The stability and durability of rocks in cold regions are significantly impacted by the degradation of mechanical properties caused by freeze–thaw (F–T) environment. In this work, we shall propose a rational multiscale nonlinear constitutive model based on thermodynamics, micromechanics, and fractional calculus theory to describe the complete deformation and failure process of F–T rocks under triaxial compression. The F–T rocks at the mesoscale are regarded as consisting of porous matrix and cracks, while porous matrix is composed of the micropores and elastic solid grains at the microscale. According to experimental observations, we assume the F–T action mainly causes micropores growth and cracks opening, and mechanical damage is resulted from the initiation and propagation of cracks. In this context, the effects of F–T and mechanical damage on effective elastic properties of rocks can be quantitatively analyzed by using the two-step Mori–Tanaka (M-T) homogenization method. After subtly deriving the total free energy function of F–T rocks under compression, we systematically develop specific criteria for describing open cracks closure deformation, mechanical damage evolution and frictional sliding induced plastic distortion. Note that to correctly capture the plastic deformation characteristics, the non-orthogonal flow rule based on fractional differential calculations is employed. Following that, analytical analyses and numerical implementation of the proposed model are conducted. The performance of the model is evaluated by the simulations with experimental data on two kinds of F–T rocks, and discussions on parameters sensitivity and effects of fractional order are followed.

中文翻译：

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三轴压缩冻融岩石的合理多尺度非线性本构模型


寒冷地区岩石的稳定性和耐久性受到冻融（F-T）环境引起的力学性能退化的显着影响。在这项工作中，我们将提出一种基于热力学、微观力学和分数阶微积分理论的理性多尺度非线性本构模型来描述F-T岩石在三轴压缩下的完整变形和破坏过程。 F-T岩石在介观尺度上被认为是由多孔基质和裂隙组成，而在微观尺度上多孔基质则由微孔和弹性固体颗粒组成。根据实验观察，我们假设F-T作用主要导致微孔生长和裂纹张开，机械损伤是由裂纹的萌生和扩展引起的。在这种背景下，F-T和机械损伤对岩石有效弹性特性的影响可以通过两步Mori-Tanaka（M-T）均质化方法进行定量分析。在巧妙地推导了压缩下 F-T 岩石的总自由能函数后，我们系统地制定了描述开放裂纹闭合变形、机械损伤演化和摩擦滑动引起的塑性变形的具体标准。请注意，为了正确捕获塑性变形特征，采用了基于分数微分计算的非正交流动法则。随后，对所提出的模型进行了分析分析和数值实现。通过对两种 F-T 岩石的实验数据进行模拟来评估模型的性能，并讨论参数敏感性和分数阶的影响。