Introduction

The development of deep coal resources is one of China’s energy development strategies, and under the influence of the high in-situ stress and the mining disturbance, the good mining conditions have deteriorated, and dynamic disasters such as underground impact pressure occur frequently, which bring great challenges to mine safety1,2,3. Although the mechanism of underground impact pressure disaster has not yet been clarified, a large number of practices have shown that protective layer mining4,5can change the stress environment of the original rock, release the elastic energy, and destroy the structure of the rock layer, and the protective layer mining technology is one of the most effective strategic measures. Thus the main countries with underground impact pressure have carried out in-depth and extensive research on the parameters of the implementation of this method which achieved significant applications, such as Russia, Poland, and China6,7,8. In 1933, France was the first country to adopt the protective layer mining technology for the prevention and control of coal and gas outbursts9, and in 1950, the former Soviet Union began to pay attention to the research on the prevention and control of impact pressure disasters by protective layer mining10, and in 1981, China began to try to apply the protective layer mining to prevent and control impact pressure disasters11.

Until the beginning of the twentieth century, many experts began to pay attention to the research on the mechanism of protective layer mining because of the frequent occurrence of impact pressure disasters in coal-producing countries around the world. Tu Xigen et al.12 explored the change rule of gas and rock pressure activities in the protective layer after protective layer mining and analyzed the mechanism of protection. Wang Luofeng et al.13 analyzed the mechanism of the decrease of effective vertical distance of the lower protective layer due to the increase of mining depth and stress elevation in the thick coal seam with a large inclination angle and strong impact. Dou Linming et al.14 used laboratory research to conclude that the protective layer mining in Jisan Mine damaged the structure of the below coal rock body, pre-released the elastic energy stored in the rock body, and the stress in the protected coal seam decreased. Xue Yi et al.15 investigated the effect of stress release and infiltration and permeability increase in the overlying coal seam, and at the same time, put forward a model of the permeability evolution in the damaged coal seam that considered the effect of damage on permeability. Chen Rongzhu et al.16 used 3DEC software to simulate the development and distribution of fissures in the underlying coal (rock) at different mining distances, and the fissures in the basement rock seam can be divided into the original state zone, high-intensity decompression, and permeability enhancement zone, and recompaction zone along the horizontal direction. Jiang Fuxing et al.17,18 proposed the impact pressure control program for mining localized protective layers conducted the mechanism research on impact pressure control and large deformation disaster prevention, and studied the static and dynamic system sources of the protective layer impact induced by the coal pillar of the upper protective layer. Yang Yongliang et al.19 investigated the influence law of cyclic stress effect on the dynamic characteristics of coal bodies generated in the process of protective layer mining. Wang Dezhong et al.20 concluded that the stress reduction in the mining field due to the mining of the upper protective layer is the fundamental reason for the unloading of the protected layer. Zhiguo Lu et al.21 evaluated the response and sensitivity of post peak features to single factor and multi factor interactions. Xuexi Chen et al.22 used FLAC3D-COMSOL coupled simulation to analyze the mechanical evolution law and pressure relief and transparency mechanism of protective layer mining under complex structural stress. Min Wang et al.23,24 studied the mechanical properties of rock like materials with pre-existing joints and circular holes. Wulin Lei et al.25 analyzed the influence of coal seam spacing, interlayer lithology, and protective layer thickness on the pressure relief effect of the protective layer by establishing a numerical simulation model. Kong Shengli et al.26, Pang Longlong et al.27, Xu Gang et al.28found that the change in the stress distribution in the mining field is the main reason for the changes in the deformation of the coal body of the protected layer, the development of fissures, the tendency to impact, and the change in the intensity of the dynamic load disturbances. Yuan Liang29, Zhao Can et al.30, Luo Yong et al.31, and Chen Liang32showed that after multiple upper protective layers are mined, the underlying protected layer will undergo multiple pressure relief processes, and the effect of multiple pressure relief is better than that of single pressure relief. According to the relative positional relationship between the protective layer and the protected layer, it is divided into upper protective layer mining and lower protective layer mining33.Regarding the pressure relief mechanism of the coal rock under the upper protective layer mining, scholars at home and abroad mainly follow the theory related to the deformation and destruction of the base plate rock layer. Mainly formed the floor plate “clamped beam“34, “plate model theory“35, “in-situ fissure and zero position damage“36,” O” ring theory37, key stratum theory38, “lower three zones theory“39, “lower four belts” theory40, etc. The above research results have a certain guiding significance for the research on the mechanism of pressure relief and impact prevention in protective layer mining. However, the upper protective layer mining to prevent impact pressure has not yet formed a mature theoretical framework and application of technology system, most of the research is only for the protective layer mining of mining field stress changes in the qualitative analysis, as well as a variety of protective layer mining field application of experimental research, can not provide sufficient theoretical and technical support for the engineering field of the upper protective layer mining design of a reasonable layout.

In summary, the deformation and pressure relief mechanism of underlying coal and rock under protective layer mining was studied through theoretical calculations. The factors affecting the pressure relief and anti scouring effect of protective layer mining were divided into four major factors: geostress environment, coal and rock damage and mechanical strength, dynamic load energy of roof fracture, energy loss structure and release space. According to theoretical calculations, it has been revealed that after upper protection mining, the residual vertical stress level in the goaf is lower than that in the goaf. This is directly related to the influence of the goaf as a free space. On the one hand, the vertical stress of the rock mass above the goaf is transferred to the deep rock mass, and cannot act on the collapsed gangue in the goaf to transmit the force to the lower release layer, which blocks the upper vertical stress. On the other hand, the underlying rock mass in the goaf has free movement space, which causes horizontal stress to accumulate to some extent in the lower elastic coal rock mass. Due to the fact that the decrease in vertical stress within a certain depth range of the goaf is greater than the change in horizontal stress, the horizontal stress is relatively high; Under lower residual pressure, high-level stress exerts a significant squeezing effect on the underlying coal rock mass, promoting its failure and the release of high ground stress. These theoretical calculations form the theoretical foundation for rock mechanics experiments, physically similar material simulation experiments, and on-site industrial experiments, providing crucial basis and directional guidance for these practical activities.

