Numerical groundwater models are regularly used to predict pore water pressures (PWPs) in open pit mines. The resulting PWPs are used in geomechanical analyses to evaluate slope stability and the need for active depressurization. These groundwater models tend to be extremely complex, both from a hydrogeological and a numerical point of view.
Important efforts have been made to improve the quality of the modelling predictions, including the use of highly discretized 3D models and the representation of hydromechanical coupled processes, if required. That said, there is still a tendency to rely exclusively on deterministic models, which limits the capacity to quantify and manage the underlying uncertainty.
Stochastic predictions of PWPs for an open pit project located in Chile are presented in Figures 1 to 4 to demonstrate the advantages of performing calibration-constrained Monte Carlo (or quasi-Monte Carlo) simulations. These figures give important information about the uncertainty of the modelling results, including the fact that the degree of uncertainty of the PWPs decreases with time in most piezometers located close to the excavation (e.g. piezometer VWP-1 in Figure 1). This behaviour is explained by the nature of the groundwater flow around the open pit, which tends to be highly conditioned by the existing seepage faces and active depressurization systems. On the contrary, the uncertainty of the calculated PWPs increases with time in piezometers that are located further away from the open pit and in the proximity to relevant geological structures (e.g. piezometer VWP-2 in Figure 2).
The stochastic simulations also reveal how the best calibrated model could display PWPs in the upper range of the stochastic results for certain periods of time (conservative result from a geomechanical point of view) and in the lower range for other periods (optimistic result from a geomechanical point of view), as shown for piezometer VWP-3 in Figure 3. This result refutes the idea that a conservative historic behaviour will necessarily lead to conservative predictions, and that the best calibrated model represents a middle point within the expected uncertainty. All of this corroborates the advantages of performing stochastic simulations, especially if the available field observations are limited.
Finally, it is concluded that the uncertainty of the decrease in PWPs grows with time in all piezometers around the mining operation (e.g. piezometer VWP-1 in Figure 4). This result reinforces the importance of analyzing in detail the type of predictive variables to consider for the objectives of the study: PWPs, decrease of PWPs, and/or rate of decrease of PWPs.
Adding stochastic capabilities to the existing MODFLOW-USG open pit model took less than a day thanks to the use of GSMOD. Running times were in the order of days due to the use of parallel computing. Preliminary results could be revised after just a couple of hours in order to correct potential issues and to have an idea of how the final stochastic results would look like.
Figure 2: PWPs in piezometer VWP-2 for 500 model runs (212 model runs with NRMS < 7.5%)
Figure 3: PWPs in piezometer VWP-3 for 500 model runs (212 model runs with NRMS < 7.5%)
Important efforts have been made to improve the quality of the modelling predictions, including the use of highly discretized 3D models and the representation of hydromechanical coupled processes, if required. That said, there is still a tendency to rely exclusively on deterministic models, which limits the capacity to quantify and manage the underlying uncertainty.
Stochastic predictions of PWPs for an open pit project located in Chile are presented in Figures 1 to 4 to demonstrate the advantages of performing calibration-constrained Monte Carlo (or quasi-Monte Carlo) simulations. These figures give important information about the uncertainty of the modelling results, including the fact that the degree of uncertainty of the PWPs decreases with time in most piezometers located close to the excavation (e.g. piezometer VWP-1 in Figure 1). This behaviour is explained by the nature of the groundwater flow around the open pit, which tends to be highly conditioned by the existing seepage faces and active depressurization systems. On the contrary, the uncertainty of the calculated PWPs increases with time in piezometers that are located further away from the open pit and in the proximity to relevant geological structures (e.g. piezometer VWP-2 in Figure 2).
The stochastic simulations also reveal how the best calibrated model could display PWPs in the upper range of the stochastic results for certain periods of time (conservative result from a geomechanical point of view) and in the lower range for other periods (optimistic result from a geomechanical point of view), as shown for piezometer VWP-3 in Figure 3. This result refutes the idea that a conservative historic behaviour will necessarily lead to conservative predictions, and that the best calibrated model represents a middle point within the expected uncertainty. All of this corroborates the advantages of performing stochastic simulations, especially if the available field observations are limited.
Finally, it is concluded that the uncertainty of the decrease in PWPs grows with time in all piezometers around the mining operation (e.g. piezometer VWP-1 in Figure 4). This result reinforces the importance of analyzing in detail the type of predictive variables to consider for the objectives of the study: PWPs, decrease of PWPs, and/or rate of decrease of PWPs.
Adding stochastic capabilities to the existing MODFLOW-USG open pit model took less than a day thanks to the use of GSMOD. Running times were in the order of days due to the use of parallel computing. Preliminary results could be revised after just a couple of hours in order to correct potential issues and to have an idea of how the final stochastic results would look like.
Figure 1: PWPs in piezometer VWP-1 for 500 model runs (212 model runs with NRMS < 7.5%)
Figure 4: Decrease in PWPs in piezometer VWP-1 for 500 model runs (212 model runs with NRMS < 7.5%)
