SUMMARYThe paper deals with two essential and related closely processes involved in the finite element slope stability analysis in two-dimensional problems, i.e. computation of the factors of safety (FOS) and location of the critical slide surfaces. A so-called -inequality, sin 1 − 2 is proved for any elasto-plastic material satisfying Mohr-Coulomb's yield criterion. In order to obtain an FOS of high precision with less calculation and a proper distribution of plastic zones in the critical equilibrium state, it is stated that the Poisson's ratio should be adjusted according to the principle that the -inequality always holds as reducing the strength parameters c and . While locating the critical slide surface represented by the critical slide line (CSL) under the plane strain condition, an initial value problem of a system of ordinary differential equations defining the CSL is formulated. A robust numerical solution for the initial value problem based on the predictor-corrector method is given in conjunction with the necessary and sufficient condition ensuring the convergence of solution. A simple example, the kinematic solution of which is available, and a challenging example from a hydraulic project in construction are analysed to demonstrate the effectiveness of the proposed procedures.

Aiming to solve, in a unified way, continuous and discontinuous problems in geotechnical engineering, the numerical manifold method introduces two covers, namely, the mathematical cover and the physical cover. In order to reach the goal, some issues in the simulation of crack propagation have to be solved, among which are the four issues to be treated in this study: (1) to reduce the rank deficiency induced by high degree polynomials as local approximation, a new variational principle is formulated, which suppresses the gradient-dependent DOFs; (2) to evaluate the integrals with singularity of 1/r, a new numerical quadrature scheme is developed, which is simpler but more efficient than the existing Duffy transformation; (3) to analyze kinked cracks, a sign convention for argument in the polar system at the crack tip is specified, which leads to more accurate results in a simpler way than the existing mapping technique; and (4) to demonstrate the mesh independency of numerical manifold method in handling strong singularity, a mesh deployment scheme is advised, which can reproduce all singular locations of the crack with regard to the mesh. Corresponding to the four issues, typical examples are given to demonstrate the effectiveness of the proposed schemes. 987 patches of nodes on the displacement boundary to constants. Having reformulated NMM with more clarity, Lin [9] explored the merits and limitations of the method. Terada et al. [10] suggested calling NMM the finite cover method (FCM), who tested a number of elasticity problems by FCM and FEM respectively and concluded that the performance deterioration due to element distortion is less serious than that in FEM. Tian and Yagawa [11] developed 2D and 3D simplex elements and associated the physical patch with a so-called generalized node having physically meaning variables. In the simulation of soil consolidation, Zhang and Zhou [12] interpolated displacement and pore pressure independently, leading to a numerically stable scheme for the coupling problems, particularly in the nearly incompressible case.Since 1995, eleven international conferences on the NMM have been held, titled 'International Conference on Analysis of Discontinuous Deformation' and abbreviated as 'ICADD-n' with n as the conference number. ICADD-11 was just held in Fukuoka, Japan, during 27th-29th August, 2013.All developments and applications of NMM have been limited to the second order problems where the control partial DEs are second order; see Ma et al. [13] for details. Recently, Zheng et al. [14] constructed an NMM space of Hermitian form and applied it to the fourth order problems. Through the application to Kirchhoff's thin plate bending problems, they demonstrated that NMM is able to rescue those elements earliest developed in the finite element history, such as Zienkiewicz's plate element, and make them regain vigor.The major advantage of NMM is to solve in a unified way the problems involving continuous and discontinuous deformation. Wu and Wong [15], Kurumatani and Terada [16], a...

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