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Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure
Journal Pre-proof Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure
Weijing Xiao, Dongming Zhang, Xiaojun Wang PII:
S0013-7952(19)30870-1
DOI:
https://doi.org/10.1016/j.enggeo.2019.105406
Reference:
ENGEO 105406
To appear in:
Engineering Geology
Received date:
10 May 2019
Revised date:
2 August 2019
Accepted date:
11 November 2019
Please cite this article as: W. Xiao, D. Zhang and X. Wang, Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure, Engineering Geology (2019), https://doi.org/10.1016/ j.enggeo.2019.105406
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© 2019 Published by Elsevier.
Journal Pre-proof
Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure Weijing Xiao a, b, Dongming Zhang a, b* , Xiaojun Wang
c
a
State Key Laboratory of Coal M ine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
b
School of Resources and Environmental Sciences, Chongqing University, Chongqing 400044, China
c
School of Resources and Environmental Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi,
China
f
Experimental study on progressive failure process and permeability
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characteristics of red sandstone under seepage pressure Weijing Xiao a,b [email protected], Dongming Zhanga,b,* [email protected], Xiaojun Wangc
a
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[email protected]
State Key Laboratory of Coal M ine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
b
School of Resources and Environmental Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi,
Pr
c
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School of Resources and Environmental Sciences, Chongqing University, Chongqing 400044, China
China *
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Corresponding author.
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Abstract: Rock masses in underground spaces often experience in-situ stress field and seepage field coupling which gives them complex mechanical behavioural and permeability characteristics. In this study, a High
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Pressure Triaxial Automated System for Rock (HPTAS) is employed in triaxial compression testing of red sandstone under different seepage pressures, and the variation laws of strength, deformation, axial strain stiffness and permeability during rock failure are analysed. The results show that with changes in the seepage pressure, there are also changes in the rock’s strength and ability to resist deformation, and the stress threshold decreases with an increase in the seepage pressure. In addition, seepage pressure does not affect the strain stiffness trend, but it affects the value. Throughout the process of stress and strain, the permeability curve firstly decreases and then increases rapidly before finally stabilizing, and the peak value of the permeability curve lags behind that of the stress-strain curve. According to the law of permeability evolution during the pre-peak progressive failure process, a piecewise functional relationship model between permeability and stress is established in this study, and theoretical values agree well with experimental results. These experimental results can be used as a reference for monitoring and controlling rock stability during geological engineering when a seepage-stress coupling action is applied. Key words: triaxial compression test; seepage pressure; rock failure; stress thresholds; permeability
*
Corresponding author. E-mail address: [email protected] (W. Xiao), [email protected] (D. Zhang), [email protected] (X. Wang).
Journal Pre-proof 1 Introduction Rock has a compact structure and a low fluid flow rate; therefore, it is often used as the main geological medium when constructing underground energy storage and nuclear waste disposal systems (Wang et al., 2018; Zhao et al., 2018). It is also a common complex medium used in the construction of water conservancy and hydropower projects, oil and gas field exploitation, underground mining projects and in deep-burial energy storage projects (Jeanpert et al., 2019; Yu et al., 2019; Giot et al., 2018). However, excavation disturbance causes changes in in-situ stress and groundwater pressure and subsequent changes in the strength and permeability characteristics of rock during the loading process, and such processes have been well-studied in the field of rock mechanics (Fisher et al. 2017; Meng et al., 2019). There is a complex relationship between water and the rock mass in the process of internal flow, and this alters with respect to the seepage pressure. Previous research achievements have shown that the presence of
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water can reduce the strength and deformation of rock. In addition, seepage pressure can reduce the effectiveness of the confining pressure of the rock, and this causes the effect of deterioration to be more complex (Masuda et al., 2001; Chen et al., 2018). In recent years, many scholars have conducted experimental
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studies based on the permeability characteristics of rock during compression, and useful results have been obtained. In this respect, Heland (2003) used sandstone as the research object to study the permeability
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characteristics of sandstone during deformation and failure processes and the evolution of rock permeability before and after failure, and Wang et al. (2014) used laboratory tests to study the hydraulic properties of
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altered rock under different confining pressures. Chen et al. (2018) also used sandstone as the research object in a triaxial compression test to conduct experimental research on the deformation characteristics,
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permeability change law and acoustic emission characteristics of the confining pressure unloading process; the test results illustrated a correlation between the deformation characteristics, acoustic emission and
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permeability of the rock during unloading. Wang et al. (2015) used a MTS815 rock mechanics test system to conduct triaxial compression tests on sandstone and limestone; their results revealed the evolutionary
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characteristics of permeability during rock failure and the relationship between rock strength, deformation and permeability before and after failure. In the study of Mitchell and Faulkner (2008), conventional triaxial compression tests were conducted on rock to monitor the evolution of permeability, the fracture development characteristics of rock deformation and the failure processes in real time. Furthermore, Chen et al. (2019) used triaxial compression tests under osmotic pressure to study the effects of different bedding angles on mechanical properties and the permeability of coal in the process of full stress-strain. Wang et al. (2013) studied the law of permeability evolution in intact coal samples during progressive failure and analysed the influence of permeability characteristics on the instability of underground coal seams. The studies of Oda et al. (2002), Chen et al. (2014) and Schulze O (2001) conducted relevant research on the permeability characteristics of rock under triaxial compression; and their research showed that rock deformation damage can affect the permeability characteristics of rock, and there is a certain correlation between rock stress, deformation and permeability. In summary, there is currently a mature qualitative understanding of the stress-strain characteristics and the permeability evolution law relating to the rock failure process under the action of seepage pressure. However, the deformation, strength and permeability in different deformation stages of rock under seepage pressure have less been studied.
Journal Pre-proof In the construction of hydraulic and hydropower projects, slope projects and mining projects, it is necessary to focus on the coupling of seepage and stress to determine the engineering stability of the rock mass. The key to conducting a coupling analysis of the seepage field and hydraulic force is to determine the permeability characteristics of the rock mass. In this respect, conducting a rationality evaluation of the permeability characteristics in different deformation stages of the rock mass is of great engineering significance when analysing the deformation, strength and stability characteristics of an engineered rock mass. In this study, red sandstone was collected from a slope engineering excavation s ite in the suburbs of Ganzhou city, Jiangxi Province (the sampling location is shown in Fig. 1), and laboratory tests using a High Pressure Triaxial Automated System for Rock (HPTAS) were conducted to study the different seepage pressures. The stress eigenvalues, axial strain stiffness and permeability during rock failure under different seepage pressures were then calculated based on the experimental results. In this paper, the relationship between axial strain
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stiffness and permeability and stress-strain during progressive rock failure is analysed, and a model of the evolution between permeability and stress is established. The results of this study can be used as a reference for monitoring and controlling geological stability during engineering under seepage-stress coupling, and they
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are also significant for guiding rock engineering des ign and construction when seepage-stress coupling is
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involved.
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Ganzhou
Jiangxi
Fig. 1 Sample collection location
2 Test equipment and methods 2.1 Test equipment The High Pressure Triaxial Automated System for Rock (HPTAS) was designed and developed by GDS Instruments (Geotechnical Digital Systems (GDS), UK) (shown in Fig. 2) and was used to conduct tests on sandstone samples . Unlike other advanced triaxial test apparatus, this test system is based on a triaxial test system with a high-pressure loading frame, and it can be used to conduct precise rock sample tests. The main components include a load frame, confining pressure, back pressure controller and a pressure chamber. The apparatus can be used for uniaxial compression, triaxial compression and rheological tests and
Journal Pre-proof temperature-seepage-stress multi-physical field coupling tests. The system is equipped with three independent systems for controlling axial pressure, confining pressure and seepage pressure, and axial and radial deformations are measured by a Linear Variable Differential Transformer (LVDT). Loading ram
Load ram
Confining pressure control system Loading frame
F
Rubber memberane
Pressure chamber
Pressurised cell fluid Top-cap
Computer Collection box
Rock specimen
O-ring
Perspex cell
Porous discs
Water volume change
Pedestal
Pore pressure
Cell pressure
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f
Temperature controller Electric machinery
ADVDPC
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Fig. 2 High Pressure Triaxial Automated System (HPTAS) for Rock
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The seepage pressure control system used in the test is a back-pressure controller (the GDS Advanced Pressure/Volume Controller (ADVDPC)), as shown in Fig. 2. The controller is a screw pump controlled by a
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microprocessor, and it can accurately measure changes in liquid pressure and volume. As a pressure source, it exerts an independent seepage pressure on rock samples and replaces the use of traditional indoor pressure sources (such as mercury columns, water pumps and air compressors). It also displays volume and pressure values in real time, is highly accurate, provides a high resolution and has excellent control capabilities.
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Furthermore, the pressure chamber can be filled with water or oil. The basic parameters of the controller are as follows: pressure range of 0–32 MPa, pressure resolution of 0.1 kPa, pressure chamber volume (rated) of
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200 cc, water volume resolution of 1 mm3 (0.001 cc), measurement accuracy of less than 0.1% and it has a mass of 20 kg. The equipment can be used independently, or it can be computer-controlled.
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2.2 Sample Preparation
The red sandstone had a reddish-brown appearance, compact structure, low porosity, and a density of 2.57 g/cm3. To reduce the dispersion between samples, all rock samples were drilled in an adjacent position of the same rock with fewer fissures. According to the ISRM recommended standard (Fairhurst and Hudson, 1999), the rock samples were processed into cylindrical standard specimens with sizes of 50 × 100 mm. Both end-faces of these rock samples were carefully polished to ensure that the error of unevenness was less than 0.05 mm. It was also essential to make the end-faces parallel within a small tolerance of 0.1 mm or less. Finally, the processed samples were treated with saturated water. The sample preparation procedure is shown in Fig. 3.
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(a) Drilling sampling
(b) Red sandstone sample
(c) Water saturation
(d) Compression test
Fig. 3 Sample preparation process
2.3 Test methods
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During the test, water was used as permeable medium, and six different permeability values were set at 2, 3, 4, 5, 6 and 7 MPa, respectively. However, in the early stage, triaxial compression tests were conducted
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using seepage pressures under 2, 4, 6 and 7 MPa only, whereas in the later stages, supplementary tests with seepage pressures of 3 MPa and 5 MPa were conducted using a THM-2 Thermal-Fluid-solid coupling test system (developed by the State Key Laboratory of Coal Mine Disaster Dynamics and Control of Chongqing
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University) to make the results more universal.
