Cracking mechanisms of a medium-grained granite under mixed-mode I-II loading illuminated by acoustic emission

Highlights

• Cracking behavior of a medium-grained granite under mixed-mode I-II loading.

• Acoustic emission excels in predicting the crack initiation in heterogeneous granite.

• Mode II loading component alters the source mechanisms of acoustic emission events.

Abstract

Cracks at various scales in rock masses are often subjected to mixed-mode I-II loadings in Earth's dynamic processes and geotechnical engineering works. Insightful understanding of the macroscopic and microscopic cracking mechanisms of rocks under this loading condition is of far-reaching significance. To investigate the effect of the loading condition and granite heterogeneity on the cracking mechanism, we conduct three-point bending tests on pre-notched semi-circular medium-grained granite specimens. For comparison, identical tests are also conducted on polymethyl methacrylate (PMMA) specimens. The results show that the initiation angles of the macrocracks in granite are less influenced by the loading condition as compared with the more homogeneous PMMA. Based on the monitoring of the acoustic emissions (AEs), we find that the microcracks under mixed-mode I-II loading do not nucleate as easily as compared with that in mode I case. For the AE event density contours characterizing the fully-developed fracture process zones, their shape is sub-circular and symmetric with respect to the pre-existing notch under mode I loading, while those under mixed-mode I-II loadings are irregular and asymmetric. Most of the macrocrack paths traverse the high AE event density region. As the mode II stress intensity factor (K_II) increases, the AE events with higher energy tend to concentrate beside the crack paths in front of the notch tips. The moment tensor inversion suggests that the presence of mode II loading component alters the AE source mechanisms in terms of the temporal evolution characteristics of event-type ratios preceding the unstable propagation of macrocracks.

Introduction

Rock cracking subjected to mixed-mode I-II loadings is ubiquitous in Earth's dynamic processes²⁰ and geotechnical engineering works.⁶³ For example, one of the formation mechanisms of strike-slip faults is associated with the coalescence of a set of subparallel joints or small fault segments whose fracture walls are generally oblique to the principal stress direction. Driven by mixed-mode I-II loadings,²⁸ new secondary cracks initiate and link the pre-existing joints or faults segments, forming the linking damage zones of strike-slip. Besides, the step-path failure of rock slopes with intermittent joints is induced by the initiation and propagation of new cracks from the pre-existing joints under mixed-mode I-II loadings. Once these new cracks propagate through the rock bridge, the key joints coalesce and form a critical sliding plane leading to the global failure of rock slopes.⁶³ Therefore, a thorough study of the cracking mechanisms of rocks under mixed-mode I-II loadings is of scientific and practical value in better understanding the fault evolution and assessing the slope stability.

For decades, a key debate regarding the cracking behavior of rocks under mixed-mode I-II loadings is when and how new cracks initiate from the pre-existing fractures. To deal with this issue, the linear elastic fracture mechanics (LEFM) proposed a number of criteria to predict crack initiation. These criteria can be generally classified into three categories, namely stress-based, strain-based, and energy-based.⁵⁶ The maximum tangential stress (MTS) criterion,¹⁷ minimum strain energy density criterion^52,53 and maximum energy release rate criterion¹⁷ are the most classic criterion of each category, representatively. When the key parameters in the criteria (i.e., stress, strain energy density, and energy release rate) reach their thresholds, new cracks initiate. These criteria have been proved to satisfactorily predict the variations of the critical stress intensity factors (i.e. fracture envelopes) and crack initiation angles of a fracture under mixed-mode I-II loadings in linear elastic homogeneous materials such as polymethyl methacrylate (PMMA).⁹ However, the criteria sometimes fail to describe the cracking behavior in rocks which are regarded as relatively nonlinear and heterogeneous materials.⁵

To further investigate the cracking behavior of rocks under mixed-mode I-II loadings, both field investigations²⁸ and laboratory tests have been extensively conducted. Laboratory tests have the advantages of controlling the loading modes by designing the corresponding loading configurations. The macroscopic cracking behavior under mixed-mode I-II loading has been experimentally studied in different rock types, such as granite,^12,44,61 limestone,4, 5, 6^,27 marble^{3,7,12,24,43,60} mudstone,^8,31 sandstone^{19,32,34,35,55} and tuff¹⁶ as well as some rock-like materials.⁶² In parallel with the laboratory tests, a number of numerical models have also been proposed to simulate the cracking behavior of different rock types²⁵⁵⁹).

