强降雨影响下盾构隧道开挖面稳定性的三维对数螺旋模型上限解

Upper limit solution for 3D logarithmic spiral model of stability on shield tunnel face under influence of heavy rainfall

目前针对盾构隧道开挖面稳定性的既有成果,还较少考虑降雨环境和地下水位的影响,尤其是强降雨入渗带来的土工影响。首先,基于分层假定Green-Ampt模型来模拟强降雨入渗过程;其次,在土体抗剪强度理论和有效应力理论的基础上,将修正后的Mohr-Coulomb准则和Darcy定律结合,推导出与降雨强度和降雨历时相关的分段形式表观黏聚力表达式;然后,基于极限分析上限理论构建三维对数螺旋破坏机制,将表观黏聚力做功引入上限定理的虚功率方程,通过优化计算,得到考虑强降雨入渗和地下水位条件下盾构隧道开挖面支护力的上限解。最后,将上限解析解与三维数值模拟结果及既有试验结果进行对比,得到了较好的一致性。此外,针对降雨强度和地下水位深度等关键参数进行了影响因素分析。结果表明:当降雨强度较小时(F/ks≤1,F为平均降雨强度,ks为饱和渗透系数),隧道开挖面极限支护力随降雨强度的增大而加速增大,随降雨历时的变化不明显,当降雨强度较大时(F/ks>1),极限支护力随降雨强度的增大而缓慢增大,随降雨历时的增加而显著增大;当地下水位深度较小时(Z_(w)/D≤3,Z_(w)为地下水位深度,D为开挖直径),极限支护力随地下水位深度的增加线性减小,当地下水位深度较大时(Z_(w)/D>3),其变化速率逐渐减小,最后趋于平稳。

The existing theoretical studies on the stability of shield tunnel excavation face have not taken into account the effects of rainfall environment and groundwater level,especially the geotechnical effects induced by heavy rainfall infiltration.Firstly,a layered hypothetical Green-Ampt model is used to simulate the heavy rainfall infiltration process.Secondly,on the basis of the shear strength theory and the soil effective stress theory,the modified Mohr-Coulomb criterion and the Darcy’s law are combined to derive the apparent cohesion expression in segmental form related to rainfall intensity and duration,and then,based on the upper bound theory of limit analysis,a three-dimensional(3D)logarithmic spiral failure mechanism is constructed,and the work done by apparent cohesion is introduced into the virtual power equation of upper bound theorem,the upper limit solution of the support force of shield tunnel excavation face is obtained under the conditions of heavy rainfall infiltration and groundwater level through optimization calculation.Finally,the theoretical upper bound solution is compared with the 3D numerical results and existing experimental results,and a good agreement is obtained.In addition,the key parameters such as rainfall intensity and water table depth are analyzed.The results show that when the rainfall intensity is small(F/ks≤1,where F is the mean rainfall intensity,and ks is the saturated infiltration coefficient),the ultimate supporting force of tunnel excavation face accelerates with the increase of rainfall intensity,but has no obvious change with rainfall duration;the ultimate supporting force increases slowly with the increase of rainfall intensity,but significantly with the increase of rainfall duration when the rainfall intensity is large(F/ks>1);the ultimate supporting force of tunnel excavation face decreases linearly when the normalized groundwater table depth is small(Z_(w)/D≤3,where Zw is the depth of groundwater level,and D is the excavation diameter);and the rate of change gradually decreases and finally becomes stable when the normalized groundwater table depth is large(Z_(w)/D>3).