渗流影响下黏弹塑性岩体隧道支护压力预测的解析模型

Analytical model for tunnel stability and support pressure prediction of viscoelastic-plastic rock masses under the influence of seepage

对于流变岩体中衬砌支护深埋圆形隧道,该文用黏弹塑性模型模拟岩石流变特性并考虑实际应力路径及非稳态渗流场的影响,推导并获得支护压力及围岩、衬砌应力及位移的精确解析解,可以更快速精准地预测与时间相关的支护结构的受力变化和围岩稳定状态。通过开挖释放荷载下的加载计算获得开挖阶段的流变位移与应力。在支护阶段,通过分离变量法获得全域全时段的非稳态孔压分布;正确考虑支护阶段的加卸载应力路径,得到渗流影响下衬砌支护力以及围岩、衬砌力场和位移场的时效解析解。对比考虑加卸载应力路径和仅按加载路径计算的结果,发现仅按加载路径而未考虑实际应力路径时围岩变形预测值偏小,支护结构按此设计将偏于危险。该文为黏弹塑性岩体中深埋圆形隧道与时间相关的支护压力预测和围岩、衬砌流变力场分析提供了快速预测的方法。

[Objective] With the advancement of traffic infrastructure development in China,an increasing number of tunnels and underground projects are being built through soft rock strata characterized by notable rheological properties in high-water-pressure environments.However,the comprehensive consideration of the stress path and unsteady seepage field during the excavation and support process has not been incorporated in predicting tunnel stability and support pressure in rheological rock masses.To solve the aforementioned problem,an analytical method is proposed to rapidly and accurately predict the time-dependent variation of the surrounding rock stability and support pressure.[Methods] The viscoelastic-plastic constitutive model is employed to simulate the rheological behavior of the surrounding rock.Based on the Mohr-Coulomb yield criterion,an exact analytical solution for stress and displacement is derived for the entire construction process of a deep-buried circular tunnel with lining.This solution incorporates the influence of the stress path and unsteady seepage field,utilizing the principles of elasticity-viscoelasticity correspondence and Laplace transformation.The construction process is categorized into two distinct stages.During the excavation stage(0-t_1),the tunnel is rapidly excavated at the onset.This stage is characterized by the absence of any water flow;hence,no additional stress is generated.During this stage,the mechanical field under the release load from the excavation needs to be considered.In the support stage(t_1-t_∞),the lining is applied when t=t_1.After the support is subjected to stress,the stress of the surrounding rock reaches a safe state,leading to the complete unloading of the original plastic zone.Long-term mechanical action may cause cracks or damage in the supporting or waterproof layer,eventually leading to water leakage and gushing.In the support stage,the influence of the seepage field needs to be considered when analyzing the mechanical field.The unsteady pore pressure distribution in the entire domain and throughout the entire period can be obtained using the separation of variables method,which enables establishing an analytical model that considers the influence of seepage on the mechanical field of the surrounding rock and lining.Furthermore,the analytical solution for the aging process of the mechanical field in the surrounding rock and the supporting force of the lining is derived,with the effect of the stress path considered correctly.[Results] Given the influence of seepage flow and the loading and unloading processes,the precise analytical solution for stress and displacement in the excavation and support stages of a tunnel was derived.This solution considered the entire construction and operation process of a deep-buried circular tunnel with lining in viscoelastic-plastic surrounding rock.The displacements at r=3.0 m and r=3.5 m over time were obtained in both the loading and unloading regions,as well as solely under the loading conditions.[Conclusions] The comparison of the results of these two cases shows that the displacement values obtained without considering unloading are considerably smaller.This observation highlights the potential for misjudging the stability of the surrounding rock,as the displacement values may be overestimated.Furthermore,this finding highlights the importance of considering the unrecoverable plastic strain in predicting time-dependent displacement and stress in the unloading zone.The derived analytical solution can serve as a valuable reference for designing support systems and construction processes in practical applications.