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J& J A v V ^ f J& JF +SS// / ## ä # 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 Borut Macuh University of Maribor Tehnična urednica Technical Editor Tamara Bračko University of Maribor Uredniki Co-Editors Jakob Likar Janko Logar Primož Jelušič Stanislav Škrabl Milivoj Vulic Bojan Žlender Geoportal d.o.o. 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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. P. Ghosh and A. Pal Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis P. Ghosh in A. Pal Nosilnost pasovnih temeljev s krili v nedreniranih pogojih s pomočjo analize zgornje mejne vrednosti Y. Y. Cai in drugi Seizmični aktivni zemeljski pritisk na toge podporne stene ob rotaciji okoli osnove ob upoštevanju rotacije glavne napetosti s psevdo-statično metodo Y Y. Cai et al. Seismic active earth pressure on rigid retaining walls under rotation about base considering principal-stress rotations by pseudo-static method M. R.Kahyaoglu in M. Vanček Numerična študija ojačenih nasipov, podprtih z obloženimi gruščnatimi stebri M. R.Kahyaoglu and M. Vanicek A numerical study of reinforced embankments supported by encased floating columns 25 M. Martin-Ruiz in drugi Stisljivost kremenovega peska pri visokih obremenitvah in temperaturi M. Martin-Ruiz et al. Quartz-sand compressibility at high stresses and temperatures F R. P. Shukla in R. S. Jakka R. P. Shukla and R. S. Jakka Določanje in napoved mejne nosilnosti pasovnih temeljev na nedreniranih glinenih pobočjih Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes 50 W. Wang in drugi W. Wang et al. HI Raziskava numeričnega modela realnih mezostruktur v ne-strižnem delu gline Research on a numerical model of real me-sostructures in the non-shear zone of clay 66 M. Ôrnek in drugi M. Ornek et al. Zasnova globine stebra avtocestne ograje glede na lastnosti tal z uporabo udarnih preizkusov z nihalom Soil based design of highway guardrail post depths using pendulum impact tests 77 ▲ Navodila avtorjem Instructions for authors 90 Acta Geotechnica Slovenica, 2019/2 1 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis UNDRAINED BEARING CAPACITY OF A SKIRTED STRIP FOUNDATION USING UPPER-BOUND LIMIT ANALYSIS NOSILNOST PASOVNIH TEMELJEV S KRILI V NEDRENIRANIH POGOJIH S POMOČJO ANALIZE ZGORNJE MEJNE VREDNOSTI Priyanka Ghosh (corresponding author) Alok Pal Indian Institute of Technology, Kanpur, Indian Institute of Technology, Kanpur, Department of Civil Engineering Department of Civil Engineering Kanpur - 208 016, India Kanpur - 208 016, India E-mail: priyog@iitk.ac.in E-mail: alok.besu2188@gmail.com https://doi.org/10.18690/actageotechslov.16.2.2-11.2019 DOI Keywords footings, limit analysis, plane strain, plasticity, skirted foundation Abstract Skirted foundations are assumed to be a wise selection in offshore geotechnical engineering. In this paper the bearing-capacity factors for a vertically loaded skirted strip foundation resting on uniform c-Q soil were obtained using an upper-bound limit analysis. The analysis is performed by choosing a kinematically admissible failure mechanism comprising multiple triangular rigid blocks. The effect of the embedment depth of the skirts on the bearing capacity is studied based on the dimensionless embedment ratio Df/Bf. A detailed parametric study is carried out by varying the Df/Bf ratio and Q for both the smooth and rough surface of the skirts. The results obtained from the present theoretical analysis are compared with the available theoretical and experimental data reported in the literature. Ključne besede temelji, mejna analiza, ravninsko deformacijski stanje, plastičnost, temelj s krili Izvleček Vgeotehničnem inženirstvu na morju so temelji s krili praviloma primeren izbor temeljenja. V tem prispevku smo s pomočjo analize zgornje mejne vrednosti določili faktorje nosilnosti za vertikalno obremenjen pasovni temelj na enakomerni c-$ zemljini. Analiza je izvedena z izbiro kinematično dopustnega porušnega mehanizma, ki je sestavljen iz več trikotnih togih blokov. Vpliv globine vpetja kril na nosilnost je preučevana na podlagi brez-dimenzijskega razmerja vpetosti, Df/Bf. Izvedena je bila podrobna parametrična študija s spreminjanjem razmerja Df/Bf in $ za gladko in grobo površino kril. Rezultati, dobljeni na osnovi predlagane teoretične analize, so bili primerjani z razpoložljivimi teoretičnimi in eksperimentalnimi podatki, ki so navedeni v literaturi. List of symbols: Df Df/ Bf Ncsk width of the skirted strip foundation embedment depth of the skirts non-dimensional embedment ratio bearing-capacity factor for an isolated skirted strip foundation with respect to the cohesion of the soil Ny Nysk Pusk V, bearing-capacity factor for surface strip foundation with respect to the unit weight of the soil bearing-capacity factor for an isolated skirted strip foundation with respect to the unit weight of the soil ultimate failure load of the skirted foundation absolute velocity of the ith triangular rigid block in the radial shear zone of the skirted foundation B 2. Acta Geotechnica Slovenica, 2019/2 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis Vj,i+i velocity of the block i+1 relative to the block i in the radial shear zone of the skirted foundation li, di length of two arms of the ith triangular rigid block in the radial shear zone of the skirted foundation n number of triangular rigid blocks in the radial shear zone of the skirted foundation qusk ultimate bearing capacity of the skirted foundation a¡, internal angles of the ith triangular rigid block in the radial shear zone of the skirted foundation aa adhesion factor for the soil 0 angle of internal friction of the soil 1 INTRODUCTION To improve the bearing-capacity and reduce settlement, skirted foundations are reported as a popular choice in geotechnical engineering. The skirts provide confinement in which the soil is stringently enclosed and perform as a single unit with the overlain foundation to transmit the superstructure load to the soil essentially at the level of the skirt tip. Skirted foundations are generally installed to increase the effective depth of the offshore foundation where scouring seems, by all accounts, to be a noteworthy concern [1-4]. Besides that, for several coastal and near-shore structures resting on granular soils with high water tables as well as for the enhancement of the bearing capacity under normal situations, skirted foundations can be an economical option. The major application of skirted foundations is affiliated with jack-up unit structures, oil and petrol gas plants, tension leg platforms, wind-turbine foundations, bridge foundations, etc. Several studies [2-21] are available to determine the bearing capacity of the skirted foundation assuming a rigid soil plug within the skirts. Having considered an equivalent embedded rigid foundation, Yun and Bransby [21] determined the bearing capacity of the skirted foundation embedded in uniform soil. The soil plug is generally presumed to act as a rigid body with uniform shear strength along the depth [14]. Keawsawasvong and Ukritchon [2] and Ukritchon and Keawsawasvong [3] determined the undrained pullout capacity of suction caissons using both upper- and lower-bound limit analyses. A number of investigations [22-28] reported in the literature address the bearing-capacity aspect of the foundation under different field conditions using various solution techniques, such as upper- and lower-bound limit analyses, and finite-element analysis. However, the few studies [13, 21] available in the literature are restricted to the experimental investigation of the skirted foundation considering the plane-strain condition and a perfectly rough foundation- soil interface. Finite-element analyses were performed by Mana et al. [14] to determine the bearing capacity of a circular skirted foundation as a function of the skirt depth, the foundation-soil interface roughness and the heterogeneity in soil strength. However, except for a few studies on suction caissons [2-4], no work is available in the literature to understand the failure of the skirted foundation through a kinematically admissible collapse mechanism along with a properly defined velocity field under the framework of a limit analysis. Therefore, there is an obvious need to develop a proper failure mechanism for exploring the bearing capacity of a skirted foundation theoretically. This study aims to determine the bearing capacity of a skirted strip foundation resting on a homogeneous soil deposit using upper-bound limit analysis [2-3, 22]. The upper-bound theorem, which assumes a perfectly plastic soil model with an associated flow rule, states that the rate of internal energy dissipation by any kinematically admissible velocity field can be equated with the rate of work done by external forces to enable a strict upper bound on the true limit load [29]. In association with the collapse mechanism similar to Pal et al. [17], a multiblock failure mechanism along with upper-bound limit analysis has been adopted to determine the bearing-capacity factors. The bearing-capacity factors with respect to the cohesion (Ncsk) and unit weight (Nysk) of the soil are obtained using a kinematically admissible velocity field. Both smooth and rough skirts are considered in the analysis. The effect of the skirt depth on the bearing capacity is studied based on the dimensionless embedment ratio. The results obtained from the analysis are suitably compared with the available data reported in the literature. 2 PROBLEM DEFINITION A single, isolated, skirted strip foundation with width Bf and depth of skirts Df rests on a uniform c-0 soil deposit. The objective is to determine the bearing-capacity factors Ncsk and Nysk considering an upper-bound limit analysis along with a multi-block failure mechanism. The collapse mechanism, as shown in Fig. 1, is supposed to determine the bearing-capacity factors for the skirted foundation. It is assumed: 1) foundation, skirt and connection between the foundation and the skirt behave as a rigid structure; 2) the analysis does not consider the effect of the installation of the skirted foundation on the surrounding soil; 3) the behavior of the soil is considered to be pressure independent, i.e., the undrained condition. 3. Acta Geotechnica Slovenica, 2019/2 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis (a) (b) Figure 1. (a) Geometry of rigid blocks and velocity vectors, (b) velocity hodograph for failure mechanism. 3 FAILURE MECHANISM The collapse mechanism, as shown in Fig. 1a, is a kine-matically admissible, symmetrical, multi-block failure mechanism with three kinematic variables (a,, fi and 9) to define the collapse mechanism. For the sake of clarity, only the right portion of the center line of the foundation is shown in Fig. 1a, where AB and BC are the half width of the foundation and the right skirt, respectively. The wedge ABCDi is assumed to move vertically as a rigid body with the same downward velocity V0 as that of the footing. The downward movement of the footing and the wedge ABCDj is accommodated by a lateral movement of the adjacent two radial shear zones on both the left and right sides. The radial shear zones on the right side CD1D2...D;...D„D,?kC are discretized into n number of triangular rigid blocks along with the last quadrilateral rigid block BCD^E. The wedge ABCDj includes a part of the soil plug formed between two skirts (left and right) and the triangular wedge shaped below the skirts, which makes an angle 9 with the horizontal. Each triangular rigid block within the radial shear zone can be defined by the internal angles ai and Pi, and by two arms li and dj, whereas the last quadrilat- 4. Acta Geotechnica Slovenica, 2019/2 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis eral rigid block, BCD^E can be defined by the angles (n/2 + aqb) and faqb, and the arm length lqb, where lqb = CDqb. The velocity hodograph for the failure mechanism and other associated geometric parameters are shown in Fig. 1b. At collapse, it is assumed that the footing and the underlying rigid block ABCD1 move as a single rigid unit in the vertical direction with a velocity V0. The number (n) of triangular rigid blocks is kept equal to 30 based on the convergence study. V1,V2,... V,... Vn are the absolute velocities of all the triangular rigid blocks within the radial shear zone, whereas V01 is the velocity of the block CD1D2 relative to the block ABCD1; Vi,i+1 is the velocity of the block i+1 relative to the block i and so on. The interfaces of all the triangular blocks are treated as the velocity-discontinuity lines. The soil mass is assumed to obey the Mohr-Coulomb failure criterion and an associated flow rule. Hence, the direction of the velocity vectors V1,V2,.V,...Vn makes an angle $ with the corresponding rupture lines. The relative velocities V01,V12,...Vi-U...Vn-1,n are also inclined at an angle $ with the velocity discontinuity lines CD1,CD2.CDi. CDn , respectively. The quadrilateral block moves with an absolute velocity Vqb, , which makes an angle $ with DqbE and an angle i(j = + Pqb - 0 - 4> - ZJLi «¡) with the skirt BC, as shown in Fig. 1b. It is worth noting that in the presence of soil cohesion, an adhesion factor (aa) is assumed to determine the internal energy dissipation along the skirt surface, which ensures no separation between the skirt and the soil. All the velocities can be computed in terms of V0 following the velocity hodo-graph, as shown in Fig. 1b. 4 ANALYSIS Various parameters along with the velocity vectors associated with the radial shear zone around the edge of the foundation can be obtained following the collapse mechanism as well as the velocity hodograph. The magnitude of Pusk can be obtained by equating the total external work done to the total internal dissipation of energy, which in turn determines the ultimate bearing capacity of the skirted foundation, qusk = Pusk/Bf. The work done by various external forces and the internal dissipation of energy along the lines of discontinuity can be obtained by following the equations provided in Appendix I and II, respectively. Among the various possible solutions obtained with different input parameters, the least upper-bound value of Pusk reveals the target solution. Hence, the objective function (the bearing capacity) is optimized with respect to different variables (geometrical parameters of the failure mechanism) to obtain the minimum value of the bearing capacity and can be expressed as qusk = = cNcsk + 0.5 yBfNySk (1) Bf The bearing-capacity factors for the smooth skirts can be expressed as NySk = "(A +h+h+h+ /s) (2a) Ncsk = (fe+h+fz+f<> + Ao)(2b) where the functions f1 - f10 are defined in Appendix I and II. However, for a detailed formulation of these functions, Chen [29] can be referred to. Similarly, the bearing-capacity factors for the rough skirts can be expressed as Nrsk = ~(fi +f2+f3+A+ /5) (3a) NCSk = (fe+f7+fe+f9+ /10 + /11) (3b) where the function f11 is defined in Appendix II. From Eqs. (2) and (3) it can be observed that Nysk is same for the foundation with smooth as well as rough skirts, whereas Ncsk varies with the roughness of the skirts. The method of superposition is employed to determine the bearing-capacity factor for the skirted foundation i.e., the c = 0, y # 0 condition is considered to determine Nysk; whereas Ncsk is obtained by considering the c # 0, y = 0 condition and hence, in the process, a true upper-bound solution might not be guaranteed. The minimum value of the bearing capacity, qusk is obtained after performing a nonlinear constrained optimization of Eq. (1) with the help of the 'fmincon' solver in MATLAB. The constraints considered in the optimization process are a) 8 + Zpij1 |3i+1, which ensures a kinematically admissible failure mechanism. c) di + (3; < u, which ensures that all the rigid blocks within the radial shear zone are triangular. d) 10°< 0 < 85°, 1°< a < 85°, 10°< fa < 170°, which are the upper and lower limits of the parameters 9, ai and fa. e) V, > 0 and Vi-1 < V, which ensure that all the velocity vectors are positive and the collapse mechanism is kinematically admissible. 5. Acta Geotechnica Slovenica, 2019/2 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis 5 RESULTS AND DISCUSSION 5.1 Smooth and rough skirts The variation of Ncsk with Df/Bf for both smooth and rough skirts is shown in Fig. 2 for different values of aa and 0. For smooth skirts, there is no energy dissipation along the skirts; whereas in the case of rough skirts the magnitude of Ncsk depends on the adhesion factor aa, which is varied from 1/3 to 1.0. From Fig. 2 it is clear that the magnitude of Ncsk increases with an increase in the Df/Bf ratio for a particular value of 0. It can also be observed that the value of Ncsk increases as the roughness of the skirts i.e., the adhesion factor (aa), increases. However, for a lower embedment ratio (Df/Bf) the roughness of the skirts has little influence on Ncsk. Hence, it is evident from Fig. 2 that the effectiveness of the skirted foundation increases with an increase in the embedment depth of the skirt. <|) = 20° 25 n "20 - 15 0.0 0.5 1.0 D/Bf (a) <|> = 30° 1.5 50 n 45 - 40 - 35 - 30 - 25 0.0 1.5 0.5 1.0 D/Bf (b) Figure 2. (a) Variation of Ncsk with Df/Bf with different aa for (a) 0 = 20°, (b) 0 = 30°. The variation of Nysk with Df/Bf for different values of 0 is shown in Fig. 3. The magnitude of Nysk is found to increase significantly with the Df/Bf ratio due to an increase in the confinement provided by the skirts. The roughness of the skirts does not affect the bearing-capacity factor Nysk as the internal energy dissipation is considered to be zero (c = 0) in the determination of Nysk. The rate of increase of Nysk is seen to be more predominant in the case of a higher angle of internal friction, which can be attributed to the larger failure domain developed in the surrounding soil. 100 n -aa= 1.0 -aa = 2/3 -aa = 1/2 -a" = 1/3 -Smooth skirts -30° -20° -aa= 1.0 -aa = 2/3 -a" = 1/2 -a" = 1/3 -Smooth skirts Figure 3. Variation of Nysk with Df/Bf for different values of 0. 5.2 Critical failure surface The critical failure surface obtained from the optimization of the collapse mechanism is shown in Fig. 4 for 0 = 30° and different Df/Bf ratios. It is clear that the size of the critical failure zone considerably increases with an increase in the Df/Bf ratio, which in turn causes an increase in the bearing capacity of the skirted foundation. Similarly, the critical failure surface for different values of aa and 0 is presented in Figs. 5 and 6, respectively. It is clear from Figs. 5 and 6 that the failure zone expands with an increase in aa and 0, resulting in an enhancement of the bearing capacity with an increasing roughness of the skirts and the angle of internal friction of the surrounding soil. 6 COMPARISON_ In Table 1 the present values of Ncsk obtained for smooth skirts with 0 = 0° are compared with those reported by Mana et al. [15], who obtained Ncsk for the foundation with smooth skirts employing finite-element limit 6. Acta Geotechnica Slovenica, 2019/2 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis (a) (b) Figure 4. Critical collapse surface for < = 30° and aa = 1.0 with (a) Df/Bf = 0.6, (b) Df/Bf = 1.4. Figure 5. Critical collapse surface for < = 30°and Df/Bf = 1.4 with different aa. Figure 6. Critical collapse surface for aa = 1.0 and Df/Bf = 1.4 with different <. analysis. The present results are found to be the lowest, but compare reasonably well with those proposed by Mana et al. [15]. In Table 2, the values of Ncsk obtained from the present analysis for rough skirts with < = 0° are compared with those provided by Yun and Bransby [21] and Mana et al. [14]. The latter determined the bearing-capacity of a skirted strip foundation resting on uniform clay soil (< = 0°) using the finite-element method. The present analysis predicts a lower value of Ncsk as compared with the existing values reported in the literature and hence it can be considered as a better solution for the skirted foundation. In Table 3, the ratio of Nysk/Ny obtained from the present analysis for different magnitudes of the Df/Bf ratio is compared with the numerical as well as the experimental results reported by Eid [11]. Eid [11] proposed the Nysk/Ny ratio in cohesionless soil through experimental 7. Acta Geotechnica Slovenica, 2019/2 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis Table 1. Comparison of Ncsk for smooth skirts with fy = 0° D/J Present analysis Mana et al. [15] 0.1 5.33 5.48 0.2 5.50 5.74 0.3 5.63 5.92 0.4 5.77 6.10 0.5 5.90 6.22 Table 2. Comparison of Ncsk for rough skirts with fy = 0°. Df/Bf Present analysis Yun and Bransby [21] Mana et al. [14] 0.00 5.14 5.20 5.22 0.20 5.65 6.00 6.10 0.30 5.86 6.35 6.50 0.50 6.23 7.00 7.25 0.75 6.62 7.70 8.00 1.00 6.95 8.50 8.80 1.20 7.19 9.00 - Table3. Comparison of Nysk/Ny ratio for different Dj/Bf. Nysk/Ny fy(°) Df/Bf Present analysis Eid [11] Numerical Experimental 0.5 1.87 1.5 - 35.0 1.0 2.80 1.8 - 1.5 3.81 2.6 - 2.0 4.88 3.2 - 0.5 1.74 - 2.10 38.5 1.0 2.52 - 3.10 1.5 3.36 - 4.05 2.0 4.25 - 5.50 0.5 1.70 1.4 1.85 40.0 1.0 2.41 2.1 2.60 1.5 3.18 2.6 3.50 2.0 4.00 3.2 4.70 0.5 1.53 1.6 1.50 45.0 1.0 2.10 2.2 2.20 1.5 2.66 2.7 2.95 2.0 3.27 3.3 4.00 as well as numerical analyses. Three different values of relative density (44%, 57% and 71%) were considered in the experimental study of Eid [11], which correspond to three different magnitudes of fy , such as 38.5°, 40° and 45° [30]. It is worth noting that the corresponding value of fy is selected as the mean value within the range of fy as proposed by Eid et al. [30]. For lower values of fy, the present values of the Nysk/Ny ratio are seen to be a little higher than those determined from the numerical study of Eid [11], whereas the experimental results of Eid [11] for all values of fy are the highest. 