Scale Dependence of Waviness and Unevenness of Natural Rock Joints through Fractal Analysis
Table 3
Fractal dimensions of waviness and unevenness of rock joint sample 2 at varying window sizes.
Point spacing (mm)
Fractal estimation
Window size ()
0.5
2.002065
2.004658
2.004025
2.004222
2.004405
2.003238
2.002918
2.003086
2.003475
2.003312
10140
40920
91850
163500
25590
366900
49870
651800
82650
963700
0.999
0.971
0.9343
0.9728
0.9756
0.981
0.9442
0.9449
0.9664
0.9589
2.01016
2.009858
2.01047
2.01013
2.009915
2.01042
2.01015
2.01075
2.01075
2.01063
10410
41620
93790
166600
26070
375600
2.01015
667200
84620
987600
0.9876
0.9893
0.9893
0.9886
0.9858
0.989
51090
0.9893
0.9719
0.9882
1.0
2.002696
2.004337
2.004687
2.004136
2.003912
2.003324
2.002957
2.003051
2.003287
2.003409
10150
40860
92090
163400
25550
367100
49890
651700
82590
964300
0.999
0.9652
0.9654
0.954
0.9623
0.9777
0.9399
0.9465
0.9604
0.9578
2.008048
2.008427
2.008947
2.008806
2.008611
2.009051
2.008796
2.008859
2.009329
2.009198
10350
41430
93410
166000
25980
374200
50900
664700
84320
983800
0.9849
0.9919
0.9902
0.9924
0.9907
0.9928
0.9934
0.9932
0.9921
0.9908
2.0
2.003945
2.005202
2.003265
2.004757
2.003571
2.003308
2.002896
2.003225
2.00347
2.003585
10190
41000
91580
163900
25520
367000
49870
652300
82640
956300
0.999
0.9499
0.9362
0.9418
0.9384
0.9771
0.9547
0.9387
0.9538
0.9417
2.00717
2.007215
2.007344
2.007052
2.006896
2.00716
2.006828
2.006952
2.00733
2.007264
10310
41290
92930
165100
25810
372100
50590
660800
83810
977700
0.9799
0.9895
0.9885
0.9919
0.9927
0.9886
0.9927
0.9909
0.9894
0.9899
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.
