Experimental study on the effect of confining pressure and interval time on the fatigue mechanical properties of mudstone

. The mudstone interlayer experiences discontinuous cyclic loading during gas storage reservoir operation. To investigate the effects of intermittent action and confining pressure on the fatigue mechanical properties of mudstone. Continuous fatigue test and graded intermittent fatigue test were conducted respectively. The results show that: 1. the fatigue life of mudstone is enhanced by the intermittent effect during the fatigue process. The presence of confining pressure under the same experimental conditions also benefits the fatigue life of mudstone.2. the average modulus of elasticity of mudstone decreases with increasing stress level during cyclic loading, and both intermittency and confining pressure help to enhance the modulus of elasticity of mudstone.3. in graded intermittent fatigue tests. In both uniaxial and triaxial tests, the residual strains generated by the post-interval cycles are smaller than those generated before the intervals.4. In the 3MPa graded interval fatigue test, negative deformation occurs in the post-interval cycle due to the release of elastic energy.


Introduction
Due to the need for energy security reserves, many underground salt cavern gas storage facilities have been built in China in recent years.During the operation of underground gas storage, with the injection and extraction of gas.The surrounding rock experiences discontinuous cyclic loading action.As shown in Fig. 1 for Germany huntorf power station daily peak pressure diagram.Unlike foreign salt rock is distributed in the form of giant salt mounds in the underground, salt rock in China is mostly distributed in the form of layered salt rock.The salt rocks contain interlayers such as mudstones.Mudstone is a weakly consolidated clay that has formed a strongly consolidated rock after a moderate degree of postgeneration [1], In general, its uniaxial compressive strength is low, belonging to the soft and weak rock, which is extremely widely distributed, and shale accounts for about 50% of the total amount of the surface [2].In order to ensure the safe operation of underground gas storage reservoirs.Considering the underground storage reservoir surrounding rock in the storage reservoir operation process by the load is often in the change, a large number of scholars so on the rock grading load under the mechanical properties of research [3][4][5][6][7].Chen Wenwu et al. [8] conducted graded loading test with red layer soft rock and found that the theoretical curve of Burgers model is basically consistent with the test curve, which can better describe the creep characteristics of red layer soft rock; Lu Gao Ming et al. [9] found that the fatigue life of yellow sandstone can be predicted by the number of cycles-upper limit stress curve under a certain condition; Xu Ying et al. [10] investigated the energy evolution and damage characteristics of mudstone under cyclic loading and unloading conditions; Cai Guojun et al [11] investigated the kinetic properties of mudstone under cyclic loading and unloading and found that there was a quadratic polynomial relationship between the damage variables and the strain of the mudstone; Guo Yindong et al [12] carried out fatigue tests under uniaxial cyclic loading of mudstone, studied the fatigue strength, deformation, and damage characteristics of mudstone, and made an analysis of the evolution of fatigue damage of mudstone under cyclic loading and the fatigue strength, deformation, and damage characteristics of mudstone under uniaxial cyclic loading.Under the action of cyclic loading, the fatigue damage evolution law of salt rock was initially explored; some scholars conducted experiments to investigate the effect of fatigue characteristics of rocks under the action of time interval, Li Zongze et al [13] found that the residual strain produced by cycling after the time interval was greater than that before the interval; Jiang Deyi et al [14] found that the intermittent fatigue life of salt rock was shortened more than 50% compared to the traditional fatigue life; Fan et al [ 15] found that with the interval time, the fatigue strength, deformation and damage characteristics of salt rock were investigated.found that the fatigue life of salt rock decreases and the residual strain increases with the increase of interval time; related studies show that factors such as temperature and humidity have an effect on the mechanical properties of rocks under cyclic loading and unloading [16 17]; Wang Ruihong et al [18] investigated the relationship between residual strength of the rock body and cyclic loading, and found that there is a negative correlation between the two; Yang Yongjie et al [19] found that the coal rock is more prone to fatigue compared to Zhu Zhuohui et al [20] found that the overall strength of the specimen decreased under uniaxial cyclic loading; He Mingming et al [21] established a damping ratio relationship model that can describe the damping behaviour during graded cyclic loading; Feng Chunlin et al [22] found that the upper limit stress and amplitude of the cyclic loading are the main factors affecting the fatigue damage process and fatigue life of white sandstone; Meanwhile, a large number of scholars have studied the relationship between residual strength of mudstone and cyclic loading in mudstone.Meanwhile, a large number of scholars have also carried out experimental investigations on the mechanical properties of mudstone under cyclic loading and unloading [23][24][25][26][27][28][29][30].
Existing studies have many results on the fatigue creep mechanical properties of rocks.There are fewer studies on the fatigue mechanical properties of mudstone.
Considering the existence of discontinuous loading in the actual operation of the gas storage reservoir, and the special layered salt rock structure in China.The weak mudstone interlayer should be studied.In this paper, by designing graded uniaxial continuous fatigue test, graded uniaxial intermittent fatigue test and graded triaxial intermittent fatigue test.It explores the influence of the presence of confining pressure and intermittent time on the mechanical properties of mudstone, which is of great significance to ensure the safe operation of the gas storage reservoir.

