soil, structure and earthquake input

Transcription

1 Few thoughts on the numerical simulation of soil, structure and earthquake input Anastasios Sextos Assistant Professor auth Aristotle University of Aristotle University of Thessaloniki Greece

2 Scope Strong evidence regarding g SSI Huge amount of research Large discrepancy of structural response for various methods Clear the SSI is a function of earthquake input content and amplitude But also too sensitive to a motion that is unknown More numerical tools available and incredible computational power Increased modeling uncertainty Need to: assess the computational simulations of different complexity quantify the relative uncertainty of physical phenomenon and numerical modelling

3 Egnatia Highway

4 Egnatia Highway 670km highway 42km of bridges

5 Egnatia Highway overpass a typical example A1 M1 M2 A2 19.0m 32.0m 19.0m 60.0m the deck is connected through two pot bearings that permit sliding along the two principal bridge axes and a sliding joint of 12cm separates the deck from the backwall Kappos, Potikas, Sextos (2007)

6 Pushover curve and seismic assessment of the system (longitudinal direction) Ultimate state due to unrecoverable abutment damage (δ=22cm) 4 plastic hinges exhausting 35-49% of the available plastic rotation Soil yielding Pier yielding Joint closure at δ=12cm E 2E Kappos, Potikas, Sextos (2007)

7 Comparative assessment in the linear range Frame bridge. Piers and Abutments replaced by Springs and Dashpots Frame bridge. Piers and Abutments on Spring and Dashpot systems Frame bridge on 3D solid embankment-foundation-abutment Distributed Simulation

8 CASE 1: Frame bridge on Spring and Dashpot systems Abutment Stiffness (CALTRANS) K abut = 11.5x0.5x6.0/1.7 5x6 0/1 = 203 MN/m Abutment Damping Zhang and Makris (2002) Abutment 6DOF dynamic impedance matrix Pier foundation 6DOF dynamic impedance matrix Pier foundation 6DOF dynamic impedance matrix Abutment 6DOF dynamic impedance matrix Pile Group Stiffness Sextos & Taskari (2008)

9 Abutment stiffness and ultimate load (CALTRANS) Based on passive earth pressure tests and the force deflection results from largescale abutment testing at UC Davis, a value for the initial embankment fill stiffness equal to 11.5kN/mm/m width of the wall is recommended by Caltrans guidelines. The initial stiffness can be adjusted proportionally to the backwall: the ultimate abutment load is assumed to be limited by a maximum passive pressure of 239kPa resisting movement at the abutment

10 California overpasses

11 Geometrical characteristics of the six abutment types Lww 1 2 i H h1 h2 b l L Lpile 1 j Table 2.1 H (m) h 1 h 2 b l L (m) L ww L pile D pile pile Soil (blow count in (m) (m) (m) (m) (m) (m) (m) group parenthesis) Route LADWP W m silty sand (15) 6m med.fine sand (27), 6m med./fine sand (40) MGR /6 1 5m rock, 5m sandy gravel Adobe m sandy silt (13) 12m clayey sil (15-20), 3m medium sand (45) La Veta m fine sand, 4m dense sand

12 FE modelling of the selected typical abutments R14 Bridge LA DWP Bridge W180 Bridge MGR Bridge Adobe Bridge La Veta Sextos, Mackie, Stojadinovic, Taskari (2008)

13 FE modelling of the abutment-embankment embankment system Embankment Soil (Mohr-Coulomb) Backfill Soil (Mohr-Coulomb, E=60MPa, φ=39 ο ) Foundation Soil (Mohr-Coulomb) Surface contact to coarse mesh Foundation Soil (Mohr-Coulomb) Foundation Soil (Mohr-Coulomb, E=15MPa, φ=15 ο, c=100kpa for Soil A and E=5MPa, φ=5 ο, c=50kpa for Soil B) Cracked pile stiffness Pile-soil contact

14 Plastic strains at the backfill the W180 bridge

15 Plastic strains at the backfill the Route 14 bridge

16 Pushover curve of the abutment-embankment embankment system Force (kn) Pushover curves (longitudinal direction) ROUTE 14 soila soilb CALTRANS Almost in all cases, the FEderived stiffness is higher compared to CALTRANS Stiffness even for Soil B Displacement (m)

