Experimental Study on the Influence of Different Loading Rates on Fatigue Mechanical Properties of Sandstone

Abstract

Underground rock engineering often encounters long-term cyclic loading and unloading. Under the influence of this effect, the mechanical characteristics of rocks will inevitably change, which will affect the stability and safety of underground engineering. Therefore, it is necessary to study the fatigue characteristics of rocks under a certain period of action. With an RDL series electronic creep relaxation testing machine, fatigue loading and unloading tests of sandstone at different loading rates were carried out, followed by uniaxial compression on the samples. The study shows that the stress–strain curves of the uniaxial compression specimens have three stages: a compaction pore fracture stage, an elastic deformation stage, and an unstable fracture developing to failure stage. The stress–strain curves of the samples with a certain number of cycles of loading and unloading give the thinning and dense phenomenon, and the axial upper limit strain and axial cumulative residual strain gradually decrease as the loading rate increases. With the increase, the uniaxial compressive strength of the reloaded samples increases gradually, which is higher than the ordinary uniaxial compressive strength. In the process of cyclic loading and unloading, the internal particles of the sample present fracture and reorganization of the fragile structure and, at the same time, compaction stability.

1. Introduction

Due to changes in the stresses on rock masses, a series of disturbing stresses are generated during the mining and excavation process, and these stresses often show cyclical changes. For an underground rock body under the action of the cycle repeated loading and unloading, the strength of the rock body will be greatly affected and the damage will gradually increase, thus causing fatigue damage of the rock body. Therefore, it is necessary to assess the evolution law of rock fatigue damage under cyclic loading.

For a long time, domestic and foreign scholars have carried out a series of studies on this aspect. The fatigue damage of rock is mostly related to the waveform, frequency, and amplitude of the test. Ge X. R. and colleagues carried out a series of tests on the single axial fatigue experiment of a variety of rocks and found that the fatigue failure of rocks is closely related to the test loading waveform, frequency, and amplitude [1,2,3,4]. Li J. T. et al. [5] conducted research on the fatigue deformation and damage characteristics of red sandstone under uniaxial cycle loading. The results showed that the red sandstone fatigue life decreases with the increasing upper stress limit, and the rate of injury development increases with the upper limit of stress. Xu Y. et al. [6] carried out a cyclic loading and unloading test and tested equal load fatigue on mudstone The results showed that the initial cyclic plastic strain under the same grade load is much larger than other cycles, defining the damage variable from the perspective of energy, and the power function relationship between fatigue life and load level is predicted. Jing L. W. et al. [7] studied the energy evolution and damage characteristics of rock under the action of graded cyclic loading and unloading, and constant load amplitude cyclic loading and unloading were studied. It was found that under the action of two kinds of cyclic loading and unloading and under the action of graded cyclic loading and unloading, the elastic modulus increases first and then decreases gradually with the increase in cyclic grade. Under the cyclic load of constant load amplitude, the elastic modulus increases first and then decreases slowly with the number of cycles. Li L. et al. [8] assessed the mechanical evolution characteristics of saturated rocks under three different loading and unloading modes: equal loading and unloading, multiple loading and unloading, and perturbation loading and unloading. The results showed that the relationship between softening stage and peak strain in each loading and unloading mode is as follows: multiple loading and unloading is greater than equal multiple loading and unloading, which is greater than the micro disturbance loading and unloading. Miao S. J. et al. [9] studied the upper limit load of different cycles of muddy quartz siltstone. Studies have shown that with an increasing upper limit load, the compressive strength increases first and then decreases. Pan B. et al. [10] studied the effects of different stress-graded cyclic loading modes on the damage characteristics and evolutionary characteristics of brittle rocks. They also defined the damage constitutive model of the cyclic loading and unloading process. Zhan K. L. et al. [11] performed an indoor cyclic load test, and the stagnant ring area of the rock was calculated using data processing software. The relationship between the area of hysteresis loop and the test times under the cyclic loading test condition was also analyzed. Yao. K. et al. [12] studied the strength, deformation, and other characteristics of granite under cyclic loading through uniaxial and triaxial loading tests. The results showed that the specimen under uniaxial cyclic loading and unloading showed columnar splitting failure, while the specimen under triaxial cyclic loading and unloading showed obvious shear failure characteristics. Huang F. et al [13] studied the mechanical properties of granite under cyclic plus unloading conditions. It was concluded that the failure modes in the two different loading modes of the uniaxial compression test and cyclic load test are very similar. The deformation modulus increases with the number of cycles, while the cohesion and the internal friction angle decrease. Song Z. Y. et al. [14] studied the mechanical properties of medium-grained sandstone under different loading and unloading rates, discussed the relationship between final strength and axial strain at failure under different loading modes, and predicted the residual fatigue life of medium-grained sandstone. Peng K et al. [15,16] studied the deformation characteristics and failure pattern of sandstone under different cycles and unloading. It was found that the lower stress limit can significantly affect the evolution of irreversible deformation. After multiple levels of loading and unloading, the evolution characteristic of the sandstone deformation parameter is gradual growth. Meng Q [17,18] studied the deformation characteristics and failure modes of sandstone under different cyclic loading and unloading. It was found that the lower limit of stress can significantly affect the evolution of irreversible deformation. After multi-stage loading and unloading, the evolution characteristics of sandstone deformation parameters showed a gradual increase. He M [19] conducted cyclic load tests on rock, and the study found that in the failure stage, the rapid expansion of the crack makes the dissipation energy of the rock increase sharply until failure occurs.

