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Soft bands may widely exist in sites, and their presence complicates the analysis of slope stability, particularly when the limit analysis method is adopted. Note that the use of the limit analysis method is capable of providing rigorous lower and upper bound solutions and hence is widely used in soil slope stability analyses. To account for soft band effects, finite-element lower-bound (FELB) and finite-element upper-bound (FEUB) approaches are introduced in this study. Finite element discretization aids in the construction of a statically allowable stress field and kinematically admissible velocity field, which are prerequisites for limit analysis. In combination with a modified pseudodynamic approach, seismic slope stability analysis is evaluated through linear programming. Lower and upper bound solutions of the slope safety factor (FoS) are optimized with an interior point algorithm, which aids in better estimating the true FoS of seismic slope stability. The nonassociated flow rule is also discussed herein. After validating the upper and lower linear programming models by limit equilibrium and FEM, the soft band's effects on seismic slope stability are discussed, and a rotational-translational failure mechanism is revealed by critical velocity fields. A less than 5.1% difference between lower- and upper-bound solutions is favourable for providing a reliable reference for slope design. [ABSTRACT FROM AUTHOR]

A lower bound limit analysis approach based on the block element method is proposed to analyze wedge stability problem. The search for the maximum value of the factor of safety is set up as a nonlinear programming problem. Sequential quadratic programming (SQP) algorithm from a reasonable initial value is applied to obtain the optimal solution. This approach provides a strict lower bound solution considering the sliding mode and rotation effect simultaneously. The deviations of the factor of safety between the present and traditional limit equilibrium methods are positively correlated with both the friction angle and the dip of the discontinuity surface. [ABSTRACT FROM AUTHOR]

A rigid block based lower bound limit analysis method for analyzing stability of fractured rock mass in 2D and 3D conditions is proposed. The rock bridge effects are considered in the general formation. No assumptions are imposed on the inter-element forces, and the solution obtained is statically admissible. The proposed method is theoretically rigorous and simple. The validation and efficiency of the proposed method have been demonstrated through three typical types of slopes, indicating that apart from the fractures, rock bridge plays a key role in stabilizing rock blocks, which should be greatly concerned in stability analysis of rock mass. [ABSTRACT FROM AUTHOR]

A finite-element upper-bound procedure is presented to assess the stability of a soil slope under reservoir drawdown and rainfall conditions. In order to overcome the scientific challenge of generating a kinematically admissible velocity field, discretizing the problem of interest into finite elements is carried out for this specific purpose, and based on which the upper bound formulation of slope safety factor is derived. The slope stability analysis is transformed to the optimization of a linear programming model under four constraint conditions, by virtue of an interior-point algorithm. Steady-state and transient water flows are discussed. Based on the soil–water characteristic curve (SWCC), matric suction above the phreatic surface is considered so as to provide a reliable assessment for unsaturated slope stability. True cohesion of soils and apparent cohesion stemmed from matric suction are combined to describe the shear strength of unsaturated soils. After validating the robustness of the proposed procedure by limit equilibrium and FEM, it is further applied to evaluate the slope stability under (rapid, general, slow) reservoir drawdown and rainfall conditions. [ABSTRACT FROM AUTHOR]

The present study presents a novel procedure to assess the seismic slope stability, using the finite-element upper-bound method combined with the pseudo-dynamic approach. A pioneering work is performed to incorporate the pseudo-dynamic accelerations into the finite-element upper-bound analysis which combines the advantages of upper bound and finite element methods. The finite element method is principally used to discretize the domain of soil mass into finite elements, aiming to construct a kinematically admissible failure mechanism based on which the external and internal rates of work can be expressed. Based on the upper bound theorem, the upper bound formulations are derived from the virtual work rate equation, in the form of slope safety factor and limit surcharge acting on the slope crest. The problem of seeking the optimal upper bound solution is transformed to solve a linear programming problem within numerous kinematically admissible velocity fields, and this is achieved by using the interior-point algorithm implemented into the MATLAB. Pseudo-dynamic solutions are calculated and compared with the pseudo-static, limit equilibrium and FLAC results. The proposed procedure is versatile in considering the homogeneity and non-homogeneity of soil strength properties in seismic slope stability analysis. A benchmark problem with 0.5 m thick weak interlayer is discussed. [ABSTRACT FROM AUTHOR]