# Experimental Study on the Influence of Borehole Angles on Fracture Grouting in Limestone Aquifers

Authors: Jianbo Li; Yanchun Xu
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Grouting is an effective method to ensure mining safety by reconstructing confined aquifers. However, the effect of grouting on deep-buried aquifers is difficult to evaluate. Therefore, the experimental means in this paper are used to study the fracture grouting effect under the influence of borehole angles. A special device composed of boreholes and fractures is designed to study the whole process of grouting in limestone fractures. Four factors are tested in the experiment, including penetration distance, water separation, slurry stone body, and sealing effect. The results show that the slurry deposition can be divided into two stages, including the initial diffusion and the second gravity deposition. The water separation of mixed slurry is an important factor affecting the grouting effect. The slurry stone body formed through deposition is the key area for blocking water, and the borehole angles are the key to ensure the second gravity deposition. For a horizontal borehole, it is difficult to completely fill the space of fractures only by deposition and a certain angle is essential to achieve the second deposition. When the filling area of the fracture section is more than 90%, the flow characteristic of the fractures after grouting is closer to the equal percentage. When the filling area is less than 90%, the flow characteristics are approximately linear. At last, the data monitored in field grouting engineering are analyzed based on the grouting mechanism obtained from the experiment and the final consolidating form of slurry in a single fracture is described. The research is helpful for the optimization of grouting technology in the fractured aquifers under coal seams before mining.


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## Body

## 1. Introduction

In practice, grouting is widely used in many fields to prevent water or mud inrush, such as tunnel excavation and remediation of dams [1–6]. For coal mines threatened by confined aquifers, grouting is also used to reconstruct water-rich faulted zone, jointed ﬁssures, and karst passages [7–9] to ensure mining safety. However, the effect of grouting in deep-buried aquifers is difficult to evaluate because the fractures are invisible.In theoretical research, many studies have been performed, mainly focusing on deformation and stiffness estimation of fractures [10], penetration grouting [11–15], grout spread and injection period [16], and prediction of groutability [17]. For grouting effect research, the experimental method is an important means to study fracture grouting and the grout properties and joint thicknesses are usually regarded as the key factors [18–21]. For simulation tests, fractures are often generalized as pipe models or plane shape models [9, 11]. In addition, the mechanisms of slurry diffusion and deposition sealing under the action of confined water are studied systematically and meticulously [22–25] although many methods on grouting reinforcement effect evaluation have been formed, including field physical detection, numerical calculation, and similar tests. However, the effect of grouting in deep-buried aquifers is difficult to evaluate because the fractures are invisible. In this paper, a special device composed of boreholes and fractures is designed and the experimental method is selected to study the fracture grouting effect under the influence of borehole angles.


## 2. Engineering Background

As shown in Figure1(a), there are three limestones, limestone IX (L9), limestone VIII (L8), and limestone II (L2), vertically from the top to bottom under the coal seam. Many fractures exist in these limestones, most of which are full of confined water with sufficient water sources. The average thickness between coal seam II1 and L8 is about 25 m. L2 is about 90 m away from the coal seam II1 floor, while the water pressure is more than 6.0 MPa. These aquifers bring great threat to coal exploitation.Figure 1
Schematic diagram of aquifer grouting in one drilling site from the roadway to aquifers: (a) a section and (b) plane figure.
(a)(b)The layout of typical grouting boreholes in the studied working face is shown in Figure1(b). In the first 500 m from the open-off cut of the mining area, more than 100 boreholes have been drilled. The total drilling length is more than 20000 m, and more than 2000 tons of cement and 1300 tons of clay were injected. Different from grouting for tunnel excavation, the length of grouting holes in coal mining is far greater than that of tunnel grouting engineering.Grouting is completed before mining. Three stages of the grouting process are shown in Figure2, including initial grouting, slurry diffusion, and final grouting. The water inflow is monitored at the borehole outlet during drilling. When the water inflow is more than 10 m3/h, grouting is done immediately. When the value is less than 10 m3/h, drilling is done through the fracture directly for a certain small distance and then it is stopped and grouted. The grouting pressure is set to be twice of the aquifer water pressure.Figure 2
Different stages of the grouting process. (a) Initial grouting. (b) Slurry diffusion. (c) Final grouting. L is the penetration distance.
(a)(b)(c)


