A Stress‐Driven Double‐Phase–Field Framework for Tensile Fracturing Processes in Transversely Isotropic Rocks

IF 3.4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2024-09-19 DOI:10.1002/nag.3830
Weihong Yuan, Yang Zhao, Bingyin Zhang
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Abstract

We present a double‐phase–field framework for tensile fracturing processes in transversely isotropic rocks. Two distinct phase‐field variables are introduced to represent smeared approximations of tensile fractures along the weak bedding planes and through the anisotropic rock matrix, respectively. Driving forces that control fracture propagation in the phase‐field framework are constructed as a stress‐based formula with a recently developed tensile failure criterion that distinguishes the two failure modes in transversely isotropic rocks. For numerical implementation, we adopt a staggered integration scheme and decouple the governing equations so that the displacement field and phase‐field variables can be updated in sequence for a given loading step. The finite element formulation of the proposed framework is introduced in detail in this paper and is implemented in an in‐house finite element code. The numerical implementation is then validated by reproducing the uniaxial tension test results of Lyons sandstone. After that, we conduct simulations on a pre‐notched square plate loaded in tension to demonstrate the features of the proposed framework. Finally, we conduct simulations of three‐point bending tests of Pengshui shale and show that the proposed model can reproduce the force–displacement curves and failure patterns of specimens with different bedding plane orientations observed in laboratory experiments.
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横向各向同性岩石拉伸压裂过程的应力驱动双相场框架
我们提出了横向各向同性岩石拉伸断裂过程的双相场框架。我们引入了两个不同的相场变量,分别代表沿弱基底面和穿过各向异性岩石基质的拉伸断裂的涂抹近似值。相场框架中控制断裂扩展的驱动力被构建为一个基于应力的公式,该公式采用了最新开发的拉伸破坏准则,可区分横向各向同性岩石中的两种破坏模式。在数值实现方面,我们采用了交错积分方案,并将控制方程解耦,从而可以在给定加载步骤中依次更新位移场和相场变量。本文详细介绍了拟议框架的有限元公式,并在内部有限元代码中实施。然后,通过再现里昂砂岩的单轴拉伸试验结果,对数值实现进行了验证。之后,我们对一块预缺口方形板进行了模拟拉伸加载,以展示所提框架的特点。最后,我们对彭水页岩的三点弯曲试验进行了模拟,结果表明所提出的模型可以再现实验室实验中观察到的不同基底面方向试样的力-位移曲线和破坏模式。
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来源期刊
CiteScore
6.40
自引率
12.50%
发文量
160
审稿时长
9 months
期刊介绍: The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.
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