ACTA GEOTECHNICA SLOVENICA Ustanovitelji Founders Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo University of Maribor, Faculty of Civil Engineering, Transporta­tion Engineering and Architecture Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo University of Ljubljana, Faculty of Civil and Geodetic Engineering Univerza v Ljubljani, Naravoslovnotehniška fakulteta University of Ljubljana, Faculty of Natural Sciences and Engineering Slovensko geotehniško društvo Slovenian Geotechnical Society Društvo za podzemne in geotehniške konstrukcije Society for Underground and Geotechnical Constructions Izdajatelj Publisher Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo Faculty of Civil Engineering, Transportation Engineering and Architecture Odgovorni urednik Editor–in–Chief Borut Macuh University of Maribor Tehni°na urednica Technical Editor Tamara Bra°ko University of Maribor Uredniki Co Editors Jakob Likar Geoportal d.o.o. Janko Logar University of Ljubljana Primož Jeluši° University of Maribor Stanislav Škrabl University of Maribor Goran Vižintin University of Ljubljana Bojan Žlender University of Maribor Posvetovalni uredniki Advisory Editors Heinz Brandl Vienna University of Technology Chandrakant. S. Desai University of Arizona Bojan Majes University of Ljubljana Pedro Seco e Pinto National Laboratory of Civil Eng. 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Baze podatkov v katerihje revija indeksirana: SCIE - Science Citation Index Expanded, JCR – Journal Citation Reports / Science Edition, ICONDA - ˜e inter­national Construction database, GeoRef. Izid publikacije je ˙nan°nopodprla Javna agencija za raziskovalno dejavnost Republike Slovenijeiz naslova razpisa za so˙nanciranje doma°ih periodi°nih publikacij. ˜e journal is published twice a year. Papers are peer reviewed by renowned international experts. Indexation data bases of the journal: SCIE - Science Citation Index Expanded, JCR – Journal Citation Reports / Science Edition, ICONDA- ˜e international Construction database, GeoRef. ˜e publication was ˙nancially supported by Slovenian Research Agency according to the Tender for co-˙nancing of domestic periodicals. A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis A FRAMEWORK FOR THE USE OF RELIABILITY METHODS IN DEEP URBAN EXCAVATIONS ANALYSIS Arefeh Arabaninezhad University of Tehran, Department of civil engineering Enghelab Ave, Tehran, Iran E-mail: arefeh.arbani@ut.ac.ir OKVIR ZA UPORABO METOD ZANESLJIVOSTI PRI ANALIZAH GLOBOKIH IZKOPOV V URBANIH OKOLJIH Ali Fakher (corresponding author) University of Tehran, Department of civil engineering Enghelab Ave, Tehran, Iran E-mail: afakher@ut.ac.ir https://doi.org/10.18690/actageotechslov.18.1.2-14.2021 deep excavation, random set ˙nite element method, globoki izkop, metoda naklju°nih nizov s kon°nimi reliability analysis, system performance; uncertainty elementi, analiza zanesljivosti, zmogljivost sistema, nezanesljivost Deep excavations in urban areas impose deformation to adjacent structures; hence the reliability of deformation analysis for the real deep excavation projects is very important to be assessed. In this study a framework is presented for the use of reliability methods in deforma­tion analysis of deep urban excavations. .e suggested framework is applied for 5 real deep excavation projects implemented during last 10 years. All studied cases were recognized as projects of high importance in urban areas, and were monitored during the excavation process. A non-probabilistic reliability analysis procedure, Random set method, in combination with ˙nite element numerical modeling is applied to obtain the probability of unsatis­factory performance for each case. .e reliability analysis results are con˙rmed by ˙eld observations and measu­rements. Typical results for the probability of analytical deformations exceeding the acceptable values along with the site observations and measured displacements for 5 real deep excavation projects show that the reliability analysis could be a bene˙cial tool for designer. It is conclu­ded that applying the suggested framework in the design stage of deep excavation projects may lead to design more appropriate systems compared to common deterministic design methods. Izvedbe globokih izkopov v urbanih obmo˜jih povzro˜ajo deformacije na sosednjih konstrukcijah; zato je zelo pomembna ocena zanesljivosti analize deformacij za dejanske projekte globokih izkopov. V tej študiji je pred­stavljen okvir za uporabo metod zanesljivosti pri analizi deformacij globokih izkopov v urbanih okoljih. Predlagani okvir je bil uporabljenih za pet dejanskih projektov globo­kih izkopov, izvedenih v zadnjih 10 letih. Vsi preu˜eni primeri so bili prepoznani kot projekti velikega pomena v urbanih obmo˜jih in so bili spremljani med izvedbo izko­pov. Za verjetnostno analizo uspešnosti izvedbe izkopov se za vsak od primerov ni uporabil postopek verjetnostne analize zanesljivosti, temve˜ metoda naklju˜nih nizov v kombinaciji z numeri˜nim modeliranjem kon˜nih elementov. Rezultate analize zanesljivosti potrjujejo teren-ska opazovanja in meritve. Tipi˜ni rezultati verjetnosti analiti˜nih deformacij, ki presegajo sprejemljive vrednosti, skupaj z opazovanji na lokaciji in izmerjenimi premiki za pet dejanskih projektov globokih izkopov kažejo, da bi bila analiza zanesljivosti lahko koristno orodje za projektante. Ugotovljeno je bilo, da uporaba predlaganega okvira v fazi na˜rtovanja projektov globokih izkopov lahko privede do zasnove ustreznejših sistemov v primerjavi s splošnimi metodami deterministi˜nega na˜rtovanja. 2. Acta Geotechnica Slovenica, 2021/1 A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis 1 INTRODUCTION As a result of the extensive development of urban areas, deep excavation design has become an increasingly pursued issue in engineering analyses in recent years. Because of the great e.ects of deep excavation-induced ground movements on the nearby structures, the assess­ment of the e.ects of deep excavations on ground move­ments has been the subject of interest of several studies [1-6]. Ignoring the deformation caused by excavating process in the design stage can cause signi˙cant damage to adjacent structures and utilities. Excessive movements can occur without a failure mechanism occurring [7], hence it should be considered in the design stage as long as the failure control. In other words, both the service­ability and ultimate limit state of the system should be evaluated in-order to design sucient support plan for a deep excavation wall. Structure failure events pose a signi˙cant threat not only to human life but also to the environment and in general to economic development. Sources of ground movement are lateral displacement of excavation wall and displacement due to support system installation [8]. Hence, in the presented study the horizontal displacement of the excavation top point (as a signi˙cant system response a.ecting the nearby facilities) is considered as the main system response to be controlled. Figure 1. Schematic ˙gure for e.ects of deep excavation on ground movement and adjacent buildings. ˜e uncertainty caused by soil and rock properties such as cohesion and elastic modulus poses a major challenge in geotechnical problems. Soils are variable, whether such variability is recognized in design or not. Address­ing uncertainty does not increase the level of safety, but allows a more rational design as the engineer can cali­brate the decisions on a desired or required performance level of a structure [9]. Reliability analysis methods represent the most important aspect of performance, namely the probability of unsatisfactory performance of a system. Using deterministic methods, excavations are designed based on the stability safety factor, deforma­tion of excavation walls and adjacent buildings, ignoring the existing uncertainties in soil properties. ˜e main advantage of reliability analysis over deterministic meth­ods in terms of safety lies in the fact that, the designer is able to provide more complete and realistic information regarding the level of safety of design. In recent years, the technology for implementing deep excavations in Iran has improved considerably. Using simple reliability analysis methods is encouraged in the design stage of the projects in order to propose optimum support system plans. In this study a framework is represented for the use of reliability methods in deep urban excavations analysis. Due to the great e.ect of deformation induced by deep urban excavations on the nearby facilities, the framework is based on controlling the horizontal displacement of the excavation top point as the main system response. ˜e Random Set Method (RS) is selected for performing reliability analysis and a ˙nite element soware was used to model the deep excavations. ˜e main reason to choose RS method is that it works well with the limited soil data available in real deep excavation projects and it takes the soil input variables in the form of intervals. Being able to select and communicate the level of performance and reduce undesired conservatism, in turn, is bene˙cial in the economic sense [9]. It also reduces the risk of incorrect decisions due to uninten­tionally optimistic modeling [10]. In order to estimate the probability of unsatisfactory performance of the system, a threshold value is considered for horizontal displacement of the excavation top point as a target value and the probability of having displacement more than this value is compared to the acceptable probability of excessive deformation. ˜e presented framework is based on applying the previously published research ˙ndings. ˜e Innovation is (I) to combine these methods in order to present a simple and practical framework and (II) applying it for 5 important deep excavation projects implemented during the last 10 years. ˜e results were compared to the site measurements and ˙eld observations on the problems encountered in reality. ˜e selected cases have been implemented in Tehran during 2010 to 2018. ˜e support system plans for all cases were implemented based on deterministic analysis methods and no reli­ability analysis had been performed at the design stage. All studied cases were recognized as projects of high importance in urban areas, and were therefore moni­tored during the excavation process. A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis 2 THE METHODOLOGY OF PRESENTED FRAMEWORK ˜e steps to implement the presented framework for reliability analysis of deep excavations in urban areas are summarized below: [Step 1]: Performing the reliability analysis for the selected deep excavation projects. [Step 2]: Selecting the target value for horizontal displacement of the excavation top point (as the main system response) and the acceptable probability of excessive deformation. [Step 3]: Comparing the probability of excessive deformation to the acceptable value and evaluating the performance of proposed support system to ˙nd out whether any revision is required or not. 3 USED RELIABILITY ANALYSIS METHOD Although various mathematical methods have been proposed and investigated for reliability analysis [11-23], applying these methods to geotechnical problems presents certain diculties. It highlights the importance of proposing methods that draw on limited input data which are available in real geotechnical project such as deep excavations in order to represent an appropriate estimate from the system performance. Accordingly, the random set method bene˙ting a simple mathematical framework for reliability analysis has been selected for the presented study. ˜e random set theory was ˙rst proposed by Kendall [24], and consequently developed by di.erent research­ers. ˜is method consists of a mathematical model that can deal with the system uncertainties when the exact input variable values are not available. Since 2000, the random set method has been applied to a certain extent in geotechnical studies, and has mostly been used in tunnel studies. Peschl [25] and Schweiger and Peschl [26] combined the random set theory with the ˙nite element method, developing the random set ˙nite element method (RS-FEM) and investigated its applicability to slope stability analysis. Nasekhian [27] conducted a tunnel project case study to investigate the advantages and disadvantages of RS-FEM for reliability analysis. Shen and Abbas [28] applied random set method in combination with distinct element method to investigate the reliability of rock slopes. Ghaziyan-Arabi & Fakher [29] and Arabaninezhad & Fakher [30] examined the use of the random set method in the ˙nite element analysis of deep excavations; however, only one case study in Tehran was considered in each study, which was not sucient for a practical conclusion. Momeni et al. [31] evaluated the random set method for reliability analysis of deep excavations using Monte Carlo technique. 3.1 Concept of Random Set Method ˜e random set theory provides a general framework for dealing with set-based information and discrete prob­ability distributions [26]. Assume that X is a non-empty set containing all possible values of a variable x. Dubois and Prade [32] de˙ned a random set on X as a pair ( ,m), where = Ai: i = 1,...,n and m is a mapping, [0,1], so that m(.) = 0 and (1) In the above, is known as the support of the random set, the sets Ai are the focal elements, and m is known as the basic probability assignment. Each set contains certain possible values for the variable x, and m(A) can be viewed as the probability that A is the range of x. Because of the imprecision of this formulation, it is not possible to calculate the precise probability of a generic x.X or generic subset E.X, but only the lower and upper bounds of this probability. With numerical modeling based on the ˙nite element method (FEM), it is possible to obtain more than one system response without making any changes to the model. ˜erefore, the random set in combination with the FEM will be a sucient reliability analysis method. Assume that function f(Ai) represents a numerical model in the RS-FEM framework. ˜e number of system input variables is N and n information sources are available. Hence, nN FE runs are required to consider all possible combinations of input variables based on the input sources of information. Because only extreme values of input random sets are considered, 2N FE runs are also required to perform interval analysis. ˜e number of all calculations nc required to determine the bounds of the system response are: (2) Assuming that input variables (A1 ,…, An) are stochasti­cally independent, the joint probability for the system response focal element obtained from each deterministic FE calculation is equal to the product of probability assignment m for each input focal element as: (3) 4. Acta Geotechnica Slovenica, 2021/1 A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis 3.2 Radom Set Finite Element Method With numerical modeling based on the ˙nite element method, it is possible to obtain more than one system response without making any changes to the model. ˜erefore, in this study, reliability analysis is accom­plished by using the random set in combination with the ˙nite element method. ˜e steps to implement random set reliability analysis in combination with numerical modeling are summarized below: [Step 1]: De˙ne the geometry of the system, prepare the ˙nite element model and select the appropriate constitu­tive model for material. [Step 2]: Provide available sources of information to de˙ne di.erent input random sets for the basic system variables. In the case that two sources of information are available, the probability of each basic variable can be set to 0.5. In this way, almost all sources of uncertainties are taken into consideration in the modeling procedure. [31] [Step 3]: Consider spatial variability in order to reduce uncertainty over the input random sets. [Step 4]: Determine the most inuential input vari­ables using sensitivity analysis to reduce the number of required FE runs. [Step 5]: Generate all possible combinations of input variables for the FEM and calculate the relevant prob­ability share for each individual run. Each combination (set) is keyed into a ˙nite element model, the model is run and the desired output is recorded. ˜is process is repeated nc times (Eq. 2) and the model outputs are recorded. ˜e probability share assigned to the model output for each combination is calculated from multiply­ing the probability of each basic variable (Eq. 3). [Step 6]: Perform FE calculations and represent the main system responses in terms of the lower and upper bounds of discrete cumulative probability functions (CDF). ˜e resulting CDF are ˙tted using a best-˙t method (Easy˙t soware [34] in this study) to achieve a continuous distribution function. [Step 7]: De˙ne suitable performance functions which can be evaluated using the reliability analysis results (bounds on continuous distribution functions of the system response) to obtain a range for the probability of failure or unsatisfactory performance. In this study an acceptable value is de˙ned for horizontal displacement of the excavation top point as a target value and the probability of having displacement more than this value which indicates the probability of unsatisfactory perfor­mance of the system can be determined. 4 SELECTED PROJECTS SPECIFICATION In-order to assess the presented framework for reli­ability analysis of deep excavation projects, a number of monitored case studies must be undertaken. Tall buildings are common in northern Tehran. In order to supply sucient space for parking, multi-story base­ments are constructed for these buildings; thus major deep excavation projects are performed to construct the basements. ˜e routine depth of a deep excava­tion is 20 to 40 m. ˜e soil layers generally consist of ˙ll materials near the ground surface (1.5 to 3 m in depth), with clayey gravel and clayey sand being mostly frequently observed in succession. In order to consider the mentioned speci˙cations of general deep excava­tions in Tehran, ˙ve excavation walls from 3 important monitored projects were selected as summarized in Table 1. ˜e excavation areas of the selected projects are large and the inclination of the ground surface causes di.erent excavation depths at di.erent parts of the same project. Table 1. General speci˙cations of selected projects. Project Excavation depth (m) Fill material depth (m) Excavation area (m2) Support system Main type of soil layers Number of walls investigated South Atlas Plaza, Commercial center 23 and 25 3 32000 nail-anchor combination clayey gravel and clayey sand 2 Shiraz Street, Golestan Administrative-commercial building 34 and 36.5 1.5 8500 nail-anchor combination clayey gravel and sti. clay 2 North Atlas, Hotel 36.5 1.5 16000 nail-anchor combination clayey gravel and clayey sand 1 A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis (a) First project site (b) Second project site (c) ˜ird project site (including case studies nos. 1 & 2.) (including case studies nos. 3 & 4.) (including case study no. 5.) Figure 2. Aerial view of intended deep excavation projects locations. Fig. 2 shows the excavation location and neighboring facilities, including buildings and roads for intended excavation projects. In the ˙rst project, as illustrated in Fig. 2(a), two walls were selected for the study because of the di.erences in horizontal displacements and surcharges. It should be noted that, according to the monitoring reports, several small cracks were observed on the ground surface near wall 2. ˜e second excavation project (Fig. 2(b)) was launched in 2012. As activities proceeded, several cracks were observed around the northern part of the excavation, leading to anxiety in resi­dents of nearby buildings; thus, excavation activities were suspended for a period in order to revise the stabilization plan. ˜e soil pro˙le that appeared during the excavation process indicated that the primary geotechnical investiga­tions were not consistent with real soil conditions. Several residential buildings exist adjacent to the street located on the north side of the project, and according to the moni­toring reports, the majority of horizontal displacements occurred in the northwestern part of the excavation; hence, reliability analysis is performed for walls nos.3 and 4 located in this region. ˜e third excavation project is located in the northern half of the ˙rst deep excavation project site as illustrated in Fig. 2(c). ˜is project was being carried out in order to construct a hotel, and during the excavation process, a building located in the southern half of the current excavation was being built. ˜e excavation support system implemented for all projects was a nail-anchor combination. Support systems were designed by geotechnical engineers applying deter­ministic methods. In the presented study the e.ect of uncertainty in soil properties on reliability of deep exca­vations has been taken into account applying RS-FEM. ˜e support system is considered to be equal in all ˙nite element runs performed for reliability analysis of each intended wall. Hence for the sake of brevity the details of support systems are not explained in detail. 5 IMPLEMENTATION OF RS-FEM Numerical modeling was done using ˙nite element so­ware [35]. Fig. 3 plots the system model cross-section for intended walls. For each soil variable, according to the geotechnical reports and engineering judgment, along with expert knowledge, two ranges with a weight of 0.5 each are suggested. In order to consider the spatial variations in soil param­eters, the primary values of the variables are modi˙ed slightly, using a variance reduction technique. In this study, the method proposed by Schweiger and Peschl [26] is applied. For the purpose of brevity, details of this method are not presented here and can be found in other studies [26, 31]. ˜e modi˙ed upper and lower bounds of the suggested ranges, and the reference values for each soil variable, are represented in Tables 2-5. (a) Case study 1 6. Acta Geotechnica Slovenica, 2021/1 A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis (b) Case study 3 (c) Case study 2 Figure 3. Cross section of the system for investigated case studies. Table 2. ˜e ranges of random sets and reference values for soil variables considering spatial variation (case studies 1, 2). Layer Cohesion c (kN/m2) Range of sets Ref Friction angle ˆ (°) Range of sets Ref Elastic modulus E50 ref (MN/m2) Range of sets Ref Fill Material Set 1 Set 2 6.93-13.21 6.07-11.79 9.65 29.29-33.29 28.71-32.71 31 26.43-46.43 23.57-43.57 35 Clayey gravel (dry) Set 1 Set 2 72.86-102.86 67.14-97.14 85 38.57-43.29 37.43-42.71 40.36 83.57-103.57 86.43-106.43 95 Clayey gravel (saturated) Set 1 Set 2 62.86-92.86 57.14-87.14 75 31.29-35.29 30.71-34.71 33 92.86-126.43 87.14-123.57 106.79 Clayey sand Set 1 Set 2 46.43-66.43 43.57-63.57 55 29.93-33.93 29.07-33.07 31 66.43-86.43 57.14-83.57 71.79 Table 3. ˜e ranges of random sets and reference values for soil variables considering spatial variation (case study 3) Layer Cohesion c (kN/m2) Range of sets Ref Friction angle ˆ (°) Range of sets Ref Elastic modulus E50 ref (MN/m2) Range of sets Ref Fill Material Set 1 Set 2 5.75-13.13 6.25-13.87 9.81 26.75-30.7527.25-31.25 29 10.75-14.75 11.25-15.25 13 Clayey gravel Set 1 Set 2 53.77-73.77 56.23-76.23 65 32.75-36.7533.25-37.25 35 33.77-67.55 36.23-72.45 53.11 A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis Table 4. ˜e ranges of random sets and reference values for soil variables considering spatial variation (case study 4). Layer Cohesion c (kN/m2) Range of sets Ref Friction angle ˆ (°) Range of sets Ref Elastic modulus E50 ref (MN/m2) Range of sets Ref Fill Material Set 1 Set 2 5.77-13.15 6.23-13.85 9.81 26.77-30.77 27.23-31.23 29 10.77-14.77 11.23-15.23 13 Clayey gravel (dry) Set 1 Set 2 33.83-67.66 36.17-72.34 53.09 32.77-36.77 33.23-37.23 35 33.83-67.66 36.17-72.34 53.09 Clayey gravel (saturated) Set 1 Set 2 13.83-33.83 16.17-36.17 25 32.77-36.77 33.23-37.23 35 33.83-67.66 36.17-72.34 53.09 Sti. Clay Set 1 Set 2 75.74-107.66 79.26-112.34 94.04 8.77-12.77 9.23-13.23 11 16.91-33.83 18.09-36.17 26.54 Table 5. ˜e ranges of random sets and reference values for soil variables considering spatial variation (case study 5). Layer Cohesion c (kN/m2) Range of sets Ref Friction angle ˆ (°) Range of sets Ref Elastic modulus E50 ref (MN/m2) Range of sets Ref Fill Material Set 1 Set 2 3.75-8.75 4.25-9.25 6.5 30.75-34.75 31.25-35.25 33 6.89-16.89 8.11-18.11 12.5 Clayey gravel (dry) Set 1 Set 2 48.77-66.89 51.23-68.11 58.44 32.75-36.75 33.25-37.25 35 11.89-26.89 13.11-28.11 20 Clayey gravel (saturated) Set 1 Set 2 38.77-60.66 41.23-64.34 51.56 32.75-36.75 33.25-37.25 35 65.66-88.77 69.34-91.23 78.45 Sensitivity analysis is carried out to identify which vari­ables exert the most inuence on the system response, and subsequently reduces the number of required ˙nite Table 6. ˜e most inuential input variables based on sensitivity analysis Case Number study of basic Basic variables no. variables 1. Cohesion of ˙ll material. 2. Elastic modulus of ˙ll material 1, 2 4 3. Cohesion of clayey sand. 4. Elastic modulus of the saturated clayey gravel layers 1. Cohesion of clayey gravel 3 3 2. Friction angle of clayey gravel 3. Elastic modulus of clayey grave 1. Cohesion of of dry clayey gravel. 4 4 2. Elastic modulus of dry/saturated clayey gravel. 3. Elastic modulus of sti. clay. 1. Cohesion of saturated clayey gravel. 2. Friction angle of saturated clayey 5 4 gravel. 3. Elastic modulus of saturated clayey gravel. 4. Elastic modulus of dry clayey gravel. element runs. In this study, the method provided by the U.S. Environmental Protection Agency (EPA) [36] generalized and made compatible with the random set approach by Peschl [25], is used. According to the sensitivity analysis conducted based on the horizontal displacement of the excavation top point, the variables listed in Table. 6 were selected as the most inuential ones for each case study. In order to establish belief and plausibility functions (for example, upper and lower bounds) for a speci˙c system response obtained from ˙nite element calculations; the probability box (p-box) of model output has been constructed. A p-box is a pair of cumulative probability distribution functions (CDFs) that represents the impre­cise probability distribution of a random variable [37]. ˜e discrete cumulative probability functions are ˙tted by means of best-˙t methods; to obtain a continuous distribution function matched with each of the upper and lower bounds of the reliability analysis results. 5.1 Acceptable value for horizontal displacement of the excavation top point Considering an acceptable (˜reshold) value for hori­zontal displacement of the excavation top point for each 8. Acta Geotechnica Slovenica, 2021/1 A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis Table 7. ˜e acceptable value for horizontal displacement of the deep excavations top point. Case study NO. Excavation depth (m) Neighboring situation Acceptable .max/H (%) ˜reshold value considered for horizontal displacement of the excavation top point (mm) 1 23 0.5 100 2 25 No important facility and building 0.5 100 3 36.5 0.2 65 Several residential buildings 4 34 0.2 65 No important infrastructure and facilities 5 36.5 0.5 150 within a distance of 2H from the excavation case study, one can estimate the probability of unsat­isfactory performance of the system. ˜e acceptable displacement depends on national codes and engineer­ing judgment to some extent [38]. Depending on project constraints, requirements with respect to control of wall and ground movements will vary. Estimates of wall and ground movements are typi­cally made using semi-empirical relationships developed from past performance data. According to federal highway administration manual [39] the maximum hori­zontal deformation, .max, for anchored walls constructed in sands and sti. clays average approximately 0.002H with a maximum of approximately 0.005H where H is the height of the wall. Navy design manual DM 7.2 [40] suggests that walls in sands and silts might displace later­ally up to 0.002H. ˜is value for sti. and so clay was recommended to be 0.005H and 0.002H, respectively. PSCG [41], based on the importance of utilities adjacent to excavation, set some criteria for excavation protection levels in Shanghai, China. According to these criteria, .max should be less than 0.003H in the case that impor­tant infrastructure or facilities exist within a distance of 1-2H from the excavation. If no important infrastructure and facilities exist within a distance of 2H from the exca­vation, then .max should not exceed 0.007H. According to the above-mentioned references the acceptable value of horizontal displacement for the intended deep excavation walls are presented in Table 7. 6 ACCEPTABLE PROBABILITY OF EXCESSIVE DEFORMATION As mentioned earlier, excessive movements can occur without a failure mechanism occurring [7], and should be considered in the design stage as long as the failure control. It is worth mentioning that the probability of excessive deformation for a deep excavation is di.erent from probability of ultimate failure or collapse. In order to decide whether the determined values for aforemen­tioned probabilities are acceptable, a target value should be considered for each one. ˜e acceptable range for the probability of failure reported in many researches is from 10-6 to 10-4 [42-45]. ˜e acceptable probability of excessive deformation (APED) is certainly higher than these values because of the catastrophic consequences of deep excavation collapse compared to excessive deformation which might cause serviceability failure. In this study the value of 0.1 is considered for APED as proposed by Momeni et al. [38]. 7 RESULTS Figures 4 to 8 represent the reliability analysis results in comparison with the acceptable horizontal displacement value and in-situ measurements for the excavation top point in all studied cases. Such ˙gures could be used as a tool for engineers to discuss on reliability of the system and improve the decision making procedure in order to represent proper support system plans. 7.1 Comparison and discussion for case study 1 RS-FEM best ˙t distibution ˜reshold value Site measurment Figure 4. Reliability analysis results compared to threshold value and in-situ measurements for case study 1. A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis Fig. 4 shows that: – ˜e site measurement values (19 mm) fall within the upper and lower bounds. ˜is observation is indicative of the appropriateness of the soil variable input values and shows the validity of the selected reliability method in estimating the deformation of system for case study 1. – Even in the most unfavorable circumstances (upper bound), the horizontal displacement of the exca­vation top point does not exceed 57 mm, which is considerably less than the threshold value (100 mm); hence, it can be concluded that the support system implemented for the investigated wall was designed conservatively during the deterministic design stage. 7.2 Comparison and discussion for case study 2 approach. However, according to the ˙eld observa­tions, the probabilities of unsatisfactory performance of these two walls were di.erent. ˜is issue is in line with the reliability analysis results and may indicate the applicability of non-deterministic methods to predicting deep excavation system performance compared to the common deterministic methods. 7.3 Comparison and discussion for case study 3 As mentioned in Section 4, due to incorrect investiga­tion of soil conditions considered during the determin­istic design stage, the horizontal displacement calculated by means of numerical modeling was less than the threshold value. ˜is inaccuracy led to the proposal of an inappropriate support system and subsequently the appearance of large cracks around the project location during excavation. Figure 5. Reliability analysis results compared to threshold value and in-situ measurements for case study 2. Fig. 5 shows that: – ˜e site measurement value of the horizontal displa­cement at the end of the excavation process is equal to 65 mm, which falls within the lower and upper bounds of the results. – Under the least favorable circumstances (upper bound), the probability that the horizontal displa­cement of the excavation top point will exceed the threshold value is equal to 0.22 which is more than the APED value of 0.1. ˜is result is in line with the small cracks observed on the ground surface near the excavation. ˜e walls investigated in case studies nos. 1 and 2 are designed by the same designers, based on identical safety factors and displacement criteria for the deterministic Figure 6. Reliability analysis results compared to threshold value and in-situ measurements for case study 3. Fig. 6 shows that: – ˜e site measurement value is 189.5 mm, which exceeds the threshold value (65 mm). ˜is indicates that the implemented support system, designed based on the deterministic approach, was not safe. – ˜e site measurement data is not placed within the range between the lower and upper bound of reliability analysis results. ˜is is because of the signi˙cant di.erences between the geotechnical site investigation data and actual condition of the soil layers. However, the horizontal displacement thre­shold value falls within the upper and lower bounds, and is very close to the lower bound of the reliability analysis results. ˜e threshold value position may be considered as a warning of the possibility of inappro­priate system performance; hence, even in such 10. Acta Geotechnica Slovenica, 2021/1 A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis circumstances, the non-deterministic approaches may provide more reliable results than deterministic analysis methods. – According to the lower bound of the results, the probability of the horizontal displacement being more than the threshold value (65 mm) is approximately 0.2. However, when considering the upper bound of the reliability analysis results, the probability of displacements being more than the threshold value is equal to 1. ˜is demonstrates the large di.erence between the lower and upper bounds of the reliability analysis results, and may serve as a signi˙cant warning to the designer regarding the input data and considered support system. 