Introduction

Gentle anti-dip rocky slopes are widely distributed in the mountainous regions of Southwest China and commonly exhibit deformation issues under the influence of mining activities. Research indicates that such landslides typically exhibit the characteristic feature of localized locked segments1, with their stability governed by the dual mechanisms of the potential sliding surface and the rock mass mechanics of the locked segment. Based on this characteristic, previous studies have defined such slopes as locked-segment landslides2. From an engineering geological perspective, the locked segment refers to the portion that plays a critical controlling role in slope stability3,4. Essentially, it represents the unconnected part of the potential sliding surface5,6,7,8. Due to their high shear strength and substantial geometric dimensions9,10,11, locked segments can significantly enhance the overall load-bearing capacity of slopes, making them crucial in the stability analysis of rock slopes. Mining activities may induce progressive failure of the locked-segment rock mass, thereby triggering landslide disasters. Therefore, an in-depth study of the shear slip damage mechanism of locked segments in gentle anti-dip rocky slopes under mining disturbances will not only help reveal the instability mechanisms of such slopes but also provide a theoretical basis for optimizing slope protection design, reducing engineering costs, and improving stability, holding significant practical value for engineering applications.

Geological disasters induced by underground mining activities are increasingly common, particularly when mining operations are conducted beneath slopes, which can easily lead to slope deformation and instability12. In recent years, related research has primarily been conducted through theoretical analysis, physical model testing, and numerical simulation. Malinowska et al.13 employed numerical models to analyze mining-induced strain fields and their effects on fracture formation; Fathi et al.14 took the instability of a high-steep slope induced by coal mining in Australia as an example, proposing that toe damage can lead to a composite sliding-toppling failure at the slope’s leading edge; Regassa et al.15 investigated the relationship between mining depth and roof collapse; Zhao et al.16 revealed the formation mechanism of the Majialing landslide using PFC numerical simulation; Yu et al.17 employed the particle flow method to analyze the deformation characteristics of the Faer coal mine slope; Sun et al.18 obtained two failure modes—bending fracture of roadway strata and interlayer slip—through 3DEC modeling; Tang et al.19 proposed a landslide deformation mechanism controlled by “key blocks”; Tian et al.20 demonstrated the “V”-shaped overburden failure pattern caused by stress release through physical simulation; Dai et al.21,22 used UDEC to study the dynamic evolution of slope deformation damage; Zhao et al.23 found that the gentle anti-dip rocky slope at Majialing, Guizhou, formed a continuous sliding surface when the mining-damaged locked segment was sheared under water pressure. Liu et al.24 simulated external excitations such as rainfall and earthquakes using a self-designed dynamic loading system to explore the progressive failure mechanism of “retaining wall-type” locked-segment landslides.

Although existing studies have revealed the influence mechanisms of mining on the deformation of gently inclined counter tilted rock slope through case analyses, theoretical models, and numerical simulations—confirming that the shearing of locked segments to form continuous sliding surfaces is a key factor triggering landslides—systematic research on the formation mechanism of potential shear slip surface in locked-segment rock masses of gentle anti-dip rocky slopes under mining disturbances remains lacking. Moreover, an effective method for quantitatively determining the spatial distribution characteristics of damage surfaces has yet to be established. Therefore, constructing a quantitative prediction model for shear slip surface in locked-segment rock masses under mining disturbances will not only provide a theoretical basis for precise early warning of landslide disasters but also offer scientific guidance for optimizing the design of engineering prevention and control measures, holding significant theoretical and practical importance.

Numerical simulation study

Basic geological condition

The Meidong Slope deformation is located in Duyun City, Guizhou Province, China, with the geographic coordinates of 107°17′30″~107°18′28″E and 26°10′35″~26°11′29″N, see Fig. 1A and B. The recoverable coal seams in the study area are mainly located in the upper and middle parts of the Xiangbai Formation, which is composed of quartz sandstone and carbonaceous shale interbedded rocks, and is a typical gentle anti-dip rocky slope, see Fig. 1C. The geotectonic position of the well field is located in the east-south part of the north-south tectonic deformation zone of Guiding and Qiannan Plateau, a sub-tectonic unit of the Yangzi quasi-plateau, and the north-west flank of the southern section of the Huangshi Dorsal Plateau in the region, whose tectonic trajectory is characterized by the near-north-south oriented groove folds.