A saturated specimen was installed in the pressure chamber and the confining pressure was applied and
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maintained at a constant 8 MPa. After the confining pressure had been stabilized, seepage pressure was applied to a predetermined value and maintained for a certain time period until the water volume in the
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back-pressure controller changed steadily and a stable seepage pressure difference and steady water flow was apparent; the test was then terminated by loading the axial pressure until the specimen was destroyed (which
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indicated that the test was terminated). In the process, the stress and strain of the sample were automatically collected and recorded by the computer, and the water volume was automatically collected by the ADVDPC. For rock materials with a permeability coefficient of k ≥ 10−7 μm2, it is preferable to use the steady-state
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method to measure permeability (Yang et al., 2015). During the test, the seepage pressure difference between the two ends of the sample was maintained at a constant value. To test and analyse permeability of the rock,
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the following assumptions were made: (1) water is an incompressible fluid; (2) initial pores and microcracks in the rock are uniformly distributed and the rock is considered to be a porous medium; (3) steady seepage under constant pressure is regarded as continuous seepage and (4) seepage conforms to Darcy's law during the process of stress-strain. Based on Darcy's law, permeability was calculated according to equation (1) (Brace et al., 1968; Jia et al., 2017) as
k
LV , Apw t
(1)
where k is average permeability, m2 ; is the dynamic viscous coefficient of water, = 1 × 10-3 Pa·s (T = 20℃); V is the volume of water that has infiltrated into the rock sample, m3 ; L is the height of the rock sample, m; t is the recording time interval, s; A is the cross-sectional area of the rock sample in m2 and pw is the seepage pressure difference between the two ends of the rock sample in Pa.
3. Analysis of test results 3.1 Stress thresholds of rock failure under different seepage pressures In the process of stress-strain, rock shows different mechanical properties at different bearing stages.
Journal Pre-proof According to rock deformation and fracture development, the concept of stress thresholds can be introduced, and the variation law of rock stress thresholds can be analysed, which is of great significance when monitoring stability during rock mass engineering projects. In the entire process of progressive stress-strain failure under triaxial compression, the corresponding stress characteristic thresholds of each stage prior to the peak are as follows: the crack closure threshold ( cc ), crack initiation threshold ( ci ), crack damage threshold ( cd ) and peak strength ( c ) (Eberhardt, 1998). According to the characteristics of pore and fissure compaction and penetration during the progressive failure of rock, the progressive failure process of rock can be divided into four stages as follows: the crack closure compaction stage (OA); linear elastic stage (AB); crack stable propagation stage (BC) and unstable crack propagation stage (CD). The points A, B, C, and D correspond to cc , ci , cd and c , respectively, in Fig. 4.
σ
f
c
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D
cd
C
pr
ci
B
Stress-Volumetric strain Stress-Axial strain Stress-Lateral strain
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cc
ε
Pr
A
O
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Fig. 4 Schematic diagram of progressive failure process of rock (Eberhardt, 1998)
Eberhardt (1998) proposed that the stress thresholds for crack initiation and damage during rock
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compression are those of the crack initiation threshold and crack damage threshold, respectively. The crack initiation threshold represents the threshold value of stress at which cracks begin to germinate in the process
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of triaxial failure, and internal cracks in the rock are in a stable stage of development when under this stress. The crack damage threshold indicates that rock deformation has entered an unstable stage of development: it is the initial stress stage of continuous expansion and rapid development of internal cracks, and following this stage, peak stress is attained and the rock is subsequently destroyed. The concept of crack volume strain ( cv ) proposed by Martin (1997) provides an effective method for
determining the crack initiation threshold ( ci ) and crack damage threshold ( cd ). By observing the volumetric strain-deviation stress curve of rock and the volumetric strain-deviation stress curve of crack, the volumetric strain of rock ( v ) and crack volume strain ( cv ) can be determined as follows,
v 1 2 3
(1 2 )( ) , cv v E 1
3
(2)
where 1 ， 3 ， v and cv are axial strain, radial strain, rock volumetric strain and crack volumetric strain, respectively, and E and are the elastic modulus and Poisson's ratio, respectively. The use of Eq. (2) enables experimental data to be processed and the volumetric strain-deviation stress curves of rocks and cracks under various seepage pressures can then be plotted, as shown in Fig. 5. The crack
Journal Pre-proof initiation threshold ( ci ) and crack damage threshold ( cd ) are determined from the following: the crack initiation threshold ( ci ) is the stress corresponding to the peak point of the crack volumetric strain-deviation stress curve, and the crack damage threshold ( cd ) is the stress corresponding to the peak point of the rock volumetric strain-deviation stress curve. 90
c cd
ci
30
f
(3)/MPa
60
Dilation
3
2 1
2
3
4
1/%
3
Crack volumetric strain Volumetric strain
0
-1 0
1
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pw
1
Pr
Contraction ε(%)
1
0
pr
-1
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0 -2
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Axial strain Lateral strain
2
ε1/%
3
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Fig. 5 Volumetric strain-deviation stress curves of rocks and cracks
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The crack closure threshold ( cc ) represents the threshold value corresponding to complete compaction of pores and fissures within the rock. The stress-strain curve is evidently concave in the initial stages, and it then transits to an elastic deformation stage. However, there is a great randomness involved, and errors can occur when determining the crack closure threshold ( cc ) using only the stress-strain curve. Therefore, in this study, it is considered more reasonable to use the method based on the axial strain difference to determine the crack closure threshold ( cc ). A schematic of the axial strain difference is shown in Fig. 6. 90
0.25 0.20
σcd 60
σcc
D
0.15
reference line
Δε1/%
Axial Stress/MPa
Stress-strain curve
30
A
0.10 0.05
O
0
0
axial strain difference 1
2
Axial Strain/%
3
0.00
B
0
20
40
(σ1-σ3)/MPa
σcd 60
80
Journal Pre-proof Fig. 6 Determination of axial strain difference using stress-strain curve
Fig. 7 Axial strain difference curve
In Fig. 6, the point O is the coordinate origin, the point D is the crack damage threshold, and the line segment OD is used as the reference line for axial strain. The difference between strain corresponding to each stress-strain curve and strain corresponding to the reference line is called the axial strain difference, which is denoted as 1 , and the equation used in calculation is as follows,
1 1
(3)
1 3 , cd cd
where 1 is the axial strain difference and cd is the axial strain corresponding to the crack damage threshold ( cd ). The axial strain difference ( 1 ) under different deviating stresses can be calculated using Eq. (3), and
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the relationship curve between the axial strain difference( 1 ) and deviatoric stress ( 1 3 ) can also be plotted, as shown in Fig. 7, where the stress corresponding to the peak point of the curve is the crack closure 90
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threshold ( cc ). pw = 2 MPa
pw = 5 MPa
pw = 3 MPa
30
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0
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Pr
60
pw = 7 MPa
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Stress/MPa
pw = 4 MPa
pw = 6 MPa
ci
cd
c
Stress thresholds
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cc
Fig. 8 Stress thresholds under various seepage pressures
According to the above calculation method, the stress thresholds of the rock failure process under different seepage pressures can be obtained, and these are plotted in the histogram in Fig. 8. An analys is shows that with an increase in the seepage pressure, the crack closure threshold ( cc ), crack initiation threshold ( ci ), crack damage threshold ( cd ) and peak strength ( c ) of the rock decrease to varying degrees. These results show that under the action of seepage pressure, the strength of the engineered rock mass (such as an underground chamber or reservoir dam) will decrease. 3.2 Deformation characteristics of progressive failure of rock The process of progressive failure of rock refers to the deformation and stress processes prior to peak stress of rock compression, and it is classified as belonging to the rock bearing deformation stage. According to the stress-strain curve, the rock failure process can be divided into the progressive failure process prior to peak stress and the post-peak failure process, as shown in Fig. 9.
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Progressive failure process Ⅰ
Ⅱ
Ⅲ
Post-destruction phase Macro-fracture
Ⅳ
ci 40 20 0
vc
vf
1
Ⅲ
2 Strain/%
3
cd
60
ci
40
Axial strain Volumetric strain
cc
0
4
vc 1
0
vf
(3)/MPa
20 vf 2
Ⅱ
Ⅲ
Ⅳ
4
5
f
cd
0
Axial strain Volumetric strain
cc vf 2
vc 1
0
3 Strain/%
Ⅰ
Macro-fracture
Ⅱ
Ⅲ
Ⅳ
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vc 1
(3)/MPa
(3)/MPa
ci 30
Axial strain Volumetric strain
cc vf
(e)
4
5
Axial strain Volumetric strain
cc
0 2 3 Strain/%
Macro-fracture
cd
60
ci
0
5
c
cd
30
4
90 Progressive failure process Post-destruction phase
Post-destruction phase
c
60
Macro-fracture
c
(d)
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(c)
Ⅰ
Ⅳ
ci
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3 Strain/%
90 Progressive failure process
5
30
Axial strain Volumetric strain
cc
0
Ⅲ
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ci
vc 1
Ⅱ
pr
60
cd
40
4
Progressive failure process Post-destruction phase Ⅰ
c
60
0
90
Macro-fracture
Pr
(3)/MPa
Post-destruction phase
Ⅳ
80
3
Strain/%
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Ⅲ
2 (b)
100 Progressive failure process Ⅱ
Macro-fracture
c
(a)
Ⅰ
Ⅳ
20
Axial strain Volumetric strain
cc
0
Ⅱ
80
cd
60
Progressive failure process Post-destruction phase Ⅰ
c
(3)/MPa
(3)/MPa
80
100
0
1 vc vf 2 3 Strain/%
4
5
(f)
Fig. 9 Stress-strain curve for rock under various seepage pressures (a) pw = 2 M Pa; (b) pw = 3 M Pa; (c) pw = 4 M Pa; (d) pw = 5 M Pa; (e) pw = 6 M Pa; and (f) pw = 7 M Pa
As evident from Fig. 9, during the progressive failure process, the internal voids of the rock are gradually compressed during the initial stage of loading (and the stress-strain curve is concave). However, with an
Journal Pre-proof increase in axial stress, the rock voids gradually germinate, expand and penetrate, and the damage gradually accumulates until the rock reaches its peak stress. During the process of post-peak failure, the bearing capacity of the rock decreases, which results in a rapid drop in the stress-strain curve and a large number of macro-cracks appear on the surface. The progressive failure process can be further analysed, and according to the stress thresholds of rock, the progressive failure process can be divided into four distinct stages: the crack closure compaction phase (region I); linear elastic phase (region II); crack stability expansion phase (region III), and the crack unsteady expansion stage (region IV). As shown in Fig. 9, the characteristics of each deformation stage are as follows: Region I: Under the combined action of confining pressure and axial pressure, the original open fracture and structural plane begin to gradually close and the volume of the rock becomes compacted; this represents the early stage of non-linear rock deformation. In this stage, the stress-strain curve of the rock is concave, and
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the end point of this stage is the crack closure threshold ( cc ). At this time, the original cracks are completely closed.
