The coal samples used throughout the present study were gathered from Xiaojihan coal mine, Yulin City in Shanxi Province, China. The sampling location was at the solid coal side of an auxiliary transportation roadway in the 11,215 working face, 2,650 m away from the mining face, that had been less affected by mining induced stresses (see in Figure 1, the red solid dot indicates the sample location). The samples were cored according to the International Society for Rock Mechanics (ISRM) Standards (Fairhurst and Hudson, 1999) with 50 mm diameter and 100 mm height.

In this experimental study, first of all, conventional tension, compression and shear tests were carried out with intact and undamaged coal specimens to obtain the basic physical and mechanical parameters of coal mass, as described in Basic Mechanical Properties of Conventional Coal Samples.

Then, based on the quantitative calculation of damage in Definition of CID, the MTS815 electro-hydraulic servo-controlled system was used to prepare coal samples with different CID values through triaxial compression tests with different loading-unloading cycles.

Finally, the CID control values were set to be 0, 0.2, 0.3, 0.4, and 0.5. Two coal specimens were selected for each CID control value, and a total of 10 CID coal samples were selected for subsequent triaxial compression tests to study the effects of different CID values on the mechanical properties of CID coal samples. Because the CID value cannot be precisely controlled when the CID coal sample is prefabricated, the coal sample whose CID value is closest to the CID control values should be selected as far as possible. For example, when the CID control value is 0.3, two coal samples with CID value of 0.312 and 0.318 are selected, as shown in Mechanical Testes of Coal With CID.

The surrounding rock in underground excavations usually undergoes multiple and often different stress loading and unloading events, depending mainly on the mining sequence. Considering that the elastic stage has little influence on the damage of coal samples in the compression test, it is necessary to ensure that the coal sample is loaded to the yield stage in order to produce certain damage (Gu et al., 2018; Walton et al., 2019), but the coal pillar is prone to splitting failure at the yield stage (Li et al., 2018). Therefore, according to Huang et al. (2021a) and Huang et al. (2021b), the preparation of the damaged coal samples was carried out using the MTS815 pressure testing machine with circumferential displacement control (to ensure that the coal samples are not be destroyed instantaneously); the loading rate of circumferential displacement was 0.002 mm/s; the circumferential displacement was increased by 1 mm per cycle; the way of axial unloading was controlled by the load; the final unloading was 1 kN; and the unloading rate of axial force was 0.1 kN/s. The loading stress path is shown in Figure 2.

An MTS815 electro-hydraulic servo rock test system was used for the tests. As shown in Figure 3, the test system consists of the loading system, control system, and measurement system. It could provide a maximum axial pressure of 4,600 kN, a maximum confining pressure of 140 MPa, and a minimum sampling interval of 50 μs.

The test procedure was as follows:

1) Activate the MTS815 electro-hydraulic servo test system oil pumps

The stress-strain curves of conventional coal samples under uniaxial compression are shown in Figure 4A, and those in tensile tests are shown in Figure 4B.

Using basic rock mechanics, the physical and mechanical properties of the conventional coal samples were obtained after testing. The test results are shown in Table 1.

Damage variables can well describe the internal damage statue of rock and can quantitatively analyze the occurrence, expansion and damage law of cracks in the process of rock failure. There are many methods to define damage variables, such as effective load area method, sound velocity method, microcrack method, acoustic emission method, elastic modulus method, plastic strain method, CT number method etc., (Basista and Gross 1997; Dhar et al., 1996; Liu et al., 2017; Muzyka, 2018; Gu et al., 2018; Ma et al., 2020), and the local energy release rate (LERR) was proposed to deal with rockbust (Su, 2006). The energy method was used to define CID in the present investigation.

According to the principle of energy conservation, the exchange of heat between the sample and the exterior is not considered during the loading process. Part of the total work done by the hydraulic press is stored inside the sample and is released completely in the form of elastic energy during unloading. The other part of the energy is used for the dissipation of damage and plastic deformation inside the sample. The total work done by the compression is expressed as follows: U = U e + U d (1) where, U _e is the elastic energy stored in the specimen during the loading process, J; and U _d is the energy dissipated during the loading process, J.

In the cyclic loading-unloading full stress-strain curve, U is the area enclosed by the stress-strain curve and the x-axis during the loading process, and U _e is the area enclosed by the stress-strain curve and the x-axis during the unloading process (see in Figure 5.)

The CID is defined as the ratio of the accumulated plastic energy to the total strain energy of the cycle, as shown in Eq. 2: C I D = U d ( i ) / U ( i ) (2) where, U d ( i ) is the accumulated plastic energy of i cycles, J, as shown in Eq. 3; and U ( i ) is the total strain energy of i cycles, J. U d ( i ) = ∑ k = 1 i U d k (3) where, U d k is the plastic energy of kth cycle, J.

According to Eq. 1, the cumulative total strain energy of i cycles can be expressed as: U ( i ) = ∑ k = 1 i U d k + U e k (4) where, U e k is the elastic energy of kth cycle, J.

