1 Introduction

The influence of groundwater on coal mining operations is difficult to avoid due to the constraints of the fugitive conditions (Fan and Ma 2018; He 2021). In recent years, incidents due to groundwater still occur from time to time and account for a high proportion of mine accidents in China. The soft muddy rock is widely distributed in the strata of coal mines in China, and its mechanical properties can be significantly affected by the presence of groundwater, which can ultimately lead to the instability of the anchorage structure in the underground roadways (Arikoglu 2014; He 2021; Ma et al. 2021; Meng et al. 2014; Zhang et al. 2009). Therefore, the failure mechanism of the soft muddy rock anchorage structures subject to the presence of groundwater needs to be investigated (Wang et al. 2015; Zuo et al. 2015).

Duo to the underground excavations, groundwater will hydrate with the surrounding rock after entering the tunnels, leading to a significant reduction in rock mechanical properties such as strength and elastic modulus (Huang and Liu 2013; Vishal et al. 2015; Yuan et al. 2019; Zhang et al. 2021). The main rock types in the soft muddy rock are quartz, calcite, feldspar, and clay, while clay is normally present in various forms including kaolinite, montmorillonite, and illite (Li et al. 2015a, 2015b). When the soft muddy rock comes into contact with water, montmorillonite and illite swell sharply and become a paste, whereas kaolinite becomes softened (Yao et al. 2021). Unstable minerals such as sodium feldspar and potassium feldspar will exchange ions with water to produce kaolinite as a by-product, which will intensify the softening of the rock (Zhang et al. 2019a, b). Because it is mainly clay particles and clastic particles undergoes cementation in the soft muddy rock, clay minerals migrate and diffuse under the scouring action of water during rock softening and expansion processes, which leads to the reduction of cementation between rock particles, and consequently results in the reduction of rock strength and integration (Chen et al. 2015; Feng et al. 2022; Zhao et al. 2020, 2021, 2015). The disintegration of soft muddy rock will further initiate fractures in the surrounding rock, leading to a significant reduction in load bearing capacity of the surrounding rock (Bian et al. 2019; Ma and Zhang 2011; Sisodiya et al. 2021; Sun et al. 2019).

The anchorage unit in underground roadways consists of the surrounding rock, bonding materials, reinforcement element and fixing device (Li et al. 2021, 2022; Windsor 1997), as shown in Fig. 1. According to the actual conditions of the project site, groundwater not only causes erosion of the surrounding rock, but also weakens the adhesive properties between the bonding materials (such as resins) and the surrounding rock, and corrodes supporting components such as bolts (Chu et al. 2021). Moreover, the presence of groundwater can increase the water to cement ratio during the bolt installation and hence reduce the grout strength, which ultimately reduce the pullout resistance of the bolts (Kim et al. 2018; Li et al. 2019, 2018; Wang et al. 2021). All these phenomena indicate that the intrusion of groundwater will greatly affect the capacity of the rock reinforcement (Jia et al. 2019; Liu and Liu 2021; Yao et al. 2019).

Fig. 1
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Anchorage unit

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In recent years, scholars have conducted a lot of research on such issues and have achieved fruitful results (Bai et al. 2016; Li et al. 2015a, 2015b; Zhang et al. 2019a, b; Zhao et al. 2013). However, most of the existing studies have focused on the effect of water on a single component of the anchorage system, such as the effect of water on the mechanical properties of rock or reinforcement elements. On the other hand, very limited research has been done on the influence of water on the overall load bearing capacity of the anchorage structure and the synergistic interaction between the various parts in the anchorage structure. It has been widely realized that the failure of the anchorage system are likely following five different forms, being bolt (cable) rupture, debonding at the bolt-anchor agent interface (Liu and Xia 2013), slippage in anchor agent, debonding at the anchor agent—surrounding rock interface, and slippage in the surrounding rock (Hutchinson and Diederichs 1996; Li et al. 2020; Li 2020). Among them, debonding at the grout-surrounding rock interface, and slippage in the surrounding rock are the main failure modes of anchorage structure in soft rock roadways and water-rich roadways (Feng 2017; You 2005), as shown in Fig. 2. As can be seen from Fig. 3, under the action of normal stress, the bolt forms a common carrier with the shallow surrounding rock of the borehole by extrusion with the rock and the adhesion of the resin, and then forms a coupled bearing structure with the deep surrounding rock by extrusion and friction between the rocks. Therefore, the mechanical properties and integrity of the rock and grout, as well as the mechanical lock and cohesion at the interface between the two are critical to the load bearing capacity of the anchorage structure.

