Va * # ff > J # v/ ^ cV ^ # cr J>\* ** * # # / ACTA GEOTECHNICA SLOVENICA ISSN: 1854-0171 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 Bojana Dolinar University of Maribor Uredniki Co-Editors Jakob Likar Janko Logar Borut Macuh Stanislav Škrabl Milivoj Vulic Bojan Žlender Geoportal d.o.o. 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Članki v reviji so recenzirani s strani priznanih mednarodnih strokovnjakov. Baze podatkov v katerih je revija indeksirana: SCIE - Science Citation Index Expanded, JCR - Journal Citation Reports / Science Edition, ICONDA - The international Construction database, GeoRef. Izid publikacije je finančno podprla Javna agencija za raziskovalno dejavnost Republike Slovenije iz naslova razpisa za sofinanciranje domačih periodičnih publikacij. The 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- The international Construction database, GeoRef. The publication was financially supported by Slovenian Research Agency according to the Tender for co-financing of domestic periodicals. 1. Yongge et al. Impacts of different factors on seepage and land uplift due to compressed-air injection Z. Yongge in drugi Vplivi različnih faktorjev na precejanje in dvigovanje zemlje zaradi vbrizgavanja stisnjenega zraka R. P. Shukla & R. S. Jakka Kritični odmik plitvega temelja na pobočju R. P. Shukla & R. S. Jakka Critical setback distance for a footing resting on slopes H. Patino in drugi Strižni modul zasičene granulirane zemljine iz preizkusa resonančne kolone H. Patino et al. Shear modulus of a saturated granular soil derived from resonant-column tests 1.1. Akinwumi in drugi Inženirske lastnosti tropske gline in bentonita modificiranih z žagovino 1.1. Akinwumi et al. Engineering properties of tropical clay and bentonite modified with sawdust Taha Taskiran Nosilnosti temeljev na nezasičenih zemljinah Taha Taskiran An unsaturated-soils approach to the bearing capacity of foundation structures P. Li in drugi Poenostavljeni pristop k ocenjevanju vpliva enega pilota na porazdelitev napetosti v tleh P. Li et al. A simplified approach to estimating the soil stress distribution due to a single pile P. H. H. Giang in drugi Učinki značilnosti delcev na strižno trdnost apnenčastih peskov P. H. H. Giang et al. Effects of particle characteristics on the shear strength of calcareous sand 32 58 76 18. Acta Geotechnica Slovenica, 2017/2 VPLIVI RAZLIČNIH FAKTORJEV NA PRECEJANJEIN DVIGOVANJE ZEMLJE ZARADI VBRIZGAVANJA STISNJENEGA ZRAKA Izvleček V tej študiji so bili, z uporabo in-situ preizkusa zračnega pretoka v Essnu, z numeričnimi simulacijami raziskani vplivi različnih faktorjev na večfazni pretok in dvigovanje zemlje med in po injektiranju s stisnjenim zrakom. Za simuliranje in situ preizkusa zračnega pretoka in primerjavo simuliranih in merjenih rezultatov smo uporabili ohlapno povezan dvofazni pretok in geomehanski modelni pristop, ki povezuje dve programski kodi (TOUGH2/EOS3 in FLAC3D). Ko se stisnjen zrak vbrizga, teče navzgor in bočno, vertikalna efektivna napetost blizu in nad injekti-ranimi območji pa se zmanjša zaradi povečanja pornega tlaka, kar povzroča razširitev ogrodja zemljine v pripadajočih območjih. Dvigovanje zemlje, ki ga povzročajo predvsem podporni vplivi iz nižjih deformiranih zemljin, je pomemben za porazdelitev povečanj poroznosti v notranjosti zemljine in se hitro povečuje med vbrizgavanjem zraka. Ko se stisnjen zrak zaustavi, se dvigovanje zemlje zaradi razpršitve nadtlaka postopoma zmanjšuje do nič. S kombinacijo intenzivnih padavin je dvigovanje zemlje nekoliko večje v bližini vrtine, znatno večje pa na oddaljenosti od vrtine kot je v primerih brez ali majhnih padavin. Pri tem stopnja vbrizgavanja zraka ostaja skoraj nespremenjena zaradi nespremenljivih pornih tlakov v bližini območja injiciranja. Ko se osnovna prepustnost povečuje ali tlak vstopnega zraka zmanjša v vbrizganih slojih, se povečata tako dvig zemlje kot tudi hitrost vbrizgavanja zraka. Čas, ki je potreben za dvigovanje zemlje, se približa vrednosti nič, če je rahlo pospešen z majhno prepustnostjo ali visokim vstopnim zračnim tlakom. Zang Yongge Tianjin University, State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072, Ljudska republika Kitajska E-pošta: zangyongge2011@163.com Sun Dongmei (vodilni avtor) Tianjin University, State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072, Ljudska republika Kitajska E-pošta: sundongmei@tju.edu.cn Feng Ping Tianjin University, State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072, Ljudska republika Kitajska E-pošta: fengping@tju.edu.cn Stephan Semprich Graz University of Technology, Institute of Soil Mechanics and Foundation Engineering 8010 Graz, Avstrija E-pošta: stephan.semprich@tugraz.at Ključne besede ohlapno povezani dvofazni pretok in geomehanski model; in-situ preskus zračnega pretoka; injektiranje s komprimiranim zrakom; večfazni pretok; dvigovanje tal; izguba zraka. 18. Acta Geotechnica Slovenica, 2017/2 IMPACTS OF DIFFERENT FACTORS ON SEEPAGE AND LAND UPLIFT DUE TO COMPRESSED-AIR INJECTION Abstract In this study, using an in-situ, air-flow test in Essen, the impacts of different factors on multiphase flow and land uplift during and after compressed-air injection were investigated using numerical simulations. A loosely coupled, two-phase flow and geo-mechanical modeling approach, linking two numerical codes (TOUGH2/EOS3 and FLAC3D) was employed to simulate the in-situ, air-flow test for comparing the simulated and measured results. As the compressed air is injected, it flows upwards and laterally, and the vertical effective stress near and above the injection zones decreases owing to the pore pressure increasing here, causing an expansion of the soil skeleton in the corresponding zones. The land uplift, induced mainly by support actions from lower deformed soils, is relevant to the distribution of the porosity increments in the soil interior, and it increases rapidly during air injection. After the compressed-air injection stops, the land uplift decreases gradually to zero due to the overpressure dissipation. With a combination of intensive rainfall, the land uplift is slightly greater near the borehole, but it is significantly greater at a distance from the borehole than the land uplift with no or low rainfall, but the air-injection rate remains almost unchanged due to the unchangeable pore pressure near the injection region. As the intrinsic permeability increases or the air entry pressure decreases in the injected strata, both the land uplift and the air-injection rate increase, but the time required for the land uplift to become zero is slightly advanced with either a small permeability or a high air entry pressure. Zang Yongge Tianjin University, State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072, China E-mail: zangyongge2011@163.com Sun Dongmei (corresponding author) Tianjin University, State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072, China E-mail: sundongmei@tju.edu.cn Feng Ping Tianjin University, State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072, China E-mail: fengping@tju.edu.cn Stephan Semprich Graz University of Technology, Institute of Soil Mechanics and Foundation Engineering 8010 Graz, Austria E-mail: stephan.semprich@tugraz.at Keywords loosely coupled two-phase flow and geo-mechanical model; in-situ, air-flow test; compressed-air injection; multiphase flow; land uplift; air loss 1 INTRODUCTION During tunnel construction below the groundwater table, due to the relatively higher groundwater pressure and the greater hydraulic conductivity, the pore-water in soil voids flows into the work space through the excavated surface, which may hinder the progress of the construction or even cause the collapse of the tunnel. It would, therefore, be advantageous to apply the compressed-air technique during the tunnel's construction [1-2]. By introducing pressurized air into the tunnel space, the groundwater inflow through the excavated surface could be prevented and the surface settlement can also be reduced, which is very critical in an urban area where the damage of settlements on the existing buildings must be concerned. It is important to note that the applied compressed-air pressure in the tunnel space must be equal to or greater than the magnitude of the groundwater pressure at the tunnel invert, so that the compressed air can permeate into the surrounding soils due to the pressure gradient. In 18. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air injection addition to this application, subsurface fluid injection has been applied extensively for energy development and environmental management, such as enhancing oil production, storing useful gas or oil in depleted gas/ oil fields, recharging an over-drafted aquifer system, arresting or mitigating land subsidence, and disposing of contaminants and hazardous wastes, and other applications [3-6]. Actually, these applications of pressurized fluid injection all involve an interaction between multiphase fluid flow and geo-mechanical processes, and they could affect the variation of the seepage and the stress state in the porous media [5, 7-9]. The simultaneous consideration of the gas phase, liquid phase, and solid phase underground could therefore produce a more realistic result. Numerical analyses, compared to analytical solutions, can dispose of the complicated initial and boundary conditions, the multi-layered soils and the complex geometry of many engineering problems, and is a better choice to analyze the coupling processes between multiphase fluid flows and soil deformation. Selvadurai and Kim developed a mathematical solution to study the caprock-storage formation interactions during the injection of fluids into a poroelastic storage formation and the ground subsidence caused by the uniform extraction of fluids from a disc-shaped region [10-11]. A loosely coupled methodology, linking two numerical codes (TOUGH2, used for solving multi-phase multi-component flow equations [12]; and FLAC3D, used for solving geo-mechanical, stress-strain equations [13]), was proposed by Rutqvist et al. [14] and Rutqvist and Tsang [15] to simulate the interactive processes between the geo-mechanical and fluid-flow processes. This coupled simulator has been widely applied in many geo-environmental situations, such as nuclear waste disposal, CO2 sequestration, geothermal energy extraction, naturally occurring CO2 upwelling with surface deformations, and gas production from hydrate-bearing sediments [16-20]. Therefore, in this study, on the platform of the in-situ, air-flow test in Essen conducted by Kramer and Semprich [1], the water-air, two-phase flow processes and soil deformation during and after compressed-air injection were investigated using the coupled TOUGH2-FLAC3D simulator. Notably, the in-situ, air-flow test was carried out to explore the behavior of the outcropping soils before the subway construction using the compressed-air technique in Essen, Germany. Then, the impacts of the different factors on the multiphase flow and land uplift during and after compressed-air injection were analyzed, including the occurrence of a rain event, and a sensibility analysis of the values of the permeability and air entry pressure of the injected strata. 2 COUPLING PROCEDURES TOUGH2/EOS3 is a module in TOUGH2 for non-isothermal, water-air, two-phase flow in three-dimensional, unsaturated-saturated porous and fractured media, in which the transformation and dissolution processes occurring between the liquid and gas phases are explained by mass-balance equations. These balance equations are discretized in space by the integral finite difference and in time by the first-order finite difference. FLAC3D is a three-dimensional and explicit finite-difference computer code for solving geo-mechanical stress-strain equations. In the coupled two-phase flow and geo-mechanical process, the seepage process affects the stress field by changing the pore pressure and the effective stress, whereas the stress field affects the seepage through changing the porosity, the capillary pressure and the intrinsic permeability. 2.1 Update of Geo-mechanical Variables In the loosely coupled procedure, the pore water pressure pi , the pore air pressure pg , and the liquid saturation Si provided by TOUGH2 (the pore pressure is referred to the local atmospheric pressure, and the same below) are sent to FLAC3D to calculate the average pore pressure p[14]: P = SiPi + (1- Si) Pg (1) This expression for the average pore pressure is applied to porous sedimentary rock [14, 21], and the medium was assumed to be porous media in this study. Then, the average pore pressure is incorporated into the calculations of the soil skeleton stress, the strain, and the effective stress u.. (a.. = a.. - pSV, where u.. is the total 'J 'J 'J V If stress and Sij is the Kronecker function (for i = j, dy = 1; for i ^ j, Sjj = 0)). The change in porosity induced by the soil deformation can be expressed as follows: = d (Vu / V) = (VtdVu - VudV,)/ V2 = = dVu / V -0odV, / V (2) where Vp is the pore volume, Vt is the total volume, and is the initial porosity at the initial stress. The total volume Vt is equal to the sum of the pore volume Vp and the solid grain volume Vs . Here, it is assumed that the deformation of the solid grains is much less than that of the soil skeleton, and can be negligible. Therefore, the change in the total volume Vt is equal to the change in the pore volume Vp , i.e., dVt= dVp , and the change in porosity can be given by i = (1 -$o)dV, / V, = (1 -¿K where ev is the volumetric strain. (3) 4. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection 2.2 Update of Hydraulic Variables The geo-mechanically induced d has an immediate effect on the fluid flow behavior, including the intrinsic permeability and the capillary pressure. The Kozeny-Carman Equation suggests that there should be a linear relation between the hydraulic conductivity k (or the intrinsic permeability AT, k = Kyw //iM,, where yw is the unit weight of water and /iM, is the dynamic viscosity of water) and e'l{\+e) (or where e is the void ratio and „ is the porosity at the time step n. Therefore, the intrinsic permeability K„ at the time step n can be defined with Eq. (5). This relationship has also been used by Taylor to estimate the unknown hydraulic conductivity at a porosity from a known hydraulic conductivity at another porosity for the same soil [23], (a V K, = K„ \ro J l-< 1-i (5) According to Rutqvist and Tsang [15], with respect to porous media, the capillary pressure is scaled with the intrinsic permeability and porosity according to a function by Leverett [24], PcLn Pc 4KJa (6) \lKJt where pcLn is the corrected capillary pressure at the time step /? and pcn is the calculated capillary pressure dependent on the liquid saturation at the time step n. 2.3 Coupling Procedure The loosely coupling process between TOUGH2 and FLAC3D is typically developed according to the procedure in Fig.l. Some input data files for TOUGH2 and FLAC3D, such as the soil properties, mesh, boundary and initial conditions, must be initially prepared. Then TOUGH2 is executed for a sufficient simulation time to obtain an initial steady state, and FLAC3D is also operated under gravitational loads to establish initial equilibrium stress gradients and outputs the initial porosity 0 from the FLAC3D element is mapped to the TOUGH2 element, which is used to update the intrinsic permeability according to Eq.5. TOUGH2 is firstly executed for the first time-step, and the capillary pressure is corrected using Eq.6. When convergence is reached at the end of this time-step, the pore water pressurepj, the pore air pressure pg, and the liquid saturation Sj of each element in TOUGH2 are obtained and are mapped to the FLAC3D nodes using a weighted distance interpolation. Then FLAC3D runs under loads of average pore pressure for each node (which can be calculated using Eq.l), until an equilibrium state is reached. At this point the change in the porosity at the FLAC3D element can be calculated according to the strain increment (by Eq.3). Afterwards, the updated porosity at the FLAC3D element is sent back to the TOUGH2 element by interpolation. Utilizing the updated porosity, the intrinsic permeability is updated again according to Eq.5, and TOUGH2 is executed for the next time-step. And then the above coupling processes are repeated until the specified simulation time (Sum-time) is reached. 3 EXPERIMENT AND NUMERICAL SIMULATION OF THE IN-SITU AIR-FLOW TEST IN ESSEN 3.1 Description of the In-situ Air-Flow Test An in-situ, air-flow test was carried out by Kramer and Semprich [1] to investigate the air permeability of the Essen soil, determine the extent of the airflow field, and analyze the effect of compressed airflow on the deformation of the soil skeleton and in particular on the surface displacement. Fig. 2 shows a schematic diagram of the experimental setup for the in-situ, air-flow test. According to the description of the related experiment [1], the soil profile in Essen can be divided into the following four distinct layers: a fill layer, a thick silt layer, a thin permeable sand layer and a thick layer of marl that is rather weathered in the upper region and presents pronounced joints. The groundwater table is approximately 4.75 m below the ground surface and is located in the silt layer. Compressed air can be introduced into the ground through a 1.5-m diameter borehole in the injection well. A thin steel pipe can be installed inside the borehole, the lower part of the pipe being perforated for air permeating into soils and the top of the pipe being connected to an air compressor (which was used to control the air pressure) [1]. In test IB under consideration here, the 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection TOUGH2 FLAC3D Set up TOUGH2-FLAC3D coupling simulation Figure 1. Flow chart for a loosely coupled algorithm. » "t J compressed air was introduced 18.0-21.0 m below the ground surface, and only the first applied pressure level Ap = 160 kPa over 27 h was considered for simplicity. The rate of air injection was monitored by a flow meter during the experiment. Several piezometers were installed near the borehole to measure the variation of the pore pressure at different depths and distances from the borehole. The land uplift was measured by geodetic leveling installed at different distances from the borehole. 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection Figure 2. In-situ, air-flow test in Essen (after Kramer and Semprich [1]). 3.2 Setting up of the Numerical Model 3.2.1 Model Domain and Soil Parameters In this study, the numerical model of the in-situ, air-flow test was established using the above coupling algorithm. Taking advantage of the axial symmetry of this problem, only one-fourth of the domain was simulated. The measured results show that the land uplift reached only 2 mm at approximately 20 m distance from the borehole. The extent of the model was just 40 m in the horizontal direction in the simulation by Ottl [25] and 100 m by Chinkulkijniwat et al. [2]. Therefore, the model domain was 100 m long in both the transverse direction (X) and the longitudinal direction (Y), and was 25 m deep in the vertical direction (Z). The mesh generation in TOUGH2 was the same as in FLAC3D, consisting of 18,259 hexahedron elements and 20,480 nodes, and is shown in Fig. 3. The domain in the vertical direction was discretized to take into account the soil layers, the groundwater table and the air-injection region. The mesh size in the horizontal directions was relatively fine near the borehole and expanded with the distance from the borehole. Y (m) o X (m) Figure 3. Meshes in the model of TOUGH2 and FLAC3D. 