Investigation of Limit Equilibrium Method and Finite Element Analyses for Ground Anchored Slopes
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Abstract: Ground anchors are commonly used to stabilize natural slopes. The Limit Equilibrium Method (LEM) is often employed to evaluate the safety factors of the slope before and after the addition of the ground anchors. Typically, the allowable capacities (forces) of the ground anchors are critical in determining the improved factor of safety for slopes. This large concentrated load can cause convergence issues in the rigorous slice methods (e.g. Spencer’ s method) and erroneous results in simplified slice methods (e.g. Simplified Bishop’ s method). To address these issues, Carpenter (1986) developed the Load Distribution Method. This method distributes the force throughout the soil mass based on Flamant’ s (1886) stress distribution model in a semi-infinite elastic half-space.

Using the Strength Reduction Method in Finite Element Analysis (FEA), we can evaluate the accuracy of the semi-infinite elastic half-space assumption. A hypothetical slope with one row of ground anchors is analyzed using both the LEM with the Load Distribution Method and the Strength Reduction Method of FEA. The resulting safety factors from the LEM and FEA are similar when a rigid surface on the slope is employed in the FEA, indicating that the Load Distribution Method provides reasonable results. However, when the tieback is locked into a flexible grid wall, the safety factor obtained from FEA is significantly lower. The resulting failure surface passes through the flexible facing. Due to its rigid-plastic assumption, the LEM cannot account for the effects of stiffness of the tieback. Results from FEA also show the corresponding shear force and bending moment of the grid wall, which can be used for structure design. In addition, FEA provides valuable deformation information of the slope, which can help determine optimal locations for ground anchors. Results from this study shows FEA is a valuable tool for designing and locating ground anchors in a slope.
Dr. Farnyuh Menq; Mr. SHIN-TOWER WANG
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