## 1 Introduction  
Transversely isotropic rock materials, especially carbonaceous slate, are widely distributed in western China [1]. Their well-developed foliation structure renders it prone to creep under prolonged exposure to tectonic stress. In tunnel engineering construction, this strong rheology has led to a series of disasters such as lining cracking and floor heaving [2], which threatens the stability, sustainability, and long-term operation of tunnels. Therefore,an in-depth exploration of the time-dependent properties of carbonaceous slate is necessary to promote the long-term stability and safety of engineering works in the western regions. Previous studies primarily examined the short-term mechanical behavior of different types of layered rocks. These studies included tests such as uniaxial and triaxial compression and Brazilian testing of sandstone with different bedding angles [3]; triaxial compression testing of shale [4] and layered mudstone [5]; and uniaxial compression testing of slate [6] and phyllite [7]. Currently, the majority of the creep experiments are conducted on isotropic rocks, including uniaxial, biaxial, and true triaxial creep testing on various types of rock such as sandstone [8], granite [9] and marble [10]. Additionally, there are creep tests that simulate complex working conditions, such as uniaxial cyclic loading creep tests on rock salt [11], tensile creep tests on granite [12], and triaxial unloading creep tests on red sandstone with single ice crack [13]. However, there is a lack of research on the creep characteristics of transversely isotropic rocks. [PERSON] et al. [14] conducted direct shear creep tests on shales with five different bedding inclinations and observed that the creep anisotropy exhibited a significant stress-dependent behavior. [PERSON] et al. [15] reported that the presence of structural anisotropy influenced the characteristics of laminated inclined rock salt in terms of transient, steady-state, and accelerated creep. [PERSON] et al. [16] employed triaxial compression tests to study the creep behavior of cox mudstone, revealing that the stable creep rate with a bedding angle \(\theta=0^{\circ}\) is higher than that at \(\theta=90^{\circ}\). The aforementioned studies largely focused on analyzing the impact of bedding on the mechanical anisotropy of creep in layered sedimentary rocks. However, the bedding in sedimentary rocks often experiences alterations in mineral composition due to tectonic movements and fluctuations in sedimentary environments during the sedimentation process [17]. Carbonaceous slates, which are a type of metamorphic rock, differ from sedimentary rocks in terms of their diagenetic mechanisms. Presently, the constitutive models for creep can be generally divided into three types: empirical models, component models, and nonlinear damage models. Classical component models like the Burgers model and the Nishihara model are extensively employed in practical research [18]. Although these models possess simple equations and proper physical implications, they cannot precisely depict the nonlinear accelerating creep stage of rock. Many scholars have enhanced classical component models by incorporating damage factors, allowing these models to better capture the accelerating creep process. [PERSON] et al. [19] proposed an improved Nishihara model by connecting a nonlinear dashpot with a strain trigger in series with the Nishihara model, and [PERSON] et al. [20] improved the components in the Nishihara model by considering the initial damage and damage evolution. Since the aforementioned models are all integer-order models, they have certain discrepancies in describing the decelerating creep stage and the characteristics of unsteady creep. [PERSON] et al. [21] and [PERSON] et al. [22] replaced the Newton dashpot in the Nishihara model with a fractional Abel dashpot to more accurately describe the accelerating creep behavior of rocks. [PERSON] et al.