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection In the numerical simulation, the capillary pressure and the relative liquid and gas permeability dependent on the liquid saturation were described by the van Genuchten model [26] and the van Genuchten-Mualem model [26-27], respectively. The expressions of these two models are described in Eq. (7), Eq. (8) and Eq. (9) pc=-p0[(srVÄ-ifÄ i-pmaxSls) (Sgr= 0) (8) (9) where S1 = (S',, — Slr) / (1 - Slr - Sgr) and Sgr is the residual gas saturation. The hydraulic and geo-mechanical parameters for four soil layers in Essen, taken from Ottl [25], are shown in Table 1, including the solid densityps, Youngs modulus E, Poissons ratio v, the initial porosity k> (kN/m2) Sis Sir X K0 (10~12 m2) Fill 2.72 20 0.33 0.36 4.0 0.2 1.0 0.8 4.95 Sût 2.90 12.47 0.35 30.0 0.2 1.0 0.5 0.495 (9.24) (0.37) Sand 2.72 21.22 0.32 0.36 4.0 0.05 1.0 0.65 9.90 Marl 2.79 14.33 0.40 0.33 12.0 0.15 1.0 0.6 2.48 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection the simulations. Then, the coupled hydraulic-mechanical process, considering the interactions between the liquid, gas and solid phases, was repeated until the injection duration of 27 h was reached. Hereafter, the material property and the volume of the elements within the injection zone were reset as the property of the marl and their actual volume, respectively, in order to investigate the variations of multiphase flow and soil deformation after the air injection stopped. The post-injection phase lasted for 100 hours. Notably, the experimental data were not recorded after the air injection stopped in the in-situ, air-flow test. 3.3 Analysis of the Experimental and Simulated Results 3.3.1 Analysis of the Discrepancy between the Simulated and Measured Results The main objective of this field test is to investigate the magnitude and scope of the land uplift as well as the air loss rate induced by compressed air injection. Fig. 4a shows the distribution of the simulated and measured land uplift at different times. After 27 hours, the simulated land uplift was much higher than the measured value at a distance from the borehole, which might be because the high permeability of the sand layer promoted radial propagation of the overpressure in the numerical simulation. Actually, according to Kramer and Semprich [1] and Ottl [25], the thin sand layer contains a considerable portion of silt in the field, reducing the permeability of the sand layer. Additionally, average values of the permeability for the marl layer were used in the above simulation, although the marl corresponds to silt containing high portions of sand and clay according to Kramer and Semprich [1]. Therefore, the possibility of high anisotropy between the horizontal and vertical soil permeability should be recognized. Fig. 4b compares the behavior over time of the measured and simulated air-injection rates during the test. The mass flux of air (unit: kg/s) injected into the soil interior through the injection zone was calculated using the numerical model and the air density under the normal conditions of atmospheric pressure and 10°C was determined by the ideal gas law, which permitted a calculation of the volume flux of air (m3/min) injected into the soil. The simulated rate was substantially the same as the measured results during the middle period, whereas there were large differences between them at the initial and final stages. In the field test, the applied air pressure was increased stepwise to 160 kPa by the compressor, as shown in Fig. 5. Before the air pressure reached 160 kPa, the matric suction in the marl layer could not surpass the air entry value of the marl, and no air penetrated into the soil. However, the applied air pressure was set Figure 4. (a) Measured and simulated land uplift at different times and (b) temporal evolution of the simulated and measured air-injection rate during compressed air injection. to 160 kPa at the beginning of the numerical simulation, so the difference between the measured and simulated results was introduced at the initial stage. Considering the low permeability of the sand layer, the anisotropy between the horizontal and vertical soil permeability of the marl layer, and the implementation process of the applied air pressure, the values of permeability in the sand and marl layer in the numerical simulations were adjusted as follows: Kx = Ky = Kz = 0.9x10-12 m2 for the sand layer and Kx = Ky = 5.58x10-12 m2, Kz = 3.38x10-12 m2 for the marl layer, and the applied pressure Figure 5. Applied air pressure and air loss versus time for test 1B (after Ottl [25]). 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection Figure 6. Measured and adjusted simulated land uplift at different times and (b) temporal evolution of the measured and adjusted simulated air-injection rate during compressed air injection. Ap in the numerical simulations was set as shown in Fig. 5, as follows: Ap = 61 kPa from 0 s to 3360 s, Ap = 78 kPa from 3360 s to 6720 s, Ap = 119 kPa from 6720 s to 10,080 s and Ap = 160 kPa from 10,080 s to 27 hours. The comparison of the adjusted simulated results and the measured results is shown in Fig. 6. There was good agreement between the adjusted simulated and measured land uplift after 27 hours (Fig. 6a). As shown in Fig. 6b, before the air pressure reached 160 kPa (the first 2.8 hours), both the simulated and measured injection rate remained zero. Hereafter, there was a slight discrepancy between the simulated and measured results from 2.8 h to 13 h, whereas they were substantially consistent from 13 h to 21 h. After 21 h, because the air flowed to the location where fractures can be present, the measured rate increased significantly. However, the medium in the numerical model was assumed to be porous media, thereby causing the difference between the simulated and measured rates. In general, the adjusted simulated results agreed well with the measured values, and the adjusted scheme was applied in the following simulation analysis. unsaturated. Moreover, because the applied air pressure was slightly greater than the maximum groundwater pressure within the air-injection regions, a small area below the injection regions also became unsaturated. The unsaturated zone was concentrated mainly above the air-injection regions. Close to the ground surface, the gas saturation near the borehole decreased because the airflow pushing caused the water to flow upwards. Fig. 7b shows the distribution of gas saturation and air flow after 75 hours (48 hours after compressed air injection stopped). As shown, after the compressed-air injection stopped, the air still flowed upwards and laterally due to the density difference and the pressure gradient, but the magnitude of the air velocity was much smaller at 75 hours than it was at 27 hours. The zone from the bottom to 10 m recovered water saturated because the air in the voids of the injection regions was displaced by the adjacent groundwater, whereas due to the continuous upward airflow, the size of the unsaturated zone from 10 m to 15 m remained substantially unchanged, and from 15 m to the water table, the unsaturated zone expanded into the shallow unsaturated zone. Figure 7. Distribution of simulated gas saturation and airflow at (a) 27 h and (b) 75 h (The blue arrows refer to the magnitude and direction of airflow velocity). 3.3.2 Analysis of Seepage and Soil Deformation Fig. 7a shows the distribution of the simulated gas saturation and airflow after 27 hours. It was expected that the injecting air would permeate into soils due to the pressure gradient and the adjacent regions became Fig. 8 shows the distribution of the simulated average pore-pressure equivalence at different times. After 27 hours, the average pore pressure near and above the injection zone increased significantly, and the 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection amplification decreased with the distance from the borehole. The affected zone extended to approximately 70 m horizontally. After 75 hours, due to the airflow dissipation, the average pore pressure near and above the injection zone decreased substantially. From the bottom to approximately 7 m, the average pore pressure recovered to its initial steady value. From 7 m to 16 m, the average pore pressure also decreased to its initial values near the borehole, while it still deviated from the initial values at a distance from the borehole. The reason might be that the gas saturation in this region reached a relatively large value within 10 m horizontally (Fig. 7b), so that it was easy for the airflow to move, but the overpressure and airflow 10 m away dissipated with relative difficulty due to its small gas saturation. Above the elevation of 16 m, the average pore pressure did not decrease to its initial value due to airflow pushing (Fig. 7b). The measured and simulated pore air pressure at the four observed points of A, B, C and D (Fig. 3) are shown in Table 2, and the measured and simulated results were substantially consistent. Fig. 9 shows the distribution of the simulated vertical effective stress at different times. After 27 hours, since the total stress acting on the soil layers remained almost unchanged (the mass of the injected compressed air was very small relative to the weight of the whole soil layers) and the stress overtaken by the fluids in the soil voids increased (Fig. 8), the stress overtaken by the solid skeleton decreased; i.e., the effective stress near and above the injection zones decreased. This release of the vertical effective stress caused an expansion of the soil skeleton in the corresponding zone. The magnitude of the porosity near and above the injection zones therefore increased, and the affected zone of the porosity increment reached approximately 32 m horizontally (Fig. 10a). After 75 hours, the vertical effective stress decreased to its initial values in most areas, while it still appeared to deviate from 12 m to 20 m vertically. Therefore, both the magnitude and scope of the porosity increments also decreased at 75 hours (Fig. 10b), and the maximum value appeared from 10 m to 20 m horizontally due to the distribution of the average pore pressure and vertical effective stress (Figs. 8b and 9). Figure 8. Distribution of simulated average pore pressure at different times at (a) initiation and at 27 h and (b) initiation and at 75 h (unit: kPa). Table 2. Locations with the measured and simulated pore air pressure for four observation points. Observation points A B C D Horizontal distance from borehole (m) 2 2 2 6 Depth below ground surface (m) 6 10 13 12.5 Measured pore water pressure (kPa) 27 70 95 90 Simulated pore water pressure (kPa) 30.5 76.5 101 95 Figure 9. Distribution of simulated vertical effective stress at different times (unit: kPa). Figure 10. Distribution of the simulated porosity increment at (a) 27 h and (b) 75 h. Because the porosity near the ground surface changed little, the land uplift was caused primarily by the expansion of deep deformed soils. As shown in Fig. 6a, after 27 hours, the maximum land uplift occurred near the borehole. The land uplift decreased with the distance from the borehole, consistent with the distribution of 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection the porosity increment within the soil. After 75 hours, the land uplift decreased due to overpressure dissipation and the flat segment within approximately 15 m from the borehole was relevant to the distribution of the porosity increment at 75 h. Fig. 11 shows the behavior over time of the maximum land uplift. During compressed air injection, the land uplift remained zero before 2.8 hours due to no air penetrating into the soil. Later, it increased rapidly and reached a maximum value at 27 hours. After the injection stop, the heave decreased rapidly at first and then gradually went to zero at approximately 110 hours. 60 Time (h) Figure 11. Time behavior of the maximum land uplift. 4. ANALYSIS OF THE IMPACTS OF DIFFERENT FACTORS 4.1 Rain Events To investigate the effects of a rain event on multiphase flow and land uplift during and after compressed-air injection, rain with intensity equal to 5 mm/h and 20 mm/h was combined with the compressed-air injection. Notably, the duration of rainfall coincided with that of the applied pressure of 160 kPa (i.e., 2.8-27 hours). The model source term in kg/s for rainfall is computed as m(t) = rwAeQr(t) , where t (s) is the time; Ae (m2) is the effective area for rainwater infiltration and is equal to the area perpendicular to the direction of rainfall; and Qr (m/s) is the rainfall intensity. The term was applied to the whole soil surface (i.e., the soil elements adjacent to the atmospheric boundary). As the compressed air injection and rainfall stopped, the source term was removed. The whole simulation time, the initial conditions and the other boundary conditions were the same as the base case. Fig. 12 shows the total stress distribution for different profiles at 27 h for the three cases. The total stress for different profiles after 27 h for the three cases was essentially consistent with that at the initial steady state, indicating that the applied rainwater amount has Figure 12. Distribution of total stress for different profiles at 27 h for the base case and rain intensities of 5 mm/h and 20 mm/h. Time rti) Figure 13. (a) Distribution of the average pore pressure for different profiles at 27 h and (b) the temporal evolution of the average pore pressure at different points for the base case and rain intensities of 5 mm/h and 20 mm/h. little effect on the total stress. The intensive rainfall produced a continued downward wetting front, which reduced the escape of pore air and compressed pore air between the wetting front and the capillary fringe. As a result, the pore pressure in the unsaturated and saturated zones increased due to airflow pushing by the advancing wetting front. However, a small amount of rainfall cannot completely seal off the ground surface, and pore air could partially escape out of the surface during rainfall and it cannot be compressed and pressurized by the moving wetting front. As shown in Fig. 13a, the average pore pressure distribution for X = 10 m 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection Figure 14. (a) Land uplift at different times and (b) changes in the maximum land uplift with time for the base case and rain intensity of 5 mm/h and 20 mm/h. Figure 15. Temporal evolution of the air-injection rate for the base case and rain intensities of 5 mm/h and 20 mm/h during compressed-air injection. at 27 h seemed to be mostly identical for the three cases, and all deviated from their initial values. The average pore pressure distributions for X = 60 m remained at their initial values for the base case and rain intensity of 5 mm/h, but they deviated from the initial state vertically from approximately 8 m to 20 m for a rain intensity of 20 mm/h. Likewise, as seen in Fig. 13b, the time evolution of the average pore pressure at points ((X = 10 m, Z = 15.12 m) and (X = 60 m, Z = 15.12 m)) was also almost identical for the base case and 5 mm/h, while it began to deviate from the variation of the above two cases at different times for 20 mm/h. Moreover, the magnitude of this deviation was smaller for X = 10 m than for X = 60 m (notably, the seemingly identical pore pressure for X = 10 m at 27 h for three cases in Fig. 13a was limited by the adopted coordinate range). As a result, the distribution of land uplift at 27 h for 5 mm/h was substantially the same as the base case, while the magnitude of the land uplift for 20 mm/h was slightly greater near the borehole, but was much greater at a distance from the borehole than that for the other cases (Fig. 14a). This phenomenon suggested that a low rain intensity (i.e., 5 mm/h in this case) hardly affected the land uplift induced by compressed-air injection, but a high rain intensity (i.e., 20 mm/h in this case) would elevate this land uplift to different levels at different positions. Additionally, as shown in Fig. 14b, it was expected that the maximum land uplift for 5 mm/h was almost consistent with the base case, except that the time required for the 5 mm/h uplift to reach zero was slightly delayed. However, the land uplift for a rain intensity of 20 mm/h began to deviate from the base-case solution at 23 hours, consistent with the variation of the pore pressure (Fig. 13b), probably because the increasing pore pressure induced by intensive rainfall needed some time. Hereafter, the land uplift for 20 mm/h decreased gradually, but its value did not reach zero at the end of the simulation period due to the increasing pore pressure. Fig. 15 shows the time evolution of the air-injection rate for the base case, rain intensity of 5 mm/h, and 20 mm/h during compressed-air injection. The behavior of the air-injection rate was almost the same for the three cases, probably because the changes in pore pressure near the injection zone were essentially identical for the three cases (Fig. 13a). 4.2 Permeability of Injected Strata The permeability of the injection zone reflects the ability of soils to conduct water and air, and it plays an important role in the permeation of compressed air into the soil. Different values were considered for the intrinsic permeability of the marl layer (i.e., the injected strata), 0.5 Kbase , Kbase and 1.5 Kbase , to analyze its effects on the multiphase flow and land lift during and after compressed air injection. Notably, Kbase represented the adjusted intrinsic permeability of the marl layer in three directions (X, Y and Z). All the other simulation conditions were the same as those for the base case. A large permeability promoted the injected air to flow into the soil voids and affected the seepage and soil deformation in the aquifer. Therefore, as shown in Fig. 16a, with a large permeability, the land uplift increased 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection at 27 hours. However, at 75 h, the land uplift near the borehole was substantially the same with a different permeability, probably because the unsaturated zone in this region was connected to the shallow unsaturated zones and the dissipation of the overpressure was almost the same. Additionally, the varying rate and the maximum value of the maximum land uplift also increased with increasing permeability during the compressed-air injection. Hereafter, the land uplift with a different permeability decreased gradually to zero, but the time required to reach zero was slightly advanced with a small permeability (Fig. 16b). Similarly, the air-injection rate through the injection section also increased as the permeability of the injected strata increased (Fig. 17). 4.3 Air Entry Pressure of Injected Strata The air entry pressure denotes the matric suction at which air begins to enter into the maximum pore space of the soils, and it is an important parameter in the soil-water characteristic curve. It is easier for air to permeate soils with a lower air entry pressure (coarse materials). Three different values were considered for the air entry pressure of the injected strata, i.e., 0.5 pbase ,Phase (base case) and 1.5 Pbase. Notably, Phase was the air entry pressure of the marl layer in the base case (Table 1). The other simulation conditions were the same as those for the base case. 4.5 -o 2 -2? h for bu» cas» - - - 7} h for bu* aw -27 h for 0 JK^ ---7}hfor0 5KM -î'Iifor IJK^, ---75 h for 1 SK^ Figure 16. (a) Land uplift at different times and (b) changes in the maximum land uplift with time for different permeabilities. 60 Time (h) Figure 18. (a) Land uplift at different times and (b) changes in the maximum land uplift with time for different air entry pressures. Time(h) Time (h) Figure 17. Temporal evolution of the air-injection rate for Figure 19. Temporal evolution of the air loss rate for different air different permeabilities during compressed air injection. entry pressures during compressed-air injection. 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection As shown in Fig. 18a, with decreasing air entry pressure, the land uplift increased at 27 h, but it varied at different positions at 75 h. Additionally, the varying rate and the maximum value of the maximum land uplift increased with the air entry pressure decreasing during air injection, but the variation of the dissipation of land uplift was similar with different air entry pressures, and the time when the land uplift reached zero was slightly advanced with a high air entry pressure (Fig. 18b). Additionally, the air injection rate increased with decreasing air entry pressure (Fig. 19). 