Research Journal of Applied Sciences, Engineering and Technology 4(22): 4607-4616, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: March 03, 2012
Accepted: March 24, 2012
Published: November 15, 2012
Displacements Prediction in Double-Arch Dam Rock Abutment Using
SPSS Software Based on Extensometer Readings Case study:
Karun 4 Concrete Dam, Iran
1
Hadi kamali Bandpey, 1Kaveh Ahangari and 2Mirsaeid Hosseini Shirvani
Department of Mining Engineering, Science and Research Branch, Islamic Azad University,
Tehran, Iran
3
Department of Computer Engineering, Sari Branch, Islamic Azad University, Sari, Iran
1
Abstract: In this study we present a method for Displacements Prediction in Double-Arch Dam Rock Abutment
Using SPSS Software Based on Extensometer Readings. Displacement in dams is the most tangible and
important parameter which could be crucial in their safety. Different elevation displacements are yielded by
various loadings and the thrust force imposed on foundation and abutment. Most concrete dams are constructed
on stone foundations. Displacements in foundation and abutment are measured by extensometers. Karun 4
Concrete dam is designed with 11 galleries, from elevation 1016 to 802 m, in the order from top elevation (dam
crest elevation 1032) to the bottom elevation (dam foundation elevation 806) within the dam body. As a whole,
19 extensometers in the left bank, 17 in the right, and one more in the middle are implemented in the dam.
Karun 4 dam has already been impounded with water up to the elevation 1003. Displacements in Karun 4 are
recorded by extensometers whence water was leveled in 7 elevations 943.68, 953.36, 973.55, 983.28, 993.17,
1003.13. In this study, using SPSS we have tried to predict the displacements for a situation in which water will
be elevated to the elevations 1013, 1023, 1032 in the future for elevations which are equipped with anchor. The
most predicted displacement pertaining to the left bank when water was leveled to the elevation 1013, was 3.65
mms by R2 = 0.9997 for the implemented anchor. Proceeding further, as water is leveled to the elevations 1023
and 1033, the most predicted displacement respectively would be 4.31 and 5.66 by R2 = 0.9941; and is related
to the anchor implemented in the elevation 936.05. The most predicted displacement for the right bank is
5.9397, 7.2347 and 8.6877 mms by R2 = 0.9995 for the elevation 888.128 m.
Keywords: Displacement, extensometer, Karun 4 concrete dam, SPSS
INTRODUCTION
Displacement in dams is the most tangible parameter
which could be easily measured. Displacement involves
all directions, but the most critical displacements occur in
the horizontal plate. Concrete dams are needed to have
equipment in order to measure displacements including
relative motion of the interior points of the dam and the
dam motion relative to a stationary exterior point. In the
current article, to achieve the amount of displacement,
extensometer instrumentation data has been utilized in the
contact surface between the dam body and the rock mass.
Accomplished researches in this field including:
Aleksandrovskaya and Urakhchin (1974) predict the
displacements of concrete gravity dams on rock
foundations and the horizontal displacements of high
concrete dams during operation in which most effective
analysis is based on use of the so-called method of
influence coefficients. The maximum and minimum
values of displacements obtained by the monograms can
serve this purpose (Aleksandrovskaya and Urakhchin,
1974). Allen and Cluff (2000) considered the effect of
active faults in dam foundations (Allen and Cluff, 2000).
Wieland et al. (2003) Considered earthquake resilience in
large concrete dams (Wieland et al., 2003). Mata and
Portela (2007) used neural network for predicting Radial
displacement by using pendulum readings in Concrete
dam (Mata and Portela, 2007), but in this paper
Extensometer readings are used for predicting mentioned
displacement by statistical study (SPSS: Statistical
Package for the Social Sciences). Wieland et al. (2008b)
Studied in potentially active faults in the foundations of
large dam and its effect on the selection of sites, dam type
and design aspects of dams to resist fault movements
(Wieland et al., 2008a, b) predict the relative crest
settlement of Concrete-Faced Rock fill Dams (CFRDs)
Corresponding Author: Hadi kamali Bandpey, Department of Mining Engineering, Science and Research Branch, Islamic Azad
University, Tehran, Iran
4607
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
sited on marl, marly limestone, cretaceous to Miocene
limestone (Fig.1) (Mahab-Ghodss Consulting Engineering
Company, 2010a).
Fig. 1: A view of Karun 4 dam (mahab-ghodss consulting
engineering company)
analyzed using an artificial neural network model. This
method can support the dam engineer in predicting the
relative crest settlement of a CFRD after impounding
(Kim and Kim, 2008). Mata (2011) interprets concrete
dam behavior with artificial neural network and multiple
linear regression models. The results of this study show
that NN models can be a powerful tool to be included in
assessments of existing concrete dam behavior (Mata,
2011).
CASE STUDY
Karun 4 dam construction site: Karun 4 dam is located
in plaited chains of Zagros Mountain which runs along
north-west to south-east. The chief bed of the reservoir is
Technical considerations on the extensometers
installed in the body of Karun 4 dam: Karun 4 dam is
designed with 11 galleries respectively from DG1
(Drainage Gallery) elevation 1016 to DG11 elevation 807
respectively from the top elevation (dam crest elevation
1032) to the bottom elevation (dam foundation elevation
806) within the body of the dam. Galleries elevations and
the elevation whose extensometer and anchors are
installed, along with their readings (displacement in the
same elevation in which the anchor is installed) in left and
right abutments are presented in Table 1 and 2. In the
right and the left bank, respectively 2 and 4 instruments
were refrained as a result of overdue installation and
lack of ideal readings and are not applied in predicting
(Table 1 and 2 with asterisks). In respective readings,
positive displacement depicts the ascent of the rod or the
subsidence of the body of dam, and negative displacement
indicates downward movement of the rod.
Extensometers are installed in dam banks (the contact
surface between dam body and rock mass) with
determined dip and azimuth. In Karun 4 dam 19
Extensometers are implemented in the left, 17 in the right
bank and one in the middle. Figure 2 illustrates the
extensometers layout in the concrete double-arch dam,
Karun 4.
