Earthquake-Soil-Structure Systems

Transcription

1 and Sashi Kunnath with Kallol Sett and Nima Tafazzoli Department of Civil and Environmental Engineering University of California, Davis

2 Outline Goals ESS Systems High Fidelity, D Models Behavior for Short and Long Period Motions Uncertain Seismic Motions Constitutive and Spatial Uncertainties Seismic Wave Propagation Through Uncertain Soils Summary

3 Focus Steady progress in software and hardware allows high fidelity, detailed performance assessment (simulations) of critical (and other) infrastructure systems (bridges, dams, buildings, ports...) Interplay of Earthquake Soil Structure systems seems to play a major role in catastrophic failures (and successes) Quantify uncertainty and variablity in soil and structural behavior Provide methodology (formulation, implementation) for probabilistic performance based engineering (PEER type) Overcome traditional performance assessment approaches used in engineering practice (design using prescriptive code!)

4 Historical Note (Full Circle?) Soil Structure Interaction phenomena first realized and described by Professor Kyoji Suyehiro Ship engineer (Professor of Naval Arch. at U. of Tokyo), Earthquake engineer (First Director of the Earthquake Research Institute at U. of Tokyo), Was in Tokyo during Great Kantō earthquake (:58am ( :8pm! slow?), st. Sept. 9) Saw earthquake surface waves travel and buildings sway (ships in the ocean) Presented his new SSI work in the USA (Caltech, UCB, Stanford, MIT) in 9... Slow and Fast earthquakes Uncertainty and variability (source, material...)

5 High Fidelity, D Models Outline Goals ESS Systems High Fidelity, D Models Behavior for Short and Long Period Motions Uncertain Seismic Motions Constitutive and Spatial Uncertainties Seismic Wave Propagation Through Uncertain Soils Summary

6 High Fidelity, D Models Detailed D, FEM model Construction process Two types of soil: stiff soil (UT, UCD), soft soil (Bay Mud) Deconvolution of given surface ground motions Use of the DRM (Prof. Bielak et al.) for seismic input Piles beam-column elements in soil holes No artificial damping (only mat. dissipation, radiation) Structural model: collaboration UCD, UCB and UW Element size issues (filtering of frequencies) model size (el) el. size f cutoff min. G/Gmax γ K. m Hz. <.5 % 5K.9 m > Hz.8. % 5K. m Hz.8. % 5K.5 m Hz. 5. %

7 High Fidelity, D Models FEM Mesh (one of) B. Jeremić and G. Jie. "Parallel Soil Foundation Structure Computations", Chapter in Book: Progress in Computational Dynamics and Earthquake Engineering; Taylor and Francis Publishers, 8.

8 ESS Systems Goals Uncertain Seismic Motions Summary High Fidelity, D Models Parallel Computer GeoWulf I I I I I Distributed memory parallel computer Multiple generation compute nodes and networks Very cost effective! Same architecture as large parallel supercomputers (SDSC, TACC, EarthSimulator...) Local design, construction, available at all times! Boris Jeremic

9 Behavior for Short and Long Period Motions Outline Goals ESS Systems High Fidelity, D Models Behavior for Short and Long Period Motions Uncertain Seismic Motions Constitutive and Spatial Uncertainties Seismic Wave Propagation Through Uncertain Soils Summary

10 Behavior for Short and Long Period Motions Northridge and Kocaeli Input Motions Displacement (m) Acceleration (m/s ) Fourier Amplitude (m) Fourier Amplitude (m/s ) Acceleration Time Series Input Motion (NORTHRIDGE EARTHQUAKE, 99) 5 6 Displacement Time Series Input Motion (NORTHRIDGE EARTHQUAKE, 99) Displacement (m) Acceleration (m/s ) Acceleration Time Series Input Motion (TURKEY KOCAELI EARTHQUAKE, 999) Displacement Time Series Input Motion (TURKEY KOCAELI EARTHQUAKE, 999) Acceleration Frequency Content Input Motion (NORTHRIDGE EARTHQUAKE, 99) Displacement Frequency Content Input Motion (NORTHRIDGE EARTHQUAKE, 99)

