Soil Foundation Structure Interaction Simulations: Static and Dynamic Issues Boris Jeremić Department of Civil and Environmental Engineering University of California, Davis 1 JB
Leitmotiv Create high fidelity models of constructed facilities (bridges, buildings, port structures, dams...). Models will live concurrently with the physical system they represent. Models to provide owners and operators with the capabilities to assess operations and future performance. Use observed performance to update and validate models through simulations. 2 JB
Presentation Overview Role of numerical simulations Static (kinematic) behavior Layered soils Pile groups Dynamic behavior Application of seismic loads (motions) Site response analysis From large scale geophysical simulations to large scale soil structure simulations Application to long bridges 3 JB
Goal Develop and use computational models in order to Design physical tests Use observed behavior to validate and improve models Use validated models to predict behavior of realistic bridge systems Educate users about new, exciting simulation tools that are now available 4 JB
Goals of Validation Quantification of uncertainties and errors in the computational model and the experimental measurements Goals on validation Tactical goal: Identification and minimization of uncertainties and errors in the computational model Strategic goal: Increase confidence in the quantitative predictive capability of the computational model Strategy is to reduce as much as possible the following: Computational model uncertainties and errors Random (precision) errors and bias (systematic) errors in the experiments Incomplete physical characterization of the experiment 5 JB
Validation Procedure Uncertainty Aleatory uncertainty inherent variation associated with the physical system of the environment (variation in external excitation, material properties...). Also know known as irreducible uncertainty, variability and stochastic uncertainty. Epistemic uncertainty potential deficiency in any phase of the modeling process that is due to lack of knowledge (poor understanding of mechanics...). Also known as reducible uncertainty, model form uncertainty and subjective uncertainty Deterministic Epistemic uncertainty Aleatory uncertainty Heisenberg principle 6 JB
Validation Experiments A validation experiment should be jointly designed and executed by experimentalist and computationalist Need for close working relationship from inception to documentation Elimination of typical competition between each Complete honesty concerning strengths and weaknesses of both experimental and computational simulations A validation Experiment should be designed to capture the relevant physics Measure all important modeling data in the experiment Characteristics and imperfections of the experimental facility should be included in the model 7 JB
Application Domain System complexity Application Domain Validation Domain System complexity Application Domain Validation Domain System complexity Application Domain Validation Domain Inference System Parameter System Parameter System Parameter Complete Overlap Partial Overlap No Overlap Inference Based on physics or statistics Validation domain is actually an aggregation of tests (points) and might not be convex (bifurcation of behavior) NEES research provides for validation domain (experimental facilities) that are mostly (if not exclusively) non overlapping with the application domain. 8 JB
