Slope stability analysis plays a crucial role in geotechnical engineering for assessing the stability of natural and engineered slopes. Finite Element Analysis has emerged as a powerful numerical tool to model and analyze slope stability, and the finite elements mesh density is one of the most critical aspects in FEA-based slope stability analysis, directly affecting the calculated reduction of parameters such as the soil friction angle (φ) and the soil cohesion (c). A coarser mesh may not capture the fine details of the soil structure and behavior, leading to less accurate predictions of cohesion and soil friction reduction. On the other hand, a denser mesh can provide more accurate results by capturing localized variations and gradients in soil properties. Increasing the mesh density allows for better representation of small-scale features, such as thin soil layers or discrete geological structures, which can affect the overall cohesion and soil friction angle reduction. Consequently, a finer mesh can yield more precise estimations of cohesion reduction along potential failure surfaces.
This article presents a study on the impact of FEA mesh density on slope stability analysis, highlighting its significance and implications for accurate assessment and prediction of the most critical slope surfaces, and the corresponding slope stability safety factor. Three scenarios, examining the effect of different levels of FEA mesh density (medium, fine and very fine), and with different water, and support conditions are presented:
CASE 1: Unsupported slope surface with frictional soils.
CASE 2: Unsupported slope surface with unconfined water flow.
CASE 3: Slope surface with soil nails.
All cases were modelled with our DeepEX – Shoring design software suite and analyzed with our DeepFEM engine. Results are also compared against traditional slope stability safety factors computed with DeepEX.
B. FINITE ELEMENT ANALYSIS OPTIONS IN DEEPEX
This scenario models a 2:1 slope utilizing a sand soil material (Friction angle= 34deg, Unit weight = 18 KN/m3, Cohesion = 5 kPa, E= 14370 kPa). The selected soil model is the exponential soil hardening FEM model, with exponent = 0.5. Figure 1 below presents the DeepEX FEM mesh density levels and options.
Figure 1: FEM Analysis Options in DeepEX – Level of Mesh Density
C1. CASE 1: Unsupported slope surface with frictional soils
This case examines the effect of changing mesh density on the global stability analysis of a slope surface with frictional soils. Figure 2 presents the horizontal displacement distribution within the soil mass, the C-Phi reduction factor and the calculated slope stability safety factor for different levels of mesh density.
Figure 2: 2:1 Slope surface - Displacement shadings, slope stability FS and C-phi reduction factor for different levels of FEM mesh density: a) Medium, b) Fine, c) Very Fine
C2. CASE 2: Unsupported slope surface with unconfined water flow
This case examines the effect of changing mesh density on the global stability analysis of a slope surface with frictional soils, where we also apply a water level drawdown, considering the effect of the unconfined water flow. Figure 3 presents the analysis results for this scenario.
Figure 3: 2:1 Slope surface with water drawdown - Displacement shadings, slope stability FS and C-phi reduction factor for different levels of FEM mesh density: a) Medium, b) Fine, c) Very Fine
C3. CASE 3: Slope surface with soil nails
This case examines the effect of varying mesh density on the global stability analysis of a slope surface with frictional soils supported by 8 rows of soil nails. Figure 4 presents the analysis results for this scenario.
Figure 4: 2:1 Slope surface with soil nails - Displacement shadings, slope stability FS and C-phi reduction factor for different levels of FEM mesh density: a) Medium, b) Fine, c) Very Fine
The examined scenarios in this article indicate that there is a direct connection between the level of Finite Element Mesh density, and the accuracy of the slope stability analysis safety factor. A coarser mesh might oversimplify the geometry and soil behavior, leading to less accurate slope stability FS calculations and c-phi reduction, as it may fail to capture localized stress concentrations or variations in soil properties, potentially resulting in inaccurate estimates of the true slope stability condition. This can lead to an overly optimistic assessment of slope stability, potentially overlooking potential failure mechanisms. Conversely, a finer mesh can provide more detailed information about stress distributions and gradients within the slope. This can lead to more accurate calculations of the safety factors and a better understanding of potential failure modes and mechanisms. A denser mesh allows for the capture of small-scale features, such as stress concentrations near geological discontinuities, which can significantly influence slope stability.
By exploring the impact of finite element analysis mesh density on slope stability analysis, this article provides valuable insights to geotechnical engineers and contractors involved in slope stability assessment and design. Understanding the significance of mesh density will enable engineers to make informed decisions and improve the reliability of slope stability analysis. In summary, a finer mesh density in FEM analysis can provide more accurate estimations of soil friction - cohesion reduction and slope stability. It allows for a better representation of small-scale features and localized variations in soil properties, resulting in more reliable predictions.