The variation law of mining induced stress in underlying coal and rock

Mechanism of preventing and controlling rockburst

The mining of protective layers is generally carried out under the conditions of coal seam clusters, and the coal seams that are first mined to eliminate or reduce the impact risk of adjacent coal seams are called protective layers; The protected layer is relative to the protective layer, which refers to the adjacent impact coal seams that eliminate or reduce the risk of impact after the mining of the protective layer, and is called the protected layer. The mining of the upper protective layer breaks the original stress balance of the coal-rock body, and the stress is redistributed with the moving deformation of the roof and floor coal-rock body. According to the change of moving deformation of the coal rock body under the floor plate, it is divided into 4 characteristic zones in the horizontal direction: undisturbed zone, compression zone, expansion zone, and compaction zone; according to the change of the stress of the coal rock under the floor plate, it is divided into 4 characteristic zones in the horizontal direction: the original stress zone, the stress concentration zone, the stress reduction zone and the stress restoration zone. As shown in Fig. 1, analyze the characteristics of coal and rock movement and deformation under the protective layer mining from the perspective of coal and rock displacement changes. If a longitudinal section is taken along the direction of the working face, during the process of advancing the protective layer working face, the underlying coal and rock under the bottom plate in front of the coal wall of the working face are in a compressed state, and the displacement is downward; The underlying coal and rock in the goaf are in an expanding state with upward displacement, resulting in a large number of mining induced fractures in the area; As the gangue in the goaf gradually collapses and compacts, the underlying coal and rock stress returns to the original rock stress state. The rock mass below the goaf is in the compacted zone, and the displacement gradually decreases. At this time, interlayer cracks are prone to occur.

Fig. 1
figure 1

Stress distribution diagram of protective seam mining.

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The stresses in the underlying coal rock body during the mining of the upper protective layer underwent a dynamic process of elevation, reduction, and recovery. At the same time, the mining field coal rock body went through a large number of deformation energy aggregation, energy sharp release, and elastic energy recovery loading and unloading process. Therefore, the following four factors constitute the prevention machine of the underground impact pressure relief in the upper protective layer mining.

  1. (1)

    Mining stress environment. Mining of the upper protective layer will make the protected layer in a certain time and space in a low-stress state, reducing the occurrence probability of impact underground pressure of the protected layer due to high ground stress environment. The formation of “upper three zones” and “lower three zones” of the mining field peripheral rock will release the elastic energy in the mining field peripheral rock in advance, changing the spatial distribution of energy in the mining field area.

  2. (2)

    Mechanical strength of coal rock. The underlying coal rock body is affected by loading and unloading during the upper protective layer mining, the coal rock body damaged fissure formation, resulting in the structural reorganization of the coal rock interior, the loss of structural linkage, for the release of energy, transfer of the requisites and foundations for the change of the physical and mechanical properties of the coal rock, reduces the elastic potential of the coal rock body and mechanical strength, weakened the tendency to impact of the coal rock body.

  3. (3)

    Dynamic load disturbance. The mining in the upper protected layer causes the roof and floor plates to be broken or to significantly develop fissures, forming the “weak structure of surrounding rock fissures” layer of the protected layer, weakening the key rock structure of the protected layer, weakening the suspending distance of the high-level, thick and hard rock layers when mining in the protected layer, and the degree of concentration of stress in the mining field, thus decreasing the dynamic energy disturbance of the roof fracture.

  4. (4)

    Energy loss space. Mining on the protective layer so that the protected layer is below its mined-out area, mined-out area collapsed gangue to form a larger range of space broken loose structure, will fully absorb the dynamic load energy, reduce the dynamic load energy accumulation and transfer role, to absorb the role of consuming dynamic load energy, reduce the occurrence probability of underground impact pressure which induced by the dynamic load energy when the protected layer mining.

Therefore, the upper protective layer mining can effectively change the mining high-stress environment of the protected layer, reduce the mechanical strength of the coal rock body in the mining field, weaken the structural strength of the roof plate of the protected layer and the dynamic load energy disturbance effect, form the loose and broken gangue structure of the mined-out area above the protected layer, and eliminate or weaken the danger of the impact underground pressure of the protected layer, shown in Fig. 2.

Fig. 2
figure 2

Pressure relief mechanism of protective seam mining.

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Mechanical model analysis

  1. (1)

    Mechanical analysis of working face tendency.

According to the theory of elastic-plastic mechanics, assuming that the underlying coal rock body is a continuous medium, the initial stress is a uniform load, and the change of abutment stress is linear, the mechanical simplification of the force state of the mining field coal rock body is carried out, and then the stress increment is used to simplify the mechanical model, to obtain the mechanical model of the tendency direction of the underlying coal rock under the action of equivalent load, as shown in Fig. 3. Considering the mining stress increment as a homogeneous load, the maximum value of the stress increment is (k-1)q0, and the average value of the residual stress is (1-k’)q0.

Fig. 3
figure 3

The effect of concentrated force on any point of semi infinite plane.

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According to elastic mechanics, it is known that the semi-infinite planar body is subjected to the effect of concentrated stress P. Through the coordinate transformation relation, the stress component generated at any point M of the underlying coal rock is:

$$\left. \begin{gathered} {\sigma _y}= - \frac{{2P}}{\pi }\frac{{{{\cos }^3}\theta }}{r} \hfill \\ {\sigma _x}= - \frac{{2P}}{\pi }\frac{{{{\sin }^2}\theta \cos \theta }}{r} \hfill \\ {\tau _{yx}}= - \frac{{2P}}{\pi }\frac{{\sin \theta {{\cos }^2}\theta }}{r} \hfill \\ \end{gathered} \right\}$$
(1)

Where: σy - Vertical component of the ground stress, MPa; σx - Horizontal component of the ground stress, MPa; τyx - Shear component of the ground stress, MPa; γ- Volumetric weight of the rock, kN/m3; P- Concentrated stress, MPa; r-Distance between point M and concentrated stress P, m; θ-angle between r and y-axis, °.

Using the relational expression \(\cos \theta =\frac{y}{r}\),\(\sin \theta =\frac{x}{r}\),\({r^2}={x^2}+{y^2}\), the above equation can be written as:

$$\left. \begin{gathered} {\sigma _y}= - \frac{{2P}}{\pi }\frac{{{y^3}}}{{{{\left( {{x^2}+{y^2}} \right)}^2}}} \hfill \\ {\sigma _x}= - \frac{{2P}}{\pi }\frac{{{x^2}y}}{{{{\left( {{x^2}+{y^2}} \right)}^2}}} \hfill \\ {\tau _{yx}}= - \frac{{2P}}{\pi }\frac{{x{y^2}}}{{{{\left( {{x^2}+{y^2}} \right)}^2}}} \hfill \\ \end{gathered} \right\}$$
(2)

As shown in Fig. 3, the AD segment at the boundary position -(L1 + L2) ≤ x ≤ (L1 + L2) range is subjected to a distributed stress of intensity q(x). To find the stress component at any point M(x, y) in the semi-infinite plane, take the micrometric element dξ on the AD segment, which is at a distance ξ from the coordinate origin O, and consider the force dp = qdξ applied on dξ as a tiny concentrated force. The stress induced by this tiny concentrated force at any point below it can be calculated by Eq. (2). In Eq. (2), x and y are the horizontal and vertical distances between the desired stress point and the point of action of the concentrated force, then the horizontal and lead distances between the point M and the concentrated force dp are (x - ξ), y. Therefore, the stress component caused by dp = qdξ at point M is as follows.

$$\left. \begin{gathered} d{\sigma _y}= - \frac{{2qd\xi }}{\pi }\frac{{{y^3}}}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}} \hfill \\ d{\sigma _x}= - \frac{{2qd\xi }}{\pi }\frac{{{{\left( {x - \xi } \right)}^2}y}}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}} \hfill \\ d{\tau _{yx}}= - \frac{{2qd\xi }}{\pi }\frac{{\left( {x - \xi } \right){y^2}}}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}} \hfill \\ \end{gathered} \right\}$$
(3)

Where: ξ-Distance of point M from the origin of coordinates, m; q-Load, MPa.

