Konar dam closuremeeting by India Water Week

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Numerical Modeling of Konar Dam Mr Ankur Agarwal

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CAD modeling 

Geometry was created using 2D sections of all blocks



Cavities, Shafts, Galleries are modeled in 3D model



Foundation was modeled.



Geometry was created in Abaqus/CAE and in CATIA V6

Non Overflow section 9

Overflow section

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Konar DAM Model

Total number of nodes: 3028358 Total number of elements: 2672744 2489221 linear hexahedral elements of type C3D8T 36326 linear wedge elements of type C3D6T 147197 quadratic tetrahedral elements of type C3D10

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Mesh Details

u → linear εµ

ε 11

∂ ∂x

→ constant

∆θ → linear

µ ∆θ − average over element

→ constant

Linear displacement, linear temperature, coupled element



Dam Blocks are meshed with brick elements. The elements used for this analysis are 8 noded coupled temperature displacement C3D8T



With these elements both thermal and mechanical loads can be applied in the same analysis.



Both temperature and displacement are output of this analysis



Foundation is meshed with tetrahedral elements. The elements used for this analysis is 10 noded quadratic tetrahedron with only displacement degrees of freedom.



Only mechanical loads can be applied on these elements.

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Material Properties (Base Model)



Concrete



Rock

Elastic Modulus: 2.1E5 Kg/cm2

Elastic Modulus: 1.2E5 Kg/cm2

Poissons ratio: 0.2

Poissons Ratio: 0.2

Density: 2400 Kg/m3

Density: 2500 Kg/m3

Thermal Conductivity: 2.33 W/(m-K)

Cohesion: 2.5Mpa

Specific Heat: 960 J/(Kg-K)

Frictional Angle: 45ᵒ

Thermal expansion: 1E-5 /c

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Sensitivity Analysis



Thermal conductivity, Specific heat and coefficient of thermal expansion is taken from Dr Pant’s report and is confirmed with USBR Engineering monograph 34.



Heat coefficient for convection between concrete-air and concrete-water is taken from report- “Effects of Changing Surrounding Conditions on the Thermal Analysis of the Moste Concrete Dam “ by Pavel Žvanut, Goran Turk and Andrej Kryžanowski.



Sensitivity analysis was carried out by changing the values of Young’s modulus, poissons ratio and coefficient of thermal expansion in order the find variation in stresses.

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Analysis Models studied

Model No.

Model Name

Youngs Modulus

Poissons Ratio

Coefficient of thermal expansion

Remarks

2D1

2d_Block8_withfoundation_2.inp (Base Model)

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

2D2

2d_Block8_withfoundation_2_YM3.inp

3.0E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

2D4

2d_Block8_withfoundation_2_YM35.inp

3.5E5 Kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

2D5

2d_Block8_withfoundation_2_MU18.inp

2.1E5 kg/cm2

0.18

1E-5/ᵒC

With foundation, without uplift, With galleries

2D6

2d_Block8_withfoundation_2_MU22.inp

2.1E5 kg/cm2

0.22

1E-5/ᵒC

With foundation, without uplift, With galleries

2D7

2d_Block8_withfoundation_2_alpha08.inp

2.1E5 kg/cm2

0.2

0.8E-5/ᵒC

With foundation, without uplift, With galleries

2D8

2d_Block8_withfoundation_2_alpha12.inp

2.1E5 kg/cm2

0.2

1.2E-5/ᵒC

With foundation, without uplift, With galleries

2D9

2d_Block8_withfoundation_2_withcrack.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

2D10

2d_Block8_withfoundation_2_nogalleries.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, No Galleries

2D11

2d_Block8_withfoundation_2_withcohuplift.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, with uplift, With Galleries

2D12

2d_Block8_withfoundation_2_cohuplift_pant_ft.in p

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, with uplift, With Galleries, initial temp 20ᵒC, solar absorvity=1, cap on solar flux

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3D Analysis Models

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Loads



Mechanical Loads Gravity Load  Varying water level,  Silt load 



Thermal Loads: Convection to air on downstream face  Radiation to ambient air temperature on down stream face  Direct Solar radiation on downstream face  Convection to water on upstream face  Convection to air above water level on upstream face  Thermal Radiation to air above water surface on upstream face 

Air and Reservoir temp 3DS.COM © Dassault Systèmes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Reference: ZHU Bofang

• • •

Air temperature data is supplied by DVC for a typical year June-may The cycle is repeated for three years Reservoir temperature is determined from ZHU Bofang eqns with time and depth of reservoir as shown

Interactions:

*Tie, name=CP-1-Block-12-1-Block-13-1, adjust=yes, type=SURFACE TO SURFACE

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Model: 3D analysis of Block 13

CP-2-Block-13-1, CP-1-Block-12-1 *Tie, name=CP-1-Block-13-1-Block-14-1, adjust=yes, type=SURFACE TO SURFACE CP-1-Block-14-1, CP-1-Block-13-1

Block -13

*Tie, name=Constraint-3, adjust=no CP-2-foundation-1, CP-2-Block-12-1 *Tie, name=Constraint-4, adjust=no CP-6-foundation-1, CP-6-Block-13-1 *Tie, name=Constraint-5, adjust=no CP-11-foundation-1, CP-11-Block-14-1

In this analysis, tie constraints are used to define interaction between blocks and foundation. This restricts slipping and opening between blocks and foundation.

