The Permeability Evolution of Sandstones with Different Pore Structures under High Confining Pressures, High Pore Water Pressures and High Temperatures

Abstract

Seepage from the pores of sandstone exposed in deep mines is difficult to block by grouting. In this paper, the permeability evolution of four subcategories of sandstone with different pore structures under different confining pressures, pore water pressures and temperatures is analyzed by experiments. (1) With increasing confining pressure, the permeabilities of the four tested subcategories of sandstone all decrease, but at different rates and to different extents. (2) With increasing pore water pressure, the permeability of subcategory I₁, I₂ and II₁ sandstones increases linearly, while that of subcategory II₂ sandstone decreases following a power function under low confining pressures and tends to be stable under high confining pressures. (3) With increasing temperature, the permeabilities of the four sandstone subcategories decrease at different rates. (4) The orthogonal experimental results show that the confining pressure has the greatest influence on the permeability, followed by the water pressure and temperature. (5) The confining pressure, pore water pressure and temperature produce stress-strain in sandstone and thus change the sandstone pore structure and permeability. The permeability evolution of sandstones varies with pore structure. The findings of this study can inform the classified grouting of deep sandstone and optimize grouting parameters.

1. Introduction

At present, water-bearing fractures and Quaternary sand are the most studied sources of water seepage in the field of groundwater prevention and control. Because the hydraulic conductivity of fractures is better than that of pores, the prevention and control of fracture water in rock has attracted considerable attention from many scholars [1,2,3,4]. Quaternary sandy soil has a loose structure and abundant pore water, which is a primary concern for hydrogeology and civil engineering projects [5,6,7,8]. However, in the past 20 years, an increasing number of deep projects, including deep coal mining, deep tunnel construction, deep oil and gas storage, and deep nuclear waste storage, have been constructed [9,10,11,12], and the mining conditions in deep areas are different from those in shallow areas, with “three-high” characteristics (“three-high” refers to a high confining pressure, high water pressure and high temperature; in this paper, water pressure refers to the pore water pressure) [13]. Accordingly, many new problems that have an impact on engineering projects have emerged, such as the problem of pore water seepage from deep sandstone.

As cemented sandstones generally have a low-to-medium permeability (0.1–500 mD), with a small amount of pore water seepage and little impact on shallow engineering projects, few researchers have studied the influence of pore seepage of cemented sandstones on shallow engineering projects. However, the situation is quite different for deep engineering projects. For example, most of the strata that are crossed by deep mining shafts are sedimentary sandstones with abundant water and developed pores [14]. Water seepage and gushing from sandstone often occur in shaft construction. Years of experience in grouting sandstone aquifers to plug water seepage in deep mining shafts have shown that even when cementing and chemical grouting are carried out in the rock mass behind the wall and the main water inflow channels (fractures) in the rock mass are effectively blocked, residual water can still seep through sandstone pores in the shaft wall. This seepage cannot be ignored, because the total water leakage exceeds the upper limit of the accepted specification (≤10 m³/h) [15,16]. The difficulty of grouting porous sandstone has become a bottleneck that restricts the rapid excavation and normal handover of shafts [14,17]. At present, pore seepage influences the production of deep shafts in many coal mines, such as some deep coal mines in the Ordos, Ningdong, Longdong and Binchang mining areas [14] and the Tangkou, Anju, Huafeng and Xiezhuang coal mines in the Southwest Shandong coalfield [18,19]. There are two main reasons for the above phenomenon: first, the deep environment is characterized by “three-high” characteristics; second, some types of sandstone pore structures can allow large-area pore seepage under these “three-high” conditions, resulting in a significant increase in the seepage flow rate, which can become fast enough to affect normal production. Therefore, the study of the permeability evolution of deep sandstones with different pore structures under the “three-high” conditions is urgent for improving the production of many deep coal mines.

To date, some researchers have studied the influence of the “three-high” factors on rock pore permeability from a theoretical perspective. Somerton (1965) conducted heating tests on a large number of sandstone cores at 400–800 °C and found that the permeability of broken cores increased by 50% [20]. Brace (1968) conducted a permeability test on granite under high pressure and found that the pore permeability of granite decreased with increasing effective confining pressure (the difference between the confining pressure and pore pressure) [21]. Heard (1982) heated Adamellite to 300 °C under different confining pressures, which made the rock fracture and its permeability increase several times [22]. Li et al. (1994) studied the permeability of Yinzhuang sandstone in the full stress-strain relationship-testing process and analyzed the relationship between the permeability and the full stress-strain evolution of this rock [23]. Jiang et al. (2014) studied the influence of water pressure on the time-dependent deformation of surrounding rock in the process of deep rock mass excavation under high stress by performing triaxial creep tests of deep sandstone from Chongqing and found that water pressure can enhance the performance of rock creep deformation [24]. Ding et al. (2019) studied the variation in sandstone permeability in the loading-unloading process of confining pressure [25]. Mohammed, S.B. and Mohammed, M.A. (2009) carried out research on the variation in the permeability of carbonate rocks and found that the permeability began to decrease when the temperature increased from 25 °C to 50 °C; the permeability decreased by approximately 59% when the temperature decreased from 100 °C to 50 °C and the confining pressure from 28 MPa to 5 MPa [26]. Zhang et al. (2020) found that the increase and decrease in the seepage flow discharge and permeability were consistent with the damage evolution trend under high temperatures and high confining pressures through an experimental study on the permeability characteristics of low-permeability Yunnan red sandstone [27].