Fig. 2
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Main failure modes of anchorage structure in soft rock roadways and water-rich roadways

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Fig. 3
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Synergy of the anchoring structure

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The load bearing capacity of the anchorage structure governs the extent of the deformation and damage in underground roadway, as such, investigation into the failure mechanism of the anchorage structure in the soft muddy rock is essential to ensure a safe working environment in underground excavations. In this paper we eliminates the influence of other components in the anchorage structure by separating the rock-grout coupled structure. Since the rock-grout is generally under a direct shear loading when it is in service on site, direct shear tests with acoustic emission (AE) aids were conducted to study the effect of hydration damage on the mechanical properties and AE characteristics of the rock-grout coupled structure under different normal stresses σn and subject to different moisture contents w. In addition, the meso-mechanical behavior of rock-grout coupled structure subject to hydration damage was simulated with PFC. The macroscopic and mesoscopic mechanisms of hydration instability of mudstone anchorage structures are discussed.

2 Materials and methods

2.1 Specimens

The mudstone used for the test was taken from the roof at the 1900 level of the pedestrian inlet inclined shaft in the Zhenggao coal mine in Guizhou Province, China. The natural moisture content of mudstone is 2.15%, the uniaxial compressive strength in the dry state is 11.68 MPa, Young's modulus is 2.29 GPa, and Poisson's ratio is 0.28. As shown in Fig. 4, the rock specimen is highly susceptible to disintegration when exposed to water.

Fig. 4
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Mudstone disintegration in water

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To determine the lithology and percentages of internal mineral components of mudstone, an X-ray diffraction test (XRD) was carried out on the rock specimens by Rigaku Ultima IV X-ray diffractometer manufactured in Japan. The mineral components of mudstone are shown in Table 1. Figure 5 shows the X-ray diffraction pattern and distribution of main mineral components in mudstone.

Table 1 Mineral composition of mudstone
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Fig. 5
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X-ray diffraction patterns

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As can be seen in the Table 1, clay minerals account for 39.4% of rock minerals, of which kaolinite and montmorillonite are predominant. Montmorillonite has strong water absorption, its volume will swell sharply and become paste when it meets water. By contrast, the dispersion of kaolinite will be significantly improved when exposed to water. Both will reduce the overall strength of the rock after absorbing water. Cubic specimens with dimensions of 100 × 100 × 50 mm were prepared. To ensure the consistency of the specimens used in the test, the non-metal ultrasonic tester was used to select specimens with similar wave speeds for subsequent tests. The specimens were shown in Fig. 6.

Fig. 6
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Mudstone specimens

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2.2 Direct shear test scheme for anchored mudstone specimens under different moisture content

During the construction of the argillaceous roadway, the surrounding rock will be fractured due to stress redistribution, leading to the generation of water-conducting channels to communicate with the aquifer. As a result, the roof of the roadway is already in a water-bearing state even before the bolt is installed. To conform to the actual engineering conditions and simulate the instability process of rock-grout structure in the argillaceous roadway, the test scheme is formulated as follows:

The cubic mudstone specimens were placed in the oven. The drying temperature was set at 65 ℃ and the drying time was 12h according to the Regulation for testing the physical and mechanical properties of rock (DZ/T0276.18–2015) (Yao et al. 2015). Since the conventional immersion method will lead to the disintegration of mudstone, YH-40B standard constant temperature and humidity curing box are used to soak dry rock specimens (humidity was set at 95%, the temperature was set at 25 ℃) until the moisture content of rock specimens reached the set value. In the process of immersion, rock specimens were taken out and weighed at various time intervals. The variation of the moisture content of mudstone with the time of immersion was shown in Fig. 7.