Computability Physical Problem Computability : (von Neumann computability) how well a mathematical model can predict the response of a mechanical system (related to validation) Computational computability : (Turing computability) discretized problem is computable if there exists an algorithm that can solve the problem in a finite number of steps (related to verification) 9 JB
Static (Kinematic) SFSI Computational geomechanics for large scale problems Single pile behavior in elastic plastic soils, effects of layers Pile group behavior 1 JB
Single Pile in Layered Soils 2 2 2 2 2 2 SAND φ = 37.1 o SAND φ = 37.1 o 1.718 1.718 Depth (m) 2 SOFT CLAY Cu = 21.7 kpa 3.436 4 SAND φ = 37.1 o 2 4 2 4 Depth (m) 2 SOFT CLAY Cu = 21.7 kpa 3.436 4 SAND φ = 37.1 o 2 4 2 4 6 6 6 6 6 6 8 8 8 8 8 8 1 1 1 2 Bending Moment (kn.m) 1 4 2 2 4 6 Shear Force (kn) 1 1 1 2 3 Lateral Resistance (kn/m) 1 1 1 2 Bending Moment (kn.m) 1 4 2 2 4 6 Shear Force (kn) 1 1 1 2 3 Lateral Resistance (kn/m) 11 JB
p y Response for Single Pile in Layered Soils Lateral Pressure p (kn/m) 3 25 2 15 1 Depth.322 Depth.537 Depth.752 Depth.966 Depth 1.181 Depth 1.396 Depth 1.611 Depth 1.825 Depth 2.4 Depth 2.255 Depth 2.47 Depth 2.684 Lateral Pressure p (kn/m) 3 25 2 15 1 Depth.322 Depth.537 Depth.752 Depth.966 Depth 1.181 Depth 1.396 Depth 1.611 Depth 1.825 Depth 2.4 Depth 2.255 Depth 2.47 Depth 2.684 5 5 2 4 6 8 1 12 Lateral Displacement y (cm) 2 4 6 8 1 12 Lateral Displacement y (cm) Influence of soft layers propagates to stiff layers and vice versa Can have significant effects in soils with many layers 12 JB
Lateral Resistance Ratio Distributions Cu=13.kPa,Eo=11kPa Cu=21.7kPa,Eo=11kPa Cu=3.3kPa,Eo=11kPa Cu=13.kPa,Eo=11kPa Cu=21.7kPa,Eo=11kPa Cu=3.3kPa,Eo=11kPa 1 y/d =.5 1 y/d =.65 2 2 Z / D 3 SAND γ=14.5kn/m 3 3 SAND γ=14.5kn/m 3 4 4 5 5 CLAY, γ=11.8kn/m 3 6.5.6.7.8.9 1 p / p homog. case CLAY, γ=11.8kn/m 3 6.5.6.7.8.9 1 p / p homog. case Influence increases as the shear strength of soft layer decreases (think of cyclic mobility of liquefaction) 13 JB
Pile Group Simulations 4x3 pile group model and plastic zones 14 JB
Out of Plane Effects Out-of-loading-plane bending moment diagram, Out-of-loading-plane deformation. 15 JB
Pile Spreading Stress Path 16 JB
Load Distribution per Pile Lateral Load Distribution in Each Pile (%) 15 14 13 12 11 1 9 8 7 Trail Row, Side Pile Third Row, Side Pile Second Row, Side Pile Lead Row, Side Pile Trail Row, Middle Pile Third Row, Middle Pile Second Row, Middle Pile Lead Row, Middle Pile 6 5 1 2 3 4 5 6 7 8 9 1 11 Displacement at Pile Group Cap (cm) 17 JB
Piles Interaction at -2.m Note the difference in response curves (cannot scale single pile response for multiple piles) 18 JB
Comparison with Centrifuge Tests Lateral Load distribution in each row (%) 45 4 35 3 25 FEM Trail Row FEM Third Row FEM Second Row FEM Lead Row Centrifuge Trail Row Centrifuge Third Row Centrifuge Second Row Centrifuge Lead Row 2 15 1 2 3 4 5 6 7 8 9 1 Lateral Displacement at Pile Group Cap (cm) 19 JB
Dynamic SFSI Application of seismic loads (motions) Site response analysis From large scale geophysical simulations to large scale soil structure simulations Application to long bridges 2 JB