To find the value of the stresses induced by all the distributed loads at the point M(x, y), it is sufficient to add the stresses induced by all the concentrated forces of all micro-units, i.e., to find the integral of the three equations above, as in the following Eq. 

$$\left. \begin{gathered} {\sigma _y}= - \frac{2}{\pi }\int_{{\left( {{L_1}+{L_2}} \right)}}^{{ - \left( {{L_1}+{L_2}} \right)}} {\frac{{q{y^3}d\xi }}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}}} \hfill \\ {\sigma _x}= - \frac{2}{\pi }\int_{{\left( {{L_1}+{L_2}} \right)}}^{{ - \left( {{L_1}+{L_2}} \right)}} {\frac{{q{{\left( {x - \xi } \right)}^2}yd\xi }}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}}} \hfill \\ {\tau _{yx}}= - \frac{2}{\pi }\int_{{\left( {{L_1}+{L_2}} \right)}}^{{ - \left( {{L_1}+{L_2}} \right)}} {\frac{{q\left( {x - \xi } \right){y^2}d\xi }}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}}} \hfill \\ \end{gathered} \right\}$$
(4)

As shown in Fig. 3, the AD section can be divided into AB, BC, CD three parts of the load, segmented into the integral calculation. The load of the AB section is \(q={{\left[ {\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}} \right]} \mathord{\left/ {\vphantom {{\left[ {\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}} \right]} {{L_1}}}} \right. \kern-0pt} {{L_1}}}\), the load of the BC section is \(q= - \left( {1 - k^{\prime}} \right){q_0}\), and the load of the CD section is \(q= - {{\left[ {\left( {k - 1} \right)\left( {x - {L_1} - {L_2}} \right){q_0}} \right]} \mathord{\left/ {\vphantom {{\left[ {\left( {k - 1} \right)\left( {x - {L_1} - {L_2}} \right){q_0}} \right]} {{L_1}}}} \right. \kern-0pt} {{L_1}}}\), to find out the stresses generated by the AB, BC, and CD sections on the point M(x, y). Since the underlying coal rock is simplified as a semi-infinite planar body without considering the gravity of the coal rock body, the stress distribution should be based on the above formula, considering the horizontal stress generated by the tectonic movement and the self-gravitational stress, then the stress calculation formula of any point of the underlying coal rock body is obtained.

$$\begin{aligned} {\sigma _y}&=\gamma \left( {y+H} \right)+\frac{{\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}}}{{{L_1}\pi }}\left\{ {\left[ {\frac{{y\left( {x+{L_1}+{L_2}} \right)}}{{{{\left( {x+{L_1}+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}}} \right]+(t{g^{ - 1}}\frac{{x+{L_1}+{L_2}}}{y} - t{g^{ - 1}}\frac{{x+{L_2}}}{y})} \right\} \\ &\quad{\text{ }}+\frac{{\left( {1 - k'} \right){q_0}}}{\pi }\left\{ {\left[ {\frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_2}} \right)}}{{{{\left( {x - {L_2}} \right)}^2}+{y^2}}}} \right]+\left( {t{g^{ - 1}}\frac{{x+{L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_2}}}{y}} \right)} \right\} \\ &\quad{\text{ }} - \frac{{\left( {k - 1} \right)\left( {x - {L_1} - {L_2}} \right){q_0}}}{{{L_1}\pi }}\left\{ {\left[ {\frac{{y\left( {x - {L_1} - {L_2}} \right)}}{{{{\left( {x - {L_1} - {L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_2}} \right)}}{{{{\left( {x - {L_2}} \right)}^2}+{y^2}}}} \right]+\left( {t{g^{ - 1}}\frac{{x - {L_1} - {L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_2}}}{y}} \right)} \right\} \\ {\sigma _x}&=\frac{\mu }{{1 - \mu }}\gamma \left( {y+H} \right)+\frac{{\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}}}{{{L_1}\pi }}\left\{ {(t{g^{ - 1}}\frac{{x+{L_1}+{L_2}}}{y} - t{g^{ - 1}}\frac{{x+{L_2}}}{y}) - \left[ {\frac{{y\left( {x+{L_1}+{L_2}} \right)}}{{{{\left( {x+{L_1}+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\ &\quad{\text{ }}+\frac{{\left( {1 - k'} \right){q_0}}}{\pi }\left\{ {\left( {t{g^{ - 1}}\frac{{x+{L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_2}}}{y}} \right) - \left[ {\frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_2}} \right)}}{{{{\left( {x - {L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\ &\quad{\text{ }} - \frac{{\left( {k - 1} \right)\left( {x - {L_1} - {L_2}} \right){q_0}}}{{{L_1}\pi }}\left\{ {\left( {t{g^{ - 1}}\frac{{x - {L_1} - {L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_2}}}{y}} \right) - \left[ {\frac{{y\left( {x - {L_1} - {L_2}} \right)}}{{{{\left( {x - {L_1} - {L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_2}} \right)}}{{{{\left( {x - {L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\ {\tau _{yx}}&=\frac{{\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}y}}{{{L_1}\pi }}\left\{ {(t{g^{ - 1}}\frac{{x+{L_1}+{L_2}}}{y} - t{g^{ - 1}}\frac{{{x_1}+{L_2}}}{y}) - \left[ {\frac{{y\left( {x+{L_1}+{L_2}} \right)}}{{{{\left( {x+{L_1}+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\ &\quad{\text{ }}+\frac{{\left( {1 - k'} \right){q_0}y}}{\pi }\left\{ {\left( {t{g^{ - 1}}\frac{{x+{L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_2}}}{y}} \right) - \left[ {\frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_2}} \right)}}{{{{\left( {x - {L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\ &\quad{\text{ }} - \frac{{\left( {k - 1} \right)\left( {x - {L_1} - {L_2}} \right){q_0}y}}{{{L_1}\pi }}\left\{ {\left( {t{g^{ - 1}}\frac{{x - {L_1} - {L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_2}}}{y}} \right) - \left[ {\frac{{y\left( {x - {L_1} - {L_2}} \right)}}{{{{\left( {x - {L_1} - {L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_2}} \right)}}{{{{\left( {x - {L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\ \end{aligned}$$
(5)

Where: k-Abutment stress concentration coefficient; k’ - Residual abutment stress concentration coefficient; H-Depth of the rock layer, m; µ-Poisson’s ratio of rock; q0 -Self-weight stress, MPa; L1 - Advanced abutment stress range, m; L2 - Half of the face length of the working face, m.

