Fracture toughness analysis of HCCD specimens of Longmaxi shale subjected to mixed mode I-II loading

Highlights

• The fracture toughness anisotropy of Longmaxi shale is studied.

• Fracture toughness of Longmaxi shale is calculated by using different methods.

• Crack initiation angles are correlated with bedding inclination angles.

• The crack initiation condition is discussed based on different fracture criteria.

Abstract

Longmaxi shale exhibits strong anisotropy due to its bedding planes induced by diagenesis. The anisotropic properties of shale have a significant effect on the stability control of geotechnical engineering. To investigate the influence of anisotropy of shale on its mixed mode fracture toughness, we performed Brazilian disc splitting tests on hollow center cracked disc shale specimens with different bedding and crack inclination angles (α and β, respectively). In this study, the fracture toughness of Longmaxi shale was calculated by the finite element method combined with either the J-integral or crack tip-opening displacement method. The results show that the dimensionless stress intensity factors and β values for pure mode-I and mode-II fractures both show anisotropic behavior by varying α. For all combinations of mode-I and mode-II loading, the fracture toughness also exhibits anisotropy by varying α; the mode-I fracture toughness decreases with increasing α when β > 30°, and the anisotropy is negligible for β = 0°. The anisotropy for mode-II fracture toughness is weak when β is small or large, whereas the anisotropy is significant when β = 45° and 60°. The effect of α on mode-I fracture toughness is greater than that on mode-II fracture toughness when β is small or large. Further, a comparison of four mixed-mode fracture criteria with the experimental results shows that the maximum tangential stress criterion for a transversely isotropic body can predict the mixed-mode fracture behavior of Longmaxi shale well. At the same time, it is suggested that the role of the T-stress should be considered to obtain more accurate prediction results.

Introduction

Under the influence of a diagenetic environment and diagenesis, rocks usually exhibit anisotropy. Sedimentary and metamorphic rocks always contain numerous structurally weak planes, such as laminations, foliations, schistosities, and joints. These fabric structures are often the source of transverse isotropy of rocks and strongly influence the stability of geotechnical engineering projects, such as underground excavation [1], [2], [3], [4], storage of radioactive substances [5], [6], [7], slope and borehole stabilization [8], [9], and oil and gas exploration [10], [11], [12]. Longmaxi shale is a typical sedimentary rock that is well known for its distinct transverse isotropy of mechanical properties. Several previous studies have explored the transverse isotropic behavior of shale, including its deformation and strength characteristics under different loading conditions [13], [14], P- and S-wave velocity [15], [16], and acoustic-emission characteristics [17], [18], [19]. In addition, some studies have revealed that the anisotropy of shale properties has an effect on the cracking evolution and failure characteristics [20], [21]. Nasseri and Mohanty showed that anisotropy plays a decisive role in subcritical crack growth and dynamic fracturing processes in rock [22]. In geotechnical engineering projects, shale rock masses usually contain numerous natural and artificial cracks due to the influence of geological processes and artificial disturbances. Therefore, quantitative characterization of the influence of anisotropy on fracture properties is of great significance for the stability control of geotechnical engineering.

Rock fracture mechanics provides an effective analytical method for the initiation and propagation of cracks subjected to loads in rock engineering problems. Fracture toughness is the most fundamental parameter in fracture mechanics as it reflects the ability of a material to resist fracture propagation [23], [24], [25]. In engineering applications of rock fracture mechanics, mode-I fracture toughness K_IC, which is the critical value of the mode-I stress intensity factor, is the most frequently used parameter. This parameter can be obtained using different testing specimens and loading configurations. Several testing methods have been developed to measure the mode-I fracture toughness of rocks, including the chevron bend (CB) method [26], cracked chevron-notched Brazilian disc (CCNBD) method [27], [28], straight-crack semi-circular bend (SCB) method [29], [30], cracked chevron-notched semi-circular bend (CCNSCB) method [31], [32], cracked straight-through Brazilian disc (CSTBD) method [33], [34], straight-notched disc bend (SNDB) method [35], [36], and hollow center cracked disc (HCCD) method [25], [37]. Because most rocks are anisotropic due to the influence of diagenetic environments and diagenesis, it is very important to analyze the influence of anisotropy on the mechanical properties of the mode-I fracture toughness of rock in rock engineering problems.

