The effect of rock discontinuity surface roughness on shear strength

In the evaluation of a slope for stability, it is important to determine useable values of various rack properties. One of the most important rock properties which must be determined is the internal angle of friction, {dollar}Phi{dollar}. Surface roughness can have a considerable effect upon the friction angle. The norm has been to adjust the friction angle for roughness by the average asperity angle, i, or to compensate by use of a Joint Roughness Coefficient.; The objective of this investigation was to develop a method of mathematically quantifying rock discontinuity surface roughness without the need for a subjective determination based upon a visual comparison with some standard. This mathematical relationship then can be used in the evaluation process of the stability of a slope based upon the limit equilibrium concept.; This investigation utilized the concept of fractal dimension to quantify the surface roughness along discontinuities in four rock types. It resulted in the development of a relationship between Joint Roughness Coefficient (JRC) and fractal dimension (D) for each of the four rock types of the form:(UNFORMATTED TABLE OR EQUATION FOLLOWS){dollar}{dollar}vbox{lcub}halign{lcub}#hfil&&qquad#hfilcr&&JRC{dollar}sb{lcub}rm Pah{rcub}{dollar} = {dollar}-{dollar}1002.11 + (1003.83)Dcr&where:&D{dollar}sb{lcub}rm Pah{rcub}{dollar} averages 1.00837crcr&&JRC{dollar}sb{lcub}rm Dwd{rcub}{dollar} = {dollar}-{dollar}995.58 + (996.92)Dcr&where:&D{dollar}sb{lcub}rm Dwd{rcub}{dollar} averages 1.00660crcr&&JRC{dollar}sb{lcub}rm Min{rcub}{dollar} = {dollar}-{dollar}925.47 + (927.90)Dcr&where:&D{dollar}sb{lcub}rm Min{rcub}{dollar} averages 1.00750crcr&&JRC{dollar}sb{lcub}rm Met{rcub}{dollar} = {dollar}-{dollar}1126.41 + (1127.84)Dcr&where:&D{dollar}sb{lcub}rm Met{rcub}{dollar} averages 1.00336.cr{rcub}{rcub}{dollar}{dollar}(TABLE/EQUATION ENDS)These equations for the relationship between JRC and D can be approximated by: JRC = 1000(D {dollar}-{dollar} 1).; It was possible to substitute this approximate relationship into Barton's equation for shear strength of discontinuities. In terms of fractal dimension, the equation takes the form: {dollar}rm Tsb{lcub}peak{rcub} = sigmasb{lcub}n{rcub}tan(Phisb{lcub}residual{rcub}{dollar} + {dollar}rm (1000(D - 1))Logsb{lcub}10{rcub}JCS/sigmasb{lcub}n{rcub}).{dollar}; This resulted in a useable equation for peak joint shear strength which does not require a subjective determination of a "Roughness Coefficient". Instead, the fractal dimension of the discontinuity surface can be precisely mathematically determined.; It was next possible to rewrite the equation for the factor of safety for the case of simple plane shear by substituting the equation for T{dollar}sb{lcub}rm peak{rcub}{dollar} into the limiting equilibrium equation. This then gave a method for estimating the factor of safety against sliding on a discontinuity given a measurement of the fractal dimension of the discontinuity surface.