A Study on the Static and Seismic Earth Pressure Problems in Anisotropic Granular Media

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:…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] Within the framework of the so-called pseudo-static method, seminally proposed by Okabe 15 and Mononobe and Matsuo, 16 the constant uniform horizontal and vertical loads are assumed to be applied on the failure wedge. [17][18][19][20][21] This method was updated by Steedman and Zeng 22 during their phase studies on the evaluation of the pseudo-static lateral earth pressure for the linear elastic backfill. Significantly extended by Choudhury and Nimbalkar, [23][24][25] the methodology was then implemented in several later studies for the seismic stability analysis of…”

Lower bound limit analysis for an axisymmetric problem in rock mass using power cone programming

“…On the other hand, for rock media, the generalized Hoek and Brown (GHB) yield criterion has been found to be the most acceptable 3–5 . Various plane strain and three‐dimensional stability problems involving foundations, 6–10 anchors, 11,12 tunnels, 13–15 retaining walls, 16 trapdoors, 17 slopes, 18,19 suction caissons 20,21 have been analyzed on the basis of the MC yield criterion with the applications of both the LB and the UB FELA techniques. The axisymmetric problems can either be solved by using a three‐dimensional approach involving three‐dimensional elements or by performing a two‐dimensional analysis with the usage of planar elements.…”