The above studies mainly focused on the relationship between sandstone pore permeability and the development process of rock fracture and mostly on ultralow-permeability rock, such as marble, granite and tight sandstone. Although these studies systematically analyzed the effects of high temperatures and high confining pressures on rock permeability and other physical properties, the test conditions were extreme; for example, the test temperatures were mostly 100–800 °C, and the effective stress was more than 80 MPa (sample fracture occurs). The “three-high” conditions (high confining pressure, high water pressure, high temperature) are quite different from those that are encountered in deep coal mines at present or that will be countered in the next 20 years.

This study focuses on the problem of sandstone pore water seepage that affects coal mining in deep coal mines at present or within the next 20 years. The research aims to solve the engineering problems concerning the realistic “three-high” conditions of deep coal mines, namely, confining pressures of 1–40 MPa, water pressures of 1–12 MPa, and temperatures of 25–65 °C. This study considers the permeability differences of sandstones with different pore structures under the actual “three-high” conditions of deep coal mines. The aim of this study is to explore a classified permeation grouting method and optimize grouting parameters for permeation grouting in deep-mine sandstone.

2. Samples and Methods

2.1. Structural Logistics Scheme of This Study

In this paper, taking the deep-mine sandstones from the Southwest Shandong coalfield where “large-area sweating” seepage once occurred as an example, a large number of sandstone samples with different pore structures were collected. First, all the samples were classified according to their differences in pore structure by analyzing various types of data, such as casting thin slice observations, scanning electron microscopy (SEM) results, mercury injection capillary pressure (MICP) test results and grain size analysis results. Then, with a Top Rock 600-50-VHT multifield coupling tester, a single-factor test and orthogonal test were used to study the permeability evolution of these deep-mine sandstones with different pore structures under “three-high” conditions. An overview of the flow of this study is shown in Figure 1.

2.2. Sample Collection

All deep-mine sandstone samples in this study were collected from the typical sections with three layers of sandstone aquifers in the deep coal mines in the Southwest Shandong coalfield, where “large-area sweating” seepage once occurred. The three most widespread layers of sandstone aquifers are Permian Shanxi Formation sandstone, Permian Shihezi Formation sandstone and Jurassic sandstone, which are widely distributed in the Southwest Shandong coalfield and have an important impact on coal mining [28]. Microscopic observation showed that most of the sandstone samples were fine sandstones composed of clastic particles (88%–95%), cement (calcite 1%–7% and silicate 3%–6%) and matrix (5%–12%). The clastic particles were mainly composed of quartz, feldspar and various rock fragments; the filler was mainly composed of clay matrix, calcite and other cements. All the deep-mine sandstone samples had different numbers of pores and could be regarded as porous media.

2.3. Sample Classification

To determine the pore structures of these sandstones and classify them by their permeability, all the sandstone samples were transported to a laboratory without disturbance and processed to undergo the four types of laboratory tests before the formal seepage experiment.

(a)

The first type of test was to obtain the porosity and permeability with STY-2 gas permeability and porosity meters. Standard plunger rock samples with a diameter of 25.4 mm and heights of 25.4–50.8 mm were made by nondestructive wire cutting for porosity and permeability tests (see Figure 2).

(b)

The second type of test was used to test the pore throat size of the sandstone with a MAP 9500 mercury porosimeter. Samples with heights of 7.0–12.0 mm and a diameter of 25.4 mm were prepared for mercury injection testing (see Figure 2).

(c)

The third type of test was used to observe the composition and texture of grains and pore structure of sandstone by a Zeiss Imaging 2 M polarizing microscope and Nova Nano SEM450. Casting thin slices were used for polarizing microscope observation, and samples with a height of 6.0 mm and diameter of 4.0 mm were used for SEM observation (see Figure 2).

(d)

The fourth type of test was used to analyze the sandstone grain size with a Mastersizer 3000 E laser grain size analyzer. The samples were processed by crushing, grinding, removing cement with hydrochloric acid and drying before grain size analysis (see Figure 2).

Some important test results reflecting the pore structure and permeability of deep-mine sandstone samples are listed in

Table 1. The permeability, porosity, average pore throat radius and sorting coefficient results of the sandstone samples.

Sample No	K (mD)	Փ (%)	Rave. (µm)	So (%)
Z1	102.1700	21.16	4.568	0.72
Z23	94.0540	20.36	4.93	0.79
Z38	70.9000	20.38	3.814	0.76
Z29	49.6370	21.16	4.116	0.78
Z27	43.8370	20.26	3.797	0.85
Z24	10.6520	17.82	3.623	1.05
Z31	7.6076	18.25	2.517	1.09
Z12	5.6690	17.50	1.128	1.11
Z9	5.5626	17.58	2.324	1.16
Z30	3.9094	17.10	1.642	1.21
Z25	2.7078	16.49	1.531	1.19
Z32	2.3820	16.66	1.423	1.20
Z46	2.1500	18.56	1.321	1.26
Z11	1.6010	13.10	1.296	1.35
Z41	0.8980	16.83	0.789	1.25
Z42	0.7270	16.62	0.756	1.25
Z13	0.7020	15.30	0.738	1.23
X9-1	0.6713	9.88	0.622	1.51
A0	0.4220	12.00	0.588	1.55
X3	0.3033	9.33	0.424	1.53
A4	0.2197	10.67	0.344	1.52
A1	0.2117	9.33	0.4	1.56
T8	0.0751	9.27	0.331	1.53
S12	0.0594	9.44	0.175	1.60
S18	0.0527	9.23	0.167	1.56
S22	0.0474	9.37	0.153	1.52
A5	0.0462	8.63	0.342	1.63
S16	0.0323	10.11	0.151	1.53
S10	0.0277	8.18	0.149	1.57
S11	0.0276	7.73	0.146	1.56
S17	0.0259	8.89	0.143	1.47
S19	0.0255	7.17	0.139	1.54
S15	0.0220	6.43	0.137	1.85
S20	0.0208	6.78	0.129	1.86
T4	0.0162	5.27	0.128	2.65
T3	0.0135	7.18	0.095	2.03
T13	0.0110	5.88	0.104	1.88
T2	0.0096	4.37	0.102	1.96
T21	0.0070	6.45	0.078	1.83
A9	0.0051	3.02	0.044	1.83
A7	0.0049	2.84	0.049	1.97
H11	0.0037	5.29	0.051	1.93
H6-2	0.0010	2.21	0.048	1.96

K—permeability (mD); Փ—porosity (%); R_ave.—average pore throat radius (µm); S_o—sorting coefficient (%).

