With the continuous exploitation of coal and the increase of abandoned goafs under weakly cemented aquifer strata in Western China, the study of the time dependent mechanical properties of the unique weakly cemented medium-grain sandstone, which is susceptible to water, is imminent. In this paper, creep mechanical properties of dry and saturated medium-grain sandstone, which represent two limit states affected by water, were studied and compared. The results showed that water greatly weakens the compressive resistance of medium-grained sandstone, but balances the volumetric compressive deformation by filling in the internal defects of rock samples with different confining pressures. The rock showed a state of volume expansion except for the first or second loading stage. Compared with short-term compressive strength, the turning point of saturated rock from viscoelasticity to viscoplasticity is earlier than that of dry rock. The short-term elastic modulus has a negative exponential relationship with deviating stress, and creep rate has a positive exponential relationship with deviating stress. Based on Burges model with exponential damage variables, the method of obtaining creep model parameters by short-term mechanical parameters of rocks was introduced, and the linear relationship between elastic modulus of medium-grained sandstone and parameters of Burgers model with damage was found. This conclusion will enrich the framework of the above-mentioned methods for obtaining time-dependent properties.
Research Article
Creep behavior of dry and saturated medium-grain sandstone and its relationship with short-term mechanical properties
https://doi.org/10.21203/rs.3.rs-3238625/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 22 Feb, 2024
Read the published version in Geomechanics and Geophysics for Geo-Energy and Geo-Resources →
You are reading this latest preprint version
Time-dependent property
Weak cementation
Medium-grain sandstone
Creep model parameters
There are many shallow coal seams with simple geological structure in Western China. With the depletion of coal resources in eastern China, the coal mining intensity in the eastern mining area is gradually increasing, and the number of abandoned mines is increasing (Ning et al. 2017; Wang et al. 2023). However, due to the late diagenetic period of medium-grain sandstone in the western coal measures, the particle cementation of the rock is poor and the rock strength is low. The characteristics of rock damage and fracture in coal seam mining are totally different from those in the eastern hard strata (Zhang et al. 2015; Tan et al. 2017; Jiao et al 2021). The ecological environment of mining areas in Western China is fragile, and the underground contains precious water resources. The rough mining of coal seams causes serious water loss and even water inrush accidents in the goaf area (Wang et al. 2012), as shown in Fig. 1. Therefore, it is of significance to grasp the unique mechanical properties of medium-grained sandstone for the safe mining and stability of goaf areas in Western China.
For the instantaneous (short-trem) mechanical properties of soft rock, great progress has been made by many researches over the years (Cao et al. 2016; Zhou et al. 2016; Lollino and Andriani 2017; Ning et al. 2017; Wang et al. 2017; Mansouriand and Ajalloeian 2018; Bian et al. 2019; Hou et al. 2019; Yang et al. 2019; Fu et al. 2022; Chen et al. 2023). However, an important feature of soft rock is that the deformation is obvious under external force, and it is time-dependent. For example, when the Tanern highway tunnel passed through chlorite and other soft rock areas, the deformation of the surrounding rock was severe and the maximum speed reached 20 cm/d, which seriously threatened the stability of the tunnel. After modification of design scheme and secondary support, the deformation of surrounding rock tended to be stable, and the convergence time of tunnel wall deformation exceeded 300 days (Xu et al. 2011). What’s more, groundwater has a great influence on soft rocks, especially added to the influence of continuous load, the mechanical properties of weak rocks which are important for rock engineering are more different.