## 3. Experimental Design

### 3.1. Test Device

The fracture is generally simplified into different shapes in similar experiments, such as plane fractures [9] and pipe fractures [11]. Considering that the device needs to have good sealing performance and the slurry diffusion can be observed, transparent glass tubes with a diameter of 3.0 cm, which can resist high water pressure, are selected to simulate fractures and boreholes, focusing mainly on the influence of borehole angles on grouting.The grouting test device is shown in Figure3. Glass tubes are divided into two sections, including the fracture section and the borehole section. The length of the glass tube for the artificial fracture is 6.0 m, which can also be extended as needed. Three boreholes of different dip angles, respectively, 30°, 45°, and 90°, can be selected freely, and four factors are tested in the experiment, including the penetration distance, water separation, slurry stone, and the efficiency of plugging confined water. In the test, the simulation of grouting with horizontal boreholes is relatively simple and carried out separately.Figure 3
Test device for simulating fractures and boreholes with three dip angles.The experimental process includes determining fracture types, applying dynamic water conditions, grout diffusion, slurry sedimentation, and water injection test in the opposite direction to grouting. Taking the borehole of 45° as an example, the experimental process is described as follows:(a)
Fracture Determination. Keep valves S1, S3, S4, and S6 closed and valves S2 and S5 open so that the middle fracture of 45 degrees is selected. Close switch C and open switches A and B. Select an overflow valve with a threshold of 0.6 MPa. Then, start the pump and inject water. When water flows out through switch A, close valve B and pressurize the water pump to 0.6 MPa. Hydrodynamic application is completed.(b)
Grouting. Open switch A and start the grouting pump. When slurry flows out at the outlet of switch A, close switch A and open switch B to start grouting. Increase the pressure gradually to 2.0 MPa, which is more than twice the water pressure.(c)
Flush the grouting pump and the grouting system by selecting the corresponding valves and switches.


### 3.2. Research Contents and Test Conditions

The research contents include the grouting effect of fractures with different dip angles of boreholes and the influence of the slurry stone body on water flow and flow velocity. In practice, clay-cement slurry is selected for better grouting effect. The cement accounts for about 20% of solid material (cement and clay), the slurry mass ratio is 1.12∼1.18 g/cm3, and the water-solid ratio is 3∼4.In the test, the slurry mass ratio is set as 1.16 g/cm3, the dynamic water pressure is 0.6 MPa, and the grouting pressure is set as 2.0 MPa. The length of artificial fractures simulated with a glass tube is 6.0 m. The water flow, water pressure, and grouting pressure are monitored in the test.


## 3.1. Test Device

The fracture is generally simplified into different shapes in similar experiments, such as plane fractures [9] and pipe fractures [11]. Considering that the device needs to have good sealing performance and the slurry diffusion can be observed, transparent glass tubes with a diameter of 3.0 cm, which can resist high water pressure, are selected to simulate fractures and boreholes, focusing mainly on the influence of borehole angles on grouting.The grouting test device is shown in Figure3. Glass tubes are divided into two sections, including the fracture section and the borehole section. The length of the glass tube for the artificial fracture is 6.0 m, which can also be extended as needed. Three boreholes of different dip angles, respectively, 30°, 45°, and 90°, can be selected freely, and four factors are tested in the experiment, including the penetration distance, water separation, slurry stone, and the efficiency of plugging confined water. In the test, the simulation of grouting with horizontal boreholes is relatively simple and carried out separately.Figure 3
Test device for simulating fractures and boreholes with three dip angles.The experimental process includes determining fracture types, applying dynamic water conditions, grout diffusion, slurry sedimentation, and water injection test in the opposite direction to grouting. Taking the borehole of 45° as an example, the experimental process is described as follows:(a)
Fracture Determination. Keep valves S1, S3, S4, and S6 closed and valves S2 and S5 open so that the middle fracture of 45 degrees is selected. Close switch C and open switches A and B. Select an overflow valve with a threshold of 0.6 MPa. Then, start the pump and inject water. When water flows out through switch A, close valve B and pressurize the water pump to 0.6 MPa. Hydrodynamic application is completed.(b)
Grouting. Open switch A and start the grouting pump. When slurry flows out at the outlet of switch A, close switch A and open switch B to start grouting. Increase the pressure gradually to 2.0 MPa, which is more than twice the water pressure.(c)
Flush the grouting pump and the grouting system by selecting the corresponding valves and switches.


