
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

73155
10.1038/s41598-024-73155-8
Article
Design and field evaluation of hydraulic fracturing boreholes for terminal mining faces
Zhang Boyang 1
Song Weiya 1
Wang Yiming yimingwang921029@126.com

2
Li Zhenhua jzlizhenh@163.com

1
Huang Huwei 1
Lin Zhibin 1
Yao Banghua 1
1 https://ror.org/05vr1c885 grid.412097.9 0000 0000 8645 6375 School of Civil Engineering, Henan Polytechnic University, Jiaozuo, 454000 China
2 https://ror.org/024nfx323 grid.469579.0 School of Resources and Civil Engineering, Suzhou University, Suzhou, Jiangsu China
20 9 2024
20 9 2024
2024
14 2193311 1 2024
13 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The terminal mining is an essential part of fully mechanized mining, and the reasonable length of the flap roof during the terminal mining is an important basis for the smooth operation of the terminal mining. With the research background of the 213 working face of the Longde Coal Mine, the contribution of this study is the influence law of hydraulic fracturing on the terminal mining mechanical behavior of the working face. Four different numerical calculation models of terminal mining hydraulic fracturing are established, and the optimal hydraulic fracturing site plan is determined according to the length of the terminal mining flap top and the working resistance of hydraulic support. The effect of hydraulic fracturing construction and the law of mechanical behavior in the terminal mining stage in the field test are analyzed. The results show that through hydraulic fracturing technology, the control of the length of the flap roof of the working face during the terminal mining period has been realized.

Subject terms

Environmental sciences
Ecology
National Natural Science Foundation of ChinaNos. 41807209 51778215 51708185 Zhang Boyang Henan Provincial Youth Talent Promotion ProgramNo. 2020HYTP003 Zhang Boyang issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The Yuheng coal area is a vital coal production base in China with a shallow depth of seam and good roof integrity, which is suitable for high-intensity mining1,2. However, this area often faces the problem of hard roofs that cannot be collapsed, which may cause the direct and basic roofs to be difficult to collapse during the initial mining period, thus causing the length of the flap top to be too long3,4. The mass collapse of the roof may cause a “hurricane” disaster, resulting in severe casualties and economic losses5,6.

Currently, hydraulic fracturing methods are widely used in Chinese coal production and an essential method to solve the problem of hard roofs that are difficult to collapse. Hydraulic fracturing technology first originated in the field of oil extraction7,8, it is now widely used in shale gas9, enhanced geothermal systems10, water well production enhancement11, in-situ stress measurements12, coal bed methane mining13, coal mining roof control14 and other fields4.

Implementing hydraulic fracturing technology for roof control in coal mines is focused on the challenges of effectively stabilising caving roofs in production faces and controlling coal bed degassing6,15. The methods and means meant for the directional hydraulic fracturing and coal degassing are described. The practical results of the method introduced in coal mines in Kuzbass are reported16. Kang and Feng analyzed the crack initiation pressure and direction of crack initiation in an arbitrary direction borehole according to the maximum tensile stress criterion and derived the variation law of crack initiation pressure with borehole azimuth angle and borehole inclination angle17,18. Thus, the method to control the fracturing and caving process of the main roof was tentatively recommended with an applied hydraulic fracture in the main roof. The results demonstrate that the stress condition was significantly improved, and the deformation was significantly decreased to an acceptable value19. Huang et al. point out that strong strata behaviors can be controlled by directional hydraulic fracturing in the overhanging roof above the gob of the adjacent mined-out working face20–22. Lu et al. proposed a hydraulic fracturing method for far-field hard roof control; a longwall mining numerical simulation method is developed, with which energy release and changes of the peak values of front abutment stress of working face after weakening far-field tight roof are analyzed23. The above researches provides a wealth of experience in the engineering practice of hydraulic fracturing technology for topside overburden control.

However, the applications of hydraulic fracturing in the terminal mining phase of the working face was infrequent. Previous studies have briefly described the hydraulic fracturing technology used during terminal mining in the Muduchaideng Coal Mine24 the Ningliuta Coal Mine25, and the Zhuzhuang Coal Mine26, which proved the feasibility of the engineering application of hydraulic fracturing in the terminal mining phase of the working face. However, there is a lack of in-depth research on the design basis, the mechanical behavior law, and the deformation law of the main retracement roadway of hydraulic fracturing in the terminal mining phase of the working face. In summary, it is not common to use hydraulic fracturing technology to control the length of the flap roof at the terminal mining, especially when there is a main withdrawal channel. However, if hydraulic fracturing is carried out, it must be done in a way that ensures the stability of the main withdrawal channel and effectively controls the length of the flap roof during terminal mining. This has not been researched by scholars in the past.

