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Research Article| November 09, 2021

Experimental Study on Seepage and Fracture Characteristics of Cemented Rock Samples under Triaxial Stress

Chong Li;

Chong Li

School of Mines

MOE Key Laboratory of Deep Coal Resource Mining

China University of Mining and Technology

Xuzhou

221116 Jiangsu

China

cumt.edu.cn

Jiangsu Laboratory of Mine Earthquake Monitoring and Prevention

China University of Mining & Technology

Xuzhou

221116 Jiangsu

China

cumt.edu.cn

[email protected]

https://orcid.org/0000-0002-2535-5583

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Sifeng He

School of Mines

MOE Key Laboratory of Deep Coal Resource Mining

China University of Mining and Technology

Xuzhou

221116 Jiangsu

China

cumt.edu.cn

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Author and Article Information

Chong Li

https://orcid.org/0000-0002-2535-5583

School of Mines

MOE Key Laboratory of Deep Coal Resource Mining

China University of Mining and Technology

Xuzhou

221116 Jiangsu

China

cumt.edu.cn

Jiangsu Laboratory of Mine Earthquake Monitoring and Prevention

China University of Mining & Technology

Xuzhou

221116 Jiangsu

China

cumt.edu.cn

Sifeng He

School of Mines

MOE Key Laboratory of Deep Coal Resource Mining

China University of Mining and Technology

Xuzhou

221116 Jiangsu

China

cumt.edu.cn

[email protected]

Publisher: GeoScienceWorld

Received: 16 Aug 2021

Accepted: 19 Oct 2021

First Online: 09 Nov 2021

Online ISSN: 1947-4253

Print ISSN: 1941-8264

Funding

Funder(s):
National Natural Science Foundation of China
- Award Id(s):
  51874277

Exclusive Licensee GeoScienceWorld. Distributed under a Creative Commons Attribution License (CC BY 4.0).

Lithosphere (2021) 2021 (Special 7): 9893399.

https://doi.org/10.2113/2021/9893399

Abstract

To study the seepage and fracture characteristics of cemented rock strata, a series of triaxial seepage tests on cemented rock samples under different confining pressures and water pressures were carried out in this study. The triaxial strength, elastic modulus, volume strain, and the permeability of the cemented rock samples were analyzed by the seepage unit connection probability model and Kozeny-Carman model. Based on test results, the stress state of cemented rock samples was divided into four stages: nonlinear compaction stage, linear elastic stage, stress yield stage, and failure and postfailure stage. The triaxial strength of the cemented rock samples gradually increased with the increase of confining pressure but decreased with the increase of water pressure. The elastic modulus of the cemented rock sample increased with the increase of confining pressure but decreased with the increase of water pressure. Besides, the volume strain of the cemented rock sample was analyzed, and the volume strain change of the cemented rock sample was also classified into three stages: the increasing stage of crack volume strain, the stable stage of crack volume strain, and the decreasing stage of crack volume strain. Based on the results of triaxial seepage tests, the evolution of permeability was divided into the declining stage, increasing stage, and redescend stage. Through the seepage unit connection probability model and Kozeny-Carman model, the evolution of crack volume was obtained, and the evolution of crack volume with axial strain was also classified into three stages: the original pore closure stage, crack network expansion stage, and crack network closure stage. The permeability evolution and the crack volume evolution were also compared. The comparison results suggest that three stages of crack volume evolution are all ahead of three stages of permeability evolution, verifying that the crack propagation induces the formation of seepage channels in cemented rock samples. This research will provide a valuable reference for the study of instability and water inrush mechanism in cemented rock strata.

1. Introduction

The fault zone is a common geological structure in coal mining activities, and the broken rocks in the fault zone are generally in a weakly cemented state [1, 2]. When the underground aquifer is adjacent to the fault zone, the evolution of the seepage field and the development of the fracture zone constantly interact with each other [3, 4]. Under three-dimensional in situ stress, water inrush and surrounding rock instability collapses are prone to occur in a fault zone, which poses a massive threat to safe mining [5, 6]. Therefore, it is necessary to deeply study the crack propagation law and hydraulic characteristics of cemented rock under triaxial stress.

Three-dimensional in situ stress is a common state of underground rock strata. Research on the evolution of the mechanical state [7–9] of surrounding rocks in the mining face and underground roadways has been widely performed. Xiao et al. [10] conducted triaxial compression tests on red sandstone under different water pressures and established the permeability-stress coupling relationship for the control of rock stability. The test results showed that the stress threshold decreased with the increase of the seepage pressure. Luo et al. [11] proposed a three-dimensional seepage-stress coupling model by using the extended finite element method and revealed the response and interaction mechanism between hydraulic fractures and natural fractures. Yin et al. [12] studied the deformation and failure mechanism of the large-section roadway. It was found that the crack network extended and penetrated at the roof separation, and the dangerous region was penetrated by cracks formed inside the roof. Wang et al. [13] proposed a crack propagation criterion to predict the crack propagation process for mode I fracture based on the stress intensity factor. The proposed numerical method can effectively predict the crack propagation process of layered composite beams. In these studies, intact rock strata have been mainly investigated. However, the mechanical characteristics of cemented rock under triaxial stress have been rarely explored.

