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 estimation
Window size ()
0.5
2.005199
2.00259
2.004366
2.00445
2.003602
2.002477
2.002543
2.00257
2.002184
2.002377
10120
40950
91870
163500
254600
364700
496700
649000
820100
957800
0.999
0.9685
0.9246
0.9634
0.9582
0.9101
0.9252
0.9042
0.9158
0.9196
2.01058
2.01056
2.01137
2.01085
2.01056
2.01103
2.01069
2.01068
2.01088
2.01061
10390
41580
93880
166900
260600
375100
510300
666400
843300
984100
0.9739
0.9859
0.9883
0.9864
0.9846
0.9883
0.9897
0.9894
0.9704
0.9858
1.0
2.004282
2.003235
2.003286
2.003104
2.003623
2.002034
2.002557
2.002896
2.001913
2.002271
10180
40600
91430
162600
25460
364100
496800
647700
819100
955500
0.999
0.9092
0.9133
0.9028
0.9321
0.9013
0.9124
0.929
0.9102
0.9049
2.00866
2.009118
2.009879
2.009258
2.008936
2.009383
2.009035
2.009148
2.009312
2.0091
10340
41410
93450
166100
259300
373400
507900
663500
839900
979800
0.9831
0.9887
0.9899
0.9893
0.99
0.9927
0.9929
0.9927
0.9915
0.9901
2.0
2.00564
2.003815
2.004073
2.00372
2.00321
2.002192
2.002969
2.003313
2.002331
2.003075
10230
40690
91750
163100
254300
364400
497600
648500
820600
963300
0.999
0.9013
0.9109
0.9069
0.9065
0.9091
0.929
0.9184
0.9347
0.9201
2.007011
2.006835
2.007341
2.006906
2.006979
2.007231
2.006903
2.007105
2.007191
2.007291
10280
41120
92820
164900
257700
371000
504600
659400
834700
977300
0.99
0.989
0.9918
0.9922
0.9922
0.991
0.9906
0.9924
0.9907
0.9921
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.