A new method for automated estimation of joint roughness coefficient for 2D surface profiles using power spectral density

https://doi.org/10.1016/j.ijrmms.2019.104156Get rights and content

Abstract

In this study, a new method for the objective and accurate estimation of the joint roughness coefficient (JRC) of surface profiles, which are extracted from terrestrial laser scanner point clouds, is proposed. The requirements of objectivity, accuracy, reliability, and suitability for automatic analysis have been the basic criteria in assessing the performance of the procedure for JRC estimation. The procedure to estimate the JRC value of a sample profile is based on a similarity measure, between the third-order polynomial function fits to the power spectral density in the spatial frequency domain of the sample surface profile and Barton's reference profiles. The procedure is tested on the one hundred and two digitized surface profiles found in the literature. Normal probability density distribution of estimation errors of the results show that the JRC estimation by the proposed method is more accurate and precise compared to the results from the three versions of the well-known and commonly used Z2 method.

Introduction

Standardized conventional procedures followed in the field for the determination of discontinuity properties of rock masses tend to be time-consuming, laborious, and costly.1 Further, they may involve safety risks and may even be impossible to realize in cases where rock faces are inaccessible. Therefore, in the last decade or so, manual field survey procedures have been mostly replaced by Terrestrial Laser Scanning (TLS) based surveying techniques that alleviate most of the disadvantages associated with the conventional manual field surveys. TLS approach allows the fast and low-cost collection of point cloud data, which are later processed to obtain the relevant properties of discontinuities, among which are the orientation, spacing, persistence, and roughness properties. TLS technique can be applied in a fully interactive manner, proceeding step by step through the processes involved.2,3 However, such an application will not allow full realization of the advantages of the approach. Therefore, semi-automatic,4,5 and fully automatic6 processing of the cloud data has been the subject of recent studies.

One of the significant outcomes in the determination of joint properties by the TLS approach is the estimation of the shear strength of rock joints to be used for the determination of the mechanical properties of rock masses. Shear strength of rock joints depends strongly on the rock joint roughness. The empirical equation proposed by Barton and Choubey7 has been the most commonly used formula for the estimation of peak shear strength of a joint,8τ=σtanJRClog10JCSσ+ϕbwhere τ is the peak shear strength of the rock joint, σ is the normal stress, JRC is the joint roughness coefficient, JCS is the strength of the joint wall, and ϕb is the basic friction angle. In this equation, it is possible to obtain all the parameters except JRC by standard tests. The JRC of a particular rock joint profile, however, needs to be estimated. The JRC value can be estimated by back-calculation from the shear test results using a rearranged form of Eq. (1) as detailed by Barton and Choubey.7 In the absence of shear test data, the estimation is done traditionally by visually comparing the sample profile with the ten standard profiles with JRC values ranging from 0 to 20 provided by Barton and Choubey.7 This approach was also adopted by the International Society for Rock Mechanics (ISRM)9,10 and has been widely used in practice since its publication.

To analyze the reliability of this traditional visual assessment method, Beer et al.11 performed a survey based on three granite block profiles with 125, 124, and 122 responses from people with different levels of experience, using an internet-based survey system. The results indicated that a wide range of JRC estimation values could be obtained even in the case of experienced survey subjects. Graselli and Egger8 randomly extracted three different profiles from different samples in the shear direction. JRC was estimated both with visual comparison and with back analysis from shear test results. The results confirmed that it was not easy to uniquely estimate the JRC value using the visual assessment method. Alameda-Hernandez et al.12 performed a similar visual estimation survey with 90 trained subjects undertaking the survey test. The results of the survey clearly showed systematic inaccuracies in the visual evaluation procedure. As a result, the conclusion that the visual assessment procedure of JRC is strongly subjective and thus not suitable for a reliable estimation has been widely stated in the literature. It is clear that the visual evaluation for the estimation of JRC is not suitable for use in a fully automated procedure either.

With the recognition of the subjectivity of the traditional assessment method, researchers turned their attention to the development of objective methods. A considerable number of publications for the determination of the JRC, mainly using statistical parameters and fractal dimension D of the joint profiles, have thus appeared in the literature.

Tse and Cruden13 investigated the correlations between JRC and surface parameters by using back-calculated JRC values of Barton and Choubey's ten reference surface profiles. As surface parameters, they adopted the root mean square of the first derivative of the profile (Z2) first suggested by Myers,14 and the structure-function (SF), which was related to the autocorrelation function proposed by Sayles and Thomas.15 They concluded that the joint roughness coefficient of a rock surface could be well predicted by Z2 and SF. Yu and Vayssade,16 while supporting the proposition that a strong correlation exists between JRC and Z2 or SF, stressed the fact that these parameters were sensitive to sampling interval and thus were insufficient in practice. Yang et al.17 showed that due to the self-affinity transformation law, scaling of the reference JRC profiles did not influence the final JRC values. Tatone and Graselli18 modified the equations relating JRC to Z2 given by Tse and Cruden13 for different sampling intervals. Zhang et al.19 modified Z2 and its application by including a dilation angle, which could be attributed as positive or negative, to account for the directional dependencies. In their literature survey, Li and Zhang20 listed 47 empirical equations for the estimation of JRC of a joint profile using Z2, SF, and other statistical parameters as the variables. They noted that previously published equations might misestimate the JRC of a profile and stressed once more that special caution should be paid when using these equations. Recently Wang et al.21 proposed still another roughness parameter PZ, including the influence of the amplitude height of the rock joint profile to the modified Z2 proposed by Zhang et al.19 The calculation of PZ requires a sophisticated analysis procedure to estimate JRC. While this study presents the most detailed treatment of the problem to this day, the calculation of PZ requires a rigorous and difficult analysis procedure to estimate JRC.