.

Based on the four recognized indicators that can reflect pore permeability, namely permeability, porosity, average pore throat radius and sorting coefficient, k-means clustering analysis was conducted for all samples. The results showed that the sandstone samples could be divided into four subcategories (I₁, I₂, II₁ and II₂), which belonged to two categories (I and II), as shown in

Table 2. Classification of the pore structure of the deep-mine sandstone.

Classification Indicators	Category I		Category II
	I1	I2	II1	II2
K (mD)	>40	0.7–40	0.025–0.7	<0.025
Փ (%)	>20	15–20	7–15	<7
Rave. (µm)	>3.7	0.7–3.7	0.138–0.7	<0.138
So	<1.00	1.00–1.40	1.40–1.60	>1.60

. The characteristics of the four subcategories of sandstone in terms of the optical microscope, SEM and MICP test results are shown in Figure 3, Figure 4 and Figure 5, respectively.

2.4. Experimental Device

A Rock 600-50-VHT multifield coupling tester was used in this study (see Figure 6). Deep-mine sandstone with different pore structures was put into the device for the permeability test.

The testing device consisted of a control system, a confining pressure system, a water seepage system, a temperature system and various special high-precision sensors (pressure, flow, temperature). The maximum confining pressure that could be applied was 60 MPa, the maximum seepage pressure of the inlet was 60 MPa, the maximum returned pressure of the outlet was 50 MPa and the controlling accuracy of the pressure was ±0.01 MPa. The load, hoop strain, fluid pressure and flow value could be recorded in real time. The load curve and the relationship curve of pore fluid pressure/flow time could be drawn synchronously. The package of the rock sample and the sensor layout are shown in Figure 7.

2.5. Experimental Principle

To obtain the permeation evolution of deep-mine sandstones with different pore structures under the “three-high” conditions over the next 20 years, the present study selected water as the seepage medium for the experiment, and the ranges of the experimental parameters were as follows: confining pressure 1–40 MPa, water pressure 1–12 MPa and temperature 25–65 °C. According to the existing research results, the stress-strain changes of all the experimental samples remained in the stage of elastic deformation under the above test conditions, and the sandstone pore seepage conformed to Darcy’s law [29]. The following assumptions were made in the present experiment [30]:

(a)

The seepage medium was groundwater, which was regarded as an incompressible fluid.

(b)

The seepage was regarded as continuous and steady under a constant pressure.

(c)

The pore distribution of sandstone was relatively uniform, so sandstone could be regarded as a porous medium.

(d)

Under the “three-high” conditions, the seepage was stable and slow, which conformed to Darcy’s law.

Therefore, the steady state method was used to measure the permeability of deep-mine sandstone in the present experiment. The permeability calculation formula of the tested sandstone sample is shown in Formula (1) [31]:

$$K_i=\frac{\mu L\Delta Q_i}{A\Delta P\Delta t_i}$$

(1)

where K_i is the average permeability of the sample within time duration Δt_i (m²); μ is the viscosity coefficient of the fluid (Pa·s); Δt_i is the interval time between recording points (s); ΔQ_i is the volume of water flowing through the sandstone sample within time duration Δt_i (m³); L is the seepage length of the water flow, namely, the height of the sandstone sample (m); A is the cross-sectional area of the sandstone sample (m²); and ΔP is the seepage pressure difference between the upstream and downstream ends of the sample, namely, ΔP = P₃–P₄, where P₃ and P₄ are the seepage pressures of the upstream and downstream ends, respectively (Pa).

2.6. Experimental Methods and Procedures

The maximum temperature of the experiment was 65 °C. As the saturated vapor pressure of the water increased with the temperature, the saturated vapor pressure of the water was 0.025 MPa at 65 °C, the minimum confining pressure in the sample pressure chamber remained above 1 MPa, and the minimum water pressure upstream and downstream of the seepage was set to 0.1 MPa to prevent the saturated water in the sandstone sample from escaping due to the temperature rise and ensure that the test was not disturbed by the vapor pressure. All sandstone samples were vacuumed and immersed in water with the same ionic concentration as the original strata for 48 hours before the test to simulate the real saturation state of the deep-mine sandstone and ensure that the seepage in the sandstone samples during the test was a single-phase flow of water. After preparation, single-factor tests and orthogonal tests were conducted on sandstones with different pore structures under different levels of confining pressure, water pressure and temperature according to the seepage test design scheme (

Table 3. The experimental scheme for investigating the seepage of the deep-mine sandstone.

