With the fast and inexpensive personal computers of today, numerical methods have become more popular in engineering science. More frequently, numerical methods used in continuum and discontinuum analysis are the finite element and finite difference methods. On the other hand, slope stability analysis is usually performed by the limit equilibrium method. In this latter approach, several important parameters cannot be dealt with, such as stress history, non-linear behavior, non-homogeneity and anisotropy of the soil outside the sliding wedge. The CA2 (Continuum Analysis, 2-dimensional) computer program is capable of solving slope stability problems, using explicit finite difference method combined with the limit equilibrium concepts. In this paper, the results of continuum numerical analyses are compared with those of limit equilibrium methods and the importance of several parameters involved is described.

In this paper, a novel numerical approach is proposed for determination of a lower bound solution for the bearing capacity of strip footings. In this method, the geometry of problem is constructed by nodes and, there is no need for mesh in the traditional sense. The gradient of stress is smoothed piecemeal by the aid of the stabilized nodal integration technique and, the equilibrium and boundary conditions are fully satisfied at the entire domain consequently. The stress field is discretized by a mesh-free technique called Shepard's method. Due to the individual properties of Shepard's shape functions, the non-yielding condition is just controlled at the nodes. Putting the objective function and the related constraints together forms a mathematical optimization problem which is solved by a linear programming technique. At the end, the accuracy and efficiency of the proposed method is investigated by solving some examples for the cohesive soils with uniform and depth dependent shear strength, and the cohesive-frictional soil.

In this research, engineering geological characteristics of the Haji-Abad tunnel site in Hormozgan province have been assessed and its stability analysis is carried out using experimental and limit equilibrium methods. The tunnel site was divided into ten geotechnical units including T1–T8 and two crushed zones in Units 5 (Tf1) and 9 (Tf2) using the BGD method. The rock discontinuities in the tunnel site have filled by calcite and clay, with dry to wet surface conditions, and low degree of weathering. The internal friction angle of the discontinuities surfaces ranges 15º–45º, their persistence is from about 3 to more than 20m, their spacing is 0.15–4m, and their opening is 0.1–5mm. The compressive strength of the site rocks, except for the two crushed zones that have different conditions, varies 20–120MPa. The moisture content of the samples obtained from the boreholes of the tunnel site were 0.12–2.87%, and their porosity were 7.33–0.32%, respectively. The tunnel site rocks are placed in the very poor to good classes with RQD values from 25 to 90. According to the RMR classification, the rocks in the tunnel site have a score of 18–62 (very poor to good). Also, by using the Q method, the rocks of different unites of the tunnel site were given a score rang of 0.04–2.83 (extremely weak to weak). The GSI method indicated that the site constructing rocks range is 15–61 (very poor to good). By using Unwedge.v.3.0 software, the maximum and minimum weight values of the formed wedges were obtained 5875 and 0.076 tons, with heights of 100.94 and 0.12m, respectively. Also, the safety factor is 0.04–112 and the wedges that had a safety factor less than 1.5 will be reached an acceptable safety factor by installing rockbolt.

Slope stability analysis is used in a wide variety of geotechnical engineering problems such as embankments, road cuts, open-pit mining, excavations, canals, landfills, etc. The limit equilibrium method is the most popular approach in slope stability analyses. In this study, a new limit equilibrium method is proposed that can satisfy the forces and moment without any assumptions. In this method, circular or non-circular slip surface has been considered and slices are intended along the radius of the slip surface. Innovation of this research is in the form of slices in circle sector which could eliminate the common simplifying assumptions in the equilibrium equations. The forces and moment equilibrium equations have been applied without any simplifying assumptions and expected that this method can achieve lower error in determining the safety factor. In order to calculate the safety factor using the proposed method, a numerical model has been developed. In this model, the soil slope characteristics such as slope geometry, soil strength properties, seismic coefficient and also water level are considered as input. Then sliding wedge is introduced and on the basis of number of divisions that the user defines, sliding wedge is discretized. In the next step, the coordinates of each node of these slices are determined. To compute the safety factor, a process should be taken that satisfies the force and moment equilibrium equations simultaneously. To achieve this goal, the iterative method (trial and error) is used in this study. In order to evaluate the proposed method and the efficiency of the developed model, several tests with different conditions are solved. The mentioned test results are in good agreement with the results of other methods that satisfy all of the equilibrium equations.

Traditional limit-equilibrium techniques are the most commonly-used analysis methods for slope stability problems. Recently, finite element method has emerged as an efficient and viable tool for analyzing various geotechnical problems. The Strength Reduction Technique (SRT) technique enables the FEM to calculate factors of safety for slopes. Despite the SRT‟ many obvious benefits, it has not yet received widespread acceptability among geotechnical engineers for routine slope stability analysis. To help change this situation this paper will compare the method‟ performance to those of the most widely used limit-equilibrium methods on a broad range of slope stability problems.

Probabilistic slope stability analysis provides a tool for considering uncertainty of the soil parameters in design. In this paper, using Slide software, the Monte Carlo simulation is used as an analytical method to develop probabilistic models of slope stability based on equilibrium methods. The limit equilibrium methods are the most popular approaches in slope stability analysis. These methods are well known to be a statically indeterminate problem, and assumptions on the inter-slice shear forces are required to render the problem statically determinate. In modeling using this methodology, the selected stochastic parameters are internal friction angle, cohesion and unit weight of soil, which are modeled using a truncated normal probability density function (pdf). In this research, the abilities offered using models were presented by using field data obtained from Cannon dam in Iran. The results obtained show that the hybrid Monte Carlo simulation and equilibrium methods can be used successfully for slopes stability assessment.

Controlling the stability of weighted concrete dams is one of the most important things in analysis and design. So far, various methods have been presented to check the stability of weighted concrete dams, among which the most important and widely used methods can be mentioned limit equilibrium and finite element methods. In this study, the stability of weighted concrete dams with different heights was investigated using the limit equilibrium method and the 2D and 3D finite element method for five earthquake spectrums. The differences in the results of the above two methods were compared in obtaining some parameters, including the amount of slip, modulus of elasticity and stress distribution of the dam bottom. The sliding of the dam on the foundation was not significant for all the range of earthquakes up to the maximum acceleration of 0.2 g, and for higher maximum accelerations, more slips occur depending on the nature of the earthquakes. In the limit equilibrium method, the displacement of the dam crest relative to the foundation floor is the same for five earthquakes, while in the finite element method, the landslides have different trends for all five earthquakes.