ABSTRACT: The modulus of deformation of a rock mass as determined by in situ testing is always less than the modulus determined from intact cores taken from the rock mass. It is generally concluded that structural features such as joints are primarily responsible for the reduction of the rock mass modulus. A quantitative expression of the effects of joints on rock mass deformation can be developed if the extent of each joint surface can be assumed to be small relative to the volume of the rock mass. The deformation effects of joints within a rock mass can be determined by first analyzing the effects of a single joint and then summing the effects of each of the joint patterns present in the rock mass. A procedure is presented that provides an expeditious method of determining the modulus of deformation of a rock mass, for use in numerical modeling analyses, using the results of physical test on core specimens recovered from exploration drilling.
1. Introduction
The modulus of deformation of a rock mass as determined by in situ testing is always less than the modulus determined from intact cores taken from the rock mass. The rock mass modulus is usually reported in the range of from 10 to 80 percent of the modulus of the intact core specimens (Deere, et al, 1967, and Stagg and Zienkiewicz, 1968).
It is generally concluded that structural features such as joints and fractures are primarily responsible for reduction of the rock mass modulus. These structural features represent plane surfaces along which relative movement may occur when the rock mass is loaded.
A quantitative expression of the effects of joints can be developed if the extent of each joint surface can be assumed to be small relative to the volume of the rock mass. The effects of joints within a rock mass can be determined first by determining the effect of a single joint and second by summing the effects for the particular joint pattern present in the rock mass of interest. A similar development has been presented by Walsh (1965) to explain the effects of grain size cracks on the deformation of laboratory specimens.
The quantitative expression developed to relate the rock mass modulus to the core specimen modulus takes the general form of:
Em = E/(1 + S13 Ki ) (1)
where:
Em = modulus of rock mass,
E = modulus of core specimen,
Ki = (¿L3/2V)(sinBCosB(sinBCosB µsin2B)),
L = average joint length for set i,
V = average joint block volume for set i,
B = angle between joint plane and the direction of determination of Em for joint set i, and
µ = coefficient of friction along joint planes in set i.
The poisson's ratio of a jointed rock mass can be determined by the expression:
vm = v + ((1 - 2v)/2)(1 - Em/E) (2)
where:
vm = poisson's ratio of the rock mass, and
v = poisson's ratio of the core specimen.