Water inrush is a crucial factor that affects the safety of subsurface engineering (Hödl & Höllrigl. 2014). In mines with aquifers, groundwater can easily cause stope and floor water inrush accidents, impacting mine safety and the ecological environment (Nikhitha et al., 2022). Relevant statistics indicate that over 70% of mine water inrush incidents occur in fault zones. Field investigations reveal that most fault zones contain continuous fault breccias and gouge mixtures. The soil–rock mixture (SRM) in these zones often demonstrates marked discontinuity and nonuniformity, leading to seepage failures such as piping and fluid soil under water's influence (Du et al., 2023; Kim et al., 2004; Vallejo, 2001; Vallejo & Mawby, 2000). A lack of understanding of SRM's seepage characteristics in fault zones would significantly jeopardize the prevention and control of engineering disasters. Therefore, it is imperative to study SRM's seepage characteristics in these zones.

As a critical parameter in geotechnical engineering seepage analysis, the permeability coefficient is vital for evaluating the hydraulic properties of geotechnical media. This coefficient is closely related to the composition of rock masses and voids. Extensive research has been conducted on the impact of SRM's rock block percentage on the permeability coefficient. Pereira (2023) posited that the rock block percentage in SRM and the nature of the infilling “soil” are primary determinants of its permeability characteristics. Gargiulo et al. (2016) examined the impact of rock content on SRM's structural changes, noting that porosity initially decreases and then increases with rock content, a pattern also observed in permeability. Indrawan et al. (2006) discovered through experiments that SRM's saturated permeability coefficient increases with coarse particle content, while its unsaturated counterpart decreases. Börgesson et al. (2003) studied a bentonite and gravel mixture used in underground nuclear waste storage, finding that the mixed filler's expansion force and permeability exceed theoretical values due to uneven mixing. Guo (1998) indicated that when the coarse particle content is below 30%, it merely fills gaps in SRM, with permeability mainly dependent on fine particles and decreasing as the rock content increases, adhering to Darcy's law. Conversely, when the coarse content surpasses 75%, the permeability coefficient abruptly increases, deviating from Darcy's law. Chen et al. (2019) explored the effects of rock proportion, size, and shape on SRM's effective permeability, revealing that the permeability coefficient decreases with increasing rock block percentage. Zhou et al. (2017) and Jin et al. (2021) investigated SRM seepage through theoretical modeling and the Lattice Boltzmann Method, respectively, concluding that SRM's permeability coefficient progressively increases with rock block percentage, particularly between 50% and 70%. These studies indicate that SRM's permeability coefficient is closely related to particle composition, rock properties, and coarse particle content.

The porosity of SRM and its influence on the permeability coefficient also constitute a significant research focus. Ghassemi and Pak (2011) used the LBM to identify the relationships between permeability and factors such as particle diameter, grain-specific surface, and porosity, determining that porosity and specific surface are crucial for permeability. Sekucia et al. (2020) analyzed the soil water retention curve using the SWRC model, incorporating a novel model that merged Dexter and Richard's (2009) model with Ross and Smettem's (1993) macro-porosity expression. This approach shows that rock content markedly influences porosity by increasing large pore content in SRM, thereby enhancing permeability. Amrioui et al. (2023) proposed a new porosity–permeability analysis model considering pore group influences on permeability calculations, thereby aligning computed and measured permeabilities in SRM more closely. Zhou et al. (2006) conducted indoor orthogonal tests, establishing that higher pore ratios correlate with increased permeability coefficients and expressing the relationship between SRM's permeability coefficient and porosity ratio. These investigations underscore the importance of structural elements in determining SRM's permeability coefficient.

The seepage test is a crucial method for examining the seepage characteristics of SRM, considering various stress states. Building on the fluid–solid coupling theoretical framework established by Biot (1955), researchers have conducted numerous seepage–stress coupling analyses (Detournay & Cheng, 1988), focusing primarily on the impact of confining pressure on SRM's permeability under triaxial compression. Arson and Pereira (2013) introduced a model that correlates permeability and porosity, applying this model to triaxial compression tests during drainage to more accurately reflect the influence of confining pressure on permeability. Nguyen et al. (2020) developed a model of stress-induced permeability increase based on linear fracture mechanics theory, uncovering the variation pattern of rock permeability under triaxial stress. Wang et al. (2016), Tan et al. (2022), and Wang and Zhang (2022) investigated the effect of confining pressure on the seepage characteristics of SRM samples with varying rock block percentages using a three-dimensional stress–seepage coupling test device, determining the permeability coefficient's variation pattern. Beyond triaxial stress–seepage tests of SRM, Zhang et al. (2022) and Malek et al. (2018) conducted uniaxial compression tests of SRM under the combined influence of the seepage and stress fields. They found that the synergistic effect of water and load leads to an increase in the permeability coefficient.

