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The average of thisrange, d//0= 0.7, was selected for this study and the interfacestrength values, calculated based on the ratio of 0.7 and the soilinterface friction angle, used for the two soil types are given inTable 1.The anchor was modeled as a one-node elastic spring elementwith a constant spring stiffness and the other end of the spring (de-fined by the equivalent length and direction) is fixed. The anchorstiffness calculated for each case was based on the anchor force obtained from the conventional design results, the cross-sectionalarea required, and the length needed to place the anchor block out-side the active and passive failure wedges behind the wall.The construction method was simulated by removing soil inlifts for excavation cases and adding soil in lifts for backfill cases.The total soil depth removed or height added was performed ineight steps, i.e. the thickness of the soil lifts was equal to one-eightof the total wall height. This resulted in 0.75, 1.125, and 1.50 m-thick soil lifts for 6, 9, and 12-m-high walls, respectively. For theexcavation cases, the anchor was installed when the excavationreached the anchor level, i.e. after 25% of the excavation was com-pleted. Similarly, the anchor was installed when 25% of the fillheight was placed behind the wall for the backfill cases. Becauseof cohesionless soils, analyses were performed considering fullydrained conditions.The Mohr–Coulomb constitutive model for soils has been com-monly used in finite element modeling of retaining wall behavior[3,7,9,13–15,24,25,29,30,32]. There are more sophisticated consti-tutivemodels available in PLAXIS and used by researchers tomodelcomplex soil behavior, i.e. soft-soil-creep model for peat [15,29]and hardening-soil model for clay [28,33]. The hardening-soilmodel uses secant modulus and unloading/reloading modulus tobetter model the soil behavior. The unloading modulus is approx-imately three times more than the loading modulus. The Mohr–Coulomb model behaves stiffer than the hardening-soil model[13]. The Mohr–Coulomb model has been successfully used forgranular soils and therefore was also employed in this study tomodel the stress–strain behavior of sands. The Mohr–Coulombmodel is a linearly elastic and perfectly plastic constitutive model.The parameters needed for the Mohr–Coulomb model are theYoung’s modulus, E, and Poisson’s ratio, m, for the elastic straincomponent of the soil behavior.
The effective strength parameterscohesion, c0, and friction angle, /0, as well as the dilatancy angle, w,are needed for the plastic strain component of the soil behavior.The properties selected for the two soil types are given in Table 1.To look at the effect of constitutive model, DD12 and LL12 caseswere also analyzed using the hardening-soil model. The resultsshowed some differences in the results (2–35% depending on thecase, construction method, and behavior investigated) comparedto the results obtained from the Mohr–Coulomb model. However,the results obtained from the hardening-soil model furtherstrengthens the conclusions drawn from this study regarding thewall behavior constructed in cut and fill conditions. The results ob-tained from the Mohr–Coulomb soil model are presented in thispaper.4. Results and analysisLateral earth pressures, wall deformations, wall bending mo-ments, and anchor forces were investigated for the 12 cases usedin the parametric study. The results of four cases are presentedin more details to evaluate the effect of soil type and wall heighteffects on the behavior of anchor walls constructed by excavationand backfilling. The four cases selected were DD12, DL12, DD6,and DL6. DD12 was selected because of the stronger and uniformsoil profile. DL12 case was selected because it was the weakestcase, with dense/heavy backfill soil over loose/weak foundationsoils. Comparisons of DD and DL cases provide information onthe effect of foundation soil strength. DD6 and DL6 cases were se-lected to investigate the effect of wall height.The numerical modeling and analyses of each case were basedon the design performed using the free earth support method.Therefore, the finite element results (i.e., earth pressures, walldeformations, bending moments, and anchor forces) presentedhere correspond to a stress state lower than the ultimate limit state. The results presented especially for the early constructionstages correspond to a stress state much lower than the ultimatelimit state.4.1. Lateral earth pressuresLateral earth pressures behind and in front of the 12-m-highwalls for DD12 and DL12 cases are shown in Fig. 3. Fig. 4 showsthe lateral earth pressures of the 6-m-high walls for DD6 andDL6 cases. The 12-m-high walls have higher lateral earth pressuresacting on the walls than the 6-m-walls, as expected.The analysis results show that lateral earth pressures in theback and front sides of the wall have similar trends in excavationand backfill methods. The stress concentration around the anchorlevel is present in all cases for both construction methods. Theexcavation cases result in higher active earth pressures above theanchor level. Both construction methods result in very comparablepassive earth pressure magnitudes and changes along the depth ofwall penetration.Fig. 5a shows the comparison of lateral earth loads, both activeand passive, of excavation and backfill methods for all 12 casesanalyzed. The ‘‘ ”in Fig. 5 and in other figures is used to representboth soil types. In all 12 cases, the lateral earth forces obtained be-hind the wall, i.e. active force, for both methods were in close prox-imity. The walls constructed by backfill method on densefoundation soil, i.e. DD and LD cases, resulted in 6% less activeloads, on average, compared to the walls constructed by excavationmethod on same soil conditions. On the other hand, when loosefoundation soils are present, i.e. DL and LL cases, the walls con-structed by backfill method resulted in 3% more active loads, onaverage, compared to the walls constructed by excavation method.The lateral earth forces in front of the wall, i.e. passive forces, werein better agreement, with the backfill method resulting in 4% morewhen the foundation soils are stronger and 3% less when the foun-dation soils are weaker compared to excavation cases.When all the12 cases are compared, the lateral earth pressures, on average,were almost equal in both excavation and backfill methods.The effect of construction method is more significant when thelocations of the resultant of lateral earth loads are considered.Fig. 5b shows the comparison of the active and passive lateral earthload application elevations for all the cases analyzed. Although the location of the resultant of the passive earth force shows a maxi-mum of 3% difference between the excavation and backfill cases,the location of the active earth load can vary as much as almost20%, with an average of 15%, when the medium dense foundation -,tnsoils are present, i.e. DD and LD cases. In these cases the locationof the resultant active force in backfill cases is at lower elevationsrelative to the excavation cases and it is independent of the wallheight. When loose soils exist at the foundation level, i.e. DL andLL cases, the location of the resultant active force in backfill casesis usually at higher elevations compared to excavation cases. Asthe wall height increases the difference becomes smaller and thelocation of the resultant active force in backfill cases may be atlower elevations compared to excavation cases.4.2. Wall displacementsLateral displacement of the 12 m and 6 m walls during the con-struction stages of excavation and backfilling are shown in Figs. 6and 7, respectively.