# An Experimental Study of Seepage Properties in Crushed Sandstone and Mudstone

Authors: Qi-Le Ding; Shuai-Bing Song
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

To study the effects of compression rate and weight ratio of sandstone to mudstone on permeability, water flow tests were performed on crushed rocks using an in-house designed and built water flow apparatus. Seepage properties of sandstone and mudstone were tested on specimens under six axial displacement levels. The weight ratios of the six specimens of sandstone to mudstone were set to 1 : 0, 4 : 1, 3 : 2, 2 : 3, 1 : 4, and 0 : 1. A non-Darcy law was adopted to calculate the permeability in the experiments based on verification of the Reynolds number. Non-Darcy flow is found to be most significant when the axial displacement or mudstone content increases. The permeability in the experiments is found to be in the range of 9.1 × 10−15–9.492 × 10−13 m2, which is calculated from a quadratic polynomial fit between the flow velocity and pressure gradient. A compression rate of 28.6% and weight ratio of sandstone to mudstone of 60% are found to be key values affecting permeability. When the axial displacement of specimen A (1 : 0) increases from 10 mm to 30 mm, the compression rate (ratio of axial displacement to original specimen height) increases from 9.5% to 28.6%, and the permeability decreases by 83.8% to 1.534 × 10−13 m2. When the axial displacement is 10 mm and the content of mudstone is increased from 0% to 60%, the permeability decreases by 77.1% to 2.172 × 10−13 m2.


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## Body

## 1. Introduction

Underground mining can lead to strata movement and loss of equilibrium of the stress state, causing deterioration in the mechanical behavior of surrounding rocks [1–3]. Schatzel et al. [4] tested water flow properties of overburden strata at a mine site and demonstrated that the permeability increased by two to three orders of magnitude as a result of mining disturbance. Advancement of the working face may result in a series of hazards, such as groundwater inrush into a coal mine from an aquifer, which is one of the most frequent forms of mining accidents [5–7]. This type of accident seriously threatens safe production of the mine, and mine workers themselves [8, 9]. Since 2000, about 500 events of mine water inrush have occurred in China and more than 3000 people have lost their lives. For example, 36 people died in a groundwater inrush accident at the Wangjialing Coal Mine in Shanxi Province, China, on 28 March 2010 [8]. In recent years, and with continuing extension to more complex coal seams containing faults, karst collapse pillars and other weak tectonic structures, the hydrogeological conditions in such mines are deteriorating [10, 11].Many scholars have studied the mechanics and the prediction and the control measures of water inrush [12–15]. Bukowski [16] proposed a risk assessment method to classify mine shafts according to the risk of water inrush. The method considers factors such as flow intensity, condition of water-bearing formations, suspended materials contained in the water, and protective coal pillars. Wu et al. [11] adopted the “three maps-two predictions” method to construct an index model of water abundance in overlying aquifers, with results shown on a map indicating potential water flow channels to aquifers.A more accurate and in-depth understanding of seepage properties is important for prediction and control of mine water inrush accidents [17], and the study of permeability of rocks is the foundation of such. Tanikawa and Shimamoto [18] carried out water permeability tests on sedimentary rocks from the western foothills of Taiwan and found that the permeability increased slightly when the pressure gradient increased. Benavente et al. [19] studied the water permeability of 15 sedimentary rock types and proposed a model for calculating permeability that considers factors such as flow velocity, water properties (density and viscosity), porosity, interfacial tension, and contact angle.Research into the permeability of rocks mainly focuses on intact rocks that have not been broken or damaged, while crushed rocks are widely distributed in fault zones, karst collapse pillars, and caved zones. These crushed rocks, of which the permeability is much higher than intact rock [20–25], may act as preferential migration pathways for groundwater into a mine [26].In this paper, the effects of compression rate and weight ratio of sandstone to mudstone on permeability are investigated using an in-house designed and built water flow apparatus. Water flow tests were performed on crushed rocks containing sandstone and mudstone. The experimental results provide an improved understanding of the mechanism of water inrush through such preferential pathway materials and serve as a reference for prediction and control of water inrush accidents.


