# How Mathcad Rocks: Mining (Part I)

Some time last year, I was brainstorming for some interesting topic to present.  We were approaching our annual technical forum, where the Mathcad team gathers in Needham, MA (PTC headquarters) for three days of knowledge exchange.  For half of one day, each application engineer gets up and shares something cool.  It can be a neat trick, fun demos, interesting content – really  just anything you want.

So I thought and thought and decided to focus on mining (of minerals, though data mining would be another fun topic with Mathcad).  I decided on mining for a few reasons.  The sales rep who covers the Rocky Mountains states had mentioned he comes across a lot of mining customers.  And there wasn’t much Mathcad content in that area.  So I did a quick Google search.  When I searched for “Mathcad mining,” I basically get one result.  CADCAM.com.au is an Australian site offering CAD/CAM ideas and they had a page on Mathcad.  And the topic is on mining, as it’s a big industry there.

The aforementioned page centered around rock strength.  As you can imagine, this is clearly a very critical factor.  The page then walks through a simple calculation of calculating the gravitational force (F=m*g) and then determining the stress acting on a rock given a force and area.  Again, these are all very important concepts, but I wished for something more detailed.  And something more specific to mining.

Now because I have no background on mining, I decided that the best place to go was the library.  I was able to immerse myself there for a few days and learn as much about mining as I could.  As expected, mining engineering is full of math, which in turn means Mathcad is perfectly suited for it.  It’s also a very broad topic, as many factors have to be considered when you’re mining.  Rock strength is important, as we’ve mentioned.  So is the hoist system you use to haul out the mined material out.  And ventilation, sometimes described as “the lifeblood of a mine,” is obviously crucial for the safety of miners.  I mention those three topics because those are the three topics on which I created Mathcad worksheets!

Let’s go through each topic.  First, rock strength, or pillar strength.  So say you’re mining for coal.  I imagined that you would just start digging and digging and basically end up with a big underground hole.  Well, if you did that and the hole got too big, you run into the chance the earth above you could cave in.  So what you actually need to do is leave behind some material to hold up the hole (or “room” in mining speak).  The material that you leave behind are called “pillars.”  You can read about room and pillar mining here.  The width and spacing of these pillars depends on the material, as you need to make sure that the pillar will be able to hold up the weight of the earth above it.

To calculate the compressive strength of coal, we use empirical relationships that come from experimental data.  An example would be the Holland Gaddy pillar strength.

In this equation, K is the Gaddy constant (in PSI), and the pillar width and height (w­­pillar and H) need to be expressed in inches.  The result is is in PSI.  As Mathcad users already know, unit conversion is handled automatically.  Well, assuming that you defined the pillar width and height in inches, the result would have an extra square root of inches in the denominator.  What we need to do is strip out the units.

The beauty of this approach is that pillar width and height can actually be defined in any units of length that you want.  Maybe you choose to define it in centimeters.  By dividing out inches, you’re converting the terms both to inches and also stripping the units.

Using this approach, I can quickly calculate the pillar strengths using other formulas – Holland and  Bieniawski.  If we want safety factors, we calculate the stress on the pillar.  PTC Mathcad’s units intelligence again comes very handy here.  We take the specific gravity and multiply it by the density of water (easy to memorize in SI units) to get the density of the coal.  And then multiply by acceleration due to gravity and depth of the coal seam to get the premining stress.  The actual pillar stress takes into account that the pillar is holding up more material than just the material directly above it.  We can specify the results to be returned in PSI.

I can divide those values by the stress of the earth above the pillar to get my safety factors.

Ok, I’ve tired myself out enough for a day.  In the next blog (Part II), I will talk about some mining examples in hoisting and ventilation calculations!

For a copy of the Mathcad worksheet I created for the pillar strength example, refer to the PTC Communities document.

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