In summary, many scholars have studied the mechanical properties of rock under cyclic loading and unloading. It has been found that rock is mainly affected by the waveform, frequency, and amplitude of the sample under cyclic loading and unloading. However, the actual rock mass is usually damaged under long-term fatigue loads. Therefore, it is necessary to study the mechanical properties of rock after a certain number of cycles of loading and unloading. In this paper, sandstone is taken as the research object. Firstly, a certain number of cyclic loading and unloading fatigue tests are carried out on the samples. On the basis of discussing the influence of different loading rates on the fatigue characteristics of sandstone, the evolution law of reloading sandstone strength characteristics is further analyzed.

2. Experimental Study

2.1. Sample Preparation

The sandstone samples used in this test were all taken from the Zhangji Coal Mine in Huainan, Anhui Province, China. To ensure the reliability of the test, the samples were collected from the same place. After retrieval from the site, it was observed that the surface is grayish white with a few dark brown spots, as shown in Figure 1a. The natural stones were processed into standard cylinders with ϕ50 mm × 100 mm, which conforms to the requirements of the Rock Mechanics Test Code formulated by the Standardization Committee for Laboratory and Field Tests of the International Society of Rock Mechanics. In order to reduce the influence of the end effect, the flatness of the sandstone surface was within 0.02 mm, as shown in Figure 1b. Considering the series of voids and cracks in the natural stones, further acoustic tests were carried out, based on which samples with similar wave velocities were selected and put into fresh bags for storage.

Next, thin rock sections were scanned and identified using a polarizing microscope. The X-ray diffraction spectrum analysis showed that the main components in the samples were quartz, argillaceous mixture, biotite, and a small amount of kaolinite, among which the content of quartz was 68%, that of clay minerals was 16%, that of siliceous rock was 11%, and that of feldspar was 5%, as shown in Figure 2. Furthermore, from the EDS energy spectrum analysis, it can be seen that there were iron compounds inside the rock.

2.2. Test Equipment

Experiments on the influence of different loading rates on the mechanical fatigue properties of sandstone were carried out in Anhui University of Science and Technology. The equipment used was an RDL series electronic creep relaxation testing machine, as shown in Figure 3. The maximum axial force of the equipment is 200 KN and the precision is 1‰.

2.3. Test Scheme

This experiment was conducted to study the influence of different loading rates on the fatigue mechanical properties of sandstone. The test scheme is shown in

Table 1. Test scheme.