The instability of the surrounding rock in the fault is the result of the interaction of multiple fields. The interaction [14–16] of the fissure field, seepage field, and stress field can induce the simultaneous occurrence of water inrush and instability. The strain-permeability coupling relationship and volume strain evolution can be obtained by the conventional triaxial compression method [17], and the transition behavior of volume strain and permeability can be explained by a connected seepage model. Zhang et al. [18] developed a temperature-stress-seepage system to study the seepage characteristics of fractured rock. It is suggested that the Darcy flow and nonlinear flow were seepage processes of permeability evolution. The horizontal seepage tests were carried out [19] under different triaxial stress states. The test results show that the permeability of the rock material has a negative power function with the hydraulic gradient. Li et al. [20] reproduced the evolution of the water inrush channel with the advance of the working face in the FLAC^3D numerical simulation tests. The results of the numerical simulation showed that the volume strain is determined by the interaction between the stress field and the seepage field. Hou et al. [8] established a creep damage constitutive model of cemented gangue-fly ash backfill (CGFB) considering the seepage-stress coupling effect and explained the relationship between creep rate and hydraulic properties. Liu et al. [21] carried out triaxial seepage tests on fractured rock mass with the fillings. The results show that the permeability coefficient peak value appears before the stress peak value, and the filling cracked rock is sensitive to the variation of confining pressure. However, these researches cannot directly reveal the disaster-causing mechanism of water inrush in the surrounding rock of the fault. It is necessary to study the hydraulic properties of cemented rock for the exploration of disaster mechanisms.

In studies on the disaster-causing mechanism of water inrush in the surrounding rock of the fault, the coupling mechanism [22, 23] of fracture development and seepage evolution has been highlighted. Zhu et al. [24] studied the permeability evolution mechanism of fractured rock mass with the fillings and proposed the permeability model of fractured rock based on the volume strain, which can well verify the test results of true triaxial seepage. Xu et al. [25] obtained a linear relationship between the crack volume strain and the permeability of sandstone samples and divided the permeability evolution into four stages. To study the seepage characteristics and crack propagation and closure, Wang et al. [26] established a continuous-discrete medium model and effectively simulated the crack evolution by the numerical calculation method based on the ABAQUS. Jiang et al. [27] conducted seepage tests on rock specimens with intrinsic fractures. The test results showed that the structural surface damage of rock samples results in the increase of seepage speed under the high confining and seepage pressure. Wei et al. [28, 29] conducted the seepage tests of rock samples with preexisting flaws under different dip angles and concluded that the increase of the fluid pressure restrained the propagation of secondary cracks and accelerated the propagation of wing cracks. Zhang et al. [30, 31] investigated the spatiotemporal characteristics of stress-fracture-seepage coupling in panel 31401 of the Bulianta Colliery and found that the redistributed stress affected the propagation and connection of the seepage channel. The Navier-Stokes $k ‐ ε$ model [22] was established to analyze the seepage characteristics of the fracture network. The results showed that water pressure negatively affected the accuracy of the radial flow cubic law. Zhang et al. [32] studied the effect of fracture width on the seepage characteristics by the water and slurry seepage and established a quadratic function between seepage velocity and hydraulic gradient. Jin et al. [33] analyzed the effect of roughness on the seepage characteristics of joint rock mass by the chemical grouting in fractures. It is found that the joint roughness coefficient is negatively related to the seepage velocity. The above literature focuses on the influence of the fracture type and evolution process on the seepage characteristics. Few literatures report the effect of seepage flow on crack propagation in the cemented rock strata.

In this study, the triaxial seepage tests were carried out on cemented rock samples, and the instability of the surrounding rock in fault was simulated under three-dimensional in situ stress. The mechanical and hydraulic properties of cemented rock samples were analyzed under different confining pressures and water pressures. The total volume strain, matrix volume strain, and crack volume strain were solved under different confining pressures and water pressures. The evolution of crack volume changing with the axial strain was analyzed based on the seepage unit connection probability model and Kozeny-Carman model.

2. Experiment Preparation and Design

2.1. Sample Preparation

The rock particle material was red sandstone, which was collected from the Chensilou coal mine fault zone. The sample preparation of cemented rock samples is as follows:

2.1.1. Screen the Rock Particles

The broken red sandstone samples were sieved through the fractal sieve to obtain rock particles with different particle sizes (as shown in Figure 1(a)).

2.1.2. Weight Distribution

After the fractal sieve operation, four kinds of rock particles with different particle sizes (2-5 mm, 5-8 mm, 8-10 mm, and 10-12 mm) were obtained. The cement and gypsum were selected as cementing materials. The cement, gypsum, and the four kinds of rock particles with different particle sizes were mixed at a ratio of 1 : 1 : 1 : 1 : 1 : 1. The weight of each component was 50 g, and the total mass of the cemented rock sample was 300 g (as shown in Figure 1(b)).

2.1.3. Concreting of Rock Sample

After adding water, the mixture was mixed and stirred evenly. The mixed slurry was injected into a model with a diameter of 50 mm and a height of 100 mm. In order to ensure the uniform distribution of broken rock particles and avoid the generated pores in the preparation process of the cemented rock sample, the mixed slurry was vibrated and tamped (as shown in Figure 1(c)).

2.1.4. Demoulding

The solidified cemented rock samples were taken out from the model and placed in a curing box for 28 days. Finally, the cemented samples were obtained with 50 mm in diameter and 100 mm in height (as shown in Figure 1(d)).