Test conditions and program 2.1 Test apparatus and specimen preparation
The mudstone used for the tests was from Changsha City, Hunan Province and had a yellowish-brown appearance.
According to the standard of International Society for Rock Mechanics (ISRM), the specimens were processed into standard cylindrical specimens with a height of 100 mm and a diameter of 50 mm (height to diameter ratio of 2:1), and in order to reduce the influence of the unevenness of the end surfaces on the test results, the top and bottom end surfaces were polished so that the unevenness of the specimens was controlled to be less than ±2 mm.Considering that the difference in water content of mudstone has a great influence on the test results, the specimens were stored in a drying box immediately after the specimens were processed to keep them dry.The specimens are shown in Fig. 1  Fig. 2 The manufactured mudstone sample, MTS815 rock mechanics testing system.

Test program
The mudstone specimens were first subjected to uniaxial compressive strength testing versus triaxial compressive strength testing with a confining pressure of 3 MPa.The test data are shown in Table I.  4: Fig. 2(a) shows a continuous fatigue test with a test load rate of 0.1 kN/s, setting the stress level at the first level of 30% of the mean uniaxial compressive strength.The stepby-step increment is 20%.The lower limit of stress is 10% of the average compressive strength.Each level of cyclic loading and unloading 10 times.Fig. 2(b) for the graded upper limit interval fatigue test(GUIF), the test load rate of 0.1kN / s, set the stress level of the first level for the average uniaxial compressive strength of 30%.The step-by-step increment is 20%.The lower stress limit is 10% of the average compressive strength.Each level of cyclic loading and unloading 10 times, every two cycles in the upper stress limit constant 4 minutes.A total of 2 sets of tests were conducted with a confining pressure of 0 MPa and a confining pressure of 3 MPa.In this paper, the number of cycles experienced by the mudstone before destruction is taken as the fatigue life.Comparing Fig. 4 (a) and (b) it can be easily seen that the intermittent time enhances the fatigue life of mudstone.
The fatigue life of the continuously graded uniaxial fatigue test is 30, and the fatigue life of the graded uniaxial intermittent fatigue test is 40.Comparing Fig. 4(b) and (c), it can be seen that the presence of confining pressure also enhances the fatigue life of the mudstone.The fatigue life of 3 MPa graded triaxial intermittent fatigue test mudstone is 50 under the same test programme as graded uniaxial intermittent fatigue test.The reason for the intermittent time to enhance the fatigue life of mudstone is.During the graded cyclic loading process, during the period of constant upper stress limit.The mudstone is loaded internal particles squeeze each other to fill, the original pore cleavage is closed under this action.The mudstone becomes denser, which improves its ability to resist damage and deformation.The ultimate load it can withstand is also greater, so the fatigue life is increased.
And the reason for the enhanced fatigue life under confining pressure is.Compared with the uniaxial test, in the triaxial test.Under axial loading, the presence of confining pressure restricts the deformation expansion of mudstone in radial direction, and under this extrusion, it causes the closure of the primary fissure pores of mudstone, and the cracks that expand during cycling also partially undergo closure under the action of confining pressure.Therefore, the fatigue life of mudstone is also enhanced by confining pressure.

Elastic modulus
The elastic modulus, also known as Young's modulus, is one of the most important and characteristic mechanical properties of rock materials and characterizes the degree of difficulty of elastic deformation of an object.During the loading process, mudstone will produce elastic and plastic deformation, while only elastic deformation can be recovered during the unloading process.In order to reflect more intuitively the influence of different test factors on mudstone deformation, we use the modulus of elasticity of mudstone during unloading as the modulus of elasticity E in this paper, which reflects the ability of mudstone to recover from elastic deformation.Its calculation formula is as follows: where   is the stress amplitude and   is the strain difference.
In order to avoid the influence of cyclic loading and unloading on the modulus of elasticity under the same grade, the modulus of elasticity of each cyclic unloading stage was counted and averaged as the modulus of elasticity of mudstone under the grade to reduce the error.
As shown in Fig. 5, the variation of the average modulus of elasticity of mudstone specimens with the stress level under different test schemes.

