University of Maribor Press * # ISSN 1854-0171 //V xST />V SS S s// //s; /// S/S// SSJ ///// * # J* r^ „CT vQ t/ 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. A. Lazar et al. Monitoring of the Belca rockfall k A. Lazar in drugi Monitoring skalnega podora Belca V Vukadin in V. jovičic S_BRICK: Konstitutivni model za zemljine in mehke kamnine V. Vukadin and V. Jovičic S_BRICK: A constitutive model for soils and soft rocks 1. Li in drugi Z. Let al. Obremenilni in razbremenilni preizkus trdnih kamnin in njihov elastoplastični model poškodbe kontakta Loading and unloading test of hard rock and its elastoplastic damage coupling model 3B G. Misir Napovedovanje izvlečne nosilnosti navpičnih sider z dvema ploščama G. Misir Predicting the uplift capacity of vertically located two-plate anchors k. B. S. Olek B. S. Olek 5B Analiza konsolidacije glinastih tal s Consolidation analysis of clayey soils pomočjo analitičnih orodij using analytical tools C. Qiang in drugi Učinki geometrijskih parametrov krožnega plitvega temelja na njegovo nosilnost na izvlek v rahlih zemljinah C. Qiang et al. The effects of the geometric parameters of a circular shallow foundation on its uplift bearing capacity in loess soil J. Stacho J. Stacho Načrtovanje sistema uvrtanih pilotov z odmikanjem z uporabo teorije razširjanja prostora The design of drilled displacement system piles using the cavity expansion theory 81 Navodila avtorjem Instructions for authors 92 MONITORING OF THE BELCA ROCKFALL MONITORING SKALNEGA PODORA BELCA Aleš Lazar (corresponding author) Geoservis, d.o.o Litijska cesta 45, 1000 Ljubljana, Slovenia E-mail: lazarales@gmail.com Tomaž Beguš Geotrias d.o.o. Dimičeva ulica 14, 1000 Ljubljana, Slovenia E-mail: t.begus@gmail.com Milivoj Vulic University of Ljubljana, Faculty of Natural Sciences and Engineering Aškerčeva cesta 12, 1000 Ljubljana, Slovenia E-mail: milivoj.vulic@guest.arnes.si https://doi.org/10.18690/actageotechslov.15.2.2-15.2018 Keywords monitoring, deformation analysis, rock fall, landslide, terrestrial laser scanning, geotechnics Ključne besede monitoring, analiza deformacij, skalni podor, plaz, terestrično lasersko skeniranje, geotehnika DOI Abstract This paper reviews the monitoring of the rock block above the forest road of Belca Jepca near the village of Belca in the municipality of Kranjska Gora, Slovenia. A rockfall in part of the block occurred in autumn 2014. Both classic and some new measurement technologies were used. The new technologies were implemented according to new findings: an unmanned aircraft was used in the hazardous and hardly accessible areas of the observation, a terrestrial laser scanner was used for the comprehensive observation of the rock slopes and large cracks were observed with the installation of invar wires. The deformation analysis uses data between 2014 and 2017, among which airborne laser scanning (ALS) data from 2014 is included. The study also includes a comparison of the airborne laser scanning and the terrestrial laser scanning. Izvleček V prispevku je podan pregled monitoringa skalnega bloka, ki se je jeseni 2014 sprožil nad gozdno cesto Belca Jepca v bližini vasi Belca v občini Kranjska gora v Sloveniji. V sklopu monitoringa je bila uporabljena tako klasična kot tudi najnovejša merska tehnologija. Metode dela smo prilagajali novim spoznanjem. Tako smo na nevarnih in težko dostopnih območjih za opazovanje uporabili brezpilotni zrakoplov, za celostno opazovanje skalnih brežin pa terestrični laserski skener. Analiza deformacij obsega podatke med letoma 2014 in 2017, med katerimi so uporabljeni tudi podatki aerolaserskega skeniranja površja, zajeti leta 2014. V raziskavi je vključena primerjava podatkov aerolaserskega skeniranja in terestričnega laserskega skeniranja. 1 INTRODUCTION This paper reviews the monitoring of a rock block located near the village of Belca in the municipality of Kranjska Gora, Slovenia. The reason to begin monitoring the area was a rockfall from some parts of the rock block in September 2014 and the possibility of a collapse of the entire block. Geotechnical measurements were used as part of the monitoring process, as well as geolo-cating measurements, complemented by field geological surveys and observations using an unmanned aircraft. Of the measurement techniques, the following were used: surveys using wire extensometers, tachometry and terrestrial laser scanning (TLS). We have also acquired lidar data from the summer of 2014, using airborne laser scanning (ALS), showing the status of the area before the rockfall. The analysis of the acquired data covers the period from 2014 to 2017. The aim of this research was to assess the risk of another rockfall, as well as finding a solution to achieve the safety and transportability of the road. We have used both classic and the latest measurement technology. In hard-to-reach areas, an unmanned aircraft was used for the observation, while a terrestrial laser scanner was used to comprehensively monitor the rock slopes. The deformation analysis also includes a data comparison between the airborne laser scanning and the terrestrial laser scanning. 1.1 An overview of related works Scaioni et al. [1] were the first to use terrestrial laser scanning for the monitoring of a rock block in the Alps, together with an interferometric synthetic aperture radar (InSAR), terrestrial photogrammetry and geotechnical measurements. Teza et al. [2] showed the monitoring of a rock block to assess the risk of a rockfall using TLS and infrared thermography (IRT). The first to try TLS for monitoring the movements and deformations were Gordon et al. [3] on an old wooden bridge. Gordon et al. [4] showed that the technology of laser scanning can be more efficient than classic methods for sensing the changes of flat objects due to the large number of acquired points. Alba et al. [5] used terrestrial laser scanning to control the stability of a big dam, while Schneider [6] used it to determine the inclination of a high water tower and the deformations of two dams. Tsakiri et al. [7] researched the required conditions to use a scanner to measure deformations, in the sense of calibrating the scanner and the processes of modelling clouds for movement sensing. The mentioned works are papers from conferences, while we found one article [8] in a scientific journal that describes using TLS for measuring deformations in an incriminating laboratory test. At the ISPRS congress in Beijing in 2008, the authors of [9, 10, 11, 12, 13] presented their work regarding the use of TLS for the measurements of deformations. Berényi et al. [14] used TLS to measure how much large bridges sag in incriminating tests, while Vezocnik et al. [15] tried to determine the movement of a gas line using the movement of concrete columns connected to underground pipes. Abellán et al. [16] dealt with the field of sensing changes in natural environments. De Asís López et al. [17] used statistical methods to compare two clouds of points, accumulated in different ways. Harmening and Neuner [18] use clouds to flatten various 3D planes and compare them with one another. 1.2 The area of research The area of interest is the right rock slope above the river Belca, which is above the forest road Belca Jepca, near the village of Belca. In the autumn of 2014 a rockfall with a volume of between 5,000 and 10,000 m3 was launched over the forest road. The terrain is rocky with some rockface on distinct slopes. The rock block is made from Upper Triassic rocks: massive dolomite and limestone, strongly tectonized: limited by open cracks. The main area of interest is the independent block between the road and the peak ridge that we call Main block. Its volume is estimated to be 150.000 m3. The most unstable block - Upper block - is clearly limited with 0.5-m-wide and 4-6-m deep cracks. The volume is estimated to be 16,000-20,000 m3. On the side of the main block some significant open cracks determine the Side block: 45,000 m3. The terrain is quite steep. Where there is no rock, the area is covered in a sparse pine forest. There are two distinct screes below the road, up to the valley of Belca, which is the main watercourse. Figure 1. The researched area, view towards the northeast. The construction of the terrain is from lidar data from 2014. Indicated are the main directions of the potential falling and the main fallen blocks of the slope. After the rockfall in autumn 2014, the area of the road was completely covered by rock to a length of 45-50 m. The waterways of the unnamed stream were also completely ruined. There were many activities during the redevelopment that provide a safe commute on the forest road: - Transportability of the road was provided by widening the road. On the wider road rubble and smaller stones can be stopped on the inner part of the road. - Monitoring during the construction works was also carried out to determine the size of the movement and alert the working crew. With the monitoring, an estimation of the stability of the entire rock block was also achieved. 2 MATERIALS AND METHODS USED_ The main methods for monitoring the rock block consisted of: - Visual monitoring of the rock block; - Installing and recording the six measuring points on the slope; - Installing extensometers on the cracks. We broadened our monitoring based on the knowledge we acquired while constructing the monitoring system and measuring: - Using an unmanned aircraft, - Recording the rock block with terrestrial laser scanning. 2.1 Visual observations The visual observations are based on geological field overviews [19, 20]. Based on these visual observations, we concluded the following: - The main part of the material has fallen off (and will probably continue to fall off) the upper part, which is limited by clear rupture cracks. This applies to the so-called upper block; - We mapped the area that fell off in autumn 2014. It is located on the upper block; the volume of the fallen material is estimated to be 5,000-10,000 m3 (rough estimate). On the opposite side of the upper block, a larger volume of rock fell off (estimated at 300 m3) a few years before. Open cracks are clearly visible in this area. We named this area the side block. Given the incursions of major discontinuities, we decided for two potential ways of material falling: falling of the upper block, or the possibility of another rockfall of the whole block from the ridge to the road. The volume of the entire block was estimated at 150,000 m3. The area is very dangerous for the observation at some points of the terrain change. Some areas are also very hard to reach, even with mountain-climbing equipment. There- Figure 2. The positions of the extensometers and measuring points in the rock block Belca. The crack that limits the main block is pictured with red. Figure 3. Left: schematic position of the wire extensometers, based on the upper block and based on the potential direction of movement; Right: a double and triple extensometer. fore, we used an unmanned aircraft to observe the dangerous and hard-to-reach areas. We captured over 400 aerial photographs. Based on aerial photogrammetry, the aerial photographs were later evaluated. The result is a photorealistic 3D model of the observed rock block, where the rock block can be viewed from any given perspective. The usability is mainly found in a better spatial orientation of the rock block and in finding a comprehensive image, which makes predicting possible outcomes easier. 2.2 Geotechnical surveying For the verification and quantification of the absolute movements of the rock block, several measuring techniques were used [21, 22, 23]. We installed geotechnical surveying instruments on the cracks, i.e., wire exten-someters. We used tacheometry, which we supplemented with terrestrial laser scanning. - The widening of the cracks on the main block was measured with five wire extensometers, and a wire extensometer with a clock on the side block, - The whole rock block was measured at six measuring points, installed at several points on the slope: two points on the upper block, with which we assess the possibility of a rockfall of the side block, and four points, with which the stability of the entire rock block is controlled. 2.2.1 Wire extensometers Wire extensometers were installed on five characteristic parts of the cracks that limit the upper rock block. They were used to transmit the potential movements on the block. We used invar wires, which largely compensated for the influence of temperature. The measurements were carried out periodically. The results are shown in the table 1, as well as pictured in Figure 4. The increased increment in 2017 is clearly visible. If we understand the values that are increasing or declining in a trend as values worth using, we can state the following: - Triple left is increasing at a constant rate and reaches a value of 2.7 cm. We can conclude that the north Table 1. Wire-extensometer measurements. DOUBLE TRIPLE date - left diff. left right diff. right left diff. left middle diff. middle right diff. right 19. 11. 2015 245.8 245.8 134.1 131.5 04. 12. 2015 245.8 0.0 245.8 0.0 134.4 -0.1 134.1 0.0 133.0 1.5 22. 01. 2016 245.7 -0.1 246 0.2 135.0 0.5 133.8 -0.3 130.5 -1.0 10. 06. 2016 244.5 -1.3 245.5 -0.3 136.5 2.0 136.0 1.9 116.8 13. 10. 2016 243.5 -2.3 245.5 -0.3 137.0 2.5 107.0 -27.1 117.0 0.2 27. 10. 2016 243.5 -2.3 245.5 -0.3 137.0 2.5 106.0 -28.1 117.5 0.7 29. 05. 2017 250.8 5.0 248.0 2.2 137.2 2.7 108.0 -26.1 128.0 11.2 Movements on the wire extensometers Figure 4. Graph of movements on the wire extensometers. part of the rock block is moving towards the south at a constant speed. - Double left and triple right increased to 5 and 11.2 cm in 2017; therefore, the rock block is moving away from the crack. - A sudden value change for the extensometer triple middle also stands out. The point is directly above a turning point of the slope into a rocky overhang. Therefore, the slope can be so loose that the anchor holding the measuring wire gives way. An extensometer for measuring the spreading of the larger crack of the rock is placed on the side block (the measuring scale shows movements of up to 65 mm). The value increased to 5 mm between January and June 2016, after that (between June and November 2016) the value was constant. Between November 2016 and May 2017 the value increased to 11 mm. 2.2.2 Geolocating We have installed six fixed measuring points using a classic polar method (tacheometry) in the most prominent areas as a part of the observational methods. They were labelled from T1 to T6: - T1, T2 on the front edge of the rock block; these two points are used to measure the movement of the entire rock block, Figure 5. Left: view of the extensometer in September 2015; Middle: view of the extensometer in June 2016; Right: view of the extensometer in May 2017. The difference is 11.0 mm. The increase of the value occurred between January and June 2016 (5 mm), as well as between November 2016 and May 2017 (6 mm). Table 2. Coordinates of points in different epochs. Measure- 02.09.2015 11.11.2015 28.10.2016 ment point x [m] Y [m] h [m] X [m] Y [m] h [m] X [m] Y [m] h [m] T1 416724.048 149131.063 909.662 416724.050 149131.061 909.651 416724.060 149131.057 909.647 T2 416726.666 149133.189 917.702 416726.670 149133.185 917.693 416726.677 149133.175 917.688 T3 416742.017 149171.512 944.830 416742.023 149171.511 944.821 416742.046 149171.508 944.811 T4 416732.672 149181.141 964.918 416732.683 149181.143 964.911 416732.715 149181.150 964.898 T5 416713.598 149207.500 998.636 416713.612 149207.509 998.613 416713.694 149207.539 998.557 T6 416710.956 149234.294 1016.681 416710.978 149234.306 1016.651 416711.081 149234.357 1016.561 - T3, T4 on the side slope, where no distinct movement is expected; they are also used to control the movement of the entire rock block, - T5 in the middle of the upper rock block; the point is used to monitor the movement of the upper block, - T6 on the first parts of the upper rock block; this point is used to monitor the movement of parts above the upper block. Three periodic measurements using a classic polar method (tacheometry) were made in 2015 and 2016. The accuracy of the measurements is 1 cm. The results are shown in the table 2. 2.2.3 Terrestrial laser scanning and airborne laser scanning The area of the Belca rockfall was scanned with an airborne laser in 2014. This is how, using publicly accessible lidar data through the eVode portal (http:// evode.arso.gov.si/), we managed to consider the state of the surface before the rockfall. We managed to do that, because the airborne laser scanning of Slovenia was carried out in the summer of 2014 in that area. We made a digital model of the relief (DMR) with a spatial resolution of 50 cm using the lidar data. Because some details remained hidden (vertical beams of reflection) while scanning and recording from the air (helicopter), we carried out a terrestrial laser scanning of the area from the first measurement on. Doing this we automatically obtained many points from the laser-beam reflections: - Measurements from 13.7.2015 have 142.4 million points, - Measurements from 11.11.2015 have 129.1 million points, - Measurements from 28.10.2016 have 145.5 million points. Speeds oi fTiovemeiits Figure 6. Graphs: size of movements - absolute (top left) and in the X-Y plane (top right); settlements (bottom left) and speeds of movements (bottom right). The relevant data used in the further implementation is acquired from these points using a variety of software tools. We use these to: - construct 3D models of the terrain, - determine the movement by comparing the point clouds of different periods of recording time. 3 RESULTS_ 3.1 Observation results Based on two or more periodic measurements of the observations of stabilized measurement points on the rock block with a classic polar method, we determined the size of the spatial movements of the object. Next, based on three or more periodic measurements, we determined the speed of the movements. The analysis of the results is shown in the graphs in Figure 6 (previous page). The graphs show that the points in the upper part (T5 and T6) clearly stand out while looking at the sizes of the movements. This indicates the intensity and ever-present events on and near the upper rock block. The movement direction clearly shows the possibility of further rockfall around the upper rock block. The values of the other points (T1-T4) also show the movement of the block. Changes are clearly seen on the upper block and around the lower spree (Figure 8 shows the colour scale going towards Figure 7. The position and labelling of the measurement points on the rock block. The arrows proportionally show the directions of movement, while the values of the absolute movements between July 2015 and October 2016 are shown on the right-hand side. red) while comparing the point clouds accumulated with terrestrial laser scanning from 11.11.2015 and 28.8.2016. We attribute the other changes (on the left- and right-hand sides of the figure) to the influence of the vegetation. 3.2 Data analysis of the airborne laser scanning and the terrestrial laser scanning Airborne laser scanning of the surface was conducted within the LIDAR survey of Slovenia in the summer ¿mm ■ £2C ¿¿Et>kjte distantK[<0.31 R-aw ■ mm METSIB # .' J* ; ■ : ¿3 . , ' h ' WW- ' .' T ■■ : J % Figure 8. Differences between the terrestrial laser scanning on 11.11.2015 and on 28.8.2016. of 2014, so a few months before the rockfall in the autumn. This gave us the chance to compare the data from before and after the rockfall. The difference in its surface is visible when comparing the inclination maps (Figure 9). The biggest fallen block of rock measures approximately 90 m x 20 m in layout dimensions, and is 33 m in height. Based on the 3D analysis of the difference between the surfaces in 2014 and 2015, we have defined the volume of the fallen rock, which measures 6,700 m3. Figure 9. Top left: a relief of the surface, made based on ALS data (summer 2014); Top right: a relief of the surface, made based on TLS data (summer 2015); Bottom: The volume differences. 4 DISCUSSION 4.1 A visualisation of the events and projections into the future Based on the field survey, measurements and detailed reviews of the measured results, we can conclude that the rock block above the forest road in Belca is still moving. Based on the measurements so far, we can also conclude that the values in the upper block are within 10-20 cm per year. Often, a graph of the reverse velocity and time values is used to estimate the launching time of a landslide. The launch time is the time when the value of the speed-1 is approaching 0. In the case of all the points from T1 to T6, the values do not asymptotically fall towards the value 0 (Figure 10). However, we must warn of the fact that the upper block is made up of pieces of dolomite, which are clearly separated between themselves with open cracks. Therefore, the falling of free blocks can still occur. Moreover, the conclusions are derived from three series of measurements, which can be a too small number of repetitions for a credible assessment. In the case of the rock block Belca, we are interested in two things: - The possibility of more rockfall in the upper block and the consequences of it falling onto the road. - The possibility of the whole block falling and making its way towards the valley of the river Belca. 4.2 The possibility of rockfall in the upper block and the consequences of rockfall to the road Smaller rockfall of the slopes and greater filling of the road with the rockfall also occur after repair work. A 10-m road segment is especially at risk. Despite the roadway being wide in this part, the road is also hit with single larger pieces of stones, with dimensions of up to a few decimetres. This area requires constant cleaning of the roadway. Because the area is relatively well shrouded, the potentially dangerous stones can be controlled by a catch fence at the bank above the road. 4.3. Basic and derived measurements With the basic examination of the terrain, a first picture of the events is made. This picture is then upgraded with new findings and new methods of work: basic recording of data was updated to terrestrial laser scanning, with which we can create a spatial assessment of the fallen block, as well as an assessment of the spatial spreading of the block. The picture of the event was completed by recording with an unmanned aircraft. 