Fig. 7
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The relation of w of mudstone with water intrusion time

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To study the effect of water on the shear mechanical properties of rock-grout, representative w of rock specimens should be selected. According to the three stages of w (moisture contents) change with soaking time in Fig. 7 (rapid growth I, slow growth II, tends to saturation III), w required for the direct shear test was selected to be 0, 3%, 6%, 9%, and 12%, respectively. At present, coal mines mainly use resin anchorage agent for bolts installation. According to previous relevant studies (Luo et al. 2022; Qiu et al. 2021), the mechanical properties of resin and grout of the coal mine roadway are consistent. And it is more suitable for the test scale because of its good fluidity, which can better simulate the mechanical properties of the grout (Chen et al. 2020; Zhang et al. 2022). Therefore, resin was selected as the grout material in this test. Its setting time was 0.5 h, and the average UCS of resin after curing 3 h was 47.68 MPa, which could meet the test requirements. After the w of the rock specimen reached the set value, it was placed into the mold, and the resin was poured into the mold and mixed well. The size of the mudstone anchorage sample was 100 × 100 × 100 mm.

The test system mainly includes the direct shear boxes with AE detection device, as shown in Fig. 8. The direct shear test facility uses YZW50B microcomputer-controlled electric stress type direct shear instrument, and the specimen loading mode is shown in Fig. 8.

Fig. 8
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Direct shear test system and AE monitoring system

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Aziz (2002) and Hyett et al. (1995) found that the confining pressure at the borehole wall is usually less than 10 MPa due to stress redistribution after bolt installation. The UCS of mudstone is 11.68 MPa, 5.91 MPa, 3.57 MPa, 2.03 MPa and 0.76 MPa respectively when w is 0, 3%, 6%, 9% and 12.04% (saturated moisture content). The normal stress, σn were set at 0.25 MPa, 0.5 MPa, 1 MPa, and 3 MPa. The loading stress path is as follows: add the normal load to the set value first, and then keep the normal force constant. The displacement rate of the shear movement is 0.01 mm/s. The testing program is shown in Table 2. Since AE localization is not studied, four AE probes are used to collect signals, which can meet the test needs. The threshold value was set as 40 dB, and the AE sampling frequency range was set at 1 kHz − 1 MHz.

Table 2 Test set value
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3 Mechanical properties of anchored mudstone specimens under shear loading subject to different w

3.1 Deformation characteristics of specimens

Figure 9 shows the shear stress–shear displacement curves of anchored mudstone specimens subject to different σn and different w. Under the condition of saturated moisture content, the bonding surface of the anchored mudstone specimen has no adhesion, and it will debond by slight disturbance. The mudstone was muddied and cracked along the weak plane (detailed failure mode is described below).

Fig. 9
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Shear stress − strain curves of anchored mudstones

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As seen in the Fig. 9, the curve at the initial stage of the test presented an upper concave shape. This can be attributed to the progressive closure of the initial pores in the mudstone as shear force increased. As the shear stress further increased, the curve tended to be straight where the shear stress is linearly proportional to the shear displacement. When the shear stress reached its peak, the bond between the mudstone and resin failed rapidly. The shear stress drops rapidly until reaching its residual strength.

The effect of w on the shear strength of anchored mudstone specimens is shown in Fig. 10a. The shear strength of the specimen increased as σn increased, and decreased as w increased. The shear strength of the specimens was reduced by 8.97%–11.63% when w = 3%; 28.25%–35.84% when w = 6%; and 47.51%–56.93% when w = 9%.

