1. Cracking In Thin Arch Concrete Dam – Nonlinear Dynamic Structural Analysis

2. Presentation Overview
Investigations
Finite Element Model
Material Properties
Loads
Static Analysis Results
Dynamic Analysis Results
Conclusions

3. Investigations
Foundation Stability Analysis

4. Geophysical Investigations Spectral Analysis of Surface Waves (SASW) Surveys
Phase I: Downstream face of Block 3 of the dam located near
the left abutment and approximately 85 feet below the crest
Phase II: Entire extent of the crack on the downstream face of the dam including Blocks 2 through 9

5. Concrete Quality vs. Velocity

6. Finite Element Model Concrete Arch Dam Existing Cracks
Overflow Spillway
Downstream
Reservoir
C Block
AB Block

7. Foundation Properties
Material Properties
Foundation Properties
Final Values
Average Density
165 lb/ft3
Young’s Modulus
8.3 x 106 lb/in2
Poisson’s Ratio
0.19
Material Properties
Water
Modulus of Elasticity
189.7 lb/in2
Poisson’s Ratio
0.4999
Density
62.4 lb/ft3
Bulk modulus K
316,166.7 lb/in2
Pressure Cutoff
0.0 lb/in2
Viscosity Coefficient
0.0
Material Properties
Concrete Testing
Average Density
147 lb/ft3
Young’s Modulus
6.5 x 106 lb/in2
Poisson’s Ratio
0.17
Compressive strength (f’c)
5,500 lb/in2
Tensile strength
300 lb/in2
Maximum aggregate size
2.5 in

8. Nonlinear Concrete Material Models
Material uses a damage parameter with a range from zero (indicating no damage) to one (indicating cracking or crushing). This parameter is displayed under the “Effective Plastic Strain” title in the output. The area of damaged concrete is shown in red in the effective plastic strain plots.
Winfrith material - damage is displayed in terms of crack orientation. The orientation matches the orientation a physical crack would take.

9. Loads Gravity Foundation uplift pressure Temperature
Seismic loads (5k,10k and 50k year)
5,000-year = 0.27g
10,000-year = 0.33g
50,000-year = 0.54g

10. Gravity Load Application
Dam
Foundation Rock Blocks
Water
Dam
Foundation Rock Blocks
Water

11. Application of Uplift Pressure
Full Uplift on Both Release Plane and AB Base Plane
Full Uplift on Release Plane and 50% Uplift on AB Base Plane
Release Plane
Full Uplift
AB Base Plane

12. Temperature Load Application
Hot Temperature, Downstream
Upstream

13. Seismic Load Application
Free-Field vs Measured Motion

14. Static Analysis Results
Reservoir Water Pressure Applied to the Upstream Face of the Dam

15. Dynamic Analysis Results
Concrete Damage in Arch Dam Under Different Seismic Loadings
5K STU, Material 159
5K STU, Winfrith
10K STU, Material 159
10K STU, Winfrith
50K STU, Material 159
50K STU, Winfrith

16. Concrete Damage in Arch Dam Under Different Temperatures
Cold Temperature, Winfrith
Cold Temperature, Material 159
Average Temperature, Winfrith
Average Temperature, Material 159
Hot Temperature, Winfrith
Hot Temperature, Material 159

17. Concrete Damage in Arch Dam under Full Uplift and 50% Uplift on AB Base Plane
50% Uplift, Material 159
50% Uplift, Winfrith
Full Uplift, Material 159
Full Uplift, Winfrith

18. Dynamic Analysis Results
Foundation Blocks Displacement
Apex of AB Block, Node C
Foundation, Node B
Apex of C Block, Node A

19. Concrete Damage Caused by Rock Block Displacement
Concrete Damage, Small Rock Block Displacement, Material 159
Concrete Damage, Large Rock Block Displacement, Material 159
Concrete Cracks, Small Rock Block Displacement, Winfrith
Concrete Cracks, Large Rock Block Displacement, Winfrith

20. Rock Block Displacement Caused by 50%Uplift and Full Uplift – Material 159
Apex of C Block, Node A
Foundation, Node B
Apex of AB Block, Node C

21. Rock Block Displacement Caused by 50%Uplift and Full Uplift – Winfrith
Apex of C Block, Node A
Foundation, Node B
Apex of AB Block, Node C

22. Conclusions
Results of the structural analysis indicate the ability for an arch dam to redistribute stresses through arch action even in a damaged state resulting in stability of the dam.
The earthquake magnitude has a significant impact on the stability of both concrete dam and foundation blocks. However a time history of displacements of the dam at various locations show that the displacements stabilize after the seismic events, indicating stability of the arch.
The uplift pressures are critical to understanding the movement of foundation blocks. The arch dam experienced more overall cracking on both upstream and downstream faces under larger uplift pressures. In general, the stability of the concrete dam is related to the magnitude of the uplift pressure at the foundation block.
The analysis showed that the ambient temperature doesn’t have a significant impact either on the arch dam cracking patterns or on the foundation block displacements