Region II: With a gradual increase in the axial pressure, the volume of the rock becomes gradually
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compacted. In this stage, the stress-strain curve of the rock is approximately linear, and its deformation mainly originates from elastic deformation within it; the end point of this stage is the crack initiation threshold ( ci ).
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Region III: In this stage, the stress of the rock exceeds the crack initiation threshold ( ci ), the internal stability fractures gradually spring up and expand and the volume of the rock is compressed. The end point of
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this stage is the crack damage threshold ( cd ). At this time, the volume strain of the rock reaches the maximum compaction point.
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Region IV: When the stress exceeds the crack damage threshold ( cd ), the cracks in the rock increase rapidly, fuse and penetrate each other, the volume of the rock begins to increase, the internal damage increases
stress.
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gradually until peak stress is reached and the progressive failure process ends w ith the occurrence of peak
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To study the variation law of volume strain during the process of progressive failure under different seepage pressures, the curve of volume strain is analysed here. As shown in Fig. 9, the progressive failure process undergoes two typical stages of volume compaction and volume expansion. When the rock volume is compressed to its minimum value, the point on the stress-strain curve is defined as the maximum volume compaction point, and the corresponding stress is defined as the damage strength ( d , namely: d cd ). According to the test results, the rock damage strength decreases with an increase in seepage pressure (62.1 MPa, 61.9 MPa, 61.7 MPa, 60.6 MPa, 60.2 MPa and 58.1 MPa in turn), which indicates that the existence of seepage pressure reduces the rock strength to a certain extent. Furthermore, the greater the seepage pressure, the stronger the weakening effect of water on the rock’s strength, which reduces the rock damage strength. It can be seen from Fig. 9, that the volumetric strain corresponding to the maximum volume compaction point of the rock under different seepage pressures is between 1.44% and 1.75%. During the process from the maximum volume compaction point to peak strength, the rock sample volume begins to expand. Therefore, when the peak stress is reached, the difference between the rock volume strain and the volume strain at the maximum volume compaction point (taking the absolute value) can be recorded as the relative value of volume strain dilatation ( vr ). The magnitude of this value can indicate the capacity of the rock to resist
Journal Pre-proof deformation after volume compaction during the rock failure process. According to Eq. (4), the calculation is as follows,
vr vf vc
,
(4)
where vr is the relative value of volume strain dilatation when stress reaches peak stress, vf is the corresponding volume strain at maximum volume compaction and vc is the corresponding volume strain when stress reaches peak strength. The calculation results are shown in Table 1. Table 1 Relative values of volumetric dilatation under various seepage pressures
vf / %
vc / %
vr / %
2
1.44
0.40
1.04
3
1.48
0.53
0.95
4
1.66
0.72
0.94
5
1.71
6
1.68
7
1.75
pr
oo
f
p w / M Pa
0.87
0.84
1.02
0.66
1.55
0.20
Table 1 shows that the relative value of volume strain dilatation ( vr ) decreases with an increase in
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seepage pressure when the peak strength is reached. These results show that in the process of rock
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compression and deformation, seepage pressure can reduce the ability of the rock to resist deformation. In addition, it promotes cracking and the volume expansion of the rock, and the rock reaches its peak strength point faster following the volume compaction stage. As the seepage pressure increases, the effect becomes
value.
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more obvious, and the relative value of volume strain dilatancy is smaller when the stress reaches its peak
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3.3 Axial strain stiffness of progressive failure process The axial strain stiffness curve can be used to reflect the ability of rock micro-elements to resist
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deformation and failure during the different stress stages. This effect can be explained as follows: the increase in axial deformation stiffness indicates that the rock has an increased ability to resist deformation and failure, otherwise the ability of the rock to resist deformation and failure would decrease. A constant value of axial strain stiffness with an increase in stress indicates that the rock is in the elastic deformation stage. As the collected experimental data are stored in the text data list in the form of data points, the use of a numerical differentiation method is proposed to calculate the axial strain stiffness corresponding to each strain data point in the progressive failure process of the rock. The calculation is as follows, 1 1 ( i 1) 1 ( i )
1 ( i ) [
2 1 ( i 1) 1 ( i )
1 ( i ) 1 ( i 1) 1 ( i ) 1 ( i 1)
]
,
(5)
where 1 is the axial strain stiffness, GPa; i is the i-th data point of the stress-strain curve data points
obtained from all monitoring; 1 ( i ) is the axial strain stiffness corresponding to the i-th data point, GPa; 1 ( i ) is the axial stress of the i-th data point in MPa and 1 ( i ) is the strain of the i-th data point.
According to the above calculation process, the variation curves of axial strain stiffness during progressive failure process under different seepage pressures can be obtained, and the results are shown in Fig.
Journal Pre-proof 10. pw=2 MPa
5
6
Test value of ε1max
pw=3 MPa
Theoretical value of ε1max
pw=4 MPa
4
pw=5 MPa
5
pw=7 MPa
ε1max/GPa
max /MPa
pw=6 MPa
3 2
4
3
1 0 0
15
30
45
60
75
2
90
2
4 pw/MPa
(1-3)/MPa
8
(b)
f
(a)
6
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Fig.10. Axial strain stiffness curve for each seepage pressure: (a) Axial strain stiffness during progressive failure process; (b)
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relationship between 1max and pw
An analysis of the variation in axial strain stiffness during progressive failure process under different
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seepage pressures, as shown in Fig.10, is presented as follows:
1) In the early stage of stress loading, axial strain stiffness ( 1 ) increases rapidly with an increase in
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stress, and there are minimal differences in the axial strain stiffness ( 1 ) values between rock samples. However, the trend shows that when seepage pressure is larger, axial strain stiffness is smaller, as shown in Fig. 10 (a).
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2) As stress gradually reaches peak strength, there is a rapid decrease in the change of the rock axial strain stiffness ( 1 ) curve under various seepage pressures until peak strength ( c ) is reached, at which time process).
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the minimum value of axial strain stiffness ( 1 ) is reached (the lowest value reached during the entire
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3) As the stress increases gradually, axial strain stiffness ( 1 ) slowly increases until it reaches the peak value of axial strain stiffness. During this stage, axial strain stiffness has an obvious correlation with seepage pressure; that is, when seepage pressure is larger, axial strain stiffness is reduced. The axial strain stiffness curves are arranged in order from top to bottom according to the magnitude of seepage pressure, and the maximum value of axial strain stiffness ( 1max ) decreases with an increase in seepage pressure (pw), as shown in Fig. 10 (b). By fitting the relationship between 1max and pw, it can be seen that 1max and pw have a good linear correlation, which indicates that when the seepage pressure is larger, the peak value of rock axial strain stiffness is smaller, and the functional relationship can be expressed using Eq. (6),
1max 0.1474 pw 4.5327 ， R2 0.9011 .
(6)
The variation trend in the axial strain stiffness curve during progressive failure process under different seepage pressure is consistent, which indicates that the effect of seepage pressure cannot change the overall trend in the axial strain stiffness of rock. However, the values of rock axial strain stiffness under different seepage pressures are obviously different, which indicates that seepage pressure can affect the value of rock
Journal Pre-proof axial strain stiffness. Further analysis shows that in the process of rock compression and deformation, internal cracks continue to deform, extend and connect, and new cracks gradually sprout. Moreover, due to the effect of seepage water pressure, the expansion of rock cracks is promoted, and the stable deformation stage of rocks with cracks is accelerated; there is then a transition to unstable deformation and ultimately to the failure stage. Simultaneously, due to the lubrication of water, there is a decrease in the friction resistance between discontinuous surfaces, and when the seepage pressure is greater the effect of reduction is more obvious. This results in a reduction in axial strain stiffness during the progressive failure process.
3.4 Permeability Evolution Characteristics 3.4.1 Characteristics of permeability evolution during rock stress-strain process Permeability in the stress-strain process is calculated by Eq. (1), and the curves of permeability change
2
B E
30 25 A
0
o
1
2 3 Axial Strain/%
(a)
A
BC
D 10
D
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(3)/MPa
60 1
2
30
3
0 1
60
B
40 E
20
3
4
5
B C
75
Post-destruction phase 100
D 16 12
(1-3) k
D
8
75
4
50
0
1
2
C
0
E
50
B
25
25 A
0 1
2
Progressive failure process A
o
0
E
A
A
0
50
B
Axial Strain/%
100
C
0
0
C
2
25
0
(3) k
5
75
(b)
Post-destruction phase 80
Progressive failure process
100
2 0
1
D
4
o
0
5
rn
90
4
6
al
0
0
(3) k
25
(1-3)/MPa
0
50
Post-destruction phase
2 3 Axial Strain/%
(c)
4
5
0
0
o
0
2 Axial Strain/%
(d)
4
k/10-6μm2
1
60
C
pr
75
D
B C
k/10-6μm2
k
1
0
Progressive failure process A
Pr
(3)/MPa
D
0
50
100
(3)
2
75
90
Post-destruction phase
3
(3)/MPa
D
e-
BC
k/10-6m2
A
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Progressive failure process
k/10-6m2
100
f
under various seepage pressures are drawn and shown in Fig. 11.
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D
Post-destruction phase
15
k
75
(3)/MPa
0 1
2
C
60 E
25
75
30
0
50
(3) k
75
0
1
2 3 Axial Strain/%
4
2
3
C
50
E
B
25
0
0 1
40
20
25
A o
0
D
D
B
0
B C
A
90
D
5
0
100 Progressive failure process Post-destruction phase 100
(3)
10
50
120
(3)/MPa
B C
k/10-6m2
A
k/10-6m2
100 Progressive failure process
o
5
A
0
0 1
2 3 Axial Strain/%
(e)
4
5
(f)
f
Fig. 11 Curve of rock permeability evolution during stress-strain process
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(a) pw = 2 M Pa；(b) pw = 3 M Pa；(c) pw = 4 M Pa；(d) pw = 5 M Pa；(e) pw = 6 M Pa；(f) pw = 7 M Pa
pr
(The grey part is an enlarged graph of the permeability evolution curve during progressive failure process)
It can be seen from Fig. 11, that permeability first decreases and then gradually increases with an
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increase in axial stress. When the peak of permeability is reached, the permeability curve rapidly decreases and finally becomes constant. In addition, the peak of the permeability curve lags significantly behind the peak of the stress-strain curve. To ensure that the figure corresponds to the order presented in Section 3.1, the
ci , cd and c are recorded as points A, B, C and D.