7.4 Comparison and discussion for case study 4 Fig. 7 shows that: – Although the geotechnical site investigation was not implemented correctly and did not represent the actual soil conditions, the ˙eld measurement of the horizon­tal displacement (152 mm) falls within the lower and upper bounds of the reliability analysis results. Figure 7. Reliability analysis results compared to threshold value and in-situ measurements for case study 4. – ˜e site measurement value (152 mm) exceeds the horizontal displacement threshold value (65 mm). As per the conclusion for the third case study, incorrect investigation of the soil condition resulted in the proposal of an inappropriate support system, and consequently, large cracks appeared around the project location during excavation activities. – ˜e probability of excessive deformation for both the upper and lower bounds of the results are equal to 1 and more than the APED; hence, in case study 4, the reliability analysis results demonstrates the inappropriateness of the support system, which was not recognized during the deterministic design stage. 7.5 Comparison and discussion for case study 5 RS-FEM Site Figure 8. Reliability analysis results compared to threshold value and in-situ measurements for case study 5. Fig. 8 shows that: – ˜e site measurement value (71mm) falls within the upper and lower bounds of the reliability analysis results. – ˜e threshold value is greater than the values of the upper and lower bounds of the reliability analysis results; hence, the reliability analysis results demon­strate that even in the least favorable circumstances (upper bound), the probability of inappropriate system performance is zero. 8 OVERALL DISCUSSION ON PROBABILITY OF UNSATISFACTORY PERFORMANCE OF STUDIED CASES ˜e threshold values for horizontal displacement of the excavation top point for case studies 1 to 5 are displayed in Table 8, along with the reliability analysis results, in order to evaluate the performance of the studied cases. ˜e conclusions drawn from the data presented in Table 8 are: For case studies 1 and 5, which encountered no prob­lems in practice, the probability of unsatisfactory system performance for both the lower and upper bounds of results is equal to zero. ˜e reliability of the system in case study 2 is worse than those of nos. 1 and 5, as A. Arabaninezhad & A. Fakher: A framework for the use of reliability methods in deep urban excavations analysis Table 8. Probability of unsatisfactory performance for all case studies. Case study NO. and related ˙g. Field observation Measured horizontal Observed cracks displacement (mm) ˜reshold horizontal displacement (mm) Probability of unsatisfactory performance Considering lower Considering upper bound bound NO.1, Fig.4 19 None 100 0 0 NO.2, Fig.5 65 Small 100 0 0.22 > (APED = 0.1) NO.3, Fig.6 189.5 Large 65 0.2 > (APED = 0.1) 1 > (APED = 0.1) NO.4, Fig.7 152 Large 65 1 > (APED = 0.1) 1 > (APED = 0.1) NO.5, Fig.8 71 None 150 0 0 small cracks were observed on the ground surface near the excavation. According to the upper bound of the results for case study 2, the probability of the horizontal displacement exceeding the threshold value is equal to 0.22 which exceeds the APED of 0.1 and is in line with the ˙eld observations. ˜e system performance for case studies 3 and 4 become signi˙cantly worse. For case study 3, in which excavation activities were suspended because of large cracks being observed around the excavation, the lower bound of the results was very close to the threshold value, and when the upper bound of results are considered, the probability of unsatisfactory system performance is equal to 1. For case study 4, in which excavation activities were suspended as in case 3, even in the most favorable circumstances (lower bound of results) the probability of unsatisfactory support system performance is equal to 1 and exceeds the acceptable value of 0.1. Hence, the reliability analysis results and actual ˙eld observations are in good agree­ment for all of the studied cases. 9 CONCLUSION In this paper the performance of 5 real deep excavation projects were evaluated by a suggested framework and the following conclusions were drawn. – When applying deterministic analysis methods, inaccurate site investigations may lead to the design of unsafe support systems for deep excavation. However, when using the reliability analysis method, the large di.erence between the upper and lower bounds of the results (as concluded for case studies 3 and 4) could be considered as a warning to evaluate the geotechnical site investigation process and revise the support system plan for deep excavation. ˜is would prevent problems that may occur as a result of improper system design. – When a system is designed very conservatively, the reliability analysis results could reveal it. For example in the case studies 1 and 5, the probability of unsatis­ factory performance of system is equal to zero accor­ding to both lower and upper bounds of the results. ˜is observation is indicative of the conservative design of the system in the deterministic design stage. Applying reliability analysis method for such cases may lead to optimize the plan. – ˜e results of reliability analysis could be used to predict unsatisfactory performance of deep exca­vation systems. For the ˙ve studied cases, wherever large cracks were observed on the ground surface near the deep excavation (case studies 3 and 4), in the least favorable circumstances, the probability of unsatisfactory system performance was equal to 1 which was more than the APED of 0.1. For the cases that encountered no problems in reality (1 and 5), the probability of unsatisfactory system performance was equal to zero according to both lower and upper bounds of the results. For the situation in which small cracks were observed on the ground surface near the excavation (case study 2), in the least favorable circumstances the probability of unsatisfactory system performance was equal to 0.22 and more than 0.1. ˜e suggested framework was applied for 5 real deep excavation projects implemented during the last 10 years. ˜e combination of ˙eld observations and site measure­ments with the probability of unsatisfactory performance determined using reliability analysis, and the APED showed that the presented framework is an applicable tool to help the designer improve the decision making procedure and represent more proper support system plans compared to deterministic analysis methods. REFERENCES [1] El Sawwaf M, Nazir AK. ˜e e.ect of deep excava­tion-induced lateral soil movements on the behav­ior of strip footing supported on reinforced sand. Journal of Advanced Research. 2012;3(4):337-44. [2] Peck, R.B. (1969) Deep Excavation and Tunneling in So Ground. 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Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique DIAMETRIC SPLITTING TESTS ON UNSATURATED EXPANSIVE SOIL WITH DIFFERENT DRY DENSITIES BASED ON PARTICLE IMAGE VELOCIMETRY TECHNIQUE Junran Zhang (corresponding author) North China university of water resources and electric powery, Henan province key laboratory of geome­chanics and structural engineering Zhengzhou, Henan 450046, China E-mail: zhangjunran@ncwu.edu.cn Miao Ren North China university of water resources and electric powery, Henan province key laboratory of geome­chanics and structural engineering Zhengzhou, Henan 450046, China E-mail: renmiao@ncwu.edu.cn DIAMETRALNI CEPITVENI PREIZKUSI NA NENASI˜ENI EKSPANZIVNI ZEMLJINI Z RAZLI˜NO SUHO GOSTOTO NA OSNOVI OPTI˜NE METODE PIV Lijin Wang Tong Jiang North China university of water resources and North China university of water resources and electric powery, electric powery, Henan province key laboratory of geome- Henan province key laboratory of geome­ chanics and structural engineering chanics and structural engineering Zhengzhou, Henan 450046, China Zhengzhou, Henan 450046, China E-mail: 201300804@stu.ncwu.edu.cn E-mail: jiangtong@ncwu.edu.cn Min Wei North China university of water resources and electric powery, Henan province key laboratory of geome­ chanics and structural engineering Zhengzhou, Henan 450046, China E-mail: 190620115@qq.com https://doi.org/10.18690/actageotechslov.18.1.15-27.2021 diametric splitting, tensile strength, unsaturated expansive soil, particle image velocimetry .ere is a close relationship between tensile strength of soil and crack development, but the tensile stress-strain in full failure process is rarely studied because challenges exist in accurately measuring shear strain using traditional methods. In this paper, we employed a newly developed diametric splitting testing apparatus and particle image velocimetry (PIV) system to study the tensile strength of compacted unsaturated expansive soil with di.erent water contents and initial dry densities. Soil water characteristic curves of compacted expansive soil with di.erent initial dry densities were determined using the ˙lter paper method. Test results show that the tensile strength increa­ses ˙rst and then decreases with increasing water content, diametri°na cepitev, natezna trdnost, nenasi°ena eks­panzivna zemljina, opti°na metoda delec-slika-meritev hitrosti (PIV) Med natezno trdnostjo zemljin in nastankom razpok obstaja tesna povezava, vendar se odnos med nateznimi napetostmi in speci˙˜nimi deformacijami v celotnem procesu porušitve redko preu˜ujejo, ker obstajajo dvomi v natan˜nost merjenja strižnih speci˙˜nih deformacij s tradi­cionalnimi metodami. V tem prispevku smo uporabili novo razvito diametralno cepilno preskusno napravo in opti˜no metodo delec-slika-meritev hitrosti (PIV) za preu˜evanje natezne trdnosti trdne, nenasi˜ene, ekspanzivne zemljine z razli˜no vlažnostjo in za˜etno suho gostoto. Krivulje zemljina-voda za trdne ekspanzivne zemljine z razli˜nimi za˜etnimi suhimi gostotami so bile dolo˜ene z metodo ˙ltrirnega papirja. Rezultati preizkusov kažejo, da se nate- J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique and there is a critical water content for the peak load vs. water content curve. .e diametric splitting test process can be divided into four stages on the basis of the plotted load-displacement curves: a stress contact adjustment stage (I); stress approximately linear increasing stage (II); tensile failure stage (III); and residual stage (IV). Under the same water content, the angle between the major directions of the displacement vector and the major crack decreases with increasing the dry density, especially when the ˙ssure appears. Using the particle image velocimetry technique, the displacement and strain during the test process recorded is helpful for better understanding the soil failure mechanism. 1 INTRODUCTION Tensile strength is an important soil-strength param­eter to describe the soil’s resistance to loading, and is considerably smaller than other aspects of soil strength [47]. Expansive soil is a typical special soil, which has the characteristics of expansion, contraction, ˙ssuring, and over-consolidation, owing to its hydrophilic minerals, such as montmorillonite. Expansive soils are particularly sensitive to climate changes. As shown in Ng et al. [25], the hydro-mechanical behavior of expansive soils was signi˙cantly a.ected by climate changes, which can lead to a severe disaster for geotechnical engineering. Desic­cation cracking is a common phenomenon during the drying and wetting cycles for expansive soils that occur in various geotechnical engineering projects, such as dams, slopes and embankments [5], [35], [38]. Previous studies have shown that the cracks change remarkably through the hydro-mechanical behavior of soils [41]. Cracks in the soils lead to a sharp increase in the permeability coecient. At the same time, the existence of cracks will aggravate the corrosion of soils and leads to an increase in the probability of geological disaster [33], [36]. Extreme drought has occurred in recent years, with increasing frequency and soil desiccation cracking [42], [34], [14]. Desiccation cracking occurs when the tensile stress in the soil exceeds a certain limit (i.e., tensile strength) [23]. Determination of the soil-cracking mechanism and improving the safety of geotechnical structures are therefore of great signi˙cance to compre­hensively understand the tensile strength of special soils, especially for expansive soil. ˜e testing methods for measuring soil’s tensile strength include direct and indirect methods. ˜e indirect tensile-test methods include the split tensile test, the beam bending test and the axial fracturing test [7], [37], zna trdnost najprej pove˜a in nato zmanjša z naraš˜anjem vlažnosti, za krivuljo najve˜ja obtežba-vlažnost pa obstaja kriti˜na vlažnost. Na podlagi izrisanih krivulj obtežba--premik lahko postopek preizkusa diametralne cepitve razdelimo na štiri stopnje: (I) stopnja vzpostavitve stika napetosti; (II) stopnja približno linearno naraš˜ajo˜e nape-tosti; (III) stopnja natezne porušitve; in (IV) rezidualna stopnja. Pri enaki vlažnosti se kot med glavnimi smermi vektorja premika in glavno razpoko zmanjšuje z nara-š˜ajo˜o suho gostoto, zlasti ko se pojavi razpoka. Uporaba opti˜ne metode PIV je koristna, ker nam posneti premiki in speci˙˜ne deformacije med preizkusnim postopkom omogo-˜ajo boljše razumevanje mehanizma porušitve zemljine. [12], [18], [24], [22], [6]. ˜e above methods are suitable for rock and concrete. For so soils, some coecients are necessary [7] to correct the test results. Most previous studies used a linear variable di.erential transducer (LVDT) to measure the deformation of the specimens with regard to the tensile strain. ˜e LVDT method is suitable for uniform soils. ˜e development of image-processing techniques in recent decades has signi˙cantly improved strain measurements. ˜e displacement and strain on the specimen’s surface can be tracking in a full process by using the particle-image­velocimetry (PIV) and digital-image-correlation (DIC) techniques [46], [11], [1]. ˜e PIV technique has the advantages of non-contact and high resolution, and it has been widely applied in geotechnical engineer­ing [45], [5], [19], [31], [44], [43], [49]. ˜ese studies reported that desiccation crack sites can be reliably predicted on the basis of the surface strain ˙eld. Many researches have focused on the tensile strength of unsaturated soil (e.g., [20], [21], [13], [4], [38], [40], [17], [47], [8], in which most studies are mainly focused on the tensile strength. However, the tensile stress-strain in a full-failure process is rarely studied, and because of that there are challenges in accurately measuring the shear strain using traditional methods. Moreover, the inuence of the initial dry density and the water content on the tensile stress of expansive soil during the tensile-test process and the failure mechanism remain unclear. It needs further study [16]. In order to study the tensile stress-strain in the full-failure process of expansive soil systematically, we have designed a new diametric splitting test with a PIV system. ˜e DIC and PIV techniques were employed to obtain the strain ˙eld. A series of diametric split­ting tests were conducted on compacted, unsaturated, expansive soil specimens with di.erent water contents 16. Acta Geotechnica Slovenica, 2021/1 J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique of 10–22 % and initial dry densities of 1.35–1.65 Mg/m3. ˜e test results are analyzed and discussed in the follow­ing, together with the PIV images. 2 MATERIAL AND METHODS 2.1 Testing apparatus ˜e diametric splitting testing apparatus with the PIV system is shown in Figure 1. ˜e diametric splitting test­ing apparatus consists of three systems: the loading test system, the data collection system, and the PIV system. During the test, the three systems were synchronized. ˜e loading system used in the tests is the CMT4000 electronic universal testing machine developed by the American Meester Company. ˜is instrument includes the loading equipment and the data-acquisition system and can automatically control the constant-velocity displacement rate. ˜e load is applied using the strain control type with the compression rate ranging from 0 to 10 mm per minute. ˜e speed selected in this study is 1.4 mm per minute. ˜e data of the load is monitored using a load cell with a maximum range of 160 N, and a working resolution of 0.001 N. During the test, the displacement and load measurements are carried out simultaneously. ˜e displacement is monitored by a LVDT with a maximum range of 100 mm and a working resolution of 0.001 mm. A high-speed CCD camera with high sensitivity and image quality was vertically mounted above the specimen and manually focused on the specimen’s surface. Seven pictures were taken per second to record the deformation in the full process. Davis8.3 soware was then used to obtain the required images and speci˙c locations were selected and analyzed using PIVview2C and Tecplot10 instruments. ˜e size range of the specimens photographed in the tests is about 38.5 × 38.5 cm2. ˜e initial specimen size used in the tests is d0 = 6.18 cm and h0 = 2 cm. 2.2 Soil sample ˜e expansive soil was collected from Nanyang City, Henan Province, China, and is similar to that used in Zhang et al. [48] but from a di.erent location. ˜e expansive soil has a liquid limit of 52.7 % and a plasticity index of 29 %. Other physical property indexes, such as speci˙c gravity, liquid limit, plastic limit, optimum water content, maximum dry density, and free swelling ratio, are listed in Table 1. Fig. 2 shows the grading curve determined by the hydrometer analyses. ˜e soil is composed of 21.1 % clay fraction (<2 ľm). According to the USCS soil classi˙ca­tion, the expansive soil from the Nanyang site is CL. Figure 2. Grading curve of the expansive soil. 2.3 Sample preparation ˜e dried and pressed sample ˙rst passed through a 2-mm sieve. ˜en the sample was mixed with distilled water. Seven groups of samples were prepared with water contents of 10 %, 12 %, 14 %, 16 %, 18 %, 20 %, and 22 %. ˜e soil samples were stored in an airtight container for 96 hours to distribute the water evenly. ˜e required quantity of samples was then put into a mold Table 1. Property indexes of expansive soil. Speci˙c Liquid limit Plastic limit Plasticity Maximum dry den-Optimum water Free swelling Uni˙ed Soil gravity Gs wL (%) wP (%) index Ip (%) sity .d,max (Mg/m3) content wopt (%) ratio (%) Classi˙cation System 2.73 52.7 23.7 29 1.68 18.9 49 CL J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique and compacted to di.erent initial dry densities of 1.35, 1.50, or 1.65 Mg/m3. ˜e specimen-preparation method is di.erent from that of specimens undergoing drying from saturated specimens to specimens with di.erent water contents [48]. It is known that in the drying process, the dry density of expansive soil will increase, and resulting in an increase in strength. 2.4 Test procedure ˜e diametric splitting tests were performed at a constant speed. ˜e speed is 0.14 mm/min in the vertical direction. ˜e tensile load and displacement were monitored during the testing. For each test group, two parallel specimens were prepared to check the procedural reproducibility. 2.5 Image processing Surface deformation was monitored during the tests using the PIV system with images taken at 7-s intervals. Aer the tests, the images were changed to grayscale images and the study area with 60 × 60 mm2 around the specimen (as shown in Figure 1) was selected and imported into the programs PIVview2C and Tecplot10 for the image analyses. Deformation information at di.erent stages was obtained by comparing the images with the reference images taken prior to the tests. ˜e length and orientation of the vectors representing the deformation are shown in the displacement vector ˙eld. 2.6 Soil-water characteristic curve test ˜e specimen-preparation method used in the soil-water characteristic curve test is the same as that used in the diametric splitting test. ˜e suction was measured at di.erent compaction water contents (6–22 %) of speci­mens with dry densities of 1.35, 1.50, and 1.65 Mg/m3 using the ˙lter-paper method. Circular quantitative ˙lter paper Whatman No. 42 was used for the ˙lter paper method and the expression for determining the matrix suction from Leong et al. [15] is formulated as follows: log s = 2.909 0.0229wf (wf  47) (1) log s = 4.945 0.0673wf (wf > 47) (2) In the above formula, s is the matrix suction, and wf is the water content of the ˙lter paper. Before the tests, the ˙lter paper was kept in an oven at 105şC for more than 16 h to ensure dryness and then put in a dryer for cooling and storage. ˜e soil specimen and ˙lter paper contacted together and were put into a sealed box, which was held at constant temperature (20ą2 şC) and humidity for two weeks. Aer that the papers were quickly, carefully, and individually removed using forceps. ˜e weight of the ˙lter paper was measured with a balance having 0.0001-g precision and the water content of the ˙lter paper was measured. ˜e weight of the soil specimen was also measured. ˜e matrix suction was calculated according to Eq. (1) or (2) and the soil-water characteristic curve (SWCC) was determined. More details about the suction measure­ment procedures can be found in Leong et al. [15]. 3 RESULTS AND DISCUSSION 3.1 Soil-water characteristic curve of expansive soil ˜e results of the soil-water characteristic curves (SWCCs) tests for the expansive soil with di.erent initial dry densities are shown in Fig. 3. ˜e water content (w) and degree of saturation (Sr) both decrease with increas­ing suction. ˜e relationships w-s and Sr-s are shown in Fig. 3a and Fig. 3b, respectively. ˜e SWCCs move le and down with increasing initial dry density when the suction is less than 5000 kPa, as shown in Fig. 3a. ˜e inuence of the initial dry density on the soil-water characteristic curve is very obvious, especially for low suction, i.e., the water content decreases with increasing dry density under the same suction. When the suction is greater than 5000 kPa, the dry density’s inuence on the SWCCs is not apparent. A similar test result for SWCCs was found by Romeroe and Vanat [27] and Gao et al. 18. Acta Geotechnica Slovenica, 2021/1 J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique [9]. In terms of the saturation degree, the SWCC curves move right and upwards with increasing dry density, as shown in Fig. 3b. ˜e inuence of the initial dry density on the soil-water characteristic curve is very obvious in the full suction range, the degree of saturation decreases with decreasing initial dry density under the same suction conditions, which is similar to that reported by Sun et al. [28], [29] and Sun and Sun [30]. 3.2 Infuence of initial dry density on the stress and strain behavior ˜e Inuence of the initial dry density on the rela­tionship between the load and the displacement of (b) w=12 % (d) w=1 6% (f) w=20 % specimens with di.erent water contents is shown in Fig. 4. For the plastic soil, the relationship between the load (a) w=10 % (c) w=14 % (e) w=18 % (g) w=22 % Figure 4. Inuence of initial dry density on the relationship between load and displacement. J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique and the displacement in the splitting tests appears as a double-peak phenomenon. However, the soil underwent substantial plastic deformation in the second peak stage, which indicates that the stage poses little signi˙cance for studying the tensile strength. We therefore focus mainly on the curves in the ˙rst peak stage. ˜e results in Fig. 4 also show that the inuence of the initial dry density on the tensile strength is very obvious. Under the same water-content conditions, the peak load increases with increasing initial dry density. As shown in Fig. 4a, when the water content is 10 %, the average peak load increases by 322.1 % and 1065.7 % as the dry density increases from 1.35 to 1.50 and from 1.35 to 1.65 Mg/m3, respectively. A similar test result was found by Blazejczak et al. [3]. ˜is is because the specimen with a higher initial dry density has more contacts between the soil particles, and the number of water bridges increased, which leads to a higher peak load. ˜e test results are more obvious, especially for expansive soil with a low water content. ˜e average increases of the peak load as the initial dry density increases from 1.35 to 1.50 Mg/m3 and to 1.65 Mg/m3 are shown in Figure 5. ˜e average increase of the peak load decreases with increasing water content. Above, a similar test result was obtained by Li et al. [16]. 3.3 Infuence of water content on tensile stress-strain behavior ˜e inuence of the initial water content on the relation­ship between the load and the displacement at di.erent initial dry densities is shown in Fig. 6, which shows that the peak load ˙rst increases and then decreases with an increasing water content. ˜e displacement where the relationship curve between the load and stress reaches the ˙rst peak value essentially increases with the water content. When the initial dry density is 1.35 Mg/m3, the peak value increases in the water content range from about 10 % to 18 %, and decreases from 18 % to 22 %. However, when the initial dry density is 1.50 and 1.65 Mg/m3, the peak value increases in the water content range from 10 % to 14 % and decreases from 14 % to 22 %. In addition, part of the slope of the curve that reaches the ˙rst peak value is larger with lower water content, which indicates that the brittleness is more appar­ent for compacted expansive soil with a low water content. (a) d = 1.35 Mg/m3 (b) d = 1.50 Mg/m3 (c) d = 1.65 Mg/m3 Figure 5. Average increase of peak load at di.erent water contents with increasing initial dry density from 1.35 to Figure 6. E.ect of water content on the relationship 1.50 Mg/m3 and from 1.50 to 1.65 Mg/m3. between load and displacement. 20. Acta Geotechnica Slovenica, 2021/1 J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique ˜ere is a close functional relationship between the tensile strength and the suction for unsaturated soils [20], [32], [40]. As soils are subjected to drying condi­tions and the suction increases during the drying [50], which increases the tensile strength [39]. ˜e peak-load characteristic curves (PLCCs) are shown in Fig. 7, which are according to relationship between the load and displacement in Fig. 6. And the soil-water characteristic curves (i.e., SWCCs) are also presented in Fig. 7. Fig. 7 indicates that the PLCCs are unimodal curves and the PLCCs is inuenced by the water content. Tang et al. [35] obtained similar results. ˜e critical water content, wc (~17.9 %, ~14.1 %, ~13 %), corresponding to the maximum peak load (65.5, 114.2, and 263.9 N) for di.erent initial dry densities of 1.35, 1.50 and 1.65 Mg/m3 are determined from Figure 7. When w is less than wc , the peak load increases with an increase in the water content. However, when the water content is higher wc , the peak load decrease with an increase in the water content. ˜e reason is as follows. ˜e change of microstructure with water content should be considered [40]. Most of the water is stored inside the aggregate pores at low water contents and it is very dicult to form liquid bridges [10]. ˜e soil’s tensile strength depends mainly on the liquid bridges among the particles. When w is less than wc , the liquid bridges form gradually with an increasing water content, and thus the peak load (tensile strength) increases with an increasing water content. When the water content increases up to wc , the liquid bridges appear at most contact points of particles. ˜e liquid bridges among the particles will disappear gradu­ally with a further increasing water content, resulting in a decrease in the tensile strength. 3.4 Effects of initial dry density and water content on the displacement vector feld Figs. 6 and 8 show that the water content has a very obvious e.ect on the tensile strength. ˜e images taken during the tests were analyzed, with the initial image taken immediately prior to the load application. ˜e PIV and DIC techniques allow characterization of the evolution of the deformation patterns. Typical results are presented in Fig. 9 and are related to specimens at low Figure 8. Typical relationship between load and displacement (d = 1.50 Mg/m3) Figure 7. PLCCs and SWCCs at di.erent initial dry densities. J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique water contents (i.e., w = 10 %), around wc (i.e., w = 14 %), and a high water content (i.e., w = 22 %) and with an initial dry density of 1.50 Mg/m3. As shown in Fig. 8, the load-displacement curve of compacted, expansive soil with di.erent water contents can be separated into four stages: a stress contact adjust­ment stage (I), for section OA, which is caused by the stress concentration of the upper and lower indenters on the contact parts of the specimens; stress approximately linearly increasing stage (II), for section AB, in which the load increases practically linearly with increasing displacement until reaching the peak (i.e., tensile strength); tensile failure stage (III), for section BC, (a) w = 10 % (b) w = 14 % 22. Acta Geotechnica Slovenica, 2021/1 J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique (c) w = 22% Figure 9. Failure process and displacement vector ˙eld for specimens with di.erent water contents. where the specimen begins to crack and the curve drops steeply aer reaching the target value; and the residual stage (IV) for section CD, where the specimen shows clear splitting cracks, the curve decreases rapidly to zero and the specimen subsequently shows a certain residual strength. With increasing stress, the crack continues to expand until it is completely destroyed. ˜e fracture propagation of specimens with di.erent water contents and their displacement vector ˙elds are shown in Fig. 9. Aer the applied load experiences the AB segment, which is an approximately straight line, no obvious crack appears when the peak stress point B is reached. Aer the load drops to point C, a splitting crack appears on the splitting surface and the load drops sharply to point D. ˜e fracture diagram and its displacement vector ˙eld of points B, C, and D are shown in Fig. 9a–9c, respectively. According to the displacement vector ˙eld in Fig. 9, the specimen at point B only underwent compression deformation without the formation of obvious cracks, owing to the plasticity of the soil mass. Aer the peak, cracks appear at point C and the displacement vector ˙eld is distributed symmet­rically on both sides of the splitting surface. At point D, the load drops to the trough and the cracks connect. ˜e failure part of the specimen is due to excessive displacement and the displacement vector ˙eld obtained by the PIV technique is a blank area. Moreover, the above phenomenon ˙rst increases and then decreases with increasing water content, which is most apparent at the optimal water content (i.e., w = 14 %), and the time required to complete the II–IV stages shows a similar trend with the increasing water content. Figs. 5 and 10 show that the initial dry density has a very obvious e.ect on the tensile strength. ˜e images taken during the tests were analyzed, with the initial image taken immediately prior to the application of the tensile load. ˜e evolution of the deformation patterns is char­acterized using the PIV and DIC techniques. ˜e typical results are presented in Fig. 11, and are related to speci­mens with di.erent initial dry densities (1.35, 1.50, and Figure 10. Typical relationship between load and displacement (w = 14 %). J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique 1.65 Mg/m3), and with a water content of 14 %. Under the same water content, the angle between the major direction of the displacement vector and the major crack decreases with increasing dry density, especially at point C, as two arrows show in middle ˙gures of Fig. 11(a), (b) and (c). ˜e above phenomenon might be caused by the specimens becoming increasingly hard as the dry density increases and the lateral displacement of the specimens decreases. Similar test results are observed for other speci­mens with di.erent water contents (w = 10 %–22 %). (a) d = 1.35 Mg/m3 (b) d = 1.50 Mg/m3 24. Acta Geotechnica Slovenica, 2021/1 J. Zhang et al.: Diametric splitting tests on unsaturated expansive soil with different dry densities based on the particle-image-velocimetry technique (c) d = 1.65 Mg/m3 Figure 11. Failure process and displacement vector ˙eld for specimens with di.erent initial dry densities. 