The Focus	The Experimental Scheme
Influence of confining pressure (single-factor analysis)	Fix the temperature at 25 °C, the water pressure of the inlet at 1.3 MPa or 6 MPa, and the water pressure of the outlet at 1 MPa; observe the variation in the permeability of sandstones with different pore structures when the confining pressure is 1.5, 5, 10, 15, 20, 30 and 40 MPa.
Influence of water pressure (single-factor analysis)	Fix the temperature at 25 °C and the confining pressure at 20 MPa, 30 MPa and 40 MPa; observe the variation in the permeability of sandstones with different pore structures when the water pressure of the outlet is 1 MPa and the water pressure of the inlet is 2, 4, 6, 8, 10 and 12 MPa.
Influence of temperature (single-factor analysis)	Fix the confining pressure at 20 MPa, the water pressure of the inlet at 6 MPa, and the water pressure of the outlet at 1 MPa; observe the variation in the permeability of sandstones with different pore structures when the temperature is 25 °C, 35 °C, 45 °C, 55 °C and 65 °C.
Coupled influence of three factors: confining pressure, water pressure and temperature (three-factors analysis)	As per the L9 (3 × 3) orthogonal table, design a orthogonal test with 3 factors and 3 levels to analyze the permeability evolution of deep-mine sandstones with different pore structures under the coupled action of a high confining pressure, high water pressure and high temperature

). The test procedures were as follows:

2.6.1. Initial Parameters Setup

The saturated samples of sandstone with different pore structures were placed into the rock sample holder of the Rock 600-50-VHT multifield coupling tester. The confining pressure was applied at a rate of 0.1 MPa/min until the minimum confining pressure was 1 MPa, and σ1 = σ2 = σ3 was realized with the mechanical self-balancing system of the device. The thermostat was heated to a minimum temperature of 25 °C with the heating system, and the temperature was maintained at a predetermined temperature level in real time by the temperature control system. The seepage pressure P₃ at the lower end of the sandstone sample and the seepage pressure P₄ at the upper end of the rock sample were increased to the minimum water pressure of 0.1 MPa.

2.6.2. Permeability Test of Sandstones with Different Pore Structures under the Sole Influence of Confining Pressure

Because the confining pressure should always be greater than the water pressure during this test, this test is divided into a low confining pressure stage and a high confining pressure stage to prevent seepage around the sample. In the low confining pressure stage, first, the water pressure of the inlet (P₃) was increased to 1.3 MPa, and the water pressure of the outlet (P₄) was 1 MPa. Next, keeping the water pressure stable at both ends, the sandstone permeability was measured under a confining pressure of 1.5 MPa and 5 MPa, respectively. In the high confining pressure stage, first, the water pressure of the inlet (P₃) was increased to 6 MPa. Then, keeping the water pressure stable at both ends, the sandstone permeability was measured under confining pressures of 10 MPa, 15 MPa, 20 MPa, 30 MPa and 40 MPa. After the test of the first sample was completed, the next sample was placed and the above steps were repeated until all samples were tested.

2.6.3. Permeability Test of Sandstones with Different Pore Structures under the Sole Influence of Water Pressure

Because the influence of water pressure on sandstone seepage varies under different confining pressures according to previous research results [25], this test was carried out in three groups under three different confining pressures of 20 MPa, 30 MPa and 40 MPa to ensure the accuracy of the test results. In the first group of tests, first, the confining pressure was fixed at 20 MPa, the water pressure of the outlet (P₄) was fixed at 1 MPa, and the water pressure of the inlet (P₃) was set at 2 MPa; the sandstone permeability was measured at a water pressure difference of 1 MPa. Then, the water pressure of the inlet (P₃) was increased to 4, 6, 8, 10 and 12 MPa, and the permeability of the sandstone sample was measured under water pressure differences of 3, 5, 7, 9, and 11 MPa. After the first group of tests was completed, the confining pressure was increased to 30 MPa and 40 MPa, and the above steps were repeated to measure the variations in the permeability in the sandstone samples with different water pressures under the confining pressures of 30 MPa and 40 MPa respectively. After the test of the first sample was completed, the next sample was placed, and the above steps were repeated until all samples were tested. The flow chart of this test is shown in Figure 8.

2.6.4. Permeability Test of Sandstones with Different Pore Structures under the Sole Influence of Temperature

The operation process was as follows: First, the confining pressure was fixed at 20 MPa, the water pressure of the inlet (P₃) was fixed at 6 MPa, and the water pressure of the outlet (P₄) was fixed at 1 MPa; the sandstone permeability was measured at 25 °C. Then, the temperature was increased to 35 °C, 45 °C, 55 °C and 65 °C, and the permeability of the sandstone sample under each temperature gradient was measured in turn. After the test of the first sample was completed, the next sample was placed, and the above steps were repeated until all samples were tested.

2.6.5. Permeability Test of Sandstones with Different Pore Structures under the Coupled Action of High Confining Pressure, High Water Pressure and High Temperature

There exists a very complex interaction between high confining pressure, high water pressure and high temperature [32,33]. In this paper, as per the L9 (3 × 3) orthogonal table, an orthogonal test with 3 factors and 3 levels (see

Table 4. Three factors and three levels of the orthogonal test.

Factors	Confining Pressure (MPa)	Water Pressure (MPa)	Temperature (°C)
Level 1	7	2	25
Level 2	10	4	35
Level 3	20	6	45

) was designed to analyze the permeability evolution of I₂ and II₂ sandstones to further study the permeability evolution of sandstone with different pore structures under the coupled action of high confining pressures, high water pressures and high temperatures and to verify the conclusions of the above single-factor test.

3. Results

3.1. The Results of the Single-Factor Test for Sandstones with Different Pore Structures

3.1.1. Influence of Confining Pressure on Permeability Evolution

The variation in the permeability of four subcategories of sandstone with different confining pressures was calculated according to the stable seepage flow measured during the permeability testing of the four subcategories of sandstone under the sole influence of confining pressure. See Figure 9 for the test results.

The test results revealed that the permeability of the four subcategories of sandstone showed a nonlinear decline with increasing confining pressure. The permeability rapidly decreased in the low confining pressure range of 0–10 MPa; for example, when the confining pressure increased from 1.5 MPa to 10 MPa, the permeability of the four subcategories of sandstone decreased by 39.65%–75.90%. As the confining pressure continued to increase, the permeability changed less and less.

