Failure of transversely isotropic rock under Brazilian test conditions
Introduction
In recent years, there has been an increased interest in the behavior of transversely isotropic rock material [1], [2], [3], [4], [5], [6]. The main reason for this is that numerous current applications deal with this type of rocks; e.g., exploitation of shale gas [7], [8], [9], drilling through shale formations in the overburden of oil and gas reservoirs [10], [11], radioactive waste disposal in clay formations [12], [13], development of excavation damage that occurs during underground construction [14], [15], and rock-cutting performance in mechanized tunneling [16], [17]. Another reason for the increased interest in transversely isotropic rock materials is that new techniques and methods have become available for conducting laboratory experiments and numerical simulations, and the behavior of these materials can be characterized more effectively than before. In recent years, several authors have successfully simulated individual fracture growth using discrete elements or other numerical codes [18], [19], [20], [21], [22], [23].
The failure of transversely isotropic rock is more complex than is often assumed. First, this statement is valid for the variation of the strength as a function of the inclination angle of the plane normal to the plane of isotropy [3], [4], [5]. Second, the induced fracture patterns are complex [6], [23], [24]. Often, when studying failure, one considers the simplest form of transverse isotropy, i.e., planar anisotropy, in which the rock mass has a set of parallel planes of weakness [25]. In the cases of uniaxial and triaxial tests, failure occurs in the configuration along a weak plane for the interval of the weak planes angle between the friction angle and a value close to the vertical orientation of the weak planes. For this interval, the variation of the axial strength with inclination angle generally follows an upward, concave curve. For other angles, the rock fails in a different direction from that of the weak planes, and the axial strength is considered constant for these angles. A similar simple model can be considered for a Brazilian test, in which the axis of the disks is parallel to the strike of the weak planes. The specimen splits below a certain inclination angle, and thus, the fracture is independent of the weak planes. However, for moderately-inclined angles, shear failure occurs along a weak plane and for very steep angles (close to 90°), the specimen splits again, but this time it splits along a weak plane. Third, the final fracture patterns are complex, both for isotropic and anisotropic rocks. This is often illustrated by recording acoustic emission during the loading and unloading of the specimen [26], [27], [28], [29]. Development of failure in quasi-brittle materials is linked with the occurrence of micro-cracks, which release energy in the form of elastic waves (i.e., acoustic emission). At the start of the loading, the amount of hits is low and diffuse over a large part of the entire specimen. When the material׳s strength is approached, the acoustic emission activity increases and is mainly situated in critically stressed regions. As damage increases and peak stress is reached, a coalescence or localization of damage occurs. During unloading further damage may occur.
The objective of this paper is to report a systematic analysis on the anisotropic behaviors in strength and fracture patterns observed during Brazilian test of various rock types. In addition to compressive or shear strength, the tensile strength is a key parameter for determining, for example, the load-bearing capacity of rocks, their deformation, damage, and fracturing, and the crushing process of rocks. It is also used to analyze the stability and serviceability of rock structures. Tensile strength plays an important role because rocks are much weaker in tension than in compression. To address the complex behavior of transversely isotropic rock material, laboratory experiments were conducted with nine different rocks. The results were compared in a relatively extensive and uniform examination, even though the experiments were conducted by three different organizations. In addition to the variation of the strength, the emphasis was on the fracture patterns that were visible after loading. In this paper, the examples are limited to Brazilian tests, in which the axis of the disk was parallel to the strike of the weak planes; in other words, the specimens were tested at various angles of the plane normal to the plane of isotropy. This means that one can consider the failure as a pseudo two-dimensional process. The concept of a comparative study was developed after the three research groups had already completed their individual tests [3], [4], [6], [23], so there are small differences in the test procedures; e.g., different diameters and different thickness-to-diameter ratios. However, in general, the ISRM suggested method [30] was followed. The dimensions of the specimens that were tested are provided in Table 1.
Section snippets
Rock materials studied
In total, nine rocks, which can be classified as transversely isotropic rock, were investigated. Each rock can be characterized by a certain degree of heterogeneity and anisotropy following its origin and geological history. Of the three basic rock classes, i.e., igneous, sedimentary, and metamorphic rocks, transverse isotropy is observed mainly among the two latter classes. Various origins of transverse isotropy are observed, including bedding, stratification, layering, foliation, fissuring,
Variation of strength as a function of inclination angle
As mentioned above and illustrated further, the induced fracture patterns can be relatively complex for transversely isotropic rock material when tested under Brazilian test conditions (i.e., diametrical loading of a core disk). The failure is not necessarily a pure tensile failure; in some cases, it even can be pure shear failure, but often it is a combination of tensile and shear failure [5], [18], [41]. In other words, the classical formula for the indirect tensile strength is not valid in
Classification of fracture patterns
To obtain a better understanding of the reasons for the different variations of strength as a function of the inclination angle, the final fracture pattern for each individual specimen was analyzed. Similar to the idea introduced by Szwedzicki [42] for UCS tests, different fracture types were suggested by Tavallali [6], [24]. As a first step, a pure geometrical classification is considered. It is only afterwards, when interpreting these observations that the link is made with the stress state
Discussion
The following two observations are made in this study comparing nine different transversely isotropic rocks. First, four different trends are observed for the variation of strength as a function of the inclination angles, as shown in Fig. 9. The four trends are as follows:
- (1)
Approximately a constant value over the entire interval.
- (2)
Constant value between 0° and about 45°, followed by a linear decrease.
- (3)
Decrease of the strength over the entire interval, but a rather systematic decrease, approximating
Conclusions
Nine rocks which are classified as transversely isotropic rock material were studied under Brazilian test conditions, and variation of strength and the final fracture patterns were compared as a function of the inclination angle of the weak planes. The nine rocks showed different trends and were grouped. The four trends for the variation of the strength as a function of the inclination angles range from little or no variation (trend 1; i.e., isotropic behavior for strength) to a sharp decrease
Acknowledgement
The financial support of the Research Council of the KU Leuven (OT-project OT/03/35) is gratefully appreciated, as it allowed the research on the Modave Sandstone. This work was also supported by the New and Renewable Energy Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) through a grant that was funded by the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20133030000240).
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