Three-Dimensional Theoretical Model for Soil Arching with Inclined Slip Surfaces

Terzaghi proposed two-dimensional (2D) arching theory through trapdoor tests based on the assumption of a vertical slip surfaces. However, the original 2D assumption is different from a real three-dimensional (3D) excavation condition and an actual slip surfaces caused by downward movement of a trapdoor is an inclined surface. Therefore, a 3D theoretical model was proposed in this study considering inclined slip surfaces. Horizontal thin layer differential element method was used to obtain the loosening soil pressure. Using the 3D theoretical model, the effects of buried depth ratio of loose area, length of loose area, soil parameters, and lateral earth pressure coefficient were investigated. The loosening earth pressure was highly affected by inclination angle of slip surface, buried depth ratio and length of loose area. Neglecting the inclined slip surface will underestimate the value of the loosening earth pressure, which will lead to the insecurity of the design. Loosening earth pressure calculated by this study was also compared with trapdoor tests. Results from this study was in good agreement with the experimental results. Compared with the traditional 2D solution, results from this study can more accurately analyze the soil arching effect in 3D excavation cases.