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

The paper focuses on the variation of relaxed water and earth pressures of shallowly-buried shield tunnels under external water infiltration and internal water exosmosis conditions. Firstly, the seepage field and hydraulic gradient considering internal water pressure were derived based on the modified image method. Then, the solution of water and earth pressures in arbitrary locations within the relaxed zone was obtained based on the modified Terzaghi’s formula considering the horizontal distribution of stress. The effectiveness of calculation model was verified by comparing with numerical modeling 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 strata’s permeability to lining’s permeability is below 1000, the internal water pressure head has significant effects on the water and earth pressure. The increase of internal water pressure head will cause the reduction on the effective stress in the relaxed zone, which induces the unloading of soil. Moreover, it will also result in the increase of total pressure at tunnel crown of the relaxed zone, implying that the growth in pore pressure dominates the variation of 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 pressure, 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.