Fig. 1
figure 1

(A) Location of Duyun City, Guizhou Province, China; (B) Location of deformation on Meidong Slope; “Figure A and B created with ArcGIS 10.8 (https://www.esri.com)” (C) Soft rock-hard rock interbeddedstructure.

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The study area has a long history of coal mining, dating back to the late 1990 s. The stratigraphy in the study area tends to the north-west, with a dip angle of 5–12°, from south-east to north-west, and the outcrops are, from old to new, the Upper Devonian Wangchengpo Formation (D3w), the Devonian Zhewang Formation (D3z), the Lower Carboniferous Tangbaigou Formation (C1t), and the Carboniferous Xiangbai Formation (C1x), and the coal-bearing stratigraphy is the Lower Carboniferous Xiangbai Formation, as shown in Fig. 2. There are only two mineable coal seams, A9 and A7, within the study area. The A9 seam is 1.71 ~ 1.95 m thick, with an average of 1.83 m, and the A7 seam is 1.61 ~ 1.81 m thick, with an average of 1.70 m. The lower part of the A9 seam is 15 ~ 25 m away from the A7 seam, and the average inclination angle of the coal seam is 7º.

Numerical modeling

Based on the engineering geological section of the Meidong Slope in Fig. 2, because the rock layer below the A7 coal seam has less influence on the simulation, it is simplified to quartz sandstone, so as to establish the numerical model of the slope mass UDEC (Universal Distinct Element Code), And six displacement monitoring lines CX1, CX2, CX3, CX4, CX5 and CX6 are established, which are located at the soft rock-hard rock interbedding, as shown in Fig. 3.

Table 1 Parameters of the rock mass in the numerical simulation.
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The numerical slope model sets the rock joint orientation at 280°∠7° with orthogonal secondary joints. Both the coal and rock mass adopt the built-in Mohr-Coulomb constitutive model in UDEC software, while the joint surfaces utilize the Mohr-Coulomb slip model. The physico-mechanical parameters of coal-rock masses and joint parameters adopted in this study were all derived from laboratory investigations by Wang et al.25,26,27 with complete parameter specifications listed in Tables 1 and 2. The model constraints are zero horizontal displacement at the left and right boundaries of the slope, zero vertical displacement at the lower boundary, and a free boundary at the upper boundary.

Table 2 Parameters of the joints in the numerical simulation.
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Fig. 2
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Plan and section of engineering geology of Meidong Slope.

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Numerical calculations simulate the mining of coal seams A7 and A9 in the study area, and the design of the coal seams mining conditions is shown in Fig. 4, in the order of A9-01→A9-02→A7-01→A7-02. According to this design, the corresponding coal seams are mined sequentially to simulate repeated mining, and the iterative calculation of rock stress balance is carried out at the end of each mining task, and the next mining task is carried out at the end of the calculation. The length of each mining task: 140 m for A9-01 working face, 110 m for A9-02 working face, 200 m for A7-01 working face, 100 m for A7-02 working face, and the lengths of coal pillars left in A9 and A7 coal seams are 20 m and 25 m respectively.

Fig. 3
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Numerical model of Meidong Slope.

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Fig. 4
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Sequence of coal seam mining.

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Numerical simulation result analysis

Figure 5 shows a map of mining cracks at the end of mining, in which only cracks with a width greater than or equal to 0.01 m after mining of the coal seam are recorded, and the areas of mining cracks are shown in red. Figure 6 shows the vector map of slope displacement after the model repeats the end of mining in mining sequence, where the arrow points to the direction of displacement and the color represents the size of displacement. The rock above the coal pillar is better preserved due to the influence of the protective coal pillar, resulting in the mining fissure being clearly separated into two zones, contributing to the division of the slope into the front end of the slope and the back end of the slope (Fig. 5).

Fig. 5
figure 5

Slope mining crack map.

