Limit Analysis of Modified Pseudodynamic Lateral Earth Pressure in Anisotropic Frictional Medium Using Finite-Element and Second-Order Cone Programming

Lower bound analysis of modified pseudo‐dynamic lateral earth pressures for retaining wall‐backfill system with depth‐varying damping using FEM‐Second order cone programming

“…In fact, as the potential failure zone systematically changes during seismic loading and is very complicated to be assumed prior to analysis, utilizing such a method to accurately predict the most possible failure surface seems to be essential. 43 Another advantage of the limit analysis method adopted in this study is its considerably higher computational speed as well as its greater efficacy to deal with complex geometries and nonconventional problems compared to the limit equilibrium technique. The complete privileges of the FELA approach over other methods have been summarized by Sloan.…”

“…46 Apart from the advantages of the FELA, as opposed to the other methods, the application of the adopted FELA to model the stability of geo-structures has been extensively validated in many previous studies implementing innovative efforts to model a variety of soil conditions. 20,21,38,43,[46][47][48][49][50][51][52][53][54][55][56] It should be noted that considering the associated flow rule and assuming dilation angle to be equal with the internal friction angle do have influence on the estimated lateral earth pressures. [60][61][62][63] Indeed, the active and passive lateral earth pressures would be slightly greater and smaller, respectively, than those estimated in the current FELA simulations depending on the value of the adopted dilation angle.…”

“…Apart from the abovementioned discussion, FELA have been commonly performed throughout the literature using the failure criterion following the associated flow rule. 20,21,38,43,[46][47][48][49][50][51][52][53][54][55][56][57]59 In particular, there exists no specific and efficient approach in the literature to account for the non-associated flow rule in the lower bound formulations. The non-associated flow rule should be implemented in the induced plastic strains; while the lower bound theorem does not take the induced strains into account and deals mainly with the stresses mobilized in the soil medium.…”

“…57,65 In order to obtain the stress field (σ x , σ y and τ xy ) within the backfill as the primary unknowns of the corresponding lower bound limit analysis problem, a number of constraints must be satisfied element-wise. 20,21,38,43,[46][47][48][49][50][51][52][53][54][55][56][57] For the element equilibrium constraint, all acting forces on the failure wedge must be in equilibrium resulting in particular constraints at nodal points. Accordingly, the stresses through each element must be in equilibrium, adopting the right-handed Cartesian coordinate system, with the acting stresses, including soil unit weight and earthquake loading, as:…”

“…The method was extensively employed by several researchers in subsequent studies. [33][34][35][36][37][38][39][40][41][42][43] A current limitation of the conventional pseudo-dynamic method is that it does not consider the effect of soil damping and the traction-free surface condition. Furthermore, in all the previous modified pseudo-dynamic analyses, the damping ratio of the soil deposit has been deemed to be constant with depth, which is discernibly incompatible with the fundamental compression implications and laboratory/field test results.…”