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This paper develops an efficient algorithm that combines polynomial-chaos kriging (PCK) and adaptive radial-based importance sampling (ARBIS) for reliability analysis. The key idea of ARBIS is to adaptively determine a sphere with the center at the origin and radius equal to the smallest distance of the failure domain to the origin, also known as the optimal β -sphere, and only those samples outside the optimal β -sphere have a possibility of failure and thus need to evaluate the limit-state function to judge their states (safe or failure). In the proposed algorithm, both the PCK model and β -sphere are updated adaptively. In each iteration of determining the optimal β -sphere, the PCK model is updated sequentially based on an active learning function, which is used to select the most informative sample from the samples between the last and current β -spheres. Once the stopping criterion is met, the learning process of PCK in this iteration terminates, and the obtained PCK model is then used to determine the next β -sphere. The updating iteration of the β -sphere proceeds until the optimal sphere is found. Five representative examples are revisited, in which the results demonstrate the high accuracy and efficiency of the proposed PCK-ARBIS algorithm. [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 kinematical approach of limit analysis has been historically employed to assess slope stability in the geotechnical community, for which most three-dimensional (3D) failure mechanisms are generally based on a composite of multiple common geometrical bodies. Although these failure mechanisms are straightforward, they may not perform well for slopes that involve multilayered soils with heterogeneous shear strength parameters. This paper aims at proposing a new 3D failure mechanism for steep slopes using a spatial discretization technique. The proposed failure mechanism is composed of a large number of elemental blocks that are generated point by point obeying the kinematically admissible velocity field and the normality condition. The discretization scheme makes it possible to simplify the calculations of internal energy dissipations and external work rates on the failure mechanism when both the soil properties and external loadings are spatially changing. The performance of the proposed method is illustrated to examine the stability of steep slopes in homogeneous soils, multilayer soils, and spatially variable soils, showing good agreements with previously published results and numerical modelings. [ABSTRACT FROM AUTHOR]

Geotechnical structures often have position-dependent soil strength parameters as a consequence of stress history, deposition process, mineralogical composition, and weathering effect. However, most available theoretical models for estimating active earth pressures focus only on homogeneous cases. By a point by point technique, this work develops a friction-angle-dependent discretized failure mechanism to evaluate the active earth pressure on backfills in the framework of the limit-equilibrium slice method. The generated failure mechanism is composed of a series of horizontal elements. Compared with previous theoretical models, the benefits of the proposed method are twofold: (1) the friction-angle-dependent failure mechanism agrees well with the actual failure surface for heterogeneous backfills; (2) not only the multilayer frictional backfill but also the backfill with a position-dependent friction angle can be accounted for. The total active earth pressure coefficient, the earth pressure distributions, and the failure mechanisms are obtained, all showing excellent agreement with the available experimental data and the existing analytical solutions. For practical use, applications to backfills with a weathered zone and spatially variable frictional angles are then conducted. Finally, the proposed model is degraded into a two-layer case in which the active earth pressure coefficients under various mechanical and geometrical parameters are tabulated. [ABSTRACT FROM AUTHOR]

• A blowout failure mechanism of elliptic tunnel faces is developed. • Blowout face pressure are sensitive to the shape of elliptical tunnel faces. • Spatially rotated anisotropy varying strength parameters are considered. • A case study is presented to demonstrate the practical use of the proposed model. Because of high space utilization, elliptical cross-section sometimes is adopted in the design of urban pedestrian underpasses, underground common ditches and subway tunnels. Nevertheless, theoretical models on the blowout failure analysis of shallow elliptical tunnel faces are quite rare. Within the framework of the kinematical approach of limit analysis, deterministic and probabilistic blowout analyses of a shallow elliptical tunnel in frictional-cohesive soils are performed in this study. With the help of the spatial discretization technique, an improved blowout failure mechanism for shallow elliptical tunnel faces is generated. Compared with previous analytical or semi-analytical ones, such an improved failure mechanism allows variable frictional angles of soils to be readily accounted for. The critical blowout face pressure is determined based on the work rate balance equation and a hybrid global optimization algorism. The deterministic model is validated by numerical simulations, existing experimental results and theoretical solutions, in which the effect of the geometrical parameter of elliptical tunnel faces and the less computational cost over numerical simulations are emphasized. Deterministic parametric analyses are conducted to investigate the influences of several significant parameters in the form of charts. Probabilistic blowout analyses of tunnel faces excavated in spatially rotated anisotropy varying soils are then conducted via a combination of the subset simulation, the random field theory and the Markov Chain Monte Carlo method, and the influence of characteristic parameters of the random field are examined. In the end, a case study is presented to demonstrate the practical use of the proposed model. [ABSTRACT FROM AUTHOR]

In this work, the stability of a reinforced tunnel face is examined by combining the homogenization method with the kinematic approach of limit analysis. A three-dimensional (3D) heterogeneous and anisotropic failure criterion for reinforced soils is first proposed according to the homogenization method, in which the possible tensile failure and pullout failure of reinforcing members are considered. The proposed homogenization method is then incorporated into the 3D rotational failure mechanism to assess the safety factor of a tunnel face by using the strength reduction technique. The applicability of the proposed method is illustrated by comparing with existing results and numerical simulations. The influences of model parameters on the calculated safety factors are finally discussed. [ABSTRACT FROM AUTHOR]

