## 2 Background
### Tri-Axial Compressive Creep Test  
In the tri-axial compressive creep test, the specimens were subjected to incremental loading at 60%, 70%, 80%, 85%, 90%, and 95% of the peak intensity, maintaining each load for 72 h. Figure 4 shows the strain-time process curve of the mudstone. [PERSON]'s method [27] was adopted to convert this curve into a strain-time curve under loading conditions, as shown in Figure 5.  
Figure 3: SEM and XRD test results: (**a**) micro- and meso-structures, (**b**) mineral composition analysis.  
According to Figures 4 and 5, the strain of the mudstone under different levels of loads can be divided into transient strain and creep strain. As the axial loading stress increases, the transient strain increases. The higher the slope of the creep curve, the more significant the creep characteristics of the rock are. By continuously increasing the axial load, the microcracks inside the rock are constantly compressed and closed, leading to volumetric compression and increase in the volumetric strain. The annular strain of the rock prior to the accelerated creep is extremely small; therefore, the volumetric strain at this stage is basically determined by the axial strain. After the accelerated creep, the volumetric strain decreases rapidly, indicating that the lateral strain increases considerably and significant dilatation failure occurs. In addition, the axial loading stress affects the creep deformation characteristics of the rock. Under the first- and second-order deviatoric stress, the strain rate tends to be zero after the transient decelerated creep, which is defined as the decay creep stage. Under the third-, fourth-, and fifth-order deviatoric stress, two stages of decelerated creep and isokinetic creep occur; this is defined as the steady creep stage. Under the last stage of deviatoric stress, the rock sample presents decelerated creep in the early stage, and then enters the steady creep stage. When the axial strain exceeds a certain limit, the rock undergoes significant accelerated deformation and ultimately fails.  
Figure 5 presents \(\varepsilon\)-\(t\) curves that have characteristics closest to those of the general Kelvin and Burgers models. As the strain rate gradually becomes constant with time, the general Kelvin model exhibits decay creep, whereas the Burgers model exhibits steady creep. The parameters in the two models are fitted for \(\sigma_{3}\) = 6 MPa, as shown in Figure 6. Tables 3 and 4 show the specific fitting values and equations used.  
Although both the general Kelvin and Burgers models have sufficient goodness-of-fit, the Burgers model shows a better performance than the general Kelvin model. For the Burgers model, except for the curve during the last stage, the goodness-of-fit of the curve in each stage reaches above 98%, reflecting creep characteristics including the transient strain, decelerated strain, and steady strain in all stages. Despite a goodness-of-fit of over 90% in the general Kelvin model, the model does not reflect the full creep characteristics similar to those exhibited by the Burgers model. Therefore, this study adopted the Burgers model to describe the creep characteristics of the mudstone in this project.