Failure characteristics of surrounding rocks along the radial direction of underground excavations: An experimental study

Highlights

• True triaxial tests with different σ₃ are conducted.

• Rock strength under different σ₃ condition are investigated

• The influence of σ₃ on the rock failure mode is studied.

• Rock failure near the boundary of underground excavations is characterzied.

Abstract

For the in situ surrounding rocks of underground excavations, the radial stress corresponding to the minimum principal stress σ₃ varies with increasing distance away from the excavated boundary. To characterize the rock failure along the radial direction of an excavation, true triaxial compression tests with different σ₃ values (0.5, 5, 10, 15, 20, 25, and 30 MPa) were performed. The characteristic stresses (including the crack initiation stress σ_i, crack damage stress σ_d, and peak stress σ_s) and failure mode of the tested specimen under different σ₃ conditions were systematically investigated. The experimental results indicate that with increasing σ₃, the characteristic stresses increase monotonically and continuously. The increasing rate of the characteristic stresses with σ₃ ranging from 0 to 10 MPa is higher than that with σ₃ ranging from 10 to 30 MPa, indicating that low σ₃ impose a greater effect on the characteristic stresses than high σ₃. In addition, the failure mode of the tested specimen changes from tensile-shear failure mode I (with vertical tensile cracks and oblique tensile-shear cracks developing along the σ₂ direction) to tensile-shear failure mode II (with oblique tensile-shear cracks developing only along the σ₂ direction) to tensile-shear failure mode III (with oblique tensile-shear cracks along both σ₂ and σ₃ directions) as σ₃ increases. Then, the failure characteristic of the surrounding rocks of the underground excavation was characterized based on the obtained experimental results. When maximum radial stress σ_r encountered near the excavated boundary is much smaller than the axis stress σ_a, the surrounding rocks will exhibit a “Ternary failure characteristic”, i.e., with an increase in the distance from the excavated boundary along the radial direction, the failure mode of the surrounding rocks after excavation changes from tensile/splitting failure mode to tensile-shear failure mode I and then to tensile-shear failure mode II. When the maximum σ_r encountered near the excavated boundary approximates the original σ_a, the surrounding rock masses will exhibit a “Quaternary failure characteristic”. Specifically, the corresponding failure mode along the radial stress direction away from the excavated boundary changes from tensile failure mode to tensile-shear failure mode I then to tensile-shear failure mode II and finally to tensile-shear failure mode III.

Introduction

During underground rock engineering, excavation significantly changes the stress state of the rocks. An opening due to excavation starts the stress state change by removing the radial stress σ_r (stress perpendicular to the wall) of rocks on the excavated boundary. Then, rocks near the excavated boundary will undergo stress redistribution, which results in a non-monotonic distribution of σ_r along the radial direction. The varied σ_r is a critical factor influencing the failure characteristics of surrounding rocks. According to the Kirsch equations, σ_r increases and then decreases to the far-field radial stress with an increase in the distance away from the excavated boundary (as shown in Fig. 1). In particular, within the region approximately 0.4 times the diameter of the tunnel near the excavated boundary, σ_r increases rapidly (Su et al. 2017d). The failure characteristics of the rocks near the excavated boundary with a low σ_r significantly differ from those with a high σ_r. Consequently, a deep investigation of the rock strength and failure mode of rocks under different σ_r conditions (corresponding to the minimum principal stress σ₃ in the lab study) can provide useful information for characterizing rock failure at different distances away from the excavated boundary. This study is very important to the supporting design, stability analysis of surrounding rocks, and long-term operation of underground excavations.

Rock strength is the peak stress that rock encounters during its failure process, which is a critical parameter to characterize the rock mechanical behavior and divides the rock failure into pre-peak and post-peak stages. Considerable investigations of the rock strength (peak stress) and its influencing factors have been conducted using different approaches, including laboratory tests, numerical simulations, and theoretical or empirical analyses (Cai 2008; Feng et al. 2019; Feng et al. 2016; Liang et al. 2015; Mao et al. 2015; Mogi 1967; Pan et al. 2012; Sangha and Dhir 1972; Si and Gong, 2020; Song et al. 2019; Xu et al. 2017; Zhang and Wong 2013; Zhao et al. 2013; Zuo et al. 2017). In addition to the peak stress σ_s, there are two characteristic stresses, namely, the crack initiation stress σ_i and crack damage stress σ_d, that can also be taken as the representative mechanical parameters to characterize the rock failure behavior. σ_i represents the stress level where new crack formation starts; this stress level is considered to be a lower bound for evaluating the onset of in situ spalling. σ_d indicates the stress level where cracks develop unstably, which is characterized by a dramatic increase in the crack density and the start of crack coalescence (occurrence of rapid damage of the rock mass); this stress is taken as the long-term strength of the in situ surrounding rocks (Cai et al. 2004; Eberhardt et al. 1998; Gong and Wu 2020; Kong et al. 2018; Zhao et al. 2015; Zhao et al. 2013). Hence, the determination of σ_i and σ_d can also provide useful information for rock failure prediction.