5 CONCLUSION_ The measurements indicate that the rock block is still in motion, being 10-20 cm/year at the upper part. We have calculated the volume of the fallen rock (the volume of the rockfall in September 2014) using a 3D deformation analysis of the state of the rock before and after the rockfall. There is a risk of a rockfall for the whole block of rock in the direction of the river Belca, in the worst case damming the river with the rockfall material. To assess the possibility of the further falling of either parts of the rock block (upper block) or the whole rock block, it is necessary to continue the monitoring process and adapt it per the results. 35 30 25 20 15 10 S 0 1 / speed of movements \V -y f r # ^ # jf # # ci> if ^ M Figure 10. Projection graph of the reverse speed values. In the monitoring process, the use of UAV flights is extremely useful in surveying the rock block. The entire block can be reconstructed and hidden details can be clearly visible. Due to a difficult visual surveying approach, which is also very dangerous, the use of UAV can become a standard tool in such operations. The only disadvantage is the low GPS positioning of the device due to the narrow, hilly terrain, which prevents a good signal. Acknowledgment We would like to thank the companies Geotrias d.o.o. and Magelan Group Ltd., which provided us with access to the collected data. We would also like to thank the municipality of Kranjska Gora for their engagement with the issues in Belca. REFERENCES [1] Scaioni, M., Arosio, D., Longoni, L., Papini, M., Zanzi, L. 2008. Integrated Monitoring and Assessment of Rockfall. V: Proceedings from International Conference on Building Education and Research, Kandalama, Sri Lanka, 10. - 15. February 2008: pp. 618-629. [2] Teza, G., Marcato, G., Pasuto, A., Galgaro, A. 2015. Integration of laser scanning and thermal imaging in monitoring optimization and assessment of rockfall hazard: a case history in the Carnic Alps (Northeastern Italy). Natural Hazards 76, 3: 15351549. doi: 10.1007/s11069-014-1545-1 [3] Gordon, S., Lichti, D., Stewart, M. 2001. Application of a high-resolution, ground-based laser scanner for deformation measurements. V: The 10th FIG International Symposium on Deformation Measurements, Orange, California, USA, 19. - 22. March 2001: pp. 23-32. [4] Gordon, S., Lichti, D., Stewart, M., Franke, J. 2003. 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RMZ - Materials and geoenvironment 55, 2, 237-258. [22] Vižintin, G, Viršek, S. 2008B. Analitical surface Appendix 1. Frontal view water forecasting system for Republic of Slovenia = Analitičen sistem napovedovanja pretokov površinskih vod v Republiki Sloveniji. RMZ -Materials and geoenvironment 55, 2, 215-224. [23] Božiček, B., Lojen, S., Dolenec, M., Vižintin, G. 2017. Impacts of deep groundwater monitoring wells on the management of deep geothermal Pre-Neogene aquifers in the Mura-Zala Basin, Northeastern Slovenia. Groundwater for sustainable development 5, 193-205. APPENDICES - Frontal view - View towards the east - View towards the west - Top view Appendix 2. View towards the east Appendix 3. View towards the west Appendix 4. Top view S_BRICK: A CONSTITUTIVE MODEL FOR SOILS AND SOFT ROCKS S_BRICK: KONSTITUTIVNI MODEL ZA ZEMLJINE IN MEHKE KAMNINE Vladimir Vukadin Institute for Mining, Geotechnology and Environment (IRGO) Slovenčeva 93, 1000 Ljubljana, Slovenia Vojkan Jovicic (corresponding author) Institute for Mining, Geotechnology and Environment (IRGO) Slovenceva 93, 1000 Ljubljana, Slovenia E-mail: vojkan.jovicic@irgo.si https://doi.Org/10.18690/actageotechslov.15.2.16-37.2018 Keywords structure, constitutive material models, soft rocks and hard soils, numerical modelling, destructuring Ključne besede struktura, konstitutivni materialni modeli, mehke kamnine in trde zemljine, numerično modeliranje, destrukturizacija DOI Abstract Materials known in the literature as hard soils and soft rocks are widely spread, natural materials that are commonly encountered in engineering practise. It was demonstrated that some of these materials can be described through the general theoretical framework for structured soils set by Cotecchia and Chandler [14], which takes into account the structure as an intrinsic property present in all natural geological materials. Based on laboratory results and existing theoretical frameworks, the development of a constitutive model for structured materials was carried out. The model formulated in strain space named BRICK [27, 29] was chosen as the base model and was further developed by adding features to model both the structure and the processes of destructuring. The new model was named S_BRICK and was first presented on a conceptual level, in which the typical results of modelling structured and structureless (reconstituted) materials on different stress paths were compared within the solutions of the Cotecchia and Chandler [14] theoretical framework. The S_BRICK model was validated on three materials, i.e., Pappadai clay, North-Sea clay and Corinth marl, thus covering a wide range of natural, structured materials. The results showed that S_BRICK was able to successfully model the stress-strain behaviour typical for hard-soil and soft-rock materials, in general. Izvleček Materiali, ki so poznani v literaturi kot trde zemljine ali mehke kamnine, so široko razširjeni naravni materiali pogosto prisotni v inženirski praksi. Pokazano je, da se določeni tovrstni materiali lahko opišejo s pomočjo teorijskega okvirja za strukturirana tla, ki so ga razvili Cotecchia in Chandler [14], in sicer na ta način, da so upoštevali notranjo strukturo, ki je prisotna v vseh naravnih geoloških materialih. Razvoj konstitutivnega modela za strukturirane zemljine je bil narejen na podlagi rezultatov laboratorijskih raziskav in z uporabo obstoječih teorijskih okvirjev. Konstitutivni model BRICK [27, 29], ki je bil razvit v prostoru relativnih deformacij, je bil izbran za osnovni model in je nadgrajen z dodatnimi lastnostmi, da bi bil lahko uporaben za modeliranje strukture in tudi procesa destrukturizacije. Novi model, imenovan S_BRICK, je najprej predstavljen na konceptualnem nivoju, v katerem so tipični rezultati modeliranja strukturiranih in ne-strukturiranih (rekonsti-tuiranih) materialov primerjani z rešitvami iz Cotecchia in Chandler-ovega [14] teorijskega okvirja. Model S_BRICK je validiran na tri materiale: pappadaiska glina, glina iz severnega morja in korintski lapor. Na ta način je validacija modela zajela široki razpon naravnih materialov. Rezultati so pokazali, da model S_BRICK lahko uspešno modelira napetostno-deformacijsko obnašanje, ki je tipično za trde zemljine ali mehke kamnine. 1 INTRODUCTION The BRICK model, developed by Simpson [27, 29] for overconsolidated clays, was chosen to be the base model for the development of the constitutive model called S_BRICK, aiming to model structured materials such as hard soils and soft rocks. This was mainly due to the BRICK model's ability to model the non-linear, stress-strain response of soil and the recent stress-history effect [5], which are both the main features of the mechanical behaviour characterised by kinematic hardening. In the first part of the paper the framework for structured soils developed by Cotecchia and Chandler [14] is presented together with a brief description of the original BRICK model. This is followed by an explanation of the S_BRICK model formulation, in which the additional features are given to account for the influence of the structure on the mechanical behaviour of natural materials. A particular feature of the S_BRICK model is its ability to model destructurisation. It was soon understood that the modelling of structured natural materials could not be successful without taking into account the processes of structure decay following the plastic deformation. The methodology of modelling destructuring in S_BRICK is explained and the parameter determination procedure is given on a conceptual level. Finally, the validation of the S_BRICK model was carried out on three natural materials: Pappadai clay, North-Sea clay and Corinth marl. While the Pappadai clay and the North-Sea clay are heavily overconsolidated clays and can be classified as hard soils, Corinth marl is a typical representative of soft rock, with a complex geological history and the resulting mechanical properties. Those three materials were chosen to demonstrate the ability of S_BRICK to cover the main features of the mechanical behaviour of a wide range of natural, structured materials. 2 THEORETICAL BACKGROUND 2.1 Structured materials Kavvadas [21] and Kavvadas and Anagnostopoulos [22] suggested that the principles of soil mechanics could be applied to the modelling of hard soils and soft rocks as long as the behaviour of the natural material is not influenced significantly by large-scale discontinuities. It is widely accepted that, apart from including the important features of the mechanical behaviour of soils, such as nonlinearity, small strain stiffness and the influence of volumetric and kinematic hardening, a constitutive model has to include the effects of structure and destructuring in order to describe the behaviour of natural geological materials [25, 10, 14, 23, 26, 7, 16, 2, 17, 11]. The origins of the structure in natural soils are complex and can be attributed to different processes and different physical and chemical conditions during and after sedimentation. Hence, there are many different classifications and definitions that take into account the different aspects of structure. Lambe and Whitman [24] stated that structure is a combination of the fabric and the bonding in which the fabric represents the arrangement of the soil particles and the bonding represents the chemical, physical or any other types of bonds between the particles. Bonding has predominant effects in rocks, while in soils the influence of fabric is more important. It is obvious that according to this definition, structure is present in both natural and reconstituted geological materials, because no matter how much material is remoulded or destructured, it still has some type of fabric. Nevertheless, from the mechanical point of view, the influence of structure in reconstituted materials is the benchmark reference state representing the lower bound for the strength and the stiffness of natural materials. An example of the influence of structure on state boundary surfaces (SBSs) for undisturbed, partly destructu-red and reconstituted Pappadai clay is shown in Figure 1 (after Cotecchia and Chandler [14]). It can be seen in the q/p' diagram (p' is mean effective stress and q is the deviator stress) normalized with the mean effective stress p'e* (taken at an isotropic reconstituted normal compression line at the same specific volume as for the intact clay) that the influence of structure is manifested by the size of the SBSs, resulting in the higher strength and stiffness of the undisturbed material in comparison with the partly destructured or reconstituted Pappadai clay. Cotecchia and Chandler [14] and Kavaddas and Anagnostopoulos [22] and the other authors differ on the classification and the mechanisms of the structure development, but they all nevertheless agree that the position of the in-situ state in volumetric space, i.e., the distance of the yield stress from the intrinsic compression line, controls the compression and the strength behaviour of natural soils. The intrinsic compression line here refers to the properties of reconstituted materials, representing the lower bound for the normal compression lines of natural materials. The key element of the structure is stability, as Baudet [6] and Baudet and Stallebrass [7] emphasise, so that the stable structure is predominantly governed by the fabric, while the unstable structure is predominantly following shearing, compression and swelling stress paths inside the SBS. However, these mechanisms of destructu-ring are still not fully understood, which was and would be an obvious obstacle to the development of the models that simulate the behaviour of natural materials. 2.2 Theoretical frameworks The proposed S_BRICK model was developed using the theoretical concepts of elasto-plasticity and critical state soil mechanics [30, 4] in a wider sense and the approach of Simpson [27] in developing the basic BRICK model. A further step in the model's development was made by using the theoretical framework for structured soils developed by Cotecchia and Chandler [14]. In this framework the influence of the structure (S) is quantified by the difference in the sizes of the SBSs of the structured and reconstituted materials, which are similar in shape. The framework is conceptually presented in Figure 2 in the q-p'-v space (v represents the specific volume), showing the two idealised boundary surfaces for reconstituted and structured materials. Cotecchia and Chandler [14] postulated that the parameter of shear sensitivity St, which is the ratio between the peak shear strengths of the natural or structured (qpeak) and the reconstituted material (q*peak), is equal to the parameter of stress sensitivity Sa which is defined as the ratio of the effective stresses for natural and reconstituted soils, taken at the same specific volume for isotropic (p'ei/p'*ei) or normal compression lines (p'era/p^era). Figure 2. Theoretical framework for structured and reconstituted material in the q-p'-v space (after Cotecchia & Chandler, [14]). p'/P; Figure 1. Influence of the structure on the SBS of undisturbed, partly destructured and reconstituted Pappadai clay (after Cotecchia & Chandler, [14]). governed by the bonding. Destructuring is caused by the plastic straining and is responsible for the decreasing of the SBS, as shown in Figure 1, and thus a reduction in the strength and the stiffness of the natural soil. The materials that show a certain degree of destructuring are classified as meta-stable, in which both elements of the structure (fabric and bonding) are still present. According to Leroueil and Vaugan [25], yielding and hence the plastic straining, causing destructuring can result by The relationship is given by the following expression: S = St = qpeak 1 %eak = Sa = P'i 1 P'i = P'eKo 1 PL (1) The value of the parameter S for the reconstituted material is equal to 1; therefore, the SBSs of the reconstituted and structured materials should coincide when plotted together in the normalized space qI(Sp'*)-p'I (Sp'e*), which takes into account the structure (S) and the volume (p'e*). The framework was validated by Cotecchia and Chandler [14] for Sibari, Bothkennar and Pappadai clays. The theoretical framework was also subsequently validated by Baudet [6] and Baudet and Stallebrass [7] for different materials, ranging from soft to hard clays. Even though the data on soft rocks in the literature are not as extensive as those on soft and hard clays, there is enough evidence to suggest that the basic concepts of this theoretical framework can also be applied to soft rocks [18, 23, 1]. 2.3 Basic concepts of the BRICK model The constitutive model for the structured soils S_BRICK originates from the BRICK model developed by Simpson [27, 29]. The BRICK model was developed to model the behaviour of over-consolidated clays, but was also successfully used to model soft or normally consolidated soils. The model includes many important features of the soil behaviour, including isotropic and kinematic hardening, and can model the stress-strain nonlinearity and the recent stress-history effect [5]. The means of formulation for the BRICK model are such that it is not obvious how the BRICK model is related to the theoretical concept of critical state soil mechanics or how the model can be extended within the theoretical framework for structured soils developed by Cotecchia and Chandler [14]. An attempt is made to underline those features of the BRICK model so that the further development to the S_BRICK model can be understood. The background and the formulation of the BRICK model are given in detail by Simpson [27, 29] and a more updated version, which includes a 3D formulation, is given by Ellison et al. [15]. The BRICK model is formulated in the strain space defined by the six strain invariants £j (i=1-6) in which the first one represents the volumetric component and other five represent the deviatoric components of the strain. The main idea is explained by the analogy of bricks and strings shown in Figure 3 a, in which a man (representing the current strain state) is pulling a certain, but definitive, number of bricks that are attached to him by strings of different lengths (representing the current strain path, causing a plastic deformation of different a) la! ' j> ik Ji fi__„ÎÎ iC—i ^ v y o Wan O Buck Gt/Gm Gt/Gm b) String length (SL) = Shear strain Step height = proportion of material represented by brick Shear strain Figure 3. The concept of the BRICK model: a) brick and string analogy and b) discretization of the S-shaped curve (after Simpson, [27]). magnitude). The analogy is essentially a way to discretise the decay of the tangent shear stiffness with the shear strain shown in Figure 3b in the shape of the normalised S-shaped curve. The strings (SL - string length) are given in a stepwise fashion, in which the height of each step indicates the proportion of the material being represented by a single brick. At very small strains the material is completely elastic, all the strings are slack and the bricks do not move. As the straining proceeds, the first brick starts to move, the plastic strain begins and there is a drop in the stiffness of the material. With continuous straining, more and more bricks are being pulled, there is more plasticity and there is a further drop in the stiffness until the material is fully plastic and the stiffness limits towards zero. When the stress path is changed initially, all the strings are slack, so that the immediate response is elastic. It should be noted though, that many stress paths starting from an in-situ state will not be fully elastic at small strains because some strings will remain taut. The plastic strain develops in the direction of the string orientation so that fully plastic behaviour does not occur until all the strings are all taut and aligned in the direction of the strain increment. With the BRICK analogy, the concepts of non-linearity, recent stress history and kinematic hardening are all being accounted for. Simpson [27] also demonstrated that the area beneath the normalized S-shaped curve is equal to sin0', and thus determines the maximum angle of shearing resistance for the effective stresses 0 defining the strength response of the model. Simpson [28] also showed how the model could be viewed as a set of nested yield surfaces, expressed in the strain space. The stiffness response of the BRICK model in the elastic range is accounted for by the parameter i that represents the correlation of the elastic volumetric modulus with the mean effective stress. The S-shaped curve and the elastic parameter i are additionally modified by a volumetric state parameter that accounts for the changes to the stiffness and the strength. Therefore, as for the other kinematic hardening models, the correct modelling of a stress history is of crucial importance for the correct model predictions. The state parameter fg, an important feature of the BRICK model, is used to the same effect of accounting for isotropic hardening as is the overcon-solidation ratio used in the theory of critical state soil mechanics. As will be explained later, the concept of state, which was defined in a similar way as proposed by Been and Jeffries [8], was used as a means to extend the BRICK model within the theoretical framework developed by Cotecchia and Chandler [14] for structured soils. The state parameter fg in the BRICK model is given by the following expression: ¥b =SU-SU0 (p'/p') (2) In this expression, fg represents the distance of the current volumetric-stress state given byp (mean effective stress) and ev (volumetric strain) from the reference state represented by the normal compression line defined by p'0, A and ev0 in the ev-lnp' plane, as shown in Figure 4. As it is assumed that the reconstituted material has not undergone any straining, ev0 is set to zero and p'0 is taken at the arbitrary (non-zero but small) value of 2 kPa. Simpson [27] introduced the influence of the state on stiffness and the strength using the parameter fi, which he subsequently divided into two parameters, fig and fiv, so that the influence of the state on the stiffness and strength, respectively, is given by the following two expressions: SL = SL ((3) (1 + Pg¥b ) [) 1 =1 current I1 + Pg¥b ) (4) It is clear from Equation 3 that the string lengths (SLs) are influenced by both the parameters fig and fiv, which means that the influence on the stiffness and the strength is not fully decoupled. In total, the BRICK model requires eight parameters, from which five can be determined using conventional laboratory testing (A, k, i, v and the shape of S curve), one that can be used as a constant (^-Drucker-Prager parameter defining the shape of a State Boundary Surface in H-plane) and the two (fig and fiv) can be determined by back-analysing conventional laboratory tests through a trial-and-error process. It will be shown later that the values of most of the parameters fall into relatively narrow intervals, so the values given by Simpson [27, 29] for London clay, given in Table 1, could be used as suitable starting values for any other clay. Furthermore, the S-shaped curve, which is given in normalized form, seems to be similar for all hard-soils and soft-rock materials, which were the subject of this research, as will be demonstrated latter. NCL N (a = x-y NCL X H'R-j AV A*- * * N C"- CSL CSL* P'o P' Inp' (kPa) Figure 4. Concept of the state parameter WB as modeled in BRICK, definition of the parameter a, and locations of the necessary triaxial tests for the parameter determination for S_BRICK. 3 FORMULATION OF THE S_BRICK MODEL The newly developed model was named S_BRICK to indicate the ability to model structured soils, while the original name was preserved, indicating that all the features of the BRICK model were preserved. A single-element program was developed as a tool for numerical simulations of soil behaviour using the S_BRICK model in 3D strain space. 