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Repeated mining has caused the roof of the goaf to collapse and deform, and the overlying rock mass is severely fragmented, producing a large number of mining cracks (Fig. 5). The overall collapse of the overlying hard rock formations in the workings A9-01 and A7-01 goaf constitutes the front end of the slope, which is constrained by the gentle anti-dip strata and undergoes shear misalignment on the side close to the face of the slope, constituting a potential slip surface. There are fewer cracks in the collapse zone directly above the goaf, and this part of the cracks is closed by the extrusion of the rock body above, which can effectively block the expansion of the cracks. The cracks are centrally distributed on both sides of the goaf and spread upward, and then expand and develop around the collapsed rock mass to the central part to form the mining crack zone, and finally extend to the slope surface and the slope shoulder. The upper rock mass breaks down and sinks, and squeezes the lower rock mass to form the extrusion crack in the position of the slope shoulder, and the front end of the slope body produces the tendency of pouring downward to the slope surface, and forms the tensile crack LF1 in the position of the rear boundary.

The mining task A9-02 and A7-02 the upper rock mass of the goaf constitute the back end of the slope body. The cracks are uniformly distributed above the goaf and extend upward to the top of the slope, so that the rock mass at the top of the slope body is broken, the back end of the slope body is extruded and sunk above the front boundary to form an extrusion crack, and the back end of the slope body is tilted forward to form a tensile crack at the rear boundary. The cracks at the top of the slope develop through each other to form tensile cracks LF1 and LF2, and cracks LF1 and LF2 are generally consistent with field conditions.

Fig. 6
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Vector plot of slope displacement.

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Repeated mining resulted in the overall subsidence of the overlying rock mass in the goaf (Fig. 6), and the mining-induced settlement was transferred upward with gradually decreasing displacement. In mining task A9-01 and A7-01, the intact rock mass near the goaf near the slope formed a lock to the broken rock mass above, and at the same time, was also subjected to the oblique extrusion of the rock mass above, “elliptical arc” shaped displacement towards the slope, and accompanied by extrusion tendency, extrusion and uplift. Under the influence of the gentle anti-dip geology, the rock fragmentation above the back of the goaf has increased, and the zone of maximum displacement vector has generally moved back. The front end of the slope produces a tendency to dip towards the slope face, squeezing the lower part of the front boundary at the front end of the slope and intensifying the fragmentation of the rock mass there, with an anomalous increase in the area of the maximum displacement vector, which extends upwards.

Fig. 7
figure 7

Vertical displacement curve of rock formation.

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Figure 7 shows the vertical displacement curves of the numerical model soft-hard rock layers, and the arrangement of monitoring lines is shown in Fig. 3. After the end of coal seam mining, the vertical displacement curves of each monitoring line show “w” shape, the vertical displacement is between 0~−3.5 m. The rock mass above the mining task has the largest subsidence, and the rock mass above the coal pillar has the smallest subsidence. Based on the above analysis and the rock subsidence curve, the slope rock mass is roughly divided into five regions, I, II, III, IV and V, according to the vertical displacement of −1 m as the dividing line. Region II has the largest amount of subsidence, followed by region IV, while regions I, III, and V are relatively stable, and the amount of subsidence at the front end of region I is positive, extrusion and uplift deformation occurs.

Gentle anti-dip rocky slope mining deformation damage, cracks in the slope mass above the through the development of the formation of a potential slip surface, and to prevent the occurrence of landslide disaster mainly rely on the goaf near the slope near the integrity of the rock mass of the locking, locking the rock mass of the shear slip damage is the key to the occurrence of landslide disaster of this type of slopes. Spatially, the deformation damage is not uniformly distributed throughout the locked rock mass, For example, different rock layers at different locations are subjected to different extrusion pressures from the upper rock mass; The locking rock mass contains carbonaceous shale beds, quartz sandstone beds, and coal beds, and the extent of damage when the rock faces of different lithologies are subjected to extrusion shear varies. Therefore, determining the potential shear slip surface of locked rock masses can provide an important basis for preventing and controlling the occurrence of such landslides.

Predictive modeling of shear slip surface in locked rock mass

Building geometric model

According to the numerical simulation results, in order to determine the potential shear slip surface of the locked rock mass, this study constructs a geometric model of the anti-dip rocky slope after mining deformation and damage, and roughly divides the rock mass of the slope into five areas: locked area (I), proximity-disturbed and fragmented area (II), coal pillar protection area (III), disturbed and fragmented area (IV) and undisturbed area (V), Fissure LF1 and Fissure LF2 are located above the rear boundaries of Areas II and IV, respectively, see Fig. 8.

