Three-Dimensional Expansion of the Terzaghi Arching Formula Considering Inclined Sliding Surfaces and Examination of Its Effects

Abstract

Terzaghi proposed a two-dimensional (2D) formula for arching based on the assumption of a vertical sliding surface induced in the upper part of soil mass attributable to the downward movement of a trapdoor. This study expands the 2D Terzaghi arching formula to a three-dimensional (3D) formula in which inclined sliding surfaces under general 3D excavation conditions are considered. The effects of the formula under various conditions were investigated. The assumption of the original 2D formula that the maximum shear strength is mobilized on a vertical surface is different from reality, because an actual sliding surface caused by downward movement of a trapdoor is an inclined surface. Furthermore, the 2D Terzaghi formula is limited to conditions of plane strain and does not consider 3D excavation conditions. Therefore, to examine the practical effects of these issues and to consider the arching effect in 3D excavation conditions, a formula was developed to expand the Terzaghi arching formula to inclined sliding surfaces under downward movement in 3D conditions. Using the expanded formula, the effects of excavation, ground, and surcharge conditions on vertical stress were examined, and the results were compared with those of the 2D Terzaghi formula. The induced vertical stress was highly affected by the inclination angle and the longitudinal excavation length. The degree of influence depended on the excavation, ground, and surcharge conditions. It is expected that the results from this study will provide a better understanding of various arching phenomena in the future.