This paper presents a numerical method to predict the temperature weakening effects on tensile and compressive strength and stiffness of granitic rock. Thermally induced cracking, leading to degradation of the material stiffness and strength, is modelled in the continuum sense by using a damage-viscoplasticity model based on the Drucker-Prager criterion with a rounded tensile cut-off surface. The governing thermo-mechanical initial/boundary value problem is solved with an explicit (in time) staggered method while using extreme mass scaling to increase the critical time step. Rock heterogeneity is described as random clusters of finite elements assigned with the constituent mineral, here Quartz, Feldspar, and Biotite, material properties further randomized by Weibull distribution. In the present approach, only Quartz thermal expansion coefficient is assumed temperature dependent due to its strong and anomalous temperature dependence upon approaching the α-β transition. In the numerical testing, the sample is first volumetrically heated to a target temperature. Then, the uniaxial tension and compression tests are performed on the cooled down numerical samples. The simulations demonstrate the validity of the proposed approach as the experimental weakening effects on the rock strength and stiffness as well as the macroscopic failure modes, both in tension and compression, are realistically predicted in a non-circular way, that is, not using the temperature dependence of any material parameter, save Quartz thermal expansion, as an input data.

中文翻译：

---

花岗岩热弱化效应的 3D 数值预测

本文提出了一种数值方法来预测温度减弱对花岗岩的抗拉抗压强度和刚度的影响。通过使用基于 Drucker-Prager 准则和圆形拉伸截止表面的损伤-粘塑性模型，对导致材料刚度和强度退化的热致开裂进行连续统一建模。控制热机械初始/边界值问题通过显式（及时）交错方法解决，同时使用极端质量缩放来增加关键时间步长。岩石异质性被描述为分配有组成矿物的有限元的随机簇，这里是石英、长石和黑云母，材料特性通过 Weibull 分布进一步随机化。在目前的方法中，只有石英热膨胀系数被假定为温度相关，因为它在接近 α-β 转变时具有强烈且异常的温度依赖性。在数值测试中，首先将样品体积加热到目标温度。然后，对冷却后的数值样品进行单轴拉伸和压缩试验。模拟证明了所提出方法的有效性，因为实验削弱对岩石强度和刚度的影响以及在拉伸和压缩中的宏观破坏模式，以非圆形方式实际预测，即不使用任何材料参数的温度依赖性，保存石英热膨胀，作为输入数据。