Step-1: Static Analysis 3DS.COM ÂŠ Dassault SystĂ¨mes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Gravity Load is applied in step-1= 9.81m/s2

In the first step, gravity load is applied on the blocks and foundation. The units are converted to units: Kg, inch, sec: 386.21inch/s2

Step-2: Coupled Temp-Displacement analysis 3DS.COM © Dassault Systèmes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Mechanical Loads

• •



Gravity Load: 9.8ms-2



Upstream Hydrostatic Pressure



Upstream Silt Load in vertical and horizontal direction

Water level is varied using DLOAD subroutine for three years Silt load is assumed to be at constant level

Step-2: Coupled Temp-Displacement analysis 3DS.COM © Dassault Systèmes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Thermal Loads

• •



Upstream convection to water below water level



Upstream convection to air above water level



Upstream radiation to air above water level



Downstream radiation to air



Downstream convection to air



Downstream solar radiation

Upstream air temperature is varied for three years Upstream water temperature is varied due to air temperature fluctuations using ZHU Bofang equations • Solar radiation is computed on a sloping surface using Radiation equations

Step-2: Coupled thermo-structural analysis 3DS.COM ÂŠ Dassault SystĂ¨mes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Horizontal and Vertical Silt Load is applied

In the second step, horizontal and vertical downward silt load is applied on dam blocks below 1584inch from the top of dam. Units are in Kg, inch, sec Horizontal silt load expression: (360 * 386.219 * ( 1584 + Z ) ) / (39.37 * 39.37 * 39.37), where z is measured negatively from the top of the dam downwards Vertical silt load expression: (925 * 386.219 * ( 1584 + Z ) ) / (39.37 * 39.37 * 39.37)

Step-2: Coupled thermo-structural analysis 3DS.COM ÂŠ Dassault SystĂ¨mes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Varying hydrostatic pressure

In the second step, varying hydrostatic pressure is applied. Water level is varied using subroutine DLOAD and hydrostatic pressure load is applied depending on the location vertically downwards from the reservoir surface. Units is Kg, inch, sec Density=0.016387162 Gravity=386.27 Pressure=density*gravity*(H-coords(3)), where H is water head and Coords(3) gives the location of load points.

Step-2: Coupled thermo-structural analysis 3DS.COM ÂŠ Dassault SystĂ¨mes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Convection on upstream face

Surface Film condition is defined on upstream face to define convection heat loss to water and air. Subroutine FILM is defined to monitor water level and heat loss to water below water surface and heat loss to air above water surface Heat coefficient water: 556 W/(m2-K) Heat coefficent air: 55.6 W/(m2-K) Water temperature and air temperature is varied as shown earlier.

Step-2: Coupled thermo-structural analysis 3DS.COM ÂŠ Dassault SystĂ¨mes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Convection to air on downstream face

Surface Film condition is defined on downstream face to define convection heat loss to air. Heat coefficent air: 55.6 W/(m2-K) Air temperature is varied as shown earlier.

Step-2: Coupled thermo-structural analysis 3DS.COM ÂŠ Dassault SystĂ¨mes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Thermal radiation heat loss to Air on downstream face

Surface radiation is defined on the downsteam face for the heat gained/loss to air Emissivity: 0.90 Air temperature is varied as shown earlier. Newtons law of cooling=

Step-2: Coupled thermo-structural analysis 3DS.COM ÂŠ Dassault SystĂ¨mes | Confidential Information | 04/08/16 | ref.: 3DS_Document_2015

Solar radiation heat flux

Solar radiation is varied on the downstream face which depends on day of the month and time in day. CBRI method is used to compute heat flux. Subroutine DFLUX is written to compute total flux on surface. n= no. of days t= time in day B=(360*(n-81)/365)*3.14/180 EOT=9.87*sin(2*B)-7.53*cos(B)-1.5*sin(B) TC=4*(85.77-82.5)+EOT LST=t+TC/60 th=15*(LST-12)+360 dec=Asin(sin(23.45*3.14/180)*sin(360*(n-81)*3.14/365/180))*180/3.14 clat=cos(23.9*3.14/180) slat=sin(23.9*3.14/180) ALT=Asin(slat*sin(dec*3.14/180)+clat*cos(dec*3.14/180)*cos(th*3.14/180))*180/3.14 Azi=180+(Acos((slat*cos(dec*3.14/180)*cos(th*3.14/180)clat*sin(dec*3.14/180))/cos(ALT*3.14/180)))*180/3.14 Zd=Acos(slat*sin(dec*3.14/180)+clat*cos(dec*3.14/180)*cos(th*3.14/180))*180/3.14 B1=Azi-165