The I region is mainly subjected to the oblique slope ward compression of the crushed rock mass within the slope, and this section impedes the sliding of the crushed rock mass towards the slope. II and IV region is affected by coal seam mining, the rock mass is broken, the vertical displacement is greater than 1 m, and because of the influence of gentle anti-dip geology, the rock mass above the back of the goaf is broken intensified, the maximum vertical displacement range is generally shifted back, and II region of the slope produces a tendency to pour to the slope surface, extrusion of the front end of the lower part of the rock mass, so that the rock mass in this place is broken intensified and the maximum vertical displacement there is paradoxical increase. In this area constitutes a potential slip surface, the for the rock mass in this region, with the slope fragmentation and stress rebalancing, the complete rock mass gradually becomes smaller, limit equilibrium analysis of the model is simplified to build a potential slip surface, only consider the upper part of the slip surface of the more complete and effective rock mass. III region is located above the protected coal pillar, and V region is located at the back of the slope, where the rock mass is preserved more intact, with a vertical displacement of less than 1 m, and is less affected by the mining of coal seams.

Fig. 8
figure 8

Geometrical modeling of slope mining damage.

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Predictive modeling of shear slip surface in locked rock masses

In order to determine the potential shear slip surface of the locked rock mass, the stability of the slope was analyzed by limit equilibrium analysis based on the geometric model of the anti-dip rocky slope after mining deformation and damage, as shown in Fig. 9.

Fig. 9
figure 9

Slope limit equilibrium analysis model; (a) Disturbed crushed zone IV rock mass; (b) Coal pillar protection zone III; (c) Locked zone II and proximity disturbed crushed zone II slip mass.

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The force analysis of the rock mass in Fig. 9(a) is:

$$\:\begin{array}{c}{G}_{i}=\frac{\left({L}_{01}+{L}_{02}\right)}{2}{h}_{i}{r}_{i}\end{array}$$
(1)
$$\:\begin{array}{c}{N}_{i}={G}_{i}{sin}\alpha\:{cos}\alpha\:\end{array}$$
(2)

where \(\:{G}_{i}\) is the mass of the effective rock mass in the upper part of area IV after the slope is stabilized by mining;\(\:{N}_{i}\)is the external force on the effective rock mass;\(\:{L}_{01}\) and \(\:{L}_{02}\) are the lower and upper base lengths of the effective rock mass;\(\:{h}_{i}\) is the height of the effective rock mass;\(\:{r}_{i}\) is the unit mass of the effective rock mass; \(\:\alpha\:\) is the angle between the lower slope of the effective rock mass and the horizontal plane.

Force analysis of the rock mass in Fig. 9(b): 

$$\:\begin{array}{c}{N}_{i}={N}_{i+1}\end{array}$$
(3)

where \(\:{N}_{i}\) and \(\:{N}_{i+1}\) are a pair of mutually balanced forces acting on the Region III rock mass.

According to the Mohr-Coulomb strength theory, the force analysis of the rock mass in Fig. 9(c) can be obtained as:

$$\:\begin{array}{c}{G}_{1}=\left[\frac{{L}_{1}^{2}}{2}{tan}\theta\:+\frac{H-{h}_{0}}{{sin}\theta\:}h\right]{r}_{1}\end{array}$$
(4)

where \(\:{G}_{1}\) is the mass of the Region II slide after slope mining stabilization;\(\:\:{L}_{1}\) is the length of the upper edge of the triangular rock mass on the upper part of the slide; \(\:H\) is the height of the slip surface; \(\:{h}_{0}\) is the height of the slip surface of Region I; \(\:h\) is the height of the trapezoidal rock mass in Region II; \(\:{r}_{1}\) is the mass per unit of the slide in Region II; \(\:\theta\:\) is the angle of the side slope.

$$\:\begin{array}{c}{F}_{1}=\left({G}_{1}{cos}\theta\:-{N}_{i+1}{sin}\theta\:\right){tan}\phi\:+C\left(\frac{H-{h}_{0}}{{sin}\theta\:}\right)\end{array}$$
(5)

where \(\:{F}_{1}\) is the slip resistance of the Region II slide; \(\:\phi\:\) and \(\:C\) are the strength parameters of the structural surface; \(\:{N}_{i+1}\) is the force of the Region III rock mass acting on the Region II slide.

