On the Slippery Slope

I have just had the pleasure of calculating the stability of pit sidewalls for a coal mine in Mpumalanga. The excavations are in excess of 20 metres deep in a number of instances and the mine wanted to if they could reduce the number of benches cut in the sidewalls without comprising safety. As you can well imagine, removing tens of thousands of unproductive overburden, stockpiling it and then returning it at the end of the mining operation is both expensive and timing consuming. In this light then we took a number of undisturbed samples from the pit sidewalls 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.

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The 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. If a soil is fully saturated, then any additional load will be carried by the water within the soil fabric and not by the soil itself. A load will lead to an increase in the pore water pressures and increases 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. This is called an ‘undrained’ analysis and should been carried out using variations in the cohesion of the various soil and rocks which occur within a slope.

Carrying out the analysis for various shear strengths allows for an assessment of the sensitivity of the analysis to differences in the shear strengths of the various soil horizons. Another 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 load 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 the soils will fail if measures are not taken to unload the soil column. The aim of any analysis is to determine the factor of safety (FoS) of a slope. An 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 a safe, practical and workable solution can generally be arrived at for any slope. 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. Some of the best geotechnical software around comes out of this stable and their credentials are impeccable.

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