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stress-strain curves corresponding to cc ,
Furthermore, the stress-strain curves and permeability curves are divided into five stages: OA, AB, BC, CD
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and DE, as shown in Fig.11. According to the stress-strain curve and permeability evolution curve, five stages of OA, AB, BC, CD
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and DE are determined and analysed. It can be seen that in the early stage of stress loading (OB stage), rock specimens are in the stage of crack compaction and elastic deformation, permeability is at a low level, and the
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OA stage is in the stage of crack compaction. Rock permeability is thus slightly decreased and the AB stage occurs slowly. The results show that cracks close gradually in the early stage of stress loading and permeability is low, which is related to the low porosity, uniform texture and compactness of red sandstone. With an increase in axial stress, and when stress reaches or exceeds
ci (BC stage), the rock fissures
gradually germinate and connect, which results in a gradual increase in rock permeability. When stress reaches
cd (CD stage), the rock is in an unstable developmental stage, and the different fissures intersect and converge with each other, which provides a seepage channel for water; therefore, permeability gradually increases. In addition, due to the rapid growth of cracks during this stage, different seepage channels are constantly formed in the new cracks but internal fractures block some of these seepage channels. The above two factors cause the rock permeability curve to increase upwards, and stress points exist where permeability decreases; however, overall, rock permeability increases rapidly during this stage. The rock breaks when the stress exceeds
c (DE stage), and the crack connected to both ends of the sample is the dominant factor
controlling the change in permeability. However, the rapid increase in permeability to its peak value lags behind the peak value of stress. Finally, under the combined action of axial and confining pressures, the penetration cracks are compacted, and permeability gradually decreases and eventually becomes stable.
Journal Pre-proof 3.4.2 Evolutionary characteristics of permeability in progressive failure process The focus of research on rock mechanics under water-force coupling in engineering practice is the evolutionary characteristics of permeability during the process of progressive failure of a rock mass prior to reaching peak strength (Alam et al., 2014). Therefore, it is particularly important to analyse the evolutionary characteristics of the rock mass during the process of progressively increasing stress. In addition to the influence of seepage pressure, permeability depends mainly on the expansion, geometric size and fractal dimensions of cracks and the degree of intersection between them. Based on experimental data, the relationship between permeability and axial strain during the progressive failure process of red sandstone prior
pw=3 MPa
pw=4 MPa
pw=5 MPa
pw=6 MPa
pw=7 MPa
20
pr
k/10-6μm2
30
pw=2 MPa
oo
40
f
to reaching peak stress under different seepage pressures is plotted and shown in Fig. 12.
0 0
e-
10
1
2
3
Pr
Axial strain/%
al
Fig. 12 Permeability change curve of progressive failure process prior to reaching peak stress
As seen from Fig. 12, permeability decreases with an increase in axial strain in the early stage of
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stress-strain, in relation to pre-test void and fracture compaction; however, permeability then increases with an increase in axial stress. An analysis of the relationship of permeability under different seepage pressures
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shows that with an increase in seepage pressure, there is a gradual increase in the amplitude of permeability in the process of stress-strain, and the permeability corresponding to peak strength also increases . With an increase in seepage pressure, the corresponding permeability in the case of rock failure is 2.512 × 10-6 μm2, 5.653 × 10-6 μm2 , 8.615 × 10-6 μm2 , 11.515 × 10-6 μm2 , 13.675 × 10-6 μm2 and 32.638 × 10-6 μm2. According to the change law of permeability during the progressive failure process, and to establish a permeability evolution model of the progressive failure process of red sandstone, strain corresponding to the minimum permeability value during the stress-strain process can be used as a boundary line, and the permeability curve of the progressive failure process can be divided into two parts (Parts 1 and 2), as shown in Fig. 13.
Journal Pre-proof Progressive failure process Part 1
Part 2
0 k min k
k min c
k min
0
c Axial strain
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f
Fig. 13 Schematic diagram of permeability change curve
According to the variation law of the permeability curve with respect to the two parts (Parts 1 and 2), a
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piecewise function is proposed to express the relationship between permeability and strain as in Eq. (7), (7)
e-
a k min k0 , 0 k min k , b k min k0， k min c
k min is axial strain corresponding to minimum permeability, %; c is axial strain corresponding to peak stress, %; a and b are the rock permeability factors of different permeability change stages; k0 is the basic permeability of rock, 10-6 μm2 ;
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where k is permeability during the stress-strain process, 10-6 μm2;
is the coefficient reflecting the relationship between permeability and average porosity and
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k min indicates the effect of rock void change on permeability. dk d
dk d d d
dk d . d d
(8)
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The relationship between permeability and stress can be expressed using Eq. (8) as follows,
If the constitutive relation during the progressive failure process is approximated to the linear relation expressed as E , then the correlation equation between rock permeability and stress can be obtained using the simultaneous Eqs. (7) and (8), and the correlation equation is as follows,
( ) k ,0 E , k ( ) k , E a
k min
0
b
k min
(9)
k min
0
k min
c
k min is deviation stress corresponding to minimum permeability, MPa, where the value is the crack closure threshold ( cc ); E is the elastic modulus of rock in MPa and c is the peak stress of rock in MPa. where
According to the test results, the model parameters of permeability and deviating stress under different seepage pressures calculated by Eq. (9) are shown in Table 2. According to the model parameters, the permeability curves during progressive failure process under different seepage pressures can be obtained, and the curves can then be compared with the experimental data curves, as shown in Fig. 14. The results show that the fitting effect of the Eq. (9) is better, which proves that the established piecewise function model can better
Journal Pre-proof reflect the relationship between permeability and deviating stress in the progressive failure process. These results can be used as a reference when conducting further study on the evolutionary characteristics of rock strength and permeability under seepage-stress coupling. Table 2 Calculated model parameters pw/M Pa Part 1
a 10
Part 2
b 10
10
7
2
3
4
5
6
7
1.460
1.468
1.528
1.598
1.684
1.903
4.481
4.874
5.576
9.658
13.857
26.178
4.003
4
9
Theoretical value of k Test value of k
Theoretical value of k Test value ofk
3
0
0
10 Theoretical value of k Test value of k
al
8
0
Pr
(a)
90
6
rn
4
0 0
Jo u
2
30
60
30 60 (3)/MPa
e-
30 60 (-3)/MPa
90
(b)
16
Theoretical value of k Test value ofk
12 k/10-6μm2
0
k/10-6m2
3
pr
1
f
2
oo
k/10-6μm2
k/10-6m2
6
8
4
0
90
0
30
60
90
(3)/MPa
(-3)/MPa
(c)
(d) 40
15
Theoretical value of k Test value ofk
Theoretical value of k Test value of k
30 k/10-6m2
k/10-6m2
10
5
20 10
0
0 0
20
40 (-3)/MPa
(e)
60
80
0
20
40 (-3)/MPa
(f)
60
80
Journal Pre-proof Fig. 14 Comparison between permeability test results and theoretical calculation values: (a) pw = 2 M Pa; (b) pw = 3 M Pa; (c) pw = 4 M Pa; (d) pw = 5 M Pa; (e) pw = 6 M Pa and (f) pw = 7 M Pa
Based on the above research, it is possible to determine that seepage pressure has a significant effect on rock strength and associated deformation characteristics. The stiffness and peak strength of rock are reduced during the rock failure process, and this is extremely important to consider when conducting engineering projects involving rock mass (such as slope engineering and reservoir dam and underground chamber construction) under the coupling action of seepage field and stress field. According to the research results of this paper, and with respect to conducting engineering geology in an environment where the seepage field and stress field are coupled, it is necessary to enhance the hydrophobic function of the underground engineering drainage system and reduce the seepage pressure of the underground space environment to ensure rock mass
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f
stability. The piecewise function model established in this paper provides a reference for monitoring and successfully distinguishing the stability and permeability of the engineering rock mass under seepage-stress
pr
coupling.
4 Conclusion
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In this study, triaxial compression tests were conducted on red sandstone samples under different seepage pressures, and the variation laws of strength, deformation, strain, stiffness and permeability during rock
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fracture under osmotic pressures were analysed. The research results provide a reference for design and construction during large rock mass engineering, and also act as guidance for monitoring and preventing engineering geological hazards under hydraulic coupling. Some of the important conclusions are as follows:
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(1) With an increase in seepage pressure, there is a decrease in the stress eigenvalues during the rock failure process. Different stress eigenvalues correspond to different deformation stages of rocks. Therefore, in
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engineering geology, stress eigenvalues are of great significance when ensuring stability during rock engineering. Appropriate reduction of seepage pressure in rock engineering environment can enhance the
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stability of rock engineering.
(2) In the progressive failure process of rock, axial strain stiffness firstly increases and then decreases with an increase in axial stress. The magnitude of seepage pressure does not affect the change trend of axial strain stiffness but it affects its magnitude: with a larger seepage pressure, there is a reduction in axial strain stiffness during the process of progressive failure process. In addition, there is a good linear relat ionship between maximum axial strain stiffness and seepage pressure. (3) In the stress-strain process, the values of permeability firstly decrease then increase. They subsequently decrease rapidly after reaching peak permeability and finally reach a stable value. During the entire process, the permeability curve is in good agreement with the stress-strain curve, but peak permeability lags behind peak stress. (4) During the progressive failure process of rock, the permeability firstly decreases and then increases with an increase in axial stress, and permeability corresponding to peak strength increases gradually with an increase in seepage pressure. The piecewise function model presented in this paper uses the crack closure threshold as the boundary point, and it accurately reflects the relationship between permeability and deviatoric stress during the progressive failure process of rock.
Journal Pre-proof Acknowledgements This study is supported by the National Science and Technology Major Project of China (Grant No. 2016ZX05045-004).
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Journal Pre-proof Title: Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure Manuscript ID: ENGEO_2019_821
Highlights: (1) Triaxial compression tests were conducted on red sandstone under seepage pressure (2) Seepage pressure can reduce the stress characteristic value of rock (3) Seepage pressure does not affect the strain stiffness trend, but it affects the value
Jo u
rn
al
Pr
e-
pr
oo
f
(4) The piecewise function model reflects permeability evolution characteristics
Weijing Xiao, Dongming Zhang, Xiaojun Wang PII:
S0013-7952(19)30870-1
DOI:
https://doi.org/10.1016/j.enggeo.2019.105406
Reference:
ENGEO 105406
To appear in:
Engineering Geology
Received date:
10 May 2019
Revised date:
2 August 2019
Accepted date:
11 November 2019
Please cite this article as: W. Xiao, D. Zhang and X. Wang, Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure, Engineering Geology (2019), https://doi.org/10.1016/ j.enggeo.2019.105406
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© 2019 Published by Elsevier.
