Rock indentation analysis based on the theories of elasticity

Abstract

A theoretical analysis based on the Von-Mises flow criteria and extension strain failure criteria, to estimate the extent of fracturing under the static indentation in rocks with and without discontinuities is presented here. The concept of relating

<span style="font-size:14.0pt;line-height:115%;font-family:" times="" new="" roman";="" mso-fareast-font-family:"times="" roman";color:black;mso-ansi-language:en-in;="" mso-fareast-language:en-in;mso-bidi-language:hi"="" lang="EN-IN">the stress distribution in materials to the ratio of Young's modulus to Shear modulus <i>(E/G) </i>in which a non-linear relationship between the elastic parameters <i>(E,G</i> and Poisson's ratio μ) is considered in the form <i>E/G </i>= 2(<i>1+μ) </i>for the rock without discontinuities and <i>E/G </i>> <i>2(1+μ) </i>for the rocks with closely spaced discontinuities. The theoretical values are validated by detailed laboratory static indentation experiments in various rock types. Related mechanical properties of these rocks have also been determined in the laboratory. Of the various criterion considered, the extension strain criteria gave a close estimation of the fracture extent in almost all the rock types for both conditions of <i>E/G </i>= 2(<i>1+μ) and E/G </i>> <i>2(1+μ). </i>The theoretical values by these failure criteria are found to be within the reasonable limits.</span>