Up to now, a lot of researches on the influence of water on creep properties of rocks have been done and some valuable results have been achieved (Waza et al. 1980; Lockner 1993; Sun 1999; Masuda 2001; Yang et al. 2007; Okubo et al. 2010; Nara et al. 2013; Tang et al. 2018; Yu et al. 2019; Li et al. 2023). For example, Lockner (1993) carried out creep tests on granite and sandstone under uniaxial stress. The results showed that creep deformation increased with the water content, and the steady creep rate of rock under dry and saturated conditions was two orders of magnitude different. Okubo et al. (2010) carried out creep tests on saturated Tage tuff for 2.5 years and 12 years, respectively. Creep strain and strain rate can be expressed as power functions of time. Sun (1999) showed that the long-term compressive strength of viscous red sandstone after saturation was only 46.3% of the corresponding strength in dry state. Yang et al. (2007) through triaxial creep tests on shales with different water-bearing states, it was considered that water content and deviatoric stress were the most important factors affecting rock creep. In a word, the effect of water on rock creep is mainly manifested in the following aspects: with the increase of water content, the mechanical parameters and strength of rock gradually decrease, the creep rate and creep rate increase, and the duration of steady creep prolongs. However, it is impossible to find a unified law of the influence of water on rock creep properties because of the different mineral composition and internal structure of different rocks. The creep properties of weakly cemented medium-grained sandstone under the influence of water need to be studied systematically.
What is more important, as the basis of design and evaluation of rock engineering, creep constitutive models established by scholars can meet the needs of rock engineering. The key is to obtain the parameters of creep models. In the past, it is a common practice to obtain the relationship between creep and time by laboratory test, and then to obtain creep model parameters by fitting experimental data with constitutive relation. This method is of high accuracy, but time-consuming and laborious. Now, a new idea of estimating creep model parameters based on instantaneous (short-term) properties of rocks is proposed (Hamzaa O and Stace R 2018). But this method has only been validated on the mechanical properties of intact and fractured muddy siltstone. It also needs to be validated in different kind of rocks and further explored to popularize this important discovery.
In this paper, the weakly cemented medium-grain sandstone which is widely attached in Western China is taken as the research object. The short-term and long-term mechanical properties of dry and saturated rocks under different confining pressures are experimentally studied to obtain its unique rheological properties and the effect of water on the rheological properties. The relationship between short-term and long-term mechanical parameters is established to enrich the new framework for estimating creep model parameters based on rock short-term properties.
2.1 Sample preparation
Medium-grain sandstone samples used in the test were taken from Ordos Mining Area, China. Medium-grain sandstone was formed in the Jurassic period. The mineralogical compositions mainly include quartz (27.75%), illite (16.18%), chlorite (8.09%) and albite (47.98%). Illite and chlorite are clay minerals, accounting for about 24% the total mineral composition of medium-grained sandstone. The microstructural morphology of rock samples indicates that medium-grain sandstones are mainly composed of mineral particles, which are located in the matrix composed of microgravity and clay minerals (Fig. 2). Most mineral particles are irregular aggregates. Some unconformity contacts between the particles form the original defects in the samples, which contribute to the time-dependent behavior of rocks.
Dry and saturated specimens for conventional triaxial compression and rheological tests were prepared in accordance with the procedures outlined by ISRM (1981). The ratio of height to diameter of medium-grain sandstone specimens used in the test is 2:1. The diameter is about 50 mm and the height is about 100 mm, and the error of the surface roughness less than 0.02 mm (Fig. 3). The drying treatment is to placed the rock samples in the laboratory with excellent ventilation and weigh it every hour until its quality remains unchanged (Zhou et al. 2016). The saturation treatment of rock samples is to immerse dry rock in clear water and weigh it every half an hour during the first 10 h and then once every hour until its quality remains unchanged (Zhou et al. 2016; Tang et al. 2018). The saturation ratio of medium-grained sandstone measured by experiment is 8.55%-9.24%.
2.2 Axial load classification
The key to the creep test of multi-axial loading is to determine the magnitude of each step load. Therefore, before the creep test, we should carry out the conventional triaxial compression test of dry and saturated medium grained sandstone. The confining pressure (σ3) is designed as 1.5 MPa, 3.0 MPa, 4.5 MPa and 6.0 MPa. The experimental results show that rock strength increases with confining pressures, and the strength of dry rock under the same confining pressure is obviously greater than that of saturated rock, as shown in Fig. 4. The compressive strength of dry sample is 26.5 MPa, 30.7 MPa, 34.3 MPa and 38.1 MPa respectively, and the compressive strength of saturated sample is 18.6 MPa, 23.8 MPa, 26.8 MPa and 29.3MPa with σ3 of 1.5 MPa, 3.0 MPa, 4.5 MPa and 6.0 MPa.
