Research Article

Scale Dependence of Waviness and Unevenness of Natural Rock Joints through Fractal Analysis

Table 4

Fractal dimensions of waviness and unevenness of rock joint sample 3 at varying window sizes.

Point spacing (mm)Fractal estimationWindow size ()

0.52.0051992.002592.0043662.004452.0036022.0024772.0025432.002572.0021842.002377
101204095091870163500254600364700496700649000820100957800
0.9990.96850.92460.96340.95820.91010.92520.90420.91580.9196
2.010582.010562.011372.010852.010562.011032.010692.010682.010882.01061
103904158093880166900260600375100510300666400843300984100
0.97390.98590.98830.98640.98460.98830.98970.98940.97040.9858

1.02.0042822.0032352.0032862.0031042.0036232.0020342.0025572.0028962.0019132.002271
10180406009143016260025460364100496800647700819100955500
0.9990.90920.91330.90280.93210.90130.91240.9290.91020.9049
2.008662.0091182.0098792.0092582.0089362.0093832.0090352.0091482.0093122.0091
103404141093450166100259300373400507900663500839900979800
0.98310.98870.98990.98930.990.99270.99290.99270.99150.9901

2.02.005642.0038152.0040732.003722.003212.0021922.0029692.0033132.0023312.003075
102304069091750163100254300364400497600648500820600963300
0.9990.90130.91090.90690.90650.90910.9290.91840.93470.9201
2.0070112.0068352.0073412.0069062.0069792.0072312.0069032.0071052.0071912.007291
102804112092820164900257700371000504600659400834700977300
0.990.9890.99180.99220.99220.9910.99060.99240.99070.9921

Note: and are fractal dimensions of waviness and unevenness, respectively. and are the coefficients during linear correlation for estimating and , respectively. and represent the coefficients of determination during linear correlations for estimating and , respectively.