Fig. 10
figure 10

Shear stress − strain curves of anchored mudstones

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Figure 10b shows the contour plot of shear strength under different conditions, and it can be found that both w and σn affect the shear strength of the specimens. Under the condition of lower w, the variation of σn had a significant effect on the strength of the specimen, and the shear strength of the specimen increased with σn. As w increased, the effect of σn on the strength of the specimen was diminished. When w was greater than 9%, the strength of the specimen was almost not affected by the change of σn. However, the strengths of the specimens were significantly affected by the variation of w regardless of σn levels.

3.2 Failure characteristics of specimens

Figures 11, 12, 13 and 14 lists the typical shear failure modes of anchored mudstone specimens under different w. It can be found, specimens under different conditions exhibit four typical failure modes:

Fig. 11
figure 11

Failure mode I (1–1, A-1, A-2, B-2, B-3, C-4)

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Fig. 12
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Failure mode II (1–2, 1–3, 1–4, A-3, A-4, B-4)

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Fig. 13
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Failure mode III (B-1, C-1, C-2, C-3)

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Fig. 14
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Failure mode IV (D-1, D-2, D-3, D-4)

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Failure mode I (see in Fig. 11): The failure mode of the specimen is mixed shear damage, that is, the fracture surface of the specimen consists of the interface and the mudstone near the interface together. The main characteristic is that the resin side was adhered with mudstone fragments and a thin layer of mudstone rock powder. The specimen was firstly damaged along the weak surface of mudstone near the interface Then, the specimen starts to break along the interface.

Failure mode II (see in Fig. 12): Damage was seen along the bonding surface (only a thin layer of rock powder has adhered to the resin side). The fracture surface was flat, and obvious friction traces can be observed.

Failure mode III (see in Fig. 13): The failure mode of the specimen shows that shear damage occurs along the mudstone, and the fracture surface was wavy.

Failure mode IV (see in Fig. 14): The strength of the mudstone anchorage specimen was seriously weakened by water, and there is no bonding force between mudstone and resin. The mudstone was argillized and cracks along the internal weak surface.

The test results show that under the conditions of low stress level and low degree of hydration damage, the weak area of the coupled structure consists of the cohesive surface and the weak surface of the rock around the cohesive surface. With increasing moisture content, the shear strength of the mudstone part decreases rapidly and the weak area shifts to the rock part. As the hydration damage intensifies, the mudstone disintegrates, the resin and mudstone lose their adhesive capacity, and the coupled structure loses its load-bearing capacity. If the mudstone is not disintegrated, the increase in normal stress will strengthen the weak surface of the rock, increase the shear strength of the rock part, and cause the weak area to shift to the adhesive surface.

4 AE characteristics of anchored mudstone specimens at different moisture contents

AE monitoring is an important method to study the mechanical properties of rock, which can effectively monitor the failure process and damage evolution of rock. AE monitoring was conducted for direct shear tests of mudstone anchorage specimens with different w, and failure mechanisms of anchored mudstone specimens subject to various moisture content levels were investigated by analyzing the AE parameters.

AE count represents the oscillation times of the signal exceeding the threshold, which can be used for AE activity evaluation. And cumulative AE count with AE count can reflect the degree of damage accumulation within the specimen. Figure 15 shows the curves of shear stress, AE counts, cumulative AE counts, and time at different w.

Fig. 15
figure 15figure 15

Shear stress-AE count-cumulative count-time curves of anchored mudstones

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In the compaction and elasticity stage of the stress–strain curve, the AE count values are relatively low, and the cumulative counts have relatively small increments in this phase. During the yielding stage, the AE counts start fluctuating significantly, and the lifting rate of the cumulative AE count increased significantly. The maximum AE counts can be observed near the peak stress. Where w = 0, the cumulative AE count of the specimens hardly increases until the yielding stage.

Combined with Fig. 16, it can be seen that the peak AE counts of the specimens at different w decreased as w increased. As w increased, the peak AE counts decreased by 27.8%–40.6% for σn = 0.25 MPa, 11.6%–39.2% for σn = 0.5 MPa, 37.3%–55.2% for σn = 1 MPa, and 68.4%–83.6% for σn = 3 MPa. And it can be found that the peak cumulative AE counts kept increasing with an increasing w. As w increased, the peak cumulative AE counts increased by 10.7%–77.7% for σn = 0.25 MPa, 49.2%–205.2% for σn = 0.5 MPa, 40.3%–151% for σn = 1 MPa, and 19.4%–40.1% for σn = 3 MPa.