5 SUMMARY AND CONCLUSIONS In this study, a loosely coupled two-phase flow and geo-mechanical model approach linking two numerical codes, TOUGH2/EOS3 and FLAC3D, was used to investigate the interaction between multiphase flow and soil skeleton deformation underground. Owing the air-flow test in Essen, the effect of different factors on seepage and soil deformation during and after the compressed-air injection was investigated using this coupled model. As compressed air is injected into the soil layer, the air mainly flows upwards and laterally and the adjacent regions become unsaturated. The average pore pressure and the vertical effective stress near and above the injection zones increases and decreases, respectively, causing the porosity in the corresponding zone to increase. After the termination of the compressed-air injection, both the magnitude and the scope of the porosity increments decrease due to overpressure dissipation. The land uplift, caused primarily by the expansion of the deep layers, reaches the maximum value at the end of the injection phase, and then it decreases to zero after a certain period. When a rain event, imposed at the ground surface, is combined with air injection underground, the seepage and soil deformation presents a complex response. If the rain intensity is too low to completely seal off the ground surface, the pore air in the unsaturated zones can easily escape out of the ground surface during rainfall, and the land uplift is substantially the same as the base case. However, if the rain intensity is so great that the pore air in unsaturated zones cannot flow easily back to the atmosphere during rainfall and is compressed by the advancing wetting front, the pore pressure in the unsaturated and saturated zones increases, causing the magnitude of the land uplift to increase, but this difference is relatively small near the borehole. Nevertheless, the air-injection rate through the injection section is scarcely affected by a rain event (high or low ran intensity). When the intrinsic perme- ability increases or the air entry pressure decreases in the injected strata, both the land uplift and the air injection rate through the injection section increase during air injection, but the time required for the land uplift to reach zero is slightly advanced with a small permeability or a high air entry pressure. Therefore, with regard to some scenarios of subsurface fluid injection, a detailed and meticulous strata exploration is required, and the soil properties can significantly affect the multiphase flow and soil deformation during fluid injection. Meanwhile, for different purposes, different strata should be chosen for injecting fluids. Additionally, as a fluid displaces another fluid in porous media, the front is usually perturbed owing to the difference in the physical properties of the fluids, for instance, viscosity, density, surface tension or permeability across the interface of two fluids, thereby causing the development of a fingering phenomenon [28-29]. Therefore, further work needs to be performed to develop a more advanced numerical model to consider the development of fingering during the process of air displacing water. Acknowledgments This work was supported by the National Nature Science Foundation of China (Grant NO. 51579170 and 51179118) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51321065). REFERENCES [1] Kramer, J., Semprich, S. 1989. E Erfahrungen über Druckluftverbrauch bei der Spritzbetonbauweise (in German). Taschenbuch für den Tunnelbau 13, 91-153. [2] Chinkulkijniwat, A., Horpibulsuk, S., Semprich, S. 2014. Modeling of Coupled Mechanical-Hydro-logical Processes in Compressed-Air-Assisted Tunneling in Unconsolidated Sediments. Transport in Porous Media 108, 1, 105-129. DOI: 10.1007/s11242-014-0295-6 [3] Selvadurai, A.P.S. 2006. Gravity-driven advec-tive transport during deep geological disposal of contaminants. Geophysical Research Letters 33, L08408. DOI: 10.1029/2006GL025944 [4] Wong, R.C.K., Lau, J. 2008. Surface heave induced by steam stimulation in oil sand reservoirs. Journal of Canadian Petroleum Technology 47, 01, 13-17. DOI: 10.2118/08-01-13-TN 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection [5] Teatini, P., Gambolati, G., Ferronato, M., Settari, A.T., Walters, D. 2011. Land uplift due to subsurface fluid injection. Journal of Geodynamics 51, 1, 1-16. DOI: 10.1016/j.jog.2010.06.001 [6] Rutqvist, J. 2012. The geomechanics of CO2 storage in deep sedimentary formations. Geotechnical and Geological Engineering 30, 3, 525-551. DOI: 10.1007/s10706-011-9491-0 [7] Selvadurai, A.P.S. 2009. Heave of a surficial rock layer due to pressures generated by injected fluids. Geophysical Research Letters 36, 14. DOI: 10.1029/2009GL038187 [8] Rutqvist, J., Vasco, D.W., Myer, L. 2010. Coupled reservoir-geomechanical analysis of CO2 injection and ground deformations at In Salah, Algeria. International Journal of Greenhouse Gas Control 4, 2, 225-230. DOI: 10.1016/j.ijggc.2009.10.017 [9] Kim, J., Selvadurai, A.P.S. 2015. Ground heave due to line injection sources. Geomechanics for Energy and the Environment 2, 1-14. DOI: 10.1016/j.gete.2015.03.001 [10] Selvadurai, A.P.S., Kim, J. 2015. Ground subsidence due to uniform fluid extraction over a circular region within an aquifer. Advances in Water Resources 78, 50-59. DOI: 10.1016/j. advwatres.2015.01.015 [11] Selvadurai, A.P.S., Kim, J. 2016. Poromechanical behaviour of a surficial geological barrier during fluid injection into an underlying poroelastic storage formation. Proc. R. Soc. A. The Royal Society 472, 2187: 20150418. DOI: 10.1098/ rspa.2015.0418 [12] Pruess, K., Oldenburg, C., Moridis, G. 1999. TOUGH2 User's Guide Version 2.0. University of California, Berkeley, USA. [13] ITASCA Consulting Group Inc. 2002. Fast Lagrangian Analysis of Continua in 3 Dimensions Version 2.10, User's Manual. ITASCA Consulting Group Inc, Minnesota. [14] Rutqvist, J., Wu, Y.S., Tsang, C.F., Bodvarsson, G. 2002. A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. International Journal of Rock Mechanics and Mining Sciences 39, 429-442. DOI: 10.1016/S1365-1609(02)00022-9 [15] Rutqvist, J., Tsang, C.F. 2003. TOUGH-FLAC: a numerical simulator for analysis of coupled ther-mal-hydrologic-mechanical processes in fractured and porous geological media under multi-phase flow conditions. In Proceedings of the TOUGH Symposium 12-14. [16] Rutqvist, J., Bäckström, A., Chijimatsu, M., Feng, X.T., Pan, P.Z., Hudson, J., Jing, L., Kobayashi, A., Koyama, T., Lee, H.-S., Huang, X.-H., Rinne, M., Shen, B. 2009. A multiple-code simulation study of the long-term EDZ evolution of geological nuclear waste repositories. Environmental geology 57, 6, 1313-1324. DOI: 10.1007/s00254-008-1536-1 [17] Rutqvist, J. 2008. Analysis of injection-induced micro-earthquakes in a geothermal steam reservoir, the Geysers Geothermal Field, California. Lawrence Berkeley National Laboratory. [18] Rutqvist, J., Moridis, G. J. 2007. Numerical studies on the geomechanical stability of hydrate-bearing sediments. In Offshore Technology Conference. Offshore Technology Conference. [19] Tsang, C. F., Birkholzer, J., Rutqvist, J. 2008. A comparative review of hydrologic issues involved in geologic storage of CO2 and injection disposal of liquid waste. Environmental Geology 54, 8, 1723-1737. DOI: 10.1007/s00254-007-0949-6 [20] Cappa, F., Rutqvist, J., Yamamoto, K. 2009. Modeling crustal deformation and rupture processes related to upwelling of deep CO2-rich fluids during the 1965-1967 Matsushiro earthquake swarm in Japan. Journal of Geophysical Research: Solid Earth 114, B10. DOI: 10.1029/2009JB006398 [21] Bear, J., Bachmat, Y. 1990. Introduction to Modeling of Transport Phenomena in Porous Media (Vol. 4). Springer Science & Business Media. [22] Chapuis, R.P., Aubertin, M. 2003. On the use of the Kozeny Carman equation to predict the hydraulic conductivity of soils. Canadian Geotechnical Journal 40, 3, 616-628. DOI: 10.1139/T03-013 [23] Taylor, D.W. 1948. Fundamentals of soil mechanics. John Wiley & Sons, New York. [24] Leverett, M.C. 1941. Capillary behavior in porous solids. Transactions of the AIME 142, 152-168. DOI: 10.2118/941152-G [25] Öttl, G. 2003. A Three-phase FE-model for Dewatering of Soils by Means of Compressed Air. Universität Innsbruck AI: Publik.-Bereich. [26] Van Genuchten, M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil science society of America journal 44, 892-898. DOI: 10.2136/ sssaj1980.03615995004400050002x [27] Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water resources research 12, 513-522. DOI: 10.1029/WR012i003p00513 [28] Homsy, G. M. 1987. Viscous fingering in porous media. Annual review of fluid mechanics 19, 1, 271-311. DOI: 10.1146/annurev. fl.19.010187.001415 10. Acta Geotechnica Slovenica, 2017/2 Z. Yongge et al.: Impacts of different factors on seepage and land uplift due to compressed-air Injection [29] Moortgat, J. 2016. Viscous and gravitational fingering in multiphase compositional and compressible flow. Advances in Water Resources 89, 53-66. DOI: 10.1016/j.advwatres.2016.01.002 10. Acta Geotechnica Slovenica, 2017/2 KRITIČNI ODMIK PLITVEGA TEMELJA NA POBOČJU Ključne besede nosilnost temeljnih tal, nekoherentna zemljina, temeljenje, razdalja odmika, pobočja Izvleček Konstrukcije so pogosto zgrajene na pobočjih v hribovitih območjih, kar ima za posledico pomanjkanje podpore tal zaradi nagnjene podlage na pobočni strani temeljenja. To povzroči zmanjšanje nosilnosti temeljenja. Čeprav obstajajo številne študije o temeljenjih na pobočjih, je večina teh študij omejena zgolj na površinsko temeljenje (to je brez upoštevanja globine temeljenja). Poleg tega v literaturi ni soglasja o vplivu razdalje odmika temelja od pobočja na nosilnost temeljnih tal. F prispevku so predstavljeni rezultati analiz s končnimi elementi za pasovne temelje, ki ležijo na stabilnih pobočjih. Analizirano je veliko število možnih nagibov pobočij z različnimi globinami temeljenja. Iz rezultatov je razvidno, da se kritična razdalja odmika poveča s povečanjem notranjega kota trenja zemljine, globine temeljenja in nagiba pobočja. Kritična razdalja odmika je med 2 do 4-kratno širino pasovnega temelja za zemljine z nizkim notranjim kotom trenja, medtem ko je več kot 10-kratna širina pasovnega temelja za zemljine z višjim notranjim kotom trenja. Na podlagi rezultatov študije je razvita tudi regresijska enačba. Predlagana enačba lahko predvidi vpliv različnih parametrov, ki vplivajo na nosilnost temeljev, ki ležijo na pobočjih. Rezultati so primerjani s prejšnjimi eksperimentalnimi in numeričnimi študijami. Rajesh Prasad Shukla IIT Roorkee, Department of Earthquake Engineering Roorkee, Indija E-pošta: rpshukla.2013@iitkalumni.org Ravi Sankar Jakka (vodilni avtor) IIT Roorkee, Department of Earthquake Engineering Roorkee, Indija E-pošta: rsjakka@iitr.ac.in 18. Acta Geotechnica Slovenica, 2017/2 CRITICAL SETBACK DISTANCE FOR A FOOTING RESTING ON SLOPES Keywords bearing capacity ratio, cohesionless soil, footing, setback distance, slopes Abstract Structures are often constructed on slopes in hilly regions, which results in a lack of soil support on the sloping side of the footings. This causes a reduction in the bearing capacity of the footings. Though there are number of studies about foundations on slopes, most of these studies are confined to surface footings only (i.e., without the depth of embedment). Furthermore, there is no consensus in the literature over the influence of the setback distance on bearing capacity. This paper presents the results of finite-element analyses on a strip footing resting on stable slopes. A very large number of possible soil slopes with different footing depths were analysed. From the results it is found that the critical setback distance increases with an increase in the internal friction angle of soil, the depth of the footing and the slope gradient. The critical setback distance is varying between 2 to 4 times the footing width for soils with a low internal friction angle, while it is more than 10 times the footing width for soils with a higher internal friction angle. A regression equation is also developed based on the outcomes of the study. The developed equation is able to predict the influence of various parameters affecting the bearing capacity of a footing resting over the slopes. The results are compared with earlier experimental and numerical studies. Rajesh Prasad Shukla IIT Roorkee, Department of Earthquake Engineering Roorkee, India E-mail: rpshukla.2013@iitkalumni.org Ravi Sankar Jakka (corresponding author) IIT Roorkee, Department of Earthquake Engineering Roorkee, India E-mail: rsjakka@iitr.ac.in 1 INTRODUCTION Structures are often built on or near a slope for several reasons, such as the unavailability of level ground, to make the structure more appealing, to construct a foundation for bridges, etc. The presence of a slope significantly affects the load-carrying capacity of a footing [1]. A footing constructed on slopes, lacks soil support on one side, which results in the failure of the foundation at a lower load compared to the identical foundations on level ground. This means that the ability of soil to support structures (i.e., bearing capacity) reduces. An estimation of the bearing capacity after accounting for the slope and foundation geometry is difficult. In these cases, the determination of the bearing capacity is different from general cases, as various additional factors influence the bearing capacity. For foundations located on a slope, the plastic zone on the side of the slope is relatively smaller than those of similar foundations on level ground [2]. Thus, the ultimate bearing capacity of the foundation is correspondingly reducing in almost all cases. The soil strength on the slope side is fully mobilised before the complete mobilization of the soil strength on the side of the level ground, and consequently the footing fails without reaching its ultimate collapse load. The geometry of the 18. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes slopes and the soil characteristics are important factors influencing the mobilization of soil strength on either side of the slope. The geometry of the slope includes the setback distance (B'), the slope gradient (horizontal: vertical) and its height. The soil characteristics include the type of soil and the strength parameters of the soil (c and 9). A number of studies considered the effect of the slope on bearing capacity of the footings. Some of the studies considered the effect of the setback distance on bearing capacity of the footing. Meyerhof [2] proposed bearing-capacity factors for a footing resting near slopes. Hansen [3] presented slope-correction factors for a footing resting precisely on the slope crest. However, the presented solution cannot be used for a footing resting with some distance from the slope crest. Shields et al. [4] experimentally evaluated the resultant bearing-capacity factor, Nyq, (the combined effect of overburden resistance and soil self-weight), for a footing resting over a slope gradient of 2 Horizontal: lVertical (2H:1V) and 1.5H:1V in cohesionless soil. It was reported that Meyerhof [2] overestimates the bearing capacity factors for a footing resting near the slope. This is due to fact that Meyerhof [2]considered equal mobilization of the soil strength on both sides of the slope. Kusakabe et al. [5] used the upper bound to estimate the bearing capacity. Model tests were also conducted, but the maximum setback distance was restricted to the footing width (B). Graham et al. [6] used method of stress characteristics to determine the bearing capacity, but the study was limited to a setback of 2B. Tatsuoka et al. [7] found the study results of Graham et al. [6] to be on the unsafe side. Bowles [8] considered a graphical approach to incorporate the effect of slopes, but the variation in the failure geometry with the slope angles and setback distance are not considered in the analysis. Saran et al. [9] used upper bound analysis and the limit-equilibrium method to determine the ultimate load. The critical setback was evaluated separately for bearing-capacity factors (Nc, Nq, and NY). The critical setback distance was found to range from 1.88B to 4.88B. The mechanism adopted in the upper-bound analysis is inconsistent with the assumed soil model as an inadmissible failure mechanism was adopted in the study [10]. Narita and Yamaguchi [11] extended the study of Kusakabe et al. [5] to the clay slope, but both studies neglected the mobilization of the shear strength of the soil on the level side of the footing. De Buhan and Garnier [12] evaluated the bearing capacity of a rectangular shallow foundation located near a slope or an excavation by using yield design theory. Lee and Manjunath [13] constrained the maximum setback distance to 5B. However, the test results clearly showed that the bearing capacity is increasing continuously, even at 5B. Huang and Kang [14] used the limit-equilibrium method and found that the critical setback distance is varying from 2.1 to 7.1B for the soil of internal friction 30 to 45°, respectively. Castelli and Motta [15] used the limit equilibrium and found that the critical setback is varying from 1.5B to 5.5B. El Sawwaf and Nazir [16] conducted tests on loose sand and found that the enhancement in bearing capacity becomes constant for a setback of 3B. Naeini et al. [17] conducted a study on a slope of 1H: 1V and found that the bearing capacity reaches the level ground at a setback of 10B. Gill et al. [18] observed in the experimental studies that the effect of the slope is significant up to a setback of 3B in coal ash slopes. Nouri [19] found the critical setback distance to be equal to 8B for soil of internal friction 35° and it can be even more than 8B for the soil of higher values of internal friction. Rostami and Ghazavi [20] used the limit-equilibrium method and found that the critical setback distance is varying between 3.1 and 5.4B. There is no consensus over the critical value of the setback distance in the literature. A few studies concluded that the setback distance does not affect the bearing capacity beyond a B'/B of 2 and 3 [6, 8, 16, 18, 21-24]. However, other studies found this value to vary up to 5 and 6 [2, 4, 9, 13, 14, 25-27]. Some studies found the B'/B values to be even more than 7-8 [14, 17, 19]. The strength contribution from the soil on the level side of a footing, the effect of the slope angle on the failure surface, the effect of driving forces acting on the sloping side and the effect of embedment depth of footing have been neglected in most of the studies. Furthermore, these studies do not incorporate the non-uniformity of the surcharge loading, especially on the slope side of the footing. Another common limitation in most of the studies is that these were restricted up to a setback distance of 5B in the analyses, even though there is a significant improvement in the bearing capacity from a setback of 4B to 5B. This means that the true value of the critical setback distance remains undetermined in the earlier studies. In the present study extensive finite-element analyses have been carried out to study the effect of the setback distance on the bearing capacity of a footing resting near the slope crest for various possible slopes and footing geometries, including the depth of the embedment. Based on the study, bearing-capacity-reduction factor (BCR) is proposed for a combination of parameters. The BCR factor is defined as the ratio of the bearing capacity of a footing resting on a slope to the bearing capacity of an identical footing resting over level ground. A regression equation is also developed to directly estimate the reduction in the bearing capacity of footings resting over the slope. 