Loosening earth pressure based on triangular slip surfaces

Soil deformation caused by karst collapse and tunnel excavation often causes uneven settlement, ground collapse and cracking in foundation. Development of approaches to determine the distribution of loose earth pressure at the top of soil structure and analyze the relationship between soil deformation and soil arching effect accurately is of much importance. A series of classical trapdoor tests with different H/B ratios is conducted to reveal the variation law of soil deformation and settlement on the loose earth pressure at the top of the structure. Based on the test results, a mathematical model is proposed to analyze the loose earth pressure with triangle as the mechanical model under different slip surfaces. The relationship among the slip surface angle, soil deformation and principal stress deflection is considered. The principal stress deflection of any horizontal differential soil layer in the slip surface is analyzed and the stress equilibrium differential equation is established. The theoretical formula of loose earth pressure is solved according to the boundary conditions under different slip surfaces. The rationality of the theoretical formula is verified by comparing with the trapdoor tests results. The main parameters (e.g. slip surface angle, coefficient of lateral earth pressure and internal friction angle) were analyzed. The results reveal that when the displacement-width ratio (1%−3%) is smaller, the stress rapidly transfers and redistributes, and the angle of initial slip surface is slightly smaller than π/4+φ/2. With the increase of H/B, the vertical stress increases slowly and finally tends to be stable; loose earth pressure of closed triangular slip surface in foundation is related to the displacement-to-width ratio and internal friction angle; the increase of internal friction angle makes full use of soil arching effect, strengthens stress transfer and reduces vertical stress; the increase of internal friction angle brings a remarkable reduction in the horizontal stress component, thereby reducing the lateral earth pressure coefficient.