Progressive Failure Mechanism Of Shield Tunnel Overlying Soil And Earth Pressure Calculation

During shield tunnel construction or service period,the relative movement direction of the shield tunnel and its overlying soil may change,resulting in the overlying soil being in different active/passive states.For example,during the construction period,the so-called ground loss causes the overlying soil to be in active state,which will lead the overlying load acting on the tunnel is the active earth pressure and causes the loosening and deformation of the ground;During the service period,the overlying soil may be in a passive state due to the surrounding environment or engineering activities.For example,a tunnel suffering from differential settlement may be uplifted to the original position by grouting technology to satisfy the operation safety;The expansive soil underlying the tunnel may squeeze the tunnel;and the surrounding grouting squeezes the tunnel to move upward.At this situation,tunnel passively squeezes the overlying soil will lead to passive earth pressure and ground compressive deformation.Therefore,the overlying soil may be in any non-limit state of"active","passive"or"static"during the entire life cycle of the tunnel.No matter which state it is,the ground movement and earth pressure will gradually develop with the ground loss or extrusion.Determining the earth pressure and the ground movement is particularly important for the fine control of the shield tunnelling and the evaluation of the load state during the maintenance.It is also the premise to ensure the safety and reliability of the tunnel and surrounding environment.However,the current earth pressure calculation is mainly based on the limit state,and the ground movement prediction method is difficult to describe the evolution process of the displacement with the development of ground loss or extrusion.In this study,theoretical analysis,experimental study,numerical simulation are comprehensively used to carry out systematic research on the prediction of soil displacement response caused by active ground loss or passive extrusion,and the calculation of overlying non limit earth pressure.The main work,contribution and conclusions are summarized as follows:(1)The active/passive failure modes of the overlying soil for the circular tunnel in the cohesive soil layer and the cohesive-friction soil layer were proposed,and the theoretical solution and empirical formula of the active/passive limit earth pressure were given,which have been verified by the existing centrifuge test or numerical solution.For tunnel stability problem,in order to overcome the problems of mesh distortion and difficult convergence by using incremental elastic-plastic analysis,using the upper bound finite element limit analysis with mesh adaptation,the plastic shear dissipation distribution and plastic velocity field of the overlying soil were obtained.Based on the simulation results,the typical failure modes in active/passive state were proposed.In active state,three blocks with three parameters failure mechanism,five blocks with four parameters failure mechanism,and the combination of logarithmic spiral continuous deformation zone and rigid sliding block failure mechanism were proposed.In passive state,three types of failure mechanisms,including deep,shallow,and deep shallow transition,related to buried depth and strength parameters,were proposed;For the passive state in cohesive soil layer,the theoretical relationship between the limit earth pressure,the buried depth ratio,and the undrained shear strength s_u was established.Based on this,the critical transformation equation of the deep and shallow buried condition was obtained.and the result indicates that critical buried depth will increase with the increasing of s_u;For the cohesive-friction soil layer,considering the contribution of the cohesion c’,internal frictionφ’,surface overloadσs and self-weightγ,the empirical formulas of the limit earth pressure were established.(2)Based on particle image velocimetry and transparent soil technology,a non-invasive observation trapdoor test system device for capturing the displacement of the ground was designed and developed.According to the vertical movement direction of the trapdoor,the active or passive state were simulated.The trapdoor tests under different trapdoor shapes(flat plate,semi-circular),active/passive state and different burial depths were carried out.The results indicate that:the semicircular trapdoor results can form a more stable arching effect and reduce the surface settlement when compared with the flat trapdoor;In the active state,the disturbance region above the trapdoor changes from"triangular mode"to"rectangular or inverted trapezoidal mode"and gradually develops to the surface.The active region(approximately consistent with the trapdoor displacement)approximates"parabolic mode"and gradually develops to the surface.(3)A stochastic medium method for prediction the ground movement evolution caused by the displacement boundary of the shield tunnelling was proposed.This method can describe the propagation characteristics of the volume loss and the diffusion behavior of the settlement,which overcomes the difficulty of describing the ground movement by the existing empirical methods.Considering the volume change characteristics and subsidence diffusion of ground loss,the stochastic medium theory was introduced,and the second-order partial differential equation for the evolution of two-dimensional ground movement is established.For the tunnel displacement boundary,five typical composite boundary modes at the tunnel-soil interface were proposed.According to the quadratic integration of the specific solution of the distribution function in the loss domain,a description method of ground movement with the composite boundary mode was established.The results show that the composite mode of"convergence-vertical displacement-ellipticization"will lead to larger settlement displacement and vertical deformation when compared with only the uniform convergence mode.(4)Based on the visualized trapdoor tests and the multiplier elastoplastic finite element analysis with mesh adaptation,the development and influencing factors of the earth pressure in the active/passive state were clarified.And the mechanism of progressive failure in different active/passive earth pressure development stages was revealed.According to active earth pressure development,the load-displacementρ～Δcurve is divided into four stages:the initial rapid decrease stage,the stable minimum stage(ρmin),load recovery stage and limit state(ρult);In contrast to the passive state,the earth pressure increases to the peak valueρmax and then gradually decreases to the limit valueρult;Elastic modulus E,poisson’s ratioν,lateral pressure coefficient k0 has almost no effect onρmin orρmax;the progressive failure can be described by the development of the inclination angleαof the shear band,and the change mechanism of the inclination angleαis related to the weakening of the dilatancy characteristics and the reduction of the compactness of the overlying soil during the trapdoor movement.When the earth pressure develops toρmin orρmax,the initial shear band is formed,and its inclination angleαis the dilatation angleψ.During the progressive failure process,the inclination angleαdecreases,the earth pressure increases(active)or decreases(passive).When the earth pressure reaches the limit stateρult,an approximately vertical shear band is formed.(5)Considering the evolution of slip surface and principal stress rotation with displacement during the development of earth pressure,a evolutionary differential horizontal slice method for calculating non-limit active/passive earth pressure is proposed.This method can not only obtain the limit state earth pressure solution,but also it reflects the development trend of overlying earth pressure with displacement and the distribution law of earth pressure.Based on the progressive failure mechanism of the overlying soil above the trapdoor,the basic governing equations for the earth pressure in the active/passive state with the cohesive soil layer and the cohesive-friction soil layer are established,and the development of the earth pressure under different burial depth conditions and different stress transfer stages is obtained.The solution is compared with the experimental results in this study,the limit analysis results in this study,and the centrifuge test results in the literature,which verifies the accuracy of the calculation model.