17 CASE 2: Frame bridge on spring supported abutment and foundation Abutment 6DOF dynamic impedance matrix Pier foundation o 6DOF dynamic impedance matrix Pier foundation 6DOF dynamic impedance matrix Abutment 6DOF dynamic impedance matrix Beam on Dynamic Winkler Spring Model (Makris & Gazetas, 1992)

18 CASE 3: Frame bridge on 3D solid embankment-foundation-abutmentabutment x10-1 x10

19 CASE 4: Distributed Simulation: Frame bridge on 3D solid embankment-foundation abutment Analysis coordinator developed at Mid-America Earthquake Center (University of Illinois at Urbana-Champaign) Primarily to coordinate remotely controlled experiments and numerical analyses Spencer et al. (2006)

20 CASE 5: Distributed Simulation: Frame bridge on 3D solid embankment-foundation abutment In the framework of the Sub-structuring approach, it is important to decide the dynamic (effective) DOF of the system and the sub-parts of the structure that can be solved separately and statically to contribute to the formulation of the stiffness matrix at every time step. Using SIMCOR as the Simulation Coordinator, the integration will take place within SIMCOR engine, involving (only) the effective DOFs, where as the substructured static modules will provide the reaction forces for the applied displacement at each time step DOFs = Dynamic DOFs + Static DOFs

21 CASE 4: Distributed Simulation: Frame bridge on 3D solid embankment-foundation abutment DOF1 DOF2 DOF3 DOF4 DOF5 DOF6 DOF7 9m n.1 n.2 n.3 n.4 n.5 n.6 n.7 Module 1 DOF1 19m 32m 19m DOF7 Module 2 Module 3 Decide the static ti modules and the effective nodes & degrees of freedom

22 CASE 4: Distributed Simulation: Frame bridge on 3D solid embankment-foundation abutment Sextos & Taskari (2008)

23 Validation of the Multi-platform model Point masses and boundary conditions match the MP model Displacem ment (m) Model 4a (SIMCOR) Model 4b (Sap2000) Time (sec) Sextos & Taskari (2008)

24 CASE 4: Distributed Simulation: Frame bridge on 3D solid embankment-foundation abutment

25 Summary of available features and performance Model Features and Performance Case 1 Case 2 Model 3 Model 4 Spring Middle piers pile group Point supported foundation stiffness Spring Frame Point Spring Fixed** Middle piers pile group damping ** ** Abutment stiffness Spring 3D on shell 3D 3D Embankment stiffness Spring Spring 3D 3D Abutment foundation stiffness 3D on shell 3D 3D Embankment mass Point mass Point mass 3D 3D Embankment soil stresses Backfill soil stresses Soil nonlinearity potential Abaqus built-in models Multiple software Spring Spring (Mohr-Coulomb Drucker- choices (Opensees, (p-y) (p-y) Prager, Cam-Clay) Abaqus) R/C nonlinearity potential Multiple software Lamped Lamped Abaqus Built-in i choices (Opensees plasticity plasticity constitutive law Zeus, FedeasLab) Computational time * 2min 4min 2 ½ hours 2 ¼ hours * Integration time refers to 10sec duration of uniform ground excitation at 0.01sec step executed on a Core 2 Duo processor, 2GB RAM.

26 Comparative assessment in the linear range Sextos & Taskari (2008) Reasonable matching given the different assumptions made Multi-platform analysis lies essentially in between the envelope of the response

27 Comparative assessment in the non-linear range Sextos & Taskari (2008)

28 Meloland Road Overcorssing (MRO) Bridge, U.S. after Zhang and Makris,(2001) Monitored bridge The 1979 Imperial Valley Earthquake (M = 6.6) was the largest recorded event at the site, with peak ground acceleration of 0.32 g.

29 Meloland Road Overcorssing (MRO) Bridge, U.S. The MRO Bridge site has a deep soft alluvium profile. The shear wave velocity ranges from 140 m/sec near the surface to 730 m/sec at the depth of 150 m.