4 CONCLUSIONS A newly designed diametric splitting testing apparatus and particle-image-velocimetry (PIV) system were employed to study the tensile stress-strain in a full-failure process of expansive soil systematically. ˜e main conclusions are as follows. (1) ˜e diametric splitting test process can be divided into four stages on the basis of the plotted peak load-displacement curves: stress contact adjustment stage (I); stress approximately linear increasing stage (II); tensile failure stage (III); and residual stage (IV). (2) ˜e water content and the initial dry density have obvious e.ects on the tensile behavior of the compac­ted expansive soil. ˜e tensile strength increases ˙rst and then decreases with increasing water content, and there is a critical water content. ˜e critical water contents are about of 17.9 %, 14.1 %, and 13 % for expansive soil specimens with initial dry densities of 1.35, 1.50, and 1.65 Mg/m3, respectively. ˜e peak load increases with increasing dry density, which is more obvious at a low water content. (3) ˜e PIV techniques can be applied to analyze the deformation during testing, which provides the displacement vector ˙eld at various stages. Under the same water content, the angle between the major direction of the displacement vector ˙eld and the major crack decreases with increasing dry density, especially when the ˙ssure appears. ˜e tensile ˙ssu-res and the directions of the propagation of major displacement vector ˙eld can be determined, which reects the tensile stress distribution characteristics in the soil. Acknowledgments ˜is study was ˙nancially supported by the National Natural Science Foundation of China (Grant No. 41602295), the Foundation for University Key Teacher by the Ministry of Education of Henan Province (Grant No. 2020GGJS-094), and the Key Scienti˙c Research Projects of Colleges and Universities in Henan Province (Grant No. 21A410002). REFERENCES [1] Adrian, R.J., 1999. Particle imaging techniques for experimental uid mechanics. Annual Review of Fluid Mechanics. 23 (1), 261-304. [2] Barzegar, A.R., Oades, J.M., Rengasamy, P., Murry, R.S., 1995. 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Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence THRESHOLD SILT CONTENT DEPENDENCY ON PARTICLE MORPHOLOGY (SHAPE AND SIZE) OF GRANULAR MATERIALS: REVIEW WITH NEW EVIDENCE ODVISNOST MEJNE VSEBNOSTI MELJA OD OBLIKE IN VELIKOSTI DELCEV ZA ZRNATE MATERIALE: PREGLED Z NOVIMI DOKAZI Abdellah Cherif Taiba (corresponding author) Youcef Mahmoudi Wiebke Baille Hassiba Ben Bouali University of Chlef, Hassiba Ben Bouali University of Chlef, Bochum Ruhr University, Laboratory of Material Sciences & Environment Laboratory of Material Sciences & Environment Laboratory of Soil Mechanics, Foundation B.P 78C, Ouled Fares Chlef 02180, Algéria B.P 78C, Ouled Fares Chlef 02180, Algéria Engineering & Environmental Geotechnics E-mail: a.cheriftaiba@univ-chlef.dz 44801 Bochum, Germany Torsten Wichtmann Mostefa Belkhatir Bochum Ruhr University, Hassiba Ben Bouali University of Chlef, Bochum Ruhr University, Laboratory of Soil Mechanics, Foundation Laboratory of Material Sciences & Environment Laboratory of Soil Mechanics, Foundation Engineering & Environmental Geotechnics B.P 78C, Ouled Fares Chlef 02180, Algéria Engineering & Environmental Geotechnics 44801 Bochum, Germany 44801 Bochum, Germany https://doi.org/10.18690/actageotechslov.18.1.28-40.2021 threshold silt content, silty sand, particle shape and size, packing density .e threshold silt content is well known as a key param­eter a.ecting the mechanical response of binary granular assemblies considering particle characteristics (size and shape). In this context, the threshold silt content (TSC) is determined from di.erent laboratory tests based on packing density response (emax and emin versus silt content ŤScť) and theoretical approaches proposed by several researchers in the specialized published literature using the characteristics of host sand and silt [emax(sand) , emin(sand) , emax(silt) , emin(silt) , Gs , Gf and x]. .e analysis of the recorded data indicates that the TSC derived from the (emax) curve appears more reliable than that obtained from the (emin) one. Moreover, it is found that the proposed analytical methods are suitable to quantify the threshold silt content (TSC) than that determined mejna vsebnost melja (TSC), meljasti pesek, oblika in velikost delcev, gostota pakiranja delcev Mejna vsebnost melja (TSC) je dobro znana kot klju˜ni parameter, ki vpliva na mehanski odziv dvojnih zrnatih sklopov glede zna˜ilnosti delcev, namre˜ velikosti in oblike. V tem okviru se TSC dolo˜i na podlagi razli˜nih laboratorijskih preizkusov, ki temeljijo na odzivu gostote pakiranja delcev (emax in emin glede na vsebnost melja, Sc) in teoreti˜nih pristopov, ki jih je predlagalo ve˜ razi­skovalcev v specializirani objavljeni literaturi z uporabo zna˜ilnosti vsebovanega peska in melja (emax(sand) , emin(sand)), emax(silt), emin(silt) , Gs, Gf in x). Analiza zabeleženih podatkov kaže, da je TSC, izpeljan iz krivulje emax, videti bolj zanesljiv kot tisti, dobljen iz krivulje emin. Poleg tega je bilo ugotovljeno, da so predlagane analiti˜ne metode primernejše za kvanti˙kacijo TSC kot tiste, ki so bile eksperimentalno dolo˜ene z uporabo gostote 28. Acta Geotechnica Slovenica, 2021/1 A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence experimentally using the packing density (emax and emin). In addition, the test results show that the new introduced ratios [(D50s×As)/(D50f×Af)] and [(Cus×As)/(Cuf×Af)] determined based on particle characteristics (shape and size) appear as appropriate parameters for predicting the threshold silt content (TSC) of sand-silt mixture of the compiled data from the published literature as well as that of the present research related to Chlef sand, Fontaineb­leau sand and Hostun sand mixed with Chlef silt. Abbreviations As = Angularity of sand Af = Angularity of silt Cus = Coecient of uniformity of sand Cuf = Coecient of uniformity of silt D10sand = E.ective diameter of sand (mm) D50s = Mean grain size of sand (mm) D50f = Mean grain size of silt (mm) emax = Maximum void ratio emin = Minimum void ratio Gs = Specifc gravity of sand Gf = Specifc gravity of silt R2 = Coecient of determination Sc = Silt content TSC = ˜reshold silt content x= Disparity of size (D10sand/d50silt) 1 INTRODUCTION ˜e contact level of soil inter-particles constitutes a fundamental index behind the evaluation of shear behavior sandy soils like the phenomenon of liquefac­tion while these particles participated in the forces chain created by monotonic and cyclic loading conditions [30]. ˜ey suggested that the relative density and conse­quently, the void ratio as key parameter in characterizing the contact between particles of sandy soils. However, the e.ectiveness of the global void ratio in sand-silt mixtures was questionable. In this context, they found that the silt particles ˙lled up the void spaces between sand particles without supporting the coarse particles, while the silt content was less than the threshold silt content (TSC) and they gave a name of intergranular void ratio for this case (Figure 1a). In contrast, they reported when the silt content increased than (TSC), the silt particle might carry out the contact of the interpar­ticle forces while the coarse particles acted as reinforced elements embedded with the matrix of silt particles and they proposed a new void ratio named as (inter˙ne void ratio) (Figure 1b). Moreover, published studies reported pakiranja delcev (emax in emin). Razen tega rezultati preizkusov kažejo, da sta na novo uvedeni razmerji (D50s×As)/(D50f×Af) in (Cus×As)/(Cuf×Af), ki temeljita na zna˜ilnostih delcev oblike in velikosti, ustrezna parametra za napovedovanje TSC za mešanico peska in melja iz zbranih podatkov iz objavljene literature, kot tudi razi­skave v zvezi s peskom Chlef, peskom Fontainebleau in peskom Hostun, pomešanim z meljem Chlef. contradictory ˙ndings on the inuence of silt content on shear behaviour of sand-silt mixtures and several technical interpretations were addressed for analyzing the experimental results of the binary granular mixtures [2, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 26 and 32]. Figure 1. Intergranular binary granular classi˙cation system [28 and 30]. [22] studied the binary packing of spherical particles by mixing of coarse spheres with six di.erent sizes of ˙ne spheres. He found that for the lower diameter of the ˙ne spheres, the greater packing density. ˜us, he explained the obtained behaviour by the fact that the ˙ne-grained soil particles ˙lled up the void spaces of the coarse-grained material with vibrating until it reached a minimum volume. In the other hand, when the vibration of coarse particles stopped, and the ˙ne particles were poured into the container and vibration continued until a minimum volume was again attained. He indicated also that the ultimate density of the packing process was independent of the formed rate which was related to the frequency and acceleration of mechanical vibration, density of materials, and number of particles per unit volume and evacuation of container during packing density (Figure 2). In this context, [17] were the ˙rst researchers who de˙ned the threshold silt content “TSC” characteristic as a relevant indicator in the change of the mechani­cal characterization of granular materials which was considered as the most important inuent parameter to A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence predict the response of sand dominated and silt domi­nated in the binary granular systems. Based on their researches, they suggested that the threshold silt content has been related to the packing density (maximum void ratio “emax” and minimum void ratio “emin”) of sand-sit mixtures (Figure 3 on the le side), where, they showed that the minimum void ratio was reached at the lowest point when the silt particles completely ˙lled up the void spaces of coarse particles and the obtained silt content was termed as the threshold silt content (TSC) (point B on the right side of Figure 3). [17] suggested an analytical method to determine the threshold silt content (TSC) based on the maximum void ratio of sand (emax(sand)) and silt (emax(silt)) accord­ing to following equation: (1) Moreover, [14] considered the speci˙c gravity di.erence of sand (Gs) and that of silt (Gf) and proposed an empiri­cal relationship based on the maximum void ratio and speci˙c gravity of the sand and silt under consideration (equation 2). (2) In addition, [35] suggested another theoretical approach to evaluate the threshold silt content (TSC) based on Figure 3. Variation of maximum and minimum void ratios with di.erent silt content [17 and 32]. 30. Acta Geotechnica Slovenica, 2021/1 A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence index properties of sand [minimum void ratio (emin(sand)) and speci˙c gravity (Gs)] and silt [minimum void ratio (emin(silt)) and speci˙c gravity (Gf)] (equation 3): (3) Figure 4. Variation of threshold silt content (TSC) with disparity ratio x. However, [28] proposed a semi-analytical relationship between the threshold silt content (TSC) based on the disparity of size (x) de˙ned as the ratio between the median size (D50f) of ˙nes and D10 which is the 10 % fractile of host sand according to the equation (4) and Figure (4). (4) On the other hand, [1, 8, 11, 12, 33] reported that sphe­ricity (S) is quanti˙ed as the ratio of the diameter of the largest inscribed sphere relative to the diameter of the smallest circumscribed sphere, however, the roundness (R) as the ratio of the average radius of curvature of surface features relative to the radius of the maximum sphere that can be inscribed in the particle. Indeed, [27] subdivided the sphericity in two classes (higher spheric-ity and lower sphericity) and the angularity in six catego­ries (very angular, angular, sub-angular, sub-rounded, rounded and well-rounded) according to Figure (5). [3] performed a series of oedometer, triaxial and resonant column tests on saturated coarse rotund sand (i.e., Leighton Buzzard Sand) mixed with ˙nes (i.e., mica) according to various mixture ratios. He found out the existence of close relationships between the transition ˙nes content and mechanical properties of mixtures through the triaxial and resonant column tests. [23] conducted a series of undrained monotonic triaxial compression tests on thirty sands with varying ˙nes contents, which were reconstituted by mixing three base sands (Sile Sands 20/30, 50/55, 80/100) with same geologic origin but with di.erent gradations and three di.erent non-plastic silts (IZ, SI and TT silts) with di.erent gradations and shape properties. ˜ey showed that the inuence of granulometric factors (CUsilt, d50-silt) Figure 5. Classi˙cation of angularity and sphericity [27]. A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence and shape characteristics (R, S) of silty grain matrix on undrained shear strength of Sile Sands was dependent on the value of ˙nes content parameter. [4] conducted a series of fall cone tests on clay-sand mixtures to explore the variation of liquid limit with sand content and the link between the undrained shear strength and water content for various sand contents in the tested mixtures. ˜ey demonstrated clearly that an approximate linear relationship between the cone penetration and the water content for both clay-NS and clay-CSS mixtures in the range of mixtures proportions used. [29] performed a series of bender element and triaxial tests on the Ottawa sand-silt mixture considering the range of 5–20 % ˙nes content. ˜ey observed that the addition of even small percentages of silt to clean sand considerably increased both the peak friction angle and the critical-state friction angle at a given initial relative density. [5] performed a series of hydraulic conductivity tests on coarse-grained soils with di.erent particle sizes and shapes. ˜ey showed that the rounded sands exhibited lower hydraulic conductivity values than the angular sands. [9] proposed new empirical correlations relating the hydraulic conductivity with the packing density and particle shape of silty sand soils. ˜ey found that the saturated hydraulic conductivity decreased according to a polynomial function with the decrease of the predicted extreme void ratios (emax and emin) of the tested materi­als. Moreover, they indicated that the saturated hydraulic conductivity (Ks) decreased polynomially with the decrease of the roundness ratio (Rr = Rhs/Rmixture) and increase of the sphericity ratio (Sr = Shs/Smixture) for the (Fc = 0 % - 30 %) range of low plastic ˙nes content of the used sand-silt mixtures. [12] demonstrated clearly that the size and shape of soil particles reected the formation history of the grains. In addition, they found through a series of experimental tests and analysis of data from published literature that the particle shape characteristics of grains impacted signi˙cantly the Table 1. Summary of the index properties of the sand-silt mixture from published literature and present study. Sources Materials Gs Gf emax emin D50s D50f Cus Cuf As Af As/Af ˜is study Chlef sand 2.652 - 0.795 0.632 0.596 - 2.634 - 0.439 - 0.70 ˜is study Fontainebleau sand 2.642 - 0.950 0.645 0.558 - 3.157 - 0.390 - 0.62 ˜is study Hostun sand 2.650 - 1.021 0.646 0.369 - 1.536 - 0.319 - 0.51 ˜is study Chlef silt - 2.667 1.563 0.991 - 0.032 - 12.66 - 0.626 - [2] Chlef sand1 Chlef silt1 2.680 - -2.700 0.876 1.137 0.535 0.720 0.68 - -- 3.36 - -- -- -- 0.80 [32] Hokksund sand Chengbei silt 2.712 - -2.739 0.949 1.413 0.572 0.731 0.44 - -0.032 2.38 - -1.95 -- -- 2.6 [31] Sxinias-Marathon sand Sxinias-Marathon silt 2.69 - -2.69 1.04 1.77 0.66 0.66 0.12 - -0.02 -- -- -- -- - [16] Mai Liao sand Mai Liao silt 2.69 - -2.71 1.125 - 0.646 - 0.123 - -0.044 1.75 - -2.79 - -- 1 [24] Alluvium sand Alluvium silt -- -- -- -- 0.778 - -0.038 5.63 - -5.43 -- -- 2.4 [34] Toyoura sand Toyoura silt 2.65 - -- 0.977 1.754 0.600 0.500 0.17 - -0.01 1.61 - -6.08 0.486 - -0.486 1 [30] OS00 sand Silica silt -- -- 0.800 2.1 0.608 0.627 0.25 - -0.01 1.69 - -7.50 -- -- 2.8 [25] M31 sand Assyros silt 2.65 - -2.66 0.841 1.663 0.582 0.658 0.30 - -0.02 -- -- -- -- 3.4 [28] Sydney sand Majura silt 2.63 - -2.49 0.855 - 0.565 - 0.27 - -0.006 1.26 - -12.50 -- -- 1 [13] Ahmedabad sand Quarry Dust silt 2.65 - -2.67 0.68 1.632 0.42 0.652 0.375 - -0.037 3.58 - -7.83 -- -- - [15] Kaohsiung sand Kaohsiung silt 2.70 - -2.70 0.696 - 0.238 - -- -- 7.92 - -- -- -- - 32. Acta Geotechnica Slovenica, 2021/1 A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence packing density and small-to-large strain mechanical properties of sandy soils, where, they found out that the increase of the angularity or eccentricity produced an increase in the extreme void ratios (emax and emin) of soils. In this context, they proposed some empirical relationships between particle shape characteristics in terms of (roundness, sphericity and regularity) and packing density of compiled data from the published literature. Finally, published literature accorded particular atten­tion to the determination of the threshold silt content (TSC) based on the packing density in terms of extreme void ratios (emax and emin), index properties in terms of speci˙c gravity (Gs and Gf) [14, 17, 35] and particle size in terms of disparity ratio (x) [28] of sand-silt mixtures. However, [35] emphasized the importance to evaluate the inuence of shape of particles and packing density to harmonize the experimental and analytical prediction of the threshold silt content (TSC). To achieve this goal, the present research intends to explore the relationships between the threshold silt content (TSC) and particle characteristics in terms of [particle size (mean grain size “D50” and coecient of uniformity “Cu”) and particle shape (angularity “A”)] through di.erent methods reported in published literature as experimentally [packing density of sand and silt “extreme void ratios index, emax and emin versus silt content Sc”] and theoretically according to the approaches of [14, 17, 28] of the compiled data from the published sources as well as those of the present research related to three di.erent sands [Chlef sand, Fontainebleau sand and Hostun sand with distinct shapes [“rounded shape”, “sub-rounded shape” and “sub-angular shape”] respectively mixed with Chlef rounded shape silt. 2 EVALUATION OF THRESHOLD SILT CONTENT USING PACKING DENSITY CHARACTERISTICS FROM PUBLISHED STUDIES Figure 6 reproduces the data from the published litera­ture [2, 15 and 32] as well as those of the present study on three di.erent sand-silt mixtures such as “Chlef rounded sand-silt mixtures, Fontainebleau sub-rounded sand-silt mixtures and Hostun sub-angular sand-silt mixtures” showing the relationship between the extreme void ratios indexes (emax and emin) with silt content ranging from (Sc =0% to Sc = 100 %). It is clear from Figure 6 that the overall extreme void ratios tendencies (emax and emin) exhibit a decrease with the increase of silt content of the range of Sc =0% to Sc = 45 %. Beyond that, they continue Figure 6. Void ratio index versus silt content of compiled data and those of the present study. (a) Minimum void ratio (b) Maximum void ratio to show a signi˙cant increasing with the increase of silt content from Sc =45% to Sc = 100 % for the collected data from the published literature [2, 15 and 32] as well as the data related to the present laboratory investigation on the di.erent tested silty sand samples as “Chlef, Fontaineb­leau and Hostun sand-silt mixtures”. Moreover, it appears that the threshold silt content of the compiled data and that of the present study ranges between Sc = 15 % and Sc = 45 % depending on the nature of the materials. In addition, Figure 6b demonstrates clearly that the A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence threshold silt content determined from the maximum void ratio (emax) curves is more reliable than that derived from the minimum void ratio (emin) curves, where it gives an indication of the possible range in which the threshold silt content (TSC) might occur. ˜ese ˙ndings are in good agreement with observations of [17]. 3 EVALUATION OF THRESHOLD SILT CONTENT FROM EXPERIMENTAL AND ANALYTICAL METHODS OF DIFFERENT PUBLISHED STUDIES In order to evlauate the threshold silt content (TSC) using the experimental method [extreme void ratios indexes “emax and emin” versus silt content “Sc”] based on packing density characteristics “emax and emin ”, the proposed analytical methods by [14, 17 and 35] and the suggested semi-analytical method by [28] for the di.er­ent data compiled from the published literature [2, 13, 25, 30, 31 and 32] inculding those of the present study related to three distinct materials such as “Chlef rounded sand, Fontainebleau sub-rounded sand and Hostun sub-angular sand”. ˜e obtained data of the curent study indicate that the threshold silt content determined by Figure 7. Comparison of di.erent methods for evaluation of threshold silt content from data of published literature and those of current study. packing density’s method presents a larger range from TSC =25% to TSC = 45 %. Indeed, same ˙ndings were observed for the threshold silt content obtained by third analytical method proposed by [35] which is less scarttered than those deteremined by method 1 and 2, where the threshold silt content values range between TSC = 25 % and TSC = 48 %. Moreover, it could be seen from the analytical approaches proposed by [14 and 17] which were based on the index properties of sand and silt “ maximum void ratio and speci˙c gravity) showed a narrower range of threshold silt content (TSC) for all di.erent silty sand soils under consideration. However, the determination of threshold silt content (TSC) from the semi-analytical approach proposed by [28] which was derived empirically from the experiemental published data and related to the sand-silt gradation (equation 4) is in good agreement with that obtained by the calculation methods 1 and 2. ˜ese ˙ndings con˙rm that the determination of the threshold silt content (TSC) from calculation approaches is better than those determined experimentally using the packing density of silty sand soils in terms of maximum void ratio (emax) and mimimum void ratio (emin). In addition, the evalu­ation of threshold silt content (TSC) from the analytical methods proposed by [14 and 17] (1 and 2) that was based on the maximum void ratio (emax) and speci˙c gravity of sand and silt (Gs and Gf) (equations 1 and 2 ) were more realistic than those determined by the third analytical approach proposed by [35] which was based on minimum void ratio (emin) and speci˙c gravity (Gs and Gf) of silty sand soils (equation 3). ˜is con˙rms that the maximum void ratio (emax) is a suitable index to evaluate experimentally and analytically the threshold silt content (TSC) of the di.erent binary granular assem­blies under consideration. 4 EVALUATION OF THRESHOLD SILT CONTENT BASED ON PARTICLE MORPHOLOGY FROM PUBLISHED LITERATURE 4.1 Particle angularity ratio (As /Af ) Figure 8 illustrates the variation of threshold silt content (TSC) with angularity ratio [angularity of sand “As ” and angularity of silt “Af ”] of compiled data from published literature [ 2, 16, 24, 28, 32 and 34] and those of the current study on three di.rent sands with dinstinct shapes [Chlef sand “rounded shape, As = 0.439”, Fontainebleau sand “sub-rounded shape, As = 0.390” and Hostun sand “sub-angular shape, As = 0.319”] mixed with Chlef silt “rounded shape, Af = 0.626”] using the di.erent methods cited above for the determination of the threshold silt content (TSC) (equations 1, 2, 3 and 34. Acta Geotechnica Slovenica, 2021/1 A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence 4) respectively. It seems that the threshold silt content (TSC) increases with the increase of angularity ratio (As/Af) for all di.erent data cited in this study. Moreover, the obtained results indicate that the threshold silt content presents a norrower range for the smallest angu­larity ratio values varying between As/Af = 0.5 and As/Af = 1 compared to the larger range of threshold silt content (TSC) for the highest angularity ratio values ranging between As/Af = 2.4 and As/Af = 2.8 for the the compiled points from published sources and those of the current study data for the experimental and analyti­cal approaches used in this research to evaluate and determine the threshold silt content (TSC). In addition, for the case of As/Af = 2.8 [30 and 35] reported that the particle shape has insigni˙cant inuence on the thresh­old silt content for the ratio beteween the larger sand particles and smaller silt particles (discussed in Figure 8). ˜eses observations indicate that the decreasing in angularity ratio (As/Af) “increasing of silt angularity” has a signi˙cant e.ect on the threshold silt content comparing to the highest values of anuglarity ratio and this indicates the e.ect of particle shape of soil grains especially that of the silt particles playing a major role on the threshold silt content and consequently on the behaviour of binary granular soils under consideration. 4.2 Mean grain size ratio (D50s /D50f ) For the purpose of analyzing the relationship between the threshold silt content (TSC) and the ratio of the mean grain size of sand (D50s) to the mean grain size of silt (D50f) of some compiled studies from published sources and data of the present study on three sands having di.erent mean grain sizes such as (Chlef sand, D50 = 0.596 mm, Fontainebleau sand, D50 = 0.558 mm, Hostun sand, D50 = 0.369 mm mixed with Chlef silt, D50 = 0.032 mm). ˜e threshold silt content was deter­mined using the analytical approaches proposed by [14, 17 28 and 35] which was based on the index properties of sand and silt (emax, emin, Gs, Gf) and grain size (D10 and D50) of sand and silt respectively. It is clear from this plot that the threshold silt content increases with the increase of the mean grain size ratio (D50s/D50f) ranging from D50s/D50f = 2.79 for the study of [16] to D50s/D50f = 25 for the study of [30] for all distinct silty sand soils evaluated in this research. Moreover, the obtained data indicate that mean grain size ratio has a signi˙cant inuence on the threshold silt content (TSC) for the intermediate value of (D50s/D50f) which varies between D50s/D50f = 10 to D50s/D50f = 20 concerning the studies of [24, 32 and 34] with the tested soils such as Chlef, Fontainebleau and Hostun sands respectively). ˜is trend was explained by [35] in the way that the nature of fabric and type of packing including the grain size of mixtures participate in changing the threshold silt content and consquently Figure 8. ˜reshold silt content versus angularity ratio of Figure 9. ˜reshold silt content versus mean grain ratio of di.erent studies from published literature and current study. di.erent studies from published literature and current study. A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence changing the mechanical behaviour of silty sand soils. In addition, for the larger mean grain size ratio D50s/D50f = 25 (the silty sand soils tested by ˜evanayagam et al. 2002), the threshold silt content (TSC) determined by analytical methods proposed by several researchers in literature ranges from TSC =20% to TSC = 48 % for the tested sand-silt mixtures. In this case, the mean grain size ratio between larger and smaller particles might be highlighted by packing density of mixtures rather than by the particle shape of silty sand soils [35]. 4.3 Coffcient of uniformity ratio (Cus /Cuf ) In the context of evaluating the variation of the thresh­old silt content (TSC) with the ratio of the coecient of uniformity of sand (Cus) to the coecient of uniformity of silt (Cuf) of nine di.erent researches based on the compiled data from the pulished literature as [2, 16, 24, 28, 32 and 34] and those of the present study related to three sands with di.erent coecients of uniformity such as (Chlef sand “Cu = 2.634”, Fontainebleau sand “Cu = 3.157” and Hostun sand “Cu = 1.536” mixed with Chlef silt with a coecient of uniformity of “Cu = 12.66”). ˜e obtained results indicate that the threshold silt content increases with the decrease of the coecient of uniformity ratio (Cus/Cuf) for the plotted points compiled from di.erent research sources using the analytical methods proposed by [14, 17, 28 and 35]. Moreover, it could be seen from this plot that the threshold silt content presents a norrower range for the coecient of uniformity ratio (Cus/Cuf) varying between Cus/Cuf = 0.1 and (Cus/Cuf = 0.3 for (Hostun sand, Chlef sand, Fontainebleau sand and the studies of [2 and 30]). ˜is con˙rms that the increase in the coecient of uniformity of di.erent silts used in the di.erent studies leads to a signi˙cant decreasing in the coecient of uniformity ratio (Cus/Cuf) inducing an important changing in the threshold silt content (TSC) and consequently a.ects in signi˙cant manner the mechanical response of sand-silt mixture samples under study. ˜erefore, the highest values of coecient of uniformity ratio (Cus/Cuf) lead to more scatter between the granular assemblies with no appreciable trend for the studies of [ 16, 24 and 24]. In addition, the obtained results from Figures 8 and 9 show that the grain size of silt in terms of mean grain size (D50) and coecient of uniformity (Cu) appear as appropriate parameters to predict and determine the threshold silt content (TSC). Indeed, their increasing leads to a decrease of the mean grain size ratio (D50s/D50f) and coecient of uniformity ratio(Cus/Cuf) of the silty sand inducing a signi˙cant e.ect on the threshold silt content and consequently on the behaviour of binary granular systems under consideration. 