Three-dimensional Limit Equilibrium Method for Stability Analysis of Dangerous Rock
In order to improve the practicality of the two-dimensional limit equilibrium method in the application of the 3D stability analysis of dangerous rock,this study established a three-dimensional approach based on the principles of limit e-quilibrium theory.The proposed method takes into consideration the effects of location and degree of the lateral penetration on the main structural planes.During force analysis,an extended three-dimensional sketch obtained by stretching and expanding the main structural surface of dangerous rock was applied.Through the comparison between the ratio of anti-slip force(anti-tor-sional moment)and slip force(torsional moment),the calculation formulas of stability coefficient of different dangerous rock masses were determined,including sliding,falling and toppling types.In addition,based on the proposed formula and numerical simulation,the influence of lateral penetration rate and upper penetration rate on the stability of dangerous rock was analyzed.The results indicate that the stability of the dangerous rock mass tends to decrease as the lateral penetration rate and the upper penetration rate increase.The proposed method is feasible and more accurate than the traditional two-dimensional limit equilib-rium method,with the relative error of calculation reduced by more than 50%,and it can be effectively applied to the stability analysis of dangerous rock mass under both completely and partially penetrated lateral conditions of main structural planes,suc-cessfully overcoming the limitation of existing two-dimensional limit equilibrium method.Moreover,it extends the two-dimen-sional limit equilibrium analysis method and enriches the theory of critical rock stability analysis.
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