## 2 Materials and Methods
\[M=\frac{F\cdot l}{4} \tag{9}\]  
Combining (8), (9) and (7) the formula could be presented as follows:  
\[y=\sigma\cdot\frac{l^{2}}{6E\cdot h} \tag{10}\]  
Substituting E by Et in Equation (10), taking into consideration Equation (6) the formula for calculating the beam deflection at the centre cross-section with time can be expressed as follows:  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]0  
The initial instantaneous beam deflection obtains the values of:  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]1  
The Equation (11) is now:  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]2  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]3 Scheme of bending and compressing test of a rock specimen. Taking logarithms of both sides of the achieved expression above, the formula is as follows:  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]4  
Setting the following terms,  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]5  
Expression (14) transforms into the first-degree equation of  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]6  
Creep parameters expressed in Equation (15) can be determined using the following formulas,  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]7  
\[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]8  
The rock beam testing performed according to the scheme presented in Figure 2 was considered at various values of concentrated load generating the following values of tensile stress: \(\sigma=1.8;2.25;2.7\) (MPa). The results representing the measured displacements are given in \[L(t,\tau)=\delta(t-\tau)^{-\alpha} \tag{3}\]9  
From the results, the values of a and b were respectively equal to \(-0.18\) and \(0.29\), thereby creep parameters \(\alpha\) and \(\delta\) were calculated as follows:  
\[ \begin{array}{l}\alpha=1-b=1-0.29=0.71\\ \delta=10^{a}(1-\alpha)=10^{-0.18}(1-0.71)=0.192\end{array} \]  
Substituting \(\alpha\) and \(\delta\) achieved above into expression (5), a new form of creep function \(\Phi\) can be proposed:  
\[\Phi=\frac{\delta\cdot t^{1-\alpha}}{1-\alpha}=\frac{0.192}{1-0.71}t^{1-0.71}= 0.662t^{0.29}\]  
The initial instantaneous beam deflection \(y_{0}\) was equal to \(0.003\) cm, corresponding to the value of tensile stress \(\sigma\) developing in the rock beam at \(2.7\) MPa. As a result, the initial instantaneous modulus of deformation of the rock beam was determined as follows:  
\[y=\sigma\cdot\frac{l}{6E\cdot l_{\,l}<->}\ 0.003=2.7\frac{14^{2}}{6E\cdot 2}.\]  
Figure 3: Result of processed output data using Equation (16). We attain E = 14,700 MPa. Substituting the obtained results in Equation (13) we obtain  
\[y(t)=y_{0}\bigg{(}1+\frac{\delta}{1-\alpha}t^{1-\alpha}\bigg{)}=y_{0}(1+\Phi)=y_{ 0}\Big{(}1+0.662t^{0.29}\Big{)} \tag{19}\]  
Comparison of results from Equation (19) with the experimental retrieved results at different values of tensile stress was demonstrated in the form of curves expressing creep rock beam deflection and time relationship, as presented in Figure 4.  
The strain modulus of rock masses is considered essential input data in the analyses of rock mass behaviours [33]. It is possible to estimate it by carrying out field tests [34], or by referring to experimental relationships obtained from tables of rock quality classification as mentioned in [35; 36] (Rock Mass Rating); by [37] (Q--System); and by [38] (Geological Strength Index--GSI). Due to the time consuming and sophisticated characteristics of conducting field tests as reported by [39], the values were determined qualitatively based on classification schemes presented by [34; 35; 36; 37; 38; 39; 40]. To simplify rock classification procedures [41], a new method named GSI was proposed which concerns the input data to design underground construction in rock material. The sole system that is relevant to technical parameters, such as Mohr-Coulomb, Hoek-Brown strength parameters, or rock mass modulus, are expressed as the GSI, in accordance with [42].