7 CONCLUSIONS_ The bearing-capacity factors for a skirted strip foundation are determined using an upper-bound limit analysis for various soil-friction angles and the embedment ratio of the skirts. The magnitude of Ncsk is found to increase with an increase in the roughness of the skirts. However, for a lower value of the Df/Bf ratio, the roughness of the skirts has little influence on the Ncsk values. It was clear that the magnitude of Ncsk increases with an increase in the Df/Bf ratio for a particular value of fy. The magnitude of Nysk was found to increase significantly with theDf/Bf ratio due to an increase in the confinement provided by the skirts. The roughness of the skirts does not affect Nysk as the internal energy dissipation is considered to be zero (c = 0) during the calculation of Nysk. APPENDIX I: EXTERNAL WORK DONE a) The external work done by the self-weight of the quadrilateral block ABCD1 below the footing (Fig. 1a) can be expressed as, yBf where, f _ tan 6 _ Ji — ~; r i AWABCD^-^IflCOfcMHVo (?) (4) b) The external work done by the self-weight of the 2n triangular rigid blocks on either side of the footing can be expressed as, 2n = ^L [f2(ai( ßj, 0)]VO (5) where, h = j=i cos (8 — 0) 2 cos2 0 sin(ß1 — 20) i I sinaisinßi SUlfai + ßi) sin2 ßj sin(aj + ßj — 20) r ^ \ j—r sin- ßj sin(aj + fSj A - 0 - 0 - ^ a, I nsm2(aj + ßj) sin(ßj+i _ 20) c) The external work done by the self-weight of the quadrilateral rigid block BCD^E (Fig. 1a) can be expressed as, 8. Acta Geotechnica Slovenica, 2019/2 P. Ghosh and A. Pal: Undrained bearing capacity of a skirted strip foundation using upper-bound limit analysis vBf AWqb = [f3(aj, ßi( 0) + f4(ai( ßi, 9) + fs(ai( ßi( 9)]V0 (6) where, cos(6 — 0) sin aqb sin ßqb h = sin 2 cos2 6 sin(aqb + ßqb) sin(ß1 — 20) ' v1 \ FT sin2 siniaj + ßj ~ 2(P) ßqb - e - 0 - ^ I[J siniaj+ßj)sin(ßj,1- 20) /4 = 2 Df cos(6 — 0) sinßqb Bf cos 9 sin(ßi — 20) sin(aqb + ßqb) ~~t sin ft sin(a.j + ßj — 20) ' r-, \t—r sm ft sin{(Xj + ßj - ¿- ^ «,]n^a,+ ft)s^ft+1-20) /s = 2D/2 cos(0 - 0) sin[(ggi, + ßqb) - n/2\ Bf2 sin(ß1 - 20) sin(aqb + ßqb) ~~t sin{aj + ßj — 20) SW ßqb — 9 — (¡) ■ ■I")U sin(ßj+1-2=40° , -9-6=20" ¿„=0.4 —•—6=30° 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 K Figure 11. Effect of the vertical seismic coefficient Figure 13. Effects of the wall-soil friction angle on tanf under different k^. 5.3 Horizontal interlayer friction coefficient Figs. 12 and 13 show the variations of the horizontal interfacial friction coefficient with these influence parameters (i.e. the internal friction angle f, horizontal seismic coefficient kh and vertical seismic coefficient kv). From Fig. 12, the horizontal interlayer friction coefficient tanf' decreases from 0.18 to 0.09 with the increase of f from 15° to 45° and with the decrease of kv from 0 to kh. From Fig. 13, the tanf' increase from 0 to 0.3 with the increase of S from 0 to f and kh from 0 to 0.2, and it is smaller than tanf = tan40° = 0.839. Moreover from Fig. 12 and Fig. 13, it can be seen obviously that influence of kh on tanf' is more significant than that of kv on tanf', and the influence of S on tanf' is more significant than that of f on tanf'. 5.4 Lateral seismic active earth pressure Figs. 14-17 show the distributions of the normalized lateral seismic active earth pressure aw f(yH) along the normalized wall height with f, S, kh and kv. From Figs. 14-17, the maximum value of the lateral seismic active earth pressure is located near the wall toe,that is consistent with the experimental results [4] for rigid retaining walls under RB mode. Moreover, the lateral seismic active earth pressure aw is concave nonlinear distribution along the wall height except for kh<0.1, and the distribution of aw varies from right-convex to concave with increase of kh from 0 to 0.2. The aw decreases with the increase of f, S and kv, respectively. But the ffw increases with the increase of kh. on kaw under different S. 19. Acta Geotechnica Slovenica, 2019/2 Y. Y Cai et al.: Seismic active earth pressure on rigid retaining walls under rotation about base considering principal-stress rotations by pseudo-static method Figure 14. Effect of the internal friction angle on ow KyH). Figure 17. Effect of the ratio between the vertical and horizontal seismic coefficients on ow KyH). Figure 15. Effect of the wall-soil friction angle on ow KyH). From Figs. 14-17, the resultant of the seismic active earth pressure respectively decreases with the increase off, S and kv, but increases with the increase of kh. 5.5 Height of the application of the seismic active earth pressure Figs. 18-19 show the variations of the normalized height of the application of the seismic active earth pressure h/H with f, S/f, kh and kv/kh. Figure 16. Effect of the horizontal seismic coefficient on ow KyH). 20. Acta Geotechnica Slovenica, 2019/2 Y. Y Cai et al.: Seismic active earth pressure on rigid retaining walls under rotation about base considering principal-stress rotations by pseudo-static method 0.345 0.318 -1-1-1-1-1-1-1-1-1-L Ti 25 27 29 31 33 35 37 39 41 43 45 ff ) (c) <5=10° Figure 18. Change of the height of the application of the lateral seismic active earth pressure with f under different % 0.32 0.31 1--J------A----1-1-1-1-'---- 0 0 0.1 0.2 0.3 0.4 0 5 0 6 0.7 OR 0.9 1.0 Sfp (a)*„=0 2, f=30' 0.31 -*-*-*-1-*-1-1-*-1- 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.R 0.9 1.0 Slip (b) ifc=0.2, (5=40* Figure 19. Change of the height of the application of the lateral seismic active earth pressure with S/f under different kv/kh. From Figs. 18 and 19, the normalized height of the application of the lateral seismic active earth pressure h/H approximately decreases linearly with the increase of f, and first decreases and then increases with the increase of S/f, but it non-linearly decreases with the increase of kh. Moreover, the h/H increases with the increase of kv/kh for S/f < 0.1 and f < 28°, but decreases with the increase of kv/kh for S/f > 0.6. The h/H is greater than 1/3 and smaller than 0.3406 for kh < 0.03, but it is smaller than 1/3 and greater than 0.319 for kh > 0.1. Moreover, the h/H is smaller than 1/3 and greater than 0.3311 for f > 33° and kh = 0.05, and it is smaller than 1/3 and greater 0.3199 for S/f < 0.8 and kh > 0, but it is greater than 1/3 and smaller than 0.3359 for 23° < f < 33° and kh = 0.05. 6 CONCLUSIONS In the proposed method, the seismic problem was simplified to the static problem using the pseudo-static method. By rotating, the seismic angle is added to the inclined angles of the wall and backfill surface in the formula of Coulomb static earth pressure, then the seismic active rupture angle was obtained according to Coulomb static earth pressure theory. Moreover, the basic equations of the seismic active earth pressure under RB mode were established by stress analysis and the static equilibrium. Then, the theoretical formulae for the seismic active earth pressure and its coefficient, the resultant of the seismic active earth pressure and its application height are put forward for the design of rigid retaining walls under RB mode considering the principal-stress rotation. The effects of main parameters (i.e. the internal friction angle of backfills, wall-soil friction angle, horizontal and vertical seismic coefficients) on the seismic active rupture angle, the coefficient of the lateral seismic active earth pressure, the horizontal interface friction coefficient, the distribution of the seismic active earth pressure, the resultant earth pressure and the height of its application were analyzed. The horizontal seismic coefficient has a greater influence on the seismic active earth pressure of rigid retaining walls than the vertical seismic coefficient, and the internal friction angle of backfills has a greater influence on the seismic active earth pressure of rigid retaining walls than the wall-soil friction angle. The comparisons of predicted and measured values of the lateral seismic active earth pressure showed that the proposed method agreed better with the experiment than M-O method. This proposed method is feasible and reasonable in the design of seismic rigid retaining walls under RB mode. Acknowledgments This research was supported by the Natural Science Foundation of China (Grant 51774147 and 51978292), Natural Science Foundation of Fujian Province of China (Grants 21. Acta Geotechnica Slovenica, 2019/2 Y. Y Cai et al.: Seismic active earth pressure on rigid retaining walls under rotation about base considering principal-stress rotations by pseudo-static method 2017J01669 and 2017J01094), Scientific Research Program of Hebei Education Department (Grant QN2018098) and Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology), China (SKLGP2018K008). All support is gratefully acknowledged. Notation The following symbols are used in this paper: Fh Fv F kh kv P g khg kvg n Y Y' S p ß ß' H H' a oi a3 oh aß dx L R x horizontal inertia force of the backfill vertical inertia force of the backfill total inertia force of the backfill horizontal seismic coefficient vertical seismic coefficient density of the backfill gravitational acceleration horizontal seismic acceleration vertical seismic acceleration seismic angle unit weight of the backfill unit weight of the backfill in rotating calculation model wall-soil friction angle internal friction angle of backfills seismic active rupture angle pseudo seismic active rupture angle height of the rigid retaining wall height of the rigid retaining wall after rotation rotational angle of principal stresses major principal stress minor principal stress horizontal stress on the vertical of the differential sliding backfill element at any point vertical stress on the horizontal of the differential sliding backfill element at any point shear stress on horizontal of the differential sliding backfill element at any point lateral earth pressure on the wall shear stress on the wall rotational angle of the principal stress at the wall shear stress on the sliding surface normal stress on the sliding surface angle between the active sliding surface and the major principal stress plane angle between the horizontal and major principal stress at the sliding surface differential length along the horizontal horizontal width of the differential flat element radius of the circular arc horizontal distance of arbitrary point in differential flat element from the wall y = depth of the differential element from the backfill surface dG = self-weight of differential sliding backfill element aav = average vertical stress on the horizontal in differential element Ta = average shear stress on the horizontal in differential element ka = coefficient of active earth pressure by Rankine kaw = coefficient of lateral seismic active earth pressure in this paper f' = horizontal interlayer friction angle tanf' = interfacial friction coefficient Eh = resultant of lateral seismic active earth pressure on the retaining wall Ea = resultant of seismic active earth pressure on the retaining wall M = moment of the lateral seismic active earth pressure about the wall base h = height of application of the seismic active earth pressure REFERENCES_ [1] Okabe, S. 1926. 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Department of Civil Engineering N.Tesla str. 3, 160 00 Praha 6, The Czech Republic 48000, Mentese-Mugla, Turkey E-mail: mvanicek@geosyntetika.cz E-mail: rkahyaoglu@mu.edu.tr https://doi.Org/10.18690/actageotechslov.16.2.25-38.2019 DOI Keywords geogrid reinforcement, geotextile encasement, surcharge, soil settlement, column bulging, sand mat Ključne besede geomreže, geotekstilna obloga, preobremenitev, posedanje zemljine, izbočenje stebra, peščena podlaga Abstract This paper presents a three-dimensional, finite-element, parametric study of a base-reinforced embankment supported by encased floating columns on soft soil. A 3D numerical model is made to study the effects of geogrid basal reinforcement and geotextile encasement on the displacement behavior of the columns. The numerical model was initially verified using measured data from a real case study. Then, parametric studies were subsequently performed, considering the effect of the encasement stiffness, the basal reinforcement stiffness and the embankment fill height, together with an examination of the effective length of the encasement. The results from this parametric study are presented here in the form of comparative graphs. The objective of this paper is to present the behavior of the embankment on floating encased columns after the soft soil consolidation for different embankment heights, basal reinforcement and column-encasement stiffnesses. Izvleček V prispevku je predstavljena tridimenzionalna parametrična študija končnih elementov ojačenega nasipa, podprtega z geotekstilom obloženimi gruščnatimi stebri na mehkih tleh. Izdelan je 3D numerični model za proučevanje učinkov osnovne ojačitve z geomrežo in geotekstilnih oblog na deformacijsko obnašanje gruščnatih stebrov. Numerični model smo sprva preverili s pomočjo študije izmerjenih podatkov na realnem primeru. Nato so bile naknadno izvedene parametrične študije ob upoštevanju učinka togosti geotekstilnih oblog, togosti osnovne ojačitve z geomrežo in višine polnilnega nasipa vzdolž raziskovane efektivne dolžine geotekstilnih oblog. Rezultati iz te parametrične študije so predstavljeni v obliki primerjalnih grafov. Cilj tega prispevka je predstaviti obnašanje nasipa ležečega na z geotekstilom obloženih gruščnatih stebrih po konsolidaciji mehkih tal za različne višine nasipov, osnovne ojačitve in togosti z geotekstilom obloženih stebrov. 1 INTRODUCTION The construction of embankments on soft soils, as part of the efforts to reclaim new areas for the construction of highways, railways, airport runways and urban infrastructure, faces several hurdles with regard to the low load-bearing capacity and high compressibility of the subsoil, as well as the tendency for excessive lateral deformations. Among the various available techniques, such as surcharging, excavation and replacement, vertical drainage, vacuum consolidation and column- Acta Geotechnica Slovenica, 2019/2 25. M. R.Kahyaoglu & M. Vanicek: A numerical study of reinforced embankments supported by encased floating columns -supported embankments, the use of column-supported embankments (CSEs) allows for a rapid construction, total and differential settlement reduction, and adjacent facility protection [1-3]. However, it is impossible to construct CSEs in very soft clays (cu < 15 kN/m2) due to the insufficient columns material lateral confinement and excessive lateral bulging of the columns [4-6]. In such soils, the required lateral confinement can be induced through the encasement of individual columns with geosynthetics [7-11]. In 1995 the first project utilizing a seamless geotextile-encased column was successfully implemented in Germany, and later, Kempfert et al. [5], Raithel and Kempfert [6] and Raithel et al. [7] tested the performance of geosynthetic-encased stone columns (GECs) using numerical and analytical models. The technique detailed in the above-mentioned projects has been adopted in Europe [8, 9] and more recently in South America [11], but with growth in the construction sector and improvements in geosynthetic production technologies, new design procedures have been developed. The performance of geosynthetic encasement on the capacity and settlement behavior of soft soils has been studied in both laboratory and field tests [12-17], while numerical studies of encased granular columns have been conducted successfully in the literature [18-27]. The cited studies investigated the influence of the geometry and material properties of encased and non-encased stone columns (SCs) on vertical stresses, excess pore-water pressures and tangential strains in the geotextile, with a focus on the effect of encasement length and stiffness, the strength of the soft ground and surcharge from the embankment fill. The benefit of encasing stone columns in terms of settlement, lateral deformation and load-carrying capacity has been underlined in the above studies, and design charts for an estimation of the maximum settlement in soil and column strain during the preliminary design are presented. In recent years, in the event of high embankment loads, one layer of geogrid has been used at the base of the embankment in combination with GECs over soft clay soils to form a geosynthetic reinforced and column-supported embankment (GRCSE) [28-30]. The application of a geogrid layer over the columns and the soft soil enhances the efficiency of the load transfer from the embankment to the columns, provides controllable deformation, minimizes soil yield, enhances global stability and eliminates the need for inclined columns to resist the horizontal thrust at the sides of the embankment [31-34]. The complicated mechanism of load transfer in GRCSEs combines with the arching effects, tension in the geosynthetic reinforcement and stress transfer from the soft soil to the column due to the different stiffness values. Over the past few years, both experimental and numerical investigations into the behavior of GRCSE have been carried out by many researchers [35, 37]. Previous studies have analyzed the performance of GECs and the time-dependent behaviors of geosynthetic-reinforced embankments supported on end-bearing columns. In some instances, when the column does not reach a hard stratum, the construction of floating columns is found to be more economical and technically feasible. The frictional force along the floating column, based on the relative deformation between the column and the surrounding soil, affects the behavior of GECs [36, 38, 39]. Although previous research has contributed valuable information to the knowledge of end-bearing columns, information about the group behavior of floating columns is still lacking, and so further research is required into the design of embankments on encased floating columns [40-42]. This paper explores the time-dependent behavior of geogrid-reinforced embankments supported by floating columns encased in geotextiles. Firstly, a real case study of GRCSE in thick soft soil was modeled numerically. Then, the numerical results and the measured data were compared, and some calibrations on the numerical model were made for the verification. Finally, parametric studies including variations of the embankment height, the stiffness of the column encasement and the base reinforcement were performed. Many of the recent studies mentioned above have dealt with the load-carrying capacities and settlement of unreinforced embankments supported with GECs; however, the effects of reinforcement to the base of the embankment have not been considered to date, nor have the load-transfer mechanism and the lateral bulging deformation patterns associated with GECs. The published literature focusing on the long-term effects of these parameters on the vertical and lateral displacement behaviors of the GECs is limited, and so in order to enhance the performance of the GECs to contribute to the above-mentioned issues, the objectives of this paper are as follows: (1) to examine the long-term behavior (100% consolidation) of a floating, column-supported embankment under different surcharges; (2) to investigate the performance of basal geogrid reinforcement; (3) to consider the effects of geotextile encasement on the lateral and vertical displacement of columns; and (4) to determine the effective length of the geotextile encasement of floating columns. 