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Abstract This paper presents a new adaptive strategy to efficiently exploit velocity discontinuities in 3D finite-element-based upper bound limit analysis formulations. Based on an initial upper bound result, obtained with a conventional approach without velocity discontinuities, possible planes of plastic flow localisation are determined at each strain-rate evaluation node and, subsequently, this information is used to sequentially introduce discontinuities into the considered discretised structure. During a few iterations, by means of introducing new and adjusting existing discontinuities, an optimal velocity discontinuity layout is obtained. For the general 3D case, the geometry of this layout is defined by the well-known level set method, standardly used to define the geometry of cracks in the extended finite element method. To make this method also applicable for orthotropic strength behaviours, traction-based yield functions defining the plastic flow across discontinuities are derived from their stress-based counterparts. This procedure is outlined in detail and the obtained traction-based yield functions are verified numerically, to guarantee a consistent strength behaviour throughout the whole discretised structure. By means of three different examples, including isotropic as well as orthotropic yield functions, the performance of the proposed strategy is investigated and upper bound results as well as failure modes are compared to reference solutions. The proposed approach delivers reliable upper bounds for each example and the majority of plastic flow takes place across the sensibly-arranged discontinuities. For this reason, very good upper bounds can be obtained with a quite coarse finite element mesh and only few introduced velocity discontinuities. This represents an attractive alternative to commonly-used adaptive mesh refinement strategies, where often a huge number of degrees of freedom need to be added to capture localised failure. Highlights • Implementing velocity discontinuities into numerical upper bound formulations. • Developing an adaptive strategy to implement discontinuities in the optimal layout. • Using traction-based yield functions for strength behaviours across discontinuities. • Deriving a projection algorithm to guarantee consistent strength behaviours. [ABSTRACT FROM AUTHOR]

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]

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]

• We determine tunnel stability in soil with a soft upper layer and hard lower layer. • The effects of multiple soil layers and different soft soil parameters on an underground tunnel in China are studied. • We present the upper-bound finite element method with a mesh adaptive strategy. • Two main reasons for tunnel instability and large surface settlement are presented. • Two construction proposals are presented to ensure normal working conditions and safety of engineering. This paper presents a limit analysis of a tunnel in non-homogeneous soil using the upper-bound limit analysis in combination with finite element technology and a mesh adaptive strategy by investigating the critical loads and failure mechanisms of a tunnel cross-section and tunnel face. A case study of an underground tunnel in China is conducted, with a focus on the effects of multiple soil layers and different soft soil parameters. This work demonstrates that the variation in the soil layering plays an important role in the initiation of tunnel collapse, possibly shifting the failure region and even changing the failure mechanism. When the soil changes from a strongly weathered conglomerate to a soft soil, not increasing the low tunnel pressure quickly enough and using the wrong excavation mode are the two main reasons for tunnel instability and large surface settlement. [ABSTRACT FROM AUTHOR]