Static elastic modulus of rocks predicted through regression models and Artificial Neural Network

Abstract

The statistical analysis of the main physical, mechanical and ultrasonic features of various sedimentary rock samples (limestone, calcarenite, marly calcisiltite and sandstone) is presented with the aim of finding reliable models to predict the static elastic modulus from known properties. Based on the relevance of the static elastic modulus Estat in engineering geological applications and on the increasing need of non-destructive procedures for its estimation, this paper attempts to establish prediction models by means of single and multiple regression approaches and Artificial Neural Network (ANN). While in the first two cases rock properties are plotted against each other to study their mutual dependence, even combining more than one independent variable, the Artificial Neural Network approach allows a self-learning model capable of predicting a target value from known input variables to be built. Results show that the static elastic modulus of tested rocks is mainly related to the rock Uniaxial Compressive Strength and it varies with respect to the seismic wave velocities (both compressional Vp and longitudinal Vs) and, consequently, to the dynamic elastic modulus Edyn calculated by ultrasonic tests. In particular, there is a numerical difference between the static and dynamic values of the elastic modulus, as the dynamic ones are generally higher than the corresponding static values. Satisfactory prediction equations were found by multiple regressions involving Vp, Edyn and the rock bulk density, thus providing useful statistical laws for the indirect calculation of Estat. The results arising from the ANN models are used herein to draft Estat prediction graphs from known variables, in the perspective of a practical utility for the quick and non-destructive estimation of the static elastic property of tested sedimentary rocks.