However, the four subcategories of sandstone also had some differences in permeability evolution. The permeability ratio (k′/K) can reflect these differences, so the concept of the permeability ratio was introduced to reveal the difference in the permeability evolution of sandstones with different pore structures under the sole influence of confining pressure in this paper. Because the permeability ratio can reflect the speed of permeability variation and quantitatively reflect a small difference between the same variation trends, many scholars use the permeability ratio to reflect the extent of variation in sandstone permeability [31]. In this paper, the permeability ratio reflected the decreasing difference between sandstones with different pore structures as the confining pressure increased. Here, the permeability value of each sandstone sample obtained under a confining pressure of 1.5 MPa was taken as the reference point, and the ratio of the permeability measured under other confining pressures and the permeability of the reference point was defined as the permeability ratio (K′/K) of the sandstone sample. Thus, the variation in the permeability ratio (K′/K) of each of the four subcategories of sandstone with confining pressure was obtained and is shown in Figure 10. Figure 10 shows that the permeability ratios (K′/K) of the four subcategories of sandstone decreased at different rates and within different ranges, and the rates of decrease gradually increased from subcategory I₁ to I₂ to II₁ to II₂.

3.1.2. Influence of Water Pressure on Permeability Evolution

The sole influence of water pressure on pore permeability was studied under three levels of confining pressure: 20 MPa, 30 MPa and 40 MPa. Under each level of confining pressure, the variation in sandstone permeability with different water pressures was calculated according to the seepage flow rate of the four subcategories of sandstone measured by the corresponding pore seepage test. The test results are shown in Figure 11.

The test results show that under the three levels of confining pressure, the permeabilities of the four subcategories of sandstone vary with the water pressure difference, but the variation trends are different. The difference is shown in the following two aspects:

(a)

The permeabilities of subcategory I₁, I₂ and II₁ sandstones increase linearly with increasing water pressure (see Figure 11a–c), but the rate of increase in the permeability gradually slows (the slope of the straight line gradually decreases) from subcategory I₁ to I₂ to II₁ (see

Table 5. Functional relationships between permeability and water pressure under different confining pressures.

Sandstone Subcategories	Fitting Curves of Permeability Vary with Water Pressures
	Confining Pressure (20 MPa)	Confining Pressure (30 MPa)	Confining Pressure (40 MPa)
Ι1	y = 25.774 + 4.281x R2 = 0.998	y = 24.108 + 3.590x R2 = 0.999	y = 22.168 + 3.176x R2 = 0.986
Ι2	y = 0.080 + 0.028x R2 = 0.998	y = 0.087 + 0.021x R2 = 0.993	y = 0.069 + 0.019x R2 = 0.998
II1	y = 0.130 + 0.004x R2 = 0.996	y = 0.123 + 0.003x R2 = 0.996	y = 0.118 + 0.002x R2 = 0.996
II2	y = 0.035x−0.522 R2 = 0.98	y = 0.004 + 0.001x −9.54 × 10−5 x2 + 4.588 × 10−6 x3 R2 = 0.969	y = 0.001 + 0.001x + 9.29 × 10−6 x3 R2 = 0.992

The independent variable x is water pressure, and the dependent variable y is permeability in the above table.

);

(b)

Under different confining pressure levels, the variations in the permeability of subcategory II₂ sandstone are different, and the permeability varies greatly and decreases as a power function under a low confining pressure (20 MPa), but the variation is small or basically stable under a high confining pressure (over 30 MPa) (see Figure 11d and Table 5).

3.1.3. Influence of Temperature on Permeability Evolution

The variations in the permeability of the four subcategories of sandstone under different temperatures can be calculated according to the stable seepage flow measured by the permeability test of the four subcategories of sandstone under the sole influence of temperature. The test results are shown in Figure 12.

The test results show that the permeabilities of the four subcategories of sandstone decreased with increasing temperature, but the variation trends were different. With increasing temperature, the permeability of subcategory I₁ sandstone decreased linearly and slowly; the permeability of subcategory I₂ and II₁ sandstones decreased as a cubic curve (decreasing slowly at the beginning, but the deceleration increased significantly when the temperature was higher than 45 °C) (see Figure 12a–c); the permeability of subcategory II₂ sandstone decreased almost as a power function (decreasing rapidly at the beginning, but the deceleration slowed significantly or with little change when the temperature was higher than 45 °C) (see Figure 12d).

3.2. Results of the Orthogonal Test of Sandstone with Different Pore Structures

The results of the orthogonal test of subcategory I₂ and II₂ sandstones are shown in

Table 6. Analysis of orthogonal test results for subcategory Ι₂ sandstone.

Numbers	Confining Pressures (MPa)	Water Pressures (MPa)	Temperature (°C)	K (mD)
1	7	2	25	0.078035
2	10	6	25	0.091888
3	20	4	25	0.062407
4	7	4	35	0.143773
5	10	2	35	0.042103
6	20	6	35	0.020217
7	20	2	45	0.055881
8	10	4	45	0.076364
9	7	6	45	0.067883
Ι	0.289691403	0.176019915	0.232330126	0.63855 (Sum)
II	0.210354872	0.282543283	0.206092635
III	0.138504721	0.179987797	0.200128234
Range value (R)	0.151186682	0.106523368	0.032201892
Range ranking	Maximum	Minimum	Median

Ι—sum of the permeability values of three tests for level 1; II—sum of the permeability values of three tests for level 2; III—sum of the permeability values of three tests for level 3; R—difference between the maximum and minimum values in I–III.

, Figure 12,

Table 7. Analysis of orthogonal test results for subcategory II₂ sandstone.

