DP与EDP模型及其在隧道稳定分析中的应用

Analysis of Tunneling Stability Using Classic and Extended Drucker-Prager Model

Drucker-Prager模型(DP)是隧道工程数值模拟中常用材料模型,随着计算方法的进步,很多有限元软件都开发了Extended Drucker-Prager模型(EDP),以弥补经典模型的不足。本文针对ANSYS中EDP模型的参数不直观的问题进行了系统深入研究,通过对各屈服函数比较,阐述了经典模型与扩展模型中参数的参数意义并指出它们相互转换关系。通过对平面应变条件下的深埋隧道有限元模拟和理论计算,对比了解析解、DP模型和EDP模型数值解。研究表明:EDP模型作为DP模型的改进模型,考虑材料的硬化特性,更符合岩土材料的实际情况; EDP模型中的参数可以通过粘聚力和内摩擦角求得;在弹塑性分析中,解析解与利用EDP和DP模型求得应力基本一致;但是,解析解求得到的塑性区半径小于数值模型求得的值。

The classic Drucker-Prager model is a popular model in numerical simulations of tunneling engineering. With progress of theory and method,many finite element software have researched and developed an Extended Drucker-Prager mode in order to cover its original shortage. According to the problem that parameters of EDP model are special,this paper studies extended Drucker-Prager model carefully in ANSYS. By comparing their different yield functions,the relation and physical mean of their input parameters were described and the parameter transfer formulas between DP model and EDP mode were given. Then under plain strain condition,a deep circular tunnel engineering stability was analyzed by an analytic stress solution and a finite element method using DP and EDP model separately. Therefore,some conclusions are drawn. Firstly,as an improvement,because of considering effect of hardening mode of material,the EDP model is more reasonable and conform the case further. Secondly,parameters value of EDP model,such as pressure sensitive parameter and yield stress of material,can be calculated from cohesion and friction angle. Thirdly,in elasto-plastic analysis for deep circular tunnel,3 stress distributions which are analyzed by an analytic stress solution and a finite element method using DP and EDP model separately are mostly agree. However,the radius of plastic zone with an analytic stress solution is smaller than one with finite element numerical method.