PSI - Issue 39

Mahsa Sakha et al. / Procedia Structural Integrity 39 (2022) 792–800 M. Sakha et al. / Structural Integrity Procedia 00 (2019) 000–000

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ence of anisotropy induces additional complexity to the problem of hydraulic fracturing. Nevertheless, the increasing demand of this technique in recent years involves a deeper investigation on hydraulic fracturing in anisotropic rocks. Anisotropy arises in rocks as a result of the preferred orientation of micro-cracks and anisotropic constituent min erals. For example, micro-cracks are dominantly oriented along the foliation and bedding planes during the formations of metamorphic and sedimentary rocks, respectively. Particularly in sedimentary rocks, the bedding plane is the re sult of the deposition and compaction processes in their formation history (Zia et al., 2018). Besides the in-situ stress state, the rock anisotropy influences the pattern of hydraulic fractures initiation and propagation in the anisotropic rock masses. For example, the anisotropy in strength can cause the hydraulic fractures to initiate and grow in an oblique direction with respect to the principal stresses. This curved trajectory can induce a complex mixed-mode I / II / III loading condition in the vicinity of the boreholes in anisotropic formations. Such fractures then turn and twist in such a way that the fracture path eventually reorients along a plane perpendicular to the minimum compressive stress at larger scales. Hence, it is important to understand how anisotropy in rocks interacts with the in-situ stress condition to determine the path of hydraulic fracture propagation. Hydraulic fracturing is a moving-boundary problem based on which rock deformation and fluid pressure can be determined over time. Therefore, before advancing the numerical solution over a time step, a criterion must be es tablished to predict the trajectory at which a fracture propagates. Irrespective of the loading condition, among all the models proposed in the literature, the maximum tangential stress (MTS) is by far the most popular criterion, and has widely been adopted to predict the onset of fracture growth in both isotropic and anisotropic solids (under dry condition Saouma et al. (1987); Lim et al. (2001); Carloni and Nobile (2005); Mohtarami et al. (2017, 2019) and under hydraulic condition Wang et al. (2016); Zeng et al. (2018)). The MTS criterion, however, becomes inappli cable as soon as a shear-based failure precedes the tensile-based one. In these cases, the maximum energy release rate (MERR), which can basically describe shear-based fracturing as well (Sakha et al., 2021), may be employed (Obata et al., 1989; Gao and Chiu, 1992; Azhdari and Nemat-Nasser, 1996, 1998; Yang and Yuan, 2000; Argatov and Nazarov, 2002; Shen and Shi, 2016). The robustness of these theories in the prediction of fracture path can be validated through experimental data. In anisotropic solids, however, most of these aforementioned studies have not been validated by any experimental data. In addition, some inconsistencies have been reported between the results of these criteria. For example, although the MTS and MERR criteria give similar predictions in isotropic materials, they cease to yield consistent predictions in anisotropic solids (Azhdari and Nemat-Nasser, 1998; Nejati et al., 2020a). Therefore, there still remains a debate on the accuracy of the fracture growth criteria in anisotropic rocks. In this study, a rigorous evaluation of different fracture growth criteria is carried out in order to determine the reliability of each criterion. To this end, the results of a large set of mixed-mode I / II fracture toughness tests on Grimsel Granite are employed to validate the predictions of different crack growth criteria on crack propagation path. The 99 metamorphic Grimsel Granite samples are subjected to four different ratios of mixed-mode I / II loading under the dry condition. The experiment results for the kink angle and the effective fracture toughness are then compared with the predictions of the proposed crack growth criteria. It is shown that the inclusion of T-stress in these criteria can yield predictions which lie closer to the experimental data. It is also demonstrated that the proposed modifications of the MERR criteria are essential to improve the predictions. We employed the asymmetrical SCB test configuration shown in Figure 1 to conduct mixed-mode I / II fracturing tests under dry conditions. This test configuration allows to obtain different combinations of mixed-mode I / II loading simply by varying the span ratio S 2 / S 1 (Nejati et al., 2019a). To achieve both positive and negative values of the mixed mode I / II loading ratio, the ratio S 1 / R is kept fixed and the span ratio S 2 / S 1 was calculated through finite element analyses in ABAQUS in such a way that the configuration can meet the desired loading condition. We subjected the Grimsel Granite samples to four different loading ratios as K II / K I = − 0 . 4 , 0 . 4 , − 1 , 1. Grimsel Granite is categorized as metamorphic rock which exhibits a clear transversely isotropic behavior within its foliation planes. Table 1 lists the elastic properties, the FPZ length, and the fracture toughness values of Grimsel Granite used in this study. Here, K Ic , 1 and K Ic , 2 are respectively the mode I fracture toughness in principal directions 1 (along the foliation) and 2 (normal to the foliation). K IIc , 1 and K IIc , 2 are also true mode II fracture toughness along principal directions 1 and 2, respectively. The relations describing the directional dependence of different measures 2. Experimental setup