Domain Reduction Method (DRM) Work by Bielak et al. (23, Bulletin of the Seismological Society of America) at CMU. Modular, two step procedure for large 3D dynamics problems. Primary unknowns: Total wave field within the local domain, Scattered wave field in the exterior domain, Free field wave field from the background structure only act on a single concave surface. 21 JB
DRM: Background Wave Field Determination using any available numerical or measurement technique, Need displacement and acceleration field Green s functions solutions, Quake system, SCEC database, SHAKE... 3D downhole arrays, Local Feature Geologic Layers Fault 22 JB
DRM: Idea Simplified original model Local geological feature P b Γ Ω u b u i Ω P b Γ u b u i Γ Ω u i P b Γ Fault P e Ω + Γ u + b u e Fault Ω + e P e + Γ u b u 23 JB
DRM: Dynamics [ M Ω ii M Ω ib M Ω bi M Ω bb [ M Ω+ bb M Ω+ be M Ω+ eb Mee Ω+ ] { } üi ü b ] { } üb + ü e + [ K Ω ii K Ω ib K Ω bi K Ω bb [ K Ω+ bb K Ω+ be K Ω+ eb Kee Ω+ ] { ui u b } ] { ub u e } Mii Ω M Ω ib ü i Mbi Ω Mbb Ω + M Ω+ bb M Ω+ be ü b M Ω+ eb Mee Ω+ ü e Kii Ω Kib Ω u i Kbi Ω Kbb Ω + KΩ+ bb K Ω+ be u b K Ω+ eb Kee Ω+ = u e { } =, in Ω Pb { } Pb =, in Ω + P e + P e Γ Ω u i u b Fault P e Ω + Γ + u e 24 JB
DRM: Change of Variables Equations of motion in Ω + for changed model [ M Ω+ bb M Ω+ be M Ω+ eb Mee Ω+ ] { ü b ü e } + [ K Ω+ bb K Ω+ be K Ω+ eb Kee Ω+ ] { u b u e } = { P b P e } P e = M Ω+ eb ü b + M Ω+ ee ü e + K Ω+ eb u b + K Ω+ ee u e Change of variables: u e = u e + w e total displacement u e free field, background structure u e residual field, relative displacement field with respect to the reference free, background field w e Mii Ω Mib Ω Mbi Ω Mbb Ω + M Ω+ M Ω+ eb bb M Ω+ be Mee Ω+ ü i ü b ẅ e + Kii Ω Kib Ω Kbi Ω Kbb Ω + KΩ+ bb K Ω+ eb K Ω+ be Kee Ω+ u i u b w e = P eff i P eff b P eff e 25 JB
DRM: Dynamic (Seismic) Forces P eff i P eff b P eff e = M Ω+ M Ω+ eb be ü e K Ω+ be ü b + KΩ+ eb u e u b Fault P e Γ e Ω + Γ u b Ω Γ + u e u i u e Seismic forces P e replaced by the effective nodal forces P eff, P eff involve only submatrices, M be,k be,m eb,k eb They vanish everywhere except in the single layer of elements in Ω + adjacent to Γ. The material inside Ω does not have to be linear elastic 26 JB
Application Examples Seismic wave propagation Effects of elastic plastic soils on free field motions Soil Structure interaction Effects of elastic plastic soils on dynamic response of pile column system 27 JB
Wave Propagation Model Acceleration (m/s 2 ). 1.8 3.3 6.3 8.8 11.8 14.8 18.3 Displacement (m). 1.8 3.3 6.3 8.8 11.8 14.8 21.8 23.3 27.3 18.3 21.8 23.3.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) 27.3.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) 28 JB
Wave Propagation Soft Soil Z Max Y 25. Max.622. 1.8 3.3.1181.127.128 21. 19.5 15. 11. 7..779.837.984.175.1129 Displacement (m) 6.3 8.8 11.8 14.8 18.3 21.8 23.3.116.176.96.846.749.678.633 Dispalacement (m) 4.3 3.6 1.8. 1.8 3.6 4.3 7. 11. 15. 19.5.1173.1178.1183.1181.1179.1174.1169.1123.169.982.837 27.3.625 21. 25..779.622.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s).5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) 29 JB
Wave Propagation Stiff Soil Displacement (m) Z. 1.8 3.3 6.3 8.8 11.8 14.8 18.3 21.8 23.3 27.3 Max.76.762.762.761.758.753.745.735.724.658.625 Displacement (m) Y 25. 21. 19.5 15. 11. 7. 4.3 3.6 1.8. 1.8 3.6 4.3 7. 11. 15. 19.5 21. 25. Max.622.715.726.737.746.754.758.759.76.76.76.759.759.754.746.737.727.715.622.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s).5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) 3 JB
