Life on the Slippery Slope

I have just had the pleasure of assessing the stability of the sidewalls of an open cast coal mine in Mpumalanga.  The excavations are in excess of 20 metres deep in a number of instances and the mine wanted to whether they could reduce the number of benches cut in the sidewalls without comprising safety.  Removing tens of thousands of unproductive overburden, stockpiling it and then returning it at the end of the mining operation is both expensive and time consuming and to be able to reduce this would assist greatly in reducing operating costs.  In this light then we took a number of undisturbed samples from the various soil and completely to highly weathered soil horizons and carried out both undrained and drained triaxial and shear box tests on the materials to determine the shear strength parameters of the different geological horizons. It was certainly hard work hacking out good sized blocks of soil, but that is only the half of it – they are surprisingly heavy, and to carry them to the vehicle and load them is no easy task in itself, bearing in mind that they do not tolerate any rough handling.

Stresses in a soil are a combination of the pore pressures (i.e. the pressure that the groundwater exerts within each individual pores of the soil) and the pressures exerted by the mass of the soil itself plus any additional loads applied, for example spoil heaps, structures and even vehicles.  For a fully saturated soil, any additional load will be carried by the water within the soil fabric and not by the soil itself due to the incompressibility of the water in the pores.  Adding a load will lead to an increase in the pore water pressures which in turn leads to increases in the total stress in a soil.  This is the period when most failures occur due to modifications to the in situ stress regime.  Over time the pore pressures will dissipate as the water table is drawn down towards the pit sidewalls.  In this case however, although the loads weren’t increased, the confining material where the pit is now located had been removed, forming a free space into which the material could fail.

The aim of any slope analysis is to determine the factor of safety (FoS) for the slope.  A FoS of 1 indicates that the forces causing failure are exactly equal to the internal forces keeping the sidewalls stable.  If the FoS falls below 1 then, theoretically, failure will or has occurred.  If the figure is greater than 1 the slope is theoretically stable.  A FoS of 1.5 is generally applied for civil engineering works where slopes have to remain stable over the design life of the structure.  By analysing for various slope morphologies and shear strength parameters, a safe, practical and workable solution can generally be arrived at for any slope.

The saturated condition, when failure is most probable, is called the ‘undrained’ state and requires an ‘undrained’ analysis.  It should be carried out using variations in the cohesion of the various soil and rocks which occur within a slope, which provides an indication of the sensitivity of the analysis to differences in the shear strengths for the various soil horizons.

Thekwini Soils Laboratory in Durban did our triaxial and shear box testing to give us our shear strength parameters.  Armed with this knowledge we began to analyse the various scenarios – which is always an interesting exercise and a scary one at times when the existing conditions on site are shown to be unstable as they currently stand.

A further critical factor in assessing the stability of a slope is determining the unit weight, that is, the weight of 1 m3 of material.  Water has a unit weight of 9.8 kilonewtons, arrived at by multiplying the mass of the water by the force of gravity, i.e., 1000 kg x 9.8 ms-2.  To simplify matters slightly, a figure of 10ms-2 for the acceleration due to gravity is often used, which gives an approximate weight of 10kNm-3.  Soils are generally in the 16 to 19 kNm-3 range.  All soils exert a downward force due to their own weight.  For example a cubic metre of soil weighing 19 kNm-3 will exert a pressure of 19 kNm-2.  A ten metre column of the same soil with a footprint of 1 m2 will therefore exert a load of 190 kNm-2.  Without lateral support (in this case the removal of the soil and rock from the excavation) the soils will fail if measures are not taken to unload the soil column – best done by cutting benches into the pit sidewalls and battering back the slopes.

There are a number of software packages available for carrying out analyses but one which I have found most useful and user friendly is the Rocscience Inc package called ‘Slide’ which not only determines the FoS but also the probability of failure.  Evert Hoek was instrumental in many ways in developing the science of rock mechanics to its current levels at Imperial College and then at Rocscience Inc in Toronto.   Some of the finest geotechnical software, particularly in rock mechanics comes out of this stable.   It has been said that if there was a Nobel Prize for Rock Mechanics, the first recipient would be Evert Hoek.

And the results of our analysis?  Well, perhaps it is best to say that it is difficult to get away with no benches in your pit slopes – the factor of safety is too low and the risks too high.