$$\:\begin{array}{c}{F}_{3}={G}_{1}\text{sin}\theta\:+{N}_{i+1}\text{cos}\theta\:\end{array}$$
(6)
$$\:\begin{array}{c}{N}_{i+2}={F}_{3}-{F}_{1}\end{array}$$
(7)

where \(\:{F}_{3}\) is the sliding force generated by the gravity of the Region II slide itself; \(\:{N}_{i+2}\) is the force exerted by the Region II slide on the Region I locked rock mass.

$$\:\begin{array}{c}{G}_{2}=\left[\frac{2{h}_{0}}{\text{sin}\theta\:}+h\text{tan}\theta\:+\frac{h}{\text{tan}\left(\theta\:+{7}^{^\circ\:}\right)}\right]\frac{h{r}_{2}}{2}\end{array}$$
(8)

where \(\:{r}_{2}\) is the unit mass of the locked rock mass; \(\:{G}_{2}\) is the mass of the locked rock mass in Area I after the slope mining stabilization;\(\:\:\theta\:+{7}^{^\circ\:}\:\)is the angle between the slope surface and the structural surface.

$$\:\begin{array}{c}{F}_{2u}={G}_{2}\text{cos}\theta\:\text{tan}\phi\:+C\frac{{h}_{0}}{\text{sin}\theta\:}\end{array}$$
(9)
$$\:\begin{array}{c}{F}_{2d}=\left[{N}_{i+2}\text{sin}\left(\theta\:+{7}^{^\circ\:}\right)+{G}_{2}\text{cos}{7}^{^\circ\:}\right]\text{tan}\phi\:+C\frac{h}{\text{sin}\left(\theta\:+{7}^{^\circ\:}\right)}+{G}_{2}\text{cos}\theta\:\text{sin}\left(\theta\:+{7}^{0}\right)\end{array}$$
(10)

where \(\:{F}_{2u}\) is the sliding resistance at the upper base of the locked rock;\(\:\:{F}_{2d}\) is the sliding resistance at the lower base of the locked rock.

$$\:\begin{array}{c}{F}_{4u}={G}_{2}\text{sin}\theta\:+{N}_{i+2}\end{array}$$
(11)
$$\:\begin{array}{c}{F}_{4d}=\left({G}_{2}\text{sin}\theta\:+{N}_{i+2}\right)\text{cos}\left(\theta\:+{7}^{^\circ\:}\right)\end{array}$$
(12)

where \(\:{F}_{4u}\) and \(\:{F}_{4d}\) are the sliding forces on the locked rock mass.

Slope stability coefficient is the ratio of anti-slip force to sliding force along the assumed sliding surface, because the tilted tensile cracks at the trailing edge of the slide mass can not provide anti-slip force, the stability coefficient of anti-dip rocky slopes after mining deformation and damage \(\:{F}_{s}\) as:

$$\:\begin{array}{c}{F}_{s}=\frac{{F}_{k}}{{F}_{x}}=\frac{{F}_{1}+{F}_{2u}+{F}_{2d}}{{F}_{3}+{F}_{4u}+{F}_{4d}}\end{array}$$
(13)

where \(\:{F}_{k}\) is the total slip resistance of the slope after mining stabilization; \(\:{F}_{x}\) is the total sliding force on the slope.

The potential shear slip surface of the locked rock mass is determined by calculating and comparing the stability coefficient \(\:{F}_{s}\) after mining deformation damage of the anti-dip rocky slopes. Therefore, in order to simplify the stability calculations and determine the potential shear slip surface of the locked rock mass, the nonlinear variation process of the external force Ni+1 in time and space is neglected in this paper. The increase of this external force will accelerate the shear slip damage of the locked rock mass, but it does not affect the determination of the potential shear slip surface, so it is assumed that the external force is 0.

