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.3. Numerical modeling procedure
3.1. Method of approachEffect of the construction method, excavation and backfill, onthe behavior of sheet pile walls and surrounding soil has beeninvestigated through a parametric study using continuummechan-ics numericalmethods. The finite elementmethod was used for theanalyses and varying wall heights and soil conditions were em-ployed. A total of 12 cases, with different soil conditions and wallheights, were analyzed for both excavation and backfill construc-tion conditions. The details of the cases studied and the analysismethods are given in the following.3.2. Wall and soil profiles studiedThe sheet pile walls can be either cantilever or anchored. Theselection of the wall type is based on the function of the wall, thecharacteristics of the foundation soils, and the proximity of thewallto existing structures [22]. While the cantilever walls are usuallyused forwall heights less than 3–4.5 m, anchoredwalls are requiredfor higherwalls orwhen the lateralwall deformations are needed tobe restricted.Three different wall heights (6, 9, and 12 m) were selected forthis study to include the size effect on the construction method.The behavior of single anchored sheet pile walls with heights upto 12 m has been studied by others [12] and higher walls usuallyrequire multiple level anchors. The numerical modeling and anal-yses were performed for these three wall heights for the soil profilecombinations considered using excavation and backfill construc-tion methods.Two different soil types were considered during this study;medium dense sand and loose sand. One-letter code designationsare used to refer to the soil types throughout the paper. Lettercodes ‘‘D” and ‘‘L” represent medium dense sand and loose sand,respectively. The properties selected, average of typical representa-tive ranges reported, for the two soil types are given in Table 1. Themodulus of elasticity, for example, is an average value selectedfrom the typical range given by Kulhawy and Mayne [23] and it is representative of secant moduli within common design stresslevels.The anchor level was fixed and it was 25% of the wall height be-low the top of wall in all cases. This anchor level was selectedbased on the results of a study performed by Bilgin and Erten[24] showing that the wall deformations are minimum when theanchor is installed at a depth of approximately 25% of the wallheight below the top of wall. Water elevation was assumed to beat the anchor level on both sides of the wall. A typical wall sectionused in the analyses is shown in Fig. 2.
For each wall height of 6, 9, and 12 m four different soil typeconfigurations were considered. Two of the cases involved thesame soil type throughout the site, i.e. both backfill and foundationsoils had the same soil type, either medium dense or loose sand.The other two cases consisted of different soil types for backfilland foundation soils. One case involved medium dense sand forbackfill soil with loose sand for foundation soil and the other caseinvolved loose backfill sand over medium dense sand foundationsoil. Each case analyzed was given a two-letter identification codeusing the soil types’ one-letter codes followed by a number indicat-ing the wall height in meters. The first letter in a two letter codeindicates the backfill soil and the second letter indicates the foun-dation soil. Therefore, the four cases analyzed for the 12 m wallwere DD12, LL12, DL12, and LD12. Case LD12, for example, refersto a case where the backfill soil is loose sand, foundation soil ismedium dense sand, and the wall height is 12 m.3.3. Conventional design calculationsThe 12 cases were designed by using conventional free earthsupport method to determine the wall penetration depth, the an-chor stiffness, and the steel sheet pile sections to be used in the fi-nite element model. The same wall penetration depths andsections were used for modeling both the excavation and backfillconstruction methods. Analyses were performed using a safety fac-tor applied to the passive pressures. The safety factor used in theconventional design methods usually ranges from 1.5 to 2.0. The calculations in this study were performed using a safety factor of1.5. The wall penetration depth, D (Fig. 2) calculated using the freeearth support method, depending on the foundation soil condi-tions, ranged from 2.47 m to 4.01 m for the 12-m-high walls, from1.85 m to 3.01 m for the 9-m-high walls, and from 1.23 m to2.00 m for the 6-m-high walls. The lower bounds of the penetra-tion depth ranges were for relatively denser foundation soil condi-tions while the upper bounds were for relatively loose soilconditions, as expected. Pile sections selected, based on the freeearth support method, were PZ27 for the 12-m- and 9-m-highwalls and PZ22 for the 6-m-high walls. The cross-sectional areaand moment of inertia were 136.9 cm2/m and 11,500 cm4/m,respectively, for PZ22 and 168.1 cm2/m and 25,200 cm4/m, respec-tively, for PZ27, with the elastic modulus of 200 GPa.3.4. Finite element analysisThe finite element modeling comprised two-dimensional planestrain analysis and analyses were carried out using PLAXIS [25].PLAXIS has been successfully used for the modeling and analysisof different types of retaining wall structures under varying load-ing conditions and the predicted performance of walls were veri-fied by field measurements. The PLAXIS finite element code hasbeen used to investigate the behavior of deep excavations [26–28], to study deep dynamic compaction induced deflections ofsheet pile walls [15,29], and to perform a study on soil–nailedwalls [30].When using a linear elastic soil in finite element analysis, thedepth of the model boundary below the dredge line has a linear ef-fect on the vertical movement of the ground surface at the top ofthe wall during construction simulation, but relatively very littleinfluence on the horizontal movement of the wall face [11]. In thisstudy, the depth of the numerical model boundary assumed to betwo times the wall height below the dredge line and the modelwidth was selected as eight times the wall height, with the wall lo-cated in the middle of the model width.Soil layers were modeled using 15-node triangular elements.The 15-node elements provide a fourth order interpolation for dis-placements and the numerical integration involves 12 stresspoints. The sheet pile wall was modeled by using five-node elasticplate elements. Interface elements had 10 nodes, five on the soilelements and five on the wall elements. A typical finite elementmodel mesh for excavation case consisted total of 1500 ± 30elements (1350 ± 25 soil elements, 51 ± 3 wall elements, and102 ± 6 interface elements). The total number of elements forbackfill cases was 1118 ± 27 (1006 ± 20 soil elements, 51 ± 3 wallelements, and 62 ± 6 interface elements). Due to a stress concen-tration in and around the wall, a finer finite element mesh wasused in these areas and mesh became coarser in the zones awayfrom the wall.An elastic–plastic model is used to describe the soil–structureinterface behavior and the interface strength, Rint, is given asRint ¼ tan dtan/0ð1Þwhere d = interface friction angle; and /0= soil friction angle. A ratioof the interface friction angle to soil friction angle, d//0, ranges from0.5 to 0.9 for the sand and steel interface [31].