2.2. Testing System and Scheme

The triaxial seepage tests were carried out by the MTS815 testing system. As shown in Figure 2, the testing system includes (1) the axial compression control system, which is used to control the axial displacement of compression platen. The sensor on the compression platen transmits the recorded stress-strain data to the data acquisition computer; (2) the triaxial compression chamber, which is the core component of the whole system. The seepage test with the triaxial compression is conducted in this part; (3) the water pressure control system, which is used to supply the stable water pressure condition for triaxial seepage tests; and (4) the confining pressure control system, which is used to provide the stable confining pressure for the triaxial compression.

Figure 3 is the schematic diagram of the triaxial seepage test. The cemented rock sample is loaded on the axial pressure $σ_{1}$ and confining pressure $σ_{3}$ ⁠. At the same time, the water pressure values at the top and bottom of the triaxial compression chamber are $P_{1}$ and $P_{2}$ ⁠, respectively. Therefore, the cemented rock sample experiences the bottom-up seepage with the triaxial compression. To investigate the hydraulic characteristics of cemented rock samples, the axial compression control system and water pressure system are paused every 10 seconds. As water flows over the cemented rock sample, the water pressure difference $Δ P$ (⁠ $Δ P = P_{2} - P_{1}$ ⁠) and the time $Δ t$ will be recorded. A series of $Δ P$ and $Δ t$ can be collected by the data collection system, which provides primary data for permeability calculation.

To investigate the effects of different water pressures and confining pressures on seepage-fracture characteristics of cemented rock samples, 12 groups of cemented rock samples were designed for the triaxial seepage tests. The detailed experimental scheme is shown in Table 1.

3. Triaxial Mechanical Characteristics of Cemented Rock Samples

According to the deviatoric stress-strain curves (in Figures 4–6) of the cemented rock samples under triaxial compression, the mechanical state of the rock samples can be divided into four stages: nonlinear compaction stage, linear elastic stage, stress yield stage, and failure and postfailure stages. In the nonlinear compaction stage, the stress mainly affects the pore compression inside the cemented rock samples. Therefore, the relationship between stress and axial strain is nonlinear in this stage. In the linear elastic stage, the stress acts on the cementing materials and rock particles of the cemented rock sample, leading to the elastic deformation of rock samples. At this stage, the stress and axial strain also present a linear relationship. In the stress yield stage, the cementing materials and rock particles inside the cemented rock sample reach the limits of elastic deformation. The rock particles and cementing materials are gradually separated from each other, and the failure of rock particles occurs. The partial stress inside the rock sample is released; with the increase of the strain, the growth rate of stress gradually decreases at this stage. In the failure and postfailure stage, the stress reaches its peak value, and the internal stress of the rock sample is ultimately released. As the axial strain increases, the stress gradually decreases.

It is worth noting that all the triaxial stress-strain curves appear a smooth variation trend, indicating that the cemented rock sample experiences stable and gradual failure during the compression process. This phenomenon can be explained by two reasons: (1) with the development of the internal pore structure of the cemented rock, the rock particles are relatively loose, and the stress mutation is hardly induced by the accumulative energy inside the rock sample, and (2) due to the coupling mechanism of seepage and stress, the ductility of rock samples is increased. As a result, gradual and steady failure is caused inside the rock samples.

As shown in Figures 4–6, the triaxial strength of the cemented rock sample gradually decreases with the increasing water pressure. This is because seepage flow erodes the internal structure and reduces the strength of the cemented rock sample. According to the stress-strain curves under different confining pressures, it is found that the triaxial strength of the cemented rock samples gradually increases as the confining pressure increases. Firstly, the confining pressure reduces the porosity between the particles of the cemented rock sample and makes the internal structure denser. Secondly, the increasing confining pressure inhibits the seepage flow inside the rock sample, which reduces the weakening effect of seepage flow to the triaxial strength. Therefore, the triaxial strength of rock samples increases with the increase of the confining pressure.

The elastic modulus [34] of the cemented rock sample is solved by the linear stage of stress-strain. The calculation method is as follows:

\begin{matrix} (1) & E = \frac{σ_{m} - σ_{n}}{ε_{1 m} - ε_{1 n}}, \end{matrix}

where

σ_{n}

is the deviator stress value at the starting point of the linear phase,

σ_{m}

is the deviator stress value at the end of the linear phase,

ε_{1 n}

is the axial strain value at the starting point of the linear phase, and

ε_{1 m}

is the axial strain value at the end of the linear phase.

The Poisson ratio [35] of the cemented rock sample is also solved by the linear stage of stress-strain. The calculation method is as follows:

\begin{matrix} (2) & ν = \frac{ε_{3 m} - ε_{3 n}}{ε_{1 m} - ε_{1 n}}, \end{matrix}

where

ε_{3 n}

is the radial strain value at the starting point of the linear phase and

ε_{3 m}

is the radial strain value at the destination of the linear phase.

