# Blasting of Unstable Rock Elements on Steep Slopes
## 2 Materials and Methods  
### Experimental Approach to Powder Factor (PF)  
Several approaches have been developed for estimating the PF in tunnel blasting and in open-air bench blasting, but not for the blasting of a single element on a slope. The PF permits summarizing information in a single parameter, even if in a very simplified way; it captures several conditions of the blasting pattern and provides an estimation regarding the blasting efficiency. Many contributions are available in the technical literature seeking correlations between PF and induced vibration, fragment size distribution, residual contour [3], and stability; as an example, key objectives in the drilling and blasting design are the determination of the powder factor, as well as the explosive weight and distribution in rock mass [4]; other studies examine the improvement of the blasting design for a more satisfying fragmentation, a more tolerable oversized fragments rate in relation to the overall blasted rock volume, and better bench stability [5; 6; 7], as well as the adoption of numerical methods for the quantitative assessment of the effectiveness of vibration reduction in line-drilling as a screening approach [8]. Interdependent factors should be studied by careful monitoring during field tests; fragmentation and environmental effects are influenced by the amount of powder factor; a higher amount of powder factor improves fragmentation and, thus, productivity--the blast-induced vibration and air-blast also rise with an increase in the powder factor. This impasse calls for an optimum powder factor for sustainable blasting operations [9]. Finally, effective parameters that influence the powder factor can be divided into three contributions, namely, rock mass, geometric, and explosive parameters [10]. Referring to the specific technical literature, [11] states regarding tunnel blasting that the PF depends on the blasting section, rock type, explosive type, and blasting pattern. The blasting section is the most relevant parameter and the PF can be estimated as follows:  
\[\text{PF}=\text{A}\,^{*}\,\text{B}\,^{*}\,\text{C}\,^{*}\,[(10/\text{S})+0.6] \tag{1}\]  
where  
* A is a coefficient that varies according to the rock type;
* B depends on the employed explosive type;
* C is related to the blasting pattern adopted;
* S is the area of the excavation section. * A, B, and C were tabulated based on the analysis of several real cases. More generally, referring to the existing formulas for the dimensioning of explosive charges, according to empirical study, these formulas include the following [12]:  
* A coefficient characteristic of the rock to be blasted;
* A coefficient characteristic of the employed explosive;
* A coefficient of \"effect\" referring to the result to be obtained with the blasting (size distribution of the blasted material, width of the zone of influence of the charge);
* A characteristic dimension of the blasting pattern geometry (normally, the line of least resistance), eventually raised to a power, or a polynomial combination of several characteristic dimensions. The more general expression of such formulas may be written as follows:  
\[\text{C}=\text{k}^{\prime}\,\text{*}\,\text{k}^{\prime\prime}\,\text{*}\, \text{k}^{\prime\prime\prime}\,\text{*}\,\text{f}(\text{I}) \tag{2}\]  
where  
* C is the explosive charge;
* k\({}^{\prime}\) represents a coefficient referring to the rock type;
* k\({}^{\prime\prime}\) depends on the employed explosive type;
* k\({}^{\prime\prime\prime}\) is the \"effect\" coefficient for fragmentation;
* I is the characteristic dimension of the rock block to be blasted;
* f(I) is a function of \"I\" raised to a power of a number varying from 2 to 3, with lower values associated with blasting along a defined failure surface and higher values referring to blasting volume. When the exponent of f(I) is 2, Equation (2) refers to a simple detachment effect, mainly based on the tensile strength of the rock. When, instead, the exponent is 3, (2) refers to a volume to be blasted.