Researchers have primarily explored the effect of confining pressure on the permeability coefficient of SRM samples via seepage–stress coupling tests, but the impact of osmotic and axial pressures has been less studied. These studies fail to comprehensively consider the stress according to the actual engineering situation. Also, the samples used in laboratory tests are different from those in engineering, which also hinders the application of test results to engineering. Moreover, while the permeability characteristics of SRM under individual stress states are often analyzed, comparative analyses of these characteristics under various stress states are scarce. In addition, there has been less focus on the sensitivity analysis of permeability coefficient to stone content. Current research mainly focuses on SRM in slopes, dam bodies, and foundations, with limited attention to SRM in fault zones. Because the SRM is located in different geological structure regions, its seepage characteristics are not the same. Previous studies cannot provide more references for the analysis of SRM's permeability characteristics in fault zones.

Therefore, in this study, the SRM in fault zones was the focus of research and its permeability characteristics under various stresses were comprehensively analyzed. First, geotechnical tests and X-ray diffraction (XRD) analysis were conducted on the SRM obtained from in situ fault zones to provide the necessary parameters for laboratory remodeling samples so as to maximize the similarity of the remodeling samples to the actual engineering samples of the SRM. Then, three test conditions were applied to investigate the variation pattern of the permeability coefficient of SRM samples, exploring the relationship between the permeability coefficient and osmotic pressure, confining pressure, and axial pressure. On this basis, the influence of the stone content in SRM on the permeability coefficient was analyzed under different stress states and the changes in the meso-structure of SRM were concurrently observed through real-time CT scanning during seepage tests. The findings demonstrate the variation and sensitivity patterns of SRM's permeability coefficient in fracture zones, providing valuable insights for water inrush prevention and control in Sanshandao Gold Mine.

2 PREPARATION FOR THE SRM SEEPAGE TEST

The SRM used in this seepage test was obtained from the F3 fault zone of the North Tunnel in Xishan Mine at a depth of −780 m. The XRD analysis of the SRM shows that the main components of the mixture are Quartz and Muscovite, with a small amount of Kaolinite. The XRD pattern and the relative mineral content are shown in Figure 1. Among them, Muscovite has high diffraction intensity, a symmetrical diffraction peak, and high crystallinity.

           

The prepared remolded SRM samples are 50 mm in diameter and 100 mm in height. According to the soil/rock threshold formula $𝑑=0.05{𝐿}_{\mathrm{C}}$ (where d represents the soil/rock threshold and LC is the sample diameter) proposed by Xu et al. (2008), the soil/rock threshold for these samples is 2.5 mm. Furthermore, the largest rock diameter in the SRM is 1/6 of the sample diameter as per ASTM standards (Feng et al., 2018), resulting in a maximum rock particle size of 8.3 mm for the SRM sample.

When the rock block percentage is between 20% and 70%, the sample composition is relatively balanced, and the rock block percentage has an obvious influence on the permeability coefficient of SRM. Therefore, six kinds of SRM samples with stone contents ranging from 20% to 70% were prepared for this study. Figure 2 shows the grain grading curves of SRM.

           

Before sample preparation, compaction tests were conducted to ensure uniform soil density in SRM samples with varying rock block percentages. The soil compaction curves for the SRM samples are depicted in Figure 3. The SRM samples were prepared with a soil density of 1.82 g/cm3.

           

Before preparing the samples, the mold was cleaned and petroleum jelly was used to facilitate release. The sieving soil and block were mixed evenly according to the determined stone content. In order to reshape the SRM samples with enhanced cementation, 9% water and 2% cement were added. The evenly mixed samples were loaded into the mold in three layers, and the interface of each layer was shaved. Then, the samples were compacted and stored in a curing box for 28 days to make sure that the strength of the reshaped sample was close to that of the original SRM. Figure 4 shows a group of SRM samples.

           

The seepage tests for the SRM samples were conducted using a self-designed small-scale fluid–solid coupling test device, as illustrated in Figure 5. The test applied axial pressure through a hydraulic jack at the bottom, confining pressure via a special Hooke pressure chamber, and osmotic pressure using an externally controlled water pump, maintaining constant pressure.