(2) Mechanical analysis of working face strike.

According to the theory of elastic-plastic mechanics, assuming that the abutment stress changes linearly, and considering the stress of the mining coal rock under the mined-out area as 0 and the stress concentration coefficient in the mined-out area as 1, the maximum value of stress increment is (k − 1)q0, and the mechanical model is simplified by adopting the stress increment to get the mechanical model of the direction of strike of the underlying coal rock under the action of the equivalent load, as shown in Fig. 4.

Fig. 4
figure 4

Calculation diagram of stress increment in strike direction.

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Taking any one of the micro-unit bodies within the underlying coal rock body, the stress component can be calculated based on the semi-infinite body subjected to normally distributed loads on the boundary. As can be seen from the figure, the load on the underlying coal rock can be divided into several parts, and the resulting stress components can be calculated separately, and then superimposed to obtain the stress component at any point in the underlying coal rock. According to the theory of elastic mechanics, similar to the derivation method of tendency direction, the expression of stress component caused by supporting pressure at any point M in the underlying coal rock is as follows.

$$\left. \begin{gathered} {\sigma _y}= - \frac{2}{\pi }\int_{{\left( {{L_3}+{L_4}} \right)}}^{{ - \left( {{L_1}+{L_2}} \right)}} {\frac{{q{y^3}d\xi }}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}}} \hfill \\ {\sigma _x}= - \frac{2}{\pi }\int_{{\left( {{L_3}+{L_4}} \right)}}^{{ - \left( {{L_1}+{L_2}} \right)}} {\frac{{q{{\left( {x - \xi } \right)}^2}yd\xi }}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}}} \hfill \\ {\tau _{yx}}= - \frac{2}{\pi }\int_{{\left( {{L_3}+{L_4}} \right)}}^{{ - \left( {{L_1}+{L_2}} \right)}} {\frac{{q\left( {x - \xi } \right){y^2}d\xi }}{{{{\left[ {{{\left( {x - \xi } \right)}^2}+{y^2}} \right]}^2}}}} \hfill \\ \end{gathered} \right\}$$
(6)

Where: L1 - distance between the stress peak in front of the coal wall and the undisturbed area, m; L2 - distance between the stress peak in front of the coal wall and the working face, m; L3 - distance between the minimum stress in the mined-out area and the coal wall of the working face, m; L4 - distance between the minimum stress in the mined-out area and the distance between undisturbed zone, m.

As in Fig. 4, the AD section is divided into three parts of the load, respectively, AB, BC, CD section, and the integration calculation is carried out in segments. The load of the AB section is \(q={{\left[ {\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}} \right]} \mathord{\left/ {\vphantom {{\left[ {\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}} \right]} {{L_1}}}} \right. \kern-0pt} {{L_1}}}\), the load of the BC section is \(q= - \left( {{{{q_0}} \mathord{\left/ {\vphantom {{{q_0}} {{L_3}}}} \right. \kern-0pt} {{L_3}}}} \right) \cdot x\), \({L_3}={{{L_2}} \mathord{\left/ {\vphantom {{{L_2}} {\left( {k - 1} \right)}}} \right. \kern-0pt} {\left( {k - 1} \right)}}\), and the load of the CD section is \(q=\left[(x-L_{3}-L_{4})(1-k)q_{0}\right]/L_{4}\), and the stress generated by the AB, BC and CD sections on the point M(x, y) are found respectively, and the stress on any point of the underlying coal rock body is obtained by taking the horizontal stress and the self-gravitational stresses along the working face strike.

$$\begin{aligned}{\sigma _y}&=\gamma \left( {y+H} \right)+\frac{{\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}}}{{{L_1}\pi }}\left\{ {\left[ {\frac{{y\left( {x+{L_1}+{L_2}} \right)}}{{{{\left( {x+{L_1}+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}}} \right]+(t{g^{ - 1}}\frac{{x+{L_1}+{L_2}}}{y} - t{g^{ - 1}}\frac{{x+{L_2}}}{y})} \right\} \\ &\quad{\text{ }}+\frac{{{q_0}}}{{{L_3}\pi }}\left\{ {\left[ {\frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_3}} \right)}}{{{{\left( {x - {L_3}} \right)}^2}+{y^2}}}} \right]+\left( {t{g^{ - 1}}\frac{{x+{L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_3}}}{y}} \right)} \right\} \\&\quad {\text{ }}+\frac{{\left( {x - {L_3} - {L_4}} \right)\left( {1 - {k^{\prime}}} \right){q_0}}}{{{L_4}\pi }}\left\{ {\left[ {\frac{{y\left( {x - {L_3} - {L_4}} \right)}}{{{{\left( {x - {L_3} - {L_4}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_3}} \right)}}{{{{\left( {x - {L_3}} \right)}^2}+{y^2}}}} \right]+\left( {t{g^{ - 1}}\frac{{x - {L_3} - {L_4}}}{y} - t{g^{ - 1}}\frac{{x - {L_3}}}{y}} \right)} \right\} \\{\sigma _x}&=\frac{\mu }{{1 - \mu }}\gamma \left( {y+H} \right)+\frac{{\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}}}{{{L_1}\pi }}\left\{ {(t{g^{ - 1}}\frac{{x+{L_1}+{L_2}}}{y} - t{g^{ - 1}}\frac{{{x_1}+{L_2}}}{y}) - \left[ {\frac{{y\left( {x+{L_1}+{L_2}} \right)}}{{{{\left( {x+{L_1}+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\&\quad {\text{ }}+\frac{{{q_0}}}{{{L_3}\pi }}\left\{ {\left( {t{g^{ - 1}}\frac{{x+{L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_3}}}{y}} \right) - \left[ {\frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_3}} \right)}}{{{{\left( {x - {L_3}} \right)}^2}+{y^2}}}} \right]} \right\} \\&\quad {\text{ }}+\frac{{\left( {x - {L_3} - {L_4}} \right)\left( {1 - {k^{\prime}}} \right){q_0}}}{{{L_4}\pi }}\left\{ {\left( {t{g^{ - 1}}\frac{{x - {L_3} - {L_4}}}{y} - t{g^{ - 1}}\frac{{x - {L_3}}}{y}} \right) - \left[ {\frac{{y\left( {x - {L_3} - {L_4}} \right)}}{{{{\left( {x - {L_3} - {L_4}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_3}} \right)}}{{{{\left( {x - {L_3}} \right)}^2}+{y^2}}}} \right]} \right\} \\ {\tau _{yx}}&=\frac{{\left( {k - 1} \right)\left( {x+{L_1}+{L_2}} \right){q_0}y}}{{{L_1}\pi }}\left\{ {(t{g^{ - 1}}\frac{{x+{L_1}+{L_2}}}{y} - t{g^{ - 1}}\frac{{{x_1}+{L_2}}}{y}) - \left[ {\frac{{y\left( {x+{L_1}+{L_2}} \right)}}{{{{\left( {x+{L_1}+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}}} \right]} \right\} \\ &\quad {\text{ }}+\frac{{{q_0}y}}{{{L_3}\pi }}\left\{ {\left( {t{g^{ - 1}}\frac{{x+{L_2}}}{y} - t{g^{ - 1}}\frac{{x - {L_3}}}{y}} \right) - \left[ {\frac{{y\left( {x+{L_2}} \right)}}{{{{\left( {x+{L_2}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_3}} \right)}}{{{{\left( {x - {L_3}} \right)}^2}+{y^2}}}} \right]} \right\} \\&\quad {\text{ }}+\frac{{\left( {x - {L_3} - {L_4}} \right)\left( {1 - {k^{\prime}}} \right){q_0}y}}{{{L_4}\pi }}\left\{ {\left( {t{g^{ - 1}}\frac{{x - {L_3} - {L_4}}}{y} - t{g^{ - 1}}\frac{{x - {L_3}}}{y}} \right) - \left[ {\frac{{y\left( {x - {L_3} - {L_4}} \right)}}{{{{\left( {x - {L_3} - {L_4}} \right)}^2}+{y^2}}} - \frac{{y\left( {x - {L_3}} \right)}}{{{{\left( {x - {L_3}} \right)}^2}+{y^2}}}} \right]} \right\} \\\end{aligned}$$
(7)

