Study on the mining stress field distribution law beneath isolated coal pillar in close coal seam and reasonable location of the roadway

Abstract

In the process of mining deep close coal seams, it is influenced by isolated coal pillars and goafs in upper coal seam, which causes the selection of roadway position in lower coal seam to be a technical problem restricting safe mining of coal seam. This study is based on the gateroad to the No. 3 coal seam working face in a mine in Guizhou Province, China. The stress evolution characteristics in the floor following the mining of the upper coal seam is investigated using a comprehensive methodology that included theoretical analysis, numerical simulation, and field observations. The rational roadway position in the underlying coal seam was identified by analyzing the deviatoric stress tensor and the evolution laws of plastic zones at various roadway positions. The results show that: (1) by establishing an analytical mechanical model of the floor after stabilization of the goafs on both sides, an analytical expression for floor stress as a function of depth is derived, revealing the stress distribution law within the floor. Numerical simulations using FLAC3D are conducted to examine the evolution of principal stress beneath isolated coal pillars in the upper coal seam. The stress propagates downward in an inclined manner and gradually attenuates, with the distribution transitioning from a bimodal to a unimodal pattern. The principal stress difference is relatively low right below the isolated coal pillar, that is, at the roof position of No. 3 coal seam. The stress distribution law obtained from theoretical calculation is generally consistent with that obtained from numerical simulation. (3) The coordinated deflection mechanism between the deviatoric stress tensor and the morphology of the plastic zone is revealed, transitioning from a stable elliptical pattern to a highly unstable butterfly-shape as the roadway location shifts from the centerline of the isolated coal pillar to either side.(4) Based on butterfly-shaped failure theory, a roadway layout zoning method is proposed that incorporates the two main influencing factors of the principal stress difference and the principal stress ratio. The roadway layout area is divided into three zones, with zone R-III identified as the optimal range. After comprehensively considering the economic benefit and safety factors of coal mine, it is recommended that the gateroad of the No. 3 coal seam be arranged directly beneath the isolated coal pillar. Field practice demonstrates that when the mining roadway in the lower coal seam is arranged beneath the isolated coal pillar, the surrounding rock deformation remains within acceptable limits, ensuring normal roadway operation.

Introduction

China is endowed with rich coal resources in close coal seams, and downstream mining has been widely applied^1,2. Because of the small inter-seam spacing, repetitive mining of the upper coal seam inevitably has a pronounced impact on the stress distribution of the surrounding rock in the lower seam^3,4. Meanwhile, plastic deformation and failure of the floor induced during upper coal seam extraction weaken the strength and integrity of the roof of the lower coal seam. The overburden pressures are further transmitted to the floor by the isolated coal pillars that remain in the upper coal seam⁵, leading to distinct stress concentration zones. The stress environment of the surrounding rock becomes increasingly complex as coal mining advances to greater depths^6,7,8,9,10, posing significant challenges for selecting appropriate roadway locations in the lower seam. Therefore, thoroughly elucidating the evolution laws of mining-induced stress in the floor under the disturbance of isolated coal pillars and goafs in the upper coal seam, it provides essential theoretical guidance for determining the optimal location of roadways in the underlying seam.

Aiming at the bottom plate stress distribution and the arrangement of the reasonable position of the roadway in the downstream mining of close coal seams, many scholars have done rich research work on this. Meng Xiangrui et al.¹¹ proposed the failure criterion for the rock body of the bottom plate based on the Mohr-Coulomb criterion by constructing a mechanical model of a point of the bottom plate of the mining field about the stress calculation; Zhao Hongbao et al.¹² established a three-stage mechanical model of the bottom plate, revealing the zonal failure characteristics of the floor rock mass, which was fully verified through numerical simulations. He Fulian et al.¹³ developed a mechanical model for remnant sectional coal pillars to reveal the propagation mechanism of principal stress difference within the floor, analyzed stress distribution characteristics at different depths beneath the pillar, and identified appropriate roadway locations. Liu Hongtao et al.¹⁴ based on the main factors causing plastic damage to the surrounding rock of floor roadways, revealed the stress distribution and plastic zone evolution at different roadway positions in the lower coal seam, and determined the rational layout of the roadways. H. Y. Liu et al.¹⁵ applied elasticity theory to elucidate the stress distribution laws within the floor following upper coal seam extraction, and demonstrated good agreement between numerical simulation results and theoretical calculations.

In addition, numerous domestic scholars have conducted in-depth studies on the mechanisms of non-uniform failure in roadway surrounding rock and the corresponding control techniques. Kang Hongpu et al.¹⁶ investigated the large-deformation mechanisms of soft coal in kilometer-deep mine roadways and proposed a combined control technique involving grouting bolts with high pressure-shotcreting in synergy, and field trials demonstrated effective surrounding rock control. Wang Weijun et al.^17,18 regarding the challenges of surrounding rock control in deep roadway with high-stress, emphasizing a shift from the deformation control ideas to stability control of new concepts, which allows roadways to reserve a “given deformation” space; Wu Yongzheng et al.¹⁹ combined theoretical analysis, numerical simulations, and field measurements to investigate the failure mechanisms of “one-water, three-weak” type roadways, and proposed a novel surrounding rock control method termed “one obstruct and three strengthen”. Yuan Chao et al.²⁰ proposed a combined reinforcement technique consisting of “bolt-mesh-shotcrete + hollow grouting anchor cables”to address severe fragmentation and deformation of surrounding rock in deep, high-stress roadways, which effectively restrains the expansion of the plastic zone within the surrounding rock of the roadway. Shang, Y. et al.²¹ elucidated the deformation and failure characteristics within the surrounding rock of the roadways under the influence of repetitive mining in close-distance coal seams through integrated field measurements, theoretical analysis, and numerical modeling. Finally, the stability control technology of “asymmetric anchor net cable + I-steel”is proposed, which has demonstrated significant effectiveness in engineering practice.