           

3 EXPERIMENTS ON SRM SAMPLES UNDER DIFFERENT STRESS STATES

3.1 Variation law of the permeability coefficient of SRM samples under osmotic pressure

As Zhang (2003) described, the steady-state method was used for the SRM sample seepage tests. In these tests, the SRM sample was placed inside the Hooke pressure chamber; no confining pressure was applied, but lateral constraints were maintained. Osmotic pressures were applied at the sample's bottom at a loading rate of 0.01 MPa/step until the permeability coefficient reached its maximum; meanwhile, the sample's top was exposed to atmospheric conditions. The test commenced once the osmotic pressure at the inlet was stabilized. Distilled water was used to enhance the test's precision.

Darcy's law states that Equation (     1) can be applied to obtain the permeability coefficient     k of an SRM sample:

      $$𝑘=\frac{\mathit{QL}{𝛾}_{\mathrm{w}}}{𝛥\mathit{hA}},$$     (1)    

where     Q denotes the amount of water passing through the sample per unit time (m     3/s);     L is the height of the sample (m); ${𝛾}_{\mathrm{w}}$ is the weight of water (kN/m     3);     Δh is the difference in the water pressure between the two ends of the sample (MPa); and     A is the cross-sectional area of the sample (m     2).

Figure 6 shows the relationship between the permeability coefficient and osmotic pressure in SRM samples with different rock block percentages. The permeability coefficients of SRM samples with stone contents of 20%, 30%, 40%, 50%, 60%, and 70% reach their maximum value at osmotic pressures of 0.14, 0.14, 0.13, 0.11, 0.10, and 0.08 MPa, respectively.

               

As demonstrated in Figure 6, increasing osmotic pressure leads to an increase in the permeability coefficient in SRM samples with varying rock block percentages. In addition, as samples near their maximum permeability coefficient, the osmotic pressure gradually decreases as the proportion of rock blocks increases. For example, at a 20% rock block percentage and 0.14 MPa osmotic pressure, the permeability coefficient peaks at 12.936 × 10−6 cm/s. Conversely, at a 70% rock block percentage and 0.08 MPa osmotic pressure, it reaches a maximum of 6.986 × 10−6 cm/s. Therefore, the permeability coefficient of SRM samples is closely related to the stone content and osmotic stress.

3.2 Variation law of the permeability coefficient of SRM samples under osmotic–uniaxial pressure

In order to explore the variation in the permeability coefficient of SRM samples with different rock block percentages under osmotic–uniaxial pressure, a constant osmotic pressure of 0.08 MPa was applied, and the axial pressure loading rate was set at 0.02−0.03 kN/step. No confining pressure was applied, but lateral constraints were maintained. Figure 7 shows the axial stress–strain curves of SRM samples with different rock block percentages. It can be seen from the figure that the peak stresses of SRM samples with stone contents of 20%, 30%, 40%, 50%, 60%, and 70% are 0.168, 0.207, 0.244, 0.313, 0.362, and 0.457 MPa, respectively. Figure 8 depicts the variation curves of the permeability coefficient with the axial pressure (within peak stress) for SRM samples under osmotic–uniaxial pressure.

               

               

As indicated in Figure 8, before the sample reaches its peak stress, the permeability coefficient monotonously decreases with an increase in the axial pressure when the rock block percentage is below 40%. The permeability coefficient decreases until the axial pressure exceeds 0.2 MPa and then increases rapidly with increasing axial pressure when the rock block percentage surpasses 40%. This trend occurs because, at a low rock block percentage, the soil predominantly bears the stress in samples. However, as the rock block percentage increases, the rock begins to assume a more significant role. When the axial pressure is low, the soil becomes more compact, its porosity decreases, and its permeability coefficient diminishes; conversely, as the axial pressure increases, the sample fractures, leading to a rapid increase in the permeability coefficient.

In order to further understand the changes in the permeability coefficient of SRM samples under osmotic–uniaxial conditions, the evolution of the internal fracture structure and the overall cracking failure of SRM samples were studied using CT scanning. During stress loading, four axial pressures were selected for CT scans on an SRM sample with a 40% rock block percentage, specifically at 0.028, 0.089, 0.153, and 0.244 MPa. The scans were conducted using the nanoVoxel-4000 system's three-dimensional X-ray microscope. The system's parameters are listed in Table 1.

Table 1. Main parameters of the computed tomography scanning equipment.

Voltage (kV)	Electric current (μA)	Exposure time (s)	Magnification	Spatial resolution (mm)	Frame number
150	150	0.8	4.6	0.127	1440

Five layers (I, II, III, IV, and V) with an interval of 20 mm in the SRM samples were selected for analyzing the CT images, and the sectional model is shown in Figure 9.

