Jack Caldwell - Mining Engineer - Robertson GeoConsultants

Monte Carlo is a principality where you can go and gamble to the profit of the royalty of a small kingdom. It is also the most powerful way to quantify the probability distribution of an outcome of an essentially random process.

I was introduced to the Monte Carlo process in an informal way about thirty-five years ago when we were engaged as consultants to quantify the probability of failure of slopes of varying inclination of a proposed coal mine in Texas. We had many boreholes drilled and profiled by others. They had rather crudely logged the soil strata above the coal layers as sand, silt, or clay. So we went in and drilled, cored, and logged a few more boreholes. We made sure our descriptions of the soil layers were accurate. For example there were more soil types than simple sand silt, and clay. There were silty sands, sandy clays, and every conceivable combination of sands, silts, and clays.

We had the original loggers log the materials as sand, silt, or clay and we set up a table that quantified the probability that their sand, silt or clay was in fact a silt sand, and silty clay, etc.

Next we did a series of lab tests to quantify the strength of the many various soil types we identified. Hence we quantified the probability of the strength of a particular soil type (ours) and hence of a sand, silt, or clay as defined by the original loggers.

Thus equipped, we proceeded to calculate the factor of safety of a slope composed of the soils as originally logged. We did this by crude computing. We set up a program that read the original log, and assigned by random numbers and the correlations we had established between their soil types and ours, strength to each particular soil layer. Hence it was easy to calculate the factor of safety of a slope of varying inclination. Do this many times over and you can define the probability of failure of each profile for a given slope inclination.

I have described this process in great detail in a paper that is available at this link.

The next exposure I had to Monte Carlo simulation was when a big oil company engaged me to work out the probable cost of cleaning-up one of their contaminated sites. Over three days of intense deliberations, I and an expert team estimated, mostly by subjective opinion, the probable range of costs for each and every work item involved in cleaning up the site.

Then a father-son team from Kansas City cameto help us. They had computerized the Monte Carlo method and its application to probabilistic cost estimating. They took our estimates of cost ranges for each activity, fed them into their code and produced probability curves for the overall cost.

Keep in mind that the essence of the Monte Carlo method is that you run the cost estimate many, many time. For each run you allow the cost of a particular activity to be assigned by a random number generator. Combined, this yields a single cost estimate. Done a sufficient number of times and you can plot a probability distribution curve of the cost.

This process is now standardized and incorporated into many commercially available computer code. It is easy to compute if you have done the hard work of defining the system and estimating the range of outcomes associated with particular activities or engineering works.

Today I cogitated on the application of Monte Carlo methods to groundwater predictive modelling. Seems the groundwater profession does not routinely use or apply Monte Carlo methods. I am told this is because it is too time-consuming and too expensive to do. Clients won’t pay consultants to do the work.

This is ridiculous. Groundwater impacts are the most significant of mining impacts. Predictive modelling is the most difficult of mining predictive activities. Why this artificial constraint on modelling of things that very much influence our decision making regarding mining processes, facilities, and impacts?

The procedures are standard, The application has been refined over thirty years of application. Yet still, due to budget constraints and professional reticence, we do not apply Monte Carlo methods as a routine groundwater modelling method in support of risk assessment and decision making.

We have come, we have conquered, yet we have not learnt or applied the method. I predict this is the future challenge for groundwater modellers. If they do not do it, so much their shame and failure. And a black eye for the whole mining industry.