3.1 Modelling of a structure The influence of structure is accounted for by the introduction of the two new parameters a and a. The first parameter a is used to proportionally increase or decrease the size of the string lengths (SLs) and thus of the area beneath the S-shaped curve. This has a direct Table 1. S_BRICK parameters for natural and reconstituted London clay, Pappadai clay, North-Sea clay and Corinth marl. Parameter London Pappadai natural Pappadai North-Sea natural North-Sea Corinth clay reconstituted Cape shore Ferder reconstituted natural Basic BRICK parameters A 0.1 0.254 0.204 0.1 0.1 0.1 0.6 K 0.02 0.029 0.046 0.02 0.02 0.02 0.005 I 0.0041 0.0048 0.0048 0.0041 0.0041 0.0041 0.0041 ßG 4 4 4 4 4 4 4 ßv 3 3 3 3 3 3 3 N 0.2 0.2 0.2 0.2 0.2 0.2 0.2 M 1.3 1.3 1.3 1.3 1.3 1.3 1.3 S-curve (as defined in BRICK and in S_BRICK for a=0.8) String Length 0.000083 0.00021 0.00041 0.00083 0.0022 0.0041 0.0082 0.021 0.041 0.08 Gtan/Gmax 0.92 0.75 0.53 0.29 0.13 0.075 0.044 0.017 0.0035 0.0 S_BRICK parameters defining structure and destructurisation a/ak 0.7/0.6 0.6/0.6 0.85/0.85 0.85/0.85 0.85/0.85 1.1/1.1 v(°) 21 21 18 25.5 25.5 25.5 33 U/ Ufr - 0.12/0 0/0 1.8/0 1.2/0 0.06/0 1.0/0 x°1 / X 2 - 20 / 80 0/0 0/200 0/500 0/0 0/3000 /1 / /2 - 0/0 0/0 0/0 0/0 0/0 0/1000 A / xh2 - 0/0 0/0 0/900 0/300 0/0 0/3000 A / A - 0/0 0/0 0/1000 0/450 0/0 0/3000 xsw1 / A - 0/0 0/0 0/200 0/500 0/0 0/0 A / yw2 - 0/0 0/0 0/0 0/0 0/0 0/0 influence on the value of the maximum angle of the shearing resistance and hence the strength response of the model. As indicated earlier, the normalized S-shaped curve for London clay was taken as a reference shape. The parameter a is implemented by modifying the string lengths using the following expression: SL = SL, ( + ß9¥B ) ( + ßc¥B ) a (5) The lower and upper range for the parameter is defined so that the maximum angle of the shearing resistance q> ranges from 18° (a=0.6) to 36° (a=1.2), which is considered as a reasonable range of q> for natural materials, which can be easily extended at both ends. With a value a=0.7, S_BRICK uses the same S-shaped curve as the basic BRICK model defined by Simpson [27]. The influence of the parameter a is graphically presented in Figure 5 for fB =0, together with its proposed range of values. Figure 5. Influence of the parameter a on S-shaped curve and its characteristic values. The second parameter w modifies the fg parameter to account for the influence of structure. The definition of w is graphically presented in Figure 4. It is best understood as an increase of the distance, in terms of volumetric strain, between the normal compression line and the critical state line of the structured material in comparison with that of the reconstituted material. In a numerical sense, the effect of parameter w is to increase the apparent overconsolidation of the soil. It is used to modify Equation 2 with the following expression: ¥b =Su-SU0 1 P'0) + œ (6) It is evident from Equations 3 and 4 that the state parameter influences both the i parameter (elastic stiffness) and the string lengths (SLs) of the normalized S-shaped curve (strength) so there would be inevitably some overlapping of the influences of the parameters a and w on the model behaviour. However, the influence of the parameter w on i and hence the stiffness is larger than the influence on the S-shaped curve and hence the strength because the S-shaped curve is modified by the ratio of the state parameters (Equation 3). The parameter w is therefore the key parameter for modelling the stiffness increase and the parameter a is the key parameter for modelling the strength increase caused by the presence of structure. 3.2 Modelling of destructuring Destructuring is modelled using the both parameters a and w. They are given in the form of normalised exponential functions of strains to account for the presumed logarithmic nature of the destructuring [18, 23]. The rates of destructuring are made dependent on the sum of the volumetric and shear components of the plastic strains, as shown in the following two expressions: <,sh,sw =at +{a-ak )exp [-( ( +SSp' ) + yC,sh,sw ( + 8e? )) œk ak*, ^k* initial values of parameters for natural materials final values of parameters for natural materials that were destructed values of structure parameters for reconstituted materials , c,sh,sw ■i > , c,sh,sw p Pl pPl °v y °s 8e/, Se5pl x c,sh,sw yi c,sh,sw X2 yi c,sh,sw c,sh,sw current values of structure parameters in compression (c), shear (sh) or swelling (sw) volumetric and shear component of plastic strain increment of volumetric and shear component of plastic strain parameters that quantify influence of volumetric and deviatoric plastic strain on destructuring of parameter a parameters that quantify influence of volumetric and deviatoric plastic strain on destructuring of parameter œ Parameters a*k and w*k are not implicitly shown in Equations 7 and 8. They are used in the model to represent the structure in reconstituted materials and also implicitly for the materials with unstable structures, for which ak and wk in the destructuring are approaching, or are equal to a*k and w*k. Destructuring in S_BRICK is implemented separately by introducing different parameters x1, x2 and y1, y2, for shearing, compression and swelling. The decoupling of the destructurisation on the volumetric and shear components of strain at different stress paths gives an additional flexibility to the model. It is also assumed that the destructuring in the shearing is governed by both volumetric and deviator components of the plastic strain. 3.3 Parameter determination for structure and destructuring For a complete parameter determination three drained and three undrained triaxial shearing tests and one triaxial compression test should be carried out on both the natural and the reconstituted material, which makes fourteen triaxial tests in total. As will be shown later, this number can be significantly reduced by the robustness of the model. The triaxial compression tests should be carried out to sufficiently high stresses so that destructuring of the natural material in compression can be determined. Triaxial tests should include measurements of the stiffness at very small strains and should be carried out at the different initial states shown in Figure 4, so that the material response is obtained for the overconso-lidated (A, A*), normally consolidated (B, C, B*, C*) and destructured states (Ad, Cd). The asterisk sign * is used here to denote the states of the reconstituted material, while the term destructured is used to denote the state in which the parameters ak and wk are approaching or are equal to a*k and w*k . The following procedure is developed for the determination of the parameters for the S_BRICK model: - The geological stress history of the material should be modelled by taking into account the parameters a and w, which describe the structure. This is necessary for all the kinematic hardening models, since the model response is governed by the initial state and the recent stress-history effects. - From the drained triaxial tests starting from states A* and C* (see Figure 4) on the reconstituted material, a maximum angle of shearing resistance, which is here attributed to the critical state angle, is obtained and a\ is determined, yielding the values of f, as explained by Simpson [27], which are given in the table in Figure 5. - Parameter w*k is always set to zero for reconstituted materials. - From the drained triaxial tests starting from states A and B the critical state angle for the natural material is obtained and the starting value for a is determined based on the values given in the table in Figure 5. - From the triaxial tests starting at state Cd the critical state angle is obtained for natural material destruc-tured during compression and a final value ak is determined based on the values given in the table in Figure 5. If the material has completely lost its structure, ak is equal to a*k. - Input parameters w and Wk are determined with a trial-and-error process so that the measured Gmax values are reproduced by the model for all three tests starting at states A, B and C. As already indicated, if the material has no structure, Wk is set to zero. - From the drained triaxial shearing tests starting at states A and C, the destructurisation parameters for shearing xsh1, xsh2, ysh1 andysh2 are determined through a comparison of the model's prediction and measured values in q-ea and G-es diagrams using a trial-and-error process. Because the volumetric deformations and hence destructuring due to volumetric deformation in shearing are prevented in undrained stress paths, the parameters ysh1 and ysh2 are determined from undrained tests. These values can be used to determine the volume change and are than used in drained tests to obtain the parameters xsh1 and xsh2. - From the results of the isotropic compression on natural material between the state points B and Cd, the destructuration parameters for the compression x°i and xc2 can be obtained. Similarly, the parameters for swelling can be obtained for recompression (xswi and xsw2) between the states B and A. Using the proposed parameter-determination procedure, a unique set of parameters is obtained for a particular material. As will be shown latter, the stress-strain behaviour was modelled to a high degree of accuracy for Pappadai clay, for which the procedure was strictly followed, and to some degree also for Corinth marl with a similar result. However, not all the materials are usually studied in such detail and many of the required tests might not be available. It is demonstrated later, on the example of North-Sea clay that a satisfactory result can also be obtained in such a case. To summarise, the full implementation of structure and destructuring as implemented here requires the determination of the additional sixteen parameters in total. As will be demonstrated later, this number can be significantly reduced due to the robustness of the model. Four of them (a, ak, w and Wk) represent the structure and twelve (xi, yi)c'sh'sw represent the rate of destructurisation in compression, swelling and shearing. A volumetric component of destructuring is present in all the drained stress paths, while shear components are present in all but the isotropic compression and swelling stress paths. It is still not clear whether or not the shear components of the plastic strains have a noticeable influence on stress paths with no significant change in the deviator component, for example, in the normal compression and the recompression stress paths. Amorosi and Kavvadas [1] argue that for those stress paths only isotropic hardening and destructuring due to volumetric plastic strain have a noticeable effect. If this is the case, then the number of necessary parameters could be reduced to twelve. It is reasonable to expect that not all the types of destructuring are present for a dominant stress path, so the necessary number of total additional parameters for destructuring can be as low as four. The modelling of destructuring is implemented in such a way that the model parameters that are not significant can be omitted without hindering the model's behaviour. 4 PRESENTATION OF THE S_BRICK MODEL ON A CONCEPTUAL LEVEL The capabilities of the S_BRICK model to simulate the structure and destructuring are presented by comparing the numerical results of the two conceptual materials taken at the different stress-strain paths for the two different states. Both materials have all the basic parameters equal, and they are the same as parameters given for London clay [27], which are summarised in Table 1, except for the amount of structure modelled. Material B represents the material with the stronger structure (aB=1.1 and wB=0.5) and material A represents the material with the weaker structure (aA=0.7 and wA=0.0). Using the structure parameters given for material A, the S_BRICK model is basically reduced to being the same as the basic BRICK model for London clay [27]. 4.1 Results of the modelling of structure on a conceptual level using S_BRICK The influence of the structure parameters a and « on the increase in strength, stiffness and the SBS is presented by comparing the S_BRICK predictions for materials A and B. The purpose of showing the comparison is to demonstrate that S_BRICK is capable of modelling the main features of the theoretical framework for structural soils proposed by Cotecchia and Chandler [14]. S_BRICK predictions for stress paths that comprise normal compression, swelling, and drained triaxial shearing for materials A and B are shown in the v-logp' plane in Figure 6. The predictions of the normal compression lines (NCLs) and the critical state lines (CSLs) for both materials are also shown in the figure. The numerical triaxial tests were taken at different states (OCR varies from 1 to 10). It is evident that the CSLB and NCLB lie to the right of the CSLA and NCLA, as is expected for the material of stronger structure. It is clear that the distance between the CSLB and NCLB is greater than the distance between CSLA and NCLA, which is also expected for a material of stronger structure. Furthermore, it can be observed that S_BRICK made a prediction, which can be interpreted for each material as an almost unique position of CSL, regardless of the state in which the shearing tests were modelled. Therefore, the unity of the position of the CSL line was anticipated in the continuation on a conceptual level to interpret the other data. The results for different drained shearing stress paths in the q-p space for normally consolidated material (OCR=1) and overconsolidated material (0CR=10) are shown in Figure 7. It was demonstrated that the material with a stronger structure (B) reached higher peak deviatoric stresses than the material with a weaker structure (A), regardless of the direction of the stress path and the state at which they were started. The stress paths in compression produced higher inclinations for the CSL lines than in the extension, which is expected. For the model of the over-consolidated test the increase of the peak deviatoric stress due to the over-consolidation and subsequent softening towards the CSL line is also evident. It was also observed, but not shown here, that the material with the stronger structure (B) has higher stiffness in the range from vary small (i.e., below 0.001%) to large strains (i.e., above 1%) in both compression and extension. The SBSs predicted by the model for both materials are shown by the dotted lines in Figure 8a, in which the results from the triaxial shearing at different levels of over-consolidation are presented. The results are shown as a normalized plot in the q/pAe - p'lp'Ae plane, where pAe represents the equivalent pressure taken on a normal compression line of the material A. (The 50% destruc-turisation case shown in the figure will be considered later.) It is evident that the material B has a much larger SBS than the material A, which is expected for a material with a stronger structure. In Figure 8b the results are further normalized with the inclusion of structure (S) in the qlSpAe - p'lSp'Ae plane. It can be seen that the normalised SBSs of the materials A and B coincide, as suggested by the theoretical framework for structured materials, given by Cotecchia & Chandler [14]. Figure 6. S_BRICK predictions of normal compression and swelling with drained triaxial shearing taken at different states for the materials A and B. Figure 7. S_BRICK predictions of drained triaxial shearing taken at different directions for the normally consolidated and overconsolidated state (OCR=10) for the materials A and B. a. 0J cr -2- a) CSLB Compression Extension Material: A Material: B Material B at 50 de structurization 2 p'/p/ CT -0.4 b) 0.2 0.4 0.6 0.8 pVSpW Figure 8. State boundary surfaces predicted by S_BRICK for materials A, B and material B with 50% destructurisation before shearing in: (a) q/pAe - p'lp'Ae plot and (b) q/Sp'Ae - p'/Sp'Ae plot. 4.2 Results of the modelling of destructuring on a conceptual level The results of destructuring as modelled by S_BRICK in compression, swelling and shearing are shown by comparing the same two conceptual materials A and B. The results of destructuring in compression are shown in Figure 9a, where the parameters a and a were reduced at different rates to 50 % of the initial values for the material B (aBk=0.9 and aBk=0.25). For demonstration purposes, the parameters x°i ,yCj (¿=1,2), describing the rate of destructuring in normal compression, are the same for the volumetric and the deviatoric component. The values that were used are x°i , yc,= 1000 for the fastest rate of destructuring; x°i , yc,=500 for the intermediate rate and x°i , yc,=200 for the slowest rate of destructuring. It is evident from Figure 9a that all three tests reach the normal compression line that lies in-between the normal Figure 9. Different rates of destructuring at normal compression and destructuring in swelling modeled with S_BRICK (a) and different levels of destructuring for the triaxial shearing modeled with S_BRICK (b). compression lines for materials A and B, but at different rates, as expected. The modelling of destructuring in swelling is also presented in Figure 9a, in which the structure parameters a and w for the material B were again allowed to reduce to 50 % of the initial values. The swelling line of the destructured material is presented together with the normal compression and swelling lines of the materials A and B. It can be seen that the slope of the swelling line of the destructured material lies in-between the swelling lines of the materials A and B. Furthermore, it can be seen that the material destructured in swelling reaches the same normal compression line after recompression as materials that were destructured in compression. The results of a triaxial shearing test after destructurisation in compression are also shown in Fig 8 in the form of normalised plots. In Figure 8a, the SBS for material B at 50 % destructurisation clearly lies in-between the SBSs for materials A and B, while in Figure 8b they all coincide, as one would expect according to the theoretical framework. Finally, the modelling of destructuring in shearing is presented in Figure 9b, where the structure parameters for material B have been allowed to reduce for 20, 50 and 80%. A clear trend of reducing the peek deviator value from material B towards material A can be seen with the increasing amount of destructurisation. Table 2. List and description of validated laboratory tests from Pappadai clay, North-Sea clay and Corinth marl. Pappadai clay North Sea clay Corinth marl Test label and type p' (kPa) prior to shearing OCR prior to testing Test label and type p' (kPa) prior to shearing OCR prior to testing Test label and type p' (kPa) prior to shearing OCR prior to testing TN-14-D 500 3.4 TT-1-D 10 31 cd-98-D 98 13.3 TN-15-D 800 2.1 TT-2-D 25 16 cd-294-D 294 4.4 TN-16-D 1300 1.3 TT-3-D 50 8 cd-500-D 500 2.6 TN-17-D 2500 1 TT-4-D 760 1 cd-3000-D 3000 1 TN-18-D 1500 1.1 TT-5-D 10 70 cd-6000-D 6000 1 TN-20-D 250 6.8 TT-6-D 25 28 cd-56-U 56 23.2 TN-5-U 700 2.4 TT-7-D 50 14 cd-315-U 315 4.1 TN-6-U 300 5.7 TT-8-D 700 1 cd-550-U 550 2.4 TN-7-U 500 3.4 TT-9-D 10 86 cd-3000-U 3000 1 TN-10-U 1300 1.3 TT-10-D 25 34 cd-5000-U 5000 1 TN-11-U 1600 1.1 TT-11-D 50 17 TN-12-U 3800 1 TT-12-D 860 1 TN-21- K0 1 TT-2r-D 25 13 TT-12r-D 800 1 D- Drained triaxial shearing U- Drained triaxial shearing K0 -Triaxial K0 compression test 5. THE S_BRICK PREDICTION OF STRESS STRAIN BEHAVIOUR OF PAPPADAI CLAY, NORTH SEA CLAY AND CORINTH MARL The S_BRICK model was validated using the laboratory results from the three different materials, which could be classified as hard soils and soft rocks according to their strength and mechanical behaviour. The Pappadai clay, North Sea clay and Corinth marl were chosen to demonstrate the ability of the S_BRICK model to cover a wide range of structured materials. The key parameters of the S_BRICK model for each natural material are given in Table 1. All the other necessary parameters for the S_BRICK model were taken as constants and were the same as the parameters for the BRICK model of London clay [27]. A list and description of the validated laboratory tests from Pappadai clay, North-Sea clay and Corinth marl are presented in Table 2. 