Nonlinear Analysis of Viaducts and Overpasses Geotechnical Modeling Issues Steve Kramer Pedro Arduino Hyung-Suk Shin University of Washington
The Problem Approach Soil Soil Soil Soil Soil Soil Soil Soil Soil Soil Bridge Bridge Abutment Soil Soil Soil Soil Piers Piers Soil Soil Approach Foundations Soil Soil Abutment Soil Soil Soil Soil
Reality Three-dimensional problem Soil Bridge Motions Finite extent Short structures - overpass Long structures - viaduct Soil behavior Nonlinear, inelastic Spatial variability Quantity / quality of data
Reality Soil-Foundation-Structure Interaction (SFSI) Effects on system stiffness Effects on system damping Effects on displacements Abutments Stiffness Failure Shallow foundations Deep foundations Time-dependent soil behavior Pore pressure generation Pore pressure dissipation Delayed failure
Three-dimensional problem Soil Bridge Motions Three-dimensional Three-dimensional OpenSees OpenSees analyses analyses Possible Possible using using brick brick elements elements Very Very long long run run times times How How to to handle handle foundations? foundations? Continuum Continuum representation representation Discrete Discrete (spring) (spring) representation representation 3-D Model
Three-dimensional problem Soil Bridge Motions 2-D Model Two-dimensional Two-dimensional OpenSees OpenSees analyses analyses Quad Quad elements elements for for soil soil Much Much shorter shorter run run times times Discrete Discrete (spring) (spring) representation representation of of foundations foundations Horizontal Horizontal and and vertical vertical input input motions motions Separate Separate analysis analysis for for out-of-plane out-of-plane response response
Three-dimensional problem Soil Bridge Motions Quasi-3D Quasi-3D OpenSees OpenSees analyses analyses Perpendicular Perpendicular 1-D 1-D soil soil columns columns Much Much shorter shorter run run times times Discrete Discrete (spring) (spring) representation representation of of foundations foundations Horizontal Horizontal and and vertical vertical input input motions motions Decoupled Decoupled response response at at different different foundation foundation locations, locations, and and in in different different directions directions
Finite extent can be important for long structures Incoherency Incoherency Due Due to to variable variable soil soil conditions conditions Due Due to to wave wave passage passage effect effect
Soil behavior Nonlinear, inelastic Spatial variability Quantity / quality of data Soil Soil Models Models Many Many parameters parameters may may be be required required Parameter Parameter identification identification may may require require numerous numerous tests tests Standard Standard parameters parameters sets sets available available for for Elgamal Elgamal models models Pressure-independent model model Pressure-dependent Pressure-dependent model model
Soil behavior Nonlinear, inelastic Spatial variability Quantity / quality of data Random Random Fields Fields Generate Generate multiple multiple realizations realizations of of anticipated anticipated soil soil properties properties Correct Correct distribution distribution (µ, (µ, σ) σ) Correct Correct auto-correlation auto-correlation function function Multiple Multiple analyses analyses required required May May be be time-consuming time-consuming
Soil behavior Nonlinear, inelastic Spatial variability Range of permanent Quantity / quality of data displacements Mean permanent displacement Random Random Fields Fields Generate Generate multiple multiple realizations realizations of of anticipated anticipated soil soil properties properties Correct Correct distribution distribution (µ, (µ, σ) σ) Correct Correct auto-correlation auto-correlation function function Multiple Multiple analyses analyses required required May May be be time-consuming time-consuming Distribution of permanent displacements
Soil behavior Nonlinear, inelastic Spatial variability Quantity / quality of data Subsurface Subsurface Investigation Investigation Soil Soil sampled sampled at at discrete discrete number number of of locations locations Laboratory Laboratory tests tests affected affected by by many many factors factors Disturbance Disturbance Stress Stress path path effects effects
Soil behavior Nonlinear, inelastic Spatial variability Quantity / quality of data Subsurface Subsurface Investigation Investigation Soil Soil sampled sampled at at discrete discrete number number of of locations locations Laboratory Laboratory tests tests affected affected by by many many factors factors Disturbance Disturbance Stress Stress path path effects effects Insitu Insitu tests tests
Soil behavior Nonlinear, inelastic Spatial variability Quantity / quality of data Correlations Correlations Parameter Parameter measured measured in in insitu insitu test test correlated correlated to to property property of of interest interest Correlations Correlations available, available, but but based based on on scattered scattered data data Leads Leads to to uncertainty uncertainty in in estimated estimated property property value value
Soil-Foundation-Structure Interaction Shallow foundations Deep foundations Continuum analysis 3-D 3-D modeling modeling Small Small elements elements required required in in nearfielfield near- Interface Interface elements elements required required Sliding Sliding Gapping Gapping Larger Larger elements elements OK OK at at greater greater distances distances Transmitting Transmitting boundaries boundaries required required for for radiation radiation damping damping