Fig. 16
figure 16

Relationship curve between AE characteristic parameters and moisture content

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All the aforementioned observations are attributed to the fact that water weakens the strength of the bonding surface and internal structure of mudstone, which ultimately reduces the energy required for bond failure between mudstone and resin, as well as the energy required for extension of fracture inside the specimen. It was also found that the strain energy released by the specimen decreased, and the peak AE counts of the specimen decreased. On the other hand, with increasing moisture content, the bonding between particles within the specimen was weakened, the mudstone structure became loose, the internal damage was easier to develop, and the peak cumulative AE count of the specimen gradually increased.

5 Shear meso-mechanical properties of anchored mudstone specimens

PFC considers materials as small granular structures such as particles and clusters of different sizes bonded through contact bonds. It uses the fracture of contact bonds to characterize the generation of microfractures, which can effectively simulate discontinuous elements such as fracture and disintegration of materials (Zheng et al. 2022, 2023). In this section, PFC2D simulation software was used to further study the mesomechanical behaviors of the specimen, such as the motion of particles and the evolution of damage during the test, based on the macroscopic test results.

5.1 Simulator scheme

Parallel-bond model is a commonly used as the contact model for simulating rock-like materials. The failure of the parallel-bond model will lead to the rapid reduction of macroscopic stiffness of the model, which is consistent with the failure mechanism of rock material. Therefore, the parallel-bond model is used in the simulation of this paper. The anchored mudstone models were established as seen in Fig. 17, and the model dimensions were all 100 × 100 mm. The initial model was generated and saved to ensure that all subsequent steps were performed under the same initial conditions.

Fig. 17
figure 17

Numerical model of anchored mudstone specimen

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After the model is created, the load is applied to the model using the walls. The bottom wall of the model is fixed, and σn is applied through the upper wall, which is achieved using a servo mechanism. After the upper wall applies constant σn to the model, the walls on both sides of the resin in the upper part are fixed, and a constant rate is applied to the lower wall on both sides moving to the left side of the model for shear loading. As the experiment involves quasi-static loading, the loading rate in PFC can meet the quasi-static loading requirements within the range of 0.016–0.2 m/s, and different loading rate changes within this range have no effect on the simulation results (Ding et al. 2014; ITASCA 2016). Therefore, a fixed loading velocity of 0.1 m/s is selected for all the tests carried out in this study.

5.2 Determination of model parameters

Based on the uniaxial compression test results of mudstone specimens and epoxy resin at different w, simulations for the uniaxial compression of mudstone and resin were carried out (Table 3). The meso-parameters were adjusted by trial-and-error until the test and simulation results agreed with each other. The resulting test and simulation stress–strain curves are shown in Fig. 18. As can be seen from the figure, the results obtained by PFC simulation are consistent with the experimental results, and the selected parameters can better capture the mechanical properties of the resin and mudstone, as shown in Table 4. Since PFC cannot simulate the physical and chemical effects of water on rocks, the parametric weakening method is used in this paper (Shi et al. 2018; Xiao 2021).

Table 3 Meso-parameters of mudstone and epoxy resin
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Fig. 18
figure 18

Stress–strain curve obtained from simulation and test

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Table 4 Meso-parameters of interface
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The difference between the experimental and simulated strains is because the specimens in the PFC simulations are loaded and calculated to the initial equilibrium to form effective contact among the particles during the loading process. In this process, the model has been compacted and self-balanced. The particles of the model are uniformly distributed, so there is no compaction stage, which does not affect the subsequent simulation results (Huang et al. 2017; ITASCA 2016; Rafiee et al. 2018; Wei et al. 2019).