Numbers	Confining Pressures (MPa)	Water Pressures (MPa)	Temperature (°C)	K (mD)
1	7	2	25	0.00507091
2	7	4	35	0.001247929
3	7	5	45	0.000760487
4	10	2	35	0.000201238
5	10	4	45	0.000405782
6	10	6	25	0.001479715
7	20	2	45	0.000078181
8	20	4	25	0.000195153
9	20	6	35	0.000815077
Ι	0.007079326	0.005350329	0.006745779	0.015755802 (Sum)
II	0.002086735	0.001848864	0.002264244
III	0.001088411	0.003055279	0.00124445
Range value (R)	0.005990915	0.003501465	0.005501329
Range ranking	Maximum	Minimum	Median

Ι—sum of the permeability values of three tests for level 1; II—sum of the permeability values of three tests for level 2; III—sum of the permeability values of three tests for level 3; R—difference between the maximum and minimum values in I–III.

and Figure 13.

The range ranking in Table 6 shows that the R value of the confining pressure was the largest and that the R value of the temperature was the smallest, indicating that the confining pressure had the largest impact on the seepage of subcategory I₂ sandstone, followed by the water pressure and the temperature.

Figure 13 shows the comparison of the sums of the resulting permeabilities of three levels of confining pressure, water pressure and temperature. Figure 13 shows that the permeability of subcategory I₂ sandstone decreased with increasing confining pressure, slowly decreased with increasing temperature, and first increased and then decreased with increasing water pressure difference.

The range ranking in Table 7 shows that the R value of the confining pressure was the largest and that the R value of the water pressure was the smallest, indicating that the confining pressure had the largest impact on the seepage of subcategory II₂ sandstone, followed by the temperature and the water pressure.

Figure 14 shows that the permeability of subcategory II₂ sandstone decreased with increasing confining pressure and rapidly decreased with increasing temperature but decreased first and then increased with increasing difference in water pressure.

4. Discussion

4.1. Influence Mechanisms of Confining Pressure, Water Pressure and Temperature on Sandstone Permeability

Permeability is a measure of liquid flowing through porous media, and is thus an intrinsic property of sandstone that depends on the pore structure of sandstone and can be directly defined by Darcy’s law, as shown in Formula (2).

$$k=-\frac{Q\mu }{A\rho g}{\left(\frac{\partial h}{\partial s}\right)}^{-1}$$

(2)

where K is the permeability of sandstone; Q is the seepage amount of liquid passing through cross-sectional area A during a unit time; µ is the fluid viscosity; ρ is the fluid density; g is the gravitational acceleration; and ∂h/∂s is the hydraulic gradient in the flow direction of s.

Darcy’s law itself does not reflect the relationship between permeability and the stress field, temperature field and seepage field of porous media; therefore, how do confining pressure, water pressure and temperature affect the permeability of sandstone?

4.1.1. Influence Mechanism of Confining Pressure

The single-factor test of confining pressure showed that the permeability of all four subcategories of sandstone decreased with increasing confining pressure, which indicated that strain was generated in the sandstone under confining pressure (see Figure 15). In the low confining pressure range of 0–10 MPa, the permeability decreased rapidly, but the change in permeability decreased with increasing confining pressure. This is because when the confining pressure began to act on the sandstone, the particles in the sandstone skeleton underwent strain, resulting in the volume compression of pores and pore throats and the rapid reduction in sandstone permeability. However, when the pores and pore throats were compressed to a certain extent, the compression effect of stress on the pores and pore throats decreased, so the changes in the permeability of the sandstone samples decreased.

4.1.2. Influence Mechanism of Water Pressure

The single-factor test of water pressure showed that the permeability of subcategory I₁, I₂ and II₁ sandstones increased with increasing water pressure. This phenomenon indicated that the sandstone pores were deformed under the action of water pressure, and the action surface of water pressure was the pore wall. Therefore, the water pressure had a certain expansion effect on the pores, which was usually shown as the reaction force of the confining pressure, and the permeability of the sandstone samples increased to a certain extent.

4.1.3. Influence Mechanism of Temperature

The single-factor test of temperature showed that the permeability of the four subcategories of sandstone decreased with increasing temperature under a fixed confining pressure of 20 MPa. This phenomenon showed that under the continuous action of high temperature, the volume of the sandstone grains expanded, causing a change in the sandstone pore structure to a certain extent. According to the grain size analysis data of sandstone in this study, the average grain size of the sandstone skeleton particles is approximately 100 µm, and the linear thermal expansion coefficient of the skeleton particles can generally be taken as 1.11 × 10⁻⁵ °C⁻¹. The pore throat radius decreased by approximately 0.011 µm when the temperature increased by 10 °C. Due to the compression effect of the 20 MPa confining pressure, the pore throats of the rock sample were compressed to a large extent and became narrow. In this case, if the sandstone skeleton experienced thermal expansion with increasing temperature, this further narrowed the pore throats, causing a certain decrease in permeability, possibly even a large decrease.

4.1.4. The Coupling Action of the “Three-High” Factors

The orthogonal test results showed that the confining pressure had the greatest influence on the permeability of deep-mine sandstone, followed by temperature and seepage pressure. The variation trends of sandstone permeability with different pore structures were the same under high confining pressures but different under high water pressures and high temperatures. This indicated that the compression effect of high confining pressures on the sandstone pore structure was significant, but the deformation caused by high water pressures and high temperatures was small and was affected to some extent by the coupling effect of confining pressure.

In conclusion, high confining pressures, high water pressures and high temperatures can change the structure of deep-mine sandstone to varying degrees through the stress-strain relationship, thus changing the pore structure of the sandstone and leading to a change in the permeability of sandstone. The influence mechanism of the “three-high” factors on sandstone permeability is characterized in Figure 16.

4.2. Analysis of the Reasons for the Differences in Permeability Evolution of Sandstones with Different Pore Structures

The following discussion of the reasons for the difference in the permeability evolution of sandstone with different pore structures is based on the results of various experiments in this study.

