A Risk Evaluation Approach for Pit Slope Design

The determination of the acceptable slope angle for open pits is a key aspect of the mineral business, as it implies seeking the optimum balance between the additional economic benefits gained from having steeper slopes, and the additional risks resulting from the consequent reduced stability of the pit slopes. The difficulty in determining the acceptable slope angle is related to geological uncertainties within the rock mass. These uncertainties are accounted for in the process of slope design and different methodologies have been used for this purpose. The traditional approach is that based on the calculation of the factor of safety (FOS), where the uncertainties are accounted for through the selection of a FOS for design larger than 1.0. A methodology more frequently used in recent years is that based on the calculation of the probability of failure (POF) of the slope, where input parameters to the deterministic model of the previous approach are represented by probability distributions to assess the probability of having a FOS less than a critical value representing the failure of the slope. Although in the POF approach uncertainties are partially accounted for, a major drawback that still persists in both the FOS and POF methodologies is the difficulty to define an adequate acceptability criterion. A methodology that aims to solve this problem is the risk analysis approach. In slope design, risk can be defined as the POF of the slope combined with the consequence or potential loss associated with the failure of the slope. The consequences can be two fold: personnel impact and economic impact. The proposed methodology of risk evaluation considers the use of non formal sources of information (engineering judgment, expert knowledge) together with hard data for the assessment of both components of the risk equation. Methods such as fault and event tree analysis are used for this purpose. The approach includes four main tasks: (1) Evaluation of the total probability of failure (POF) representative of the stability conditions of slopes. (2) Evaluation of the consequences of slope failure on safety of personnel. (3) Evaluation of the consequences of slope failure in terms of economic losses associated with impact on equipment and production. (4) Evaluation of options for risk mitigation for those cases where acceptable risk levels are exceeded. This paper describes the risk analysis methodology for slope design and presents some examples of actual projects where the methodology has been successfully applied. 2. FACTOR OF SAFETY, PROBABILITY OF FAILURE AND RISK ANALYSIS 2.1. Uncertainties in Slope Design The optimum design of a pit requires the determination of the most economic pit limit which normally results in steep slope angles as in this way the excavation of waste is minimized. In general, as the slope angle becomes steeper, the stripping ratio (waste to ore ratio) is reduced and the mining economics improves. However, these benefits are counteracted by an increased risk to the operation. Thus the determination of the acceptable slope angle is a key aspect of the mining business. The difficulty in determining the acceptable slope angle stems from the existence of uncertainties associated with the stability of the slopes. Table 1 summarizes the main sources of uncertainty in pit slopes. These uncertainties are accounted for during the process of design of the slopes and different methodologies have been used for this purpose. The uncertainty might be due to a random variability of the aspect under analysis or to lack of knowledge of that aspect. Field data collection and site investigations are used to reduce these uncertainties and to define the inherent natural variability. Table 1. Sources of Uncertainty in Pit Slopes Slope Aspect Source of Uncertainty Geometry Topography Geology / Structures