5 EXPLORING THE RELATIONSHIP BETWEEN THRESHOLD SILT CONTENT WITH THE MEAN GRAIN SIZE AND PARTICLE ANGULARITY For the purpose of suggesting suitable ˙ttings and exploring eventual new correlations between the threshold silt content and particle characteristics in terms of [Coecient of uniformity “Cu ”, mean grain size “D50 ”, Angularity “A”] of sand and silt based on the proposed analytical methods [17 “1”, 14 “2”, 35 “3” and 28 “4”] by several researchers to evaluate the threshold silt content, Figure 11 illustrates the variation of threshold silt content (TSC) with the ratio between the particle morphology index of sand (D50s×As) and that of silt (D50f ×Af) of di.erent silty sand soils. As it could be seen in Figure 11, a polynomial relationship may express the variation of the threshold silt content (TSC) as a function of the ratio [(D50s×As)/(D50f ×Af)] for all the considered analytical methods used in this study to determine the transitional point between sand dominated and silt dominated for the di.erent granular assemblies. Moreover, the obtained results indicate that method 1 of [17] and method 2 of [35] present good polynomial correlations with higher coecient of determination (R˛ = 0.75 and R˛ = 0.99 respectively) comapred to the anlaytical method proposed by [14] and 36. Acta Geotechnica Slovenica, 2021/1 A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence (a) First analytical method (1) (b) Second analytical method (2) (c) ˜ird analytical method (3) (d) Rahman's method Figure 11. Variation of the threshold silt content as function of the ratio (D50s×As)/(D50f ×Af) for di.erent methods. the semi-analytical approach proposed by [28] where the cocient of determination were (R˛ = 0.498 and R˛ = 0.221) respectively. ˜e obtained trend indicates that the new introduced ratio [(D50s×As)/(D50f ×Af)] and consquently the particle size and shape characteristics of sand and silt impact signi˙cantly the packing denisty properties [emax in equation (1) and emin, Gf and Gs in equation (3)] for the considered binary granular mixtures. On the other hand, this ˙nding con˙rms that the particle size (mean grain size of sand and silt) and particle shape parameter (angularity of sand and silt) and consequently the ratio [(D50s×As)/ (D50f ×Af)] appear as suitable parameter to pridect the threshold silt content (TSC) of binary granular systems according to the following expressions : TSC = 0.043 × [(D50s×As)/(D50f ×Af)]˛ + (5) 0.23× [(D50s×As)/(D50f ×Af)] + 25.607 ; R˛ = 0.75 TSC = 0.0106 × [(D50s×As)/(D50f ×Af)]˛ (6) 0.434 × [(D50s×As)/(D50f ×Af)] + 26.397 ; R˛ = 0.99 6 EXPLORING THE RELATIONSHIP BETWEEN THRESHOLD SILT CONTENT AND THE COEFFICIENT OF UNIFORMITY AND PARTICLE ANGULARITY ˜e data related to the correlation between the threshold silt content (TSC) and the ratio[(Cus×As)/ (Cuf ×Af)] [ratio between coecient of uniformity and particle angularity of sand with the cocient of uniformity and particle angularity of silt] of di.erent silty sand soils selected from the published sources as well as those of this study on (Chlef, Fontainebleau and Hostun sands) are discussed in this section. ˜e analysis of the obtained data from Figure 12 con˙rm the existence of a power function relationship that may relate the threshold silt content (TSC) to the ratio [(Cus×As)/(Cuf ×Af)] for the selected calculation methods used in this research as (Lade’s method, Hazirbaba’s method, Zuo’s method and Rahman’s method). As it can be seen, the Lade’s method shows a good power function with a coecient of deter- A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence (a) First analytical method (1) (b) Second analytical method (2) (c) ˜ird analytical method (3) (d) Rahman's method Figure 12. Evaluation of threshold silt content based on the ratio of (Cus×As)/(Cuf ×Af) for di.erent methods. mination of (R˛ = 0.87) compared to the Hazirbaba’s approach (R˛ = 0.006), Zuo’s approach (R˛ = 0.82) and Rahman’s method (R˛ = 0.63). ˜is observation demon­strates clearly that the coecient of uniformity and particle angularity of sand and silt and consquently the ratio [(Cus×As)/(Cuf ×Af)] exhibits a consequent impact on the evolution of the threshold silt content (TSC) calculated through the packing density (emax) using the approach of [17] compared to the other proposed approaches suggested by several researchers in published literature. ˜e obtained soil trend con˙rms that particle characteristics in terms of cocient of uniformity and angularity may a.ect considerably the changing thresh­old silt content points between the sand dominated and silt dominated in the sand-silt matrix under study. the following equation is suggested to express the relation­ship between the threshold silt content (TSC) and the ratio [(Cus×As)/(Cuf ×Af)] for the di.erent binary granu­lar assemblies under consideration. TSC = 18.74*[(Cus×As)/(Cuf ×Af)]-0.249 ; R˛ = 0.87 (7) 7.CONCLUSION ˜e threshold silt content (TSC) represents a key parameter in the physical identi˙cation and mechanical characterization of binary granular mixtures. It has been reported by many researchers that it is the boundary condition explaining the di.erent properties of the sand dominated or silt dominated in the overall matrix sand-silt under consideration. ˜is parameter was determined experimentally using laboratory tests (emax and emin versus Sc) curves and theoretically according to analyti­cal and semi-analytical approaches that were proposed by several researchers in the published literature. In this context, the main results of this research are summa­rized as follows: 1. ˜e analysis of the compiled data and those of the present study indicates that the theshold silt content may be established according to the variation of the extreme void ratios indexes (emax and emin) with silt content (Sc) for the tested silty sand soils. Indeed, the 38. Acta Geotechnica Slovenica, 2021/1 A. C. Taiba et al.: Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence threshold silt content determined from the (emax) curve is more reliable than that derived from the (emin) curve, where it represents an indicator charac­terizing the possible range in which the (TSC) might exist. 2. ˜e recorded data from published literature and those of the present study show that the calculation methods used in the evaluation the threshold silt content give more clari˙cation compared to the TSC calculated experimentally according to the packing density of binary granular assemblies. Moreover, the analysis of the collected data demonstrates clearly that the threshold silt content (TSC) increases with the increase of the ratio of [particle angularity of sand to that of silt “As/Af ”] and the ratio of [mean grain size of sand to that of silt “D50s/D50f ”] of sand-silt mixtures. However, it exhibits an increase with the decrease of the ratio of the coecient of unifor­mity of sand (Cus) to that of silt (Cuf) for the di.erent silty sand soils under investigation. 3. ˜e data collected from published literature and those of the present laboratory study con˙rm the existence of good correlations relating the threshold silt content (TSC) to the particle characteristics in terms of size and shape for the considered binary granular systems. Where, the new introduced ratios [(D50s×As)/(D50f ×Af)] and [(Cus×As)/ (Cuf ×Af)] appear as pertinent parameters that could be used to predict the threshold silt content (TSC) derived from the compiled data from the published literature and those related to this study on (Chlef sand, Fontaineb­leau sand and Hostun sand mixed with Chlef silt). Acknowledgments ˜is research work was performed in the context of mutual scienti˙c cooperation between the Laboratory of Material Sciences & Environment, Hassiba Ben Bouali University of Chlef (Algeria) and the Laboratory of Soil Mechanics, Foundation Engineering & Environmental Geotechnics, Bochum Ruhr University (Germany). ˜e authors are grateful for the ˙nancial support received from the Directorate General for Scienti˙c Research and Technological Development, Algeria. REFERENCES [1] Barrett, P. J. 1980. ˜e shape of rock particles, a critical review. Sedimentology. Vol. 27, pp. 291-303. [2] Belkhatir, M., Arab, A., Missoum, H., Della, N., Schanz,T. 2011. Laboratory study on the liquefac­tion resistance of sand-siltmixtures: e.ect of grad­ing characteristics. Granular Matter 13:599–609 [3] Cabalar , A,F 2010. Applications of the triaxial, resonant column and oedometer tests to the study of micaceous sands. 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Acta Geotechnica Slovenica, 2021/1 A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand SMALL SCALE MODEL TEST MODELNI PREIZKUS V MAJH­ ON LATERAL BEHAVIORS OF NEM MERILU ZA BO˜NO PILE GROUP IN LOOSE SILICA OBNAŠANJE SKUPINE PILOTOV SAND V SILIKATNEM PESKU RAHLEGA GOSTOTNEGA STANJA Amir Vakili Seyed Mohammad Ali Zomorodian Arash Totonchi Islamic Azad university, (corresponding author) Islamic Azad university, Dep. of civil engineering, Najafabad branch Islamic Azad university, Dep. of civil engineering, Najafabad branch Najafabad, Iran Dep. of civil engineering, Najafabad branch Najafabad, Iran Najafabad, Iran Islamic Azad university, Shiraz University, Dep. of civil engineering, Marvdasht branch Dep. of water engineering Marvdasht, Iran Shiraz, Iran E-mail: mzomorod@shirazu.ac.ir https://doi.org/10.18690/actageotechslov.18.1.41-54.2021 pile group, lateral load, p-y method, load angle, group reduction factor .e accurate predictions of load- deection response of the pile group are necessary for a safe and economical design. .e behavior of piles under the lateral load embedded in soil, is typically analyzed using the Winkler nonlinear springs method. In this method, the soil-pile interaction is modeled by nonlinear p-y curves in a way that the single pile p-y curve is modi˙ed using a p-multiplier (Pm) for each row of piles in the group. .e average Pm is called the group reduction factor. .e Pm factor depends upon the con˙guration of pile group and the pile spacing (S). .e present study was conducted to investigate the e.ects of various parameters, such as the pile spacing in the group, di.erent layouts and the lateral load angle () change as a new parameter on the Pm factor and group eciency based on the 1-g model test. .e Pm factor is well comparable with the results of the full-scale test on pile group. However, based on the results, the calculated values of the Pm factor for 3×3 pile groups under 2.5-diameter spacing was estimated about 0.38 and under 3.5-diameter spacing was estimated skupina pilotov, bo°na obtežba, p-y metoda, naklon obtežbe, koli°nik redukcije skupine pilotov Za varno in ekonomi˜no zasnovo skupine pilotov so potrebne natan˜ne napovedi odziva obtežba-pomik. Obnašanje vpetih pilotov obremenjenih s pre˜no obtežbo, se obi˜ajno analizira z uporabo Winklerjeve metode neli­nearnih vzmeti. S to metodo se interakcija zemljina-pilot modelira z uporabo nelinearnih krivulj p-y na na˜in, da se krivulja p-y enega pilota spremeni s p-multiplikatorjem (Pm) za vsako vrsto pilotov v skupini. Povpre˜ni Pm se imenuje koli˜nik redukcije skupine pilotov. Faktor Pm je odvisen od kon˙guracije skupine pilotov in razmika med piloti (S). V pri˜ujo˜i študiji se raziskujejo u˜inki razli˜nih parametrov, kot so razmik med piloti v skupini, razli˜ne postavitve pilotov in kot bo˜ne obtežbe () kot novega parametra, ki vpliva na koli˜nik Pm ter u˜inkovitost skupine pilotov na podlagi 1-g preizkusnega modela. Tako dobljen koli˜nik Pm je zelo primerljiv z rezultati celovitega testa na skupini pilotov. Na podlagi rezultatov pa so bile izra˜unane vrednosti faktorja Pm za skupine pilotov 3×3 pri medsebojnem razmiku 2,5 premera ocenjene na približno 0,38, pri medsebojnem razmiku 3,5 premera A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand about 0.52, so the calculated values at S/D=3, obtained from interpolation the values of group reduction factor at S/D=2.5 and S/D=3.5, are close to the AASHTO recommendation. 1 INTRODUCTION When the piles act in a group, the strength and lateral-bearing of the individual piles are reduced by soil-pile interaction. In general, the pile group will exhibit less lateral capacity than the sum of the lateral capacities of the individual piles. In the pile group, each pile pushes against the soil in front of it, creating a shear zone in the soil, which expand with increasing lateral loading. ˜e overlap that occurs between the piles in the same row is called "edge e.ects", while the overlapping created between the di.erent rows of piles in the group is called the "shadowing e.ect". ˜ese shadowing and edge e.ects are signi˙cant factors in the bearing capacity of pile groups, which may reduce the lateral resistance of each individual pile in the group [1, 2]. ˜e overlapping of the shear zones created in the pile group is shown in Figure 1. Several methods have been proposed to model lateral pile group response. For example, Ooi and Duncan (1994) developed a group ampli˙cation procedure. pa približno 0,52. Zato so izra˜unane vrednosti koli˜nika redukcije skupine pri S/D=3, dobljene z interpolacijo vrednosti koli˜nika redukcije skupine pri S/D=2,5 in S/D=3,5, blizu priporo˜ilu AASHTO. However, they are neither able to estimate the distribu­tion of loads among piles within a group nor take into account the pile group arrangement [3]. ˜e group e.ects in pile groups are taken account of by reducing the subgrade modulus. Pise and Patra (2001) carried out lateral loading model 1-g tests on ˙xed head model piles and small pile groups in sand to investigate the ultimate lateral resistance of a pile group. Similar to Ooi and Duncan’s procedure (1994), this method is not able to calculate the distribution of loads among piles in a group [4]. ˜e lateral response of piles is typically analyzed using the beam on nonlinear Winkler springs model. ˜e nonlinear springs are based on the p-y curves proposed by the American Petroleum Institute (API), where p indi­cates the soil resistance around the pile and y is the lateral deection [5, 6]. One of the most common methods of accounting for the group e.ects in the Winkler model is to modify the single pile p-y curves using a Pm factor, as suggested by Brown et al. (1988). In this approach, the p-multiplier was determined by comparing with the p-y curves obtained in laterally loaded single pile tests as shown in ˙gure 2. ˜e value of the Pm coecient for the leading row (the row which has the longest distance from the lateral load) is higher and for the trailing row is considered less because of the shadowing e.ects [7]. ˜e leading and trailing rows interchange during the seismic and dynamic loading. ˜erefore, an average value of Pm is sometimes used for all the piles in the group. ˜e aver­age of the Pm coecient is called "group reduction factor" (Brown et al., 2001) [8]. Figure 1. Overlapping of failure zones (shadowing) Figure 2. De˙nition of p-multiplier (Pm) and Ps horizontal and gap formation behind piles [1]. resistance of soil for single pile [8]. 42. Acta Geotechnica Slovenica, 2021/1 A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand Table 1. ˜e group reduction factor from previous studies. Reference Soil type Test type Pile con-˙gura­tion Pile type D (cm) S/D Pile head condi­tion 1 p-multiplier for row 2 3 4 5 6 7 Groupreduc­tion factor Brown et al. (1988) [7] medium dense sand full scale 3×3 steel pipe 27.3 3 free 0.8 0.4 0.3 - - 6 - 0.5 Morrison and Reese (1988) [14] medium dense sand full scale 3×3 steel pipe 27.3 3 free 0.8 0.4 0.3 - - - - 0.5 medium loose sand centrifuge 3×3 steel pipe 43 5 free 1 0.85 0.7 - - - - 0.85 McVay et al. (1995) [9] medium dense sand medium loose sand centrifuge centrifuge 3×3 3×3 steel pipe steel pipe 43 43 5 3 free free 1 0.65 0.85 0.45 0.7 0.35 -- -- -- -- 0.85 0.48 medium dense sand centrifuge 3×3 steel pipe 43 3 free 0.8 0.4 0.3 - - - - 0.5 sand centrifuge 3×3 squaresteel 42.9 3 ˙xed 0.8 0.4 0.3 - - - - 0.5 sand centrifuge 3×4 squaresteel 42.9 3 ˙xed 0.8 0.4 0.3 0.3 - - - 0.45 McVay et al. (1998) [10] sand centrifuge 3×5 squaresteel 42.9 3 ˙xed 0.8 0.4 0.3 0.2 0.3 - - 0.4 sand centrifuge 3×6 squaresteel 42.9 3 ˙xed 0.8 0.4 0.3 0.2 0.2 0.3 - 0.37 sand centrifuge 3×7 squaresteel 42.9 3 ˙xed 0.8 0.4 0.3 0.2 0.2 0.2 0.3 0.34 Huang et al. (2001) [15] Rollins and Sparks (2002) [16] Rollins et al. (2005) [17] Walsh (2005) [18] Christensen (2006) [19] Rollins et al. (2006) [20, 21] Kim and Yoon (2011) [11] silty clay silty clay sand sand sand sti. clay sand full scale full scale full scale full scale full scale full scale small scale 2×3 3×3 3×3 3×5 3×3 3×3 3×3 RC steel pipe steel pipe steel pipe steel pipe steel pipe steel pipe 150 32.4 32.4 32.4 32.4 32.4 1.2 3 3 3.3 3.92 5.65 5.65 3 ˙xed ˙xed free free free free ˙xed 0.93 0.6 0.8 1 1 0.95 0.69 0.7 0.74 0.38 0.43 0.4 0.4 0.5 0.35 0.7 0.65 0.88 0.77 0.35 0.3 ---0.3 --- ---0.4 --- ------- ------- 0.79 0.47 0.53 0.51 0.78 0.87 0.5 ˜e group reduction factor can be obtained using laboratory studies or full-scale tests. Full-scale tests are the best means for investigating the behavior of laterally loaded piles. It is, however, very expensive and dicult to perform a full-scale test on a pile group. ˜e capacity of the loading equipment also limits the size of the pile group that can be tested. ˜erefore, full-scale tests are oen performed on small models of pile groups at close distance between piles. Centrifuge test is considered as a useful alternative to full-scale test, which can be used to study the "group reduction factor" (McVay et al., 1995 and 1998) [9, 10]. Kim and Yoon (2011) proposed the response assessment of a laterally loaded pile group in 3, 4 and 6-diameter pile spacing based on laboratory modeling and suggested that pile spacing of more than six times the pile diameter in group seemed to be large enough to eliminate the group e.ects of the pile [11]. Soomro et al. (2018), presented lateral responses of an existing 2×2 pile group for advancing side-by-side twin tunnels at various depths in dry sand. [12]. Al-Shamary A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand et al. (2018) used three-dimensional ˙nite-element approach to assess the responses of lateral pile and pile group subjected to pure lateral load. Based on the results, the behavior of the pile group 2×2 was close, but not the same as the behavior of pile group 2×1. Regard­ing the group 3×2, the lateral pile displacement and lateral soil resistance had similar values for the ˙rst and second trailing rows. ˜e values of the p-multiplier (pm) for leading pile are always greater than those obtained for ˙rst and second trailing pile [13]. Table 1 indicates a list of full-scale, small-scale, and centrifuge experimental studies. Most experiments have been conducted on pile groups with 3×3 arrangement, with free head conditions, center to center spacing of 3 pile diameters (S/D = 3). A review of past researches reveals that few studies are available on the behavior of the pile group under lateral loads on a small-scale model in the laboratory. In addi­tion, small-scale models, compared to full-scales studies, are easier and have lower cost. In small-scale modeling, group pile can also be created with small spaces for inves­tigating the soil-pile interaction on ultimate lateral resis­tance, group eciency and group reduction factor based on the 1-g model test. Finally, since the arrangement of piles with small spaces in full-scale models is very dicult, the results are generalized to full-scale studies and used to control their results. Due to the possibility of changing the lateral load direction during the lifetime of the pile structure, the e.ect of lateral load angle change as a new parameter on the group eciency and group reduction factor is investigated. Since the group reduction factor is directly a.ected by the stress zone overlapping, evaluation of this parameter is expected to yield new results. 2 MATERIALS AND METHODS 2.1 Soil ˜e type of soil is dry silica sand, which was passed through a sieve size of 100. In addition, the Standard soil Figure 3. Grain size distribution curve for the silica sand. Table 2. Physical properties of used silica sand. Parameters Quantity ASTM Standard Comments Gs 2.67 D854 Pycnometer Test ˆ (deg) 31.5 D3080-90 Direct Shear Test d,min (kN/m3) 15.4 D4254 Dry Pour Test d,max (kN/m3) 17.6 D4253 Dynamic Cyclic Loading d (kN/m3) 16.2 D7263 In-situ Density Dr [%] 39.5 - - D10 , D30 , 0.09, 0.15, - - D50 & D60 0.19 & 0.23 Cc & Cu 1.09 & 2.56 - - tests were carried out on the soil to determine the soil properties and the results are shown in Table 2. ˜e grading test was performed according to the ASTM D421-87 standard [22]. ˜e used sand was classi˙ed as poorly graded sand (SP) based on the uni˙ed soil clas­si˙cation system (USCS). ˜e grain size distribution for the silica sand is shown in Figure 3. 2.2 Pile ˜e model pile used for the lateral loading tests was 20 mm and 16 mm in external and internal diameter respectively and 200 mm in length. Pile rigidity can be evaluated based on the criteria presented in the Elhakim et al.’s (2014) study, where the piles are considered as rigid when (L/T < 2) and exible when (L/T > 4), where L indicates the pile length and T shows the elastic length calculated by using Equation 1 [2]: (1) Where, Ep indicates the elastic modulus of the pile material, Ip shows the moment of inertia of the pile (Ep Ip is 966 Nm2), and nh is considered the empirical value which depends on the sand relative density. ˜e nh value for loose sand was considered as 1900 kN/m3, (Terzaghi, 1955) [23]. ˜e estimated values of T and (L/T) are 0.22m and 0.91, respectively, for piles embedded in loose sand. Broms (1964) suggested that for a pile, the embedded length of the pile to be considered as a short rigid pile, must be smaller than 2T and for considering as a long exible pile, the value must be greater than 4T [24]. Since the tests were carried out on the piles with the length of 0.2 m and this length is less than 2T, so the pile categorized as short rigid pile. ˜e characteristics of model piles is shown in Table 3. 44. Acta Geotechnica Slovenica, 2021/1 A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand Table 3. ˜e characteristics of model piles. pile external free embedded spacing/di- thickness diameter length length (mm) ameter (S/D) (mm) (mm) (mm) 20 4 150 50 1.5, 2.5, 3.5 ˜e pile arrangement of the group pile used in the model tests is shown in ˙gure 4. ˜e piles were placed in a layer of sand in single position and in ˙ve group arrangements with center to center spacing of 1.5, 2.5, and 3.5 diameters of the piles. 2.3 Model pile group test A side view of the model pile group test during the static ˙xed-head testing and the dimensions of test box and pile cap plan for 3×3 pile group are shown in Figure 5 a, and b. Based on the studies conducted on the lateral loading of piles, it was shown that the size of the model box must be suciently large enough to minimize side e.ects. Dong et al. (2018) studied the boundary condition e.ects on laterally loaded pile behavior both numerically and experimentally and suggested that the ratio of dimensions of the model box in the plan to the pile diameter must be more than 15 in order to ignore the boundary condition e.ects [25]. Based on some other studies, when pile groups are under lateral loading, the e.ect of the stress zone extends up to 8-12D and 3-4D in the directions of lateral loading and perpendicular to the loadings, respectively (Poulos and Davis, 1980; Zomoro­dian and Dehghan, 2011; Memar et al., 2019) [26, 27, 28]. However, in order to validate the dimensions which were chosen for test box, a numerical analysis was executed using a commercially available ˙nite-element program Abaqus3D. ˜e geometry of a typical ˙nite-element model veri˙ed for the analysis is shown in ˙gure 6. According to the numerical modeling performed with the mentioned soware, it was determined that the area under the e.ec­tive stress of the soil mass did not reach the boundary of the model and no changes developed at the model bound­ary. ˜erefore the test box was made of steel cubes with the length of 1m and the width and height of 0.8 m with a special frame with a thickness of 3 mm. A place on the test box was considered for installing the pneumatic jack which was used for loading in a horizontal direction. Figure 5. (a) Side view of reservoir and loading system and (b) Dimensions of test box and pile cap plan for 3×3 pile group in S/D = 3.5. A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand 2.4 Testing procedure and equipment ˜e loading system should provide lateral force by hydraulic, pneumatic (air pressure) or electrical loading to apply the lateral load on the pile group. In this test, a pneumatic pressure control panel and an air compressor connected which were used to apply the controlled force via the jack. In this panel, a regulator was used to adjust the output pressure and a pair of automatic valves to apply force on two opposite directions. In addition, a load cell with a maximum load capacity of 1000 (N) was used to measure the total loads applied to the loading plate. Further, the loading plate consisted of rectangular plate and a pile cap that was essentially rigid compared with the lateral pile sti.ness. Since obtaining the rate of stress and tolerable force by each pile of the group was considered as the main objective, appropriate measure­ments should be made regarding the total lateral load and distribution of loads among piles in a group. In addition, the measurement was performed through load transduc­ers in the laboratory model. Load transducers were made of steel, which were connected to the pile cap from one side and the piles from the other side to form the system rigidity and the transducer resolution is classi˙ed in class A with ą0.05 relative error (Figure 5). ˜e displacement of the pile group during the test was measured using a linear variable di.erential transducer (LVDT), which were attached to the centerline of the loading plate. ˜e measured total load applied to the loading plate transferred lateral load to each pile, and the displacement data from the load cell, load transducer, and LVDT were simultaneously stored on a computer data acquisition system. ˜e advantage of this method is that the load share of each pile could be obtained from the total group load and the p-y curve of each pile could be easily drawn. ˜e test box was ˙lled using a sand precipitation method through a mechanized device. ˜e sand precipitation was conducted through a series of netted plates connected to the bottom of the calibrated precipitation funnel which could move up and down through a reel and frame and holder arm. ˜e system provides the possibility of adjusting the precipitation heights and the horizontal motion of the precipitation funnel along the length of the test box easily. Before starting the main experiments, the precipitation of the sand was determined using a series of trial and error tests, with a speci˙ed outow and from a certain height, in order to reach the intended relative density. ˜e use of sand precipitation method created a very homogeneous sand mass so that the relative density changes in the test box were determined to be less than 1 %. During the testing process, the relative density of the soil inside the box was checked to determine whether it is constant and uniform by placing small cans with speci˙c dimensions in di.erent places of the test box. In this way, aer the sand falls from a certain height (30 cm), the amount of weight and volume of the soil inside the cans are obtained and ˙nally, the amount of soil dry unit-weight and relative density are obtained and controlled. 3 LABORATORY RESULTS A series of 34 model pile group tests were performed to determine the e.ects of pile spacing, type of pile group arrangement and lateral load angle change on the average lateral resistance of the group pile. Table 4 indicates the experimental and numerical model plan. In addition, the e.ect of the case study parameters on the load-displacement response of the loaded piles were evaluated, along with the load distribution within pile groups with ˙xed head condition. ˜e load on a single pile and pile group was increasingly applied to obtain a horizontal deection versus nonlin­ear load diagram. A large number of data were obtained based on the lateral load and displacement of the piles cap. It is worth noting that the tests were conducted on a single pile, as well as on pile groups up to the lateral deection of about 4 mm (the ratio of lateral deection to diameter is 0.2). ˜e result of the lateral load-normalized deection curve of the single pile embedded 46. Acta Geotechnica Slovenica, 2021/1 A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand Table 4. Experimental model plan. Number Pile Lateral Type of Variable of pile spacing load angle modeling Pile Normalized lateral de˜ection (Y/D) arrange­ 1, 2, 3, 4, 1.5D, 2.5D small  = 0° ment 6 & 9 & 3.5D scale Pile 1.5D, 2.5D small 4, 6 & 9  = 30° spacing & 3.5D scale Lateral 1.5D, 2.5D small load 4, 6 & 9  = 45° & 3.5D scale angle in loose sand is shown in Figure 7. ˜e results indicated that when (Y/D) is less than 0.1 the Q - (Y/D) slope is increased rapidly comparing to (Y/D) more than 0.1. (a) (b) Figure 8. (a) Schematic view of lateral load applied to the pile group and (b) Lateral load–normalized deection response for the 2×2 pile group in di.erent ratio of S/D. Acta Geotechnica Slovenica, 2021/1 47. A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand 3.1 Lateral load – defection response of pile groups Figure 8 (a, and b) displays a schematic view of lateral load applied to the pile groups and the piles spacing e.ect on lateral load-normalized deection response for the 2×2 pile group with square arrangement. Based on the results, the measured average lateral resistance increases with an increase in pile spacing. Figure 9 shows the response of the variations of the lateral deection to diameter ratio versus the average lateral load for the pile group in two square and parallel modes (at S/D = 3.5) and also single pile. For a constant ratio of lateral deec­tion to diameter (about 0.2), the average lateral resistance levels for each pile in the 2×2 and 3×2 pile groups were Ratio of each row load to group lateral load about 34 % and 39 % less than the single pile, respectively. ˜e ratio between the average lateral load carried by a pile in each row and the total loads carried by a pile group (pile groups 2×2, 3×2 and 3×3) is shown in Figure 10. Based on the results, the front and rear piles carry 56 % and 44 % of the total pile group loads (at pile group results, the measured average lateral resistance increases with changing lateral load angles from 0° to 45°. Regard­ ing a constant ratio of lateral deection to diameter 2×2) and the front, middle and rear piles carry 44 %, 32 % and 24 % (at pile group 3×2) and 46 %, 31 % and 23 % (at pile group 3×3) of the total pile group loads, (about 0.2), the average lateral resistance levels for each pile in the group at S/D = 3.5 under angular lateral loads in  = 0 °,  = 30 °, and  = 45 ° were about 34 %, 24 %, and 20 % less than the single pile, respectively. ˜ =0° - S/D = 3.5 Normalized lateral de˜ection (Y/D) Figure 9. Lateral load– normalized deection response for the pile groups (pile models 2×2 and 3×2). respectively. ˜e ratio of each row load to group lateral load for a leading row is higher than this ratio for a trail­ing row because of the shadowing e.ect. Due to the possibility of changing the lateral load direc­tion, the e.ect of load angle change on ultimate lateral resistance is investigated. Figure 11 (a, and b) displays a schematic view of angular lateral loads applied to the pile groups and the di.erent load angles e.ect on the lateral load-normalized deection response for the 2×2 pile group with square arrangement. Based on the (a) Load per pile, Q(N) 48. Acta Geotechnica Slovenica, 2021/1 A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand Normalized lateral de˜ection (Y/D) Normalized lateral de˜ection (Y/D) (b) Figure 11. (a) Schematic view of angular lateral load applied to the pile groups and (b) Lateral load–normalized deection response in di.erent load angles for the 2×2 pile group. Load per pile, Q(N) Load per pile, Q(N) A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand 3.2 Group effciency ˜e eciency of the group is important to estimate the resistance of the pile group from the result of the single pile resistance. ˜e eciency of the group , in a speci˙c deection here, in terms of ultimate lateral resistance of the pile group to that of the single pile is expressed as: (2) Where, QLG is the lateral resistance of the pile group, QLS is the lateral resistance of the single pile, n1 is the number of rows in the pile group, and n2 is the number of columns in the pile group. Wakai et al. (1999) conducted the 1-g model test on pile group under lateral load (3×3 piles group at S/D = 2.5) and reported a group eciency of about 0.7 (when the deection reached 0.1D) [29]. Figure 12 shows the relationship between the eciency of the group versus the spacing to diameter ratio of the piles in the group at di.erent arrangements. Based on the results, the measured group eciency increases with an increase in pile spacing to diameter ratio. For the case of a 2×2 pile group, the eciency of the group varied from about 0.3 to 0.65 by increasing the pile spacing to diameter ratio from 1.5 to 3.5. As expected in Figure 13, the group reduction factor decreases with an increase in the number of piles in the group, and the trend is dependent on the pile spacing and number of piles in the group. Figure 14 shows the e.ect of the lateral load angles on the group eciency for the 2×2 and 3×3 pile groups. Also, the results showed that the e.ects of overlapping stress zones (shadowing e.ect) decrease and the group eciency increases by changing the angle of lateral load from 0° to 45° due to the change in the trajectory of stress. Group pile 2×2 (PAT 3) Group e°ciency (°) Group e°ciency (°) Figure 12. Group eciency - normalized pile spacing relationship in pile groups. Load angle (˜) 3.3 Calculation of the group reduction factor from model test As previously mentioned, modifying the single pile p-y curves by using a group reduction factor (Pm) for each row of piles in the group is considered as one of the most Figure 12. E.ects of the number of pile (n) on group eciency () common and useful methods to evaluate the interac­ 50. Acta Geotechnica Slovenica, 2021/1 A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand Table 5. p-multiplier factors for laterally loaded pile groups with di.erent arrangements in =0°. Y/D S/D Group layout Average Pm P1 P2 P3 p-multiplier factors P4 P5 P6 P7 P8 P9 0.2 1.5 2×1 0.46 0.38 0.54 - - - - - - - 0.2 2.5 2×1 0.54 0.46 0.62 - - - - - - - 0.2 3.5 2×1 0.81 0.74 0.87 - - - - - - - 0.2 1.5 3×1 0.39 0.24 0.33 0.59 - - - - - - 0.2 2.5 3×1 0.52 0.37 0.50 0.71 - - - - - - 0.2 3.5 3×1 0.71 0.53 0.69 0.93 - - - - - - 0.2 1.5 2×2 0.31 0.20 0.20 0.41 0.41 - - - - - 0.2 2.5 2×2 0.48 0.37 0.37 0.59 0.59 - - - - - 0.2 3.5 2×2 0.66 0.59 0.59 0.74 0.74 - - - - - 0.2 1.5 3×2 0.29 0.18 0.18 0.25 0.25 0.45 0.45 - - - 0.2 2.5 3×2 0.42 0.27 0.27 0.42 0.42 0.57 0.57 - - - 0.2 3.5 3×2 0.60 0.44 0.44 0.58 0.58 0.80 0.80 - - - 0.2 1.5 3×3 0.28 0.17 0.17 0.17 0.29 0.29 0.29 0.40 0.40 0.40 0.2 2.5 3×3 0.38 0.24 0.24 0.24 0.38 0.38 0.38 0.52 0.52 0.52 0.2 3.5 3×3 0.52 0.36 0.36 0.36 0.50 0.50 0.50 0.71 0.71 0.71 tion e.ects in pile groups. Based on the results of the experimental modeling, Tables 5 and 6 indicate the sets of average p-multiplier factors for the pile groups with di.erent arrangements, di.erent spacing to diameter ratio, and di.erent lateral load angles. ˜e values of the Pm factors given in the Table are actually the average of multiplier factors of each pile located in the group. ˜ese factors for the lead row are independent of the type of pile group arrangement and pile spacing, but for the middle and trail rows of the pile groups are, however, highly dependent on the type of arrangement and pile spacing. As shown in Table 5, the factor of Pm obtained for the lead row is higher, while it is lower for the trail Table 6. Average p-multiplier for di.erent lateral load angles in pile groups with di.erent arrangements. Y/D S/D Group layout Average p-multiplier (Pm)  = 45°  = 30°  = 0° 0.2 1.5 2×2 0.31 0.37 0.43 0.2 2.5 2×2 0.48 0.51 0.62 0.2 3.5 2×2 0.66 0.77 0.81 0.2 1.5 3×2 0.29 0.36 0.43 0.2 2.5 3×2 0.42 0.49 0.59 0.2 3.5 3×2 0.60 0.64 0.74 0.2 1.5 3×3 0.28 0.35 0.40 0.2 2.5 3×3 0.38 0.48 0.55 0.2 3.5 3×3 0.52 0.61 0.69 rows. In the pile group, each pile pushes against the soil in front of it, creating a shear zone in the soil. ˜ese shear zones begin to enlarge and overlap as the lateral load increases and more overlapping occurs if the piles are closely spaced to each other. ˜e overlap in the shear areas are signi˙cant factors in the bearing capacity of pile groups, which may reduce the lateral resistance of pile groups. As shown in Table 6, the factor of Pm increases by changing the angle of lateral load from 0° to 45°, due to more diameter distances between the piles. ˜e e.ect of spacing piles in the group, the number and layout of piles on the average value of the group A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand reduction factors (Pm) in  = 0° is shown in Figure15. Based on the results, the value of the Pm factor increases signi˙cantly by increasing pile spacing from 1.5 to 3.5 diameter. Also the value of the Pm factor for pile groups for di.erent layouts were estimated from 0.38 (3×3 pile group) to 0.54 (2×1 pile group) in 2.5-diameter spacing and were estimated from 0.52 (3×3 pile group) to 0.81 (2×1 pile group) in 3.5-diameter spacing, respectively. ˜ese results are very close to the average Pm factor values of about 0.5 and 0.53, conducted by Mcvay et al. (1998), for 3×3 pile group at S/D = 3 on a centrifuge experiment and Rollins et al. (2005), for 3×3 pile group at S/D = 3.3 on a full-scale experiment based on the results in Table1 respectively [10, 17]. Table 7 indicates the evaluation of the group reduction factors and comparison of the results against those recommended in di.erent design guidelines such as AASHTO (2017). ˜e calculated values of the Pm factor for lateral load (in  = 0°) at S/D = 3, obtained from the interpolation of the values of group reduction factor at S/D = 2.5 and S/D = 3.5, are close to the ones recommended by AASHTO [30]. However, regarding angular lateral load (in  = 30°, 45°), the results indicated that AASHTO underestimates the group reduction factors and the lateral resistance, especially for the ˙xed pile head condition. ˜e AASHTO recommendations for choosing p-multipliers are based on data from free head pile group tests. Fixed head group reduction factors are close and slightly lower than free head factors at S/D = 3. ˜is means that group e.ects in ˙xed pile head groups are more pronounced than in free head pile groups. Table 7. Comparison between p-multiplier suggested in AASHTO (2017) and Modeling results. Test Load angle Group Reference S/D Pm type  (°) pile AASHTO Full 0 3×3 3 0.5 (2017) scale Modeling Small 0 3×3 3 0.45 results scale Modeling Small 30 3×3 3 0.55 results scale Modeling Small 45 3×3 3 0.62 results scale 4 EFFECTS OF SCALE AND LIMITATIONS Since a lot of time and cost are spent on full-scale models in situ testing, laboratory tests on small-scale models were used as a method herein. In the experi­ments, the model piles were made smaller by speci˙c scale, while the sand used in the small-scale of the laboratory model was the same as in the real models. ˜erefore, it is possible for both the pile and the sand, in a small scale, to have a di.erent behavior in reality, and this might inuence the experimental results, referred to as scale e.ects. ˜e diameter of the pile (D) used in the experiments was more than 100 times bigger than the average diameter of aggregates (D50). Ovesen (1979) proposed that the ratio of pile diameter (D) to the average diameter of aggregates (D50) is required to be greater than 40 [31]. Based on the experimental results on small-scale models, it is impossible to predict the real in situ behavior. However, the present study showed comparable results of the small-scale tests (laboratory models), which could be generalized to the results of full-scale tests. 