Table 2 shows the elastic modulus and Poisson ratio of cemented rock samples under different water pressures and confining pressures. As shown in Figure 7(a), the elastic modulus gradually decreases with the increase of water pressure, indicating that seepage flow can reduce the elastic modulus of the cemented rock sample. According to Figure 7(b), the results show that the elastic modulus gradually increases with the increase of confining pressure. This is because the confining pressure increases the elasticity of cemented rock samples and causes the denser particle arrangement of the cemented rock samples. According to Figure 8, the Poisson ratio increases from 0.24 to 0.29, and the Poisson ratio has no noticeable change with the confining pressure and water pressure. This is because the porosity distribution and seepage channels inside the cemented rock sample are irregular.

4. Crack Volume Strain Evolution of Cemented Rock Samples

In the triaxial stress state, the volume strain of cemented rock samples can be calculated from the scale of the microunit body. The side length of a rectangular microunit body is taken as

d x

⁠,

d y

⁠, and

d z

⁠; then, the volume of the microunit body is

\begin{matrix} (3) & d v = d x d y d z . \end{matrix}

When the cemented rock sample is loaded on triaxial stress, its strains in the three directions are

ε_{x}

⁠,

ε_{y}

⁠, and

ε_{z}

⁠, and the volume increment after deformation is

\begin{matrix} (4) & d v + Δ d v = (1 + ε_{x}) d x (1 + ε_{y}) d y (1 + ε_{z}) d z . \end{matrix}

The volume increment after deformation is expressed as follows:

\begin{matrix} (5) & Δ d v = [(1 + ε_{x}) (1 + ε_{y}) (1 + ε_{z}) - 1] d v . \end{matrix}

Expanding equation (), the higher-order terms are omitted; then, the approximate volume increment can be expressed as follows:

\begin{matrix} (6) & Δ d v = (ε_{x} + ε_{y} + ε_{z}) d v . \end{matrix}

The total volume strain of the microunit body is expressed by

\begin{matrix} (7) & ε_{v}^{t} = \frac{Δ d v}{d v} = ε_{x} + ε_{y} + ε_{z} . \end{matrix}

In the normal triaxial stress state,

ε_{y} = ε_{z}

⁠; therefore, the total volume strain can be expressed by

\begin{matrix} (8) & ε_{v}^{t} = |ε_{1} + 2 ε_{3}|, \end{matrix}

where

ε_{1}

is the axial strain and

ε_{3}

is the radial strain.

However, it is difficult to measure the crack volume strain directly. Generally, the crack volume strain is reflected by the difference between the total volume strain and the matrix volume strain of the rock material. Generalized Hooke’s law is as follows [36]:

\begin{matrix} (9) & \{\begin{cases} ε_{1}^{m} = \frac{1}{E} [σ_{1} - ν (σ_{2} + σ_{3})], \\ ε_{3}^{m} = \frac{1}{E} [σ_{3} - ν (σ_{1} + σ_{2})], \end{cases} \end{matrix}

where

ε_{1}^{m}

refers to the axial strain of rock matrix and

ε_{3}^{m}

refers to the radial strain of rock matrix.

Therefore, the matrix volume strain can be described by

\begin{matrix} (10) & ε_{v}^{m} = ε_{1}^{m} + 2 ε_{3}^{m} = \frac{1 - 2 ν}{E} (σ_{1} + 2 σ_{3}) . \end{matrix}

Hence, the crack volume strain is

\begin{matrix} (11) & ε_{v}^{c} = ε_{v}^{t} - ε_{v}^{m} = ε_{v}^{t} - \frac{1 - 2 ν}{E} (σ_{1} + 2 σ_{3}) . \end{matrix}

According to Figures 9–11, the total volume strain and matrix volume strain curves and the deviatoric stress-strain curves have the same change law. The total volume strain and matrix volume strain first increase and then decrease with the increase of the axial strain. According to the change curve of crack volume strain with axial strain, the evolution of crack volume strain can be divided into three stages: (1) The first stage is the increasing stage of crack volume strain. In this stage, the total volume strain is more than the matrix volume strain, because the pore compression and crack propagation will contribute to the total volume strain. (2) The second stage is the stable stage of crack volume strain. In this stage, there is a stable difference between the total volume strain and the matrix volume strain, namely, the stable value of the crack volume strain. The stable difference corresponds to an equilibrium state of crack propagation in the rock sample. (3) The third stage is the decreasing stage of crack volume strain. In this stage, the total volume strain is still more than the matrix volume strain, but the difference between them is getting smaller. The crack network formed in the previous stage gradually closes, and the crack volume strain of the rock sample gradually decreases. It can be found that the first and third stages obviously exist in the evolution of the crack volume strain, corresponding to the beginning and ending states of crack propagation of rock samples. However, the stable stage of crack volume strain (the second stage) is an equilibrium limitation state and does not necessarily exist. The existence of the second stage is related to the individual differences of cemented rock samples.

5. Hydraulic Characteristics and Crack Evolution Mechanism

5.1. Hydraulic Characteristics of Cemented Rock Samples

Based on the assumption that the fluid in the cemented rock sample is considered the continuum medium, permeability $k$ can be calculated by Darcy’s flow law. The detailed calculation process is as follows.

The bulk modulus

K_{f}

of the fluid can be defined as:

\begin{matrix} (12) & K_{f} d V = - V d P, \end{matrix}

where

V

is the volume of fluid and

P

is the fluid pressure.

According to the mass conservation equation, it can be derived that

\begin{matrix} (13) & V d ρ + ρ d V = 0, \end{matrix}

where

ρ

is the fluid density.