4.2.1. The Reason for the Permeability Difference under the Sole Influence of Confining Pressure

The single-factor test of confining pressure showed that the rate and extent of permeability reduction for the four subcategories of sandstone were different with increasing confining pressure, and the rate and extent of permeability reduction gradually increased from subcategory I₁ to I₂ to II₁ to II₂ (see Figure 10). This phenomenon was related to the difference in sandstone structure (see

Table 8. The sorting coefficients of four subcategories of sandstone.

Sandstone Subcategories	I1	I2	II1	II2
So	<1.00	1.00–1.40	1.40–1.60	>1.60

). From subcategory I₁ to I₂ to II₁ to II₂, the grain sorting worsened, namely, the grain grading of the sandstones improved in this order. Therefore, from subcategory I₁ to I₂ to II₁ to II₂, the compactness of the sandstone increased faster, and the porosity and permeability decreased more under the continuous action of a high confining pressure.

4.2.2. The Reason for the Permeability Difference under the Sole Influence of Water Pressure

The single-factor test of water pressure showed that the permeability evolutions of the four subcategories of sandstones were obviously different. From subcategory I₁ to I₂ to II₁, the permeability of these three subcategories of sandstone increased, but the rate of increase in permeability slowed with increasing water pressure. This is because the porosity and average pore throat radius decreased in turn (see

Table 9. The porosities and average pore throat radii of the four subcategories of sandstone.

Sandstone Subcategories	I1	I2	II1	II2
Փ (%)	>20	15–20	7–15	<7
Rave. (µm)	>3.7	0.7–3.7	0.14–0.7	<0.14

), causing the contact surface between the water pressure and pore wall to decrease, and the effect of water pressure on pore volume expansion decreased in turn. However, the permeability of subcategory II₂ sandstone fluctuated greatly under a low confining pressure of 20 MPa, but changed little under a high confining pressure above 30 MPa with increasing water pressure. This is because the porosity of subcategory II₂ sandstone was generally less than 7%, and the corresponding average pore throat radius was less than 0.14 μm (see Table 9). The pore expansion effect caused by the water pressure in the small pores and pore throats can still be observed under low confining pressure, but it can hardly be observed under high confining pressures above 30 MPa because this pore expansion effect was offset by the compression effect of high confining pressure on pores.

4.2.3. The Reason for the Permeability Difference under the Sole Influence of Temperature

The single-factor test of temperature showed that the permeabilities of the four subcategories of sandstone decreased with increasing temperature, but the variation trends were different. The reason were the differences was that the pore structures of the four subcategories of sandstones are different. Subcategory I₁ sandstone had high porosity and a large average pore throat radius (see Table 9). The skeleton grains of this sandstone expanded slowly, resulting in the slow shrinkage of the primary pores and pore throats. Accordingly, the permeability of subcategory I₁ sandstone decreased linearly and slowly with increasing temperature. The porosity and the average pore throat radius of the sandstones in subcategories I₂ and II₁ were moderate (see Table 9). With increasing temperature, the primary pores and pore throats of sandstones slowly shrank, and the pore permeability slowly decreased at the beginning. However, an increasing number of pores and pore throats began to close when the temperature was higher than 45 °C, and the closure of pores led to a rapid decline in permeability. For this reason, the permeability of subcategory I₂ and II₁ sandstone decreased slowly at the beginning, but the deceleration increased significantly when the temperature was higher than 45 °C. The porosity of subcategory II₂ sandstone was low, the average pore throat radius was small (see Table 9), and the number of connected pores was very small, and a light pore throat change caused by temperature change led to the plugging of the pores. Therefore, the permeability decreased rapidly at the beginning of the temperature rise, but when the temperature continued to increase to more than 45 °C, the deformation of the sandstone pores was increasingly smaller, and the change in the permeability value was increasingly smaller.

4.2.4. The Reason for the Permeability Difference under the Coupling Action of the “Three-High” Factors

The comparison of the orthogonal test results of subcategory I₂ and subcategory II₂ sandstones showed that different subcategories of deep-mine sandstones behaved differently:

(a)

The order of factors influencing the seepage of subcategory I₂ sandstone was confining pressure > water pressure > temperature, while that of subcategory II₂ sandstone was confining pressure > temperature > water pressure.

(b)

The permeability of subcategory I₂ sandstone first increased and then decreased with increasing water pressure difference, while that of subcategory II₂ sandstone first decreased and then increased with increasing water pressure difference.

(c)

The permeability of subcategory I₂ sandstone decreased slowly with increasing temperature, while that of subcategory II₂ sandstone decreased rapidly with increasing temperature.

The reason for the above results is that the porosity and average pore throat radius of subcategory I₂ sandstone were larger than those of subcategory II₂ sandstone, and the water pressure thus had a more obvious expansion effect on the pore walls, while the fine pore throats of subcategory II₂ sandstone were more sensitive to the microscale volume change caused by the temperature change.

4.3. Analysis of Similarities and Differences between the Results of This Study and the Findings of Previous Researchers Mentioned in the Literature Review

Comparing the results of this study with the works of the previous researchers mentioned in the literature review, it is evident that the works of some researchers are similar to the results of this study. For example, Brace (1968) found that the pore permeability of granite decreased with increasing effective confining pressure [21]. Jiang et al. (2014) studied the influence of water pressure on the time-dependent deformation of surrounding rock in the process of deep rock mass excavation under high stress, and found that water pressure can enhance the performance of rock creep deformation [24]. Mohammed, S.B. and Mohammed, M.A. (2009) carried out research on the variation in the permeability of carbonate rocks and found that the permeability began to decrease when the temperature increased from 25 °C to 50 °C [26]. However, the works of some researchers are inconsistent with the results of this study. For example, Somerton (1965) conducted heating tests on a large number of sandstone cores at 400–800 °C and found that the permeability of broken cores increased by 50% [20]. Heard (1982) heated adamellite to 300 °C under different confining pressures, which made the rock fracture and its permeability increase several times [22].