11 ESS Systems Goals Uncertain Seismic Motions Summary Behavior for Short and Long Period Motions Parametric Simulation Results Freefield Input Motion Freefield Input Motion Boris Jeremic Moment (kn*m) Freefield Input Motion Moment (kn*m) 6.5 Moment (kn*m) Moment (kn*m) Moment (kn*m) Freefield Input Motion Freefield Input Motion Freefield Input Motion Freefield Input Motion.5 Moment (kn*m).5 Fourier Amplitude (m/s) Fourier Amplitude (m/s). Fourier Amplitude (m/s ). 6 Freefield Input Motion.5.5 Fourier Amplitude (m/s ) Fourier Amplitude (m/s). Fourier Amplitude (m) Fourier Amplitude (m/s ) Fourier Amplitude (m).6..7 Freefield Input Motion Freefield Input Motion. Acceleration (m/s) Acceleration (m/s)... Freefield Input Motion. Displacement (m) Displacement (m) Displacement (m).. Acceleration (m/s).. Displacement (m). Freefield Input Motion Acceleration (m/s) Fourier Amplitude (m/s) Fourier Amplitude (m/s) Displacement (m) Acceleration (m/s) Fourier Amplitude (m) Fourier Amplitude (m/s) Displacement (m).. Acceleration (m/s)

12 Behavior for Short and Long Period Motions Northridge Input Motions Displacement (m) Acceleration (m/s ) Acceleration Time Series Input Motion (NORTHRIDGE EARTHQUAKE, 99) 5 6 Displacement Time Series Input Motion (NORTHRIDGE EARTHQUAKE, 99) Fourier Amplitude (m) Fourier Amplitude (m/s ).. Acceleration Frequency Content Input Motion (NORTHRIDGE EARTHQUAKE, 99) Displacement Frequency Content Input Motion (NORTHRIDGE EARTHQUAKE, 99)

13 Behavior for Short and Long Period Motions Short Period E.: Left Bent, Structure and Soil, Disp... Displacement (m) Motion Freefield Input. Displacement (m)

14 Behavior for Short and Long Period Motions Short Period E.: Left Bent, Structure and Soil, Acc.Sp. Fourier Amplitude (m/s ) Freefield Input Motion Fourier Amplitude (m/s )

15 Behavior for Short and Long Period Motions Short Period E.: Left Bent, Structure and Soil, M. Moment (kn*m) B. Jeremić, G. Jie, M. Preisig and N. Tafazzoli. "Soil Foundation Structure Interaction in non Uniform Soils", in review in Earthquake Engineering and Structural Dynamics, 8.

16 Behavior for Short and Long Period Motions Kocaeli Input Motions Displacement (m) Acceleration (m/s ) Acceleration Time Series Input Motion (TURKEY KOCAELI EARTHQUAKE, 999) Displacement Time Series Input Motion (TURKEY KOCAELI EARTHQUAKE, 999) Fourier Amplitude (m/s ) Fourier Amplitude (m) Acceleration Frequency Content Input Motion (TURKEY KOCAELI EARTHQUAKE, 999) Displacement Frequency Content Input Motion (TURKEY KOCAELI EARTHQUAKE, 999)

17 Behavior for Short and Long Period Motions Long Period E.: Left Bent, Structure and Soil, M. Moment (kn*m)

18 Constitutive and Spatial Uncertainties Outline Goals ESS Systems High Fidelity, D Models Behavior for Short and Long Period Motions Uncertain Seismic Motions Constitutive and Spatial Uncertainties Seismic Wave Propagation Through Uncertain Soils Summary

19 Constitutive and Spatial Uncertainties Problem Setup Incr. D el pl: dσ ij = { Dijkl el Del ijmn m } mnn pq Dpqkl el n rs Drstu el m tu ξ r dɛ kl phase density ρ of σ(x, t) varies in time according to a continuity Liouville equation (Kubo 96) Continuity equation written in ensemble average form (eg. cumulant expansion method (Kavvas and Karakas 996)) van Kampen s Lemma (van Kampen 976) < ρ(σ, t) >= P(σ, t), ensemble average of phase density is the probability density

20 Constitutive and Spatial Uncertainties Eulerian Lagrangian FPK Equation + P(σ(x t, t), t) t Z t =»jfi fl η(σ(x t, t), D el (x t), q(x t), r(x t), ɛ(x t, t)) σ» η(σ(xt, t), D el (x t), q(x t), r(x t), ɛ(x t, t)) dτcov ; σ ff η(σ(x t τ, t τ), D el (x t τ ), q(x t τ ), r(x t τ ), ɛ(x t τ, t τ) P(σ(x t, t), t)»jz t + dτcov σ»η(σ(x t, t), D el (x t), q(x t), r(x t), ɛ(x t, t)); ff η(σ(x t τ, t τ), D el (x t τ ), q(x t τ ), r(x t τ ), ɛ(x t τ, t τ)) P(σ(x t, t), t) B. Jeremić, K. Sett, and M. L. Kavvas, "Probabilistic Elasto Plasticity: Formulation in D", Acta Geotechnica, Vol., No., pp 97-, 7.

