Other Readings

By Jack Caldwell - Mining Engineer - Robertson GeoConsultants

There are many books, papers, computer code user manuals, and guidelines on all the topics we deal with above. The best are the ASTM standards for groundwater modelling. Consult them if you need more detail.

Conceptual models are key aspects of mine modelling, analysis, and decision making. With our limited thinking ability, we need concepts, or models, of reality before we can fully comprehend, understand, and mentally manipulate reality.

Thus arise the key questions:

· What is a conceptual model?

· How do we formulate a conceptual model?

The answers depend on whom you ask. There are different answers if the responder is a mining engineer, a civil engineer, or a groundwater expert. The mining engineer needs a conceptual model of the ore body so that he may formulate ways to mine the ore. The civil engineer, charged with designing, operating, and closing the mine’s waste disposal facilities, needs conceptual models to evaluate slope stability, erosion, seepage, and impact on the environment. The groundwater specialist needs a conceptual model so that they may do those groundwater analyses that predict impact or absence of impact on precious water resources at and around the mine.

Like any model, a conceptual model is a pale reflection of reality. A model is an attempt to capture the essential features of a real situation in words, figures, and numbers. Being a model, it may cannot and need not replicate the infinite variety and complexity of reality. It is a model after all: a simplification of essential aspects of reality. A toy that helps us think, analyze, judge, and decide. For if a conceptual model has any use, it is to be the basis of numerical calculations and analyses.

If you need to calculate the factor of safety of the perimeter slope of a tailings facility, you need a conceptual model of the real situation so that you can put pen to paper, or turn on and run the computer code, and do the numerical calculations that result in a number that is the ratio of resisting to disturbing forces.

If you need to quantify the change in the concentration of a contaminant emanating from the waste rock dump, seeping through attenuative clays, and emerging into a creek where the salmon spawn, you need a conceptual model before you undertake simplistic calculations using high-school maths or sophisticate computer codes.

So what is a conceptual model? Simply stated, it is a description in words, figures, and numbers of reality. Perforce, it is a simplified representation of reality. It is a replication of reality that our limited, human mind can conceive and work with. It is the basis of a further step in science and engineering: namely the process of using equations and numerical analyses to quantify the probable performance of reality. And maybe study the range of possible and statistically probable performances of the real thing.

In the mining context, a conceptual model must incorporate at least the following.

The domain of the mining facility under consideration. Examples include: the distribution of rich ore, the open pit slope; the tailings impoundment and seepage therefrom; and the groundwater hydraulic regime and the passage of contaminants from the waste facility to receptors.

The Boundary Conditions. Examples include: the location of stata that contain valuable ore; pools on the tailings facility that generally are kept at an established elevation; and the watershed divides away from which all groundwater seeps.

The Geology and Its Strata. Examples include: the soil or rock layers in which the valuable gold, platinum, oil, or iron ore resides; the aquifers and aquitards that allow and limit flow of pollution from waste facilities; and the faults that may limit groundwater seepage and force water to the surface to springs, creeks, and rivers.

The Properties of the Principal Strata. Examples include: the ounces of gold per ton of rock; the pollution concentrations in waste facility waters; and the hydraulic conductivity of the soils & rocks through which seepage will occur.

To formulate your conceptual model, first gather all the data you can about the field situation you need to model and make decisions about. Document these data in words, figures, and tables. That is your conceptual model.

Get colleagues and peer reviewers to examine your conceptual model. For your concepts may be faulty; your understanding of reality limited; you intellect too rusty to jump to elegant models; and your prejudices too ingrained to admit your preferences and biases.

Once you have an agreed conceptual model, you may proceed to the next step: definition and selection of numerical models and analytical methods to put numbers to the performance of the model and hence a pale numerical replication of reality.

But that is another topic.