Therefore, four different hydraulic fracturing construction methods are designed for the specific geological conditions of the 213 working face of the Longde Coal Mine in this paper. The optimal hydraulic fracturing design is determined through FLAC3D. Meanwhile, the field tests are conducted according to this design to analyze the field construction effect of hydraulic fracturing, the law of mechanical behavior at the terminal mining phase of the 213 working face, and the deformation law of the main retracement roadway.

Study area overview

Longde Coal Mine of Huadian Coal Industry Group Co., Ltd. is located southwest of Shenmu County, Yulin City, Shaanxi Province, and belongs to the eastern part of the Jurassic coalfield in northern Shaanxi. The field test site in this paper is located at the 213 fully mechanized mining face of the Longde Coal Mine, with a strike length of 3042.3 m, a slope length of 291.2 m, and an average coal seam thickness of 4.33 m. An overview of the study area is shown in Fig. 1.

Fig. 1 Location of Longde coal mine.

The coal seam in the 213 working face has an attitude with a strike ranging from 8° to 188° and a dip of 278°. It is thinner near the cut-eye and thicker at the withdrawal area, characteristic of a stable coal seam. Geological survey data show that the coal seam dips to the northwest with an angle of less than 1°, exhibiting a gentle monocline structure. The working face is mined on an upward slope, with the lowest point at the cut-eye section and the highest at the withdrawal section. The overall topography is higher in the southeast and lower in the northwest, with a height difference of 25.0 m. During the exposure process, a total of six normal faults were found, and the fault drop was between 1.2 and 1.6 m and dip angles between 43° and 67°.

The 213 main retracement roadway is located in the southeast of the 213 fully mechanized mining face, with a length of 291.2 m, a width of 5.3 m, and a height of 3.8 m. The auxiliary and rubber transport roadway connected to the 213 main retracement roadway and the data of borehole BK10 near the 213 working face of Longde Coal Mine are shown in Fig. 2. The roof of the 2−2 coal seam is mainly composed of fine-grained sandstone and siltstone, and the basic roof thickness is 15.1 m.

Fig. 2 Overview of the 213 working face and its terminal mining area.

Terminal mining hydraulic fracturing location selection

Roof rock physical and mechanical test

We carried out a part of laboratory tests on site sampling, before carrying out hydraulic pressure field tests in this area. The load-displacement curves of the Brazilian disk splitting test are shown in Fig. 3, and the stress-strain curves of the conventional triaxial test of siltstone are shown in Fig. 4. And the final numerical simulation parameters were determined by combining the previous test data of the 201 working face27 in the same disk area of this coal mine, and the final test data comparison results are shown in Table 1.

Fig. 3 Brazilian disc splitting test on various types of rocks.

Fig. 4 Triaxial stress-strain curve of siltstone.

Table 1 Physical and mechanical parameters of different rock masses.

Parameters	Type	Siltstone	Fine-grained sandstone	Medium sandstone	Sand-coal interbedding	Coal	
Elasticity modulus (GPa)	Test results	7.15	7.56	6.62	4.71	2.54	
Wang 2018	5.7–7.9	5.7–7.9	5.7–7.9	–	–	
Numerical simulation	7.1	7.5	6.6	4.7	2.5	
Prepeak cohesion (MPa)	Test results	2.77	2.98	2.42	1.71	1.22	
Wang 2018	2.43–9.57	2.43–9.57	2.43–9.57	–	–	
Numerical simulation	2.7	2.9	2.4	1.7	1.2	
Internal friction angle (°)	Test results	34	35	32	30	31	
Wang 2018	33–42	33–42	33–42	–	–	
Numerical simulation	34	35	32	30	31	
Poisson’s ratio	Test results	0.25	0.23	0.24	0.30	0.31	
Wang 2018	–	–	–	–	–	
Numerical simulation	0.25	0.23	0.24	0.30	0.31	
Tensile strength (MPa)	Test results	2.51	2.79	2.09	1.61	1.09	
Wang 2018	2.91–8.01	2.91–8.01	2.91–8.01	–	–	
Numerical simulation	2.5	2.8	2.1	1.6	1.0	

