Effect of the Confining Pressure on the Dynamic Compression Properties of Transversely Isotropic Rocks

,e dynamic compression properties of transversely isotropic rocks and their dependence on the confining pressure and bedding directivity are important in deep underground engineering activities. In this study, a slate is characterized using a split Hopkinson pressure bar (SHPB) test. Five groups of samples with preferred bedding directions (dip angles of 0°, 30°, 45°, 60°, and 90°) are subjected to coupled axial impact loading (low, medium, and high) under confining pressure (0, 5, and 10MPa). ,e failure mode, dynamic strength, and Young’s modulus are investigated. ,e test results show that the tensile splitting effect is significant when there is no confining pressure. However, under a confining pressure (5 and 10MPa) condition, the cracks that develop along the loading direction can be significantly constrained and the samples are forced to fail along the bedding plane. With increasing confining pressure, the critical dynamic strength significantly increases, and Young’s modulus increases when θ≥ 45° while it decreases when θ≤ 30°.


Introduction
Transversely isotropic rocks, which are widely distributed on the surface of the earth, are a specific form of anisotropic rock.Differ from the isotropic rock has identical properties in all directions, the properties of transversely isotropic rocks vary as the bedding plane direction changes (i.e., the rock contains one dominant direction of planar anisotropy) [1]. is description generally applies to the intact laminated, stratified, bedded sedimentary class, and certain intact foliated metamorphic rocks (e.g., slates, shales, sandstone, and coal) [2,3].
Over the past several decades, numerous tests, numerical simulations, and analytical calculations on failure modes and mechanical properties have been completed [4][5][6][7].e fracture behaviour under triaxial pressure has been found to differ from that under uniaxial pressure [8].As the confining pressure is increased, the anisotropic rocks become more ductile [9].However, most of the previous research has focused on the static state of stress.Many engineering applications, such as blasting and drilling, expose rocks to dynamic loading, potentially inducing underground engineering accidents such as collapse, roof fall, rock burst, and gush events.erefore, understanding the properties of rocks under dynamic loading is important for engineers to optimize design and construction.
Recently, the dynamic property of anisotropy has received major attention.Dai et al. [10] and Liu et al. [11] studied the dynamic properties of Barre granite with respect to the three principle directions.Qiu et al. used static and dynamic uniaxial compression tests on coal rock to characterize the bedding directivity [12].Li et al. studied the dynamic tensile properties of phyllite with five dip angles (0 °, 30 °, 45 °, 60 °, and 90 °) [13].Koerber et al. described recent advances in the SHPB, namely, by using an image-based approach to investigate polymer-based composite materials [14].
ese studies focused primarily on uniaxial impact compression tests.In general, the impact splitting effect is easily detectable in one-dimensional impact tests [15].However, the test results may not fully characterize the actual properties of the rocks, particularly at deep depths.
In natural conditions, the rock properties are affected by the state of in situ stress in the strata before blasting and boring.Multiple blasting engineering observations and laboratory experiments have indicated that properties such as transmission of the impact wave and the effect of blasting and rock fragmentation differ between triaxial and uniaxial pressure [16].e confining pressure is generally used in dynamic tests to simulate the in situ stress.Christensen et al. [16] was the first to test rock with confining pressure and dynamic loading [17].
en, the triaxial split Hopkinson pressure bar (SHPB) test system for rocks was quickly implemented worldwide [18].However, despite its importance, relevant research on transversely isotropic rocks is still relatively scarce.
In this study, we aim to investigate the effect of confining pressure on the failure mode and dynamic compression properties of transversely isotropic rocks.e bedding directivity is also of interest; therefore, five groups of samples (θ � 0 °, 30 °, 45 °, 60 °, and 90 °) were tested using an SHPB at three load levels (low, medium, and high) and three confining pressures (0 MPa, 5 MPa, and 10 MPa).Testing was conducted with 0 MPa confining pressure for the dynamic uniaxial compression test.en, the results were analysed to determine how the confining pressure affects the physical properties of the rock samples.
is apparatus can achieve a strain rate of 10 1 -10 4 s −1 , which can match typical dynamic loads associated with rock fragmentation.As shown in Figure 1, a dynamic test was conducted using a 50 mm SHPB system at the Central South University (Hunan, China).A coneshaped striker was used to generate a half-sine incident wave and provided a constant strain rate to the point of sample failure [23,24]. is method is suitable for testing rock-like materials.e confining pressure device shown in Figure 2 consists of a steel frame with an associated oil cylinder, a rubber sleeve, and oil inlet/outlet valves.e confining pressure is provided by the oil pressure in the chamber (as pressurized by hand pumping).e confining pressure can reach 200 MPa if necessary.
Based on the one-dimensional stress wave theory [25] and the assumption that stress equilibrium is achieved during dynamic loading (i.e.ε i + ε r � ε t ), the commonly used formulas for calculating strain rate _ ε(t), strain ε(t), and stress σ(t) are as follows: where C is the P-wave velocity of the bars, E is Young's modulus of the bars, and l 0 is the length of the sample, A and A 0 are the cross-sectional areas of the bars and samples, respectively.e indexing i, r, and t refer to incident, reflected, and transmitted, respectively.