Several researchers have studied the anisotropy of fracture toughness for rocks. Nasseri et al. [22], [38] used the CCNBD method to measure the fracture toughness of four granitic rocks. They found that the relationship between fracture toughness and microstructural properties has a strong correlation. The anisotropy due to microcrack distribution and orientation plays a decisive role in determining the fracture toughness in HCCD specimens. Chen et al. [25] and Ke et al. [39] studied the mixed mode (I-II) fracture toughness of anisotropic Hualien marble using HCCD and CSTBD tests by the boundary element method. They concluded that the fracture toughness of anisotropic rocks usually depends on the rock properties, crack inclination angle β, and orientation of the axes of elastic symmetry. Lee et al. [40] investigated the influence of bedding orientation on the mode-I fracture toughness of Marcellus shale using the SCB test. Their results showed that the bedding parallel to the base of the specimen produced the highest mode-I fracture toughness, and the 30° inclined base had the lowest. Chandler et al. [41] measured the fracture toughness of Mancos shale along three principal fracture orientations – divider, short transverse, and arrester – using a modified short-rod methodology. They reported that the mode-I fracture toughness of Mancos shale has strong anisotropy; the crack plane normal to the bedding produced the highest mode-I fracture toughness and was parallel to the bedding with the lowest. The ratio between the maximum and minimum values was found to be approximately 3.5. Shi et al. [42] studied the mode-I dynamic fracture toughness of anisotropic black shale using NSCB specimens. Their results showed that the loading rate has a significant effect on the fracture toughness, and the fracture toughness increases with the loading rate for all loading angles [43]. For the static case, the fracture toughness increases with increasing loading angle, and the maximum fracture toughness is 1.75 times the minimum.

However, cracked rock masses are often subjected to complex mixed mode I-II conditions. Consequently, it is essential to investigate rock fracture in various combinations of modes I and II. CCNBD specimens are often used to explore the fracture properties under mixed loading conditions [43]. HCCD specimens not only benefit from the merits of CCNBD ones but also have a simpler preparation process, so they have been used to investigate the rock fracture in various combinations of mode-I and mode-II loading. Many researchers have studied the fracture toughness of various rocks under mixed loading using different specimens, such as sandstone [44], granitic rocks [45], marble [46], and limestone [47]. The main research objectives of most of these studies have been based on isotropic media. Only limited studies on the fracture toughness of anisotropic rock materials have been conducted. In addition, previous studies have investigated the fracture toughness of anisotropic rock materials using a fracture model based on an isotropic medium.

According to fracture mechanics theory, the major objective in determining fracture toughness is to determine the stress intensity factors (SIFs) near the crack tip for a given body under certain loading conditions. At present, the calculation methods for SIFs mainly include analytical , numerical, experimental, and estimative methods [25]. Among these, the finite element method is the most commonly used. Especially for anisotropic media, determining SIFs is very complicated, and it is usually impossible to obtain them analytically. However, the finite element method can provide an effective solution for the above problems by applying the M-integral, J-integral, or displacement extrapolation method [48], [49], [50], [51].

In this study, the HCCD method was chosen to measure the fracture toughness of Longmaxi shale under mixed mode loading for its simplicity of specimen preparation, equipment, and testing process. The fracture toughness of HCCD specimens with several bedding inclination angles was calculated according to the J-integral and crack tip-opening displacement (CTOD) methods. Then, the anisotropy of the fracture toughness in the mixed model was investigated with respect to the bedding orientation. Moreover, the experimental results for SIFs and crack initiation angles for Longmaxi shale were theoretically assessed using different fracture criteria. Section 2 presents the calculation methods for HCCD specimens for transversely isotropic media obtained by FEM; the ABAQUS code and setups of the numerical models are also introduced. In Section 3, the fracture experiment for Longmaxi shale is described in detail, followed by a comprehensive description and analysis of the experimental results in Section 4. Theoretical assessment of experimental results is presented in Section 5, and the discrepancy is analyzed and discussed. Finally, the main conclusions are summarized in Section 6.