Fig. 2: A view of the extensometers installed in foundation and abutment of Karun 4 dam
4608
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
Table 1: Information on the extensometers installed in the right bank (Karun 4) (Mahab-Ghodss Consulting Engineering Company, 2010b)
Displacement readings in 7 water elevation
Instrument coding and
Anchors
-------------------------------------------------------------------------------------------------------------start point elevation
Rodlength elevation
943.68
953.36
963.91
973.55
983.28
993.17
1003.13
EX30-FBI
9
978.0000
*
987
12
975.0000
18
969.0000
30
957.0000
EX30-FB2
9
972.0000
*
981
12
969.0000
18
963.0000
30
951.0000
EX36-18-974/2
12
970.6958
0.20
0.28
0.35
0.49
0.65
0.89
1.26
974.8
18
968.6436
0.34
0.44
0.58
0.80
1.07
1.44
1.99
24
966.5915
0.43
0.55
0.74
1.02
1.39
1.86
2.52
36
962.4873
0.55
0.72
0.97
1.34
1.81
2.49
2.32
EX36-18-974/3
12
971.0918
0.19
0.24
0.32
0.43
0.59
0.83
1.19
974.8
18
969.2377
0.29
0.38
0.50
0.68
0.92
1.28
1.78
24
967.3836
0.40
0.52
0.71
0.93
1.28
1.69
2.44
36
963.6754
0.52
0.70
0.96
1.28
1.81
2.52
3.45
EX36-16-953/3
12
948.3521
0.04
0.05
0.05
0.10
0.13
0.15
0.26
953.8
18
945.6282
0.06
0.08
0.11
0.21
0.28
0.28
0.41
24
942.9042
0.06
0.07
0.12
0.24
0.31
0.31
0.41
36
937.4563
0.13
0.22
0.38
0.65
0.75
0.83
1.31
EX36-16-953/2
12
947.8000
0.08
0.09
0.10
0.13
0.15
0.19
0.35
953.8
18
944.8000
0.13
0.17
0.20
0.24
0.21
0.31
0.58
24
941.8000
0.15
0.21
0.25
0.29
0.21
0.29
0.61
36
935.8000
0.16
0.24
0.33
0.36
0.09
0.11
0.62
EX45-14-932/2
9
928.1000
0.09
0.10
0.12
0.14
0.11
0.27
0.47
932.6
15
925.1000
0.12
0.17
0.20
0.24
0.25
0.36
0.62
24
920.6000
0.23
0.29
0.35
0.40
0.33
0.47
0.87
45
910.1000
0.38
0.53
0.74
0.90
0.88
1.01
1.53
EX45-14-932/3
9
928.5141
0.07
0.09
0.11
0.15
0.12
0.30
0.47
932.6
15
925.7901
0.11
0.16
0.21
0.26
0.24
0.45
0.68
27
920.3423
0.20
0.27
0.41
0.52
0.61
0.93
1.22
45
912.1704
0.28
0.51
0.78
0.98
1.30
1.84
2.27
EX54-12-911/2
9
907.3000
0.01
0.01
-0.04
0.03
-0.03
-0.11
-0.09
911.8
15
904.3000
0.02
0.02
-0.02
0.05
0.02
-0.03
0.06
27
898.3000
0.04
0.06
0.03
0.14
0.10
-0.06
-0.10
54
884.8000
0.04
0.14
0.20
0.45
0.39
0.18
0.14
EX54-12-911/3
12
906.5395
0.09
0.10
0.11
0.23
0.25
0.34
0.50
911.8
18
903.9093
0.17
0.24
0.29
0.47
0.56
0.72
0.96
27
899.9640
0.25
0.41
0.54
0.86
1.08
1.40
1.81
54
888.1280
0.75
1.11
1.58
2.27
2.89
3.81
4.80
EX54-10-890/2
9
885.1149
0.02
0.01
-0.01
0.04
0.02
0.06
0.15
890.9
15
881.2582
0.00
0.00
-0.02
0.05
0.04
0.08
0.19
27
873.5447
0.07
0.10
0.12
0.26
0.28
0.35
0.49
54
856.1895
0.09
0.22
0.41
0.77
1.02
1.31
1.57
EX54-10-890/3
12
884.0171
0.11
0.12
0.11
0.21
0.24
0.36
0.55
890.9
18
880.5756
0.16
0.24
0.27
0.42
0.51
0.70
0.95
27
875.4134
0.29
0.42
0.55
0.82
1.04
1.36
1.75
54
859.9269
0.35
0.58
0.92
1.53
2.14
3.04
4.06
EX54-08-869/2
12
861.3147
0.08
0.10
0.10
0.22
0.21
0.26
0.36
869.8
18
857.0721
0.10
0.13
0.14
0.26
0.25
0.31
0.42
27
850.7081
0.14
0.20
0.22
0.37
0.45
0.51
0.62
54
831.6162
0.12
0.20
0.30
0.50
0.65
0.89
1.17
EX54-08-869/3
12
861.7704
0.16
0.21
0.24
0.38
0.41
0.52
0.69
869.8
21
855.7483
0.25
0.31
0.36
0.54
0.58
0.69
0.87
36
845.7113
0.41
0.53
0.66
0.95
1.05
1.28
1.54
54
833.6669
0.62
0.80
0.96
1.39
1.62
2.00
2.40
EX54-06-848/2
9
841.3676
0.04
0.04
0.02
0.08
0.05
0.03
0.13
848.74
15
836.4527
0.05
0.06
0.04
0.11
0.09
0.07
0.16
27
826.6229
0.03
0.00
-0.01
0.08
0.04
0.08
0.11
54
804.5058
0.05
0.06
0.03
0.12
0.06
0.09
0.17
EX54-06-848/3
12
839.5575
0.17
0.20
0.21
0.32
0.32
0.39
0.51
848.75
18
834.9612
0.31
0.36
0.40
0.57
0.58
0.70
0.86
4609
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
Table 1: (Continue)
Instrument coding and
start point elevation
Ex54-04-827/3
827.58
Rodlength
30
54
9
15
27
54
Anchors
elevation
825.7687
807.3836
820.0320
814.9999
804.9359
782.2918
Displacement readings in 7 water elevation
-------------------------------------------------------------------------------------------------------------943.68
953.36
963.91
973.55
983.28
993.17
1003.13
0.41
0.50
0.58
0.77
0.83
1.03
1.21
0.46
0.65
0.79
1.06
1.23
1.50
1.80
0.03
0.03
0.02
0.08
0.02
-0.01
0.07
0.08
0.10
0.10
0.16
0.10
0.08
0.16
0.13
0.14
0.15
0.23
0.19
0.15
0.24
0.09
0.11
0.12
0.18
0.16
0.15
0.25
Table 2: Information on the extensometers installed on the left bank (Karun 4)
Displacement readings in 7 water elevation
Instrument coding and
Anchors
-------------------------------------------------------------------------------------------------------------start point elevation
Rodlength elevation
943.68
953.36
963.91
973.55
983.28
993.17
1003.13
EX54-19-1016/1
27
1015.047
*
1017.4
36
1014.262
45
1013.478
54
1012.694
EX24-19-1016/3
9
1014.723
*
1016.9
15
1013.271
24
