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Abstract A plastic-dissipation-based mesh adaptive algorithm is first introduced into the upper-bound finite-element method to determine the stability of axisymmetric problems using an equivalent plane strain model. The failure loads for two geotechnical examples were presented in the form of dimensionless stability numbers. The refined meshes and power dissipations were also plotted to highlight evolutional characteristics of failure mechanisms. Comparisons are given to verify the effectiveness of the mesh adaptive strategy. The advantage of the present method lies in the improved accuracy of the upper-bound solution and the ability to provide failure patterns with greater clarity. [ABSTRACT FROM AUTHOR]

Response surface methods are widely used in slope reliability analysis due to the high efficiency. However, they are often criticized of the curse of high dimensionality, problem-dependent accuracy, and mechanism-free interpretation. To address these issues, this study proposes a response surface-guided adaptive slope reliability analysis method for slopes in spatially varying soils. A sparse quadratic polynomial is initialized using a two-fold dimensionality reduction technique. The response surface-based preliminary slope reliability analysis is successfully corrected to an unbiased, finite element-based target slope reliability analysis, during which the response surface updates iteratively with an increasing high accuracy from special emphasis nearby the failure domain. Two spatially varying soil slopes are investigated. Results indicate that the proposed method can provide an efficient and unbiased estimation of finite element-based target slope failure probability with a low variability, develop a more accurate and problem-oriented response surface model for slope reliability analysis, and explore failure mechanisms of slope stability in spatially varying soils. Its performance is insensitive to the accuracy of initial response surface. Additionally, it prominently outperforms both response surface and finite element-based subset simulations, regardless of high-dimensional or low-failure-probability problems. These advantages significantly enhance the application of response surface on practical slope reliability analysis. [ABSTRACT FROM AUTHOR]

A lower bound (LB) axisymmetric limit analysis formulation is presented for Mohr-Coulomb materials using finite elements and semidefinite programming (SDP). The details of the application of SDP to the axisymmetric LB finite element method for Mohr-Coulomb materials are described in this paper. Through the use of the SDP, the axisymmetric Mohr-Coulomb yield criterion can be directly applied in its native form in terms of principal stresses without any smoothing of the parent yield surface, and no assumption needs to be made about σ θ. A node-stress-based adaptive mesh algorithm is also introduced into the proposed method to obtain an accurate high-accuracy LB solution. The proposed method is then applied to estimate the collapse load of circular footings and the stability of an unlined vertical circular excavation. The results are also compared with those reported in the literature; the results obtained from the proposed method are accurate and can provide failure patterns with greater clarity. [ABSTRACT FROM AUTHOR]