# A Study of Constitutive Model of Rock Damage under the Joint Effect of Load and Moisture
## 1 Introduction  
Rock, as one of the common natural materials in engineering projects, often is featured with various degrees of internal macrostructure flaws. Rock failure tends to occur when rock damage continues to accumulate, exceeding the load-bearing capability [1, 2]. It is common in the natural environment that rock is surrounded or submerged in water. Water can change the macrostructure of rock through physical, chemical, and mechanical interactions, resulting in decreases in strength, and geological disasters [3, 4, 5]. Therefore, studying rock damage variances under the joint effect of load and water content through the constitutive model can provide insightful guidance to engineering project development and implementation [6, 7, 8]. The interaction between rock and rock was first proposed by [PERSON] from the Soviet Union. Since then, the study of water and rock interaction has been transformed into multi-field and interdisciplinary, especially regarding the physical and mechanical characteristics of rock [9, 10, 11, 12]. In the mechanical study of rock, compared with the study of elasticity and the study of plastics, the damage theory was launched at a later time. In the year 1958, [PERSON] first introduced some basic concepts in the study of rock damage, such as the effective stress and continuous factors, marking the beginning of rock damagestudy [13]. In the year 1976, [PERSON] first applied damage mechanics to rock study [14], followed by [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON], who studied the damage mechanics of rock by taking advantage of different definitions of damage variables, damage parameters, yield principles, and conditions. Now, damage theory has become one of the effective approaches to the study of rock [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. Rock damage mechanic behaviors can be described using the damage variables and the constitutive formulas, which have been studied intensively by domestic and overseas scholars. The constitutive model based on the statistic damage theory has been consistently proven effective. Commonly used probability distribution functions for rock damage models based on statistical theory include the Weibull distribution function, normal distribution function, power function, etc. The statistical damage constitutive model of structure has been proven to be effective in fitting rock constitutive relations and describing the process of rock deformation and failure [27; 28; 29; 30; 31]. For example, [PERSON] and [PERSON] [32] quantified the effects of water content on the mechanical properties of rocks and developed a method for estimating rock strength and deformability based on physical properties. [PERSON] and his team [29; 33] established a rock statistical damage constitutive model considering the changes of the elastic module, combined with a rock strain softening statistical damage simulation method based on the characteristics of the pore compaction stage. [PERSON] and his team [34] proposed an anisotropic damage model for mudstone based on the Drucker-Prager criterion, which takes into consideration the degradation of the mudstone pore matrix and the changes in hydro-mechanical properties caused by damage. [PERSON] and his team [35] adopted the Hoek-Brown strength criterion to describe the micro-element strength of rock and deduced the statistical damage constitutive model of rock under three-dimensional stress conditions. [PERSON] et al. [36] established a seepage-damage coupling model of mudstone by introducing the damage variables into the seepage-stress coupling control equation. [PERSON] [37] et al. deduced the modified damage-softening constitutive model of sandstone following a nonlinear fitting method based on the characteristic that rock damage variables comply with the Weibull distribution. Based on the unified strength theory, [PERSON] et al. [38; 39] established an elastic-plastic damage constitutive model of rock, reflecting the dynamic and static load characteristics of rock.