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This paper presents an analytical framework for predicting three-dimensional (3D) seismic active earth pressures for soils governed by a nonlinear strength criterion. The kinematic limit analysis method that incorporates a pseudodynamic approach is used to carry out the analysis. A generalized tangential technique is adopted to realize transition of the nonlinear criterion into the commonly used linear form. A 3D failure mechanism of rigid rotation is employed. Because the use of the modified pseudodynamic approach leads to a variation of seismic forces along the depth, the work rate due to earthquake effects is calculated by using a horizontal layer–wise summation method. By virtue of the balance equation of work and energy, the thrust of active earth pressures is determined, and the final solutions are expressed as dimensionless active earth pressure coefficients. A comparison between the solutions obtained in this paper and those of the existing studies shows the effectiveness of the developed method. A parametric analysis is carried out to investigate the influences of several parameters. The findings of this work can help understand the service behavior of retaining structures subjected to seismic loadings, which could provide references for designs. [ABSTRACT FROM AUTHOR]

The prediction of active earth pressure was generally implemented under the assumptions of two-dimensional conditions and cohesionless soils. However, in practice, the soils usually display a considerable level of cohesion, and the collapse of retained slopes exhibits a three-dimensional (3D) nature. Considering this fact, this paper intends to predict the 3D active earth pressure in cohesive soils based on the kinematic limit-analysis method and a 3D rotational collapse mechanism. The influence of cracks is considered, including a crack forming before the failure of retained soil masses (open crack) and a crack forming simultaneously with the failure (formation crack). The active earth pressure coefficient is estimated based on the work-energy balance principle. In order to facilitate direct application, several design charts are provided. It is shown that accounting for soil cohesion and 3D effects results in a notable decrease in the active earth pressure, whereas considering the existence of cracks would increase the pressure value. This paper develops the studies on active earth pressure, which considers the presence of cohesion, cracks, and 3D effects together for the first time. The results of this paper can offer references in designs of retaining structures for cohesive slopes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The calculation of active earth pressure has commonly been performed under dry or saturated conditions. However, in practice soils are usually unsaturated. With the aim of estimating active earth pressure under steady unsaturated flow conditions, this paper describes a new method within the framework of the kinematic approach of limit analysis. A closed-form formula is adopted to estimate the suction stress of unsaturated soils subjected to vertical steady flow. A rotational failure mechanism composed of a log-spiral curve and a vertical crack is presented for calculations of the external work rate and internal energy dissipation rate. Pre-existing cracks as well as cracks that form as part of the failure mechanism are considered in the present work. The maximum depth of cracks is determined by requiring the vertical crack boundary to be stable. Explicit expressions about the thrust of active earth pressure for different crack types are derived from the work–energy balance equation, and the most critical solutions are obtained by optimizing the variables from the failure mechanism. Numerical results for different parameters are calculated and given in the form of graphs for practical use. A parametric study is performed to investigate the impact of different parameters on the active earth pressure. [ABSTRACT FROM AUTHOR]

This paper adopts a three-dimensional (3D) rotational failure mechanism to calculate the static and seismic active earth pressure acting on rigid retaining walls within the framework of the kinematic approach of limit analysis. The failure mechanism can be generated through rotating a varying circle defined by two log-spirals, and a plane strain block is inserted into the mechanism for consideration of retaining walls with different widths. Quasi-static representation using the seismic coefficient concept is applied to consider horizontal earthquake effects for the seismic active earth pressure calculation. Two cases with the different points of action of resultant earth pressure are included in this study. In the realm of soil plasticity, the new expressions about 3D active earth pressure are educed from the work-energy balance equation. The critical solution is obtained from an optimization scheme where the maximum of active earth pressure is obtained. Numerical results for different parameters are calculated and presented in the forms of graphs and tables, which may serve as a useful tool for practical application. Compared with existing 2D and 3D solutions, the validity of the proposed method is shown. A parametric study is conducted to investigate the effects of different parameters on the static and seismic active earth pressure under 3D conditions. [ABSTRACT FROM AUTHOR]

This work presents a probabilistic analysis of three-dimensional (3D) seismic active earth pressures acting on rigid retaining walls that are designed to support cohesive-frictional soil masses. The analysis is implemented using sparse polynomial chaos expansions (SPCE) to represent the physical model responses. The deterministic evaluation of 3D seismic active earth pressures is conducted with the application of the kinematic approach of limit analysis combined with a pseudo-static method. All of the input parameters are deemed as random variables. After the SPCE metamodels are determined, the method of Monte Carle simulations is applied to perform the probabilistic analysis of 3D seismic active earth pressures. The effects of uncertainty levels and correlation relationships of input parameters are investigated. Several illustrative examples of the reliability-based design of retaining walls are shown. Results indicate that uncertainties in input parameters possess a notable effect on 3D seismic active earth pressures, suggesting the need to investigate the problem from a stochastic perspective. In most cases, the soil cohesion, internal friction angle, and seismic coefficient are found to be three of the parameters that affect the final response the most significantly. It is also indicated that considering 3D effects and soil cohesion has a favorable effect on increasing the stability of retained slopes. [ABSTRACT FROM AUTHOR]

The active earth pressure evaluation was typically conducted assuming dry backfills and/or two-dimensional collapse mechanisms. In practice, retained slope collapse usually shows a three-dimensional (3D) feature and soils are usually unsaturated. The present work develops a framework for evaluating the 3D active earth pressure under transient unsaturated flow conditions. The framework is implemented by using the kinematic approach of limit analysis, in conjunction with a closed-form solution for the transient unsaturated flow. Based on a 3D horn-like failure mechanism, the active earth pressure coefficient is determined. Results for three hypothetical soils of fine sand, silt, and clay are calculated. It emerges that the inclusion of 3D effects and unsaturated transient flow leads to a smaller active earth pressure coefficient. The 3D effects are mainly influenced by the width-to-height ratio of walls; several certain cases analyzed in this paper show that the difference in the active earth pressure coefficient with and without considering 3D effects can be as much as about 27% when the width-to-height ratio equates to 2, whereas this difference decreases to about 10% and 5% when the ratio reaches to 5 and 10. The contribution of transient flow is mainly affected by the soil types; considering the unsaturated flow effect in clay can approximately reduce the active earth pressure of 67%, whereas this difference corresponds to 34% and 22% in silt and fine sand. The obtained results can help to quantitatively understand changes in the active earth pressure due to 3D effects and the presence of transient infiltration. [ABSTRACT FROM AUTHOR]