1. Numerical analysis of Concrete Face Rockfill Dams based on Lade’s model and gradient plasticity P. Dakoulas, E. Stavrotheodorou, A. Giannakopoulos University of Thessaly Volos, Greece

2. Realistic prediction of slab performance during impoundment, creep and dynamic settlements Motivation: Campos Novos Dam Zipingpu Dam

3. Topics Behavior and modelling of rockfill Lade’s constitutive model A simple gradient plasticity approach Numerical model Concrete slab performance: o effect of dam height o effect of rockfill stiffness Conclusions

4. Oroville dam rockfill Pyramid dam rockfill σ 3 = 4413 kPa 2896 965 207 σ 3 =207 kPa 965 2896 4413 excellent quality average quality σ 3 = 4413 kPa 2896 965 207 σ 3 =207 kPa 965 2896 4413 (Marachi et al. 1972)

5. Lade’s constitutive model for geomaterials stress-strain relationship with hardening and softening behaviour yield surfaces at different levels of plastic work and failure surface (Dakoulas and Sun 1993) yield surface

6. Lade’s constitutive model for geomaterials The model offers the following advantages: Continuous variation of the tangent Young’s modulus based on the stress state during the analysis Realistic description of volumetric strains due to shearing Realistic handling of the softening behaviour

7. Simulation of rockfill behavior: isotropic compression Oroville rockfillPyramid rockfill (using Lade’s model implemented in ABAQUS as a user material)

8. Oroville rockfill behavior: triaxial compression

9. Pyramid rockfill behavior: triaxial compression

10. Possible numerical convergence issues Intense softening behaviour (e.g. due to major rockfill breaking above a critical confining stress, as in Mohale dam) Local areas of possible large strain concentration abutment interface material zone interface slope surface intense softening behaviour

11. A simple gradient plasticity approach deviatoric plastic strain: gradient coefficient:where: = gradient of = intrinsic length (rockfill size) = reference strain (limit of elastic range) (Bassani 2001)

12. A simple gradient plasticity approach

13. Numerical models of three dams 100 m 200 m Dam A Dam B concrete panels material zones Aspect ratio: L/H = 2 Shape factor: A s /H 2 = 2.1

14. 300 m Dam C material zones Numerical models of three dams Aspect ratio: L/H = 2 Shape factor: A s /H 2 = 2.1

15. Fiber reinforced concrete based on mixing plain concrete with f c = 37 MPa and steel fiber (Reinforcing Index = 2.5%) Numerical modelling of concrete slab panels Geometry: slab width = 15 m slab thickness = 0.30+0.003 h (h = depth of overlying water) Material: Uniaxial compression Uniaxial tension

16. Elastic Young’s modulus at the end of construction H= 200m Oroville rockfill Pyramid rockfill Elastic Young’s modulus: = model parameters = Poisson’s ratio = stress invariants = atmospheric pressure Young’s modulus is derived from unloading test (i.e. purely elastic behavior)

17. Distribution of settlements at midsection H = 300 m -> S/H = 0.40% H = 300 m -> S/H = 1.47% H = 200 m -> S/H = 0.30% (measured on Oroville dam S/H=0.31%)

18. Construction settlements narrow canyons

19. Concrete slab deflection after impoundment Oroville rockfill Pyramid rockfill H = 200 m

20. Slab deflection after impoundment after long-term creep and dynamic settlements Assumption: Max long-term settlements at crest is 50% of max. construction settlement

21. Tensile plastic strains in the concrete slab H= 300 m

22. Compressive stress after impoundment H= 200 m H= 300 m

23. Compressive stresses after impoundment H= 200 m H= 300 m x y

24. Compressive stress after long-term settlements H= 200 m H= 300 m

25. Compressive stresses after long-term settlements x y 3D strength: 57 MPa

26. after long-term settlements Maximum compressive stress vs dam height after impoundment

27. Horizontal movement of slab panels after impoundment Oroville rockfill

28. Horiz. movement of slab panels after long-term settlements Oroville rockfill

29. CONCLUSIONS Lade’s model for rockfill allows a realistic simulation of the stress-strain behavior and volumetric strains in a wide range of confining stresses. Comparison of measured construction settlements of dams in narrow canyons showed good agreement with the numerical predictions of the study. Use of excellent quality rockfill at void ratios 0.2 allows small construction settlements even for the 300 m dam Measured slab deflections due to impoundment from 18 CFRDs at various void ratios are in good agreement with the predicted slab deflections

30. CONCLUSIONS The use of excellent quality rockfill at void ratios of 0.2 yields small slab deflections even for the 300 m dam during impoundment and long-term settlements Compressive stresses in the slab reach a maximum at about 40% of the height during impoundment, but may reach a larger value near the crest due to long-term settlements For the excellent quality rockfill, compressive stresses remain at low levels compared to the strength of concrete For the average quality rockfill, compressive stresses become very high, especially after long-term settlements Thank you for your attention!

31. Acknowledgements This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF)-Research Funding Program: Heracleitus II. Investing in knowledge society through the European Social Fund.