1011.094
EX24-17-998/3
9
990.7673
*
999.5
15
984.9456
24
976.2129
30
970.3911
EX54-17-998/1
27
972.6027
0.05
0.09
0.19
0.27
0.52
0.95
1.39
999.5
36
963.6370
-0.05
-0.02
0.08
0.13
0.39
0.70
1.10
45
954.6712
-0.01
0.02
0.11
0.17
0.40
0.65
0.97
54
945.7055
-0.02
0.01
0.10
0.14
0.39
0.55
0.81
EX36-15-974/3
12
971.8969
0.00
-0.01
-0.01
0.01
0.05
0.09
0.20
974.8
18
970.4454
0.07
0.13
0.19
0.29
0.43
0.63
1.00
24
968.9939
0.10
0.19
0.30
0.43
0.64
0.88
1.39
45
963.9135
0.14
0.22
0.34
0.53
0.74
1.05
1.59
EX36-15-974/2
9
971.7218
*
974.8
15
969.6697
24
966.5915
36
962.4873
EX42-13-953/2
9
949.3000
0.07
0.08
0.07
0.09
0.11
0.15
0.20
953.8
15
946.3000
0.10
0.13
0.14
0.18
0.08
0.10
0.20
24
941.8000
0.08
0.11
0.13
0.15
0.15
0.15
0.20
42
932.8000
0.12
0.20
0.30
0.38
0.41
0.45
0.54
EX42-13-953/3
15
947.4607
0.11
0.16
0.25
0.38
0.52
0.65
0.85
953.8
21
944.9250
0.07
0.14
0.26
0.43
0.61
0.77
1.04
27
942.3893
0.08
0.16
0.30
0.51
0.74
0.95
1.29
42
936.0500
0.10
0.15
0.38
0.72
1.13
1.49
2.34
EX45-13-932/3
9
928.3000
0.15
0.23
0.34
0.47
0.65
0.86
1.13
932.8
18
923.8000
0.18
0.29
0.43
0.60
0.82
1.09
1.42
24
920.8000
0.18
0.30
0.64
0.66
0.91
1.20
1.56
45
910.3000
0.29
0.47
0.67
0.97
1.30
1.81
2.38
EX-LDGI
9
929.3247
-0.04
-0.03
-0.01
0.04
0.07
0.13
0.23
932.55
24
923.9492
0.00
0 .02
0.04
0.25
0.28
0.31
0.42
left
33
920.7239
-0.05
-0.04
-0.02
0.37
0.40
0.42
0.56
39
918.5736
-0.03
-0.01
0.01
1.63
1.63
1.68
1.77
EX45-13-932/2
12
925.9171
0.10
0.15
0.20
0.29
0.41
0.53
0.71
932.8
18
922.4756
0.25
0.35
0.47
0.62
0.81
1.05
1.38
27
917.3134
0.06
0.19
0.38
0.52
0.74
1.01
1.34
45
906.9891
0.23
0.37
0.61
0.86
1.19
1.52
1.96
EX54-11-911/2
12
905.8000
0.18
0.22
0.23
0.39
0.37
0.44
0.53
911.8
18
902.8000
0.15
0.21
0.23
0.40
0.40
0.49
0.63
24
899.8000
0.21
0.31
0.36
0.53
0.54
0.67
0.85
57
883.3000
0.23
0.56
0.80
1.25
1.24
1.42
1.78
EX54-11-911/3
12
906.9192
0.09
0.13
0.13
0.24
0.23
0.33
0.46
911.8
18
904.4787
0.19
0.26
0.31
0.47
0.50
0.66
0.79
27
900.8181
0.21
0.31
0.42
0.65
0.73
0.95
1.19
4610
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
Table 2: (Continue)
Instrument coding and
start point elevation
EX54-09-890/3
890.8
EX54-09-890/2
890.6
EX54-09-869/3
869.8
EX54-09-869/2
869.8
EX54-07-848/3
848.881
EX54-07-848/2
848.761
EX54-05-827/3
827.829
EX42-00-806/3
806.4
Rodlength
54
9
15
27
45
9
15
27
54
9
15
27
54
9
18
27
54
12
18
24
54
9
15
27
54
9
15
27
54
9
15
24
42
Anchors
elevation
889.8362
885.8982
882.6304
876.0947
866.2912
884.8149
880.9582
873.2447
855.8895
864.6378
861.1964
854.3134
838.8269
863.4360
857.0721
850.7081
831.6162
840.1048
835.7166
831.3285
809.3879
841.3886
836.4737
826.6439
804.5268
820.9346
816.3383
807.1458
786.4626
800.0361
795.7934
789.4295
776.7016
Displacement readings in 7 water elevation
-----------------------------------------------------------------------------------------------------------943.68
953.36
963.91
973.55
983.28
993.17
1003.13
0.41
0.71
1.04
1.50
1.93
2.49
3.04
0.10
0.11
0.12
0.24
0.23
0.29
0.39
0.15
0.19
0.21
0.38
0.41
0.50
0.33
0.10
0.14
0.13
0.42
0.46
0.52
0.53
0.07
0.11
0.13
0.64
0.65
0.73
0.41
0.11
0.11
0.11
0.27
0.24
0.29
0.35
0.14
0.17
0.16
0.44
0.38
0.45
0.54
0.24
0.30
0.32
0.60
0.61
0.69
0.41
0.15
0.30
0.45
1.01
0.97
0.94
0.42
0.18
0.22
0.23
0.38
0.48
0.46
0.59
0.34
0.41
0.47
0.69
0.74
0.88
1.07
0.59
0.74
0.87
1.17
1.32
1.59
1.86
0.66
0.86
1.07
1.43
1.62
1.88
2.20
0.13
0.15
0.15
0.27
0.29
0.33
0.41
0.20
0.25
0.24
0.39
0.44
0.48
0.55
0.39
0.47
0.53
0.75
0.81
0.97
1.06
0.46
0.66
0.76
1.12
1.27
1.51
1.55
0.23
0.28
0.32
0.46
0.46
0.47
0.64
0.40
0.47
0.56
0.72
0.76
0.88
1.11
0.48
0.58
0.69
0.91
1.01
1.17
1.41
0.67
0.89
1.09
1.40
1.67
1.93
2.25
0.14
0.18
0.19
0.27
0.25
0.30
0.43
0.17
0.24
0.28
0.36
0.38
0.43
0.59
0.24
0.32
0.38
0.50
0.52
0.60
0.78
0.28
0.32
0.43
0.64
0.70
0.79
0.94
0.22
0.25
0.26
0.38
0.33
0.36
0.45
0.37
0.43
0.45
0.60
0.60
0.65
0.78
0.55
0.65
0.74
0.92
0.97
1.07
1.25
0.65
0.79
0.94
1.23
1.36
1.52
1.88
0.14
0.16
0.16
0.26
0.24
0.30
0.42
0.38
0.44
0.47
0.60
0.64
0.75
0.94
0.51
0.61
0.68
0.85
0.92
1.06
1.33
0.55
0.64
0.73
0.95
1.05
1.22
1.47
Table 3: Results of displacement prediction in the right bank using cubic, linear, and quadratic models
Anchor points ( a1-a60 )
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Water elevvation a1
a2
a3
a4
a5
a6
a7
a8
a9
a10
a11
a12
a13
a14
a15
a16
a17
943.68
0.2000 0.3400 0.4300 0.5500 0.1900 0.2900 0.4000 0.5200 0.0400 0.0600 0.0600 0.1300 0.0800 0.1300 0.1500 0.1600 0.0900
953.36
0.2800 0.4400 0.5500 0.7200 0.2400 0.3800 0.5200 0.7000 0.0500 0.0800 0.0700 0.2200 0.0900 0.1700 0.2100 0.2400 0.1000
963.91
0.3500 0.5800 0.7400 0.9700 0.3200 0.5000 0.7100 0.9600 0.0500 0.1100 0.1200 0.3800 0.1000 0.2000 0.2500 0.3300 0.1200