In summary, numerous scholars have conducted extensive studies on stress distribution in the surrounding rock of lower seams in close coal seams, rational roadway layout, and surrounding rock control techniques. These research findings have provided valuable insights into clarifying floor failure mechanisms and stress evolution in close coal seams under shallow burial conditions or reserved sections with narrow coal pillars. However, the mechanical behavior of isolated coal pillars and goafs in deep closer coal seams remains complex; as a result, there has been relatively little investigation into the stress response characteristics of surrounding rock caused by upper coal seam mining. To thoroughly investigate the mechanical behavior of surrounding rock in lower-seam roadways beneath isolated coal pillar and goafs throughout the full service life of the isolated coal pillar. The No. 3 coal seam mining roadway in a mine serves as the case subject for this investigation in Guizhou Province, China. By integrating a synergistic approach of theoretical analysis, numerical simulation, and field measurements, the correlation between floor stress distribution law under the influence of isolated coal pillar and goafs and surrounding rock failure characteristics of the lower-seam roadway is examined. Based on the principal stress ratio, principal stress difference, and the extent of the plastic zone in the surrounding rock of the lower-coal seam roadway, a rational layout position for the lower-coal seam roadway is proposed and verified through an in field industrial test. The findings provide a theoretical reference for roadway layout under similar conditions and have significant practical engineering value.

Project overview

A mine has a designed production capacity of 600,000 t/a in Guizhou Province, China. The coal seams are deeply buried and contain high gas content, classifying it as a high-gas mine. The hydrogeological conditions are simple, and coal seams No. 1, 3, 4, 17, and 21 are fully mineable across the entire area.

The mined seam is No. 1, with a burial depth of approximately 510 m and an average thickness of 3 m. Both the 1110 and 1112 working faces have strike lengths of 500 m, with incline lengths of 175 m and 150 m, respectively. Currently, both faces have been fully mined and are approaching stability, leaving a remnant isolated coal pillar with a tendency length of 55 m in the No. 1 seam. The currently mined seam is No. 3, with an average thickness of 1.3 m. A layer of clayey siltstone approximately 12 m thick separates the No. 1 and No. 3 seams, which are classified as closely spaced coal seams and are significantly affected by mining-induced disturbances. The mining relationship and the columnar section of coal and rock layers are shown in Fig. 1.

Fig. 1

Mining–excavation relationship and coal-rock columnar diagram. (a) coal-rock columnar diagram, (b) Mining–excavation relationship.

Stress distribution characteristics beneath isolated coal pillars

A coal mine in Guizhou Province, China, the isolated coal pillar in the No. 1 seam is flanked by mined-out areas on both sides. These goaf zones have stabilized through processes such as caving and compaction. The corresponding engineering geological model is shown in Fig. 2a. Assuming that the influence of tectonic stress and original rock stress on the model is ignored, the isolated island coal pillar is subjected to the support pressure of the goafs on both sides and the force exerted by the roof falling and compacted rock mass on both sides of the goaf area on the bottom plate is simplified. The corresponding mechanical model is shown in Fig. 2b.

Fig. 2

Engineering geological model and mechanical model after stabilization of double-side goafs. (a) Engineering geological model, (b) mechanical model.

As shown in Fig. 2b, for the floor force model after stabilization of the goafs on both sides of the isolated coal pillar, the force distribution functions corresponding to each stage can be expressed as follows^22,23,24:

$$\left. \begin{gathered} {F_1}(\xi )=\gamma H,(0 \leqslant \xi \leqslant a) \hfill \\ {F_2}(\xi )=\frac{{{K_1}\gamma H - \gamma H}}{{b - a}}(\xi - a),(a \leqslant \xi \leqslant b) \hfill \\ {F_3}(\xi )=\frac{{ - {K_1}\gamma H}}{{c - b}}(\xi - c),(b \leqslant \xi \leqslant c) \hfill \\ {F_4}(\xi )=\frac{{\gamma {H_m}}}{{d - c}}(\xi - c),(c \leqslant \xi \leqslant d) \hfill \\ {F_5}(\xi )=\gamma {H_m},(d \leqslant \xi \leqslant e) \hfill \\ {F_6}(\xi )=\frac{{ - \gamma {H_m}}}{{f - e}}(\xi - f),(e \leqslant \xi \leqslant f) \hfill \\ {F_7}(\xi )=\frac{{{K_2}\gamma H}}{{g - f}}(\xi - g),(f \leqslant \xi \leqslant g) \hfill \\ \end{gathered} \right]=q(\xi )=\left[ \begin{gathered} {F_8}(\xi )=r{\xi ^2}+w,(f \leqslant \xi \leqslant g) \hfill \\ {F_9}(\xi )=\frac{{ - {K_3}\gamma H}}{{i - h}}(\xi - i),(h \leqslant \xi \leqslant i) \hfill \\ {F_{10}}(\xi )=\frac{{\gamma {H_m}}}{{j - i}}(\xi - i),(i \leqslant \xi \leqslant j) \hfill \\ {F_{11}}(\xi )=\gamma {H_m},(j \leqslant \xi \leqslant k) \hfill \\ {F_{12}}(\xi )=\frac{{ - \gamma {H_m}}}{{l - k}}(\xi - l),(k \leqslant \xi \leqslant l) \hfill \\ {F_{13}}(\xi )=\frac{{{K_1}\gamma H}}{{m - l}}(\xi - l),(l \leqslant \xi \leqslant m) \hfill \\ {F_{14}}(\xi )=\frac{{ - {K_1}\gamma H}}{{n - m}}(\xi - n),(m \leqslant \xi \leqslant n) \hfill \\ {F_{15}}(\xi )=\gamma H,(n \leqslant \xi \leqslant o) \hfill \\ \end{gathered} \right.$$

(1)

In these expressions, γ is the unit weight of the rock strata; H is the burial depth; Hm is the height of the caving zone in the goaf; K₁ is the stress concentration factor of the boundary coal pillar in the mechanical model; K₂ and K₃ are the stress concentration factors on the left and right sides of the isolated coal pillar close to the goafs, respectively. Segments “O-a” and “n-o” represent the range over which the in-situ stress acts within the coal seam. Segments “a–b” and “n-m” denote the zone where the in-situ stress increases to the peak lateral abutment pressure. Segments “b-c”, “f-g”, “h-i”, and “l-m” indicate the distance between the goaf edge and the location of the peak lateral abutment pressure on the coal pillar. Segments “c-d”, “e-f”, “i-j”, and “k-l” correspond to the zones where stress in the caved rock mass within the goaf gradually recovers. Segments “d-e” and “j-k” represent the zones of stress recovery after the compaction of the caved rock mass. Segment “g-h” defines the range over which the peak abutment pressure acts within the isolated coal pillar.

The rock layers in the floor of the No. 1 coal seam in a mine are approximated as ideal elastic media. Within the range of applied loading, an infinitesimal element dξ located at a distance ξ from the origin O is selected for analysis. The calculation expressions for σ_x, σ_z, and τ_xz at an arbitrary point within this element are given as follows^25,26:

$$\left\{ \begin{gathered} {\sigma _x}= - \frac{\pi }{2}\int_{{ - u}}^{v} {\frac{{q(\xi )z{{(x - \xi )}^2}}}{{{{\left[ {{z^2}+{{(x - \xi )}^2}} \right]}^2}}}{\text{d}}\xi } \hfill \\ {\sigma _z}= - \frac{\pi }{2}\int_{{ - u}}^{v} {\frac{{q(\xi ){z^3}}}{{{{\left[ {{z^2}+{{(x - \xi )}^2}} \right]}^2}}}{\text{d}}\xi } \hfill \\ {\tau _{xy}}= - \frac{\pi }{2}\int_{{ - u}}^{v} {\frac{{q(\xi ){z^2}(x - \xi )}}{{{{\left[ {{z^2}+{{(x - \xi )}^2}} \right]}^2}}}{\text{d}}\xi } \hfill \\ \end{gathered} \right.$$

(2)

In these expressions, σ_x denotes the horizontal stress at an arbitrary point in the floor strata; σ_z is the vertical stress at that point; and τ_xz is the shear stress. Parameters a and b define the ranges over which the stress increments act, and q(ξ) represents the stress distribution function applied to the floor.

By substituting the stress functions corresponding to each segment into Eq. (2), the calculation expressions for σ_x, σ_z, and τ_xz at a given point P(x, z) in the floor after mining on both sides of the isolated coal pillar can be derived. Based on in-situ stress measurements, the average ratio of axial stress to vertical stress is 1.03; Therefore, the stress expressions are given as follows:

$${\sigma _x}= - \frac{2}{\pi }\left[ \begin{gathered} \int_{0}^{a} {\frac{{\gamma Hz{{(x - \xi )}^2}d\xi }}{{{{({{(x - \xi )}^2}+{z^2})}^2}}}} +\int_{a}^{b} {\left( {\frac{{({K_1} - 1)\gamma H(\xi - a)}}{{b - a}}+\gamma H} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{b}^{c} {\left( {\frac{{ - {K_1}\gamma H(\xi - c)}}{{c - b}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } \hfill \\ +\int_{c}^{d} {\left( {\frac{{\gamma {H_m}(\xi - c)}}{{d - c}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{d}^{e} {\left( {\gamma {H_m}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{e}^{f} {\left( {\frac{{ - \gamma {H_m}(\xi - f)}}{{f - e}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{f}^{g} {\left( {\frac{{{K_2}\gamma H(\xi - g)}}{{g - f}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{g}^{h} {\left( {r{\xi ^2}+w} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{h}^{i} {\left( {\frac{{ - {K_3}\gamma H(\xi - i)}}{{i - h}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{i}^{j} {\left( {\frac{{\gamma {H_m}(\xi - i)}}{{j - i}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{j}^{k} {\left( {\gamma {H_m}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{k}^{l} {\left( {\frac{{ - \gamma {H_m}(\xi - l)}}{{l - k}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{l}^{m} {\left( {\frac{{{K_1}\gamma H(\xi - l)}}{{m - l}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{m}^{n} {\left( {\frac{{ - {K_1}\gamma H(\xi - n)}}{{n - m}}} \right)\frac{{z{{(x - \xi )}^2}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{n}^{o} {\frac{{\gamma Hz{{(x - \xi )}^2}d\xi }}{{{{({{(x - \xi )}^2}+{z^2})}^2}}}} } } \hfill \\ \end{gathered} \right]$$

(3)

$${\sigma _z}= - \frac{2}{\pi }\left[ \begin{gathered} \int_{0}^{a} {\frac{{\gamma H{z^3}d\xi }}{{{{({{(x - \xi )}^2}+{z^2})}^2}}}} +\int_{a}^{b} {\left( {\frac{{({K_1} - 1)\gamma H(\xi - a)}}{{b - a}}+\gamma H} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{b}^{c} {\left( {\frac{{ - {K_1}\gamma H(\xi - c)}}{{c - b}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } \hfill \\ +\int_{c}^{d} {\left( {\frac{{\gamma {H_m}(\xi - c)}}{{d - c}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{d}^{e} {\left( {\gamma {H_m}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{e}^{f} {\left( {\frac{{ - \gamma {H_m}(\xi - f)}}{{f - e}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{f}^{g} {\left( {\frac{{{K_2}\gamma H(\xi - g)}}{{g - f}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{g}^{h} {\left( {r{\xi ^2}+w} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{h}^{i} {\left( {\frac{{ - {K_3}\gamma H(\xi - i)}}{{i - h}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{i}^{j} {\left( {\frac{{\gamma {H_m}(\xi - i)}}{{j - i}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{j}^{k} {\left( {\gamma {H_m}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{k}^{l} {\left( {\frac{{ - \gamma {H_m}(\xi - l)}}{{l - k}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{l}^{m} {\left( {\frac{{{K_1}\gamma H(\xi - l)}}{{m - l}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{m}^{n} {\left( {\frac{{ - {K_1}\gamma H(\xi - n)}}{{n - m}}} \right)\frac{{{z^3}d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{n}^{o} {\frac{{\gamma H{z^3}d\xi }}{{{{({{(x - \xi )}^2}+{z^2})}^2}}}} } } \hfill \\ \end{gathered} \right]$$

(4)

$${\sigma _y}=1.03{\sigma _z}$$

(5)

$${\tau _{xz}}= - \frac{2}{\pi }\left[ \begin{gathered} \int_{0}^{a} {\frac{{\gamma H{z^2}(x - \xi )d\xi }}{{{{({{(x - \xi )}^2}+{z^2})}^2}}}} +\int_{a}^{b} {\left( {\frac{{({K_1} - 1)\gamma H(\xi - a)}}{{b - a}}+\gamma H} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{b}^{c} {\left( {\frac{{ - {K_1}\gamma H(\xi - c)}}{{c - b}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } \hfill \\ +\int_{c}^{d} {\left( {\frac{{\gamma {H_m}(\xi - c)}}{{d - c}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{d}^{e} {\left( {\gamma {H_m}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{e}^{f} {\left( {\frac{{ - \gamma {H_m}(\xi - f)}}{{f - e}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{f}^{g} {\left( {\frac{{{K_2}\gamma H(\xi - g)}}{{g - f}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{g}^{h} {\left( {r{\xi ^2}+w} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{h}^{i} {\left( {\frac{{ - {K_3}\gamma H(\xi - i)}}{{i - h}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{i}^{j} {\left( {\frac{{\gamma {H_m}(\xi - i)}}{{j - i}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{j}^{k} {\left( {\gamma {H_m}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{k}^{l} {\left( {\frac{{ - \gamma {H_m}(\xi - l)}}{{l - k}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}} } } \hfill \\ +\int_{l}^{m} {\left( {\frac{{{K_1}\gamma H(\xi - l)}}{{m - l}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{m}^{n} {\left( {\frac{{ - {K_1}\gamma H(\xi - n)}}{{n - m}}} \right)\frac{{{z^2}(x - \xi )d\xi }}{{{{\left( {{{(x - \xi )}^2}+{z^2}} \right)}^2}}}+\int_{n}^{o} {\frac{{\gamma H{z^2}(x - \xi )d\xi }}{{{{({{(x - \xi )}^2}+{z^2})}^2}}}} } } \hfill \\ \end{gathered} \right]$$

(6)

Based on engineering geological data from a mine in Guizhou, statistical analysis of rock pressure observations during longwall mining, and empirical data, the relevant parameters for the mechanical calculation model of the rock mass at the base of isolated coal pillars under repeated mining conditions are presented in Tables 1 and 2.

Table 1 Calculation model parameters.

Table 2 Widths of individual segments in the calculation model.

By substituting the relevant parameters from Tables 1 and 2 into Eq. (3–6), the stress values at a given point in the floor beneath the isolated coal pillar can be obtained. Visualization using appropriate software yields the stress contour maps of σ_x, σ_z, σ_y and τ_xz, as shown in Fig. 3.

Fig. 3

Stress distribution laws of the floor rock mass. (a) σ_x, (b) σ_z, (c) σ_y, (d) τ_xz.

As shown in Fig. 3, a significant increase in stress is observed on both sides of the goaf, while the goaf itself exhibits a distinct stress reduction zone. The rock mass stress beneath the two ends of the isolated coal pillar adjacent to the goaf is relatively high, propagating diffusely toward the deeper strata of the floor. Furthermore, the σ_x, σ_y, σ_z, and τ_xy values of the No. 1 coal seam floor exhibit an asymmetric “saddle-shaped” distribution centered on the middle position of the isolated coal pillar. This poses a major obstacle to the rational layout of the No. 3 coal seam roadway. Therefore, it is imperative to conduct numerical experiments to investigate the stress evolution laws and plastic zone distribution characteristics at different roadway locations beneath the isolated coal pillar, thereby providing scientific basis for rational roadway planning.

Numerical simulation analysis

Numerical model construction and Goaf backfill parameter calibration

The finite-difference software FLAC3D is widely utilized to simulate the mechanical response of roadways subjected to excavation and mining disturbances, specifically regarding stress redistribution, surrounding rock deformation, and the expansion of plastic zones^27,28,29,30. This study focuses on the isolated coal pillars and the 3# coal seam working face mining roadways at a mine in Guizhou Province, China. Based on geological data provided by the mine and field survey results, a three-dimensional numerical model was constructed, as shown in Fig. 4. The numerical model has dimensions of 480 m (length) × 300 m (width) × 80 m (height), comprising 4,082,160 elements and 4,174,673 nodes. To eliminate boundary effects inherent to numerical simulations, 50 m coal pillars were placed at the lateral boundaries. The mesh was refined around the roof and floor of the isolated coal pillar to improve the accuracy of the results. The bottom and side surfaces of the model were fixed in displacement. To simulate the weight of the overlying strata, a compensating stress of 10.75 MPa was applied to the top of the model. Based on in-situ stress measurements, the lateral stress coefficient is 1.63, and corresponding horizontal stresses were applied around the model. The rock and coal strata were modeled using the Mohr-Coulomb constitutive model. The mechanical parameters of the strata used in the model are listed in Table 3.

Fig. 4

Numerical simulation model.

Table 3 Numerical calculation parameters.

According to the on-site mining and excavation sequence in underground coal mines, this study simulates the damage effect of the isolated coal pillar formed after the excavation of the 1110 and 1112 working faces on the floor. By revealing the stress distribution law prior to the excavation of the mining roadway in the 3# coal seam working face, the stress distribution characteristics of the floor induced by the isolated coal pillar and the goafs on both sides, as well as the influencing factors governing the reasonable layout of the roadway, can be further elucidated. The working face mining employs the retreating strike longwall mining method, with roof management implemented via the caving method. Over time, the caved rock blocks are gradually compacted to form a reconstructed load-bearing medium capable of sustaining the load of the overlying strata, which exerts a significant influence on the stress redistribution around the stope. Therefore, considering the compaction effect of caved gangue in the goaf^31,32,33,34, the Double-yield model is adopted for goaf filling in this simulation.