Design basis of hydraulic fracturing for terminal mining

Usually, the hydraulic fracture borehole for coal roof pressure relief is designed as an L-borehole and S-borehole, where the vertical height of the L-borehole is similar to or lower than the basic top height, and the vertical height of the S-borehole is similar to or greater than the height of the main roof22,28,29. Due to the existence of support for the main retracement roadway of the terminal mining and the need to hang the net during the terminal mining, if the fracturing location is arranged around the main retracement roadway of the terminal mining, on the one hand, it will destroy the support for the main retracement roadway of the terminal mining; on the other hand, it affects the construction (hanging net, etc.) during the terminal mining. Therefore, the design location of the terminal mining hydraulic fracturing should be considered to control the penultimate or penultimate third periodic weighting of the working face.

We plan to design 4 different scenarios, the first scope without hydraulic fracturing construction as a comparison sample, the other three corresponding to different fracturing areas, to ensure as much as possible the approximation of the scope of the lead hammer fracturing (due to the construction of drilling holes must be opened in the main retraction channel and the general limitations of the length of each fracturing of 3 m, it is difficult to maintain complete consistency of the scope of the lead hammer fracturing, we chose the closest to the design), and change the scope of the horizontal fracturing.

According to the roof behavior monitoring data of 213 working face of the Longde Coal Mine, the overall incoming pressure step is about 10 m, while the flap top length of 4 ~ 6 m is most favorable for the withdrawal of the hydraulic support during the terminal mining period30,31. Therefore, we propose the following four design schemes (as shown in Fig. 3):

Scheme (1) No terminal mining hydraulic fracturing (as shown in Fig. 5a; Table 2).

Scheme (2) The length of the fractured section of the L-borehole is about 18 m. The vertical height is about 19 m. The length of the fractured section of the S-borehole is about 15 m. The vertical height of the S-borehole is all about 23 m, and the horizontal section area of the fractured section is from 6.00 ~ 28.67 m (as shown in Fig. 5b; Table 2).

Scheme (3) The length of the fractured section of the L-borehole is about 18 m. The vertical height is about 19 m. The length of the fractured section of the S-borehole is about 15 m. The vertical height of the S-borehole is all about 23 m, and the horizontal section area of the fractured section is from 9.64 ~ 32.91 m (as shown in Fig. 5c; Table 2).

Scheme (4) The length of the fractured section of the L-borehole is about 18 m. The vertical height is about 19 m. The length of the fractured section of the S-borehole is about 15 m. The vertical height of the S-borehole is all about 23 m, and the horizontal section area of the fractured section is from 10.61 ~ 39.20 m (as shown in Fig. 5d; Table 2).

Fig. 5 Different hydraulic fracturing schemes in the terminal mining phase of the 213 working face.

Table 2 Borehole design for different hydraulic fracturing schemes.

Scheme	Borehole type	Dip angle (°)	Length (m)	Vertical height (m)	Horizontal length (m)	Fracturing horizontal range (m)	
Scheme 1	No	No	No	No	No	No	
Scheme 2	L borehole	35	35/33	20.08/19.93	28.67/27.03	12.29 ~ 28.67	
S borehole	60	28/27	24.25/23.38	14.00/13.50	6.00 ~ 14.00	
Scheme 3	L borehole	30	38/36	19.00/18.00	32.91/31.18	15.59 ~ 32.91	
S borehole	50	31/30	23.75/22.98	19.93/19.28	9.64 ~ 19.93	
Scheme 4	L borehole	27	44/42	19.98/19.07	39.20/37.42	21.38 ~ 39.20	
S borehole	45	34/33	24.04/23.33	24.04/23.33	10.61 ~ 24.04	

Establishment of the numerical calculation model

According to the borehole data such as BK10 (Fig. 2) around the 213 working face, the numerical simulation model of the 213 working face is established by FLAC3D, as shown in Fig. 6. The boundary conditions of the model are defined as a free top surface, constrained normal displacement all around, and a fixed bottom surface. The model has a width of 210 m, a height of 229.73 m, and a thickness of 6 m (the support length of one hydraulic chock for the retracement roadway), and consists of 136,728 nodes and 9,0720 hexahedral elements, each with a width of approximately 1 m. The modeling range is from the surface to the fine-grained sandstone under the 2−2 coal seam.

Fig. 6 Numerical simulation model of the terminal mining phase of the 213 working face.

The initial stress of the model should be calculated before the layout of the retracement roadway. According to the rock stress-strain characteristics, the intrinsic rock model is set as a strain-softening model, which follows the Mohr-Coulomb damage criterion, as shown in Fig. 7.

