Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures 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

“…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:…”

“…Eventually, all these constraints are then assembled into the { } ≤ [ ]{ ; } ≤ { } form to acquire the stress field behind the wall as the target objective functions. 43,[53][54][55][56]58,67 This is achieved by the second-order cone optimization 75 employing the primal-dual interior-point algorithm. 76 It is worth noting that the implementation of the primal-dual interior-point algorithm for solving second-order cone optimization is based on a homogeneous and self-dual model, which handles rotated quadratic cones directly, and employs a Mehrotra type predictor-corrector extension and sparse linear algebra to improve the computational efficiency.…”

“…76 Accordingly, adopting the objective function as the horizontal stresses acting alongside the retaining wall, the active state of the stress field is obtained by maximizing the equation ( { ; }) in order to find the maximum pressure which is required to maintain the backfill against failure; while the passive state is evaluated by minimizing it ( { ; }) in order to find the minimum pressure which causes the backfill failure. 43,55,56…”