5 CONCLUSION ˜e group reduction factor is considered as a parameter which is commonly used in spring models of pile groups to account for the group e.ects in soil-pile interaction analysis. ˜ere are various guidelines to determine the average of group reduction factors. ˜ese guidelines are derived from several available experiments that are oen conducted on full-scale pile group with limited spaces, and mostly under free head conditions [30, 32]. ˜e group reduction factors can be obtained using labora­tory (small-scale) and in-situ (full-scale) tests. However, creating and performing a full-scale test on pile groups is very dicult and costly. ˜erefore, small-scale criteria were used to study the pile groups under the lateral load in ˙xed head conditions. For this purpose, several di.er­ent models of pile groups were prepared in di.erent arrangements and were studied by changing the spaces between the piles and lateral load angles in the group in each case. Based on the results, the following conclu­sions are made: - Load–deection behavior of piles in a group was more exible than single-pile behavior. ˜is di.e­rence in behavior was reduced due to the reduction of shadow overlap e.ects, when the spaces between the piles increased in the groups. – By increasing the ratio of spacing to diameter piles in the group, the eciency coecient of the group as well as the group reduction factors (Pm) increased. For a 2×2 pile group, the group eciency varied from about 0.3 to 0.65 by increasing the ratio of spacing to diameter piles from 1.5 to 3.5. – By changing the angle of lateral load from 0° to 45°, the group eciency increases, due to the change of trajectory of stress and decreasing the e.ects of over­lapping stress zones (shadowing e.ect). 52. Acta Geotechnica Slovenica, 2021/1 A. Vakili et al.: Small scale model test on lateral behaviors of pile group in loose silica sand – For ˙xed head pile groups, the leading row of the group tolerated the highest load, while the middle and trailing rows tolerated less load for the certain deection value. ˜e group reduction factors in 3×2 pile group arrangement, and in S/D = 2.5, were esti­mated to be 0.57, 0.42 and 0.27, respectively, for the leading, middle, and trailing rows. – ˜e results of small-scale tests in laboratory were comparable and veri˙ed with the results of full-scale experiments on pile group under lateral load. ˜ere-fore, the experimental results of the pile group under the lateral load on a small-scale can be useable. – ˜e calculated values of the Pm factor for the lateral load ( = 0°) at S/D = 3, were close to the ones recommended by AASHTO. 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[25] Dong, J., Chen, F., Zhou, M. and Zhou, X., 2018, “Numerical analysis of the boundary e.ect in model tests for single pile under lateral load”, Bulletin of Engineering Geology and the Environ­ment, 77(3), PP.1057-1068. [26] Poulos, H.G., and Davis E.H., 1980, “Pile founda­tion analysis and design”, John Wiley & Sons Inc., New York. [27] Zomorodian, M.A. and Dehghan, M., 2011, “Lateral resistance of a pile installed near a rein­forced slope”, International Journal of Physical Modelling in Geotechnics, 11(4), PP. 156-165. [28] Memar, M., Zomorodian, M.A. and Vakili, A.H., 2019, “E.ect of pile cross-section shape on pile group behaviour under lateral loading in sand”, International Journal of Physical Modelling in Geotechnics. [29] Wakai, A., Gose, S., and Ugai, K., 1999, “3-D elasto-plastic ˙nite element analysis of pile founda­tions subjected to lateral loading”, Soil and Foun­dation, Tokyo, Vol. 39, No. 1, PP. 97-111. [30] AASHTO, 2017, “AASHTO LRFD bridge design speci˙cation”. 6th ed. American Association of State Highway and Transportation Ocials (AASHTO), Washington, D.C. [31] Ovesen, N.K., 1979, “˜e use of physical models in design: ˜e scaling law relationship”, Proc., 7th European Conf. on Soil Mechanics and Founda­tion Engineering, 4, PP. 318-323. [32] FEMA, 2012, “Foundation analysis and design”, FEMA p-751. In NEHRP recommended provi­sions: design examples. Federal Emergency Management Agency. National Institute of Build­ing Sciences, Building Seismic safety Council, Washington, D.C., chapter 5. 54. Acta Geotechnica Slovenica, 2021/1 S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis IMPROVED GENERAL SLICE METHOD OF LIMIT EQUILIB­RIUM FOR SLOPE STABILITY ANALYSIS Shiguo Xiao (corresponding author) Southwest Jiaotong university, Ministry of education, Key laboratory of high-speed railway engineering Chengdu 610031, China Southwest Jiaotong University, Department of Geological Engineering Chengdu 610031, China E-mail: xiaoshiguo@swjtu.cn IZBOLJŠANA SPLOŠNA LAMELNA METODA MEJNEGA RAVNOVESJA ZA STABILNO­STNE ANALIZE POBO˜IJ Tingjun Chen Southwest Jiaotong University, Department of Geological Engineering Chengdu 610031, China https://doi.org/10.18690/actageotechslov.18.1.55-64.2021 slope stability, limit equilibrium, slice method, non-linear programming; interslice force For traditional slice methods of limit equilibrium used to analyze slope stability, some hypothetical conditions on interslice force are generally introduced to solve the problem. In order to reduce the defect theoretically due to the related hypothesis, more rigorous constraints of inter-slice force are completely considered in light of static equi­librium conditions and energy dissipation principle of the interface between two adjacent slices. Without hypothesis of interslice force, the slope stability analysis is transformed consistently into a non-linear programming problem to be solved. So, a generally improved solution of slice method of limit equilibrium to slope stability is put forward. In parti­cular, inuence of the dilation angle of soil on slope stability can be involved in the method. .e proposed method can be utilized for any slopes with arbitrary slip surfaces. 1 INTRODUCTION Limit equilibrium methods of slope stability analysis are easily operated and widely used in practical slope engineering [1]. In 1916, Petterson and Hultin proposed circle sliding surfaces for stability analysis of undrained stabilnost pobo°ja, mejno ravnovesje, lamelna metoda, nelinearno programiranje, medlamelna sila Za tradicionalne lamelne metode mejnega ravnovesja, ki se uporabljajo za analizo stabilnosti pobo˜ij, so za rešitev problema glede medlamelne sile na splošno uvedene nekatere predpostavke. Da bi teoreti˜no zmanjšali napake zaradi teh predpostavk, se glede na stati˜na ravnovesna stanja in na˜elo disipiranja energije na kontaktu med dvema sosednjima lamelama upoštevajo strožje omejitve za medlamelne sile. Brez predpostavke o medlamelni sili se analiza stabilnosti pobo˜ij dosledno spremeni v reševanje problema nelinearnega programiranja. Predlagana je torej splošno izboljšana rešitev lamelne metode mejnega ravnovesja stabilnosti pobo˜ij. Pri tej metodi je mogo˜e zlasti vklju˜iti vpliv kota dilatacije zemljine na stabilnost pobo˜ij. Predlagano metodo lahko uporabimo za vsa pobo˜ja s poljubnimi drsnimi površinami. soil slopes [2], which is later called the Swedish circle method and marks the beginning of the application of limit equilibrium method for slope stability. In 1926, Fellenius introduced both cohesive and frictional strength of soil into slope stability analysis using the circular sliding surface. ˜us, the Fellenius method S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis is regarded as one of the signi˙cant limit equilibrium methods with fully considering soil strength for slope stability analysis [3]. Later, Lorimer once used Euler spiral or clothoid instead of circular slip surface to explain failure mode of soil slope by referring to experi­ments and investigations. In these methods, potential slide mass is divided vertically into ˙nite slices with small width. And interslice forces on the two sides of a slice are assumed to be a pair of balance forces. Bishop (1955) [4] improved further the assumption of interslice force with neglecting the di.erence between their vertical components and proposed the simpli˙ed Bishop method for the soil slope with circular slip surface. Janbu (1954) [5] also neglected the tangent component of interslice force but provided the simpli˙ed Janbu method used for the soil slope with arbitrary slip surface. In order to reduce the disadvantage of the previous methods without considering the tangent component of interslice force, Lowe and Kara˙ath (1960) [6] assumed that the dip angle of the interslice force is equal to the average of the dip angle of the top and bottom of the slice. ˜e US Army Corps of Engineers (1967) [7] recommended that the dip of interslice force is equal to the average of the dip angles of all slices (Corps of Engineers #1) or the dip of the top of the slice (Corps of Engineers #2). However, for the Imbalanced ˜rust Force Method (ITFM) [8], the dip angle of the interslice force is assumed to be consis­tent with the dip of the bottom of the previous slice. Since these methods mentioned above cannot include all equilibrium equations of force and moment of a slice, analysis results of slope stability by them sometimes are not possibly certainly reasonable [9]. Morgenstern and Price (1965) [10] proposed a general slice method which satis˙es both force and moment equilibrium by assuming that the ratio of tangential over normal component of interslice force is a speci˙ed function. Spencer (1967) [11] presumed that the ratio is an unknown constant. In fact, it is a special case of the Morgenstern-Price method (MPM). Janbu (1973) [12] obtained the solution of slice method by considering all static equilibrium conditions and assuming the location of action point of the interslice force. Fredlund and Krahn (1977) [13] provided an alternative derivation for the Morgenstern-Price method and fully exhibited the rela­tionship between factor of safety and the scaling param­eter de˙ned in the MPM. Sarma (1979) [14] proposed a method of non-vertical slicing with considering interfaces between adjacent slices to be in the limit state, which is widely used for stability analysis of rock slope. Chen and Morgenstern (1983) [15] improved the MPM and promoted the function of interslice force further to approximate practical condition. Correia (1988) [16] assumed the shear force on the slice sides to be a function characterizing the shape of the shear force across the slide mass multiplied by a scaling parameter with the unit of force. Zhu (2001) [17] presented a new concise formula­tion of force and moment equilibrium equations within the framework of the MPM. Although these methods involved completely in both force and moment equilib­rium conditions of slices, they all stemmed from assump­tions of the direction or magnitude of interslice force. ˜erefore, rationality of slice methods of limit equilib­rium depends to great extent on whether interslice force is reasonably coped with. Rigorously speaking, although some investigations [9,15] indicate assumptions of interslice force tend to have possibly small e.ects on the results of the slice method, the minimum value of the factor of safety of slope stability by the slice method in theory has not been completely demonstrated. From the perspective of rigorous theory, in spite of various assumptions of interslice force adopted in the previous studies, acceptable hypotheses of interslice force based on the practically physical sense are that: (1) ˜e shear forces on the sides of slices should not exceed the related shear resistances; (2) ˜ere is no tensile stress between adjacent slices [9]. On the basis of the two elementary constrain conditions, this paper provided a more rigorous derivation for the slice method satisfying all static equilibrium conditions of slices and boundary conditions of the slope without introducing any prescribed relationship between the tangential and normal force on the slice sides. As far as the calculation procedure in mathematics is concerned, the slope stabil­ity analysis is transformed rigorously into a non-linear programming problem to ensure the solution of the minimum factor of safety. 2 BASIC PROCEDURE A typical analysis model of slope stability by slice method is shown in Fig. 1. ˜e key points of slope stability analysis can be regarded essentially as solving the unknown forces on potential sliding surfaces and sides of slices under various factors of safety. Based on the general slice method [10], each slice must satisfy the static equilibrium conditions. Namely, there are two force equilibrium and one moment equilibrium equa­tions for each slice. ˜erefore, for the ith slice the three static equilibrium equations can be expressed as (the meaning of all symbols are explained in the Notation) (1) (2) 56. Acta Geotechnica Slovenica, 2021/1 S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis (a) Potential slide mass and its slices. (b) Forces on the ith slice. Figure 1. Analysis model of a general slope. (3) Besides, the bottom of each slice is in the limit state. So according to the Mohr-Coulomb strength criterion and shear strength reduction strategy [18] for the factor of safety, there is (4) In fact, vertical interfaces subjectively divided between slices of potential slide soil mass are not certainly in the limit state, which is di.erent from the hypothesis assumed by Sarma (1979) [14]. In other words, shear force on the sides of the slice is not over the related shear resistance. Namely, (5) Introducing a non-negative coecient Ki no more than 1, Eq. (5) can be rewritten as (6) where Ei is not less than zero due to the fact that there is no tension between slices. We can suppose that there is a thin transition layer with a small thickness of . between two adjacent slices (see Fig. 2). And there are average tangential and normal stress on the layer. ˜us, general energy dissipation rate in the transition layer can be expressed as [19] (7) According to the geometric relationships, one can get (8) Further, based on the conception of the average stresses on the layer, there is (9) Substituting Eqs. (8) and (9) into Eq. (7), one can obtain (10) ˜en, taking into account that the energy dissipation rate in the transition layer should not be negative (D 0), one can further get (11) Since the transition layer is not necessarily in the limit state, the shear stress on it is not beyond the related shear strength. Further, the corresponding actual shear strain is not more than the ultimate shear strain. So, one can get (12) According to the admissible failure mechanism of kinematical system of soil mass which can be reasonably used in slope stability analysis [19], the ratio of normal velocity over tangential velocity in the transition layer is the tangent value of dilation angle  of the soil. ˜us, Substituting Eq. (12) into Eq. (11) one can obtain (13) ˜erefore, Eq. (13) exhibits that the dip angle of the resultant interslice force should be not less than the dila­tion angle of the soil. S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis ˜en, the problem of slope stability analysis is equivalent to solving the minimum value of the factor of safety under the control conditions of Eqs. (1) to (4) and restraint conditions of Eqs. (6) and (13). A potential slide mass is divided into n slices, and for the last slice, there are En+1 = 0, Xn+1 = 0 and hn+1= 0. So for each slice there are ˙ve unknowns: Ni , Ti , Ei , Xi , and hi. In addition, the factor of safety of slope stability Fs is another unknown. Consequently, there are totally 5n+1 unknowns. Based on Eqs. (1) to (4), one can obtain 4n independent equations. And for the ˙rst slice, there are E1 = 0, X1 = 0 and h1 = 0. ˜us, solving the factor of safety of a slope with potential slide mass divided into n ( 3) slices can be actually regarded as an n-2 dimensional non-linear programming problem to ˙nd the minimum factor of safety. As long as the factor of safety is sought out, the other variables including the tangential and normal force on the sides of all slices can be also obtained simultaneously. As for the speci˙cally operating procedure, Sequential Quadratic Program­ming (SQP) method in MATLAB soware can be used to solve this programming problem [20]. ˜ere is a locally optimal solution to the problem with constrained variables, and it can be carried out via the inserted fmincon function (Constrained nonlinear minimization) of the optimization tool in MATLAB [20]. 3 VERIFICATION EXAMPLES AND DISCUSSION In order to verify the proposed method, ˙ve examples are taken next. Since experiments show that the dilation angle of soil is smaller than the internal friction angle [21], the dilation angle is adopted as ˆ, 3ˆ/4, ˆ/2, ˆ/4, and 0, respectively to suciently reect the inuence of dilation angle on the analysis results of slope stability. 3.1 Example 1: a homogeneous clay slope with circular slip surface and Fs >1 Fig. 3 shows an example of a soil slope with a circular slip surface and 10 m height [10]. Point Oc is the rota­tion center of a potential slip surface, and the potential slide mass of the slope is divided into 9 slices. Point O is the top point of the slip surface. ˜e factors of safety ˙gured out by SQP are exhibited in Table 1, where the symbols of MPM-I, MPM-II, MPM-III, and MPM-IV represent correspondingly four cases that the function f(x) of interslice force is assumed as constant, custom unimodal curve, custom unimodal curve with two valleys, and straight line, respectively. Besides the results by the non-circular analysis method, circular analysis result (Slip circle analysis) is also listed aer Morgen-stern and Price (1965) [15]. ˜e results show the maxi­mum relative error between the proposed method and MPM is 5 %. Moreover, the factors of safety obtained by the proposed method are not more than those by the non-circular MPM and circular analysis method. ˜e reason is that the proposed method is actually able to obtain the optimal solution of the factor of safety using the optimization search procedure with considering all constraint equations of slices, rather than introducing the assumption of interslice force function as does the MPM. ˜erefore, the proposed method is more general and rigorous than existing methods and can theoreti­cally ˙nd the minimum value of the factor of safety. Also, Table 1 shows the factor of safety obtained using the proposed method increases very slightly with the increase of the dilation angle. If the dilation angle varies from 0 to ˆ, the factor of safety increases only about 0.2 %. So it means the dilation angle has little e.ect on the analysis results of slope stability. In fact, a numerical simulation model of the example via FLAC3D (see Fig. 4) is established to reect further the inuence of the dilation angle on the factor of safety. ˜e numerical model consists of 11632 quadrangle elements and 23780 nodes. Perfectly elastoplastic constitutive model and Mohr-Coulomb strength principle are assumed to simu­late the slope soil. As shown in Fig. 5, the factor of safety by FLAC3D is marginally increasing with the dilation angle and has only 0.8 % growth if  = ˆ. ˜e tendency of Fs varied with /ˆ by the proposed method is in good agreement with that by FLAC3D, which also indicates the proposed method is acceptable. In order to indicate the directions of interslice force or interslice thrust line obtained by various methods, f(x) [10] is still cited here to express the ratio of tangential over normal force on the side of slice. (14) 58. Acta Geotechnica Slovenica, 2021/1 S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis As shown in Fig. 6, there are remarkable di.erences of the dip angles of interslice forces among the various methods including classical Lowe and Kara˙ath method (LKM) [6], Corps of Engineers #1 method (CEM1) [7], Corps of Engineers #2 method (CEM2) [7], ITFM [8], and MPM-I [10]. However, the results obtained by the ITFM are relatively close to those calculated using the proposed method. Fig. 7 indicates further that there are distinct alterations of the interslice thrust lines between Table 1. Analysis results of example 1. Methods Fs Proposed method ( = ˆ) 2.044 Proposed method ( = 0.75ˆ) 2.042 Proposed method ( = 0.5ˆ) 2.041 Proposed method ( = 0.25ˆ) 2.041 Proposed method ( = 0) 2.04 Slip circle analysis 2.098 Figure 6. Variation of dip angle of interslice forces in example 1. MPM-I 2.045 MPM-II 2.136 MPM-III 2.134 MPM-IV 2.044 Unit weight 20kN/m3 Cohesion 20kPa Figure 7. Variation of ratio of tangential force over normal Figure 4. Numerical simulation model of example 1 via FLAC3D. force on the sides of slices in example 1. Acta Geotechnica Slovenica, 2021/1 59. S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis the proposed method and the MPM. It can be compre­hensively seen from Table 1 and Fig. 7 that the more approximate the interslice force function selected in the MPM is to that by the proposed method, the closer the factor of safety by the MPM is to the minimum value or that obtained by the proposed method. In this regard, the proposed method is fairly helpful to conducting the selection of the interslice force function in the MPM. 3.2 Example 2: a homogeneous clay slope with circular slip surface and Fs close to 1 Fig. 8 shows a soil slope with a circular slip surface and 10m height [22], which is one of the examinations of slope stability by Australia Computer Aided Design Society (ACADS). A potential slide mass of the slope is divided into 10 slices. ˜e results of the ratio of tangential force over normal force on the sides of slices are shown in Fig. 9, where MPM-V represents the case that the function of interslice force is semi-sinusoidal curve. It can be seen that the ratios obtained by the proposed method under various dilation angles are almost consistent in trend. For the slices with the higher ratio, the dilation angle has no e.ect on the ratio; but for the slices with the lower ratio, the dilation angle has Figure 8. Sketch map of the slope example 2. Figure 9. Variation of ratio of tangential force over normal force on the sides of slices in example 2. only small e.ect on the ratio. ˜e factor of safety by the proposed method increases only about 0.05 % with the increase of dilation angle, and they are very close to the results by the MPM. But the factor of safety under  = 0 is not more than that by the MPM. Fig. 10 shows the variations of dip angle of interslice forces by several classical slice methods such as the LKM, CEM1, CEM2, ITFM, and MPM-I. ˜e results also indicate that the dip angles assumed by the ITFM are rather closer to those computed by the proposed method. 3.3 Example 3: a nonhomogeneous soil slope with circular slip surface Fig. 11 shows an example of a nonhomogeneous soil slope with two layers [23]. ˜e potential slide mass of the slope is divided into 9 slices. As shown in Fig. 12, the ratios of tangential force over normal force on the sides of slices obtained by the proposed method are clearly di.erent from those computed by the MPM. Similar to the analysis results of the examples mentioned above, the factor of safety obtained by the proposed method under  = 0 is the minimum. And it is about 0.1 % less than that by the MPM. Also, there are obvious di.erences of 60. Acta Geotechnica Slovenica, 2021/1 S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis the dip angles of interslice forces between the proposed method and the classical slice methods, but the dip angles assumed by the ITFM are relatively closer to those obtained using the proposed method (see Fig. 13). Figure 12. Variation of ratio of tangential force over normal force on the sides of slices in example 3. Figure 13. Variation of dip angle of interslice forces in example 3. 3.4 Example 4: a nonhomogeneous cohesionless slope with non-circular slip surface As shown in Fig. 14, potential slide mass of a nonho­mogeneous cohesionless slope with non-circular slip surface is divided into 5 slices. It can be seen from Fig. 15 the values of f(x) obtained by the proposed method are close to those by MPM-I and MPM-III, but appar­ently di.erent from those by MPM-II. ˜e proposed factor of safety is almost identical with that by MPM. Moreover, there are observable di.erences of the dip angles of interslice forces between the proposed method and ITFM as well as CEM2, but the proposed dip angles are fairly closer to those by CEM1 and LKM (see Fig. 16). In particular, the dip angles using the proposed method are between 16° and 20°. ˜erefore, the calcula­tion results show further the dip angles are between  and ˆ as demonstrated theoretically above. Figure 14. Sketch map of the slope example 4. Figure 15. Variation of ratio of tangential force over normal force on the sides of slices in example 4. Figure 16. Variation of dip angle of interslice forces in example 4. S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis 3.5 Example 5: a nonhomogeneous clay slope with non-circular slip surface Fig. 17 shows a nonhomogeneous clay slope with non-circular slip surface and potential slide mass divided Figure 17. Sketch map of the slope example 5. Figure 18. Variation of ratio of tangential force over normal force on the sides of slices in example 5. Figure 19. Variation of dip angle of interslice forces in example 5. 62. Acta Geotechnica Slovenica, 2021/1 into 4 slices. As shown in Fig. 18, f(x) by the proposed method are evidently di.erent from those computed by MPM-I, but relatively closer to those by MPM-II and MPM-III. ˜e proposed values are observably inuenced by  in the example. Similarly, the factor of safety obtained by the proposed method is very close to that by MPM. Besides, there are still noticeable di.er­ences of the dip angles of interslice forces between the proposed method and the classical slice methods (see Fig. 19). 4 CONCLUDING SUMMARY ˜e general slice method with satisfying all equilibrium conditions of slices for slope stability analysis can be improved further without assuming the direction or magnitude of interslice forces. Based on the admis­sible failure mechanism of kinematical system of soil mass which can be used in slope stability analysis, it is demonstrated that the dip angles of interslice forces should not be less than the dilation angle of the slope soil. ˜erefore, the slope stability analysis can be trans­formed equivalently into a non-linear programming problem to be solved with clear ranges of the directions of interslice forces. Moreover, the closed-form solu­tion of the slice method for slope stability analysis is obtained. ˜e proposed method is applicable to both homoge­neous and nonhomogeneous soil slopes without any limitation of potential slip surfaces. Compared to clas­sical slice methods of limit equilibrium, the proposed method can more rigorously ˙nd the minimum value of the factor of safety of slope stability. ˜e e.ect of the dilation angle of slope soil on the factor of safety is involved in the proposed method, but analysis results of some examples show the dilation angle has little e.ect on the slope stability. In addition, among the classical slice methods with di.erent assumption of the dip angle of interslice force for stability analysis of slopes with circular slip surfaces, the directions of interslice forces obtained by the ITFM are fairly closer to those computed using the proposed method. However, for slopes with non-circular slip surfaces, there are obvious di.erences of the interslice force directions between the proposed method and ITFM. Acknowledgments ˜e research was supported by the National Natural Science Foundation of China (Grant Nos. 51578466 and 51278430) and the Program for New Century Excellent Talents in University (NCET-13-0976). S. Xiao & T. Chen: Improved general slice method of limit equilibrium for slope stability analysis Notation c= Cohesion of the slope soil di = Height of the interface between slice i and slice i-1 D= Internal energy dissipation rate of the thin transition layer between adjacent slices Ei = Normal force on the interface between slice i and slice i-1 Fs = Factor of safety of slope stability hi = Height of action point of the interslice force between slice i and slice i-1 i= Number of the ith slice Ki = Development coecient of shear limit resis­tance on the interface between slice i and slice i-1 li = Length of the bottom of slice i n= Total number of slices of the potential slide mass of a soil slope vertically divided Ni = Normal force on the bottom of slice i t= Minimal time Ti = Tangential force on the bottom of slice i Wi = Weight of slice i x= Horizontal coordinate with respect to the origin O Xi = Tangential force on the interface between slice i and slice i-1 y= Vertical coordinate with respect to the origin O i = Dip angle of the bottom of slice i = Unit weight of slope soil .