21 Constitutive and Spatial Uncertainties Euler Lagrange FPK Equation Advection-diffusion equation P(σ, t) t = σ [ N () P(σ, t) { N() P(σ, t) }] σ Complete probabilistic description of response Solution PDF is second-order exact to covariance of time (exact mean and variance) It is deterministic equation in probability density space It is linear PDE in probability density space Simplifies the numerical solution process Template FPK diffusion advection equation is applicable to any material model only the coefficients N () and N () are different for different material models K. Sett, B. Jeremić and M.L. Kavvas, "The Role of Nonlinear Hardening/Softening in Probabilistic Elasto Plasticity", International Journal for Numerical and Analytical Methods in Geomechanics, Vol., No. 7, pp , 7

22 Constitutive and Spatial Uncertainties Spectral Stochastic Elastic Plastic FEM N N P M K mn d ni + d nj C ijk K mnk = F mψ i [{ξ r }] n= n= j= k= K mn = B n DB m dv K mnk = B n λk h k B m dv D D C ijk = ξ k (θ)ψ i [{ξ r }]ψ j [{ξ r }] F m = φn m dv SFEM: Ghanem and Spanos Material variables random field represented through a finite number of random variables using KL-expansion Unknown solution random variables represented using polynomial chaos of (known) input random variables Fokker Planck Kolmogorov approach based probabilistic constitutive integration at Gauss integration points D

23 Seismic Wave Propagation Through Uncertain Soils Outline Goals ESS Systems High Fidelity, D Models Behavior for Short and Long Period Motions Uncertain Seismic Motions Constitutive and Spatial Uncertainties Seismic Wave Propagation Through Uncertain Soils Summary

24 Seismic Wave Propagation Through Uncertain Soils Uniform CPT Site Data

25 Seismic Wave Propagation Through Uncertain Soils Random Field Parameters from Site Data Maximum likelihood estimates of correlation length Finite Scale Typical CPT q T Fractal

26 Seismic Wave Propagation Through Uncertain Soils Seismic Wave Propagation through Stochastic Soil Soil as.5 m deep D soil column (von Mises Material) Properties (including testing uncertainty) obtained through random field modeling of CPT q T q T =.99 MPa; Var[q T ] = 5.67 MPa ; Cor. Length [q T ] =.6 m; Testing Error =.78 MPa q T was transformed to obtain G: Assumed transformation uncertainty = 5% G =.57MPa; Var[G] =.MPa Cor. Length [G] =.6m G/( ν) =.9q T Input motions: modified 98 Imperial Valley

27 Seismic Wave Propagation Through Uncertain Soils Surface Displacement Time History Displacement (mm).5.5

28 Seismic Wave Propagation Through Uncertain Soils Mean ± Standard Deviation Displacement (mm).5.5

29 Seismic Wave Propagation Through Uncertain Soils PDF of Surface Displacement Time History PDF at the finite element nodes can be obtained using, e.g., Edgeworth expansion (Ghanem and Spanos ) Probability Density of Displacement Displacement (m) 5 Numerous applications, especially where extreme statistics are critical

30 Seismic Wave Propagation Through Uncertain Soils Most Probable Solution Mode =. m 8 PDF Displacement (m)

31 Seismic Wave Propagation Through Uncertain Soils Tails of PDF P[. < Displacement <.] =.65 8 PDF Displacement (m)

32 Seismic Wave Propagation Through Uncertain Soils Probability of Exceedance Probability that displacement exceeds.5 m =.85 = CDF Displacement (m)

33 Seismic Wave Propagation Through Uncertain Soils Derivative Applications PDF Performance based engineering Reliability index (β) Probability of damage and/or failure (p f ) Load Mode Mean Resistance p f Margin = Reistance Load PDF βσ Margin µmargin Value of Load or Resistance Sensitivity analysis Financial risk analysis Margin In general, useful for applications where mean, mode and extreme statistics are important

34 Summary Steady progress in software and hardware allows for high fidelity Model Based Simulations for performance assessment of infrastructure systems Interplay of Earthquake(s) with Soil and Structure Systems plays a major role in catastrophic failures (and successes) Probabilistic performance based engineering (uncertainty in soil and structural behavior, earthquake motions...) Overcome traditional performance assessment approaches used in engineering practice (design using prescriptive code!)