In summary, the conclusions about the influence of confining pressure and water pressure on the permeability evolution of sandstone are similar, but the conclusions about the influence of temperature on the permeability evolution of sandstone have both similarities and differences. Further analysis shows that when the temperature range was similar to that of this study, the conclusion was consistent with that of this study; but when the temperature variation range was very different from that of this study, the conclusion was different. The reason for this phenomenon is that the temperature variation range in this study was small, and only a small elastic deformation occurred in sandstone with increasing temperature. When the temperature was too high, such as 800 °C, the sandstone was broken and produced a large number of fractures, which led to a sharp increase in sandstone permeability. At the current mining depth of deep coal mines, the underground temperature was generally less than 60 °C. Therefore, the conclusions of these researchers are of little significance for the prevention of water seepage from sandstone pores in deep coal mines at present.

4.4. The Practical Significance of the Results of the Study to Guide Grouting

It can be seen from Section 4.1 and Section 4.2 that the pore seepage characteristics of deep-mine sandstone are the result of the comprehensive action of the pore structure of sandstone itself and the external environmental factors (confining pressure, water pressure, temperature) deep underground (see Figure 17). Therefore, during the design and construction of pore grouting, it is necessary to comprehensively analyze various influencing factors to make the correct grouting plan and obtain the best grouting effect. The following illustrates the practical significance of the research results for guiding grouting.

Understanding the actual effects and mechanisms of the “three-high” factors on pore seepage under the current coal mining environment is helpful to guide future grouting construction design. For example, according to the results of this study, under the environmental conditions of coal mining in the next 20 years, the increase in high confining pressure and high temperature will mainly produce elastic deformation in deep-mine sandstone, resulting in a reduction in pore throat volume, which will lead to a reduction in sandstone permeability. Therefore, in the grouting design of deep sandstone with “large-area sweating” seepage, the grouting holes should be mainly arranged in the high-permeability sandstones, such as subcategory I₁, I₂ and II₁ sandstones, because the low-permeability sandstones, such as subcategory II₂ sandstone, will have fewer pores, and the seepage flow will decrease under the continuous action of the higher confining pressure and high temperature.

Understanding the difference in the permeability evolution of sandstone with different pore structures under the influence of the “three-high” factors can inform the correct selection of grouting parameters. For example, the permeability changes in sandstone with different pore structures vary greatly with increasing water pressure. When grouting low-permeability sandstone with a small porosity and average pore throat radius, it is not appropriate to apply too high a grouting pressure at the beginning of the grouting treatment. The pressure should be increased incrementally by considering the size of the pore throat; starting from low-pressure grouting, the grouting pressure should be adjusted continuously according to the change in pore structure, and different grouting parameters should be selected to obtain the best grouting effect.

5. Summary and Conclusions

In this study, deep-mine sandstones with pore seepage problems were selected as the test samples. The permeability evolution of sandstones with different pore structures under high confining pressures, high water pressures and high temperatures was studied by single-factor and three-factor orthogonal tests. The main conclusions are as follows:

(1)

The single-factor test of confining pressure showed that the permeability of the four subcategories of sandstone nonlinearly decreased with increasing confining pressure, and the permeability rapidly decreased in the low confining pressure range of 0–10 MPa. However, the rate and extent of permeability reduction for the four subcategories of sandstone were different, gradually increasing from subcategory I₁ to I₂ to II₁ to II₂.

(2)

The single-factor test of water pressure showed that under the three levels of confining pressure tested, the permeabilities of the four subcategories of sandstone varied with the water pressure difference, but the variation trends were different. The difference was shown in the following two aspects: (a) subcategory I₁, I₂ and II₁ sandstones increased linearly with increasing water pressure, but the rate of increase in the permeability gradually slowed from subcategory I₁ to I₂ to II₁. (b) Under different confining pressure levels, the variations in the permeability of subcategory II₂ sandstone were different; the permeability varied greatly and decreased as a power function under a low confining pressure (20 MPa), but the variation was small or basically stable under a high confining pressure (over 30 MPa).

(3)

The single-factor test of temperature showed that the permeability of the four subcategories of sandstone decreased with increasing temperature, but the variation trends were different. With increasing temperature, the permeability of subcategory I₁ sandstone decreased linearly and slowly; the permeability of subcategory I₂ and II₁ sandstone decreased as a cubic curve (decreasing slowly at the beginning, but the deceleration increased significantly when the temperature was higher than 45 °C); the permeability of subcategory II₂ sandstone decreased almost as a power function (decreasing rapidly at the beginning, but the deceleration slowed significantly, with little change when the temperature was higher than 45 °C).

(4)

The orthogonal test results showed that the confining pressure had the greatest influence on the permeability of deep-mine sandstone, followed by temperature and seepage pressure. Under the action of high water pressures and high temperatures, the variations in the permeability of sandstones with different pore structures were different. Sandstone with many pores and large pore throat radii corresponded to a more obvious expansion effect on the pore walls by the water pressure, while sandstone with fine pore throats was more sensitive to the microscale volume change caused by the temperature change.

(5)

High confining pressures, high water pressures and high temperatures can change the pore structure of deep-mine sandstone through the stress-strain relationship, leading to a change in the pore permeability of sandstone. The permeability evolution of sandstones with different pore structures varies under the same external conditions. Hence, the pore seepage of deep-mine sandstone was the result of the comprehensive influence of the pore structure of the sandstone itself and factors such as high confining pressure, high water pressure and high temperature. This conclusion can be used in guiding classified grouting of deep sandstone and optimizing grouting parameters.