Resolution of the mining stress field calculations

To make the mechanical model more intuitive, the theoretical calculation and solution with the geological and mining conditions of the Hulusu coal mine can get the vertical and horizontal stress values of the underlying coal rock body at any point of different depths in the strike and tendency directions. According to the relevant data of the working face of the Hulusu coal mine, the thickness of the protective coal layer m = 2.5 m, the burial depth H = 640 m, the average volumetric weight of rock γ = 25 kN/m3; the abutment stress concentration coefficient of the tendency direction k = 3, and the influence range of the abutment stress is 40 m. The tendency length of the working face is 2L2 = 320 m, and the residual abutment stress concentration coefficient of the mined-out area is 0.3; the increasing coefficient of the abutment stress of the strike direction k1 = 3.5. The influence range of advanced abutment stress is 50 m, the distance of advanced abutment stress from the coal wall is L2 = 15 m, and the lateral pressure coefficient of horizontal stress is 1.2. Substitute the above values into Eqs. (7) and (9) respectively, and utilize Matlab software to analyze and calculate the above-derived equations and draw the graphs to study the distribution of stress and the rule of change of the law in the underlying coal and rock body after the mining of the protective layer.

Figure 5 shows the stress distribution of the underlying coal rock mass at different depths in the inclined direction, with the horizontal axis representing the inclined direction of the working face and 0 representing the center of the goaf; The vertical axis represents vertical stress, with negative compressive stress and positive tensile stress. As shown in Fig. 5 (a), after the upper protective layer is mined, the position of the coal pillar in the section is the pressurized area, and the range of the goaf is the depressurized area. The minimum value of vertical stress is located in the middle of the goaf, and the vertical stress gradually increases towards both sides of the goaf. According to the geological conditions of the mine, the original vertical stress at a depth of 630 m in the protective layer is approximately − 12.83 MPa. Within the goaf area, after the unloading of the upper protective layer, the vertical stress of the coal rock mass at depths of 5 m, 10 m, 20 m, and 40 m from the bottom plate to the upper protective layer is −2.34 MPa- 3.14 MPa- 4.71 MPa and − 8.21 MPa decreased to 18.24%, 24.47%, 36.71%, and 63.99% of the initial vertical stress, respectively, indicating varying degrees of pressure relief effects in the coal rock mass within the goaf, and the degree of pressure relief in the coal rock mass decreased with increasing depth. Within the range of the section coal pillar, after the mining and unloading of the upper protective layer, the vertical stresses of the coal rock mass at depths of 5 m, 10 m, 20 m, and 40 m from the bottom plate to the upper protective layer are − 32.23 MPa- 27.24 MPa- 21.70 MPa and − 17.31 MPa increased to 251.21%, 212.31%, 169.13%, and 134.92% of the initial vertical stress, respectively, indicating stress concentration in the coal rock mass below the coal pillar, and the degree of stress concentration in the coal rock mass decreases with increasing depth. As shown in Fig. 5 (b), the horizontal stress of the underlying coal rock mass is −13.12 MPa at depths of 5 m, 10 m, 20 m, and 40 m from the protective layer, respectively- 10.38 MPa- At 6.85 MPa and 0.11 MPa, the horizontal stress within the goaf is compressive stress when the depth is small, and the compressive stress value gradually decreases with increasing depth; Horizontal stress is tensile stress at greater depths, and the tensile stress value gradually increases with increasing depth. The horizontal stress of the coal rock mass below the section coal pillar is tensile stress, which gradually decreases with increasing depth. The horizontal stress variation of the underlying coal rock mass in the goaf is opposite to the vertical stress variation.

Fig. 5
figure 5

Stress distribution of floor coal and rock mass at different depths.

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Figure 6 shows a schematic diagram of the stress distribution of the underlying coal rock body at different depths in the direction of the strike. As shown in Fig. 6(a), after the upper protective layer is mined, the vertical stress in a certain range of the underlying coal rock body in the mining mined-out area decreases, and this area is the pressure relief area. Vertical stress increases in a certain range of the underlying coal rock body in front of the coal wall of the working face, and this area is the pressurized zone. Vertical and horizontal stresses first increase and then decrease along the direction of working face advancement, and vertical and horizontal stresses are inversely proportional to depth. As shown in Fig. 6(b), the horizontal stress in the range of the mined-out area decreases gradually with the increase of depth, and the horizontal stress changes from compressive stress to tensile stress; the horizontal stress is concentrated in the coal wall position, and it is easy to be affected by the extrusion to produce the bottom drum phenomenon. The horizontal stress in the floor plate in front of the coal wall of the working face is different from the vertical stress, and the horizontal stress gradually decreases with the increase of depth until it stabilizes.

Fig. 6
figure 6

Stress distribution of floor coal and rock mass at different depths.

