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**U.S. ARMY CORPS OF ENGINEERS**

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

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**Introduction Project overview The JFP model Designing from the model**

Properties Troubleshooting & Lessons Learned Designing from the model Running the model Seismic input

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**The Folsom JFP LS-DYNA Model Overview**

Control Structure Reservoir (*MAT_NULL) Foundation (*MAT_ELASTIC, E = 3500ksi) Backfill (*MAT_PSEUDO_TENSOR) Shear Zone (*MAT_ELASTIC, E = 324ksi)

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**The Folsom JFP LS-DYNA Model Control Structure**

Non-Flow Monoliths Flow-Through Monoliths Non-Flow Monolith

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**The Folsom JFP LS-DYNA Model Flow-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

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Rigid Bodies & SOFT Symptom Unrealistic spikes in forces at the radial gate Corrected Peak force/length along pier during earthquake

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Rigid Bodies & SOFT Reasons Gates defined using *MAT_RIGID Reservoir is merged with the gate to obtain correct hydrostatic pressures Solution Optional Card A: SOFT = 0 uses a penalty formulation, interface stiffness is based on the bulk modulus

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Reservoir Contacts Symptom During an earthquake, some fluid elements lose pressure Reason Structure displacements created a free surface

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**Reservoir Contacts Solution 1. Split the reservoir at monolith joints**

2. Define a contact surface between reservoir parts

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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 calculator HSF = 0.5*γ*H2*b

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**Hydrostatic Pressures**

Complex topography can cause incorrect pressures Idealized geometry ensures the loads to the structure are more realistic

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**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

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**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

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**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

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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)

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**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

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**Running the Model Step 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

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**Running the Model Step 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_REFLECTING should replace all SPCs This allows the seismic waves to exit the model, simulating an unbounded condition

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**Running the Model Step 3 Apply the seismic loads**

*LOAD_SEGMENT_SET_NONUNIFORM Each direction of motion has its own load curve

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**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)

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**Non-Reflecting Boundary**

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

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**Seismic Input Seismic Input Location and Minimum Foundation Size**

Plane within foundation (*NODE_SET) Deconvolved ground motions Methods used to Deconvolve (Typ. 2D) NR Note: If model is too narrow seismic energy will exit through side of model.

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**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)

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**Seismic Input Spectral Matching (preferred method) Advantages**

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

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**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.

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**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

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Seismic Input Example of Spectrally Matched Ground Motions

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Seismic Input Example of Spectrally Matched Ground Motions

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