Abstract

The scale effect is known to hinder reliable shear strength estimation of large-scale discontinuities. Recently, a stochastic approach was proposed to predict shear strength of large discontinuities directly at problem scale, thereby bypassing the scale effect. One aspect of the stochastic approach seeks to use the available roughness information from the 1D profile of a discontinuity to create a series of statistically representative 3D synthetic rock surfaces, via a rigorous random field model. The application procedure for producing such synthetic surfaces was validated at small scale; however, preliminary large-scale applications were not quite satisfactory. It was found that the absence of consideration for the multiscale nature of discontinuity roughness contributed to the issues encountered. This paper presents the details of the revised multiscale-based 2D LAS approach for producing representative large-scale synthetic surfaces with an emphasis on the effect of sampling interval, called segment length, on the statistics of the synthetic surfaces.

Introduction

The estimation of shear strength is a significant factor in design and stability analysis encompassing engineering scale rock masses, however, its prediction for in-situ discontinuities at this scale is still challenging. This is largely to the hindrance encountered by the limited surface roughness information available from in situ discontinuities and acknowledged scaling effects.

Recently, Casagrande et al. [1] proposed a new approach for estimating the shear strength of large in situ discontinuities based on stochastic analysis. Essential to this approach is the ability to generate a series of synthetic surfaces, via a random field model using roughness statistics of the daylighting discontinuity profile as input parameters. In its original version, the method for generating the synthetic surfaces did not require to distinguish different scales of roughness. However, Buzzi and Casagrande [2] identified an issue with the generation of large synthetic surfaces in that the distribution of gradients of synthetic surfaces did not reflect the distribution of the visible reference profile, a problem that was not met when generating small scale surfaces. Due to the mismatch of gradient distributions, the semi-analytical model for shear strength estimation which is reliant on the gradients for the estimation of shear resistance, resulted in very large shear strength prediction errors. It is essential, for the reliability and robustness of the stochastic method for shear strength estimation, to be able to generate large scale synthetic surfaces with roughness statistics matching the input statistics as best as possible.

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