= ˜ickness of the thin transition layer between adjacent slices = Normal strain in the thin transition layer ˆ= Internal friction angle of the slope soil = Shear strain in the thin transition layer f(x) = Assumed function of the ratio of tangential force Xi over normal force Ei of slices, where  is a dimensionless coecient Average normal stress on the thin transition layer Average shear stress on the thin transition layer s Shear stress on the thin transition layer in the plastic limit state  Dilation angle of the slope soil v Resultant velocity of a rigid slice, where subscript i and i-1 denote slice i and i-1, respectively vs Tangential velocity of slice i relative to slice i-1 vn Normal velocity of slice i relative to slice i-1 ( vs)limit Tangential velocity of slice i relative to slice i-1 in the plastic limit state REFERENCES [1] Huang, Y.H. 2014. 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Associated and non-associated visco-plasticity and plasticity in soil mechanics. Géotechnique 25(4), 671-689. http://doi:10.1680/ geot.1975.25.4.671. [19] Chen, W.F. 1975. Limit analysis and soil plasticity. Elsevier Scienti˙c Publishing Company, Amster­dam, the Netherlands. [20] ˜e MathWorks Inc. 2018. Global Optimiza­tion Toolbox: User's Guide (R2018b). Retrieved September 2018, available from: http://www.math­works.com/help/pdf doc/gads/gads tb.pdf (cited November 10, 2018). [21] Giampa, J.R., Bradshaw, A.S., Schneider, J.A. 2016. Inuence of dilation angle on drained shallow circular anchor upli capacity. International Jour­nal of Geomechanics 17(2), 04016056. http://doi: 10.1061/(ASCE)GM.1943-5622.0000725. [22] Donald, I., Giam, P. 1992. ˜e ACADS slope stabil­ity programs review. In Proceedings of the 6th International Symposium on Landslides, Christch­urch, New Zealand, February 10-14, Vol. 3, pp. 1665–1670. [23] Xiao, S.G., Guo, W.D., Zeng, J.X. 2018. Factor of safety of slope stability from deformation energy. Canadian Geotechnical Journal 55(1), 296-302. http://doi: 10.1139/cgj-2016-0527. 64. Acta Geotechnica Slovenica, 2021/1 Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam DYNAMIC ANALYSIS OF EARTH DAM USING NUMERI­CAL METHOD – A CASE STUDY: DOYRAJ EARTH DAM Ahmad R. Mazaheri (corresponding author) Ayatollah Borujerdi University, Engineering Faculty, Department of Civil Engineering Borujerd, Iran E-mail: a.mazaheri@abru.ac.ir Majid Veisi Ayatollah Borujerdi University, Engineering Faculty, Department of Civil Engineering Borujerd, Iran DINAMI˜NA ANALIZA ZEMELJ­SKE PREGRADE Z UPORABO NUMERI˜NE METODE: ŠTUDIJA PRIMERA ZEMELJ­SKE PREGRADE DOYRAJ Mehdi Komasi Ayatollah Borujerdi University, Engineering Faculty, Department of Civil Engineering Borujerd, Iran Masoud Nasiri Razi University, Engineering Faculty, Department of Civil Engineering Kermanshah, Iran https://doi.org/10.18690/actageotechslov.18.1.65-78.2021 case study, dynamic analysis, earth dam študija prakticnega primera, dinamicna analiza, 2D metoda koncnih razlik zemeljska, pregrada .e precise study of the response of earth dams to earthquakes is one of the most complex issues in the ˙eld of soil structures. In this research, dynamic analysis of earth dam structures (a case study: Doyraj dam in the west of Iran) have been performed using 2D Finite Di.erence Method (2D F.D.M.). .e aim of this study is to investigate accelerations, lateral (horizontal) and vertical displace­ments (i.e. settlements) due to earthquake occurrence. .e results of dynamic analysis indicate that the performance of the dam is satisfactory for each one of the seismic scenarios considered in this investigation. .e maximum settlements at the dam crest is considerably smaller than that of the dam freeboard, with maximum value of 540 mm, which is comparable to recommendation of the Department of Safety of Dams (DSOD). Depth of sliding surfaces is better shown in the Finn model, and the settlements based on the Finn model is about 2.5 times higher than that of Mohr model. In contrast to what is commonly accepted Eno najbolj zapletenih vprašanj na podro˜ju zemljinskih konstrukcij predstavlja natan˜na študija odziva zemelj­skih pregrad na potres. V tej raziskavi je bila izvedena dinami˜na analiza konstrukcije zemeljske pregrade (študija primera: jez Doyraj na zahodu Irana) z uporabo 2D metode kon˜nih razlik (2D FDM). Cilj te študije je raziskati pospeške, bo˜ne (vodoravne) in navpi˜ne premike (tj. posedke) zaradi pojava potresa. Rezultati dinami˜ne analize kažejo, da je zmogljivost pregrade zadovoljiva za vsakega od potresnih scenarijev, obravna­vanih v tej preiskavi. Najve˜je posedanje na grebenu jezu je bistveno manjše kot pri prosti višini jezu, z najve˜jo vrednostjo 540 mm, kar je primerljivo s priporo˜ilom Ministrstva za varnost jezov (DSOD). Globina drsnih površin je bolje prikazana v Finnovem modelu, posedki, ki temeljijo na Finnovem modelu, pa so približno 2,5-krat ve˜ji kot pri Mohrovem modelu. V nasprotju s splošno sprejetimi vrednostmi potresnih pospeškov (pove˜anje Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam about earthquake acceleration (the increase in earthquake potresnega pospeška od dna do vrha jezu), ugotavljamo, acceleration from the base to the top of the dam), it cannot da se ne more posploševati na vse primere in je lahko generalize to all cases, and it can be limited to very strong omejeno na zelo mo˜ne jezove ali pa potrese majhnih dams or can be related to poor earthquakes. intenzitet. 1 INTRODUCTION Damage and loss of life caused by earthquakes are immense. ˜is is ampli˙ed when accompanied by the collapse of essential infrastructures, such as a dam or a power plant, which have the potential of destroying the entire cities. ˜e water and power supplied by dams are essential for the survival of a community. However, when a dam fails, the destruction is oen deadly, causing irreparable damage to the land, the people, and to the economy [1]. In fact, the deformations resulting from the earthquake may cause overtopping of water from the dam, leading to severe damages [2]. Earth dams are widely used throughout the world due to the avail­ability of suitable materials and their exibility. ˜ere are numerous earth dams in each country, including Iran. Dams are used for irrigation, food mitigation, and hydroelectric power generation purposes. Due to soil nature and its exibility, the earth dams have better seismic performances in comparison to concrete dams. However, many earth dams were damaged during strong earthquake, and even collapsed in some serious cases [3]. It is essential to carry out post-earthquake investigation and analysis on the earth dams; however, researches have been focused in this feld [4-7]. As Iran lies in one of the world's most seismically active areas, the main issue in dam management and construction is seismic safety. ˜erefore, to assure dam safety, proper evaluation of dynamic analysis is crucial. In general, the assessment of the seismic stability of new or existing dams can be performed via (a) pseudo-static analysis [8], (b) displacement-based (Newmark or sliding block) methods [9-11], and (c) dynamic stress-deformation numerical analysis [12]. ˜ese above-mentioned analyses provide insight into the seismic response of zoned earth dams and homogeneous embankments and ascertain the relative signifcance of various parameters. Such parameters included excitation characteristics (intensity and frequency content), dam geometry (height and existence of stabilizing berms), foundation soil conditions, and the dam’s operation phase (‘‘end of construction’’ and ‘‘steady-state seepage’’ conditions). Note that in addition to the excitation char­acteristics, the other parameters under study are crucial to the static stability of earth dams, but their signifcance in terms of seismic loading is unknown [13]. Although dam failures are rare, studies have been conducted based on such events to understand the causes of those failures. One example is the failure of the Teton dam, an earth dam located in Idaho, the United States. ˜e dam failed on June 5th in 1976, as it was being flled for the frst time, owing to internal erosion known as “piping”. ˜e failure caused a huge food that damaged the city downstream, which cost about 2 billion US$ [14]. ˜e Lower San Fernando dam, which was a 40-meter-high hydraulic-fll earth dam located in San Fernando, California, failed on February 9th in 1971 [3]. In Japan, the Aratozawa dam is a rock-fll imper­vious-core dam with the height of 74.4 m, located in Kurihara. ˜e Iwate–Miyagi Nairiku earthquake in 2008 caused huge landslides occurred in the le bank of the reservoir from the dam. ˜is caused settlement of the core zone about 20 cm. ˜ere was no evidence of severe damage to the dam structure, but it was taken out of operation because of safety concerns [15]. Tschuschke, et al. [16] investigated quality control for construction of tailings dam, they also examine the e.ects of the applied technology on the condition of the natural environment. Other researchers have also evaluated the safety of earth dams. For example, Soralump, et al. [17] conducted a dynamic response analysis on the Srinagarind dam by using 213 records of 35 earthquake events and the equiv­alent linear method for the nonlinear behavior of dam materials. Similarly, Fallah and Wieland [18] conducted an evaluation on earthquake e.ects and the safety of the Koman concrete-faced rock-fll dam in Albania, by using a 2D F.E. models for the maximum cross section. ˜eir study was undertaken using the equivalent linear method. ˜e dam was checked for the safety evaluation against earthquake with a peak ground acceleration of the horizontal component of 0.45g. ˜is study aims to gain insight into the behavior of the Doyraj dam (a case study in Iran) in case of the earth­quake by using the 2D F.D.M. numerical modeling. In order to select the input motion, seismic hazard analysis was performed by deterministic and probabilistic methods of probable horizontal and vertical acceleration in the dam area. ˜en, the nearest earthquake record for the region has been selected from the earthquakes that occurred in all around the world as a baseline earthquake. By completing modeling and performing dynamic analyzes, the results have been discussed. ˜e 66. Acta Geotechnica Slovenica, 2021/1 Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam importance of such research is not only to examine the behavior of a dam or the level of damage it can sustain, but also to preserve it against future earthquakes. 2 NUMERICAL MODELLING 2.1. Analysis Approach During a seismic event, stress waves propagate through soils and attenuate with distance. Energy dissipation, volume changes, and sti.ness degradation of the materi­als are the factors, which a.ect this attenuation. During shaking, soils exhibit continuous hysteresis modulus degradation resulting in increasing levels of damping, which in turn decrease the amplitudes of the stress waves. ˜e representation of this material behavior is important in seismic analysis of embankment dams. Two approaches are conventionally used in simulation of inelastic characteristics of soils subjected to cyclic load­ing: Equivalent Linear Methods (E.L.M.) and nonlinear numerical methods [19]. In the E.L.M. nonlinear behav­ior of soil is simulated by adjusting the shear modulus and damping ratio as functions of maximum shear strain in the soil. On the other hand, nonlinear methods use nonlinear constitutive models to represent the nonlinear behavior during cyclic loading. Constitutive equations used in predicting inelastic cyclic behavior of soils can become quite complex and may require various material parameters. Alternatively, simple elastic–plastic consti­tutive models may be used with additional damping added, to represent inelastic damping behavior [19]. ˜e latter method has been adopted in the present study. Damping in soils is primarily hysteretic, since energy dissipation occurs when grains slide over one another [20]. During dynamic analysis, as e.ective stresses decrease with increase in pore pressure, the soil begin to yield and increments of permanent deformation are accumulated. Simultaneous coupling of pore pressure generation with non-linear, plasticity based, stress analy­sis produces a more realistic dynamic response than that can be achieved with the equivalent linear method [20]. ˜e above-described approach has been veri˙ed in the literature through analysis of well-documented case histories [21] and was adopted herein for the dynamic analysis of embankment dams with a center core. In the present study, a bilinear elastic-perfectly plastic stress–strain relationship with a Mohr–Coulomb failure criterion has been used in the dynamic analyses. In this model, energy dissipation is achieved by plastic ow when shear stresses reach the yield strength. For cycles generating shear stress levels remaining in the elastic range, energy dissipation is achieved by viscous damping. Rayleigh damping consisting of two viscous elements is generally used in the numerical analyses. ˜e two elements of Rayleigh damping are both frequency dependent; one increases linearly with frequency (sti.­ness damping as a function of strain rate) and the other decreases exponentially with increase in frequency i.e. mass damping as a function of particle velocity [20]. ˜e ˙nite di.erence grid dimensions were selected taking into account the maximum frequency, f, of the shear wave that the model could respond to during earthquake loading [22]. 2.2. Doyraj Earth Dam Doyraj Reservoir Dam is located on the river Doyraj at about 13 km north of Moosian and southwest of Ilam province, in Iran. ˜e main purpose of Doyraj dam construction was irrigation of about 10,000 acres of agricultural land in Moosian Plain. ˜e normal level of operation in this dam is 226.5 meters and the level of the river bed is 176 meters above sea level. Seismic monitor­ing equipment has been located in di.erent parts of the Doyraj dam. ˜e location of the project, and Doyraj dam layout is shown in Figure 1. ˜e maximum height of the Doyraj dam is 58 meters and the operational reservoir Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam surface is 50 meters. ˜e length of the dam is 1160 m and the crest width is 10 m. In numerical modelling, the dam body was modeled in 8 layers of the same thickness, so that the conditions for the construction of the dam can be simulated. 2.3 Geometry and properties of Doyraj dam Two-dimensional plane strain models of the embank­ment were considered in the parametric analyses of this study. ˜e geometry of the model is shown in Figure 2. Doyraj Dam is mainly composed of silty soil and sand. ˜e ˙lter and drainage layers are composed of ˙ne-grained sand for drainage of water leakage and variable deformations between the core and the crater embankment. Suitable materials were used for the core Table 1. Properties of materials used in 2D F.D.M. analysis. Materials dry(kN/m3) kx (m2/s) E (MPa) c (kPa) . (°) Founda­ tion Rock 22.0 1.0×10-9 300.0 0.3 0.0 32 Layer Founda­ tion Clay 20.0 3.9×10-5 200.0 0.25 0.0 28 Layer Gravel Shell 21.0 1.0×10-7 100.0 0.33 0.0 38 Gravel Drainage 19.5 1.0×10-3 90.0 0.25 0.0 39 Clay Core 20.5 1.0×10-9 75.0 0.25 50.0 13 Filter 19.5 1.0×10-5 35.0 0.3 0.0 35 Figure 2. Cross section of Doyraj earth dam. 68. Acta Geotechnica Slovenica, 2021/1 Figure 3. Grain size distribution of Doyraj dam materials. and cutting o. the clay and concrete. In fact, the area of gravel levee and embankment were constructed with the excavated materials near site of the project. ˜e particle size distribution for di.erent materials of the Doyraj dam is shown in Figure 3. Physical and mechanical properties of the embankment and foundation soils used in the numerical models, are presented in table 1. 2.4. Finite difference modelling ˜e technique of layered construction was employed in the static stress analyses. Since pore pressure genera­tion during construction was a concern, the following procedures were used to model the static e.ective stress conditions: (a) Embankment materials were divided into eight layers and placed sequentially. Following the placement of each layer, other layers were added to the layer and the model was set to run for a time period equal to the estimated time required for actual construc­tion of the layer under ˙eld conditions. ˜e time needed was calculated by assuming an embankment construction with rate of 1000 m3/day and multi­plying this by the total ˙ll volume of each layer. (b) ˜e water level was then raised to full the pool. Boundary water pressures were applied along the interior dam surface and the reservoir bed to account for water pressures. (c) Seepage analysis was performed to achieve steady state conditions within the embankment and the foundation. (d) Mechanical adjustment of stresses was allowed by performing mechanical calculations in which, ow calculations turned o., and forcing the model to reach equilibrium. Once initial stresses for the steady state condition were achieved, the following steps were taken to prepare the model for dynamic analyses: (a) Apply dynamic boundary conditions. In order to enforce free ˙eld conditions in the numerical boun­daries of the discretized half space foundation, free ˙eld boundary conditions available in the code were adopted for the lateral boundaries. For the horizontal boundary, the simulation of outward propagating waves in the foundation was achieved by employing the absorbing boundary conditions which are also available in the ˙nite di.erence code. Absorbing boundaries have been shown to be e.ective in absor­bing outward propagating waves, and hence simu­lating half space conditions. ˜e viscous boundaries developed by Lysmer and Kuhlemeyer [23] are adop­ted in the ˙nite di.erence code, and were employed in the analyses herein. One restriction in applying absorbing boundaries in numerical modeling for dynamic analysis is that such boundary conditions cannot be simultaneously applied to a model, where acceleration or velocity input is applied; since prescribing acceleration or velocities to a boundary would nullify the e.ect of the absorbing boundary. In such situations it is necessary to convert accelera­tion or velocity inputs into stress waves, as described below. (b) Prepare input motion and apply seismic loading to the numerical model. Horizontal component of the acceleration record from Loma Preita earthquake was applied to the base of the model. Since quiet boundaries were already attributed to the horizontal boundary, the acceleration time history of the input motion was converted to shear stress waves, as described above. A nearly perfect match between the input acceleration time history and the time history recorded aer applying the shear wave time history, con˙rmed the validation of the process employed in this paper. Aer preparing the input motion by ˙ltering the acceleration time history and converting it to a shear stress time history, the resulting shear stress time history was prescribed to each of the Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam grid points at the horizontal boundary in which, absorbent boundary conditions were previously prescribed. (c) Rayleigh damping was assigned to each element of the model in the mid-range between the natural frequency of the model and the predominant frequency of the input motion. ˜e value of Rayleigh damping was chosen based on shear strains recorded from undamped analysis, by taking 65 % of the peak recorded strain. ˜e damping ratios obtained by this procedure ranged from 3 % to 7 %. (d) Dynamic analysis was performed for the duration of the earthquake, and results were extracted for inter­pretation and further assessment. It should be mentioned that for simpli˙cation purposes, the hydrodynamic interaction e.ects of the dam reservoir were neglected. Furthermore, the vertical components of the seismic input were not considered in the seismic loading, since the present study aims to provide qualitative results of the behaviour of a dam under seismic loading conditions. ˜e maximum shear modulus of materials used in the dam body, derived from empirical relationships. In these relationships, the shear modulus can be determined by the porosity of the materials. ˜e relationships to determine the Gmax for materials of di.erent areas of the dam body used in this research, are presented in table 2. In order to determine the most probable horizontal and vertical acceleration due to the earthquake in the study area, two approaches of determination of the earthquake magnitude have been considered. 1) De˙nitive determi- Table 2. Shear Modulus of dam materials. Materials Gmax Foundation Rock 1.62 GPa Layer Foundation Clay 1.62 GPa Layer Gravel Shell [24] Kokusho & Esachi (1981) Gravel Drainage [24] Kokusho & Esachi (1981) Clay Core [25] Hardin & Black (1968) Filter [26] Seed & Idriss (1970) nation and 2) probabilistic determination. In the de˙ni­tive determination of the earthquake magnitude based on seismic studies and earthquake studies, the most important seismic spring relative to the site of the Doyraj Dam is the hidden fault of the Black Sea Anticline "SZ4". ˜is fault has the maximum seismicity (Ms = 7.0) at 42 km north of the dam site and approximately 13.6 km of the earth surface; with the maximum horizontal and vertical acceleration of 0.3 and 0.19 g, respectively. As compared to other seismic springs, that is the highest one. In the probabilistic method for determining the earthquake magnitude, a large return period has been estimated for the radial range of 100, 150 and 200 kilo­meters around the Doyraj Dam site using Gothenburg-Richter preparatory method, the ˙nal ˙t method, and the maximum likelihood estimator or probable maximum (KIKO) method. By comparing the various methods presented for determining the maximum return magnitude, it is concluded that the method of estimating the maximum exponential (KIKO method) is closer to reality because this approach has been used besides the use of the Guthenberg-Richter cumulative distribution function of historical earthquakes. Figure 4 shows the graphs of the return periods of surface magnitudes in the studied areas. Finally, the results of calculations based on a range of 100 km with a conserva­tive view and appropriately ˙tted to seismic springs for earthquake hazard analysis are attributed. In this regard, an earthquake event with a magnitude of Ms = 5.5 has a return period of about 100 years, an earthquake with magnitude given af Ms = 6.1 has a return period of about 500 years, an earthquake with Ms = 6.3 has a return period of about 1000 years, and an earthquake with Ms = 6.6 will have a return period of about 2000 years. However, seismicity exceeding Ms = 6.6 corresponds to a return period over 2000 years. By studying maximum acceleration of probabilistic method for the 1000-year return period, the maximum horizontal and vertical acceleration were projected to be 0.24 and 0.16 g, respectively. In order to study the seismic behavior of earth dams in this study, the time history of Loma Prieta earthquake acceleration was selected as the input movement in the dam foundation section. Horizontal time histories of the desired earthquake were considered as a two-way input to the dam base for a period of 40 seconds in the dynamic analysis. In the Loma Prieta earthquake, the maximum horizontal and vertical acceleration at high level of the MCL design for this accel­eration is 0.367 and 0.28 g, respectively. ˜is historical history has the closest horizontal and vertical acceleration to the most probable predictable earthquake in that area. Record of the earthquake input is shown in Figure 5. 70. Acta Geotechnica Slovenica, 2021/1 Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam Figure 4. Return period of earthquakes according to surface magnitude in the radial ranges of 100, 150 and 200 km. Figure 6. ˜e model of Doyraj dam in F.D.M. analysis. ˜e Meshing of the Doyraj dam contained 15360 quad-3 RESULTS AND DISCUSSION rangular and triangular elements. For investigating of the displacements in the static and dynamic analyses, a nonlin­ 3.1 Static Analysis of Doyraj Dam ear model with Mohr-Coulomb failure criterion has been used to simulate the elasto-plastic behavior of the founda-Prior to studying the dam response to earthquake load-tion material and the embankment body of the dam. For ing, the construction of the earth dam was simulated to the pore water pressure analysis, the ˙ne model is used. reproduce the initial state of e.ective stress. Actually, Figure 6 shows the model built in the F.D. environment. static analysis has been performed with the aim of Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam reviewing and controlling the static behavior of the Doyraj dam. ˜e horizontal and vertical displacement of the Doyraj dam at the time of completion (10/02/2013; and before impounding) and at the ˙rst impounding is shown in Figure 7. ˜e horizontal displacement changes of the dam is presented in Figure 7.a and aer impound­ing is shown in Figure 7.b. ˜e results of vertical defor­mations of the dam at the time of construction and aer impounding are shown in Figures 7.c and 7.d, respec- (b) Horizontal displacement aer impounding. (c) Settlement pattern before dewatering. (e) ˜e pore water pressure distribution derived from the seepage analysis; height of retained water is 51 m. Figure 7. ˜e amount of settlements, pore water pressure and horizontal displacements in the Doyraj dam. (a) Settlements of the core. (b) Settlements of Doryaj dam over the time. (c) Excess pore pressure pattern over time. Figure 8. Excess pore pressures and computed settlement pro˙les. 72. Acta Geotechnica Slovenica, 2021/1 Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam tively. In Figure 7.e, the pore water pressure is shown in which, the dam located at the impounding stage. Due to the construction process of the embankment, the clay core has vertical settlements about 530 mm. With reference to Figure 8.a, it is observed that with the di.erent heights of the embankment in the central axis of the core, which has not yet been completed, the most settlements are located at about one third of the center of the clay core, which is approximately 540 mm. However, there is not much change in the amount of settlements aer impounding and before impounding in the clay core. In Figure 7.b, it is clear that the amount of hori­zontal displacement variations has doubled compared to before impounding, increasing from 60 mm to 120 mm. In fact, the increase in horizontal displacements in the dams is due to increased reservoir pressure. In the case of a reservoir drop stage, the elastic deformation of the dam material because of impounding can be improved due to discharge of the reservoir. Figure 8.b shows the consoli­dation process at di.erent times in the downstream verti­cal axis. As it can be seen, the amount of change in the consolidation settlements with the increase in time is not much noticeable and the validity of this issue can be seen in Figure 8.c, so there is not much excess pore pressure in the dam. Furthermore, as shown in this ˙gure, the excess pore water pressure is reduced over time. In the analysis stage of the permanent leakage of the dam, it is assumed that the reservoir water height has its maximum value (approximately 51 meters). ˜erefore, an analysis of the steady state seepage was performed for the water level of 51 m. Steady state seepage analysis was performed separately from the mechanical analysis. ˜erefore, according to the patterns, the maximum sum of the settlements is located at one third of the dam height from the foundation, with maximum value of 540 mm. ˜e maximum pore water pressure is also obtained at around 700 kPa. 3.2 Dynamic Analysis of Doyraj Dam Dynamic analysis performed to investigate the probable behavior of the dam during an earthquake. Using the initial stress state obtained from the previous static anal­ysis, the dam has been analyzed using the Loma Prieta earthquake history as an input quake. ˜e earthquake time incoming on the dam was about 40 seconds. 3.2.1 Acceleration Distribution Inside the Dam Body Acceleration contours showed that the maximum accel­eration at the end of the earthquake was about 2 m/s2. But the history of acceleration at the dam crest and the maximum acceleration at the crest of the analy­sis in 8 seconds step, was calculated about 5.3 m/s2. Figure 9. Horizontal and vertical acceleration changes on upstream and downstream slopes. Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam History of acceleration time for 6 points from the upstream slope and downstream slope of the dynamic ˙nite di.erence analysis indicated in Fig. 9 (Point d-f and a-c). Peak acceleration at 6 points in front of its height is depicted in Figure 9, showing that from the base of the dam to its crest, it ˙rst increased and then slightly decreased. As it can be seen, the amount of horizontal and vertical acceleration changes is higher than the rest of the points in the middle third part of the upstream and downstream shells; this is also indicative of the possibility of slipping wedges in these areas. In addition, the horizontal acceleration is higher than the vertical acceleration peak in the dam. Given that the motion of the bed is stronger in the vertical direction, it is clear that the dam is substantially strengthened in the direction of the horizontal motion of the earth. Peak acceleration direction at 6 points is also shown in Figure 9. Peak acceleration in the upstream of slope is mainly down­ward to upstream, while in the downstream of slope, is oen upward. Finally, at the same elevation, the peak acceleration in the upstream of slope is larger than the downward of slope indicating that there is more seismic deformation on the upstream side of the dam. Another matter that can be stated is that, the acceleration at the point H located at the bed of the foundation is slightly higher than the rest of the points, and the cause can be attributed to the e.ect of the shear force caused by the earthquake on the base of the foundation and where the earthquake force it enters. So, with respect to this, we can say that Finn model is not very successful in accelera­tion analysis in the model based on performance of this model which proves the opposite belief about this model. As shown in Figure 10, in relation to the acceleration on the crown and the base of the foundation, the two Finn and Mohr models have been the opposite of each other. 3.2.2 Deformations Deformations can be used to assess the safety of the dam due to the loss of free height. Aer dynamic analysis, the calculated changes for comparing the damping behavior presented in Figure 11, which show horizontal and vertical contours, respectively. Deformations contour indicate that the maximum settlement at the dam was 61 cm. It is obvious that the settlements in the clay core have continued to the crest. However, horizontal defor­mations in the clay core are less than the upstream and downstream shells. Patterns show that the maximum horizontal displacements occur in the downstream shell, 74. Acta Geotechnica Slovenica, 2021/1 Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam which is approximately 60 cm in size. Of course, the depth of horizontal displacements is not much on the downstream slope. ˜e results of this section are based on Mohr model. Figure 12 show the location of the monitoring points. As shown in this ˙gure, these points have experienced the modest changes in horizontal displacements. Figure 12.a shows the history of horizontal displacement during dynamic loading based on the Mohr model in the monitoring point. Figure 12.c also shows the history of horizontal displacement during dynamic loading based on the Finn model in the monitoring point. It is observed that the most horizontal displacement in the Mohr model occurred about 38 cm at the point “f”. However, in the Finn model, the maximum horizontal displacement of about 46 cm occurred at the same point. Figure 12.b and 12.d show the history of the vertical displacements at the monitoring points based on the Mohr and Finn models, respectively. It is observed that the maximum settlements at the point “f” occurred on both models. But the di.erence between the amounts of settlements in two models is considerable. ˜e settlement based on the Finn model is about 2.5 times higher than that of Mohr model. ˜is proves that the Finn model shows the displacements more than the predicted value. In general, according to the obtained results, the lasting displacement in the side of the crest of the dam has its highest value. 3.2.3 Strains Shear strain provide information for understanding the locations inside the dam that may have been damaged during severe earthquake stimulations. Shear contours (a) Horizontal displacements based on Mohr model. (c) Horizontal displacements based on Finn model. (d) Vertical displacements based on Finn model. Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam of dynamic analysis for di.erent models are shown in Figure 13. Most parts of the dam body have experienced a small amount of shear strain. Shear strains can be seen in the upper part and close to the crest. In fact, at 6 seconds from the occurrence of the earthquake, the shear strain had more penetration in the dam body. ˜ereaer, the occurrences of large shear strain can be observed clearly on both sides of the dam in the middle and bottom portions of the slope downstream. As seen in Figure 13.a, in Mohr model, all the shear strains have occurred on a slope downstream, but in the Finn model (Figure 13.b.), all shear strains happened in the upper slope of the dam. ˜is shows that the Finn model considers saturated areas more critical. It is even observed that the depth of shear strain penetration in the Finn model is more than that of Mohr model. (b) Shear strain based on Finn model. Figure 13. Counter of shear strains at di.erent times of dynamic analysis. 