Journal Pre-proof
Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure Weijing Xiao a, b, Dongming Zhang a, b* , Xiaojun Wang
c
a
State Key Laboratory of Coal M ine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
b
School of Resources and Environmental Sciences, Chongqing University, Chongqing 400044, China
c
School of Resources and Environmental Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi,
China
f
Experimental study on progressive failure process and permeability
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characteristics of red sandstone under seepage pressure Weijing Xiao a,b [email protected], Dongming Zhanga,b,* [email protected], Xiaojun Wangc
a
pr
[email protected]
State Key Laboratory of Coal M ine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
b
School of Resources and Environmental Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi,
Pr
c
e-
School of Resources and Environmental Sciences, Chongqing University, Chongqing 400044, China
China *
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Corresponding author.
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Abstract: Rock masses in underground spaces often experience in-situ stress field and seepage field coupling which gives them complex mechanical behavioural and permeability characteristics. In this study, a High
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Pressure Triaxial Automated System for Rock (HPTAS) is employed in triaxial compression testing of red sandstone under different seepage pressures, and the variation laws of strength, deformation, axial strain stiffness and permeability during rock failure are analysed. The results show that with changes in the seepage pressure, there are also changes in the rock’s strength and ability to resist deformation, and the stress threshold decreases with an increase in the seepage pressure. In addition, seepage pressure does not affect the strain stiffness trend, but it affects the value. Throughout the process of stress and strain, the permeability curve firstly decreases and then increases rapidly before finally stabilizing, and the peak value of the permeability curve lags behind that of the stress-strain curve. According to the law of permeability evolution during the pre-peak progressive failure process, a piecewise functional relationship model between permeability and stress is established in this study, and theoretical values agree well with experimental results. These experimental results can be used as a reference for monitoring and controlling rock stability during geological engineering when a seepage-stress coupling action is applied. Key words: triaxial compression test; seepage pressure; rock failure; stress thresholds; permeability
*
Corresponding author. E-mail address: [email protected] (W. Xiao), [email protected] (D. Zhang), [email protected] (X. Wang).
Journal Pre-proof 1 Introduction Rock has a compact structure and a low fluid flow rate; therefore, it is often used as the main geological medium when constructing underground energy storage and nuclear waste disposal systems (Wang et al., 2018; Zhao et al., 2018). It is also a common complex medium used in the construction of water conservancy and hydropower projects, oil and gas field exploitation, underground mining projects and in deep-burial energy storage projects (Jeanpert et al., 2019; Yu et al., 2019; Giot et al., 2018). However, excavation disturbance causes changes in in-situ stress and groundwater pressure and subsequent changes in the strength and permeability characteristics of rock during the loading process, and such processes have been well-studied in the field of rock mechanics (Fisher et al. 2017; Meng et al., 2019). There is a complex relationship between water and the rock mass in the process of internal flow, and this alters with respect to the seepage pressure. Previous research achievements have shown that the presence of
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f
water can reduce the strength and deformation of rock. In addition, seepage pressure can reduce the effectiveness of the confining pressure of the rock, and this causes the effect of deterioration to be more complex (Masuda et al., 2001; Chen et al., 2018). In recent years, many scholars have conducted experimental
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studies based on the permeability characteristics of rock during compression, and useful results have been obtained. In this respect, Heland (2003) used sandstone as the research object to study the permeability
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characteristics of sandstone during deformation and failure processes and the evolution of rock permeability before and after failure, and Wang et al. (2014) used laboratory tests to study the hydraulic properties of
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altered rock under different confining pressures. Chen et al. (2018) also used sandstone as the research object in a triaxial compression test to conduct experimental research on the deformation characteristics,
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permeability change law and acoustic emission characteristics of the confining pressure unloading process; the test results illustrated a correlation between the deformation characteristics, acoustic emission and
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permeability of the rock during unloading. Wang et al. (2015) used a MTS815 rock mechanics test system to conduct triaxial compression tests on sandstone and limestone; their results revealed the evolutionary
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characteristics of permeability during rock failure and the relationship between rock strength, deformation and permeability before and after failure. In the study of Mitchell and Faulkner (2008), conventional triaxial compression tests were conducted on rock to monitor the evolution of permeability, the fracture development characteristics of rock deformation and the failure processes in real time. Furthermore, Chen et al. (2019) used triaxial compression tests under osmotic pressure to study the effects of different bedding angles on mechanical properties and the permeability of coal in the process of full stress-strain. Wang et al. (2013) studied the law of permeability evolution in intact coal samples during progressive failure and analysed the influence of permeability characteristics on the instability of underground coal seams. The studies of Oda et al. (2002), Chen et al. (2014) and Schulze O (2001) conducted relevant research on the permeability characteristics of rock under triaxial compression; and their research showed that rock deformation damage can affect the permeability characteristics of rock, and there is a certain correlation between rock stress, deformation and permeability. In summary, there is currently a mature qualitative understanding of the stress-strain characteristics and the permeability evolution law relating to the rock failure process under the action of seepage pressure. However, the deformation, strength and permeability in different deformation stages of rock under seepage pressure have less been studied.
Journal Pre-proof In the construction of hydraulic and hydropower projects, slope projects and mining projects, it is necessary to focus on the coupling of seepage and stress to determine the engineering stability of the rock mass. The key to conducting a coupling analysis of the seepage field and hydraulic force is to determine the permeability characteristics of the rock mass. In this respect, conducting a rationality evaluation of the permeability characteristics in different deformation stages of the rock mass is of great engineering significance when analysing the deformation, strength and stability characteristics of an engineered rock mass. In this study, red sandstone was collected from a slope engineering excavation s ite in the suburbs of Ganzhou city, Jiangxi Province (the sampling location is shown in Fig. 1), and laboratory tests using a High Pressure Triaxial Automated System for Rock (HPTAS) were conducted to study the different seepage pressures. The stress eigenvalues, axial strain stiffness and permeability during rock failure under different seepage pressures were then calculated based on the experimental results. In this paper, the relationship between axial strain
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stiffness and permeability and stress-strain during progressive rock failure is analysed, and a model of the evolution between permeability and stress is established. The results of this study can be used as a reference for monitoring and controlling geological stability during engineering under seepage-stress coupling, and they
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are also significant for guiding rock engineering des ign and construction when seepage-stress coupling is
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involved.
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Ganzhou
Jiangxi
Fig. 1 Sample collection location
2 Test equipment and methods 2.1 Test equipment The High Pressure Triaxial Automated System for Rock (HPTAS) was designed and developed by GDS Instruments (Geotechnical Digital Systems (GDS), UK) (shown in Fig. 2) and was used to conduct tests on sandstone samples . Unlike other advanced triaxial test apparatus, this test system is based on a triaxial test system with a high-pressure loading frame, and it can be used to conduct precise rock sample tests. The main components include a load frame, confining pressure, back pressure controller and a pressure chamber. The apparatus can be used for uniaxial compression, triaxial compression and rheological tests and
Journal Pre-proof temperature-seepage-stress multi-physical field coupling tests. The system is equipped with three independent systems for controlling axial pressure, confining pressure and seepage pressure, and axial and radial deformations are measured by a Linear Variable Differential Transformer (LVDT). Loading ram
Load ram
Confining pressure control system Loading frame
F
Rubber memberane
Pressure chamber
Pressurised cell fluid Top-cap
Computer Collection box
Rock specimen
O-ring
Perspex cell
Porous discs
Water volume change
Pedestal
Pore pressure
Cell pressure
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f
Temperature controller Electric machinery
ADVDPC
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Fig. 2 High Pressure Triaxial Automated System (HPTAS) for Rock
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The seepage pressure control system used in the test is a back-pressure controller (the GDS Advanced Pressure/Volume Controller (ADVDPC)), as shown in Fig. 2. The controller is a screw pump controlled by a
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microprocessor, and it can accurately measure changes in liquid pressure and volume. As a pressure source, it exerts an independent seepage pressure on rock samples and replaces the use of traditional indoor pressure sources (such as mercury columns, water pumps and air compressors). It also displays volume and pressure values in real time, is highly accurate, provides a high resolution and has excellent control capabilities.
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Furthermore, the pressure chamber can be filled with water or oil. The basic parameters of the controller are as follows: pressure range of 0–32 MPa, pressure resolution of 0.1 kPa, pressure chamber volume (rated) of
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200 cc, water volume resolution of 1 mm3 (0.001 cc), measurement accuracy of less than 0.1% and it has a mass of 20 kg. The equipment can be used independently, or it can be computer-controlled.
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2.2 Sample Preparation
The red sandstone had a reddish-brown appearance, compact structure, low porosity, and a density of 2.57 g/cm3. To reduce the dispersion between samples, all rock samples were drilled in an adjacent position of the same rock with fewer fissures. According to the ISRM recommended standard (Fairhurst and Hudson, 1999), the rock samples were processed into cylindrical standard specimens with sizes of 50 × 100 mm. Both end-faces of these rock samples were carefully polished to ensure that the error of unevenness was less than 0.05 mm. It was also essential to make the end-faces parallel within a small tolerance of 0.1 mm or less. Finally, the processed samples were treated with saturated water. The sample preparation procedure is shown in Fig. 3.
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(a) Drilling sampling
(b) Red sandstone sample
(c) Water saturation
(d) Compression test
Fig. 3 Sample preparation process
2.3 Test methods
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During the test, water was used as permeable medium, and six different permeability values were set at 2, 3, 4, 5, 6 and 7 MPa, respectively. However, in the early stage, triaxial compression tests were conducted
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using seepage pressures under 2, 4, 6 and 7 MPa only, whereas in the later stages, supplementary tests with seepage pressures of 3 MPa and 5 MPa were conducted using a THM-2 Thermal-Fluid-solid coupling test system (developed by the State Key Laboratory of Coal Mine Disaster Dynamics and Control of Chongqing
pr
University) to make the results more universal.
