Calculation of ultimate supporting forces of shield tunnels in unsaturated sandy soils considering soil arching effects

Due to the influences of grouting parameters and tunnelling parameters in the actual construction, the soil arching effects caused by the ground loss gradually in-crease, and the shear stress on the sliding surface increases to the shear strength gradually. The contribution of the apparent cohesion of unsaturated sandy soils to the shear stress should be also considered. However, the above factors are not considered in Terzaghi's formula. In order to solve the problem, based on the principal stress rotation theory, the expressions for the lateral pressure coefficient of unsaturated sandy soils at different positions are deduced. Based on with the theoretical formula for the apparent cohesion and the experimental data, a piecewise function for the apparent cohesion related to the matric suction is obtained, and the formula for loosening soil pressure as well as the formula for ultimate supporting force is derived in consideration of different soil arching effects. The results of the example show that with the soil arching effects, at the same depth, the loosening soil pressure decreases gradually and it is always less than the self-weight stress. With the increase of water content, there is a threshold value for the loosing earth pressure. Under different soil arching effects, with the increase of the depth, the loose earth pressure at the arch crown of strata with different saturations will tend to different constant values. Meanwhile, the formula for the limit supporting forces of shield tunnels has the same law. This research results will provide theoretical guidance for controlling reasonable chamber pressure of shield tunnelling in the unsaturated sandy soils, and ensure the safety of construction.