$$\:\begin{array}{c}{F}_{S}=\frac{\left[{G}_{1}+{G}_{2}-{G}_{1}\text{s}\text{i}\text{n}\left(\theta\:+7^\circ\:\right)\text{t}\text{a}\text{n}\phi\:\right]\text{c}\text{o}\text{s}\theta\:\text{t}\text{a}\text{n}\phi\:+C\left[\frac{H-\left(H-{h}_{0}\right)\text{s}\text{i}\text{n}\left(\theta\:+7^\circ\:\right)\text{t}\text{a}\text{n}\phi\:}{\text{s}\text{i}\text{n}\theta\:}+\frac{h}{\text{s}\text{i}\text{n}\left(\theta\:+7^\circ\:\right)}\right]+\left({G}_{1}\text{s}\text{i}\text{n}\theta\:\text{t}\text{a}\text{n}\phi\:+{G}_{2}\text{c}\text{o}\text{s}\theta\:\right)\text{s}\text{i}\text{n}\left(\theta\:+7^\circ\:\right)}{\left[2{G}_{1}+{G}_{2}+{G}_{2}\text{c}\text{o}\text{s}\left(\theta\:+7^\circ\:\right)\right]\text{s}\text{i}\text{n}\theta\:-\left(1+\text{c}\text{o}\text{s}\left(\theta\:+7^\circ\:\right)\right)\left[{G}_{1}\text{c}\text{o}\text{s}\theta\:\text{t}\text{a}\text{n}\phi\:+C\left(\frac{H-{h}_{0}}{\text{s}\text{i}\text{n}\theta\:}\right)\right]}\end{array}$$
(14)

In the formula, \(\:\theta\:\) is 32°, \(\:{L}_{1}\) is taken as 45.31 m, \(\:h\) is taken as 32 m, and \(\:{r}_{1}\) is taken as 23.54 kN/m3, \(\:H, {h}_{0}\:\text{a}\text{n}\text{d}\:{r}_{2}\:\)are changed with the change of the calculation of the locking rock mass rock face. The slope stability coefficients of the locking rock mass at each level are calculated according to Eq. (14), and the calculation results are shown in Table 3.

Table 3 Calculation of damage surface prediction model.
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When the stability coefficient is 1, the slope resistance is equal to the sliding force, at this time the slope is in the limit state of critical slip; when the ratio is less than 1, the slope is damaged; greater than 1, the slope is stable, and the larger the ratio the more stable the slope is; Define the difference of slope stability coefficient of each layer of locked rock mass is called stability difference, in which A9 coal seam is compared with the hypothetical damage surface, i.e., the difference of hypothetical damage surface with slope stability coefficient of 1. The slope stability coefficients and stability differences of each layer of locked rock mass are obtained as shown in Fig. 10.

Fig. 10
figure 10

Slope stabilization coefficients for the various formations of the locked rock mass.

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As can be seen from the data in Table 3 and the trends in Fig. 10, after the mining deformation damage of this anti-dip slope, the slope as a whole is still in a more stable state, and by comparing the slope stability coefficients, it is determined that the potential shear slip surface of the locking rock mass is the A9 coal seam. The mathematical model can provide a reference for predicting the shear slip damage level of locked rock mass after mining deformation damage of anti-dip rocky slopes to enhance landslide disaster prevention.

Physical test validation

Experimental design

The main parameters of the similarity simulation test include geometric size L, deformation modulus E, densityγ, cohesion C, internal friction angle φ, and Poisson’s ratioµ, According to the similarity theory and the similarity theorem, and taking into account the effective scale of the test platform, it is determined that the similarity constant of the test is selected to be C = 200, so that CL = CE = Cγ = CC = 200,Cφ= Cµ = 1。The symbol C denotes the similarity ratio and the subscripts indicate the corresponding physical parameters. From the similarity constants combined with the engineering geological profile of the Meidong Slope (Fig. 2), the dimensions of the test model were determined as: length × width × height = 200 cm×30 cm×105 cm。The test uses soil pressure sensors (T1 ~ T22) to collect the model data, 3D Full-field Deformation Measurement and Analysis System to monitor the slope deformation data, the specific parameters of the testing instrument are shown in Table 4, and the arrangement of soil pressure sensors in the model is shown in Fig. 11.

Fig. 11
figure 11

Physical model design.

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Table 4 Specification of measuring instruments for the physical model test.
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Based on the previous study on the rock parameters of Meidong Slope28, the similar materials consisted of barite powder, river sand, gypsum and cement, quartz sandstone composition (gypsum: cement: river sand: barite powder = 4: 2: 15: 15), carbonaceous shale composition (gypsum: cement: river sand: barite powder = 10: 1: 3: 2) and coal rock composition (gypsum: cement: river sand: barite powder = 1: 0: 10: 0), the mechanical parameters of similar materials are shown in Table 5.

Fig. 12
figure 12

Test platform building.

