# New Method to Estimate Rock Mass Deformation Modulus Based on BQ System
## 4 Estimation of Deformation Modulus Based on BQ
Code 2 in the figure refers to the Chinese Code for engineering geological investigation of water resources and hydropower (GB50487-2008) [22], which also gives proposed values for the rock mass deformation modulus according to the rock mass quality classification. Although this classification uses an independent system, it is roughly consistent with Code 1 when transforming the classification index into a BQ value (Table 9). As shown in Figure 3, the deformation moduli suggested by Code 2 are very close to the fitting curve, showing that Formula (3) established in this paper provides good predictions of the deformation modulus of a dam foundation rock mass based on the BQ value. Indirect Estimation of the Deformation Modulus Based on the Relationship between BQ and Other Classification Schemes  
Many methods of indirect estimation of the deformation modulus have been studied and used in practical engineering, including the RMR and Q-system methods. Table 10 lists the formulas widely used in the above methods. Code 1 puts forward a regression equation relating BQ to RMR based on statistical analysis of more than 200 sets of measured data:  
\[BQ=80.786+6.0943 RMR\ \ r=0.81 \tag{4}\]  
[PERSON] et al. (2012) also established a correlation between BQ and RMR when studying the rock mass quality at Maerdang hydropower station:  
\[RMR=1.4185 BQ^{0.6241}\ \ r=0.8245 \tag{5}\]  
The above two formulas establish a bridge between BQ and RMR. Also, RMR has the following correlations with the Q-system classification:  
\[RMR=15 lgQ+50 \tag{6}\]  
These relationships and the correlations listed in Table 10 can be used to develop a series of formulas for predicting the rock mass deformation modulus from the BQ value (Table 11). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Correlations (E\({}_{\text{m}}\) in GPa)** & **References** \\ \hline \(\text{E}_{\text{m}}=2\text{RMR}-100\) & \(\text{RMR}>50\) & [PERSON] (1978) [1] \\ \(\text{E}_{\text{m}}=10^{(\text{RMR}-10)/40}\) & \(\text{RMR}\leq 50\) & [PERSON] and [PERSON] (1983) [23] \\ \(\text{E}_{\text{m}}=300\text{exp}\ (0.07\text{RMR})\times 10^{-3}\) & [PERSON] (1993) [24] \\ \(\text{E}_{\text{m}}=0.1(\text{RMR}/10)^{3}\) & [PERSON] et al. (1999) [25] \\ \(\text{E}_{\text{m}}=0.0097\text{RMR}^{3.54}\times 10^{-3}\) & [PERSON] (1997) [26] \\ \(\text{E}_{\text{m}}=0.0736\text{exp}(0.0755\text{RMR})\) & [PERSON] et al. (2003) [7] \\ \(\text{E}_{\text{m}}=100\text{Q}_{1}^{1/3}\) & \(\text{Q}_{\text{c}}=\text{Q}(\text{g}_{\text{c}}/100)\) & [PERSON] (2002) [2] \\ \(\text{E}_{\text{m}}=100\left(\frac{1-D^{2}}{1+\left(\frac{1-D  
Figure 4 shows the curves derived from Formulas (7)-(14) to predict the deformation modulus of a rock mass, plus the measured mean values of the deformation modulus for class I to V rock masses according to Code 1 and the values recommended by Code 2. It should be noted that Code 1 is a general standard that is applicable to various rock projects, while Code 2 was designed for dam foundations, where there is a heavy load. This difference may be the main reason for the difference between the values recommended by the two codes. As mentioned above, the deformation modulus is related to the test load. Within a certain range, the modulus of a poor quality rock mass may differ little under different loads. However, for a rock mass of good quality, a large test load can cause more deformation than a small load, thus making the modulus value lower. In general rock mass engineering (not including projects with a large load such as the foundation of a high dam), it can be seen from Figure 4 that Formulas (8), (10) and (11) provide good fits for the measured mean values (according to Code 1); Formulas (3), (12)