沉积岩水力压裂问题数值模拟及解析解研究

Numerical Simulation and Analytical Solution of Hydraulic Fracturing in Sedimentary Rock Tunnels

在岩体隧道工程的勘测、施工、运营整个过程中,水力压裂是一种需要重点关注的力学机制。文章针对层理性沉积岩材料,运用有限元断裂损伤模拟和解析推导两种手段开展水力压裂问题研究。基于多场耦合有限元分析软件,结合线弹性断裂准则与损伤本构模型,二次开发了可以表征微裂纹的渗流-应力-损伤耦合岩石模型,并应用于饱和渗流岩体水力压裂过程,通过引入弥散的平行微裂纹表达沉积岩的层理,建立沉积岩圆筒模型模拟孔径注水、外加围压条件下的水力压裂行为,研究其压裂破坏模式及渗流分布模式。另外,通过变化孔径和围压,探讨临界起裂水压与围压、试件孔径的定量关系。为了验证数值模拟所得起裂压力规律,基于渗流理论和弹性力学基本方程,结合模拟中得到的张拉破坏模式,推导了均质线弹性渗流岩体圆筒的临界起裂水压公式。解析与数值计算结果对比显示,两种途径得到的起裂压力吻合很好,偏差呈现在3%以内;围压越大,起裂压力越大,两者近似呈线性关系;孔径越小,起裂压力越大,两者在一定范围内近似呈负斜率线性关系。同时,起裂压力解析解总是略大于数值解,这反映出解析方法与数值方法基本材料假设不同所造成的影响。在材料性质参数一致时,基于理想线弹性体假设得到的起裂压力会大于引入初始损伤层理的材料算得的起裂压力。

In the whole process of survey, construction and operation of rock tunnels, hydraulic fracturing is a mechanical mechanism that needs to be focused. In this paper, numerical simulation for fracture damage constitutive model and analytical formula were used to study the hydraulic fracturing of stratified sedimentary rocks. Based on multi-field coupling finite element analysis software, and combining the linear elastic fracture criterion with the damage constitutive model, a seepage-stress-rock damage coupling model is redeveloped, in which micro cracks can be characterized, and applied to study the hydraulic fracturing of rock mass in the saturated seepage process. By introducing dispersed parallel micro cracks for simulating the beddings of sedimentary rocks, the sedimentary rock cylinder model was established to simulate the hydraulic fracturing behaviors under injecting water into apertures and acting of confining pressure, in order to study the fracturing failure modes and seepage distribution patterns. In addition, the quantitative relationship between the critical water pressure for initial cracking and the confining pressure, the pore diameter of specimens was discussed by changing the pore diameter and confining pressure. In order to verify the cracking initiation pressure law obtained by numerical simulation, based on the seepage theory and the basic equation of elastic mechanics, and combined with the tensile failure mode obtained in the simulation, the formula of critical water pressure for cracking initiation in the rock cylinder with uniform linear elastic seepage was derived. The results of analytical solution and numerical calculation show that the cracking initiation pressure obtained by the two methods is in good agreement with the deviation within 3%. The larger the confining pressure, the larger the cracking initiation pressure, with the approximate linear relationship. The smaller the aperture, the larger the cracking initiation pressure, with the approximate negative slope linear relationship in a certain range. At the same time, the cracking initiation pressure by the analytical solution is always slightly greater than that of the numerical solution, which reflects the impact caused by the difference of the basic material hypothesis between the analytical method and the numerical method. When the material property parameters are consistent, the cracking initiation pressure based on the assumption of ideal linear elastomer will be greater than that of the material introduced into the initial damage bedding.