## 3.2. Research Contents and Test Conditions

The research contents include the grouting effect of fractures with different dip angles of boreholes and the influence of the slurry stone body on water flow and flow velocity. In practice, clay-cement slurry is selected for better grouting effect. The cement accounts for about 20% of solid material (cement and clay), the slurry mass ratio is 1.12∼1.18 g/cm3, and the water-solid ratio is 3∼4.In the test, the slurry mass ratio is set as 1.16 g/cm3, the dynamic water pressure is 0.6 MPa, and the grouting pressure is set as 2.0 MPa. The length of artificial fractures simulated with a glass tube is 6.0 m. The water flow, water pressure, and grouting pressure are monitored in the test.


## 4. Test Results

### 4.1. Water Separation and Slurry Stone Body

#### 4.1.1. Water Separation

The relationship between slurry concentration and water separation rate has been obtained [26, 27], as shown in Figure 4. When the water-to-solid (clay and cement) ratio is 3 and the cement accounts for 20% of the dry material, the water separation rate of the slurry is 50%, as shown in Figure 4.Figure 4
Water separation rate of clay-cement slurry [26, 27] with different water-solid ratios. W/S is the ratio of water to dry materials.


#### 4.1.2. Slurry Stone Body

The slurry deposition and filling effect were studied by the special experiment focusing on the deposition shape and the effective sealing distance, as shown in Figure5. The grouting pressure is 2.0 MPa and the water pressure is 0.6 MPa. In the final stage of grouting, the grouting pressure is kept constant for 30 min. During this period, the slurry separates water and the slurry stone body is formed.Figure 5
Slurry stone and water separation under the action of flowing water. The figure in the upper right corner is obtained in the experiment. L is the penetration distance, and l is the distance of the second deposition in the simulated fractures.The slurry deposition experiences two stages, including the first slurry diffusion stage and the second gravity deposition in the stable grouting stage. The effective plugging distancel of the slurry stone mainly depends on the gravity deposition, which is a key area for preventing water inrushes.In the slurry diffusion stage, the deposition surface presents a linear gradient and the slurry diffusion distance isL. The distance of the second gravity deposition in the fracture is l.


### 4.2. Influence of Dip Angles on the Slurry Stone Body

The slurry concentration is 1.16 g/m3, and the slurry deposition shapes and the interfaces between water and slurry stone obtained under three different dip angles are shown in Figure 6. It is difficult to completely fill the space of fractures by deposition in a horizontal hole, and a certain angle is indispensable to ideally complete the second deposition. The minimum flow limit under constant grouting pressure for a period of time is important to the formation of the slurry stone body.Figure 6
Interfaces of water and slurry stone body after water separation with different dip angles. L is the penetration distance, and H is the diameter of the glass tube (fracture height).When grouting through horizontal boreholes, the interface between slurry stone body and water is linear. When grouting through an inclined borehole, the deposition interface is divided into two sections, linear and approximate arc shape.When a horizontal borehole is used to grout the fracture with the slurry concentration of 1.16 g/m3, the stone body cannot completely fill the fracture, as shown in Figure 6. The slurry stone body formed by the second gravity deposition after grouting is the key area for effective sealing of fractures. The dip angle of boreholes is the key factor to ensure the second deposition of the slurry. In fact, in order to ensure the groutability of slurry, the slurry concentration is always not too high. The effective plugging distance is the key area formed by gravity deposition on the basis of the first deposition, which is much smaller than the diffusion area.The effective thrust forces between particles in vertical drilling holes are greater than those in inclined drilling holes, while the forces in horizontal drilling are the smallest. For a single particle, the effective thrusts between particles in the boreholes are, respectively,mg and mgsinα, as shown in Figure 7.Figure 7
Mechanical mechanism of particle gravity deposition in the second gravity deposition of the (a) inclined borehole and (b) vertical borehole.
(a)(b)


