# Research on Mechanical Properties and Damage Constitutive Model of Water-Bearing Coal
## 1 Introduction  
Coal is a sedimentary rock composed of organic and inorganic materials that plays an essential role in the global energy structure as a relatively inexpensive and abundant fossil fuel [1, 2]. In many developing countries, coal is the primary energy source. For example, 2.74 billion tons of coal were consumed in China in 2018, providing 59% of the country's overall primary energy usage [3]. Ensuring coal mine safety in production has positive relevance for global energy security and steady supply. In the practice of coal mining, coal seam water injection operations are carried out to prevent rock bursts, suppress gas emissions, and reduce the dust concentration at the working face; waterproof coal pillars are laid out to prevent mine water from entering the roadway; and hard top coal is hydraulically fractured for effective top coal cave mining [4, 5, 6, 7, 8, 9, 10]. Variable degrees of water-rock interaction will occur between water and coal in the above water-related engineering, resulting in the deterioration of coal's mechanical properties and concealing threats to production safety [11, 12, 13]. It is necessary to investigate the macroscopic mechanical properties and damage constitutive model of water-bearing coal for safe mining. Scholars have conducted many studies on the macroscopic mechanical properties of water-bearing coal. [PERSON] et al. [14], [PERSON] et al. [15], and [PERSON] [16] investigated the attenuation law of strength and the elastic modulus of saturated coal samples through uniaxial compression experiments. [PERSON] et al. [17] investigated the strength of saturated water-bearing coal samples versus natural water-bearing coal samples under uniaxial and triaxial compression, discovering that the former is always weaker than the latter. [PERSON] et al. [18] performed uniaxial compression experiments on coal samples with four moisture contents and investigated the link between moisture content and mechanical properties of coal samples and crack propagation characteristics. [PERSON] et al. [19] investigated the impact of water on the mechanical properties and acoustic emission characteristics of raw coal samples by loading experiments, and they discovered that as moisture content increased, the uniaxial compressive strength of the coal samples and the cumulative ring count of acoustic emission gradually decreased. [PERSON] et al. [20], [PERSON] et al. [21], [PERSON] et al. [22], and [PERSON] et al. [23] also obtained similar experimental results: the uniaxial compressive strength and Young's modulus of coal samples decline monotonically as moisture content rises. [PERSON] et al. [24], [PERSON] et al. [25], and [PERSON] et al. [26] performed uniaxial compression experiments on briquetic coal samples varying in moisture content and found that with increasing moisture content, the mechanical strength indexes such as uniaxial compressive strength (UCS) and Young's modulus first increased and then decreased, which were different from the experimental phenomena of raw coal samples [19; 20; 21; 22; 23]. There was no systematic study of the difference between the two experimental phenomena. The authors hypothesized that the difference was related to the porosity and permeability of the coal samples, and that the mechanical strength index of the water-bearing coal samples with higher porosity and permeability would first grow and subsequently decline. In this paper, raw coal samples with large porosity and high permeability are selected for uniaxial compression tests at different loading rates to explore the macroscopic mechanical properties of water-bearing coal. At present, there is little basic research on the damage constitutive models of water-bearing coal, and some researchers have developed some damage constitutive models of water-bearing hard rock. [PERSON] et al. [27] developed a statistical damage constitutive model suitable for rock and other materials by integrating the continuous damage concept with the statistical strength concept for the first time. [PERSON] et al.