973.55
0.4900 0.8000 1.0200 1.3400 0.4300 0.6800 0.9300 1.2800 0.1000 0.2100 0.2400 0.6500 0.1300 0.2400 0.2900 0.3600 0.1400
983.28
0.6500 1.0700 1.3900 1.8100 0.5900 0.9200 1.2800 1.8100 0.1300 0.2800 0.3100 0.7500 0.1500 0.2100 0.2100 0.0900 0.1100
993.17
0.8900 1.4400 1.8600 2.4900 0.8300 1.2800 1.6900 2.5200 0.1500 0.2800 0.3100 0.8300 0.1900 0.3100 0.2900 0.1100 0.2700
1003.13
1.2600 1.9900 2.5200 2.3200 1.1900 1.7800 2.4400 3.4500 0.2600 0.4100 0.4100 1.3100 0.3500 0.5800 0.6100 0.6200 0.4700
Prediction1013 1.2603 2.0142 2.5785 2.8417 1.1769 1.7883 2.4286 3.5030 0.2459 0.4361 0.4626 1.3427 0.3075 0.4974 0.5017 0.3983 0.3957
Prediction1023 1.4282 2.2799 2.9192 3.1878 1.3358 2.0272 2.7511 3.9773 0.2795 0.4940 0.5240 1.5259 0.3454 0.5560 0.5553 0.4297 0.4482
Prediction1032 1.5961 2.5456 3.2599 3.5339 1.4947 2.2661 3.0736 4.4516 0.3131 0.5519 0.5854 1.7091 0.3833 0.6146 0.6089 0.4611 0.5007
0.9192 0.9291 0.9362 0.9438 0.9043 0.9194 0.9178 0.9261 0.8602 0.9470 0.9541 0.9446 0.7604 0.7045 0.5894 0.1348 0.6620
R2 (linear)
Prediction1013 1.5970 2.5166 3.1931 2.9321 1.5293 2.2690 3.0737 4.4185 0.3275 0.4814 0.4777 1.5156 0.4340 0.6917 0.6817 0.5706 0.6203
Prediction1023 2.0163 3.1579 3.9932 3.3472 1.9513 2.8687 3.8796 5.5802 0.4216 0.5749 0.5500 1.8284 0.5665 0.8961 0.8703 0.7308 0.8397
Prediction1032 2.4914 3.8826 4.8953 3.7777 2.4317 3.5486 4.7929 6.8947 0.5291 0.6764 0.6247 2.1700 0.7200 1.1329 1.0889 0.9196 1.0961
R2 (Quadratic) 0.9951 0.9977 0.9991 0.9452 0.9957 0.9972 0.9941 0.9982 0.9620 0.9609 0.9552 0.9621 0.9351 0.8660 0.7280 0.2184 0.9074
Prediction1013 1.7638 2.6494 3.3135 2.1089 1.6725 2.4318 3.3561 4.6713 0.3579 0.4406 0.4113 1.7364 0.5372 0.9749 1.1185 1.4214 0.8299
Prediction1023 2.4153 3.5199 4.3051 1.2712 2.3063 3.2828 4.6047 6.2193 0.5085 0.4406 0.3690 2.3583 0.8425 1.6221 1.9443 2.8357 1.3757
Prediction1032 3.2494 4.6046 5.5063 -0.2493 3.1157 4.3546 6.2089 8.1357 0.7051 0.4406 0.2637 3.1780 1.2670 2.5499 3.1519 4.9726 2.1411
0.9995 0.9997 0.9999 0.9783 0.9998 0.9999 0.9988 0.9999 0.9692 0.9616 0.9648 0.9688 0.9806 0.9760 0.9436 0.7781 0.9766
R2 (Cubic)
a18
a19
a20
a21
a22
a23
a24
a25
a26
a27
a28
a29
a30
a31
a32
a33
a34
943.68
0.1200 0.2300 0.3800 0.0700 0.1100 0.2000 0.2800 0.0100 0.0200 0.0400 0.0400 0.0900 0.1700 0.2500 0.7500 0.0200 0.0000
953.36
0.1700 0.2900 0.5300 0.0900 0.1600 0.2700 0.5100 0.0100 0.0200 0.0600 0.1400 0.1000 0.2400 0.4100 1.1100 0.0100 0.0000
963.91
0.2000 0.3500 0.7400 0.1100 0.2100 0.4100 0.7800 -0.0400 -0.020 0.0300 0.2000 0.1100 0.2900 0.5400 1.5800 -0.0100 -0.0200
973.55
0.2400 0.4000 0.9000 0.1500 0.2600 0.5200 0.9800 0.0300 0.0500 0.1400 0.4500 0.2300 0.4700 0.8600 2.2700 0.0400 0.0500
983.28
0.2500 0.3300 0.8800 0.1200 0.2400 0.6100 1.3000 -0.0300 0.0200 0.1000 0.3900 0.2500 0.5600 1.0800 2.8900 0.0200 0.0400
993.17
0.3600 0.4700 1.0100 0.3000 0.4500 0.9300 1.8400 -0.1100 -0.030 -0.0600 0.1800 0.3400 0.7200 1.4000 3.8100 0.0600 0.0800
1003.13
0.6200 0.8700 1.5300 0.4700 0.6800 1.2200 2.2700 -0.0900 0.0600 -0.1000 0.1400 0.5000 0.9600 1.8100 4.80000 0.1500 0.1900
4611
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
Table 3: (Continue)
Anchor points ( a1-a60 )
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Water elevvation a18
a19
a20
a21
a22
a23
a24
a25
a26
a27
a28
a29
a30
a31
a32
a33
a34
Prediction1013 0.5555 0.7427 1.5029 0.4199 0.6332 1.2488 2.4444 -0.1069 0.0254 -0.0545 0.3018 0.4959 1.0017 1.9354 5.1880 0.1159 0.1613
Prediction1023 0.6244 0.8234 1.6654 0.4781 0.7161 1.4124 2.7712 -0.1258 0.0275 -0.0756 0.3222 0.5620 1.1303 2.1925 5.8267 0.1345 0.1895
Prediction1032 0.6933 0.9041 1.8279 0.5363 0.7990 1.5760 3.0980 -0.1447 0.0296 -0.0967 0.3426 0.6281 1.2589 2.4496 6.5003 0.1531 0.2177
R2 (linear)
0.7890 0.6721 0.8943 0.7428 0.8149 0.9311 0.9695 0.59410 0.0197 0.2891 0.0900 0.8969 0.9564 0.9724 0.9742 0.5788 0.7311
Prediction1013 0.7509 1.0061 1.6602 0.6221 0.8577 1.5264 2.8120 -0.1520 0.0555 -0.2339 -0.0813 0.6309 1.1743 2.2211 5.9029 0.2126 0.2591
Prediction1023 0.9679 1.2854 1.9399 0.8316 1.1082 1.8994 3.4157 -0.2043 0.0794 -0.3892 -0.3473 0.7986 1.4332 2.6924 7.1397 0.3026 0.3610
Prediction1032 1.2179 1.6089 2.2456 1.0747 1.3959 2.3190 4.0810 -0.2640 0.1081 -0.5743 -0.6769 0.9889 1.7211 3.2113 8.5017 0.4084 0.4793
R2 (Quadratic) 0.9255 0.8239 0.9114 0.9281 0.9377 0.9880 0.9954 0.6619 0.0924 0.7217 0.7478 0.9757 0.9930 0.9974 0.9995 0.8896 0.9171
Prediction1013 1.0045 1.4685 2.1766 0.8021 1.0805 1.6656 2.9624 -0.1284 0.1087 -0.3239 -0.2073 0.6441 1.2103 2.2335 5.9397 0.2666 0.3123
