Rock mass substitute geometry theory (SGT) and 3D centroid sliding pyramid (CSP) method

Abstract

Discontinuous analysis methods are typically used for the stability analysis of fractured rock masses with multiple sets of joints. Among various discontinuous methods, the key block theory (KBT) requires less data input, has a higher computational efficiency, and is suitable for wide-ranging engineering applications. Classical discontinuous numerical methods typically require complete boundary information for rock block units. However, current information-gathering methods can only capture information on rock surfaces. The proposed rock mass substitute geometry theory (SGT) overcomes this limitation by using local geometric information to equivalently represent the original geometric body simplifying subsequent analyses. A 3D centroid sliding pyramid (CSP) method is introduced for motion state analysis of a rock block that uses only the collinear faces of a block’s free surfaces. A comparison of CSP with KBT proves that CSP not only addresses the issue of collecting only surface information of rock masses but it significantly minimizes the computation scale. Additionally, a 3D discontinuous analysis program was developed, encompassing the entire process of rock mass information gathering, 3D discontinuous modeling, and 3D CSP analysis. The effectiveness and efficiency of the method were validated using stochastically generated models, while its practical engineering applicability was demonstrated at an engineering site.