# Blasting of Unstable Rock Elements on Steep Slopes
## 3 Results  
Starting from the antecedents cited in Section 2.4, the formula presented here for determining and dimensioning the blasting of an unstable rock element on a rock slope assumes the following expression:  
\[\text{PF}=\text{K}^{*}\left(\text{S}/\mathcal{O}_{\text{d}}\right)^{*}\text{R}^ {*}\text{E}^{*}\left(\text{F}^{*}\text{D}\right) \tag{4}\]  
where  
* K is a numerical coefficient depending on the rock behavior at failure;
* S is the spacing between two holes of the same row;
* \(\mathcal{O}_{\text{d}}\) is the drilling hole diameter;
* R is a coefficient referring to rock type;
* E is a coefficient referring to explosive features;
* F is the desired fragmentation effect;
* D is the desired displacement of the blasted material.  
It can be observed that (S/\(\mathcal{O}_{\text{d}}\)) represents the ratio of the rock's resistance surface to the surface (represented by the diameter of the hole) on which the pressure of the explosion gases is applied.  
K is taken as 0.0059. According to [11], the rock coefficient R takes the values shown in Table 2.  
Table 3, related to explosives, applies the same reference but reproduces the types of explosives currently used.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case Studies** & **Rock Type** & \begin{tabular}{c} **Total** \\ **Volume (m’)** \\ \end{tabular} & **Fragmentation** & \
\begin{tabular}{c} **Prevalent** \\ **Explosive Type** \\ \end{tabular} &
\begin{tabular}{c} **Drilling** \\ **Diameter (mm)** \\ \end{tabular} & **Spacing in Row (m)** \\ \hline Meiringen (Switzerland) & Limestone & 60,000 & high & ANFO & 85 & 3.0 \\ \hline Quebec motorway (Canada) & Precambrian andestic genesis & 800 & very high & ANFO & 63 & 1.5 \\ \hline Cravagliana (VC), Italy & Weathered gabbro rock & 2500 & very high & slurry & 41 & 1.25 \\ \hline Le Cave (VC), Italy—Slab & Porphyrock & 1300 & high & slurry & 41 & 1.1 \\ \hline Perrero (TO), Italy—Catas & Minute genesis & 640 & normal & dynamite & 34 & 1.0 \\ \hline Balmoreglio quarry (VB), Italy & Serizzo (genesis) & 6000 & normal & watergel & 51 & 2.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Overview of the main parameters.  
\begin{table}
\begin{tabular}{c l c} \hline \hline
**Class** & **Rock Type** & **R** \\ \hline
1 & quartzites and compact porphyries & 1.30 \\ \hline
2 & sound granitoid rocks, graises, basalts, gabbro rock & 1.00 \\ \hline
3 & compact limestone and dolomite, gres, highly cemented sandstone & 0.90 \\ \hline
4 & phyllites, hard shale day, serpentine & 0.80 \\ \hline
5 & marl and soft limestone, gypsum, poorly cemented sandstone & 0.50 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Division into classes for rock types.  
\begin{table}
\begin{tabular}{c l c} \hline \hline
**Class** & **Rock Type** & **R** \\ \hline
1 & quartzites and compact porphyries & 1.30 \\ \hline
2 & sound granitoid rocks, graises, basalts, gabbro rock & 1.00 \\ \hline
3 & compact limestone and dolomite, gres, highly cemented sandstone & 0.90 \\ \hline
4 & phyllites, hard shale day, serpentine & 0.80 \\ \hline
5 & marl and soft limestone, gypsum, poorly cemented sandstone & 0.50 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Division into classes for explosive types.  
To increase the degree of fragmentation of the blasted rock, as well as to move the heap of the blasted material, additional energy is needed, which is provided with an increase in the employed explosive. The coefficients F and D in Tables 4 and 5 increase the estimated value of PF according to these concepts.  
By applying Equation (4) to the real cases described in Section 2.4, the following results are obtained: