**1. Introduction**

The gas disaster is one of the major disasters that threaten coal mine safety production. With the development of coal resources gradually extending to the depths, the difficulty of gas control is increasing. Borehole drainage is the basic gas control measure. At present, gas pre-drainage mainly includes the borehole drilling in the bedding coal seam and the penetrating borehole in the bottom roadway, which can penetrate the coal seam so that the gas easily flows into the boreholes along the bedding plane, which can effectively reduce the gas content in the coal seam [1–4]. Buried pipe drainage, high-level drilling, and roof directional drilling are mainly used for gas control in the goaf during mining. Because the

**Citation:** Wang, Z.; Yang, X.; Wang, G.; Gong, H. Study on Instability Characteristics of the Directional Borehole on the Coal-Seam Roof: A Case Study of the Tingnan Coal Mine. *Processes* **2023**, *11*, 1675. https:// doi.org/10.3390/pr11061675

Academic Editor: Raymond Cecil Everson

Received: 13 April 2023 Revised: 11 May 2023 Accepted: 14 May 2023 Published: 31 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

roof directional borehole is located in the fracture zone of the coal seam, where the horizon is high and less affected by mining disturbance, the borehole and gas drainage life cycle is long, which can effectively solve the problem of gas overflow in the upper corner of the goaf [5–8].

However, the openings of roof directional boreholes are often located in the coal seam, and they have to pass through mudstone and sandstone before entering the fracture zone. Due to the large diameter of the borehole (typically around 160 mm), the boreholes are susceptible to loss of stability resulting in deformation and collapse. Therefore, the stability of the directional borehole on the roof through the strata directly affects its drainage effect. Borehole diameter, lithology, and other parameters are important parameters affecting borehole stability [9,10].

Research on the influencing factors of borehole stability and borehole failure modes in the bedded coal seam has been conducted by scholars at home and abroad. The influencing factors of borehole stability mainly include rock strength, gas pressure, stress and strain, burial depth, lateral pressure coefficient, and anisotropic permeability [11–14]. Yang et al. [15] indicated that rock mechanics is the main theoretical basis for ensuring good stability, sand production, or casing damage. Karatela et al. [12] investigated the stability of boreholes in fractured rock using the discrete element method. The results show that the stability of boreholes depends largely on the strength of the rock. The tensile and shear failure of the borehole increases with increasing fluid velocity and pore pressure. Ding et al. [16] found that the large difference in permeability of rock layers around the borehole would lead to the change in stress state, damage area, collapse pressure, and fracture pressure around the borehole. Zhao et al. [17] studied the instability characteristics of the borehole under steady vertical load using the gas drainage borehole collapse dynamic monitoring devices. The attenuation of the borehole circumferential strain is an important symbol for the prediction and warning of borehole instability and collapse. A borehole may be damaged resulting from the integrated effect of stratigraphic and structural factors. Katanov et al. [18] proposed a model based on neural simulation to analyze the deformation of rock layers with different strength characteristics. Ma et al. [19] solved the problem of severe borehole deviation in coal mine gas drainage by summarizing the borehole deviation law and improving the precision directional drilling tool. Dychkovsky et al. [20] simulated the influence of geological faults on the stress and deformation state of rock mass by FLAC 5.00 and established a three-dimensional network visualization by computer simulation results and data interpolation method. The research shows that in the Lviv-Volyn coal basin, the geological fault of up to 3 m distance has a great influence on the stress and deformation state of the rock mass. Based on the parameters of the geo-mechanical model developed and confirmed, Petlovanyil et al. [21] have determined the reasonable range of inclination angle and key parameters of the radius of curvature when using underground gasification technology to develop thin coal seams. Zhang et al. [22] numerically simulated the deformation characteristics of boreholes with different burial depths, and the results showed that the deeper the burial depth, the more obvious the deformation. The form of instability and failure was the collapse of the upper part, and the fracture of the left and right sides formed the fracture area. Qu et al. [23] found that the stability of coal seam borehole was affected by the time lag effect based on field tests and numerical simulation; they found that the change of pore pressure was the main factor affecting the time lag effect, and the rich cleat was the internal factor. Niu et al. [24,25] studied the monitoring and evaluation of borehole stability through experiments and simulations, proposed an index to calculate the degree of borehole damage based on the residual area, and fitted the functional equation between the relative pressure of the sensor (the difference between the real-time pressure of the sensor and the coupling pressure of the borehole wall) and the degree of borehole damage. Combined with the amount of gas extracted, it was verified that the borehole deformation first increased and then became stable with time, and then increased and then decreased with depth. Zhang et al. [26] established the gas migration channel zoning model and determined the parameters of the optimal directional long borehole in

the working face by using UDEC and COMSOL software. Xu et al. [27] found that when the borehole is shallow, the friction resistance between the drill pipe and the borehole wall increases linearly. With the increase of borehole depth, the friction resistance gradually develops into an exponential relationship. In addition, Liu et al. [28] concluded that the effective drainage radius of a directional long drilling hole has an exponential relationship with the distance from the drilling opening. Yuan et al. [29,30] conducted the combined drilling method of curtain grouting in underground deep wells, which can significantly reduce the risk of water inrush in deep mining with complex hydrogeological conditions. A mathematical model to describe the unstable pressure dynamics in stress-sensitive coalbed methane reservoirs was proposed by Wang et al. [31]. Wang et al. [32] proposed the gradient recognition and memory-cutting method for the continuous advancement of non-uniform coal seams, such as coal seams with folded structures on long-arm working-face.