### 4.3. Sealing Effect

The verification of sealing efficiency is completed by a water injection test. Because the surface of the glass tube is smooth and the friction between the glass tube and the slurry stone body is small, the stone body is easy to be damaged by high water pressure during the reverse water injection. In the water injection test, the applied water pressure is not too high. Different sealing efficiencies are expressed by the proportion of the slurry stone body of the cross sections of the simulated fractures. Three filling effects, 20%, 60%, and 100%, of the fracture section are shown in Figure8.Figure 8
Flow characteristics of valves and filled fractures. For fractures, percent open refers to the ratio of an unfilled section to the whole section of the fracture.The slurry stone body is like a valve in the cross section of the designed fracture. Three flow characteristics of the filled fractures under the condition of flow water pressure are shown in Figure8. For fractures, percent open refers to the ratio of an unfilled section to the whole section of the fracture before grouting. When the filling area is more than 90% (percent open 10%), the flow characteristic of the fractures is closer to the equal percentage. When the filling area is less than 90%, the flow characteristics are approximately linear.Two flow patterns are observed, including free flow and fracture flow. When the grouting section is less than 90% (percent open is more than 10%), free flow occurs. When the filling degree is 90% to 100%, the water flow fluctuates obviously and the free flow gradually changes into fracture flow or Darcy flow.The effective deposition area of plugging water is much smaller than the diffusion distance of the slurry. In practice, in order to check the grouting effect, the secondary verification borehole was constructed, as shown in Figure9.Figure 9
Verification of plugging effect by the second drilling. L is the diffusion distance of the slurry, and l is the effective water plugging area.When the stone body completely seals the fracture, there is no water flowing out of the borehole. Indeed, it is the left stone of the effective plugging areal that can be used to effectively prevent water inrush. When the left effective sealing area cannot resist the water pressure, the confined water flows out of the borehole. The slurry stone is very important to prevent water inrushes.


### 4.4. Penetration Distance

#### 4.4.1. Theoretical Penetration

A cement-based grout can be described as a fluid characterized by viscosity and yield stress. At the final stage of grouting, the injection pressure is balanced by the shear stress towards the fracture walls, and the grout penetration,I, in a parallel slot with an aperture of d can thus be calculated as follows:(1)I=pg−pwd2τ,where pg-pw is the difference between the injection and water pressures and τ is the yield stress of the slurry. d is the equivalent fracture width.Through equation (1), the diffusion distance is related to grouting pressure, fracture width, and slurry yield stress. In practice, experiences of grouting have shown that grout has to be injected to a full stop in order to obtain an ideal result. For a Bingham material, the formula of 1D flow rate, Q, can be obtained [16, 28] and written as follows:(2)Q=wH2c3η1−ξ22+ξξ,where ξ is the ratio of the spread to the span (the maximum spread).Hence, the effective diffusion distance,Ieff, is obtained by the following equation:(3)Ieff=ξ·I.


#### 4.4.2. Penetration Distance in the Test

Because the fracture width is relatively large (the diameter is 3 cm), the slurry can easily diffuse to the outlet of the designed fracture under the condition that grouting pressure is 2.0 MPa and dynamic water pressure is 0.6 MPa. In the test, the distances of the diffusion in the fracture with three different angles are approximately equal. The penetration distance obtained from the total grout amount is as follows:(4)L=4Vgπd2,where Vg is the grout amount in the test, d is the diameter, and L is the diffusion distance.Considering the water separation rate of the slurry is 50%, the volume of the stone body can be obtained asVg/2. The distribution form of the slurry stone body is as shown in Figure 6.


