## 2 Materials and Methods  
Considering one of the hereditary creep theories, presented in [30; 31], the authors took into account the nonlinear properties of the material and compared these with the time taken. The creep theory was also applied in slope stability-related research, showing a broad approach of numerical and empirical application [32]. Hereditary creep allows for the manifesting of material deformation over a long period, taking into consideration the history of the loading processes. According to hereditary creep theory, materials continue deforming after being loaded and unloaded. The strains are proportional to the stress values at various intervals and accumulate gradually. The equation to present the relationship of nonlinear strain and stress, taking into account the time factor according to [PERSON]'s hereditary creep theory [30], is shown as follows:  
\[\epsilon(t)=\frac{1}{E}\left[\sigma(t)+\int\limits_{0}^{t}L(t,\tau)\cdot \sigma(\tau)d\tau\right] \tag{2}\]  
where \(\epsilon\)(t), \(\sigma\)(t) are the strain and stress at moment t, respectively; E stands for the instantaneous modulus of the elasticity of rocks; \(\tau\) is the time before instant t; and L(t, \(\tau\)) is a creep kernel function characterising the strain rate. Based on the hereditary properties of rock, the creep kernel L(t, \(\tau\)) can be presented as follows:  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]  
The strain archived from the creep test for a rock specimen by loading with a constant load, \(\sigma=\sigma_{0}=\text{const obeys the law as follows:}\)  
\[\epsilon(t)=\frac{\sigma_{0}}{E_{0}}(1+\Phi) \tag{4}\]  
Nowadays, there are various laboratory methods to determine the creep parameters of rock specimens. One of them is the bending compression test performed on rock specimens with a beam of a cross-section of 20 \(\times\) 20 \(\times\) 160 mm; the testing scheme is represented in Figure 2. The laboratory tests were performed using the creep apparatus comprised of a stainless-steel test cylinder sealed at both ends and equipped with externally linked pistons. By ensuring that the pistons share the same diameter, this setup facilitated the deformation of the specimen without altering the volume in the pressure chamber. The axial load or differential stress on the specimen was applied via an overhanging pan atop the yoke of the apparatus, loaded with the desired weights. The contraction of the specimen was gauged using an Ames dial gauge affixed to the upper-end piece of the specimen assembly. In accordance with [3], creep function \(\Phi\) is expressed as follows:  
\[\Phi=\frac{\delta\cdot t^{1-\alpha}}{1-\alpha} \tag{5}\]  
where \(\Phi\) is the creep function; \(\sigma 0\) is tensile stress due to the bending moment, MPa; E is the strain modulus of rock, and GPa; \(\alpha\) and \(\delta\) are dimensionless and dimensional empirical parameters, respectively. Taking into consideration Equation (4) the time-varying deformation modulus can be expressed as:  
\[E_{t}=\frac{E}{1+\Phi} \tag{6}\]  
The deflection of the rock beam was determined using the following formula,  
\[y=\frac{F\cdot l^{3}}{48\cdot E\cdot J} \tag{7}\]  
where: J is the moment of inertia of the beam cross-section. The tensile stress arising from bending the rock beam was calculated using the following formula,  
\[\sigma=\frac{M\cdot h}{2J} \tag{8}\]  
where: M is the maximum bending moment at the centre beam cross-section, and h is the beam height.