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According to the model design in Fig. 11, a physical test platform is built, as shown in Fig. 12. The model is stacked in layers, the similar materials are mixed well, and mica flakes are added to simulate the joint damage of the rock layer, after stacking one layer, a layer of mica flakes is sprinkled to simulate the structural surface of the rock layer, and the earth pressure transducer is buried in the corresponding position, and then the next layer of the model is stacked again. Mining action was simulated in the tests by manual excavation of similar material and adjustment of the bedrock support frame, and the coal seam was excavated in the same sequence as in Fig. 4.

Table 5 Mechanical parameters of similar materials.
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Characterization and analysis of model deformation

The experiment uses the 3D Full-field Deformation Measurement and Analysis System to monitor slope deformation data. By processing the collected data, we obtain the displacement evolution maps and strain field evolution contour maps of the model under various design conditions. The displacement maps show the deformation of the model under coal mining conditions, while the strain maps represent the strain distribution under these conditions. Displacement maps focus on the absolute changes in position, whereas strain maps focus on the relative changes in internal material stress.

Fig. 13
figure 13

Physical model combined displacement evolution cloud map.

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The evolution of the ensemble displacements generated by the model with each design condition mining is shown in Fig. 13. Figure 13a shows the initial shape of the model. When mining task A9-01 (Fig. 13b) and A9-02 (Fig. 13c), the overlying hard rock rock layer in the goaf collapses, the other rock mass combined displacement range is mainly distributed between 0.125 ~ 0.500 mm, and the locking rock mass does not have obvious change characteristics. When mining task A7-01 (Fig. 13d), under the influence of coal seam mining, the displacement of the slope mass increased greatly, mainly distributed between 0.250 ~ 1.625 mm, the displacement of the rock mass above the goaf of mining task A9-01 was larger, around 1.500 mm, and the displacement of the intact rock mass close to the slope surface was relatively small, below 1.000 mm, thus forming an obstacle to the sinking of the rock mass above the locking rock mass is initially formed by the shear effect. For the locking rock mass, it mainly contains carbonaceous shale rock layer, quartz sandstone rock layer and coal seam, in which the A9 coal seam is located in the ___location of the upper carbonaceous shale rock layer and the lower quartz sandstone rock layer compared with the larger displacement, more prone to shear slip damage. When mining task A7-02 (Fig. 13e), the slope displacement further increased, mainly distributed between 0.375 and 2.000 mm, and the displacement of the rock mass above the front end of the goaf in mining task A9-01 was the largest, reaching 2.000 mm, which formed a tiny shear misalignment with the intact rock mass close to the slope surface at the vicinity of the goaf and constituted a locking rock mass, hindering the dumping and sliding of the rock mass above in the direction of the slope surface The maximum amount is 2,000 mm, and the maximum amount is 2,000 mm; The sinking of the upper rock mass also further squeezes the locking rock mass, and the locking rock mass is squeezed and sheared towards the slope face, and because the displacement of the A9 coal seam in the locking rock mass is significantly larger than that of the other rock seams, it proves that it is subjected to greater shear damage and is more likely to be subjected to shear slippage, and it is most probable that the potential shear slippage damage surface of the locking rock mass is the A9 coal seam.

A cloud diagram of the evolution of the strain field of the model with the mining task is shown in Fig. 14. Figure 14a shows the initial shape of the model. From Fig. 14b and c, the strain of the slope mass at mining task A9-01 and A9-02 is small, mainly concentrated in the rock mass above the goaf of mining task A9-01 and close to the slope, which is conducive to the formation of the locking rock mass. In mining task A7-01 (Fig. 14d) and A7-02 (Fig. 14e), the strain on the rock above the front end of the goaf in mining task A9-01 is larger, and the strain on the rock near the slope in the annex of the goaf is smaller, thus constituting a locking rock mass, which hinders the dumping and sliding of the rock above it in the direction of the slope. At this stage, the locked rock mass of the slope is controlled by shear stress, and at the same time, the slope continues to creep and slip, and the deformation increases, resulting in creep and slip damage to the locked rock mass and bulging. The strain of the rock stratum where the A9 coal seam is located in the locked rock mass is more than 70%, which is obviously larger than the other rock seams, proving that the disruption by deformation is more serious at this place, and the potential shear slip surface of the locked rock mass is the most likely for the A9 coal seam.

Fig. 14
figure 14

Cloud diagram of the evolution of the strain field for physical models.

