Study On Continuous Upper Bound Limit Analysis Methods For The Transverse Failure Mode And Necessary Support Pressure Of Shallow Shield Tunnels

For lateral stability analysis of shallow shield tunnels in cohesive-frictional(clayey-sandy)soils,a composite volume loss model and corresponding complex variables solution are used to establish the theoretical model of continuous upper bound limit analysis and to calculate the the most critical slip line position and the necessary supporting pressure to maintain the stability of the tunnel by using the numerical iteration or intelligent optimization algorithm;other theoretical solutions and model test results in the literature are compared to verify the rationality of the established model and the solution method.The main research contents and results are as follows:(1)For a 'convergence-oval deformation-vertical translation(sagging or uplifting)' composite volume loss model of shallow shield tunnels in pure clays and the corresponding complex variables solution,a continuous upper bound limit analysis theoretical model is established to calculate and analyze the effects of tunnel sagging,uplifting and oval deformation on the displacement field,the stress field,the position of the most critical slip line and the supremum of the stability number.Illustrative calculations reveal: with the increase of the tunnel sagging coefficient or oval-deformation coefficient,the ground surface settlement increases mainly in magnitude but minor in trough width;the influence of the tunnel uplifting coefficient on ground displacement is similar in pattern but opposite in direction to that of the tunnel sagging coefficient;the effect of the tunnel oval-deformation coefficient on the supremum of the tunnel stability number is more significant than that the tunnel sagging/uplifting coefficient;the uniformconvergence volume loss model can reflect the most critical pattern of tunnel instability and the most critical tunnel stability number with sufficient accuracy.(2)For shallow shield tunnels in cohesive-frictional(clayey-sandy)soils,a composite volume loss model and corresponding complex variables solution are used to establish the theoretical model of continuous upper bound limit analysis.The optimization objective is to minimize the internal dissipation energy of the ground instability around the tunnel,and the constraint conditions are the Mohr Coulomb yield criterion,the associated flow rule,the parameter range of tunnel volume loss and the boundary displacement conditions of the region instability.Particle swarm optimization algorithm is used to solve the minimum required tunnel support pressure.The results show that: the infimum of the necessary tunnel support pressure decreases with the increases of the angle of internal friction of the soil,and the extent for such decrease is slightly affected by the surface load;the infimum of the necessary tunnel support pressure increases with the tunnel cover-diameter ratio and the increase of the tunnel cover-diameter ratio weakens the influence of internal friction angle on the zone of ground instability;with the increase of the surface load,the infimum of the necessary tunnel support pressure increases,and the surface load to expanding the zone of ground instability is more prominent for smaller tunnel cover-diameter ratios.(3)Considering the influence of groundwater seepage on the stability of shallow shield tunnel in cohesive-frictional(clayey-sandy)soils,the pore water pressure is regarded as an external force substituted into the upper bound theorem equation of continuous upper bound limit analysis,the expression of necessary support pressure for maintaining the stability of tunnel under seepage condition is derived,and the infimum of necessary support pressure is calculated by optimization.The results show that: both the infimum of the necessary tunnel support pressure and the region of ground instability increase when the hydraulic head at the ground surface increases,when the surface water level is large,the effect of effective internal friction angle on the infimum of the necessary tunnel support pressure is weakened;under the influence of stress field and seepage field,the tunnel influx increases,the infimum of the necessary tunnel support pressure required to maintain the stability of the tunnel decreases,and the region of ground instability also decreases.