26. Acta Geotechnica Slovenica, 2019/2 26. M. R.Kahyaoglu & M. Vanicek: A numerical study of reinforced embankments supported by encased floating columns 2 NUMERICAL MODELLING 2.1 Model verification A case study of a stone-column-supported embankment constructed in Kebun-Malaysia, the details of which can be found in Raju (1997) [43], was modelled numerically. The soil profile for the Kebun Interchange project contained marine clay where th e CPT tip resistance values for the top 11 m are 0.1-0.3 MPa (Fig 1). Stone columns with a 1.1-m diameter were installed at a 2.2-m rectangular spacing to a depth of 12 m under the 2.6-m-high embankment. Settlement gauges were placed on the top of the stone columns and the total settlement was read as 0.4 m. A 1-m settlement was observed for untreated ground under the same circumstances. The results of the settlement in the soft soil and the encased column after the completion of the embankment construction from our numericalm odel were compared with measured settlements from the Kebun project. This comparison presented in Fig. 2 shows that the numerical model followed the trends of the measured data. The vertical stress transmitted to both the stone column and the soft soil was verified with measured values, and this consistency indicates that the numerical model is appropriate for a parametric study. / A s / --- // n / X * J ✓ / ✓ jf H = 2.6m LC = 12m —•—Measured (Soil) --Calculated (Soil) —■—Measured (Column) --Calculated (Column) - // // It r '} ✓ / // / t lt St 6t 8t 1tt 12t 1st 16t 18t Itt Time (day) Figure 2. Comparison between the calculated and measured settlements of the column and the soil. 2.2 Parametric study GRCSE in 40-m-thick soft soil lying on a rigid and firm layer were modeled and studied numerically. The water level was modelled at the original ground surface. Floating columns having a diameter of 1 m (D) were arran- 11 it si st 0) 31 3t 11 lt Acta Geotechnica Slovenica, 2019/2 27. M. R.Kahyaoglu & M. Vanicek: A numerical study of reinforced embankments supported by encased floating columns ged in a square-grid pattern with a 3-m center-to-center spacing, giving an area replacement ratio of 8.7 percent. All the stone columns were encased with geotextiles of the best geosynthetic type for the encasement of the floating columns [20]. A 1-m-thick sand mat, acting as a working platform below the embankment (2V:1H side slopes), was established on top of the natural clay soil prior to the embankment fill to allow equipment access and to provide drainage for the columns. Furthermore, one layer of geogrid was laid to provide a basal reinforcement for the embankment. The numerical analyses were carried out using an available PLAXIS 3D Foundation package [44]. The displacements and the vertical stresses on the column and the surrounding soil, as well as the tensile strains and tangential tensile forces acting on the geosynthetics, were calculated. The details of the cross-section of the Figure 3a. Cross-section of the model. model and the finite-element mesh are shown in Fig. 3, representing the right half of the domain on account of the symmetry. In the analyses, the model limits were 50 m in the vertical direction and 220 m in the horizontal direction, being five times the width of half of the embankment base, so as to minimize the boundary effect. Fig. 4 shows the finite-element mesh used in the 3D numerical simulations. The soil clusters were modeled using 10-noded tetrahedral elements, whereas the geosynthetic elements are represented by 6-noded triangle surface elements. A horizontal displacement was not permitted on the vertical boundaries of the model; however, the bottom boundary was fixed securely in both the vertical and horizontal directions. The embankment fill construction to the top surface was simulated in four stages. For each stage 20 days was envisaged for the construction of a 2-m layer and 90 days for the consolidation from its surcharge. The consolidation analyses were carried out during and after each construction stage. After the completion of the embankment construction, the calculations were continued until the excess pore-water pressure dissipation at mid-depth of the clay layer had reached 1 kPa. A closed consolidation boundary was applied to the sides of the model parallel to the embankment axis to prevent lateral drainage. Both the embankment fill and the sand mat (assumed to be Sacramento River sand) were modeled using the Mohr-Coulomb failure criterion under a drained condition. Kaliakin et al. [45] discussed the determination of the values from experimental data for Sacramento River sand based on the tests carried out by Lee and Seed [46]. The column material was modeled as granular soil, in Figure 3b. Cross-section of the finite-element model. 28. Acta Geotechnica Slovenica, 2019/2 28. M. R.Kahyaoglu & M. Vanicek: A numerical study of reinforced embankments supported by encased floating columns Figure 4. 3D finite-element model. line with the suggestions of Ambily and Gandhi [47]. The soft soil was idealized using the modified Cam Clay (MCC) model. The MCC parameters considered in this study were adopted from the geotechnical parameters of soft Kebun clay soil encountered in a recent soft-ground improvement project [43]. Khabbazian et al. [37] stated that the use of the MCC model is preferable over the Mohr-Coulomb or linear elastic models, in that it allows a more accurate modeling of the behavior of the soft soil. The geosynthetics used for both the reinforcement and the encasement were modeled as linear elastic material with no bending stiffness, as recommended by Muru-gesan and Rajagopal [19] and Liu et al. 2007 [13]. The stiffness of the geosynthetic reinforcement (J=EA) was determined as the tensile force at 3% elongation divided by that elongation (3%). Perfect adhesion between the stone and the surrounding soil were assumed, and thus interface elements with a rigid interface were used at the interfaces of either the stone column and the encasement, or the encasement and the soft clay [22, 23]. In fact, a large number of researchers have been investigating so much to characterize the interface working mechanism and propose fruitful achievements on the constitute models of the soil-geosynthetic interface. The parameters used in the numerical analyses are summarized in Table 1. Stone columns are installed using vibro-displacement and vibro-replacement methods. The stone material is laterally expanded, which is accompanied by an increase in the horizontal earth pressure and the excess pore-water pressure in the soft soil during and after the column's installation. However, any influence related to the installation of the columns was disregarded in this study. Table 1. Material parameters used in the numerical analyses. Parameter Column Material Stone Soil (Ambily and Gandhi 2007) Embankment Fill Sacramento River Sand (Kaliakin 2012) Working Platform Sacramento River Sand (Kaliakin 2012) Soft Clay Kebun Clay (Raju 1997) Model Type Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Modified Cam Clay Unit Weight, y(kN/m3) 24 22.5 20 15 Effective Friction Angle, ^>'(°) 42 36 32 - Effective Cohesion, c'(kPa) 1 1 1 - Dilation Angle, f'(°) 10 4 3 - Elastic Modulus, E(kPa) 55000 20000 15000 - Poisson's Ratio, v 0.3 0.3 0.3 0.3 Slope of Swelling Line, K - - - 0.02 Slope of the Virgin Consolidation Line, X - - - 0.4 Void Ratio at Unit Pressure, e - - - 1.0 Slope of the Critical State Line, M - - - 1.0 Permeability, k(m/s) 1x10-2 1x10-3 1x10-3 1x10-6 Acta Geotechnica Slovenica, 2019/2 29. M. R.Kahyaoglu & M. Vanicek: A numerical study of reinforced embankments supported by encased floating columns In order to cover all the cases in the embankment-construction scenarios, parameters such as the embankment height (H), column-encasement stiffness (Je), and basal reinforcement stiffness (Jr) were varied, as summarized in Table 2. Table 2. Parameters evaluated in the parametric analyses. Parameter Embankment Height, 2 4 6 8 H (m) Geogrid Reinforcement Stiffness, JR (kN/m) 1000 2000 3500 5000 6500 Column Length, LC (m) 16 Geotextile Encasement 500 1000 1500 2000 2500 Stiffness, JE (kN/m) For the case of the 8-m-high embankment, the critical length of a floating column according to the analytical equation developed by Satibi [40] was determined as 15 m. Based on this critical length, the lengths of the columns are determined to be 16 m (Lc=16m) for the whole parametric study. A comparison is made of the surface settlement of the column and the soft soil, the column bulging, the vertical stresses on the floating column (Lc=16m) and the soft soil, and the tangential force in the geogrid reinforcement. A similar parametric study with several variables for reinforced shallow foundations was performed by Jelusic and Zlender [48, 49]. 3. RESULTS OF THE PARAMETRIC STUDY The results of the parametric study evaluating the variation of the embankment height, column encasement and basal reinforcement stiffnesses were categorized according to the effects on the stress strain behavior of the GRCSE in the following subsections. 3.1 Surface settlement Fig. 5 shows the surface-settlement behavior of the encased columns and the soft soil for different unreinforced embankment cases. The results reveal a significant decrease in the settlement with the encasement, which is thought to be a direct consequence of the column bulging reduction by additional confining pressure produced by the geotextile encasement along the column length. It is also clear that an increase in the stiffness of the encasement improves the performance of the GEC. The settlement curves (Fig. 5) also indicate that geotextile encasement reduces the total settlement, but generates some differential settlement. The soft soil closer to the embankment centerline is subjected to greater vertical stresses when compared to the soil near the embankment edges, leading the settlement values to decrease with the distance from the centerline of the embankment. The value of the maximum settlement of the column close to the middle is about 30 percent greater than that of the column near the edge. The settlement response of the GECs also depends strongly on the surcharge from the embankment's self-weight. When the embankment height is less than 4.0 m (H < 4 m), the surface settlements are small. 60 Ï 1 ¿4 5 Q. ~ ~ 4 5 Vi\ \ / ti % tj ' \ H=6m Lc=16m 6 /5 6 JR= 0 kN/m ? 7 1 f / i1

-p=o k- P=10 K- p=20 — P=30 -p=5 -p=15 P=25 ■p=35 3 6 c„/(YB) 12 (c) (d) Figure 6. Effect of soil strength on the relative bearing capacity: (a) b/B=0, (b) b/B=1, (c) b/B=2, (c) b/B=3, (c) b/B=4. (c) (d) Figure 7. Effect of soil strength on the failure mechanism: (a) cu/(yB) =0.7, (b) cu/(yB) =1.4, (c) cu/(yB) =2.8, (d) cu/(yB) =5.7. failure. It can also be stated that the severe effect of the slope decreases with an increase in the strength of the soil. Therefore, the edge distance at which the strength of the soil mobilizes optimally decreases with the increase in the soil strength. Although the magnitude of the safe slope inclination increases with the soil strength, the critical edge distance is found to decrease. 4.4 Effect of the edge distance The typical variation in the BCR with edge distance is presented in Fig. 8 for a footing of different embedment ratios resting over a soil having cu/(yB)=2.85. The degree of strength mobilization of the soil located on the level side increases with an increase in the edge distance. 56. Acta Geotechnica Slovenica, 2019/2 R. P. Shukla and R. S. Jakka: Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes Consequently, it increases the bearing capacity and the stability of the footing. The footing located near to the slope fails due to the local shear failure and the mode of failure changed to general shear or punching shear failures with an increase in the edge distance. At a particular edge distance, both sides of the soil contribute with an equal amount and the footing behaviour becomes independent of the slope. At this critical edge distance, the failure pattern becomes symmetrical about the footing axis. At a small edge distance and a steep slope, the failure is one sided (slope side only), and the soil on the side of the level ground does not fully contribute to the bearing capacity. Therefore, the measured BCR is small for a footing resting precisely (a) (b) 0.6 -»-p=o ¡=5 0.4 -*-p=15 ¡=20 —1—P=30 [ 1=35 0.2 —P=45 -■-f ¡=50 0 0 1 2 B'/B (c) Figure 8. Effect of edge distance on the bearing capacity enhancement for a footing: (a) Df/B=0, (b) Df/B=0.5, (c) D(/B=1.0. on a slope crest or near to the slope crest. The degree of strength mobilization of the soil located on the level side increases with an increase in the edge distance (Fig. 9). The passive resistane increases with an increase in the edge distance, resulting in the increases in the bearing capacity [36]. Varzaghani and Ghanbari [37] also stated that the stiffness of the foundation increases with the setback distance increases, which leads to an increase in the bearing capacity of the soil. The typical effect of edge distance on the failure mechanism is shown in Figure 9. It shows that the failure mechanism changes significantly with an increase in the edge distance. The elastic wedge below the footing is unsymmetrical for a small setback and becomes a symmetrical and higher edge distance. Also, the shear dissipation on the level side of the footing also increases with an increase in the edge distance. The footing becomes independent of the slope with an increase in the edge distance, and at a particular edge distance, the footing becomes independent of the slope inclination. On the basis of the numerical analyses, the limiting edge distance is identified for the various combinations (a) (b) (c) (d) Figure 9. Effect of edge distance on the failure mechanism: (a) b/B=0, (b) b/B=1, (c) b/B=2, (d) b/B=3. 57. Acta Geotechnica Slovenica, 2019/2 R. P. Shukla and R. S. Jakka: Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes of parameters. The limiting edge distance evaluated in the present study is presented in Table 2. The increase in the critical edge distance is primarily observed (Table 2) due to the increased slope inclination in the soils, rather than an increase in the soil strength as even a steep slope is stable in cohesive soils due to the higher strength. Table 2. Limiting edge distance for strip footing on a cohesive soil slope. Undrained shear cu (kPa) cJiyB) Depth ratio (D/B) Critical b/B Optimum b/B 20 0.7 0-20 0-1.0 1-5.0 1.0-2.5 40 1.4 0-35 0-1.0 1.0-4.5 1.0-2.0 80 2.8 0-50 0-1.0 1.0-4.5 1.0-1.5 160 5.7 0-55 0-1.0 0.5.0-4.0 0.5-1.0 320 11.4 0-80 0-1.0 0.5.0-3.0 0.5 The International Residential Code [38] and the Uniform Building Code [39] suggest the maximum edge distance can be a minimum of H/3 and 12 m. The Indian standard IS: 1904-1986 recommends maintaining a minimum distance of 0.9 m from the slope surface. However, the code does not provide any guidelines to locate a footing resting near to the slope crest (edge distance). In the present study, the critical edge distance is found to vary from 1 m to 9 m (or 0.05H to 0.45H). However, from the present numerical study, it is observed that the critical setback distance depends not only on the slope height, but also on the slope inclination, the depth of footing, the width of footing, and the strength of the soil (cu/(yB)). However, in practice, it is not always possible to locate a footing at a critical setback distance. Therefore, an optimum value of the edge distance needs to be identified, at which the reduced bearing capacity (due to the slope effect) is reasonably negligible. In the present study, the optimum value of the edge is determined by considering a BCR value equal to 0.75-0.8 and varies from 0.5B to 2.5B (0.05H to 0.05H), depending on the footing depth, the soil strength and the slope inclination. The obtained values of the optimum setback (0.05H to 0.05H) are significantly less than the values suggested in the codes. The significant difference highlights the fact that a constant value of the edge distance, as suggested in the standards/codes, irrespective of the soil properties, foundation characteristics and slope geometry is not appropriate, and needs to be improved. 5 COMPARISON WITH THE BEHAVIOUR OF A FOOTING RESTING ON COHESIONLESS SOIL SLOPES The results of the present study have been compared with the results of Shukla and Jakka [2], where footings resting on cohesionless soil slopes were studied in detail. From the comparison of the results, it is observed that the BCR decreases with an increase in the slope inclination and the embedment depth in both cohesive and cohesionless soil slopes. However, the influence of the soil strength on the critical edge and the BCR is the opposite in cohesive and cohesionless soils. Unlike cohe-sionless soils, the critical edge distance decreases with an increase in the strength of the cohesive soils. Furthermore, the range of the critical edge distance is found to be narrow (1B to 5B) in cohesive soils, compared to cohesionless soil, where it is varying from 2B to more than 12B. Despite the increase in the bearing capacity with the soil strength in cohesive soil, as well as cohe-sionless soils, the BCR increases with the soil strength in cohesive soil and decreases in cohesionless soil. The effect of the strength parameters (f, cu/(yB)) on the BCR and the bearing capacity factor for a footing resting at an edge distance of 1B is presented in Fig. 10. Further discussions are made here to understand the reasons for the observed opposite trends in the case of the critical edge distance and the BCR. The bearing capacity factor (Nyq) in cohesionless soil increases exponentially with the soil strength in cohesionless soils, especially for level ground (Fig. 10 a), while its increase rate is moderate or low for steep slopes. As the BCR represents the normalized bearing capacity with respect to level ground, the BCR decreases with an increase in the soil strength due to a large and sharp increase in the bearing capacity in level ground compared to the slopes (Fig. 10 a). However, in clayey slopes, the bearing capacity factor (Ncq) increases sharply for steep slopes in comparison to gentle slopes (Fig. 10 b). This opposite observation in cohesionless soil and cohesive soil leads to a difference in the observations made in the BCR (Fig. 10 c-d). To further understand the contradictory observations, the failure mechanisms of footings in both types of soil have been studied. The variation in the failure mechanism for cohesive soil and cohesionless soil is presented in Figs. 7 and 11, respectively. The area contributing to the bearing capacity increases with the increase in the internal friction of cohesionless soil and the undrained strength of cohesive soil. The increase in the area within the rupture surface leads to an increase in the bearing-capacity factor. The contribution from the level side of 58. Acta Geotechnica Slovenica, 2019/2 R. P. Shukla and R. S. Jakka: Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes (a) (b) 1 rfr. o40.5 O PQ -»-p=o — P=5 —p=10 -*-p=15 —p=20 P=25 0 0 —I—p=30 3 -P=35 cu/(yB) 9 12 (c) (d) Figure 10. Effect of strength parameters: (a) on the bearing capacity factor in cohesionless soil, (b) on the bearing capacity factor in cohesive soil, (c) on the bearing capacity ratio in cohesionless soil, (d) on the bearing capacity ratio in cohesive soil. (c) (d) Figure 11. Effect of the angle of internal friction on the failure mechanism: (a) 9=25°, (b) 9=30°, (c) 9=35°, (d) 9=40°. the footing reduces sharply in cohesionless soils (Fig. 11 a-d). The reduction in the area of the shear zone on the level side of the footing contributes to a reduction in the BCR with an increase in the angle of the internal friction of the soil. This means that the adverse effect of the slope reduces with an increase in the soil-strength parameter in cohesive soil, unlike in the cohesive soil. In cohesionless soils, the slip surface is a log spiral and extends to longer lateral dimensions and greater depths than the cohesive soil. This contributing area increases significantly with the angle of the shearing resistance of the soil. Therefore, a larger edge distance is required in cohesionless soils. In cohesive soils, the failure surface is circular and only a small area contributes to the bearing capacity. The slip surface extends to a very small area beyond the footing width in cohesive soils. Also, the failure mechanism changes from slope failure to bearing-capacity failure with an increase in the strength for a given edge distance. Therefore, the critical edge distance decreases with an increase in the soil strength in cohesive soils. 