### 4.5. Prediction of Grouting Effect and Its Application

#### 4.5.1. Prediction of Grouting Effect in a Single Fracture

The description of sealing effect of a single fracture during grouting engineering is drawn in Figure10. In grouting practice, the slurry diffuses to both sides of the fractures with the borehole as the center and the penetration distances on both sides are different. The penetration distance on the side against the water flow direction is less than the distance along the water flow direction, when the condition of high water pressure is considered.Figure 10
Prediction of filling effect in a single fracture: (a) before grouting and (b) after grouting.
(a)(b)


#### 4.5.2. Changes in the Monitored Water Volume and Pressure

The grouting quantity, water-solid ratio, and basic parameters of typical boreholes during grouting engineering are listed in Table1. The changes in water volume and water pressure are related to the plugging degree. The patterns of the grouting effect are classified into two types after grouting. For some boreholes, only the water flow is reduced but water pressure remains unchanged (D17-2 and D21-2). For other boreholes, both water pressure and water flow are reduced.Table 1
Slurry volume, water-solid ratio, and basic parameters of typical boreholes.
BoreholesLength (m)Dip angle (°)Water discharge (m3/h)Water pressure (MPa)Cement/solidSlurry volumeBeforeAfterBeforeAfterD17-21982520.24.54.50.19238.14D17-31473610.243.80.19127.54D17-51912810.24.34.00.19219.07D17-62352310.24.64.50.19218.01D19-1014234.550.25.55.00.19236.02D19-111603010.343.80.19236.02D19-13n1214710.34.23.80.19231.78D21-2197262.61.045.85.80.19256.14D21-71563510.25.35.10.19213.77


## 4.1. Water Separation and Slurry Stone Body

### 4.1.1. Water Separation

The relationship between slurry concentration and water separation rate has been obtained [26, 27], as shown in Figure 4. When the water-to-solid (clay and cement) ratio is 3 and the cement accounts for 20% of the dry material, the water separation rate of the slurry is 50%, as shown in Figure 4.Figure 4
Water separation rate of clay-cement slurry [26, 27] with different water-solid ratios. W/S is the ratio of water to dry materials.


### 4.1.2. Slurry Stone Body

The slurry deposition and filling effect were studied by the special experiment focusing on the deposition shape and the effective sealing distance, as shown in Figure5. The grouting pressure is 2.0 MPa and the water pressure is 0.6 MPa. In the final stage of grouting, the grouting pressure is kept constant for 30 min. During this period, the slurry separates water and the slurry stone body is formed.Figure 5
Slurry stone and water separation under the action of flowing water. The figure in the upper right corner is obtained in the experiment. L is the penetration distance, and l is the distance of the second deposition in the simulated fractures.The slurry deposition experiences two stages, including the first slurry diffusion stage and the second gravity deposition in the stable grouting stage. The effective plugging distancel of the slurry stone mainly depends on the gravity deposition, which is a key area for preventing water inrushes.In the slurry diffusion stage, the deposition surface presents a linear gradient and the slurry diffusion distance isL. The distance of the second gravity deposition in the fracture is l.


## 4.1.1. Water Separation

The relationship between slurry concentration and water separation rate has been obtained [26, 27], as shown in Figure 4. When the water-to-solid (clay and cement) ratio is 3 and the cement accounts for 20% of the dry material, the water separation rate of the slurry is 50%, as shown in Figure 4.Figure 4
Water separation rate of clay-cement slurry [26, 27] with different water-solid ratios. W/S is the ratio of water to dry materials.