Soil-Foundation-Structure Interaction Shallow foundations Deep foundations Continuum analysis 3-D 3-D modeling modeling Small Small elements elements required required in in nearfielfield near- Interface Interface elements elements required required Sliding Sliding Gapping Gapping Larger Larger elements elements OK OK at at greater greater distances distances Transmitting Transmitting boundaries boundaries required required for for radiation radiation damping damping
Soil-Foundation-Structure Interaction Shallow foundations Deep foundations Continuum analysis
Soil-Foundation-Structure Interaction Shallow foundations Deep foundations Discrete analysis nonlinear springs and dashpot Discrete Discrete interaction interaction elements elements Springs Springs to to represent represent soil soil stiffness stiffness Dashpots Dashpots to to represent represent damping damping Hysteretic Hysteretic damping damping in in near-field near-field Radiation Radiation damping damping in in far-field far-field Must Must account account for for gapping gapping Must Must account account for for pore pore pressure pressure effects effects Soil profile p-y spring t-z spring q-z spring
Abutment models Stiffness modeling abutment module Bridge module Discrete Discrete interaction interaction elements elements Nonlinear Nonlinear springs springs Stiffness Stiffness Strength Strength Interface Interface elements elements Bearing Bearing elements elements Bearing pad module Pile foundation module Soil module
Abutment models Stiffness modeling Discrete Discrete interaction interaction elements elements Nonlinear Nonlinear springs springs Stiffness Stiffness Strength Strength Interface Interface elements elements Bearing Bearing elements elements
Abutment models Stiffness modeling Strength modeling Discrete Discrete interaction interaction elements elements Nonlinear Nonlinear springs springs Stiffness Stiffness Strength Strength Interface Interface elements elements Bearing Bearing elements elements
Abutment models Stiffness modeling Strength modeling Discrete Discrete interaction interaction elements elements Nonlinear Nonlinear springs springs Stiffness Stiffness Strength Strength Interface Interface elements elements Bearing Bearing elements elements
Abutment models Stiffness modeling Strength modeling Discrete Discrete interaction interaction elements elements Nonlinear Nonlinear springs springs Stiffness Stiffness Strength Strength Interface Interface elements elements Bearing Bearing elements elements Complex failure surface geometry
Time-dependent soil behavior Pore pressure generation Pore pressure redistribution Pore pressure dissipation Effective Effective stress stress analysis analysis Constitutive Constitutive model model Modulus Modulus degradation degradation Phase Phase transformation transformation Hysteretic Hysteretic damping damping High frequency Low frequency High frequency
Time-dependent soil behavior Pore pressure generation Pore pressure redistribution Pore pressure dissipation Effective Effective stress stress analysis analysis Constitutive Constitutive model model Modulus Modulus degradation degradation Phase Phase transformation transformation Hysteretic Hysteretic damping damping Diffusion Diffusion equation equation solution solution
Time-dependent soil behavior Pore pressure generation Pore pressure redistribution Pore pressure dissipation Effective Effective stress stress analysis analysis Constitutive Constitutive model model Modulus Modulus degradation degradation Phase Phase transformation transformation Hysteretic Hysteretic damping damping Diffusion Diffusion equation equation solution solution Post-liquefaction Post-liquefaction settlement settlement
Geotechnical Modeling - Example Example: Bridge on liquefiable soil deposit Five-span bridge Approach embankments Variable thickness of liquefiable soil Clay Liquefiable sand Dense sand
Geotechnical Modeling - Example reinforced conrete column (column A 4 ft) prestressed reinforced concrete bridge spring connection abutment simplified abutment (roller or spring) steel pipe pile (8 ft diameter)
Geotechnical Modeling - Example Horizontal displacements 95 cm 200 cm Vertical displacements 26 cm 70 cm
Geotechnical Modeling - Example Ground failure Lateral spreading Settlement Different form of loading on bridge
Geotechnical Modeling - Example 50% 50% // 50 50 yrs yrs 10 10 motions Scaled Scaled so so that that mean mean S a (T a (T o ) o ) = target target S a (T a (T o ) o )
Geotechnical Modeling - Example 10% 10% // 50 50 yrs yrs 10 10 motions Scaled Scaled so so that that mean mean S a (T a (T o ) o ) = target target S a (T a (T o ) o )
Geotechnical Modeling - Example 2% 2% // 50 50 yrs yrs 10 10 motions Scaled Scaled so so that that mean mean S a (T a (T o ) o ) = target target S a (T a (T o ) o )
Geotechnical Modeling - Example Ground surface settlement
Geotechnical Modeling - Example Ground surface settlement
Geotechnical Modeling - Example Ground surface settlement Max heave: 29 cm Max settlement: 82 cm
Geotechnical Modeling Conclusions: Many complex geotechnical aspects to complete modeling of bridge-soil system OpenSees has capabilities for addressing nearly all of these in fairly rigorous fashion OpenSees is unique in level of rigor with which soil and structural response can be modeled in coupled manner OpenSees calculations are time-consuming for rigorous model Several approximations can be made w/r/t dimensions, geometry for soil model, foundation models Results of analyses provide insight into response, damage mechanisms