3.1.1. Determination of Key Parameters

In order to analyze the differential damage and failure process of the roadway in the steeply inclined coal seam, the UDEC (universal distinct element code) numerical software is used to carry out a simulation study. The UDEC is a discontinuous mechanics method that uses discrete element method theory to provide accurate analyses for geotechnical engineering and mining engineering. It simulates the mechanical response of a jointed rock stratum under static or dynamic load, such as stress, displacement, and crack evolution [16,17]. The Trigon module in the software can realistically simulate the generation, expansion, and coalescence of cracks in brittle materials [18,19]. It was developed by Gao and Stead [20] on the basis of the Voronoi algorithm, which mainly divides a randomly generated polygonal mesh into triangular blocks. The resulting model has less dependence on a mesh, improves the problem of the post-peak strain hardening of rocks, and can realistically simulate fracturation as well as crack evolution in mining engineering.

In the discrete element model the mechanical parameters of the block and contact surface jointly determine the mechanical properties of a rock mass. The parameters of the block include density and the bulk as well as shear moduli, while those of the contact surface include normal stiffness, tangential stiffness, cohesion, and internal friction angle. The bulk modulus, *K*, and shear modulus, *G*, in the model are determined by the elastic modulus, *E*, and Poisson's ratio, *ν*; the specific conversion relationship (see Equations (1) and (2)) is as follows [21]:

$$K = \frac{E}{\Im(1 - 2\nu)}\tag{1}$$

$$G = \frac{E}{2(1+\nu)},\tag{2}$$

In the Trigon module the elastic modulus of the triangular block depends on the normal stiffness and tangential stiffness of the contact surface of the block, and its calculation formula (see Equations (3) and (4)) is as follows [22]:

$$k\_n = 10 \left[ \frac{K + \frac{4}{3}G}{\Delta Z\_{\text{min}}} \right],\tag{3}$$

$$k\_s = 0.4k\_{n\_f} \tag{4}$$

where *kn* is the normal stiffness of the contact surface, *ks* is the tangential stiffness of the contact surface, and Δ*Z*min is the minimum side length of the block.

Therefore, in order to determine the mechanical parameters of the model block and the contact surface, it is necessary to obtain those of the real rock stratum in combination with laboratory experiments to verify the rationality of the model parameters.

#### 1. Determination of Rock Mass Parameters

The parameters of coal–rock samples, i.e., rock parameters, are obtained through experiments, while the parameters applied in UDEC are rock mass parameters; therefore, the conversion of mechanical parameters is required.

Zhang and Einstein [23] proposed the conversion formula between the elastic modulus of rock mass and the elastic modulus of rock, as shown in Equation (5):

$$\frac{E\_m}{E\_r} = 10^{0.0186RQD - 1.91} \tag{5}$$

where *Er* is the rock elastic modulus; *Em* is the rock mass elastic modulus; and *RQD* is the rock quality index, which is obtained by peeping from a borehole in the ventilation roadway of Working Face 1961.

Singh and Seshagiri [24] found that there is a strong linear relationship between the *n*th power of the ratio of the rock mass elastic modulus to the rock elastic modulus and the ratio of the rock mass compressive strength to the rock compressive strength, as shown in Equation (6):

$$\frac{\sigma\_{cm}}{\sigma\_{\rm c}} = \left(\frac{E\_m}{E\_r}\right)^j,\tag{6}$$

where *σ<sup>c</sup>* is the rock compressive strength; *σcm* is the rock mass compressive strength; and the general value of *j* is 0.56.

The rock mass tensile strength is shown in Equation (7):

$$
\sigma\_{\rm trr} = k \sigma\_{\rm cm} \tag{7}
$$

Hoek and Brown [25] proved that the value of *k* is generally 0.05–0.1, so its value is 0.1 this time.

The rock mechanical parameters are converted into rock mass mechanical parameters by calculation and filled into Table 1.


**Table 1.** Conversion of rock parameters and rock mass parameters.

#### 2. Verification of Model Parameters

The micro-parameters of the contact surface are calculated with rock mass parameters according to Equations (1) to (4). A 5 × 10 m plane model is established by the UDEC to carry out uniaxial compression simulation experiments and obtain simulated mechanical parameters, such as the compressive strength and elastic modulus of each rock stratum. The obtained simulated values are compared with the experimental values. If the error between the simulated and experimental values is large, it is necessary to adjust the rock stratum parameters again for another simulation, and so on.

After many simulation adjustments, the microscopic parameters with an error of less than 5% are set as the final mechanical parameters of the model, as shown in Table 2.


**Table 2.** Mechanical parameters of each rock stratum in the model.

#### 3.1.2. Model Establishment

The UDEC model is designed according to the geological occurrence of the ventilation roadway of Working Face 1961, and the model size is 50 m × 50 m. It can be seen from Figure 5 that the model is divided into twenty layers, including five lithologies, namely coal, argillaceous siltstone, carbonaceous mudstone, siltstone, and fine-grained sandstone, and that the dip angle of each rock stratum is set to 53◦. The model adopts the mechanical parameters calibrated in Section 3.1.1, as shown in Table 2. The origin of the model is set at the lower-left corner, and the surrounding zone of the roadway (the red part in Figure 5) is the key observation zone. The rock mass joints in this zone are densified in order to observe the distribution of cracks in the surrounding rocks.

**Figure 5.** Model layout.

According to the geological data, the average burial depth of the ventilation roadway of Working Face 1961 is 450 m. If the lateral pressure coefficient is taken as 1, the vertical stress and horizontal stress applied by the model are both 11.76 MPa. The model is a plane strain model, the block is an elastic body, and the contact surface adopts the Mohr–Coulomb yield criterion. When the roadway module is deleted, this indicates that the excavation of the roadway has begun.

The cutting equipment for the ventilation roadway of Working Face 1961 is an EBZ260 TBM. Due to the limitation of the surrounding rocks around the roadway, the surrounding rock stress is reduced gradually rather than completely released at one time [26], so the Fish function "ZONK.FIS" (Itasca, 2012) in the UDEC is used to simulate the real process of stress release after excavation unloading of the roadway. The surface stress of the roadway is gradually released in ten stages, namely Stages <sup>1</sup> , <sup>2</sup> , <sup>3</sup> , <sup>4</sup> , <sup>5</sup> , <sup>6</sup> , <sup>7</sup> , <sup>8</sup> , <sup>9</sup> , and <sup>10</sup> . Of the surface stress, 10% is released in each stage until it drops to zero by Stage 10. The stress release coefficient is set as R, and the R of these ten stages is 0.1, 0.2, 0.3 ... ~1.0, respectively, as shown in Figure 6. Four operation steps, namely four stress states, are selected to analyze the time-dependent failure law of the roadway. The operation steps are a (0.2 × 104), b (2.5 × 104), c (5.0 × 104), and d (10.0 × 104), and the stress release coefficients are 0.1, 0.7, 1.0, and 1.0, respectively.

**Figure 6.** Surface stress evolution curve of the roadway.