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Sun tracker

Jan’13

July’13

Apr’13

Oct’13

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Results

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Model-2D1: 2d_Block8_withfoundation_2.inp

Upper Gallery: S22

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Model-2D4: 2d_Block8_withfoundation_2_YM35.inp

Upper Gallery: S22

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Model-2D8: 2d_Block8_withfoundation_2_alpha12.inp Upper Gallery: S22

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Model-2D10: 2d_Block8_withfoundation_2_nogalleries.inp Upper Gallery: S22

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Summary: Analysis Models studied

Model No.

Poiss ons Ratio

Coefficient of thermal expansion

Model Name

Youngs Modulus

2D1

2d_Block8_withfoundation_2.inp (Base Model)

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

100%

2D2

2d_Block8_withfoundation_2_YM3.inp

3.0E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

165%

2D4

2d_Block8_withfoundation_2_YM35.inp

3.5E5 Kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

180%

2D5

2d_Block8_withfoundation_2_MU18.inp

2.1E5 kg/cm2

0.18

1E-5/ᵒC

With foundation, without uplift, With galleries

100%

2D6

2d_Block8_withfoundation_2_MU22.inp

2.1E5 kg/cm2

0.22

1E-5/ᵒC

With foundation, without uplift, With galleries

103%

2D8

2d_Block8_withfoundation_2_alpha12.inp

2.1E5 kg/cm2

0.2

1.2E-5/ᵒC

With foundation, without uplift, With galleries

113%

2D9

2d_Block8_withfoundation_2_withcrack.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

2D10

2d_Block8_withfoundation_2_nogalleries.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, No Galleries

2D11

2d_Block8_withfoundation_2_withcohuplift.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, with uplift, With Galleries

2D12

2d_Block8_withfoundation_2_cohuplift_pant_f t.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, with uplift, With Galleries, initial temp 20ᵒC, solar absorvity=1, cap on solar flux

Remarks

Max S22

68.4%

Summary: Analysis Models studied

Model No.

Poiss ons Ratio

Coefficient of thermal expansion

Model Name

Youngs Modulus

2D1

2d_Block8_withfoundation_2.inp (Base Model)

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

100%

2D2

2d_Block8_withfoundation_2_YM3.inp

3.0E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

165%

2D4

2d_Block8_withfoundation_2_YM35.inp

3.5E5 Kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

180%

2D5

2d_Block8_withfoundation_2_MU18.inp

2.1E5 kg/cm2

0.18

1E-5/ᵒC

With foundation, without uplift, With galleries

2D6

2d_Block8_withfoundation_2_MU22.inp

2.1E5 kg/cm2

0.22

1E-5/ᵒC

With foundation, without uplift, With galleries

103%

2D8

2d_Block8_withfoundation_2_alpha12.inp

2.1E5 kg/cm2

0.2

1.2E-5/ᵒC

With foundation, without uplift, With galleries

113%

2D9

2d_Block8_withfoundation_2_withcrack.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, With galleries

2D10

2d_Block8_withfoundation_2_nogalleries.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, without uplift, No Galleries

2D11

2d_Block8_withfoundation_2_withcohuplift.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, with uplift, With Galleries

2D12

2d_Block8_withfoundation_2_cohuplift_pant_f t.inp

2.1E5 kg/cm2

0.2

1E-5/ᵒC

With foundation, with uplift, With Galleries, initial temp 20ᵒC, solar absorvity=1, cap on solar flux

Remarks

Max S22

68.4%

Observation



Severe reduction in stresses seen when upper gallery is plugged



There is reduction of stresses when the upper gallery is plugged ranging from 32% to 56%

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Results: With Galleries and Without Galleries

Upper Gallery: S22

Rehabilitation measures considered



Stitching of cracks, provision of steel liners, plugging of Upper gallery blocks or combination of these procedures with enhanced continuous observation of cracks.



Rehabilitation of the inspection gallery in a phased manner starting from the central portion i.e. starting from central Blocks 13 & 14 and adding one block each towards abutments with a year interval for thermal redistribution and observation. 

This is based on the FEM analysis outcome for Stress redistribution without gallery, which indicates a considerable reduction of stresses



Extensive mapping of the existing cracks using LIDAR, followed by grouting of all surface cracks



Instrumentation for closure monitoring of Dam behavior after plugging the gallery



Periodical remapping of cracks using LIDAR to monitor effects/success of rehabilitation design