Utilizing the uncertainty matrix in estimation of rock mass deformation modulus on the basis of empirical relations

Uncertainty in required parameters in analysis and design of structures is an important issue that is usually considered by rock engineers. This uncertainty is due to the developed relations and also rocks’ nature. Modulus of deformation is one of the geo-mechanical parameters that is widely utilized in design and analysis. But estimating this parameter according to the empirical relations is associated with uncertainty and this causes mistakes in decision making of engineers. Purpose of this paper is to develop a novel concept entitled uncertainty matrix for practical prediction of deformation modulus with high level of confidence. Therefore, modulus of deformation is obtained based on the uncertainty matrix and statistical methods. Later, using the uncertainty matrix and t distribution, a domain for variation of deformation modulus is determined. In order to do a case study and also defining the elements of uncertainly matrix, models that are function of rock mass rating and data sets of sand-stone slopes in Kahar formation are applied. Results indicate that, prediction of deformation modulus for rock mass according to the developed method in comparison with the general methods is more reliable. In addition, deformation modulus with the probability of 95% for the studied sand-slope is in the range 23.67 to 30.00(GPa).