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In summary, the deformation and pressure relief mechanism of underlying coal and rock under protective layer mining was studied through theoretical calculations. The factors affecting the pressure relief and anti scouring effect of protective layer mining were divided into four major factors: geostress environment, coal and rock damage and mechanical strength, dynamic load energy of roof fracture, energy loss structure and release space. According to theoretical calculations, it has been revealed that after upper protection mining, the residual vertical stress level in the goaf is lower than that in the goaf. This is directly related to the influence of the goaf as a free space. On the one hand, the vertical stress of the rock mass above the goaf is transferred to the deep rock mass, and cannot act on the collapsed gangue in the goaf to transmit the force to the lower release layer, which blocks the upper vertical stress. On the other hand, the underlying rock mass in the goaf has free movement space, which causes horizontal stress to accumulate to some extent in the lower elastic coal rock mass. Due to the fact that the decrease in vertical stress within a certain depth range of the goaf is greater than the change in horizontal stress, the horizontal stress is relatively high; Under lower residual pressure, high-level stress exerts a significant squeezing effect on the underlying coal rock mass, promoting its failure and the release of high ground stress. These theoretical calculations form the theoretical foundation for rock mechanics experiments, physically similar material simulation experiments, and on-site industrial experiments, providing crucial basis and directional guidance for these practical activities.

Mechanism of changes in mechanical strength of coal and rock during mining

In the process of mining the upper protective layer, the mining disturbance destroys the stress equilibrium state in which the underlying coal rock body is located, leading to the redistribution of the stress suffered by the underlying coal rock body in the working face, so that the coal rock body experiences the dynamic stress process of stress elevation and lowering, which is essentially the process of loading and unloading of the coal rock body, which will lead to different degrees of damage to the coal rock body, and then change the mechanical properties of the coal rock. Therefore, the cyclic loading and unloading mechanical test can be used to realize the stress state of coal rock under different strengths of upper protected seam mining, and to study the deformation and damage of coal rock materials and the evolution of mechanical properties during the loading and unloading process, which is of great significance for the study of the mechanism of pressure relief in upper protective layer mining.

Mechanical test of loading and unloading coal samples

According to the “Method for Determining the Physical and Mechanical Properties of Coal and Rock”, coal samples taken from Hulusu Coal Mine are made into standard cylindrical specimens with a diameter of 50 mm and a height of 100 mm. The specimens must ensure that the two end faces are parallel, smooth, without significant scratches, and the parallelism of the two end faces is less than 0.02 mm, the flatness of the two end faces is less than 0.5 mm, and the diameter deviation of the two end faces is less than 0.02 mm. The processing accuracy of the specimens must meet the requirements of the national standard for rock mechanics testing.

Table 1 Cyclic loading and unloading test scheme.
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Fig. 7
figure 7

The stress-strain curve of samples.

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Fig. 8
figure 8

The axial strain curve of samples.

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In this experiment, four sets of specimens were designed to unload stress at 0 MPa, 4 MPa, 8 MPa, and 10 MPa, respectively, with a displacement loading rate of 0.3 mm/min. The HCT-106 microcomputer controlled electro-hydraulic servo pressure testing machine was used to conduct deformation tests on coal samples under different loading and unloading stresses. The test results are shown in Table 1. When the loading and unloading stresses increased from 0 MPa to 4 MPa, 8 MPa, and 10 MPa, the uniaxial compressive strength of the specimens decreased by 1.97%, 5.49%, and 11.26%, respectively, indicating that the uniaxial compressive strength decreased with the increase of loading and unloading stresses. The peak axial strain increased from − 3291 µ ε to −3788 µ ε- 4267 µ ε- 5259 µ ε increased by 15.11%, 29.66%, and 59.79%, respectively, indicating that with the increase of loading and unloading stress, the damage and deformation of coal samples increase, making them more susceptible to damage, as shown in Fig. 7. The plastic strains generated by the damage of coal specimens are − 254 µ ε- 522 µ ε- 623 µ ε indicates that the damage to the specimen increases with the increase of loading and unloading stress, as shown in Fig. 8. When the loading and unloading stress reaches the ultimate critical stress, the stress-strain curve of repeated loading and unloading will eventually intersect directly with the peak of the coal rock stress-strain curve, resulting in coal rock failure. The strength of coal rock failure is lower than the peak strength, and the strength value of failure at this time is called fatigue strength. The results indicate that with the increase of loading and unloading stress, the damage and deformation of coal and rock increase, making them more susceptible to damage and more conducive to the release of their own elastic energy. The uniaxial compressive strength of coal rock decreases with the increase of loading and unloading stress, while the damage variable of coal increases with the increase of loading and unloading stress.

Change rule of impact tendency of coal samples during unloading and loading test

Impact propensity is the ability to identify the impact damage of coal and rock masses, and to determine whether they have inherent mechanical properties that pose a risk of impact. In engineering practice, coal or rock samples are taken from different locations in a certain coal rock layer or area on site, and rock mechanics tests are conducted in the laboratory to measure indicators that characterize the impact tendency of the coal rock mass. Based on this, it is determined whether the coal rock layer or area has impact inclination. According to the Determination, Monitoring and Prevention Methods of Rock Burst Part 2: Classification of Coal Burst Tendency and Determination Method of Coal Burst Index41, the determination indicators of middling coal’s impact propensity are divided into four categories: dynamic failure time, elastic energy index, impact energy index and uniaxial compressive strength.

According to the uniaxial compressive strength of coal, the impact tendency of coal can be classified into three categories: Rc < 7 MPa for category I, no impact tendency; 7 ≤ Rc < 14 MPa for category II, weak impact tendency; Rc ≥ 14 MPa for category III, strong impact tendency.

The uniaxial compressive strength of the coal samples in the conventional uniaxial compression mechanical test is 15.78<MPa, which has a strong impact tendency. The uniaxial compressive strength of the coal samples decreased to 15.47<MPa, 14.92 MPa, and 14.01 MPa at the loading and unloading stresses of 4 MPa, 8 MPa, and 10 MPa, indicating that the impact tendency of the coal samples decreased with the increase of the loading and unloading stress levels.

According to the impact energy index of coal, the impact tendency of coal can be divided into three categories: KE<1.5 for category I, no impact tendency; 1.5 ≤ KE < 5.0 for category II, weak impact tendency; KE ≥ 5.0 for category III, strong impact tendency.

The impact energy index is the ratio of the deformation energy Es accumulated before the peak of the complete stress-strain curve of the coal sample in uniaxial compression to the deformation energy Ex consumed after the peak, which is calculated by the equation:

$${K_E}=\frac{{{E_S}}}{{{E_X}}}$$
(8)

Where, KE- impact energy index, which can visualize the process of energy storage and dissipation in rocks during uniaxial compression, showing the nature of the impact tendency of coal; ES - deformation energy accumulated before the peak; EX - deformation energy consumed after the peak.

The impact energy index of the coal samples in the conventional uniaxial compression mechanical test is 7.2, which has a strong impact tendency. At loading and unloading stresses of 4 MPa, 8 MPa, and 10 MPa, the impact energy indexes of the coal samples are 6.3, 5.2, and 4.5, indicating that the impact energy indexes of the coal samples decreased with the increase of loading and unloading stress levels.