The accumulated plastic energy and total strain energy can be obtained from the area enclosed by the stress-strain curve and the x-axis in the cyclic loading-unloading test. The CID can be obtained by combining Eqs 2–4 as follows: C I D = ∑ k = 1 i U d k / ( ∑ k = 1 i U d k + U e k ) (5)

According to the definition of the damage variable in Eq. 2, the equivalent values of the total strain energy, the elastic strain energy and the plastic strain energy of coal samples with different degrees of CID are calculated.

As shown in Table 2, the values of all damage variables are in the range of 0–1. The damage variable increases with the increase of loading and unloading times, which indicates that the number of times of cyclic loading can increase the degree of damage, which agrees with the basic properties of rock mechanics.

Based on triaxial compression test data of coal samples with different degrees of CID, each data is divided into 0, 0.1–0.2, 0.2–0.3, 0.3–0.4, 0.4–0.5, 0.5–0.6 ranges to calculate the corresponding average CID and deviatoric stress value. The relationship curve between the deviating stress of coal samples and the CID was obtained.

As can be seen from Figure 7, the relationship between the CID and deviating stress of a coal sample is a quadratic function. With the increase in the initial damage variable value, the deviating stress of the coal sample decreases. When the initial damage variable value is increased from 0 to 0.521, the average deviating stress of coal sample decreases from 34.9 to 23.9 MPa, i.e., a decrease of 31.4%. It can be observed that initial damage has a great influence on the strength of the coal sample. Before the initial damage value exceeds 0.40, the peak deviational stress decreases sharply, and after that the peak deviational stress decreases gradually. This is because the CID makes cracks in the coal sample develop and the bearing capacity of some structures decreases.

Figure 8 illustrates the relationship between the CID and the peak strain of the coal samples is a quadratic function. With an increase in the initial damage variable, the peak strain of the coal samples decreases. When the initial damage variable is increased from 0 to 0.521, the average peak strain of the coal samples decreases from 1.057 to 0.659; a decrease of 37.7%.

According to the triaxial compression stress-strain curves of coal samples with different degrees of CID, the relationship between the volumetric strain and the deviating stress, and the relationship between the deviating stress and the damage variable at the starting point of expansion of the coal samples were extracted.

As for the volumetric strain, the positive value means the sample is under compression condition while the negative value indicates volume expansion state. Also, when the volumetric strain decreases, it means that the specimen is experiencing the process of volumetric expansion; when the volumetric strain increases, it means that the specimen is experiencing the process of volumetric compression. Thus, as shown in Figure 9, the triaxial compression expansion characteristics of coal samples with different degrees of CID had the following characteristics:

1) From the curves of different initial damage degrees and deviating stress, it can be seen that there are strain inflections and expansion starting points in the volume strain. Which indicates that coal samples begin to expand from the compression state, while the expansion starting point indicates that the coal samples begin to expand with initial damage;

Ductility reflects the deformation capacity of coal and rock media from yield point to maximum bearing capacity. By defining the ductility coefficient as the ductility index of the coal and/or rock media, the mechanism of the brittle-ductile transformation of the coal and rock media can be analyzed quantitatively. The expression for the ductility coefficient is as follows (Zhang 2012): η = ε c / ε s (6) where, ε _c is the strain at peak stress, and ε _s is the strain at the 80% stress.

The change in the ductility coefficient with CID is shown in Table 3.

Figure 10 shows that the relationship between the value of the CID and the ductility coefficients of the coal samples is a quadratic function. With an increase in the value of the initial damage variable, the peak strain of the coal samples increases. When the initial damage variable value increased from 0 to 0.521, the ductility coefficient of the coal samples increased from 1.278 to 1.361; an increase of 6.49%. It is evident that an increase in the cumulative effect of the initial damage changed the failure mode of the coal samples and increased their ductility.

A TESCAN VEGA3 Scanning Electron Microscope (SEM) was used to scan the fracture surface of CID coal samples, as shown in Figure 11, which shows images of the microstructural features of coal samples after triaxial compression failure under different values of CID.

According to Mao (2018), the brittle fracture of coal and rock sample mainly includes transgranular fracture and intergranular fracture. The main difference between the two fracture is whether the crack develops through the inside of the grain or along the grain boundary. And the main characteristic morphologies of transgranular fracture include cleavage step, lamellar tear fracture and “tongue” pattern. Compared with brittle fracture, ductile fracture is a kind of fracture related to the plastic deformation process of coal and rock. Its main characteristic morphology is dimple which is mainly shown as continuous large pits in the section, and there are significant tearing failure characteristics around the pits. Dimples are formed by the growth and accumulation of cavities within the rock under load, eventually forming macroscopic fracture surfaces.

The failure fracture of coal samples with different CID values showed great differences. In Figure 11, both brittle fracture and ductile fracture can be observed, and some representative morphological features are identified. When CID = 0, the coal sample basically has no initial damage, and its internal structure is complete with strong integrity. After destruction, as shown in Figure 11A, its section is basically brittle fracture with cleavage steps, lamellar tearing and other morphological features, and there are small pits and holes dispersed, but they have not developed into contiguous dimples. When CID = 0.5221, a considerable degree of initial damage has been accumulated in the CID coal sample before loading. Then after triaxial loading, the internal damage further develops. After the failure, as shown in Figure 11B, there are brittle fractures mainly composed of cleavage steps and lamellar tearing in the fracture surface. There are also a large number of ductile fractures, mainly dimples.