Fig. 7 Simplified stress-strain diagram of rock strain-softening model before and after hydraulic fracturing.

Before hydraulic fracturing, the peak compressive strength of the original rock is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{a}$$\end{document}. The residual compressive strength is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{c}$$\end{document}. After hydraulic fracturing, the rock becomes damaged, reducing its peak compressive strength to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{b}$$\end{document}. The residual compressive strength remains constant at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{c}$$\end{document}, then the rock damage coefficient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:D$$\end{document} value32,33 caused by hydraulic fracturing can be defined as shown in Eq. (1):1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:D=\frac{{\sigma\:}_{a}-{\sigma\:}_{b}}{{\sigma\:}_{a}-{\sigma\:}_{c}},$$\end{document}

Cohesion force and internal friction angle

The angle of internal friction of the rock changes very little after damage occurs and can be considered essentially constant34,35. Therefore, the compressive strength of rock before and after hydraulic fracturing is in direct proportion to its cohesion, as shown in Eq. (2). The cohesion value of rock after hydraulic fracturing can be obtained by combining Eq. (1), as shown in Eq. (3):2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\left\{\begin{array}{c}{\sigma\:}_{a}=\frac{2{c}_{a}\cdot\:\text{c}\text{o}\text{s}\phi\:}{1-\text{s}\text{i}\text{n}\phi\:}\\\:{\sigma\:}_{b}=\frac{2{c}_{b}\cdot\:\text{c}\text{o}\text{s}\phi\:}{1-\text{s}\text{i}\text{n}\phi\:}\\\:{\sigma\:}_{c}=\frac{2{c}_{c}\cdot\:\text{c}\text{o}\text{s}\phi\:}{1-\text{s}\text{i}\text{n}\phi\:}\end{array}\right.$$\end{document}

3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{b}=\left(1-D\right){c}_{a}+D{c}_{c},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\phi\:$$\end{document} is the internal friction angle of rock mass, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{a}$$\end{document} is the initial cohesion of rock mass before hydraulic fracturing, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{c}$$\end{document} is the residual cohesion of rock mass before hydraulic fracturing and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{b}$$\end{document} is the cohesion of rock mass after hydraulic fracturing.

Elastic modulus

Without considering the effect of crack closure and opening in the rock, it can be considered that the plastic deformation of the rock is not recoverable at different stages, whereas the elastic deformation can be completely recovered. According to Fig. 5, the elastic modulus of rock before and after hydraulic fracturing is shown in Formula (4):4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{b}=\frac{{\sigma\:}_{b}}{{\sigma\:}_{a}}{E}_{a}=\frac{{c}_{b}}{{c}_{a}}{E}_{a}=\left[\left(1-D\right)+D\frac{{c}_{c}}{{c}_{a}}\right]{E}_{a},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{a}$$\end{document} is the initial elastic modulus of rock mass before hydraulic fracturing and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{b}$$\end{document} represents the elastic modulus of rock mass after hydraulic fracturing.

Tensile strength

Since the failure mode of the pressure-splitting circle is similar to that of the Brazilian disk-splitting method, Zhang36 deduced the equation of the pressure-splitting circle tensile strength of rock based on the shear strength parameters of various geotechnical tests. In virtue of Eq. (3), the tensile strength of rock after hydraulic fracturing can be obtained as shown in Eq. (5):5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{tb}=\frac{{c}_{b}}{{c}_{a}}{\sigma\:}_{ta}=\left[\left(1-D\right)+D\frac{{c}_{c}}{{c}_{a}}\right]{\sigma\:}_{ta},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{ta}$$\end{document} is the initial tensile strength of rock mass before hydraulic fracturing and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{tb}$$\end{document} is the tensile strength of rock mass after hydraulic fracturing.

From the definition of damage coefficient, it is known that the damage coefficient value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:D$$\end{document} of the rock takes values between 0 and 1. According to the influence of Hoek-Brown parameters on the model30,31, the damage coefficient value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:D$$\end{document} of the rock after hydraulic fracturing is taken as 0.6 in this paper. According to the above formula, the material of the rock specimen in this paper is taken from the core of the adjacent working face borehole22, and the physical and mechanical parameters of the rock before and after hydraulic fracturing are shown in Table 3.

Table 3 Physical and mechanical parameters of different rock masses.