Dynamic Testing Scheme.
e critical failure of the samples at different dip angles is measured using a method that uses high-to-low loading steps to test the samples.e assessment standard is based on rock rupture and debris peeling.en, the loading of critical failure is defined as the low loading level.ree different loading level (low, medium, and high) are used to test samples of five groups.During the test, the loading level is dependent on the barometric value in the launcher.e barometric values at various confining pressures are shown in Table 1.

Sample Preparation.
Five groups of different bedding dip angles (0 °, 30 °, 45 °, 60 °, and 90 °) were included in this study.e dynamic test samples were prepared at a slenderness ratio of 0.5 (50 mm diameter and 25 mm length), as shown in Figure 3.To ensure that at least 3 results could be obtained per loading level and confining pressure, 150 rock samples were prepared at five dip angles.

Geological and Mechanical Characteristics of the Slate
e studied slate was from Jiangxi Province, China.A chemical composition analysis of the slate yielded the following composition: 59.05% SiO 2 , 18.56% Al 2 O 3 , 6.87% Fe 2 O 3 , 0.24% CaO, 1.84% MgO, 3.47% K 2 O, and 2.03% Na 2 O. e microscopic structure has been observed by a scanning electron microscope (SEM).As shown in Figure 4, two major layers exist within this slate, which are the stiffer layer and softer layer, respectively.e stiffer layer mainly contains the schistose structure and close arrangement.e crack is undeveloped in this layer.On the contrary, the softer layer is relatively fragmentized and the crack is significantly developed in this layer.e uniaxial compressive strength (σ bc ) and Young's modulus (E) are listed in Table 2.

Test Results and Discussion
4.1.Dynamic Equilibrium and Strain Rate. Figure 5 shows a typical result: here, specimen 60-1 is subjected to 5 MPa confining pressure.To apply the cone-shaped striker as intended, the constant strain rate loading is applied until sample failure.Figure 6 shows that the sum of incident stress and the reflected stress waves are almost equal to the transmitted strain wave, which indicates that the force balance on both ends of the sample is maintained during all of the dynamic tests, including those on samples subjected to confining pressure.

Failure Modes.
Firstly, the failure mode of the slate samples at the low loading level is analysed.Figure 7 shows failure patterns of the samples with different bedding angles at the low loading level and three different confining 2 Advances in Civil Engineering pressures.Four typical failure modes with di erent dip angles under three di erent con ning pressure can be summarized as follows: (I) tensile splitting across the bedding, (II) shear sliding across the bedding, (III) slide failure along the bedding, and (IV) tensile splitting along the bedding.Table 3 lists the critical failure modes of the slate samples under di erent con ning pressures.e failure modes of the slate at di erent con ning pressures are similar at θ 0 °, 45 °, 60 °, and 90 °.However, at θ 30 °, the failure mode changes from II to III with the increases of the con ning pressure.
e di erence may result from the con ning pressure constraining the development of fractures along the loading direction.In addition, due to the small angle intersection of bedding plane and con ning pressure direction, the con ning pressure may open the microfractures inherent the bedding planes.us, cracks may be prior to develop along the bedding planes.
Figure 8 presents the failure mode of θ 45 °at high loading level under con ning pressure 0 MPa and 10 MPa.When the con ning pressure is 0 MPa, the failure pattern of the θ 45 °sample transitions from a single failure mode (III) to a mixed mode (III + I) with the loading level changes from low to high [25].However, when the conning pressure is 10 MPa, although many ne cracks develop along the loading direction, the mainly failure mode is still sliding along the bedding plane.It may because the con ning pressure can e ectively weaken the impact splitting e ect and constrain the cracks develop along the loading direction.9 shows the typical stress-strain curve of the five groups of samples (0 °, 30 °, 45 °, 60 °, and 90 °) subjected to three different confining pressures (0 MPa, 5 MPa, and 10 MPa).For samples in the entire groups, the plastic stage significantly increases relative to the results of the one-dimensional impact test.e stress-strain curves of the one-dimensional impact tests indicate brittle failure.By contrast, under the confining pressure condition, particularly at a relatively high level (10 MPa), the stressstrain curves present typical characteristics of elastoplastic behaviour.For example, when the value of θ is 30 °, a plateau appears at the peak of the curves, indicating the samples transition from a brittle mode to a ductile mode as the confining pressure increases.At θ 90 °, the plastic stage is not easily detected when the con ning pressure is 0 MPa. is result indicates that the cracks develop rapidly throughout the samples during dynamic loading.
is phenomenon may result from the following two factors: (1) the impact splitting e ect in onedimensional dynamic tests and (2) the weak planes being parallel to the loading direction.erefore, the failure patterns at θ 90 °are split along the bedding plane.However, when the con ning pressure increases, the plastic stage emerges again.It is clear that the con ning pressure can constrain the development of cracks along the loading direction.