Prediction1023 1.6079 2.4605 3.2459 1.2816 1.6952 2.2695 3.7797 -0.1603 0.2094 -0.6142 -0.6664 0.8496 1.5273 2.7425 7.2347 0.4335 0.4910
Prediction1032 2.4599 3.8949 4.7816 1.9447 2.5529 3.0510 4.7760 -0.1900 0.3571 -1.0093 -1.2969 1.1009 1.9061 3.3223 8.6877 0.6584 0.7283
R2 (Cubic)
0.9923 0.9654 0.9681 0.9704 0.9819 0.9933 0.9965 0.6629 0.1561 0.7531 0.7697 0.9768 0.9936 0.9975 0.9995 0.9145 0.9307
a35
a36
a37
a38
a39
a40
a41
a42
a43
a44
a45
a46
a47
a48
a49
a50
a51
943.68
0.0700 0.0900 0.1100 0.1600 0.2900 0.3500 0.0800 0.1000 0.1400 0.1200 0.1600 0.2500 0.4100 0.6200 0.0400 0.0500 0.0300
953.36
0.1000 0.2200 0.1200 0.2400 0.4200 0.5800 0.1000 0.1300 0.2000 0.2000 0.2100 0.3100 0.5300 0.8000 0.0400 0.0600 0.0000
963.91
0.1200 0.4100 0.1100 0.2700 0.5500 0.9200 0.1000 0.1400 0.2200 0.3000 0.2400 0.3600 0.6600 0.9600 0.0200 0.0400 -0.0100
973.55
0.2600 0.7700 0.2100 0.4200 0.8200 1.5300 0.2200 0.2600 0.3700 0.5000 0.3800 0.5400 0.9500 1.3900 0.0800 0.1100 0.0800
983.28
0.2800 1.0200 0.2400 0.5100 1.0400 2.1400 0.2100 0.2500 0.4500 0.6500 0.4100 0.5800 1.0500 1.6200 0.0500 0.0900 0.0400
993.17
0.3500 1.3100 0.3600 0.7000 1.3600 3.0400 0.2600 0.3100 0.5100 0.8900 0.5200 0.6900 1.2800 2.0000 0.0300 0.0700 0.0800
1003.13
0.4900 1.5700 0.5500 0.9500 1.7500 4.0600 0.3600 0.4200 0.6200 1.1700 0.6900 0.8700 1.5400 2.4000 0.1300 0.1600 0.1100
Prediction1013 0.5131 1.8027 0.5183 0.9688 1.8545 4.2701 0.3718 0.4345 0.6858 1.2444 0.7129 0.9198 1.6717 2.5986 0.0957 0.1401 0.1117
Prediction1023 0.5817 2.0609 0.5872 1.0949 2.0956 4.8869 0.4172 0.4856 0.7676 1.4187 0.7979 1.0212 1.8603 2.8986 0.1057 0.1544 0.1278
Prediction1032 0.6503 2.3191 0.6561 1.2210 2.3367 5.5037 0.4626 0.5367 0.8494 1.5930 0.8829 1.1226 2.0489 3.1986 0.1157 0.1687 0.1439
R2 (linear)
0.9439 0.9885 0.8338 0.9346 0.9661 0.9512 0.9086 0.9268 0.9760 0.9639 0.9491 0.9674 0.9843 0.9804 0.3267 0.5525 0.6056
Prediction1013 0.5947 1.9372 0.7206 1.1866 2.1617 5.2368 0.4243 0.4870 0.7309 1.4698 0.8251 1.0099 1.7912 2.8541 0.1406 0.1699 0.1563
Prediction1023 0.7238 2.2955 0.9408 1.4764 2.6332 6.5775 0.5107 0.5791 0.8461 1.8147 0.9939 1.1781 2.0683 3.3465 0.1847 0.2074 0.2043
Prediction1032 0.8663 2.6760 1.1946 1.8026 3.1559 8.0790 0.6063 0.6804 0.9687 2.1976 1.1813 1.3611 2.365 3.8817 0.2364 0.2501 0.2593
R2 (Quadratic) 0.9706 0.9940 0.9822 0.9931 0.9987 0.9996 0.9371 0.9498 0.9820 0.9985 0.9831 0.9827 0.9922 0.9954 0.4689 0.6082 0.6894
Prediction1013 0.6119 1.7212 0.7706 1.2766 2.1749 5.2500 0.4479 0.5002 0.6533 1.4934 0.8791 1.0507 1.7676 2.7877 0.1898 0.2303 0.0959
Prediction1023 0.7597 1.7514 1.0868 1.7014 2.6842 6.6285 0.5547 0.6301 0.6712 1.8587 1.1248 1.2580 2.0243 3.1655 0.3298 0.3464 0.0653
Prediction1032 0.9303 1.6210 1.4926 2.2376 3.2679 8.1910 0.6803 0.7924 0.6447 2.2716 1.4313 1.4991 2.2910 3.5207 0.5334 0.5101 -0.0007
R2 (Cubic)
0.9708 0.9982 0.9873 0.9960 0.9988 0.9996 0.9374 0.9517 0.9851 0.9985 0.9851 0.9830 0.9922 0.9958 0.5642 0.6485 0.7243
a52
a53
a54
a5500 a56
a57
a58
a59
a60
943.68
0.0500 0.1700 0.3100 0.4100 0.4600 0.0300 0.0800 0.1300 0.0900 953.36
0.0600 0.2000 0.3600 0.5000 0.6500 0.0300 0.1000 0.1400 0.1100 963.91
0.0300 0.2100 0.4000 0.5800 0.7900 0.0200 0.1000 0.1500 0.1200 973.55
0.1200 0.3200 0.5700 0.7700 1.0600 0.0800 0.1600 0.2300 0.1800 983.28
0.0600 0.3200 0.5800 0.8300 1.2300 0.0200 0.1000 0.1900 0.1600 993.17
0.0900 0.3900 0.7000 1.0300 1.5000 -0.010 0.0800 0.1500 0.1500 1003.13
0.1700 0.5100 0.8600 1.2100 1.8000 0.0700 0.1600 0.2400 0.2500 Prediction1013 0.1474 0.5183 0.8982 1.2914 1.9500 0.0398 0.1397 0.2312 0.2369 Prediction1023 0.1635 0.5722 0.9878 1.4239 2.1700 0.0412 0.1468 0.2451 0.2583 Prediction1032 0.1796 0.6261 1.0774 1.5564 2.3900 0.0426 0.1539 0.2590 0.2797 2
R ( linear )
0.5187 0.9260 0.9558 0.9775 0.9889 0.0099 0.2016 0.4538 0.7525 Prediction1013 0.1990 0.5941 0.9882 1.4043 2.0929 0.0475 0.1331 0.2167 0.2593 Prediction1023 0.2531 0.7047 1.1453 1.6214 2.4200 0.0551 0.1356 0.2205 0.2963 Prediction1032 0.3156 0.8279 1.3174 1.8573 2.7709 0.0641 0.1371 0.2205 0.3367 2
R (Quadratic) 0.6233 0.9640 0.9759 0.9923 0.9976 0.0173 0.2043 0.4618 0.7662 Prediction1013 0.2766 0.6301 1.0014 1.4443 2.1461 0.1139 0.2459 0.2935 0.3257 Prediction1023 0.4280 0.7988 1.1963 1.7004 2.5500 0.2361 0.4037 0.3945 0.4773 Prediction1032 0.6396 1.0129 0.6294 1.9943 3.0199 0.4251 0.6451 0.5451 0.6977 2
R ( Cubic )
0.6663 0.9670 0.9765 0.9924 0.9979 0.2021 0.4395 0.5119 0.8286 -
Table 4: Model summary and parameter estimates (using SPSS software), Dependent variable: a32
Model summary
Parameter estimates
-------------------------------------------------------------------------------------------------------------------------------------------F
df1
df2
Sig.