Strata	Density (kg/m3)	Elasticity modulus (GPa)	Prepeak cohesion (MPa)	Residual cohesion (MPa)	Internal friction angle (°)	Poisson’s ratio	Tensile strength (MPa)	
Aeolian sand	2000	0.06	0	0	30	0.3	0	
Red soil	1900	0.046	0.04	0.04	28	0.32	0	
Siltstone	2700	7.1 (4.6)	2.7 (1.3)	0.3	34	0.25	2.5 (1.5)	
Fine-grained sandstone	2750	7.5 (4.9)	2.9 (1.4)	0.4	35	0.23	2.8 (1.7)	
Medium sandstone	2630	6.6 (4.2)	2.4 (1.1)	0.2	32	0.24	2.1 (1.3)	
Sand-coal interbedding	2550	4.7 (3.3)	1.7 (0.9)	0.4	30	0.3	1.6 (1.0)	
Coal	1400	2.5 (1.8)	1.2 (0.7)	0.3	31	0.31	1.0 (0.6)	
The values in brackets represent the corresponding parameter values of the rock after hydraulic fracturing.

Analysis of numerical simulation results

Overburden failure law

The fracture zones of the coal roof of scheme 1, scheme 2, scheme 3 and scheme 4 are shown in Figs. 8, 9, 10 and 11, respectively. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ar}$$\end{document} represents the distance of the working face from the main retracement roadway.

From the fracture zone distribution spacing of the top slab at different mining advance distances, under the condition of no hydraulic fracturing, the distribution of fracture zones on the roof rock mass is shown in Fig. 8. As the working face continues to advance towards the retreating roadway, new vertical fracture zones will be generated in the roof rock mass behind the working face every 10–15 m, resulting in periodic collapse of the roof rock mass. Under the condition of hydraulic fracturing, the distribution of the fracture zone of the roof rock mass is shown in Figs. 9, 10 and 11. When the working face is more than 40 m away from the retreating roadway, the hydraulic fracturing has little influence on the damage characteristics of the roof rock mass because the range of hydraulic fracturing is far away from the working face, and the roof rock mass of the working face shows the characteristics of cyclic collapsing and bending damage. When the working face is less than 40 m away from the retreat roadway, due to the low strength of the rock mass within the hydraulic fracturing range and the obvious development of fissures, the rock mass within the hydraulic fracturing range will have obvious bending and sinking phenomenon when the new fracture zone of the roof rock mass passes through it, resulting in the lower rock mass collapsing every 5–10 m instead of every 10–15 m, which greatly reduced the cantilever length of the roof rock mass above the mining hollow area.

Fig. 8 Fracture zone distribution map of coal seam roof in the 213 working face of scheme 1.

Fig. 9 Fracture zone distribution map of coal seam roof in the 213 working face of scheme 2.

Fig. 10 Fracture zone distribution map of coal seam roof in the 213 working face of scheme 3.

Fig. 11 Fracture zone distribution map of coal seam roof in the 213 working face of scheme 4.

This greatly reduces the cantilever length of the rock above the mining zone. it can be seen that in this model, outside the hydraulic fracturing influence zone (working face is 40 ~ 120 m from the main retracement roadway), the working face periodic weighting step of scheme 1 to scheme 4 is about 10 ~ 15 m. While in the hydraulic fracturing influence zone (working face is 0 ~ 40 m from the main retracement roadway), the working face periodic weighting step of scheme 1 is still about 10 ~ 15 m. The periodic weighting step of the hydraulic fracturing zone of scheme 2 to scheme 4 becomes 5 ~ 10 m. Due to the different scope of hydraulic fracturing of the terminal mining from scheme 2 to scheme 4, there are significant differences in the length of the flap top of the terminal mining. The flap top lengths of scheme 1, scheme 2, scheme 3, and scheme 4 are about 8 m, about 9 m, about 5 m, and about 7 m respectively. The comparative analysis shows that the flap top length of scheme 3 is most suitable for the terminal mining of 213 working face.

Working resistance of hydraulic support

The variation curves of hydraulic support working resistance with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ar}$$\end{document} (the distance of the working face from the main retracement roadway) under different hydraulic fracturing schemes are shown in Fig. 12. It can be seen that in scheme 1 (Fig. 12a), there are 10 times of periodic roof pressure in the study area, and the maximum working resistance of the hydraulic support during the terminal mining period (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ar}$$\end{document}<30 m) reached 50.7 MPa. While there are about 12 times of periodic roof pressure in schemes 2 to 4, and the maximum working resistances of the hydraulic support during the terminal mining period in schemes 2 to 4 (Fig. 12b–d) are 40.2 MPa, 29.1 MPa, and 33.1 MPa, respectively.

