Comparison of Pillar Strengths Calculated Using Empirical Equations and Finite Elements

Mechanical properties typical of coal are used in the comparisons of pillar strengths based on finite elements and the empirical equations of Holland-Gaddy, Salamon-Munro, Obert¬Duvall, and Bieniawski-PSU. A correlation among the strength parameters which are employed in the empirical equations, in Mohr-Coulomb and Hoek-Brown failure criteria is established. Emphasis is given to the important distinction between the mechanical properties of small rock specimens and those related to the rock mass. An elastoplastic version of Hoek-Brown criteria has been developed and implemented in a finite elements code. The strengths calculated using the empirical equations showed a good agreement when the ratio width by height of the pillars varied from I to 8, except for Holland-Gaddy equation which exhibited lower values. Under the hypothesis of associative perfect elastoplasticity used, pillar strength calculated using Mohr¬Coulomb yield criterion became excessively high for all the models having a pillar width by height ratio above 2. The finite elements solution based on Hoek-Brown criterion predicted strengths around fifty percent larger than Bieniawski-PSU equation when the pillars width by height ration varied from 3 to 8, showing good agreement below that range. It has been concluded that, under the hypothesis of percfect plasticity, stress analysis techniques may overestimate the strength of rock structures subjected to high confining stresses.