Sample Number	h/mm	d/mm	Wave Velocity (m/s)	Protocol
CU-1	100.22	49.83	4.414	Uniaxial compression.
CU-2	99.98	50.10	4.326
CU-3	99.99	50.11	4.361
LC-1	99.76	50.04	3.967	Loading rate 15 KN/min fatigue test. Then, the uniaxial loading test was carried out.
LC-2	100.54	50.09	4.388
LC-3	100.32	50.08	4.192
MC-1	99.76	50.04	3.967	Loading rate 30 KN/min fatigue test. Then, the uniaxial loading test was carried out.
MC-2	100.54	50.09	4.388
MC-3	100.32	50.08	4.192
HC-1	99.76	50.04	3.967	Loading rate 30 KN/min fatigue test. Then, the uniaxial loading test was carried out.
HC-2	100.54	50.09	4.388
HC-3	100.32	50.08	4.192

. The specific steps were as follows:

(1) Initially, three groups of uniaxial compression tests were carried out on the testing equipment to obtain the uniaxial strength of the samples.

(2) After obtaining the uniaxial strength, the fatigue loading test was conducted on the sandstone sample. Load control was taken in the fatigue loading test (loading rates were 15 KN/min, 30 KN/min, and 60 KN/min). The amplitude was controlled (0–50% of the uniaxial peak strength of rock). The test loading waveform was triangular, and the frequency was 0.1 Hz. The sample was loaded 60 times altogether. The loading waveform is shown in Figure 4. The fatigue characteristics of samples with different loading rates were observed.

(3) Uniaxial compression was brought to these samples after 60 times of fatigue loading to obtain the uniaxial strength after fatigue loading and unloading.

3. Experimental Results

3.1. Uniaxial Compression Test Results

In view of the discretization problem caused by large differences in samples, this experiment was repeated three times to avoid the deviation of test results caused by such problems. Thus, the uniaxial strength of the sample was 60.4 MPa, 71.2 MPa, and 51.3 MPa, respectively, and the average uniaxial compressive strength of the sample was 61.3 MPa. To better study the change in the stress–strain curve and failure mode of the rock during uniaxial loading, the stress–strain curve and failure mode of sample CU-1 were selected for analysis.

According to the sample stress–strain curve in Figure 5, under the action of external load, the stress–strain curve of sandstone samples is relatively smooth before they reach the failure strength. The whole process curve of stress and strain develops as an upper concave curve, and the process can be summarized into three stages: a compaction pore fracture stage, an elastic deformation and microfracture stable development stage, and an unstable fracture development until complete failure stage. (1) Compaction pore fracture stage: At this stage, with the external load under the constant action of external force, the microcracks or open structural planes in the sample are closed and compressed, showing an initial nonlinear trend. (2) Elastic deformation stage: At this stage, the internal stress–strain curve is nearly a straight line. The strain increases when the stress does, and the ratio of stress and strain is approximately proportional. (3) Unstable fracture developing to failure stage: After the continuous loading, the elastic deformation of rock is transformed into plastic deformation, and the volumetric strain rate and axial strain rise continuously. In this stage, the change range of rock cracks increases. Obvious cracks appear on the rock surface, and the rock reaches its yield strength. When it comes to the peak strength, the rock is destroyed and develops into a cross-penetrating fracture surface. Subsequently, the rock sample still has a certain bearing capacity, which decreases with the sample deformation going up, and the block in the section is in a state of slip.

During the uniaxial loading test, the sandstone samples showed obvious cracks at the initial stage of stress loading. As the load keeps going up, the stress on the sample tends to be stronger, resulting in the appearance of microcracks and the development of macroscopic cracks. When the load reaches its peak strength, the cracks on the surface change continuously and the slight gaps become wider and longer until the sample is completely destroyed. At the same time, the process is accompanied by a breaking sound. Under uniaxial loading, typical tensile failure occurs, which is shown in Figure 5. The occurrence of tensile failure is influenced by the Poisson effect. The load leads to the increase in axial compressive stress and makes the transverse tensile stress continue to act in the rock.