               

Figure 10 illustrates the CT scan results of SRM samples with a 40% rock block percentage under four axial stresses. As can be seen from the figure, under low axial pressure, the microcracks and pores in the soil are closed due to pressure, thus enhancing the sample's shear strength and reducing its permeability coefficient. As the axial pressure increases, cracks initially form at the soil–rock interface and then gradually propagate around the soil boundary. This phenomenon results from the differing deformation moduli of rock and soil and the dislocation sliding at the soil–rock interface. When the sample reaches its peak strength, numerous cracks are formed internally. Without confining pressure, the internal stones continue to move outward, showing significant expansion and severe deformation, particularly in the middle of the sample. The failure progresses from local to complete, entering the cracking failure stage, and the emergence of large cracks leads to a sharp increase in the samples' permeability coefficients. Thus, during loading, the SRM sample's permeability coefficient decreases and increases with an increase in the axial pressure.

               

3.3 Variation law of the permeability coefficient of SRM samples under osmotic–triaxial pressure

The SRM samples were subjected to osmotic–triaxial pressure tests under three confining pressure conditions (0.10, 0.14, and 0.18 MPa), with osmotic pressure maintained at 0.08 MPa and axial pressure controlled by displacement. The stress–strain curves of SRM samples with different rock block percentages under osmotic–triaxial pressure are shown in Figure 11. The strain of SRM was maintained within 12% to ensure test result accuracy. Figure 12 shows the variation in the permeability coefficient of SRM samples with 20% and 40% rock block percentages under osmotic–triaxial pressure.

               

               

Figure 12 illustrates that (1) Under three types of confining pressures, the permeability coefficient of SRM samples generally decreases as the axial pressure increases. (2) In the initial loading phase, the permeability coefficient of SRM samples decreases with an increase in the confining pressure, and its variation range gradually narrows under identical axial pressure as the confining pressure increases. (3) The permeability coefficient of the samples does not undergo an order of magnitude change with the increase in axial and confining pressures, mainly because most pores in the samples are compacted before testing, decreasing the external load's impact on the permeability coefficient.

4 RESEARCH ON THE RELATIONSHIP BETWEEN THE PERMEABILITY COEFFICIENT AND STRESS STATES OF SRM SAMPLES

4.1 Relationship between the permeability coefficient and osmotic pressure of SRM samples

Five samples with 20%–70% stone contents were selected for seepage tests under the condition of only changing osmotic pressure in order to mitigate the effects of variables such as the shape and distribution of rocks in SRM samples on the experimental outcomes. The correlation between the permeability coefficient and osmotic pressure in SRM with varying rock block percentages can be represented by the power function in the below equation.

      $$𝑘={𝑘}_0+𝑎{𝑝}_{\mathrm{w}}^{𝑏},$$     (2)    

where     k     0 is the initial permeability coefficient (cm/s);     p     w represents the osmotic pressure (MPa); and     a and     b are fitting parameters.

Figure 13 presents the correlation between the permeability coefficient and osmotic pressure in SRM samples with diverse rock block percentages. All SRM samples show permeability coefficient and osmotic pressure relationship curves with fitting percentages exceeding 93%.

               

4.2 Relationship between the permeability coefficient and axial pressure of SRM samples

The relationship between the permeability coefficient and axial pressure of SRM samples can be fitted non-linearly, which can be expressed by the exponential function

      $$𝑘={𝑘}_0{\mathrm{e}}^{-𝑎𝜎},$$     (3)    

where $𝜎$ is the axial stress (MPa).

The fitting results for the relationship between the permeability coefficient and axial pressure in SRM samples with various rock block percentages are depicted in Figure 14, showing a fitting accuracy exceeding 88%.

               

5 INFLUENCE OF ROCK BLOCK PERCENTAGE ON THE PERMEABILITY COEFFICIENT OF SRM SAMPLES

5.1 Variation law of the permeability coefficient with rock block percentage

Figure 15 illustrates the relationship between the SRM samples' permeability coefficient and rock block percentage under different osmotic and axial pressure levels.

               

It can be observed that (1) As the rock block percentage increases, the permeability coefficient of SRM samples initially decreases, and then increases up to its minimum at a 40% rock block percentage under different stress conditions. This occurs because the soil's dominance in the sample results in reduced internal porosity, and the presence of rock blocks obstruct the soil's seepage channels, thereby decreasing the permeability coefficient when the rock block percentage lies between 20% and 40%. When the rock block proportion exceeds 40%, the primary seepage channels, now surrounded by blocks, increase the porosity, creating a larger seepage slope at the soil–rock interface. This in turn leads to a rapid increase in the permeability coefficient. (2) The variation in the permeability coefficient of SRM samples gradually increases with an increase in osmotic pressure. For example, the difference in the permeability coefficient between SRM samples with 20% and 40% rock block percentages is 0.225 × 10−6 cm/s at an osmotic pressure of 0.03 MPa, compared to 4.795 × 10−6 cm/s at 0.13 MPa. (3) With an increase in axial pressure, the permeability coefficient of SRM samples with varying rock block percentages decreases, and so does the disparity in permeability coefficients, due to the samples becoming denser and less porous under axial pressure.

