ABSTRACT: A three-dimensional (3D) analysis method of rock block stability, based on the sliding mechanism of arch dam abutment and rock slope failure with multiple rock wedges, is presented. The method of vector analysis was employed in the description of block geometry and force equilibrium equations. Based on limit equilibrium and strength reduction concept, a series of nonlinear force equilibrium equation of each block was established. An iterative, back-substitute procedure is used to solve overall factor of safety of multiple blocks. As the application of the 3D analysis for multiple rock blocks sliding, an arch dam abutment of a large hydropower station and a rock slope in a large water reservoir were analyzed. Based on comparisons with 3D one wedge sliding analysis, 2D finite element method, and 2D slices method of the rock slope, the 3D multiple blocks failure analysis method was generally found to be suitable in predicting the stability of slopes and arch dam abutment with complicated type of rock sliding and wedge failure.
Three-dimensional (3D) analysis is used for many slope stability problems. In soil mechanics, most researches in 3D slope analysis are concentrated on 3D column methods [1, 2, 3, and 4]. The slope soil was divided into vertical columns which is the extension of the 2D general limit equilibrium method. The intercolumn shear force of each column can be neglected or assumed to distribute as a certain function. The overall factor of safety can be calculated by force or moment equilibrium of all columns.
For rock slopes, a single wedge failure solution, based on the rigid-body mechanics, in threedimension is a routine tool of rock slope engineering [5, 6, and 7]. Multiple blocks, sliding along multiple planes is the most complicated planar type of sliding. Multiple wedges can be formed by the intersection of four or more sets of discontinuities (Fig. 1), and usually find in arch dam abutment (Fig. 2) and high rock slope failure. computer program for the factor of safety in such cases are not readily available.
This paper aimed to calculate the factor of safety of multiple block systems using vector analysis method in the description of block geometry and force equilibrium equations. A computer program was developed to complete the analysis. Several case studies were finished and proved that the 3D multiple blocks failure analysis method was suitable in predicting the stability of slopes and arch dam abutments with complicated type of rock sliding and wedge failure.