## 2. Experimental Materials and Testing Procedures

### 2.1. Experimental Materials

The sandstone and mudstone used in the experiments were collected from the 21105 working face of the Pingshuo Coal Mine in Shanxi Province, China. The mineral composition of the tested sandstone and mudstone was composed of feldspar, quartz, kaolinite, chlorite, siderite, and small amounts of other minerals. The sandstone and mudstone blocks were crushed using a hammer, piercer, and rock crusher in the laboratory. A sieve was used to separate the particles in the 10–15 mm size range, as shown in Figure1. This size range closely correlates with site conditions, as 10–15 mm size sandstone and mudstone grains are typically widely distributed in fault zones, collapse pillars, and caved zones. Six specimens were made, each with a different weight ratio of sandstone to mudstone. These specimen were A (1 : 0), B (4 : 1), C (3 : 2), D (2 : 3), E (1 : 4), and F (0 : 1), the ratios of sandstone to mudstone shown in parentheses.Figure 1
Illustration of the geological conditions and sample material showing (a) working faces of the Pingshuo coal mine, (b) borehole log showing the lithologies, (c) crushed mudstone, and (d) crushed sandstone.


### 2.2. Experimental Equipment and Testing Procedures

The experimental apparatus is illustrated in Figure2. The details of the apparatus setup are provided in the figure caption.Figure 2
Water flow testing system. A, pressure transducer; B, supercharger; C, relief valve; D, voltage stabilizer; E, differential pressure transducer; F, drainage; S1–S15, switches; 1, crushed rocks; 2, platen; 3 and 8, rubber seal rings; 4, piston; 5, perforated plate; 6, felt pad; 7, cylindrical barrel; 9, plate; 10, spring; 11, valve core; 12, valve chest; and 13, screw.The testing procedures are conducted in two main steps, as described in detail as follows.(1)
The axial displacement (S) is applied. Six axial displacement levels were set: 10 mm, 15 mm, 20 mm, 25 mm, 30 mm, and 35 mm. The target value was applied to the specimen and maintained until step (2) was completed, as shown in Figure 3. The porosity (φ) of the crushed rocks was calculated as follows:(1)φ=AHn−m/ρAHn,where A is the cross sectional area of the inner wall of the cylindrical barrel (1.27 × 10−2 m2), m is the mass (1.7 kg), ρ is the density, and Hn is the height of specimen at a given axial displacement and is calculated as follows:(2)Hn=H−110−hn−h2+h3,where H is the height of the cylindrical barrel (180 mm), hn is the length of part of piston that is outside of the cylindrical barrel (variable according to the six different axial displacement levels), h2 is the thickness of the perforated plate (9 mm), and h3 is the thickness of the felt pad (3 mm).(2)
Water flow testing is undertaken. When the axial displacement becomes stable, a pore pressure control system is used to produce four different piston velocities: 10, 20, 30, and 35 mm/min. The relation between water flow velocity (Vs) and piston velocity (Vp) is written as follows:(3)Vs=dpds2Vp,where ds and dp are the respective diameters of the specimen and the piston (12.7 cm and 5.5 cm, respectively). Thus, it is possible to obtain the pressure gradient and corresponding water flow velocities.Figure 3
Water flow testing procedure of the crushed sandstone and mudstone samples.


## 2.1. Experimental Materials

The sandstone and mudstone used in the experiments were collected from the 21105 working face of the Pingshuo Coal Mine in Shanxi Province, China. The mineral composition of the tested sandstone and mudstone was composed of feldspar, quartz, kaolinite, chlorite, siderite, and small amounts of other minerals. The sandstone and mudstone blocks were crushed using a hammer, piercer, and rock crusher in the laboratory. A sieve was used to separate the particles in the 10–15 mm size range, as shown in Figure1. This size range closely correlates with site conditions, as 10–15 mm size sandstone and mudstone grains are typically widely distributed in fault zones, collapse pillars, and caved zones. Six specimens were made, each with a different weight ratio of sandstone to mudstone. These specimen were A (1 : 0), B (4 : 1), C (3 : 2), D (2 : 3), E (1 : 4), and F (0 : 1), the ratios of sandstone to mudstone shown in parentheses.Figure 1
Illustration of the geological conditions and sample material showing (a) working faces of the Pingshuo coal mine, (b) borehole log showing the lithologies, (c) crushed mudstone, and (d) crushed sandstone.


