Directing Energy Dissipation in Earthquake-Soil-Structure Systems
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1 Directing Energy Dissipation in Earthquake-Soil-Structure Systems, Nima Tafazzoli, Mahdi Taiebat, Guanzhou Jie Department of Civil and Environmental Engineering University of California, Davis CompDyn9
2 Outline Motivation Modeling and Simulation Seismic Energy Input Seismic Energy Dissipation Examples of Energy Dissipation Use of Soft Soil Use of Liquefaction Summary
3 Motivation Motivation Improving seismic design for infrastructure objects Use of high fidelity numerical models in analyzing seismic behavior of soil structure systems Accurately (high fidelity modeling and simulations) following the flow of seismic energy in the soil structure system Directing, in space and time, seismic energy flow in the soil structure system
4 Motivation Hypothesis Interplay of Earthquake with Soil and Structure plays major role in (catastrophic) failures (and successes). Timing and spatial location of energy dissipation determines location and amount of damage. If timing and spatial location of energy dissipation can be controlled, we could optimize soil structure systems for Safety and Economy
5 Motivation First Published Work on Soil Structure Interaction Professor Kyoji Suyehiro Ship engineer (Professor of Naval Arch. at U. of Tokyo), Was in Tokyo during Great Kantō earthquake (11:58am(7.5), 12:1pm(7.3), 12.3pm(7.2) (shaking until 12:8pm), 1st. Sept. 1923) Saw earthquake surface waves travel and buildings sway Founding Director of the Earthquake Engineering Research Institute Univ. of Tokyo), Records shows 4 (four) more damage to soft wooden buildings on soft ground
6 Motivation Modeling and Simulation Examples of Energy Dissipation Summary Motivation Northridge Example [Trifunac and Todorovska 1998] Boris Jeremic
7 Seismic Energy Input Outline Motivation Modeling and Simulation Seismic Energy Input Seismic Energy Dissipation Examples of Energy Dissipation Use of Soft Soil Use of Liquefaction Summary
8 Seismic Energy Input Seismic Energy at the Source Large energy releases, Northridge, 1994, M Richter = 6.7, E r = J Loma Prieta, 1989, M Richter = 6.9, E r = J Sumatra-Andaman, 24, M Richter = 9.3, E r = J Valdivia, Chile, 196, M Richter = 9.5, E r = J Rhodes, 28, M Richter = 6.5, E r = J Part that energy is radiated as waves ( ) and makes it to the surface For comparison, specific energy of TNT is J/kg. Rhodes earthquake was.1kt.
9 Seismic Energy Input Seismic Energy and the SFS System Kinetic energy flux through closed surface Γ includes both incoming and outgoing waves (using Domain Reduction Method by Bielak et al.) [ ] E flux = ; M Ω+ be ü e K Ω+ be u e; M Ω+ eb ü b + K Ω+ eb u b u i i Alternatively, E flux = ρac t u2 i dt Outgoing kinetic energy is obtained from outgoing wave field (w i, in DRM) Incoming kinetic energy is then the difference. P e (t) Ω + Ω u b u e Local feature u i u e Γ Γe Γ+
10 Seismic Energy Dissipation Outline Motivation Modeling and Simulation Seismic Energy Input Seismic Energy Dissipation Examples of Energy Dissipation Use of Soft Soil Use of Liquefaction Summary
11 Seismic Energy Dissipation Seismic Energy Dissipation for Soil Structure Systems Mechanical dissipation outside of SFS domain: wave reflection SFS system oscillation radiation Mechanical dissipation/conversion inside SFS domain: plasticity of soil (different subdomains) viscous coupling of porous solid with pore fluid (air, water) plasticity/damage of the structure (different parts) viscous coupling of structure with surrounding fluids potential kinetic energy Numerical energy dissipation/production