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes 2 PARAMETERS CONSIDERED IN THE ANALYSIS 3 METHOD OF ANALYSIS All the different parameters affecting the performance of a strip footing resting near the slopes, such as the soil friction angle, the slope inclination, the depth of the footing and the setback distance were considered in the analysis. The ranges of the parameters used in the study are summarized in Table 1. It is commonly accepted that the angle of internal friction of soil can vary between 27° and 42° [28], But to maintain the uniformity in the results, the present study considered a range of friction angles varying from 25° to 45°. The slope angle considered in the analysis depends on the friction angle of the soil. To ensure the stability of the soil slope, the slope angle is assumed to be always less than the angle of internal friction of the soil. Additionally, slope-stability analyses were carried out to avoid unstable slopes. Two unit weights, 16 and 17 kN/m3, are considered in the analysis. The stiffness and the Poissons ratio of the soil are assumed to be 12500 kN/m2 and 0.3, respectively. The normalized parameters, depth ratio and setback ratio are defined and used for the interpretation of the results. The depth ratio is defined as the depth of the foundation normalized with respect to the width of the footing, while the setback ratio is the setback distance for a footing normalized with respect to the width of the The finite-element analysis was performed using a two-dimensional finite-element program. A plain-strain analysis was used to simulate the strip footing resting near the slope. A software programmeOptumG2 was used for the FEM analysis. Fig. 1 shows a typical finite-element model used in the study. It was assumed that the slope gradient is uniform along the length of the footing. The model domain was kept large enough to minimize the boundary effects. The area of the domain was selected based on the slope geometry and the setback distance. For a larger slope gradient and setback distance, a larger area of domain was selected to minimize the effect of the boundaries on the results of analysis. The number of elements in the analysis and the area of the model domain were varied with the slope gradient and the setback distance. Fifteen nodded gauss elements were used in the analysis. The elements use a cubic interpolation of the stresses and the quartic interpolation of the displacements. A small number of elements are sufficient for steep slopes with a smaller setback distance, whereas a larger number of elements are 25 1/10, 1/7, 1/5, 1/4, 1/3 0, 0.5 and 1 0, 1, 3, 5 and 7 75 30 1/10, 1/7, 1/5, 1/4, 1/3 and 1/2 0, 0.5 and 1 0, 1, 3, 5 and 7 90 35 1/10, 1/7, 1/4, 1/3, 1/2 and 1/1.5 0, 0.5 and 1 0, 1,3, 5,7 and 9 108 40 1/10, 1/7,1/4, 1/3, 1/2, 1/1.5 and 1/1.4 0, 0.5 and 1 0, 1, 3, 5, 7 and 9 108 45 1/10, 1/7, 1/4, 1/3, 1/2, 1/1.5 and 1/1.2 0, 0.5 and 1 0,1,3, 5, 7, 9 and 11 147 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes considering a critical case using the mesh adaptively option of Optum. The mesh adaptivity was earlier used by several studies to refine the mesh to obtain accurate results [30-32]. It was found that 3-4 iterations are enough to obtain consist results. Conservatively, a total of 6 adoptive iterations were considered in the analyses. In the first iteration, the number of elements was fixed to 5000. Finally, a total of 7000 elements were found to be adequate for the analysis. The same number of elements are used for all the cases in the final adoptive iteration. The six-nodded interface is idealized as an element of zero thickness between the soil and the footing. Details of the analysis can be found in Krabbenhoft et al. [29]. Sand was modelled as a drained material, and a Mohr-Coulomb model was used to represent the shear strength. The soil friction angle (9) was assumed to be constant throughout the soil strata, i.e., the relative density of soil is not varying with the depth. The foundation was considered as a weightless rigid material. The load was applied to the footing in terms of a load multiplier, and was increased to the point of foundation failure. 4 RESULTS AND DISCUSSIONS_ The effects of the setback distance on BCR were analysed for various slope inclinations, the depth of footing and the internal friction angles of the soil. The critical setback distance was estimated for various different combinations of these parameters. The effects of these parameters are discussed separately in the following four sections, i.e., the effect of setback distance, the effect of the slope gradient, the effect of the depth ratio and the effect of the friction angle of the soil. The critical setback distance is defined as a minimum distance, where the setback distance does not influence the BCR significantly. Some of the typical results are presented for soil of internal friction 35° only. The BCR increases with a relatively higher rate up to a setback ratio (B'/B) of 3, and this rate of increase in the BCR reduces for the higher value of the setback distance. It is evident from Fig 2 (a, b and c) that for a particular slope gradient and setback distance, the BCR is reducing with an increase in the foundation depth. The BCR is higher in the case of a gentle slope and the BCR is becoming constant for a small setback distance. The rate of increase in the BCR is higher in the case of a slope with a steep gradient. Increasing the B'/B value more than 5 does not improve the BCR significantly. The curves are relatively steeper in the case of the footing with a higher depth ratio, and it indicates that the rate of increase in the BCR is higher in the case of a footing with a higher depth ratio. The increase in the setback distance reduces the instability caused by the slope. Thus, the improvement in BCR and the confinement of the (a) 0.8 0.6 o «0.4 0.2 0.8 0.6 Pi O «0.4 0.2 j/ —♦—10H:V —■- 7H:V —•— 4H:V —■- 3H:V —2H:V B'/B —♦—10H/V — 7H/V —♦—5H/V —«-3H/V —2H/V (b) B'/B 4.1 Effect of the setback distance Though the effect of the setback distance on the BCR is determined for all the cases presented in Table 1, the results here are presented for a soil of internal friction 35°. The typical variation in BCR with the setback distance for a soil of friction angle of 35° is presented in Fig 2. The variation in BCR with the setback distance for depth ratios of 0, 0.5 and 1 are presented in Figs 2 a, b and c, respectively. In all the cases, the BCR is found to be improving with an increase in the setback distance due to an increase in the soil confinement on the slope side of the footing. (c) 0.8 0.6 0.4 0.2 0 B'/B —♦—10H/V —■- -7H/V —♦—5H/V —■- -3H/V —A—2H/V Figure 2. Effect of setback distance on BCR for a footing resting on soil of internal friction 35° for different depth of embedment: (a) D/B=0.0, (b) D/B=0.5 and (c)D/B=1. 1 0 0 2 4 6 8 0 0 2 4 6 8 0 2 4 6 8 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes soil is observed with larger setback distances for a given slope gradient and an embedment depth of footing. The BCR improves with the increase in the setback distance due to the lesser effect of the instability caused by the slope. Passive resistance also increases with an increase in the setback distance due to an increase in the amount of surcharge loading and the effective soil weight contributing to the bearing capacity. Mobilization of the soil strength on the level side of the footing is also increasing with an increase in the setback distance, which is the main reason for the higher rate of improvement in the BCR at lower setback distances. The stiffness of the foundation increases with the setback. The increase in the stiffness of the soil foundation system also improves the bearing capacity of soil [33]. The results presented here for a depth of embedment of zero are comparable with earlier studies by Rostami and Ghazavi [20] and Keskin and Laman [26]. However, both studies were confined to surface footings. The testing was limited to a few relative densities, three slope angles and a maximum setback of 5B, which further restricted the authors to determine the true critical setback distance. A detailed comparison of the results with Keskin and Laman [26] is presented later in the section 'Validation of the equation with experimental data and analytical analysis'. The effect of the setback distance on soil deformation is shown in Fig. 3. Though the analysis is carried out for a large range of soil, the results are presented for the soil of internal friction angle 35°, and slope gradient of 2H: V. The setback distance was varied from 0 to 7B. Fig. 3 (a and b) clearly shows that at a higher setback distance, the strength of the soil on the sloping side contributes to the strength of footing, while no or a partial mobilization of the soil strength is observed for smaller setback distance. This means that the behaviour of the footing at a low setback distance is entirely governed by the soil on the sloping side. Increasing the setback distance more than a certain value enables the contribution of the soil strength from both sides of the footing. The effect of the slope becomes insignificant at a setback distance of 5B. Ausilio [27] also observed that for soil with an internal friction of 35°, the effect of the slope diminished at the setback of 5B for the footing resting on the ground surface. Fig. 3 (f) shows that for a setback distance of more than the critical setback, the behaviour of the footing becomes independent of the slope geometry. At this stage the mobilization of soil strength on both sides of the footing becomes almost equal to each other, as depicted by the symmetrical failure surface on either side of the footing. So the effect of the slope on the footing's performance can be minimized by maintaining a proper distance between the slope edge and the footing. The setback distance at which the behaviour of the foundation becomes independent of the slope depends on the slope angle as well as the soil's internal friction. 4.2 The effect of the slope gradient The effect of the slope inclination on the BCR is studied for a large range of slope gradients for stable soil slopes. The typical variations of the BCR with the slope gradient for different foundation depths on a soil with an internal friction of 35° are shown in Fig. 4. The graphs are plotted for different amounts of setback distance. The BCR decreases with an increase in the slope gradient, and this decrease in the BCR is depending on the depth of the foundation embedment and the relative location of the footing from the slope crest. The reduction in the BCR with an increase in the slope gradient is very significant when the footing is resting near the slope crest. The effect of the setback distance is becoming more evident with an increase in the slope gradient. Comparing Figs 4 (a, b and c), it is observed that the reduction in the bearing capacity with an increase in the slope gradient is marginally higher for a footing resting at a relatively higher depth. 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes (a) 0.8 Q0.6 pq 0.4 0.2 —♦—B'/B=0 —*-B'/B=5 0 0 0.1 0.2 (b) 1 0.8 g0.6 pq 0.4 0.2 0 1 0.8 Ö0.6 pq 0.4 0.2 (c) 0 -B'/B=1 -B'/B=7 -B'/B=3 0.3 0.4 0.5 Slope gradient (H/V) 0.6 L-Jft f - -*-* B'/B=0 -■- B'/B=1 '/B=3 *-B'/B=5 0.1 0.2 B'/B=7 0.3 0.4 0.5 Slope gradient (H/V) 0.6 '/B=3 B'/B=5 0.1 0.2 -B'/B=7 0.3 0.4 0.5 Slope gradient (H/V) 0.6 Figure 4. Effect of slope gradient on BCR for a soil of internal friction 35°. (a) D/B=0, (b) D/B=0.5 and (c) D/B=1.0. In the case of large setback distances, the BCR remains relatively unaffected by a change in the slope gradient. The effect of the slope gradient on the soil deformation is shown in Fig. 5. The results are presented for a soil of internal friction 35°. The setback distance and the depth ratio of the footing were maintained equal to 3B and 0.5, respectively, and only slope gradient was varied for analysis. The soil deformation further increases with an increase of the slope gradient and the maximum deformation is observed at a steep slope gradient. Figs. 5 (a-d) show that the orientation of the soil movement and failure surface is similar to a normal footing when the slope gradient is relatively very small. It also shows that the soil failure surface and the soil deformation are oriented towards the ground surface at a smaller slope gradient, and both are leaning gradually downward, 1.e., towards the slopping surface with an increase in the slope gradient. Similar observations were made in the experimental studies conducted by Chang et al. [34]. 4.3 The effect of embedment depth of footing Fig. 6 shows the effect of the footing embedment depth on the BCR for various slope gradients. The BCR decreases with an increase in the embedment depth of footing, in spite of the increase in bearing capacity. The effect of the footing embedment depth is significant when the footing is resting near the slope crest, and gradually becomes negligible with an increase in the setback distance. This is due to the fact that for a setback distance, more than or equal to the critical setback, the BCR 1 0 o (a) ^tffl i (b) 1 1 «^uH (d) . _ Figure 5. The deformation profile of soil slope for various slope gradients for soil of internal friction 35°: (a) 5H: V (b) 4H: 1V, (c) 3H: V and (d) 2H: V. 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes 0.8 g0.6 pq ■- I m— =3 ♦- ------- ---- ---- 0.4 0.2 (a) -B'/B=0 B'/B=3 -B'/B=7 -B'/B=1 -B'/B=5 0.2 0.4 0.6 0.8 Depth ratio (B/D) (b) 1 r If- -* 0.8 - -■ 0.6 -♦ 0.4 0.2 —♦—B'/B= 0 -» B'/B=1 —B'/B= =3 —X-B'/B=5 0 —*-B'/B= =7 0 0.2 0.4 0.6 0.8 1 Depth ratio (B/D) 1 X-*-* * 1-1 0.8 --A q 0.6 -- m ---- 0.4 0.2 (c) 0 -B'/B=3 -B'/B=7 3'/B=1 -B'/B=5 0. 2 0.4 0.6 0.8 Depth ratio (B/D) Figure 6. Effect of depth ratio of the footing on the BCR of soil with angle of internal friction 35°. (a) 10H: V, (b) 4H: V, and (c) 2H:1. remains almost constant, irrespective of the slope inclination. Similar to the present study, Narita and Yamaguchi [11] also found that the effect of the embedment depth of the footing is significant at a low setback distance. Two observations can be made from Figs. 6 (a, b and c). First, the BCR decreases with an increase in the depth ratio of the footing, especially in the case of a steep slope, and second, for a particular setback distance, the difference in the BCR is becoming more evident with an increase in the depth ratio of the footing. In the case of level ground, the effect of the depth ratio of the footing is relatively more significant for a soil with a low friction angle or loose soil, and a similar observation is also made in the present study for a footing resting over the slope. Castelli and Motta [15] also found that the effect of the depth of the embedment on BCR is not significant; however, the critical setback distance increases with the embedment depth. Garnier et al. [22] found the coefficient of reduction for a surface footing is always greater than 0.2 in soil with an angle of internal friction 40.5°, even when the slope is steep (3V:2H). A similar observation is also made in the present study for the footings resting over the ground surface. In addition to the surface footing, studies are also extended to a depth ratio of 0.5 and 1. For a soil with an angle of internal friction 40.5°, the coefficient of reduction (BCR) is found to be 0.15 and 0.1, respectively, for depth ratios of 0.5 and 1.0. 4.4 Effect of the angle of internal friction of soil The effect of the angle of internal friction of soil on the BCR of a footing resting on a different slope gradient is presented in Fig. 7. The results are presented for the surface footing only. For a particular setback distance, the angle of the slope, and the depth of footing, the BCR is decreasing with an increase in the friction of the soil (or relative density). Furthermore, the reduction in the BCR is varying with the angles of shearing resistance of soil, and this variation is depending significantly on the magnitude of the setback distance and slope gradient. The reduction in the BCR with an increase in the friction angle of soil is higher for a small setback distance and a steep slope gradient. The relationship between the BCR and the friction angle of soil is linear for gentle slopes, and it is becoming non-linear with an increase in the slope gradient. In comparison to the soil with a low internal friction angle, the pressure is distributed over a relatively large area in the case of soils with higher friction angle. To mobilize the strength of the soil completely, the footing resting on the dense sand requires a relatively large setback distance. In the loose sands, the failure is either a local shear failure or a punching shear failure, and in both cases the footing sinks without affecting the surrounding area, so these soils need a relatively small setback distance to compensate for the effect of the slope inclination. This reduction in the BCR with an increase in the internal friction angle of soil is increasing with an increase in the slope angle and a decrease in the setback distance. Rostami and Ghazavi [20] observed a similar behaviour in the case of a footing resting over the ground surface. Based on the numerical results, the critical setback distance is identified for different slope angles, depth of foundation and soil friction angles. The normalised setback distance is represented in a tabular form in Table 2. A detailed table is included in the annexure (Table 3). Though Meyerhof [2] considered only a limited range of setback distances (0 to 6B) and depth of footing, the presented critical setback distances are compared with the Meyerhof [2]. 0 0 0 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes o SB 1 * 0.8 0.6 ^0.4 0.2 (a) 0 25 1 0.8 0.6 Pi o P3 0.4 0.2 (b) 0 25 1 0.8 0.6 0.4 0.2 0 25 3 B'/B=0 B'/B=5 B'/B=1 B'/B=7 30 35 40 (|) (degree) B'/B=3 45 B'/B=0 B'/B=5 B'/B=1 B'/B=7 30 35 40 <|> (degree) B'/B=3 45 (c) B'/B=0 -■ B'/B=1 B'/B=5 -*-B'/B=7 30 35 40 (|) (degree) B'/B=3 45 Figure 7. Effect of friction angle on BCR for a footing of zero embedment resting over soil of internal friction 35°. (a) 10H: V, (b) 4H: 1V and (c) 3H: 1V Table 2. Normalised critical setback distance for cohesionless soils. Friction Slope gradi- Critical Setback Meyerhof angle (90) ent, G distance (B'/B) from [6] (V/H) present study 25 1/10-1/3 2-3 - 30 1/10-1/4 3 - 1/3-1/2 4-5 3 35 1/10-1/4 4-5 - 1/2 -1/1.5 6-7 5 40 1/10-1/5 5-6 >6 1/4 -1/3 6-7 >6 1/2-1/1.3 8-9 - 45 1/10-1/4 8-9 - 1/3-1/2 9-10 - 1/1.5-1/1.2 >10 - A steep slope of low relative density soil (low angle of internal friction) loses its stability with the application of a small magnitude load. In this condition, the slope sometimes fails itself and sometimes the foundation soil fails by means of local or punching shear failure (small area of shear zone). In both conditions a very small volume of soil is involved in the strength mobilization, without affecting the large mass of soil. In contrast, in the dense sand, failure is normally a general shear failure (a large area of shear zone). The larger area of soil contributes to the resistance against failure, and a large setback distance requires to mobilize the full strength of the soil. Chang et al. [34] and Raftari et al. [35] also found that the depth and the area of the shear zones increase with an increase in the setback distance in the reinforced slope. Similar to the present study, almost all previous studies also found that the critical distance increases with the increase in the angle of shearing resistance or the relative density of the soil. 5 STATISTICAL ANALYSES_ Statistical analyses were also performed to determine the factors affecting the BCR using the results of numerical analyses. A simple multiple regression and correlation analysis along with other statistical tests were performed to derive an equation to determine the BCR of a footing resting over cohesionless soil. As it can be seen from the numerical analysis, a total of four independent parameters (i.e., setback distance, slope gradient, soil friction angle and depth ratio of footing.) are influencing the bearing capacity of a footing resting near the slope. The results of the numerical study show that the relationship between the independent parameters and the bearing capacity ratio is not linear, and hence it is necessary to consider the nonlinearity in order to develop an equation for the BCR calculation. As an exact nonlinearity in the relationship is not known initially, it was assumed that the BCR is not only depending on these four parameters, but also upon various derivatives as well. Initially, a total of 96 parameters, which are the function of these 4 independent variables, are considered in the regression analysis. T-Tests were performed to determine the dependency of the BCR on these parameters. Along with the probability level, the R2 value was used to determine the critical factor affecting the BCR. The degree of multicol-linearity was used to remove the insignificant parameters. It was found from these studies that only 12 parameters, including the four basic parameters, critically affect the bearing-capacity ratio. Later these 12 variables were used to develop the equation for the bearing capacity ratio. 