The axial load of the test starts from about 50%-60% of the compressive strength. The difference between two adjacent loads is 2.0 MPa. The load difference between two adjacent confining pressures at the beginning of creep is 2.5MPa. The specific implementation scheme is shown in Table 1.
|
Rock sample |
σ3 (MPa) |
σ1-σ3 (MPa) |
|||||||
|---|---|---|---|---|---|---|---|---|---|
|
Dry |
1.5 |
12.5 |
14.5 |
16.5 |
18.5 |
20.5 |
22.5 |
24.5 |
… |
|
3.0 |
15 |
17 |
19 |
21 |
23 |
25 |
27 |
… |
|
|
4.5 |
17.5 |
19.5 |
21.5 |
23.5 |
25.5 |
27.5 |
29.5 |
… |
|
|
6.0 |
20 |
22 |
24 |
26 |
28 |
30 |
32 |
… |
|
|
Saturated |
1.5 |
9.5 |
11.5 |
13.5 |
15.5 |
17.5 |
19.5 |
21.5 |
… |
|
3.0 |
12 |
14 |
16 |
18 |
20 |
22 |
24 |
… |
|
|
4.5 |
14.5 |
16.5 |
18.5 |
20.5 |
22.5 |
24.5 |
26.5 |
… |
|
|
6.0 |
17 |
19 |
21 |
23 |
25 |
27 |
29 |
… |
|
2.3 Creep test equipment and procedures
Triaxial creep test was carried out on RLJW-2000 servo-controlled testing machine (Gu et al. 2019; Tan et al. 2019). The creep characteristics of rock specimens under constant temperature (25 ± 1.5 ℃) were tested by multi-axial loading on a single specimen with equal confining pressure. At the beginning of the test, the confining pressure is loaded to the set value at the rate of 0.05 MPa /s, then the axial deviating stress is loaded to the first level at the rate of 0.06 mm /min. The axial pressure is maintained for 6 hours before loading to the second level, and so on until the specimen is destroyed.
3.1 Time-Dependent Strain of Medium-grain Sandstone
3.1.1 Behavior of Axial Strain with Time
The creep deformation of saturated and dry medium-grain sandstone with time is shown in Fig. 5. The instantaneous strain of the specimen is obvious at each stage of deviatoric stress, and the instantaneous strain is the largest under the first stage of axial loading. The first-stage instantaneous deformation of saturated rock under different confining pressure differs slightly and remains at about 0.35%, while the first-stage instantaneous deformation of dry rock decreases with the increase of confining pressure, which shows that confining pressure restrict the instantaneous deformation of dry rock more obviously. After the first stage of loading, with the increase of loading level, the instantaneous deformation increases gradually, and the gap between saturated and dry rock axial deformation increases. This also confirms the view that confining pressure has great restrictive effect on dry rock.
When the deviatoric stress is not large enough, such as confining pressure 3.0 MPa and deviatoric stress less than 14 MPa, the rock samples only show instantaneous deformation and decay creep, and the rock deformation reaches a stable state in a short time. When the deviatoric stress increases to a certain extent, the deformation of rock shows obvious time correlation. At this time, it takes a long time for the rock deformation to reach a stable state. With the increase of loading level, the steady creep rate of rock increases gradually until accelerated creep occurs, which eventually leads to rock failure.
The increase of confining pressure improves the maximum deformation and bearing capacity of medium-grain sandstone. When saturated rock is failure, the loading level is low and the axial strain is large, which indicates that the deformation capacity of medium-grain sandstone under the influence of water is increases and the bearing capacity decreases.
3.1.2 Behavior of Lateral Strain with Time
The trend of lateral strain is similar to that of axial strain, as shown in Fig. 5. However, the dynamic principle of lateral deformation and axial deformation is different (Zhang et al. 2016). In the early stage of creep test, the lateral compactness of primary cracks and voids in specimens is generally less than the axial strain. With the increase of deviatoric stress, the original defect is compacted to the minimum, and the restructuring of particles in rock enhances the lateral strain, and the time dependence of lateral strain is greater than that of axial strain. Thereafter, the lateral deformation of rock increases significantly and eventually leads to lateral dilatancy failure in the loading stage near rock failure.