To accurately characterize the gradual stress recovery of caved rock masses in goafs, the Double-yield model integrated in FLAC3D software was employed. A calibrated model with dimensions of 1 m × 1 m × 1 m was established. Prior to numerical calculations, transverse and longitudinal displacements were sequentially fixed at the bottom of the three-dimensional model, and longitudinal displacements were restricted on both sides of the model³⁵. A corresponding velocity (typically 10⁻⁵ m/step) was applied to the top of the model. Double-yield simulated compression tests were repeatedly conducted using the trial-and-error inversion method, with the detailed verification process illustrated in Fig. 5. The calibrated results of the numerical simulation were generally consistent with the stress-strain curve obtained from theoretical calculations. Therefore, the physical and mechanical parameters of the caved zone rock masses are presented in Table 4.

Fig. 5

Calibration process of the double-yield model for the goaf.

Table 4 Physical and mechanical parameters of rock mass in caving zone.

Principal stress distribution law of the 1# coal seam

The goafs on both sides of the 1# coal seam and the isolated coal pillar exert a certain influence on the 3# coal seam and the surrounding rock of the roadway. To obtain the stress states at different positions along the y-axis direction in the numerical model, slices were taken at distances of 90 m, 150 m, and 210 m from the model boundary to comparatively analyze the principal stress distribution characteristics. Figure 6 presents the principal stress contour maps, where (1) denotes the maximum principal stress contour map, (2) the minimum principal stress contour map, and (3) the principal stress difference contour map. Meanwhile, Figs. (a), (b), and (c) sequentially represent the sliced principal stress contour maps at the three positions of 90 m, 150 m, and 210 m.

As can be seen from Fig. 6, the principal stress distribution laws obtained from slices at different positions are roughly consistent. The stress concentration degree at the position of the isolated coal pillar adjacent to the goaf is significantly higher than that near the coal wall, which is consistent with the aforementioned floor stress analysis results. Due to the different tendency lengths of the goafs on both sides of the isolated coal pillar, there are differences in the manifestation of stress concentration on the two sides. At the 90 m slice position, all three types of stress accumulate on both sides of the isolated coal pillar. The maximum principal stresses at 23.4 m from the centerline of the isolated coal pillar (left and right sides) are 46.18 MPa and 46.75 MPa, with stress concentration coefficients of 3.42 and 3.46, respectively. As the slice position changes along the y-axis direction, affected by the boundary effect, the stress concentration range in the middle of the model is larger than that in other parts, and the stress peak value also increases accordingly. At the 150 m slice position (i.e., the middle of the model), the maximum principal stress concentration coefficient on the left side of the isolated coal pillar increases from 3.42 to 3.80, and that on the right side increases from 3.46 to 3.87. At the 210 m slice position, the maximum principal stress concentration coefficient on the left side of the isolated coal pillar decreases from 3.80 to 3.34, and that on the right side decreases from 3.87 to 3.37. Similarly, the variation laws of the minimum principal stress and principal stress difference show the same trend as the maximum principal stress distribution: with the increase of the slice position, the stress peak value and stress concentration coefficient first increase and then decrease.

Fig. 6

Principal stress distribution contour map.

Taking Fig. 6(3) as an example, an analysis was conducted on the 150 m slice. The difference between the maximum principal stress at both ends of the isolated coal pillar is relatively large, with stress concentration observed on both sides of the pillar. The stress propagation and diffusion angle ranges approximately from 32° to 45°. The roof rock strata of the goaf adjacent to the isolated coal pillar are relatively loose and fragmented; however, due to the large width of the reserved coal pillar, the internal part of the isolated coal pillar can still maintain a stable state. There are significant differences in the distribution of principal stress differences in the floor rock strata of the isolated coal pillar. It propagates in a diffused manner toward the deep part of the floor on both sides of the coal pillar floor, showing an inhomogeneous distribution state. The farther away from the isolated coal pillar floor, the larger the propagation and diffusion range, but it exhibits a gradual attenuation characteristic. The principal stress difference in the shallow part of the isolated coal pillar floor is relatively large, approximately 10 – 18 MPa, while that in the middle part of the coal pillar floor is smaller, about 8–10 MPa. The stress distribution state gradually evolves from a “double-peak” to a “single-peak” pattern. Moreover, the maximum principal stress difference at the roof of the 3# coal seam (directly below the isolated coal pillar) is obviously in a relatively low state, only about 4 – 6 MPa. Thus, it can be concluded that under the dual effects of the 55 m large isolated coal pillar for roadway protection and stress propagation attenuation, the stress concentration degree at the roof of the 3# coal seam directly below the isolated coal pillar is relatively small. If the roadway is arranged here with reasonable support measures, the surrounding rock control can maintain a relatively stable state.

Fig. 7

Layout of stress monitoring lines.

To investigate the stress propagation laws of the isolated coal pillar within the floor and determine the optimal position of underlying roadways, as described above, since the middle part of the model is in a relatively high stress state, 11 monitoring lines are arranged along the floor of the 1# coal seam at y = 150 m to reveal the variation law of the principal stress in the roof and floor of the 3# coal seam. As illustrated in Fig. 7, the stress distribution curves of the 11 monitoring lines are presented in Fig. 8.

Fig. 8

Principal stress distribution curve. (a) The maximum principal stress, (b) The minimum principal stress, (c) The principal stress differences.