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes Figs. 8 (a) and (b) respectively show the residues of the BCR (observed BCR-predicted BCR) versus the percentage of the value for 96 and 12 variables. The equation was developed as a consequence of a comparative study carried out to develop an equation that can predict the effect of the slope inclination and the foundation geometry very effectively. Based on a regression analysis and a comparative analysis, an equation is proposed to estimate the BCR. For this, various type of functions, such as logarithmic, linear, polynomial and exponential func- tions, were assumed and the best relationship is used to develop the equation. It was found that R2 is reduced from 0.9947 to 0.987, when the number of insignificant variable were removed from the analysis. It ensures that the other assumed dependents parameters are not affecting the bearing capacity, as assumed in the initial phase of the regression analysis. Based on the T Test, the probability level and the degree of multicollinearity, the following order can be assigned to the factors, critically affecting the bearing capacity: Slope > Setback distance Figure 8. Residuals versus percentage of values (a) for 156 independent variables (b) for 12 independent variables. 20. Acta Geotechnica Slovenica, 2017/2 R. P Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes > Friction angle > Depth ratio of footing. The effect of the depth ratio of the footing on the bearing capacity is very nominal, as compared to the other three factors. Equation 1 shows the BCR equation developed to determine the influence of the slope geometry and the angle of internal friction of the soil. Annexure shows an equation that is relatively complex, but it can predict a change in the bearing capacity with a higher accuracy. BCR = 1 + 0.044B'/B(1 - 0.14B7B + 0.09D/B + 3.4$ + 0.06D/B(D/B - 1) - 0.4^(1 + 0.35ft + 0.8 D/B + 2.1tanp) + tanp(1 - 1.2 tamp - 0.15D/B + 0.15B7B) (1) where BCR = Bearing capacity ratio, B' = setback distance, B = width of footing, D = depth of footing, ft = soil slope in radian and p = angle of internal friction of the soil. 5.1 Validation of the equation with experimental and analytical analysis The proposed Eq. 1 is validated with the experimental results of Keskin and Laman [26]. Fig. 9 shows a reasonably good agreement between the BCR predicted from the proposed equation and the experimentally measured BCR values of Keskin and Laman [26]. The predicted BCR values up to the setback distance of 4B are a little higher than Keskin and Laman [26], but these differences are within the acceptable ranges (0-15%). This variation might be attributed to the scaling effect as the numerical modelling was carried out on a prototype model, while Keskin and Laman [16] performed small-scale model testing in the laboratory. Keskin and Laman [26] used the relative density of the sand in the analysis, and it has been converted to the friction angle of the soil using a relationship given by Schmertmann [36] for comparing the results. This might be another reason responsible for the minor differences observed between the experimental values and the values predicted from the developed regression equation. The results are also compared with the analytical analysis results of Huang and Kang [14]. To make this comparison, the results were reproduced in a different form. Here, BCR represents the ratio of the bearing capacity of the footing resting some distance from the slope crest to the bearing capacity of the footing resting precisely on the slope crest. Fig. 10 shows the comparison of the results with Huang and Kang [14]. Graphs with dotted lines show the results of Huang and Kang [14], and the solid lines show the results of the present study. The results of the former study show that the BCR become constant precisely after a certain value of the setback distance. Whereas in the present case, though BCR is not becoming constant, but the rate of increase in the BCR becomes insignificant after a 1 0.8 0.6 o PQ 0.4 0.2 (a) 0 1 0.8 (b) 0.6 Pi O pq 0.4 0.2 0 (c) 0 1.00 0.80 0.60 Pi O m 0.40 0.20 (d) 0.00 Keskin and Laman (2013) Present study 4 5 23 B'/B r Keskin and Laman (2013) 2 3 B'/B "Keskin and Laman (2013) -Present study 23 B'/B 4 —♦—K Leskin and Laman (2013) Present study 2 3 B'/B Figure 9. Variation of BCR with setback distance. (a) for soil slope 30°, 9=32°, (b) for soil slope 25°, 9=32°, (c) for soil slope 20°, 9=32° and (d) for soil slope 30°, 9=40°. certain value of setback distance. In comparison to the results of Huang and Kang [14], the BCR measured in the present study is higher for the small slope. Whereas 0 0 1 4 5 1 5 0 1 4 5 28. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes (a) 3.5 3 2.5 2 Pi 1 0.5 0 5 4 3 6 CONCLUSION (b) pR o pq (c) 15 (d) P=5 2 p=15 4 6 B'/B P=25 B=25 —•— P=30 -p=5 -A--B=25 -»-P=35 P=25 P=15 4 6 B'/B |3=5 P=15 3=35 [ i=25 15 B'/B 12 B'/B Figure 10. Comparison of results with analytical results of Huang and Kang [14] shown by dashed lines for surface footing resting on slope. (a) 9=30°, (b) 9=35°, (c) 9=40° and (d) 9=45°. in the case of a higher slope angle, the BCR evaluated from the present study is smaller than the BCR of the former studies. The slopes have an adverse effect on the bearing capacity of a footing. The slope gradient, setback distance, angle of internal friction of the soil and the depth ratio of footing affects the bearing capacity of a footing resting over the slope. The bearing capacity decreases with an increase in the slope gradient. The reduction in the bearing capacity with the slope gradient is relatively higher for a footing of large embedment depth and when the footing is resting near the slope crest. Particularly for dense sand, the effect of the slope gradient on the reduction in the bearing capacity is observed, even up to very large setback distances of 11B. Soil deformation also increases with an increase in the slope gradient. At a low slope gradient, the orientation of the failure surface and the soil deformation are very much similar to the footing resting on the level ground. Both the failure surface and the direction of propagation of soil deformation oriented downwards and towards the slope surface with an increase in the slope gradient. The soil confinement and strength mobilization on the level side of the footing increase with an increase in the setback distance; therefore, the bearing capacity increases. The critical setback distance is increasing with an increase in the friction angle of the soil, the slope gradient and the depth of footing. The reduction in the bearing capacity with slope inclination increases with an increase in the internal friction of the soil and the depth of footing. The effect of the depth of foundation on the reduction in the BCR is relatively higher when the footing is resting near the slope crest. The predicted BCR is well matching with the BCR determined in the previous analytical and experimental studies. REFERENCES [1] Sarma, S. K., Chen, Y. C. 1995. Seismic bearing capacity of shallow strip footings near sloping ground. The 5th SECED conference on European seismic design practice, Balkema, Rotterdam, 505-512. [2] Meyerhof, G. G. 1957. The ultimate bearing capacity of foundation on slopes. 4th Int. Conf. on Soil Mech. and Foundation Eng., 3, 384-386. [3] Hansen, J.B. 1970. A revised and extended formula for bearing capacity. Dan. Geotech. Ins., Bulletin 28. [4] Shields, D., Chandler, N., Garnier, J. 1990. Bearing capacity of foundations in slopes. Journal of geotechnical engineering 116, 3, 528-537. 0 8 0 2 8 8 6 2 0 0 3 6 9 0 3 9 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes [5] Kusakabe, O., Kimura, T., Yamaguchi, H. 1981. Bearing capacity of slopes under strip loads on the top surfaces. Soils and Foundation, JGS 21, 4, 29-40. DOI: http://doi.org/10.3208/ sandf1972.21.4_29. [6] Graham, J., Andrews, M., Shields, D. H. 1988. Stress characteristics for shallow footings in cohe-sionless slopes. Canadian Geotechnical Journal 25, 2, 238-249. DOI: http://dx.doi.org/10.1139/t88-028 [7] Tatsuoka, F., Huang, C.C., Morimoto, T., Okahara, M. 1989. Stress characteristics for shallow footings in cohesionless slopes. Discussion. Canadian Geotechnical Journal 26, 4, 748-755. DOI: http:// dx.doi.org/10.1139/t89-088 [8] Bowles, J.E. 1988. Foundation engineering and design. 5th Edition, McGraw-Hill, Inc. [9] Saran, S., Sud, V., Handa, S. 1989. Bearing capacity of footings adjacent to slopes. Journal of geotechnical engineering 115, 4, 553 - 573. DOI: http://dx.doi.org/10.1061/(ASCE)0733-9410(1989)115:4(553) [10] Michalowski, R. L. 1991. Discussion of bearing capacity of footings adjacent to slopes by Swami Saran, VK Sud and SC Handa. Journal of Geotechnical Engineering 117, 7, 1125-1127. DOI: http://dx.doi.org/10.1061/(ASCE)0733-9410(1991)117:7(1125.2) [11] Narita, K., Yamaguchi, H. 1990. Bearing capacity analysis of foundations on slopes by use of log-spiral sliding surfaces. Soils and Foundation, JGS 30, 3, 144-152. DOI: http://doi.org/10.3208/ sandf1972.30.3_144 [12] De Buhan, P., Garnier, D. 1998. Three dimensional bearing capacity analysis of a foundation near a slope. Soils and Foundations, JGS 38, 3, 153-163. DOI: http://doi.org/10.3208/sandf.38.3_153. [13] Lee, K. M., Manjunath, V. R. 2000. Experimental and numerical studies of geosynthetic-reinforced sand slopes loaded with a footing. Canadian Geotechnical Journal 37, 828-842. DOI: http://doi. org/10.1139/t00-016 [14] Huang, C.C., Kang, W.W. 2008. The effects of a setback on the bearing capacity of A surface footing near a slope. Journal of GeoEngineering 3, 1, 25-32. DOI: http://doi.org/10.6310/jog.2008.3(1).3 [15] Castelli, F., Motta, E. 2010. Bearing capacity of strip footings near slopes. Geotechnical and Geological Engineering 28, 2, 187-198. DOI: http://doi.org/10.1007/s10706-009-9277-9 [16] El Sawwaf, M. 2010. Experimental and numerical study of strip footing supported on stabilized sand slope. Geotechnical and Geological Engineering 28, 4, 311-323. DOI: http://doi.org/10.1007/ s10706-009-9293-9 [17] Naeini, S. A., Rabe, B. K., Mahmoodi, E. 2012. Bearing capacity and settlement of strip footing on geosynthetic reinforced clayey slopes. Journal of Central South University 19, 4, 1116-1124. DOI: http://doi.org/10.1007/s11771-012-1117-z [18] Gill, K. S., Choudhary, A. K., Jha, J.N., Shukla, S. K. 2013. Large model footing load test on reinforced coal ash slope. International Journal of Geotechnical Engineering 7, 3, 257-265. DOI: http://doi.org/10.1179/1938636213Z.00000000040 [19] Nouri, M. 2014. Interaction domain of shallow foundations on the top of a slope. Master Dissertation, Department of Civil, Environmental and Land Management Engineering, Polytechnic University of Milan. Itly. [20] Rostami, V., Ghazavi, M. 2015. Analytical solution for calculation of bearing capacity of shallow foundations on geogrid-reinforced sand slope. IJST, Transactions of Civil Engineering 39, C1, 167-182. [21] Andrew, M. 1986. Computation of bearing capacity coefficients for shallow footing on cohesionless slopes using stress characteristics. M.Sc. thesis, University of Manitoba, Winnipeg, Manitoba. [22] Gamier, J., Canepa, Y., Corte, J.F., Bakir, N.E. 1994. Etude delaPortance de Foundations enBorddeTa-lus. 13 th Int. Conf. on Soil Mechanics and Foundation Engineering 2, 705-708. [23] Georgiadis, K. 2010. Undrained bearing capacity of strip footings on slopes. Journal of Geotechnical and Geoenvironmental Eng. 136, 5, 677-685. DOI: http://doi.org/10.1061/(ASCE)GT. 19435606.0000269 [24] Altalhea, E. B., Taha, M.R., Abdrabbob Fathi, M. 2015. Behavior of strip footing on reinforced sand slope. Journal of Civil Engineering and Management 21, 3, 376-383. DOI: http://doi.org/10.3846/1 3923730.2014.890646 [25] Jao, M., Ahmed, F., Muninarayana, G., Wang, M. C. 2008. Stability of eccentrically loaded footings on slopes. Geomechanics and Geoen-gineering 3, 2, 107-111. DOI: http://doi. org/10.1080/17486020802010772 [26] Keskin, M.S., Laman, M. 2013. Model studies of bearing capacity of strip footing on sand slope. KSCE Journal of Civil Engineering 17, 4, 699-711. DOI: http://doi.org/10.1007/s12205-013-0406-x [27] Ausilio, E. 2014. Seismic bearing capacity of strip footings located close to the crest of geosynthetic reinforced soil structures. Geotechnical and Geological Engineering 32, 4, 885-899. DOI: http://doi.org/10.1007/s10706-014-9765-4 [28] Peck, R. B., Hanson, W. E., Thornburn, T. H. 1974. Foundation engineering. (Second edition), Wiley, New York. 20. Acta Geotechnica Slovenica, 2017/2 R. P. Shukla & R. S. Jakka: Critical setback distance for a footing resting on slopes [29] Krabbenhoft, K., Lyamin, A., Krabbenhoft, J. 2015. Optum computational engineering, (www. optumce.com). [30] Keawsawasvong, S., Ukritchon, B. 2016. Finite element limit analysis of pullout capacity of planar caissons in clay. Computers and Geotechnics 75, 12-17. DOI: http://dx.doi.org/10.1016/j. compgeo.2016.01.015 [31] Lyamin, A. V., Sloan, S. W., Krabbenhoft, K., Hjiaj, M. 2005. Lower bound limit analysis with adaptive remeshing. International Journal for Numerical Methods in Engineering 63, 14, 19611974. DOI: http://doi.org/10.1002/nme.1352 [32] Martin, C. M. 2011. The use of adaptive finite-element limit analysis to reveal slip-line fields. Géotechnique Letters 1, 2, 23-29. DOI: http:// dx.doi.org/10.1680/geolett.11.00018 [33] Varzaghani, I. M., Ghanbari, A. 2014. A new analytical model for determination of seismic settlement of foundations adjacent to slope. Geomechanics and Engineering 6, 561-575. DOI: http://dx.doi.org/10.12989/gae.2014.6.6.561 [34] Chang, J. C., Liao, J. J., Pan, Y.W. 2008. Bearing behavior and failure mechanism of a shallow foundation located on/behind the crest of a poorly cemented artificial sandstone. International Journal of Rock Mechanics and Mining Sciences 45, 8, 1508-1518. DOI: http://doi.org/10.1016/j. ijrmms.2008.01.013 [35] Raftari, M., Kassim, K.A., Rashid, A.S.A., Moayedi, H. 2013. Settlement of shallow foundations near reinforced slopes. EJGE 18, Bund. D, 797-808. [36] Schmertmann, J. H. 1978. Guidelines for cone penetration test: Performance and Design, FHWA-TS-78-209 (report), U.S. Dept. of Transportation. Table 3. Normalised critical setback distance for cohesionless soil. Friction Slope Depth of Critical Set- Meyerhof angle gradient, Embedment back distance et al. [5] (/) G (V/H) (B/D) (S/B) 25 1/10-1/5 0.5 2 - 1/5-1/3 1 3 - 0 2 2 1/10-1/4 0.5 3 30 1 3-4 0 3 3 1/4-1/2 0.5 3-4 1 4-5 0 4-5 1/10-1/5 0.5 5 1 5-6 0 5-6 35 1/4-1/2 0.5 6 1 6-7 0 5-6 1/2-1/1.5 0.5 6-7 1 7-8 1/10-1/5 0 5-6 1 6-7 40 1/5 -1/2 0 6-7 >6 1 7-8 1/2-1/1.3 0 7-8 >5 1 8-9 >7 1/10-1/4 0 7-8 1 8-9 45 1/4-1/2 0 8-9 1 10-11 1/2-1/1.2 0 >12 1 >12 Annexures: The equation to calculate the bearing-capacity ratio more accurately BCR = 0.047B7B + 0.32D/B + 4.46tanp -0.02(B'/B)2(1 - 0.34D/B - 0.75tanp + 0.15ß) -ß2(1 + 0.2ß - 1.9tanp - 0.36D/B + 0.19b/B) -6.45tanp2(1+ 0.45tanp + 0.16ß - 0.04D/B + 0.01b/B) -D/B2(1 - 0.7D/B + 0.017b/B - 0.22ß - 0.04tanp) + 0.034(b/B)D/B(1 - 2.35tanp) + 0.42(b/B)ß(1 - 0.07D/B) + 0.1(b/B)tanp(1 - 1.23ß) - 0.2(D/B)tanp(1 + 0.5ß) -ß(1 - 0.24tanp + 0.55D/B) 20. Acta Geotechnica Slovenica, 2017/2 STRIŽNI MODUL ZASIČENE GRANULIRANE ZEMLJINE IZ PREIZKUSA RESONANČNE KOLONE Izvleček V prispevku so predstavljeni rezultati 120 preizkusov določitve strižnega modula (G) zasičenih granuliranih zemljin (20-40 odstotni Ottawa pesek) v različnih pogojih relativne gostote (Dr), efektivnega konsolidacijskega tlaka (o') in nivoja torzijske indukcije (T). Uporabljena je bila resonančna kolona, ki jo je izdelal Wykeham Farrance. Preizkusi so bili izvedeni z relativnimi gostotami 20, 40, 60 in 80 %, efektivnimi konsolidacijskimi tlaki 50, 100, 150, 200, 250 in 300 kPa ter nivoji torzijskih indukcij 0.025, 0.05, 0.1, 0.2 in 0.4 voltov (V), da smo dobili strižne specifične deformacije (y) med 0.002 % in 0.023 %. Rezultati so privedli do zelo preprostih empiričnih izrazov za strižni modul kot funkcijo strižne specifične deformacije za različne vrednosti efektivnih konsolidacijskih tlakov in količnikov por. H. Patiño Universidad Politécnica de Madrid (UPM) Madrid, Španija E. Martínez Universidad Politécnica de Madrid (UPM) Madrid, Španija Jesús González Universidad Politécnica de Madrid (UPM) Madrid, Španija E-pošta: jesus.gonzalezg@upm.es A. Soriano Universidad Politécnica de Madrid (UPM) Madrid, Španija Ključne besede resonančna kolona; resonančna frekvenca; strižni modul; relativna gostota; efektivni konsolidacijski tlak; dinamični strižni modul 18. Acta Geotechnica Slovenica, 2017/2 SHEAR MODULUS OF A SATURATED GRANULAR SOIL DERIVED FROM RESONANT-COLUMN TESTS Keywords resonant column; resonant frequency; shear modulus; relative density; effective consolidation pressure; dynamic shear modulus Abstract This paper presents the results of 120 determinations of the shear modulus (G) of a saturated granular soil (20-40 Ottawa sand) in different conditions of relative density (Dr), effective consolidation pressure (o'J and level of torsional excitation (T). The equipment used was a resonant-column apparatus manufactured by Wykeham Farrance and the tests were performed with relative density values of20, 40, 60 and 80%, effective consolidation pressures of50, 100,150, 200, 250 and 300 kPa, and torsional excitations of0.025, 0.05, 0.1, 0.2 and 0.4 volts (V), leading to shear strains (y) between 0.002% and 0.023%. The results led to very simple empirical expressions for the shear modulus as a function of the angular strain for different effective consolidation pressures and void-ratio values. 1 INTRODUCTION The dynamic behaviour of granular soils has been intensively studied around the world for several decades now and the results obtained from various research programs are disseminated through the proceedings of international conferences and indexed journals related to geotechnical engineering. Since there is abundant information on the dynamic behaviour of granular soils and many of the topics dealt with are commonplace; this paper will only focus on references directly related to resonant-column tests, either from the point of view of the development of the test itself or from their utilization to obtain shear-wave velocities, shear-stiffness moduli and damping ratios. The resonant column was first used by Ishimato and Iida (1937) [1] and Iida (1938, 1940) [2, 3] to test Japanese soils, and then nearly two decades later by Bishop (1959) [4]. Since the 1960s, this technique has been widely used in many countries and has been subjected to countless modifications in the restraints applied to the specimen ends. Some of the many works on this matter are described below. For the sake of clarity, the references have been grouped by the main objective of the research rather than following a chronological order. Appearing first are the most relevant analyses of the test apparatus itself and of how to use the resonant column. Wilson and Dietrich (1960) [5] used one of the most novel - at that time - resonant columns in the USA to test clay samples. Hall and Richard (1963) [6] designed and developed a "fixed-free" resonant-column apparatus, i.e., the specimen is fixed at the base and free at the upper end, therefore allowing the soil samples to be subjected to torsional and longitudinal vibrations. Drnevich et al. (1966, 1967) [7, 8] developed equipment for hollow H. Patiño Universidad Politécnica de Madrid (UPM) Madrid, Spain E. Martínez Universidad Politécnica de Madrid (UPM) Madrid, Spain Jesús González Universidad Politécnica de Madrid (UPM) Madrid, Spain E-mail: jesus.gonzalezg@upm.es A. Soriano Universidad Politécnica de Madrid (UPM) Madrid, Spain 18. Acta Geotechnica Slovenica, 2017/2 H. Patino et al.: Shear modulus of a saturated granular soil derived from resonant-column tests cylindrical soil specimens, to determine the shear modulus and the damping ratio under large deformations; the reason for using hollow specimens being related to the difficulty in obtaining a representative value of the angular strain in solid samples. In addition, they developed the theory in which the interpretation of the results obtained from the resonant column test is based. The operational principle of resonant-column equipment, the calibration recommendations, the processing of the data and the interpretation of the results were clearly described by Drnevich et al. (1978) [9]. Menq (2003) [10] developed a resonant-column apparatus that allows testing of specimens up to 15 cm in diameter that was used to study the dynamic properties of sand and gravel. Clayton et al. (2009) [11] used aluminium rods of various diameters to evaluate the polar moment of inertia of