For medium-grain sandstone in coal measures, the instantaneous lateral strain under deviatoric stress is less than the instantaneous axial strain, and the lateral deformation of rock increases faster than the axial deformation after load stabilization. Under the same confining pressure, the difference of lateral strain between saturated and dry rock samples is very small, which indicates that the maximum lateral deformation ability of both samples is similar, and their maximum lateral strain decreases with the increasing of confining pressure.
3.1.3 Behavior of Volumetric Strain with Time
Volume deformation of rock generally includes two stages: volume compaction and creep dilatation (Zhang et al. 2016; Belmokhtar 2017). The volume compaction of medium-grain sandstone is usually reflected in the first or two loading stages, and the subsequent loading stages are characterized by dilatancy behavior. The strain rate in compaction stage is smaller than that in dilatancy stage, and the dilatancy strain increases sharply when rock is near failure.
The maximum volumetric compressive strain of dry rock increases with the confining pressure, and the maximum dilatancy strain decreases with the increasing of confining pressure[]. For saturated rock samples, the difference of volumetric compressive strain under different confining pressure is very small, which remains about 0.2%, while the volume dilatancy under low confining pressure is the most obvious. In addition, the maximum volumetric compression strain of saturated rock is larger than that of dry rock, and the maximum volumetric dilatation strain is smaller than that of dry rock, and these differences gradually decrease with the increase of confining pressure.
3.2 Instantaneous elastic modulus
In multi-axial creep loading, both instantaneous loading and constant axial stress can cause rock damage, and the damage between two adjacent loading levels can be indirectly compared by the elastic modulus between them (Zhao et al. 2017). Based on this, we calculate the elastic modulus of rock samples during each instantaneous loading, as shown in Fig. 6. The elastic modulus of saturated and dry medium-grain sandstone decreases exponentially with the increasing of deviatoric stress. That is to say, with the increase of deviatoric stress, the rock damage increases, which indirectly indicates that the damage of medium-grain sandstone increases exponentially with the increasing of deviatoric stress.
3.3 Strain rate analysis
To study the difference of axial creep rate between saturated and dry medium-grain sandstone under different confining pressures, the creep rate of rock samples under three kinds of deviatoric stress is shown in Fig. 7. At the same deviatoric stress level, the creep rate decreases with the increasing of confining pressure, and the influence becomes more significant with the increasing of deviatoric stress. The reason may be that the confining pressure increases the compressive strength of rock and weakens the creep mechanical properties. Under the same confining pressure, the creep rate of saturated rock sample is higher than that of dry rock sample, and with the increase of confining pressure, the creep rate of saturated rock sample decreases more greatly. In practical engineering, support and reinforcement can effectively improve confining pressure and long-term stability of the project.
Ma et al. (2006) pointed out that the steady state creep rate of tuff lava has a power function relationship with deviatoric stress, and the higher the stress, the more obvious the exponential relationship is. In this paper, the exponential function relationship (y = AeBx) between steady creep rate and deviatoric stress of medium grain sandstone in is shown in Fig. 8. A and B are both experimental parameters, which are greater than 0. The fitted exponential relation is consistent with the conclusion that the elastic modulus decreases exponentially with deviatoric stress. That is, the higher the deviatoric stress, the faster the damage of rock and the faster the creep rate.
3.4 Creep model analysis
The creep experimental data can be analyzed and displayed through constitutive models. The parameters in these models can correspond to the inherent creep characteristics of rock materials. so it is important to quantitatively obtain the creep characteristics of materials for engineering stability prediction and engineering design.