Fig. 12 Working resistance curves of hydraulic support in terminal mining phase of the 213 working face.

The above calculations show that the hydraulic fracturing construction of scheme 3 can effectively control the flap top length of the working face and ensure the low working resistance of the hydraulic support during the terminal mining phase. This can effectively ensure the successful completion of the withdrawal of the frame during the terminal mining of the 213 working face in Longde Coal Mine. Therefore, scheme 3 was selected for the field test.

Analysis of field test results

Field hydraulic fracturing construction and effect analysis

Field hydraulic fracturing construction process

Hydraulic fracturing refers to the splitting effect of high-pressure fluid on the roof rock mass, which causes the weak surface of the roof rock mass to open, expand, and extend, forming an intertwined multi-fracture connected network, resulting in the reduction of the overall strength of the roof rock mass, and the realization of the uniform depressurization. The schematic diagram of the principle of using construction hydraulic fracturing equipment is shown in Fig. 13. Hydraulic fracturing construction is divided into 2 sets of water pipes. The first set is the main water pipe for hydraulic fracturing, which is pressed into the five high-pressure steel pipes by the 1-high-pressure pump in Fig. 13 to finally provide water pressure for hydraulic fracturing construction in the 7-fracturing section. The second set provides sealing pressure for the borehole sealer, and the water enters the 6-borehole sealer by the 2-borehole sealer pressure pump in Fig. 13.

Fig. 13 Hydraulic fracturing construction schematic. 1—High-pressure pump and water tank; 2—Borehole packer pressure pump; 3—Valve; 4—Pressure gauges; 5—High pressure steel pipe; 6—Borehole sealer; 7—Fracturing section.

The length of the hydraulic fractured section of the L-borehole and S-borehole of scheme 2 to scheme 4 are 18 m and 15 m, respectively. Where L-borehole is fractured every 3 m for a total of 6 times of hydraulic fracture. The S-borehole was fractured once every 3 m, with a total of 5 times of hydraulic fractures. Hydraulic fracturing time for 3 times at the inside of the borehole was 30 min or water is obviously outflow near the drilling. Hydraulic fracturing time for 2 times at the outside of the borehole was 20 min or water is obviously outflow near the drilling. Whether or not water can be observed outflow of the adjacent borehole is an important indicator to evaluate the effectiveness of fracturing visually.

Field hydraulic fracturing effect analysis

The construction design of the terminal mining hydraulic fracturing boreholes at the 213 working face of the Longde Coal Mine is shown in Fig. 14. Borehole L1 is 7 m away from the transport roadway, borehole S12 is 8 m away from the return airway. The distance between adjacent boreholes is 12 m. The length of the L-borehole with an odd number is 38 m, and the length of the L-borehole with an even number is 36 m. The length of the S-borehole with an odd number is 31 m, and the length of the S-borehole with an even number is 30 m.

Fig. 14 Hydraulic fracturing borehole design in terminal mining phase of the 213 working face.

The water outflow probability of the adjacent boreholes during the hydraulic fracturing of the L-borehole is shown in Fig. 15a. Water outflow from adjacent boreholes indicates that water has formed a pathway in the rock formation. The extent of hydraulic fracture extension can be roughly determined from the location of the water outlet holes. For the probability of water outflow in the L-borehole, the hydraulic fracturing was conducted on the whole section, as well as the inside and outside sections three times each. The probabilities for water outflow were 84.44%, 75.00%, and 94.44%, respectively. Notably, the water outflow probability was significantly larger in the outside section compared to the inside section. The water outflow probability of the adjacent boreholes during the hydraulic fracturing process of the S-borehole is shown in Fig. 15b. For the probability of water outflow in the S-borehole, the hydraulic fracturing was conducted on the whole section, as well as the inside three times and outside sections two times. The probabilities for water outflow were 56.67%, 54.17%, and 58.33%, respectively. Notably, the water outflow probability of inside 3 times and outside 2 times were similar. Boreholes L1 and S12 were adjacent to the roadway with only one observation borehole around them, and the water outflow probability of the adjacent boreholes was significantly lower than that of the same type of boreholes, which was also consistent with previous construction experience20,26,27. Overall, the water outflow probability of the adjacent boreholes during hydraulic fracturing exceeded 70%, which indicated that the hydraulic fracturing construction had achieved the expected results.