A saturated specimen was installed in the pressure chamber and the confining pressure was applied and
e-
maintained at a constant 8 MPa. After the confining pressure had been stabilized, seepage pressure was applied to a predetermined value and maintained for a certain time period until the water volume in the
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back-pressure controller changed steadily and a stable seepage pressure difference and steady water flow was apparent; the test was then terminated by loading the axial pressure until the specimen was destroyed (which
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indicated that the test was terminated). In the process, the stress and strain of the sample were automatically collected and recorded by the computer, and the water volume was automatically collected by the ADVDPC. For rock materials with a permeability coefficient of k ≥ 10−7 μm2, it is preferable to use the steady-state
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method to measure permeability (Yang et al., 2015). During the test, the seepage pressure difference between the two ends of the sample was maintained at a constant value. To test and analyse permeability of the rock,
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the following assumptions were made: (1) water is an incompressible fluid; (2) initial pores and microcracks in the rock are uniformly distributed and the rock is considered to be a porous medium; (3) steady seepage under constant pressure is regarded as continuous seepage and (4) seepage conforms to Darcy's law during the process of stress-strain. Based on Darcy's law, permeability was calculated according to equation (1) (Brace et al., 1968; Jia et al., 2017) as
k
LV , Apw t
(1)
where k is average permeability, m2 ; is the dynamic viscous coefficient of water, = 1 × 10-3 Pa·s (T = 20℃); V is the volume of water that has infiltrated into the rock sample, m3 ; L is the height of the rock sample, m; t is the recording time interval, s; A is the cross-sectional area of the rock sample in m2 and pw is the seepage pressure difference between the two ends of the rock sample in Pa.
3. Analysis of test results 3.1 Stress thresholds of rock failure under different seepage pressures In the process of stress-strain, rock shows different mechanical properties at different bearing stages.
Journal Pre-proof According to rock deformation and fracture development, the concept of stress thresholds can be introduced, and the variation law of rock stress thresholds can be analysed, which is of great significance when monitoring stability during rock mass engineering projects. In the entire process of progressive stress-strain failure under triaxial compression, the corresponding stress characteristic thresholds of each stage prior to the peak are as follows: the crack closure threshold ( cc ), crack initiation threshold ( ci ), crack damage threshold ( cd ) and peak strength ( c ) (Eberhardt, 1998). According to the characteristics of pore and fissure compaction and penetration during the progressive failure of rock, the progressive failure process of rock can be divided into four stages as follows: the crack closure compaction stage (OA); linear elastic stage (AB); crack stable propagation stage (BC) and unstable crack propagation stage (CD). The points A, B, C, and D correspond to cc , ci , cd and c , respectively, in Fig. 4.
σ
f
c
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D
cd
C
pr
ci
B
Stress-Volumetric strain Stress-Axial strain Stress-Lateral strain
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cc
ε
Pr
A
O
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Fig. 4 Schematic diagram of progressive failure process of rock (Eberhardt, 1998)
Eberhardt (1998) proposed that the stress thresholds for crack initiation and damage during rock
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compression are those of the crack initiation threshold and crack damage threshold, respectively. The crack initiation threshold represents the threshold value of stress at which cracks begin to germinate in the process
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of triaxial failure, and internal cracks in the rock are in a stable stage of development when under this stress. The crack damage threshold indicates that rock deformation has entered an unstable stage of development: it is the initial stress stage of continuous expansion and rapid development of internal cracks, and following this stage, peak stress is attained and the rock is subsequently destroyed. The concept of crack volume strain ( cv ) proposed by Martin (1997) provides an effective method for
determining the crack initiation threshold ( ci ) and crack damage threshold ( cd ). By observing the volumetric strain-deviation stress curve of rock and the volumetric strain-deviation stress curve of crack, the volumetric strain of rock ( v ) and crack volume strain ( cv ) can be determined as follows,
v 1 2 3
(1 2 )( ) , cv v E 1
3
(2)
where 1 ， 3 ， v and cv are axial strain, radial strain, rock volumetric strain and crack volumetric strain, respectively, and E and are the elastic modulus and Poisson's ratio, respectively. The use of Eq. (2) enables experimental data to be processed and the volumetric strain-deviation stress curves of rocks and cracks under various seepage pressures can then be plotted, as shown in Fig. 5. The crack
Journal Pre-proof initiation threshold ( ci ) and crack damage threshold ( cd ) are determined from the following: the crack initiation threshold ( ci ) is the stress corresponding to the peak point of the crack volumetric strain-deviation stress curve, and the crack damage threshold ( cd ) is the stress corresponding to the peak point of the rock volumetric strain-deviation stress curve. 90
c cd
ci
30
f
(3)/MPa
60
Dilation
3
2 1
2
3
4
1/%
3
Crack volumetric strain Volumetric strain
0
-1 0
1
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pw
1
Pr
Contraction ε(%)
1
0
pr
-1
e-
0 -2
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Axial strain Lateral strain
2
ε1/%
3
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Fig. 5 Volumetric strain-deviation stress curves of rocks and cracks
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The crack closure threshold ( cc ) represents the threshold value corresponding to complete compaction of pores and fissures within the rock. The stress-strain curve is evidently concave in the initial stages, and it then transits to an elastic deformation stage. However, there is a great randomness involved, and errors can occur when determining the crack closure threshold ( cc ) using only the stress-strain curve. Therefore, in this study, it is considered more reasonable to use the method based on the axial strain difference to determine the crack closure threshold ( cc ). A schematic of the axial strain difference is shown in Fig. 6. 90
0.25 0.20
σcd 60
σcc
D
0.15
reference line
Δε1/%
Axial Stress/MPa
Stress-strain curve
30
A
0.10 0.05
O
0
0
axial strain difference 1
2
Axial Strain/%
3
0.00
B
0
20
40
(σ1-σ3)/MPa
σcd 60
80
Journal Pre-proof Fig. 6 Determination of axial strain difference using stress-strain curve
Fig. 7 Axial strain difference curve
In Fig. 6, the point O is the coordinate origin, the point D is the crack damage threshold, and the line segment OD is used as the reference line for axial strain. The difference between strain corresponding to each stress-strain curve and strain corresponding to the reference line is called the axial strain difference, which is denoted as 1 , and the equation used in calculation is as follows,
1 1
(3)
1 3 , cd cd
where 1 is the axial strain difference and cd is the axial strain corresponding to the crack damage threshold ( cd ). The axial strain difference ( 1 ) under different deviating stresses can be calculated using Eq. (3), and
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the relationship curve between the axial strain difference( 1 ) and deviatoric stress ( 1 3 ) can also be plotted, as shown in Fig. 7, where the stress corresponding to the peak point of the curve is the crack closure 90
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threshold ( cc ). pw = 2 MPa
pw = 5 MPa
pw = 3 MPa
30
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0
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Pr
60
pw = 7 MPa
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Stress/MPa
pw = 4 MPa
pw = 6 MPa
ci
cd
c
Stress thresholds
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cc
Fig. 8 Stress thresholds under various seepage pressures
According to the above calculation method, the stress thresholds of the rock failure process under different seepage pressures can be obtained, and these are plotted in the histogram in Fig. 8. An analys is shows that with an increase in the seepage pressure, the crack closure threshold ( cc ), crack initiation threshold ( ci ), crack damage threshold ( cd ) and peak strength ( c ) of the rock decrease to varying degrees. These results show that under the action of seepage pressure, the strength of the engineered rock mass (such as an underground chamber or reservoir dam) will decrease. 3.2 Deformation characteristics of progressive failure of rock The process of progressive failure of rock refers to the deformation and stress processes prior to peak stress of rock compression, and it is classified as belonging to the rock bearing deformation stage. According to the stress-strain curve, the rock failure process can be divided into the progressive failure process prior to peak stress and the post-peak failure process, as shown in Fig. 9.
Journal Pre-proof 100
Progressive failure process Ⅰ
Ⅱ
Ⅲ
Post-destruction phase Macro-fracture
Ⅳ
ci 40 20 0
vc
vf
1
Ⅲ
2 Strain/%
3
cd
60
ci
40
Axial strain Volumetric strain
cc
0
4
vc 1
0
vf
(3)/MPa
20 vf 2
Ⅱ
Ⅲ
Ⅳ
4
5
f
cd
0
Axial strain Volumetric strain
cc vf 2
vc 1
0
3 Strain/%
Ⅰ
Macro-fracture
Ⅱ
Ⅲ
Ⅳ
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vc 1
(3)/MPa
(3)/MPa
ci 30
Axial strain Volumetric strain
cc vf
(e)
4
5
Axial strain Volumetric strain
cc
0 2 3 Strain/%
Macro-fracture
cd
60
ci
0
5
c
cd
30
4
90 Progressive failure process Post-destruction phase
Post-destruction phase
c
60
Macro-fracture
c
(d)
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(c)
Ⅰ
Ⅳ
ci
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3 Strain/%
90 Progressive failure process
5
30
Axial strain Volumetric strain
cc
0
Ⅲ
e-
ci
vc 1
Ⅱ
pr
60
cd
40
4
Progressive failure process Post-destruction phase Ⅰ
c
60
0
90
Macro-fracture
Pr
(3)/MPa
Post-destruction phase
Ⅳ
80
3
Strain/%
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Ⅲ
2 (b)
100 Progressive failure process Ⅱ
Macro-fracture
c
(a)
Ⅰ
Ⅳ
20
Axial strain Volumetric strain
cc
0
Ⅱ
80
cd
60
Progressive failure process Post-destruction phase Ⅰ
c
(3)/MPa
(3)/MPa
80
100
0
1 vc vf 2 3 Strain/%
4
5
(f)
Fig. 9 Stress-strain curve for rock under various seepage pressures (a) pw = 2 M Pa; (b) pw = 3 M Pa; (c) pw = 4 M Pa; (d) pw = 5 M Pa; (e) pw = 6 M Pa; and (f) pw = 7 M Pa
As evident from Fig. 9, during the progressive failure process, the internal voids of the rock are gradually compressed during the initial stage of loading (and the stress-strain curve is concave). However, with an
Journal Pre-proof increase in axial stress, the rock voids gradually germinate, expand and penetrate, and the damage gradually accumulates until the rock reaches its peak stress. During the process of post-peak failure, the bearing capacity of the rock decreases, which results in a rapid drop in the stress-strain curve and a large number of macro-cracks appear on the surface. The progressive failure process can be further analysed, and according to the stress thresholds of rock, the progressive failure process can be divided into four distinct stages: the crack closure compaction phase (region I); linear elastic phase (region II); crack stability expansion phase (region III), and the crack unsteady expansion stage (region IV). As shown in Fig. 9, the characteristics of each deformation stage are as follows: Region I: Under the combined action of confining pressure and axial pressure, the original open fracture and structural plane begin to gradually close and the volume of the rock becomes compacted; this represents the early stage of non-linear rock deformation. In this stage, the stress-strain curve of the rock is concave, and
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f
the end point of this stage is the crack closure threshold ( cc ). At this time, the original cracks are completely closed.