As can be seen from Fig. 8, when only considering the influences of the goafs and the isolated coal pillars, the distribution characteristics of the principal stress curves under their respective floors are different: with the increase of the horizontal monitoring position, the stress curve in Fig. 8a, b under the goaf floor generally shows a trend of first decreasing rapidly, then increasing slowly, and finally decreasing gradually, reaching a minimum at the goaf boundary; The stress curve in Fig. 8c exhibits variation characteristics in the shallow surrounding rock (z ≤ 2 m) that are similar to those shown in Fig. 8a, b; when z > 2 m, the principal stress difference curve presents a trend of first increasing, then decreasing, and finally increasing, reaching a maximum value at the goaf boundary. Under the isolated coal pillar of the 1# coal seam, the maximum principal stress curve generally exhibits an asymmetric “M-shaped double-peak” distribution in the shallow surrounding rock area (z ≤ 12 m), characterized by a small value at the coal pillar centerline and large values on both sides. When z > 12 m, the distribution law of the maximum principal stress transitions from the “M-shaped double-peak” to a “platform-type”, as shown in Fig. 8a. In the shallow surrounding rock area (z ≤ 8 m) of the isolated coal pillar floor in the 1# coal seam, the minimum principal stress curve also presents an “M-shaped double-peak” distribution; when z > 8 m, the distribution law of the minimum principal stress transitions from the “M-shaped double-peak” to a “single-peak type”, as shown in Fig. 8b. The farther the rock stratum below the isolated coal pillar is from the isolated coal pillar, the smaller the principal stress differences; however, the distribution law of the principal stress differences consistently maintains an “M-shaped double-peak” distribution in the vertical direction, as shown in Fig. 8c.

Based on the comprehensive analysis above, affected by the isolated coal pillar, due to its large reserved width, significant stress changes are observed at the goaf floor boundary and the areas on both sides below the isolated coal pillar, while relatively slight stress changes occur in the middle area below the isolated coal pillar. If the roadway is excavated in the 3# coal seam at this location, it will be less affected by stress.

Study on the optimal location of roadways

Analysis of the second invariant of deviatoric stress and distortion energy

Deviatoric stress mainly controls the shape deformation of coal and rock masses and is the primary driving force for their plastic failure and deformation. The second invariant of deviatoric stress and distortion energy parameters related to the deviatoric stress tensor can be used to characterize the shear stress and deformation energy of surrounding rock. Evaluating the instability and failure characteristics of roadway surrounding rock using the second invariant of deviatoric stress and distortion energy offers significant advantages, as they overcome the limitations of single vertical or horizontal stress and other independent indicators. For this purpose, the eighth-order implicit equation relating to the second invariant of deviatoric stress at any point of the roadway surrounding rock to the radius is derived as follows^36,37:

$$\begin{gathered} J_{2} = \frac{{9B^{2} }}{4}\left( {\frac{a}{r}} \right)^{8} - \left[ {3B^{2} + \frac{3}{2}AB\cos 2\theta } \right]\left( {\frac{a}{r}} \right)^{6} + \left[ {\left( {\frac{5}{2} + \frac{1}{3}(2\mu - 1)^{2} } \right)B^{2} \cos ^{2} 2\theta + \frac{1}{4}A^{2} + AB\cos 2\theta - \frac{1}{2}B^{2} \sin ^{2} 2\theta } \right]\left( {\frac{a}{r}} \right)^{4} \hfill \\ + \left[ {B^{2} (\sin ^{2} 2\theta - \cos ^{2} 2\theta ) + AB\left( {\frac{2}{3}\mu - \frac{5}{6}} \right)\cos 2\theta - \frac{2}{3}p_{y} B(2\mu - 1)\cos 2\theta } \right]\left( {\frac{a}{r}} \right)^{2} + \left[ {\frac{{B^{2} }}{4} + \frac{{A^{2} }}{{12}} - \frac{1}{3}(A - p_{y} )} \right] \hfill \\ \end{gathered}$$

(7)

The expression of distortion energy can be represented by the second invariant of deviatoric stress:

$$W = \frac{{J_{2} }}{{2G}}$$

(8)

where J₂ denotes the second invariant of deviatoric stress; A = p_x+p_z and B = p_x−p_z, where p_x and p_z are the stresses in the x and z axes, respectively; p_y is the stress in the y axes ; a is the roadway radius; r is the distance from a rock mass element to the roadway center;θ is the angle between the position of the rock mass element and the horizontal direction; µ is the Poisson’s ratio of the surrounding rock; W is the distortion energy; and G is the elastic modulus.

Evolution law of deviatoric stress tensor at different roadway positions

Numerical models were established for different roadway layout positions under the influence of the isolated coal pillar. The expressions for the second invariant of deviatoric stress and distortion energy were compiled using the FISH language embedded in FLAC3D, which was then imported into the software for calculation. Finally, the contour maps of the second invariant of deviatoric stress (J₂) and distortion energy(W) in the vicinity of the surrounding rock of the underlying roadway were extracted.

Figure 9 illustrates the evolution law of the second invariant of deviatoric stress (J₂) for roadways at different layout positions. At the location 0 m directly below the isolated coal pillar, J₂ presents a symmetrical distribution. When the roadway position shifts from the centerline toward the lower left side of the isolated coal pillar, J₂ exhibits a clockwise deflection to the right. Conversely, when the roadway position moves from the centerline toward the lower right side of the isolated coal pillar, J₂ exhibits a clockwise deflection to the right, ultimately presenting a severely asymmetric distribution. The further away from the centerline, the stress peak first increases and then decreases, while the stress concentration range continues to expand.

Fig. 9

Evolution law of the second invariant of deviatoric stress (J₂) at different roadway positions.

Fig. 10

Evolution law of distortion energy density at different roadway positions.

Figure 10 illustrates the evolution law of distortion energy density when the roadway is located at different positions. At 0 m directly below the isolated coal pillar, the distribution of distortion energy density is consistent with that of the second invariant of deviatoric stress (J₂), generally presenting a quasi-“elliptical” distribution. As the distance from the centerline of the isolated coal pillar increases, the roadway is increasingly significantly affected by the stress transmitted by the isolated coal pillar. The distribution pattern of distortion energy density transforms from a relatively stable “elliptical” shape to an extremely unstable “pseudo-butterfly” shape. The farther the roadway position, the more uneven the expansion of the “pseudo-butterfly” shape.

It can be inferred therefrom that the deviatoric stress tensor varies with the change of roadway positions. The farther away from the coal pillar centerline (the 0 m position), the larger the aggregation range of the deviatoric stress invariant. To protect the roadway surrounding rock from severe damage and large deformation, the roadway should be arranged as close to the coal pillar centerline as possible.