For medium-grained sandstone, the rock presents deceleration creep and steady creep under deviating stress, i.e. linear creep. This creep behavior can be well described by Burgers model. However, according to the above experimental results, the damage of medium-grain sandstone accumulates exponentially under multi-axial creep loading, and the isochronal stress-strain relationship changes nonlinearly. Therefore, we should use the damage Burgers model to describe the creep behavior of medium-grain sandstone, and its expression is as follows (Zhu et al. 2010):
where ε is the strain, σ is the stress, t is time, E0 M, η0 M, E0 K, η0 K are viscoelasticity coefficient of damage Burgers model, εc is viscous strain.
|
σ3 (MPa) |
E0 M (GPa) |
P-E0 M (GPa) |
η0 M (GPa h) |
P-η0 M (GPa h) |
E0 K (GPa) |
P-E0 K (GPa) |
η0 K (GPa h) |
P-η0 K (GPa h) |
|---|---|---|---|---|---|---|---|---|
|
Saturated |
||||||||
|
1.5 |
6.12 |
6.36 |
5.83 |
6.56 |
52.43 |
61.92 |
158.47 |
146.89 |
|
3.0 |
6.78 |
7.49 |
8.15 |
7.72 |
68.75 |
72.20 |
159.71 |
169.16 |
|
4.5 |
9.27 |
8.47 |
8.89 |
8.73 |
91.05 |
81.20 |
188.54 |
188.66 |
|
6.0 |
10.86 |
9.32 |
10.41 |
9.63 |
113.76 |
92.27 |
203.46 |
209.13 |
|
Dry |
||||||||
|
1.5 |
9.31 |
9.66 |
9.51 |
9.35 |
96.64 |
105.51 |
138.50 |
139.96 |
|
3.0 |
10.08 |
10.80 |
9.52 |
10.45 |
110.52 |
116.94 |
153.28 |
153.81 |
|
4.5 |
12.48 |
11.52 |
11.89 |
11.15 |
121.95 |
124.16 |
164.26 |
162.57 |
|
6.0 |
14.17 |
12.79 |
13.05 |
12.21 |
134.83 |
135.57 |
177.26 |
174.65 |
It can be seen from Formula (1) that there is a non-linear term (1/e− mεc) in the Burgers model with damage, which is consistent with the conclusion that the damage increases exponentially with the deviatoric stress. m is a coefficient related to rock properties. The greater the m value, the more serious the material damage is under the same viscous strain. Based on the research results of Zhu et al. (2010), the satisfactory fitting result can be obtained by fitting the curve with m = 40.
Based on the creep test results, the Levenberg-Marquardt algorithm is introduced into the least squares method for solving nonlinear problems to identify the parameters in the creep model. The identified parameters of Burgers model with damage are shown in Table 2. The model was found to be suitable to describe the experimental data with good accuracy (R2 = 0.91 − 0.99).
The results in Table 2 show that the saturated rocks with smaller stiffness also have smaller creep parameters than the dry rocks, which results in larger creep deformation. The creep parameters of medium-grain sandstone increase with the confining pressure, and the relationship between rock stiffness and confining pressure is also positive. Therefore, we can infer that the creep model parameters of medium-grained sandstone correspond to its elastic modulus. This inference will make it possible for us to obtain the parameters of creep model based on the instantaneous deformation parameters of rocks.
Maxwell parameter E0 M reflects the instantaneous deformation of rock specimen under axial loading. E0 M in Table 2 shows that the instantaneous deformation of rock before accelerated creep increases with the increase of confining pressure. As for the variation of E0 M with deviatoric stress, taking 4.5 MPa confining pressure as an example, the relationship of E0 M with deviatoric stress as shown in Fig. 9 shows that the instantaneous deformation of medium-grain sandstone increases with the increase of deviatoric stress, which reflects the non-linear characteristics of rock creep, and also confirms the phenomena illustrated by the isochronal stress-strain curve. In addition, the first creep (deformation recoverable) and the second creep (deformation non recoverable) properties of rocks can be reflected by Kelvin parameters η0 K and Maxwell parameter η0 M, respectively. It is found that the Maxwell viscosity η0 M of medium-grain sandstone is usually much smaller than the Kelvin viscosity η0 K, indicating that non recoverable deformation is more easier to produce on medium grain sandstone.