Constant
b1
b2
b3
Equation
R2
Linear
0.974
180.355
1
5
0.000
-63.696
0.068
Quadratic
0.999
201.512
1
5
0.000
-30.681
0.000
3.496E-5
Cubic
0.999
3734.820
2
4
0.000
346.997
-0.565
0.000
2.227E-7
The independent variable is water elevation
Table 5: Model summary and parameter estimates (by using of SPSS software), Dependent variable: a56
Model summary
Parameter estimates
-------------------------------------------------------------------------------------------------------------------------------------------2
F
df1
df2
Sig.
Constant
b1
b2
b3
Equation
R
Linear
0.988
408.404
1
5
0.000
-20.539
0.022
Quadratic
0.997
472.956
1
5
0.000
-9.749
0.000
1.141E-5
Cubic
0.997
760.711
2
4
0.000
59.150
-0.101
0.000
4.322E-8
The independent variable is water elevation
4612
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
Table 6: Results of displacement prediction in the right bank using cubic, linear, and quadratic equations
Anchor points (a1- a68 )
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Water elevvation
a1
a2
a3
a4
a5
a6
a7
a8
a9
a10
a11
a12
a13
a14
a15
a16
a17
943.68
0.050
-0.050 -0.010 -0.020 0.000 0.070 0.100 0.140 0.070
0.100 0.080 0.120 0.110 0.070 0.080
0.100
0.150
953.36
0.090
-0.020
0.020
0.010 -0.010 0.130 0.190 0.220 0.080
0.130 0.110 0.200 0.160 0.140 0.160
0.150
0.230
963.91
0.190
0.080
0.110
0.100 -0.010 0.190 0.300 0.340 0.070
0.140 0.130 0.300 0.250 0.260 0.300
0.380
0.340
973.55
0.270
0.130
0.170
0.140 0.010 0.290 0.430 0.530 0.090
0.180 0.150 0.380 0.380 0.430 0.510
0.720
0.470
983.28
0.520
0.390
0.400
0.390 0.050 0.430 0.640 0.740 0.110
0.080 0.150 0.410 0.520 0.610 0.740
1.130
0.650
993.17
0.950
0.700
0.650
0.550 0.090 0.630 0.880 1.050 0.150
0.100 0.150 0.450 0.650 0.770 0.950
1.490
0.860
1003.13
1.390
1.100
0.970
0.810 0.200 1.000 1.390 1.590 0.200
0.200 0.080 0.120 0.110 0.070 0.080
0.100
0.150
Prediction1013
1.362
1.076
0.972
0.835 0.170 0.967 1.360 1.574 0.192
0.158 0.204 0.610 0.913 1.120 2.351
2.351
1.362
Prediction1023
1.578
1.261
1.132
0.973 0.201 1.111 1.559 1.803 0.212
0.165 0.221 0.677 1.037 1.281 2.714
2.714
1.578
Prediction1032
1.795
1.447
1.293
1.110 0.231 1.255 1.759 2.032 0.233
0.171 0.237 0.744 1.160 1.443 3.076
3.076
1.795
2
R (linear)
0.869
0.876
0.897
0.916 0.747 0.891 0.907 0.913 0.817
0.099 0.891 0.975 0.973 0.974 0.925
0.925
0.869
Prediction1013
1.932
1.548
1.339
1.111 0.290 1.297 1.773 2.047 0.259
0.174 0.197 0.558 1.048 1.293 3.034
3.034
1.932
Prediction1023
2.576
2.089
1.777
1.456 0.411 1.690 2.284 2.629 0.328
0.193 0.208 0.586 1.275 1.584 3.909
3.909
2.576
Prediction1032
3.315
2.709
2.276
1.846 0.551 2.139 2.864 3.289 0.408
0.214 0.219 0.607 1.525 1.905 4.899
4.899
3.315
R2(Quadratic)
0.994
0.995
0.997
0.992 0.985 0.990 0.989 0.994 0.987
0.113 0.893 0.986 0.998 0.998 0.993
0.993
0.994
Prediction1013
2.098
1.652
1.416
1.111 0.327 1.501 2.026 2.257 0.299
0.378 0.274 0.635 1.008 1.275 1.583
3.201
1.446
Prediction1023
2.975
2.365
1.951
1.456 0.506 2.184 2.923 3.165 0.408
0.687 0.383 0.761 1.196 1.548 1.926
4.308
1.830
Prediction1032
4.073
3.256
2.599
1.846 0.737 3.083 4.105 4.335 0.546
1.158 0.543 0.931 1.388 1.841 2.291
5.657
2.284
2
R (Cubic)
0.997
0.997
0.997
0.992 0.993 0.999 0.9979 0.999 0.992
0.626 0.964 0.991 0.999 0.998 0.998
0.994
1.000
a18
a19
a20
a21
a22
a23
a24
a25
a26
a27
a28
a29
a30
a31
a32
a33
a34
943.68
0.180
0.180
0.290
-0.040 0.000
-0.050 -0.030 0.100 0.250
0.060 0.230 0.180 0.150 0.210 0.230
0.090
0.190
953.36
0.290
0.300
0.470
-0.030 0.020
-0.040 -0.010 0.150 0.350
0.190 0.370 0.220 0.210 0.310 0.560
0.130
0.260
963.91
0.430
0.640
0.670
-0.010 0.040
-0.020 0.010 0.200 0.470
0.380 0.610 0.230 0.230 0.360 0.800
0.130
0.310
973.55
0.600
0.660
0.970
0.040 0.250
0.370 1.630 0.290 0.620
0.520 0.860 0.390 0.400 0.530 1.250
0.240
0.470
983.28
0.820
0.910
1.300
0.070 0.280
0.400 1.630 0.410 0.810
0.740 1.190 0.370 0.400 0.540 1.240
0.230
0.500
993.17
1.090
1.200
1.810
0.130 0.310
0.420 1.680 0.530 1.050
1.010 1.520 0.440 0.490 0.670 1.420
0.330
0.660
1003.13
1.420
1.560
2.380
0.230 0.420
0.560 1.770 0.710 1.380
1.340 1.960 0.530 0.630 0.850 1.780
0.460
0.790
Prediction1013
1.192
1.506
1.666
2.495 0.229
0.486 0.687 2.440 0.741
1.437 1.440 2.116 0.570 0.669 0.899
2.013
0.460
Prediction1023
1.353
1.709
1.888
2.838 0.272
0.560 0.800 2.811 0.841
1.620 1.649 2.404 0.628 0.746 0.999
2.256
0.518
Prediction1032
1.514
1.913
2.109
3.180 0.315
0.634 0.913 3.183 0.941
1.803 1.857 2.692 0.686 0.824 1.100
2.499
0.575
2
R (linear)
0.962
0.966
0.966
0.955 0.915
0.928 0.881 0.789 0.953
0.958 0.975 0.977 0.935 0.953 0.967
0.963
0.902
Prediction1013
1.416
1.768
1.868
3.006 0.318
0.508 0.679 2.050 0.891
1.699 1.665 2.416 0.599 0.729 0.966
1.862
0.565
Prediction1023
1.744
2.170
2.241
3.729 0.427
0.598 0.786 2.128 1.105
2.079 2.041 2.930 0.679 0.851 1.118
1.992
0.699
Prediction1032
2.109
2.616
2.648
4.538 0.551
0.691 0.890 2.141 1.343
2.502 2.454 3.494 0.762 0.982 1.281
2.095
0.850
2
R (Quadratic)
1.000
1.000
0.982
0.999 0.992
0.930 0.882 0.807 0.999
0.999 0.998 1.000 0.939 0.964 0.977
0.971
0.961
Prediction1013
1.829
2.061
3.109
0.331 0.371
0.409 0.561 0.939 1.789
1.772 2.416 0.576 0.741 1.080 2.085
0.607
0.959
Prediction1023
2.309
2.742
4.005
0.478 0.285
0.111 -1.617 1.193 2.304
2.302 2.930 0.635 0.901 1.387 2.579
0.836
1.142
Prediction1032
