Effect of rock loading rate on fissure expansion and propagation

Uniaxial DIC test chart

The failure of deformation of rock materials occurs due to the development of localization of deformation in the rock system under most conditions. At present, the analysis of rock deformation and failure process through the development of deformation localization has become one of the important methods for researching rock mechanics, among which the method of digital image correlation has received wide attention from scholars at home and abroad. DIC, the digital image correlation method, is a non-destructive full-field optical measurement method, which was first proposed in the 1980s.26,27,28.

As shown in Figure 4, a uniaxial DIC test is performed to explore the influence of the loading rate of the rock, and the test system consists of a test loading system and a data image acquisition system. The loading system is realized by hydraulic servo testing machine, and displacement control is used for axial loading. Selecting the red sandstone for the sample and processing it into a cuboid as \(50\;{\text{mm}}\times 50\;{\text{mm}}\times 100\;{\text{mm}}\). The six sides of the sample are sanded to ensure that the end of the sample is smooth. Based on related research1,29,30,31loading rates of 0.02 mm/min, 0.1 mm/min and 0.5 mm/min are specified, five sets are performed at each loading rate, and the test scheme is shown in Table 1.

Figure 4

Uniaxial DIC image of the test system.

Table 1 Experiments and uniaxial DIC parameters.

The specific operating steps of the test are as follows:

  1. (1)

    First of all, the matte white paint is sprayed on the surface of the sandstone sample as the base color, and then the matte black paint is sprayed on the white background to form artificial spots, which are randomly distributed, and the size of one spot is greater than three pixels. The ratio of the spot area to the area of ​​the base color on the sample surface is close to 1:1.

  2. (2)

    Adjust the aperture and focal length of the camera to make the viewfinder roughly parallel to the surface of the sandstone sample.

  3. (3)

    The good quality spray spot samples are put on the testing machine, and clamped under a certain pressure.

  4. (4)

    Set the test machine load rate and camera acquisition frequency.

  5. (5)

    Collect DIC system image information, while the test device is compressed.

  6. (6)

    When subjected to a certain stress, obvious macroscopic damage occurs and the download and image collection stops at the same time. Select the appropriate patch on the sandstone sample for image processing and analysis, and obtain the deformation field of the sandstone sample surface.

Analysis of Uniaxial Rock Test Results – DIC

Five sets of tests are conducted at each load rate level. Filter a set of data with better test results under each set of load rates. The stress-strain curve of the sandstone sample during loading is shown in Figure 5, and the test results are shown in Table 2.

Figure 5
Figure 5

Load curves at different load rates.

Table 2 Test results at different strain rates under uniaxial stress.

According to the stress-strain curve of sandstone and test results, the peak strength and modulus of elasticity of sandstone increases with the increase in the loading rate, and the time required for sandstone sample to reach the peak stress gradually decreases. Figures 6, 7 and 8 show the relationship between loading rate and peak stress, time to reach peak stress, elastic modulus and strain rate, respectively. As we can see, the peak strain increases with increasing loading rate, which is positively correlated, while the time required to reach the peak strain shows the opposite variance. The stress rate increases with the increase in the logarithm value of the loading rate. By fitting, it is found that the two are non-linear and positively correlated. When the loading rate is small, the stress rate increases relatively slowly.

Figure 6
Figure 6

Relationship between peak stress and loading rate.

Figure 7
Figure 7

The relationship between modulus of elasticity and loading rate.

Figure 8
Figure 8

Relationship between stress rate and loading rate.

Taking 0.1 mm/min as an example to analyze the stress development properties of sandstone during loading. As shown in Figure 9, images of spots on the surface of rock samples at the start of loading are selected as reference images. Based on the digital spot correlation method to analyze the speckle images in the loading process, and then obtain a sandstone stress field evolution cloud map.

In the first stage of loading, the internal micro-cracks in the sandstone are closed under pressure from the open state in the initial state, which leads to significant local stress and random distribution of the stress field. According to the analysis in the previous chapter, the deformation of the rocks before reaching the compressive strength has elastic deformation, and the stress localization zone begins to appear near the peak strength. The stress localization phenomenon is the phenomenon of stress concentration in a small area of ​​compacted sandstone before the macroscopic failure. The area is narrow and constantly evolving, and rock collapse can be expected accordingly. When the sandstone enters the stress softening stage, the strain localization region gradually becomes narrower, and then the stress localization shear region is formed in the strain localization region and extends through the entire sandstone sample, followed by the sandstone macroscopic failure region. After peak strength is reached, as the pressure decreases, fine cracks in the sandstone continue to expand. In the process of sandstone deformation and failure, the elastic energy is released, and the released elastic energy keeps the further expansion of the cracks. When the sandstone enters the residual strength phase, the cracks slide along the plane of the macroscopic fracture. At this time, stress concentration occurs in the stress-localized shear band, while the stress field is evenly distributed outside the localized shear band and the deformation is relatively uniform. At this time, the sandstone is still in the elastic deformation stage. The location of the localized shear zone, i.e. the final macroscopic fracture surface. The above phenomena can be verified by the stress field evolution cloud map.

When the sandstone sample obtains the normal state and undergoes no loading, the energy in the rock is relatively dispersed, and the energy field is distributed almost evenly. Meanwhile, taking into account the heterogeneity and internal friction characteristics of the rocks, the internal energy of the rocks under pressure will preferentially accumulate in the region with poor mechanical properties, resulting in the uneven distribution of the energy field. Prior to reaching peak strength, energy is continually introduced into the rock system through axial loading. Most of the energy is accumulated in the form of elastic energy, and only a small part of the energy is used in the form of dispersive energy to close the original micro-cracks in the rock and form new cracks in the crop stage. As shown in Figure 9, by integrating with the schematic diagram of the strain evolution of sandstone at different times under 0.1 mm/min loading, it can be found that the rock localization area begins to incubate from the left side of the upper part of the sample, and the deformation localization area is approximately parallel to the sample axis. Before reaching peak strength, there is no obvious penetrating crack on the surface of the rock. When the peak force is exceeded, as the load continues to increase, the energy is transferred to the area below and accumulated, causing micro-cracks on the sample surface that gradually expand. When the energy reaches the rock’s energy storage limit, large cracks form and eventually enter through the entire sample, causing the rock to fail in general. The total failure of the sample is accompanied by the release of energy. The accumulation and release of energy is the essence of the destruction of rocks and other materials. According to the analysis, more energy is accumulated in the pre-peak phase, while in the post-peak phase, more energy is released, which leads to fusion of cracks in the rocks and leads to instability of rock materials.

Figure 9
Figure 9

Nephograms for the evolution of the field of deformation (0.1 mm/min).

Due to space limitation, the paper only lists the comparison between the peak stress cloud of the rock and the true failure condition, as shown in Figure 10. The true failure condition of the rock is shown on the left, the surface of the rock sample fault is marked with a red line, and the stress field evolution cloud is shown on the right . The ultimate failure of sandstone under three different loading rates consists of both macroscopic and multiple microfractures. In addition, under the influence of different loading rates, the tensile mechanical properties of the main fracture tip are mainly tensile.

Figure 10
Figure 10

Peak deformation field and final failure shape for samples under three loading rates.

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