Displacements Prediction in Double-Arch Dam Rock Abutment Using SPSS Software Based on Extensometer Readings Case study: Karun 4 Concrete Dam, Iran

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, 1 Kaveh Ahangari and 2 Mirsaeid Hosseini Shirvani 1 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 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 R 2 = 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 R 2 = 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 R 2 = 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

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

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

Table 1: (Continue) 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 30 825.7687 0.41 0.50 0.58 0.77 0.83 1.03 1.21 54 807.3836 0.46 0.65 0.79 1.06 1.23 1.50 1.80 Ex54-04-827/3 9 820.0320 0.03 0.03 0.02 0.08 0.02-0.01 0.07 827.58 15 814.9999 0.08 0.10 0.10 0.16 0.10 0.08 0.16 27 804.9359 0.13 0.14 0.15 0.23 0.19 0.15 0.24 54 782.2918 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

Table 2: (Continue) 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 54 889.8362 0.41 0.71 1.04 1.50 1.93 2.49 3.04 EX54-09-890/3 9 885.8982 0.10 0.11 0.12 0.24 0.23 0.29 0.39 890.8 15 882.6304 0.15 0.19 0.21 0.38 0.41 0.50 0.33 27 876.0947 0.10 0.14 0.13 0.42 0.46 0.52 0.53 45 866.2912 0.07 0.11 0.13 0.64 0.65 0.73 0.41 EX54-09-890/2 9 884.8149 0.11 0.11 0.11 0.27 0.24 0.29 0.35 890.6 15 880.9582 0.14 0.17 0.16 0.44 0.38 0.45 0.54 27 873.2447 0.24 0.30 0.32 0.60 0.61 0.69 0.41 54 855.8895 0.15 0.30 0.45 1.01 0.97 0.94 0.42 EX54-09-869/3 9 864.6378 0.18 0.22 0.23 0.38 0.48 0.46 0.59 869.8 15 861.1964 0.34 0.41 0.47 0.69 0.74 0.88 1.07 27 854.3134 0.59 0.74 0.87 1.17 1.32 1.59 1.86 54 838.8269 0.66 0.86 1.07 1.43 1.62 1.88 2.20 EX54-09-869/2 9 863.4360 0.13 0.15 0.15 0.27 0.29 0.33 0.41 869.8 18 857.0721 0.20 0.25 0.24 0.39 0.44 0.48 0.55 27 850.7081 0.39 0.47 0.53 0.75 0.81 0.97 1.06 54 831.6162 0.46 0.66 0.76 1.12 1.27 1.51 1.55 EX54-07-848/3 12 840.1048 0.23 0.28 0.32 0.46 0.46 0.47 0.64 848.881 18 835.7166 0.40 0.47 0.56 0.72 0.76 0.88 1.11 24 831.3285 0.48 0.58 0.69 0.91 1.01 1.17 1.41 54 809.3879 0.67 0.89 1.09 1.40 1.67 1.93 2.25 EX54-07-848/2 9 841.3886 0.14 0.18 0.19 0.27 0.25 0.30 0.43 848.761 15 836.4737 0.17 0.24 0.28 0.36 0.38 0.43 0.59 27 826.6439 0.24 0.32 0.38 0.50 0.52 0.60 0.78 54 804.5268 0.28 0.32 0.43 0.64 0.70 0.79 0.94 EX54-05-827/3 9 820.9346 0.22 0.25 0.26 0.38 0.33 0.36 0.45 827.829 15 816.3383 0.37 0.43 0.45 0.60 0.60 0.65 0.78 27 807.1458 0.55 0.65 0.74 0.92 0.97 1.07 1.25 54 786.4626 0.65 0.79 0.94 1.23 1.36 1.52 1.88 EX42-00-806/3 9 800.0361 0.14 0.16 0.16 0.26 0.24 0.30 0.42 806.4 15 795.7934 0.38 0.44 0.47 0.60 0.64 0.75 0.94 24 789.4295 0.51 0.61 0.68 0.85 0.92 1.06 1.33 42 776.7016 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 R 2 (linear) 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 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 R 2 (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 R 2 (Cubic) 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 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

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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 - - - - - - - - R 2 ( 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 - - - - - - - - R 2 (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 - - - - - - - - R 2 ( 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 ----------------------------------------------------------------------- ---------------------------------------------------------------------- Equation R 2 F df1 df2 Sig. Constant b1 b2 b3 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 ------------------------------------------------------------------------- -------------------------------------------------------------------- Equation R 2 F df1 df2 Sig. Constant b1 b2 b3 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

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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 R 2 (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 4613

