# Mechanical and Acoustic Emission (AE) Characteristics of Rocks under Biaxial Confinements
## 1 Introduction  
The underground rocks in the vicinity of underground engineering boundaries are subjected to a static biaxial compressive geo-stress state (the minimum principal stress \(\sigma_{3}\) unloading to 0, and the maximum principal stress \(\sigma_{1}\) and the intermediate principal stress \(\sigma_{2}\) reaching a new balanced state) after the excavation operations [1, 2, 3, 4, 5, 6], as shown in Figure 0(a). Thus, the studies of the load-carrying ability and failure behaviors of rocks under biaxial confinements are fundamental for a better understanding of the rock disasters and for effective design and construction of underground engineering [7, 8, 9]. Many researchers have made great efforts in this field and have achieved many results. The biaxial compression tests were initially carried out using a hollow cylinder and cubes coal specimens by [PERSON] [10], but not long after that, the cubic rock specimens became more widely used, and a growing number of research findings in biaxial compression tests have been reported [11]. The cubic sandstone specimens with a side length of 75 mm have been used in biaxial compression tests to determine the biaxial compressive characteristics of rocks. It was found that the biaxial compressive strength \(\sigma_{\text{bcs}}\) is significantly increased with the increase of lateral confinement. Besides, the failure is generally initiated by rock spalling at the free faces at the early stage of loading, and the ultimate failure occurs in a form of an out-of-plane shear failure [12]. Under a high \(\sigma_{2}\), the microcracks and fracturesin the rocks can only develop in the plane of \(\sigma_{1}\)-\(\sigma_{2}\), which leads to the anisotropic failure behaviors of rocks [13]. Furthermore, the \(\sigma_{2}\) has a limited influence on the peak strength of the rock near the excavation boundary [14]. The \(\sigma_{2}\) in a plastic potential function has a significant impact on the evolution of volumetric plastic strain, thereby exerting an influence on the overall stability of rock mass structures [15]. The specimen's failure and crack coalescence are at the same time under compression, while crack coalescence occurs first, and then failure occurs in the state of biaxial confnements [16]. More energy would be required for rock failure under equal biaxial compression than under unequal biaxial compression [17]. Under biaxial confnements, structural failure occurred mainly in the specimens when the number of natural cracks in the rock is small, and the specimen appears local failure with the increase of the number of natural cracks, and under the state of low initial stress can accelerate the propagation of a large number of cracks [18; 19]. The \(\sigma_{\text{bcs}}\)-\(\sigma_{2}\) envelopes of rocks in biaxial compression tests (\(\sigma_{1}\geq\sigma_{2}\geq 0\), \(\sigma_{3}=0\)) from other literature [19; 20; 21; 22] are shown in Figure 1b, and the results are concluded as follows: (1) The uniaxial compressive strengths \(\sigma_{\text{ucs}}\) of limestone and granite are approximately equal to the biaxial compressive strengths \(\sigma_{\text{bcs}}\) under the biaxial compression with \(\sigma_{1}=\sigma_{2}\), while the \(\sigma_{\text{bcs}}\) of red sandstone, sandstone, and salt are much bigger than \(\sigma_{\text{ucs}}\); (2) The \(\sigma_{\text{bcs,peak}}\) (the maximum value of \(\sigma_{\text{bcs}}\)) of limestone, red sandstone, granite, sandstone, and salt is 21%, 53%, 63%, 85%, and 87% higher than their \(\sigma_{\text{ucs}}\), respectively; (3) When the \(\sigma_{2}\) is about 0.5\(\sigma_{\text{ucs}}\), the \(\sigma_{\text{bcs}}\) of limestone and granite reaches the \(\sigma_{\text{bcs,peak}}\), and the \(\sigma_{\text{bcs,peak}}\) of red sandstone, sandstone, sandstone, and salt can be obtained under the condition of biaxial compression with \(\sigma_{2}=0.8\sigma_{\text{ucs}}\), \(\sigma_{2}=\sigma_{\text{ucs}}\), and \(\sigma_{2}=\sigma_{\text{ucs}}\), respectively.