Fig. 15 Significant water outflow probability of adjacent boreholes during hydraulic fracturing.

Analysis of mechanical behavior law

Mechanical behavior law of terminal mining face

Using the measured data of 34 hydraulic supports’ working resistance in the field, the working resistance variation of hydraulic support in the 213 working face was plotted as shown in Fig. 16. In order to facilitate the analysis of the law, the 213 working face were divided into the upper measuring area, the middle measuring area, and the lower measuring area. The upper measuring area was near the 211 working face mining void area, and the lower measuring area was near the 215 working face (unmined). It can be seen from Fig. 16 that:

There were 8 areas where the working resistance of the hydraulic supports reached 41.48 ~ 47.40 MPa, including 4 areas in the middle measuring area, 1 at the intersection of the upper measuring area and the middle measurement area, 3 in the upper measuring area, none in the lower measurement area. The maximum support pressure in the lower measuring area was between 35.55 and 41.48 MPa. This indicates that the hydraulic support presents the highest resistance in the middle measuring area, followed by the upper measuring area, with the lowest resistance in the lower measuring area during periodic roof pressure. The main reason is that the upper measurement area was close to the 211 working faces goaf, but the protective coal pillar between the two working faces had a certain bearing capacity, the hydraulic support working resistance in the upper measuring area was smaller than that in the central measuring area, and the closer to the coal pillar area, the smaller the hydraulic support working resistance. The central measuring area was in suspension because there is no solid coal on both sides, and the hydraulic support had the greatest working resistance. The lower measuring area was near the solid coal, and the hydraulic support had the least working resistance because the solid coal can effectively share the overburden load.

The periodic roof pressure steps of the upper, central, and lower measuring areas on the working face were not uniform, among which the periodic roof pressure steps of the upper and lower measuring areas were larger, while the periodic roof pressure steps of the central measuring area were smaller. However, on the whole, the periodic roof pressure steps of the 213 working face were between 9 and 12 m.

The flap top length at the terminal mining phase of the 213 working face is 4–6 m, and the numerical simulation of the average flap top length of the terminal mining phase is 5 m in Fig. 10, which is basically consistent with the numerical simulation results and can effectively ensure the smooth withdrawal of the hydraulic support at the terminal mining phase.

Fig. 16 Cloud diagram of hydraulic support working resistance of the 213 working face.

Selected working resistance for preliminary determination of overburden periodic weighting:6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{p}_{m}^{{\prime\:}}={p}_{m}+{\delta\:}_{mp}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{p}_{m}^{{\prime\:}}$$\end{document} is the support dynamic pressure criterion, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{p}_{m}$$\end{document} is the working resistance average value of each support during the observation period and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\delta\:}_{mp}$$\end{document} is the mean square deviation of working resistance.

The measuring point 11# and measuring point 21# in the central measuring area were taken as an example to analyze the periodic roof pressure step and coefficient of roof weighting of each measuring area. In the light of Eq. (6), the working resistance curves of the support with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ae}$$\end{document} of measuring points 11# and 21# in the central measuring area was shown in Fig. 17. From Fig. 17, it can be seen that:

The 11 # and 21 # measuring points had 9 and 10 times of the periodic roof pressure, respectively, and the periodic roof pressure step was 9.37 m and 11.25 m, respectively.

When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ae}$$\end{document} was 4 m to 6 m, the working resistance of the support was increased. The flap top length at the terminal mining phase of 213 working face was 4 ~ 6 m, which was consistent with the results in Figs. 10 and 16.

The working resistance was reduced by 10.2%, 3.2%, and 18.6% in the upper, middle, and lower measuring areas, respectively. The observed average reduction of 9.7% followed the pattern of the numerical simulation results shown in Fig. 12.

Fig. 17 The variation curves of hydraulic support working resistance in the central measuring area with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ae}$$\end{document}.

Deformation law of main retracement roadway in terminal mining

The variation curves of the nearer quantity from roof to floor with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ae}$$\end{document} is shown in Fig. 18. 10 measurement points of nearer quantity from roof to floor were arranged in the 213 main retracement roadway. The 1# measuring point in upper measuring area, 5# measuring point in the central measuring area and 9# measuring point in the lower measuring area are selected in Fig. 18. From the figure, it can be seen that:

The variation stages of the nearer quantity from roof to floor of the main retracement roadway with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ae}$$\end{document} can be roughly divided into two stages: slow deformation stage and fast deformation stage. The slow deformation stage and fast deformation stage lasted for 8 d and 3 d, respectively, corresponding to the range of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ae}$$\end{document} from 112.0 to 26.5 m and 26.5–0 m.