Moreover, scholars have conducted a great number of field tests and research on a series of borehole protection technologies, such as borehole reinforcement, regional solidification, and screen protection. Xue et al. [33] found that increasing the casing strength and thickness can effectively control the borehole instability and greatly improve the gas extraction effect through field tests. To improve the stability of the borehole. Zhai et al. [34] conducted research on the technology of screen pipe protection. By comparing the maximum AE event technology and energy dissipation rate, it was found that the screen pipe can effectively resist external stress disturbance, prevent hole collapse, and improve the drainage effect of the borehole. Di et al. [35] proposed the regional solidification pore formation method for soft coal seams, which can solidify the strength of the rock surrounding the borehole and improve the pore formation rate. Qi et al. [36] tested the full-hole deep screen mesh tube drainage technology to solve the problem of internal collapse and negative pressure loss of deep coal seam drainage boreholes, which can effectively control the collapse and deformation of boreholes and reduce the negative pressure loss. Compared with conventional drainage, after 90 days, the gas drainage concentration increased by 101% and the gas flow increased by 97%, so the gas drainage rate increased significantly. Li et al. [37] proposed to integrate the technology of borehole digging, protection, and sealing in the construction of the borehole site, so as to strengthen the stability of the borehole and solve the problems of difficult borehole formation, poor drainage effect and high danger of coal seam explosion in soft coal seams.

Currently, the research on borehole stability mainly focuses on the surrounding rock stress, burial depth, lateral pressure coefficient, anisotropic permeability, and other influencing factors, and the failure characteristics of the borehole in the bedding coal seam, while the research on the stability and borehole protection technology of roof directional long borehole is still lacking. Compared with the traditional high-position alley gas extraction technology, the roof directional long borehole has the advantages of a short construction period, low investment, and long extraction period. Therefore, the stability of the roofdirectional long borehole with different lithology and borehole diameters was analyzed by numerical simulation in this paper. The compression experiments were carried out to study the protective effect of different internal support structures in the directional borehole, which is beneficial to realize the effective hole formation of the directional long borehole on the roof and high-efficiency gas extraction in the goaf treatment of the coal mine face. This paper will provide some guidance for the popularization and application of directional long boreholes on the roof technology, and also gradually realize the "replacing alley with borehole" in goaf gas treatment. The rest of this study is organized as follows. Section 2 analyzes the deformation characteristics of boreholes under different coal and rock conditions, and simulates the stress, strain, and plastic deformation of rocks around boreholes with different diameters. In Section 3, the experiment on the influence of the internal support hole protection tube on the stability of the hole wall was carried out. Section 4 analyzes the mechanism of numerical simulation and laboratory experiment results. Finally, the conclusions are presented in Section 5.

#### **2. Numerical Simulation of the Borehole Stability**

Lithology, borehole diameter, and borehole protection tubing have a great influence on the stability of the borehole; for example, the strength of the rock will affect the rate of hole formation and the durability of the borehole. The larger the diameter of the borehole, the closer it is to the uniaxial compressive strength of the rock and the easier it is to destroy the stability of the borehole in the rock formation. The shear strength of the casing is also closely related to the effectiveness of the casing [38–40]. Therefore, this section takes the 208-working face of Tingnan Coal Mine in Xianyang, Shaanxi Province, China as an object to conduct numerical simulation research to analyze the influence of lithology, borehole diameter, borehole protection pipe, and other factors on borehole stability. Tingnan Mine Field is mainly covered by Quaternary loess and Tertiary red soil, and the Lower Cretaceous Luohe Formation is exposed in major valleys along the Heihe River and Jinghe River. The strata in the minefield of Tingnan Coal Mine are, from top to bottom, Holocene (Q4), Upper Pleistocene Malan Formation (Q3), Quaternary-Middle Pleistocene Lishi Formation (Q2), Huachi Formation (K1h), Luohe Formation (K11), Lower Cretaceous Yijun Formation (K1y), Anding Formation (J2a), Zhiluo Formation (J2z) and Middle Cretaceous Yanan Formation. The Jurassic Yan'an Formation is a coal-bearing layer, and the Triassic Hujiahe Formation is a direct or indirect sedimentary basement. The surface and overlying strata are basically the same, and the aquifer of the Luohe Formation is in the upper part. The minefield is located in the middle part of the anticline (Lujia–Xiaolingtai), and the stratum in the middle is close to the level. The terrain in the south wing is gentler than that in the north wing, and the dip angle in the north wing is 4◦~6◦. The back of the syncline is Mengcun, which is connected with the north wing of the anticline from Lujia to Xiaolingtai. The strike of the layer is N 20◦ E and the dip angle is about 2◦. The north wing crosses the Great Buddha Temple to the south and the occurrence of the southeast corner of the layer changes. The anticline structure affects the change of layer thickness, coal seam thickness, and occurrence in the minefield. Tingnan coal mine is a high-gas mine, and the 4# coal seams belong to the type II spontaneous combustion coal seams, and the coal dust is explosive. The coal seam thickness of the 208-working face varies greatly, with the average coal seam thickness being 11.5 sm. The base roof of the working face is coarse-grained sandstone, which is grey and mainly composed of quartz and feldspar. The immediate roof is mudstone, dark grey and lumpy, containing a large number of plant fossils and locally a small number of calcite veins. The direct floor is aluminum mudstone, light grey, dense, and contains plant root fossils. The base is fine-grained sandstone, light grey, chestnut, and hard, with sandy muddy breccias. The 208-working face is located in the west wing of the second panel, with a total length of 2527 m. The description of formation lithology characteristics is shown in Table 1.

**Table 1.** The description of formation lithology in 208 working-face.

