Kinematical analysis of 3D passive earth pressure with nonlinear yield criterion

Summary Analyses of three‐dimensional slope failures can be elaborate because of the complexity owed to the geometry of the failure mechanism that needs to conform to an admissible kinematics of the slope collapse. This admissibility is imposed by the soil limit state condition, the normality plastic flow rule, and the boundary conditions. The kinematic approach of limit analysis is employed, and a rotational 3D slope failure is revisited. The study leads to the conclusion that some geometric constraints used in previous studies limit the range of admissible mechanisms resulting in overestimating stability factors. A set of results is presented that was obtained using an algorithm that allowed eliminating limitations present in previous studies. The largest improvements in the solutions were found for undrained failures of narrow slopes. For a 30° slope limited in width by the width‐to‐height ratio of 0.6, the stability factor calculated in previous studies overestimated the current calculations by nearly 39%. This overestimation is smaller for drained failures, and it drops significantly with an increase in the width of the failure mechanism.

Section: Rotational 3d Failure Mechanismmentioning

confidence: 99%

Section: Curvilinear Cone Failure Surfacementioning

confidence: 99%

Intricacies in three‐dimensional limit analysis of earth slopes

Park

Michałowski²

2018

“…The kinematic limit‐analysis approach is employed to obtain the solution, which has been proved to be an effective method in addressing geotechnical stability problems. The kinematic approach indicates that for an arbitrary valid collapse mechanism, the internal dissipated rate does not exceed the external work rate.…”

Section: Methodsmentioning

confidence: 99%

Three‐dimensional active earth pressure from cohesive backfills with tensile strength cutoff

Yang

2020

Self Cite

Summary Most of previous analyses on the active earth pressure were performed in two‐dimensional cases using the Mohr‐Coulomb (M‐C) failure function to describe the soil strength. However, all failures of retained slopes indicate a somewhat three‐dimensional (3D) feature, and the M‐C function is found to overestimate the tensile strength of cohesive soil. In this work, a kinematic limit analysis–based approach is developed for computing the 3D active earth pressure resulting from cohesive backfills. The concept of tensile strength cutoff is adopted to implement the reduction or elimination of tensile strength from the strength envelope. An extended 3D horn failure mechanism that is associated with the modified strength envelope is developed to characterize the collapse of retained slopes. The resultant of active earth pressure is evaluated from the work rate balance equation and expressed as an unfactored coefficient. The obtained results indicate that less support provided by the wall is required when allowing the existence of soil cohesion and 3D effects and that eliminating the tensile strength can observably increase the active earth pressure, especially for the backfill with a great level of cohesion.

“…Compared with the limit equilibrium method, a much more rigorous method for assessing the stability of geostructures became available with the advent of the limit theorems of classical plasticity in the 1950s . Thus, the upper bound theorem‐based kinematic approach has been widely applied to investigate the stability of saturated and/or dry soil slopes . However, because it is difficult to construct 3D admissible failure mechanisms in frictional/cohesive soils, the limit analysis method has not been applied to assess the stability of unsaturated soil slopes with tension cracks under 3D condition.…”

Section: Introductionmentioning

confidence: 99%

“…37 Thus, the upper bound theorem-based kinematic approach has been widely applied to investigate the stability of saturated and/or dry soil slopes. 11,[38][39][40][41][42] However, because it is difficult to construct 3D admissible failure mechanisms in frictional/cohesive soils, the limit analysis method has not been applied to assess the stability of unsaturated soil slopes with tension cracks under 3D condition.…”

Section: Introductionmentioning

confidence: 99%

3D stability of unsaturated soil slopes with tension cracks under steady infiltrations

Wang

et al. 2019

Summary Most classical approaches for evaluating the stability of soil slopes with cracks are performed under two‐dimensional (2D) condition. Three‐dimensional (3D) effect and suction‐induced effect of unsaturated soils are generally neglected in assessing the slope stability. This paper develops a 3D limit analysis method to evaluate the stability of an unsaturated soil slope with tension cracks under steady infiltrations. The boundary‐value problem is formulated based on the 3D rotational failure mechanism by taking the effects of suction, effective unit weight, and tension crack into account. A simplified method is proposed to calculate the work rate of unsaturated soil weight. A layer‐wise summation method is developed based on the divergence theorem to calculate the internal energy dissipation rate. Detailed discussions are conducted to investigate the effects of suction and Poisson's ratio on the stability of unsaturated soil slopes. Examples are given to illustrate the 3D effect, the suction‐induced effect as well as the effects of infiltration and water in cracks on the slope stability.