Nonlinear Modeling of Dynamic Soil-Structure Interaction: A Practitioner s Viewpoint By (Arul) K. Arulmoli Earth Mechanics, Inc. Fountain Valley, California Workshop on Nonlinear Modeling of Geotechnical Problems: From Theory to Practice Johns Hopkins University, Baltimore, Maryland November 3 & 4, 25
Factors Affecting Industry Use of Advanced Computer Programs for Dynamic Soil-Structure Interaction Problems Too complex Complex model parameters Verification lacking Limitations on structural elements and soil-structure interfaces Lack in-house expertise More $ and time to projects Difficult to sell to client (structural) and/or owner
Uncertainties in Ground Motion Response Spectra (Input from Geologists/Seismologists) Average +42% Average -27% Average +47% ACCELERATIONRESPONSE SPECTRA FOR THE PORT OF LOS ANGELES Average -32% BASED ON DETERMINISTIC EVALUATION USING DIFFERENT MEAN SOIL ATTENUATION RELATIONSHIPS TYPICAL PERIOD RANGE FOR POLA CONTAINER WHARVES
Dynamic Soil-Structure Interaction Analysis Analysis Cross Section Container Wharf Problem (Port of Los Angeles, Berth 147) Elevation (ft) -5-1 Backfill Loose to med. dense silty SAND Soft to stiff CLAY and SILT Soft to med. stiff lean CLAY Stiff lean CLAY Dense to very dense SAND Wharf Deck Cutoff Wall Dike Row G F D C B Row A MLLW = El. ' 24-inch octagonal prestressed concrete piles -15-4 -3-2 -1 1 2 3 Distance (ft)
Dynamic Soil-Structure Interaction Analysis FLAC Model (Port of Los Angeles, Berth 147) Soil Grid Beam Elements Design Water Level = El. +5' Elevation (ft) -5-1 -15 Pile Elements (minimum discretization length = 2.5') -4-3 -2-1 1 2 3 Distance (ft)
Dynamic Soil-Structure Interaction Analysis Structure Discretization Beam Elements Dike Pile Elements Idealized Soil Profile Legend Structural Element Node Rigid Joint
Dynamic Soil-Structure Interaction Analysis Soil Model Parameters -5 Elevation (ft) -1-15 -4-3 -2-1 1 2 3 Distance (ft) Material Layer Material Description Elevation (ft) Total Unit Weight (pcf) Cohesive Strength, c (psf) Internal Angle of Friction, φ' (degrees) Design Poisson's Ratio Design Shear Modulus (ksf) Loose to medium dense silty SAND (SM) above G.W.T. +15 to +5 12 32.35 79 Loose to medium dense silty SAND (SM) below G.W.T. (Liquefied) +5 to -15 12 4.45 652 Soft to stiff CLAY and SILT (CL/ML) Soft to medium stiff lean CLAY (CL) Stiff lean CLAY (CL) Dense to very dense SAND (SP) -15 to -3-3 to -6-6 to -85-85 to -18 115 11 115 125 See Next Slide See Next Slide See Next Slide 38.45.45.45.35 See Next Slide See Next Slide See Next Slide See Next Slide Backfill (SP) +15 to -6.4 12 32.35 128 Quarry Run +8 to -65 135 2 45.25 294
Dynamic Soil-Structure Interaction Analysis Modeling Profiles POLA Station Number 48+ 47+ 46+ 45+ 44+ 43+ 42+ Proposed Berth 147 Facility Idealized Section Profile Vertical discretization of soil profile at wharf location Loose to medium dense SAND above GWT (SM) Loose to medium dense SAND below GWT (SM) Elevation (ft) -5 Stiffness Variation Strength Variation Soft to stiff CLAY and SILT (CL/ML) Soft to med. stiff lean CLAY (CL) Stiff lean CLAY (CL) -1-15 Dense to very dense SAND (SP) 1 8 6 4 2 Shear Stiffness (ksf) 2 4 6 8 1 Shear Strength (psf) Idealized Soil Profile Strength and Stiffness Variation for Modeling Purposes
Dynamic Soil-Structure Interaction Analysis Surcharges and Dynamic Boundary Conditions Static Conditions = 1 psf Seismic Conditions = 6 psf Container Handling Surcharge = 25 psf (static and seismic condtions) 75' Refer Note 2 Refer Note 3 Refer Note 2 Slaved boundary (refer Note 1) Horizontal Input Motion (applied to base of model) Notes: 1. A slaved boundary is defined by neighboring gridpoints (at the same elevation) forced to move as one in the horizontal and vertical directions. 2. Horizontal static forces mobilized from static analysis applied at boundaries. 3. Wharf deck constrained to move in horizontal direction only. Slaved boundary (refer Note 1)
Dynamic Soil-Structure Interaction Analysis Deconvolution of Surface Motion using SHAKE91 Acc. (g).6.4.2. -.2 -.4 -.6 Vel. (ft/s) 4 3 2 1-1 -2-3 -4 Displ. (in) 2 1-1 -2 Within Motion at El. -18' Surface Motion 5 1 15 2 25 3 35 Time (second)
Dynamic Soil-Structure Interaction Analysis Deformed Shape at End of Shaking Undeformed structures Maximum displacement = 11.1 inches Deformed shape Elevation (ft) -5-1 -15-4 -3-2 -1 1 2 3 Notes: 1. Undeformed soil grid not shown for clarity. 2. Magnification factor for plotted displacement = 1. Distance (ft)
Dynamic Soil-Structure Interaction Analysis Row G (Landside) Pile Structural Profiles Horizontal Displacement (inches) -5 5 1 15 Shear Force (kips) -3-15 15 3 Bending Moment (kip-ft) -6-3 3 6 t = Seismic Surcharge t = 5 sec -2 t = 1 sec t = 15 sec t = 2 sec -4 t = 25 sec t = 25.3 sec Elevation (ft) -6-8 -1-12
Dynamic Soil-Structure Interaction Analysis A Consultant s Disclaimer! Accuracy of FLAC Analysis Results: The results of FLAC should be used as a guide in estimating the overall performance of the embankmentwharf system. In evaluating the FLAC results, one should keep in mind the program limitations, modeling assumptions and other uncertainties inherent in any nonlinear deformation analysis and in estimation of ground motion time histories.
Dynamic Soil-Structure Interaction Analysis What is a Reasonable Approach for the Practitioner? A simplified geotechnical approach, with some built-in conservatism, would be reasonable to provide structural engineers with the necessary design Input.
Soil-Pile-Structure Interaction Container Wharf rock fill inertial interaction displacement demand from structural analysis kinematic Loading - lateral spread displacement demand soft clay or liquefaction zone potential plastic hinge locations The two loading conditions induce maximum moments in separated upper and lower regions of pile The two loading conditions also tend to induce maximum moments at different times during the earthquake
SSI - Inertial Loading - Three Dimensional Effects Center of Rigidity (CR) e=49 ft Seismic Piles Center of Mass (CM) Center of Mass (CM) and Center of Rigidity (CR) do not coincide Two orthogonal earthquake components Non-symmetrical in the longitudinal direction Non-seismic Piles
SSI-Kinematic Interaction Analysis Simplified Newmark Time History Analyses Widely Used to Evaluate Seismic Stability of Slopes Displacement Based Performance Criteria Assumes a Rigid Sliding Block on Critical Failure Surface Yield Acceleration from Stability Analysis Acceleration-Time History at Base of Sliding Block is Used
SSI-Kinematic Interaction Analysis Pseudo Static Slope Stability Planar Failure Surfaces
SSI-Kinematic Interaction Analysis Newmark Sliding Block Analysis Results for CLE Motion (k y =.11g) NEWMARK DISP. (IN) NEWMARK VEL. (IN/S) 2 1-1 Max= 13.1 in Min=. in -2 5 1 15 2 25 4 2-2 Max= 25.9 in/s Min=. in/s -4 5 1 15 2 25.5 INPUT ACC. (g) Max=.48 g Min= -.38 g -.5 5 1 15 2 25 TIME (SECOND)
SSI-Kinematic Interaction Analysis CLE: Newmark Displacement vs. Yield Acceleration 5. 4.5 4. Displacement (ft) 3.5 3. 2.5 2. 1.5 1..5...1.2.3 Yield Acceleration, k y (g)
Assumed fixity for displacements Pile Pinning: Simplified Structural 1 Calculations 5D 8 P=7 kips P=5 kips P=3 kips Plastic hinge 2D 4 ft.sliding layer MOMENT (kip.in) 6 4 2 CLE Curvature P=1 kips P= 24 in. PILE; PRESTRESSED SECTION; 16X.6in STRANDS 5D 2D Plastic hinge Assumed fixity for displacements.1.2.3 CURVATURE (1/in) Plastic Hinge (PH) length: 36 in. Yield curvature: 2E-6/in PH curvature: 8E-6/in Results for maximum sliding layer displacement: Yield: 2.8 in PH: 5.9 in (Courtesy, Dr. Nigel Priestley)
SSI-Kinematic Interaction Analysis FLAC Liquefaction Example Pile Pinning Effect Horizontal Displacements at Row A (Thin Liquefied Layer Case) 2 1-1 Pile -2 Soil with Piles Elevation (ft) -3-4 -5 -Liquefied Layer Soil without Piles -6-7 -8-9 -1 -.8 -.6 -.4 -.2. Horizontal Displacement (ft)
SSI, Simplified Kinematic Interaction Analysis Pile Pinning: Geotechnical Calculations X=2D Plastic hinge Assumed fixity for displacements Plastic hinge Fy H ft. My Fy My X=2D Weak Soil layer Fy = 2My (H+2X) Additional Shear Strength due to Pile Pinning Effects: Spp = Fy A PT A PT Pile Tributary Area Assumed fixity for displacements
Dynamic Soil-Structure Interaction Evaluation Summary and Conclusions Use of advanced computer program for dynamic SSI problem in the industry is limited Simplified approaches, supported by complex analyses, provide reasonable solutions to dynamic SSI problems Collaboration between geotechnical and structural engineers is critical for improving the use of computer programs in the industry Collaboration in the industry as well as academia (research) is vital Structural based computer programs, with geotechnical capabilities, appear to be more viable for dynamic SSI problems