# Blasting of Unstable Rock Elements on Steep Slopes
## 2 Materials and Methods
### Design Criteria  
Even if, in the case of blasting an unstable rock element on a slope, the design criterion is most of the time more similar to ornamental stone cutting, the most straightforward parameter to check a blasting scheme remains the powder factor (PF). It is important to conduct possible surveys with direct access to the slope with the help of climbers (specifically for joints conditions) and also by full recognition by means of unmanned vehicles (drones) to fully build a digital optical twin to describe distances and volumes; the use of drones is now complimentary for quick and complete volume descriptions and for supporting blasthole pattern configurations. Geostructural, visual, and topographical surveys are also essential after blasting in order to verify the residual condition of joint surfaces and remove, by means of scaling techniques, unstable small blocks in order to finally proceed with the eventual protective/reinforcing works (typically drapery systems) and monitoring of major joints (crackmeters, topographic targets). Moreover, residual risk assessment after scaling and reinforcing remains of great concern for civil infrastructure, such as roads and tunnels [15] or for quarry yards. The blasting criterion aims in this case to simply detach from the mountain the rock to be demolished, exploiting gravity. Compared to a situation where fragmentation is sought (e.g., a blasting operation for aggregates or industrial minerals), the operating philosophy is completely different: here, the effects sought are only those of detachment and, possibly, of rock displacement, which must detach from the original rock mass, falling downstream with the help of gravity; this operation is correctly referred to as cutting and not as demolition. As proof of this, the specific consumption found in these cases is much lower than normal for industrial materials. The cut is normally obtained by a series of side-by-side holes, often of small diameter (normally ranging from 48 mm to 51 mm). The blasting design essentially consists of determining the distance between the holes and the charge per hole. A very simple design method based on a quasi-static approach to the explosion phenomenon is now described. It is assumed that the force generated by the pressure of the explosion gases in the holes must overcome the tensile strength of the rock between two adjacent holes, as exemplified in Figure 1.  
The pressure Ph inside the hole is a function of the specific pressure of the explosive (Pe). The input parameters are as follows:  
* Type of explosive. * Drilling (\(\mathcal{O}_{\mathrm{d}}\)) and explosive (\(\mathcal{O}_{\mathrm{e}}\)) diameter (i.e., cartridge diameter). * Length of hole (L\({}_{\mathrm{h}}\)). * Explosive length (L\({}_{\mathrm{e}}\)). * Tensile strength of rock (T). By imposing the static equilibrium of the system, the following formula for calculating the Spacing (S) between the holes in the same row can be obtained [16]:  
\[\mathrm{S}=\mathcal{O}_{\mathrm{d}}+\frac{\mathcal{O}_{\mathrm{d}}}{\mathrm{ kT}}\mathrm{P}_{\mathrm{h}}\rho_{\mathrm{e}}\bigg{(}\frac{\mathrm{L}_{\mathrm{e}}}{ \mathrm{L}_{\mathrm{h}}}\bigg{)}\left(\frac{\mathcal{O}_{\mathrm{e}}}{ \mathcal{O}_{\mathrm{d}}}\right)^{2} \tag{3}\]  
where  
* \(\rho_{\mathrm{e}}\) is explosive volumetric mass;
* k is a coefficient that takes into account the effect of the alignment of the holes, which ranges from 0.5 (if the spacing between the holes is less than 10
* \(\mathcal{O}_{\mathrm{d}}\)) to 1 when the spacing is higher (more than 30-40  
The tensile strength of rocks is not always easy to obtain, especially when considering factors like schistosity. Schistose rocks indeed pose challenges due to their varying strengths in different directions. In the first hypothesis, we can refer to the uniaxial compressive strength, assuming that the tensile strength is on average 1/20 of the uniaxial compressive strength.