Investigation of the relationship between dynamic and static deformation moduli of rocks

Seyed Morteza Davarpanah,Peter Ván,Balázs Vásárhelyi

doi:10.1007/s40948-020-00155-z

Abstract

The determination of deformation parameters of rock material is an essential part of any design in rock mechanics. The goal of this paper is to show, that there is a relationship between static and dynamic modulus of elasticity (E), modulus of rigidity (G) and bulk modulus (K). For this purpose, different data on igneous, sedimentary and metamorphic rocks, all of which are widely used as construction materials, were collected and analyzed from literature. New linear and nonlinear relationships have been proposed and results confirmed a strong correlation between static and dynamic moduli of rock species. According to rock types, for igneous rocks, the best correlation between static and dynamic modulus of elasticity (E) were nonlinear logarithmic and power ones; for sedimentary rocks were linear and for metamorphic rocks were nonlinear logarithmic and power correlation. Moreover, with respect to different published linear correlations between static modulus of elasticity (Estat) and dynamic modulus of elasticity (Edyn), an interesting correlation for rock material constants was established. It was found that the static modulus of elasticity depends on the dynamic modulus only with one parameter formula.

Highlights

An accurate estimate of geomechanical properties of rocks is crucial for almost any form of design and analysis in geomechanical projects
The results show that there is a good correlation between static and dynamic elasticity modulus, rigidity modulus and bulk modulus
Some other researchers adopted the linear correlation as wellfitted regression line (Belikov et al 1970) for Granite

Summary

Introduction

An accurate estimate of geomechanical properties of rocks is crucial for almost any form of design and analysis in geomechanical projects. The strength and deformation behavior of rocks have been studied by many authors Xiong et al (2019), Yang et al (2016), Zhao et al (2017), Ranjith et al (2004), Rahimi and Nygaard (2018), Davarpanah et al (2019) and Berezovski and Van (2017). Among these properties modulus of elasticity (E), modulus of rigidity (G) and bulk modulus (K) are the basic parameters used in rock engineering. Moduli are calculated from the stress–strain curves of the rock material This is characteristic of the modulus of elasticity. For the non-destructive one, the most common method is an ultrasonic test, measuring both longitudinal and shear wave velocities

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Results

Conclusion