Evolution law of plastic zone at different roadway positions

A three-dimensional numerical model was established using the finite element software FLAC3D to simulate roadways at different positions under the influence of an isolated coal pillar. The distribution patterns of the plastic zones corresponding to different roadway positions were extracted, as illustrated in Fig. 11. Based on the expansion characteristics of the plastic zones in the underlying roadway, a comprehensive analysis was conducted to determine the reasonable layout positions of the roadway.

As can be seen from Fig. 11, with the position directly below the coal pillar defined as the origin, the roadway layout position is assigned to a negative value when the roadway is arranged to the left and a positive value when arranged to the right. Obviously, at the 0 m position (i.e., directly below the isolated coal pillar), the underlying roadway is subjected to a complex stress environment dominated by horizontal tectonic stress. Consequently, the roof and floor of the roadway suffer relatively severe failure with a relatively deep plastic zone, while the two sides of the roadway experience minor failure, and the plastic zone of the roadway presents an elliptical distribution. This indicates that the surrounding rock of the roadway maintains good overall stability; with a reasonable support scheme, the normal operation of the roadway can be guaranteed. This finding is consistent with the analysis results of the principal stress differences presented earlier. At the position of -5 m, the range of shallow shear failure on the two sides of the roadway increases, and the depth of the plastic zone at the right shoulder corner rises. The overall plastic zone of the roadway surrounding rock tends to expand, leading to a marked increase in support difficulty compared with the 0 m position. At the position of -10 m, the range of shear failure on the two sides of the roadway further expands, and the scope of the plastic zone at the right shoulder corner further increases, which poses greater challenges to surrounding rock support. At the position of -15 m, although the depth of the plastic zone in the roadway roof decreases, the range of shallow shear failure on the two sides of the roadway remains large. In addition, it exacerbates the degree of shear failure at both the left and right shoulder corners, increasing the difficulty of support for the shoulder corners. At the position of -20 m, the failure range at the left shoulder corner further expands, resulting in the connection between the plastic zone of the left roadway side and the plastic zone of the goaf floor via the left shoulder corner. This greatly impairs the anchoring performance of the bolts (cables) at the left side and left shoulder corner, and the surrounding rock is at risk of potential large deformation. At the position of -25 m, both the left roadway side and the left shoulder corner are fully connected with the plastic zone of the goaf floor. If the support scheme is unreasonable, the probability of inducing large deformations in the surrounding rock will surge sharply. Moreover, the range of shear failure directly below the roadway floor and at the right bottom corner increases drastically, bringing new difficulties to floor support.

Similarly, when the roadway is arranged on the right side of the isolated coal pillar floor within the range of 5 – 25 m, the malignant expansion of the surrounding rock gradually deflects toward the right side and right shoulder corner of the roadway. As the distance from the centerline of the isolated coal pillar increases, the failure range of the right side and right shoulder corner obviously expands progressively, accompanied by the phenomenon that the plastic zone connects with the plastic zone of the goaf floor. Meanwhile, the range of shear failure at the roadway floor and left bottom corner gradually increases, resulting in severe asymmetric large deformation.

Fig. 11

Evolution law of plastic zone at different roadway positions.

Relationship between J ₂ and plastic zone

As can be seen from the above analysis, the second invariant of deviatoric stress (J₂) has a close corresponding relationship with the plastic zone. Due to the symmetrical distribution of J₂ about the coal pillar centerline, it is sufficient to focus on the analysis of J₂ and the plastic zone on only one side of the coal pillar centerline. The relationship between them is shown in Fig. 12.

As can be seen from Fig. 12, the distribution pattern of the plastic zone is highly correlated with the second invariant of deviatoric stress (J₂). When the roadway layout is shifted from the edge of the isolated coal pillar toward the centerline, J₂ exhibits a severely asymmetric distribution at the position of -25 m, which is mainly concentrated at the left shoulder corner of the roadway and the area of the right side near the right bottom corner. In addition, the J₂ concentration zone at the left shoulder corner is connected with that of the goaf floor. Therefore, the failure of the plastic zone in the roadway surrounding rock also primarily occurs at the left shoulder corner and the area of the right side near the right bottom corner, while the plastic zone at the left shoulder corner is connected with that of the goaf floor. As the position shifts, the J₂ concentration zone deflects counterclockwise and gradually migrates toward the roof and the two sides of the roadway, generally showing a symmetrical elliptical distribution. Correspondingly, the plastic zone also deflects counterclockwise.

From the above analysis, it can be confirmed that when the roadway is arranged within the range of 0 to − 10 m or 0 – 10 m, although plastic damage exists around the roadway, the shear and tensile failure of the surrounding rock is mainly concentrated in the roof and two sides. The plastic zone distribution is generally symmetrical, and its influence is limited. The roadway is easy to maintain, and the control of floor heave can be realized through the “side fixing and roof controlling” support strategy. When the roadway is arranged at the positions of -15 m and 15 m, the plastic damage deflects toward the left shoulder corner of the roadway roof, the left side and the right side of the floor, which increases the maintenance difficulty of the left shoulder corner, the left side and right bottom corner. When the roadway is arranged within the range of − 20 to − 25 m and 20 –25 m, the plastic damage of the surrounding rock expands in the left shoulder corner area, and the degree of shear and tensile failure of the floor intensifies. This results in an extremely asymmetric distribution of the plastic damage range, which is prone to causing large deformation of the surrounding rock.

Fig. 12

Relationship between J₂ and plastic zone.

Reasonable layout range of the roadway

Based on the analysis of the principal stress ratio in the butterfly-shaped failure theory^38,39,40, the larger the value of the principal stress ratio, the more likely the plastic zone will undergo malignant expansion, eventually evolving into an extremely unstable butterfly-shaped pattern. Therefore, roadway layout should be designed to avoid the formation of butterfly-shaped plastic zones as much as possible. Only by confining the plastic failure of the roadway surrounding rock to a circular or elliptical distribution pattern to the greatest extent can the secondary expansion of the plastic zone be prevented. Since the principal stress difference can be used to indirectly characterize the shear stress controlling surrounding rock failure⁴¹, a larger principal stress difference indicates a higher risk of shear failure in the rock mass, whereas a smaller value corresponds to a lower probability of rock mass failure. The selection of the principal stress difference and principal stress ratio as two evaluation indices for determining the reasonable position of the roadway has certain reference significance.