30 Overview of the approach adopted Fragility Analysis Inelastic Dynamic analysis with and without SSI effects 1-D site response analysis with and without soil liquefaction and plasticity Kwon, Sextos & Elnashai (2008) Selection of 3x6=18 outcrop records (recorded in California) 0.05g, 0.1g, 0.2g, 0.3g, 0.4g, 0.5g Generation of 3x6=18 artificial records

31 Overview of the approach adopted Fragility Analysis Inelastic Dynamic analysis with and without SSI effects Case A: Bridge Fixed, No Liquefaction Case B: SSI - No Liquefaction Case C: SSI Global Liquefaction (below pier and abutments) Case D: SSI Local Liquefaction (below pier only). Asynchronous excitation

32 Overview of the approach adopted Total 36 records x 4 cases = 144 inelastic Fragility Analysis dynamic analyses Local Damage Index = Local and Global damage indices are assumed identical Damage limit state I: repairable damage 0.11<DI<0.40 Damage limit state II: irrepairable damage, 0.40<DI<0.77 Damage limit state III: collapse, 0.77<DI<1.00) a global factor of β dsi = 0.6 was used to account for all sources of uncertainty

33 Stress-strain strain relationship at various depths - Excitation case: C01 Depth -2.50m. Medium clay. Vs = 200m/sec Depth -4.00m. Medium sand. Vs = 200m/sec Liquefied Depth -7.00m. Stiff clay. Vs = 290m/sec Depth m. Medium sand. Vs = 200m/sec Liquefied

34 Excess pore pressure time histories at various depths. Excitation case: C01 Depth -4.00m. Medium sand. Vs = 200m/sec Liquefied Depth m. Medium sand. Vs = 200m/sec Kwon, Elnashai, Sextos (2008) Liquefied

35 Inelastic Response of Pier with and without liquefaction consideration NO LIQUEFACTION LIQUEFACTION CONSIDERED M-Φ at bottom of central pier Surface motion Bedrock motion

36 fragility analysis results: collapse damage limit state (III) Probabi lity of exceed ding Damage State III Bedrock PGA (g) Rigid - No Liquefaction (Case A) SSI - No Liquefaction (Case B) SSI - Global Liquefaction (Case C) SSI - Local Liquefaction at Central Pier (asynchronous excitation), ti (Case D) Global liquefaction reduces the imposed input accelerations to the level of the critical acceleration (0.25g-0.29g) Global liquefaction prevents the structure from reaching the critical collapse limit state (III) Hence, no such fragility curve exists

37 Proposal of an Alternative Damage Index Local Damage Index Damage Index Expression Damage States Structural Damage Index (SDI) Lateral Soil Displacement Damage Index (LDI) I: 0.11<DI<0.40 II: 0.40<DI<0.77 III:0.77<DI<1.00 I: 2.5cm <u<10 cm II: 10cm <u<25 cm III:25cm <u<40 cm Foundation Rotation I: <θ<1.0 II: 1.0 <θ<3.0 Damage (RDI) III:3.0 <θ<4.0 Pile Bending Failure Damage (PDI) GDI sev = max{sdi, LDI, RDI, PDI} I: u<53 cm II: 53cm <u<80 cm III:80cm <u<106 cm Kwon, Sextos & Elnashai (2009) Seismic Fragility of a Bridge on Liquefaction Susceptible Soil, ICOSSAR, Osaka

38 Refined modeling versus input and response uncertainty Global damage index? liquefaction? spatial variability of ground motion?

39 Spatial Variability of Ground Motion (SVGM) Loss of Coherency Wave passage θ jk( (ω) = tan -1 (Im[γ jk (ω)]/ Re[γ jk (ω)]) x n N i (t ) = 2 Ljm( ωml ) Δω cos[ ωmlt + θ jm( ωml ) + φml ] m= 1l = 1 Transfer Function

40 Inertial interaction Foundation Input Motion Kinematic Interaction Free field motion

41 Physical interpretation of spatial variability multi-parametric problem (and frequency dependent) more uncorrelated motions do not necessarily produce more critical response effect of spatial variability cannot be assessed in advance

42 Open issues regarding spatial variability 1. WHEN?: is the problem significant for the structural response 2. HOW?: can one predict this significance with simple tools or expressions 3. WHERE?: should the designer focus

43 Alternative bridges studied 28 Alternative bridges 5 actual bridges 271 different SVGM scenarios 192 different spring/dashpot p systems