3.2. Failure Characteristics of Specimens with Different Rates under Fatigue

3.2.1. Stress–Strain Curves of Fatigue Loading at Different Rates

Figure 6 shows the fatigue stress–strain curves of the samples under different loading rates, in which we can see the same change in the stress–strain curves with different loading rates. The loading curves of the samples present a trend of being first loose and then dense. As the loading process keeps going, the stress–strain curves of the samples give a stable trend, and the overlap degree of loading and unloading curves becomes higher. The main reason for this situation is that there are still some small cracks in the samples at the early loading stage. Under the loading and compression action, these microcracks inside the samples gradually close, during which the strain of the samples varies greatly to show a phenomenon of stress–strain curve loosening. With the loading process going, the inside cracks close gradually and the curves become dense. Considering that fatigue loading is a damage accumulation process, the plastic strain generated by the sample continues to increase.

It can be further seen from Figure 6 that with the loading rate rising, the fatigue stress–strain curves of the samples at each stage change more and more, indicating that as the loading rate increases, the elastic modulus of the samples under loading and unloading gradually increases and the resistance to deformation comes to be stronger.

3.2.2. Deformation Characteristics of Samples under Fatigue Loading at Different Rates

The deformation characteristics of rock can well reflect the ability of rock to resist deformation. In order to better understand the deformation of samples during fatigue loading and unloading, samples after different unloading times (1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60) and the corresponding upper strain limit (upper limit of each load stress and corresponding axial strain), axial cumulative residual strain (each unloading limit stress and corresponding axial strain), and axial residual strain increment (the axial strain difference corresponding to the lower stress limit under one loading and unloading) were selected to study.

In Figure 7, the axial upper strain limit of rock samples under the same loading times but different loading rates decreases as the loading rate increases. The reason behind that is that the loading speed is a little fast, so the deformation reaction of the particles inside the samples becomes slow. However, under the condition of slow loading speed, the particles inside will have enough time to deform, which makes the upper strain limit large. Under the same loading rate, the upper strain limit of the sample increases first and then varies slowly. It is mainly due to a gap between particles inside the rock, and the particles appear to close under the action of external load at the initial loading. With the loading, the cracks in this part suffer compression and close, and with this, all the upper strain limit changes tend to be stable. As shown in Figure 8, under the same loading times and different loading rates, the axial cumulative residual strain of sandstone sample goes down with the increasing loading rate. For the same loading rate, the axial cumulative strain of the sample presents first upward and then slow variation. Furthermore, Figure 9 shows that the axial residual strain of the sample decreases first and then changes slowly as the number of cycles increases, which is related to the closure of cracks inside the sample.

The above described information indicates that the slow loading rate leaves the internal cracks of sandstone enough time to crack, and the slow one prolongs the duration of cyclic loading and promotes the damage process of rock. This is because the cracks inside the rock are continuously loading and unloading to close and open in the cyclic load test. The slow loading rate causes the original cracks to expand and recombine when the number of cycles increases, which greatly eases the crack opening and leads to greater damage to the rock samples due to the accelerated development of internal cracks. However, larger loading rates are more likely to cause sudden fracture, and that is what we commonly call rock burst.

3.2.3. Strength Characteristics of Samples under Fatigue Loading at Different Rates

Furthermore, a uniaxial compression test was carried out on the samples with a certain number of cycles of loading and unloading. The compression test results are shown in

Table 2. Uniaxial loading strength of the sample.

Sample Number	Loading Rate (KN/min)	Compressive Strength (MPa)	Average Compressive Strength (MPa)
LC-1	15	68.2	65.6
LC-2	15	69.1
LC-3	15	59.5
MC-1	30	73.1	69.33
MC-2	30	60.69
MC-3	30	74.2
HC-1	60	68.9	72.1
HC-2	60	75.3

. From Table 2, we can see that under the loading rates of 15 KN/min, 30 KN/min, and 60 KN/min, the average compressive strength of the samples was 65.6 MPa, 69.3 MPa, and 72.1 MPa, respectively. Compared with the normal uniaxial state, the growth rates of compressive strength were 7.1%, 13.1%, and 17.6%, respectively. The loading rate has a strengthening effect on sandstone. The main reason is that the cyclic loading and unloading effect compresses and closes the micro-particles and voids inside the rock, which changes the structure inside the rock, making the internal structure closer and the strength of the rock larger. After many cycles of loading and unloading, some microcracks and slight gaps in the rock are created, which reduce the strength of the rock. However, it matters little in terms of changing the increasing strength effect of rock. Therefore, the strength of the sample under fatigue load is higher than that of ordinary rock.

