基于非线性强度特征的深埋隧道围岩有限应变求解

Finite strain solution for the surrounding rock of deeply buried tunnels based on the nonlinear strength characteristics

深埋隧道的围岩强度随着围压的增大而呈现出明显的非线性变化,且其具有高地应力这一显著特征使得准确评估隧道掘进过程中围岩的力学响应难以实现。引入岩石的非线性强度特征,建立深埋隧道围岩的对数应变方程,并考虑已有研究中大多忽略的岩石应变硬化特性,在有限差分循环迭代过程中使用当前节点的塑性剪切应变进行内部变量求解,提出基于统一应变硬化−应变软化本构模型和非线性剪胀模型的围岩弹塑性耦合有限应变解析方法。模型退化为小应变分析时,解析结果与经典理论解答基本一致,可以验证方法的有效性。影响参数分析表明:忽略岩石剪胀系数的非线性衰减将低估有限应变围岩的塑性区范围;随岩石剪胀特性的增强,洞壁位移、残余区半径和塑性区半径逐渐增加,且其增加幅度随围压减小而明显。岩石应变软化特性主要影响围岩残余区和软化区的占比,引起围岩位移的变化,其特性增强将显著减小塑性区半径。是否考虑岩石应变硬化特性对围岩塑性区范围的评估至关重要,但应变硬化特性的增强对塑性区的半径影响较小,其特性增强主要表现为对围岩软化区和硬化区占比的改变。采用该方法可有效评估深埋隧道有限应变围岩的塑性区范围,并为支护结构体系的设计提供理论指导。

The strength of the surrounding rock in deeply buried tunnels exhibits obvious nonlinear variation with increasing confining pressure,and its significant characteristic of high in-situ stress makes it difficult to accurately assess the mechanical responses of the surrounding rock in the tunnel excavation.This paper introduced the nonlinear strength characteristics of rock and established a logarithmic strain equation for the surrounding rock of deeply buried tunnels.Considering the commonly overlooked strain-hardening characteristics of rock in previous studies,the internal variables were solved using the plastic shear strain of the current node during the iterative finite difference process.An analytical method coupling elasto-plasticity with finite strain for surrounding rock was proposed,based on the unified strain-hardening,strain-softening constitutive model and the nonlinear dilatancy model.When the model reverted to small strain analysis,the analytical results aligned with classical theoretical solutions,validating the effectiveness of the proposed method.Analysis results of influential parameters reveal that neglecting the nonlinear attenuation of the rock dilatancy coefficient leads to an underestimation of the plastic zone range of the finite strain of surrounding rock.As the rock dilatancy characteristics increase,the displacement of the tunnel wall,the radius of the residual zone and the plastic zone gradually increase,and the increment is pronounced with decreasing confining pressure.The strain�softening characteristics of rock predominantly affect the proportion of the residual and softening zones of the surrounding rock,leading to changes in displacement of the surrounding rock.Enhancing this characteristic significantly reduces the radius of the plastic zone.The consideration of rock strain-hardening characteristics is crucial for evaluating the plastic zone range of surrounding rock.However,the increased strain-hardening characteristics exerts minor impact on the radius of the plastic zone,primarily altering the proportion between the softening and hardening zones of the surrounding rock.The method proposed in this paper can effectively evaluate the plastic zone range of finite strain of surrounding rock in deeply buried tunnels,offering theoretical guidance for the design of the supporting structure system.