Guided by the butterfly-shaped failure theory, the reasonable layout range of the roadway is determined as illustrated in Fig. 13. R-Ⅰ denotes the surrounding rock failure zone where the influence of the principal stress difference is minor while that of the principal stress ratio dominates. R-Ⅱ represents the most unfavorable influence range for roadway layout, corresponding to the intersection area most adversely affected by both the principal stress ratio and the principal stress difference. R-Ⅲ refers to the optimal layout range of the roadway, which is the area subjected to the minimal influence of both the principal stress ratio and the principal stress difference. Within the R-Ⅲ zone, arranging the mining roadway directly below the isolated coal pillar can not only facilitate surrounding rock maintenance but also be conducive to panel division, thereby realizing the safe and efficient mining of the lower coal seam working face.

Fig. 13

Reasonable layout range of the roadway.

Engineering validation

Regarding the influence of the isolated coal pillar on the layout of the mining roadway in the lower coal seam, in-depth analysis shows that arranging the roadway directly below the isolated coal pillar is the most favorable. To verify the rationality of the above research results, engineering practice was conducted on the layout of the mining roadway of the 3# coal seam working face, located directly below the isolated coal pillar in a certain mine in Guizhou Province, China.

Roadway support conditions

The above theoretical analysis shows that the plastic zone of the surrounding rock in a roadway directly beneath an isolated coal pillar has a stable elliptical distribution. The extent of plastic failure in the roof is greater than that in the ribs and the floor, indicating that roof deformation control is particularly critical. To accommodate roof deformation while maintaining adequate tensile resistance, sufficiently long anchor cables are required to fully mobilize their deformation capacity. Accordingly, 8.3 m-long anchor cables are adopted to suspend the roof rock mass within deeper, stable strata, thereby restraining the severe expansion of the plastic zone in the coal mass of roadway ribs caused by compression.

The roadway was driven along the floor of the 3# coal seam, with a designed rectangular cross-section of 5.0 m net width × 3.0 m net height. For the roof support, left-handed ribless threaded steel anchor bolts with specifications of Ø22 mm × 2500 mm were installed at a spacing and row distance of 900 mm × 1100 mm, supplemented by steel strand anchor cables of Ø21.8 mm × 8300 mm arranged at a spacing, and when three anchor cables are installed, the spacing is 1800 mm × 2200 mm; when four anchor cables are installed, the spacing is 1500 mm × 2200 mm. For the support of the two roadway sides, left-handed ribless threaded steel anchor bolts of Ø22 mm × 2200 mm were adopted at a spacing and row distance of 800 mm × 1000 mm. In every second row, from the roof toward the floor corner, the first and third anchor bolts are replaced with Ø21.8 mm × 3800 mm steel strand anchor cables. The detailed support scheme is illustrated in Fig. 14.

Fig. 14

Support scheme. (a) Support method, (b) Planar graph of roof support, (c) Planar graph of ribs support, (d) Engineering practice.

Roadway displacement monitoring

To verify the surrounding rock support effect of the mining roadway after excavation directly below the isolated coal pillar, multiple sets of displacement monitoring stations were installed in the middle of the test section of the mining roadway for a monitoring period of approximately 40 days. Field monitoring was conducted on the convergence displacement of the roadway roof and two sides, as illustrated in Fig. 15. During the first 10 days of monitoring, the deformation of the roadway surrounding rock was observed to be in a rapid growth stage; after 10 days, the deformation rate gradually decreased, and the deformation basically stabilized by the 30th day of monitoring. The overall surrounding rock deformation of the roadway followed the trend of roof-floor convergence > side convergence, with the peak displacements reaching 156.2 mm and 112.1 mm, respectively. The overall deformation of the roadway was within the allowable range, indicating that this support scheme can ensure the normal operation of the mining roadway.

Fig. 15

Surrounding rock convergence of the roadway.

Conclusions

• 1. A simplified mechanical model for the isolated coal pillar in the upper coal seam was established, the expression of stress varying with depth in the floor of the isolated coal pillar was derived, and the distribution law of stress in the rock mass of the coal seam floor was obtained.

• 2. The evolution characteristics of the principal stress in the floor beneath the isolated coal pillar and goaf in close coal seams were revealed via numerical simulation. In the horizontal direction, the degree of principal stress concentration at the position of the isolated coal pillar adjacent to the goaf is significantly higher than that near the coal wall. In the vertical direction, there are considerable differences in the evolution characteristics of the maximum principal stress, minimum principal stress, and principal stress difference with the variation of depth. Through the comparative analysis of the theoretical calculation results and numerical simulation results, it is concluded that the two are in good agreement.

• 3. With the variation of roadway layout positions, the second invariant of deviatoric stress (J₂) is highly correlated with the distribution pattern of the plastic zone. When the roadway shifts from the centerline of the isolated coal pillar to the left side, both J₂ and the distribution pattern of the plastic zone deflect clockwise toward the right; when the roadway shifts from the centerline to the right side, both J₂ and the distribution pattern of the plastic zone deflect counterclockwise toward the left. Eventually, both J₂ and the plastic zone evolve into a heterogeneous and asymmetric distribution law.

• 4. Taking the principal stress difference and principal stress ratio as the basis for dividing the reasonable position of the roadway, R-Ⅲ was defined as the optimal layout range of the roadway, and the mining roadway of the 3# coal seam working face was ultimately determined to be arranged directly below the isolated coal pillar. Engineering practice shows that the overall deformation of the roadway is within the allowable range, which can ensure its normal operation.

While these findings provide valuable insights, they are not without limitations. The optimal position of roadways in the lower coal seam is mainly dependent on the width of isolated coal pillars in the upper coal seam, the inter-seam spacing, and on-site mining geological conditions. Consequently, practical applications should involve a tailored analysis that accounts for these unique variables.