According to the data in Table 3, direct shear simulations of the anchored mudstone specimen at σn = 1 MPa and different w were carried out. The macro-mechanical properties of the specimen obtained from the test and simulation were compared to obtain the meso-parameters of the mudstone-resin interface under different w. And the obtained meso-parameters were used to perform a direct shear simulation of anchored mudstone specimens at σn = 3 MPa, to verify the validity of the results. The obtained interface parameters are shown in Table 4. As can be seen in Fig. 19, the obtained simulation results are in a good agreement with the test.

Fig. 19
figure 19

Stress–strain curve obtained from simulation and test

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5.3 Microfracture distribution of specimens

(1) Microfracture distribution of specimens with different w.

Figure 20 shows the damage pattern of the models at σn = 1 MPa and different water content, and the area in black colour is formed by the agglomeration of microfractures.

Fig. 20
figure 20

Failure mode of the model under σn = 1 MPa and different w

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As can be seen in the figure, the failure mode of the models obtained from the simulation is consistent with the test. As w increases, the failure region of the models gradually shifts from the bonding surface to the mudstone part. When w is high, the portion of mudstone close to the interface will be damaged, leading to a debonding of the interface and ultimately resulting in a significant reduction in the load bearing capacity of the rock-grout coupled structure.

(2) Microfracture distribution of models under different σn.

The failure mode of the simulation is shown in Fig. 21. It can be found that the shear strength of mudstone is significantly enhanced by increasing σn, with a reduced number of microfractures in the rock part. The load bearing capacity of the model is increased mainly through compacting internal fractures and pores of the rock by σn.

Fig. 21
figure 21

Failure mode of the model under different σn and w = 6%

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5.4 Shear stress evolution of the model

(1) Evolution of shear stress in models with different w.

The simulation results at σn = 1 MP and vairous w including 0, 6%, and 9% are taken as examples to analyze the evolution of shear stress under the influence of w. Figure 22a shows the shear stress distribution of particles (σps) at different loading stages under the condition of w = 0 (damage along the interface), and the corresponding shear stresses levels are 60%, 70%, 80%, 90%, 100% of the peak strength and 75% of the peak strength at the post-peak stage (for the convenience of observation, the smaller shear stress area is removed, and the scale corresponds to the range of 0.15σpsmax ~ σpsmax). As can be seen in the figure, in the pre-peak stage, with increasing shear displacement, the σps concentration area is formed in the middle of both sides of the model and gradually expands to the interior of the model. Finally, a σps concentration area with the interface as the middle line and covering the resin and rock in a certain range around the interface is formed. The interface bonding performance is intact under this condition, which can effectively link the surrounding resin and rock to resist external load and form a common bearing area. In the post-peak stage, with the failure of interface bonding, the range of σps concentration area decreases continuously, indicating that the common bearing area shrinks continuously.

Fig. 22
figure 22figure 22

Shear stress distribution of particles under different w and σn = 1MPa. a σn = 1 MPa and w = 0. b σn = 1 MPa and w = 6%. c σn = 1 MPa and w = 9%

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Figure 22b shows the σps distribution at different loading stages under the condition of w = 6% (mixed damage). As can be seen in the figure, the distribution of σps under this condition shows the same trend, but the σps is significantly lower in the region. It shows that the interfacial bonding performances deteriorated due to hydration, which weakens the bond strength between resin and rock. Some rocks near the interface are damaged along the weak surface, which impairs the bearing performance of the common bearing area. At 75% of the peak strength in the post-peak stage, σps is mainly concentrated in the mudstone part, and the co-bearing capacity of the model shows a higher decay rate.

Figure 22c shows the σps distribution at different loading stages under the condition w = 9% (fail along the rock part). The expansion rate and the area of the σps concentration region are significantly reduced, and the σps in the region is significantly reduced as it is difficult to form a common bearing region. And according to Fig. 20, the fracture of the bond between rock particles at the interface accelerates the decoupling between resin and rock, and the model has lost its load-bearing capacity at 75% of the peak strength in the post-peak stage.