the excitation system (Io) and found that this value depended on the stiffness of the rod employed in calibrating their apparatus. However, calibrating the resonant column employed for our research led to a constant Io value. Clayton (2011) [12] refers to some in-situ and laboratory methods to estimate the stiffness and analysed in detail factors influencing the stiffness value obtained from very-small-strain tests, like the range of strains, anisotropy and velocity of loading. Recently, some manufacturers of equipment for obtaining dynamic parameters have marketed relatively sophisticated models for resonant column tests that allow better control and better simulation during execution of the tests; among others Wykeham Farrance in the UK, which made the device used for this investigation. A detailed description of the equipment is presented later on. In general, the resonant column test is the most commonly used laboratory technique to measure the dynamic properties of soils subjected to a low level of deformation. The various designs developed so far imply the application of axial or torsional harmonic loads to solid or hollow specimens by means of electro-magnetic systems capable of accurately controlling the frequency and amplitude of the different types of waves that can be generated. On the other hand, Al-Sanad and Aggour (1984) [13] applied random loads and Tawfig et al. (1988) [14], impulsive loads. Resonant-column tests also make it possible to determine the velocity of shear waves and to analyse their influence on other test parameters. Some researches on this point are presented below. Hardin and Richart (1963) [15] measured the shear-wave propagation velocity in samples prepared with Ottawa sand, with crushed quartz sand and with crushed quartz silts, subjected to small strains, and they proposed empirical correlations to calculate the shear modulus as a function of the void ratio and the effective consolidation pressure. Hardin (1965) [16], based on the theory of linear vibrations of a cylindrical rod, presents an expression to calculate the shear wave propagation velocity (Vs) as a function of the resonant frequency, the polar moment of inertia, the height of the specimen and the polar moment of inertia of the system. Richart et al. (1970) [17] proved mathematically that proportionality exists between the resonant frequency of the specimen and the corresponding shear-wave propagation velocity. Santamarina and Cascante (1996) [18] used a resonant column apparatus capable of applying both compressive and tensile devia-toric stresses to measure the velocity of shear and damping waves under small strains. These velocities turned out to depend mainly on the isotropic stress, while the deviatoric stress played a lesser role. Probably, the factor most often analysed with this equipment has been the shear modulus, obtained in cyclic shear tests. Kuribayashi et al. (1975) [19] found that the shear modulus of several materials is not a function of the relative density, but rather of the void ratio. Iwasaki et al. (1978) [20] present the average variation trend of the shear modulus in eight different types of sand as a function of the angular strain. In addition, they found that in the case of Toyura sand, within a wide range of deformations, a linear relationship exists between the shear modulus and the effective consolidation pressure. Tatsuoka et al. (1979) [21] determined that the shear modulus, within a wide range of deformations, is not affected by the initial structure of the tested specimens. Alarcon-Guzman et al. (1989) [22] investigated the effect of the principal stress ratio on the shear modulus, concluding that this factor has a less important effect on the determination of the maximum shear modulus, but drastically affects the secant shear modulus. Saxena et al. (1989) [23] extensively reviewed empirical relations for obtaining Gmax and the damping (D) under small strain and conducted resonant-column tests on Monterey No. 0 Sand and showed that published relations overestimated Gmax and underestimated D for this sand. Lo Presti et al. (1997) [24] evaluated the influence of the strain rate in the determination of the shear modulus of granular soils, and found that this factor has a very small effect on the maximum shear modulus. Diaz-Rodriguez and Lopez-Flores (1999) [25] proposed an empirical function (a potential expression) between the shear modulus and the isotropic consolidation stresses (ct C). Wichtmann and Triantafyllidis (2004) [26] analysed the influence of the history of dynamic loading on the properties of dry sands; the results thus obtained indicated that a dynamic pre-stressing moderately affects the shear modulus under small deformations. Gu et al. (2013) [27] used bender 34. Acta Geotechnica Slovenica, 2017/2 H. Patino et al.: Shear modulus of a saturated granular soil derived from resonant-column tests elements to test three different sands subjected to small strains and found that both Go (shear modulus) and M0 (constraint modulus) increase with the density and the confining pressure. They found Go to be more sensitive to E0 (Young's modulus) and proposed empirical relations between the Poisson ratio and Go and M0. Finally, some works are presented that analyse how the soil identification properties (grading, particle shape, etc.) influence results. Chang and Ko (1982) [28] tested 23 samples of Denver sand and found that the maximum shear modulus is - to a large extent - a function of the coefficient of uniformity, whereas the effect of the mean size of the particles is minimal. Koono et al. (1993) [29] executed what can be regarded as a field resonant-column test in a gravel deposit. Wichtmann and Triantafyllidis (2009, 2013 and 2014) [30, 31, 32] evaluated the influence of the coefficient of uniformity and of the grain size distribution for 27 types of clean sand in the determination of the maximum shear modulus: the results obtained indicate that for equal values of the void ratio and of the effective consolidation pressure, the maximum shear modulus decreases as the coefficient of uniformity increases, whereas it does not change with the mean particle size. Martinez (2012) [33] studied the influence of the soil index properties on the determination of the dynamic parameters of a saturated granular soil. Senetakis et al. (2012) [34] tested sands with different grading curves, particle origin and shape under very small strains. Volcanic sands showed significantly lower Go values than those of quartz sands, whereas their D0 were only slightly lower compared to quartz sands. Yang and Gu (2013) [35] found that, in the range of small strains, the shear modulus varies very little in terms of particle size. Senetakis and Madhusudhan (2015) [36] tested quartz sands and angular-grained gravels and they proposed potential functions to relate Go with p'. The exponent nG was shown to be dependent on the specimen preparation procedure. Finally, Payan et al. (2016) [37, 38] observed that the published formulae cannot accurately relate the shear modulus under small strain with the void ratio and confining pressure, probably because the particle shape was not taken into account. Based on critical-state theories, they propose a new expression, including the effect of grading curves and particle shapes. Taking into account the background information presented above, the objective of this investigation is an in-depth study of the influence of the relative density, effective consolidation pressure and torsional excitation values on the shear modulus of a saturated granular sand and to develop simple empirical functions to correlate these parameters. 2 MATERIAL USED The tests were performed on 20-40 Ottawa sand (maximum, minimum and average particle sizes are 0.85, 0.43 and 0.64 mm, respectively). It is a standard material employed in many other investigations into the behaviour of granular soil. Its main characteristics are: very hard, uniform particles (the coefficient of uniformity turned out to be Cu = 1.35), fine and rounded grains and nearly pure quartz in composition. The index properties of particles passing mesh 20 and retained in mesh 40 are as follows: specific gravity Gs = 2.669, maximum void ratio emax= 0.754, and minimum void ratio emin = 0.554. The initial properties of the specimens tested are presented in Table 1. Table 1. Properties of specimens tested. Relative density, Dr, % Height, H, mm Diameter, D, mm Mass, g Dry density Pd, g/cm3 Void ratio, e 20 105 49.5 314.59 1.557 0.714 40 105 49.5 322.13 1.594 0.674 60 105 49.5 330.05 1.633 0.634 80 105 49.5 338.36 1.675 0.594 2.2 Description of the equipment used The resonant-column apparatus consists of a forced oscillation system with a single torsional degree of freedom that makes the specimen vibrate within a range of frequencies in which its first natural mode can be found. In this particular investigation, the specimen remained fixed at its base and was free to vibrate at its upper end. Testing was performed with the resonant-column device manufactured by Wykeham Farrance, Fig. 1. The frequency of the resonant-column tests is higher than 10 Hz, while in cyclic torsional shear mode the equipment typically operates at frequencies below 2 Hz. In this research, the frequency range was between 74 Hz and 140 Hz. This instrumented and automated equipment provides a series of advantages, among which mention can be made of the following. It combines resonant-column and simple torsional shear functions. It determines automatically the resonant frequency, the shear-wave velocity, the shear modulus, the angular strain and the damping ratio, this latter parameter by using the Half-Power 34. Acta Geotechnica Slovenica, 2017/2 H. Patino et al.: Shear modulus of a saturated granular soil derived from resonant-column tests Figure 1. Resonant-column apparatus manufactured by Wykeham Farrance. method or the Free Vibration Decay method. There is no need to externally use either an oscilloscope or a function generator. The internal floating structure for the excitation system allows the execution of tests in which the specimens can experience large axial deformations during consolidation. It makes it possible to visualize, in real time, the response of the sensors during the test. The equipment is basically constituted by two polycarbonate hollow cylindrical cells allowing, by means of the internal cell, the application of the consolidation pressure to the specimen through a fluid, without the electronic components being submerged, and - through the external cell - the application to the fluid of a confining pressure provided by a pneumatically operated system; a lower base through which the back pressure is applied and drainage of the specimen is allowed during the consolidation stage; a corrugated head piece with no possibility of drainage, to transmit the torsional forces to the specimen; a driving mechanism constituted by eight coils and four magnets to apply the torsional load to the specimen; an accelerometer attached to the mechanism to generate the torsional action and to provide the information necessary to calculate the shear-wave propagation velocity (Vs); an LVDT to measure axial deformations (with a stroke of +/- 12.5 mm and an accuracy of 0.2%), two proximity transducers to measure angular deformations in case the data supplied by the accelerometer is not used to calculate them; three pressure transducers to measure the chamber pressure (ctc), the back pressure (Bp) and the pore water pressure (u); a transducer to register volume changes during the consolidation stage; a compact unit fitted with a power source, a manual pressure regulator, two electric pressure regulators, eight electronic components for signal conditioning and a control and data-acquisition module; and a computer for equipment control and data acquisition. 3 THEORETICAL BACKGROUND_ According to the theory of torsional vibrations in a cylindrical rod, expression (1) relates the shear-wave propagation velocity (vs) to the shear modulus (G) and to the unit mass density (p). vs=M (i) \p Expression (2), obtained by Hardin (1965) [13], calculates the shear-wave propagation velocity (vs) as a function of the resonant frequency (Fr), the polar moment of inertia of the excitation mechanism about its symmetry axis (Io), the polar moment of inertia of the specimen about its symmetry axis (I) and the height of the sample (h). „ „ I , „ 2^-R h , x P ■ tan/? = —; where ft =-r— (2) I0 Vs Implicit equation (2) can be represented graphically as a function of ft, as depicted in Fig. 2. Figure 2. Graphical representation of the implicit equation (2). Equation (3) is obtained from (1) and (2). G = fi2 F; (3) For this particular equipment the height of the specimen and the polar moment of the excitation mechanism are fixed constants. Their values are: h = 10.5 cm Io = 13.1kg ■ cm2. Io was obtained by calibration with two rods of the same dimensions and made up of different materials and turned out to be independent of the rod's stiffness. However, Clayton et al. (2009) [11] found that, in their equipment, Io was dependent on the rod's stiffness. Our Io value lies outside the range reported by them (2.99 to 4.32 kg-cm2) and it seems as though low values of Io will depend on the rod's stiffness, while high Io values will not. The specimen diameter is D = 4.95 cm. 34. Acta Geotechnica Slovenica, 2017/2 H. Patino et al.: Shear modulus of a saturated granular soil derived from resonant-column tests The densities of the samples used for this experiment range from psat(min)=1.974 gr/cm3 to psflt(max)=2.048 gr/cm3 or psat= 2.011 ± 0.037 gr/cm3 For the central value, psat = 2 gr/cm3, the value of the polar moment of inertia of the specimen is: 1= -L7rD4hp= 1.24 kg • cm2 (4) The corresponding value of ¡5; obtained from equation (2) p-tgfi= 0.0946 is /3 = 0303 rd (/?= 17.4°) The shear-wave velocity can be obtained from the resonant frequency, Fr, measured during the test Vs= 2^Fr-h = 21gFr m (FrenHz) (5) P s and the corresponding value of the shear modulus G = vs2 ■ p = 9.51 Fr2 kN/m2 (Fr en Hz). 3.1 Experimental program This investigation was aimed at determining the effect of the relative density, the effective consolidation pressure and the magnitude of the torsional excitation on the shear modulus. A total of 120 determinations of the resonant frequency for saturated specimens were made in specimens measuring 49.5 millimetres in diameter and 105 millimetres in height. They all had a height-to-diameter ratio equal to 2.12, thus eliminating the uncertainty related to the slenderness of the specimens; the ratio specimen diameter to particle diameter was of about 120, therefore eliminating the scale effect. The total number of tests is a result of the combination of relative densities equal to 20, 40, 60 and 80%, effective consolidation pressures equal to 50, 100, 150, 200, 250 and 300 kPa and amplitudes of sinusoidal waves equal to 0.025, 0.05, 0.1, 0.2 and 0.4 volts. The frequency varied between 74 Hz and 140 Hz, which corresponds to angular deformations between 0.002% and 0.023%. The backpressure was equal to 400 kPa for all the tests. 3.2 Preparation and setting of specimens The accessories depicted in Fig. 3 that are necessary for making specimens with the sedimentation method were used to carry out the tests reported herein. 34. Acta Geotechnica Slovenica, 2017/2 Figure 3. Basic elements for the specimen preparation: 1) lifting device of the three-part mould; 2) fixed lower base; 3) porous stone; 4) three-part split mould; 5) latex membrane; 6) O-Ring; 7) O-Ring stretcher; 8) extension of three-part mould; 9) 500-cm3 beaker with de-aired water; and 10) loading head. The sample-preparation procedure was similar to other laboratory tests using sand. The need to reproduce specimens complying with a certain relative density led to a setting process that was very careful and repetitive. 3.3 Effect of the sample density on the ratio Fr The value of the ratio between the shear modulus and the square of the resonant frequency, G/F2, turns out to be only slightly affected by the sample density. In fact, the theoretical value of that ratio is: (6) F; P' When the density, p, increases, the value of p also increases and the result is that the value of R is almost unchanged. In fact, taking the derivative of R with respect to p, we obtain: dR=R_2R_d/? ^ dp p p dp From equation (2), and taking the previously indicated value of I, we obtain: „■tg/^^-p (8) Differentiating with respect to p gives: dP dp to obtain: f r, \ tg cos2 J6 P^P (9) H. Patino et al.: Shear modulus of a saturated granular soil derived from resonant-column tests M = 1. dp p 1 + a being a = —^^ sen 2/3 (10) and, with the help of equation (7) dR = dp(a-f R p va+1 With a > 1, any increase in the density always produces an increase in the value of R. (11) For the particular case of psat = 2 gr/cm3 equations (10) and (11) are: a = = 1.064 and dR= 0.032 ^. sen 20 R p The amplitude of the range of densities for this experimental program is 0 037 = 0 019 and, as a P 2 zlR consequence, the relative variation of R is = 0.00061. Thus, the rationale for normalizing G with respect to Fr2 is that, for practical purposes and for the density range of the samples tested in this investigation, the ratio G/Fr2 can be considered to be a constant that depends on the equipment characteristics, but it does not depend on the density of the sample being tested. 4 RESULTS_ The results of the 120 determinations of the resonant frequency, the angular strains measured and the values of the shear modulus G thus obtained are presented in tables 2 and 3. Table 2. Results corresponding to relative densities equal to 20 and 40%. Table 3. Results corresponding to relative densities equal to 60 and 80%. o'c T e Dr = 20% Dr = 40% Fr G Y Fr G Y kPa V Hz MPa % Hz MPa % 50 0.025 85.5 69.2 0.004 86.6 72.2 0.005 50 0.05 84.4 67.5 0.006 85.7 70.6 0.007 50 0.1 82.6 64.6 0.009 84.1 68.1 0.011 50 0.2 80.1 60.8 0.014 82.0 64.7 0.017 50 0.4 74.7 52.8 0.019 77.2 57.4 0.023 100 0.025 105.0 104.0 0.002 107.0 110.0 0.005 100 0.05 104.0 102.0 0.004 106.0 107.0 0.007 100 0.1 102.0 98.1 0.008 106.0 107.0 0.011 100 0.2 99.7 94.1 0.014 103.0 101.0 0.016 100 0.4 95.0 85.5 0.022 99.0 94.0 0.023 150 0.025 116.0 128.0 0.003 119.0 135.0 0.004 150 0.05 115.0 126.0 0.005 118.0 132.0 0.007 150 0.1 113.0 122.0 0.009 117.0 131.0 0.010 150 0.2 111.0 117.0 0.014 115.0 126.0 0.015 150 0.4 107.0 108.0 0.022 111.0 117.0 0.022 200 0.025 125.0 147.0 0.003 128.0 155.0 0.004 200 0.05 123.0 144.0 0.005 126.0 152.0 0.006 200 0.1 122.0 142.0 0.009 126.0 151.0 0.010 200 0.2 120.0 137.0 0.014 123.0 145.0 0.015 200 0.4 117.0 129.0 0.020 120.0 137.0 0.020 250 0.025 131.0 163.0 0.003 135.0 172.0 0.004 250 0.05 130.0 160.0 0.005 134.0 170.0 0.006 250 0.1 128.0 156.0 0.009 133.0 168.0 0.009 250 0.2 127.0 153.0 0.014 131.0 162.0 0.014 250 0.4 123.0 143.0 0.019 127.0 154.0 0.017 300 0.025 137.0 178.0 0.003 141.0 188.0 0.003 300 0.05 136.0 175.0 0.005 140.0 185.0 0.005 300 0.1 135.0 174.0 0.009 139.0 183.0 0.009 300 0.2 133.0 167.0 0.014 137.0 178.0 0.014 300 0.4 129.0 158.0 0.017 134.0 171.0 0.016 Fr G Y Fr G Y kPa V Hz MPa % Hz MPa % 50 0.025 87.4 73.4 0.005 88.8 74.7 0.003 50 0.05 84.9 69.3 0.007 87.7 72.8 0.006 50 0.1 84.1 68.1 0.010 86.6 71.1 0.009 50 0.2 80.9 63.0 0.015 83.4 66.0 0.014 50 0.4 77.7 58.0 0.022 79.0 59.2 0.020 100 0.025 104.0 104.0 0.004 109.0 113.0 0.004 100 0.05 104.0 103.0 0.007 108.0 111.0 0.006 100 0.1 103.0 101.0 0.011 107.0 108.0 0.009 100 0.2 100.0 96.3 0.016 104.0 103.0 0.014 100 0.4 96.4 88.8 0.023 100.0 94.9 0.021 150 0.025 117.0 131.0 0.004 121.0 140.0 0.004 150 0.05 117.0 129.0 0.007 120.0 136.0 0.006 150 0.1 116.0 127.0 0.010 118.0 132.0 0.009 150 0.2 114.0 123.0 0.015 117.0 130.0 0.014 150 0.4 110.0 115.0 0.022 113.0 120.0 0.021 200 0.025 126.0 152.0 0.004 131.0 163.0 0.003 200 0.05 126.0 150.0 0.006 130.0 159.0 0.006 200 0.1 125.0 148.0 0.010 128.0 155.0 0.009 200 0.2 123.0 144.0 0.015 127.0 153.0 0.013 200 0.4 120.0 136.0 0.020 123.0 144.0 0.019 250 0.025 134.0 170.0 0.004 138.0 181.0 0.003 250 0.05 133.0 168.0 0.006 137.0 179.0 0.005 250 0.1 131.0 163.0 0.009 136.0 174.0 0.009 250 0.2 130.0 161.0 0.014 134.0 171.0 0.013 250 0.4 126.0 151.0 0.018 131.0 163.0 0.017 300 0.025 140.0 187.0 0.003 145.0 198.0 0.003 300 0.05 139.0 184.0 0.006 143.0 195.0 0.005 300 0.1 138.0 180.0 0.009 142.0 191.0 0.008 300 0.2 137.0 177.0 0.014 141.0 188.0 0.013 300 0.4 133.0 167.0 0.016 136.0 175.0 0.015 Dr = 60% Dr = 80% T e 34. Acta Geotechnica Slovenica, 2017/2 H. Patino et al.: Shear modulus of a saturated granular soil derived from resonant-column tests Although the void ratio or the sample density is little modified under the static conditions of consolidation, at low pressures, this effect was taken into account in this research. In fact, the software implemented in the equipment evaluates the G-module from the conditions of the specimens at the end of the consolidation phase and obviously using equation (3). The results obtained make it possible to evaluate the effect of factors such as angular strain, effective consolidation pressure and relative density in the determination of the shear modulus through the execution of the resonant-column test. 4.1 Shear modulus versus angular strain In general, the angular strain experienced by the material increases as the level of torsional excitation increases. Fig. 4 shows this fact; however, only the results corresponding to Dr = 20% are included herein. The shear strain in Fig. 4 and 5 is the average shear strain (ym), obtained as 2*ymax/3, where ymax is the maximum shear strain measured by the accelerometer. .0«77Vr. -«« ■ own » ioo With these considerations, the following degradation equation can be proposed: G = G0(1-A-^Z) (15) where A = dimensionless constant that would mainly depend on the shear strength of the tested sand, Tf. The value of y,.ej would then be given by the following expression: *>-<& <16) Furthermore, it is known that G0 increases with the square root of a'c and, as a consequence, a value of yref increasing with the square root of a'c should be expected. For this reason, a value of y,eycan be found to reasonably fit the data with an expression involving (< r -15.2 -15.1 S 0) CO -15.0 _3 -14.9 z -14.8 -14.7 -14.6 Sawdust content (%) Figure 6. Variation of the compaction characteristics of the clay with sawdust. 