3.2.4 Stability of Doyraj Dam Changes in the coecient of slope stability of an earth dam can occur during di.erent periods from construc­tion to operation time; therefore, stability analysis of the upstream and downstream slopes of the earth dams in di.erent conditions, the operation of the reservoir of dams, execution of the body at the end of construction are important. Signi˙cant parts in this matter are the design, implementation and operation of the dam body at various stages. ˜erefore, in the present study, static and seismic properties of the Doyraj earth dam located in Ilam province, which is in operation at the moment, have been investigated. For this purpose, F.D.M. and Newmark methods have been used. ˜e results show that the dam has a ˙xed stability in the static and seismic states. FOS for upstream and downstream in F.D.M. analysis was 1.57 and 1.49, whilst for Newmark method the values were 1.44 and 1.55, respectively. ˜e results of deformation analysis for the Loma Prieta earthquake are shown in Figure 14. ˜e amount of permanent deformation obtained by this analytical method is about 470 mm, which is close to the results of F.D.M. analysis. Although the Newark Slip Block Method cannot fully model the mechanism of settle­ments occurrence in an earth dam in the case of an earthquake, the previous studies have shown that if the appropriate assumptions were considered in the analysis, the displacement values could be in good agreement with both elasto-plastic dynamic analysis and the method used in this research (Newmark Slip Block). 4 CONCLUSION Based on 2D F.D. analysis of a case study earth dam located in the west of Iran (Doyjay earth dam) the following results obtained: In the static state, major settlements occur at the center of the core. ˜e maximum settlement of the dam body is 530 mm at the end condition which occurs in the middle of the core. ˜e maximum horizontal displacement at the end of the construction is about 6 cm. In fact, the 76. Acta Geotechnica Slovenica, 2021/1 Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam increase in horizontal displacements in the dams is due to increased reservoir pressure, since the amount of hori­zontal displacement variations has doubled compared to before impounding. ˜e impounding does not change the amount of settlements, but the horizontal displace­ment of the dam reaches 120 mm. In this investigation for the ssettlements of the crest dam, the assumption of a sliding circles runway from the middle section of the upstream and downstream slopes (Middle Dam), are more critical. ˜e maximum amount of sustained settlements by the Newmark sliding block method is 47 cm which is far less than the Free Board, accelerated magni˙cation values at the crest of the dam in the seis­mic analysis for accelerated mapping used between 2 and 5, indicating signi˙cant acceleration in the dam body. Nonlinear analysis showed that the amount of cyclic shear strains inside the core are very small compared to other parts of the dam. Deformations contour indicate that the settlements in the clay core have continued to the crest. However, horizontal deformations in the clay core are less than the upstream and downstream shells. ˜e static stability coecients of the downstream slope are close, in all cases. ˜is demonstrates that in a static state, the safety of embankment is not a.ected by changes in water level in the reservoir. ˜e maximum shear strains distribution in the dam body, especially on the upstream and downhill slopes, are obtained by the accelerograms, which can represent a lower coecient of certainty against the failure of susceptible levels of slippage. Sliding surfaces is shown deeper in the Finn model. Contrary to what is commonly accepted (the increase in earthquake acceleration from the base to the dam is always expected), this is not a general phenom­enon and it can be limited to very strong dam (whose behavior remains earthquake-resistant, i.e. elastic) or related to poor earthquakes. Conversely, due to strong earthquakes, some parts of the dam may reach plasticity. Earthquake acceleration does not increase along the altitude. However, at the same time, the body of the dam gradually surrenders and may collapse. REFERENCES [1] Charatpangoon, B., Kiyono, J., Furukawa, A., and Hansapinyo, C. (2014). "Dynamic analysis of earth dam damaged by the 2011 O. the Paci˙c Coast of Tohoku Earthquake". Soil Dynamics and Earth­quake Engineering, 64, pp 50–62. [2] Rampello, S., Cascone, E., and Grosso, N. (2009). "Evaluation of the seismic response of a homoge­neous earth dam". Soil Dynamics and Earthquake Engineering, 29(5), pp 782–798. [3] Seed, H. B., Idriss, I. M., Lee, K. 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"Mechanisms of landslides." Engineering geology (Berkey), Geological Society of America. [9] Newmark, N. (1965). "E.ects of earthquakes on dams and embankments". Geotechnique, 15(2), pp 139–60. [10] Franklin, A. G., and Chang, F. K. (1977). "Perma­nent displacements of earth embankments by Newmark sliding block analysis." Report 5, Miscel­laneous paper S-71-17, US Army Corps of Engi­neers, Waterways Experiment Station, Vicksburg, Mississippi. [11] Yegian, M. K., Marciano, E. A., and Gharaman, V. G. (1991). "Earthquake-induced permanent deformations: probabilistic approach". Journal of Geotechnical Engineering, ASCE, 117(1), pp 35–50. [12] Seed, H. B., Lee, K. L., Idriss, I. M., and Makdisi, R. (1973). "Analysis of the slides in the San Fernando dams during the earthquake of Feb. 9 1971". Report No. EERC 73–2, Earthquake Engineering Research Center, University of California, Berke­ley, p. 150. [13] Andrianopoulos, K. I., Papadimitriou, A. G., Bouckovalas, G. D., and Karamitros, D. K. (2015). "Insight into the seismic response of earth dams with an emphasis on seismic coecient estima­tion". Computers and Geotechnics, 55, pp 195-210. [14] Randall, M. J., and Knopo., L. (1970). “˜e mech­anism at the focus of deep earthquakes”. Journal of Geophysical Research, 75(26), pp 4965-4976. [15] Yamaguchi, Y., Iwashita, T., and Mitsuishi, S. Ahmad R. Mazaheri et al.: Dynamic analysis of earth dam using numerical method – a case study: Doyraj earth dam (2008). "Preliminary investigation of dams stricken by the Iwate–Miyagi Nairiku Earthquake in 2008". In Proceedings of the 5th East Asian regional dam conference international symposium on co-exist­ence of environment and dams. [16] Tschuschke, W., Wryska, M., and Wierzbicki, J. (2017). “Quality control for the construction of a tailings dam” ACTA GEOTECHNICA SLOVENICA, 2017/1. Pp. 3-9. [17] Soralump, S., and Tansupo, K. (2009). "Safety anal­yses of Srinagarind dam induced by Earthquakes using dynamic response an analysis method". In Proceedings of the international conference on performance-based design in earthquake geotech­nical engineering, IS-Tokyo, pp 987–994. [18] Fallah, H., and Wieland, M. (2010). "Evaluation of earthquake safety of Koman Concrete Face Rock ˙ll Dam in Albania". In Proceedings of the 3rd Asian conference on the Earthquake engineering, ACEE, Bangkok, ˜ailand. [19] Han, Y., and Hart, R. (2006). "Application of a simple hysteretic damping formulation in dynamic continuum simulations". In Varona P, Hart R, editors. In Proceedings of the 4th international FLAC symposium on numerical modeling in geomechanics, Madrid, Spain. [20] Zhai, E., Roth, W., Dawson, E., and Davis, C. (2004). “Seismic deformation analysis of an earth dam a comparison study between equivalent-linear and nonlinear e.ective-stress approaches”. In Proceedings of the 13th world conference on earth­quake engineering, Vancouver, BC, Canada. [21] Roth, W.H., Dawson, E., Somerville, P., Davis, C., and Plumb, C. C. (2004). “Evaluating the seismic performance of Stone Canyon Dam with 2-D and 3-D analyses”. In Proceedings of the 13th world conference on earthquake engineering, Vancouver, BC, Canada. [22] Kuhlemeyer, R. L., and Lysmer, J. (1973). “Finite element method accuracy for wave propagation problems” Journal of Soil Mechanics and Founda­tion Engineering Division, ASCE, 99 (SM5). pp. 421–427. [23] Lysmer, J., and Kuhlemeyer, R. L. (1969). “Finite dynamic model for in˙nite media”. Journal of Engineering Mechanics; 95 (EM4), pp 859–877. [24] Kokusho, T., and Esachi, Y. (1981). “Cyclic triaxial test on sands and coarse materials, In Proceed­ings of the Xth International Conference on Soil Mechanics and Foundation Engineering, Stock­holm, Vol. 1. [25] Hardin, B. O., and Black, W. L. (1968). “Vibration Modulus of Normally Consolidated Clay,” Journal of the Soil Mechanics and Foundations, ASCE. 94 (SM2), pp 353–369. [26] Seed, H. B., and Idriss, I. M. (1970). “Soil Module and Damping factors for dynamic response analy­ses”. Report EERC 70-10, earthquake engineering Research center, University of California, Berkeley. 78. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation INVESTIGATION OF THE END PREISKAVA NOSILNOSTI BEARING LOAD IN PILE GROUP KONICE V MODELU SKUPINE MODEL IN DRY SOIL UNDER PILOTOV V SUHIH TLEH OB HORIZONTAL EXCITATION VODORAVNEM VZBUJANJU Mohammed Y. Fattah Hussein H. Karim Makki K. M. Al-Recaby University of Technology, University of Technology, University of Technology, Civil Engineering Department Civil Engineering Department Civil Engineering Department Baghdad, Iraq Baghdad, Iraq Baghdad, Iraq E-mail: myf_1968@yahoo.com E-mail: Hussein_karim@yahoo.com E-mail: Makki_Recaby@yahoo.com https://doi.org/10.18690/actageotechslov.18.1.79-106.2021 pile group, horizontal shaking, dry sand, end bearing A series of 94 laboratory tests were conducted to measure the response of pile foundation when subjected to dynamic loads. Eight tests were conducted on single pile in dry soil at relative density 30 % (loose) and 50 % (medium); 66 tests on group of piles with di.erent spacings and patterns. All tests were carried out under operating frequencies 0.5, 1 and 2 Hz under horizontal shaking. All tests were achieved with one embedment ratio (L/d = 30). .ese tests were grouped in three di.erent numbers of piles; 2 piles in row and line patterns, 3 piles and 4 piles; and three pile spacing ratios (s/d = 3, 4 and 5). .e results of dry soil indicating the mechanism of dynamic response of piles and soil subjected to dynamic horizontal shaking include the variation and distribution of acceleration with time in di.erent states of soil in addition to the vertical and horizontal displacements, end-bearing load, peak acceleration and the peak velocity of foundation. It was concluded that for a dry soil bed, the acceleration amplitudes increase with frequency for both soil relative densities (loose and medium) and di.erent pile patterns (number; single or group and di.erent spacing ratios s/d). .e maximum acceleration in the foundation is lower than in the soil bed for all operating shaking frequencies, pile spacing ratios and soil states. .e decreasing of the maximum acceleration recorded in the foundation as skupina pilotov, horizontalno tresenje, suha zemljina, nosilnost konice Izveden je bil niz 94 laboratorijskih preizkusov za merjenje odziva temeljenja na pilotih, ki so bili izpostavljeni dina­mi˜nim obtežbam. Osem preizkusov je bilo izvedenih na posami˜nem pilotu v suhi zemljini z relativno gostoto 30 % (rahlo gostotno stanje) in 50 % (srednje gostotno stanje); 66 testov na skupini pilotov z razli˜nimi razmiki in vzorci. Vsi preizkusi so bili izvedeni pri delovnih frekvencah 0,5, 1 in 2 Hz pri horizontalnem tresenju. Vsi preizkusi so bili izvedeni z enim razmerjem vpetosti (L/d = 30). Ti preizkusi so bili združeni v tri skupine z razli˜nimi števili pilotov; 2 pilota v vrsti in linijskem vzorcu, 3 piloti in 4 piloti; ter tri razmerja razmika med piloti (s/d = 3, 4 in 5). Rezultati za suho zemljino kažejo mehanizem dinami˜nega odziva pilotov in zemljine, izpostavljenih dinami˜nemu vodoravnemu tresenju, dodatno k vertikalnim in vodorav­nim premikom, nosilnostim na konici, najve˜jemu pospešku in najve˜ji hitrosti temeljenja vklju˜ujejo še spreminjanje in porazdelitev pospeška s ˜asom v razli˜nih stanjih zemljine. Ugotovljeno je bilo, da se za suho zemljinsko osnovno plast amplitude pospeševanja s frekvenco pove˜ujejo tako za rela­tivni gostoti zemljine (rahlo in srednjo gosto gostotno stanje) kot za razli˜ne vzorce pilotov (število; posami˜ni pilot ali skupina pilotov in razli˜na razmerja razmika s/d). Pri vseh delovnih frekvencah tresenja, razmerjih razmikov med piloti in stanji zemljine je najve˜ji pospešek v temelju nižji kot v zemljinski osnovni plasti. Zmanjšanje najve˜jega pospeška, M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation compared to that in the soil bed is between 10-100 % for loose and medium state of soil, and the decrease in loose state is more than in medium state. .is means that there is damping e.ect or attenuation of vibration waves. .e amplitudes of recorded acceleration in the pile cap are much higher than in the soil bed for single pile and pile group with di.erent pile spacing ratios, also these amplitu­des are increasing with increase of shaking frequency and relative density of the soil. 1 INTRODUCTION ˜e pile foundations response under dynamic loading is comparatively more complicated than that for static loading. Unfortunately till now, the piled foundation system performance subjected to cyclic loads or during earthquakes is not completely understood [22]. ˜e soil-pile-foundation interaction is one of the main vital issues in the dynamic analysis which needs more understanding. However, a very little information is available on observed dynamic behavior of pile founda­tions which is due to diculties in performing such tests involving the several variables related to both soils and piles. Numerous shaking table tests have been conducted on sand soils, with and without the pile models. ˜ese practical examinations include tests to study ground responses and behavior of the sand, and model pile tests to evaluate the pile behaviors and soil-pile interactions under shakings. Further tests and analyses of the shak­ing test data are required for a better understanding of behaviors of soil, soil-pile interaction, and combining between the generated movement and pile responses under earthquake shakings. ˜e shaking table test data may be used for veri˙cation of analysis methods and numerical modeling for ground responses and soil-pile interactions during earthquake shakings. Full-scale tests are generally assessed to submit the most reasonable results but, are limited because of their high costs. ˜e limitations highlight the two main diculties of carrying out ˙eld full-scale tests on piles subjected to earthquake excitation, essentially the diculty in modeling bedrock excitation and providing enough energy to excite large pile groups in addition to their signi˙cant cost, time and e.ort. However, a number of studies dealt with centrifuge and shaking table model testing. ˜e most common previous studies on dynamic testing of piles have been achieved with full scale piles are; Maxwell et al. [19], Novak and Grigg [20], Gui [17]; on small scale tests; Fattah et al. [14][15]. zabeleženega v temelju, v primerjavi s pospeškom v zemljin-ski osnovni plasti znaša med 10 % in 100 % za zemljine v rahlem in srednje gostem gostotnem stanju, zmanjšanje za rahlo gostotno stanje pa je ve˜je kot za srednje gostotno stanje. To pomeni, da pride do dušenja ali oslabitve vibra­cijskih valov. Amplitude zabeleženih pospeškov v blazini pilotov so veliko ve˜je kot v zemljinski osnovni plasti za en pilot in skupino pilotov z razli˜nimi razmerji razmikov med piloti, prav tako pa se te amplitude pove˜ujejo s pove˜anjem frekvence tresenja in relativne gostote zemljine. Brown [12] studied dynamic and static lateral load­ing on pile groups using di.erent full-scale ˙eld tests carried out on groups of piles of six to 12 piles, both driven and bored, in relatively cohesionless and so cohesive soils. All the pile groups were loaded laterally statically reaching large deections, and instrumented pipe pile groups were also tested under dynamic loads reaching large deections, equivalent to those that might the pile be subjected to due to major impact of ships and earthquakes. Dynamic loading was exerted by a number of impulses of increasing magnitude adopting a horizontally mounted Statnamic device. While this loading did not cover the characteristics of lateral load­ing and ground motion that may cause development of high pore water pressures, it did cover the damping that occurs at high levels of pile deections and the inertial e.ects of the structure. Banerjee [9] presented the behavior of pile foundations under earthquake loading. ˜e study investigated the interaction between soil behavior, pile sti.ness and superstructure inertial loading on pile response during earthquake. It was noted that the soil around the piles does not just support the piles, it also exerts inertial loading on the piles. Pile head loading cannot replicate this e.ect. Experimental data have been deduced from a centrifuge modeling, which then used as a basis for vali­dating and calibrating numerical analyses. ˜e research involved four major components: (1) characterization of the dynamic properties of kaolin clay through element testing using the cyclic triaxial and resonant column apparatus; (2) dynamic centrifuge testing on pure kaolin clay beds (without structure) followed by 3-D ˙nite element back-analyses; (3) dynamic centrifuge testing on clay-pile-ra systems and the corresponding 3-D ˙nite element back-analyses and (4) parametric studies lead­ing to the derivation of a semi-analytical closed-form solution for the maximum bending moment in a pile under seismic excitation. Boominathan et al. [11] carried out a study by full-scale lateral dynamic pile load testing to determine the dynamic characteristics of soil-pile system. ˜e results of 80. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation two full-scale ˙eld dynamic lateral pile load tests carried out at two di.erent sites in India (Chennai and Hazira) and the results of a nonlinear three-dimensional ˙nite element analysis of piles under dynamic lateral loads using the program ABAQUS were presented. ˜e non­destructive technique known as Multichannel Analysis of Surface Waves (MASW) was used for determination of the shear wave velocities of di.erent layers up to a depth of 12.5 m below the ground level based on the average SPT-N value and for evaluation the sti.ness (maximum dynamic shear modulus) of the subsurface required ˙nite element analysis. A steady state sinusoidal force was generated with a 5-tonne capacity mechanical oscillator. ˜e forced vibration response of the piles was measured using two acceleration transducers ˙xed at the mid height of the pile cap, and at the pile cut o. level. Aer every steady state lateral vibration test, the eccentricity of the oscillator was increased to raise the dynamic force and the test was repeated to cover a wide range of lateral displacements expected during a typical dynamic loading of the pile. Janalizadeh and Zahmatkesh [18] applied a pseudo-static method for estimation of the response of pile during dynamic loading. ˜e geometry and the soil modeling parameters have been de˙ned, and then the numerical model was veri˙ed by means of the centrifuge test. Next, the behaviors of piles were studied with the e.ects of various parameters such as soil layering, kinematic and inertial forces, boundary condition of pile head and ground slope. A method for analysis of piles in lique˙able soil under seismic loads has been presented. ˜ree cases were considered to evaluate the e.ects of variations in sti.ness and lateral resistance of the p-y curves on the testing results. ˜e dynamic response of pile foundation in dry sandy soil excited by two opposite rotary machines was considered experimentally by Fattah et al. [15]. A small scale physical model was manufactured to accomplish the experimental work in the laboratory. ˜e physical model consists of two small motors supplied with eccentric mass (0.012 kg) and eccentric distance (20 mm) representing the two opposite rotary machines, an aluminum sha as the pile, and a steel plate a pile cap. ˜e experimental work was achieved taking the following parameters into considerations: pile embed-ment depth ratio (L/d, where L is the pile length and d is its diameter) and operating frequency of the rotary machines. All tests were conducted in medium dense ˙ne sandy soil with 60 % relative density. To predict precisely the dynamic load that will be induced from the rotary machines, a mini load cell with a capacity of 100 kg was mounted between the aluminum plate (the machine base) and the steel plate (pile cap). ˜e results revealed that, before machine operation, the pile tip load was approximately equal to the static load (machine and pile cap), whereas during machines’ operation, the pile tip load decreased for all embedment depth ratios and operating frequencies. ˜is reduction was caused by the action of skin friction that was mobilized along the pile during operation, and as a result the factor of safety against pile bearing failure increases. For all operating frequencies and pile lengths, the factor of safety against bearing failure increased during machines’ operation, where the pile tip load became less than its value before starting operation. During operation, the skin friction resistance mobilized along pile length led to decrease the bearing load. ˜e objectives of the present study are determination of the frequency independent dynamic response of both single pile and group of piles to lateral vibration for di.erent patterns and spacings, calculation of a velocity and acceleration- time history in addition to displacement - time history of pile groups subjected to earthquake excitation, and investigating the e.ect of soil con˙nement due to pile spacing on the load transfer in pile groups. 2 TESTING APPARATUS AND METHODOLOGY ˜e testing device (the manufactured model) is a metal structure, which consists of three main interrelated parts. All these parts have the ability to slide (slip) one against the other by means of ball bearings, which can work together giving a relative horizontal motion between them as shown in Figure 1a. ˜e two parts have been linked by a piece of metal connected by steel screws to ˙x these movable sliding parts. In the second part (slide II), a metal holder (with dimensions 800 mm wide and 400 mm long) is mounted which is also being slided by ball bearings along the longitudinal axis with a distance more than 600 mm in the two directions (sides). But in this work, this distance was limited to only 50 and 60 mm. A steel piece (plate) of L-shape (with dimensions of 900 mm wide, 1000 mm long and 300 mm high) is mounted while strengthening its edge and base by three triangular sti.eners to avoid any rush or slippage of interior or exterior parts as shown in Figure 1b. Another two ball bearings with internal diameters of 45 mm are mounted within the bracket base in which a connectivity and installation screw (PIN) enters to get a reciprocating motion as shown in Figure 1c. A decentralized source motion must be generated and connected via an arm to the L-shaped base plate which is installed on the M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation (a) (b) (c) (d) Figure 1. Slides and base bracket system during manufacturing of shake box. (a) (b) (c) (d) Figure 2. CAMA and pin connected during manufacturing of the shaking box. metal holder. ˜en, a linear reciprocating movement must be determined at distances of 50 mm and 60 mm that means a dri from the center by 25 mm or 30 mm radius from every direction as illustrated in Figure 1d. Two decentralized Cama which is a rotating pin for translation of movement (with diameter of 95 mm) have been manufactured with downward dri distance of 25 mm or 30 mm from the center as shown in Figure 2c. ˜ey were mounted on three-phase engine, with capacity of 3 horsepower. A rotation speed of 1450 rpm was used as an incentive for the rotational motion as shown in Figure 2. ˜is decentralized Cama rotates inside the bearing ball (needle bearing) which is linked by a 400 mm long connecting arm (or connecting rod) to the eccentricity installed by a pin as shown in Figure 2. As the test in this research requires obtaining the reciprocating motion at di.erent speeds and frequencies, so an electric current controller (AC Inverter from Hyundai Company) for di.erent rotational speeds of the engine was chosen. ˜e inverter is used to determine the type and speed of rotation. To get the required velocities in this research, the inverter has been linked to a gear box (Con˙guration Gear Box through the sha) to reduce the speed by around 3 folds. 3 STEEL BOX ˜e other part of the manufactured device is the steel box, which is used for model tests. Its dimensions are (800 × 800) mm for its base and 1000 mm height, it is connected with the L-shaped steel plate by four screws M12 for installation and to prevent any movement as shown in Figure 3. A side slot 400 mm wide and 700 mm high of the steel box has been made to facilitate the process of discharging sand or soil as shown in Figure 3. A steel angle has been installed at the top of the steel box to make a platform for the devices and sensors used in the test as shown in Figure 3. During tests di.erent velocities are used from slow to rapid motion (1 up to 14) Hz, the motion is slow without any strong vibrations. But, with increasing the rotational velocity, the motion is converted to be a linear speed accompanied with the appearance of a direction change aer the cycle end for outgoing and return giving unacceptable vibrations due to the great moving mass, which generates a high momentum and high inertia (I). A little change of soil mass for di.erent model tests has a limited e.ect on (I) but the speed is of greatest value in increasing the value of (I), so when the velocity is incre­ 82. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation Figure 3. Steel box. ased, the linear mass starts to move quickly making it dicult to change the direction smoothly, therefore this problem has been solved by adding operating dampers to absorb the surging mass momentum at the end of the half, then give the initial speed in the opposite direction of the movement aer the arrival of the CAMA to the tipping point as shown in Figure 4. It is worthy to mention that in order to make the damping value variable in correspondence to the change (increase or decrease) in the linear speed; the dampers have been connected with source of pneumatic pressure from the compressor tank added to the system. ˜e compressor contains a regulator valve for air pressure to provide air to the dampers at di.erent pressures accor­ding to the selected speeds as shown in Figure 4. 4 RAINING TECHNIQUE To obtain a homogeneous ˙ll of sand with speci˙c relative densities inside the steel box, a sand raining technique device had been manufactured with dimen­sions (700×700×200) mm3. ˜e device is supplied with perforated cone holes distributed in an adequate way in correspondence to the speed of the sand falling, height of fall and the required relative density. ˜is technique regulates the mechanism of sand fall, ˙lling method, and the homogeneity of distribution, Figure 5. ˜is box is ˙tted from its four corners by hooks and steel chain M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation through a mechanism allowing its vertically upward and downward movement for the required distances of sand fall. ˜e sand box is supplied in its bottom by mecha­nical gates. Wherever the height reached, the gates are opened simultaneously. ˜e main job of this gate is to open the holes and allowing sand fall and vice versa. ˜e "raining technique" is used to deposit the soil in the testing tank at a known and uniform density, and in preparing the tested soil. ˜e device consists of a steel tank, with dimensions of 700 mm length, 700 mm width and 200 mm height. 5 DATA ACQUISITION SYSTEMS ˜e system of data acquisition was utilized so that all data could be scanned and recorded automatically, this system consists of the following: 1. Strain gauge data logger 2. Pile's tip load data system 3. LVDT data system 4. Accelerometer Data System 5. Vibration data system 6 MODEL PILES ˜e model pile used has a diameter of 18 mm. ˜e size of pile's model was chosen aer reviewing the literature about the suitable pile size that could be considered representative. Although, Vesic [23] stated that " scale e.ects will be complex for model of piles smaller than 35 mm in diameter", many researchers used smaller diameters in their tests: Al-Mhaidib [1] used steel piles with 30 mm in diameter, Boominathan and Lakshmi [10] used aluminum pile with a diameter of 19 mm and Al-Mhaidib [2] used steel piles with (25 mm) in diame­ter. ˜e dimensions of the pile model that will be used in this study were also selected to minimize the boundary e.ects of the soil container in the experimental setup. ˜e ratio between the equivalent ground plane diameter of tank and the structural plane size of the test object (pile) was taken equal to 44. ˜is equivalent diameter is large enough, so as the circumferential circle radius exce­eds the extent far beyond the zone of primary compaction around the pile in sand; therefore, the e.ect of lateral boundaries of container is minor and could be ignored. 7 SOIL In this work, poorly grained ˙ne to medium dry sand taken from one of the sites middle of Baghdad city at a depth of 10 to 15 m was used to study the responses of piles subjected to dynamic actions. ˜e soil properties are given in Table 1. Table 1. Physical properties of sandy soil used for testing. Standard of the test Value Property Grain size analysis E.ective size, D10 ASTM D 422 and 0.14 (mm) ASTM D 2487 (2007) Mean size, D50 ASTM D 422 and 0.22 (mm) ASTM D 2487 (2007) Coecient of ASTM D 422 and 1.70 uniformity, Cu ASTM D 2487 (2007) Coecient of ASTM D 422 and 0.96 curvature, Cc ASTM D 2487 (2007) Classi˙cation ASTM D 422 and SP (USCS)* ASTM D 2487 (2007) Speci˙c gravity, Gs 2.69 ASTM D 854 (2006) Dry unit weights Maximum, d(max.) ASTM D 4253 - kN/m3 15.2 (2000) Minimum, d(min.) ASTM D 4254 - kN/m3 13.2 (2000) Maximum void 0.99 -------------------­ ratio, emax Minimum void 0.74 ------------------­ ratio, emin Initial dry unit 13.74 ,14.13 -------------------­ weight, d(test) 8 PILES ˜e pile's model used in the present study is made of smooth aluminum tube having outer diameter of 18 mm and inner diameter of 15 mm covered with plastic sleeve to protect strain gauges. Pile-embedment ratio (depth-to diameter) (L/d) used in testing single and group piles was (30). four di.erent arrangements of the pile groups (2×1,1×2, triangle and 2×2) with di.erent spacing ratios (S/d) (3, 4 and 5) are used for testing a group of piles. ˜e mechanical properties of pile used are shown in Table 2. Table 2. Mechanical properties of aluminum pile used. Embedded Outer Wall Bending sti.­ length (mm) diameter (mm) thickness (mm) ness , EPIP (kNmm2) 540 18 1.5 0.18 × 106 ˜e piles were instrumented with 8 pairs of strain gauges on each pile attached along the sha to measure bending 84. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation strain by pasting (8) electrical- resistance-half bridge type strain gauges at distances of (0 L, l/4 L, l/2 L, and 3/4 L) from the top of the pile for single and group of piles tested in dry soil. Each strain gauge has a length of 5 mm, gauge factor of 2.10, and resistance of (350 ), and was ˙xed with its axis corresponding to the pile axis. ˜e wires of strain gauges were passed on a longitudinal pile covered with waterproof past to avoid damage. 9 LOAD CELLS Mini load cell with a diameter of 20 mm and a capacity of 100 kg was mounted at the tip of the pile, in a way to prevent the load cell from splitting from the pile and to predict the end-bearing load as shown in Figure 6. 