Then, the bulk modulus

K_{f}

can be expressed as

\begin{matrix} (14) & K_{f} d ρ = ρ d P . \end{matrix}

Assuming that

m

represents the mass flow, the mass of liquid flowing out of the tank per unit time is

m d t

⁠, and

S

represents the cross-section of the rock sample, then

\begin{matrix} (15) & A d ρ = - m d t, \\ (16) & m = ρ S v, \end{matrix}

where

A

is the volume of the water container,

t

is the time, and

v

is the flow velocity.

Combined with equations (), (), (), and (), equation () can be derived:

\begin{matrix} (17) & \frac{d P}{d t} = - \frac{K_{f} S v}{A} . \end{matrix}

The mass of fluid inflow and outflow per unit time is the same, and

p_{1}

increases while

p_{2}

decreases; therefore,

\begin{matrix} (18) & v = \frac{A H}{2 K_{f} S} \frac{d ζ}{d t}, \end{matrix}

where

ζ

is the pressure gradient,

ζ = - (P_{2} - P_{1}) / H

⁠, and

H

is the height of the sample.

According to Darcy’s law [37], the relationship between the flow velocity and the pressure gradient is

\begin{matrix} (19) & ξ = - \frac{μ}{k} v, \end{matrix}

where

μ

is the dynamic viscosity and

k

is the permeability.

Substituting equation () into equation (), it can be derived:

\begin{matrix} (20) & \frac{d ζ}{d t} = - 2 \frac{K_{f} S k}{A H μ} ζ . \end{matrix}

ζ_{0}

and

ζ_{1}

are the initial and final pressure gradient.

Δ t

is the total time of the seepage test, and it can be derived:

\begin{matrix} (21) & \ln \frac{ζ_{0}}{ζ_{1}} = 2 \frac{K_{f} S k Δ t}{A H μ} . \end{matrix}

The permeability of the rock sample is obtained as follows:

\begin{matrix} (22) & k = \frac{A H μ}{2 Δ {t K}_{f} S} \ln \frac{ζ_{0}}{ζ_{1}} . \end{matrix}

In order to facilitate the study of the influence of confining pressure and water pressure on hydraulics and crack volume evolution characteristics, 6 groups were selected from 12 groups of data for analysis. Table 3 shows the initial permeability and initial crack volume of the cemented rock samples. The results show that the initial permeability gradually increases with the increase of water pressure. As the confining pressure increases, the initial permeability gradually decreases. The initial crack volume has the same variation trend as the initial permeability.

According to Figure 12, the evolution of permeability with axial strain can be divided into three stages. The first stage is the declining stage, the second stage is the increasing stage, and the third stage is the redescend stage. As shown in Figure 12(a), as the water pressure gradually increases, the average permeability of the three stages gradually increases, because high water pressure can promote the seepage flow. As the water pressure increases, the duration of the three stages is gradually lengthened. From Figure 12(b), as the confining pressure increases, the variation amplitude in permeability at each stage decreases gradually. This is because the confining pressure compacts the particles of the cemented rock sample and inhibits the formation of seepage channels. Therefore, the variation of permeability is inhibited.

5.2. Evolution of Crack Propagation Induced by Seepage Flow of Cemented Rock Sample

The cemented rock sample is composed of rock particles and cementing materials. The seepage unit connection probability model is applied in this section, and the connection probability of any two adjacent seepage units is represented by

p

⁠. The dynamic evolution of the crack volume under the action of external load is determined by the failure of the microunit in the rock sample. According to the conceptions of the connection probability and failure probability, the connection probability

p

can be expressed by the failure probability of the microunit. Considering the failure randomness of the microunits inside the cemented rock sample, the failure of the microunits can be assumed as the Weibull distribution model [38]. The density distribution function of the failure probability of the microunits is expressed as follows:

\begin{matrix} (23) & p (λ) = \frac{η}{λ_{0}} {(\frac{λ}{λ_{0}})}^{η - 1} \exp [- {(\frac{λ}{λ_{0}})}^{η}], \end{matrix}

where

λ

is the strength of microunit of cemented rock sample and

λ_{0}

and

η

are two parameters of the Weibull distribution model.

The connection of the microunits directly determines the formation of the seepage channel. Therefore, the connection probability factor

P

of the cemented rock sample seepage unit is expressed by

\begin{matrix} (24) & P (λ) = \int_{0}^{λ} p (x) d x = 1 - \exp [- {(\frac{λ}{λ_{0}})}^{η}] . \end{matrix}

The connection probability factor

C

can be regarded as the damage variable of the rock sample. Hence, the connection probability of the cemented rock sample seepage unit can be described by

\begin{matrix} (25) & C = ε_{1} (1 - P) . \end{matrix}

The microunit strength can be described by the axial strain of the rock sample. Therefore, equation () can be written as follows:

\begin{matrix} (26) & C = ε_{1} \exp [- {(\frac{ε_{1}}{λ_{0}})}^{η}], \end{matrix}

where

ε_{1}

is the axial strain of the cemented rock sample. In addition, the connection probability of the seepage unit of the cemented rock sample satisfies the following boundary conditions:

\begin{matrix} (27) & \{\begin{cases} ε_{1} = ε_{1 m}, C = C_{m}, \\ \frac{\partial C}{\partial ε_{1}}| (ε_{1 m}, C_{m}) = 0 . \end{cases} \end{matrix}

Based on equation (), equation () can be derived:

\begin{matrix} (28) & \{\begin{cases} ε_{1 m} \exp [- {(\frac{ε_{1 m}}{λ_{0}})}^{η}] = C_{m}, \\ ε_{1 m} \exp [- {(\frac{ε_{1 m}}{λ_{0}})}^{η}] [1 - η {(\frac{ε_{1 m}}{λ_{0}})}^{η}] = 0, \end{cases} \end{matrix}

where the most connection probability

C_{m} = k_{m} / k_{0}

⁠,

k_{0}

and

k_{m}

are the initial and most permeability of the cemented rock sample.