5.2 Sensitivity analysis of the permeability coefficient to stone content

The sensitivity coefficient     c     k was defined by Wang et al. (     2018). It reflects the sensitivity of the permeability coefficient of the SRM samples to the change in stone contents. The larger the value, the stronger the sensitivity.

      $${𝑐}_{\mathrm{k}}=\frac{\mathrm{\Delta }𝑘}{{𝑘}_{20}\mathrm{\Delta }𝑝},$$     (4)    

where     k     20 denotes the permeability coefficient of SRM samples with a stone content of 20% (cm/s); Δ     k is the absolute value of the difference between the permeability coefficient and     k     20 (cm/s); and Δ     p is the difference between the stone content and 20% (%).

Figures 16 and 17 demonstrate the sensitivity coefficient of SRM samples to changes in rock block percentage under various osmotic pressures, confining pressures, and axial pressures.

               

               

As can be observed, (1) Under solely osmotic pressure, the sensitivity coefficient remains small when this pressure is less than 0.05 MPa. This occurs because, in conventional water pressure tests, there is typically no damage or hydraulic fracturing in the SRM samples, and the water within the cracks shows laminar flow, conforming to Darcy's law. Consequently, its permeability coefficient can be regarded as constant. However, as the osmotic pressure exceeds 0.05 MPa, the water flow in the cracks becomes turbulent, adhering to the non-Darcy law. (2) The sensitivity coefficient initially increases and then decreases with the increase in stone content under both osmotic and osmotic–uniaxial pressures. The sensitivity is pronounced when the rock block percentage lies between 30% and 40%, whereas it falls below 1.0 for percentages between 50% and 70%. This trend occurs because, beyond a 50% rock block percentage, the rock skeleton in the SRM becomes more apparent, and additional cracks form at the soil–rock interface under pressure. Without confining pressure, the SRM sample fractures and expands under stress, resulting in a high permeability coefficient at this stage. Nonetheless, a further increase in rock block percentage marginally affects the sensitivity of the permeability coefficient's variation in the sample. (3) The sample shows poor sensitivity when the rock block percentage is below 40%, reaching its first peak at 40% under osmotic–triaxial pressure. The sample undergoes a transition from soil-dominated to rock-dominated at rock block percentages of 40%–60%. During this phase, minor changes in rock block percentage lead to significant alterations in the samples' porosity, hence a large sensitivity coefficient, reaching its second peak at 60%. Beyond 60%, variations in rock block content minimally impact the sample's porosity, leading to a reduced sensitivity coefficient.

6 CONCLUSION

In this study, the seepage characteristics of SRM in Sanshandao Gold Mine fault zones under three stress conditions were studied by field sampling and laboratory remodeling. The effects of rock block percentages and stress states on the permeability coefficient of SRM samples were mainly analyzed, and the samples' crack development and deformation were revealed by CT scanning to further substantiate the observed fluctuation in the SRM sample's permeability coefficients.

The permeability coefficient of SRM samples is minimal under all stress states at a 40% rock block percentage. The relationship between the permeability coefficient and osmotic pressure of SRM samples can be modeled by a power function $𝑘={𝑘}_0+𝑎{𝑝}_{\mathrm{w}}^{𝑏}$ . Similarly, the relationship between the permeability coefficient and axial pressure can be represented by an exponential function $𝑘={𝑘}_0{\mathrm{e}}^{-𝑎𝜎}.$

Under both osmotic and osmotic–uniaxial pressures, the sensitivity coefficient initially increases and then decreases with an increase of rock block percentages. The sensitivity is more pronounced when the rock block percentage is between 30% and 40%, and yet, it decreases below 1.0 when this percentage exceeds 50%. Two sensitivity coefficient peaks are observed at 40% and 60% rock block percentages under osmotic–triaxial pressure.

As the samples used in this study are remolded, their structures and natural states have changed. In this case, the research results will be slightly different from the actual seepage situation of the SRM in the fault zones. However, the variation regularity of the permeability coefficient is applicable to practical engineering, and the influence of rock block percentages and stress states on the permeability coefficient and the sensitivity coefficient of SRM can still provide references for engineering.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.