44 EARTHQUAKE ENGINEERING BY THE BEACH Villa Orlandi, Anacapri, Italy A comprehensive approach for accounting for SVGM, Site Effects, SSI Wave passage Coherency loss Site Effects Soil Soil--Pile Kinematic Interaction Different accelerograms and dynamic stiffness matrix at each support Sextos, A., Pitilakis, K and A. Kappos (2003) pt. 1, EESD, Vol. 32(4) Sextos, A., Kappos, A. & Pitilakis, K. (2003) pt. 2, EESD, Vol. 32(4)

45 Generation of artificial records Spectrum compatible Acceleration Time History Spring-dashpot (pierdependent) system Displac cement (cm) Spatial Variability Generator Time (sec) -8.0 A Spatially variable displacement seismic input 45 A1 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11

46 ratio used for comparison Ratio ρ = Response due to αsynchronous excitation Response due to synchronous excitation

47 Effect of wave passage only

48 Effect of wave passage + incoherency Pier base bending moments ratio Wave passage only Incoherency only Wave passage + incoherency Deck displacement ratio

49 Higher modes excitation Fundamental mode (transverse) Τ1 =1.21 sec sec 2 ) χυνση (m/ m/s επιτάχ Symmetric mode Τ3 =0.66 sec Excited antisymmetric mode Τ2 =0.92 sec Incoherency only Περίοδος Τ (sec) Synchronous excitation Wave passage only Wave passage and incoherency

50 Relative impact of analysis complexity Wave passage + incoherency + site effects + kinematic interaction + inertial interaction Wave passage + incoherency + site effects + kinematic interaction Deck displacement ratio Wave passage + incoherency + site effects Wave passage + incoherency SYNCHRONOUS EXCITATION Wave passage only Sextos & Kappos (2009) BEE

51 Relative impact of various phenomena Wave passage + incoherency + site effects + kinematic interaction + inertial interaction Pier base bending moments Wave passage + incoherency + site effects + kinematic interaction Wave passage + incoherency + site effects Wave passage + incoherency SYNCHRONOUS EXCITATION Wave passage only Sextos & Kappos (2009) BEE

52 SVGM vs.angle of incidence in a curved bridge Sextos, Kappos & Mergos (2004) BEE

53 SVGM vs.angle of incidence in a curved bridge

54 SVGM vs.angle of incidence in a curved bridge

55 SVGM vs.angle of incidence in a curved bridge

56 SVGM vs.angle of incidence in a curved bridge 700m 0m 240 Sextos, Taskari & Kappos (2008) 6GRACM

57 SVGM vs.angle of incidence in a curved bridge Athens earthquake A1 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 A2 The influence of the excitation i direction i depends d on the earthquake motion characteristics

58 Relative impact of analysis assumptions Deck displacement ratio Pier base bending moments ratio Sextos & Kappos (2009) Bulletin of Earthquake Engineering.

59 Critical length Beneficial effect Detrimental effect EC8 limit (soil Β) ) Dispersion of bending moment ratio ρ Sextos & Kappos (2009) Bulletin of Earthquake Engineering.

60 Eurocode 8 new provisions Ε ΑΦΟΣ 1. Analytical approach(der Kiureghian et al.) 2. Simplified method

61 Eurocode 8 simplified approach Set A Displacements Set B Displacements

62 Eurocode 8 software plug-in for ASING

63 EC8 simplified method vs. Comrehensive approach Sextos & Kappos (2009) Bulletin of Earthquake Engineering.

64 Conclusions Modeling refinement alone does not improve assessment reliability SSI cannot be assessed independent of earthquake input Earthquake input should reflect for site conditions angle of incidence spatial variability Spatial variability cannot be predicted as wave passage effect only EC8 simplified approach leads to negligible effect unless corrected coefficients are used. A more refined approach is preferable.

65 Acknowledgements KAPPOS, Andreas, Aristotle University of Thessaloniki, Greece TASKARI, Olympia, Aristotle University of Thessaloniki, Greece MANOLIS, George, Aristotle University of Thessaloniki, Greece ELNASHAI, Amr, University of Illinois at Urbana-Champaign, United States KWON, Oh-Sung, University Missouri Science & Technology, United States MACKIE, Kevin, University of Central Florida, United States STOJADINOVIC, Bozidar, University of California Berkeley, United States