基于黏聚力弱化边界面模型的深部洞室响应分析

Analysis on response of deep circular tunnel based on a cohesion-weakening bounding surface model

在原位地应力和开挖卸载作用下,深部洞室围岩呈现硬化-软化响应,这一特性对洞室力学响应评估和支护结构设计有着重要影响。为研究开挖后深部围岩的硬化-软化响应,基于边界面理论框架,引入黏聚力弱化机制,结合改进的Rowe应力-剪胀规律,构建了深部围岩黏聚力弱化边界面模型,将常见的屈服面-峰值强度面-残余强度面简化为初始(峰值)边界面-残余边界面,避免了屈服面参数测量误差对计算结果的影响。在该本构模型增量化应力-应变关系的基础上,引入Hencky应变以评估洞室大变形工况,并引入辅助变量完成坐标转换,推导了描述深部圆形洞室周围应力场分布的常微分方程组。进一步地,结合深部圆形洞室的地应力环境等边界条件,对常微分方程组进行求解,获得所研究工况下的深部洞室应力分布,并将所得结果与现有解答进行对比校验。随后,分别讨论了相同支护力与不同地应力组合,以及相同地应力与不同支护应力组合等工况下的洞室应力分布。此外,基于所得深部洞室应力分布解答,计算围岩特征曲线并与相关文献进行对比,并讨论残余黏聚力取值对围岩特征曲线的影响。相关结果表明:黏聚力弱化边界面模型可以较好地描述岩石试样的硬化-软化力学行为。采用黏聚力弱化边界面模型可以有效描述深部洞室周围的应力分布,并能为支护设计提供参考。所得的围岩特征曲线能有效反映围岩的响应特征,在中段同支护力下预测的变形值比经典解答略大,残余黏聚力取值对围岩特征曲线影响较大。本文相关结论可为深部洞室支护理论构建、施工方法研发和保障深部洞室安全提供参考。

Surrounding rock of deep tunnels may exhibit certain type of hardening-softening response under the coupling effect of in-suit stress and excavation unloading.This feature would have a strong influence on the evaluation of the opening response and the design of the support structure.In order to capture the hardening-softening response of deep surrounding rock after excavation,a cohesion-weakening bounding surface constitutive model was developed within the framework of bounding surface theory.It was derived by introducing a cohesion-weakening mechanism and a modified Rowe stress-dilatancy rule.Prediction errors caused by the uncertainties in yield surface parameter measurements were avoided by simplifying the yield surface-peak strength-residual strength system in classical constitutive models to the initial(peak)bounding surface-residual bounding surface in the proposed model.Controlling ordinary differential equations(ODEs)of the stress distributions around the deep circular tunnel were derived based on the incremental stress-strain relationship of the proposed constitutive model.The Hencky strain was introduced to capture large deformations and an auxiliary variable was introduced to reduce the controlling equation system.The ODEs were solved under given boundary conditions such as earth pressure,and the stress distributions of the deep circular tunnel were calculated and validated by comparison with existing solutions.In addition,the stress distributions of the deep tunnel under different combinations of support pressures and earth pressure were derived and investigated.Furthermore,the ground response curve was derived by exploiting the stress distribution solution in this paper and the influences of residual cohesion are also investigated.Results show that:the proposed cohesion-weakening bounding surface model could reasonably capture the hardening-softening behavior of rock.The proposed constitutive model could accurately predict the stress distributions of the deep tunnel and could be used as a reference for the design of the support structure.The ground response curve(GRC)derived in this paper could reflect the response characteristics of the surrounding rock but provide slightly larger prediction on deformation on the middle of the GRC under same the supporting pressure value.The value of residual cohesion has a strong influence on the ground response curve.The conclusions of this paper could provide an effective reference for the development of support design and construction methods and the safety of deep tunnels.