By solving equation (), it can be obtained:

\begin{matrix} (29) & \{\begin{cases} η = \frac{1}{\ln (ε_{1 m} / C_{m})}, \\ λ_{0} = \frac{1}{ε_{1 m}} {(\frac{1}{η})}^{1 / η} . \end{cases} \end{matrix}

Up to now, all the parameters of the connection probability model of the seepage unit can be solved.

Based on the Kozeny-Carman equation [39, 40], the relationship between permeability and crack volume can be described:

\begin{matrix} (30) & k = k_{0} {(\frac{V_{c}}{n_{0}})}^{3}, \end{matrix}

where

V_{c}

is the volume of porosity and crack network of the cemented rock sample and

n_{0}

is the initial porosity of the cemented rock sample. Considering the connection probability of the seepage unit, equation () is introduced into the above formula; then, equation () can be derived:

\begin{matrix} (31) & k = k_{0} ε_{1} \exp [- {(\frac{ε_{1}}{λ_{0}})}^{η}] {(\frac{V_{c}}{n_{0}})}^{3} . \end{matrix}

The variation of the crack volume of the cemented rock sample under the triaxial compression is induced by the microunit strain. Therefore, the crack volume and volume strain satisfy the following relationship:

\begin{matrix} (32) & \{\begin{cases} V_{c} = {ω ε}_{v}, \\ ω = \frac{ε_{v}^{c}}{ε_{v}^{t}} . \end{cases} \end{matrix}

Equation () can be transformed into

\begin{matrix} (33) & \frac{k}{k_{0}} ω (2 ν + 1) {n_{0}}^{3} = {V_{c}}^{4} \exp [- {(\frac{V_{c}}{λ_{0} ω (2 ν + 1)})}^{η}] . \end{matrix}

Taking the logarithm of both sides of equation (), then

\begin{matrix} (34) & C = 4 \ln V_{c} + {A V}_{c}^{η} . \end{matrix}

In this equation,

\begin{matrix} (35) & \{\begin{cases} A = - {[{ω λ}_{0} (2 ν + 1)]}^{- η}, \\ C = \ln [ω {n_{0}}^{3} (2 ν + 1) \frac{k}{k_{0}}], \end{cases} \end{matrix}

where

C

⁠,

A

⁠, and

η

in equation () are all known constants. The solution of equation () can be used to obtain

V_{c}

of the cemented rock sample.

Figures 13(a)–13(d) show the evolution curves of $V_{c}$ with the change of axial strain under the confining pressure of 3 MPa and water pressures of 0.5 MPa, 1.0 MPa, 2.0 MPa, and 5.0 MPa. Figures 13(c), 13(e), and 13(f) show the evolution curves of $V_{c}$ with the change of axial strain under the water pressure of 2 MPa and confining pressure of 1 MPa, 3 MPa, and 5 MPa, respectively. By comparison, it is suggested that the confining pressure has an effect on the initial value of $V_{c}$ ⁠, and the initial value of $V_{c}$ decreases as the confining pressure increases. However, the water pressure has no obvious effect on the initial value of $V_{c}$ ⁠.

According to the variation trend of $V_{c}$ with axial strain [41], the curve can be divided into three stages. The first stage is the initial pore closure stage. In this stage, the cemented rock sample mainly experiences the closure of the original pores. At the same time, partial fissures are initiated inside the rock sample. The volume of the closed pores is much more than that of the newly generated partial cracks. Therefore, $V_{c}$ shows a gradual decreasing tendency with the increase of axial strain at this stage. The second stage is the crack network expansion stage. In this stage, the cemented rock samples mainly experience the formation of the new crack network. At the same time, the unclosed pores in the previous stage are gradually closed. The volume of the new crack network is much more than the volume of closed pores. Therefore, the volume of the cracks shows a gradually increasing tendency with the increase of axial strain. The third stage is the crack network closure stage. In this stage, the cemented rock sample mainly experiences the closure of the crack network. The crack volume shows a decreasing trend with the increase of axial strain. According to the evolution curves of the three stages, it can be known that the pore closure and crack initiation compete with each other to determine the evolution of $V_{c}$ in the early stage. The extension and closure of the crack network mainly determine the evolution of $V_{c}$ in the later stage.

By comparing the three stages of permeability and $V_{c}$ with the increase of axial strain, it is found that the variation of $V_{c}$ is ahead of the variation of permeability. The initial pore closure stage is ahead of the declining stage of permeability. This is because the closure of the original pores hinders the formation of permeable channels and reduces the permeability of cemented rock samples. The crack network extension stage is ahead of the increasing stage of permeability. This is because the formation of the new crack network increases the probability of connection between seepage units of the cemented rock sample, thereby promoting the formation of seepage channels and increasing the permeability of cemented rock samples. The closure stage of the crack network is ahead of the redescend stage of permeability. This is because the closure of the crack network directly inhibits the formation of seepage channels and reduces the permeability of the cemented rock sample.