In Table 2, as the loading rate rises, the reloading strength of the sample gradually increases as the particles inside the sample are compressed more closely with the loading rate increasing. Therefore, we can determine that the reloading strength of the sample increases as the loading rate goes up.

4. Microscopic Features

The microscopic morphology, structure, and composition of the cyclic samples were obtained by microscopic observation. Then, the internal damage to sandstone caused by cyclic load was analyzed. From the microscopic perspective, the evolution law of rock under cyclic load is discussed.

It is shown in Figure 10 that after a certain number of cycles of loading and unloading, the connection between internal particles is closer and the gap between is smaller. What is more, there are few microcracks inside the opening of the sample. In the process of cyclic loading and unloading, the original microcracks and natural pores in the rock fracture and reorganize under the action of external stress. The cementation ability of calcite and other clay minerals is limited. Although the structure can remain stable in a natural state, as subjected to external forces, the sand particles in the rock are prone to loosening and displacement, which results in further changes in the instability of the microstructure. Meanwhile, with the increasing number of cyclic load tests, the internal clay and rock debris keep filling the gaps and coarse sands in the sample, which also undergo continuous crushing, filling, compaction, and stability to make the rock mechanical properties in the microstructure constantly change during the cycle. Hence, the connection between the sample particles is closer after a certain number of cycles of loading and unloading.

Further, the change in the internal damage of rocks under cyclic loading and unloading is a complex process. There are cracks in the natural rock, and under cyclic loading and unloading, the internal cracks of the sample gradually expand. However, although these cracks expand under the loading and unloading, the gap between the cracks is gradually compressed. The process is shown in Figure 11. It can be seen from Figure 10 that there are natural cracks in the rock, and the original cracks of the sample expand under the cyclic load, which causes the change in the mechanical properties of the sample. However, due to the repeated compression of the cyclic load, the gaps between the cracks of the sample are gradually densified, which enhances the mechanical properties of the sample. This effect is greater than the loss of mechanical properties caused by the crack growth of the sample.

5. Conclusions

In this paper, the fatigue characteristics of sandstone under different loading rates for a certain number of cycles were tested. The evolution law of the fatigue mechanical properties of sandstone under different loading rates for a certain number of cycles was studied. The mechanism of loading rate effect and fatigue damage on rock mechanical properties is explained. The following conclusions can be drawn:

(1) A uniaxial compression test was conducted for a test sample, and the rock stress–strain curve can be divided into three stages: a compressed pore fissure stage, an elastic deformation stage, and an unstable fissure development to failure stage. The sample showed typical tensile split failure after uniaxial compression damage.

(2) The stress–strain curve of the specimen under a certain number of cycles of loading and unloading showed a sparse dense phenomenon, and the axial upper strain limit and the axial cumulative residual strain of the specimen decreased gradually with the increase in the loading rate. Under the same loading rate, the axial upper strain limit and axial cumulative residual strain of the specimen increased first and then changed slowly. The axial residual strain of the sample decreased first and then changed slowly with the increase in the number of cycles.

(3) After a certain number of cycles, the uniaxial reloading compressive strength of the sample increased compared with the uniaxial compressive strength of ordinary rock. The sample uniaxial reloading strength increased gradually as the loading rate increased.

(4) Through microscopic observation, it could be seen that the internal cracks of the specimen expanded under the action of cyclic loading and unloading, and the gap between single cracks was gradually reduced. The impact of the specimen cracks being compressed on the mechanical properties was greater than the impact of crack expansion.

In this paper, the fatigue damage characteristics of the specimen under a certain number of cycles of loading and unloading were studied, but it does not consider the damage characteristics of the specimen under the cyclic loading and unloading. We will continue to carry out related research in future work, and the research results of this paper can provide some reference value for future related research.