Energy dissipation characteristics of sandstone under triaxial extension with different confining pressures

Abstract

After excavation, some of the surrounding rock mass is in a state of triaxial extension, exhibiting tensile or shear fracture modes. To study the energy mechanism of tensile fracture turning to shear fracture, a series of triaxial extension tests were conducted on sandstone under confining pressures of 10, 30, 50 and 70 MPa. Elastic energy and dissipated energy were separated by single unloading, the input energy ut, elastic energy ue, and dissipated energy ud at different unloading stress levels were calculated by the integrating stress−strain curves. The results show that tensile cracks dominate fracture under lower confining pressure (10 MPa), and shear cracks play an increasingly important role in fracture as confining pressure increases (30, 50 and 70 MPa). Based on the phenomenon that ue and ud increase linearly with increasing ut, a possible energy distribution mechanism of fracture mode transition under triaxial extension was proposed. In addition, it was found that peak energy storage capacity is more sensitive to confining pressure compared to elastic energy conversion capacity.

1. Introduction

Numerous rock engineering projects indicate that the initial failure of surrounding rocks is often induced by tensile cracks [1, 2], and laboratory observation has also proven this [3−5]. The in-situ rock mass is initially in a stable stress state (σ1>σ2>σ3), and the elastic recovery caused by excavation unloading can lead to cracks in the rock mass, which is also the principle of some in-situ stress measurement methods [6−8]. As shown in Figure 1, under triaxial extension (σ1≈σ2>σ3), these unloading-induced cracks further propagate, forming spalling (see Figure 1(c)) or V-shaped notches (rockburst under high in-situ stress, see Figure 1(d)). Some in-situ observations indicate that the surrounding rock mass fails when the maximum tangential stress is much less than the uniaxial compressive strength of the rock [11, 12]. Therefore, considering the excavation stress path, true triaxial unloading tests were frequently conducted to study the mechanism behind this phenomenon. Although spalling and rockburst can be reproduced by conducting true triaxial compression tests, the maximum principal stress in the laboratory is still much greater than the in-situ maximum principal stress [13 −15]. So far, spalling and rockburst caused by excavation have not been well explained, and the underlying mechanisms still need further research.

In addition to true triaxial compression tests, the triaxial extension test (also known as the confined direct tension test) is often used to study the propagation of unloading-induced cracks under confining pressure. But previous researchers mainly focused on loading equipment improvement [16 −19], strength [20 −23], and fracture characteristics [24 −28]. The energy conversion characteristics in triaxial extension tests were rarely reported. HUANG et al [22] provided a preliminary explanation of the energy conversion characteristics of granite in triaxial extension tests, but the energy calculation is based on the elastic modulus. However, the elastic modulus is only a parameter used to roughly estimate the deformation characteristics of rocks, and it varies with the external forces on rocks. Sometimes, it is even used to evaluate rock damage [29]. For a certain rock, the elastic modulus is not a constant property to some extent, so the energy calculation method based on the elastic modulus may be unreasonable. In comparison, unloading can better separate dissipated energy and elastic energy. Hence, the energy distribution characteristics under triaxial extension need to be further explored.

In engineering, after excavation, the energy originally contained in the natural rock mass accumulates towards the excavation surface [30 −33]. The surrounding rock mass will fail when the energy tolerance limit is reached [34, 35]. In the laboratory, the testing machine inputs energy to the specimen, and then the specimen fails [36]. Energy dominates the mechanical behavior of rock. Therefore, studying the mechanism of rock failure from the perspective of energy can fundamentally understand the reasons for the instability of rock engineering, and provide an important reference for the formulation of engineering disaster prevention measures [37, 38].