A large number of deep buried tunnels have been constructed in western China in recent years, and many of these tunnels have been excavated in metamorphic and sedimentary rocks with evident structural anisotropy, such as phyllite, shale, schist, and slate. Field observations have revealed that structural anisotropy causes obvious asymmetric tunnel deformation associated with the orientation of the bedding planes of the surrounding rocks (Meng et al., 2013; Chen et al., 2019; Liu et al., 2021). The deformation often exhibits pronounced time-dependent characteristics when the tunnel is under high geo-stress relative to the strength of the surrounding rocks (Panthi and Shrestha, 2018; Lee et al., 2019). It has been reported that the anisotropic time-dependent deformation of the surrounding rocks has significant adverse effects on the long-term structural stability of tunnels and should be considered during the design of the support system (Tian et al., 2022).
The effects of structural anisotropy on the time-independent mechanical parameters of anisotropic rocks, including the compression strength and elastic modulus, have been extensively studied. A series of uniaxial and triaxial compression tests were conducted on shale, slate, schist, and phyllite to investigate the strength anisotropy of rocks (Niandou et al., 1997; Nasseri et al., 2003; Saroglou and Tsiambaos, 2008; Saeidi et al., 2013; Ali et al., 2014; Singh et al., 2015; Singh et al., 2022). All the results showed that structural anisotropy caused the rock strength to vary with the dip angle of the bedding plane α. The variations in the compression strength with α are divided into three types: U-shaped, shoulder-shaped, and wavy-shaped (Ramamurthy, 1993), as shown in Fig. 1(a). The minimum strength is often observed at α values ranging from 30° to 60°, and the maximum strength is observed either at α = 90° or α = 0°. Furthermore, the effects of the structural anisotropy on the elastic modulus have also been studied. According to Nasseria et al. (2003), the variations in the elastic modulus with α under uniaxial compression conditions can be categorized into two broad types: those with U-shaped and those with increasing order-shaped curves, as shown in Fig. 1 (b). Compared to the extensive studies on the time-independent anisotropic behavior of rocks, few studies have focused on the effect of structural anisotropy on the time-dependent behavior of rocks. In previous studies, the anisotropic time-dependent behaviors of rocks were mainly investigated by creep tests, in which the loading stress was kept constant, and the compression strain increased with time. Naumann et al. (2007) conducted true triaxial compression creep tests on Opalinus clay specimens with the orientation of the bedding plane α = 0° and 90° and found that the bedding plane had a more significant effect on transient creep rather than steady creep. Triaxial creep tests of Callovo-Oxfordian argillite showed that when the creep stress σcr was 82% of its failure stress σc, the steady creep rate of the specimen with horizontal bedding planes (α = 0°) was slightly greater than that of the specimen with vertical bedding planes (α = 90°) (Liu et al. 2015). Kwasniewski and Nguyen (1988) conducted a series of uniaxial creep tests on three types of shales with different bedding angle orientations. The results showed that when the creep stress was 70% of σc, the steady creep rate exhibited a decreasing order-shaped anisotropy, as shown in Fig. 2(a). The minimum creep rate was observed at α = 60–90°, and the maximum creep rate was observed at α = 0°. Wu et al. (2018) studied the anisotropic creep behavior of greenschists under uniaxial compression tests loaded using a stepwise method. The results showed that when the creep stress was greater than 22% of σc, the steady creep rate showed an inverted U-shaped or shoulder shaped anisotropy. The maximum creep rate occurred at α = 35° and 45°, and the minimum creep rate was observed at α = 0° and 90°, which differed from the results obtained by Kwasniewski and Nguyen (1988), as shown in Fig. 2(b).
To further understand the influence of structural anisotropy, researchers used the discrete element method (DEM) to simulate the development of microcracks and failure processes of anisotropic rocks (Duan et al., 2015; Park and Min, 2015; Chong et al., 2017; Xu et al., 2018). The anisotropic behaviors induced by soft structures were observed at the microscopic and mesoscopic levels. However, numerical simulations may display distinct differences from actual rocks and cannot reflect the overall mechanical properties of anisotropic rock (Yang et al., 2019). Thus, many attempts have been made to develop advanced observation methods such as digital image correlation (DIC) measurement techniques. DIC can calculate the spatial distribution of the displacement and strain of a rock during the loading process by using the measured moire fringe, speckle interferometry, high-definition digital images, or X-ray tomography images (Cheng et al., 2017; Wang et al., 2018). Louis et al. (2007) used two-dimensional (2D) DIC to map the spatial distribution of the compressive strain in Rothbach sandstone and investigated the effect of the bedding planes on the development of strain localization. Zhou et al. (2021) used DIC to investigate the influence of structural anisotropy on the failure process of foliated gneiss with various schistosity orientations. Cheng et al. (2017) and Yang et al. (2019) used three-dimensional (3D) DIC to observe crack and strain evolution before and after peak strength in uniaxial and triaxial compression tests. They studied the damage evolution processes, failure modes, and failure mechanisms of composite rocks. To date, DIC has rarely been used to observe the time-dependent anisotropic behaviors of rocks. Yang et al. (2011) verified the feasibility of DIC for observing the time-dependent behavior of argillaceous rocks at different scales (from 100 µm to cm). Shi et al. (2021) used DIC to investigate the correlations between major cracking patterns and strain concentration zones during creep tests of clay-rich rocks, and found that the effects of structural anisotropy on instantaneous strain were different from those of creep strain.
Owing to the high variability of natural rocks caused by the formation process, geological environment, weathering, and mineral composition, it is difficult to obtain a large number of natural rock specimens with desired properties (Tien et al., 2006). Therefore, many researchers have used artificial rock-like specimens to investigate the behavior of anisotropic rocks. Tien et al. (2006) used laboratory-made composite rock composed of sand, micro silica, kaolinite, and cement to investigate the failure modes of anisotropic rocks. They found that the failure of rocks induced by structural anisotropy could be classified into two modes: sliding failure along the discontinuities and non-sliding failure along the discontinuities. Cheng et al. (2017) and Yang et al. (2019) used artificial composite rocks composed of cement, gypsum, kaolinite, and sand to investigate the strength and deformability of transversely isotropic rocks. With the development of three-dimensional printing (3DP) technology, 3DP has been used to print rock-like specimens with special internal structures in the past few years (Feng et al., 2019). Jiang et al. (2015) and Vogler et al. (2017) found that 3DP sand-powder specimens have tensile and compression failure modes similar to those of natural sandstone. Tian and Han (2017) tested the failure mode of printed specimens with different angles of pre-existing flaws under uniaxial compressive conditions and found that 3DP is an effective and efficient technique for studying the mechanical mechanisms of rock materials.
In this study, uniaxial compression creep tests were conducted on composite rock specimens prepared using 3DP technology. During the creep tests, variations in the full-field displacement and strain of the specimens were monitored using DIC technology. First, the Burgers model was used to analyze the anisotropic creep behavior of the composite rocks. Subsequently, based on the DIC observations, we analyzed the non-uniform distributions of the uniaxial compression strain and shearing slip between the hard material and soft layer. Finally, the influence of creep processes on the failure modes of the composite rock was analyzed.