Significant discrepancies are sometimes observed between the experimental results (e.g. fracture envelop and crack initiation angle) and those predicted by these three classic LEFM-based criteria.¹² They may be accounted for by the presence of fracture process zones (FPZs) in front of the rock fracture tip. Preceding the initiation of macrocracks in rocks, the stress-induced microcracks (~μm) form the FPZ.²³ The FPZ keeps developing as the microcracks further nucleate and grow. The status of FPZ immediately before the initiation of macrocracks is defined as the fully-developed FPZ (FD-FPZ). The relatively large FD-FPZs make the LEFM no longer approximating the actual fracture tip stress field.⁵⁶ Besides, the heterogeneity of rock or pre-existing weak planes (~mm) near the fracture tips may also control the local stress distribution and significantly affect the crack initiation behavior.⁵⁸ Given the effect of FPZs on the validity of the theoretical criteria to predict cracking behavior in rocks, it is important to comprehensively investigate the microcracking behavior and associated FPZ features.

The formation processes of microcracks are often accompanied by emanating elastic waves known as acoustic emission (AE).^37,38 The AE technique has been used as a robust tool to study the microcracking mechanisms and the FPZ features in rock fracturing laboratory tests.^15,23,36,40, 41, 42^,45,57,63,64 While the microcracking mechanisms of brittle rock under mode I loading has been comprehensively studied using the AE technique^{22,23,26,3050,54,5765}; only a few have investigated those of limited rock types such as sandstone under mixed-mode I-II loadings .^33,34

Using the AE and digital image correlation (DIC) techniques, Lin et al.^33,34 monitored the evolution of AE events and displacement field in the mixed-mode I-II loading tests on pre-notched sandstone specimens with grain size ranging from 0.1 mm to 0.8 mm. The results offer a good understanding of the development of the microcracks in the sandstone, but whether the same microcracking mechanisms also occur in granite remains elusive. Some open questions related to the macrocracking and microcracking behavior of granite include (1) What are the microcracking mechanisms of the granite under mixed-mode I-II loadings? (2) How does the loading condition affect microcracking mechanisms? (3) How are the microcracking mechanisms correlated with the macrocracking behavior?

To advance the understanding of the above questions, we elaborately choose a medium-grained granite (average grain size of 0.99 mm) and conduct asymmetric three-point bending tests on the straight-through notched semi-circular bend (SNSCB) granite specimens, aka asymmetric semi-circular bending (ASCB) tests. To apply various mixed-mode I-II loadings to the notch (i.e. artificial fracture) tip, we vary the span of one of the supporting rollers in the bending test. Three sets of ASCB tests together with the symmetric semi-circular bending (SSCB) test are conducted on the granite specimens (Section 2). The AEs are continuously monitored during the bending tests to study the microcracking processes. To assess the influence of local grain-scale heterogeneity of the granite on the macroscopic cracking behavior, identical SCB tests are conducted on PMMA specimens. In Section 3, features of the surface macrocracks developed in the granite and PMMA specimens are studied and compared. The microcracking mechanisms of the granite are analyzed by interpreting the AE signatures. The surface crack paths are compared with the distribution of AE events of the fully-developed FPZs to elucidate the relation between the macroscopic and microscopic cracking behavior. Lastly, the moment tension inversion is conducted to further study the variations of AE source mechanisms. In Section 4, the microcracking behavior of relatively heterogeneous granite is compared with that of relatively homogeneous sandstone which was investigated in .³⁴ At the end of this paper, the influencing mechanisms of the loading condition on the microcracking behavior of the granite are summarized.