## 4.1.2. Slurry Stone Body

The slurry deposition and filling effect were studied by the special experiment focusing on the deposition shape and the effective sealing distance, as shown in Figure5. The grouting pressure is 2.0 MPa and the water pressure is 0.6 MPa. In the final stage of grouting, the grouting pressure is kept constant for 30 min. During this period, the slurry separates water and the slurry stone body is formed.Figure 5
Slurry stone and water separation under the action of flowing water. The figure in the upper right corner is obtained in the experiment. L is the penetration distance, and l is the distance of the second deposition in the simulated fractures.The slurry deposition experiences two stages, including the first slurry diffusion stage and the second gravity deposition in the stable grouting stage. The effective plugging distancel of the slurry stone mainly depends on the gravity deposition, which is a key area for preventing water inrushes.In the slurry diffusion stage, the deposition surface presents a linear gradient and the slurry diffusion distance isL. The distance of the second gravity deposition in the fracture is l.


## 4.2. Influence of Dip Angles on the Slurry Stone Body

The slurry concentration is 1.16 g/m3, and the slurry deposition shapes and the interfaces between water and slurry stone obtained under three different dip angles are shown in Figure 6. It is difficult to completely fill the space of fractures by deposition in a horizontal hole, and a certain angle is indispensable to ideally complete the second deposition. The minimum flow limit under constant grouting pressure for a period of time is important to the formation of the slurry stone body.Figure 6
Interfaces of water and slurry stone body after water separation with different dip angles. L is the penetration distance, and H is the diameter of the glass tube (fracture height).When grouting through horizontal boreholes, the interface between slurry stone body and water is linear. When grouting through an inclined borehole, the deposition interface is divided into two sections, linear and approximate arc shape.When a horizontal borehole is used to grout the fracture with the slurry concentration of 1.16 g/m3, the stone body cannot completely fill the fracture, as shown in Figure 6. The slurry stone body formed by the second gravity deposition after grouting is the key area for effective sealing of fractures. The dip angle of boreholes is the key factor to ensure the second deposition of the slurry. In fact, in order to ensure the groutability of slurry, the slurry concentration is always not too high. The effective plugging distance is the key area formed by gravity deposition on the basis of the first deposition, which is much smaller than the diffusion area.The effective thrust forces between particles in vertical drilling holes are greater than those in inclined drilling holes, while the forces in horizontal drilling are the smallest. For a single particle, the effective thrusts between particles in the boreholes are, respectively,mg and mgsinα, as shown in Figure 7.Figure 7
Mechanical mechanism of particle gravity deposition in the second gravity deposition of the (a) inclined borehole and (b) vertical borehole.
(a)(b)


## 4.3. Sealing Effect

The verification of sealing efficiency is completed by a water injection test. Because the surface of the glass tube is smooth and the friction between the glass tube and the slurry stone body is small, the stone body is easy to be damaged by high water pressure during the reverse water injection. In the water injection test, the applied water pressure is not too high. Different sealing efficiencies are expressed by the proportion of the slurry stone body of the cross sections of the simulated fractures. Three filling effects, 20%, 60%, and 100%, of the fracture section are shown in Figure8.Figure 8
Flow characteristics of valves and filled fractures. For fractures, percent open refers to the ratio of an unfilled section to the whole section of the fracture.The slurry stone body is like a valve in the cross section of the designed fracture. Three flow characteristics of the filled fractures under the condition of flow water pressure are shown in Figure8. For fractures, percent open refers to the ratio of an unfilled section to the whole section of the fracture before grouting. When the filling area is more than 90% (percent open 10%), the flow characteristic of the fractures is closer to the equal percentage. When the filling area is less than 90%, the flow characteristics are approximately linear.Two flow patterns are observed, including free flow and fracture flow. When the grouting section is less than 90% (percent open is more than 10%), free flow occurs. When the filling degree is 90% to 100%, the water flow fluctuates obviously and the free flow gradually changes into fracture flow or Darcy flow.The effective deposition area of plugging water is much smaller than the diffusion distance of the slurry. In practice, in order to check the grouting effect, the secondary verification borehole was constructed, as shown in Figure9.Figure 9
Verification of plugging effect by the second drilling. L is the diffusion distance of the slurry, and l is the effective water plugging area.When the stone body completely seals the fracture, there is no water flowing out of the borehole. Indeed, it is the left stone of the effective plugging areal that can be used to effectively prevent water inrush. When the left effective sealing area cannot resist the water pressure, the confined water flows out of the borehole. The slurry stone is very important to prevent water inrushes.


