A.0 IDUKKI ARCH DAM - ANALYSIS FOR VARIOUS LOAD CASES AND DISCRETISATIONS

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1 Annexure A.0 IDUKKI ARCH DAM - ANALYSIS FOR VARIOUS LOAD CASES AND DISCRETISATIONS In this Annexure, Idukki arch dam chosen for case study is analyzed with the developed program for various load conditions and discretisations as required for arch dams and a comparison made with the available results. The out put of the program gives nodal data, connectivity, boundary conditions, band width, element stiffness matrices, element load vectors, global load vectors, deflection at all the nodes in the three directions, stresses and strains in the six directions at the 27 gauss points of each element, nodal points, average elemental stresses, upstream and downstream elements face centre stresses, original profile, deflected profile, plans at various levels and elevation. Since presenting all the results is rather extensive, only the major values of deflection and stresses at crown section are tabulated and plotted. A. 1 G E O M E T R Y A N D D I S C R E T I S A T I O N - 1 S E L E C T E D The Idukki arch dam geometry derived by 80 nodal points with degree of polynomial 7 in length, 1 in thickness and 4 in height directions is discretised to 28 elements as arrived in section and taken for analysis. The mesh of the dam with node numbering is shown in Fig. A.1. Displacement is restricted at the 78 boundary 164

2 nodes assuming the sides and bottom faces fixed as given in Table A.1. The nodal connectivity as arrived by the program is tabulated below in Table A.2. Fig A.1: Idukki arch dam Node numbering pattern 28 elements Table A.1: Idukki arch dam Nodes at which displacements prescribed 28 elements Node u v w Node u v w Node u v w

3 Table A.2: Idukki arch dam Nodal connectivity 28 elements Element

4 A D e a d L o a d O n l y Modulus of elasticity = kn/m 2 Poisson s ratio = 0.2 Unit weight of dam material = kn/m 3 Global displacement obtained for the crown portion is shown in Table A.3 and elemental stresses in Table A.4. Radial deflection and hoop stress at crown cantilever section are plotted in Fig A.2 and Fig A.3 respectively. Table A.3: Global displacement array -Load Case I. Node Displ X cm Displ Y cm Displ Z cm

5 Table A.4: Element stresses as average of Gauss points in kg/cm 2 - Load case 1 Element Sig x Sig y Sig z Sig xy Sig yz Sig xz Height in m Radial deflection in cm Fig A.2: Radial deflection at crown cantilever section - Load case 1 168

6 Height of Dam in m Hoop stress in kg/cm2 Downstream Upstream Fig A.3: Hoop stress at crown cantilever section- Load case 1 A D e a d L o a d, M a x i m u m W a t e r a n d M a x i m u m S i l t Unit weight of reservoir water =10 kn/m 3 Unit weight of silt material = kn/m 3 Reference datum of reservoir Reference datum of reservoir = m = m Global displacement obtained for the crown portion is shown in Table A.5 and elemental stresses in Table A.6. Radial deflection and hoop stress at crown cantilever section are plotted in Fig A.4 and Fig A.5 respectively. TableA.5: Global Displacement at Crown Cantilever -Load Case 2 Node Displ X cm Displ Y cm Displ Z cm

7 Table A.6: Element stresses as average of Gauss points in kg/cm 2 -Load case 2 Element sig x sig y sig z sig xy sig yz sig xz

9 Height of dam in m Radial deflection in cm Fig A.4: Radial deflection at crown cantilever section -Load case 2 Height of Dam in m Hoop stress in kg/cm2 Downstream Upstream Fig A.5: Hoop stress at crown cantilever section- Load case 2 172

10 A D e a d L o a d, N o r m a l W a t e r, M a x i m u m S i l t a n d E a r t h q u a k e C = g Unit weight of reservoir water = 10 kn/m 3 Unit weight of silt material = kn/m 3 Reference datum of reservoir Reference datum of reservoir = m = m Table A.7: Global Displacement at crown cantilever- Load case 3 Node Displ X cm Displ Y cm Displ Z cm

11 Table A.8: Element stresses as average of Gauss points in kg/cm 2 -Load case 3 Element sig x sigy sigz sigxy sigyz sigxz Global displacement obtained for the crown portion is shown in Table A.7 and elemental stresses in Table A.8. Radial deflection and hoop stress at crown cantilever section are plotted in Fig A.6 and Fig A.7 respectively. 174

12 Height of dam in m Radial deflection in cm Fig A.6: Radial deflection Vs Height of dam - Load case 3 height of dam in m Hoop stress in kg/cm2 Fig A.7: Hoop stress Vs Height of dam- Load case 3 Downstream Upstream

13 A D e a d L o a d, N o r m a l W a t e r, M a x i m u m S i l t a n d E a r t h q u a k e C = 0. 1 g Global displacement obtained for the crown portion is shown in Table A.9 and elemental stresses in Table A.10. Radial deflection and hoop stress at crown cantilever section are plotted in Fig A.8 and Fig A.9 respectively. Table A.9: Global Displacement at crown cantilever - Load case 4 Node Displ X cm Displ Y cm Displ Z cm Table A.10: Element stresses as average of Gauss points in kg/cm 2 - Load case 4 Element sigx sigy sigz sigxy sigyz sigxz

14 height of dam in m Radial deflection in cm Fig A.8: Radial deflection Vs Height of dam - Load case 4 177

15 Height of dam in m Fig A.9: Hoop stress Vs Height of dam - Load case 4 Downstream Upstream A D e a d L o a d, N o r m a l W a t e r, M a x i m u m S i l t, E a r t h q u a k e C = 0. 1 g a n d H y d r o d y n a m i c E f f e c t Global displacement obtained for the crown portion is shown in Table A.11 and elemental stresses in Table A.12. Radial deflection and hoop stress at crown cantilever section are plotted in Fig A.10 and Fig A.11 respectively. Table A.11: Global Displacement at crown cantilever - Load case 5 Node Displ X cm Displ Y cm Displ Z cm