Region II: With a gradual increase in the axial pressure, the volume of the rock becomes gradually
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compacted. In this stage, the stress-strain curve of the rock is approximately linear, and its deformation mainly originates from elastic deformation within it; the end point of this stage is the crack initiation threshold ( ci ).
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Region III: In this stage, the stress of the rock exceeds the crack initiation threshold ( ci ), the internal stability fractures gradually spring up and expand and the volume of the rock is compressed. The end point of
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this stage is the crack damage threshold ( cd ). At this time, the volume strain of the rock reaches the maximum compaction point.
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Region IV: When the stress exceeds the crack damage threshold ( cd ), the cracks in the rock increase rapidly, fuse and penetrate each other, the volume of the rock begins to increase, the internal damage increases
stress.
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gradually until peak stress is reached and the progressive failure process ends w ith the occurrence of peak
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To study the variation law of volume strain during the process of progressive failure under different seepage pressures, the curve of volume strain is analysed here. As shown in Fig. 9, the progressive failure process undergoes two typical stages of volume compaction and volume expansion. When the rock volume is compressed to its minimum value, the point on the stress-strain curve is defined as the maximum volume compaction point, and the corresponding stress is defined as the damage strength ( d , namely: d cd ). According to the test results, the rock damage strength decreases with an increase in seepage pressure (62.1 MPa, 61.9 MPa, 61.7 MPa, 60.6 MPa, 60.2 MPa and 58.1 MPa in turn), which indicates that the existence of seepage pressure reduces the rock strength to a certain extent. Furthermore, the greater the seepage pressure, the stronger the weakening effect of water on the rock’s strength, which reduces the rock damage strength. It can be seen from Fig. 9, that the volumetric strain corresponding to the maximum volume compaction point of the rock under different seepage pressures is between 1.44% and 1.75%. During the process from the maximum volume compaction point to peak strength, the rock sample volume begins to expand. Therefore, when the peak stress is reached, the difference between the rock volume strain and the volume strain at the maximum volume compaction point (taking the absolute value) can be recorded as the relative value of volume strain dilatation ( vr ). The magnitude of this value can indicate the capacity of the rock to resist
Journal Pre-proof deformation after volume compaction during the rock failure process. According to Eq. (4), the calculation is as follows,
vr vf vc
,
(4)
where vr is the relative value of volume strain dilatation when stress reaches peak stress, vf is the corresponding volume strain at maximum volume compaction and vc is the corresponding volume strain when stress reaches peak strength. The calculation results are shown in Table 1. Table 1 Relative values of volumetric dilatation under various seepage pressures
vf / %
vc / %
vr / %
2
1.44
0.40
1.04
3
1.48
0.53
0.95
4
1.66
0.72
0.94
5
1.71
6
1.68
7
1.75
pr
oo
f
p w / M Pa
0.87
0.84
1.02
0.66
1.55
0.20
Table 1 shows that the relative value of volume strain dilatation ( vr ) decreases with an increase in
e-
seepage pressure when the peak strength is reached. These results show that in the process of rock
Pr
compression and deformation, seepage pressure can reduce the ability of the rock to resist deformation. In addition, it promotes cracking and the volume expansion of the rock, and the rock reaches its peak strength point faster following the volume compaction stage. As the seepage pressure increases, the effect becomes
value.
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more obvious, and the relative value of volume strain dilatancy is smaller when the stress reaches its peak
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3.3 Axial strain stiffness of progressive failure process The axial strain stiffness curve can be used to reflect the ability of rock micro-elements to resist
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deformation and failure during the different stress stages. This effect can be explained as follows: the increase in axial deformation stiffness indicates that the rock has an increased ability to resist deformation and failure, otherwise the ability of the rock to resist deformation and failure would decrease. A constant value of axial strain stiffness with an increase in stress indicates that the rock is in the elastic deformation stage. As the collected experimental data are stored in the text data list in the form of data points, the use of a numerical differentiation method is proposed to calculate the axial strain stiffness corresponding to each strain data point in the progressive failure process of the rock. The calculation is as follows, 1 1 ( i 1) 1 ( i )
1 ( i ) [
2 1 ( i 1) 1 ( i )
1 ( i ) 1 ( i 1) 1 ( i ) 1 ( i 1)
]
,
(5)
where 1 is the axial strain stiffness, GPa; i is the i-th data point of the stress-strain curve data points
obtained from all monitoring; 1 ( i ) is the axial strain stiffness corresponding to the i-th data point, GPa; 1 ( i ) is the axial stress of the i-th data point in MPa and 1 ( i ) is the strain of the i-th data point.
According to the above calculation process, the variation curves of axial strain stiffness during progressive failure process under different seepage pressures can be obtained, and the results are shown in Fig.
Journal Pre-proof 10. pw=2 MPa
5
6
Test value of ε1max
pw=3 MPa
Theoretical value of ε1max
pw=4 MPa
4
pw=5 MPa
5
pw=7 MPa
ε1max/GPa
max /MPa
pw=6 MPa
3 2
4
3
1 0 0
15
30
45
60
75
2
90
2
4 pw/MPa
(1-3)/MPa
8
(b)
f
(a)
6
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Fig.10. Axial strain stiffness curve for each seepage pressure: (a) Axial strain stiffness during progressive failure process; (b)
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relationship between 1max and pw
An analysis of the variation in axial strain stiffness during progressive failure process under different
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seepage pressures, as shown in Fig.10, is presented as follows:
1) In the early stage of stress loading, axial strain stiffness ( 1 ) increases rapidly with an increase in
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stress, and there are minimal differences in the axial strain stiffness ( 1 ) values between rock samples. However, the trend shows that when seepage pressure is larger, axial strain stiffness is smaller, as shown in Fig. 10 (a).
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2) As stress gradually reaches peak strength, there is a rapid decrease in the change of the rock axial strain stiffness ( 1 ) curve under various seepage pressures until peak strength ( c ) is reached, at which time process).
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the minimum value of axial strain stiffness ( 1 ) is reached (the lowest value reached during the entire
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3) As the stress increases gradually, axial strain stiffness ( 1 ) slowly increases until it reaches the peak value of axial strain stiffness. During this stage, axial strain stiffness has an obvious correlation with seepage pressure; that is, when seepage pressure is larger, axial strain stiffness is reduced. The axial strain stiffness curves are arranged in order from top to bottom according to the magnitude of seepage pressure, and the maximum value of axial strain stiffness ( 1max ) decreases with an increase in seepage pressure (pw), as shown in Fig. 10 (b). By fitting the relationship between 1max and pw, it can be seen that 1max and pw have a good linear correlation, which indicates that when the seepage pressure is larger, the peak value of rock axial strain stiffness is smaller, and the functional relationship can be expressed using Eq. (6),
1max 0.1474 pw 4.5327 ， R2 0.9011 .
(6)
The variation trend in the axial strain stiffness curve during progressive failure process under different seepage pressure is consistent, which indicates that the effect of seepage pressure cannot change the overall trend in the axial strain stiffness of rock. However, the values of rock axial strain stiffness under different seepage pressures are obviously different, which indicates that seepage pressure can affect the value of rock
Journal Pre-proof axial strain stiffness. Further analysis shows that in the process of rock compression and deformation, internal cracks continue to deform, extend and connect, and new cracks gradually sprout. Moreover, due to the effect of seepage water pressure, the expansion of rock cracks is promoted, and the stable deformation stage of rocks with cracks is accelerated; there is then a transition to unstable deformation and ultimately to the failure stage. Simultaneously, due to the lubrication of water, there is a decrease in the friction resistance between discontinuous surfaces, and when the seepage pressure is greater the effect of reduction is more obvious. This results in a reduction in axial strain stiffness during the progressive failure process.
3.4 Permeability Evolution Characteristics 3.4.1 Characteristics of permeability evolution during rock stress-strain process Permeability in the stress-strain process is calculated by Eq. (1), and the curves of permeability change
2
B E
30 25 A
0
o
1
2 3 Axial Strain/%
(a)
A
BC
D 10
D
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(3)/MPa
60 1
2
30
3
0 1
60
B
40 E
20
3
4
5
B C
75
Post-destruction phase 100
D 16 12
(1-3) k
D
8
75
4
50
0
1
2
C
0
E
50
B
25
25 A
0 1
2
Progressive failure process A
o
0
E
A
A
0
50
B
Axial Strain/%
100
C
0
0
C
2
25
0
(3) k
5
75
(b)
Post-destruction phase 80
Progressive failure process
100
2 0
1
D
4
o
0
5
rn
90
4
6
al
0
0
(3) k
25
(1-3)/MPa
0
50
Post-destruction phase
2 3 Axial Strain/%
(c)
4
5
0
0
o
0
2 Axial Strain/%
(d)
4
k/10-6μm2
1
60
C
pr
75
D
B C
k/10-6μm2
k
1
0
Progressive failure process A
Pr
(3)/MPa
D
0
50
100
(3)
2
75
90
Post-destruction phase
3
(3)/MPa
D
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BC
k/10-6m2
A
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Progressive failure process
k/10-6m2
100
f
under various seepage pressures are drawn and shown in Fig. 11.
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D
Post-destruction phase
15
k
75
(3)/MPa
0 1
2
C
60 E
25
75
30
0
50
(3) k
75
0
1
2 3 Axial Strain/%
4
2
3
C
50
E
B
25
0
0 1
40
20
25
A o
0
D
D
B
0
B C
A
90
D
5
0
100 Progressive failure process Post-destruction phase 100
(3)
10
50
120
(3)/MPa
B C
k/10-6m2
A
k/10-6m2
100 Progressive failure process
o
5
A
0
0 1
2 3 Axial Strain/%
(e)
4
5
(f)
f
Fig. 11 Curve of rock permeability evolution during stress-strain process
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(a) pw = 2 M Pa；(b) pw = 3 M Pa；(c) pw = 4 M Pa；(d) pw = 5 M Pa；(e) pw = 6 M Pa；(f) pw = 7 M Pa
pr
(The grey part is an enlarged graph of the permeability evolution curve during progressive failure process)
It can be seen from Fig. 11, that permeability first decreases and then gradually increases with an
e-
increase in axial stress. When the peak of permeability is reached, the permeability curve rapidly decreases and finally becomes constant. In addition, the peak of the permeability curve lags significantly behind the peak of the stress-strain curve. To ensure that the figure corresponds to the order presented in Section 3.1, the
ci , cd and c are recorded as points A, B, C and D.
