In order to investigate the mechanical behavior of shale rock under cyclic loading and unloading condition, two kinds of incremental cyclic loading tests were conducted. Based on the result of the short-term uniaxial incremental cyclic loading test, the permanent residual strain, modulus, and damage evolution were analyzed firstly. Results showed that the relationship between the residual strains and the cycle number can be expressed by an exponential function. The deformation modulus
Rock mass in underground is exposed to systematic cyclic loading during drilling, mechanical excavation, or due to mine seismology [
Laboratory testing is the main method to understand the mechanical behaviors of rock mass. Over the past few decades, considerable efforts have been made to assess the mechanical response of rock under cyclic loads. Liu et al. [
It is noteworthy that the abovementioned studies mainly focus on the mechanical behavior of rock under cyclic compressive loading and unloading condition and that while the instability of many geotechnical engineering does not appear immediately, such as underground excavation, mining tunnel, and drilling, it will last for some time after excavation. So, it is also very necessary to consider the time-dependent mechanical behavior of rock mass under cyclic loading.
Shale rock may suffer cyclic loading during drilling, fracturing, and refracturing. To better understand the mechanical behavior of rock mass, the short-term and creep tests of a type of shale rock were conducted under uniaxial cyclic loading. Based on the short-term experimental test results, the deformation, modulus, and damage evolution were first analyzed. Then, in accordance with the creep experimental results, the creep behavior of the shale rock was obtained. Finally, by considering the characteristics of the Burgers creep model, a viscoelastic-plastic creep model was proposed through viscoplastic mechanics and its parameters were identified. Results can help better understand the failure mechanism of shale under cyclic loading, which has important practical significance for accurately assessing the effect of hydraulic fracturing and long-term stability of borehole.
The specimen used for the cyclic tests in this research was shale rock, a type of soft sedimentary rock, which was sampled from a Longmaxi formation on the east of the Sichuan Basin in China. Longmaxi Shale is the most commercially developed shale gas reservoir in China [
The natural rock sample with the average unit weight about is 2668 kg/m3, and with the same bedding orientation (horizontal), the natural water content of the rock sample is about 6%. According to the method suggested by the ISRM [
Shale rock specimens.
Both conventional uniaxial compression experiments and cyclical experiments of specimens were carried out on a TFD-2000 rheology testing system, as shown in Figure
TFD-2000 rheology testing system.
Due to the shale gas pressure and fracturing fluid pressure, the surrounding rock is always subjected to cyclic loading in the development of shale gas field [
The sketch of (a) short-term cyclic loading test and (b) cyclic loading creep test.
Before setting up the testing procedure, the uniaxial compression tests were conducted firstly to obtain the uniaxial compressive strength and the typical stress-strain curve of the shale rock specimen as shown in Figure
The typical stress-strain curve of the shale rock specimen.
The short-term cyclic loading and unloading test (Figure
The procedure for the uniaxial creep test under cyclic loading condition (Figure
To prevent the effects of variation in diurnal temperature, a constant indoor temperature was maintained at 20 ± 0.1°C during the entire tests.
Figure
Curve of stress-strain under short-term uniaxial cyclic loading condition.
As shown in Figure
Relationship between the residual strain and the cycle number.
It can be also obtained that the rupture stress is 53.18 MPa, which is 97.91% of the uniaxial compressive strength. Figure
Schematic view of the shale rock specimen after failure.
Figure
Relationship between each peak stress and
Relationship between each peak stress and
The deformation modulus
The elastic modulus
From Figures
The existed initial cracks or bedding planes within shale make the quantity of damaged parts increase, and the area expands when the shale is under cyclic loading situation, and the increased damage causes the effective stress on a microscale to increase. All sorts of the mesoscopic flaws in shale rock are randomly distributed because rock is a product of long geological history [
Based on the stress-strain curve of the rock mass under cyclic loading, we can calculate the constitutive energy and the dissipated energy at a given stress state, as shown in Figure
Calculation model of dissipated energy and constitutive energy.
According to the results from cyclic loading test on the shale rock, the damage variable can be calculated by using (
Calculated damage variables of shale rock and its fitted curve.
In accordance with the testing procedure shown in Figure
Curves of axial strain versus time of shale rock specimens under cyclic loading.
It can be deduced from Figure
Form Figure
Illustration of the viscoelastic-plastic creep model.
where
The creep equation of the viscoelastic-plastic creep model can be written as follows:
By using the viscoelastic-plastic creep model (
Parameters of the viscoelastic-plastic creep model.
Stress level (MPa) |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
27.16 | 13667.22 | 120846.50 | 1123865.91 | 3356791.52 | 0.02 | 2.58 | 0.988 |
35.16 | 12528.82 | 457903.91 | 2265214.34 | 219.08 | −7.65 | 0.08 | 0.997 |
43.16 | 11899.18 | 63875.70 | 1.45 |
51177.93 | −2.65 | 0.19 | 0.959 |
51.16 | 11520.01 | 432090.97 | 110414.84 | 999684.64 | −8.34 |
7.80 | 0.990 |
Comparison between calculated results and experimental results below the stress level of 51.16 MPa.
Test results and model calculation curves of specimen under stress levels of 51.16 MPa.
Two different kinds of cyclic loading and unloading tests were conducted in this study for characterizing the mechanical behavior of shale rock, which were short-term uniaxial incremental compressive cyclic loading and unloading test and long-term uniaxial incremental compressive cyclic loading and unloading creep test. From the test results, the following conclusions can be drawn: The relationship between the residual strains and the cycle number can be expressed by an exponential function. The deformation modulus and elastic modulus first increase and then decrease with increase of peak stress under the loading condition, and both of them increase approximately linearly with increase of the peak stress under the unloading condition. The cyclic loads formed hysteretic loops, and the area of the hysteretic loops increased with the increasing of the loading stress, which can be used to interpret energy dissipation of the specimen. Based on the energy dissipation, the damage variables under short-term cyclic loading condition were analyzed, and it shows an exponential increasing with the strain at peak stress. There exist obvious instantaneous strain, decay creep, and steady creep under each loading or unloading stage, and under the stress of 51.16 MPa, the specimen shows the accelerated creep stage. A viscoelastic-plastic creep model was proposed. Comparison of the test results with the model predictions shows that the proposed viscoelastic-plastic creep model is capable of describing the creep behavior of shale rock subjected to cyclic loading and unloading condition.
Finally, it should be noted that further studies both in triaxial tests and in theory are necessary to gain more relative data for better understanding the cycle load mechanical behavior of shale rock. Numerical simulation of engineering projects associated with shale rock should also be taken into account in the future.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study was partially supported by the National Natural Science Foundation of China (Grant no. 41302223), Science and Technology Plan Projects of Chongqing Administration of Land, Resources and Housing (KJ-2015047), Chongqing No. 3 Colleges and Universities Youth Backbone Teachers Funding Plans and Chongqing Research Program of Basic Research and Frontier Technology (cstc2016jcyjA0074, cstc2016jcyjA0933, and cstc2015jcyjA90012), and Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1713327 and KJ1600532). The authors also thank Professor Yang Mijia for his valuable suggestions and English improvement of this manuscript, which comes from Department of Civil and Environmental Engineering, North Dakota State University.