## 2.2. Experimental Equipment and Testing Procedures

The experimental apparatus is illustrated in Figure2. The details of the apparatus setup are provided in the figure caption.Figure 2
Water flow testing system. A, pressure transducer; B, supercharger; C, relief valve; D, voltage stabilizer; E, differential pressure transducer; F, drainage; S1–S15, switches; 1, crushed rocks; 2, platen; 3 and 8, rubber seal rings; 4, piston; 5, perforated plate; 6, felt pad; 7, cylindrical barrel; 9, plate; 10, spring; 11, valve core; 12, valve chest; and 13, screw.The testing procedures are conducted in two main steps, as described in detail as follows.(1)
The axial displacement (S) is applied. Six axial displacement levels were set: 10 mm, 15 mm, 20 mm, 25 mm, 30 mm, and 35 mm. The target value was applied to the specimen and maintained until step (2) was completed, as shown in Figure 3. The porosity (φ) of the crushed rocks was calculated as follows:(1)φ=AHn−m/ρAHn,where A is the cross sectional area of the inner wall of the cylindrical barrel (1.27 × 10−2 m2), m is the mass (1.7 kg), ρ is the density, and Hn is the height of specimen at a given axial displacement and is calculated as follows:(2)Hn=H−110−hn−h2+h3,where H is the height of the cylindrical barrel (180 mm), hn is the length of part of piston that is outside of the cylindrical barrel (variable according to the six different axial displacement levels), h2 is the thickness of the perforated plate (9 mm), and h3 is the thickness of the felt pad (3 mm).(2)
Water flow testing is undertaken. When the axial displacement becomes stable, a pore pressure control system is used to produce four different piston velocities: 10, 20, 30, and 35 mm/min. The relation between water flow velocity (Vs) and piston velocity (Vp) is written as follows:(3)Vs=dpds2Vp,where ds and dp are the respective diameters of the specimen and the piston (12.7 cm and 5.5 cm, respectively). Thus, it is possible to obtain the pressure gradient and corresponding water flow velocities.Figure 3
Water flow testing procedure of the crushed sandstone and mudstone samples.


## 3. Permeability Calculation Based on a Non-Darcy Flow

The Forchheimer equation has been proven to accurately quantify water flow in crushed rock when water flow is stable [27, 28]. The value of the pressure gradient relative to flow velocity can be expressed as follows:(4)∂p∂x=−μkVs+βρwVs2,where μ is the dynamic viscosity (tap water was used in the experiment: μ = 1.01 × 10−9 MPa·s), k is the permeability, ρw is the mass density of the fluid medium (1.0 × 10−6 kg/mm3), and β is a factor of non-Darcy seepage.The non-Darcy equation (4) adopted in the experiments is verified by the Reynolds number Re, which is calculated as follows:(5)Re=ρwdVsφμ,where d is the average grain size of the crushed rocks (10–15 mm). Earlier studies have shown that the upper limit of Re is 5 when using Darcy law, and non-Darcy flow can be adopted when Re > 5. In our experiments, the minimum and maximum values of Re were 0.72 and 10.09, respectively. Thus, non-Darcy flow is more applicable.There is a difference between the base pressurePb and top pressure Pt of the specimen, and the pressure gradient, shown in (6), is approximately equal to the ratio of pressure difference to specimen height h. The downstream end is open to the atmosphere in the testing system, thus Pt = 0:(6)∂p∂x=−pb−pth=−pbh.The permeabilityk is calculated from the quadratic polynomial fit between the flow velocity and the corresponding pressure gradient as follows:(7)μk=∑i=1n∂p/∂xiVii∑k=1nVk4k−∑i=1n∂p/∂xiVi2i∑k=1nVk3k∑i=1nVi2i∑k=1nVk4k∑i=1nVi3i∑k=1nVk3k.