5.1 S_BRICK prediction of the stress strain behaviour of Pappadai clay Pappadai clay has been extensively studied over the years and its behaviour is well documented [13, 12, 14]. It is a hard over-consolidated clay with a weak cementation. According to Cotecchia and Chandler [13], the geological history of Pappadai clay followed four stages: 1) normal consolidation with the structure formation at the end Figure 10. S_BRICK prediction of Pappadai clay history in normal compression in: (a) v-logp' (b) q-p' plots. of sedimentation, 2) overconsolidation, 3) desiccation, history of Pappadai clay, modelled by S_BRICK, is shown oxidation and weathering and 4) unloading caused by the in Figure 11, along with the Cotecchia and Chandler [13] rise of the water table to the present level. The geological interpretation in both v-logp' and q-p' planes. c*=18°) and the natural clay (ipcs=21°), given by Cotecchia and Chandler [14], was taken, leading to the values of a*=0.6 and a=0.7. The values of a^, a and were also determined using the procedure previously explained. The numerical procedure of the modelled strength and stiffness response gave an indication that the destructuring was certainly present in compression, while in recompression and shearing no destructuring was evident, so it was not accounted for. Consequently, only six additional parameters were necessary to take into account the structure and destructurisation of Pappadai clay using the S_BRICK model. For the S_BRICK model, as for the other kinematic hardening models, it was necessary to model the geological history of the Pappadai clay in order to arrive at the current in-situ state. The sedimentation was modelled with the parameters for the reconstituted clay and at the end of sedimentation phase (formation of structure), the parameters describing the structure were added. Swelling to the in-situ state and sampling was therefore modelled using the parameters for the natural clay. This was the starting point for all the further A-class predictions of the results of laboratory tests, i.e., no changes to any S_BRICK parameters were made from this point onwards. The S_BRICK predictions of the stress and strain behaviour of the drained triaxial shearing of Pappadai clay are shown in Figure 11. The figure shows separately (a) the compression behaviour in the v-logp' plane, (b) the mobilisation of the deviator stress q with the shear strain £s, (c) the variation of the volumetric strain ev with the shear strain es and (d) the degradation of the secant shear modulus Gsec against the logarithmic shear strain es. For clarity, only the three tests TN-20 (OCR=6.8), TN-16 (OCR=1.3) and TN-17 (NC, 0CR=1.0) are shown in Figure 11b-d, while the results of the tests of the other samples were qualitatively similar. It can be seen that S_ BRICK gave generally excellent predictions of the strength and stiffness behaviour for the entire range of deformations, regardless of the level of overconsolidation. Somewhat less successful were the predictions of the post-peak softening (Figure 11b) and the volumetric behaviour of the sample TN-17 in which the volumetric response was clearly over-predicted. As can be seen from Figure 11a, the sample TN-17 was isotropically consolidated beyond the initial SBS, so a destructurisation in compression was modelled, which could be a reason for the over-prediction of the volumetric response. When a normalization of a p'-q plane is applied, dividing p' and q by p*e, it can be seen in Figure 12a that S_BRICK correctly predicts the position of the stress path for TN-17, which lies in between the SBS for the natural and reconstituted clay, while all the other results also correctly predict the shape of the SBS for the natural Pappadai clay. When further normalization, that includes the structure (S) is applied (Figure 12b), the SBS for the natural, reconstituted and destructured clay coincides for all the S_BRICK predictions as well as for the samples of Pappadai clay. The undrained shearing tests were also modelled using the same set of parameters given in Table 1 for Pappadai clay. The S_BRICK predictions of the stress and strain behaviour of the undrained triaxial test are shown in Figure 13a-d in the following diagrams: (a) compression behaviour in the v-logp' plane, (b) mobilisation of the deviator stress q with the mean effective stress p', (c) mobilization of the deviator stress q with the shear strain es and (d) degradation of the secant shear modulus Gsec against the logarithmic shear strain es. For clarity, only the three tests TN-7 (OCR=3.5), TN-10 (OCR=1.3) and TN-12 (NC, OCR=1.0) are shown, while the results of the tests of the other samples were qualitatively similar. Generally, it can be concluded that the S_BRICK model gave good predictions of the undrained shear strength and stiffness decay with the deformation of the Pappadai clay samples. It was slightly less successful in modelling the post peak behaviour (Figure 13c) and it predicted somewhat different stress paths in the q-p' plane (Figure 13b) for the over-consolidated samples. When the normalization for p'*e (Figure 14a) is applied, it can 0.2 0.4 0.6 0.8 P'/Sp'e /\D Yielding surface A/ Fa / / Loading / /Unl0ading --/---r I P -W B G Figure 3. Loading and unloading stress path in the p-q plane. Oj -a3/MPa -0.012 -0.008 -0.004 0 0.004 0.C Figure 4. Loading and unloading stress-strain curve under the confining pressure of 5MPa. curve under the 5MPa confining pressure. The elastic modulus decreases, while the plastic deformation increases with the loading process. As is well known, the weakness of the elastic modulus is related to the evolution of the damage. Thus, the elastoplastic damage evolution is accompanied by the loading process of the T2b marble. Fig.5 shows the envelope line for the loading-unloading test curve. The envelope line also stands for the yield surface before the yield and the subsequent yield surface after the yield. (a) Figure 5. Envelope line of the loading-unloading test curve of the T2b marble: (a) axial stress-axial strain curve, (b) volumetric strain—axial strain curve. 2.2 Test result analysis The plastic characters in the loading process can be seen from Fig.5: a) The stress-strain test curve is approximately linear under a low confining pressure. The elastic deformation at failure increases with the increasing confining pressure. After a threshold the test curve shows obvious non-linearity and plasticity, b) The confining pressure influences the strength and the deformation. With the increasing confining pressure, the strength and axial strain increases, while the volumetric strain seems restrained, c) In the case of a low confining pressure, the sample fails in a strain softening character, while strain hardening shows for the high confining pressure, d) There is a transition from volumetric compression to dilation. At first, the micro-fissures were compressed. Then the loading propagates the cracks after a threshold and dilation occurs. However, with the increasing confining pressure, the dilation is slow to happen and appears to be suppressed. In the meantime, the fissures in the T2b marble have such a sequence of evolution due to damage: a) Under low applied loading stress, the microcracks are compressed and the volume decreases, b) With the increasing loading stress, local instability leads to meso-scopic fracture, c) Mesoscopic fracture propagates and extends, d) The mesoscopic fracture develops into the penetrating crack and the sample fails. To sum up, there is a coupling elastoplastic and damage effect in the loading process of the T2b marble. When the load is not large enough, the microfissures are compressed and the material is elastic. With the increasing loading pressure, cracks propagate and dislocation occurs. Plastic deformation induces damage and, conversely, there is a further development of the plastic deformation. Therefore, it is necessary to use the coupled elastoplastic damage theory in the loading analysis of the T2b marble [10], 3 ELASTOPLASTIC DAMAGE-COUPLING MODEL There is no obvious anisotropic character in T2b marble. So the isotropic theory is used in the analysis. It is presumed that the weakness due to the mesoscopic fissures can be described by the macroscopical isotropic damage. The damage process is defined by the damage variable in a scalar form. Under isothermal conditions, the state variables in the loading process are listed as the total strain tensor e, the damage variable a>, the elastic strain tensor ee and the plastic strain tensor ep. The full variable form and incremental form of strain can be expressed £=£e + ep ,de = dee +dep (1) It is assumed that there is a thermodynamic potential coupling the damage and plasticity. The thermodynamic potential can be expressed as :C(co):s!+y/p(K,co) (2) where fp is the thermodynamic potential describing the strain hardening of the damaged material, k is the internal variable for plastic hardening, which can be described by the plastic deformation, such as the plastic strain or the equivalent plastic shear strain. C(co) is the fourth order of the elastic tensor. For isotropic material, C(co) is expressed as [11] C(©) = 2G(©)K + 3Är(©)j (3) where G and K are the shear modulus and bulk modulus, respectively. IK and J are the isotropic fourth tensor, which can be expressed as K = I-JU=-5®5 (4) 3 where S is a second-order unit tensor. I is a symmetric fourth-order unit tensor. For a second-order tensor E, we have JJ: E = , K: E = E . The partial derivative operation is done with equation (2) and we have dee ^ ' (5) Considering the damage to the elastic parameters, thus equation (5) can be rewritten in incremental form as da = C((d):dee 3.1 Damage description © 0(0 : 8 dco (6) In the framework of the irreversible energy, many damage models have been established. In these models, the damage evolution is determined by the evolution function with a damage variable. The test shows that there is a shear bond penetrating the sample and particles slide along the microcrack with damage evolution. Thus, in this paper the damage driving force Ya is Ymax is the maximum damage variable. The parameter Bc controls the kinetics of the compressive damage and can be determined by using a uniaxial compression test. The parameter Ya)0 is the damage threshold. To sketch the damage evolution during the loading process, the damage-evolution curve for the T2b marble under a confining pressure of 40MPa is shown in Fig.6. 300 -, 250 - 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 E1 Figure 6. Damage-evolution curve for T2b marble under confining pressure of 40MPa. 3.2 Plasticity description According to the test research, rock has the characteristic of pressure sensitivity[13]. In other words, the strength increases with the increasing confining pressure or hydrostatic pressure. In this paper, the value of the variable is positive when the stress is tensile. Inspired by Chen et al, the strength criterion is adopted as r r \ q - + c g(8)/c0 "U(0)/CoJ q -- fcO = 0 (9) 1 wherep is the hydrostatic pressure expressed as p—fr (o). q is the equivalent shear stress expressed as a = J—S :S . S is the deviatoric shear tensor V 2 i expressed as S ~a--[tra)8 ,fc0 is the uniaxial strength determined by the uniaxial test. The parameters q, c2 and c3 define the curvature of the failure surface and can be determined by plotting the failure surface. g(9) determines the effect of the Lode angle on the strength. In the loading path in this paper, g(9) is simplified as g(0)=l. It is noted that equation (9) is the Drucker-Prager criterion in the case of c2=0 for the simplified calculation. The loading equation similar to equation (9) is /s=?-asg(8)ac=0 (10) c1+ 0, as ■ an • For Yp ■co, a. •1. 3.3.1 (a) da»0, fs=0 In this case, the plastic flow and the damage evolution are activated. The damage variable increment is determined by 5/co d(ù = d\,„ = dX„ dZ, -co. D max <: (16) o)] where d\a is the damage multiplier, which can be determined by the damage-consistency condition The generation of microcracks is accompanied by the plastic deformation. To express the weakness the loading function is expressed as fs=q-asg(Q) ("cl + Jci+4 cl{c2-pl fco) Ico /co=0 (13) L-(ö)-ö)y^, ü)f is the threshold of where fc0 =/co(1~(Cl the damage to the plasticity. When the damage variable is larger than ay, the loading curve shrinks and the strength decreases. The symbol (x) is expressed as: (x) = 0 when x<0 and (x) = x when x>0. The test shows that the volumetric deformation changes from compression to dilation and this effect decreases with the increasing confining pressure. To express the deformation character, inspired by the work[14, 15], the plastic potential function is gs + fl' yhj = 0 (14) where I = -p + c^fcQ . The parameter I0 determines the intersection point of the plastic potential surface and the coordinate/). The threshold of the volumetric compression to dilation can be determined by ^gs _ q , expressed as SI /™=^-^(0)(-jP + c3/co) = ° (15) where the parameter ¡¿s defines the slope of the boundary between the compressibility and dilatancy domains. Its value can be obtained by plotting the transition boundary line in the p-q plane. 3.3 The damage and plasticity coupling numerical process In a general loading path, the plastic flow and damage evolution can be activated regarding the loading law, respectively. There are two kinds: a) da)>0,fs=0. b) da)>0,fs<0. oYm oco ®max^c dZ dZ exP \ßc (^co ~ ^coo )] V de From equations (16) and (17) we have — : dze + —: dzp + c/co = 0 dzp (17) dXm=-\^:dEe+^:dEp I (18) ,8ee 8ep For plasticity, the plastic strain increment is dep = dl^ s da (19) where dXs is the plastic multiplier, which can be determined by the plastic consistency condition as dfsJA:da+ÈL^:dEP + dAd^ o da dyp dep dco (20) From equations (19) and (20), the plastic multiplier is determined as — :da + — da> dX, - - da dco &YP dsp ' da (21) Substitute (16) into (21) and (19) into (18), the simultaneous equations are obtained and thus we get the plastic multiplier and the damage multiplier. The constitutive function in incremental form can be expressed as da ~ C(co): I dz-d\s^~ —d À,,. co, z> 'max nc 3C( (22) co exp[5c(rffl-rffl0)] ÔCO - : e 3.3.1 (b)flk»0, fs<0 For/s<0, the stress point is in the elastic range and no plastic flow happens. da)>0 and there is only damage evolution. Accordingly, the plastic strain increment is 0. Therefore, dep=0. The damage-variable increment is expressed as equation (16). Similar to equation (17), the damage-consistency condition is expressed as oYm öco (23) exP \ßc (Y' - 30°) 0.00 Poisson's Ratio 0.25 Elasticity Modulus, E (kN/m2) 30.000 Rinter 0.10 (a) (b) Figure 1. Mesh grid of topographic model. (a) Single-plate anchor; (b) Two-plate anchors Figure 2. Typical finite-element mesh. The one-plate anchor system was modelled to obtain the reference bearing capacities. In the analyses, the upper-plate depth (H/D) was changed from 1 to 7 and the spacing between the two plates (s/D) for each different H/D value was changed from 0.5 to 7. Consequently, 84 analyses were performed for this study. In the finite-element analysis the axi-symmetric model was used since the geometry and the loading conditions of the problem provide axi-symmetry. Only half of the geometry is considered in the PLAXIS 2D analysis of axi-symmetric problems. The thickness (t) and the diameter (D) of the plate were 1 cm and 20 cm, respectively. The soil was modelled as an isotropic elasto-plastic continuum with failure described by the Mohr-Coulomb yield criterion. The parameters of the sandy soil were listed in Table 1. The anchor was modelled as being much stiffer than the soil as a discrete plate element. Although it is likely that, shaft friction contributes to the capacity, the term is generally ignored in the anchor design because of the uncertainties involved (Merifield [21]). So, the interface element was defined around the shaft and the interaction between the shaft and the surrounding soil was neglected. Also, the interaction was neglected between the plate bases and the soil under the plates (Fig 2). The rationale of the finite-element method is one in which continuous media is divided into finite elements with different geometries. The mesh configuration can be generated automatically for the desired refinement and each element is compatible with the structural and interface elements. During the generation of the mesh, 15-node triangular elements were selected in preference, to provide greater accuracy in the determination of the stresses. In this study, in order to select the suitable mesh refinement, preliminary analyses were conducted at five different mesh coarseness. The fine-mesh coarseness was used in all analyses, since there is a remarkable difference observed for the coarser mesh sizes. A typical finite-element mesh that is composed of the soil, multiplate circular anchors, boundary conditions and the geometry of the model used, is shown in Fig. 2. The uplift behavior of the plate anchor was analyzed by using the displacement-definition approach. The common opinion about the failure criteria is in the range of 10% of the plate's diameter. However, the determination of the failure criteria was based on the comparisons of the experimental and theoretical results, as indicated in the literature (Sakr [27], Elsherbiny and Hesam El Naggar [28], Sakr [29]). The 5% displacement criterion has been recommended as a failure criterion to satisfy the serviceability requirements. For this purpose, the failure criterion was selected as 5% of the plate diameter (20 cm). Therefore, the vertical stresses above the horizontal plates were used to calculate the total ultimate load Fy, which was obtained against the 1-cm movement of the two-plate anchor system in the analyses. 3 NUMERICAL ANALYSIS_ 3.1 Single-Plate Anchor The uplift capacity of the single-plate anchor at seven different embedment ratios (H/D) from 1 to 7 was analyzed using PLAXIS 2D. The results of the singleplate anchor analysis were only used to compare the results with the literature and to assess the performance change that would occur in a two-plate case. The analyses were performed until the collapse of the soil was observed. The criterion of the displacement-defined analysis was increased up to the collapse of the soil to obtain the same ultimate situation as in the literature. Uplift capacities are often expressed in dimensionless form as breakout factor (BF), as given below: BF = - F ïAplH (1) where BF is the breakout factor, Fu is the maximum uplift resistance, y is the soil unit weight, H and Apj are the anchor embedment depth and plate area, respectively. The graph in Figure 3 presents the variation of the relationship between the breakout factor and the embedment ratio (H/D) at a 30° constant angle of the shearing resistance of the soil, for a single-plate anchor in sand. Figure 3. Comparison of the breakout factor for a single plate. According to the graph, the breakout factor that was obtained from PLAXIS 2D are in accordance with the literature (Hanna et al. [19], Merifield et al. [30], Sarac [31], Koutsabeloulis and Griffiths [32]). The breakout factors obtained from the PLAXIS 2D are slightly below the results of the literature, especially at the large embedment depths. Consequently, the validation of the model and the parameters that are used in the analysis have been approved in the literature by dimensionless values. 3.2 Two-Plate Anchors A total of 77 different analyses were performed. The analysis program is listed in Table 2. Evaluations were made at the maximum vertical stresses caused by a 1-cm plate's movement. The stress distributions were presented together with the upper and lower plates, and they were compared with the single-plate condition for each embedment ratio, as seen in Figure 4. Table 2. Analysis program. Plate Diameter Constant Value Variable Value Embed- (D) cm ment Ratio, Spacing Ratio, s/D H/D 20 1 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0 20 2 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0 20 3 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0 20 4 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0 20 5 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0 20 6 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0 20 7 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0 Figure 4. Vertical stress versus spacing ratio for the constant embedment ratios. According to Figure 4, the maximum vertical stress (with a 5% vertical movement) on the single plate was obtained as being similar to the upper plate of the two- plate anchor system at the same embedment depth ratio. An average absolute error of 3% was obtained for all the 7 embedment depth ratios. While the upper-plate stresses were obtained about a constant value, independent of the spacing ratio, the lower-plate stresses were in a trend of increasing with an increase of the spacing ratio. Figure 5. Vertical stress distribution at the bottom plate. 100 ? 10 ♦ H/D ■ H/D a H/D XH/D xH/D • H/D + H/D d =1 =2 =3 =4 =5 =6 =7 A vX 2 ¥ i + A A A $ $ (a) 2 3 4 5 6 7 Spacing Ratio (s/D) (b) Figure 6. Performance variation. (a) Two-plate case; (b) Optimum value (s/D=3.5%) The stress distribution in a logarithmic form on the lower plate was in a trend of increasing until a 3.5 spacing ratio and the trend of the stress was transformed into an asymptote for the larger values of the spacing ratios (Figure 5). It can be concluded that using a spacing value between the plates wider than 3.5D has no significant effect on the vertical stress on the lower plate. Therefore, the uplift capacity of the two-plate anchor system has become constant for a constant value of H/D and for any values of the spacing ratios s/D>3.5. The performance variation of the two-plate anchors according to the single-plate anchor system (N) was described as N=FdoublJ Fsingle. In Figure 6, the N values increase when the spacing ratio (s/D) increases in a non-linear form. According to the graph, the maximum performance in a two-plate anchor system was obtained as 20 times, compared with the single-plate case, for the lowest embedment depth ratio, H/D=1 (Figure 6.a). As described earlier, the optimum spacing ratio was obtained as 3.5D for the performance increments. The graph of the performance variation against the embedment depth ratio was given in Figure 6.b for the specific spacing ratio of 3.5D. From the graph it can be concluded that, the N values decrease when the embedment ratio increases significantly until H/D=4, but it is more or less constant for the values of H/D>4. 4 STATISTICAL ANALYSIS_ For predicting the performance of the systems, empirical estimation methods are generally used in civil-engineering applications, including geotechnical engineering (Rao and Prasad [33], Niroumand and Kassim [34]). Regression analysis is one of the most commonly used empirical methods to examine the relationship between a dependent variable and a set of independent variables. Correlation and regression analysis are related in the sense that both deal with the relationships among variables. Neither regression nor correlation analyses can be interpreted as establishing cause and effect relationships. The correlation coefficient (R) measures only the degree of linear association between two variables and also the coefficient of determination (R2) is used as a measure of the quality of the regression. The method that is used in this study is preferred as a similarity model and can be adopted for pullout capacities of double-plate anchor systems because the independent variables used are explicit and the dimensionless variables are physically bounded (Misir and Laman [35]). The formulation was derived from 84 numerical analysis results with different embedment and spacing ratios. The developed formulation contains the dimensionless parameters of the embedment ratio (H/D) with a range of 1 to 7 and a spacing ratio (s/D) with a range of 0.5 to 7 for a double-plate anchor. After the studies in the literature were examined, it was decided that the curve type controlling of the plate stress ratio is a function of the exponential behavior, as seen in Eq. 2. 5 RESULTS AND DISCUSSION a yy bottom a yy sin gle y = a * e/ -7.11 + 10.98* H U _127.19 (2) D ) ÎH, 0.424 * H |-5.4 (3) Regression analysis is a technique used to estimate values that are unknown using known values. It is important to know the shape and the degree of the functional relationship between the variables. The value of the correlation coefficient indicates the degree of reliability for the estimated values (Misir and Laman [35]). The comparison of the vertical stresses on the bottom plate of the two-plate anchors and the single-plate anchor Oyy bottom/ayy single in dimensionless form obtained from PLAXIS and the formulation results is shown in Figure 7. The relationship between the PLAXIS and the formulation (Eq. 3) results are very comparable, with the line of y=x having a high coefficient of determination equal to 0.995 (Figure 7). 