6. Conclusions

To study the seepage-crack characteristics of cemented rock strata, a series of triaxial seepage tests on cemented rock samples were carried out in this study. The main conclusions are drawn as follows:

(1)
The stress state of the cemented rock sample experiences four stages, including nonlinear compaction stage, linear elastic stage, stress yield stage, and failure and postfailure stages. Test results show that the triaxial strength of the cemented rock samples gradually increases with the increase of the confining pressure but decreases with the increase of the water pressure. The elastic modulus of the cemented rock sample increases with the increase of confining pressure but decreases with the increase of water pressure. The confining pressure and water pressure have no obvious effect on the Poisson ratio of the cemented rock sample
(2)
Based on the total volume strain and rock matrix volume strain, the crack volume strain was obtained. By analyzing the volume strain evolution of the cemented rock sample, it is found that the cemented rock sample experiences the increasing stage of crack volume strain, the stable stage of crack volume strain, and the reducing stage of crack volume strain
(3)
During the triaxial seepage of the cemented rock sample, the evolution of permeability experienced the declining stage, increasing stage, and redescend stage. The duration of each stage increases with the increase of water pressure, and the variation amplitude in permeability at each stage decreases gradually with the increase of confining pressure. The evolution of $V_{c}$ was solved based on the seepage unit connection probability model and Kozeny-Carman model. It is indicated that the evolution of $V_{c}$ with the axial strain can also be divided into three stages: initial pore closure stage, crack network expansion stage, and crack network closure stage. The comparison result suggests that three evolution stages of $V_{c}$ are all ahead of three evolution stages of permeability, which verifies that the evolution of $V_{c}$ determines the formation of seepage channels of cemented rock samples

Data Availability

The experimental data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare no competing financial interest.

Acknowledgments

This research was financially supported by the National Natural Science Foundation of China (Grant No. 51874277).

Figure 1

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Sample preparation process.

Figure 2

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Testing system.

Figure 3

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Triaxial compression chamber.

Figure 4

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Triaxial stress-strain curves of cemented rock samples under 1 MPa confining pressure and different water pressures: (a) $P_{w} = 0.5 MPa$ ⁠, (b) $P_{w} = 1.0 MPa$ ⁠, (c) $P_{w} = 2.0 MPa$ ⁠, and (d) $P_{w} = 5.0 MPa$ ⁠.

Figure 5

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Triaxial stress-strain curves of cemented rock samples under 3 MPa confining pressure and different water pressures: (a) $P_{w} = 0.5 MPa$ ⁠, (b) $P_{w} = 1.0 MPa$ ⁠, (c) $P_{w} = 2.0 MPa$ ⁠, and (d) $P_{w} = 5.0 MPa$ ⁠.

Figure 6

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Triaxial stress-strain curves of cemented rock samples under 5 MPa confining pressure and different water pressures: (a) $P_{w} = 0.5$ MPa, (b) $P_{w} = 1.0$ MPa, (c) $P_{w} = 2.0$ MPa, and (d) $P_{w} = 5.0$ MPa.

Figure 7

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The variation of elasticity modulus of cemented rock samples: (a) with water pressure; (b) with confining pressure.

Figure 8

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The variation of Poisson ratio of cemented rock samples.

Figure 9

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The evolution of volume strain with axial strain under 1 MPa confining pressure and different water pressures: (a) $P_{w} = 0.5$ MPa, (b) $P_{w} = 1.0$ MPa, (c) $P_{w} = 2.0$ MPa, and (d) $P_{w} = 5.0$ MPa.

Figure 10

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The evolution of volume strain with axial strain under 3 MPa confining pressure and different water pressures: (a) $P_{w} = 0.5$ MPa, (b) $P_{w} = 1.0$ MPa, (c) $P_{w} = 2.0$ MPa, and (d) $P_{w} = 5.0$ MPa.

Figure 11

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The evolution of volume strain with axial strain under 5 MPa confining pressure and different water pressures: (a) $P_{w} = 0.5$ MPa, (b) $P_{w} = 1.0$ MPa, (c) $P_{w} = 2.0$ MPa, and (d) $P_{w} = 5.0$ MPa.

Figure 12

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The evolution of permeability with axial strain: (a) $σ_{3} = 3$ MPa; (b) $P_{w} = 2.0$ MPa.

Figure 13

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The evolution of $V_{c}$ and $k$ with axial strain: (a) $σ_{3} = 3$ MPa, $P_{w} = 0.5$ MPa; (b) $σ_{3} = 3 MPa, P_{w} = 1.0 MPa$ ⁠; (c) $σ_{3} = 3 MPa, P_{w} = 2.0 MPa$ ⁠; (d) $σ_{3} = 3 MPa, P_{w} = 5.0 MPa$ ⁠; (e) $σ_{3} = 1 MPa, P_{w} = 2.0 MPa$ ⁠; (f) $σ_{3} = 5 MPa, P_{w} = 2.0 MPa$ ⁠.

Table 1

Detailed test scheme.