## 4. Test Results and Discussion

As the water flow tests began, the pore pressure gradually increased, reaching a stable state after about 20 seconds (Figure4). It was found that a piston velocity of 10 mm/min corresponds to the first axial displacement level in the water flow test, and the 10 mm/min curves show more significant changes than other curves as time increases.Figure 4
Graphs of pore water pressure vs. time at various axial displacement levels of specimen A (1 : 0): (a) axial displacement 10 mm (compression rate 9.5%); (b) axial displacement 15 mm (compression rate 14.3%); (c) axial displacement 20 mm (compression rate 19.0%); (d) axial displacement 25 mm (compression rate 23.8%); (e) axial displacement 30 mm (compression rate 28.6%); (f) axial displacement 35 mm (compression rate 33.3%).
(a)
(b)
(c)
(d)
(e)
(f)The positions and distributions of the constituent grains changed as the tests continued, leading to the unstable state of the curves. The 10 mm/min curve in Figure4(a) and the 20 mm/min curve in Figure 4(c) both show a significant decrease before the water flow stabilized. This resulted from the evolution of water flow channels. When the water flow tests were started, the channels through which water flows had not formed completely, and pore pressure was increasing sharply. As water flow continued, the channels became smoother, leading to a decrease in pore water pressure.Values of water flow velocity (Vs), the corresponding pressure gradient, and the calculated permeability k are provided in Table 1, and the relationship between the pressure gradient and the flow velocity is shown in Figures 5 and 6. As the axial displacement and the content of mudstone increase, the curves of pressure gradient vs. flow velocity change from straight lines to curves. That is, the phenomenon of non-Darcy flow is most significant when the porosity decreases. The relationship between the pressure gradient and the axial displacement is shown in Figure 7. The permeability k was calculated from the quadratic polynomial fitting between the pressure gradient and flow velocity (Vs).Table 1
Pressure gradient and flow velocity parameters of specimen A (1 : 0).
Axial displacementS (mm)
Piston velocityVp (mm/min)
Flow velocityVs (m/s)
Pressure gradient∂p/∂x (MPa/m)
Permeabilityk (m2)
10
10
3.13 × 10−5
−0.09
9.49 × 10−13
20
6.25 × 10−5
−0.33
30
9.38 × 10−5
−0.60
35
1.09 × 10−4
−0.87
15
10
3.13 × 10−5
−0.12
6.84 × 10−13
20
6.25 × 10−5
−0.38
30
9.38 × 10−5
−0.85
35
1.09 × 10−4
−1.06
20
10
3.13 × 10−5
−0.14
5.83 × 10−13
20
6.25 × 10−5
−0.41
30
9.38 × 10−5
−0.95
35
1.09 × 10−4
−1.16
25
10
3.13 × 10−5
−0.19
3.05 × 10−13
20
6.25 × 10−5
−0.53
30
9.38 × 10−5
−1.12
35
1.09 × 10−4
−1.38
30
10
3.13 × 10−5
−0.31
1.53 × 10−13
20
6.25 × 10−5
−0.75
30
9.38 × 10−5
−1.53
35
1.09 × 10−4
−1.83
35
10
3.13 × 10−5
−0.44
1.12 × 10−13
20
6.25 × 10−5
−1.08
30
9.38 × 10−5
−2.09
35
1.09 × 10−4
−2.63Figure 5
Flow velocity and corresponding pressure gradient of specimen A (1 : 0) under different axial displacements (S).Figure 6
Flow velocity and corresponding pressure gradient of all the specimens when the axial displacement is 10 mm.Figure 7
Axial displacement and corresponding pressure gradient of specimen A (1 : 0) under different piston velocities.Table2 shows that the permeability of crushed rocks in the tests was in the range of 9.1 × 10−15–9.492 × 10−13 m2, which is an approximate two orders of magnitude increase compared to fractured sandstone [29].Table 2
Porosity (φ) and permeability (k) at various axial displacements for all the specimens.
Specimen number
Properties
Axial displacement (mm)
10
15
20
25
30
35
A (1 : 0)
φ
0.427
0.396
0.360
0.320
0.275
0.223
k (×10−14)
94.92
68.43
58.31
30.51
15.34
11.20
B (4 : 1)
φ
0.420
0.387
0.352
0.311
0.266
0.214
k (×10−14)
47.80
38.40
39.72
18.85
11.81
8.23
C (3 : 2)
φ
0.409
0.377
0.341
0.300
0.254
0.201
k (×10−14)
45.99
33.81
27.97
16.32
6.31
5.11
D (2 : 3)
φ
0.400
0.368
0.331
0.290
0.244
0.191
k (×10−14)
21.72
20.35
12.46
9.30
3.94
2.98
E (1 : 4)
φ
0.389
0.356
0.319
0.277
0.231
0.177
k (×10−14)
12.79
8.94
7.32
4.60
3.34
1.20
F (0 : 1)
φ
0.376
0.343
0.305
0.263
0.216
0.161
k (×10−14)
6.16
4.71
3.38
2.62
1.06
0.91Figure8 demonstrates that the permeability is closely correlated with the compression state and, when the axial displacement increases, the porosity decreases, resulting in a decrease in permeability. The decreasing rate is most significant when the axial displacement increased from 10 mm to 30 mm. As the axial displacement of specimen A (1 : 0) increased from 10 mm to 30 mm, the compression rate (ratio of axial displacement to original specimen height) increased from 9.5% to 28.6%, the porosity decreased from 0.427 to 0.275, and the permeability decreased by 83.8% from 9.492 × 10−13 to 1.534 × 10−13 m2. When the axial displacement increased to 35 mm, the permeability decreased slightly and the difference in permeability among different specimens decreased when the axial displacement increased.Figure 8
Permeability as a function of porosity of all the specimens (A–F).For specimens with the same axial displacement, a higher content of mudstone led to a decrease in porosity and thus a decrease in permeability (Figure9). When the content of mudstone increased from 0% to 60%, the changing rate of permeability was most significant. When the axial displacement was 10 mm and the content of mudstone increased from 0% to 60%, the porosity decreased from 0.427 to 0.400 and the permeability decreased by 77.1% from 9.492 × 10−13 to 2.172 × 10−13 m2. The decreasing rate of permeability declined when the content of mudstone was >60%. As the mudstone content increased, the difference in permeability among different axial displacement levels decreased.Figure 9
Permeability as a function of increasing mudstone content in samples subjected to different axial displacements (S).