70 60 50 40 30 - 20 > > b 10 0 0 10 20 30 40 50 60 70 s yy bottom/syy single Formulation Figure 7. Correlation of the predicted results from the formulation data and PLAXIS. 5.1 Analytical Determination of the Uplift Capacity There have been numerous theoretical studies that address the uplift capacity of a single horizontal anchor. The majority of these studies, however, assume a condition of plane strain for the case of a continuous strip anchor or axi-symmetric for the case of circular anchors. In recent years the failure mechanisms and the pullout capacities of multi-plate anchor systems have been investigated and current approaches are now being developed. The most common approach is to categorize the multiplate anchor system according to their failure mechanisms. For this purpose, the pullout capacities of the multiple anchor systems can be calculated based on the failure mechanisms in two groups as individual bearing or cylindrical shear. The important point in this approach is that the designer should know the critical embedded ratio and the spacing ratios to distinguish the behavior of the failure between the shallow and deep anchors. However, in this study the double-plate anchor system and failure mechanisms have not been categorized as either a shallow or deep individual bearing versus cylindrical shear. All of the models that have been analyzed comprise a combination of both the deep and shallow anchor systems. Unlike the general approaches in the literature, in this study the pullout capacity was calculated from the vertical stress variation over the plate surface during the vertical movement caused by the pulling force. A similar semi-empirical approach was used by Meyerhof and Adams [3] to include the circular anchors by extending the strip anchor results by modifying the passive earth pressures with a shape factor. To obtain the pullout capacity, the maximum vertical stresses corresponding to the defined vertical displacement over the plates were collected and the effective stresses at the plate depth levels were subtracted from this value (Eq. 4) F = 5.2 \a + g \ yybottom yyupper y *D* An, *| 2H + — r 1 D D , (4) Comparison of the PLAXIS results with those obtained from Eq. (4) The pullout capacities can be obtained from the conventional formulation given in Eq. (4) with the known vertical stresses, from the upper (single-plate analysis results from PLAXIS 2D) and the lower plate (statistical approach). The graph in Figure 8 shows the comparison e of the uplift capacities obtained from the PLAXIS 2D analysis and the developed approach that are given in Equation 4 for the double-plate anchor system. The linear 1:1 line was also plotted in this figure in order to discuss the performance of the statistical models. It can be seen from the figure that by using Eq. (4) the location points of the numerical and the predicted pullout capacity values are scattered around the 1:1 line with a high coefficient of determination equal to 0.982. 0 3 6 9 12 15 18 21 24 27 Uplift Capacity Obtained from Formulation tkN) Figure 8. Comparison of the uplift capacities obtained from PLAXIS and formulation (Eq. 4). As seen from Table 3, the pullout capacities between the results of the numerical analysis and the proposed approach were obtained in a close fit. The variables in Table 3 include the embedment ratio H/D and the anchor spacing ratio s/D. The comparisons between the numerical and proposed methods were given as the rate of the pullout capacities (FDeveloped/Fpiaxi) For the majority of cases, the calculated capacities are approximately within +3% of the measured values, which is adequate for design purposes as an average. As seen in Table 3, the developed FDevehped/FPkxis parameters, especially for H/D=1, 2 and s/D=0.5, 1.0, 1.5, are well below the prescribed limit value of 1. Especially for these six values, the difference is caused from the exponential part of the formulation for the shallow embedded depths and the close spacing ratios. In summary, the implementation steps of the proposed approach are as follows: 1. The single-plate anchor model is generated at the desired embedment ratio (H/D) in the numerical analysis. But the most important thing is that the H/D value must be the same with the upper plate depth in the two-plate anchor model. 2. The single-plate model should be analyzed at a 5% vertical displacement ratio with PLAXIS 2D. 3. The maximum vertical stress value on the circular plate can be obtained from this analysis. 4. This vertical stress value corresponds to the upper plate in the case of two plates because of the same effective stress and the same vertical movement. 5. The stress value on the bottom plate can be calculated from the statistical formulation as given in Eq. (3) by using the embedded and spacing ratios. 6. After the two last steps, the vertical stresses are the known parameters to obtain the pullout resistance for the desired vertical displacement. 7. Finally, the uplift capacity of the two-plate anchor system can be calculated using Eq. (4). Limitations The results reported in the present study are only valid for the embedment and spacing ratios referred to herein. The breakout factors and the failure mechanisms and also the size and scale effects of the plate anchors have not been investigated. Therefore, the results obtained from this study should not be used in practice without a verification based on experimental studies. 6 CONCLUSIONS On the basis of the analysis of the results obtained from the present investigation, the following main conclusions can be drawn: - The aim of the single-plate anchor modelling was to understand the effect of the embedment depth of the anchor. The results of this group of analyses were used as a reference analysis to make a transition to the two-plate anchor model. The breakout factors' variation of the single-plate anchor according to the versus embedment ratios from 1 to 7 (H/D) at a constant 30° angle of the shearing resistance of sandy soil were in good agreement with the literature. - The vertical stress distribution at a predetermined vertical displacement (1 cm) on the upper plate was obtained as similar to the single-plate anchor model at a constant embedment ratio. Also, the maximum vertical stress on the upper plate increased with the increment of the embedment ratios, but it was independent of the spacing ratios (s/D) for a 1cm movement of the anchor system. - In the two-plate anchoring case, the maximum Table 3. Comparison of the results of the Plaxis analysis and the developed formulation. H/D s/D F (kN) Developed F (kN) Plaxis FDeveloped/ FPlaxis H/D s/D F (kN) Developed F (kN) Plaxis FDeveloped/ FPlaxis 7 0.5 9.063 9.494 0.95 3 0.5 1.880 2.626 0.72 7 1 10.990 10.462 1.05 3 1 2.233 2.771 0.81 7 1.5 13.651 10.914 1.25 3 1.5 3.401 3.575 0.95 7 2 16.041 12.277 1.31 3 2 4.965 4.518 1.10 7 2.5 18.006 15.023 1.20 3 2.5 6.573 6.076 1.08 7 3 19.598 16.776 1.17 3 3 8.076 7.615 1.06 7 3.5 20.895 17.838 1.17 3 3.5 9.428 9.243 1.02 7 4 21.962 19.528 1.12 3 4 10.626 10.304 1.03 7 5 23.597 20.370 1.16 3 5 12.611 11.517 1.09 7 6 24.775 20.735 1.19 3 6 14.159 12.390 1.14 7 7 25.651 21.237 1.21 3 7 15.381 13.459 1.14 6 0.5 8.229 8.149 1.01 2 0.5 0.421 1.257 0.33 6 1 9.371 8.677 1.08 2 1 0.617 1.766 0.35 6 1.5 11.338 9.764 1.16 2 1.5 1.464 1.828 0.80 6 2 13.290 11.247 1.18 2 2 2.719 3.154 0.86 6 2.5 14.987 12.686 1.18 2 2.5 4.084 3.707 1.10 6 3 16.411 15.011 1.09 2 3 5.406 5.473 0.99 6 3.5 17.600 17.103 1.03 2 3.5 6.624 6.648 1.00 6 4 18.595 18.083 1.03 2 4 7.722 7.622 1.01 6 5 20.149 19.528 1.03 2 5 9.578 9.431 1.02 6 6 21.288 20.251 1.05 2 6 11.050 10.267 1.08 6 7 22.147 20.954 1.06 2 7 12.227 10.568 1.16 5 0.5 7.125 7.025 1.01 1 0.5 0.057 0.415 0.14 5 1 7.933 7.678 1.03 1 1 0.063 0.622 0.10 5 1.5 9.657 8.363 1.15 1 1.5 0.750 1.131 0.66 5 2 11.547 10.122 1.14 1 2 1.880 1.960 0.96 5 2.5 13.286 11.014 1.21 1 2.5 3.179 2.645 1.20 5 3 14.799 13.107 1.13 1 3 4.483 3.682 1.22 5 3.5 16.093 14.382 1.12 1 3.5 5.715 5.334 1.07 5 4 17.199 15.293 1.12 1 4 6.846 5.862 1.17 5 5 18.960 17.668 1.07 1 5 8.795 7.779 1.13 5 6 20.280 18.730 1.08 1 6 10.372 9.337 1.11 5 7 21.292 18.856 1.13 1 7 11.651 9.550 1.22 4 0.5 4.463 4.574 0.98 4 1 5.024 5.133 0.98 4 1.5 6.505 6.063 1.07 4 2 8.300 6.729 1.23 4 2.5 10.046 8.972 1.12 4 3 11.620 10.487 1.11 4 3.5 13.002 11.448 1.14 4 4 14.204 12.717 1.12 4 5 16.158 14.527 1.11 4 6 17.654 15.400 1.15 4 7 18.818 15.714 1.20 vertical stress distribution on the bottom plate was in a trend of increasing, depending on the increasing spacing ratio. - The vertical stress on the bottom plate remained unchanged at the larger spacing ratios from 3.5D. At the smaller values from 3.5D, the vertical stresses increased with the spacing ratios. Therefore, the maximum performance of the bottom plate was obtained at a spacing ratio of 3.5. - When the performance increment on the two-plate anchor system was plotted on the graph for the optimum 3.5D plate spacing, the effect of the second plate increased the system performance to 20 times for the embedment depth of H/D=1. This increase was continued in a trend of decreasing up to H/D=4 and resulted in an average 2.3 times increase in the system performance with values of greater than H/D=4. - Based on the analysis, the vertical stresses on the lower plate were formulated using a statistical analysis based on dimensionless parameters such as the H/D and s/D ratios. When compared with the values obtained from this formula and the values obtained from PLAXIS, the vertical stress value on the lower plate was estimated with a high correlation coefficient of 0.995. - When a proportional relationship between PLAXIS and the developed approach is established, the Fy developed / Fypbxis ratio, which should be 1 in the ideal solution, was obtained in average as 1.03 for all the analyses. - It can be concluded that, the perspective of the developed approach is quite promising for the prediction of the ultimate pullout capacity of two-plate anchor system as a preliminary design work. REFERENCES_ [1] Mitsch, M.P., Clemence, S.P. 1985. The uplift capacity of helix anchors in sand. In Uplift Behaviour of Anchor Foundations in Soil. Proceedings of a Session Sponsored by the Geotechnical Engineering Division of the American Society of Civil Engineers, Michigan. American Society of Civil Engineers, New York, pp. 26-47. [2] Ghaly, A., Hanna, A., Hanna, M. 1991. 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Periodica Polytechnica Civil Engineering 61(3), 434-446. https://doi.org/10.3311/PPci.9578 CONSOLIDATION ANALYSIS OF CLAYEY SOILS USING ANALYTICAL TOOLS ANALIZA KONSOLIDACIJE GLINASTIH TAL S POMOČJO ANALITIČNIH ORODIJ Barttomiej Szczepan Olek Tadeusz Kosciuszko University of Technology, Warszawska 24, 31-155 Krakow, Poland E-mail: bartlomolek@gmail.com https://doi.org/1Q.1869Q/actageotechslov.15.2.58-73.2Q18 Keywords consolidation; clay; filtration; coefficient of consolidation; optimization Ključne besede konsolidacija; glina; filtracija; koeficient konsolidacije; optimizacija Abstract The uncoupled Terzaghi consolidation equation (excess pore pressure only) is widely used to predict the rate and magnitude of settlements in clayey soils. The theoretical solution is based on the approach of considering the soil permeability and compressibility as one parameter obtained by experimental methods - the coefficient of consolidation cv. This article presents two analytical tools that allow us to determine the consolidation coefficient, which is independent of a single measurement point and represents the consolidation behavior for the significant progress of settlements. The presented methods were based on the process of optimizing the coefficient of consolidation value and the quasi-constant approach, which assumes the identification of a quasi-filtration consolidation phase using the log cv - U relationship. To assess the validity of each method, the experimental results were compared to the theoretical solution and quantified using a new statistical parameter dn. Izvleček Nevezana Terzaghija enačba vertikalne konsolidacije (upoštevan samo porni nadtlak) se pogosto uporablja za napovedovanje hitrosti in velikosti pomikov v glinastih tleh. Teoretična rešitev temelji na pristopu upoštevanja prepustnosti tal in stisljivosti v enem parametru, pridobljenem z eksperimentalnimi metodami - koeficient vertikalne konsolidacijske cv. V članku sta prikazani analitični orodji, ki omogočata določitev koeficienta vertikalne konsolidacije, ki je neodvisen od posamezne merilne točke in opisuje konsolidacijsko vedenje za značilen časovni razvoj posedkov. Predstavljene metode temeljijo na procesu optimizacije vrednosti koeficienta vertikalne konsolidacijske in kvazi - konstantnega pristopa, ki predpostavlja identifikacijo faze kvazifiltracijske konsolidacije z uporabo relacije log cv - U. Veljavnost obeh metod smo ocenili s primerjavo eksperimentalnih rezultatov in teoretičnih rešitev ter kvantitativno ovrednoteli z uporabo novega statističnega parametra dn. DOI 1 INTRODUCTION Studying the properties of geomaterials is one of the basic aspects involved in predicting the soil-structure interaction and planning any soil-strengthening modifications. Geomaterials include all the natural, processed or produced and improved materials used in geotechnical applications. Natural geomaterials are mainly soils and rocks, as well as mixed material behaving as a transient between soil and rock. Natural soils, especially soft clays, muds and expansive soils, can be problematic and may cause a potential threat to a construction. During the design of foundations and embankments on clayey soil, it is crucial to predict the magnitude and rate of settlements. The accuracy of predictions in the design stage depends on the input value of the coefficient of consolidation cv. A correct assessment of the real values of this parameter and the impact of the factors influencing it is a difficult problem. It has been a serious challenge for researchers and has not yet been fully resolved. The consolidation process is a combination of two phenomena: permeability, which controls the rate at which water is removed from the pore space (and thus the rate of the settlement at any time) and compressibility, which controls the evolution of the distribution of excess pore-water pressure (and thus the duration of the consolidation process). The widely used Terzaghi theory is based on a linear stress-strain relationship and constant permeability. Theoretical solutions were based on a consideration of all the soil properties as one parameter - the coefficient of consolidation cv, obtained with experimental methods ([1]). Over the past 50 years, difficult and time-consuming attempts have been made to develop appropriate methodologies and interpretations of consolidation tests. The valuable material refers to the studies on the standardization of time-compression data analysis and can be found in ([2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]). The achievements of the above-mentioned researchers relate to the commonly accepted Terzaghi theory and could be used for a uniform, initial, pore-pressure distribution. Solutions for a non-uniform and sinusoidal initial pore-pressure distribution can be found in Lovisa et al. [13] and Lovisa and Sivakugan [14], respectively. The existing methods for calculating the consolidation coefficient were collected in Table 1, where the experimental and theoretical relations considered during the analysis were included as well as the individual expressions for the coefficient of consolidation. The realistic application of Terzaghi's theory for determining the consolidation coefficient assumes the identification of a primary consolidation range. This recognition can be conducted by the fitting procedure of the theoretical relationship between different variations of the degree of consolidation and the dimensionless time factor U - Tv to the measured deformation with time or the pore-water pressure dissipation. This kind of procedure is carried out on the basis of the similarity between the observed and theoretical curves, which can be presented and interpreted in various ways. Consolidation coefficients determined on the basis of fitting procedures are characterized by a large dispersion, which results from choosing different reference points on the experimental curve and a different way of determining the start and the end of the primary consolidation. Cohesive soils are variable due to the nature of their formation (genesis) and the impact of environmental processes. Recognizing the coefficient of consolidation as a constant parameter is the main disadvantage of Terzaghi's conventional theory. It is known that the consolidation properties of the soil should be treated in an independent manner, and considering them as one coefficient makes it difficult to relate the experimental course of the process with the theoretical solution. The main goal of the work was to develop a reliable interpretation tool for consolidation studies based on the optimization procedure. Special attention was paid to the secondary consolidation effect on the filtration nature of the process and on the relative duration of the quasi-filtration consolidation phase. During the analysis, three basic assumptions resulting from Terzaghi's theory were examined: (i) the quasi-constant consolidation coefficient; (ii) the convergence between the theoretical and the experimental course of the consolidation curves; and (iii) parallelism in the course of the curves of the pore-pressure dissipation and deformation. This paper examines those aspects based on an analysis of the consolidation data with settlement and pore-water pressure measurements during the consolidation using a Barden-Rowe hydraulic consolidometer. Tests conducted on various soils with different liquid and plastic limits have been evaluated and the coefficient of consolidation has been determined. Two methods for computing the coefficient of consolidation were presented in the study. Table 1. Comparison of existing methods for determining the coefficient of consolidation. Method Experimental relation Expression Form of the theoretical curve Reference Metoda log t S - log t 0,196H2 Casagrande & Fadum [15] Metoda Vt Slope method S - Vt S - Vt 0,848H2 J ... V cv 4 \ ^EQP j H2 Taylor [16] Al.-Zoubi ([17], [18]) Rectangular hyperbola method t/S - t c = 0.24 MH2 Sridharan et al. [4] Logarithmic method log S - log t (n / 4)H2 Sridharan & Prakash [6] Inflection point method Early stage method S - log t S - log t 0.405H2 t 0.0385H2 t Mesri & Feng [19] Robinson & Allam [20] SRS method dS/dt - S m1H 2,468 Al-Zoubi [21] S-dS/dt method S - dS/dt c = — 4H2 Tewatia et al. [10] S-log dS/dt method S - log dS/dt 0.2566v ,,2 U - log dU/dTv a** Tewatia et al. [10] Velocity method / log dS/dt - log t Improved velocity 0.793H2 Parkin [22] Pandian et al. [23] One point method logío(H2/t) - U TH2 c =—- v t. Sridharan et al. [24] logmUP/O-U c 2 c =- v s 50 2 PRINCIPLES OF TERZAGHI'S CONSOLIDATION THEORY u = - for T & 0.197(U < 50%) (6) The one-dimensional differential equation that governs the consolidation and pore-water-pressure dissipation process is expressed as follows: du d2u , N = TT dt dz where t is the time variable, u is the pore-water pressure, and z is the depth below the top of the soil layer. By introducing the dimensionless variables: Z = Z (2) H V ; and ^ c t T = "r v H (3) equation (1) is as follows: du _ dju_ dT ~ Cv ~dŽ2 c^—2 (4) The dimensionless time factor Tv defined by equation (3) is related to the average degree of consolidation U, which determines the progress of the process. The solution to equation (4) for the initial uniform excess pore-water pressure inside the soil layer is given by: m=ta i U = 1-Y—, to m 2 (5) The theoretical velocity of consolidation U=dU/dt is a product of the differentiation of the relationship between U and Tv with respect to Tv. Depending on the degree of consolidation, the following approximations can be used: U = 2e~[ v ' for Tv > 0.197(U > 50%) (7) 3 COURSE OF CONSOLIDATION_ Considering one-dimensional strain, volume changes are caused by the initial or immediate compression, the primary consolidation, and the secondary (rheological) consolidation. It should be noted that rheological conditions depend on the soil skeleton's susceptibility to plastic deformations. The progress of the consolidation process is assessed on the basis of pore-pressure dissipation or the relative settlement of the consolidated layer (Fig. 1). The initial compression occurs almost immediately after the load application due to the expulsion and compression of air in the voids. Primary consolidation is a time-dependent deformation caused by the excess of pore water pressure. Tewatia et al. [21] separated three phases of this deformation using the relationship between the compression and the compression rate. The first primary phase is characterized by the smallest impact of secondary consolidation effects and the calculated values of the coefficient of consolidation are the highest. After that the transition from first primary to second primary phase occurs. The second primary phase in many soils is characterized by a constant coefficient of consolidation value for a considerable percentage of the total settlement. Olek and Wozniak [22] separated this phase using the criterion of a quasi-constant value of the coefficient of consolidation and the relationship between the degree of consolidation and the coefficient of consolidation. As the s. 100 80 S a w to s a. S? £ 60 40 20 Settlement -curve • c. •••• o o 0 0 o Pore pressure curve 0 N. o \ » 27,5 27 "g" £ 26,5 3. 