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Studying the relationship between energy consumption and crushed size of shale under different loading conditions is the key to efficient shale cracking. The split Hopkinson pressure bar system was used to study the dynamic mechanical properties of shale under parallel- and vertical-bedding loading, and energy dissipation in the impact tests was calculated. Relationships between the average crushed size of shale fracture products and energy dissipation and between the fractal dimension and dissipated energy were studied using fractal theory. The experimental results showed that the dynamic compressive strength of shale under parallel- and vertical-bedding conditions had an obvious positive correlation with the strain rate. Dissipative energy of the shale samples under loading in both directions increased with the increase of strain rate. The increase of the strain rate enhanced crushing of the sample. The vertical-bedding shale samples had stronger ability to absorb energy and more internal crack propagation. Dissipative energies of the shale samples in the parallel- and vertical-bedding impact tests were positively related to the fractal dimension. The fractal dimension increased with the increase of dissipative energy during sample failure; with further increase in the dissipative energy, its effect on the change of fractal dimension gradually weakened.

The core purpose of shale-gas mining technology is to carry out reservoir reconstruction of shale-gas reservoirs and to break the rock formation using techniques such as hydraulic fracturing. With the development of new fracturing technologies, such as through-liquid gunpowder high-energy gas fracturing and others, dynamic shale fracturing is expected to become an effective technology to increase production. It is therefore necessary to study the dynamic mechanical response of shale during dynamic fracturing [

The split Hopkinson pressure bar (SHPB) is an effective method for studying mechanical properties of rock under impact loading. Yue et al. [

Macroscopic fracture of rock is the final result of the continuous development, expansion, aggregation, and penetration of its internal defects. Progress from mesoscopic damage to macroscopic fracture is an energy-dissipation process and has fractal properties. From the perspective of energy, the deformation and failure of rock have been analyzed and the relationship between rock failure and energy change is established. Sujatha and Chandra Kishen [

Owing to the irregularity of fracture surfaces of rock, it is difficult to approximate its simulation using a flat surface [

Under impact loading conditions, shale exhibits significant anisotropy. Studying the relationship between its energy consumption and crushed size under different loading conditions is the key to efficient shale cracking. In this work, impact compression tests on parallel- and vertical-bedding shale samples were carried out using an SHPB device to study the energy dissipation under impact loads at 0° and 90° to the bedding directions. The relationship between the loading rate and energy dissipation of the shale under dynamic impact was established. Fractal theory was used to calculate the average crushed size and fractal dimension. Fractal characteristics of the fractured block were analyzed. Relationships between the average crushed size and energy dissipation of the fracture product and between the fractal dimension and dissipation energy were obtained.

The samples used in this work were taken from outcrop shale of the Longmaxi Formation in the Changning area of Sichuan Province, China. To avoid large dispersion of the test results due to sampling differences, the samples were taken from the same batch of rock. A 75 mm cylindrical sample was drilled in the parallel-bedding and vertical-bedding directions using a core drill, as shown in Figure

Schematic diagram of coring of the shale sample.

Using a 75 mm diameter SHPB device for dynamic rock testing, different strain rates were achieved by changing the magnitude of the impact gas pressure. The impact gas pressure was selected from five settings: 0.62, 0.64, 0.66, 0.68, and 0.70 MPa. Each experiment was carried out in triplicate.

The Hopkinson bar test system was used to dynamically impact the rock. From the start of loading to failure of the sample, the energies carried by the incident, reflected, and transmitted waves were

The two end surfaces of the sample were coated with petroleum jelly as a lubricant, so energy dissipation caused by friction between the sample and the contact end surfaces of the incident and transmission bars during the loading process did not need to be considered in the energy analysis.

Energy dissipated in the test sample was calculated using the following formula [

Typical stress-strain curves obtained in these tests are shown in Figures

Typical stress-strain curves of parallel-bedding shale samples at different strain rates.

Typical stress-strain curves of vertical-bedding shale samples at different strain rates.

Comparison of Figures

As the rock is loaded under different schemes, the type of rock damage will change. When subjected to dynamic loads, a rock will converge a large amount of energy in a very short time, which will cause cracks within the rock to crack in different directions under high-speed impact. The failure mechanism of rock under high-speed impact is close to the failure mode in actual engineering. Figure

Typical shale rupture morphology: (a) parallel bedding; (b) vertical bedding.

The compressive strength and strain rate of the test sample were obtained by data processing. The curves after fitting the data are shown in Figure

Dynamic compressive strength as a function of strain rate for parallel- (P-) bedding and vertical- (C-) bedding samples.