Comprehensive analysis, in the process of protective layer mining, the protected layer is loaded and unloaded by different levels of stress, so that the coal samples are sent to irreversible plastic deformation, resulting in the damage deformation of the coal samples, reducing the uniaxial compressive strength of the coal samples and the impact energy index, attenuating the impact tendency of the coal samples, and preventing and controlling the disaster of underground impact pressure in the protected layer.

Characterization of mining disturbances in the upper protective layer and the protected layer

Physical similar simulation test

Taking the Hulusu coal mine as the research object. The average thickness of the coal seam is 2.6 m, the average dip angle is 0–3°, and the average burial depth is 635 m. The mining method is strike-longwall mining with top coal caving, and all collapse method is used to manage the roof. The test rock (coal) layer uses river sand, fly ash, and clay as aggregate; gypsum, and calcium carbonate as cementing material; mica powder as layering material, and water as mixing material. A planar stress model with a length×width×height of 3000 × 200 × 1350 mm is constructed, with a geometric similarity ratio of 1:50, a volumetric weight similarity ratio of 1:1.56, and a strength similarity ratio of 1:234. Due to the height limitation of the model, the overlying rock layer on the mining model 2.83 m is not paved and needs to be loaded to achieve it. This experiment adopts the iron brick loading method. Due to the geometric similarity ratio of 150, the top of the model needs to be loaded with 2717 kg of iron bricks, and the weight of a single iron brick is 5 kg. Therefore, 543 iron bricks need to be loaded on the top of the model. A BOTDA distributed fiber optic monitoring system, a total station displacement monitoring system, and a floor pressure transducer monitoring system are used in the testing process to form a multi-directional multi-field monitoring system for the surface of the model and the internal displacement, strain, and stress. The system is shown in Fig. 9. The strike length of the coal seam is 3000 mm in the simulated model, 300 mm boundary pillars are left on each side of the model, the total advancing length of the coal seam is 2400 mm, the mining step distance is 30 mm/knife, 20 knives are excavated every day, the mining progress is 600 mm/d, and the mining lasts for 4 days.

Fig. 9
figure 9

Model test monitoring system.

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Overlying strata migration law based on BOTDA sensing comparison analysis

Vertical sensing fiber is used to monitor the deformation of mining overlying strata, buried in the 500 m ___location in front of the open-off cut of the working face, the length of the fiber is 1300 mm, the monitoring resolution is 5 mm, Fig. 10 shows the internal strain distribution of the overlying strata migration monitored by the fiber optic in the process of mining of the upper protective layer and the protected layer. As shown in Fig. 10(a), when the working face advances to 400 mm, the strain of fiber optic in the upper protective layer working face should become negative in the range of 0 –400 mm of the overlying strata height, and the minimum strain value is −520.3 µε. The strain of fiber optic in the working face of the protected layer should become negative in the range of 0 –300 mm of the overlying strata height, and the minimum strain value is −403.5 µε. The result shows that the fiber optic is influenced by the advanced abutment pressure in front of the working face when the working face advances to the position of the fiber optic, and the fiber is in a pressurized state. Comparing the influence range and strain value, the migration intensity of the protected layer overlying strata is smaller than that of the upper protective layer working face in the same mining position. When the working face advances to 510 mm, the working face passes through the vertical fiber optic position, the fiber optic strain value changes from negative to positive, and it is considered that the overlying strata change from being subjected to compressive stress to being subjected to tensile stress. The height of the fractured zone monitored by the fiber optic of the working face of the protected layer is 400 mm, and the maximum tensile strain is 497.4 µε, while the height of the fractured zone monitored by the fiber optic of the working face of the upper protective layer is 420 mm, and the maximum tensile strain is 866.4 µε, which shows that the effect of the mining of the protected layer on the fiber optic is smaller than that of the mining of the upper protective layer. As shown in Fig. 10(b), when the working face advances to 840 mm, the strain distribution of the fiber optic in both the protected layer and the upper protective layer mining overlying strata is in the form of a single peak, and the strain peaks are 1685.4 µε and 2040.8 µε, and the range of influence of the strain curve peaks of the protected layer mining overlying strata is smaller than that of the upper protective layer. When advancing to 1350 mm, the strain peaks of both the protected layer and the upper protective layer mining overlying strata increase, indicating that with the mining overlying strata migration continues to expand upward, the strain peaks are 1790.8 µε and 3102.2 µε; when the working face advances to 1770 mm, the fiber optic strain peak is unchanged in ___location but the peak increase, indicating that the overlying strata of the high-level key stratum is undermined once again and the broken rock is deformed by rotation, which causes a sudden increase of the tensile stress of the optical fiber, and the peak values of the strain are 2778.3 µε and 5656.3 µε.

Comprehensive comparative analysis, the upper protective layer mining makes the roof and floor plates of the mining field broken or fissures significantly developed, forming the “surrounding rock fissures weak structure” layer of the protected layer, weakening the strength of the protected layer surrounding rock of the mining field so that the degree of movement and deformation of the overlying strata of the mining face of the protected layer is small compared with the upper protective layer mining. This shows that the mining of the upper protective layer weakens the strength of the mining field stress concentration and the roof dynamic load disturbance intensity during the mining process of the protected layer.

Fig. 10
figure 10

Optical fiber strain characterization of overburden movement and deformation.

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Comparative analysis of deformation intensity of key strata based on BOTDA sensing

Figure 11(a) shows the fiber optic monitoring strain characterization of the key thick sandstone strata in the process of mining the upper protective layer. The working face advances from the open-off cut, and the strain curve of the key strata is in the form of a single peak, and the strain peak is increasing. When advancing to 840 mm, the strain of the key strata reached the maximum peak, and the strain curve changed from a single peak to a double peak, with the strain peak at the mined-out area being 6584.7 µε and that at the front of the mined-out area being 6372.9 µε, indicating that the first fracture of the key thick sandstone strata occurred. In the range of 920 mm to 2400 mm, the strain peak value decreases, and the strain peak value behind the mined-out area zone is about 5142.6 µε, and the position of the peak value is unchanged. The strain peak at the front of the mined-out zone shifted forward with mining, and the strain peak varies within the range of 4334.6 µε − 4707.8 µε. Figure 11(b) shows the strain characterization of the fiber optic monitoring of the key thick sandstone strata during the mining of the protected layer. At the early stage of the working face mining, the fiber strain curve does not produce obvious changes because the key sandstone strata where the fiber is located are far away from the coal seam and have not been affected by mining. When advancing to 420 mm, the fiber optic monitors the movement and deformation of the key strata, and the strain curve is in the form of a single peak. When advancing to 630 mm, the strain reaches the maximum peak, and the strain curve changes from a single peak to a double peak, with the strain peak at the back of the mined-out zone being 4797.5 µε, and the strain peak at the front of the mined-out zone being 4674.8 µε, which indicates that the key strata of thick sandstone has been initially fractured and it is affected by the effect of tensile stress. In the range of advancing distance from 840 mm to 2400 mm, the peak strain value decreases, and the peak strain value at the back of the mined-out area is about 3950.3 µε, and the position of the peak value is unchanged. The ___location of the strain peak behind the mined-out zone moves forward with mining, and the influence range of the peak increases, and the strain peak varies within the range of 3536.1 µε − 3817.4 µε.