26 25,5 25 24,5 24 10 100000 100 1000 10000 Consolidation time, log t[s] Figure 1. Typical experimental course of consolidation for clayey soil. 1000000 « ■c t to CO 1 consolidation progresses, the impact of the soil's secondary consolidation increases. The transient behaviour is characterized by obtaining different temporary values of cv. The deformations in this phase result from both the pore pressure dissipation and the elasto-plastic nature of the soil skeleton's compression. The last phase is a pure creep, time-dependent deformation under a virtually constant effective stress. It should be noted that not all the phases are observed in all the soils. The pore pressure dissipation curve is characteristic. In research practice, the mobilization delay characterized by an increase in the pore pressure is usually observed. Dobak and Paj^k [23] indicated some soil properties (particle size distribution, nature of micro-pore connections, content of minerals prone to swelling) that determine the delay of the load transfer on the liquid phase. The character of the pore pressure increases and reaches its stabilized maximum value Ub,max. As the pore pressure is mobilized, the larger but not fully developed influence of the limited permeability of soil causes a delay in the deformation. It can also be seen that the volume of the soil is temporarily reduced after loading due to compression or releasing gases from the sample. The courses of the uniaxial strains and the pore-pressure dissipation do not usually overlap. Regarding the theoretical assumptions, changes in the voids ratio e are not proportional to the changes in the effective stress, and the compressibility and permeability parameters for a relatively high stress applied, decrease during the consolidation process. The explanation of the above can be made on the basis of three definitions of the degree of consolidation, referring to excess pore water pressure, changes in the effective stress and changes in the strain. Comparing them with each other, some irregularities can be encountered. Terzaghi's theory assumes that the change in the effective stress is almost linearly dependent on the deformation or change in the voids ratio. However, this is not correct, because this change is proportional to the change in the logarithm of the effective stress. During the consolidation process, the thickness of the loaded soil layer decreases due to the decrease in the voids ratio. The corresponding settlement of the layer at any time is expressed as a percentage of the total settlement and is called the average degree of consolidation Uavg. The average degree of consolidation can be expressed as follows: |-z=2H (• z=2H . , \ , I udz I (Ac- u )dz U„„ = 1 -= -^-----(8) 2H x un 2H xAct' where H refers to the layer thickness, u0 is the initial excess pore water pressure caused by the load applica- tion. The consolidation process can be considered as completed when the total excess pore water pressure is dispersed due to the load increase. However, because of the absence of a linear relationship between the changes in the pore pressure and the voids ratio, the average degree of consolidation over time calculated on the basis of the pore water pressure measurements Uu is not r r avg equal to the average degree of consolidation determined on the basis of the registration of settlements . This can be expressed as follows: U" * U avg avg and 1 - f2 J0 udz * 1 - f2 0 (9) s dz 2H x(Act') f 0 (10) s,=Jz 4 RELIABILITY OF THE CONSOLIDATION ANALYSIS_ In this section the two methods for determining the coefficient of consolidation are briefly described together with preliminary studies of the usefulness of the considered solutions. 4.1 Optimisation method for the coefficient of consolidation and the convergence criteria Using Terzaghi's model to describe the consolidation process has certain consequences. The course of the consolidation caused by the flow of water through the soil is determined by a set of curves. A fixed value of the consolidation coefficient is assigned to each curve. The compatibility between the experimental data and the theoretical solution can be the criterion for compliance with Terzaghi's model. In this study, the theoretical characteristics of the consolidation progress with the smallest possible discrepancy were assessed using the statistical parameter dn: ^ U . -U'.\ y J-Lx w . U n-l d. =-^- (11) Zw . n,i w .=- U'.- U'. , n,i-1 U'.+1 - U'. n,i+1 n,i (12) where Un i is an experimental consolidation degree, U*n. is a consolidation degree calculated for a theoretical solution on the basis of the modified dimensionless time factor Tvmod and wn i is a range around each theoretical point U*ni characterizing the dispersion. In Figure 2 a graphical presentation of this approach is shown, where the dashed line refers to the experimental course and the continuous line to the theoretical one. The best-fitted model curve with the corresponding consolidation coefficient is the one for which the dn parameter is the smallest. The use of a particular type of weighted average allowed us to determine accurately the representation of individual measurements under changing axial deformation or the speed of the pore water pressure dissipation conditions, taking into consideration the real environment of each point. A similar comparison of the consolidation was conducted by Mikasa and Takada [24] based on the curve-rule method, Lovisa, Sivakugan & Read [25] using the variance method and Sebai & Belkacemi [26] using a probabilistic method and a minimization of the sum of the squared residual (SSR). In the second and third approaches, the authors applied ranges of probable values for d0, d100 and cv. U* U* v.. u* _____ \ \\ \ \ \ "3 I 0,4 0,6 0,8 1000 10000 Consolidation time , t [s] S ■3; 0,2 0,1 0,6 o,s C c, = 1.56E-08 c,„= 1.54E-08 Sample S1 1 = 0 - Expertn — — Theore — — Theore mental curve tical curve (c„) ical curve (c,J Consolidation time , t fs] Figure 6. Consolidation behaviour of reconstituted clay paste with and without additional sand content: A) predominance of the rheological factor over the filtration factor; B) predominance of the filtration factor over the rheological factor; and C) similar course of consolidation in terms of filtration and creep factors. pore water pressure. The assumed presence of the sand fraction influenced the extension of the quasi-filtration phase and the reduction of the secondary consolidation phase, which can be seen in the U - t, log10(H2/t) - U and log cv - U diagrams. The range of the separated phase is in the highest compliance with the theoretical model in the case of the SI and S2 samples, i.e., 70% and 69%, Table 3. Results of consolidation parameters' interpretation obtained with the Quasi- constant, Optimisation and Casa- cv [m2/s] Course parameters Sample Strain q-c Pore pressure q-c Optimisation Log t n dn,min S1 1.56-08 1.54-08 1.56-08 1.82-08 0.033 0.0032 S2 1.60-08 1.49-08 1.61-08 1.85-08 0.073 0.0030 C1 1.27-08 8.00-09 1.28-08 1.46-08 0.59 0.0038 C2 1.31-08 2.20-08 1.31-08 1.36-08 -0.40 0.0034 respectively. Table 3 presents the consolidation parameters obtained from the current analysis. 6.2 Comparison of the Optimisation, Quasi-constant, Taylor, and Casagrande methods in terms of cv and dn The selected experimental consolidation courses together with the best-fitting model curve obtained for a reconstituted clay (study no 5) and for an organic soil (study no. 6) are shown in Figures 7 and 8, respectively. For each of the load increments the experimental U - Tv data was plotted against the theoretical curve from which the dn parameter was calculated. Both example sets of U - Tv curves demonstrate the high quality of the fit associated with the dn parameter, irrespective of the physical properties of the tested soils. It can be observed that the secondary consolidation essentially starts around U = 60% for the clay samples and U = 40-60 % for the organic soil samples. It indicates that the inves- qj 10 100 1000 10000 100000 1000000 ^ Consolidation time, t [s] Figure 7. Experimental consolidation courses versus the best-fitting model curves for reconstituted clay. tigated organic soil is prone to significant secondary deformations. It was found by the optimization method that Terzaghi's consolidation model is able to capture a slight range of the total deformation. This is mainly due to the postulation that the consolidation process is regarded as purely filtration [32]. Figs 7-8 show that the greater is the discrepancy between the experimental and theoretical curves, the greater is the presence of secondary consolidation. The coefficient of consolidation for the clay sample computed using Eq. (6) and (7) and those obtained using the Taylor (t1/2 ) and Casagrande (log t) methods with reference to the dn parameter are shown in Figure 9. The optimal cv value of each curve was determined based on the lowest value of the dn parameter. This value represented the best agreement between the experimental and theoretical curves. The results of the analysis for clay and organic soil in Tables 4-5 showed that the accuracy of the determined cv with the quasi-constant method in relation to the best analytical solution increases together with the rise of the consolidation load. The cqv values were slightly higher than those determined on the basis of the optimization. However, the largest discrepancies were observed for loads of 25 and 50 kPa. Nevertheless, both methods are characterized by good compliance and the cv values correspond with each other. Using the optimization method, the value of cv changed, which refers to the distance from the theoretical curves imposed on the experimental curve, which should be chosen very carefully. In turn, in the quasi-constant method, a very precise distinction of the quasi-filtration phase for which the value of cv will be calculated is crucial. Making mistakes at this stage of the analysis could result either in an inadequate shape of the dn - cv curve as well as in a lack of assumed linearity of part of the cv - U curve. The lowest values of the dn parameter were obtained for the optimization method and the quasi-constant method. The highest values were Figure 8. Experimental consolidation courses versus the best-fitting model curves for organic soil. Figure 9. Coefficient of consolidation for all increments by various methods with reference to the changes of the dn parameter. The optimal values of the coefficient of consolidation related to the lowest dn parameter are marked with red crosses. Table 4. Consolidation parameters for the reconstituted clay obtained from the interpretation of the consolidation tests using the quasi-constant approach, the optimization method, the log(i) method the and i1/2method. Load Quasi-constant Method Optimization Method log(i) Method i1/2 Method cv x10-8 m2/s 11.5 10.4 17.3 26.3 25 dn,min 0.0011 0.0010 0.0035 0.0070 Ueop % 69.1 69.3 - - cv x10-8 m2/s 10.4 9.60 15.1 22.1 50 dn,min 0.0013 0.0011 0.0034 0.0067 Ueop % 70.7 72.1 - - cv x10-8 m2/s 6.73 6.60 9.86 13.3 75 dn,min 0.0005 0.0005 0.0021 0.0040 Ueop % 61.0 62.0 - - cv x10-8 m2/s 1.89 1.85 4.88 9.47 100 dn,min 0.0005 0.0004 0.0052 0.0099 Ueop % 58.0 59.8 - - cv x10-8 m2/s 1.67 1.65 2.0 7.8 125 dn,min 0.0011 0.0011 0.0012 0.0078 Ueop % 51.0 51.0 - - Table 5. Consolidation parameters for the organic soil obtained from an interpretation of the consolidation tests using the quasi-constant approach, the optimization method, the log(t) method the and t1/2method. Load Quasi-constant Method Optimization Method log(t) Method t1/2 Method cv x10-8 m2/s 11.39 11.40 11.60 8.40 25 dn,min 0.0011 0.00054 0.0035 0.0070 Ueop % 61.0 61.0 - - cv x10-8 m2/s 18.90 19.50 24.00 17.00 50 dn,min 0.0013 0.00093 0.0034 0.0067 Ueop % 70.7 40.0 - - cv x10-8 m2/s 6.73 13.00 15.50 10.50 75 dn,min 0.0005 0.0005 0.0021 0.0040 Ueop % 61.0 62.0 - - cv x10-8 m2/s 9.66 9.53 9.89 8.00 100 dn,min 0.0005 0.0010 0.0052 0.0099 Ueop % 58.0 43.0 - - cv x10-8 m2/s 8.48 9.50 9.21 7.50 125 dn,min 0.0011 0.0011 0.0012 0.0078 Ueop % 51.0 51.0 - - obtained with the t1/2 method, indicating a significant discrepancy between the laboratory measurements and the theoretical fitting. For individual load levels, the conformity of the calculated cv for the three methods was obtained only in one case. For the load of 125 kPa on the basis of the optimization method, the quasi-constant and log(t) methods, the dnmin values were calculated as 0.0011, 0.0011 and 0.0012, respectively. Similar results were obtained in the case of the organic soil. The cv values of the reconstituted clay obtained using the log t method and the t1/2 method were significantly higher than those determined on the basis of the optimization and the quasi-constant approaches. The differences between those two methods and the optimisation method are discussed using the obtained ratios of the cv values. This method is often adopted in geotechnical practice and was used, among others, in the works of Sridharan and Prakash [6], Robinson [8], Al - Zoubi [17] and Cortellazzo [33]. The first and second ratios compare the cv values determined using log t and t1/2 methods with those determined using the optimisation method. The cv values determined using the log t and t1/2 methods were approximately 1.5 to 2.7 and 2 to 5 times higher than those obtained with the optimization method, respectively. The third relation compared the log t and t1/2 methods and was calculated as from 1.5 to 4. This regularity is confirmed by previous analyses carried out for various clay soils by Sridharan et al. [20], Feng and Lee [27], Chan [34] and Shukla et al. [35]. In the case of the organic soil the cv values obtained using the log t method were significantly higher and using the t1/2 method were significantly lower than those determined on the basis of the optimization and the quasi-constant approaches. The cv values determined using the log t method were approximately 1.0 to 1.3 times higher than those obtained from the optimization method. The cv values determined by the t1/2 method were approximately 0.6 to 0.9 times lower than those obtained from the optimization method. The ratio compares the cv values determined using the log t method with those determined using the t1/2 method, which were always higher than 1.0 and lower than 2.0. Figure 10. Comparison of cv - ac curves obtained for different load steps. Figure 10 illustrates the values of the coefficient of consolidation obtained for different load steps. A downward trend of the cv-dc relationship was observed in the case of the reconstituted clay for all four methods and was the largest for the t1/2 method. The shapes of the calculated cv-a curves for the organic soil were generally similar. It is also evident from Fig. 10 that a drastic decrease in the cv-a curve appeared near the vertical yield stress dvy. 7 CONCLUSIONS_ Mathematical modelling, including a comparison of the experimental data with the sets of theoretical solutions, is a promising interpretation approach in consolidation studies. Terzaghi's consolidation theory does not take into account both the initial and secondary effects, hence the cv values are dependent upon the theoretical solution and refer to the primary consolidation only. Analytical tools made it possible to determine the coefficient of consolidation cv with the smallest value of the statistical dn parameter that led to the best fitting of the laboratory data. In this study the dn parameter was identified as an error function between the experimental and theoretical solutions. The optimization method based on the process of minimizing this function can be implemented in computer spreadsheet programs that are commonly used in various geotechnical applications. Furthermore, the dn error calculated between the experimental and theoretical degree of consolidation was generally quite low, and always less than the error associated with the log t and t1/2 cv values. The optimization method was also used to assess the reliability of the results of the quasi-constant method. Using the log cv - U relationship, the variability of the coefficient of consolidation in relation to the entire experimental course of consolidation was examined. The analysis of the relationship between the coefficient of consolidation and the degree of consolidation showed the presence of a region with semi-established cv values. Based on the results of oedometer tests on various soils, the cv values estimated by the quasi-constant approach were in good agreement with those obtained from the optimization method. The coefficient of consolidation determined by the graphic methods, e.g., log t and t1/2, is highly variable, due to the assumption of different reference points on the experimental curve. In the case of reconstituted clay the t1/2 method gave higher cv values and higher dn values than those obtained from both of the presented methods and the log t method. In the case of the organic soil the t1/2 method gave lower cv values than those obtained from both the presented methods and the log t method. In general, the values of cv calculated using the log t method were greater than those determined using other methods. REFERENCES_ [1] Leroueil, S. 1987. Tenth Canadian geotechnical colloquium: recent developments in consolidation of natural clays. Canadian Geotechnical Journal 25, 1, 85-107. 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DOI:10.3328/IJGE.2009.03.01.89-108 THE EFFECTS OF THE GEOMETRIC PARAMETERS OF A CIRCULAR SHALLOW FOUNDATION ON ITS UPLIFT BEARING CAPACITY IN LOESS SOIL UČINKI GEOMETRIJSKIH PARAMETROV KROŽNEGA PLITVEGA TEMELJA NA NJEGOVO NOSILNOST NA IZVLEK V RAHLIH ZEMLJINAH Cui Qiang Zhenhua Zhang (corresponding author) China Electric Power Research Institute, Transmission and Transformation Eng. Dep. Hefei University of Technology, School of Civil Engineering Beijing 102401, China Hefei 230009, China E-mail: everjsl@126.com E-mail: zenithzhang@sina.com Ruiming Tong Zhongcheng Lv China Electric Power Research Institute, Transmission and Transformation Eng. Dep. Jinshuitan Hydropower Plant of State Grid, Zhejiang Beijing 102401, China electric power co., Ltd. E-mail: 18613839823@163.com Lishui 323000, China https://doi.org/10.18690/actageotechslov.15.2.74-80.2018 Keywords field uplift tests; circular shallow foundation; orthogonal test method; the uplift bearing capacity Ključne besede terenski preizkusi na izvlek; krožni plitvi temelj; ortogo-nalna preizkusna metoda; nosilnost na izvlek DOI Abstract In order to revel the effect of the geometric size parameter of a circular shallow foundation on its uplift capacity in loess soil, the shaft diameter d, the enlarge angle of the slab 9 and the embedment ratio ht/D of the shallow foundation were chosen to determine the field test schemes using the orthogonal test method. The field uplift tests were carried out on the tested foundations at a site located in Gangu County, Tianshui City, Gansu Province, China. The uplift load vs. the outward displacement curves of all the test foundations were recorded using automatic electronic measuring instrument. The test results revel that all the uplift load vs. outward displacement curves of the tested foundations are non-linear and take on an obvious three stages. Through the analysis on all the uplift load vs. outward displacement curves, the uplift capacities are achieved using the L1-L2 graphic method. By analyzing the relationship between the uplift capacities and the geometric parameters (enlarge angle of slab 9, the embedment ratio ht/D and the shaft diameter d) of the tested foundations, it is concluded that the uplift capacities of all the tested foundations increase with the increase of 9, ht/D and d, and the influencing degree of the three geometric factors on the uplift capacity of the circular shallow foundation is 9 > d > ht/D. Izvleček Za ugotovitev vpliva geometrijske velikosti krožnega plitvega temelja na njegovo nosilnost na izvlek v rahlih zemljinah, so bili izbrani parametri premer temelja d, povečevalni kot plošče 9 in razmerje vkopanja h/D plitvega temelja, s katerimi je določena shema terenskega preizkusa z uporabo ortogonalne preizkusne metode. Terenski preizkusi na izvlek so bili izvedeni na preizkušenih temeljih na gradbišču v okrožju Gangu, v mestu Tianshui, provinca Gansu, Kitajska. Krivulje odnosa med obremenitvijo na izvlek in zunanjih pomikov smo za vse preizkusne temelje zabeležili z avtomatskim elektronskim merilnim instrumentom. Rezultati preizkusa kažejo, da so vse krivulje obremenitev na izvlek - zunanji pomik na preizkušenih temeljih nelinearne, in da imajo izražene tri faze. Pri analiziranju krivulj obremenitev na izvlek - zunanji pomik so bile nosilnosti na izvlek dobljene z uporabo grafične metode L1-L2. Z analizo razmerja med nosilnostjo na izvlek in geometrijskimi parametri (povečevalni kot plošče 9, razmerje vkopanja h/D in premer temelja d) preizkušenih temeljev smo zaključili, da se nosilnost na izvlek pri vseh preizkušenih temeljih poveča s povečanjem 9, ht/D in d, ter da je vplivna stopnja treh geometrijskih parametrov na izvlek krožnega plitvega temelja v razmerju 9 > d > ht/D. INTRODUCTION 2 FIELD CONDITIONS Transmission towers not only transmit heavy compressive loads but also bear a considerable amount of uplift loads. The transmission towers need footings to fix them, which can anchor these towers with competent strata. Shallow foundations are widely used to bear the transmission towers. A circular shallow foundation is a very popular type of shallow foundation to support a transmission tower. Since the controlling design load for this type foundation is normally the uplift load stipulated by codes, the determination of the uplift bearing capacity of this kind of foundation is a key job for the foundation design. In deed, the factors to affect the uplift bearing capacity of a circular shallow foundation include the soil shear strength around the foundation, the geometric parameter of the foundation, the material of the foundation, etc. Many researchers have studied how the factors influence on the uplift bearing capacity of shallow foundations. The studies were mostly conducted using indoor model experiments [1, 2, 3, 4, 5, 6, 7, 8, 9]. It is known to all that the results obtained by indoor model experiments are hard to use as a guide prototype foundation design because model experiments are always not satisfied with similarity theory. Therefore, some researchers carried out prototype pullout tests to discuss the features of the uplift load vs. outward displacement curves and the uncertainties of the parameters to fit the curves of the foundations in the Gobi field in the Northwest of China [10]. However, how multiple geometric parameters of shallow foundation influence the uplift capacity is hardly observed in the literature. Although the effects of the geometric parameters of a shallow foundation on its uplift bearing capacity have been reported in many studies, only a limited number study the effects using prototype experiments [11,12,13]. Moreover, the prototype uplift tests reported in the literature mentioned above almost do not care for the effects of geometric parameters such as the enlarge angle of slab 9, the embedment ratio ht/D and the shaft diameter d on the uplift bearing capacities of shallow foundations, except for