Progressive failure behaviors and crack evolution of rocks under triaxial compression by 3D digital image correlation
Introduction
The investigation on the progressive failure of rocks is crucial for the design of large underground structures under different loading conditions because the damage around the excavation may impair stability and safety (Liu et al., 2017; Feng et al., 2018).”
Fractures of brittle rocks have been extensively investigated. The stress-strain curve of rocks during compression is usually divided into five stages (Fig. 1): (I) crack closure stage, (II) linear elastic deformation stage, (III) crack initiation and stable crack extension, (IV) crack damage and unstable crack growth, and (V) failure and post-peak behavior (Bieniawski, 1967a, Bieniawski, 1967b; Brace et al., 1966). The stress thresholds between every two adjacent stages are σcc (crack closure stress), σci (crack initiation stress), σcd (crack damage stress), and σc (peak stress). Wen et al. (2018) summarized existing methods for determining these thresholds.
These thresholds are the key parameters for estimating progressive fractures of rocks in engineering projects. For example, the lower limit of spalling rock mass strength was reliably estimated with crack initiation stress in uniaxial compression tests (Diederichs et al., 2004; Martin and Christiansson, 2009). Turichshev and Hadjigeorgiou (2016) indicated the difference between the estimations of spalling rock mass strength based on UCS alone and that based on crack initiation stress. Munoz et al. (2016a) obtained a strong correlation between the crack damage stress, the peak stress and several brittleness indices. In addition, the lower and upper limits of long-term strength can be obtained with crack initiation stress and crack damage stress and the lower limit is usually used to analyze spalling in tunnels (Xue et al., 2014). These thresholds can be employed as warning indicators of rock mass damage and breakouts (Pepe et al., 2017). The thresholds and crack evolution of rock materials under unconfined conditions had been explored in details. Pepe et al. (2017) and Xue et al. (2014) reviewed the commonly used methods and the data of rock materials for determining the thresholds under unconfined conditions in recent decades.
Lee and Rathnaweera (2016) reported the progressive fracturing-combined acoustic emission and petrographic analysis method under uniaxial and triaxial stress conditions. Turichshev and Hadjigeorgiou (2016) explored the influences of mineral veins on the behaviors of rocks and discussed related implications. Yang (2016) found that the peak stress and crack damage parameters of hollow sandstone were affected by confining pressure and hole diameter. Wen et al. (2018) proposed a new method to determine crack initiation stress and indicated that the ratio of crack initiation stress to peak strength was approximately 0.55 under the triaxial condition. Chen et al. (2016) investigated the pre-failure damage characteristics of granite under triaxial compression by experiments and numerical simulation and indicated that the damage increased slowly before the reversal of volumetric strain and increased remarkably afterwards. However, compared to the previous results obtained under uniaxial conditions, the effects of confining pressures on progressive failure of rocks were seldom explored (Taheri and Munoz, 2016). Furthermore, the evolution of field strain and localization of rocks under triaxial compression was seldom reported.
In this paper, a series of conventional triaxial compressive tests were carried out on Emochi andesite samples to explore the effects of confining pressure on progressive failure behaviors of rocks. Based on the experimental results, the effects of confining pressure on the stress thresholds and energy evolution during crack extension were discussed. A novel three-dimensional digital image correlation (3D-DIC) instrument with six cameras was used to capture the full-field strain patterns. Damage and crack evolution under confining pressure were presented and discussed. Furthermore, the stress-strain response inside and outside the localization zone were discussed based on the measured results of virtual extensometers by DIC technique. A method of confirming the stress level of localization initiation is proposed based on DIC measurements.
Section snippets
Specimen descriptions and preparation
Emochi andesite is a kind of pyroxene andesite produced in Fukushima Prefecture of Japan. It is homogeneous, dense and fire-resistant and usually used as the building material in Japan. Its main mineral components include plagioclase, ordinary pyroxene, purple augite, magnetite and a small amount of biotite. The uniaxial compressive strength is about 68 MPa. The Young's modulus is about 8.9 GPa. The Poisson's ratio is 0.25 and the density is 2.21 g/cm3. All the specimens were cored in the same
Stress/strain data
Axial stress σ1, axial strain ε1, lateral strain ε3 and confining pressure σ3 can be directly obtained from the experiment. Then volumetric strainεv, elastic volumetric strain εve, and crack volumetric strain εvc can be calculated as follows (Martin and Chandler, 1994).
Based on the σ1-ε1curve, εv-ε1curve, and εvc-ε1curve, the thresholds of crack initiation stress σci, crack damage stress σcd, and peak stress σc can be calculated according to the method of Martin
Effects of confining pressure on thresholds
Typical results of Emochi andesite under different confining pressures are shown in Figs. 8(a~d). Axial, lateral and volumetric strains vs deviator stress curves are presented. Under uniaxial compression, the strength of andesite specimen fast decreases to the lower stress and the failure occurs in the post-peak region. When the confining pressure increases, the axial stress-axial strain curves become more and more flat in the post-peak region. The volumetric strain-axial strain curve and the
Discussion
Although DIC method had been widely applied in rock mechanics (Dautriat et al., 2011; Munoz and Taheri, 2017; Patel and Martin, 2017; Yang et al., 2015) and could be used to measure the full-field strain, the field strain patterns and crack evolution were different under different observation directions and the 3D-DIC system with two cameras was not applicable to observe the whole deformation pattern of specimen in the test. Moreover, the previous studies on the triaxial condition are less than
Conclusions
In the study, a series of triaxial compressive tests with Emochi andesite were performed. With 3D-DIC technique and transparent triaxial cell, the progressive failure behaviors of Emochi andesite were investigated. The characteristic thresholds, energy evolution, full-field strain pattern and crack evolution in different stages of rock failure were analyzed under different confining pressures. The conclusions are drawn below.
- 1)
In the range of tested confining pressures, σci, σcd, and σc of Emochi
Acknowledgments
This work was supported by the National Natural Science Foundation of China (51434003), Basic and Frontier Research Projects of Chongqing (cstc2016jcyjA0117), and the Fundamental Research Funds for the Central Universities (106112017CDJQJ248825).
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