180- 160- 140- =1 120-öi Ü £ loo- I 80- 60- ■ Liquid Limit ■Plastic limit ^Jasticit^ndex 0 2 4 6 8 Sawdust content (%) Figure 5. Variation of Atterberg limits of the bentonite with sawdust. Sawdust content (%) Figure 7. Variation of the compaction characteristics of the bentonite with sawdust. 48. Acta Geotechnica Slovenica, 2017/2 I. I. Akinwumi et al.: Engineering properties of tropical clay and bentonite modified with sawdust treated samples required more water in order to attain the MDUW. This is because some of the water in the sawdust-modified samples gets absorbed by the sawdust. However, the MDUW achieved decreased with increasing sawdust content. This can be attributed to the lower specific gravity of the sawdust. The MDUW are lower and the OMC greater for the modified bentonite. 3.2.4. Strength Characteristics The variation of the unconfined compressive strengths (UCS) of the clay and the bentonite are shown in Fig. 8. The UCS of a soil is a measure of the maximum load it can withstand per unit area, when its lateral confining pressure is zero. The UCS of the treated samples decreased with increasing sawdust content. The sawdust has a low density and compressive strength compared with that of the clay and bentonite. This explains why the UCS of the treated clay and bentonite decreases as their sawdust contents progressively increased. S awdust content (%) Figure 8. Variation of the UCS of the clay and bentonite with sawdust. 3.2.5. Permeability The variation of the permeability of the treated clay and bentonite with their sawdust contents are presented in Fig. 9. The permeability of a soil gives a measure of the ease with which water flows through it. Fig. 9 shows that the higher the sawdust content, the easier it is for the water to flow through the sawdust-treated clay and sawdust-treated bentonite. This is attributed to the increasing pore space in the treated clay and bentonite as their sawdust content increases. The SEM morphology for the natural soil and for the soil admixed with varying percentages of sawdust (Fig. 10) show increasing Sawdust content (%) Figure 9. Variation of the permeability of the clay and benton-ite with sawdust. pore space as the percentage of the sawdust in the clay increases. The pore size of the bentonite also increased as its sawdust content increased (Fig. 11). A typical clay liner material should have a hydraulic conductivity (permeability) less than or equal to 1 x 10-7 cm/s and a strength greater than 200 kN/m2 [31, 32]. The coefficients of permeability of the clay and bentonite are less than 1 x 10-7 cm/s, which is generally specified as the hydraulic conductivity requirement that clays need to satisfy in order to be used as landfill-liner materials. The UCS of the clay and bentonite are greater than 200 kN/m2, indicating that a layer of a lining system using this clay or bentonite can sufficiently support the load from landfilled wastes that may be imposed on it. Also, the modification of the clay with 8% or less sawdust and that of the bentonite with 4% or less sawdust satisfy these permeability and strength requirements. The National Rivers Authority (NRA) [33] stated that a soil to be used as a clay liner should have its liquid limit and plasticity index less than 90% and 65%, respectively, and clay content greater than 10%. The bentonite and its modification with sawdust have their liquid limits greater than 90%. Therefore, this makes the bentonite and its modification with sawdust unstable and unsuitable for use as a landfill liner. 4. CONCLUSIONS The clay and bentonite samples contain silica, alumina and iron III oxide as their predominant oxides. The clay mineral in the clay is kaolinite, whereas that in the bentonite is montmorillonite, which is highly expansive. 48. Acta Geotechnica Slovenica, 2017/2 I. I. Akinwumi et al.: Engineering properties of tropical clay and bentonite modified with sawdust Figure 10. SEM micrograph of the clay with sawdust. 48. Acta Geotechnica Slovenica, 2017/2 I. I. Akinwumi et al.: Engineering properties of tropical clay and bentonite modified with sawdust Figure 11. SEM micrograph of the bentonite with sawdust. 48. Acta Geotechnica Slovenica, 2017/2 I. I. Akinwumi et al.: Engineering properties of tropical clay and bentonite modified with sawdust The clay is of high plasticity, while the bentonite has an extremely high plasticity. The modification of the clay with an increasing percentage of sawdust caused a reduction in its specific gravity, plasticity, MDUW and UCS, while it caused an increase in its OMC and permeability. Consequently, improving the workability of the clay, but reducing its strength. The modification of the bentonite with the sawdust resulted in a reduction in its specific gravity, MDUW and UCS, while it increased its plasticity (slightly), OMC and permeability. The clay and bentonite both have sufficiently low permeability to satisfy the hydraulic conductivity requirement for use as clay liners. The clay and sawdust-modified clay also satisfy the clay content, Atterberg limits and UCS requirements for use as landfill liners, whereas the bentonite and sawdust-modified bentonite did not satisfy the Atterberg limits and UCS requirements (for modification with more than 4% sawdust). An 8% sawdust application to a clay having similar properties as that of this study is recommended for modifying it for use in a landfill-liner system. Following Bulut and Tez's [18] recommendation of sawdust as a low-cost adsorbent of heavy metals, the implication of these findings is that modification of a clay (having similar properties as that studied and suitable for use as a landfill liner) with sawdust has the potential of improving the removal of hazardous metals from landfills and protecting groundwater. Also, the use of sawdust -which is usually disposed improperly and thereby constitutes a nuisance to the environment and public health - gives assurance of the sustainable development of people and society. The increase in the permeability of the clay and benton-ite with increasing sawdust content indicate that when soil drainage is important to a construction project, sawdust can be used to improve the drainage capacity of clays of very high plasticity by the addition of an appropriate proportion that will not compromise the stability of the layer of earthworks. Sand may be added to the mixture of bentonite and sawdust using a proportion that ensures that the resulting lining system is stable, while the composite satisfies the permeability and strength requirements for use as a landfill liner. Acknowledgments Isaac Akinwumi thanks the Commonwealth Scholarship Commission in the UK for the award of a split-site PhD Scholarship. REFERENCES [1] Aqeel, A. 2016. Investigation of expansive soils in Obhor Sabkha, Jeddah-Saudi Arabia. Arabian Journal of Geosciences 9, 314, 1-14. DOI: 10.1007/ s12517-016-2341-x [2] Wyoming Office of Homeland Security, 2016. 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Acta Geotechnica Slovenica, 2017/2 NOSILNOSTI TEMELJEV NA NEZASIČENIH ZEMLJINAH Ključne besede nezasičene zemljine, nosilnost temeljev na nezasičenih zemljinah, sukcijska trdnost, načrtovanje temeljenja Izvleček Raziskovanje nezasičenih zemljin je zelo pomembno, še vedno pa je treba raziskati številne tehnične vidike takšnih zemljin. F prispevku je predlagana nova tehnika, ki napoveduje spreminjanje nosilnosti nezasičenih zemljin z matrično sukcijo. Predlagana metoda je razširitev konven-cionalnih teorij nosilnosti in konceptualno temelji na logaritemskem modelu strižne trdnosti nezasičenih zemljin, ki vključujejo le en neznan nezasičen parameter (vstopno vrednost zraka, AEV). Možnost napovedi nosilnosti nezasičenih zemljin kažejo efektivni parametri zasičene strižne trdnosti c 'in 0' in AEV iz retencijske krivulje zemljina--voda (SWRC). Glede na to, da je potrebno nove metode potrditi s podatki drugih raziskovalcev, se je predlagana enačba preizkusila s pomočjo avtorjeve objavljene eksperimentalne študije nezasičenih zemljin ter nekaterih poročanih eksperimentalnih študij o strižni trdnosti za nezasičene zemljine in modelne obremenitve temeljev na nezasičenem pesku pod nadzorovanimi sukcijskimi pogoji. Rezultati študije kažejo, da obstaja dobra primerjava med "nezasičenimi nosilnostmi", dobljenimi s predvidenimi in izmerjenimi nezasičenimi parametri trdnosti (ctotal, 0), pa tudi med izmerjenimi/izračunanimi vrednostmi nosilnosti modela obremenjenega temeljenja. Izkazalo se je, da za to ni potrebe po kompleksnih nezasičenih preskusnih napravah, ter da se lahko s pomočjo predlagane enačbe napove nosilnost nezasičenih drobnozrnatih in peščenih zemljin, za katere potrebujemo samo en nezasičen parameter, ki ga je mogoče pridobiti iz SWRC ali predvideti z uporabo osnovnih indeksnih lastnosti zemljin. Taha Taskiran Dicle University, Faculty of Engineering, Department of Civil Engineering 21280, Diyarbakir, Turčija E-pošta: taha@dicle.edu.tr E-pošta: tahtaskiran@gmail.com 18. Acta Geotechnica Slovenica, 2017/2 AN UNSATURATED-SOILS APPROACH TO THE BEARING CAPACITY OF FOUNDATION STRUCTURES Keywords unsaturated soils, unsaturated bearing capacity, suction strength, foundation design Abstract Unsaturated soils are maintaining their importance for researchers and there is still much need to investigate the many engineering aspects of these soils. A new technique is proposed here to predict the variation of the bearing capacity of unsaturated soils with matric suction. The proposed method is an extension of conventional bearing-capacity theories and conceptually based on the logarithmic model of the shear strength of unsaturated soils, which only include one unknown, unsaturated parameter (the air-entry value, AEV). The possibility of predicting the unsaturated bearing capacity of soils is shown by the saturated effective shear-strength parameters c and 0' and the AEV from the soil-water retention curve (SWRC). Considering the necessity of validating new methods with other researchers' data, the proposed equation is tested using the published unsaturated experimental study by the author, in addition to some reported experimental studies on the shear strength for unsaturated soils and also a model footing loading on unsaturated sand under controlled suction conditions. The results of the study indicate that there is a good comparison between the "unsaturated bearing capacities" obtained via predicted and measured unsaturated strength parameters (ctotal , 0) and also between the measured/calculated bearing values of a model footing loading. Consequently, it is shown that, without needing complex unsaturated testing facilities, the proposed equation is capable of predicting the unsaturated bearing capacity for both fine-grained and sandy soils, requiring only one unsaturated parameter, which can be obtained from the SWRC or predicted using the basic soil-index properties. Taha Taskiran Dicle University, Faculty of Engineering, Department of Civil Engineering 21280, Diyarbakir, Turkey E-mail: taha@dicle.edu.tr E-mail: tahtaskiran@gmail.com 1 INTRODUCTION One of the important engineering properties required for the design of shallow foundations is the bearing capacity. Several approaches are available in the literature for a determination of the bearing capacity of soils based on the saturated shear-strength parameters ([1], [2]). However, in some situations, shallow foundations are located above the ground-water table where the soil is under capillary tension and thus in a state of unsaturated condition. Besides, many kinds of natural soils, such as desiccated silts and clays, transported soils, residual soils and artificial compacted soils, are found in the unsaturated condition where uw<0. Nevertheless, the bearing capacities of soils are often determined by assuming fully saturated conditions, ignoring the influence of the capillary stresses or the matric suction. Therefore, a bearing-capacity estimation of the shallow foundations using conventional approaches may not be reliable, leading to uneconomic designs. 18. Acta Geotechnica Slovenica, 2017/2 T. Taskiran: An unsaturated-soils approach to the bearing capacity of foundation structures Several researchers performed investigations on the bearing capacity of unsaturated soils ([3], [4], [5], [6], [7]) All these studies have shown that there is a significant contribution of the matric suction to the bearing capacity of unsaturated soils. However, limited theoretical research work is reported in the literature with respect to the interpretation of the bearing capacity of unsaturated soils ([3], [8]). In this study, a semi-empirical equation is proposed to predict the variation of the bearing capacity of unsatu-rated soils with matric suction, using the saturated shear-strength parameters c' and 0' and the air-entry value. The equation presented in this paper is developed by extending the concepts for predicting the shear strength of unsaturated soils proposed by Kayadelen et al. [9]. The equation proposed here is exercised for other studies reported in the literature that include a variation of the cohesion with the matric suction for fine-grained soils and also a sand-box model footing bearing capacity test results of unsaturated coarse-grained soils. In the content of this study, benefiting from the previously reported, unsaturated test results, unsaturated bearing capacities for a typical square footing (B=L=1m) were calculated based on unsaturated, experimental soil properties and ones obtained with the theoretical equation proposed here and a comparison was made between the bearing capacities. The studies presented in this paper show that there is a good comparison between the bearing capacities of an example square footing via theoretically and experimentally obtained soil parameters. 2 REVIEW OF THE BEARING CAPACITY OF UNSATURATED SOILS_ Meyerhof [2] proposed an equation for predicting the bearing capacity of shallow strip footings for the soil failure mechanism. This equation is valid for strip footings resting in a homogenous soil and subjected to a vertical loading. qu = c'Ncec + qNq£q + O.SByNy&y (1) where: qu = ultimate bearing capacity, kPa q = overburden pressure, kPa c' = effective cohesion, kPa £c , £q , £y = shape factors due to cohesion, overburden and unit weight Nc , Nq , Ny = bearing capacity factors due to cohesion, surcharge and unit weight, respectively Y = soil unit weight, kN/m3 B = footing width, m As in the case of saturated soil, the bearing capacity of unsaturated soils is similarly calculated using two different methods, which are the 'effective stress approach' (ESA) and the 'total stress approach' (TSA). Oloo [4] proposed a method to predict the bearing capacity of surface footing on unsaturated fine-grained soils as extending the effective stress approach (ESA) as follows: Qult(unsat) = {c' + (ua - uw)b tan 0' + [((ua - uw) -(ua-uw)b]tan0b}Nc + O,5ByNY (2) where; (ua - uw)b = Air - entry value of soil (ua - uw) = Matric suction Due to the limitations that the bearing capacity varies linearly and decreases beyond the residual water content for the coarse-grained soils, and converges to a certain value for fine-grained soils, which is not the general behaviour for the equation proposed by Oloo [4], Vana-palli and Mohammed [6] proposed a relationship that contains a nonlinear variation of the bearing capacity of unsaturated soils with respect to the matric suction for surface footings extending the ESA approach. The term S9 tan0' considers the non-linear variation of the shear strength of unsaturated soils using a fitting parameter, 9. Equation (3) can be used to predict the bearing capacity of unsaturated soils that desaturate on the application of a matric suction. qu = [c' + (ua - uw)b(l - S* tan 0') + (ua - uw)avrS

