Influence of Mesh Size, Number of Slices, and Number of Simulations in Probabilistic Analysis of Slopes Considering 2D Spatial Variability of Soil Properties

Abstract

The Random Limit Equilibrium Method (RLEM) is a relatively new method of probabilistic slope stability analysis which uses a combination of 2D random field theory, limit equilibrium methods, and Monte Carlo simulation. The Random Finite Element Method (RFEM) uses a combination of 2D random field theory, finite element method of analysis, strength reduction method, and Monte Carlo simulation. In this paper, the effects of mesh size, number of slices, and number of Monte Carlo simulations on computed probability of failure are investigated using both approaches. Computation times using both methods to solve the same slope problem are also compared. Recommendations for mesh size, number of slices, and number of Monte Carlo simulations, with respect to the spatial correlation length, using RLEM are presented.

Discussion of “Probabilistic seismic slope stability analysis and design”

“…The noncircular RLEM, introduced by Cami et al (2018), is a combination of the Cuckoo search method, the Surface Altering Optimization technique, and the LEM (Morgenstern-Price method) together with the random field theory. The Cuckoo search is a very fast and efficient global optimization method (metaheuristic approach), which is used for locating critical noncircular slip surfaces.…”

“…When used in conjunction with a noncircular search, this optimization method can be very effective and efficient at locating (searching out) slip surfaces with lower safety factors. Cami et al (2018) showed that noncircular RLEM was able to find the weakest failure path using local and global optimization techniques similar to the failure path using the RFEM approach. The run time for the noncircular RLEM was shown to be at least 40% less than running the same example using the RFEM method with the same output.…”

“…Accurate modeling of a spatially variable domain in a digital circumstance entails minimizing the discretization error (i.e., the difference between solutions in a continuous and discretized medium), which would be achieved by an appropriate mesh size associated with the variability of the soil. Phoon (2013a, 2013b), Huang and Griffiths (2015), Ching and Hu (2016), Cami et al (2018), andTabarroki andChing (2019) explored the effect of the mesh density used in finite element models with spatially variable soil properties. Ching and Phoon (2013b) introduced a critical ratio (i.e., scale of fluctuation (␦) / domain size), beyond which the discretization error would be minimum, and reported the effect of the auto-correlation model (i.e., single or squared exponential model), discretization method (i.e., element-level averaging and midpoint strategy), spatial variability pattern (i.e., isotropic and anisotropic), and stress states (i.e., pure shear or compression) on this ratio.…”

“…Through a series of sensitivity analyses, Cami et al (2018) investigated the effect of correlation length and mesh size on the reliability of the slope. By adopting RLEM, a worst-case mesh size was detected between 0.1 and 0.5 m (related to the maximum probability of failure for that cases of /H = 0.5, 0.2, and 0.1) which was not tried through the RFEM software (MRSLOPE2D) of Fenton and Griffiths (2008), presumably due to the convergence problems.…”

“…In the paper under discussion, Burgess et al ( 2019) have limited their results to a specific mesh size (i.e., 0.5 × 0.5) for a wide range of correlation lengths (i.e., /H = 0.1, 0.2, 0.3, 0.5, 0.7, 2, 3, 5, 7, 10). As is evident in recently published papers (e.g., Huang and Griffiths 2015;Cami et al 2018), mesh size plays a primary role in the determination of the worst-case correlation length as well as in the thorough consideration of spatial variability of the soil. Regarding the relationship introduced by Huang and Griffiths (2015) between the correlation length and the element size, for the smallest correlation length (i.e., = 0.5), the corresponding element sizes (i.e., /2 = 0.25, 0.15) will result in drastic changes in the results, which have been neglected in the paper under discussion.…”