This paper extends the numerical manifold method (NMM) for complete rock slope failure analysis. A fracturing algorithm based on the Mohr-Coulomb criterion with a tensile cutoff is implemented into the NMM code. The developed program is first calibrated through two typical crack problems and then applied to analyze the potential footwall slope instability. Parametric studies are carried out. Numerical results indicate that the developed program can simulate the sliding along pre-existing discontinuities, fracturing through intact rock, as well as kinematics of failed slope, and can reproduce the major failure mechanisms observed in footwall slope collapses. The NMM is promising for such problems and deserves to be further developed to be practically used in rock slope stability analysis and open pit slope design.


Open pit mining is a very cost-effective mining method. In open pit mining, pit slopes are formed. With the mining depths steadily increased to 500 meters or even higher, design of open pit slope angles is becoming more and more important. Small change in the overall pit slope angle has significant influence on the overall economy. An ideal design method must be able to

  • predict where and under what conditions a failure surface may develop;

  • predict the kinematics of the failed slope.

Current design methods can be distinguished into four groups:

  1. empirical design method;

  2. physical model tests;

  3. limit equilibrium methods;

  4. numerical methods.

Among them, numerical methods have become popular in recent years. Currently existing numerical methods can be generally grouped into two categories: continuum methods (e.g. FDM, FEM, BEM, etc.) and discontinuum methods (e.g. the distinct element method with the commercial codes as UDEC, 3DEC, etc. and the discontinuous deformation analysis (DDA) [1]). Existing continuum codes are able to simulate the location and shape of the failure surface developing in a slope. However, an actual failure surface discontinuity is not formed. Pre-existing fractures are usually not incorporated. Discontinuum codes model the discontinuities presented in rock mass explicitly and have been successfully used to simulate structurally controlled failures. They are, however, difficult to simulate failures through intact rock. Actual slope failure involves both sliding along pre-existing discontinuities as well as fracturing through intact rock. A general method which can simulate the actual slope failure becomes essential. In this paper, the recently developed numerical manifold method (NMM) [2] is explored to account for complete rock slope failure process. Footwall slope is considered. Footwall slopes are often excavated parallel to dip and extensive along both strike and down-dip. When mining continues down-dip, the length of the exposed footwall slope increases and the potential instability of the slope may arise. Footwall slope instability is a relatively common occurrence in open pit mines situated in area of steeply dipping strata particularly where mountainous topography exists. The importance of footwall instability has long been recognized. Failures only occur along the pre-defined discontinuities. In this paper, non-persistent joints are allowed, both sliding along pre-existing discontinuities and fracturing through intact rock will be captured.

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