2.876
3.630
5.085
0.663 0.108
-0.415 -5.116 1.491 2.937
2.953 3.494 0.688 1.093 1.790 3.252
1.137
1.348
R2 (Cubic)
1.000
0.988
1.000
0.995 0.942
0.911 0.881 0.999 1.000
0.999 1.000 0.939 0.965 0.983 0.977
0.969
0.987
a35
a36
a37
a38
a39
a40
a41
a42
a43
a44
a45
a46
a47
a48
a49
a50
a51
943.68
0.210
0.410
0.100
0.150 0.100
0.070 0.110 0.140 0.240
0.150 0.180 0.340 0.590 0.660 0.130
0.200
0.390
953.36
0.310
0.710
0.110
0.190 0.140
0.110 0.110 0.170 0.300
0.300 0.220 0.410 0.740 0.860 0.150
0.250
0.470
963.91
0.420
1.040
0.120
0.210 0.130
0.130 0.110 0.160 0.320
0.450 0.230 0.470 0.870 1.070 0.150
0.240
0.530
973.55
0.650
1.500
0.240
0.380 0.420
0.640 0.270 0.440 0.600
1.010 0.380 0.690 1.170 1.430 0.270
0.390
0.750
983.28
0.730
1.930
0.230
0.410 0.460
0.650 0.240 0.380 0.610
0.970 0.480 0.740 1.320 1.620 0.290
0.440
0.810
993.17
0.950
2.490
0.290
0.500 0.520
0.730 0.290 0.450 0.690
0.940 0.460 0.880 1.590 1.880 0.330
0.480
0.970
1003.13
1.190
3.040
0.390
0.330 0.530
0.410 0.350 0.540 0.410
0.420 0.590 1.070 1.860 2.200 0.410
0.550
1.060
Prediction1013
0.853
1.284
3.351
0.403 0.505
0.669 0.789 0.384 0.609
0.678 0.979 0.643 1.143 2.015 2.419
0.439
0.609
Prediction1023
0.952
1.446
3.792
0.451 0.553
0.754 0.888 0.427 0.679
0.735 1.072 0.713 1.264 2.228 2.676
0.487
0.670
Prediction1032
1.052
1.608
4.233
0.499 0.602
0.839 0.987 0.471 0.750
0.791 1.165 0.783 1.385 2.440 2.934
0.535
0.731
2
R (linear)
0.973
0.979
0.988
0.912 0.652
0.879 0.558 0.865 0.856
0.467 0.317 0.936 0.972 0.987 0.995
0.938
0.951
Prediction1013
0.936
1.419
3.689
0.464 0.362
0.624 0.429 0.407 0.609
0.401 0.199 0.673 1.240 2.157 2.493
0.483
0.631
Prediction1023
1.099
1.683
4.381
0.558 0.305
0.677 0.260 0.468 0.681
0.250 -0.292 0.765 1.433 2.477 2.806
0.564
0.708
Prediction1032
1.275
1.969
5.129
0.663 0.225
0.722 0.031 0.533 0.754
0.052 -0.913 0.861 1.642 2.820 3.130
0.652
0.789
2
R (Quadratic)
0.987
0.993
1.000
0.945 0.764
0.884 0.709 0.870 0.856
0.702 0.777 0.940 0.984 0.996 0.996
0.954
0.954
Prediction1013
1.433
3.652
0.464
0.015 0.337 -0.357 0.364 0.502 -0.126 -0.677 0.599 1.217 2.144 2.481 0.447
0.565
1.081
Prediction1023
1.734
4.286
0.558
-0.544 -0.034 -1.721 0.331 0.420 -1.049 -2.498 0.575 1.389 2.427 2.756 0.469
0.527
1.049
Prediction1032
2.081
4.943
0.663
-1.403 -0.647 -3.810 0.246 0.255 -2.446 -5.189 0.489 1.568 2.709 3.019 0.466
0.428
0.927
R2 (Cubic)
0.993
1.000
0.945
0.943 0.941
0.924 0.884 0.866 0.930
0.949 0.947 0.984 0.996 0.996 0.958
0.964
0.988
a52
a53
a54
a55
a56
a57
a58
a59
a60
a61
a62
a63
a64
a65
a66
a67
a68
943.68
0.460
0.230
0.400
0.480 0.670
0.140 0.170 0.240 0.280
0.220 0.370 0.550 0.650 0.140 0.380
0.510
0.550
953.36
0.660
0.280
0.470
0.580 0.890
0.180 0.240 0.320 0.320
0.250 0.430 0.650 0.790 0.160 0.440
0.610
0.640
963.91
0.760
0.320
0.560
0.690 1.090
0.190 0.280 0.380 0.430
0.260 0.450 0.740 0.940 0.160 0.470
0.680
0.730
973.55
1.120
0.460
0.720
0.910 1.400
0.270 0.360 0.500 0.640
0.380 0.600 0.920 1.230 0.260 0.600
0.850
0.950
983.28
1.270
0.460
0.760
1.010 1.670
0.250 0.380 0.520 0.700
0.330 0.600 0.970 1.360 0.240 0.640
0.920
1.050
993.17
1.510
0.470
0.880
1.170 1.930
0.300 0.430 0.600 0.790
0.360 0.650 1.070 1.520 0.300 0.750
1.060
1.220
1003.13
1.550
0.640
1.110
1.410 2.250
0.430 0.590 0.780 0.940
0.450 0.780 1.250 1.880 0.420 0.940
1.330
1.470
Prediction1013
1.181
1.830
0.659
1.150 1.506
2.472 0.419 0.598 0.809
1.041 0.461 0.814 1.331 1.991 0.412
0.956
1.366
Prediction1023
1.299
2.026
0.721
1.263 1.659
2.736 0.461 0.660 0.892
1.155 0.496 0.879 1.445 2.190 0.455
1.044
1.495
Prediction1032
1.416
2.221
0.784
1.375 1.812
3.000 0.502 0.722 0.975
1.269 0.531 0.944 1.558 2.389 0.498
1.132
1.623
2
R (linear)
0.981
0.976
0.920
0.966 0.984
0.996 0.875 0.945 0.963
0.978 0.843 0.950 0.986 0.981 0.869
0.945
0.961
Prediction1013
1.212
1.755
0.681
1.255 1.610
2.576 0.485 0.652 0.869
1.063 0.469 0.845 1.361 2.111 0.493
1.083
1.508
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Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
Table 6: (Continue)
Water elevvation
Prediction1023
Prediction1032
R2 (Quadratic)
Prediction1013
Prediction1023
Prediction1032
R2 (Cubic)
Anchor points (a1- a68 )
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------a52
a53
a54
a55
a56
a57
a58
a59
a60
a61
a62
a63
a64
a65
a66
a67
a68
1.353
1.895
0.762
1.444 1.840
2.918 0.576 0.754 0.995
1.194 0.510 0.931 1.495 2.400 0.597
1.265
1.744
1.500
2.022
0.846
1.650 2.087
3.277 0.678 0.866 1.534
1.327 0.553 1.023 1.634 2.708 0.714
1.468
2.003
0.983
0.979
0.923
0.982 0.993
0.999 0.918 0.960 0.973
0.979 0.844 0.954 0.987 0.988 0.932
0.984
0.986
1.485
0.754
1.362
1.651 2.540
0.616 0.778 0.971 0.997
0.522 0.874 1.415 2.178 0.571 1.150
1.635
1.733
1.220
0.951
1.705
1.920 2.824
0.881 1.073 1.270 1.013
0.640 1.017 1.626 2.581 0.772 1.446
2.064
2.027
0.717
1.217
2.149
2.225 3.092
1.251 1.486 1.677 0.966
0.802 1.198 1.884 3.069 1.038 1.829
2.624
2.364
0.990
0.932
0.987
0.993 0.999
0.954 0.985 0.985 0.982
0.854 0.956 0.988 0.989 0.942 0.989
0.992
0.993
Table 7: Model summary and parameter estimates (using SPSS software), Dependent variable: a56
Model summary
Parameter estimates
-----------------------------------------------------------------------------------------------------------------------------------------F
df1
df2
Sig.