Table 6: (Continue) Anchor points (a1- a68 ) ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Water elevvation a52 a53 a54 a55 a56 a57 a58 a59 a60 a61 a62 a63 a64 a65 a66 a67 a68 Prediction1023 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 Prediction1032 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 R 2 (Quadratic) 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 Prediction1013 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 Prediction1023 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 Prediction1032 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 R 2 (Cubic) 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 ----------------------------------------------------------------------- -------------------------------------------------------------------- Equation R 2 F df1 df2 Sig. Constant b1 b2 b3 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 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. 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 Quadratic: (With correlation coefficient 0.999) Y= 3.496*10-5 * (x 2 ) 30.681 Cubic: (With correlation coefficient 0.999) Y = 2.227*10-7 * (x 3 ) 0.656 (x) + 346.997 Resulted relations using Table 5 are as follows: Linear: (With correlation coefficient 0.988) Y = 0.022(x) 20.539 Quadratic: (With correlation coefficient 0.997) Y = 1.141*10-5 * (x 2 ) 9.794 Cubic: (With correlation coefficient 0.997) Y = 4.322*10-8 * (x 3 ) 0.101 (x) + 59.150 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: Linear: (With correlation coefficient 0.984) Y = 0.027(x) 24.547 Quadratic: (With correlation coefficient 0.993) Y = 1.371*10-5 * (x 2 ) 11.579 Cubic: (With correlation coefficient 0.997) Y = 3.185*10-8 * (x 3 ) - 0.0064 (x) + 34.174 Displacement (mm) 5 4 3 2 1 Observed Linear Quadratic Cubic 0 940.00 960.00 980.00 1000.00 Water elevation (m) Fig. 3: Regression diagram resulted by anchor 32a data, using SPSS 4614

Displacement (mm) 1.75 1.50 1.25 1.00 0.75 0.50 Observed Linear Quadratic Cubic 940.00 960.00 980.00 1000.00 Water elevation (m) Fig. 4: Regression diagram resulted by anchor 56a data, using SPSS Displacement (mm) 2.50 2.00 1.50 1.00 Observed Linear Quadratic Cubic 0.50 940.00 960.00 980.00 1000.00 Water elevation (m) Fig. 5: Regression diagram resulted from anchor a56 using SPSS software 10 9 8 7 6 Water elevation: 1013 m Water elevation: 1023 m Water elevation: 1032 m 5 4 3 2 1 0-1 970.6957583 966.5915166 971.0917961 967.3835921 948.3521140 942.9040855 928.1000000 920.6000000 928.5140855 920.3422565 928.5140855 906.5395462 899.9639790 885.1149115 873.5447345 884.0170828 875.4134362 816.3147186 Fig. 6: Predicted displacement diagram for the right bank 8.00 6.00 Water elevation: 1032 m Water elevation: 1032 m Water elevation: 1032 m Displacement (mm) 4.00 2.00 0.00-2.00 972.6027 971.8969 949.3 944.925 923.8 923.9492 902.8 882.6304 880.9582 880.9582 835.7166 836.4737-4.00-6.00 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

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 R 2 = 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 R 2 = 0.9941and refer to the anchor installed in elevation 936.05. REFERENCES Aleksandrovskaya, É.K. and V.P. Urakhchin, 1974. Prediction of the displacements of concrete gravity dams on rock foundations. Power Technol. Eng., 8(5): 419-427. Allen, C.R. and L.S. Cluff, 2000. Active faults in dam foundations: An update. Proceeding of 12 th World Conference on Earthquake Engineering, Auckland, New Zealand. Kim, Y.S. and B.T. Kim, 2008. Prediction of relative crest settlement of concrete-faced rock fill dams analyzed using an artificial neural network model. Comput. Geotech., 35: 313-322. Mahab-Ghodss Consulting Engineering Company, 2010a. Soil mechanics and foundation & abutment geology study report. Karun 4 Dam, Phase 3. Mahab-Ghodss Consulting Engineering Company, 2010b. Instrumentation and behaviography of Karun 4 dam and power station. Appendix No. 2-4, Impounding Report No. 6: The Map of Enlongatometers Layout of the Dam Body and the Results of the Enlongatometers of the Dam Body. Mata, J., 2011. Interpretation of concrete dam behavior with artificial neural network and multiple linear regression models. Eng. Struct., 33: 903-910. Mata, J. and E.T.A. Portela, 2007. Application of neural networks to dam safety control. 5the International Conference on Dam Engineering, 14-17 February, Congress Centre of Line Lisbon, Portugal. Wieland, M., R.P. Brenner, and P. Sommer, 2003. Earthquake resilience of large concrete dams: Damage, repair and strengthening concepts. Trans. 21 st International Congress on Large Dams, Montreal, Q83-R10, 3, pp: 131-150. Wieland, M., R.P. Brenner and A. Bozovic, 2008a. Potentially active faults in the foundations of large dams part I: Vulnerability of dams TO seismic movements in dam foundation. Special Session S13, Proceeding of 14th World Conference on Earthquake Engineering, Beijing, China, October 12-17. Wieland, M., R.P. Brenner and A. Bozovic, 2008b. Potentially active faults in the foundations of large dams Part 2: Design aspects of dams to resist fault movements. Special Session S13, Proceeding of 14th World Conference on Earthquake Engineering, Beijing, China, October 12-17. 4616