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stress-strain curves corresponding to cc ,
Furthermore, the stress-strain curves and permeability curves are divided into five stages: OA, AB, BC, CD
al
and DE, as shown in Fig.11. According to the stress-strain curve and permeability evolution curve, five stages of OA, AB, BC, CD
rn
and DE are determined and analysed. It can be seen that in the early stage of stress loading (OB stage), rock specimens are in the stage of crack compaction and elastic deformation, permeability is at a low level, and the
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OA stage is in the stage of crack compaction. Rock permeability is thus slightly decreased and the AB stage occurs slowly. The results show that cracks close gradually in the early stage of stress loading and permeability is low, which is related to the low porosity, uniform texture and compactness of red sandstone. With an increase in axial stress, and when stress reaches or exceeds
ci (BC stage), the rock fissures
gradually germinate and connect, which results in a gradual increase in rock permeability. When stress reaches
cd (CD stage), the rock is in an unstable developmental stage, and the different fissures intersect and converge with each other, which provides a seepage channel for water; therefore, permeability gradually increases. In addition, due to the rapid growth of cracks during this stage, different seepage channels are constantly formed in the new cracks but internal fractures block some of these seepage channels. The above two factors cause the rock permeability curve to increase upwards, and stress points exist where permeability decreases; however, overall, rock permeability increases rapidly during this stage. The rock breaks when the stress exceeds
c (DE stage), and the crack connected to both ends of the sample is the dominant factor
controlling the change in permeability. However, the rapid increase in permeability to its peak value lags behind the peak value of stress. Finally, under the combined action of axial and confining pressures, the penetration cracks are compacted, and permeability gradually decreases and eventually becomes stable.
Journal Pre-proof 3.4.2 Evolutionary characteristics of permeability in progressive failure process The focus of research on rock mechanics under water-force coupling in engineering practice is the evolutionary characteristics of permeability during the process of progressive failure of a rock mass prior to reaching peak strength (Alam et al., 2014). Therefore, it is particularly important to analyse the evolutionary characteristics of the rock mass during the process of progressively increasing stress. In addition to the influence of seepage pressure, permeability depends mainly on the expansion, geometric size and fractal dimensions of cracks and the degree of intersection between them. Based on experimental data, the relationship between permeability and axial strain during the progressive failure process of red sandstone prior
pw=3 MPa
pw=4 MPa
pw=5 MPa
pw=6 MPa
pw=7 MPa
20
pr
k/10-6μm2
30
pw=2 MPa
oo
40
f
to reaching peak stress under different seepage pressures is plotted and shown in Fig. 12.
0 0
e-
10
1
2
3
Pr
Axial strain/%
al
Fig. 12 Permeability change curve of progressive failure process prior to reaching peak stress
As seen from Fig. 12, permeability decreases with an increase in axial strain in the early stage of
rn
stress-strain, in relation to pre-test void and fracture compaction; however, permeability then increases with an increase in axial stress. An analysis of the relationship of permeability under different seepage pressures
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shows that with an increase in seepage pressure, there is a gradual increase in the amplitude of permeability in the process of stress-strain, and the permeability corresponding to peak strength also increases . With an increase in seepage pressure, the corresponding permeability in the case of rock failure is 2.512 × 10-6 μm2, 5.653 × 10-6 μm2 , 8.615 × 10-6 μm2 , 11.515 × 10-6 μm2 , 13.675 × 10-6 μm2 and 32.638 × 10-6 μm2. According to the change law of permeability during the progressive failure process, and to establish a permeability evolution model of the progressive failure process of red sandstone, strain corresponding to the minimum permeability value during the stress-strain process can be used as a boundary line, and the permeability curve of the progressive failure process can be divided into two parts (Parts 1 and 2), as shown in Fig. 13.
Journal Pre-proof Progressive failure process Part 1
Part 2
0 k min k
k min c
k min
0
c Axial strain
oo
f
Fig. 13 Schematic diagram of permeability change curve
According to the variation law of the permeability curve with respect to the two parts (Parts 1 and 2), a
pr
piecewise function is proposed to express the relationship between permeability and strain as in Eq. (7), (7)
e-
a k min k0 , 0 k min k , b k min k0， k min c
k min is axial strain corresponding to minimum permeability, %; c is axial strain corresponding to peak stress, %; a and b are the rock permeability factors of different permeability change stages; k0 is the basic permeability of rock, 10-6 μm2 ;
Pr
where k is permeability during the stress-strain process, 10-6 μm2;
is the coefficient reflecting the relationship between permeability and average porosity and
al
k min indicates the effect of rock void change on permeability. dk d
dk d d d
dk d . d d
(8)
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rn
The relationship between permeability and stress can be expressed using Eq. (8) as follows,
If the constitutive relation during the progressive failure process is approximated to the linear relation expressed as E , then the correlation equation between rock permeability and stress can be obtained using the simultaneous Eqs. (7) and (8), and the correlation equation is as follows,
( ) k ,0 E , k ( ) k , E a
k min
0
b
k min
(9)
k min
0
k min
c
k min is deviation stress corresponding to minimum permeability, MPa, where the value is the crack closure threshold ( cc ); E is the elastic modulus of rock in MPa and c is the peak stress of rock in MPa. where
According to the test results, the model parameters of permeability and deviating stress under different seepage pressures calculated by Eq. (9) are shown in Table 2. According to the model parameters, the permeability curves during progressive failure process under different seepage pressures can be obtained, and the curves can then be compared with the experimental data curves, as shown in Fig. 14. The results show that the fitting effect of the Eq. (9) is better, which proves that the established piecewise function model can better
Journal Pre-proof reflect the relationship between permeability and deviating stress in the progressive failure process. These results can be used as a reference when conducting further study on the evolutionary characteristics of rock strength and permeability under seepage-stress coupling. Table 2 Calculated model parameters pw/M Pa Part 1
a 10
Part 2
b 10
10
7
2
3
4
5
6
7
1.460
1.468
1.528
1.598
1.684
1.903
4.481
4.874
5.576
9.658
13.857
26.178
4.003
4
9
Theoretical value of k Test value of k
Theoretical value of k Test value ofk
3
0
0
10 Theoretical value of k Test value of k
al
8
0
Pr
(a)
90
6
rn
4
0 0
Jo u
2
30
60
30 60 (3)/MPa
e-
30 60 (-3)/MPa
90
(b)
16
Theoretical value of k Test value ofk
12 k/10-6μm2
0
k/10-6m2
3
pr
1
f
2
oo
k/10-6μm2
k/10-6m2
6
8
4
0
90
0
30
60
90
(3)/MPa
(-3)/MPa
(c)
(d) 40
15
Theoretical value of k Test value ofk
Theoretical value of k Test value of k
30 k/10-6m2
k/10-6m2
10
5
20 10
0
0 0
20
40 (-3)/MPa
(e)
60
80
0
20
40 (-3)/MPa
(f)
60
80
Journal Pre-proof Fig. 14 Comparison between permeability test results and theoretical calculation values: (a) pw = 2 M Pa; (b) pw = 3 M Pa; (c) pw = 4 M Pa; (d) pw = 5 M Pa; (e) pw = 6 M Pa and (f) pw = 7 M Pa
Based on the above research, it is possible to determine that seepage pressure has a significant effect on rock strength and associated deformation characteristics. The stiffness and peak strength of rock are reduced during the rock failure process, and this is extremely important to consider when conducting engineering projects involving rock mass (such as slope engineering and reservoir dam and underground chamber construction) under the coupling action of seepage field and stress field. According to the research results of this paper, and with respect to conducting engineering geology in an environment where the seepage field and stress field are coupled, it is necessary to enhance the hydrophobic function of the underground engineering drainage system and reduce the seepage pressure of the underground space environment to ensure rock mass
oo
f
stability. The piecewise function model established in this paper provides a reference for monitoring and successfully distinguishing the stability and permeability of the engineering rock mass under seepage-stress
pr
coupling.
4 Conclusion
e-
In this study, triaxial compression tests were conducted on red sandstone samples under different seepage pressures, and the variation laws of strength, deformation, strain, stiffness and permeability during rock
Pr
fracture under osmotic pressures were analysed. The research results provide a reference for design and construction during large rock mass engineering, and also act as guidance for monitoring and preventing engineering geological hazards under hydraulic coupling. Some of the important conclusions are as follows:
al
(1) With an increase in seepage pressure, there is a decrease in the stress eigenvalues during the rock failure process. Different stress eigenvalues correspond to different deformation stages of rocks. Therefore, in
rn
engineering geology, stress eigenvalues are of great significance when ensuring stability during rock engineering. Appropriate reduction of seepage pressure in rock engineering environment can enhance the
Jo u
stability of rock engineering.
(2) In the progressive failure process of rock, axial strain stiffness firstly increases and then decreases with an increase in axial stress. The magnitude of seepage pressure does not affect the change trend of axial strain stiffness but it affects its magnitude: with a larger seepage pressure, there is a reduction in axial strain stiffness during the process of progressive failure process. In addition, there is a good linear relat ionship between maximum axial strain stiffness and seepage pressure. (3) In the stress-strain process, the values of permeability firstly decrease then increase. They subsequently decrease rapidly after reaching peak permeability and finally reach a stable value. During the entire process, the permeability curve is in good agreement with the stress-strain curve, but peak permeability lags behind peak stress. (4) During the progressive failure process of rock, the permeability firstly decreases and then increases with an increase in axial stress, and permeability corresponding to peak strength increases gradually with an increase in seepage pressure. The piecewise function model presented in this paper uses the crack closure threshold as the boundary point, and it accurately reflects the relationship between permeability and deviatoric stress during the progressive failure process of rock.
Journal Pre-proof Acknowledgements This study is supported by the National Science and Technology Major Project of China (Grant No. 2016ZX05045-004).
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pr
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e-
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Journal Pre-proof Title: Experimental study on progressive failure process and permeability characteristics of red sandstone under seepage pressure Manuscript ID: ENGEO_2019_821
Highlights: (1) Triaxial compression tests were conducted on red sandstone under seepage pressure (2) Seepage pressure can reduce the stress characteristic value of rock (3) Seepage pressure does not affect the strain stiffness trend, but it affects the value
Jo u
rn
al
Pr
e-
pr
oo
f
(4) The piecewise function model reflects permeability evolution characteristics