## 5. Conclusions

Based on the work presented, the following conclusions can be drawn regarding the experiment and the results thereof:(1)
Stable water flow in the flow tests is achieved after about 20 seconds, and the pore water pressure showed most significant changes at the first velocity levels for each axial displacement.(2)
Non-Darcy flow was adopted for calculations of the permeability, based on the verification of the Reynolds number. Non-Darcy flow was most significant when the axial displacement or the mudstone content increased.(3)
Permeability of the crushed rock samples was in the 9.1 × 10−15–9.492 × 10−13 m2 range, which correlates closely with the level of axial displacement and mudstone content.(4)
The permeability decreases most significantly when the axial displacement increased from 10 mm to 30 mm. When the axial displacement of specimen A (1 : 0) increased from 10 mm to 30 mm, the compression rate increased from 9.5% to 28.6%, the porosity decreased from 0.427 to 0.275, and the permeability decreased by 83.8% from 9.492 × 10−13 to 1.534 × 10−13 m2. When the mudstone content was increased from 0% to 60%, the changing rate of permeability was most significant. When the axial displacement was 10 mm and the mudstone content increased from 0% to 60%, the porosity decreased from 0.427 to 0.400, and the permeability decreased by 77.1% from 9.492 × 10−13 to 2.172 × 10−13 m2.



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*Source: 6537571-2019-06-18.xml*