some test results on the effects of normalized embedment depths (H/D) on the uplift performance of shallow foundations reported in these studies [11,12,13]. In order to understand well the effects of the geometric size parameters (enlarge angle of slab 9, embedment ratio ht/D and shaft diameter d) of a shallow foundation on its uplift bearing capacity, in this paper, prototype uplift field tests were performed in loess soil located in northwest China, and variations of the uplift bearing capacities of the circular shallow foundations with different geometric parameters are discussed. The field tests were conducted at a site located in the place of the 750-kV substation to be built in Gangu County, Tianshui City, Gansu Province, China. All the tested foundations were buried in one soil layer with relatively homogeneous loess soil. Both laboratory and in-situ tests were performed to determine the physical and mechanical parameters of the loess soil (Table 1). Table 1. Physical and mechanical parameters of the loess soil. Index properties for loess Test result Water content / % 16.5 Nature density / kg-m-3 1.89 Degree of saturation /% 43.2 Void ratio e 0.92 Liquid limit / % 30.2 Plastic limit / % 20.5 Modulus of compressibility/ kPa 15.2 Cohesion / kPa 14.8 Angle of internal friction / ° 23.1 3 TEST SCHEME DESIGN The orthogonal experimental design method is a mathematical statistical method to use an orthogonal table to study a specific indicator law determined by multiple factors. Users do fewer tests, and the regulations resulting from the tests can be found using this method [14]. The key steps of orthogonal experimental design are selecting factors for tests and determining the levels of each factor. For the purpose of studying the effects of geometric parameters on the uplift bearing capacity of the circular shallow foundation, the orthogonal experimental design method was adopted to design the test schemes. The uplift bearing capacities of the tested foundations, which consists of a cylindrical shaft and a circular slab (Figure 1), are affected by geometric parameters such as the foundation shaft diameter d, the enlarge angle of slab 9 and the embedment ratio ht/D. Different geometric parameters have different effect degrees on the uplift bearing capacity of the foundation. In order to comprehensively analyze the effects of the three parameters on the uplift bearing capacity, the geometric parameters d, 9, and ht/D were chosen for study. Each of the three factors (the three geometric parameters) were divided into three levels (Table 2). The parameters ht/D, 9 and d are indicated by A, B and C, respectively, in Table 2, and other geometric parameters are shown in Table 3. W IT hi \ê j Table 3. Other geometric parameters of the tested foundations. hi uu -D- D = d + 2h1 tan d Figure 1. Schematic diagram of the tested foundations. The standard orthogonal test table for the geometric parameters was used to develop the test schemes [15]. The test indicators are the uplift bearing capacity values of the tested foundations, whose geometric parameters are shown in Table 2 and Table 3. The test schemes are shown in Table 4, where E indicates a blank column, and the orthogonal table of factors and levels is shown in Table 4. Table 2. Factors and levels of geometric parameters. Factors (geometric parameters) index A B C ht/D e (°) ¿(mm) 1 1.5 15 900 2 2 30 1200 3 2.5 45 1500 parameter value/mm hi 600 200 200 Table 4. Test schemes obtained by orthogonal experiment for L9 (34). Number 1 2 3 4 D value in A B C E figure 1 No.1 1(1.5) 1(15) 1(900) 1 1221 No.2 1(1.5) 2(30) 2(1200) 2 1892 No.3 1(1.5) 3(45) 3(1500) 3 2699 No.4 2(2.0) 1(15) 2(1200) 3 1521 No.5 2(2.0) 2(30) 3(1500) 1 2192 No.6 2(2.0) 3(45) 1(900) 2 2099 No.7 3(2.5) 1(15) 3(1500) 2 1821 No.8 3(2.5) 2(30) 1(900) 3 1592 No.9 3(2.5) 3(45) 2(1200) 1 2399 4 PREPARATION OF THE TESTED FOUNDATIONS The circular shallow foundations were constructed in the field. The construction procedure is a borehole with a certain size made using the manual digging method; then the reinforcement cage was placed into the (a) Preparation for construction (b) Excavation of borehole (c) Make of reinforcement cage (d) Installation of reinforcement cage (e) Installation of locking nut Figure 2. Construction process for the tested foundations. (f) Pouring of concrete h 2 e borehole; after that the concrete with the compression strength of 30 MPa was placed into the hole. Finally, the foundation construction was cured for 28 days. After the process of construction, the foundation can be used for uplift tests. The construction process of the circular shallow foundation is shown in Figure 2. 5 UPLIFT TESTS 5.1 Uplift-test setup The test setup was designed according to the criteria recommended in the Chinese Nation Code GB50007 [16] and the China Electric Power Industry Standard DLl T 5219 [17]. The uplift test setup is a loading device shown in Figure 3. The loading device is composed of concrete supporting blocks, reaction beams made of reinforced steel plate and stiffeners, tension connecting bolts, etc. To allow the test foundations to develop possible rupture surfaces extending to the ground, the reaction beams were placed 10 m apart, perpendicular to the concrete supporting blocks. All the reaction beams were reinforced by welded steel plates and stiffeners to increase their stiffness. Based on the anticipated ultimate uplift bearing capacity of the tested foundations, tensile loading was applied by two 5000-kN hydraulic jacks using automatic electronic control with a stroke of 250 mm through the loading reaction beams. During each test, the head displacement of the tested foundation was measured by electronic gauges with a range of 50 mm. These gauges were attached to the reference beams installed over the tested foundation. The reference beams were of sufficient stiffness to support the instrumentation so that excessive variations did not occur. The same loading, reaction, and data-acquisition systems were used for all the tests. The loading direction supplied by the device is along the axial direction of the tested foundations. 5.2 Process of the uplift test In general, the uplift test procedures of the tested foundation were conducted in accordance with the Chinese Nation Code GB50007 [16] and the China Electric Power Industry Standard DLIT 5219 [17]. All the tests were conducted with static loading, without load cycling. The process of the uplift test can be described as involving the following steps: (1) The slowly maintained load method [17] was adopted to load on the tested foundation, that is to say, the uplift loading was applied in increments of 10% of the anticipated ultimate load for each individual foundation, and the foundation was allowed to move under each maintained-load increment until a certain rate of displacement was achieved. (2) Each load increment was maintained after loading until the change rate of the outward displacement was less than 0.1 mmlh. (3) Then the next load increment was applied. The uplift test was continued up to the point of failure, at which the foundation was completely pulled out from the loess, or the uplift test was terminated after the last load was maintained for 24 h with the change rate of displacement exceeding 0.1mmlh. 6 TEST RESULTS 6.1 Uplift load vs. outward displacement curves The measured uplift load vs. outward displacement curves for all the tested foundations are presented in Figure 4. It is clear from Figure 4 that the uplift load vs. displacement curves exhibit the same three stages, which are segment oa, segment ab and segment bc in the curve (Figure 5). Steel plate-Steel plate Dial gauge Reference beam Embedded bolt -1- Hydraulic jack Reaction beam _Tension connecting bolt Concrete supporting blocks -Connecting steel plate _ Tested foundation Figure 3. Loading device for uplift tests. Ground surface Figure 4. Uplift load vs. outward displacement curves of tested foundations. Outward displacement s /mm Figure 5. Three stages of uplift load vs. displacement curve. Among these segments, segment oa is a straight line, where elastic deformation can be thought to occur in the loess soil around the tested foundation, and compressive deformation of the soil is dominant at this stage; the middle segment ab is a curve as the transition stage, indicating that plastic deformation occurs in the soil occasionally with elastic-plastic deformation, and the soil mainly takes on compressive and shear deformation; the terminal segment bc is a straight line with a gentle slope, and the main deformation is shear deformation in this stage. (1) the first step is extending the terminal segment bc from the last point (point c in Figure 5) in the uplift load vs. outward displacement curve, and then finding the intersection (point b in Figure 5) between the middle section ab and the terminal section bc; (2) the second step is finding the value of the vertical coordinate in point b, and the value is the uplift bearing capacity (Ql2 in Figure 6). Table 5. The uplift capacities of the test foundations. Numbers h/D enlarge angle e/° shaft diameter d/mm uplift bearing capacities Qun/kN No.1 15 900 269 No.2 1.5 30 1200 943 No.3 45 1500 2037 No.4 15 1200 581 No.5 2.0 30 1500 1638 No.6 45 900 1319 No.7 15 1500 1403 No.8 2.5 30 900 1108 No.9 45 1200 2422 Figure 6. Graphical expression of the uplift bearing capacity of the tested foundation. 6.2 Uplift capacity of the tested foundations Based on the uplift load vs. outward displacement curves, the uplift bearing capacities of the tested foundations can be determined using the L1-L2 graphic method [18]. The method takes two steps to determine the uplift capacity of the tested foundation. Specifically, the two steps are illustrated as the following. 7 DISCUSSION The uplift bearing capacities and geometric parameters of all the tested foundations are presented in Table 5. The effects of various geometric parameters on the uplift bearing capacities are discussed in terms of the test results mentioned above. It has been shown in Table 5 that when the embedment ratio (ht/D) equals 1.5, the uplift bearing capacities Qnu increase with the increase in the enlarged angle of the slab (9 =15, 30 and 45°). Nevertheless, when the embedment ratio (ht/D) equals 2.0 or 2.5, Qnu does not increase anymore with the increase in enlarged angle of the slab 9 due to the effect of the shaft diameter (d). Therefore, the uplift bearing capacities Qnu of the tested foundations are influenced jointly by multiple geometric parameters of the foundation. For analyzing the effects of multiple geometric parameters (ht/D, 9 and d) on the uplift bearing capacities Qnu of the tested foundations, an orthogonal analysis was made on the test results, and the analysis results were listed in Table 6. In Table 6 the three lines Ki, K2 and K3 represent, respectively, the sum of the three Qnu values at Level 1, 2 and 3 of each factor (A, or B, or C), and K1, K2 and K3 are the averages of the three Qnu values at Level 1, 2 and 3 of each factor (A, or B, or C). It is clear from Table 6 that for the column of factor A (embedment ratio ht/D), K1 d > ht/D. Acknowledgment We acknowledge the National Natural Science Foundation of China under Grant No.51108435. REFERENCES [1] Matsuo, M. 1967. Study on the Uplift Resistance of Footing (1). J. Soils and Foundations 7, 4, 1-37. Doi:10.3208/sandf1960.7.4_1 [2] Matsuo, M. 1968. Study on the Uplift Resistance of Footing (2). J. Soils and Foundations 5, 4, 62-98. Doi:10.3208/sandf1960.8.18 [3] Dickin, E.A., Leung, C. F. 1990. Performance of piles with enlarged bases subject to uplift force. Canadian Geotechnical Journal 27, 5, 546-556. Doi:10.1139/t90-070 [4] Dickin, E.A., Leung, C.F. 1992. The influence of foundation geometry on the uplift behavior of piles with enlarged bases. Canadian Geotechnical Journal 29, 3, 498-505. Doi:10.1139/t92-054 [5] El Naggar, M.H., Wei, J.K. 2000. Uplift behavior of tapered piles established form model piles. Canadian Geotechnical Journal 37, 1, 56-74. Doi:10.1139/t99-090 [6] Liu, W.B., Zhou, J., Temuer, M.K. 2003. Uplift tests and calculations of under-reamed piles. Industrial Construction 33, 4, 42-45 (in Chinese). [7] Chen, R.P., Zhang, G.Q., Kong, L.G., etc. 2010. Large-scale tests on uplift ultimate bearing capacities of enlarged base piles in saturated and unsaturated silty soils. Chinese Journal of Rock Mechanics and Engineering 29, 5, 1068-1074 (in Chinese). [8] Yu, H. 2011. Influence of Pile Deformation Resistance to Pull Enlarged end of Performance Factors. Logistics Engineering and Management 33, 5, 120-121 (in Chinese). Doi:10.3969/j [9] Li, B.Z., Chen, Y. 2015. The bearing capacity analysis on straight chimney excavation foundation with different chimney and enlarged bottom. Industrial Construction 45, S1, 1019-1022 (in Chinese). [10] Lu, X.L., Qian, Z.Z., Tong, R.M. 2014. Uplift load-movement response of bell pier foundations in Gobi gravel. Geotechnical Engineering 164, 4, 380-389. Doi:10.1680/geng.12.00072 [11] Consoil, N.C., Ruver, C.A., Schnaid, F. 2013. Uplift Performance of Anchor Plates Embedded in Cement-Stabilized Backfill. Journal of Geotechnical and Geoenvironmental Engineering 139, 3, 511-517. Doi:10.1061/(ASCE)GT.1943-5606.0000785 [12] Consoli, N.C., Ruver, C.A., Girardello, V. etc. 2012. Effect of polypropylene fibers on the uplift behavior of model footings embedded in sand. Geosyn-thetics International 19, 1, 79-84. Doi:10.1680/ gein.2012.19.1.79 [13] Consoli, N.C., Thomé, A., Girardello, V. etc. 2012. Uplift behavior of plates embedded in fiber-reinforced cement stabilized backfill. Geotextiles and Geomembranes 35, 107-111. Doi: 10.1016/j. geotexmem.2012.09.002 Geotextiles [14] Box, G.E.P., Hunter, W.G., Hunter, J.S. 1978. Statistics for experimenters. Wiley-Interscience, New York. Doi:10.2307/1267766 [15] Yang, Z.X. 1978. Construction of orthogonal tables. Shandong People Press, JI Nan (in Chinese). [16] China Ministry of housing and construction 2010. Code for design of building foundations GB50007-2011. China Architecture and Building Press, Beijing (in Chinese). [17] ZhongNan Engineering Corporation Limited 2015. Technical code for design of foundation of overhead transmission line DL/T5219-2014. China Electric Power Press, Beijing (in Chinese). [18] Chen, Y.J., Chu, T.H. 2012. Evaluation of uplift interpretation criteria for drilled shafts in gravelly soils. Can. Geotech. J. 49, 1, 70-77. Doi : 10.1139/ T11-080 THE DESIGN OF DRILLED DISPLACEMENT SYSTEM PILES USING THE CAVITY EXPANSION THEORY NAČRTOVANJE SISTEMA UVRTANIH PILOTOV Z ODMIKANJEM Z UPORABO TEORIJE RAZŠIRJANJA PROSTORA Stacho Jakub Slovak University of Technology in Bratislava, Faculty of Civil Engineering Radlinskeho 11, 810 05 Bratislava, Slovakia E-mail: jakubstacho22@gmail.com https://doi.Org/10.18690/actageotechslov.15.2.81-91.2018 DOI Keywords pile foundation, drilled displacement system pile, cavity expansion theory, static load test Ključne besede temeljenje na pilotih, sistem uvrtanih pilotov z odmikanjem, teorija razširjanja prostora, statični obremenilni preizkus Abstract Drilled Displacement System (DDS) piles are an innovative technology for pile foundations. These DDS piles are created by rotary drilling with a simultaneous full displacement of the soil in a horizontal direction. The optimal design of DDS piles can be obtained in sandy soils and fine-grained soils that allow for a horizontal displacement, which causes an increase in the shaft's resistance. This article deals with the use of Cavity Expansion Theory (CET) for a complex analysis of DDS piles. This method makes it possible to take into account the impact of the technology in pile design. A general view of the CET is presented and is described step by step for the solution of the present problem. The results of the calculations are compared and analysed with the results of three instrumented static load tests. The analyses include a comparison of the load-settlement curve as well as the load distribution over the piles length, which was measured using strain gauges. The results of the analyses show very good agreement between the calculations and the measurements. The difference between the calculated and measured load-settlement curves did not exceed a 10% degree of accuracy. The possibilities for the future use of CET are also discussed. Izvleček Uvrtani piloti z odmikanjem (DDS) predstavljajo inova-tivno tehnologijo za temeljenje pilotov. Pilote izvedemo po tehnologiji DDS z rotacijskim vrtanjem in hkratnim polnim odmikanjem tal v vodoravni smeri. Optimalno obliko DDS pilotov lahko dobimo v peščenih in drobnozr-natih zemljinah, ki omogočajo vodoravno odmikanje, kar povzroči povečanje nosilnosti pilota na plašču. Ta članek obravnava uporabo teorije razširjanja prostora (CET) za kompleksno analizo pilotov DDS. Ta metoda omogoča upoštevanje vpliva tehnologije pri načrtovanju pilotov. Predstavljen je splošen pregled CET ter opisani vsi koraki reševanja obravnavanega problema. Rezultate izračunov smo analizirali in primerjali z rezultati treh statičnih obremenilnih preizkusov. Analize vključujejo primerjavo krivulje obremenitev-pomik in porazdelitve obremenitve po dolžini pilota, ki je bila izmerjena z uporabo merilcev specifičnih deformacij. Rezultati analiz kažejo zelo dobro ujemanje izračunanih in izmerjenih vrednosti. Razlika med izračunanimi in izmerjenimi krivuljami obreme-nitev-pomik ni presegala 10 %. Predstavljene so tudi možnosti prihodnje uporabe CET. 1 INTRODUCTION Piles are the most frequently used elements of deep foundations that are used to transfer a load from a structure to a suitable bearing stratum when the soil mass immediately below a construction is unsuitable for the direct bearing of footings. New technologies for the execution of pile foundations are constantly being developed due to the stricter requirements of modern structures. The most appropriate way of categorizing piles according to their technology is as large displacement, small displacement, and replacement piles [1]. This article focuses on Drilled Displacement System (DDS) piles. DDS technology is also known as DD (Drilled Displacement), FDP (Full Displacement Pile), or APGD (Auger Pressured Grouted Displacement) piles. DDS piles are rotary drilled piles with the full displacement of the soil in the horizontal direction, which leads to a higher bearing capacity of the pile in comparison with replacement piles (see for example [2, 3, 4]). Brown [5] published a general review of DDS technology and its advantages and disadvantages in comparison with other pile technologies. In the past, several calculation methods for determining the ultimate resistance and load-settlement curve of the pile have been developed, for example [6, 7, 8, 9]. Zhang et al. [10] classified the calculations into five categories: simplified analytical methods, load-transfer curve methods, finite-element methods (FEMs), boundary-element methods (BEMs), and variation methods. The selection of the most appropriate method for a pile design depends on experience and availability, and plays a very important role in the accuracy of the solution. This article deals with the use of Cavity Expansion Theory (CET), published by Mecsi [11, 12], for an analysis of pile displacement. The CET theory seems to be one of the most appropriate methods for a given case, because the principles which are assumed, i.e., creating a cylindrical space (a pile body) and the horizontal displacement of the soil to the surrounding area, are very similar to the real installation process of a DDS pile. The method makes it possible to calculate the changes in soil properties that are affected by the cylindrical displacement of the soil and take them into account in the calculation. It is difficult to summarize the results of all previous researchers, because the CET has been used for the design or analysis of many geotechnical constructions. An analysis using CET leads to useful solutions for a variety of problems in geotechnical engineering [11, 13, 14]. Examples of the applications are the bearing capacity of a displacement pile (or a partial displace- ment pile) [15], interpretation of a pressure meter [11, 16, 17] and cone penetration tests (CPT), for example [18], and an analysis of the deformation around tunnels. The application of CET to many geotechnical solutions was published by Yu [19]. CET can be classified into a pressure-controlled cavity expansion and a displacement-controlled cavity expansion [20]. CET used for analytical solutions assumes various constitutive laws of the medium around the cavity, for example, linear elastic or elastic perfectly plastic, with or without accounting for the volume variation [21]. These theories were adopted for the soil behaviour under a small strain as well as a large strain [14, 22,]. With the advent of numerical modelling, various numerical models were used to analyse some of the problems of a cylindrical cavity for different tasks, for example [23]. Many published simulations, for example [13, 14, 24], assumed that the soil around the cavity is homogeneous and isotropic. Due to the change in the sedimentary environment and a consolidated environment, however, the initial stress in the soil layer is usually anisotropic [24]. The use of the axisymmetric CET to investigate the effect of soil parameters on the ground movement in the vicinity of static pipe-bursting operations was studied by Fernando and Moore [25]. They present a parametric study which shows that the ground movements are controlled by the soil strength and dilatancy, rather than by the elastic soil properties. The case studies prepared by Rao et al. [26] showed that it is necessary to consider the effect of the coefficient of horizontal earth pressure K0. Analytical solutions based on K0 = 1 overestimate the critical expansion pressure and the ultimate expansion pressure as well as the plastic zone around the cavity. Li et al. [27] presented a solution that investigates the effect of the initial stress anisotropy and the initial stress-induced anisotropy on the cavity expansion by adopting parametric studies with different over-consolidation ratios (OCRs). The results of fully instrumented static load tests on DDS piles are analysed and compared with the results of calculations using the CET. The analysis includes a comparison of the load-settlement curves as well as a comparison of the measured and calculated load distributions over the pile's length measured using strain-gauges. Detailed analyses of three tested DDS piles are presented in the article. 