Dynamic Soil Structure Interaction.ppt
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The document is a presentation by Prof. Samirsinh P. Parmar on soil-structure interaction (SSI) in geotechnical engineering, focusing on the problems and analysis methods related to structures during earthquakes. It explores various effects of SSI on structural dynamics, including inertial and kinematic interactions, and details methods for analyzing these interactions through finite element methods (FEM) and boundary element methods (BEM). Additionally, it covers lumped parameter models and their applications in understanding foundation behavior under seismic loads.
Dynamic Soil Structure Interaction.ppt
- 1. Prof. Samirsinh P Parmar Mail: samirddu@gmail.com Asst. Prof. Dept. of Civil Engg. Dharmsinh Desai University, Nadiad, Gujarat , Bharatvarsh. Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 1
- 2. Content of the Presentation • SSI – Problem Definition • SSI Effects • Methods of Analysis • Interaction Analysis • FEM, BEM Analysis • Governing Equations • Staggered Solutions • Lumped Parameter Model • Travelling Wave effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 2
- 3. SSI – Problem Definition Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 3 Earthquake Analysis Structures supported by rigid foundations Earthquakes=>Specified motion of base Rigid Base Analysis Tall Buildings Acceptable • Light & Flexible • Firm Foundations • Methods focus on modeling of structure • Displacements wrt fixed base • Finite Element Methods Nuclear Power Plants Wrong Assumption • Massive & Stiff • Soft Soils • Interaction with supporting soils becomes important
- 4. SSI – Problem Definition Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 4 Machine Foundation Parameters •Local Soil Conditions •Peak Acceleration •Frequency Content of Motion •Proximity to Fault •Travel Path etc Inertial Interaction Inertial forces in structure are transmitted to flexible soil Kinematic Interaction Stiffer foundation cannot conform to the distortions of soil TOTAL=INERTIAL + KINEMATIC Seismic Excitation
- 5. SSI Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 5 0.00E+00 2.50E-05 5.00E-05 7.50E-05 1.00E-04 1.25E-04 1.50E-04 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 w/wn Amplitude in ft. SSI - Proposed BE-FE SSI - Spring Dashpot Model Proposed BE-FE, Stiff Soil Fixed Base Analysis Posin( w t) Half Space 2b H
- 6. SSI Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 6 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 0 25 50 75 100 125 150 175 200 225 250 Time x 1.08x10-4 (sec) Horizontal Amplitude U1 SSI - Relative U1 Fixed Base U2 SSI - Relative U2 Fixed Base P(t) Half Space m m
- 7. Cross Interaction Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 7 1. Moment is applied 2. Waves Propagate… 3. …Reach Receiver… 4. …and life goes on…
- 8. SSI Effects • Alter the Natural Frequency of the Structure • Add Damping • Through the Soil Interaction Effects • Traveling Wave Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 8
- 9. Methods of Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 9 Objective: Given the earthquake ground motions that would occur on the surface of the ground in the absence of the structure (control or design motions), find the dynamic response of the structure.
- 10. Methods of Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 10 Methods Idealized Complete Direct MultiStep
- 11. Complete Interaction Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 11 • Account for the variation of soil properties with depth. • Consider the material nonlinear behavior of the soil • Consider the 3-D nature of the problem • Consider the nature of the wave propagation which produced the ground motion • Consider possible interaction with adjacent structures. High Degree of Complexity
- 12. Idealized Interaction Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 12 Idealization Horizontal Layers Simplified Wave Mechanisms etc
- 13. Idealized Interaction Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 13 Preliminary description of free field motion before any structure has been built The definition of the motion itself the control motion in terms of response spectra, acceleration records etc. The location of the control motion free surface, soil-rock interface The generation mechanism at the control point vertically or obliquely incident SH or SV waves, Rayleigh waves, etc.