(2) Evolution of shear stress in models under different σn.

The simulation results at w = 6% are used as an example to analyze the evolution of shear stress under the influence of w, as shown in Fig. 23 (from top to bottom, σn = 0.25, 0.5, 3 MPa, and from left to right, corresponding to 90%, 100% of the peak shear stress in the pre-peak phase and 75% of the peak shear stress in the post-peak phase). As can be seen in the figure, the trend of σps evolution under different σn is consistent. As σn, increases, the magnitude of σps in the stress concentration region increases, but the shear stress concentration range does not change significantly. It is shown that the increase of σn can enhance the load bearing capacity of rock-grout coupled structure, but the enhancement of the linkage capacity of the bonding surface is limited, and the load bearing capacity of the model is mainly enhanced by strengthening the mechanical properties of the rock part.

Fig. 23
figure 23

Shear stress distribution of particles under different σn and w = 6%

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5.5 Energy evolution of the model

From the perspective of energy evolution, the motion of particles and fracture of contact bonds between particles, microfracture agglomeration, specimen deformation, and the final occurrence of macroscopic damage are the consequences of the internal energy accumulation and transformation. Since there is no heat exchange from the system to the outside during the simulation, all the work done by the wall on the model is converted into internal dissipation energy and strain energy for particle transport and fracture development. The strain energy of the PFC model consists of linear strain energy Ek with parallel-bond strain energy \(\overline{E}_{k}\), and the internal dissipation energy including particle kinetic energy Ec, bond slip friction energy Eμ, total energy consumed by the buffer Eβ, and local damping energy Eda. The formulas for calculating linear strain energy and parallel-bond strain energy are as follows:

$$E_{k} = \frac{1}{2}\left[ {\frac{{\left( {F_{n}^{l} } \right)^{2} }}{{k_{n} }} + \frac{{\left\| {F_{s}^{l} } \right\|^{2} }}{{k_{s} }}} \right]$$
(1)
$$\overline{E}_{k} = \frac{1}{2}\left( {\frac{{\overline{F}_{n}^{2} }}{{\overline{k}_{n} \overline{A}}} + \frac{{\left\| {\overline{F}_{s} } \right\|^{2} }}{{\overline{k}_{s} \overline{A}}} + \frac{{\overline{M}_{t}^{2} }}{{\overline{k}_{s} \overline{J}}} + \frac{{\left\| {\overline{M}_{b} } \right\|^{2} }}{{\overline{k}_{n} \overline{I}}}} \right)$$
(2)
$$\overline{A} = \pi \overline{R}^{2}$$
(3)
$$\overline{I} = \frac{1}{4}\pi \overline{R}^{4}$$
(4)
$$\overline{J} = \frac{1}{2}\pi \overline{R}^{4}$$
(5)

where \(F_{n}^{l}\) represents the normal linear force, \(F_{s}^{l}\) denotes the shear linear force, Fn signifies the normal parallel bonding force, and Fs represents the tangential parallel bonding force. \(\overline{R} = \overline{\lambda }\min (R^{\left( 1 \right)} ,R^{\left( 2 \right)} )\) (ball-ball contact), \(\overline{R} = \overline{\lambda }R^{\left( 1 \right)}\) (ball-facet contact), while R(1) and R(2) represent the radius of particles on both sides of the bond. \(\overline{\lambda }\) represents the radius multiplier (\(\overline{\lambda }\) = 1 in this paper). \(\overline{M}_{t}\) and \(\overline{M}_{b}\) represent the parallel bending moment and parallel torque moment respectively.

As shown in Fig. 24, the simulation results at σn = 1 MPa are used as an example to analyze the energy evolution of the models at different w. At the beginning of the direct shear test, Ek and \(\overline{E}_{k}\) accumulates as shear displacement increases, and the slope of the curve increase continuously. The rate of Ek and \(\overline{E}_{k}\) accumulation increases with increasing shear displacement. On the other hand, there is only a small increase in the dissipation energy, where Ec is small. In this case, the deformation process of the model is more gentle, and only a small number of microfractures are generated at this stage. When the shear stress is close to the peak strength, the strain energy accumulated inside the model is rapidly released, while the dissipation energy increases abruptly and a large amount of energy acts with the development of microfractures.