Seismic stability of slopes reinforced with soil nails has been traditionally investigated by two-dimensional limit equilibrium method. In this paper, the strength reduction method in combination with the kinematic approach of limit analysis is employed to assess the factor of safety (Fos) of slopes reinforced by soil nails using the three-dimensional rotational failure mechanism. The pseudo static approach is used to represent the seismic effects. Both the tensile failure and pull-out failure of soil nails are considered in the computations of internal energy dissipations. Comparisons are made to validate the proposed approach, which shows that the implemented approach is an efficient design tool for evaluating the factor of safety of slopes reinforced by soil nails. Parametric analysis is conducted to discuss the influence of model parameters, including nail length, nail density, soil shear strength and seismic forces, on slope stability. A set of stability charts is finally provided for fast assessments of slope safety. [ABSTRACT FROM AUTHOR]

The available theoretical models for evaluating seismic active earth pressures are limited to plane strain analyses and linear failure criterion. To fill this research gap, with a combination of the kinematical approach of limit analysis, the spatial discretization technique as well as the pseudo-static approach, this work develops a discretized three-dimensional failure mechanism of sloping backfills that is composed of an end cap and a central plane-strain insert to estimate the seismic active earth pressure coefficient under nonlinear failure criterion. Compared with the existing three-dimensional kinematically admissible failure mechanisms, the developed one has three significant merits: (1) the normality condition is strictly satisfied in the generation of the end cap; (2) the work rates can be computed by a summation of elementary work rates conveniently instead of tedious integral schemes; (3) the considerations of the nonlinear failure criterion and the sloping backfill. Comparisons with the existing upper bound solutions and experimental results in terms of active earth forces or active earth pressure coefficients are conducted to verify the proposed model. Parametric studies are performed to study the influences of model parameters, including the seismic coefficient, the sloping angle of backfills as well as the nonlinear parameters, on the active earth pressure coefficients. [ABSTRACT FROM AUTHOR]

This study aims to propose an effective approach to estimate the earthquake-induced displacements of a slope in heterogeneous soils considering the tensile strength cut-off. In the framework of the upper-bound limit analysis theory, an improved failure mechanism generated from the slope crest using the discretization technique is developed to determine the critical seismic acceleration coefficients with tensile strength cut-off. By using the Newmark's method, the earthquake-induced displacements of slopes are then estimated based on the proposed failure mechanism. The proposed method is validated by comparisons with experimental results and numerical modellings in terms of the predicted displacements and failure surfaces. Finally, the displacements induced by a real earthquake are presented for two heterogeneous slopes with considering tensile strength cut-off. [ABSTRACT FROM AUTHOR]

Slope stability analysis based on different stratigraphic boundary conditions may have significant differences in terms of factor of safety (FS) and the location of the critical slip surface. Therefore, traditional reliability analysis of layered slopes that assumes the stratigraphic boundary between two soil layers being a deterministic line or surface can be misleading. This study aims to investigate the influence of the stratigraphic boundary uncertainty (SBU) arising from limited site investigation data on slope stability analysis with the consideration of soil spatial variability. A modified one-dimensional conditional Markov chain model is proposed to model the SBU. Cholesky decomposition technique is subsequently utilized to simulate the inherent spatial variability of soil properties based on the simulated stratigraphic boundary within the framework of Monte Carlo simulation. A sample example on a two-layered soil slope with limited number of boreholes shows that the proposed method can well simulate the stratigraphic boundary based on limited borehole information. The statistics of FS and probability of failure are found not to increase or decrease monotonically with the number of boreholes, but can converge to the correct results if the number of boreholes increases. Moreover, the conventional reliability analysis with an implicit assumption of deterministic stratigraphic boundary condition can significantly overestimate the reliability of the slope, but this overestimation decreases with the increase in the scale of fluctuation. [ABSTRACT FROM AUTHOR]

Three-dimensional upper-bound analysis of rock slopes subjected to seepage flows is a classical problem in geotechnical engineering. However, it is difficult to obtain a rigorous upper-bound solution of the safety factor of slopes when seepage flows are involved. In order to address this problem, the three-dimensional (3D) hydraulic head distributions inside a slope under steady state hydraulic conditions are solved numerically. The obtained numerical hydraulic head distributions are further employed to compute the seepage forces applying to the 3D discretized rotational failure mechanism to assess the stability of a rock slope. The Hoek-Brown yield criterion is employed to characterize the failure of rock masses. The generalized tangential technique is employed to formulate the problem as a classical optimization problem. The particle swarm optimization algorithm combined with the Nelder-Mead simplex algorithm is used to search for the best solutions of slope safety factor. The proposed approach is validated by comparing with 2D plane strain analysis results in the literature. Parametric analysis shows that the safety factor increases as m i or GSI increases, but decreases with the increase of the slope angle β and B / H. It is also found that the 3D influence is significant for B / H smaller than 10, beyond which it becomes negligible. The computational results in the form of design tables are presented for practical use in rock engineering. [ABSTRACT FROM AUTHOR]

The existing analytical models for predicting earth pressures based on the kinematical approach of limit analysis are limited to soil masses with homogeneous internal frictional angles. To overcome this drawback, this work proposes a discretised failure mechanism to calculate the location of earth forces and evaluate the active and passive earth pressures against inclined retaining walls with horizontal backfills for the first time. Comparisons with other existing analytical solutions, numerical simulations and experimental tests are made to verify the proposed method for the cases of single-layer and multi-layer backfills. Practical design tables are presented for a two-layer case. Application of the proposed model to three-layer backfills with a middle weak layer is presented. The influence of the position of the weak layer on the critical earth pressures and failure mechanisms is discussed. [ABSTRACT FROM AUTHOR]