59. Acta Geotechnica Slovenica, 2019/2 R. P. Shukla and R. S. Jakka: Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes 6 PREDICTION OF THE BEARING CAPACITY The numerical analysis results were used to carry out a regression analysis and an artificial neural network (ANN). The purpose of using both of the methods is to predict the BCR and the bearing-capacity factor accurately. It is observed from the numerical analyses that a total of four independent variables (i.e., b, p, cJ(yB) and D/B) influences the bearing capacity factor of a footing resting near to the slope crest. The linear multiple regression (LMR) analysis was carried out initially to predict the BCR and Ncq . The regression coefficient (R2) is found to be 0.81 and 0.68 for Ncq and BCR, respectively. This means that LMR is not efficient to model and predict the bearing capacity of a footing on a slope as the relationship between the independent variables and the dependent variable is nonlinear. Therefore, it is necessary to consider the nonlinearity in developing regression equations. To consider the nonlinearity, it is assumed that Ncq and BCR are dependent not only on these four variables, but also upon a number of other variables. These other variables are a function of the initially assumed four independent variations. Considering these derivatives, a nonlinear multiple regression analysis (NMRA) and correlation analysis, along with other statistical tests, were performed to derive an equation to predict the bearing-capacity factor (Ncq) considering the combined effect of the soil cohesion and the surcharge loading above the footing base. Another equation is also developed to determine the change in the bearing capacity (BCR). Various types of functions, such as linear, exponential and polynomial functions, were initially assumed, and finally the best relationship was used to develop the equation. Initially, a total of 24 variables, which are functions of four independent variables, were considered in the regression analysis to develop equations to compute BCR and Ncq. Co-linearity can produce serious problems and ordinary least-squares approximations can be very different from the true values. Therefore, the degree of multi-collinearity was used to remove the insignificant variables. It was found that only eight variables out of 24 affect the Ncq) significantly. Later, these eight variables were used to develop an equation to predict Ncq. It was found that R2 reduces from 0.994 to 0.975, when a number of insignificant variables were removed from the analysis. This reduces the number of variables in the regression equation significantly, without reducing the R2 value by much. It ensures that all the assumed dependent variables are not affecting the bearing capacity significantly with respect to those assumed in the initial phase of the regression analysis. Similarly, 13 derivatives were used in the development of an equation to predict the normalized bearing relative to the level ground (BCR) out of 32 derivatives. It reduces the regression coefficient from 0.992 to 0.953. The ultimate bearing capacity of a footing located adjacent to a slope can be determined precisely by using either Eqn. 4 or Eqn. 5. Therefore, it is suggested to use the BCR values (using Eqn. 2) and Eqn. 4 to determine the effect of the slope geometry on the footing bearing capacity of a footing on a slope. In equations (1) to (5) cu is the undrained cohesion of the soil, Ncq is the bearing-capacity factor, ft is the slope inclination in radians, D is the depth of the footing, B is the width of the footing, y is the unit weight of the soil and b is the edge distance. b b D D D c „ c N = 5.18 - 2.20+ —0(1 - 0.016— + 0.27—) + 3.6—(1 - 0.48--0.280) + — 0(0.4- 0.03—) cq B B B B B yB yB , c D -1.850 (1 -0.180-0.04^-0.14—) (1) YB B BCR = 1 -0.4/+ 0.065/(1 - 0.068) + 0.17b /(1 - 0.15b) - 0.28/(1 - 0.038- 0.2/3- 0.12D) YB yB B B YB B Db -0.072 — /(1 - 0.22—) (2) BB Ncq on slope = N ^ on level ground (BCR) (3) UMm^e bearmg rap^ ^ = N (^ > c (4) Ultimate bearing capacity = (5.16^ +J D)BCR (5) 60. Acta Geotechnica Slovenica, 2019/2 R. P. Shukla and R. S. Jakka: Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes Hansen [40] and Vesic [41] have also developed equations considering the slope inclination and cu/(yB) only. Later, Bowles [42] also developed an equation and the soil strength was considered in the developed equation. Recently, Georgiadis [7] proposed an equation to calculate Nc (slope) based on a rigorous finite element analysis. However, the developed equation is complex and does not consider the effect of the footing depth that is an important factor affecting the bearing capacity. The presented Eqns. 1 and 2, consider the effects of all these factors together in single equation to determine the effect of the slope inclination on the bearing capacity. The slope height was not considered in the presented equation as only the foundation failure was considered in the analysis, not the slope failure (toe and base failure). Initially, the slope height (H/B) was also considered in the analysis, but it was observed that its effect is very nominal with respect to the bearing capacity. However, in marginally stable slopes, the slope height has a significant influence. In a marginally stable slope, the slope failure induced by the footing loading governs the capacity, not the shear failure, which can be clearly seen from Figs. 3(f) and Fig. 7(a). A linear multiple regression analysis was also performed to determine the critical factors affecting the bearing capacity. Based on the P values, the order of significant factors affecting the bearing capacity is also evaluated. The order of the factors is cu/(yB) > Slope inclination > Embedment depth of footing > Edge distance. The relative importance of all these factors was again assessed based on Garson's algorithm [43], and a similar order was obtained in this case also. The relative importance of these variables is presented in Table 3. Acharyya and dey [19] have also provided a similar rating for the c-q> soil slope based on an ANN. This indicates that the bearing (c) U 03 0.9 0.8 0.7 0.6 0.5 0.4 NLMR y = 1.0216J R2 = 0. c - 0.0343 9531 r CPq] < /rs O 0.4 0.5 0.6 0.7 0.8 BCR(evaluated) 0.9 (d) Figure 12. Comparison of the predicted values with the determined values: (a) Ncq(slope) using NLMR analysis, (b) Ncq(slope) using ANN, (c) BCR using NLMR analysis, (d) BCR using ANN. 61. Acta Geotechnica Slovenica, 2019/2 R. P. Shukla and R. S. Jakka: Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes capacity is greatly affected by the soil strength, followed by the steepness of the slope, which is a destabilizing factor, and the embedment depth of the footing and the edge distance have the least influence on the BCR. In contrast to cohesive soils, the influence of the depth ratio is found to be less than the edge distance in cohesionless soils. This is due to the fact that the slip line/fracture surface spread over a larger lateral extent in the cohe-sionless soil than in the cohesive soil, which makes the lateral dimension (edge distance) more important than the vertical dimension (depth of footing). Table 3. Relative importance of all four variables. Factors Rating Relative importance cJ(yB) 1 45.6 % Slope inclination (3) 2 40.5 % Depth ratio (D/B) 3 8.5 % Edge distance (b/B) 4 5.4 % An artificial neural network (ANN) model was also developed to determine the bearing capacity of the footing on the slope using the Levenberg-Marquardt algorithm and MATLAB. The ANN was added to compare the efficiency of the regression analysis with a regression analysis. In the model, 70% of the data (420) was used for training purposes and the remaining 30% of the data (180) was used for testing and validation purposes. Similar to the regression analysis, a total of four independent variables (i.e., b, p, cJ(yB) and D/B) were used as the input, and BCR and Ncq were the output variables. Eight hidden layers were used in the study. Each hidden layer had 10 hidden neurons, which is based on the formula 2(n + 1). Here, 'n is the number of input variables, which is equal to four in the present cases. A comparison of the predicted values with the determined values of Ncq with a nonlinear multiple regression analysis (NLMR) and the ANN is presented in Figs. 12 (a) and 12 (b), respectively. Similarly, a comparison of the predicted values with the determined values of the BCR with the NMRA and ANN is presented in Figs. 12 (c) and 12 (d), respectively. Both methods predict the Ncq and BCR accurately (as R2 is relatively high for both methods); however, the efficiency of the ANN of is found to be relatively higher than the NMRA. This means the ANN modeled the nonlineariarity more accurately than the MMRA. However, the ANN method has many limitations due the black-box approach [44]. NLMR also has an advantage over ANN, as it gives simple equations to predict the bearing capacity factor and BCR, which can be easily used by researchers and engineers. 7 VALIDATION OF THE PROPOSED EQUATION To validate the presented equation, the predicted values are compared with the results of previous studies and are presented in Fig. 13. Fig. 13 (a-b) presents the normalised bearing capacity (q/yB) for various values of cu/(yB) for cohesive soil. These plots show that the bearing-capacity values are close to those determined by Kusakabe et al. [4]. Kusakabe et al. [4] also presented the (q/yB) values determined by other researchers, i.e., Bishop [45], Kotter and Bishop. These values have also been used for comparison purposes. As seen from Fig. 13 (a), the solution obtained with the presently used finite element model is less than the upper-bound solution of Kusakabe et al. [4], Bishop [45] and Kotter's solution. However, the values of the present study are found to be always greater than the lower-bound solution of Kusakabe et al. [4] and Fellenius's solution. Fig. 13 (b) shows that the bearing capacity factor values predicted from the NLMR analysis are close to those determined in the numerical analysis and the previ- 90 75 60 Ä 45 30 15 0 • Upper bound (Ï T4Ï) Cusakabe et al. - Presenl study - A- Upper bound (] M~l\ jf et al. ** Bishop a - - " 1*, j j ^ 2 3 c„/(yB) (a) Meyerh Leshchinsky < Bowles [42] -Wang [46] -NLMR ANN 20 40 ß° (b) 60 80 100 Figure 13. Comparison of the predicted values with previous studies: (a) Effect of cu/(yB), (b) Effect of slope inclination. 62. Acta Geotechnica Slovenica, 2019/2 R. P. Shukla and R. S. Jakka: Determination and prediction of the ultimate bearing capacity of a strip footing on undrained clayey slopes ously determined values of Meyerhof [1], Bowles [42] and the experimental study of Wang [46]. The values of the predicted bearing capacity factor are close to the experimental study result of Wang [46] for a small slope inclination. However, the predicted values are slightly higher than the experimentally determined values of Wang [46] and lower than the values of Bowles [42]. The predicted bearing capacity factors are found to be close to the values proposed by Meyerhof [1]. However, for steep slopes (3 > 40°), the values are lower than the Meyerhof [1] values. This similar observation was made in previous studies of a cohesionless soil slope [47-48]. The values predicted from the ANN are less than the earlier studies, except for the experimentally determined values of Wang et al. [40]. Similar to the present study, a number of other studies also found that small-scale model testing generally underestimates the bearing capacity of a footing on a slope [49]. 8 CONCLUSION_ The presence of a slope, close to a footing, influences the bearing capacity of the footing. The severity of the slope effect depends on the footing location, the soil strength and the slope geometry. However, the slope effects are found to be independent of the soil strength in the case of a stable slope (in the case of bearing-capacity failure). The bearing capacity is a minimum when the footing is resting exactly on the slope crest and it increases with the increase in the edge distance. The critical edge distance varies from 1B to 5B, depending on various factors. In contrast to the present finding, currently codes suggest the critical setback distance mainly based only on the slope inclination and the slope height. The range of critical setbacks in cohesive soils is significantly less than in cohesionless soils. The increase in the bearing capacity with the edge distance is relatively large and non-linear in the case of the steep slopes and footings of the higher depth of the embedment. The critical value of the edge distance is identified in the present study and it is found to increase with an increase in the slope inclination and the embedment depth of the footing. In gentle slopes, shear failure governs the footing capacity. Two failure mechanisms, i.e., slope failure and bearing-capacity failure, can co-exist in steep slopes. In a few cases, the slope fails due to the stress generated from the footing loading itself. The influence of the strength parameter on the BCR and the critical edge distance is different in cohesive soils, compared to cohesionless soils. The BCR decreases with an increase in the strength of a cohesionless soil, whereas it increases with an increase in the undrained strength in cohesive soils. In contrast to cohesionless soils, the critical edge distance is found to decrease with an increase in the undrained strength of the cohesive soil. This contradictory behavior is ascribed to the differences in the failure mechanisms of the cohesive and noncohesive soils. The range of the critical edge distance is found to vary from 1B to 5B in cohesive soil. Both the ANN and NLMR analyses were used to predict the BCR and Ncq (slope). The developed nonlinear regression equations are found to be efficient in predicting the bearing capacity factor on the slope and the BCR accurately. However, the ANN is found to be relatively more efficient at predicting the BCR and the Ncq (slope) values, compared to the NLMR analysis. Acknowledgment Authors are thankful to the anonymous reviewers for their valuable suggestions. Authors are also grateful to the Optum Computational Engineering for providing the OptumG2 program free of cost and their constant support throughout the study. REFERENCES_ [1] Meyerhof, G.G. 1957. The ultimate bearing capacity of foundation on slopes, 4th Int. Conf. on Soil Mech. and Foundation Eng. 3, 384-386. 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Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay RESEARCH ON A NUMERICAL MODEL OF REAL MESO-STRUCTURES IN THE NON-SHEAR ZONE OF CLAY RAZISKAVA NUMERICNEGA MODELA REALNIH MEZO-STRUKTUR V NE-STRIŽNEM DELU GLINE Wei Wang (corresponding author) Binghua Zhao Nanjing Institute of Technology, Nanjing Institute of Technology, Institute of Civil Engineering and Architecture Institute of Civil Engineering and Architecture 211167, Nanjing, China 211167, Nanjing, China E-mail: ww1177114@163.com Liwu Yu Deheng Zhang Nanjing Institute of Technology, Nanjing Institute of Technology, Institute of Civil Engineering and Architecture Institute of Civil Engineering and Architecture 211167, Nanjing, China 211167, Nanjing, China https://doi.Org/10.18690/actageotechslov.16.2.66-76.2019 DOI Keywords clay; mesoscopic model; numerical analysis; real mesostructures Ključne besede glina; mezoskopski model; numerična analiza; realne mezostrukture Abstract The conventional numerical simulations of rock and soil are mainly concerned with the macroscopic continuous model or the pseudo-microscopic model established using the discrete-element method (DEM). However, these adopted models are not completely consistent with actual soil samples. To explore the evolution law of the internal stresses of soil samples from the mesoscopic perspective, we proposed an image-finite-element method for studying the deflection angles and the shear stresses at four points in the non-shear zone of clay with real mesostructures. The approach allowed for a realistic distribution of the pore structures and avoided any virtualization, thereby significantly improving the veracity of the mesoscopic model. It worked by using a microscopic lens and a charge-coupled device (CCD) to capture the two-dimensional (2D) meso image in the non-shear zone, and then convert this digital image into a vector image recognized by the finite-element software (ABAQUS) through image-processing techniques, and import it into a numerical model, and then carry out a numerical calculation. For the purposes of performing a Izvleček Konvencionalna numerična simulacija kamnin in zemljin se v glavnem ukvarja z makroskopskim kontinuiranim modelom ali psevdo-mikroskopskim modelom, določenim z metodo diskretnih elementov (DEM). Ti modeli niso popolnoma skladni z dejanskimi vzorci zemljin. Za raziskavo pravila napredovanja notranjih napetosti vzorcev zemljin iz mezoskopske perspektive, predlagamo slikovno metodo končnih elementov za proučevanje odklonskih kotov in strižnih napetosti na štirih mestih v ne-strižnem delu gline z realnimi mezostruktu-rami. Takšen pristop omogoča realistično porazdelitev struktur por in preprečuje virtualizacijo, kar bistveno izboljša verodostojnost mezoskopskega modela. Deluje z uporabo mikroskopskih leč in senzorjem CCD za zajemanje dvodimenzionalne (2D) mezo-slike v ne-strižnem območju in nato pretvorbo te digitalne slike v vektorsko sliko. S tehnikami obdelave slik jo prepozna programska oprema s končnimi elementi (ABAQUS), uvozimo jo v numerični model, nato pa izvedemo numerični izračun. Za izvedbo korelacijske analize je bil na istem vzorcu 66. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay correlation analysis, the unconfined-compression (UC) test was also carried out on the same specimen. The numerical results show that there is no shear failure in the meso numerical model, which is consistent with the UC test results for the same region. And, the quantitative analysis results show that: (1) under load, the yield zones in the meso numerical model are obviously located around the pores; (2) the evolution laws of the deflection angles and the meso shear stresses at four points are different in the compression process; and (3) the pore structures play a significant role in the evolution of the deflection angles and meso shear stresses, especially around the larger and denser pores. opravljen tudi enoosni preizkus (UC). Numerični rezultati kažejo, da v mezo-numeričnem modelu ni strižne porušitve, kar je skladno z rezultati enoosnega preizkusa v istem območju. Rezultati kvantitativne analize kažejo: (1) da so pod obremenitvijo plastična območja v mezo--numeričnem modelu očitno locirana okoli por; (2) da se pravila napredovanja odklonskih kotov in mezo-strižnih napetosti v štirih točkah v procesu stiskanja razlikujejo; in (3) da imajo strukture por pomembno vlogo pri povečanju odklonskih kotov in mezo-strižnih napetosti, zlasti okoli večjih por in gosteje razporejenih por. 1 INTRODUCTION Understanding the connection between internal stresses from the mesoscopic perspective and the shear failure mechanism of soil is a fundamental challenge in geomechanics research. Works on the theory, testing and numerical simulations of soil from microscopic and macroscopic perspectives have led to many great achievements. For example, in theory, Boria et al. investigated the effect of the spatially varying degree of saturation on triggering a shear band in granular materials and presented variational formulations for the porous solids whose voids were filled with liquid and gas [1]. Lu and Yang pointed out that the development of shear bands was affected by the coupling strain rate and pore pressure of a material using the momentum equations of water and grains by the mixture theory [2]. Gutierrez introduced a simple elastoplastic constitutive model that adequately captured the monotonic response of granular soils under biaxial loading conditions and developed a strain-localization criterion expressed in terms of constitutive parameters [3]. As a matter of fact, these theoretical studies take into account the effects of the physical properties of the particles and macroscopic parameters on the shear failure of soil samples [4], but do not involve the influence of internal stresses from the meso-scopic perspective. In tests, developments in meso experimental techniques, like scanning electron microscopy (SEM), computer tomography (CT), ultrasonic or digital camera, etc., made the real microscopic features of soil samples more deeply understood. Most importantly, these techniques enable the precise detection of the particles' (or aggregate particles') morphology, providing a detailed position of the local pores. The observations, made by Shan et al, indicate that the soil particles were rearranged in an orientation parallel to the direction of the maximum principal stress and the maximum shear stress [5]. Bo et al. demonstrated how to determine the mineralogical properties of ultra-soft soils using X-ray diffraction and scanning electron microscope techniques [6]. Zhang et al. calculated the volume porosity of the whole specimen by analyzing the tomography images with an error of only 3.93% compared with the experimental porosity [7]. However, compared with the digital camera method, the complexity of the soil samples' preparation and the high cost of the test equipment mentioned above limit their application. For this reason, a digital camera or a microscope lens were another choice for revealing the mesostructures of geomaterials [8-10]. Yue Z Q et al. carried out quantitative investigations of the orientations, distributions and shapes of aggregates about asphalt concrete using a conventional digital camera [11]. Ghalehjough et al. showed that the shear failure mechanism of the soil changed from general towards punching shear failure with increasing particle roundness by analysing the photographs taken from a high-resolution digital camera [12]. Shao et al. developed a series of geotechnical test instruments based on a digital image measurement system [13]. Amy et al. found that the shear band thickness ranged between 6 and 9.5 times D50 and pointed out that the grain shape, angularity, and size distribution can also affect the shear band thickness using the digital image correlation (DIC) method [14]. Although the aforementioned image methods have successfully obtained the mesostructures of soil and investigated its influence on the macroscopic properties, these results only focus on the particle characteristics of the soil and do not take into account the influence of the internal pore characteristics, nor do they involve the internal stresses from the mesoscopic perspective. In numerical simulations, some researchers have simulated the effect of mesoscopic characteristics on the macro performance by setting a "weak" element in the finite-element software. For instance, Jiang et al. performed a series of biaxial-compression-test simulations by increasing the void ratio of element No.105 on methane hydrate-bearing sediment samples to simulate 67. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay the influence of the nonuniform density (mesostructures) and showed that the bifurcation of the stress and volumetric response of the elements within the shear band is more obvious during the tests [15]. Certainly, the most typical method for simulating the microscopic model of soil is DEM, which helps to study the deformation behaviour of the particle system. Bayesteh et al. developed a 2D DEM computer program to simulate the mechanism that controlled the behaviour of a granular assembly after local and random particle loss [16]. Nicot et al. discussed the dependency of the mechanical response to the imposed volumetric strain by presenting the numerical simulation with a discrete element model and micromechanical approaches [17]. Li et al. showed that it was possible to capture, using DEM, the essential features of the mechanical behaviour of granular materials under a complex stress state [18]. However, the DEM method mainly simulates granular materials, such as sand, soil-rock mixtures, and concrete, and assumes that the soil particles are rigid spheres adopted in the numerical model, which is not in accordance with the mechanical properties of actual geomaterials. In short, the mesoscopic mechanism of the soil samples' macroscopic properties, especially the evolution laws of the internal real meso structure and its meso stress, need to be further studied. To address the issue, this paper introduced an image-finite-element method (IFEM) on the basis of previous achievements [19]. It incorporated a real meso image and a finite-element model, respectively, for investigating the evolution of the deflection angles and the internal stresses from a mesoscopic perspective on the unconfined compression simulation test. Due to the large magnification of the microscopic imaging system, the acquisition field of view is small and it is difficult to locate exactly the position of the initiation of the shear band. Therefore, the evolution of the internal stresses from the mesoscopic perspective in the non-shear zone was studied in this paper. As for the evolution of the internal stresses in the shear zone, it needs to be studied after the equipment is improved in the next step. Figure 1. Equipment combining microscopic lens and UC test. 2.1 Clay sample preparation The materials used in the test were clay, which was quarried from a construction site around the Nanjing Institute of Technology. Its plastic limit and liquid limit values were 18.36 and 39.14, respectively. The traditional cylindrical clay sample was divided into two parts from the symmetrical surface and the semi-cylindrical shape was taken as the test object (see Figure 2). The semi-cylindrical clay sample was placed on the pedestal of the UC test, and the symmetrical plane was thrown directly at the microscopic lens. Figure 2. Schematic diagram of a clay sample divided into two parts. 2 UNCONFINED-COMPRESSION SIMULATION TEST Because the unconfined-compression (UC) test is by far the most popular technique for soil shear testing, this paper uses the UC test and the mesoscopic image-acquisition system to form a set of soil samples for the macro and micro test equipment (see Figure 1), which cannot only obtain the clay meso image conveniently, but also carry out the macroscopic compression test at the same time. In this way, the numerical results and the experimental results can be compared and analyzed. 2.2 Mesoscopic image acquisition Since the surface of the cylindrical clay sample is curved, it is not convenient to collect images using the mesoscopic acquisition system with a microscopic lens and a CCD. According to the axisymmetric principle, the symmetrical surface of a semi-cylindrical clay sample was selected as the observation surface. This not only ensures that the observed area is plane, but also can collect the mesoscopic characteristics of the clay. So, the tests were carried out on the air-dried clay samples (not considering 68. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay Original meso-image Figure 3. The original meso-image acquistion diagram. the influence of pore water) with a 39.1-mm diameter and an 80-mm height. Then, the original images (768x576 pixels) with real mesoscopic features before loading were obtained using the mesoscopic acquisition system. Figure 3 shows a schematic diagram of the image collected by the mesoscopic acquisition system (the image has a physical resolution of 0.0014 mm). 2.3 Image processing The original meso image contains the true distribution characteristics of the clay particle aggregates and pores, which is the basis for establishing the meso numerical model. In order to embody the mesoscopic information in the numerical model, it is also necessary to pre-process the meso image, including denoising and binarization. The image data can be affected by the noises from the device elements and the surrounding lights. Since the adaptive median filter algorithm can preserve the edges in an image, it was chosen for the de-noise operation in this paper. For studying the effects of internal stresses and pores, it is necessary to distinguish the particle aggregates from the pores, so the particle aggregates and pores were expressed in black and white using Otsu's binarization method, respectively. In fact, Otsu's method is an image binarization technique, which cannot only avoid the interference of artificial factors, but also automatically calculates the maximum threshold of intra-class variances. In this way, the real boundaries of the clay particle aggregates and pores were fully identified. The threshold of the meso image was obtained using the formula (1). Q(k) = (Ave x W (k) - Aver(k))2 W (k) x (1 - W (k)) (1) respectively, the mean of the grey-level class and the sum of the grey-class histograms, which can be calculated via the equations k k Aver(k) = £(z + 1)Phs(i) and W(k) = £Phs( ; i=0 i=1 Phs(i) is the probability function of the grey level; i is the grey level, and 0 < i < 255. When the Q(k) value is the largest, the optimal threshold (T) is found. That is T=k-1. Obviously, the threshold values of the meso images are entirely different. In this study, the meso image threshold was 0.1775. So, the meso image can be processed using Otsu's method after the median filtering and the binary resultant image was obtained successfully (see Figure 4). where Q(k) is the separation index of the grey class; Ave is the average of the grey-value; Aver and W(k) are, Figure 4. Binary resultant image. 2.4 Establishing the numerical model Because the meso image is a digital image and cannot be identified by the finite-element software, it is necessary to vectorize the digital image. With the help of vector 69. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay software CorelDRAW, the digital image can be converted into a vector graph, and the numerical model containing the pore meso features can be established by importing the finite-element software (ABAQUS). In this way, the 2D numerical model with the clay real mesostructures was established successfully. Figure 5(a) shows the numerical model and Figure 5(b) gives the mesh result using the triangular element. I i i i—i—i—r Uniformly distributed loading Free boundary (a) 1mm (b) Figure 5. (a) Numerical model; (b) mesh resultant. 3 NUMERICAL ANALYSES AND RESULTS 3.1 Determination of the model parameters and the boundary conditions In this paper, the internal stresses evolution of the air-dried clay under uniaxial compression considering the effect of pore meso characteristics is discussed. Therefore, it was assumed that the clay sample was in accordance with the Mohr-Coulomb model. The model is easy for obtaining the parameters of the material required by the finite-element software (ABAQUS) using the triaxial drained test: cohesion (c) and friction angle (f, no dilatancy here), which is, respectively, adopted as 50 KPa and 28.51°. According to the UC test conditions, the boundary conditions of the numerical model were set up, as shown in Figure 5(a). Then, the compression process of the clay sample can be simulated by applying the same load as the UC test. 3.2 Simulation results Based on the numerical results of the Mohr-Coulomb model, the partial regions (the red parts shown in Figure 6) present the shear yield. This is due to the fact that the shear stress in this part of the region exceeds the shear yield stress, while the others are still in an elastic state, such as the blue region shown in Figure 6. It can be seen that there is only a local yield and no through shear band in the observed region collected by the mesoscopic acquisition system, which qualitatively indicates that the numerical simulation results of the region are consistent with those of the UC test in the same region. In addition, it can be seen from Figure 6 that the yield regions are mostly like an "X" shape and mainly distributed near larger pores. AC YIELD (Avg: 75%) r +1.000e+00 +Q 1fi7e-m tS, 1 Of B~U 1 - +8.333e-01 - +7.500e-01 - +6.667e-01 - +5.833e-01 - +5.000e-01 - +4.167e-01 - +3.333e-01 - +2.500e-01 - +1.667e-01 +8.333e-02 +0.000e+00 Figure 6. Profile of shear yield area. 70. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay In order to study the evolution of the internal stresses from the mesoscopic perspective, four typical points were selected, as shown in Figure 6. The first point is marked No. 4679 element in the blue region of a large pore boundary. The second point is labelled No. 845 element in a band of the red region between the two pores. The third point is located in the blue area away from the pores and labelled as the No.14473 element. The last one labelled No.11363 element is in the red region near a pore. Here are the quantitative results of the four points of the minor principle stress (a3), the major principle stress (oi), the shear stress (r), the normal stress (a), the shear strength (if), and the deflection angle (0). By using the image-finite-element method, the minor principle stress, the major principle stress and the shear stress of the whole field in the observed area can be directly obtained. Tables 1 and 2 show the results at only four points. It can be seen from the data in the table that the stress values at each point are not only different but also positive and negative. It is shown that the stress states of each point are different from the mesoscopic perspective, which should be the result of the influence of the pore structures. Although it is also in the blue region, the major principle stress at point No. 4679 near the pore is about 2-2.5 times the value of the major principle stress at the No. 14473 point, far away from the pore. Similarly, even in the red region, the point No. Table 1. Quantitative results of two points located in the red region. Time (s) NO. 845 element NO. 11363 element ff3 (KPa) a1 (KPa) r (KPa) a (KPa) rf (KPa) e a3 (KPa) a1 (KPa) r (KPa) a (KPa) rf (KPa) e 0.010 -0.47 -15.75 4.84 14.02 57.44 19.67 1.12 -6.11 1.34 5.72 53.04 16.31 0.020 -0.94 -31.41 9.69 27.92 64.82 19.77 2.26 -12.23 2.69 11.44 56.07 16.36 0.035 -1.60 -54.72 17.00 48.57 75.78 19.91 3.98 -21.42 4.73 20.03 60.63 16.44 0.058 -2.51 -89.27 28.01 79.02 91.94 20.12 6.61 -35.25 7.82 32.93 67.48 16.57 0.091 -4.13 -140.19 43.87 124.16 115.91 20.09 10.70 -56.13 12.56 52.34 77.78 16.80 0.104 -4.82 -159.22 49.74 141.06 124.88 20.07 12.35 -64.04 14.40 59.65 81.66 16.94 0.105 -4.81 -160.98 50.31 142.61 125.70 20.07 12.52 -64.79 14.57 60.35 82.03 16.95 0.105 -4.81 -161.02 50.32 142.64 125.72 20.07 12.52 -64.81 14.58 60.36 82.04 16.95 0.105 -4.81 -161.08 50.34 142.69 125.75 20.07 12.53 -64.83 14.58 60.39 82.06 16.95 0.105 -4.80 -161.17 50.37 142.77 125.79 20.07 12.54 -64.87 14.59 60.43 82.08 16.96 0.105 -0.57 -169.69 55.89 148.58 128.87 20.70 12.58 -64.94 14.62 60.48 82.10 16.99 0.105 -0.58 -169.73 55.91 148.60 128.88 20.70 12.60 -65.03 14.64 60.56 82.15 16.99 0.106 -0.60 -169.79 55.95 148.64 128.90 20.71 12.63 -65.16 14.67 60.68 82.21 16.99 0.106 -0.63 -169.88 56.00 148.69 128.93 20.73 12.67 -65.36 14.72 60.87 82.31 16.99 0.106 -0.68 -170.01 56.09 148.77 128.97 20.75 12.74 -65.66 14.79 61.14 82.46 17.00 0.107 -0.76 -170.22 56.21 148.89 129.04 20.79 12.84 -66.11 14.89 61.56 82.68 17.00 0.108 -0.86 -170.52 56.38 149.07 129.13 20.84 12.99 -66.79 15.04 62.19 83.01 17.01 0.110 -1.01 -170.95 56.63 149.32 129.26 20.91 13.21 -67.81 15.28 63.13 83.51 17.02 0.112 -1.23 -171.57 57.00 149.69 129.46 21.01 13.56 -69.34 15.63 64.55 84.26 17.05 0.116 -1.55 -172.48 57.52 150.22 129.74 21.16 14.07 -71.63 16.16 66.67 85.39 17.09 0.121 -0.86 -170.52 58.56 147.06 128.06 21.84 14.87 -75.09 16.97 69.85 87.08 17.16 0.129 -0.31 -168.96 58.83 145.05 126.99 22.13 16.08 -80.29 18.21 74.63 89.61 c 0.142 -0.20 -168.65 59.52 144.01 126.44 22.50 17.97 -88.15 20.09 81.83 93.44 17.47 0.160 -0.51 -169.53 60.57 143.95 126.41 22.90 21.12 -100.40 23.03 93.03 99.38 17.77 0.164 -0.66 -169.94 60.79 144.20 126.54 22.96 22.54 -104.11 24.05 96.26 101.10 18.08 0.169 -0.78 -170.28 60.98 144.38 126.64 23.02 22.16 -105.47 24.46 97.53 101.77 17.99 0.176 -0.65 -169.92 60.11 144.86 126.90 22.64 23.57 -101.51 27.15 90.50 98.04 22.09 71. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay Table 2. Quantitative results of two points located in the blue region. Time (s) NO. 4679 element NO. 14473 element ff3 (KPa) (KPa) T (KPa) a (KPa) Tf (KPa) 9 a3 (KPa) a1 (KPa) T (KPa) a (KPa) Tf (KPa) 9 0.010 -16.82 -13.59 3.94 12.10 56.42 20.72 -0.03 -5.46 0.18 5.45 52.89 1.87 0.020 -33.89 -27.20 7.94 24.17 62.83 20.92 -0.07 -10.91 0.36 10.90 55.79 1.91 0.035 -60.05 -47.67 14.05 42.22 72.41 21.21 -0.12 -19.10 0.65 19.08 60.13 1.97 0.058 -100.57 -78.48 23.46 69.17 86.72 21.66 -0.19 -31.39 1.12 31.35 66.64 2.06 0.091 -157.27 -121.25 37.54 105.55 106.03 22.69 -0.30 -49.90 1.90 49.82 76.45 2.20 0.104 -171.82 -133.87 42.52 115.48 111.30 23.40 -0.32 -56.88 2.22 56.80 80.15 2.25 0.105 -173.01 -135.16 43.11 116.40 111.79 23.52 -0.33 -57.55 2.25 57.46 80.50 2.25 0.105 -173.04 -135.19 43.13 116.43 111.80 23.53 -0.33 -57.56 2.25 57.47 80.51 2.25 0.105 -173.08 -135.24 43.15 116.46 111.82 23.53 -0.33 -57.58 2.25 57.50 80.52 2.25 0.105 -173.14 -135.31 43.18 116.51 111.84 23.54 -0.33 -57.62 2.25 57.53 80.54 2.25 0.105 -172.02 -135.73 43.58 116.62 111.91 23.68 -0.31 -57.67 2.28 57.58 80.56 2.28 0.105 -172.15 -135.87 43.65 116.73 111.96 23.70 -0.31 -57.75 2.28 57.65 80.60 2.28 0.106 -172.33 -136.10 43.76 116.88 112.04 23.72 -0.31 -57.86 2.29 57.77 80.67 2.28 0.106 -172.61 -136.44 43.92 117.12 112.17 23.76 -0.31 -58.04 2.29 57.95 80.76 2.28 0.106 -173.03 -136.94 44.17 117.47 112.35 23.81 -0.31 -58.30 2.31 58.21 80.90 2.28 0.107 -173.64 -137.70 44.54 117.99 112.63 23.88 -0.31 -58.69 2.33 58.60 81.11 2.29 0.108 -174.56 -138.84 45.09 118.78 113.05 24.00 -0.31 -59.29 2.35 59.19 81.42 2.29 0.110 -175.91 -140.54 45.91 119.94 113.67 24.17 -0.31 -60.18 2.40 60.09 81.90 2.30 0.112 -177.86 -143.06 47.15 121.66 114.58 24.43 -0.32 -61.53 2.46 61.43 82.61 2.30 0.116 -181.47 -146.74 48.75 124.38 116.02 24.66 -0.32 -63.55 2.55 63.45 83.68 2.31 0.121 -188.86 -151.37 50.43 128.08 117.99 24.80 -0.32 -66.60 2.69 66.49 85.29 2.33 0.129 -197.46 -158.94 53.50 133.86 121.06 25.13 -0.33 -71.17 2.91 71.05 87.72 2.36 0.142 -209.74 -169.86 58.06 142.01 125.38 25.64 -0.31 -78.11 3.27 77.97 91.39 2.41 0.160 -227.86 -185.52 64.78 153.39 131.42 26.40 -0.25 -88.83 3.84 88.66 97.06 2.49 0.164 -232.24 -190.16 67.05 156.40 133.02 26.74 -0.20 -91.58 4.00 91.40 98.52 2.51 0.169 -237.63 -194.77 69.31 159.33 134.58 27.09 -0.11 -94.39 4.19 94.20 100.00 2.55 0.176 -245.24 -200.93 72.57 162.86 136.45 27.69 0.22 -98.73 4.56 98.52 102.30 2.65 845 is significantly larger than the major principle stress at point No. 11363 because it is in a structure similar to a'slender column". Then, using the following equation (2), which is transformed from the formula r = ai2"3 sin 2 9, the deflection angle 9 at four points can be solved at every loading state. 1 -Jt (2) „1 . 2t 8 = - arcsin- 2 "i-<>3 Figure 7 (a), (b), (c) and (d) are the evolution curves of the deflection angles inclined in the direction of the major principal plane, respectively. As shown in Figure 7, we can learn that, in both the red and blue regions, the deflection angles of the four points increase with the increasing load. Obviously, when the load is increased from 0 to 50% loads, although the initial deflection angle of each point is different, the evolution curve is an increasing trend, but the slope is different. This suggests that the equilibrium of the internal and external forces of the clay sample at this stage is realized by the clay particles' deflection. This is an interesting phenomenon. The deflection angle at point No. 845 is almost unchanged between 25% and 50% of the load, which may be a sign that the "slender column" reached a critical equilibrium. But, as the load continues to increase, the deflection angle at point No. 845 suddenly jumps significantly, and then increases rapidly until the maximum load. A small jump occurs at the point No. 4679 near the pore at 50% loads, like the point No. 845, 72. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay 23.50 23.00 „ 22.50 ■5, 22.00 c CU c 21.50 o jy 21.00 M- 10.00 ju Tu □ 5.00 (a) NO. 845 element 0.05 0.10 Time (s) (b) NO. 11363 element 30.00 25.00 20.00 u> c 10 c 15.00 0 u 1 10.00 a 5.00 0.00 0.10 Time (s) (c) NO. 4679 element 3.00 2.50 ^ 2.00 BO c nj c 1.50 o t> v = 1.00 a 0.50 0.00 0.10 Time (s) (d) NO. 14473 element Figure 7. Evolution curves of deflection angle. but not at the other two points. It can be seen that the mesoscopic pore characteristics will affect the movement of the clay particles. The curve slope of the point No. 845 after 50% loads is obviously higher than that of the other points, and the deflection angle is shifted from 20 degrees to 23 degrees. This indicates that there is a lack of effective constraints on the "slender column" in the area, which makes the clay particles deflect easily, thus exacerbating the growth of the major principal stress and the meso shear stress and making the region enter the plastic zone very quickly. Moreover, until near the maximum load, the deflection angle at the point No.11363 suddenly increased by 4 degrees, indicating that there might be a large dislocation at this point to cause small cracks. This might be due to the continued expansion of the local band plastic zone in which the point No. 11363 is located, as can be seen from Figure 6. In addition, the change in trend of the deflection angles at the two points No.4679 and No. 14473 in the blue region is relatively gentle, and the amplitude is not large. It can be seen that the blue part of the observed region is the main force-bearing body, which is called the main carrier, while the red part is the secondary carrier. From the above analysis, it can be concluded that the secondary carrier first enters the plastic zone under the action of the load, and gradually affects the main carrier through the adjustment until a new secondary carrier is formed. The main reason is that there are a number of weak structures in the clay sample, which are formed by the existence of pores. Further, the normal stresses at the four points, given in Tables 1 and 2, were calculated using the following equation (3). o-l+QI Pi-a3___t n On —2----2— (3) Next, according to the Mohr-Coulomb yield theory, the shear strength at the four points can be drawn easily using the formula Tf = c+an tan^. Figure 8 (a), (b), (c) and (d) show the curves of the meso shear stresses and the meso shear strengths at the four points with the increasing of loads, respectively. Figure 8 also describes the relationship between the meso shear stress and the meso shear strength at the same point. It can be seen from Figure 8 that the meso shear strength is obviously greater than that of the meso shear stress, indicating that the clay particle aggregates in the observed area are still able to withstand external loads. From Figure 8 (a) it can 73. Acta Geotechnica Slovenica, 2019/2 W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay Time (s) (a) NO. 845 element Time (s) (b) NO. 11363 element Time (s) (c) NO. 4679 element Time (s) (d) NO. 14473 element Figure 8. Profiles of meso shear stress and meso shear stress with load. 74. Acta Geotechnica Slovenica, 2019/2 be seen that the variation curve of the meso shear stress and the meso shear strength at the point No.845 after 50% loads tends to be horizontal, which indicates that the stress state of the point No. 845 is no longer changing. Because there are pores on both sides of the site, the secondary carrier cannot affect the main carrier, and can only be connected with the main carrier through both ends. Therefore, after a certain degree of stress, the middle part cannot continue to bear a larger load. Figure 8 (b) shows that the meso shear strength at the point No.11363 begins to decrease near the maximum load, while the meso shear stress still keeps increasing. It can be seen that the dislocation of the clay particles can lead to the initiation of tiny cracks, but it does not cause damage. This is consistent with the previous conclusion. The curve slope of meso shear stress and meso shear strength at the point No.4679 is almost the same, shown in Figure 8 (c), and the final meso shear stress value is similar to that of the point No.845, which is related to the compactness degree of the clay particles weakened by its unilateral pores. A significant difference from the other points is that the meso shear stress at the point No.14473 is very slow to reach about 5 KPa (see Figure 8 (d)), which is slightly smaller than the shear strength 12 KPa of the clay sample obtained by the UC test. This indicates that the clay particle aggregates far away from pores are the main carrier, and the meso shear stress and the shear strength of the clay samples are basically in the order of magnitude. But the internal cause of shear failure of the clay samples is the evolution of secondary carriers. In short, some of the secondary carriers undergo adjustment, yielding to cracking until multiple subcarriers are connected to a single through shear band and destroyed. In fact, the meso numerical model is capable of withstanding loads, and mainly depends on the stress network intertwined by main carriers and secondary carriers. The evolution of the stress and strength in shear band should be further studied by improving the testing equipment and material parameters. 4 CONCLUSIONS In this paper, a two-dimensional numerical analysis method for clay is proposed, which reflects the real mesoscopic characteristics, and it can also be extended to other materials. The method is to convert the digital image containing meso features information into a numerical model for the calculation and analysis. With the powerful post-processing function of the finite-element software (ABAQUS), not only can the yield position in the observed area be obtained, but also the principal stress and meso shear stress of the whole field can be easily obtained. W. Wang et al.: Research on a numerical model of real mesostructures in the non-shear zone of clay The evolution laws of deflection angles and meso shear stresses at four points are different in the compression process. The change of deflection angle for each point is to adapt to the external loads, they all increase with the increasing of loads, but the change range near the pores is larger, and the plastic zone is prone to dislocations appearing. Moreover, the variation of the meso shear stress and the meso shear strength at each point is also affected by the internal pore characteristics. The weak structure formed by the pores is prone to the plastic zone, which leads to the evolution of secondary carriers. Obviously, the pore structures play a significant role in the evolution of the deflection angles and the meso shear stresses, especially around the larger and denser pores. Clay samples depend on a stable backbone of the stress network with main and secondary carriers before failure. Once multiple secondary carriers form a through shear band, the clay samples will be destroyed. The evolution of meso stress and the influence of pore characteristics in the shear band need further study. REFERENCES [1] Borja, R.I., Song, X.Y., Wu, W. 2013. Critical state plasticity. Part VII: Triggering a shear band in variably saturated porous media. Compu. Meth. Appl. Mech. Eng. 261-262, 66-82. DOI: 10.1016/j. cma.2013.03.008 [2] Lu, X. B., Yang, Z.S. 1999. Development of the shear band in saturated soil. Journal of Shanghai University 3, 199. D0I:10.1007/s11741-999-0058-8 [3] Gutierrez, M.S. 2007. Effects of constitutive parameters on shear band formation in granular soils. 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DOI: 10.1007/s 11204-014-9248-x 76. Acta Geotechnica Slovenica, 2019/2 M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests SOIL BASED DESIGN OF HIGHWAY GUARDRAIL POST DEPTHS USING PENDULUM IMPACT TESTS ZASNOVA GLOBINE STEBRA AVTOCESTNE OGRAJE GLEDE NA LASTNOSTI TAL Z UPORABO UDARNIH PREIZKUSOV Z NIHALOM Murat Örnek (corresponding author) Iskenderun Technical University, Faculty of Engineering and Natural Sciences, Civil Engineering Department 31200, Iskenderun, Hatay, Turkey E-mail: murat.ornek@iste.edu.tr Ali Osman Atahan Istanbul Technical University, Civil Engineering Faculty, Civil Engineering Department 34469, Istanbul, Turkey E-mail: atahana@itu.edu.tr Yakup Türedi Iskenderun Technical University, Faculty of Engineering and Natural Sciences, Civil Engineering Department 31200, Iskenderun, Hatay, Turkey E-mail: yakup.turedi@iste.edu.tr M. Musab Erdem Murat Buyuk Iskenderun Technical University, Sabanci University, Faculty of Engineering and Natural Sciences, Integrated Manufacturing Technologies R&A Center Civil Engineering Department 34956, Istanbul, Turkey 31200, Iskenderun, Hatay, Turkey E-mail: muratbuyuk@sabanciuniv.edu E-mail: musab.erdem@iste.edu.tr https://doi.Org/10.18690/actageotechslov.16.2.77-89.2019 DOI Keywords guardrail; post; post embedment depth; soil properties; post-soil interaction; pendulum test Abstract Guardrails are passive road restraint systems (RRS) used at roadsides and medians to improve road safety. In the case of inadequate post embedment depth of soil driven posts may not function as intended and design cannot provide adequate safety nor security for the impacting vehicles. In general, the height of the steel guardrails varies between 1600 and 2400mm. However, the characteristics of the soil where the guardrails are driven are not taken into consideration. In other words, a constant depth of guardrail is used regardless of the type of soil. Post embedment depths (PED) in steel guardrail systems are currently determined based on strong soil properties. The crash performance of these designs may not be appropriate for locations where soil conditions are weaker than tested conditions. In this study, a series of field impact tests were performed on soil embedded posts to determine optimum PED for Ključne besede ograja; steber; globina vpetja; lastnosti tal; interakcija steber-tla; preizkus z nihalom Izvleček Varovalne ograje so pasivni cestni zadrževalni sistemi (RRS), ki se uporabljajo ob robovih in na sredini cest za izboljšanje varnosti v cestnem prometu. V primeru nezadostne globine vpetja stebrov, vtisnjenih v zemljino, se lahko zgodi, da ne delujejo kot je predvideno, zato konstrukcija ne more zagotoviti zadostne varnosti ali varnosti za vozila, ki udarijo v njo. Na splošno je višina jeklene varnostne ograje med 1600 in 2400 mm. Vendar pa se lastnosti tal, v katerih so vgrajene varnostne ograje, praviloma ne upoštevajo. Z drugimi besedami, ne glede na vrsto tal, se izvaja konstantna globina vpetja stebrov zaščitne ograje. Globine vpetja stebrov (PED) v sistemih jeklenih zaščitnih ograj so trenutno določene na podlagi visokih trdnosti tal. Zmogljivost teh modelov za trk ni primerna za lokacije, kjer so trdnostne karakteristike tal nižje od predpostavljenih v osnovnem izračunu. V tej študiji so bili opravljeni terenski udarni preizkusi na stebre vpete v tla, da bi določili optimalno globino vpetja Acta Geotechnica Slovenica, 2019/2 77. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests three different soil conditions, namely hard, medium hard and soft soil. A pendulum device is used to perform dynamic impact tests on C type (C120x60x4), H type (H150x90x6) and S type (S100x50x4.2) posts. Seven different PED values were used for each type of soil. A total of 63 impact tests proved that increased soil stiffness resulted reduction in PED for the posts. Optimum PED values are determined based on energy absorption of posts. With the use of optimum length guardrail posts considerable amount of installation time, labor and material savings are expected. stebrov za tri različne trdnostne razmere v tleh, in sicer trdo, srednje trdo in mehko zemljino. Nihalno napravo uporabljamo za izvedbo dinamičnih udarnih preizkusov na stebrih tipa C (C120x60x4), H (H150x90x6) in S (S100x50x4.2). Za vsako vrsto tal je bilo uporabljenih sedem različnih vrednosti globin vpetja stebrov. Skupno je bilo tako izvedenih 63 udarnih preizkusov, s čimer se je dokazalo, da je povečana togost tal povzročila zmanjšanje globine vpetja stebrov. Optimalne vrednosti globine vpetja stebrov se določijo na podlagi absorpcije energije stebrov. Z uporabo optimalne dolžine stebrov zaščitne ograje se pričakuje precej prihranka pri času za vgradnjo, delu in materialu. 1 INTRODUCTION The roadside can be defined as the area between the outside shoulder edge of a road and the right-of-way limits [1]. The utilization of engineering treatments in this area to improve traffic safety is referred to as roadside safety design and guardrails are one of the most widely used passive safety devices for roadsides. Most guardrail designs in the world are made out of steel or concrete. Concrete barrier designs usually do not contain a foundation and they are simply placed on the road surface. Thus soil-barrier interaction is not an issue for concrete barriers. However, this is not the case for steel designs. Posts of the steel guardrail designs have to be either bolted to a concrete deck or driven into the soil. Therefore, the connection and any details of this connection have to be designed properly for a steel guardrail to perform as intended. Steel-guardrail designs are mostly installed in soil, since the number of bridges in a standard highway project is limited. For steel guardrails' post-soil interaction the properties of the soil and the extent of the post embedment depth (PED) become essential parameters affecting the impact performance [2,5,6]. With a lack of post-soil interaction or an inadequate PED a steel guardrail might not function as intended and the design cannot provide adequate safety nor security for the impacting vehicles. In general, the height of the steel guardrails varies between 1600 and 2400 mm. However, the characteristics of the soil where the guardrails are driven are not taken into consideration. In other words, a constant depth of guardrail is used, regardless of the type of soil. Unfortunately, the PEDs in steel guardrail systems are currently determined based on strong soil properties [3]. The crash performance of these designs might not be appropriate for locations where the soil conditions are weaker than the tested conditions. The European crash-test standard EN131 is a performance-based standard. In other words, regardless of the properties of the guardrail elements, only the impact-response behavior of the guardrail is considered [4]. The adequacy of guardrail systems is evaluated using the EN1317 standard and successful designs receive certification for highway use. This standard has been mandatory in Turkey since 2011 and it provides crash-test procedures and acceptance criteria for crash tests. Even though the guardrail post-soil interaction and the soil properties are of importance in crash tests, EN1317 does not provide detailed information on this topic. There are not many studies in the literature about the post-soil interaction based on experimental or numerical analyses. This is why the crash-test standards do not contain any details or details of the soil properties. The behavior of sigma-type posts under semi-static and dynamic loading on gravel soil were investigated with experimental and numerical modeling by Wu and Thomson [6]. They used a standard PED in the tests and modelled in the numerical analyses. Atahan and Cansiz [2] analyzed the crash tests of the guardrails of circular wooden posts used in the United States. Full-scale crash-test results were simulated and detailed LS-DYNA analyses were carried out. It is recommended that the PED can be reduced in order to improve the behavior of the guardrail system and energy absorption. The behavior of a vehicle impacted guardrails applied on surfaces with variable inclination was investigated by Atahan [7]. The study was based on the crash effect of the vehicle existing in the slopes. In the study, the slopes are modelled as 1:1, 2:1, 4:1, 6:1, 8:1 and 10:1 (horizontal: vertical) and the stability of the vehicle and the adequacy of the guardrail system during the vehicle crash are examined using a software LS-DYNA program. The results showed that vehicles on 4:1 and more slopes could interact more securely with the guardrail system. A similar study was carried out by Marzougui et al. [8]. The purpose of this study is to investigate the use of rope guardrails in safety zones. The rope guardrails with different geometries, vehicles and surface inclinations 78. Acta Geotechnica Slovenica, 2019/2 78. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests were studied as variables using the LS-DYNA program. Vehicle safety was studied and used to determine the most suitable configurations for rope guardrails. Polivka et al. [9] investigated the vehicle stability by driving a 2:1 (horizontal: vertical) slope guardrail system. The study involved an actual crash test and the guardrail system was able to stop the crashing vehicle safely. A study was conducted by Reid [5] to demonstrate road safety using the LS-DYNA program. In this study it was shown that how efficient the LS-DYNA program is and how accurately it can predict the dynamic interactions. Sheikh and Bligh [10] conducted a study on the effect of the inclination of the refugees on vehicle behavior and accordingly the selection of the concrete barrier locations. An optimization study was carried out on the selection of the location of concrete barriers for different slopes using the LS-DYNA program. In addition, Bonin et al. [11] and Atahan et al. [3] conducted a structural efficiency analysis of many road-safety structures using the LS-DYNA program. The structures examined in these studies are crossing guardrails, bridge barriers, energy-absorbing crash posts and guardrails. The effects of water content, lime content and compaction energy on the compaction characteristics of lime-treated loess highway embankments were investigated using laboratory and in-situ compaction tests [14]. The maximum dry density and the optimum water content of loess with different lime contents were determined. The results indicate that the maximum dry density increases due to the increase of the water content. It was also reported that a higher water content and compaction energy is needed for the optimum compaction. Woo et al. [15] used the conventional 3D finite-element approach and the hybrid approach that combines Lagrange and SPH (smoothed particle hydrodynamics) elements to evaluate the response of a laterally loaded single guardrail post with a square tube embedded in the sloping ground. They reported that these approaches seem to be suitable to model the ground slope, as well as to obtain the response of the soil-post system dominated by bending deformations. El-Maaty [16] investigated the effect of including different reinforcement types on reducing the rapid accumulation of pavement damage caused by freeze-thaw cycles or the low strength of a silty pavement foundation. The CBR strength and freeze-thaw behavior were tested with the inclusion of randomly distributed fibers, chemical additives and waste or by-product materials. It is concluded that the unsubmerged samples reinforced with waste materials provided a significant improvement in the CBR strength and the best performance was observed with the submerged samples treated with chemical additives of 10%. Grouting is an effective way to improve the strength characteristics significantly and can also contribute to the stabilization of sand. Gamil et al. [17] developed a simulation and instrumental setup to be used for cement grouting. The shear strength of the sand was recorded before and after the grouting procedure. They reported that the shear strength increased after injecting the sand with cement and the setup produced accurate grouted samples with an even distribution of the cement mix. Hussain [18] examined the effect of the compaction energy of the engineering properties, i.e., compaction characteristics, unconfined compressive strength, California bearing ratio and the swell percentage of the soil. Substantial improvements in these properties were obtained in the tests. It is reported that compacting the soil at higher compaction energy levels can provide an effective approach to the stabilization of expansive soils up to a particular limit. The swell potential is increased due to the reduction in the permeability of the soil when the soil is compacted more than this limit. As seen from studies in the literature, the design of the guardrail systems are planned without soil conditions. In general, a constant depth of guardrail is used regardless of the type of soil. Actually, the soil conditions directly affect the post embedment depths (PEDs) in steel guardrail systems. In other words, it is not a proper engineering approach to use the same PEDs for different soil characteristics. This study focused directly on the performance of the guardrails under different soil conditions. In this study, a series of field pendulum-impact tests were conducted in Iskenderun, Hatay, Turkey. These tests were performed on soil embedded posts to determine the optimum PED for three different soil conditions, i.e., hard, medium-hard and soft soil. A pendulum device was used to perform the dynamic impact tests on C-type (C120x60x4), H-type (C150x90x6) and S-type (S100x50x4.2) posts. Seven different PED values were used for each type of soil. These values are varied from 600 mm to 900 mm for C-type posts; varied from 700 mm to 1300 mm for H-type and S-type posts. A total of 63 impact tests performed proved that the increased soil stiffness resulted a reduction in the PED for the posts. Optimum PED values were determined based on the energy absorption of the posts. With the use of optimum-length guardrail posts a considerable amount of installation time, labor and material savings are expected. 