Fig. 24
figure 24

Energy evolution law of specimens under σn = 1 MPa and different w

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It can be found that with increasing w, the strain energy and dissipation energy of the model is significantly reduced, and Ek and \(\overline{E}_{k}\) at the peak stress are reduced by 38.87% ~ 75.57% and 40.61% ~ 78.45%, respectively. It shows that as the hydration damage of models intensifies, the bonding strength between rock and resin particles, and between rock and rock particles keeps decreasing. The energy required for bond break decreases, and the energy storage limit within the model decreases.

6 Discussion

The weakening damage process of the rock-grout coupled structure after water erosion is extended from the mesoscale to the macroscale. Therefore, the hydration destabilization process of the rock-grout coupled structure is analysed by combining the results of SEM tests of specimens under the conditions of w = 0, 6% and 12.04%.

As can be seen in Fig. 25, the resin and rock can be effectively bonded under dry conditions, with no obvious separation interface, and the interface shows a coupling area of some width. The rock part is intact, without obvious holes or cracks.

Fig. 25
figure 25

Diagram of hydration damage of soft muddy rock anchorage structure

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At this point, the anchor, the resin, and the surrounding rock can form a cooperative support under the action of interfacial bonding, friction between the rock blocks, and the ambient pressure. When the groundwater intrudes into the extraction space, it can be seen that a large number of fissures and dissolution holes are formed inside the rock under the action of hydration. The friction between the rock blocks is weakened under the action of water infiltration, and the self-supporting capacity of the surrounding rock is damaged. It can be observed that there is an obvious separation interface between the rock and the resin, and the rock near the interface is in a fractured state. The interfacial bonding effect is deteriorated. At this point, the anchorage structure still has some load-bearing capacity under the action of ambient pressure, weak interfacial adhesion, and weak friction between the resin and the rock and rock mass. As the hydration damage intensifies, the degree of rock fragmentation increases. And as the main cement (clay minerals) between the rock particles swell and softens, the surrounding rock muddies and disintegrates, losing its self-supporting capacity. Due to the influence of free water and the muddying of the rock particles, the resin and the rock lose their ability to bond. The anchor cannot form a coupled bearing structure with the surrounding rock through the resin, and the deformation of the surrounding rock is not effectively restrained, leading to instability of the anchoring structure (Fig. 25).

7 Conclusion

Based on direct shear tests and PFC simulations of anchored mudstone specimens at different w, the macro- and meso- mechanism of hydration destabilization of rock-grout coupled structure were investigated. The conclusions are as follows:

  1. (1)

    Water has a significant weakening effect on the load bearing capacity of rock-grout in a way that the load bearing capacity of the structure decreases rapidly as w increases. When it is fully saturated, the rock-grout losses its load bearing capacity.

  2. (2)

    As w increases, the energy required for the bond break between rock and resin as well as fracture penetration inside specimen decreases, and the peak AE count of anchored mudstone specimen keeps decreasing. However, the increase in w weakens the bonding ability between particles, making it easier to be damaged within the specimen and the peak cumulative AE counts keep increasing.

  3. (3)

    The shear damage mode of rock-grout structure has four main forms: rock-grout mixed debonding failure, debonding failure of the interface between rock and grout, detachment of anchored rock, interface debonding and mudification of surrounding rock, which is jointly affected by w and σn.

  4. (4)

    The aggravation of hydration will weaken the bond strength of the interface, and reduce the energy required for bond break within the specimen, which will ultimately weaken the load bearing capacity of the resin and rock.

  5. (5)

    The key to control the muddy roadway is to reduce the erosion of groundwater to surrounding rock, and ensure that the surrounding rock, grout and supporting components can form a co-bearing structure.