### Abstract

A written computer programme to estimate the box fractal dimension (D_{B}) is verified by estimating D_{B} of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated DB is evaluated using the same Koch curve. The employed size range of the applied box networks was found to be the parameter which has the strongest influence on the accuracy of estimated D_{B}. This indicated the importance of finding the range of self-similarity or self-affinity for the object considered to select the proper range for the box sizes and, in turn, to obtain accurate estimates of D_{B}. By calculating D_{B} for different block sizes sampled from three generated two-dimensional joint patterns, it is shown that D_{B} can capture the combined effect of joint-size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of D_{B} along a 350 m stretch of a tunnel in the shiplock area of the Three Gorges dam site is computed using the joint data mapped on the walls and the roof of the tunnel. This spatial variation of D_{B} is used, along with the visual geological evaluation of the joint trace maps of the tunnel, in making decisions about statistical homogeneity of the rock mass around the tunnel. The results obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homogeneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variation of D_{B}. It is recommended that the spatial variation of D_{B} is used, along with the results of other methods such as contingency table analysis and equal area plots, which incorporate the effect of joint orientation distribution, in addition to the geology of the site, in determining the statistically homogeneous regions of jointed rock masses.

Original language | English (US) |
---|---|

Pages (from-to) | 217-229 |

Number of pages | 13 |

Journal | Engineering Geology |

Volume | 48 |

Issue number | 3-4 |

State | Published - Dec 1997 |

### Fingerprint

### Keywords

- Accuracy
- Box fractal dimension
- Case study
- Discontinuity geometry
- Proper box sizes
- Rock masses
- Statistical homogeneity
- Theoretical

### ASJC Scopus subject areas

- Geotechnical Engineering and Engineering Geology

### Cite this

*Engineering Geology*,

*48*(3-4), 217-229.

**Box fractal dimension as a measure of statistical homogeneity of jointed rock masses.** / Kulatilake, Pinnaduwa; Fiedler, Reno; Panda, Bibhuti B.

Research output: Contribution to journal › Article

*Engineering Geology*, vol. 48, no. 3-4, pp. 217-229.

}

TY - JOUR

T1 - Box fractal dimension as a measure of statistical homogeneity of jointed rock masses

AU - Kulatilake, Pinnaduwa

AU - Fiedler, Reno

AU - Panda, Bibhuti B.

PY - 1997/12

Y1 - 1997/12

N2 - A written computer programme to estimate the box fractal dimension (DB) is verified by estimating DB of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated DB is evaluated using the same Koch curve. The employed size range of the applied box networks was found to be the parameter which has the strongest influence on the accuracy of estimated DB. This indicated the importance of finding the range of self-similarity or self-affinity for the object considered to select the proper range for the box sizes and, in turn, to obtain accurate estimates of DB. By calculating DB for different block sizes sampled from three generated two-dimensional joint patterns, it is shown that DB can capture the combined effect of joint-size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of DB along a 350 m stretch of a tunnel in the shiplock area of the Three Gorges dam site is computed using the joint data mapped on the walls and the roof of the tunnel. This spatial variation of DB is used, along with the visual geological evaluation of the joint trace maps of the tunnel, in making decisions about statistical homogeneity of the rock mass around the tunnel. The results obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homogeneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variation of DB. It is recommended that the spatial variation of DB is used, along with the results of other methods such as contingency table analysis and equal area plots, which incorporate the effect of joint orientation distribution, in addition to the geology of the site, in determining the statistically homogeneous regions of jointed rock masses.

AB - A written computer programme to estimate the box fractal dimension (DB) is verified by estimating DB of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated DB is evaluated using the same Koch curve. The employed size range of the applied box networks was found to be the parameter which has the strongest influence on the accuracy of estimated DB. This indicated the importance of finding the range of self-similarity or self-affinity for the object considered to select the proper range for the box sizes and, in turn, to obtain accurate estimates of DB. By calculating DB for different block sizes sampled from three generated two-dimensional joint patterns, it is shown that DB can capture the combined effect of joint-size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of DB along a 350 m stretch of a tunnel in the shiplock area of the Three Gorges dam site is computed using the joint data mapped on the walls and the roof of the tunnel. This spatial variation of DB is used, along with the visual geological evaluation of the joint trace maps of the tunnel, in making decisions about statistical homogeneity of the rock mass around the tunnel. The results obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homogeneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variation of DB. It is recommended that the spatial variation of DB is used, along with the results of other methods such as contingency table analysis and equal area plots, which incorporate the effect of joint orientation distribution, in addition to the geology of the site, in determining the statistically homogeneous regions of jointed rock masses.

KW - Accuracy

KW - Box fractal dimension

KW - Case study

KW - Discontinuity geometry

KW - Proper box sizes

KW - Rock masses

KW - Statistical homogeneity

KW - Theoretical

UR - http://www.scopus.com/inward/record.url?scp=0031412438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031412438&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031412438

VL - 48

SP - 217

EP - 229

JO - Engineering Geology

JF - Engineering Geology

SN - 0013-7952

IS - 3-4

ER -