Designing large long-hole stopes in the 70’s

It might surprise young mining professionals to learn that we were using Finite Element Analysis to design large long-hole stopes more than forty years ago. Admittedly, we struggled to determine the stress field and had to assume a homogenous rock mass, but the results still pointed the way for installing rock support or modifying the stope shape.

Each project began with three table-sized sheets of paper. The stope was drawn in the centre of the first sheet, at about the size of a milk carton. Then dots (nodes) were added around the perimeter of the stope shape and triangles were drawn around it from the nodes out to the edge of the sheet of paper, each ring of triangles bigger than the last. The second, intermediate, sheet just reproduced the outer ring of triangles and added more to the limits of the paper. The third sheet picked up the triangles from the second, and extended the array of triangles to a final boundary, which was a rectangle. Thus ended day two (or three) of the project for the young engineer.

Next came numbering. Every node was given a number, starting in the lower left hand corner, and working in expanding circles. It was important not to miss a node, because part of the computation involved a matrix inversion that had its bandwidth determined by the maximum difference in node numbers around any triangular element. After a day spent numbering, it might all have to be re-done if a node had been missed. The computer could not handle large bandwidths.

Then the x-y co-ordinates of each node had to be measured with a scale rule and entered into a data sheet. Hundreds and hundreds of them. We were now into the second week. The data sheets became punch cards, thanks to the ladies in the punch room. They were inserted into the programme card set, with other cards defining rock properties and the stress field. Then the project was ready to run, always on afternoon shift, because the commercial department owned the computer. The young engineer stood expectantly outside the viewing window of the computer room, watching the programme loaded by the operator. If there was an error, and there always was, a replacement punch card could be made on the spot using a manual card puncher.

The programme took all night to run. If it didn’t drop out, which it often did, a printout of computer paper about 50 mm thick was on the young engineer’s desk next morning. Then followed several days of plotting point stresses back onto the inner grid, and manually drawing contour diagrams. These were handed to the senior geotech engineer, while the young engineer turned to the next stope.

In the 1930s the author Neville Shute was chief mathematician for an airship company. He described the end of a finite difference analysis of an airship structure as “akin to a religious experience”. His took six weeks, and his “computer” was a team of young women with slide rules. We had come a long way by the early 1970s, but there was certainly a sense of achievement when each stope analysis was completed.

The task I have described could be completed interactively using a modern computer software package in a few minutes from beginning to end. Why isn’t mining productivity vastly improved on 40 years ago? Why are mining costs in real dollars not much better than they were? I don’t have the answer, but it certainly bothers me.