1500 $ 1000 m 500 0 quit ( Eqn 9 with measured parameters) quit (Eqn 9 with calculated parameters) 50 100 200 300 400 Soil suction (kPa) 2500 2000 £ 1500 o CO CO O O) C CO CD m 1000 500 quit ( Eqn 9 with measured parameters) quit ( Eqn 9 with calculated parameters) 50 80 120 Soil suction (kPa) 200 140 120 —100 CO CL ^ 80 c 1 60 .c o o 40 20 0 Measured cohesion, Gan et. al 1988 Calculated cohesion with Eqn 8 50 100 200 300 Soil suction (kPa) 400 100 90 80 ■ 70 . 60 50 c o V) £ 40 30 20 10 0 Measured cohesion, Mlao et al. 2302 Calculated cohesion with Eqn 8 50 80 120 Soil suction (kPa) 200 Figure 3. Comparison of calculated bearing capacities and total cohesions with measured values. Figure 4. Comparison of calculated bearing capacities and total cohesions with measured values. 0 0 0 0 0 60. Acta Geotechnica Slovenica, 2017/2 T. Taskiran: An unsaturated-soils approach to the bearing capacity of foundation structures Table 5. Comparison of calculated and measured bearing capacities and total cohesions. Residuel clay (kPa) 0 50 100 200 400 Measured cohesion(ctotal) 14.82 35.24 46.72 69.56 98.32 Calculated cohesion ctotal () 14.82 37.6 52.65 74.86 102.91 qult (bearing capacity, Eqn 9, with measured parameters by Kayadelen et. al. 2007) 403,69 896 1173 1724 2417 qult (bearing capacity calculated by Eqn 9) 403,69 953 1316 1852 2528 Nanyang expansive soil prepared with predetermined water contents using the static compaction effort. The unsaturated tests are performed by controlling the suction in us = (ua - uw), = 50, 80, 120 and 200 kPa using unsaturated tri-axial apparatus. The cohesion calculated by Eqn. (8), bearing capacities results using measured / calculated unsaturated parameters (ctotal , 0'), by Eqn. 9 are presented in Table 4 and Fig. 4, respectively. The series of laboratory tests were performed by author (Kayadelen et. al. [9], author in)) using a tri-axial shear test on saturated/unsaturated residual clayey soil, including high contents of semectite and chlorite minerals. The tests were conducted on the undisturbed soil specimens under consolidated and drained conditions. A total of 12 unsaturated tests were performed and axis translation technique, as described by Fredlund and Rahardjo [7], was applied to the specimens. The air-entry value was also calculated by the method proposed by Aubertin et al [20] using %10 and % 60 passing in the grain size distribution chart and the liquid limit. The air-entry value was calculated as 40 kPa, the same as the air-entry value obtained from the experimental SWCC. The shear strength tests were performed on both saturated and unsaturated soil specimens, which have varying matric suctions ranging from 50 to 400 kPa. The measured cohesion and calculated values with Eqn. (8), bearing capacities results, using measured/calculated unsaturated parameters (ctotal , 0'), by Eqn. (9 were presented in Table 5 and in Fig. 5, respectively.) Vanapalli and Fathi [6] performed a number of bearing-capacity tests by means of 100 mm x 100 mm square model footing in test tank by imposing matric suction to compacted coarse-grained soil in the range 0 to 6 kPa. By adjusting the water table level in the test tank, fully saturated and unsaturated conditions of the compacted sand in the test tank were achieved. In the testing program, they measured the bearing capacity of the model footing for 0, 2, 4 and 6 kPa imposed suctions of the foundation soil. They found that a considerable increase in the bearing capacity observed due to the contribution of matric suction for unsaturated condition. 120 100 £ 80 c o I ■ •*.. . -h '* VS4: 500nrnfi 0 0 33 0.66 1 Disc-rod Index. (L-iy(L-S) .. iSpbtçpsl. :. ^¿eçSQic?:-;. " > r f . S4 500)im< D<630)im 0 0.33 0 66 1 Dlsc-rod index. (L-IV(L-S) 0 0 33 0 66 1 Dlsc-rod Index. (L-iy(L-S) (e) N=281 i Spheres : p9mpac< • .. v j ' 7 Discs Blades . Rods Extreme » VS6 1mm 35 c _ P i-:: _Q D « » i ■ o D B 25 - £ 0 5 ■n W 3 £ 04 ^ tJ o £ 20 5 15 T3 m 10 a) * 5 0 cc 03 1 2 01 0 ■50kPa • 10C* Pa »200kPa 02 04 06 0 Mean grain size. D 6 1 12 50 (mm) 02 04 06 08 1 1 Mean grain size, D^tmm) (a) Relationship between shear properties and D50 1 09 08 or > 0 6 (O ¡8 0 4 S 0 3 0.2 0.1 9 3 n O o O 0 44 0 46 0 48 0 5 0 5? Sphericity, SPH 0 54 45 40 -6- a> 35 C7> C 30 CO c o 25 o 20 w "co 15 3 10 73 trt a> "> ir 0 ■ SOkPa • 100kPa a 200kPa 0 44 0 46 0 48 0 5 0.52 Sphericity, SPH 054 (b) Relationship between shear properties and sphericity (SPH) Figure 10. Relationship between shear properties and particle characteristics (D50, SPH) at various normal stress for medium dense samples. 78. Acta Geotechnica Slovenica, 2017/2 P. H. H. Giang et al.: Effects of particle characteristics on the shear strength of calcareous sand 80%) are shown in Figure 9a. As expected, an increase in the initial relative density and normal stress leads to an increase in the peak shear stress determined for both sands. In Table 2, the SMol sand has higher shear strengths and friction angles at the peak and residual states than Mol sand. Under constant normal stress, the difference in residual stresses between the samples at 40% and 80% of the initial relative density for Mol sand is less than that in SMol sand. These results indicate that the initial relative densities of the samples have an influence on the shear strength and friction angle at the residual state (y = 10%), which is significant for calcareous sand. From the literature, the critical state is found to be independent of the initial relative density, suggesting that to reach a critical state in each test, the tests should be performed to a higher shear strain (e. g, Y = 15% or 20%). Figure 9a further shows that dilation is observed in most of the tests at the end of shearing. The dense samples are found to have a higher dilation than the medium dense samples. Figure 9a strongly indicates that during shearing the volume change response of the samples in both sands is dependent on the normal stress. The greater the loading, the lower the dilation. In addition, Table 2 shows that at similar initial relative densities, the SMol samples with higher void ratios are compressed easily, leading to having smaller dilation angles in comparison with the Mol samples. The maximum dilation angle (■ymax) ranges from 2.3° to 11.2° for the calcareous sand and 4.8° to 13.9° for the silica sand. Interestingly, although the peak and residual strengths of the SMol samples are higher than those of the Mol samples, the Mol samples reach higher stresses than the SMol samples at small shear strains in the early state of shearing. This trend can be seen clearly in the dense samples (Dr = 80%). It is suggested that the various grain morphologies in the samples leading to greater particle interlocking and an increase in the number of inter-particle contacts causes the increase in shear strength properties for SMol sand, especially during the dilation process. 3.2.2 Effect of mean grain size D50 on the shear strength properties The variation of the shear strength properties with the grain size for calcareous sand is shown in Figure 9b. In all the samples, the shear stress increases and reaches a residual state at y = 10% without any indication of the peak. As expected, the vertical displacement is found to increase with increasing normal stress for all the samples. For each particle size, the results also show an increase in the residual friction angle at a higher normal stress, as summarized in Table 2. In Figure 9b, it is clear that the sample with larger particles having less SPH and stronger interlocking causes higher shear strength. In addition, the contractive and dilative behaviors of the samples are significantly dependent on normal stress. Although the shear stress reaches a residual state without any indication of the peak, the dilation occurs for the sample with larger particles under low normal stress. Under the normal stress of 50kPa, the sample with larger particles shows much more dilation phase than the sample with smaller particles, indicating that the dilation angle increases with increasing particle size under low load. However, this trend starts to divert under the higher normal stress of 100kPa, and finally, the completely opposite tendency is observed under 200kPa, where the sample of larger particles shows more contraction. This phenomenon is caused by the difference in particle movement, dependent on the particle size, and is explained as follows. Under a low normal stress, the sample with larger particles having greater particle hardness, greater particle angularity (or less particle SPH) and the uniformity of particle size in the sample can provide an interaction between the particles where the contact points of the particle edges (roughness) are strong enough to restrain the particle movement. However, under a higher load, the particle movement increases owing to the contributions of higher void ratio and particle polishing. In short, the volume change of the samples is dependent on the normal stress and the compression or dilation increases with the increase in particle size. Further, the relationship between shear strength properties and particle size is demonstrated in Figure 10a. It is observed that the shear strength and friction angle at residual state increase as the particle size increases for various normal stresses. 3.2.3 Correlations between shear strength properties and sphericity Using Eq. 1, the SPHs interpolated for other uniform particle sizes are calculated and listed in Table 3. Table 3. Particle characteristics of the tested sands. Sand Sieve size (mm) D50 (mm) Sphericity, SPH S2 0.16-0.25 0.205 0.532 S3 0.315-0.5 0.408 0.517 S4 0.5-0.63 0.565 0.506 S5 0.63-1 0.815 0.485 S6 1-1.25 1.135 0.461 78. Acta Geotechnica Slovenica, 2017/2 P. H. H. Giang et al.: Effects of particle characteristics on the shear strength of calcareous sand The correlations between the shear strength properties and particle shape corresponding to the effect of D50 are proposed for the calcareous sand under the various normal stresses (50, 100 and 200 kPa) shown in Figure 10b. The results show that the residual shear strength and friction angle decrease with an increasing SPH. Also, in Figure 10b the best-fit lines of the SPH and friction angle are proposed. The distance between the lines becomes smaller at higher normal stresses (100 and 200 kPa). It can be suggested that the correlations converge to a straight line under high normal stress. 4 CONCLUSIONS The 3DA on the particles of the calcareous and silica sands is studied based on the data collected using X-ray CT. The particles of calcareous sand are found to show smaller sphericity (SPH) than those of silica and crushed calcareous sands. For calcareous sand, the particle shapes in descending order are blades, rods, discs and spheres; whereas silica sand contains more spheres and blades compared to rods and discs. These findings are consistent with the results obtained from the experiments of the maximum and minimum void ratios of the tested sands. It is proved that the SPH increases with decreasing grain size. However, in each sample, the smaller particles have lower SPH than the larger particles. Further, the 3DA gives smaller particle sizes than the sieve analysis (SA). Particle shape is found to be the main factor affecting the SA results. This is due to particle interlocking caused by various particle shapes, especially for the calcareous sand. In this study, the correlations between the 3D particle shape and the size (D50) are established. From the direct shear drained test results, the main conclusions can be drawn as follows: - At the same Cu, the behavior of calcareous and silica sands are quite different. Although the calcareous sand with particles has more angularity and less SPH is formed at a higher void ratio, it gives higher peak and residual shear strength properties and tends to reach a lower shear strength at a small shear strain and a lower dilation than the silica sand. This tendency is seen clearly in the dense sample. The variety of particle shapes increases with the particle interlocking and the number of inter-particle contacts and causes increasing shear strength properties, especially during the dilation process. - For calcareous sand, the increase in the particle size D50 leads to the growth in shear strength properties in the residual state. The compression and dilation curves of the calcareous sands are affected strongly by the normal stress. The range of compression and dilation phases increases with increasing particle size. The sample with larger particles, showing less particle movement for re-arrangement under low stress, causes more dilation, whereas the sample with smaller particles giving less particle movement under high stress shows less compression. - The critical state may not be reached in this study. This supposes that the ultimate state for calcareous sand can be indicated at higher shear strain than silica sand. REFERENCES [1] Hassanlourad, M., Rasouli, M.R., Salehzadeh, H. 2014. A comparison between the undrained shear behavior of carbonate and quartz sands. Int. J. Civ. Eng. 12, 4, 338-350. [2] Safinus, S., Hossain, M.S., Randolph, M.F. 2013. Comparison of stress-strain behaviour of carbonate and silicate sediments. Proc. 18th Int. Conf. on Soil Mechanics and Geotechnical Engineering, pp. 267-270. [3] Brandes, H.G. 2011. Simple shear behavior of calcareous and quartz sands. Geotech. Geol. Eng. 29, 1, 113-126. DOI: 10.1007/s10706-010-9357-x [4] Cho, G.C., Dodds, J., Santamarina, J.C. 2006. 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Three-dimensional analysis of high-resolution X-ray computed tomography data 78. Acta Geotechnica Slovenica, 2017/2 P. H. H. Giang et al.: Effects of particle characteristics on the shear strength of calcareous sand with Morpho+. Microscopy and Microanalysis 17, 2, 252-63. DOI: 10.1017/S1431927610094389 [34] JIS A 1224. 2009. Test method for minimum and maximum densities of sands. Japanese Geotechnical Society, Soil Testing Standards, Tokyo, pp.136138. 78. Acta Geotechnica Slovenica, 2017/2 NAVODILA AVTORJEM NAVODILA AVTORJEM Vsebina članka Članek naj bo napisan v naslednji obliki: - Naslov, ki primerno opisuje vsebino članka in ne presega 80 znakov. - Izvleček, ki naj bo skrajšana oblika članka in naj ne presega 250 besed. Izvleček mora vsebovati osnove, jedro in cilje raziskave, uporabljeno metodologijo dela, povzetek izidov in osnovne sklepe. - Največ 6 ključnih besed, ki bi morale biti napisane takoj po izvlečku. - Uvod, v katerem naj bo pregled novejšega stanja in zadostne informacije za razumevanje ter pregled izidov dela, predstavljenih v članku. - 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 več 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 oštevilčene. - Predložen članek ne sme imeti več kot 18 strani (brez tabel, legend in literature); velikost črk 12, dvojni razmik med vrsticami. V članek je lahko vključenih največ 10 slik. Isti rezultati so lahko prikazani v tabelah ali na slikah, ne pa na oba načina. - Potrebno je priložiti imena, naslove in elektronske naslove štirih potencialnih recenzentov članka. Urednik ima izključno pravico do odločitve, ali bo te predloge upošteval. Enote in okrajšave V besedilu, preglednicah in slikah uporabljajte le standardne označbe in okrajšave SI. Simbole fizikalnih veličin v besedilu pišite poševno (npr. v, T itn.). Simbole enot, ki so sestavljene iz črk, pa pokončno (npr. Pa, m itn.). Vse okrajšave naj bodo, ko se prvič pojavijo, izpisane v celoti. Slike Slike morajo biti zaporedno oštevilčene in označene, 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 priporočamo CDR format (CorelDraw), saj so slike v njem vektorske in jih lahko pri končni obdelavi preprosto povečujemo ali pomanjšujemo. Pri označevanju osi v diagramih, kadar je le mogoče, uporabite označbe veličin (npr. v, T itn.). V diagramih z več krivuljami mora biti vsaka krivulja označena. Pomen oznake mora biti razložen v podnapisu slike. Za vse slike po fotografskih posnetkih je treba priložiti izvirne fotografije ali kakovostno narejen posnetek. Preglednice Preglednice morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot preglednica 1, preglednica 2 itn. V preglednicah ne uporabljajte izpisanih imen veličin, ampak samo ustrezne simbole. K fizikalnim količinam, npr. t (pisano poševno), pripišite enote (pisano pokončno) v novo vrsto brez oklepajev. Vse opombe naj bodo označene 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 priporočajo v seznamu literature, navedejo pa se lahko v besedilu, če 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 referenčna številka. Primer: ».....kot je razvidno [1,2]. Brandl and Blovsky [4], sta pridobila drugačen rezultat...« V seznamu: Literaturni viri so oštevilčeni po vrstnem redu, kakor se pojavijo v članku. Označimo jih s številkami v oglatih oklepajih. Sklicevanje na objave v revijah: [1] Jelušič, P., Žlender, B. 2013. Soil-nail wall stability analysis using ANFIS. Acta Geotechnica Slovenica 10(1), 61-73. 90. Acta Geotechnica Slovenica, 2017/2 INSTRUCTIONS FOR AUTHORS Sklicevanje na knjigo: [2] Šuklje, L. 1969. Rheological aspects of soil mechanics. Wiley-Interscience, London Sklicevanje na poglavje v monografiji: [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 Rheological Implications, CMS Workshop Lectures, Vol. 4, The 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. Če so poznani drugi podatki (DOI, imena avtorjev, datumi, sklicevanje na izvorno literaturo), se naj prav tako dodajo. INSTRUCTIONS FOR AUTHORS Format of the paper The 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. The 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 after the abstract, provide a maximum of 6 keywords; - An Introduction, which should provide a review of recent literature and sufficient background information to allow the results of the paper to be understood and evaluated; - A Theoretical 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 figures and tables where appropriate; - A Discussion section, which should describe the relationships shown and the generalisations made possible by the results and discuss the significance Podatki o avtorjih Članku priložite tudi podatke o avtorjih: imena, nazive, popolne poštne naslove, številke telefona in faksa, naslove elektronske pošte. Navedite kontaktno osebo. Sprejem člankov in avtorske pravIce Uredništvo si pridržuje pravico do odločanja o sprejemu članka 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@uni-mb.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. - The submitted text of Research Papers should cover no more than 18 pages (without Tables, Legends, and References, style: font size 12, double line spacing). The number of illustrations should not exceed 10. Results may be shown in tables or figures, 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 figures. 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 92. Acta Geotechnica Slovenica, 2017/2 INSTRUCTIONS FOR AUTHORS be in plain text (e.g. Pa, m, etc.). All abbreviations should be spelt out in full on first 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 final 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 figure 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. The 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. The 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 different result ..." List: Number the references (numbers in square brackets) in the list in the order in which they appear in the text. Reference to a journal publication: [1] Jelusic, P., Zlender, B. 2013. Soil-nail wall stability analysis using ANFIS. Acta Geotechnica Slovenica 10(1), 61-73. Reference to a book: [2] Suklje, 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 Rheological Implications, CMS Workshop Lectures, Vol. 4, The 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 The 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 The 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. The 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@uni-mb.si 92. Acta Geotechnica Slovenica, 2017/2 NAMEN REVIJE AIMS AND SCOPE Namen revije ACTA GEOTECHNICA SLOVENICA je objavljanje kakovostnih teoretičnih člankov z novih pomembnih področij geomehanike in geotehnike, ki bodo dolgoročno vplivali na temeljne in praktične vidike teh področij. ACTA GEOTECHNICA SLOVENICA objavlja članke s področij: mehanika zemljin in kamnin, inženirska geologija, okoljska geotehnika, geosintetika, geotehnične konstrukcije, numerične in analitične metode, računalniško modeliranje, optimizacija geotehničnih konstrukcij, terenske in laboratorijske preiskave. 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, field and laboratory testing. Revija redno izhaja dvakrat letno. The journal is published twice a year. AVTORSKE PRAVICE Ko uredništvo prejme članek v objavo, prosi avtorja(je), da prenese(jo) avtorske pravice za članek na izdajatelja, da bi zagotovili kar se da obsežno razširjanje informacij. Naša revija in posamezni prispevki so zaščiteni z avtorskimi pravicami izdajatelja in zanje veljajo naslednji pogoji: Fotokopiranje V skladu z našimi zakoni o zaščiti avtorskih pravic je dovoljeno narediti eno kopijo posameznega članka za osebno uporabo. Za naslednje fotokopije, vključno z večkratnim fotokopiranjem, sistematičnim fotokopiranjem, kopiranjem za reklamne ali predstavitvene namene, nadaljnjo prodajo in vsemi oblikami nedobičk-onosne uporabe je treba pridobiti dovoljenje izdajatelja in plačati določen znesek. Naročniki revije smejo kopirati kazalo z vsebino revije ali pripraviti seznam člankov z izvlečki za rabo v svojih ustanovah. COPYRIGHT Upon acceptance of an article by the Editorial Board, the author(s) will be asked to transfer copyright for the article to the publisher. This transfer will ensure the widest possible dissemination of information. This review and the individual contributions contained in it are protected by publisher's copyright, and the following terms and conditions apply to their use: Photocopying Single photocopies of single articles may be made for personal use, as allowed by national copyright laws. Permission of the publisher and payment of a fee are required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Subscribers may reproduce tables of contents or prepare lists of papers, including abstracts for internal circulation, within their institutions. Elektronsko shranjevanje Za elektronsko shranjevanje vsakršnega gradiva iz revije, vključno z vsemi članki ali deli članka, je potrebno dovoljenje izdajatelja. Electronic Storage Permission of the publisher is required to store electronically any material contained in this review, including any paper or part of the paper. ODGOVORNOST Revija ne prevzame nobene odgovornosti za poškodbe in/ali škodo na osebah in na lastnini na podlagi odgovornosti za izdelke, zaradi malomarnosti ali drugače, ali zaradi uporabe kakršnekoli metode, izdelka, navodil ali zamisli, ki so opisani v njej. RESPONSIBILITY No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of product liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. •L - A* v nt/ / V? - • 4.0. ¿v /S// j>V 9771854017001