3.5 Relationship between instantaneous and creep parameters
From the above analysis, it can be seen that there is a corresponding relationship between short-term deformation characteristics and creep deformation characteristics (Hamzaa O and Stace R 2018). Therefore, the creep model parameters under different confining pressures are normalized, i.e. the creep model parameters are divided by the elastic modulus (E) under the same confining pressure. The creep parameters after normalization are shown in Fig. 10. The results show that the regularity of creep properties of saturated and dry medium-grain sandstones after normalization is more obvious, which further shows that the instantaneous properties of rocks are proportional to the time-dependent properties.
Therefore, parameters of Burgers model with damage and elastic modulus (E) are plotted in Fig. 11. It is found that the relationship between them can be described by a linear function, and the accuracy of the description is more than 0.89. That is to say, the creep parameters of saturated and dry medium-grain sandstones can be calculated according to the formula parameter = a + bE when the elastic modulus (E) of rocks is known. The values of a and b are given in Table 3.
|
E0 M (GPa) |
η0 M (GPa h) |
E0 K (GPa) |
η0 K (GPa h) |
|
|---|---|---|---|---|
|
Saturated |
||||
|
a |
-0.1134 |
-0.1346 |
2.4596 |
18.1160 |
|
b |
1.7521 |
1.8101 |
16.0702 |
34.8047 |
|
R2 |
0.9475 |
0.9689 |
0.8979 |
0.9749 |
|
Dry |
||||
|
a |
-2.3363 |
-2.2295 |
-14.7205 |
-5.9461 |
|
b |
2.3252 |
2.2448 |
23.3022 |
28.2757 |
|
R2 |
0.9652 |
0.9657 |
0.9929 |
0.9991 |
The main purpose of this study is to investigate and compare the triaxial creep behavior of saturated and dry medium-grain sandstone, which represents two extreme states of rock mass in water environment. The relationship between instantaneous (short-term) properties and creep model parameters of two states of rocks is further discussed.
(1)The first-loading instantaneous deformation of saturated rock under different confining pressures is similar, but that of dry rock decreases with the increase of confining pressure, which indicates that confining pressure has greater restriction on dry rock. Thereafter, the instantaneous and creep deformation of the specimens increase with the increase of deviatoric stress, and the decay creep gradually develops into stable creep and then accelerated creep.
(2)The lateral strain after load stabilization increase faster than that of axial strain. The volume of rock sample is gradually compressed in the first or two stages of axial loading and then expanded in other loading stages. Water fills the defects in rock, resulting in a small difference in the maximum volumetric compressive strain of saturated samples under different confining pressures. This improves the compressive deformation capacity of medium-grain sandstone, but the shear resistance of rock samples after water absorption is greatly weakened.
(3)The creep deformation of medium-grain sandstone has non-linear characteristics, that is, the creep of medium-grain sandstone under multi-axial loading is a process from viscoelastic deformation to viscoplastic deformation. The negative exponential relationship of elastic modulus and deviatoric stress and the positive exponential relationship of creep rate and deviatoric stress also reveal this conclusion. It also reflects the exponential relationship between rock damage and deviatoric stress.
(4)Based on Burgers creep model with exponential damage, the fitting of creep test data under different confining pressures is successfully realized. Compared with dry rock, saturated rock with smaller stiffness has smaller creep parameters. The linear relationship between elastic modulus or slope of stress-lateral strain curve and parameters of Burgers model with damage is found. This discovery enriches a new framework for estimating creep model parameters based on instantaneous (short-term) properties of rocks, and is also conducive to the establishment of a unified constitutive model of short-term and long-term in the next step.
Ethics Approval Not applicable.
Conflict of interest The author(s) declared no potential conflict of interest with respect to the research, authorship, and/ or publication of this article.
Data availability The data used to support the findings of this research are included within the paper.
Author Contribution Conceptualization, Gu QH and Tan YL; methodology, Gu QH and Zhao GM; experiment, Gu QH; formal analysis, Mneg XR and Cheng X; writing—original draft preparation, Gu QH; writing—review and editing, Gu QH and Cheng X. All authors have read and agreed to the published version of the manuscript.
Funding This research was funded by Anhui Provincial Natural Science Foundation (No. 2208085QE143), National Natural Science Foundation of China (No. 51974009, 52074168), Anhui Province Science and Technology Major Project (No. 202203a07020011), Anhui Province “Provincial Special Expenditure Plan” Leading Talent Project (No. T000508), Collaborative Innovation Project of Anhui Province Universities (GXXT-2021-075), State and Local Joint Engineering Laboratory for Gas Drainage & Ground Control of Deep Mines (Henan Polytechnic University (No. SJF2208), and Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology (No. 2021yjrc20).
Consent to publish The Author confirms that the work described has not been published before (except in the form of an abstract or as part of apublished lecture. review, or thesis), and its publication has been approved by all co-authors.
- Belmokhtar M, Delage P, Ghabezloo S, Conil N (2017) Thermal volume changes and creep in the Callovo-Oxfordian claystone. Rock Mech Rock Eng 50(9): 2297–2309.
- Bian K, Liu J, Zhang W, Zheng XQ, Ni SH, Liu ZP (2019) Mechanical behavior and damage constitutive model of rock subjected to water-weakening effect and uniaxial loading. Rock Mech Rock Eng 52(1): 97–106.
- Cao P, Wen YD, Wang YX, Yuan HP, Yuan BX (2016) Study on nonlinear damage creep constitutive model for high-stress soft rock. Environ Earth Sci 75(10): 900.
- Chen G, Li Y, Li T, Zhang G (2023) Experimental study on the mechanical properties of intermittent jointed sandstone considering water-rock interaction and confining pressure effect. Bull Eng Geol Environ 82, 113. https://doi.org/10.1007/s10064-023-03156-w.
- Fu JW, Labuz JF, Cheng HX, Hou RB, Zhu WS (2022) Simulating progressive failure in fractured saturated rock under seepage condition using a novel coupled model and the application. Geomech Geophys Geo-energ Geo-resour 8, 42.
- Gu QH, Ma Q, Tan YL, Jia ZC, Zhao ZH, Huang DM (2019) Acoustic emission characteristics and damage model of cement mortar under uniaxial compression. Constr Build Mater 213: 377–385.
- Hamzaa O, Stace R (2018) Creep properties of intact and fractured muddy siltstone. Int J Rock Mech Min Sci 106: 109–116.
- Hou RB, Zhang K, Tao J, Xue XR, Chen YL (2019) A nonlinear creep damage coupled model for rock considering the effect of initial damage. Rock Mech Rock Eng 52(5): 1275–1285.
- ISRM (1981) Rock characterization, testing and monitoring. In: Brown ET (ed) ISRM (International Society for Rock Mechanics) suggested methods. Pergamon, Oxford.
- Jiao YY, Wu KB, Zou JP, Zheng F, Zhang XF, Wang C, Li X, Zhang C (2021) On the strong earthquakes induced by deep coal mining under thick strata-a case study. Geomech Geophys Geo-energ Geo-resour 7, 97.
- Li JD, Gao Y, Yang TH, Zhang PH, Deng WX, Liu FY (2023) Effect of water on the rock strength and creep behavior of green mudstone. Geomech Geophys Geo-energ Geo-resour 9, 101.
- Lockner D (1993) Room temperature creep in saturated granite. J Geophys Res-Sol Ea 98(B1): 475–487.
- Lollino P, Andriani GF (2017) Role of brittle behaviour of soft calcarenites under low confinement: laboratory observations and numerical investigation. Rock Mech Rock Eng 50(7): 1863–1882.
- Ma L, Daemen JJK (2006) An experimental study on creep of welded tuff. Int J Rock Mech Min Sci 43(2): 282–291.
- Mansouri H, Ajalloeian R (2018) Mechanical behavior of salt rock under uniaxial compression and creep tests. Int J Rock Mech Min Sci 110: 19–27.
- Masuda K (2001) Effects of water on rock strength in a brittle regime. J Struct Geol 23(11): 1653–1657.
- Nara Y, Yamanaka H, Oe Y, Kaneko K (2013) Influence of temperature and water on subcritical crack growth parameters and long-term strength for igneous rocks. Geophys J Int 193: 47–60.
- Ning JG, Wang J, Tan YL, Zhang LS, Bu TT (2017) In situ investigations into mining-induced overburden failures in close multiple-seam longwall mining: A case study. Geomech Eng 12(4): 657–673.