Fig.5 Variation of Elastic Modulus with Stress Level
It can be found by observing Fig. 5. Whether in uniaxial continuous fatigue test, graded uniaxial fatigue test or graded triaxial fatigue test, the average modulus of elasticity of mudstone decreases gradually with the increase of stress level.This is because as the stress level increases, the increase in stress amplitude leads to greater damage to the mudstone by the loading action, and the modulus of elasticity characterizes the ability of the rock to resist deformation damage.The modulus of elasticity is a characterization of the ability of rocks to resist deformation and damage.
The average modulus of elasticity in the triaxial test is significantly higher than that in the uniaxial test.This is because the presence of confining pressure in the triaxial test restricts the expansion of radial deformation of mudstone, which enhances the ability of mudstone to resist deformation damage, and therefore the modulus of elasticity of the triaxial test is larger than that of the uniaxial test under the same amplitude ratio.

Residual strain
The deformation of rock produced during loading consists of a combination of recoverable characteristic strain and unrecoverable residual strain of deformation.
Where the upper stress limit corresponds to the strain that is  , the lower stress limit corresponds to the strain that is r  , e  is the elastic strain.
The initial cycle of each stress level is the first cycle, then the cycle before the interval period in the loading process is recorded as the A cycle, and the cycle after the interval period is recorded as the B cycle, and the residual strains generated in the process of A and B cycles are counted respectively, as shown in Fig. 3. Fig. 6(a) shows the residual strain of uniaxial graded upper limit intermittent fatigue test, and Fig. 6(b) shows the residual strain of 3MPa graded upper limit intermittent fatigue test.Both uniaxial intermittent fatigue test and triaxial intermittent fatigue test.The residual strain before the interval is greater than the residual strain after the interval.This is because during the cycling process.Under the action of the upper limit constant pressure load, the mudstone is compacted by extrusion.Therefore, the residual strain before the interval is larger than the residual strain after the interval.Meanwhile, it can be found that in the triaxial intermittent fatigue test, a negative deformation phenomenon occurs after the interval.This is because a large amount of elastic energy is stored inside the mudstone during loading and constant pressure loading.In the unloading stage, the release of elastic energy led to the recovery of deformation and the generation of negative deformation.To reflect the development law of residual strain under different stress levels more clearly, graded uniaxial intermittent fatigue test is taken as an example.The average residual strain of mudstone under each stress level was counted.As shown in Fig. 7. Fig. 7 GUIF test average residual strain (σc=0MPa,Δt=4min) As can be seen in Fig. 7, the average residual strain at each stress level tends to increase nearly as an exponential function as the stress level increases.This is due to the fact that the stress amplitude increases as the stress level rises, and the loading action increases the destructive capacity of the mudstone, thus generating more irreversible deformation, which is also known as residual strain.So the average residual strain increases with increasing stress level.

Conclusion
During the operation of underground gas storage reservoirs, the surrounding rock experiences discontinuous cyclic loading action.To investigate the effect of intermittent action on the fatigue mechanical properties of mudstone, this paper sets up continuous fatigue test and graded uniaxial intermittent fatigue test as a control.Considering the horizontal stress on the rock under the actual burial depth, this paper sets graded triaxial intermittent fatigue test and graded uniaxial intermittent fatigue test as a control.By analyzing the data obtained from the tests, it is found that the fatigue mechanical properties of mudstone under the intermittent action and confining pressure It has certain reference value for the construction and stable development of gas storage.For example, when setting the frequency of gas injection and extraction, the constant load period of the upper stress limit should be extended appropriately.And the gas confining pressure injected in the cavity should be controlled in a reasonable range to prevent the collapse of the surrounding rock.For this indoor test, there are mainly the following conclusions: 1. the fatigue life of mudstone is enhanced by the intermittent effect during the fatigue process.The presence of confining pressure under the same experimental conditions also benefits the fatigue life of mudstone.2. the average modulus of elasticity of mudstone decreases with increasing stress level during cyclic loading, and both intermittency and confining pressure help to enhance the modulus of elasticity of mudstone.3. in graded intermittent fatigue tests.In both uniaxial and triaxial tests, the residual strains generated by the post-

Fig. 1
Fig.1 Diagram of a day's operating pressure of a pressurized gas storage plant (a).The test was carried out in the State Key Laboratory of Coal Mine Hazard Dynamics and Control of Chongqing University, and the instrument used was the MTS815 Rock Mechanics Test System produced by MTS Corporation of the United States of America, which is mainly used to test the mechanical properties and seepage characteristics of rock, concrete, and coal under complex stress conditions, such as splitting, uniaxial compression, triaxial compression, and cyclic loading and unloading tests.The testing accuracy is high performance and stable, and can be used for high and low speed data acquisition, with force, displacement axial strain, lateral strain and other control modes.The equipment axial maximum loading load up to 2800KN, confining pressure up to 80MPa, pore water pressure up to 80MPa, temperature up to 200 ℃.The test equipment is shown in Fig.1(b).

Fig. 3
Fig.3 Schematic diagram of test scheme