Comprehensive analysis shows that the key thick sandstone strata of the mining field have developed significant fissures after the mining of the upper protective layer, the key thick sandstone strata has been fractured and deformed, and the overlying strata structure of the mining field is loose and weak. When the protected layer is mined, the key strata structure of the protected layer is weakened, the strain peak value of the key thick sandstone strata has been reduced from 6584.7 µε to 4797.5 µε, and the breaking span has been reduced from 840 mm to 630 mm, which reduces the dynamic load energy disturbance effect of the roof fracture.

Fig. 11
figure 11

Strain characterization of H1 optical fiber under working face weighting.

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Comparative analysis of the law of mine pressure behavior in the working face

During the mining process of the upper protective layer and the protected layer working face, the changes in the peak abutment stress of the working face monitored by the pressure sensor are shown in Fig. 12. As shown in Fig. 12 (a), during the mining process of the upper protective layer, the peak abutment stress of the working face ranges from 16.2 MPa to 33.3 MPa, and the stress concentration coefficients are from 1.1 to 2.4, and three obvious periodic weighting occurred at the positions of advancing distance of 840 mm, 1350 mm, and 1770 mm; and the peak abutment stresses were 31.2 MPa, 29.1 MPa, and 33.3 MPa. As shown in Fig. 12 (b), during the mining of the protected layer, the peak abutment stress at the working face ranges from 7.84 MPa to 29.4 MPa, and the stress concentration coefficients are from 0.6 to 2.1, with three obvious periodic weighting at the positions of advancing distances of 630 mm, 990 mm, and 1410 mm; and the peak abutment stresses are 29.4 MPa, 24.2 MPa, and 25.2 MPa; on both sides of the working face, the peak abutment stresses are only 7.84 MPa, 9.64 MPa, 8.12 MPa, 9.64 MPa, and the peak abutment stresses are less than original stress.

Comprehensive analysis, (1) the periodic weighting interval is smaller than the upper protective layer working face during the mining of the protected layer working face, indicating that under the influence of the upper protective layer mining, the overlying strata structure of the protected layer working face has been weakened as a whole, and the limiting suspending span of the key thick sandstone strata has become smaller, and the degree of stress concentration in the mining field has been reduced; (2) The intensity of periodic weighting is smaller than that of the upper protective layer working face during the mining of the protected layer working face, which indicates that due to the influence of strata fracture in the mined-out area of the upper protective layer, the mined-out area of the protected layer is easy to be filled up quickly, resulting in the reduction of fracture slewing space of the high-level key thick sandstone strata, the suspending and breaking span are both reduced, and the dynamic load energy released during the first weighting and periodic weighting of the working face is weakened.

Fig. 12
figure 12

Peak distribution of abutment pressure in working face.

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On-site engineering practice inspection

To further explore the changing law of stress in the underlying coal rock body during the mining of the upper protective layer, fiber optic sensing technology is used in the test mine to monitor the effect of pressure relief in real time42. In the working face of the upper protective layer along the strike, boreholes are drilled under the floor plate. The diameter of the drill hole is 110 mm, the azimuth angle of 200 °, the dip angle of 20 °, and the length of 108 m. Ten 3 m fixed-point fiber grating sensors are implanted in the drill hole, the use of portable Si155 fiber grating demodulator to collect the signal of the fiber grating.

After the mining of the upper protective layer, the pressure relief effect of the protected layer can be evaluated using the stress release rate as an indicator, which is the ratio of the difference between the original stress and the mining stress to the original stress. The greater the stress release rate, the higher the degree of pressure relief after mining, and the more obvious the pressure relief effect of the upper protective layer. The positive value of the stress release rate indicates that the coal rock body is in the state of pressure relief; the negative value of the stress release rate indicates that the coal rock body is in the state of stress concentration. The stress release rate of the coal rock body at different depths during the mining process of the upper protective layer is shown in Table 2, and the stress release rate of the underlying coal rock body is in the pressurized state in the stage of advanced stress concentration, which increases and then decreases; in the stage of rapid growth of pressure relief state, which increases rapidly; and in the stage of slow recovery of pressure relief state, which decreases until it is stable and unchanged. The stress release rate in all three stages decreases with the increase in depth. Taking the stress release rate of 10% as the critical value of pressure relief, the critical pressure relief depth of the underlying coal rock body in the upper protective layer mining is 29.0 –32.5 m. Moreover, after mining the upper protective layer working face, the stress recovery rate of the coal rock body in the deeper part is faster than that in the shallower part, and the time required is shorter.

Table 2 Cyclic loading and unloading test scheme.
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Conclusion

(1)A four-factor mechanism is proposed for preventing and controlling underground impact pressure in upper protected layer mining, namely, the mining stress environment, the mechanical strength of coal and rock, the dynamic load disturbance effect of mining, and the energy loss space. Upper protective layer mining releases the elastic energy in the coal and rock strata, changes the environment of the high-stress zone in the protected layer, reduces the elastic potential and mechanical strength of the coal rock body, weakens the key strata structure of the protected layer, and reduces the accumulation and transfer of dynamic load energy.

(2)Establishment and analysis of the mechanical model of the underlying coal rock body in the upper protective layer mining. In the range of coal pillar, both vertical stress and horizontal stress decrease with the increase of depth; in the range of mined-out area, vertical stress increases with the increase of depth, and horizontal compressive stress value in the shallow part gradually decreases with the increase of depth, and tensile stress value in the deep part with the increase of depth increases.

(3)The pre mining stress concentration and post mining unloading of the upper protective layer have changed the mechanical strength of the coal rock mass, and the mining of the upper protective layer has weakened the overlying rock structure of the protected layer in the mining area. When the protective layer is mined, the degree of deformation caused by the collapse of the overlying rock decreases, and the distance of the overlying rock and key thick sandstone layers from the top to the top becomes smaller. The interval and strength of the working face decrease, that is, the energy released by the rock layer fracture decreases.

(4) In the process of upper protective layer mining, the underlying coal rock body experiences three stages of advanced stress concentration, the rapid growth of pressure relief, and the slow recovery of pressure relief, and the stress release rates decrease with the increase of depth. Compared with the shallow part, the stress recovery rate of the deep coal rock body is faster and the time required is shorter.