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The earth pressure monitoring of the model as the workings are mined is shown in Fig. 15, and the layout of the earth pressure sensors is shown in Fig. 11. As can be seen from Fig. 16, the T1 sensor is located above the A7 coal seam in the locked rock body, and the normal stress varies from − 5 to 10 kPa.After the end of mining of the working face A7-01, the stress redistribution of the side slopes leads to the decrease and then the increase of the positive stress above the A7 coal seam. This is due to the influence of the collapse of the overlying rock layer and the slow anticlinal strata in the mining hollow area, the positive stresses suffered from the A7 coal seam in the locked rock body can be released to reduce, again Because of the redistribution of stress in the rock mass leads to the concentration of stress at the front end, the positive stress increases sharply. The T3 sensor is located above the A9 coal seam of the locked rock body, and the positive stress varies in the range of 0 ~ 2 kPa, which indicates that this ___location is first affected by the stress redistribution of the overlying rock layer in the mining area, and the positive stress increases, and then is supported by the collapsed rock body of the mining area after the end of the redistribution of the pressure of the slope rock body, and the positive stress decreases. Therefore, the positive stress on the A7 coal seam is greater than that on the A9 coal seam, which makes the slope slip resistance increase, and the potential shear slip surface of all locked rock bodies is most likely to be the A9 coal seam.

Fig. 15
figure 15

Physical model normal stress monitoring.

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Fig. 16
figure 16

T1 and T3 normal stress monitoring.

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In summary, after the end of coal seam mining, the analysis of the combined displacement change, strain field evolution and normal stress change of the slope mass can determine the potential shear slip surface of the locking rock mass for the A9 coal seam, which is consistent with the results of the prediction model of the shear slip surface of the locking rock mass in this paper, and it proves that the prediction model can effectively predict the potential shear slip surface of the locking rock mass of the anti-dip slope under the mining action.

Limitation

Although the predictive modeling test for the potential shear slip surface of a rock body locked by a slow reverse slope under mining action has achieved relatively satisfactory results, there are still areas that need to be improved. First, the proposed model, due to the limitation of experimental conditions, only considers the influence of coal seam excavation on the model, but not the influence of external triggering factors, such as the time-varying process of rainfall and the creep behavior of the rock body. Secondly, although the prediction results of the potential shear-sliding damage surface of the rock body locked by the slow reverse slope were demonstrated by physical experiments, the experiments were carried out only once, and the reproducibility of the experiments needs to be fully considered. Finally, the feasibility of the model in the experiment was only verified in the laboratory, and its practical use needs to be further investigated to strengthen its practical relevance.

Conclusion

This study systematically investigates the prediction of potential shear slip surface in locked rock mass of gently inclined counter tilted rock slope under mining effects through an integrated approach combining numerical simulation, physical testing, and theoretical analysis. The main conclusions are as follows:

(1) The failure characteristics and formation mechanisms of locked rock masses in counter-tilted slopes under mining disturbance were investigated. The results demonstrate that the closer the mining position is to the slope surface, the more pronounced its impact on slope stability. Under gently counter-tilted stratigraphic conditions, the intact rock mass near the slope surface forms locked segments that create a restraining effect on the fractured slope above the goaf. The shear slip failure of these locked segments serves as a critical controlling factor triggering instability in such slopes.

(2) A predictive model for the potential shear slip failure surface of locked rock masses in counter-tilted slopes under mining action was established. Based on numerical simulation results, the slope rock mass was innovatively divided into five characteristic zones: locked area (I), proximity-disturbed and fragmented area (II), coal pillar protection area (III), disturbed and fragmented area (IV) and undisturbed area (V). The two-dimensional limit equilibrium method was then applied to analyze the stress state of the rock mass, constructing a predictive model capable of both quantifying the safety factor of mining-affected slopes and precisely locating the potential slip surface of locked rock masses. This model provides theoretical foundations and technical support for engineering reinforcement design.

(3) The predictive model was validated through numerical simulation and similarity simulation tests. The study reveals that post-mining slope deformation exhibits a composite “toppling-compression-shear” failure pattern. Comprehensive analysis of displacement fields, strain fields, and stress fields identified the A9 coal seam as the potential shear slip surface of the locked rock mass. These findings show excellent agreement with model predictions, confirming the accuracy and applicability of the proposed model.