Sample number	Confining pressure (MPa)	Water pressure (MPa)	Mass (g)
$S_{1}$	1.0	0.5	301.21
$S_{2}$		1.0	300.89
$S_{3}$		2.0	299.15
$S_{4}$		5.0	298.98

$S_{5}$	3.0	0.5	301.35
$S_{6}$		1.0	300.45
$S_{7}$		2.0	299.78
$S_{8}$		5.0	300.99

$S_{9}$	5.0	0.5	299.36
$S_{10}$		1.0	298.36
$S_{11}$		2.0	299.54
$S_{12}$		5.0	300.23

Sample number	Confining pressure (MPa)	Water pressure (MPa)	Mass (g)
$S_{1}$	1.0	0.5	301.21
$S_{2}$		1.0	300.89
$S_{3}$		2.0	299.15
$S_{4}$		5.0	298.98

$S_{5}$	3.0	0.5	301.35
$S_{6}$		1.0	300.45
$S_{7}$		2.0	299.78
$S_{8}$		5.0	300.99

$S_{9}$	5.0	0.5	299.36
$S_{10}$		1.0	298.36
$S_{11}$		2.0	299.54
$S_{12}$		5.0	300.23

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Table 2

The elasticity modulus and Poisson ratio of cemented rock samples.

Sample number	Confining pressure	Water pressure	Elasticity modulus	Poisson ratio
$S_{1}$	1 MPa	0.5 MPa	1.013 GPa	0.263
$S_{2}$		1 MPa	0.838 GPa	0.285
$S_{3}$		2 MPa	0.639 GPa	0.276
$S_{4}$		5 MPa	0.479 GPa	0.288

$S_{5}$	3 MPa	0.5 MPa	1.302 GPa	0.269
$S_{6}$		1 MPa	0.979 GPa	0.287
$S_{7}$		2 MPa	0.805 GPa	0.268
$S_{8}$		5 MPa	0.668 GPa	0.246

$S_{9}$	5 MPa	0.5 MPa	1.581 GPa	0.256
$S_{10}$		1 MPa	1.211 GPa	0.239
$S_{11}$		2 MPa	1.038 GPa	0.246
$S_{12}$		5 MPa	0.966 GPa	0.261

Sample number	Confining pressure	Water pressure	Elasticity modulus	Poisson ratio
$S_{1}$	1 MPa	0.5 MPa	1.013 GPa	0.263
$S_{2}$		1 MPa	0.838 GPa	0.285
$S_{3}$		2 MPa	0.639 GPa	0.276
$S_{4}$		5 MPa	0.479 GPa	0.288

$S_{5}$	3 MPa	0.5 MPa	1.302 GPa	0.269
$S_{6}$		1 MPa	0.979 GPa	0.287
$S_{7}$		2 MPa	0.805 GPa	0.268
$S_{8}$		5 MPa	0.668 GPa	0.246

$S_{9}$	5 MPa	0.5 MPa	1.581 GPa	0.256
$S_{10}$		1 MPa	1.211 GPa	0.239
$S_{11}$		2 MPa	1.038 GPa	0.246
$S_{12}$		5 MPa	0.966 GPa	0.261

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Table 3

$V_{c 0}$ and $k_{0}$ of cemented rock samples.

Water pressure (MPa)	Confining pressure (MPa)	$k_{0}$ (10^-12 mm²)	$V_{c 0}$ (%)
3	0.5	8.742	7.124
	1.0	16.124	7.726
	2.0	21.118	7.335
	5.0	27.924	7.245

1	2.0	24.926	7.512
5	2.0	7.125	7.397

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Experimental Study on Seepage and Fracture Characteristics of Cemented Rock Samples under Triaxial Stress

Abstract

1. Introduction

2. Experiment Preparation and Design

2.1. Sample Preparation

2.1.1. Screen the Rock Particles

2.1.2. Weight Distribution

2.1.3. Concreting of Rock Sample

2.1.4. Demoulding

2.2. Testing System and Scheme

3. Triaxial Mechanical Characteristics of Cemented Rock Samples

4. Crack Volume Strain Evolution of Cemented Rock Samples

5. Hydraulic Characteristics and Crack Evolution Mechanism

5.1. Hydraulic Characteristics of Cemented Rock Samples

5.2. Evolution of Crack Propagation Induced by Seepage Flow of Cemented Rock Sample

6. Conclusions

Data Availability

Conflicts of Interest

Acknowledgments

Data & Figures

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Experimental Study on Seepage and Fracture Characteristics of Cemented Rock Samples under Triaxial Stress

Abstract

1. Introduction

2. Experiment Preparation and Design

2.1. Sample Preparation

2.1.1. Screen the Rock Particles

2.1.2. Weight Distribution

2.1.3. Concreting of Rock Sample

2.1.4. Demoulding

2.2. Testing System and Scheme

3. Triaxial Mechanical Characteristics of Cemented Rock Samples

4. Crack Volume Strain Evolution of Cemented Rock Samples

5. Hydraulic Characteristics and Crack Evolution Mechanism

5.1. Hydraulic Characteristics of Cemented Rock Samples

5.2. Evolution of Crack Propagation Induced by Seepage Flow of Cemented Rock Sample

6. Conclusions

Data Availability

Conflicts of Interest

Acknowledgments

Data & Figures

About GSW

Resources

Explore

Connect

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