In this paper, the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading. Firstly, a coupled damage variable was derived, which contains two parts, i.e., the compaction-induced damage and the cracking-induced damage. The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage, and the cracking-induced damage variable was established based on the statistical damage theory. Secondly, based on the total damage variable, a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions, whereafter, the application of this model is extended to cyclic loading and unloading conditions. To validate the proposed monotonic and cyclic constitutive equations, a series of mechanical tests for marble specimens were carried out, which contained the monotonic uniaxial compression (MUC) experiment, cyclic uniaxial compression experiments under the variable amplitude (CUC-VA) and constant amplitude (CUC-CA) conditions. The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic, i.e., the damage variable firstly decreases, then increases no matter under the conditions of MUC, CUC-VA or CUC-CA. Then a reasonable consistency is observed between the experimental and theoretical curves. The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors, such as the initial compaction, the strain hardening and the strain softening. Furthermore, the shapes of the theoretical curves are controlled by the modified coefficient, compaction sensitivity coefficient and two Weibull distributed parameters.

本文提出了循环本构方程来描述循环加载和卸载的本构行为。首先，导出了耦合损伤变量，该变量包含压实损伤和开裂损伤两部分。压实致损伤变量来源于初始压实阶段的非线性应力-应变关系，开裂致损伤变量是基于统计损伤理论建立的。其次，基于总损伤变量，提出了描述岩石在单调单轴压缩条件下的本构关系的损伤本构方程，并将该模型的应用扩展到循环加卸载工况。为了验证所提出的单调和循环本构方程，对大理石试样进行了一系列力学试验，包括单调单轴压缩（MUC）实验、变幅（CUC-VA）和等幅（CUC-CA）条件下的循环单轴压缩试验。结果表明，所提出的总损伤变量综合反映了损伤演化特征，即无论在MUC、CUC-VA还是CUC-CA条件下，损伤变量都是先减小后增大的。然后在实验曲线和理论曲线之间观察到合理的一致性。所提出的循环本构方程可以模拟整个循环加载和卸载行为，如初始压实、应变硬化和应变软化。此外，