Effect of Element Size in Random Finite Element Analysis for Effective Young’s Modulus

Abstract

In random finite element analysis (RFEA), continuous random fields must be discretized. The critical element size to achieve acceptable accuracy in effective Young’s modulus for an elementary soil mass is investigated. It is observed that the discrepancy between the continuous and discretized solutions is governed by the discretization strategy (element-level averaging versus midpoint), spatial variability pattern, and the adopted autocorrelation function. With the element-level averaging strategy, RFEA with element size less than (scale of fluctuation)/5 will not induce significant discrepancy from the continuous solution. Moreover, the element-level averaging strategy is more effective than the midpoint strategy.

Discussion of “Probabilistic seismic slope stability analysis and design”

“…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.…”

Smart determination of borehole number and locations for stability analysis of multi-layered slopes using multiple point statistics and information entropy

“…The bi-directional resolution is 0.1m, resulting in a total of 45000 points. The resolution is determined based on mesh size commonly adopted in numerical modelling of geotechnical analysis, e.g., about 0.1m -1.0m for finite element/difference modelling of foundation, deep excavation, or slope stability analysis (e.g., Ching and Hu 2016;Liu and Deng 2019;Sazzad et al 2015) or conventional sampling interval used in geotechnical site investigation, e.g., a sampling interval of about 1m for standard penetration tests (e.g., Kulhawy and Mayne 1990). Both outcrops and stratigraphic boundaries separating different soil layers are delineated by five quadratic lines (i.e., I, II, III, IV and V in Fig.…”

Faults as Volumetric Weak Zones in Reservoir-Scale Hydro-Mechanical Finite Element Models—A Comparison Based on Grid Geometry, Mesh Resolution and Fault Dip

“…A general recommendation is to use a finer mesh in those areas where stress and strain gradients are large. To identify the regions where greater mesh density or local grid refinement is required, preliminary simulations with a coarse mesh appear useful [53,[87][88][89].…”

“…The higher stress values ultimately cause higher plastic strain, which is also observed in the finer mesh resolution. The second issue is that models with a lower mesh resolution, i.e., with less elements, appear to be somewhat stiffer, while increasing the number of elements softens the model slightly and improves the accuracy of the stiffness integration [89,95]. Therefore, the slightly higher stress and strain values for the models using a higher resolution may originate from the lower effective stiffness at the fault tips.…”