Analysis and Design of Large-Scale Civil Works Structures Using LS-DYNA®

1. PRESENTED BY THE U.S. ARMY CORPS OF ENGINEERS Analysis and Design of Large-Scale Civil Works Structures Using LS-DYNA® Eric Kennedy, P.E. Structural Engineer Sacramento District Ryan Tom American River Design Sacramento District David Depolo, M.S., P.E. Structural Engineer Sacramento & Philadelphia Districts Thomas Walker, P.E. Structural Engineer Sacramento District NON-PRESENTING CO-AUTHORS LSTC International Users’ Conference June 7, 2010

2. Introduction • Project overview • The JFP model • Properties • Troubleshooting & Lessons Learned • Designing from the model • Running the model • Seismic input

5. The Folsom JFP LS-DYNA ModelOverview Reservoir (*MAT_NULL) Control Structure Foundation (*MAT_ELASTIC, E = 3500ksi) Backfill (*MAT_PSEUDO_TENSOR) Shear Zone (*MAT_ELASTIC, E = 324ksi)

6. The Folsom JFP LS-DYNA ModelControl Structure Non-Flow Monoliths Flow-Through Monoliths Non-Flow Monolith

7. The Folsom JFP LS-DYNA ModelFlow-Through Monoliths Headwall Piers (Designed using LS-DYNA output) Trunnion Girders Pier Struts (Designed using LS-DYNA output) Radial Gates (Rigid, defined individually) Invert Slab Gate Arms

8. Rigid Bodies & SOFT • SymptomUnrealistic spikes in forces at the radial gate Corrected Peak force/length along pier during earthquake

9. Rigid Bodies & SOFT • ReasonsGates defined using *MAT_RIGIDReservoir is merged with the gate to obtain correct hydrostatic pressures • SolutionOptional Card A:SOFT = 0uses a penalty formulation, interface stiffness is based on the bulk modulus

10. Reservoir Contacts • SymptomDuring an earthquake, some fluid elements lose pressure • ReasonStructure displacements created a free surface

11. Reservoir Contacts • Solution1. Split the reservoirat monolith joints 2. Define a contact surface between reservoir parts

12. Reservoir Contacts • For troubleshooting, split contacts so you can focus on problem areas(each conduit has its own set of contacts) • For verification, split contacts into pieces that are easily replicated with a calculatorHSF = 0.5*γ*H2*b

13. Hydrostatic Pressures • Complex topography can cause incorrect pressures • Idealized geometry ensures the loads to the structure are more realistic

14. Post-Tensioned Anchorage • Option 1: Constrained Nodes • Each trunnion girder is constrained to nodes that represent the dead ends of the anchors • *CONSTRAINED_EXTRA_NODE_SET • Pros • Simple, easy to implement • Transfers all forces directly to the slab • Cons • Ignores elastic behavior of anchors • Creates a rigid plane in the slab

15. Post-Tensioned Anchorage • Option 2: Beam Elements • Hughes-Liu (Type 1) or Truss (Type 3) • Tied Node-to-Surface contacts at both ends • More realistic than constrained nodes – pressure between trunnion girder and pier changes during the earthquake

16. Post-Tensioned Anchorage • Hughes-Liu beams use *INITIAL_STRESS for post-tensioning • 100% Applied initialization – no option to ramp with gravity loads • Truss elements require pressure loads on surfaces to simulate post-tensioning • Stress in beam is the change from the post-tensioning stress

17. Design • Nodal contact forces recorded at pier/slab interface and two higher contacts • Force and moment demands calculated for each nodal group at each output time (dt = 0.01sec)

18. Design • Site constraints required an optimized reinforcing design • Generate an interaction diagram for each reinforcing pattern • Axial force determines moment capacity and affects shear capacity • This design would have been much more difficult without LS-DYNA

19. Running the ModelStep 1 • Run the model with gravity loads first • Use *LOAD_BODY_PARTS to apply gravity to everything except the foundation • Apply Single Point Constraints (SPCs) at all boundaries • *DATABASE_SPCFORC

20. Running the ModelStep 2 • Apply the equilibrium forces to the model • *LOAD_NODE_POINT with output in the spcforc database • Ramp these forces on the same load curve as the gravity loads • *BOUNDARY_NON_REFLECTINGshould replace all SPCs • This allows the seismicwaves to exit the model, simulating anunbounded condition

21. Running the ModelStep 3 • Apply the seismic loads • *LOAD_SEGMENT_SET_NONUNIFORM • Each direction of motion has its own load curve

22. Seismic Input • Selection of Time Histories • Characterize Design Earthquake Magnitude • Distances from source to site • Subsurface conditions • Duration of Strong Shaking • Available Records or Simulated Time Histories • Deterministic and Probabilistic • Deterministic MCE’s (3 records/per direction) • Probabilistic OBE’s (3 records/per direction)

23. Ground DAM HORIZONTAL PLANE FOR GROUND MOTIONS Non-Reflecting Boundary Seismic Input • Seismic Input Methods • Displacement Time History • Velocity Time History • Acceleration Time History • Force (or Stress) Time History (preferred)

24. NR Seismic Input • Seismic Input Location and Minimum Foundation Size • Plane within foundation (*NODE_SET) • Deconvolved ground motions • Methods used to Deconvolve (Typ. 2D) Note: If model is too narrow seismic energy will exit through side of model.

25. Seismic Input • Modifying Time Histories to Develop Design Records • Simple (Uniform) Scaling • Determine Natural Period of Structure • Deconvolved earthquake applied to foundation model w/o structure to develop response spectrum • Compare recorded and smooth design spectrums • Apply single factor so that response spectrum of scaled motion is a close match to design spectrum at the natural period • Disadvantages • More EQ records required (min. of 3) • Natural Period of structure must be determined • Agreement of response spectrums could vary significantly at other periods • Scaling for different directions of motion (1 factor for all directions vs. different factors for each direction)

26. Seismic Input • Spectral Matching (preferred method) • Modifying frequency content of input motion so that recorded response spectrum is a close match to the design response spectrum at all periods • Deconvolved vs. Free Field Motion • Advantages • Sufficient to have one time history for each direction • Multiple structures at a site with varying periods would not need scaling for each structure • The energy of the time history is not greatly altered

27. Seismic Input • Precautions • Ensure the character of the scaled record in the time domain is fairly similar in shape, sequence, and number of pulses with respect to the original time history.

28. Seismic Input • Spectral Matching Procedure • Outcrop acceleration time history for each component • FFT of Outcrop acceleration time history • Apply Outcrop motion at depth in model as force time history and record acceleration of node on surface of foundation model • FFT of computed acceleration time history • Compute correction factor in Frequency Domain as the ratio of the Outcrop to Computed motion amplitudes • Apply correction factor to the input motion in the frequency domain • Inverse FFT of corrected motion to return to time domain • Compute corrected force time history • Repeat procedure if necessary

29. Seismic Input Example of Spectrally Matched Ground Motions

30. Seismic Input Example of Spectrally Matched Ground Motions