2 METHODOLOGY OF THE PILE DESIGN USING THE CAVITY EXPANSION THEORY General definitions of the soil stress deformations and volume changes in the soil as well as an examination of the cylindrical expansion for a given CET were presented by Mecsi [11]. He showed that the volume changes occurring in the soil are attributed to the laws of the soil stress forming around a cylinder. The hardening of the soil and the impact of the soil mass around the cylinder on the stress-strain state are taken into account in the calculation. The presented theory supposes an axisymmetric stress state in the normally consolidated soil with incompressible soil grains. The anisotropic stress-strain state is taken into account in the initial conditions. It means that the compressive stresses in the vertical direction and the earth pressure at rest in the horizontal direction of the soil are assumed. The zone, where the soil density increased due to a process of enforced expansion, is also taken into account. The basic characteristics of the calculation model used are: - application of the Mohr-Coulomb (MC) conditions (plastic stress state), - force equilibrium, - nonlinear relationship between increasing soil stress and soil strain, - assumption of the elastic behaviour for the decrease of the soil stress, - changes in the soil density are obtained as a result of the strain in three mutually perpendicular directions (the 3D effect of the soil deformation is included). In the initial stress state, the original geostatic stress in the vertical direction and the horizontal stress at rest are considered. Because the soil volume is changed (compressed), the plastic stress state is reached according to the MC law. The soil volume continues to change (increase) after the plastic stress state has been reached. The following effects are applied in the calculation model: In the area outside the zone of compaction (elastic zone): - a nonlinear relation between the radial deformations and stresses for the compaction, and a linear one for the expansion, - the soil density (volume) is not changed. At the border of the compaction zone: - the same effects are applied as for the outside zone with some supplements, - the MC relation comes into effect. Within the plastic stress state zone (a zone of the compaction): - the MC relation is applied, - a nonlinear relationship between the radial deformations and the stresses for the compaction and a linear one for the expansion. Individual assumptions and the steps of the calculations are simply described for the presented analyses, due to the extensiveness of the theory used. The basic assumption of the presented theory is shown in Fig. 1. Figure 1. Description of the soil stresses near the bottom of the pile according to [11]. The distribution of the soil stresses acting beneath the pile bottom varies in the different directions. The soil immediately below the pile base becomes significantly harder after loading and a zone called the "rigid compacted soil" is created. The theory presented assumes that this fully compacted zone directly transfers a compressive load to the surrounding soil below the pile base. The radius of the fully compacted zone (rigid compacted soil) is equal to the pile radius r in the calculations. Based on this supposition, the base area of the pile in equation (5) is simply assumed to be nr2. When the load is applied to the pile, a spherical compacted zone is created from the bottom of the pile with the radius (p). In the first step of the calculations it is necessary to calculate the soil stresses at the boundary of the compacted zone (ory in the vertical and o,h in the horizontal directions) with respect to the initial soil stresses (oy in the vertical and Oh in the horizontal directions) using equations (1) and (2). The derivation process of both equations was described by Mecsi [11] in a step-by-step fashion. m = 0 : ctm M I1 - «K a(1-a) (1-a) U p,H UH (1 - a )• E0 - 2 •- < • E0 «H ^ E0 JP,R P,V (1) (2) where mr is the change in the volume in the radial direction, and mt is the change in the volume in the tangential direction; ou is the unconfined soil strength; E0 is the modulus of elasticity; and a is a parameter of the nonlinearity described below. This makes it possible to calculate the radius of the compaction zone p (extended plastic stress state), where the ultimate stress onHjimit is also taken into account. P= r0 ■ 1+sinp' 2-sinp' tan^' °P,H + tan q> ' (3) The definition of the nonlinear deformation of the soil is one of the important points of the calculation. The effect of soil compaction is determined by changing the secant modulus using the parameter a. The parameter a can be determined according the results of an oedometer test. The secant modulus, which depends on the geostatic stress, is given by equation: ES = E0 f \ a \°rCf J (4) The size of the vertical limit stress for the calculation of the ultimate pile base resistance Qb,ummate is given by the difference between the vertical stress at the bottom of the pile under the load on 0y and the initial geostatic stress Oy. The value of or0y is given by equation (5). It is recom- mended that the calculation be divided into more loading steps (from interval 0 to Qb,ummate) for the calculation of the load-settlement distribution under the pile base. Qb n- r (5) The distributions of the radial soil stress (orad) and the tangential soil stress (otan) as well as the distribution of the soil displacement (ZAuni) allow a determination of the base resistance-soil displacement (compaction) curve. The distribution of soil stresses within the compacted (plastic) zone is statically determined under the force equilibrium and the Mohr-Coulomb conditions. The derivation process of the final equations presented was described in detail by Mecsi [11]. The radial soil stress distribution is given by the following equations: - Inside the zone of compaction (if r < p): c' } | p V+smp' c' a. /11 I 1 ' W tanç J ^ r J tanç (6) - Outside the zone of compaction (if r > p): r Y -|+av (7) ( \ ,v =(a-,v -av J where ow represents the pressure of the water in the pores. The change of the strain (in compression) is given by the equation: (_a) _ (1-a) A^r 7 E (8) 11 _ a )• E0 and the change of the radial soil displacement is equal to: Asr,_1 + Asr, Au .=- - ir- r-1 ) (9) The shaft resistance and finally the load-settlement curve of the pile can be subsequently calculated after all the previous steps. The ultimate stress in the horizontal direction for the calculation of the ultimate shaft resistance is equal to: k-oh 2 • c' ,H,limit = + " « (10) where k is a multiple factor for the impact of the technology. Based on the Mohr-Coulomb relationship, the ratio of the principal stresses £ can be expressed with the following correlation: 4 = 1 - sin^' (11) 1 + sin^' The ultimate shaft resistance of the pile is given by the ultimate shear strength along the pile using Coulomb's relationship: Tult =°r,H,limit • tan^' + c' (12) and the shear resistance is given by the following equation: m c CT c a tult UZ 'Tult (13) where Uz is the diameter of the pile at a depth z from the top of the pile. the pile base and the pile shaft (settlement of the soil below the pile base and the axial compression of the pile body). When the value of Am is reached, the plastic stresses are taken into account. Generally, the shear resistance is given by the equation: 3 u t = s • t (14) GEOLOGICAL CONDITIONS OF THE TESTED AREA Elastic behaviour is considered up to the displacement Am, which is required for the full mobilization of the shaft friction and u^+s is the sum of the deformation of The geological conditions of the tested area consist of very soft layers with a thickness of about 13-15 m and very dense coarse-grained soils below them. The geologi- DDS Pile/TP1 o 5 -a S 0;00 -4,30 -6,10 _ -8.20 -9.90 -10.50 -1O.80 -13,90 C-, K -15.00 g -15,40 -16.50 -17 91 MG Y MS MS Y MS SM G-F Pl. -2.10 stable PL -13.90 encountered 0.00 -0.90 -2.80 -3.50 S -5.60 -o B DDS Pile / TP2 Surface PL -2.10 -7.30 ■a -10.80 OKI M -12.00 A -13.20 E. -13.60 « -14.00 g -14.90 -15.88 MG MS Y CL ML-CL stalnic Y CL SM G-F I'L -13.20 j, encountered P Š O i •5 S 0.00 -0.80 -1.90 -2.90 -4.60 -5.30 -7.60 -9.00 DDS Pile /TP3 II -10.20 ^ -11.00 » -11.70 I -12.65 • -13.20 3 -13.90 -14.50 Û -15.00 -17.00 -17.02 CL CH CL CH Cll Ml! CH MH CH MH CH MS G-F GM Pl. -2.10 subie PL -14.50 ^ encountered Figure 2. Geotechnical models of the analysed piles. Figure 3. Results of CPT tests in the tested area. M Table 1. Soil properties used in the calculation. Test pile TP1 TP2 TP3 Symbol of soil F S G F S G F G Depth (m) - 13.90 16.50 - 13.20 14.00 - 14.50 Thickness (m) 13.90 2.60 1.41 13.20 0.80 1.88 14.50 2.52 Y (kN.m-3) 19 18 19 19 18 19 19 19 Ysat (kN.m-3) 20 20 21 20 20 21 20 21 v' (°) 20 28 37.5 20 28 37.5 20 37.5 c' (kN.m-2) 20 10 1 20 10 1 20 0 Es (kN.m-2) 5160 28140 112000 6990 28140 117600 6600 119900 a (-) 0.5 0.4 0.1 0.5 0.4 0.3 0.5 0.3 cal profiles for the tested piles are shown in Fig. 2. The stratum of soft soil (0.00 to 13.20~14.50) is especially represented by sandy silts (MS), stiff silts, clays with low plasticity (ML-CL), and layers of organic clays (Y). In the case of TP3, soft soils were classified as clays with high plasticity (CH) and silts with high plasticity (MH). In the cases of TP1 and TP2, coarse-grained soils consist of silty sands (SM) of a thickness of 2.6 m (TP1) and 0.8 m (TP2). Very dense gravels with fine soils (G-F) are located below the sandy layers. In the case of TP3, coarse-grained soils consist of gravels with fine soils (G-F) and silty gravels (GM) immediately below the soft stratum. An engineering-geological survey that was executed on the area of the tested piles included many in-situ tests and also standard laboratory tests [28]. The following were executed: 48 SPT tests, 54 CPT tests, 17 DPH tests, 10 piezometers and core drillings. The distributions of qc and Eoed obtained using the correlation from the CPT test in the area of the tested piles are shown in Fig. 3. The soil properties used in the calculation are shown in Table 1. Based on the results of the in-situ tests, the soft layers (0 to 13.20~14.50) have about the same mechanical soil properties. For this reason, the soft stratum is considered as homogeneous (separately in all profiles). The layer is marked using the symbol F (Table 1). The effective shear strength parameters f and c were taken into account according to the results from the test report [28]. The impact of the groundwater was taken into account as a phreatic level under the pressure. The pore pressure was estimated as the difference between the encountered and the stable groundwater level (for example, TP2: (13.20 m to 2.10 m) * 10 kN.m-3 = 111 kN.m-2). 4 EXECUTION OF THE STATIC LOAD TEST A static load test (SLT) is the most accurate method for pile design [7]. The fully instrumented SLT makes it possible to obtain a complex overview of the interaction between the pile and the soils. The tested piles (TPs) were about 15 to 18 m long with a diameter of 410 mm. TP1 is 17.91 m long and anchored over 4.01 m into coarse-grained soils; TP2 is 15.88 m long and anchored over 2.68 m into coarse-grained soils; TP3 is 17.02 m long and is anchored over 2.52 m (Fig. 2). The settlement of the pile head, the horizontal aberration, the uplift of the reaction piles, and the distribution of the load over the pile's length using strain-gauges were recorded during the SLT and this allowed for a detailed analysis of the DDS pile. The static load tests were executed in 333-kN steps up to a maximum load of 2000 kN, including the unloading steps. As an example of the execution of the SLT of TP2: in the first phase of the SLT, the vertical load reached 1333 kN in four loading steps. After the unloading in the second step, the vertical load was increased to 2000 kN (in 333 kN steps) in the third phase. The unloading to 0 kN was carried out in the last Figure 4. Details of the set up for the sensors in the static load test. phase. The details of the set up for the sensors in the static load test are shown in Fig. 4. 5 COMPARISON OF THE RESULTS CALCULATED USING THE CET WITH THE RESULTS OBTAINED BY THE SLT_ The load-settlement curves and the load distributions over the pile's length, which are calculated using the CET, are compared and analysed with the results of measurements obtained from the SLT. The analysis of the load-settlement curve and the load distribution over the pile's length plays a significant role and confirms the correctness of the calculation, because an analysis of only load-settlement curves could lead to a mistake in the evaluation of the pile resistance, as has been presented by, for example, Tosinini et al. [29]. The analysis of TP2 is presented in detail, step by step, according to the previous description of the calculation methodology. Initially, the calculations of the pile-base resistance as well as the displacement below the pile base are presented. The increase in the radial stress a^j in comparison with the geostatic stress aVi under the pile base is presented in Fig. 5. The values of a^i are shown from a depth of z = 0.205 m, which is a rigid compaction of the soil, and is equal to the radius of the pile. The distributions of the tangential soil stress under the pile base otani, compared with the horizontal geostatic stress at the rest aH j, are also shown in Fig. 5. Resistance of pile base R,, (kN) 0 100 200 300 400 500 60C E 2- 3- 2 4- - 5- 6- ,0.60 1 1 1 ¡2 ] "I.... J. 37 ■ ■ N' ro "" >0.06 i ii i j*.. i i i i i ... 11 i Figure 6. Resistance of the pile base-settlement curve - TP2. The results presented are shown only for the magnitude of the vertical ultimate resistance of the pile base Qb,"ltimate , which is equal to the value of 519 kN. The resistance of the pile base depending on the soil displacement (compaction) is shown in Fig. 6. In the next steps the ultimate stress ar,iimjt and the ultimate shaft resistance, T"it and "t, are determined using equations (10), (12), and (13). The deformations required for full mobilization of the shaft friction Am play a significant role in the calculation of the shaft resistance. The value of Am was equal to 1.0 mm for Figure 5. Distribution of the radial and tangential soil stresses below the pile base - TP2. Figure 7. Distribution of the shaft friction over the pile length - TP2. the coarse-grained soils and 10 to 20 mm for the fine-grained soils. The multiple factor k was calculated according to the formulas for the displacement piles [11]. The distribution of the shaft friction over the pile's length is shown in Fig. 7. The presented curves are determined according to the results of the pile base (in the range from 0 to Rb,uit). The ultimate shaft friction tuu is equal to the full mobilization of the shaft resistance (ultimate stress is moving in the plastic stress state). These results make it possible to obtain a load distribution over the pile's length, as shown in Fig. 8. The calculated distribution of the load over the pile's length is compared with the measurements obtained using strain gauges in the static load test. This comparison confirms the correctness of the calculations. The difference between the calculated base resistance (519 kN) and the measured one (554 kN - SLT) is a 6% degree of accuracy. The difference at the boundary between the soft stratum and the coarsegrained soils (13.2 m) is a 4% degree of accuracy. The comparison of the load-settlement curves obtained by the static load test and calculated using the CET is shown in Fig. 9. The comparison also includes the ratio of the pile base resistance to the total pile resistance. The results of the calculations are in good agreement with the measurements. The difference between the calculations and the measurements is less than about a 10% degree of accuracy. l oad (kN) 0 500 1000 1500 2000 Figure 9. Load-settlement curve of DDS pile - TP2. The results of the analyses of TP1 and TP3 are presented in the following part. The comparison of the calculated and measured load distributions over the pile's length (TP1) is shown in Fig. 10, and the comparison of the load-settlement curves is shown in Fig. 11. As can be seen in Fig. 10, the calculated load distribution over the pile's length again provides a sufficient reliability. The difference between the calculated and measured load-settlement curves is less than a 5% degree of Load (kN) 0 500 1000 1500 2000 18 Loading step Rbk - 100--- 300 --- 519 --- 200 --- 400 - 554 (SLT) Figure 8. Distribution of the load over the pile's length - TP2. Loud (kN) 0 500 1000 1500 2000 20 Loading step R ■. ----100 -- 300 — --663 --■ 200 --- 400 — - 772(SLT) Figure 10. Distribution of the load over the pile's length - TP1. Figure 11. Load-settlement curve of DDS pile - TP1. accuracy. A lower accuracy (< 15 %) is obtained for the pile-base resistance. It could be caused by insufficiently precise soil-strength parameters for the calculation of the pile base in this case, but the results are considered to be good enough. The results of the analyses of TP3 are presented in Fig. 12 and Fig. 13. Coarse-grained soils in the tested area of TP3 consist only of very dense gravels without any sand or sandy layers (Fig. 2), which leads to a higher bearing capacity. Figure 13. Load-settlement curve of DDS pile - TP3. The vertical settlement of TP3 was significantly less than the previous ones. The use of the CET also allowed reliable results to be obtained in this case (TP3), while other methods (FEM and the Limit Load Curve Method according to Masopust [7]) were insufficiently accurate to reflect this difference [30]. In addition, CET makes it possible to calculate the changes of the stress state, the displacements, and the compaction around the pile that are affected by the pile technology. There are two different options for determining the pile resistance for a verification of the Ultimate Limit State (ULS). The first one is a determination of the pile resistance from a calculated load-settlement curve for a settlement equal to 10% of the pile diameter (41 mm in this case). The second one is the application of the presented theory in analytical calculation models. It is recommended that the characteristic values of the shaft resistance of the DDS pile can be calculated according to equation (15), taking into account the methodology presented. D ZLh (,i -°or,i ■ tanV'd+ Cd) (15) where K^j is the coefficient of the horizontal earth pressure, which takes into account the impact of the technology; oori is the geostatic stress at the middle of the i - layer; and fd and cd are the effective parameters of the shear strength of the soil. Based on the CET method presented, the coefficient K^j can be calculated using the following equation: ■ K P,H ,i (16) Figure 12. Distribution of the load over the pile's length - TP3. where oVi is the vertical geostatic stress, i is the horizontal geostatic stress and Ka,Hj is the coefficient of the horizontal geostatic stress at the boundary of the compacted zone. This coefficient can be calculated using equation (2) or simply determined by using the diagrams presented by Mecsi [11]. 6 CONCLUSION REFERENCES Drilled Displacement System (DDS) piles are an innovative technology for pile foundations. DDS piles are created by rotary drilling, accompanied by a full horizontal displacement of the soil. The use of this technology can lead to a more effective and economical design in comparison with traditional pile technologies. Suitable geological conditions for DDS piles include sands, sandy gravels, and fine-grained soils, where a horizontal displacement can cause compaction of the surrounding soil. This process leads to an increase in the pile shaft's resistance. The results of the three static load tests of the DDS piles are presented and analysed. These analyses include comparisons of the calculated load-settlement curves and load distributions over the pile length with the results of the static load test. A simple description of the methodology of CET is presented in the analysis of the test pile TP2. The detailed calculations include the distribution of the radial and tangential soil stresses, which are reflected in the pile base resistance-settlement curve. The calculations of the pile shaft's resistance include a determination of the shaft friction, the load distribution over the pile's length, and the load-settlement curve of the DDS pile. The analysis also includes changes to the soil stress state and the soil properties around the pile, which are affected by the pile technology. The results of the analysis show very good agreement between the measurements and the calculations. The maximum difference between the load-settlement curves obtained using CET and SLT is equal to about a 10% degree of accuracy. The comparisons of the calculated and measured load distributions over the pile length provide the required degree of accuracy and confirm the correctness of the calculation methodology. The analyses confirm the suitability of the CET for the design of displacement piles. The CET allows a calculation of the soil properties, which are directly affected by the impact of the technology. These soil properties make it possible to take into account the impact of the DDS technology in analytical solutions of the pile resistance and they could also be used for numerical modelling. Acknowledgments The paper is one of the outcomes of the Grant VEGA agency No. 1 /0882/16: Influence of boundary conditions to limit states of geotechnical structures. [1] Tomlinson, M., Woodward, J. 2007. Pile design and construction practice. 5th ed., Taylor & Francis e-Library. [2] Viggiani, C., Mandolini, A., Russo, G. 2012. Piles and pile foundations. Taylor & Francis, UK. [3] NeSmith, W. 2002. Static capacity analysis of augered, pressure-injected displacement piles. Int. Deep Foundations Congress, Florida, USA, pp. 1174-1186. [4] Zhussupbekov, A.Z., Ashkey, Y., Bazilov, R., Bazarbaev, D., Alibekova, N., Zhussupbekov, A. 2012. 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Calculation of drilled displacement pile resistance by finite element method. Proc. Advances in Architectural, Civil and Environmental Engineering, 23rd Annual PhD Student Conf., Bratislava, Slovakia, pp. 498-505 [in Slovak]. 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. 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 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 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. 9771854017001