In uence of the Con ning Pressure on the Dynamic
Strength and Young's Modulus. Figure 10 shows the relationship between the dynamic strength (σ m ), Young's modulus (E), and strain rate at di erent con ning pressures.
e solid and dashed lines indicate σ m and E, respectively.
As shown in Figure 10, the rst points of the stress lines indicate the critical dynamic strength, and it is the stress least likely to cause a dynamic failure of the rock sample.e critical dynamic strength increases as the con ning pressure increases.It may be because that the con ning pressure is perpendicular to the loading direction and makes the samples hard to split, particularly for θ 0 °and θ 90 °.For 30 °≤ θ ≤ 60 °, the con ning pressure can also increase the normal stress on the bedding plane.us, the friction on the bedding planes becomes larger and makes it need a higher stress to make the samples sliding failure along the bedding plane.
e strain rate e ect is signi cant at all dip angles when the con ning pressure is 5 MPa and 10 MPa.However, it di ers when θ 60 °and con ning pressure is 0 MPa [25].It may because the con ning pressure can reduce the in uence of impact splitting e ect and make the failure mode of the specimen relatively simple under the medium or high loading level.
Although the rock samples were screened by a P-wave test to minimize the e ect of the di erence in the dynamic testing results, there is no clear tendency of Young's modulus can be detected when comparing di erent loading levels at one con ning pressure.Lu et al. indicated that E, as one of the mechanical properties of the materials, is not sensitive to the strain rate [27].
In addition, the general trend of E is to increase with increasing con ning pressure when θ ≥ 45 °.It may because the con ning pressure force the microfracture in bedding planes closes at these dip angles.For θ 0 °and θ 30 °the  Advances in Civil Engineering direction of bedding planes and con ning pressure is quite similar.e con ning pressure may force the microfracture in bedding planes open.us, the general trend of E is to decrease with increasing con ning pressure at these two angles.

Conclusions
e compression dynamic characteristics of the transversely isotropic rocks subjected to the con ning pressure have been investigated using an improved SHPB test.e con ning pressure can signi cantly constrain crack development and breakthrough.us, the plastic stage of the stress-strain curves is extended when the samples are subjected to con ning pressure, indicating that the samples change from brittle to ductile.By constraining the cracks developed along the loading plane, con ning pressure forces the samples to fail along the bedding plane.
Furthermore, con ning pressure can improve the integrity and dynamic strength of the rock samples by inducing normal stress on the bedding plane.At a giving dip  Advances in Civil Engineering angle and confining pressure, Young's modulus of the slate is not sensitive to the strain rate.However, it increases with increasing confining pressure when the dip angle θ ≥ 45 °while it decreases when the dip angle 30 °≤ θ.

Figure 4 :
Figure 4: Microscopic structure of the slate.

Figure 7 :Figure 8 :
Figure 7: Recovered samples of the slate subjected to a low loading level.

Figure 9 :
Figure9: Stress-strain curves of samples subjected to various con ning pressures and dip angles.

8
Advances in Civil EngineeringFour main failure patterns are observed from the dynamic tests.

Figure 10 :
Figure 10: Strength and Young's modulus versus con ning pressure.

Table 1 :
Barometric values at various con ning pressures and dip angles.

Table 2 :
Mechanical parameters of the slate.

Table 3 :
Critical failure modes of the slate samples under di erent con ning pressure.