## 4.4. Penetration Distance

### 4.4.1. Theoretical Penetration

A cement-based grout can be described as a fluid characterized by viscosity and yield stress. At the final stage of grouting, the injection pressure is balanced by the shear stress towards the fracture walls, and the grout penetration,I, in a parallel slot with an aperture of d can thus be calculated as follows:(1)I=pg−pwd2τ,where pg-pw is the difference between the injection and water pressures and τ is the yield stress of the slurry. d is the equivalent fracture width.Through equation (1), the diffusion distance is related to grouting pressure, fracture width, and slurry yield stress. In practice, experiences of grouting have shown that grout has to be injected to a full stop in order to obtain an ideal result. For a Bingham material, the formula of 1D flow rate, Q, can be obtained [16, 28] and written as follows:(2)Q=wH2c3η1−ξ22+ξξ,where ξ is the ratio of the spread to the span (the maximum spread).Hence, the effective diffusion distance,Ieff, is obtained by the following equation:(3)Ieff=ξ·I.


### 4.4.2. Penetration Distance in the Test

Because the fracture width is relatively large (the diameter is 3 cm), the slurry can easily diffuse to the outlet of the designed fracture under the condition that grouting pressure is 2.0 MPa and dynamic water pressure is 0.6 MPa. In the test, the distances of the diffusion in the fracture with three different angles are approximately equal. The penetration distance obtained from the total grout amount is as follows:(4)L=4Vgπd2,where Vg is the grout amount in the test, d is the diameter, and L is the diffusion distance.Considering the water separation rate of the slurry is 50%, the volume of the stone body can be obtained asVg/2. The distribution form of the slurry stone body is as shown in Figure 6.


## 4.4.1. Theoretical Penetration

A cement-based grout can be described as a fluid characterized by viscosity and yield stress. At the final stage of grouting, the injection pressure is balanced by the shear stress towards the fracture walls, and the grout penetration,I, in a parallel slot with an aperture of d can thus be calculated as follows:(1)I=pg−pwd2τ,where pg-pw is the difference between the injection and water pressures and τ is the yield stress of the slurry. d is the equivalent fracture width.Through equation (1), the diffusion distance is related to grouting pressure, fracture width, and slurry yield stress. In practice, experiences of grouting have shown that grout has to be injected to a full stop in order to obtain an ideal result. For a Bingham material, the formula of 1D flow rate, Q, can be obtained [16, 28] and written as follows:(2)Q=wH2c3η1−ξ22+ξξ,where ξ is the ratio of the spread to the span (the maximum spread).Hence, the effective diffusion distance,Ieff, is obtained by the following equation:(3)Ieff=ξ·I.


## 4.4.2. Penetration Distance in the Test

Because the fracture width is relatively large (the diameter is 3 cm), the slurry can easily diffuse to the outlet of the designed fracture under the condition that grouting pressure is 2.0 MPa and dynamic water pressure is 0.6 MPa. In the test, the distances of the diffusion in the fracture with three different angles are approximately equal. The penetration distance obtained from the total grout amount is as follows:(4)L=4Vgπd2,where Vg is the grout amount in the test, d is the diameter, and L is the diffusion distance.Considering the water separation rate of the slurry is 50%, the volume of the stone body can be obtained asVg/2. The distribution form of the slurry stone body is as shown in Figure 6.


## 4.5. Prediction of Grouting Effect and Its Application

### 4.5.1. Prediction of Grouting Effect in a Single Fracture

The description of sealing effect of a single fracture during grouting engineering is drawn in Figure10. In grouting practice, the slurry diffuses to both sides of the fractures with the borehole as the center and the penetration distances on both sides are different. The penetration distance on the side against the water flow direction is less than the distance along the water flow direction, when the condition of high water pressure is considered.Figure 10
Prediction of filling effect in a single fracture: (a) before grouting and (b) after grouting.
(a)(b)


### 4.5.2. Changes in the Monitored Water Volume and Pressure

The grouting quantity, water-solid ratio, and basic parameters of typical boreholes during grouting engineering are listed in Table1. The changes in water volume and water pressure are related to the plugging degree. The patterns of the grouting effect are classified into two types after grouting. For some boreholes, only the water flow is reduced but water pressure remains unchanged (D17-2 and D21-2). For other boreholes, both water pressure and water flow are reduced.Table 1
Slurry volume, water-solid ratio, and basic parameters of typical boreholes.
BoreholesLength (m)Dip angle (°)Water discharge (m3/h)Water pressure (MPa)Cement/solidSlurry volumeBeforeAfterBeforeAfterD17-21982520.24.54.50.19238.14D17-31473610.243.80.19127.54D17-51912810.24.34.00.19219.07D17-62352310.24.64.50.19218.01D19-1014234.550.25.55.00.19236.02D19-111603010.343.80.19236.02D19-13n1214710.34.23.80.19231.78D21-2197262.61.045.85.80.19256.14D21-71563510.25.35.10.19213.77


## 4.5.1. Prediction of Grouting Effect in a Single Fracture

The description of sealing effect of a single fracture during grouting engineering is drawn in Figure10. In grouting practice, the slurry diffuses to both sides of the fractures with the borehole as the center and the penetration distances on both sides are different. The penetration distance on the side against the water flow direction is less than the distance along the water flow direction, when the condition of high water pressure is considered.Figure 10
Prediction of filling effect in a single fracture: (a) before grouting and (b) after grouting.
(a)(b)


## 4.5.2. Changes in the Monitored Water Volume and Pressure

The grouting quantity, water-solid ratio, and basic parameters of typical boreholes during grouting engineering are listed in Table1. The changes in water volume and water pressure are related to the plugging degree. The patterns of the grouting effect are classified into two types after grouting. For some boreholes, only the water flow is reduced but water pressure remains unchanged (D17-2 and D21-2). For other boreholes, both water pressure and water flow are reduced.Table 1
Slurry volume, water-solid ratio, and basic parameters of typical boreholes.
BoreholesLength (m)Dip angle (°)Water discharge (m3/h)Water pressure (MPa)Cement/solidSlurry volumeBeforeAfterBeforeAfterD17-21982520.24.54.50.19238.14D17-31473610.243.80.19127.54D17-51912810.24.34.00.19219.07D17-62352310.24.64.50.19218.01D19-1014234.550.25.55.00.19236.02D19-111603010.343.80.19236.02D19-13n1214710.34.23.80.19231.78D21-2197262.61.045.85.80.19256.14D21-71563510.25.35.10.19213.77


## 5. Conclusions

A special device composed of boreholes and fractures is designed to study the whole process of grouting in limestone fractures. The boreholes angles are important conditions for the grouting effect. For a horizontal borehole, it is difficult to completely fill the space of fractures by deposition and a certain angle is necessary to achieve the second gravity deposition. The effective thrust forces between particles in vertical drilling holes are greater than those in inclined drilling holes, while those in horizontal drilling are the smallest.The slurry deposition experiences two stages, including the initial diffusion stage and the second gravity deposition stage. The water separation of the slurry used in grouting is also an important factor affecting the grouting effect, and the slurry stone body is the key area for blocking water. The minimum flow limit under constant grouting pressure for a period of time is important to the formation of stone. When the filling area of the fracture section is more than 90%, the flow characteristic of the fractures after grouting is closer to the equal percentage of valves. When the filling area is less than 90%, the flow characteristics are approximately linear. When the filling degree is more than 90%, the water flow fluctuates obviously.The changes in water volume and water pressure are related to the plugging degree. The hydrological data of typical boreholes in field grouting engineering show that both water pressure and water flow are reduced for some boreholes after grouting and for other boreholes, only the water flow is reduced but water pressure remains unchanged. Based on the experimental result, the final consolidated form with the dynamic water pressure in a single fracture was obtained. The research is helpful in the grouting reinforcement in the fractured aquifers under coal seams during mining.



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*Source: 3267279-2022-04-29.xml*