To obtain σ_i and σ_d, several strain-based methods, including the volumetric strain method (Brace et al., 1966), crack volumetric strain method (Martin and Chandler 1994), lateral strain method (Lajtai 1974; Stacey 1981), extensional strain method (Stacey 1981), instantaneous Poisson's ratio method (Diederichs 2007), and lateral strain response (LSR) method (Nicksiar 2012), are proposed. In addition, because of its high sensitivity to crack initiation, propagation, and coalescence in stressed rocks, acoustic emission (AE) and its parameters are also involved (Eberhardt et al. 1998; Moradian et al. 2016; Wu et al. 2020; Zhao et al. 2015; Zhao et al. 2013). Using these methods, experimental investigations of σ_i and σ_d have been intensively performed by conducting uniaxial and conventional triaxial tests (Bruning et al. 2018; Eberhardt et al. 1998; Zhao et al. 2015; Zhao et al. 2013). According to the experimental data obtained, many criteria, always described by the deviatoric stress (σ₁-σ₃) limits, for determining σ_i and σ_d have been proposed (Cai et al. 2004; Martin and Chandler 1994; Zhao et al. 2013). However, these experimental results may be inadequate to characterize the σ_i and σ_d of deep underground rocks because these rocks are under true triaxial conditions and their intermediate principal stress σ₂ cannot be neglected. Consequently, a corresponding study by using true triaxial compression tests is required. Kong et al. (2018) and Gao et al. (2018) investigated σ_i and σ_d under different σ₂ conditions and found that σ₂ significantly influences σ_i and σ_d. Moreover, from an engineering point of view, the characteristic stresses under different σ₃ conditions should be investigated to describe the rock failure at different distances away from the excavated boundary, which can provide a scientific basis for evaluating the stability of the sounding rock mass and support design, such as the length of the rock bolt. However, the corresponding study of σ_i and σ_d under true triaxial compression conditions, especially when different σ₃ values are encountered, has been given little consideration.

In addition to the characteristic stresses (σ_i, σ_d, and σ_s), the failure mode is also generally used to characterize rock failure. A good understanding of the failure mode is essential for characterizing how the peripheral stress around an underground excavation causes the failure in rock masses (Hudson 1989) and enables a better interpretation of the strength obtained in lab tests (Basu et al. 2013; Hudyma et al. 2004). Experimental studies have been conducted to characterize or classify the failure mode in the lab. In conventional triaxial tests (σ₁ > σ₂ = σ₃), rocks generally fail in a shear fashion with oblique cracks, and the dip angle of the oblique crack is postulated to be constant when the Mohr-Coulomb criterion is involved (Song et al. 2019) but exhibits a decreasing variation with the increasing confining pressure (Haimson and Chang 2000). In addition, the confining pressure not only acts as the changer of the failure mode in terms of the dip angle of the oblique cracks but also renders a more complicated failure characteristic. Typically, the failure mode can be classified into three types with increasing confining pressures (Santarelli and Brown 1989; Yao et al. 2016): (i) failure by axial splitting under the zero confining pressure condition, (ii) failure that occurs classically along a shear plane inclined to the vertical under intermediate confining pressure conditions, and (iii) failure by multiple shear planes under high confining pressure conditions. In true triaxial compression tests (σ₁ > σ₂ > σ₃), the confining pressure includes a higher σ₂ and lower σ₃. In this situation, cracks generally develop steeply striking along σ₂ and dipping towards σ₃ (Haimson and Chang 2000). The failure mode under different σ₂ conditions has also been investigated (Haimson and Chang 2000; Song et al. 2019; Su et al. 2017b). In a recent experimental study, Kong et al. (2018) and Gao et al. (2018) investigated the failure mode under true triaxial compression condition with different σ₃. However, only a few σ₃ conditions or low-magnitude σ₃ values were involved. A further study that considers the gradual increase in σ₃ from 0 to σ₂ needs to be conducted to systematically investigate the influence of σ₃ on the rock failure mode. In addition, modified true triaxial compression tests with “one free face, five stressed faces” are conducted to simulate the intensive rock failure (rockburst) during underground excavation at depth (Jiang et al. 2020; Su et al. 2017b). However, these tests just describe the stress state of the surrounding rock on the excavated boundary; further investigations on the rock failure near the excavated boundary under true triaxial compression stress state are needed.

The major goal of this study is to characterize the failure of in situ surrounding rock along the radial direction of underground excavations. To achieve this goal, a true triaxial compression test on granite with different minimum principal stresses σ₃ is conducted. Then, the characteristic stresses (including crack initiation stress σ_i, crack damage stress σ_d, and peak stress σ_s) and failure mode of the tested specimens are investigated. Based on the obtained experimental results, the influence of the radial stress on the failure of the surrounding rock masses of excavation is discussed. Finally, the main conclusions are drawn.