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SUMMARY A closed-form solution (CFS) satisfying both equilibrium of moments and forces for the stability analysis of earth slopes in 2D is proposed. The sliding surface is assumed circular and treated as a rigid body, allowing the internal state of stress to be ignored. The proposed solution can be applied to both homogenous and non-homogenous slopes of either simple or complex geometry, and can also deal with any kind of additional loading. The method is based on the fact that, all possible forces acting on the slope can be projected onto the failure surface where they are broken into driving and resisting ones. Comparison of the safety factors obtained by the proposed CFS and those obtained by traditional limit equilibrium methods, as applied to several test examples, indicates that the proposed method is more conservative, whereas moreover, it gives a more realistic point of view for the formation of tension crack in slopes. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT The infinite slope method is widely used as the geotechnical component of geomorphic and landscape evolution models. Its assumption that shallow landslides are infinitely long (in a downslope direction) is usually considered valid for natural landslides on the basis that they are generally long relative to their depth. However, this is rarely justified, because the critical length/depth ( L/H) ratio below which edge effects become important is unknown. We establish this critical L/H ratio by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two-dimensional slopes, assuming that the difference between the predictions is due to error in the infinite slope method. We test the infinite slope method for six different L/H ratios to find the critical ratio at which its predictions fall within 5% of those from the finite element method. We repeat these tests for 5000 synthetic slopes with a range of failure plane depths, pore water pressures, friction angles, soil cohesions, soil unit weights and slope angles characteristic of natural slopes. We find that: (1) infinite slope stability predictions are consistently too conservative for small L/H ratios; (2) the predictions always converge to within 5% of the finite element benchmarks by a L/H ratio of 25 (i.e. the infinite slope assumption is reasonable for landslides 25 times longer than they are deep); but (3) they can converge at much lower ratios depending on slope properties, particularly for low cohesion soils. The implication for catchment scale stability models is that the infinite length assumption is reasonable if their grid resolution is coarse (e.g. >25 m). However, it may also be valid even at much finer grid resolutions (e.g. 1 m), because spatial organization in the predicted pore water pressure field reduces the probability of short landslides and minimizes the risk that predicted landslides will have L/H ratios less than 25. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Most finite element (FE) software uses numerical integration to compute FE stiffness matrices. In the case of straight-sided isoparametric triangular elements, numerical integration is exact, provided a sufficient number of integration points are used. In this paper, the same integrations are performed analytically in closed form with the help of computer algebra software for 3-, 6-, 10- and 15-noded triangles. The resulting analytical expressions have been converted into Fortran 95 subroutines and compared with the conventional numerical integration methods. The analytical routines produce exactly the same results as their numerical counterparts, but run significantly faster. All Fortran 95 code developed in this study is available on the first author's Web site. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A simple method for analyzing laterally loaded piles is to consider the problem as a beam on an elastic foundation. In this representation, the finite element method is used to solve the governing differential equation, in preference to the more popular finite difference approaches. The pile is modelled using beam elements, and two different methods are compared for introducing the soil stiffness. The ‘consistent’ approach, where the governing differential equation is discretized using a Galerkin formulation, is shown to be considerably more accurate than a ‘lumped’ approach. The improvement is particularly noticeable when the finite element discretization becomes coarser. Some examples are presented to illustrate the differences, and comparisons are made with closed-form solution. [ABSTRACT FROM AUTHOR]