2 FIELD TESTS 2.1 Site Characterization Three different soil pits were prepared for the field impact testing. The dimensions of these pits were 1.0 m wide x 60.0 m long x 1.5 m deep, as shown in Figure 1. A total of 63 posts with 1.0 m spacing were installed Acta Geotechnica Slovenica, 2019/2 79. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests Figure 1. Preparation of soft, medium hard and hard soil pits for post installation. in these three soil pits. The dimensions of the soil pits were selected based on the largest PED used in the study, potential post removal during tests, prevention of any interaction between posts and economic considerations. The soil used in the pits represents the standard base granular material used by the Turkish Road Authorities [12]. To determine the geotechnical properties of the granular material to be used in these pits a series of laboratory tests, such as grain-size analysis, moisture content, field density, unit weight, shear box, standard and modified proctor tests were performed. The results of these experiments are presented in Table 1. The grading curve of the granular material used in the tests is given in Figure 2. After the laboratory tests, selected granular materials were used to construct the pits. Sand Cone and California Bearing Ratio tests were used to verify the density of the granular material for hard, medium-hard and soft soil conditions. The results of these field tests are listed in Table 2. As shown, acceptable soil stiffness levels were reached before the initiation of the post-installation procedure. At the same time, the density indices of the soil pits are 80%, 88% and 95% for the loose, medium-hard and hard soil conditions, respectively. Table 1. Geotechnical properties of the soil from laboratory tests. Parameter Property Soil classification SP (USCS); A3 (AASHTO); Sand (triangular classification) Water content 4 % Dry density max: 21.0 kN/m3; min: 16.0 kN/m3 Particle density 25.3 kN/m3 Internal friction angle soft: 36°; medium hard: 44°; hard: 48° Max. dry density and ykmax = 21.0 kN/m3; uopt = 8% optimum water content (standard proctor test) Max. dry density and ykmax = 22.0 kN/m3; ^ = 7% optimum water content (modified proctor test) Table 2. Geotechnical properties of the soil from field tests. Name Test Result Loose: 17.0 kN/m3 Sand Cone Test Medium dense: 18.5 kN/m3 Dense: 20.0 kN/m3 Loose: 36% CBR Test Medium dense: 64% Dense: 95% "-t ft S 100.00 10.00 1.00 0.10 0.01 Diameter(mm( Figure 2. Grading curve of the granular material used in the tests. 2.2 Details of guardrail posts used and experimental setup Three different shaped posts, i.e., C-type (C120x60x4), H-type (H150x90x6) and S-type (S100x50x4.2) are used in this study. Typical views of the posts are given in Figure 3. As shown in Tables 3-5, the PED ranged from 650 mm to 900 mm for C-type posts, ranged from 700 mm to 1300 mm for H-type and S-type posts for all three soil conditions. In this table from the test codes, the letter gives the soil type and the numbers indicate the PED values. The posts were driven into the soil using a post-installation machine and a picture of the installation procedure is shown in Figure 4. To deliver the impact forces to the posts, a 1 kg pendulum device was 80. Acta Geotechnica Slovenica, 2019/2 80. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests (a) C type posts i.'--.--: ' ' sr.:. - v r-i -, ■ . : ■ - . ■ ... - mmm - J * 'f^mmm m (b) H type posts Figure 3. Typical views of the posts used in the study. (c) S type posts used. The pendulum was raised 1.5 m using an electric motor and the impacted posts about 550 mm above ground level. This distance represents the bumper height of an average small car. In this test setup, the pendulum applied 14.7 kJ of kinetic energy to the posts. A picture of the pendulum used in this study is shown in Figure 5. An accelerometer was installed on the pendulum to measure the acceleration-time history during impact. As shown in Figure 6, a data-acquisition system is setup to transfer the acceleration data in the x, y and z directions from the accelerometer to an 8-channel data collector and from there to a computer. The acceleration-time histories for all 63 impact tests are recorded in Excel format. This history is used to calculate the velocity-time and eventually the displacement-time histories. The force is calculated based on the mass multiplied by the measured acceleration. Eventually, a force-displacement history is obtained from all 63 impact cases. The area under these curves represented the work done, in other words, the energy absorbed by the post-soil interaction. Table 3. Details of guardrail posts tested (C type). Post Designation x Vo X O PED (mm) 600 650 700 750 800 850 900 600 650 700 750 800 850 900 600 650 700 750 800 850 900 Soil Characterization H (Hard) M (Medium Hard) S (Soft) Code H-600 H-650 H-700 H-750 H-800 H-850 H-900 M-600 M-650 M-700 M-750 M-800 M-850 M-900 S-600 S-650 S-700 S-750 S-800 S-850 S-900 Table 4. Details of guardrail posts tested (H type). Post Designation 6 x PED (mm) 700 800 900 1000 1100 1200 1300 700 800 900 1000 1100 1200 1300 700 800 900 1000 1100 1200 1300 Soil Characterization H (Hard) M (Medium Hard) S (Soft) Code H-700 H-800 H-900 H-1000 H-1100 H-1200 H-1300 M-700 M-800 M-900 M-1000 M-1100 M-1200 M-1300 S-600 S-650 S-700 S-750 S-800 S-850 S-900 Acta Geotechnica Slovenica, 2019/2 81. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests Table 5. Details of guardrail posts tested (S type). Post Designation PED (mm) Soil Characterization Code S 700 H-700 800 H-800 900 H-900 1000 1100 H (Hard) H-1000 H-1100 1200 H-1200 1300 H-1300 700 M-700 800 M-800 900 1000 1100 M (Medium Hard) M-900 1200 1300 M-1000 M-1100 M-1200 M-1300 700 S-600 800 S-650 900 S-700 1000 S (Soft) S-750 1100 S-800 1200 S-850 1300 S-900 Figure 4. Installation of posts in soil. Figure 5. Pendulum test device used in dynamic impact tests with three dimensional accelerometer. Figure 6. Data acquisition setup used during dynamic pendulum testing (1) data cable between accelerometer and data collector box, (2) 8-channel data collector, (3) recording data in a computer. 3 TEST RESULTS AND DISCUSSION 3.1 Visual inspections A total of 63 impact tests were performed using the pendulum device. Each of the test results was recorded visually and analytically. The general views for the different soil conditions (soft-S, medium hard-M and hard-H soil) after the tests where C-type posts were used are given in Figure 7. And then a qualitative evaluation of all the tests is presented in Tables 6-8. In general, when an insufficient PED is used the posts exhibited an upwards movement and in some cases were almost completely removed from the soil. On the other hand, when sufficient PED is used, the posts remained in the soil with minimal upward motion and in some cases post buckling was observed. 82. Acta Geotechnica Slovenica, 2019/2 82. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests Table 6. Qualitative evaluation of the pendulum test results (C-type post). PED Soil Stiffness (mm Hard (H) Medium hard (M) Soft (S) 600 1 The post moved upwards in the ground, but was not completely removed from the soil. The soil body is collapsed. The pendulum slowed down after impact Same as H-600 The post moved upwards in the ground and completely removed from the soil. The soil body is collapsed. The pendulum movement continued. 650 The post movement in the soil is less than H-600, but the soil body is collapsed. The pendulum stopped after the impact. Same as M-600 Same as S-600 700 The post's upwards movement is not observed and minimal soil movement occurred. The post-soil interaction and energy absorption are acceptable. Somewhat improvement compared to the M-650 case. The soil body is collapsed. The pendulum stopped after the impact. Same as H-600 750 Due to sufficient PED, slight post buckling is observed. Post-soil interaction and energy absorption are acceptable. Same as H-700 Same as M-700 800 Post buckling becomes more visible. Post-soil interaction and energy absorption is acceptable. Same as H-750 Same as H-700 850 Same as H-800 Same as H-800 Same as H-800 900 Same as H-800 Same as H-800 Same as H-800 Figure 7. General views of the soil for C-type posts after the impact tests. Acta Geotechnica Slovenica, 2019/2 83. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests Table 7. Qualitative evaluation of the pendulum test results (H-type post). PED Soil Stiffness (mm Hard (H) Medium hard (M) Soft (S) 700 The post moved upwards in the ground but was not completely removed from the soil. The soil body is collapsed. The pendulum movement continued. The post moved upwards in the ground and the soil body collapsed. The pendulum movement continued. The maximum post movement was observed and the soil body collapsed. The pendulum movement continued. 800 The post movement in the soil is less than H-700, but the soil body is collapsed. The pendulum stopped after the impact. The post movement in the soil is less than M-700 and the soil body is collapsed. The pendulum stopped after the impact. The post movement in the soil is less than S-700 and the soil body is collapsed. 900 Due to sufficient PED, slight post buckling is observed. Post-soil interaction and energy absorption are acceptable. Due to sufficient PED, slight post buckling is observed. Post-soil interaction and energy absorption are acceptable. Due to sufficient PED, slight post buckling is observed. The post movement in soil is great compared with hard and medium-hard soil types. 1000 Post-soil interaction and energy absorption are acceptable. Same as H-1000 Same as H-1000 1100 Same as H-1000 Same as H-1000 Same as H-1000 1200 Same as H-1000 Same as H-1000 Same as H-1000 1300 Same as H-1000 Same as H-1000 Same as H-1000 Table 8. Qualitative evaluation of the pendulum test results (S-type post). PED Soil Stiffness (mm Hard (H) Medium hard (M) Soft (S) 700 The post moved upwards in the ground, but was not completely removed from the soil. The soil body is collapsed. The pendulum movement continued. Same as H-700 The maximum post movement was observed and the soil body collapsed. The pendulum movement continued. The post movement in the soil is less than The post movement in the soil is less 800 H-700, but the soil body collapsed. The pendulum stopped after impact. Same as H-800 than S-700 and the soil body collapsed. The pendulum movement continued. The post's upwards movement is not ob- The post movement in the soil is less 900 served and minimal soil movement occurred. Post-soil interaction and energy absorption are acceptable. Same as H-900 than S-800, but the soil body is collapsed. The pendulum stopped after the impact. Due to sufficient PED, slight post buckling 1000 is observed. Post-soil interaction and energy absorption are acceptable. Same as H-1000 Same as H-1000 1100 Post buckling becomes more visible. Soil movement is negligible. The post's upwards movement is not observed and minimal soil movement occurred. Same as H-1100 1200 Post buckling becomes more visible. Due to sufficient PED, slight post buckling is observed. Same as M-1100 1300 Same as H-1200 Same as H-1200 Same as M-1200 3.2 Analytical Calculations The maximum measured accelerations and the energy absorbed, calculated using the area under the forcedeformation curve for all 63 impact tests, are presented in Table 9. In the pendulum test, the mass of 750kg was lifted 1.5m each time and then released free. A kinetic energy of 11.04 kJ was applied to the posts by the pendulum. This value was determined using the standard kinetic energy formula after calculating the velocity that the post had just before the impact. Compared to the energy levels applied to the guardrail systems by the vehi- 84. Acta Geotechnica Slovenica, 2019/2 84. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests Table 9. Maximum energy absorption and acceleration calculations for the pendulum tests. Soil Stiffness Post PED Hard (H) Medium hard (M) Soft (S) type (mm) Max. Energy Absorbed (kJ) Max. Accel. (g) Max. Energy Absorbed (kJ) Max. Accel. (g) Max. Energy Absorbed (kJ) Max. Accel. (g) 600 0.72 - 2.88 0.66 - 2.06 0.49 - 1.08 O 650 2.93 - 4.05 2.11 - 2.90 1.77 - 2.45 ^ X 0 6 X 0 2 700 3.27 - 4.52 2.35 - 3.25 2.14 - 2.96 750 4.58 - 6.33 3.29 - 4.55 2.89 - 3.99 800 5.75 - 11.95 4.14 -10.72 3.31 - 7.93 0 850 6.86 - 18.48 4.94 -16.83 4.01 - 13.54 900 7.92 - 25.85 6.13 -24.47 5.19 - 18.87 700 10.03 -34.81 9.56 -33.21 8.89 -31.65 K 800 10.65 -35.05 10.12 -34.54 9.34 -32.68 6 X 0 9 X 0 5 900 11.04 -35.26 10.74 -35.12 10.01 -33.84 1000 11.04 -35.32 11.04 -35.51 10.71 -34.82 1100 11.04 -35.45 11.04 -35.47 11.04 -35.21 0 1200 11.04 -35.41 11.04 -35.61 11.04 -35.52 1300 11.04 -35.56 11.04 -35.55 11.04 -35.49 700 3.32 -4.59 3.07 -4.24 0.92 -1.27 So 800 5.31 -7.34 5.11 -7.06 2.22 -3.07 .2 900 6.61 -9.14 6.39 -8.83 2.95 -4.08 X 0 5 1000 7.51 -10.38 7.17 -9.91 3.61 -8.99 X 0 0 1100 8.05 -18.13 7.77 -17.74 4.26 -15.89 0 1200 8.44 -19.67 8.01 -18.07 6.03 -16.84 1300 9.61 -25.28 8.31 -23.21 7.93 -21.75 2.5 2.0 1.5 S 1.0 o K 0.5 £ o.o -0-5 -1.0 -1.5 r \ 130 Hz Fitter r 1 \ v JK \ / \ r 0-72 fei \ \ I V 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Deformation (m) Figure 8. Typical force-deformation curve after the impact test. cles in the actual crash tests, the 11.04 kJ is a reasonable energy level that can be used to determine the impact behavior of the post driven into the soil. The following equations were used to calculate the energy level. m g h = 0.5 m V2 (1) V = (2 g hf5 = (2 x 9.81 x 1.5)0.5 = 5.43 m/s (2) E = 0.5 m F2 = 0.5 x 750 x 5.432 =11.04 kJoule (3) During the impact, this energy is absorbed by the post and the absorption depends directly on the post material's strength, the PED and the soil properties. The impact of the pendulum on the posts means that all its energy transmits to the post. A typical force-deformation curve is given in Figure 8 for the C-type posts, 600mm of PED and the hard-soil condition. Acta Geotechnica Slovenica, 2019/2 85. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests VPL= constant (700 mm for C and S types) —^ constant (1200 mm for H type) 1.5 m Posts 60.0 m Figure 9. Cross-sections of the soil pits and the PEDs. 4 EVALUATION OF FIELD TEST RESULTS In this study, three different post shapes, i.e., C type (C120x60x4), H type (H150x90x6) and S type (S100x50x4.2) are used. The PED ranged from 650 mm to 900 mm for the C-type posts and ranged from 700 mm to 1300 mm for the H-type and S-type posts for all three soil conditions. The visible post length (VPL) above the soil was kept constant at 700 mm for the C- and S-type posts and 1200 mm for the H-type post. Figure 9 shows cross-sections of the soil pits and PEDs. The posts were embedded in soft, medium-hard and hard soil conditions, for which the soil properties are given above. The relations of the post embedment depth/ visible post length (PED/VPL), energy-absorption capacity (EAC) for different soil (soft, medium-hard and hard) and post types (C, H and S type) are given in Figure 10. As shown in this figure, there is a linear relationship between the PED/VPL ratio and the magnitude of the energy-absorption capacity increases when the PED/VPL ratio increases for all the types of soil and post. For the C-type posts given in Figure 10a, the energy-absorption capacity increases from 4.44% to 47.01% when the PED increases from 600 mm to 900 mm in a soft-soil environment. Similarly, in the case of medium-hard soil, when the PED increases from 600 mm to 900 mm, the energy-absorption capacity increases from 5.98% to 55.53%. In the hard-soil conditions, this value increases from 6.52% to 71.74%. Similar observations are obtained for the H-type and S-type posts, given in Figure 10b and c. The internal friction angle of the soil (0) - EAC (%) relation of the C-, H- and S-type posts that embedded in soft, medium-hard and hard soils are presented in Figure 11. These relationships are given for different PED values. In these figures, the soft, medium-hard and hard soils are represented by internal friction angles of 36°, 44° and 48°, respectively. As shown in these figures there is a linear relationship between the internal fric- 1.4 1.2 1.0 a. 0.8 > a O.b a. 0.4 0.2 0.0 1.2 1.0 O.S 0. > 0.6 □ a. 0.4 0.2 0.0 ^>^ OHanJ-Ctype ¿Medium -Ctype " OSoft - Ctype (a) C type posts 40 EAC [%) iS ST/Jtk cr^A--- " O Hard - H type A Medium - H tvpe O Soft - H type (b) H type posts 70 80 SO EAC (%| 100 110 2.0 1.8 1.5 1.3 1.0 0.8 0.5 0.3 0.0 ,<5 M O Hard - S type ¿1 Medium - S type - OSoft-Stype (c) S type posts 20 40 60 80 100 EAC [%) Figure 10. EAC-PED/VPL relationship according to the soil conditions. 86. Acta Geotechnica Slovenica, 2019/2 86. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum Impact tests 48 36 o AO □ X X + o AO □ X X + O PED=600mm A PED=6S0mm O PED=700mm □ PED=750mm ❖ AO □ X X + iK PED=8Q0mm X PED=850mm + PED=900mm 20 40 EAC (a) C type posts so so so - _ 50 - o A □ X X + o A □ X X + O PED=600mm APED=650mm o A □ X X + O PE[)=700mm □ PEt>-75Qmm X PED=BOOmm XPED=S50mm + PED=900mm 20 40 EAC (a) C type posts 60 80 a- 40 H -5- 32 O PED-700mm APED=S00mm O a m O PE0=9OOmm □ PED=1000m m ❖ A o m. XPED=1100mm X PED=1200m m + PED=1300mm o A O □ x 70 75 80 85 90 EAC (%) (b) H type posts 95 100 105 40 36 - 32 OPE[>=700mm APED=B00mm o A o □ XX + OPED =900mm □ PED=1000mm *PED=1100mm o A o □ >x+ XPED=1200mm + PED=1300mm <> A o □ x X + EAC |?4| (c) S type posts Figure 11. EAC-$ relationship according to the PED values. so 3 60 ■ £ O PE[>-700mm A R APED=300mm O PED=900mm □ PE[>-1000m m X PED=1100m m <> A R X PED=120Cm m + PED=1300mm o A □ X 70 75 SO 35 90 EAC !%) (b) H type posts 95 100 105 100 _ 60 E K DO u 40 -\ o A □ XX + o A □ XX+ O A □ X X + O PED=700mm □ PED=1000mm + PED=1300mm APED=800rmm X PED-1100m m O PED=900mm XPED-1200mm 20 40 60 EAC (%) SO 100 (c) S type posts Figure 12. EAC-CBR relationship according to the PED values. tion angle and the magnitude of the energy-absorption capacity. Note that the EAC increases when $ increases for all the types of soil and post. For the H-type posts given in Figure 11b, the energy-absorption capacities are 97.01%, 100.0% and 100.0%, for the soft ($=36°), medium-hard ($=44°) and hard ($=48°) soil conditions, respectively. For the same soil stiffness (for example, $=48°) the energy-absorption capacity increases with an increase in a certain value of the PED and then it remains constant. For the H-type posts, for PED values 700 mm, 1000 mm and 1300 mm, the EAS are 90.85%, 100.0% and 100.0%, respectively. Acta Geotechnica Slovenica, 2019/2 87. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests The European crash-test standard EN1317 is a performance-based standard. In other words, the impact-response behavior of the guardrail designs are considered, regardless of the guardrail material, geometry or soil properties. This study focused on this phenomenon and evaluated the safety performance of the guardrail posts when they are installed into various soil types, such as soft, medium-hard and hard. In this study it is agreed that the post behaves in a similar way to laterally loaded piles [13]. In the case of axially loaded piles, loads are transferred to the soil by shaft friction and base resistance. This total resistance resulted from the shaft resistance and end-bearing resistance, providing the equilibrium conditions. In the end-bearing piles, it is essential to have the pile base inserted into a stronger soil layer, such as dense sand, stiff clay or rock. If no such strong layer is available at the site, then the loads are carried only by the shaft friction. In the laterally loaded pile phenomenon, piles behave as transversely loaded beams. The lateral load is transferred to the surrounding soil mass by using the lateral resistance of the soil. A part or complete pile tends to shift horizontally in the direction of the applied load, causing pile bending, pile rotation or pile translation, depending on the post's stiffness, load value and soil property. The soil mass lying in the direction of the applied load generates compressive and shear stresses and strains in the soil that offers resistance to the pile movement. The soil-based results are interpreted in terms of the laterally loaded pile mechanism. In the current study, dynamic pendulum tests were performed to determine the optimum PED values for different soil conditions. Based on a total of 63 test results, the suggested optimum PED values for different types of soil and posts are given in Table 10, including the application standard. As seen clearly from Table 10, the optimum PEDs suggested in this study are smaller than the applied ones, especially in the hard and medium-hard soil conditions. Table 10. Suggested and applied PED values. Optimum post embedment depth (PEDopt) Post Hard soil Medium-Hard soil Soft soil PEDsuggested / PEDapplied C type 750mm / 950mm 850mm / 950mm 950mm / 950mm S type 1000mm / 1200mm 1100mm / 1200mm 1200mm / 1200mm H type 800mm / 1230mm 900mm / 1230mm 1000mm / 1230mm Table 11 gives the amount of saving percentages for one post for each type of post and soil used. It was determined that significant savings were made, especially in C- and H-type posts and also for hard-soil conditions. Considering the optimum length in the guardrail post design, significant savings can be achieved for a mile of road. In other words, with the use of the optimum length of guardrail posts, a considerable amount of installation time, labor and material savings are expected. This study has shown that the optimum embedment depths of the guardrail posts can be decided by determining the soil properties in the light of the standard geotechnical experiments to be performed on the roads where the guardrail post is to be installed. Table 11. Amount of savings according to PED0pt. Post Hard soil Medium-Hard soil Soft soil C type 21.05% 10.53% 0.00% S type 16.67% 8.33% 0.00% H type 34.96% 26.83% 18.70% 5 CONCLUSIONS In this study a series of field pendulum-impact tests were performed on soil-embedded posts to determine the optimum PED for three different soil conditions, namely, hard, medium-hard and soft soil. A pendulum device was used to perform the dynamic impact tests on C-type (C120x60x4), H-type (C150x90x6) and S-type (S100x50x4.2) posts with seven different PED values used for each type of soil. Based on the research findings, the following specific conclusions can be drawn: - Dynamic pendulum tests proved that an increased soil stiffness resulted in a reduction in PED for the posts due to an improved post-soil interaction. - It is determined that the posts tend to move upwards, get out of the soil quickly and thus could not provide enough resistance when the PED is insufficient. - Soil stiffness has an important effect on the impact-response behavior of the guardrail posts. There is a linear relationship between the internal friction angle and the magnitude of the energy-absorption capacity increases when 0 increases for all the types of soil and post. Similar behavior was observed from a CBR perspective. - It has been determined that significant savings have been made, especially in C- and H-type posts and also for hard soil conditions. - When comparing the optimum values with the standards, the savings obtained for hard soils can reach up to 35% for H-type posts. These savings are about 20% for C-type posts and about 15% for S-type posts. - Considering the larger PED in similar guardrail systems in use today, designs with optimum PED will help save a considerable amount of installation time, labor and material. 88. Acta Geotechnica Slovenica, 2019/2 88. M. Ornek et al.: Soil based design of highway guardrail post depths using pendulum impact tests Acknowledgments The work presented in this paper was carried out with funding from TUBITAK (Scientific and Technological Research Council of Turkey), Grant No. 213M516. REFERENCES [1] AASHTO. 2014. Roadside design guide. American Association for State Highway and Transportation Officials. 4th Edition, Washington, D.C. [2] Atahan, A.O., Cansiz, Ö.F. 2005. Improvements to G4(RW) strong-post round-wood W-beam guardrail system. ASCE Journal of Transportation Engineering 131(1), 63-73. DOI: 10.1061/ (asce)0733-947x(2005)131:1(63) [3] Atahan, A.O., Bonin, G., Cicinnati, L., Ya^arer, H.I. 2008. Development of a crashworthy end terminal TWINY for thrie-beam guardrail. ASCE Journal of Transportation Engineering 133(4), 467-476. DOI: 10.1061/(ASCE)0733-947X(2008)134:11(467) [4] CEN. 2017. European Crash Testing Standard EN1317. Performance classes, impact test acceptance criteria and test methods for safety barriers, Brussels. [5] Reid, J.D. 2004. LS-DYNA simulation influence on roadside hardware. Transportation Research Board Annual Meeting, Paper No. 04-2619, Washington D.C. DOI: 10.3141/1890-04 [6] Wu, W., Thomson, R.A. 2007. A study of the interaction between a guardrail post and soil during quasi-static and dynamic loading. International Journal of Impact Engineering 34, 883-98. DOI: 10.1016/j.ijimpeng.2006.04.004 [7] Atahan, A.O. 2003. Impact behavior of G2 steel weak-post W-beam guardrail on nonlevel terrain. Heavy Vehicle Systems, A series of the International Journal of Vehicle Design 10(3), 209-223. DOI: 10.1504/IJHVS.2003.003207 [8] Marzougui, D., Mohan, P., Kan, C.D., Opiela, K.S. 2007. Performance evaluation of low tension three strand cable median barriers, Transportation Research Board Annual Meeting, Washington D.C. DOI: 10.3141/2025-03 [9] Polivka, K.A., Sicking, D.L., Faller, R.K., Bielenberg, R.W. 2000. Development of a W-beam guardrail system for use on a 2:1 Slope. Transportation Research Record 1743, 80-87. [10] Sheikh, N.M., Bligh, R.P. 2006. Analysis of the impact performance of concrete median barrier placed on or adjacent to slopes, Report No. FHWA/ TX-06/0-5210-1, Texas A&M University, Texas. [11] Bonin, G., Cantiasani, G., Loprencipe, G., Ranzo, A., Atahan, A.O. 2009. Retrofit of an existing Italian bridge rail for H4a containment level using simulation, Heavy Vehicle Systems, A series of the International Journal of Vehicle Design 16(1/2), 258-270. DOI: 10.1504/IJHVS.2009.023864 [12] TRA. 2016. Handbook of properties of road construction materials. General Directorate of Turkish Roads, Turkish Road Association, Ankara, Turkey. [13] Teng, T.L., Liang, C.C., Hsu, C.Y., Shih, C.J., Tran, T.T. 2016. Effect of soil properties on safety performance of Wbeam guardrail. International Conference on Advanced Material Science and Environmental Engineering (AMSEE 2016), 34-36. DOI: 10.2991/amsee-16.2016.10 [14] Zhang, Y., Ye, W., Wang, Z. 2017. Study on the compaction effect factors of lime-treated loess highway embankments. Civil Engineering Journal 3(11), 1008-1019. DOI: 10.28991/cej-030933 [15] Woo, K.W., Lee, D.W., Ahn, J.S. 2018. Impact behavior of a laterally loaded guardrail post near slopes by hybrid SPH model. Advances in Civil Engineering, Article ID 9479452, 12 pp. DOI: 10.1155/2018/9479452 [16] El-Maaty, A.E. 2016. Enhancing the CBR strength and freeze-thaw performance of silty subgrade using three reinforcement categories. Civil Engineering Journal 2(3), 73-85. [17] Gamil, Y., Bakar, I., Ahmed, K. 2017. Simulation and development of instrumental setup to be used for cement grouting of sand soil. Italian Journal of Science and Engineering 1(1), 16-27. [18] Hussain, S. 2017. Effect of compaction energy on engineering properties of expansive soil. Civil Engineering Journal 3(8), 610-646. DOI: 10.28991/ cej-030988 Acta Geotechnica Slovenica, 2019/2 89. NAVODILA AVTORJEM NAVODILA AVTORJEM Vsebina članka Članek naj bo napisan v naslednji obliki: - Naslov, ki primerno opisuje vsebino članka in ne presega 80 znakov. - Izvleček, ki naj bo skrajšana oblika članka in naj ne presega 250 besed. Izvleček mora vsebovati osnove, jedro in cilje raziskave, uporabljeno metodologijo dela, povzetek izidov in osnovne sklepe. - Največ 6 ključnih besed, ki bi morale biti napisane takoj po izvlečku. - Uvod, v katerem naj bo pregled novejšega stanja in zadostne informacije za razumevanje ter pregled izidov dela, predstavljenih v članku. - Teorija. - Eksperimentalni del, ki naj vsebuje podatke o postavitvi preiskusa in metode, uporabljene pri pridobitvi izidov. - Izidi, ki naj bodo jasno prikazani, po potrebi v obliki slik in preglednic. - Razprava, v kateri naj bodo prikazane povezave in posplošitve, uporabljene za pridobitev izidov. Prikazana naj bo tudi pomembnost izidov in primerjava s poprej objavljenimi deli. - Sklepi, v katerih naj bo prikazan en ali več sklepov, ki izhajajo iz izidov in razprave. - Vse navedbe v besedilu morajo biti na koncu zbrane v seznamu literature, in obratno. Dodatne zahteve - Vrstice morajo biti zaporedno oštevilčene. - Predložen članek ne sme imeti več kot 18 strani (brez tabel, legend in literature); velikost črk 12, dvojni razmik med vrsticami. V članek je lahko vključenih največ 10 slik. Isti rezultati so lahko prikazani v tabelah ali na slikah, ne pa na oba načina. - Potrebno je priložiti imena, naslove in elektronske naslove štirih potencialnih recenzentov članka. Urednik ima izključno pravico do odločitve, ali bo te predloge upošteval. Enote in okrajšave V besedilu, preglednicah in slikah uporabljajte le standardne označbe in okrajšave SI. Simbole fizikalnih veličin v besedilu pišite poševno (npr. v, T itn.). Simbole enot, ki so sestavljene iz črk, pa pokončno (npr. Pa, m itn.). Vse okrajšave naj bodo, ko se prvič pojavijo, izpisane v celoti. Slike Slike morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot sl. 1, sl. 2 itn. Posnete naj bodo v katerem koli od razširjenih formatov, npr. BMP, JPG, GIF. Za pripravo diagramov in risb priporočamo CDR format (CorelDraw), saj so slike v njem vektorske in jih lahko pri končni obdelavi preprosto povečujemo ali pomanjšujemo. Pri označevanju osi v diagramih, kadar je le mogoče, uporabite označbe veličin (npr. v, T itn.). V diagramih z več krivuljami mora biti vsaka krivulja označena. Pomen oznake mora biti razložen v podnapisu slike. Za vse slike po fotografskih posnetkih je treba priložiti izvirne fotografije ali kakovostno narejen posnetek. Preglednice Preglednice morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot preglednica 1, preglednica 2 itn. V preglednicah ne uporabljajte izpisanih imen veličin, ampak samo ustrezne simbole. K fizikalnim količinam, npr. t (pisano poševno), pripišite enote (pisano pokončno) v novo vrsto brez oklepajev. Vse opombe naj bodo označene z uporabo dvignjene številke1. Seznam literature Navedba v besedilu Vsaka navedba, na katero se sklicujete v besedilu, mora biti v seznamu literature (in obratno). Neobjavljeni rezultati in osebne komunikacije se ne priporočajo v seznamu literature, navedejo pa se lahko v besedilu, če je nujno potrebno. Oblika navajanja literature V besedilu: Navedite reference zaporedno po številkah v oglatih oklepajih v skladu z besedilom. Dejanski avtorji so lahko navedeni, vendar mora obvezno biti podana referenčna številka. Primer: ».....kot je razvidno [1,2]. Brandl and Blovsky [4], sta pridobila drugačen rezultat...« V seznamu: Literaturni viri so oštevilčeni po vrstnem redu, kakor se pojavijo v članku. Označimo jih s številkami v oglatih oklepajih. Sklicevanje na objave v revijah: [1] Jelušič, P., Zlender, B. 2013. Soil-nail wall stability analysis using ANFIS. Acta Geotechnica Slovenica 10(1), 61-73. 90. Acta Geotechnica Slovenica, 2019/2 INSTRUCTIONS FOR AUTHORS Sklicevanje na knjigo: [2] Šuklje, L. 1969. Rheological aspects of soil mechanics. Wiley-Interscience, London Sklicevanje na poglavje v monografiji: [3] Mitchel, J.K. 1992. Characteristics and mechanisms of clay creep and creep rupture, in N. Guven, R.M. Pollastro (eds.), Clay-Water Interface and Its Rheological Implications, CMS Workshop Lectures, Vol. 4, The clay minerals Society, USA, pp. 212-244.. Sklicevanje na objave v zbornikih konferenc: [4] Brandl, H., Blovsky, S. 2005. Slope stabilization with socket walls using the observational method. Proc. Int. conf. on Soil Mechanics and Geotechnical Engineering, Bratislava, pp. 2485-2488. Sklicevanje na spletne objave: [5] Kot najmanj, je potrebno podati celoten URL. Če so poznani drugi podatki (DOI, imena avtorjev, datumi, sklicevanje na izvorno literaturo), se naj prav tako dodajo. INSTRUCTIONS FOR AUTHORS Format of the paper The paper should have the following structure: - A Title, which adequately describes the content of the paper and should not exceed 80 characters; - An Abstract, which should be viewed as a mini version of the paper and should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation and the methodology employed; it should also summarise the results and state the principal conclusions; - Immediately after the abstract, provide a maximum of 6 keywords; - An Introduction, which should provide a review of recent literature and sufficient background information to allow the results of the paper to be understood and evaluated; - A Theoretical section; - An Experimental section, which should provide details of the experimental set-up and the methods used to obtain the results; - A Results section, which should clearly and concisely present the data, using figures and tables where appropriate; - A Discussion section, which should describe the relationships shown and the generalisations made possible by the results and discuss the significance Podatki o avtorjih Članku priložite tudi podatke o avtorjih: imena, nazive, popolne poštne naslove, številke telefona in faksa, naslove elektronske pošte. Navedite kontaktno osebo. Sprejem člankov in avtorske pravIce Uredništvo si pridržuje pravico do odločanja o sprejemu članka za objavo, strokovno oceno mednarodnih recenzentov in morebitnem predlogu za krajšanje ali izpopolnitev ter terminološke in jezikovne korekture. Z objavo preidejo avtorske pravice na revijo ACTA GEOTECHNICA SLOVENICA. Pri morebitnih kasnejših objavah mora biti AGS navedena kot vir. Vsa nadaljnja pojasnila daje: Uredništvo ACTA GEOTECHNICA SLOVENICA Univerza v Mariboru, Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo Smetanova ulica 17, 2000 Maribor, Slovenija E-pošta: ags@um.si of the results, making comparisons with previously published work; - Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion; - A list of References, which comprises all the references cited in the text, and vice versa. Additional Requirements for Manuscripts - Use double line-spacing. - Insert continuous line numbering. - 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 91. Acta Geotechnica Slovenica, 2019/2 INSTRUCTIONS FOR AUTHORS be in plain text (e.g. Pa, m, etc.). All abbreviations should be spelt out in full on first appearance. Figures Figures must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Figures may be saved in any common format, e.g. BMP, JPG, GIF. However, the use of CDR format (CorelDraw) is recommended for graphs and line drawings, since vector images can be easily reduced or enlarged during final processing of the paper. When labelling axes, physical quantities (e.g. v, T, etc.) should be used whenever possible. Multi-curve graphs should have individual curves marked with a symbol; the meaning of the symbol should be explained in the figure caption. Good quality black-and-white photographs or scanned images should be supplied for the illustrations. Tables Tables must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Table 1, Table 2, etc. The use of names for quantities in tables should be avoided if possible: corresponding symbols are preferred. In addition to the physical quantity, e.g. t (in Italics), units (normal text), should be added on a new line without brackets. Any footnotes should be indicated by the use of the superscript1. LIST OF references Citation in text Please ensure that every reference cited in the text is also present in the reference list (and vice versa). Any references cited in the abstract must be given in full. Unpublished results and personal communications are not recommended in the reference list, but may be mentioned in the text, if necessary. Reference style Text: Indicate references by number(s) in square brackets consecutively in line with the text. The actual authors can be referred to, but the reference number(s) must always be given: Example: "... as demonstrated [1,2]. Brandl and Blovsky [4] obtained a different result ..." List: Number the references (numbers in square brackets) in the list in the order in which they appear in the text. Reference to a journal publication: [1] Jelusic, P., Zlender, B. 2013. Soil-nail wall stability analysis using ANFIS. Acta Geotechnica Slovenica 10(1), 61-73. Reference to a book: [2] Suklje, L. 1969. Rheological aspects of soil mechanics. Wiley-Interscience, London Reference to a chapter in an edited book: [3] Mitchel, J.K. 1992. Characteristics and mechanisms of clay creep and creep rupture, in N. Guven, R.M. Pollastro (eds.), Clay-Water Interface and Its Rheological Implications, CMS Workshop Lectures, Vol. 4, The clay minerals Society, USA, pp. 212-244. Conference proceedings: [4] Brandl, H., Blovsky, S. 2005. Slope stabilization with socket walls using the observational method. Proc. Int. conf. on Soil Mechanics and Geotechni-cal Engineering, Bratislava, pp. 2485-2488. Web references: [5] As a minimum, the full URL should be given and the date when the reference was last accessed. Any further information, if known (DOI, author names, dates, reference to a source publication, etc.), should also be given. Author information The following information about the authors should be enclosed with the paper: names, complete postal addresses, telephone and fax numbers and E-mail addresses. Indicate the name of the corresponding author. Acceptance of papers and copyright The Editorial Committee of the Slovenian Geotechnical Review reserves the right to decide whether a paper is acceptable for publication, to obtain peer reviews for the submitted papers, and if necessary, to require changes in the content, length or language. On publication, copyright for the paper shall pass to the ACTA GEOTECHNICA SLOVENICA. The AGS must be stated as a source in all later publication. For further information contact: Editorial Board ACTA GEOTECHNICA SLOVENICA University of Maribor, Faculty of Civil Engineering, Transportation Engineering and Architecture Smetanova ulica 17, 2000 Maribor, Slovenia E-mail: ags@um.si 92. Acta Geotechnica Slovenica, 2019/2 NAMEN REVIJE AIMS AND SCOPE Namen revije ACTA GEOTECHNICA SLOVENICA je objavljanje kakovostnih teoretičnih člankov z novih pomembnih področij geomehanike in geotehnike, ki bodo dolgoročno vplivali na temeljne in praktične vidike teh področij. ACTA GEOTECHNICA SLOVENICA objavlja članke s področij: mehanika zemljin in kamnin, inženirska geologija, okoljska geotehnika, geosintetika, geotehnične konstrukcije, numerične in analitične metode, računalniško modeliranje, optimizacija geotehničnih konstrukcij, terenske in laboratorijske preiskave. ACTA GEOTECHNICA SLOVENICA aims to play an important role in publishing high-quality, theoretical papers from important and emerging areas that will have a lasting impact on fundamental and practical aspects of geomechanics and geotechnical engineering. ACTA GEOTECHNICA SLOVENICA publishes papers from the following areas: soil and rock mechanics, engineering geology, environmental geotechnics, geosynthetic, geotechnical structures, numerical and analytical methods, computer modelling, optimization of geotechnical structures, field and laboratory testing. Revija redno izhaja dvakrat letno. The journal is published twice a year. AVTORSKE PRAVICE Ko uredništvo prejme članek v objavo, prosi avtorja(je), da prenese(jo) avtorske pravice za članek na izdajatelja, da bi zagotovili kar se da obsežno razširjanje informacij. 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