- Okubo S, Fukui K, Hashiba K (2010) Long-term creep of water-saturated tuff under uniaxial compression. Int J Rock Mech Min Sci 47: 839–844.
- Sun J (1999) Rheology of rock and soil materials and its application in engineering. Beijing: Chinese Architecture and Building Press.
- Tan YL, Gu QH, Ning JG, Liu XS, Jia ZC, Huang DM (2019) Uniaxial compression behavior of cement mortar and its damage-constitutive model based on energy theory. Materials 12(8): 1309.
- Tan YL, Liu XS, Ning JG, Lv YW (2017) In situ investigations on failure evolution of overlying strata induced by mining multiple coal seams. Geotech Test J 40(2): 244–257.
- Tang SB, Yu CY, Heap MJ, Chen PZ, Ren YG (2018) The influence of water saturation on the short-and long-term mechanical behavior of red sandstone. Rock Mech Rock Eng 51(9): 2669–2687.
- Wang FT, Wei XQ, Shao DL, Zhang C (2023) The progressive failure mechanism for coal pillars under the coupling of mining stress and water immersion in underground reservoirs. Bull Eng Geol Environ 82, 103. https://doi.org/10.1007/s10064-023-03151-1.
- Wang Y, Yang WF, Li M, Liu X (2012) Risk assessment of floor water inrush in coal mines based on secondary fuzzy comprehensive evaluation. Int J Rock Mech Min Sci 52: 50–55.
- Wang Q, Pan R, Jiang B, Li SC, He MC, Sun HB, Luan YC (2017) Study on failure mechanism of roadway with soft rock in deep coal mine and confined concrete support system. Eng Fail Anal 81: 155–177.
- Waza T, Kurita K, Mizutani H (1980) The effect of water on the subcritical crack growth in silicate rocks. Tectonophysics 67: 25–34.
- Xu WY, Nie WP, Zhou XQ, Shi C, Wang W, Feng SR (2011) Long-term stability analysis of large-scale underground plant of Xiangjiaba hydro-power station. J Cent South Univ T 18(2): 511–520.
- Yang CH, Wang YY, Li JG, Gao F (2007) Testing study about the effect of different water content on rock creep law. J China Coal Soc 7: 695–670.
- Yang W, Zhang Q, Ranjith PG, Yu R, Luo G, Huang C, Wang G (2019) A damage mechanical model applied to analysis of mechanical properties of jointed rock masses. Tunn Undergr Sp Tech 84: 113–128.
- Yu CY, Tang SB, Tang CA, Duan D, Zhang YJ, Liang ZZ, Ma K, Ma TH (2019) The effect of water on the creep behavior of red sandstone, Eng Geol 253: 64–74.
- Zhang JH, Wang LG, Li QH, Zhu SS (2015) Plastic zone analysis and support optimization of shallow roadway with weakly cemented soft strata. Int J Min Sci Tech 25(3): 395–400.
- Zhang Y, Shao JF, Xu WY, Jia Y (2016) Time-dependent behavior of cataclastic rocks in a multi-loading triaxial creep test. Rock Mech Rock Eng 49(9): 3793–3803.
- Zhang ZT, Gao WH (2020) Effect of different test methods on the disintegration behaviour of soft rock and the evolution model of disintegration breakage under cyclic wetting and drying. Eng Geol 279, 105888.
- Zhao YL, Zhang LY, Wang WJ, Wan W, Li SQ, Ma WH, Wang YX (2017) Creep behavior of intact and cracked limestone under multi-level loading and unloading cycles. Rock Mech Rock Eng 50(6): 1409–1424.
- Zhou Z, Cai X, Cao W, Li X, Xiong C (2016) Influence of water content on mechanical properties of rock in both saturation and drying processes. Rock Mech Rock Eng 49(8): 3009–3025.
- Zhu JB, Wang B, Wu AQ (2010) Study of unloading triaxial rheological tests and its nonlinear damage constitutive model of jinping hydropower station green sandstone. Chin. J Rock Mech Eng 29(3): 528–534.
No competing interests reported.