- 14. Idealized Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 14 Idealized Interaction Analysis Tools: FEM, BEM, FDE, Analytical solutions Direct Methods Evaluation of Dynamic Response in a Single Step MultiStep Methods Evaluation of Dynamic Response in Several Steps SUPERPOSITION • Two-Step Kinematic+Inertia Interaction • Three-Step Rigid Foundations Lumped Parameter Models • Substructure Division to Subsystems Equilibrium & Compatibility True Nonlinear Solutions
- 15. Finite Element Method (FEM) Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 15 Governing Equation • Modal Analysis • Direct Integration • Fourier Analysis - Complex Response Solution Techniques
- 16. FEM Solution Techniques Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 16 Selection Criteria Cost and Feasibility Paramount Consideration Accuracy Differences - Handling of Damping - Ability to Handle High Frequency Components of Motion
- 17. FEM - Modal Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 17 Damping is neglected during early stages Actual displacements are damped Damping is considered in arbitrary manner Structural Dynamics: First few modes need to be evaluated (<20) SSI: Acceleration response spectra over a large frequency range and large number of modes need to be considered (>150) Not recommended for Direct SSI - Stiff Massive Structure Soft Soil OK for Substructure
- 18. FEM - Direct Integration • Time Marching Schemes Newmark’s Methods, Wilson Methods, Bathe and Wilson Cubic Inertia Method • Small Time Step for Accuracy • Stability and Convergence • Choice of Damping Matrix Frequency Dependent Damping Ratio - filters out high frequency components Proportional Damping • Good Choice if True Dynamic Nonlinear Analysis is feasible Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 18
- 19. FEM - Complex Response • Fourier Transformation - Transfer Functions • Transfer Functions Independent of External Excitation • Control of Accuracy • Efficient • Only Linear or Pseudo non-linear analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 19
- 20. FEM - Geometric Modeling Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 20
- 21. FEM Modeling Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 21 Matrix Mass Mixed 5 1 Matrix Mass Consistent 8 1 Matrix Mass Lumped 8 1 max s s s h Max Element Size Governed by Highest frequency which must be transmitted correctly within the element
- 22. FEM Modeling of Infinite Space Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 22
- 23. FEM Modeling of Infinite Space Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 23 Modeling Introduces Artificial Boundaries that Reflect Waves
- 24. FEM Modeling of Infinite Soil • Absorbing Boundaries Viscous Boundary Variable Depth Method Damping proportional to Wave Velocities • Radiating Boundaries (Hyper elements) Satisfy Boundary Conditions at Infinity Eigenvalue Analysis Frequency Domain Analysis Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 24
- 25. SSI – FEM Methods Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 25 FEM Advantages • Non-Linear Analysis • Well Established Shortcomings • Finite Domains • Volume Discretization's
- 26. Boundary Element Methods Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 26 j j ii j ij i u f u c u c c , 2 2 , 2 2 2 1 Governing Equation Small Displacement Field Homogeneous Isotropic Elastic
- 27. Boundary Element Method Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 27 GOVERNING EQUATION BOUNDARY INTEGRAL EQUATION Dynamic Reciprocal Theorem Indirect DIRECT Transform Domain TIME DOMAIN Dirac- Step Impulse B-SPLINE System of Algebraic Equations Time Marching Scheme
- 28. Boundary Element Method Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 28 BOUNDARY INTEGRAL EQUATION B-SPLINE FUNDAMENTAL SOLUTIONS SPATIAL DISCRETIZATION TEMPORAL DISCRETIZATION BOUNDARY INTEGRAL EQUATION IN A DISCRETE FORM TIME MARCHING SCHEME & B-SPLINE IMPULSE RESPONSE RESPONSE TO ARBITRARY EXCITATION N N H Ff
- 29. BEM – Methods Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 29 BEM Advantages • Infinite Media • Surface Discretization Shortcomings • Non-symmetric matrices • Not Efficient for Nonlinear
- 30. SSI Methods Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 30 Combined BEM-FEM eliminate disadvantages of each method and retain advantages Approach • FEM Approach • BEM Approach • Staggered Solutions
- 31. Governing Equations Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 31 j j ii j ij i u f u c u c c , 2 2 , 2 2 2 1 t t t t f Ku u C u M
- 32. FEM Method Time Marching Scheme Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 32 t t t t f Ku u C u M N N f Du Governing Equation Discrete Form in Time
- 33. FEM-BEM Coupling Staggered Solutions Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 33 Can be Solved in a Staggered Approach... N N BEM N BEM H Ff u N FEM N FEM f Du BEM FEM
- 34. FEM-BEM Coupling Staggered Solutions Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 34 Compatibility of Displacements at Interface BEM Solver FEM Solver Equilibrium of Forces at Interface External Excitation External Excitation int FEM u int BEM u int FEM f int BEM f At Every Time Step...
- 35. FEM-BEM Coupling Advantages Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 35 Independent Solutions for BEM and FEM Independent Time Step Selection Smaller Systems of Equations BEM System of Reduced Size In the Absence of Incidence Displacement Field in Soil, BEM does not require Solution.