According to the energy calculation formula obtained from the Hopkinson bar experimental principle and the stress-wave data obtained from the tests, the incident, reflected, and transmission energies and the energy consumed by the sample rupture during the test were calculated and the data were processed. Statistical results for different energies were obtained and the data were fitted, as shown in Figures

Relationship between dissipative and incident energies when parallel (P) and vertical (C) beddings were loaded.

Relationship between dissipative energy and strain rate for parallel- (P-) bedding and vertical- (C-) bedding samples.

Figure

Figure

Combining the data in Figures

The crushed shale products of the dynamic impact tests were collected and combined in size fractions according to standard laboratory sieve sizes of 2.36, 4.75, 9.5, 16, 19, 26.5, 31.5, 37.5, and 53 mm. A high-sensitivity electronic balance was used to weigh the mass accumulated on each sieve after screening, and the data were recorded for block size analysis.

To more intuitively and accurately represent the particle size distribution of the shale sample after fracture, we introduced the physical quantity of the average crushed size, calculated as follows [

Vibration sieve machine.

Examples of the shale sample after screening.

From the perspective of fractal analysis, the fracture shape of the block after rock rupture is similar to the shape of the enlarged fracture; that is, various geometric shapes after rock rupture have self-similarity. The fractal dimension of the broken block of a shale sample can be obtained from the following formula [

The posttest data were collated, and the average crushed size and strain rate under parallel and vertical beddings of shale were, respectively, fitted to obtain the relationship curves shown in Figure

Relationship between the average crushed size and the strain rate of shale under dynamic compression loading of parallel (P) and vertical (C) beddings.

Figure

Relationship between the average crushed size and the dissipative energy of parallel-bedding shale under dynamic compression.

Relationship between the average crushed size and the dissipative energy of vertical-bedding shale under dynamic compression.

The average crushed size after dynamic impact compression was reduced with an increase of the dissipation energy, but as the dissipation energy increased gradually, the slope of the fitted curve began to decrease and the effect on crushed size was reduced. The relationship between the macroscopic fracture of the shale sample and the energy absorbed (dissipative energy) is relatively tight. As the incident energy increased, the dissipated energy absorbed by the sample increased and there was an increase in the number of cracks generated. The larger the number of block products after crushing, the smaller their size after the sample was broken.

The test data were further sorted, and the dissipative energy for the parallel- and vertical-bedding samples was matched with the fractal dimension of the broken block. The curves of the fitted relationships are shown in Figure

Relationships between the fractal dimension of parallel- and vertical-bedding samples and rupture dissipation energy.

Analysis of Figure

The dynamic mechanical properties of shale were experimentally studied. Parallel-stratification and vertical-bedding shale samples were subjected to dynamic impact compression loading tests using an SHPB test system. The dynamic compressive strength, stress-strain relationship, and failure mode of the two shale types under impact loading were analyzed, and the energy consumption and fractal characteristics were determined. The following conclusions were drawn:

Dynamic compressive strength of shale under parallel- and vertical-bedding conditions had an obvious correlation with the strain rate and increased with the increase of the strain rate in an approximately linear manner. When the strain rates were similar, the peak stress of the parallel-bedding shale sample was larger than that of the vertical-bedding sample; the peak strain of the parallel-bedding-loaded shale sample was smaller than that of the vertical-bedding sample.

Analysis of the energy consumption of parallel- and vertical-bedding shale under a dynamic impact load showed that, with the increase of the strain rate, the dissipative energy absorbed by the sample increased, indicating that the strain rate increased. This effect enhanced crushing of the shale samples. The energy absorbed by the vertical-bedding shale sample was greater than that absorbed by the parallel-bedding sample, reflecting their difference in energy absorption capacity. The stronger the ability of the shale to absorb energy, the greater the number of internal cracks propagated.

By analyzing the particle size distribution of the shale sample after failure and introducing fractal theory, it was shown that the average crushed size obtained from dynamic impact compression damage increased with the dissipation energy for both the parallel-bedding and vertical-bedding shale samples. The variation in the average crushed size following dynamic compression with the increase of dissipative energy was more obvious for the vertical-bedding shale, and the crushed size was smaller. Dissipative energy had a positive correlation with the fractal dimension of the rock mass. The fractal dimension increased as the dissipative energy increased during failure of the sample. With the increase of dissipative energy, the influence of the variation of dissipative energy on the change of the fractal dimension gradually weakened. Compared with parallel-bedding shale, the fractal dimension and crushed size of vertical-bedding shale were more affected by the variation of dissipation energy.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This paper was supported by the opening project of State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology (no. KFJJ19-10M).