12 Seismic Energy Dissipation Energy Dissipation by Plasticity Plastic work (W = σ ij dɛ pl ij ) Energy dissipation capacity for different soils Energy Dissipated (J/m 3 ) Stiff Clay Dense Sand Loose Sand Soft Clay Shear Strain Cycle (%)
13 Seismic Energy Dissipation Energy Disipation by Viscous Coupling Viscous coupling of porous solid and fluid Energy loss per unit volume is E vc = n 2 k 1 ( U i u i ) 2 Natural in u p U formulation: 2 4 (M s) KijL (M f ) KijL ü Lj p N U Lj (K EP ) KijL (G 1 ) KiM (G 1 ) LjM P MN (G 2 ) LjM (G 2 ) KiL Z (C (1,2,3) ) KijL = Ω N (u,u,u) K (C 1 ) KijL (C 2 ) KijL (C 2 ) LjiK (C 3 ) KijL n 2 k 1 ij N (u,u,u) L dω u Lj p M U Lj 3 5 = u Lj ṗ N U Lj f solid Ki f fluid Ki
14 Seismic Energy Dissipation Numerical Energy Dissipation Newmark and Hilber Hughes Taylor can be made non dissipative for elastic system α =., β =.25; γ =.5, Or dissipative (for elastic) for higher frequency modes: N: γ.5, β =.25(γ +.5) 2, HHT:.3 3 α, γ =.5(1 2α), β =.25(1 α) 2 For nonlinear problems, energy cannot be maintained Energy dissipation for steps with reduction of stiffness Energy production for steps with increase of stiffness R e R e u i u i
15 Use of Soft Soil Outline Motivation Modeling and Simulation Seismic Energy Input Seismic Energy Dissipation Examples of Energy Dissipation Use of Soft Soil Use of Liquefaction Summary
16 Use of Soft Soil Earthquake Soil Bridge System Inelastic soils (el pl, Armstrong-Frederick, stiff and soft), inelastic structure (columns), inelastic piles, DRM for seismic input, Construction process Deconvolution osurface ground motions No artificial damping, only plastic dissipation and radiation Plastic Domain Decompisition Method for parallel computing 1.6 M DOFs (15cm element size)
17 Use of Soft Soil Northridge and Kocaeli Input Motions Acceleration (m/s 2 ) Displacement (m) Acceleration (m/s 2 ) Displacement (m) Acceleration Time Series Input Motion (NORTHRIDGE EARTHQUAKE, 1994) Time (s) Displacement Time Series Input Motion (NORTHRIDGE EARTHQUAKE, 1994) Acceleration Time Series Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999) Time (s) Time (s) Displacement Time Series Input Motion (TURKEY KOCAELI EARTHQUAKE, 1999) Time (s)
18 Use of Soft Soil Northridge Energy: Strain (dissipated) and Kinetic 4 SSS CCC 3 2 Moment (kn*m) Relative Velocity Energy [J/kg] Time (s) CCC SSS Time [s]
19 Use of Soft Soil Kocaeli Energy: Strain (dissipated) and Kinetic 4 SSS CCC 3 2 Moment (kn*m) Time (s).7 CCC.6 SSS Relative Velocity Energy [J/kg] Time [s]
20 Use of Liquefaction Outline Motivation Modeling and Simulation Seismic Energy Input Seismic Energy Dissipation Examples of Energy Dissipation Use of Soft Soil Use of Liquefaction Summary
21 Use of Liquefaction Uniform and Layered Soils loose (e=.96,.875) medium dense (e=.8) medium dense (e=.8)
22 Use of Liquefaction Acceleration Time History
23 Use of Liquefaction Excess Pore Pressure Ratio
24 Use of Liquefaction Plastic Energy Dissipation in Uniform Soils Cumulative Energy (Uniform) [kj] time [s]
25 Use of Liquefaction Plastic Energy Dissipation in Layered Soils.6.5 Cumulative Energy (Layered) [kj] time [s]
26 Use of Liquefaction Kinetic Energy at the Top Energy (Layered) [J/kg] Uniform Layered Time [s]
27 Use of Liquefaction Void Ratio Variation (Potential Energy)
28 Summary Interplay of Earthquake, Soil and Structure plays a major role in catastrophic failures and great successes Opportunity to improve design: following the flow of seismic energy in the soil structure systems Directing in space and time, seismic energy flow in the soil structure system might/will lead to increase in safety and economy
29 Colossus of Rhodes: What if?
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