Compressive strength of a mine pillar is a function of uniaxial compressive strength (UCS) of rock mass (pillar) and width-toheight ratio of the pillar. Determination of UCS of rock mass is difficult and expensive test. UCS is estimated generally by scale (size) effect equations with considering the discontinuities of rock mass. From extrapolating laboratory and in situ test results, the relationship between compressive strength and size of various groups of cubic coal specimens was derived. Effect of width-toheight ratio on the compressive strength and failure mechanism of mine pillars were investigated by physical modelling, as all factors affecting the strength could be controlled and kept constant. The specimens with width-to-height ratio from 0.25 to 2.0 had brittle behaviour and failed completely after yielding but differences in the yielding strength (yielding specimens at the periphery) and breaking strength inside the specimens were increased by an increase in width-to-height ratio from 2 to 3.5. The core of pillar specimens behaved in a ductile fashion when W/H>3.5. As W/H>4, the axial load was increased more than twice after yielding at the periphery and a high percentage of the inside of specimens which had ductile behaviour was intact. The ductile behaviour of pillar increased also from periphery to the centre. For W/H>5, specimens failed at their lateral surfaces. A rapid increase in the compressive strength of the specimens was observed with an increase in the width-to-height ratio from 5.0 to 5.54 and 6.0. For width-to-height ratio from 6.0 to 10, the load pointer of the testing machine remained constant. At this stage all specimens failed at periphery under high pressure and for one of the specimens having width-to-height ratio of 6.0, exploded under high pressure. The width-to-height ratio of 5.0 is a critical value with regard to the effect of width-to-height ratio of the square pillar specimens on the strength. Effect of width-to-height ratio on the compressive strength is comparable with the effect of confining pressure on the axial compressive strength, as horizontal stresses inside a pillar related to end frictional stresses increase with an increase in the width-to-height ratio. Strength-shape relationship is applicable up to brittle-ductile transition and the upper limit of width-to-height ratio is estimated at the transition. After that, not only a pillar fails at the periphery under the same axial stress with an increase in width-to-height ratio but also there is a high value of deformation for a pillar under high stresses and a high level of stored energy.
Rock contains various discontinuities. The compressive strength, as a function of discontinuities, increases with a decrease in size of rock specimens. The effect of size on the compressive strength of a pillar has been investigated by conducting tests both in the laboratory and in situ. Most of the experimental results available are for coal and are concerned especially with the compressive strength of cubes of various edge dimensions.