SSI Model. Acceleration (m/s 2 ) 4. 8. 12. 16. 2. 28. 3. Displacement (m). 4. 8. 12. 16. 2. 38. 28..5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) 38. 3..5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) 31 JB
SSI Model Free Field Stiff Elastic Plastic Soil Z(m) Max Z(m) Max..22 34.. 4..1947 Displacement (m) 8. 12. 16. 2..1576.1219.1183.1142 Displacement (m) 26. 24. 16. 12..124.1139.1231.1261 28. 3..155.52 8..1749 4..1937 38....22 1 2 3 4 5 6 7 8 9 1 Time (s) 1 2 3 4 5 6 7 8 9 1 Time (s) 32 JB
SSI Model: Pile Column Stiff Elastic Plastic Soil Y(m) Max Z(m) Max 34....291 4..1899 26..124 8..1496 24..1139 Displacement (m) 12. 16. 2..1222.1183.1142 16. 12. Displacement (m).1232.1262 28. 3..155.52 8. 4..1751.1935 38....291 1 2 3 4 5 6 7 8 9 1 Time (s) 1 2 3 4 5 6 7 8 9 1 Time (s) 33 JB
SSI Model Free Field Soft Elastic Plastic Soil Z(m) Y(m) 34. Max...3158 4. 8..2823.1622 26. 24..362.1338 Displacement (m) 12. 16. 2..1261 Displacement (m).119.196 16. 12..1512.1567 28. 3..971.14 8. 4..2545.289 38....3158 1 2 3 4 5 6 7 8 9 1 Time (s) 1 2 3 4 5 6 7 8 9 1 Time (s) 34 JB
SSI Model: Pile Column Soft Elastic Plastic Soil Z(m) Max 34....368 26. Displacement (m) 4. 8. 12. 16. 2. 28. 3..2448.1328.1227.127.194.976.14 24..356.1331 16. 12..1497.1549 8..2536 4..2896 38....368 1 2 3 4 5 6 7 8 9 1 Time (s) 1 2 3 4 5 6 7 8 9 1 Time (s) 35 JB
SSI Model: Pile Column Behavior.4.25.3.2.15.2.1 Displacemnt (m).1 Displacement (m).5.5.1.1.15.2.2.3 1 2 3 4 5 6 7 8 9 1 Time (s).25 1 2 3 4 5 6 7 8 9 1 Time (s) Stiff soil Soft soil 36 JB
I 88 Bridge SFSI Issues Seismic response of I 88 viaduct using performance based engineering Hierarchical set of SFSI simulations models developed to represent engineering demand parameters (EDP) Local site conditions (inelastic SFSI interaction problem) Wave propagation over the bridge length (scale problem) Single point (spatial) far field input motions Stochastic distribution of materials (properties) over spatial scales 37 JB
Geologic and Soil Conditions Jeremic, UCLA Seminar Series, May 24 38 B J
Local Site Conditions Adjacency of foundations in soft and stiff soil Spatial distribution of soil materials Jeremic, UCLA Seminar Series, May 24 39 B J
Soil Foundation System Models Hierarchical set of models used to estimate performance Reducing epistemic uncertainty as much as possible 1.5 7.2.6 1.5 1.5 1.5 1.5.6 21.2 7.2.6.6.6.6.6 4 JB
I 88: Hierarchy of Models 41 JB
I 88: Seismic Input Coupling free field motions to SFSI system (Domain Reduction Method) Wave propagation over the bridge length Fault 42 JB
Seismic Amplification Adjacent bents Foundation will survive but the superstructure or joints might not Z(m) Max Z(m) Max..1946..6928 4..18 4..6258 8..1248 8..3961 Displacement (m) 12. 16. 2..878.844.791 Displacement (m) 12. 16. 2..1227.1161.112 28. 3..783.77 28. 3..879.224 38.. 38.. 5 1 15 2 25 3 35 4 Time (s) 5 1 15 2 25 3 35 4 Time (s) Stiff soil Soft soil 43 JB
Concluding Remarks Static (kinematic) SFSI issues Layered soils Piles in liquefied soils (layers) Dynamic (seismic) SFSI issues Free field vs. SFSI motions Very large scale coupling (with geophysical simulations) 44 JB
Thank you Jeremic, UCLA Seminar Series, May 24 45 B J