- 36. Lumped Parameter Models for SSI Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 36 P(t) m Half Space P(t) m Spring-Dashpot Model Stick Model
- 37. Lumped Parameter Foundation Models Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 37 Reissner (1936) Analytic Solutions to Vertical Vibration of Circular Footing Due to Harmonic Excitation Assumptions: Elastic ½-space Material G,v,r Uniform Vertical Pressure Formed Basis of Almost All Analytical Studies
- 38. Lumped Parameter Foundation Models Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 38 Quinlan and Sung Assumed Different Pressure Distributions Richart & Whitman Effects of Poisson’ Bycroft (1956) Displacement Functions Hsieh K and C in terms of Soil and Foundation Parameters
- 39. Lumped Parameter Foundation Models Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 39 Lysmer Analog Constant Lumped Parameters Richart Hall & Wood(1970) Gazetas (1983) Wolf (1988)
- 40. Lumped Parameter Foundation Models Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 40 Representative Lumped Parameter Values - Square
- 41. Lumped Parameter Foundation Models Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 41 Mode K C B D Vertical (z) n 1 4 o Gr G ro r n 2 1 4 . 3 3 4 1 o r m r n z B 425 . 0 Sliding (x) n 2 8 o Gr G ro r n 2 2 6 . 4 3 8 2 o r m r n x B 288 . 0 Rocking () n 1 3 8 3 o Gr n r B G ro 1 1 8 . 0 4 5 8 1 3 o r I r n B B 1 15 . 0 Torsional () 3 6 3 o Gr r B G B 2 1 4 5 o r I r B 2 1 5 . 0 Representative Lumped Parameter Values Circular
- 42. Lumped Parameter Foundation Models Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 42 Stehmeyer and Rizos (2003) Properties k, and c are known to be frequency (w) dependent The Real System Equivalent SDOF System n n m c M K w w 2
- 43. Lumped Parameter Foundation Models Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 43 Horizontal Displacement with Horizontal Impulse Applied -0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 Time Displacement Discrete BEM Solution Simplified Closed Form Solution 2b B(t) Half Space y z x B(t) wn = 3.3 = 0.975
- 44. SSI Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 44 0.00E+00 2.50E-05 5.00E-05 7.50E-05 1.00E-04 1.25E-04 1.50E-04 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 w/wn Amplitude in ft. SSI - Proposed BE-FE SSI - Spring Dashpot Model Proposed BE-FE, Stiff Soil Fixed Base Analysis Posin( w t) Half Space 2b H
- 45. SSI Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 45 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 0 25 50 75 100 125 150 175 200 225 250 Time x 1.08x10-4 (sec) Horizontal Amplitude U1 SSI - Relative U1 Fixed Base U2 SSI - Relative U2 Fixed Base P(t) Half Space m m
- 46. SSI Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 46 Based on the Simplified Lumped Parameter Models it can be shown that k k k k T T h h 2 1 ~ P(t) m Longer Period of Foundation-Structure System
- 47. SSI Effects – Cross Interaction Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 47 Receiver Foundation Source Foundation
- 48. SSI Effects – Cross Interaction Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 48 0.0E+00 5.0E-11 1.0E-10 1.5E-10 2.0E-10 2.5E-10 0 0.5 1 1.5 2 2.5 3 3.5 4 Dimensionless Frequency ao Horizontal Amplitude 1 Source M=10 Receiver M=10 Source M=5 Receiver M=5 Source M=1 Receiver M=1 Receiver Foundation Receiver Foundation Source Foundation Source Foundation Receiver Foundation Receiver Foundation Source Foundation Source Foundation
- 49. SSI Effects – Cross Interaction Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 49 0.0E+00 5.0E-11 1.0E-10 1.5E-10 2.0E-10 2.5E-10 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 Dimensionless Frequency ao Horizontal Amplitude d/a=0.25 Source Foundation d/a=1.00 d/a=2.00 d/a=3.00 d/a=0.25 Receiver Foundation d/a=1.00 d/a=2.00 d/a=3.00 Receiver Foundation Receiver Foundation Source Foundation Source Foundation Receiver Foundation Receiver Foundation Source Foundation Source Foundation
- 50. Traveling Wave Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 50 After Betti et al.
- 51. Traveling Wave Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 51 After Betti et al.
- 52. Traveling Wave Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 52 After Betti et al.
- 53. Traveling Wave Effects Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 53 After Betti et al.
- 58. Traveling Wave Effects • Inertia Effects were Not Important but yet SSI significantly affects the response • Asynchronous Motion Excite Antisymmetric Vibration Modes • SSI effects cannot be ignored Prof. S.P.Parmar,M.Tech Geotechnical Engineering. DDU-CL. 58 After Betti et al.