16 Table A.12: Element stresses as average of Gauss points in kg/cm 2 - Load case 5 Elements sig_x sig_y sig_z sig_xy sig_yz sig_xz

17 height in m Radial deflection in cm Fig A.10: Radial deflection Vs Height of dam - Load case 5 180

18 Height in m Hoop Stress in kg/cm2 Fig A.11: Hoop stress Vs Height of dam - Load case 5 Downstream Upstream A comparison of global displacements at crown cantilever section due to hydrostatic, seismic and hydrodynamic effects is tabulated in Table A.13. It is found that radial deflection due to combined hydrodynamic and seismic effects exceeds 30% approximately than the hydrostatic effect. 181

19 Table A.13: Comparison of Global displacements due to Seismic and Hydrodynamic effect Dead load, Normal water and Maximum silt Dead load, Normal water, Maximum silt and Earthquake C=0.1g Dead load, Normal water, Maximum silt, Earthquake C=0.1g and Hydrodynamic effect Node Displ X cm Displ Y cm Displ Z cm Displ X cm Displ Y cm Displ Z cm Displ X cm Displ Y cm Displ Z cm

A. 2 G E O M E T R Y A N D D I S C R E T I S A T I O N - 2 S E L E C T E D The dam geometry generated as shown above; with 80 nodal points, is tried for a finer discretisation, (112 elements) with

20 A. 2 G E O M E T R Y A N D D I S C R E T I S A T I O N - 2 S E L E C T E D The dam geometry generated as shown above; with 80 nodal points, is tried for a finer discretisation, (112 elements) with number of divisions 8 in height and 14 in length. The generated mesh is plotted in Fig A.12. Fig A.12: Descretisation with 112 elements The dam is analyzed for the following load cases: 1. Dead load, Normal water, Maximum silt 2. Dead load, Normal water, Maximum silt and Earthquake C=0.1g 3. Dead load, Normal water, Maximum silt, Earthquake C=0.1g and Hydrodynamic effect. The deflected profile in the Load cases 2 & 3are shown in Fig A

21 Fig A.13: Deflected profile in Load cases 2 & 3 A D e a d L o a d, N o r m a l W a t e r, M a x i m u m S i l t Global displacement obtained for the crown portion is shown in Table A.14 and elemental stresses in Table A.15. Element stresses are plotted in Fig A.14. Table A.14: Global Displacement at crown cantilever - Load case 1 Node Displ X Displ Y Displ Z Coord X Coord Y Coord Z

23 Table A.15: Element stresses as average of Gauss points in kg/cm 2 - Load case 1 Element Sig x Sig y Sig z Sig xy Sig yz Sig xz

26 Fig A.14: Element stresses - Load case 1 A D e a d L o a d, N o r m a l W a t e r, M a x i m u m S i l t a n d E a r t h q u a k e C = 0. 1 g Global displacement obtained for the crown portion is shown in Table A.16 and elemental stresses in Table A.17. Element stresses are plotted in Fig A.15. Table A.16: Global displacement at crown cantilever - Load case 2 Node Displ X Displ Y Displ Z Coord X Coord Y Coord Z

28 Table A.17: Element stresses as average of Gauss points -Load case 2 Element Sig x Sig y Sig z Sig xy Sig yz sigxz

30 Fig A.15: Element stresses - Load case 2 193

31 A D e a d L o a d, N o r m a l W a t e r, M a x i m u m S i l t, E a r t h q u a k e C = 0. 1 g a n d H y d r o d y n a m i c E f f e c t Global displacement obtained for the crown portion is shown in Table A.18. Elemental face centre stresses of upstream and downstream are shown in Table A.19 and A.20. Element stresses are plotted in Fig A.16 and hoop stresses at crown cantilever section in Fig A.17. Table A.18: Global Displacement at crown cantilever - Load case 3 Node Displ X Displ Y Displ Z

33 Table A.19: Upstream Element face centre stresses in kg/cm 2 - Load case 3 Element sigx sig y sig z sig xy sig yz sig xz

35 Table A.20: Downstream Element face centre stresses in kg/cm 2 - Load case 3 Element sigx sig y sig z sig xy sig yz sig xz element

37 Fig A.16: Element stresses - Load case 3 200

38 Height in m Hoop stress in kg/cm2 Upstream Crown Downstream crown Fig A.17: Hoop stress at crown cantilever- Load case 3 A. 3 G E O M E T R Y A N D D I S C R E T I S A T I O N - 3 S E L E C T E D The same dam geometry arrived as above with 80 nodal points is tried for a finer discretisation with number of divisions 8 in height and 7 in length and 2 in thickness; 112 elements. Since this is a thick arch dam, it is checked for better results with multilayer in thickness. A D e a d L o a d, M a x i m u m W a t e r, M a x i m u m S i l t The dam is analysed for this load case. The deflected profile is shown in Fig A.18. Global displacement obtained for the crown portion is shown in Table A

Elemental face centre stresses of upstream and downstream are shown in Table A.22 and A.23. Hoop stress at crown cantilever section is shown in Fig A.

39 Elemental face centre stresses of upstream and downstream are shown in Table A.22 and A.23. Hoop stress at crown cantilever section is shown in Fig A.19. Fig A.18: Deformed profile due to self weight and water pressure No. of elements = 112 Table A.21: Global displacement at crown cantilever - Load case Node Displ X m Displ Y m Displ Z m e e e

Finite Element Method in Geotechnical Engineering

Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps