Model for calculating water and earth pressures of shallowly buried pressurized shield tunnels under external water infiltration and internal water exosmosis conditions

Focusing on the variation of relaxed water and earth pressures of shallowly shield tunnels under external water infiltration and internal water exosmosis conditions, the seepage field and hydraulic gradient considering internal water pressure are firstly, derived based on the modified image method. Then, the solutions for the water and earth pressures in arbitrary locations within the relaxed zone are obtained based on the modified Terzaghi's formula considering the horizontal distribution of stress. The effectiveness of the computational model is verified by comparing with the numerical results. It is shown that the principal stress path in either an arc or a parabola form can effectively capture the stress distribution within the relaxed zone over the tunnel crown. When the ratio of permeability of strata to that of linings is below 1000, the internal water pressure head has significant effects on the water and earth pressures. The increase of internal water pressure head will cause the reduction on the effective stress in the relaxed zone, which induces the unloading of soils. Moreover, it will also result in the increase of the total pressures at the tunnel crown of the relaxed zone, implying that the growth in pore pressure dominates the variation of the water and earth pressures. The linear regression of five-parameter orthogonal analysis suggests that the buried depth and tunnel radius have significant positive impacts on the earth pressures, while the influences of friction angle and cohesion are negative. Under the scenarios of relatively low-permeable strata, the influences of internal water head on the total and effective earth pressures at the tunnel crown are significantly negative and positive, respectively.