Another approach for the estimation of JRC values has been the use of fractal dimension. Brown and Scholz,22 and Develi and Babadagli23 noted that fracture surfaces fitted well to self-affine fractal behavior. Thus, surfaces have been evaluated in terms of their fractal dimension through methods that are applicable to self-affine fractal objects. For the determination of the fractal dimension of a rock joint profile compass-walking (also known as divider) method24, 25, 26 or box-counting method27 has been commonly used. It is possible, however, to obtain different values of D using the two methods for the same profile as indicated by Li and Huang.28 On the other hand, Outer et al.29 investigated the characterization of roughness of a discontinuity in terms of a fractal and/or fractal dimension and concluded, from the relations between the JRC and fractal dimension, that either the roughness profiles were not fractals or the divider method was not suitable for determining the fractal dimension. Nevertheless, a large number of studies have been conducted on the relation between fractal dimension and JRC, among which are Lee et al.,30 Huang et al.,31 Xu et al.,26 Jang et al.32 In these studies, the fractal dimension has been found to correlate reasonably well with JRC values and numerous empirical equations were proposed for estimating JRC using fractal dimension. Nineteen such empirical equations were collected and examined critically by Li and Huang.28 They noted that each equation reflected the method used by the authors to determine the value of D, the differences between the profiles assessed, and the data collection and processing procedures followed. They further noted that the empirical equations showed inconsistencies, sizable variations from one another, and most of them appeared to be correct only over specific ranges of D and JRC.

In an early assessment of these methodologies for joint roughness coefficient determination, Hsiung et al.33 concluded that none of the methods might be capable of providing a reasonable JRC value. This conclusion seems to be still valid. Whether one selects the statistical parameter Z2 and its variants or the fractal dimension for the estimation of JRC, it is difficult to choose one of the many equations proposed for use in the application in mind. Each equation seems to give good results for the samples analyzed by the authors. However, tests of proposed equations for the accuracy of JRC estimation for samples tested/analyzed by other researchers are not easily found in the literature. As a result of this critical examination of the major methods related to the determination of JRC of rock masses, one may conclude that there exists no universally accepted method for the accurate and reliable estimation of the value of JRC of a sample surface profile yet, in spite of a large number of research studies carried out since the publication of the major reference study by Barton and Choubey7 almost half a century ago.

Recent technological developments, including the development of TLS and computer software for processing cloud data, have made it possible to obtain discontinuity surfaces on long scan lines. There is still left the long and tedious task of estimating the JRC values for the large number of profiles obtained from these surfaces. Thus, the aim of this study is the development of a simple, accurate, and reliable method suitable for use in a fully automatic procedure for the estimation of the JRC of large numbers of surface profiles obtained from TLS point clouds; rather than to rigorously analyze and understand the relation between estimated JRC values and the peak shear strength of rock joints by back calculations from test samples.

A procedure is developed and proposed for the estimation of the JRC range of sample profiles based on a similarity measure between the polynomial functions fitted to the power spectral density (PSD) functions of a given sample surface profile and Barton's ten template profiles. As distinct from previous attempts making use of the PSD as an intermediate tool, the proposed method is based on the direct application of the PSD of the reference and sample surface profiles. The procedure is tested on the one hundred and two digitized surface profiles found in the literature. To illustrate the accuracy and precision of the method, the normal probability density distribution of estimation errors of the results for the JRC estimation are compared with the results from the three versions of the well-known and commonly used Z2 method.

Section snippets

Methodology

PSD has been used in a diverse list of applications such as surface characterization of optical components,34,35 surface generation in ultra-precision machining,36 evaluation of surface changes in laser milling operations,37 and road surface classification.38

In a visual assessment of the roughness of a surface profile, the amplitude and the frequency content of the profile are the two major parameters that influence the perception of the level of roughness. In the literature, the effects of the

Discussion of results

To evaluate the performance of the proposed procedure, tests are carried out using the source data provided by Li and Zhang,20 which include twelve digitized profiles from Graselli,52 twenty-six profiles from Bandis,51 and 64 profiles from Bandis.53 The back-calculated JRC values from tests are also available for these surface profiles. Estimated JRC values for these sample profiles obtained using the proposed method are compared with the back-calculated JRC values in Fig. 6.

The Gaussian

Conclusions

Applications requiring analyses of discontinuity surfaces of rock masses on very long scan lines involve the assessment of large numbers of surface profiles for JRC estimation. This task is time consuming, laborious, and costly. Obtaining JRC values by standard tests is not practical, either. The use of the popular methods available in the literature, on the other hand, presents the engineer in charge to choose among a large number of equations proposed for the same purpose. Further, some of

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication.

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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