Constant
b1
b2
b3
Equation
R2
Linear
0.984
990.695
1
5
0.000
-24.547
0.027
Quadratic
0.993
1232.424
1
5
0.000
-11.579
0.000
1.371E-5
Cubic
0.999
1393.985
2
4
0.000
34.174
-0.064
0.000
3.185E-8
The independent variable is water elevation
Cubic: (With correlation coefficient 0.997)
Y = 4.322*10-8 * (x3) – 0.101 (x) + 59.150
DISPLACEMENT PREDICTION
Using the extensometer readings in 7 elevations
distancing 10 m from each other, a hidden relation
between pieces of data would be unveiled. The interesting
point is that the recorded displacements in right-left banks
except a series of anchors which are poorly installed or
those having improper readings, all prove to have high
rate of regression coefficient.
Left bank: Taking all the correlation coefficients in the
left bank and bearing in mind Table 6 among
extensometer anchors, the highest correlation coefficient
belongs to the anchor a56 (Table 7) pertaining to the first
anchor installed at the depth of 54 m EX54-07-848/3.
Resulted relations using Table 7 are as follows:
Right bank: Taking all the correlation coefficients in the
right bank, noting Table 3 among the extensometer
anchors, the highest correlation coefficient in anchors
(Table 4) a32 and (Table 5) a56 are respectively related to
the anchors first installed at a depth of 54 m from
extensometers EX54-12-911/3 and EX54-06-848/3.
Figure 3, 4, 5 and 6 shown results our methods.
Considering Table 4, results for the right bank are as
follows:
Linear: (With correlation coefficient 0.973) Y = 0.o68(x)
– 63.696
Linear: (With correlation coefficient 0.984)
Y = 0.027(x) – 24.547
Quadratic: (With correlation coefficient 0.993)
Y = 1.371*10-5 * (x2) – 11.579
Cubic: (With correlation coefficient 0.997)
Y = 3.185*10-8 * (x3) - 0.0064 (x) + 34.174
5
Displacement (mm)
Quadratic: (With correlation coefficient 0.999) Y=
3.496*10-5 * (x2) – 30.681
Cubic: (With correlation coefficient 0.999)
Y = 2.227*10-7 * (x3) – 0.656 (x) + 346.997
Resulted relations using Table 5 are as follows:
3
2
1
0
940.00
Linear: (With correlation coefficient 0.988)
Y = 0.022(x) – 20.539
Quadratic: (With correlation coefficient 0.997)
Y = 1.141*10-5 * (x2) – 9.794
4
Observed
Linear
Quadratic
Cubic
960.00
980.00
Water elevation (m)
1000.00
Fig. 3: Regression diagram resulted by anchor 32a data, using
SPSS
4614
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
1.50
Observed
Linear
Quadratic
Cubic
Observed
Linear
Quadratic
Cubic
2.50
Displacement (mm)
Displacement (mm)
1.75
1.25
1.00
0.75
2.00
1.50
1.00
0.50
940.00
960.00
0.50
940.00
1000.00
980.00
Water elevation (m)
Fig. 4: Regression diagram resulted by anchor 56a data, using
SPSS
960.00
980.00
Water elevation (m)
1000.00
Fig. 5: Regression diagram resulted from anchor a56 using
SPSS software
Water elevation: 1013 m
Water elevation: 1023 m
Water elevation: 1032 m
10
9
8
7
6
5
4
3
2
1
816.3147186
875.4134362
884.0170828
873.5447345
885.1149115
899.9639790
906.5395462
928.5140855
920.3422565
928.5140855
920.6000000
942.9040855
928.1000000
967.3835921
948.3521140
971.0917961
966.5915166
-1
970.6957583
0
Fig. 6: Predicted displacement diagram for the right bank
8.00
Water elevation: 1032 m
Water elevation: 1032 m
Water elevation: 1032 m
4.00
2.00
836.4737
835.7166
880.9582
880.9582
882.6304
902.8
923.9492
923.8
944.925
949.3
-2.00
971.8969
0.00
972.6027
Displacement (mm)
6.00
-4.00
-6.00
Fig. 7: Predicted displacement diagram for the left bank
CONCLUSION
With the observation of the high rate of the cubic
correlation coefficient, the predicted displacement in the
right bank and the left bank are as follows:
Among the extensometers installed in the right bank,
extensometers with instrument coding EX36-16-953/2
(a13-a16), EX54-12-911/2 (a25-a28), EX54-06-848/2
(a49-a52), and EX54-04-827/3 (a57-a60) are of no
efficient correlation coefficient and could be refrained as
4615
Res. J. Appl. Sci. Eng. Technol., 4(22): 4607-4616, 2012
a matter of poor installation or improper reading; but the
rest are of high rate of correlation coefficient. Therefore,
displacements using 44 anchors with a high correlation
coefficient are due to occur.
Among the 68 extensometer installed in the left flank,
only the anchor installed in elevation 946.3 pertaining to
the extensometer with the coding EX42-13-953/2 has a
low correlation coefficient and the rest have a high
correlation coefficient. We could conclude that in
comparison to the right bank, the left bank benefits from
a higher correlation coefficient. So in the case of the left
bank, displacement is predicted using 67 anchors with a
high correlation coefficient:
For instance, taking Fig. 7 into account the most
predicted displacement for the left bank when water is
leveled at elevation 1013 equals 3.65 mms with R2 =
0.9997 referring to the anchor installed in elevation
889.8362. Consecutively, when water is leveled at
elevations 1023 and 1033, the most predicted
displacements are in the order 4.31 and 5.66 mms with R2
= 0.9941and refer to the anchor installed in elevation
936.05.
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