10 PILE CAP AND PAYLOAD Two steel plates with dimensions of (100 × 100 × 10) mm3 and (150 × 150 × 10) mm3 were used to simulate the pile caps, Figure 7. ˜e purpose of using steel plate rather than aluminum plate is to ensure the rigidity of the pile cap with respect to the piles. Also another steel plates were used as payloads on the pile foundation. A set of measurements have been performed aer applying di.erent loads which were induced by static payload which represent the vertical allowable load carried by pile. 11 MODELS PREPARATION Preliminarily experiments were conducted to determine the uniformity of the process and how sand density changes with raining from di.erent heights. Results from raining the sand from di.erent elevations over known volume molds placed on the model oor demonstrated that uniform sand density could be achieved across the width of the model. By adjusting the pluvation height, di.erent sand densities were obtained. ˜e trial results suggested that the distance between the raining box and top of the sand should be 550 mm and 850 mm in order to produce uniform loose sand of relative density 30-50 %. In order to attain the selected relative densities of (30 %) and (50 %), the heights of the free fall were found to be 55 mm and 85 mm, respectively. While the sand tank parts were placed together, sand layers were prepared so that the sand layers were not disturbed and consequently any change to the required density of the sand did not happen. Aer ˙lling the raining box (tank) with sand and choosing the proper height of drop, the sand was poured into the test tank by moving the box Figure 7. Steel plate used as pile cap and payloads. M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation Figure 8. Steel plate used as pile cap and payloads. forth and rear. ˜e soil layer was prepared in 10 layers with 100 mm constant height for each one to attain the last elevation of 1000 mm from the bottom of container. To minimize the inuence of buried instruments on the soil deformation, miniature earth pressure cells (EPCs) and miniature accelerometers were used. ˜e active EPCs diameter to grain size ratio (D/d50) is 12, which is twice the recommended minimum to ensure a continuum response between the soil and the EPC active face [24]. Details of the instrumentation used in this work are shown in Figure 8. ˜e EPCs were used to measure the total pressure on the soil at the target locations and for estimating the total stresses. Instrumentation records were acquired and recor­ded by multi data acquisition systems model. 12 RESULTS AND DISCUSSION 12.1 Variation of the vertical displacement of founda­tion with time Figures 9 to 11 illustrate the variation of vertical displacement and settlement (permanent displacement when shaking is stopped) with time of the single pile and group of piles with s/d = 3 ratio, di.erent number of piles and di.erent frequencies and soil states. Generally, it can be observed that the vertical displace­ment increased with frequency for all cases regardless the soil type and pile number and spacing. ˜e rate of settlement increase in loose sandy soil is greater than that in dense sandy soil. From the results, it can be seen that the vertical displacements slightly increased with time with short shaking period then stayed constant to the end of the test, then the settlements increased signi­˙cantly. Aer that, the values are increasing gradually and slightly with time in all cases. For all cases and at di.erent frequencies, the records of the ˙rst period (around 50-100 sec.) show sharp increase in the vertical displacement with time. While, gradual increase (or slight increase to steady) is observed in the rest times. ˜e reason for these cases may be due to that the soil gradually densi˙ed during shaking which provided low settlement and more response. It is also observed that some records particularly under 2 Hz frequency using pile group (triangle and 2×2) show sharp increase with time (more than 25 mm). In comparison of single pile with pile group, the vertical displacement values are lower in group with respect to single pile foundation and decrease with the increase of pile spacing in groups. Also, the values decreased with increasing the soil relative density. 86. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation During the shearing, a granular material will typically values recorded due to densi˙cation of soil during have a net gain or loss of volume. If it had been shaking. originally in a dense state, then it typically, gains volume, a characteristic known as a Reynolds In general, it was noticed that the sandy soil rebound dilatancy. If it had originally been in a very loose state, represents small part of settlement as the device shut then compaction may occur before the shearing down. ˜erefore, it is important to mention that begins or in conjunction with the shearing. It was the plotted values of total settlement represent the observed that the increasing of shaking frequency leads settlement taken simultaneously as the shaking stops. to reduction in the oscillation of wave propagation ˜us, the residual or rebound displacements represent 88. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation the settlement of the foundation. As well as, the rate of 12.2 Variation of the end-bearing load of the piles settlement increase in loose sandy soil is greater than with time that of dense sandy soil. ˜e net (due to the dynamic e.ect only) bearing It is worth mentioning that the (+) sign means that the loads of piles were measured and recorded using displacement into the le and upward for the horizontal miniature load cells with diameter 20 mm placed at and vertical moving, respectively and vice versa, also the tip of piles. ˜e variations of the end bearing load in net displacement means the displacement for dynamic single pile and some groups of piles with time for shaking to the end of test (without initial static case). s/d = 3 ratio and di.erent number of piles and di.erent M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation frequencies and states of soil are illustrated in Figures 12 to 17. Aer careful examination of these ˙gures, it can be seen that at the end of shaking, some piles maintain their values while others reset to zero load. ˜e end bearing load values increase with frequency for both loose and medium soil states. Also, the end bearing load values increase with increasing number of piles for both states of soil. In general, the end bearing load values increase when s/d ratio increases from 3 to 4 while they decrease with s/d = 5. For triangle group, an increase in end bearing load is observed with increasing the pile spacing. When the spacing ratio is below s/d = 5, the pile group behaves as one mass, therefore, the inertia load becomes high which reects the high percent of load transferred to the pile ends. 90. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation 92. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation 94. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation ˜e ˙gures show that the behavior of the net bearing load at the tip of piles seems to be constant for a long period of test. On the other hand, the values of the net bearing load are 0.25 to 3.5 N in single pile for models in loose and medium sand, respectively. At the start of vibration, there will be a rapid mobi­lization of skin friction along piles, then aer a short period of time, the skin friction and end bearing reach a plateau and no noticeable change in the components was recorded. ˜e most important result is that, the pile tip load (net end bearing load) during shaking operation increased or decreased depending on many factors: number of piles, pile spacing, operating frequency, as well as, the state of soil. From all ˙gures, it is noted that, the oscillation of the frequented values decreases with increasing the shaking frequency. When the frequency of vibration is high, there will be no enough time for sand particles to move over each other, so that the oscillation in the measured displacements and end bearing load decreases. Fattah et al. [16] found that the ˙nal settlement of the foundation increases with increasing the amplitude of dynamic force, operating frequency and degree of saturation. Meanwhile, it is reduced with increasing the relative density of sand, modulus of elasticity, and embedding inside soils. During operation, the skin friction resistance mobilized along the pile length due to increasing in settlement and densi˙cation (increase in pile soil interaction e.ect of soil) led to increase in the bearing load. ˜is increase becomes clear as the spacing between piles increases. A small settlement occurs due to low operating frequency, which means a small skin friction resistance along the pile mobilizes, which reduces more due to the interaction e.ect of piles, and that mobilized resistant is less than the induced dynamic load. As a result, the pile's tip load increases. When increasing the operating frequency, the settlement increased, which means that increasing the mobilized resistance, and the increasing in pile's tip load became less. In general, the increasing in pile tip load is not more than the applied dynamic load divided by the number of piles. During shaking, when the end bearing load reaches a steady condition, the pile group behaves in a manner similar to the system under static loads; the load applied on the pile group is divided between the skin resistance and end bearing and no contribution is observed to the inertia e.ects. Ercan [13] concluded that load developed in outer piles is about 1.25 times the load developed in inner piles. On the other hand, lateral deection increased considerably as pile spacing decreased from 5D to 2D. However, this behavior was seen more clearly in the ˙rst two row piles. Pile spacing a.ects load distribution in pile groups signi­˙cantly. As pile spacing increases, pile load decreases. As pile spacing increases, maximum bending moment occurred decreases under the same load applied. 12.3 Variation of the peak acceleration of the foun­dation with time ˜e variation of peak acceleration of the foundation in the axis of shaking was measured using a vibration meter (vibrometer) in addition to the previous measurements of acceleration of the foundation and soil bed using accelerometer. Figures 18 to 23 display the variation of the acceleration of the single pile and some groups of M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation 98. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation piles with time for s/d = 3 and 4 and di.erent number of piles and operating frequencies for both states of soil. From these ˙gures, in general it can be seen the increase in acceleration measured by vibration meter with time and frequency for both states of soil and for di.erent number of piles in the group and di.erent spacings. ˜e ˙gures also show the slight decrease in the rate of vibration with increasing s/d ratio of the pile group. Concerning the e.ect of type of soil, the rate of vibra­tion, in general, or the acceleration decreases when the soil is of higher relative density (medium). ˜e horizontal acceleration of foundation (pile cap) ranges between (0.65-8) m/sec2 and (0.65-9) m/sec2 for single pile in loose and medium sand, respectively for shaking frequency (0.5-2) Hz. For group of piles, the acceleration ranges from (0.45-7.5) m/sec2 and (0.45-7.5) m/sec2 for loose and medium sand respectively for the same shaking frequency. ˜is means that there is a small attenuation of vibration due con˙nement o.ered by pile groups. ˜e above observation indicates that there is a small attenuation of vibration due con˙nement o.ered by pile groups. 12.4 Variation of the peak velocity of the foundation with time ˜e variation of velocity of the foundation measured using a vibration meter was also detected and recorded. Figures 24 to 29 display the variation of the velocity of some groups of piles with time for s/d = 3 and 4, di.er­ent number of piles, operating frequencies and states of soil. It can be shown from these ˙gures that the peak velocity measured using the vibration meter increases with time and frequency for both soil and di.erent number of piles and pile spacing. ˜e ˙gures also show a decrease in the rate of vibration with increasing s/d ratio and relative density. 13 CONCLUSIONS In the light of experimental tests on model piles in sand and analysis of the results and other observations during the experimental approach, the following major conclu­sions drawn from the test are summarized as follows: 1. For a soil bed in dry state, the acceleration ampli­tudes increase with frequency for both soil relative 100. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation 102. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation 104. Acta Geotechnica Slovenica, 2021/1 M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation densities (loose and medium) and di.erent pile patterns (number; single or group and di.erent spacing ratios s/d). ˜e maximum acceleration in the foundation is lower than in the soil bed for all operating shaking frequencies, pile spacing ratios and soil states. ˜e decreasing of the maximum acce­leration recorded in the foundation as compared to that in the soil bed is between 10-100 % for loose and medium state of soil, and the decrease in loose state is more than in medium state. ˜is means that there is damping e.ect or attenuation of vibration waves. ˜e amplitudes of recorded acceleration in the pile cap are much higher than in the soil bed for single pile and pile group with di.erent pile spacing ratios, also these amplitudes are increasing with increase of shaking frequency and relative density of the soil. 2. ˜e increase in shaking frequency leads to reduce the oscillation of wave propagation values recorded due to densi˙cation of soil during shaking. 3. ˜e pile tip load (net end bearing load) during shaking operation increases or decreases depending on number of piles, pile spacing, operating frequency and the soil state. During operation, the skin friction resistance mobilized along the pile length due to increasing in settlement and densi˙cation (increase in pile soil interaction e.ect of soil) led to increase the bearing load. 4. ˜ere is increase in acceleration and peak velocity of the foundation measured by vibration meter with time and frequency for both states of soil and for di.erent pile numbers and spacings. 5. ˜e most important result is that, the pile tip load (net end bearing load) during shaking operation increased or decreased depending on many factors: number of piles, pile spacing, operating frequency, as well as, the state of soil. ˜e oscillation of the frequented values decreases with increasing the shaking frequency. 6. ˜e pile group deects signi˙cantly more than the isolated single pile when loaded to similar average load per pile. Moreover, the row position had an e.ect on the eciency of the individual piles. ˜e front row (leading row) piles exhibited sti.er respon­ses than the trailing rows (second and third row). ˜e pile spacing is an important indicator that a.ects the acceleration and time frequency characteristics of the displacement at pile top. With the increasing of S/D, the internal forces are slightly reduced. REFERENCES [1] Al-Mhaidib A. I., (1999), "Bearing capacity of a model pile in sand under di.erent loading rates", Proceedings of the (9th) International o.shore and Polar Engineering Conference, Brest, France, Vol. 1, pp. 724-730. [2] Al-Mhaidib A. I., (2006), "Experimental investiga­tion of the behavior of pile groups in sand under di.erent loading rates", Journal of Geotechnical and Geological Engineering, Vol. 24, pp. 889-902. [3] American Society of Testing and Materials (ASTM) (2006), "Standard test method for particle size-analysis of soils" ASTM D422-63 (2002), West Conshohocken, Pennsylvania, USA. [4] American Society of Testing and Materials (ASTM) (2006), "Standard test method for speci˙c gravity of soil solids by water pycnometer" ASTM D854, West Conshohocken, Pennsylvania, USA. [5] American Society of Testing and Materials (ASTM) (2006), "Standard test method for maximum index density and unit weight of soils using a vibratory table " ASTM D4253-00 (2006), West Consho­hocken, Pennsylvania, USA. [6] American Society of Testing and Materials (ASTM) (2006), "Standard test method for minimum index density and unit weight of soils and calculation of relative density " ASTM D4254-00 (2006), West Conshohocken, Pennsylvania, USA. [7] American Society of Testing and Materials (ASTM) (2006), "Standard test method for permeability of granular soils (constant head)" ASTM D2434-68, West Conshohocken, Pennsylvania, USA [8] American Society of Testing and Materials (ASTM) (2006), "Standard test method for classi˙cation of soils for engineering purposes (uni˙ed soil classi˙cation system)" ASTM D2487-06, West Conshohocken, Pennsylvania, USA. [9] Banerjee S., (2009), “Centrifuge and numeri­cal modelling of so clay-pile-ra foundations subjected to seismic shaking”, Ph.D. ˜esis, Department of Civil Engineering National Univer­sity of Singapore. [10] Boominathan A. and Lakshmi T., (2000), "Dynamic characteristics of pile group under vertical vibration ", ˜e 12th world conference on Earthquake Engineering, Auckland, New Zealand, pp. 1-8. [11] Boominathan A., Subramanian. R. M., Krishna Kumar S., (2015), “Lateral dynamic response and e.ect of weak zone on the sti.ness of full scale single piles”. Indian Geotechnical Journal, J 45(1): 43–50, DOI 10.1007/s40098-014-0106-6. [12] Brown D. A. (2001), “Static and dynamic lateral loading of pile groups”, National Academy press Washington, D.C. 2001. [13] Ercan A., (2010), “Behavior of pile groups under lateral loads”, M.Sc. thesis. ˜e Graduate School M. Y. Fattah et al.: Investigation of the end bearing load in pile group model in dry soil under horizontal excitation of Natural and Applied Sciences of Middle East Technical University, Turkey. [14] Fattah, M. Y., Karim, H. H., Al- Recaby, M. K. M., (2016), "Dynamic Behavior of Pile Group Model in Two – Layer Sandy Soil Subjected to Lateral Earth­quake Excitation", Global Journal of Engineering Science and Research Management, Vol. 3, No. 8, pp. 57-80. [15] Fattah, M. Y., Zabar, B. S., Mustafa, F. S., (2017a), "Vertical Vibration Capacity of a Single Pile in Dry Sand", Marine Georesources & Geotechnology, doi.org/10.1080/1064119X.2017.1294219, Vol. 35, No. 8, pp. 1111-1120, Taylor & Francis. [16] Fattah, M. Y., Al-Mosawi, M. J., Al-Ameri, A. F. I., (2017b), "Dynamic Response of Saturated Soil – Foundation System Acted upon by Vibration", Journal of Earthquake Engineering, Vol. 21, No. 7, pp. 1158-1188, Taylor & Francis Group, LLC, DOI: 10.1080/13632469.2016.1210060. [17] Gui M. W., (1995), "Centrifuge and numerical modeling of pile and penetrometer in sand “, Ph.D. Dissertation, University of Cambridge. [18] Janalizadeh A, Zahmatkesh A. (2015), “Lateral response of pile foundations in lique˙able soils”, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 7, pp. 532-539. [19] Maxwell A. A., Fry Z. B., and Poplin J.K., (1969), "Vibratory loading of pile foundation" Special Technical Publication, ASTM, STP 444, pp. 338-361. [20] Novak M. and Grigg R. F., (1976), "Dynamic experiments with small pile foundation", Canadian Geotechnical Journal, Vol. 13, p.p. 372-395. [21] Pathak S.R. and Dalvi R.S., (2011), "E.ect of sample preparation method on liquefaction of sandy soil", Electronic Journal of Geotechnical Engineering, Vol.16, pp. 1411-1426. [22] Prusty S. K., (2010), “Dynamic response of pile foundations under coupled vibration”, Final year project submitted to National Institute of Tech­nology, Rourkela for the award of the degree of Bachelor of Technology. [23] Vesic A. S., (1977), "Design of pile foundation, national cooperative highway research program", Synthesis of Highway Practice, No. 42, Transporta­tion Research Board, Washington, D.C. [24] Weiler W. A. and Kulhawy F. H. (1982), “Factors a.ecting stress cell measurements in soil”, Journal of Geotechnical Engineering, ASCE, 108(12), 1529-1548. 106. Acta Geotechnica Slovenica, 2021/1 NAVODILA AVTORJEM NAVODILA AVTORJEM Vsebina ˜lanka ˆlanek naj bo napisan v naslednji obliki:  Naslov, ki primerno opisuje vsebino °lanka in ne presega 80 znakov.  Izvle°ek, ki naj bo skrajšana oblika °lanka in naj ne presega 250 besed. Izvle°ek mora vsebovati osnove, jedro in cilje raziskave, uporabljeno metodologijo dela, povzetek izidov in osnovne sklepe.  Najve° 6 klju°nih besed, ki bi morale biti napisane takoj po izvle°ku.  Uvod, v katerem naj bo pregled novejšega stanja in zadostne informacije za razumevanje ter pregled izidov dela, predstavljenih v °lanku.  Teorija.  Eksperimentalni del, ki naj vsebuje podatke o postavitvi preiskusa in metode, uporabljene pri pridobitvi izidov.  Izidi, ki naj bodo jasno prikazani, po potrebi v obliki slik in preglednic.  Razprava, v kateri naj bodo prikazane povezave in posplošitve, uporabljene za pridobitev izidov. Prika­zana naj bo tudi pomembnost izidov in primerjava s poprej objavljenimi deli.  Sklepi, v katerih naj bo prikazan en ali ve° sklepov, ki izhajajo iz izidov in razprave.  Vse navedbe v besedilu morajo biti na koncu zbrane v seznamu literature, in obratno. Dodatne zahteve  Vrstice morajo biti zaporedno oštevil°ene.  Predložen °lanek ne sme imeti ve° kot 18 strani (brez tabel, legend in literature); velikost °rk 12, dvojni razmik med vrsticami. V °lanek je lahko vklju°enih najve° 10 slik. Isti rezultati so lahko prikazani v tabe­lah ali na slikah, ne pa na oba na°ina.  Potrebno je priložiti imena, naslove in elektronske naslove štirih potencialnih recenzentov °lanka. Urednik ima izklju°no pravico do odlo°itve, ali bo te predloge upošteval. Enote in okrajšave V besedilu, preglednicah in slikah uporabljajte le standardne ozna°be in okrajšave SI. Simbole ˙zikalnih veli°in v besedilu pišite poševno (npr. ., T itn.). Simbole enot, ki so sestavljene iz °rk, pa pokon°no (npr. Pa, m itn.). Vse okrajšave naj bodo, ko se prvi° pojavijo, izpisane v celoti. Slike Slike morajo biti zaporedno oštevil°ene in ozna°ene, v besedilu in podnaslovu, kot sl. 1, sl. 2 itn. Posnete naj bodo v katerem koli od razširjenih formatov, npr. BMP, JPG, GIF. Za pripravo diagramov in risb priporo°amo CDR format (CorelDraw), saj so slike v njem vektorske in jih lahko pri kon°ni obdelavi preprosto pove°ujemo ali pomanjšujemo. Pri ozna°evanju osi v diagramih, kadar je le mogo°e, uporabite ozna°be veli°in (npr. v, T itn.). V diagramih z ve° krivuljami mora biti vsaka krivulja ozna°ena. Pomen oznake mora biti razložen v podnapisu slike. Za vse slike po fotografskih posnetkih je treba priložiti izvirne fotogra˙je ali kakovostno narejen posnetek. Preglednice Preglednice morajo biti zaporedno oštevil°ene in ozna°ene, v besedilu in podnaslovu, kot preglednica 1, preglednica 2 itn. V preglednicah ne uporabljajte izpisanih imen veli°in, ampak samo ustrezne simbole. K ˙zikalnim koli°inam, npr. t (pisano poševno), pripišite enote (pisano pokon°no) v novo vrsto brez oklepajev. Vse opombe naj bodo ozna°ene z uporabo dvignjene številke1. Seznam literature Navedba v besedilu Vsaka navedba, na katero se sklicujete v besedilu, mora biti v seznamu literature (in obratno). Neobjavljeni rezultati in osebne komunikacije se ne priporo°ajo v seznamu literature, navedejo pa se lahko v besedilu, °e je nujno potrebno. Oblika navajanja literature V besedilu: Navedite reference zaporedno po številkah v oglatih oklepajih v skladu z besedilom. Dejanski avtorji so lahko navedeni, vendar mora obvezno biti podana referen°na številka. Primer: ť..... kot je razvidno [1,2]. Brandl and Blovsky [4], sta pridobila druga°en rezultat…Ť V seznamu: Literaturni viri so oštevil°eni po vrstnem redu, kakor se pojavijo v °lanku. Ozna°imo jih s številkami v oglatih oklepajih. Sklicevanje na objave v revijah: [1] Jeluši°, P., Žlender, B. 2013. Soil-nail wall stability analysis using ANFIS. Acta Geotechnica Slovenica 10(1), 61-73. INSTRUCTIONS FOR AUTHORS Sklicevanje na knjigo: [2] Šuklje, L. 1969. Rheological aspects of soil mechan­ ics. Wiley-Interscience, London Sklicevanje na poglavje v monogra˙ji: [3] Mitchel, J.K. 1992. Characteristics and mechanisms of clay creep and creep rupture, in N. Guven, R.M. Pollastro (eds.), Clay-Water Interface and Its Rheo-logical Implications, CMS Workshop Lectures, Vol. 4, ˜e clay minerals Society, USA, pp. 212-244.. Sklicevanje na objave v zbornikih konferenc: [4] Brandl, H., Blovsky, S. 2005. Slope stabilization with socket walls using the observational method. Proc. Int. conf. on Soil Mechanics and Geotechnical Engi­neering, Bratislava, pp. 2485-2488. Sklicevanje na spletne objave: [5] Kot najmanj, je potrebno podati celoten URL. ˆe so poznani drugi podatki (DOI, imena avtorjev, datumi, sklicevanje na izvorno literaturo), se naj prav tako dodajo. INSTRUCTIONS FOR AUTHORS Format of the paper ˜e paper should have the following structure:  A Title, which adequately describes the content of the paper and should not exceed 80 characters;  An Abstract, which should be viewed as a mini version of the paper and should not exceed 250 words. ˜e Abstract should state the principal objectives and the scope of the investigation and the methodology employed; it should also summarise the results and state the principal conclusions;  Immediately aer the abstract, provide a maximum of 6 keywords;  An Introduction, which should provide a review of recent literature and sucient background informa­tion to allow the results of the paper to be under­stood and evaluated;  A ˜eoretical section;  An Experimental section, which should provide details of the experimental set-up and the methods used to obtain the results;  A Results section, which should clearly and concisely present the data, using ˙gures and tables where appropriate;  A Discussion section, which should describe the relationships shown and the generalisations made possible by the results and discuss the signi˙cance Podatki o avtorjih ˆlanku priložite tudi podatke o avtorjih: imena, nazive, popolne poštne naslove, številke telefona in faksa, naslove elektronske pošte. Navedite kontaktno osebo. Sprejem ˜lankov in avtorske pravIce Uredništvo si pridržuje pravico do odlo°anja o sprejemu °lanka za objavo, strokovno oceno mednarodnih recenzentov in morebitnem predlogu za krajšanje ali izpopolnitev ter terminološke in jezikovne korekture. Z objavo preidejo avtorske pravice na revijo ACTA GEOTECHNICA SLOVENICA. Pri morebitnih kasnejših objavah mora biti AGS navedena kot vir. Vsa nadaljnja pojasnila daje: Uredništvo ACTA GEOTECHNICA SLOVENICA Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo Smetanova ulica 17, 2000 Maribor, Slovenija E-pošta: ags@um.si of the results, making comparisons with previously published work;  Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion;  A list of References, which comprises all the refer­ences cited in the text, and vice versa. Additional Requirements for Manuscripts – Use double line-spacing.  Insert continuous line numbering.  ˜e submitted text of Research Papers should cover no more than 18 pages (without Tables, Legends, and References, style: font size 12, double line spacing). ˜e number of illustrations should not exceed 10. Results may be shown in tables or ˙gures, but not in both of them.  Please submit, with the manuscript, the names, addres­ses and e-mail addresses of four potential referees. Note that the editor retains the sole right to decide whether or not the suggested reviewers are used. Units and abbreviations Only standard SI symbols and abbreviations should be used in the text, tables and ˙gures. Symbols for physical quantities in the text should be written in Italics (e.g. v, T, etc.). Symbols for units that consist of letters should 108. Acta Geotechnica Slovenica, 2021/1 be in plain text (e.g. Pa, m, etc.). All abbreviations should be spelt out in full on ˙rst appearance. Figures Figures must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Figures may be saved in any common format, e.g. BMP, JPG, GIF. However, the use of CDR format (CorelDraw) is recommended for graphs and line drawings, since vector images can be easily reduced or enlarged during ˙nal processing of the paper. When labelling axes, physical quantities (e.g. v, T, etc.) should be used whenever possible. Multi-curve graphs should have individual curves marked with a symbol; the meaning of the symbol should be explained in the ˙gure caption. Good quality black-and-white photographs or scanned images should be supplied for the illustrations. Tables Tables must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Table 1, Table 2, etc. ˜e use of names for quantities in tables should be avoided if possible: correspond­ing symbols are preferred. In addition to the physical quantity, e.g. t (in Italics), units (normal text), should be added on a new line without brackets. Any footnotes should be indicated by the use of the superscript1. LIST OF references Citation in text Please ensure that every reference cited in the text is also present in the reference list (and vice versa). Any refer­ences cited in the abstract must be given in full. Unpub­lished results and personal communications are not recommended in the reference list, but may be mentioned in the text, if necessary. Reference style Text: Indicate references by number(s) in square brack­ets consecutively in line with the text. ˜e actual authors can be referred to, but the reference number(s) must always be given: Example: “... as demonstrated [1,2]. Brandl and Blovsky [4] obtained a di.erent result ...” List: Number the references (numbers in square brackets) in the list in the order in which they appear in the text. INSTRUCTIONS FOR AUTHORS Reference to a journal publication: [1] Jeluši°, P., Žlender, B. 2013. Soil-nail wall stability analysis using ANFIS. Acta Geotechnica Slovenica 10(1), 61-73. Reference to a book: [2] Šuklje, L. 1969. Rheological aspects of soil mechan­ics. Wiley-Interscience, London Reference to a chapter in an edited book: [3] Mitchel, J.K. 1992. Characteristics and mechanisms of clay creep and creep rupture, in N. Guven, R.M. Pollastro (eds.), Clay-Water Interface and Its Rheo-logical Implications, CMS Workshop Lectures, Vol. 4, ˜e clay minerals Society, USA, pp. 212-244. Conference proceedings: [4] Brandl, H., Blovsky, S. 2005. Slope stabilization with socket walls using the observational method. Proc. Int. conf. on Soil Mechanics and Geotechni-cal Engineering, Bratislava, pp. 2485-2488. Web references: [5] As a minimum, the full URL should be given and the date when the reference was last accessed. Any further information, if known (DOI, author names, dates, reference to a source publication, etc.), should also be given. Author information ˜e following information about the authors should be enclosed with the paper: names, complete postal addresses, telephone and fax numbers and E-mail addresses. Indicate the name of the corresponding author. Acceptance of papers and copyright ˜e Editorial Committee of the Slovenian Geotechnical Review reserves the right to decide whether a paper is acceptable for publication, to obtain peer reviews for the submitted papers, and if necessary, to require changes in the content, length or language. On publication, copyright for the paper shall pass to the ACTA GEOTECHNICA SLOVENICA. ˜e AGS must be stated as a source in all later publication. For further information contact: Editorial Board ACTA GEOTECHNICA SLOVENICA University of Maribor, Faculty of Civil Engineering, Transportation Engineer­ing and Architecture Smetanova ulica 17, 2000 Maribor, Slovenia E-mail: ags@um.si NAMEN REVIJE Namen revije ACTA GEOTECHNICA SLOVENICA je objavljanje kakovostnih teoreti°nih °lankov z novih pomembnih podro°ij geomehanike in geotehnike, ki bodo dolgoro°no vplivali na temeljne in prakti°ne vidike teh podro°ij. ACTA GEOTECHNICA SLOVENICA objavlja °lanke s podro°ij: mehanika zemljin in kamnin, inženirska geologija, okoljska geotehnika, geosintetika, geotehni°ne konstrukcije, numeri°ne in analiti°ne metode, ra°unal­niško modeliranje, optimizacija geotehni°nih konstruk­cij, terenske in laboratorijske preiskave. Revija redno izhaja dvakrat letno. AVTORSKE PRAVICE Ko uredništvo prejme °lanek v objavo, prosi avtorja(je), da prenese(jo) avtorske pravice za °lanek na izdajatelja, da bi zagotovili kar se da obsežno razširjanje informacij. Naša revija in posamezni prispevki so zaš°iteni z avtorskimi pravicami izdajatelja in zanje veljajo naslednji pogoji: Fotokopiranje V skladu z našimi zakoni o zaš°iti avtorskih pravic je dovoljeno narediti eno kopijo posameznega °lanka za osebno uporabo. Za naslednje fotokopije, vklju°no z ve°kratnim fotokopiranjem, sistemati°nim fotoko­piranjem, kopiranjem za reklamne ali predstavitvene namene, nadaljnjo prodajo in vsemi oblikami nedobi°k­onosne uporabe je treba pridobiti dovoljenje izdajatelja in pla°ati dolo°en znesek. Naro°niki revije smejo kopirati kazalo z vsebino revije ali pripraviti seznam °lankov z izvle°ki za rabo v svojih ustanovah. Elektronsko shranjevanje Za elektronsko shranjevanje vsakršnega gradiva iz revije, vklju°no z vsemi °lanki ali deli °lanka, je potrebno dovoljenje izdajatelja. ODGOVORNOST Revija ne prevzame nobene odgovornosti za poškodbe in/ali škodo na osebah in na lastnini na podlagi odgo­vornosti za izdelke, zaradi malomarnosti ali druga°e, ali zaradi uporabe kakršnekoli metode, izdelka, navodil ali zamisli, ki so opisani v njej. AIMS AND SCOPE ACTA GEOTECHNICA SLOVENICA aims to play an important role in publishing high-quality, theoretical papers from important and emerging areas that will have a lasting impact on fundamental and practical aspects of geomechanics and geotechnical engineering. ACTA GEOTECHNICA SLOVENICA publishes papers from the following areas: soil and rock mechan­ics, engineering geology, environmental geotechnics, geosynthetic, geotechnical structures, numerical and analytical methods, computer modelling, optimization of geotechnical structures, ˙eld and laboratory testing. ˜e journal is published twice a year. 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