深埋软岩非线性流变模型及隧道施工时效性规律研究

The elastoplastic theory is often one of the main methods for tunnel mechanical analyses so far, but it can’t be used for interpretation and prediction of the time-dependent behavior of rock deformation that can usually be well overcome by the rheological theory. The existed rheological constitutive models have disadvantages of description error and parameter uncertainty, and are very difficult to be utilized in actual projects. A more accurate and easy-used constitutive model and analysis method is obviously needed. This study is to investigate a new constitutive model based on the fractional calculus theory and damage theory. The main research of this study is as follows. Firstly, a new rheological constitutive model is to be established based on the fractional calculus theory and damage theory, and the constitutive equation and creep equation is derived. Secondly, a finite difference transforming form of the constitutive equation and its application in numerical analysis is then studied. Thirdly, a study on analytical solution of time-dependent deformation is carried out by taking account of the construction process of the soft rock tunnel with a deep overburden. Finally, a three-dimensional simulation model of soft rock tunnel with deep overburden is established in order to examine the rheological characteristics and the design method of reserved rock deformation. The research method to be used in this study includes three-dimensional rheological compression test, theoretical analysis and numerical modeling. The research achievement helps to reveal the time-dependent pattern of soft rock tunnel with a deep overburden, and to promote the development of rheological theory and its application in tunnel engineering.

弹塑性理论是常用的隧道力学分析的主要手段之一，然而它无法解释和预测隧道围岩变形所表现出的时效性特征，流变理论能较好的克服这一缺点。现有流变本构模型存在一定的描述偏差和参数不确定性，难以推广应用到实际工程中。因此，需要更为准确且易于使用的本构模型及分析方法。本课题在引入分数阶微积分理论和损伤理论的基础上，探索一种新的基于分数阶非线性蠕变损伤模型。主要研究内容为：（1）建立基于分数阶非线性蠕变损伤的本构模型，并推导出本构方程和蠕变方程；（2）研究本构方程的有限差分转化形式及其在数值分析中的应用方法；（3）考虑深埋软岩隧道施工过程，研究围岩蠕变位移的数学解析表达；（4）建立深埋软岩隧道三维仿真模型，研究其流变特征和开挖预留变形量设计方法。研究手段包括等围压三轴蠕变压缩试验、理论解析和数值分析。研究成果有助于深入揭示深埋软岩隧道施工时效性规律，促进流变理论的发展及其在隧道工程中的应用。

本项目以深埋软岩隧道流变特性为研究背景，基于相关试验和现场测试，采用理论分析及数值仿真等方法，从岩石流变本构模型出发，研究了适合于描述软岩隧道流变特性的几种本构模型，并将新建本构模型用于隧道流变变形解析解及数值仿真方面的分析。主要研究成果包括：（1）结合流变本构模型理论和等围压三轴压缩蠕变试验结果，建立了岩体强度随应变增量变化的损伤函数和三参量（H-K）蠕变损伤本构模型，该本构模型可较好的反映岩体蠕变的三个阶段；（2）根据Riemann-Liouville分数阶微积分理论，提出了统一采用基于分数阶微积分形式表达的四元件非线性粘弹塑性流变模型，给出了该模型的本构方程及蠕变方程，并将该模型与试验数据分别进行了拟合对比，结果表明该模型可以有效反映岩石三个阶段的蠕变特性，并且起到了减少模型元件个数及参数的作用；（3）利用有限差分程序FLAC3D二次开发平台，通过FISH语言在计算过程中动态评估和修正蠕变参数，实现了将三参量（H-K）蠕变损伤本构模型应用于隧道数值仿真分析，为隧道流变变形分析提供了新的方法和思路；（4）基于三参量（H-K）蠕变损伤本构模型，采用有限差分程序FLAC3D探讨了软岩隧道在不同埋深及侧压力系数时的蠕变变形特征、掌子面对隧道流变的影响、施工停止时间对隧道流变的影响以及台阶法开挖对隧道流变的影响，为隧道施工预留变形量及支护措施的优化提供了参考。课题研究成果有助于深入揭示深埋软岩隧道施工时效性规律，促进流变理论的发展及其在隧道工程中的应用。