# Evaluation of Rock Brittleness Index under Dynamic Load
## 1 Introduction
Based on the post\(-\)peak failure characteristics of brittle rocks, [PERSON] and [PERSON] [8; 25] considered the relative magnitude and absolute rate of post\(-\)peak stress drop in stress-strain curves, and proposed brittleness indices \(B_{4}\) and \(B_{5}\). Based on the total stress-strain curve, [PERSON] [26] proposed a brittleness index, \(B_{6}\), based on stress reduction rate and elastic energy. Based on the energy relationship, [PERSON] and [PERSON] [22] proposed the brittleness index \(B_{7}\), which measured rock brittleness by the ratio of elastic energy to total energy at failure. [PERSON] and [PERSON] [27] proposed brittleness indices \(B_{8}\) and \(B_{9}\) under two different failure modes, considering the energy balance relationship in the post\(-\)failure region of the rock. [PERSON] [28] defined brittleness as the ability of rock to accumulate elastic energy in the pre\(-\)peak stage and self\(-\)sustaining fracture propagation in post\(-\)peak stage, and proposed brittleness indices \(B_{10}\) and \(B_{11}\). The above brittleness indices indican be obtained by conventional mechanical tests (mainly uniaxial compression tests). In addition, the brittleness index of rock also includes a brittleness index based on mineral composition, a brittleness index based on elastic parameters, etc., which will not be discussed here. \begin{table}
\begin{tabular}{l l l} \hline
**Brittlness Index** & **Parameter** & **Source** \\ \hline \(B_{1}=\sigma_{c}/\sigma_{p}\) & \(\sigma_{c}\) is uniaxial compressive strength, \(\sigma_{l}\) is uniaxial tensile strength & [PERSON] and [PERSON] (1974) [22] \\ \(B_{2}=\sigma_{c}/\sigma_{c}/\sigma_{2}\) & \(\sigma_{c}\) is the recoverable strain after loading, \(\epsilon_{c}\) is the total strain of loading & [PERSON] and [PERSON] (1974) [22] \\ \(B_{2}=\epsilon_{c}/\sigma_{p}\) & \(\sigma_{p}\) is the peak intensity, \(\sigma_{c}\) is the residual strength & [PERSON] and [PERSON] (2015) [8] \\ \(B_{5}=(\sigma_{p}-\sigma_{r})\times[\log[k_{\mathrm{ex}}/10]\) & \(k_{\mathrm{ex}}\) is the slope of a straight line from the peak strength point to the starting point of & [PERSON] and [PERSON] (2015) [8] \\ \(B_{6}=\mathrm{P}_{\mathrm{post}}+B_{\mathrm{E}}=\frac{(\gamma-\alpha)}{\alpha- \gamma_{p}}+\frac{(\gamma_{p}-\alpha)}{\alpha+\gamma_{p}}\) & \(\frac{(\gamma_{p}-\alpha)}{\alpha+\gamma_{p}}\) & \(\frac{\sigma_{p}}{\alpha+\gamma_{p}}\) is the peak stress, \(\sigma_{p}\) is the residual strain & [PERSON] (2017) [26] \\ \(B_{7}=\mathrm{W}_{\mathrm{r}}/\mathrm{W}_{\mathrm{l}}\) & \(W_{\mathrm{l}}\) is recoverable strain energy. \(W_{\mathrm{l}}\) is the total strain energy \\ \(B_{8}=(M-\mathrm{E})/M\) & \(E\) is the pre\(-\)peak elastic modulus, and \(M\) is the post\(-\)peak elastic modulus & [PERSON] and Das (1974) [22] \\ \(B_{9}=E/M\) & \(U_{\mathrm{s}}\) is the fracture energy, \(U_{\mathrm{d}}\) is the dissipated energy, \(U_{\mathrm{s}}\) is the elastic strain energy, \(U_{\mathrm{d}}\) is the energy absorbed or released after the peak & [PERSON] (2016) [28] \\ \(B_{11}=U_{\mathrm{s}}/(U_{\mathrm{d}}+U_{\mathrm{d}})\) & \(U_{\mathrm{s}}\) is the energy absorbed or released after the peak & [PERSON] (2016) [28] \\ \hline \end{tabular}
\end{table} 
Table 1: List of common brittleness indices. In practical engineering, rock mass is often subjected to dynamic load, and many researchers have carried out a significant number of studies on the relevant mechanical characteristics of rock under dynamic load [29; 30; 31]. However, studies on brittleness change and brittleness index tend to focus on static loading rather than dynamic loading. [PERSON] [32] carried out dynamic compression tests on sandstone and analyzed the brittleness characteristics of coal measure sandstone under dynamic load. However, there has been no discussion regarding which brittleness index is suitable for measuring rock brittleness under dynamic load.