# New Method to Estimate Rock Mass Deformation Modulus Based on BQ System
## 4 Estimation of Deformation Modulus Based on BQ  
It can be seen from the above that the rock masses at the test sites are mainly moderately or slightly weathered, with only two being intensely weathered. The BQ values at the test sites range between 284 and 681, corresponding to rock mass ratings of I to IV. Table 8 shows the range and mean value of the deformation moduli obtained via the plate loading tests of rock masses of different grades at the three hydropower stations, and Figure 2 reflects the relationship between these deformation moduli and the BQ value. As shown in Figure 2, the relationship between the deformation moduli of the rock masses and their BQ values can be expressed as the power function:  
\[E_{m}=2\times 10^{-8}\times BQ^{3.302}\ \ \ R^{2}=0.6066 \tag{3}\]  
where \(E_{m}\) is the deformation modulus of the rock mass in GPa. Although the rock mass deformation modulus has a good relationship with the BQ value, it still lies within in a certain range at the same BQ value. It is therefore necessary to fit upper and lower bounding curves to the scatter data (Figure 3). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Number** & **Test Position** & **Rock Types** & **Degree of Weathering** & **Deformation Modulus GPa** & **Loading Direction** & **BQ Value** \\ \hline E07 & PD03 (15 m) & & & 6.29 & 397 \\ E08 & PD03 (18 m) & & 7.80 & & 434 \\ E09 & PD03 (24 m) & & 9.74 & & 446 \\ E13 & PD04 (15 m) & & 4.36 & & 391 \\ E14 & PD04 (22 m) & & 4.72 & & 458 \\ E15 & PD04 (28 m) & & 5.73 & & 422 \\ E10 & PD03 (44 m) & marble & & 11.75 & & 446 \\ E11 & PD03 (58 m) & & 13.71 & & 550 \\ E12 & PD03 (65 m) & & slightly & 14.34 & & 489 \\ E16 & PD04 (51 m) & & 12.51 & & 415 \\ E17 & PD04 (64 m) & & 18.86 & & 531 \\ E18 & PD05 (70 m) & & 22.39 & & 452 \\ E01 & PD01 (8 m) & & 6.36 & vertical & 403 \\ E02 & PD01 (17.5 m) & & 9.53 & & 415 \\ E06 & PD02 (50 m) & & 7.53 & & 385 \\ E05 & PD02 (38 m) & & 7.14 & & 415 \\ E19 & PD05 (20.5 m) & & 5.80 & & 434 \\ E20 & PD05 (29 m) & & 7.21 & & 452 \\ E23 & PD06 (53.2 m) & & 8.82 & & 489 \\ E24 & PD06 (64 m) & & 12.39 & & 550 \\ E03 & PD01 (48 m) & & 33.86 & & 580 \\ E04 & PD01 (71 m) & & 36.62 & & 598 \\ E21 & PD05 (52 m) & & 21.65 & & 458 \\ E22 & PD05 (63 m) & & 23.14 & & 470 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Deformation modulus of rock mass at Zhen’an pumped storage power station. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rock Mass Rating** & **I** & **II** & **III** & **IV** \\ \hline Average BQ value & 610 & 493 & 415 & 313 \\ Number of samples & 24 & 19 & 20 & 3 \\ Minimum value & 48.99 & 23.14 & 24.05 & 8.34 \\ Maximum value & 10.72 & 4.72 & 0.90 & 1.62 \\ Average value & 28.15 & 14.31 & 8.56 & 4.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Deformation modulus of rock mass at the Zhen’an pumped storage power station. In addition, the deformation moduli suggested by the Chinese current specifications are also scattered in Figure 3. \"Code 1\" in the figure refers to the Chinese Standard for engineering classification of rock masses (GB/T50218-2014) [14]. It can be seen that the recommended values of the specification are located between the fitting median and the highest values, more closely approaching the upper fit line. As mentioned before, the deformation test results quoted by Code 1 are derived from various rock mass projects, most of which require a relatively lower test load than is relevant for hydropower projects. The Code 1 dataset will have yielded relatively high values because a lower test load corresponds to a higher deformation modulus, especially  
Figure 3: Measured and suggested values and fitting curve. Figure 2: The relationship between deformation modulus and BQ value. for a high-quality rock mass (the first loading-unloading cycle should be excluded, as most joint closure takes place during this stage).