In the slow deformation stage, the nearer quantity from roof to floor at measuring points 1#, 5#, and 9# were 20.1 mm, 45.8 mm, and 26.7 mm, respectively, with change rates of 2.5 mm/d, 5.7 mm/d, and 3.3 mm/d, respectively. In the fast change phase, the nearer quantity from roof to floor at measuring points 1#, 5#, and 9# were 51.1 mm, 200.6 mm, and 38.9 mm, respectively, with change rates of 17.0 mm/d, 66.9 mm/d, and 13.0 mm/d, respectively.

The maximum nearer quantity from roof to floor of the 213 main retracement roadway was about 246 mm. This allowed for the successful completion of the terminal mining work on the 213 working face, indicating that hydraulic fracturing construction during the terminal mining phase played an effective role in the successful withdrawal of hydraulic support in the terminal mining phase.

Fig. 18 The nearer quantity from roof to floor in the 213 Main retracement roadway.

Conclusion

In order to study the influence of hydraulic fracturing on the overburden strata control in terminal mining phase, four different hydraulic fracturing borehole designs were designed for the specific geological conditions of the 213 working face of the Longde Coal Mine. FLAC3D software was used to build a model to compare and analyze the length of flap top and the working resistance of hydraulic supports under various schemes, and the optimal scheme was selected for field tests to analyze the effect of hydraulic fracturing and the law of mechanical behavior at the 213 working face. The research results show that:

Hydraulic fracturing construction can effectively control the flap top length of the working face and reduce the working resistance of the hydraulic support during the terminal mining period.

The numerical simulation results of scheme 3 indicate that the length of the flap top should be 5 m for effective hydraulic support withdrawal during the terminal mining phase. This design is also the most suitable for pressure relief during the terminal mining of the Longde Coal Mine’s 213 working face. The field test results showed that the flap top length in the terminal mining phase was 4–6 m, which was basically the same as the numerical simulation results.

The water outflow probability of the adjacent boreholes during hydraulic fracturing exceeded 70%, which indicated that the hydraulic fracturing construction had achieved the expected results.

After the completion of hydraulic fracturing, the top and floor of the main retracement roadway increased from 2.5 to 5.7 mm/d in the slow deformation stage to 13.0–66.9 mm/d in the fast deformation stage when the remaining recoverable length of the working face was less than 26 m, the maximum nearer quantity from roof to floor was about 246 mm., which met the requirements for safe evacuation of the shelf.

List of symbols

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{a}$$\end{document} The initial cohesion of rock mass before hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{b}$$\end{document} The cohesion of rock mass after hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{c}$$\end{document} The residual cohesion of rock mass before hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:D$$\end{document} Rock damage coefficient, 1

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{a}$$\end{document} The initial elastic modulus of rock mass before hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{E}_{b}$$\end{document} The elastic modulus of rock mass after hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{L}_{ar}$$\end{document} The distance of the working face from the main retracement roadway, m

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{p}_{m}$$\end{document} The working resistance average value of each support during the observation period, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{p}_{m}^{{\prime\:}}$$\end{document} The support dynamic pressure criterion, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\delta\:}_{mp}$$\end{document} The mean square deviation of working resistance, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{a}$$\end{document} The peak compressive strength of the original rock before hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{b}$$\end{document} The peak compressive strength of the original rock after hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{c}$$\end{document} The residual compressive strength, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{ta}$$\end{document} The initial tensile strength of rock mass before hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\sigma\:}_{tb}$$\end{document} The tensile strength of rock mass after hydraulic fracturing, MPa

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\phi\:$$\end{document} The internal friction angle of rock mass, °

Acknowledgements

The work was supported by Henan Province young backbone teachers, (No. 2023GGJS057), the Henan Polytechnic University Outstanding Youth Fund, (No. J2024-1), the National Natural Science Foundation of China (Nos. 52374087, 41807209, 51778215, and 51708185), the Henan Provincial Youth Talent Promotion Program (No. 2020HYTP003). The authors want to acknowledge these financial assistances.

Author contributions

B.Y. Zhang, and Y.M. Wang conceived and designed the experiments. Z.H. Li and H.W. Huang performed the experiments. Z.B. Lin, W.Y. Song and B.H. Yao analyzed the data. B.Y. Zhang, W.Y. Song and Y.M. Wang wrote the paper.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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