Seismic Site Response (Site Amplification)

Transcription

1 Seismic Site Response (Site Amplification) An Introduction to Shear Beam Analysis (Part II) Ahmed Elgamal (Initial version prepared in 2006 in collaboration with Drs. Liangcai He and Zhaohui Yang)

2 Equivalent Linear Site Response 2

3 SHAKE / SHAKE 91 A. Elgamal and T. Lai (notes; original version) References P. B. Schnabel, J. Lysmer, and H. B. Seed, Shake: A Computer Program For Earthquake Response Analysis of Horizontally Layered Sites, Report No. EERC 72-12, University of California at Berkeley, December I. M. Idriss, and J. I. Sun, Shake 91: A Computer Program for Conducting Equivalent Linear Seismic Response Analyses of Horizontally Layered Soil Deposits, Modified based on Original Program Shake, University of California, Davis, August T. Iwasaki, F. Tatsuoka, and Y. Takagi, Shear Moduli of Sands Under Cyclic Torsional Shear Loading, Soils And Foundations, JSSMFE, Vol. 18, No. 1, pp P. W. Mayne and G. J. Rix (1993), Gmax-qc Relationships for Clays, Geotechnical Testing Journal, ASTM, Vol. 16, No. 1, pp H. B. Seed, R. T. Wong, I. M. Idriss, and K. Tokimatsu, Moduli and Damping Factors for Dynamic Analyses of Cohesionless Soils, Report No. UCB/EERC-84/14, Earthquake Engineering Research Center, University of California, Berkeley, Ca, M. Jamiolkowski, S. Leroueil, and D. C. F. Lo Presti (1991), Theme Lecture: Design Parameters from Theory to Practice, Proc. Geo-Coast 91, Yokohama, Japan, pp

4 T. Imai and K. Tonouchi, Correlation of N-Value with S-Wave Velocity and Shear Modulus, Proc. 2nd European Symposium on Penetration Testing, Amsterdam, The Netherlands, pp E. Kavazanjian, Jr., N. Matasovic, T. Hadj-Hamou, and P. J. Sabatini, Geotechnical Engineering Circular No. 3 Design Guidance: Geotechnical Earthquake Engineering for Highways, Design Principles, Volume 1, SA (NTIS # PB ) E. Kavazanjian, Jr., N. Matasovic, T. Hadj-Hamou, and P. J. Sabatini, Geotechnical Engineering Circular No. 3 Design Guidance: Geotechnical Earthquake Engineering for Highways, Design Examples, Volume 2, SA (NTIS # PB ) NRC 2000, Seeing into the Earth, Committee for Noninvasive Characterization of the Shallow Subsurface for Environmental and Engineering Applications, P. R. Roming, Chair, 129 pp. M. Vucetic and Ricardo Dobry, Effect of Soil Plasticity on Cyclic Response, Journal of Geotechnical Engineering, ASCE, Vol. 117, No. 1, January H. B. Seed and I. M. Idriss, Soil Moduli and Damping Factors for Dynamic Response Analyses, Report No. EERC 70-10, Earthquake Engineering Research Center, University of California, Berkeley, CA, H. B. Seed, Robert T. Wong, I. M. Idriss and K. Tokimatsu, Moduli and Damping Factors for Dynamic Analyses of Cohesionless Soils, Journal of Geotechnical Engineering, ASCE, Vol. 112, No. 11, November,

5 Free Surface Motion Rock Outcrop Motion Incident Wave Reflected Wave Rock Base Rock Motion 5

6 Wave Equation Solution for Homogeneous and Isotropic Soil t z u η z u G t u ρ + = ( ) t i z k i z k i i i i F E t z u iω 1 i i e e e ), ( = + = K i Wave Number ω i Frequency E i Amplitude of Incident Wave at Frequency ω i F i Amplitude of Reflected Wave at Frequency ω i 6

7 Layer Coordinates Propagation Properties No System Direction 1 z1 u 1 F 1 =E 1 E 1 G 1 β 1 ρ 1 h 1 i i+1 N zi u i u i+1 zi+1 zn u N F i F i+1 Particle Motion F N Reflected Wave E i+1 E N Incident Wave E i G i β i ρ i h G i h G + 1 β i+ 1 ρi+ 1 i+ 1 N β N ρ N i h N = 7

8 Properties G, β, ρ, h are known (shear modulus, damping ratio, mass density, and layer height) Unknown in system: 2N (E i, F i ) Boundary Conditions: Displacement continuity at all interfaces: N-1 Stress continuity at all interfaces: N-1 Zero stress at free surface: 1 + Given motion at any one layer: 1 Motions at any layer are determined 8

9 Equivalent Linear Soil Properties From (FHWA-SA ) 9

10 Equivalent Linear Properties From (FHWA-SA ) 10

11 Sand Curves: Seed and Idriss 1970 From (FHWA-SA ) 11

12 Effect of Confinement Sand (Iwasaki et al. 1978) From (FHWA-SA ) 12

13 Clays Vucetic and Dobry (1991) From (FHWA-SA ) 13

14 See also: Darendeli, M. B. (2001). Development of a new family of normalized modulus reduction and material damping curves. PhD dissertation, Univ. of Texas at Austin, Austin, Texas. Darendeli, M.B., and K. H. Stokoe, II (2001). Development of a new family of normalized modulus reduction and material damping curves, Geotech. Engrg. Rpt. GD01-1, University of Texas, Austin, Texas. Menq, F.-Y. (2003). Dynamic Properties of Sandy and Gravelly Soils. PhD Dissertation (supervisor: Prof. Kenneth H. Stokoe), Department of Civil Engineering, The University of Texas at Austin, May. 14

15 = mean effective stress, OCR = Overconsolidation ratio = CPT tip resistance, N 1 )60 = SPT corrected resistance (blow count) From (FHWA-SA ) 15

16 Properties G, β, ρ, h are known What SHAKE can do? Free Surface Motion Prediction When motions at depth are known (either rock outcrop (incident) or total motion Deconvolution When motions at surface are known (does not work well for nonlinear cases) 16

17 Input motion as outcrop motion (changed to incident motion) Input motion as inlayer motion (Total motion) Layer height definition Units Caution when using SHAKE 17

18 SHAKE Output Acceleration Time History Strain and Stress History Response Spectrum Fourier Spectrum Amplification Spectrum Strain Compatible Soil Properties (Equivalent Linear Option) 18

19 Equivalent Linear Concept G/Gmax (Effective Strains are Employed) Shear Strain (%) 19

20 Caution when using SHAKE (equivalent linear option) Layer Height Definition (more layers result in additional accuracy, even for constant velocity profile). Ratio of Effective Strain to Maximum affects the result Deconvolution (may not work)! 20

21 Ratio of Effective Strain to Maximum Effective Strain Ratio=(Magnitude of EQ -1)/10 Idriss, [0.4, 0.85] Ray Seed, as low as

22 What can SHAKE do? See also (General Refs.): Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures, Annie O. L. Kwok, Jonathan P. Stewart, Youssef M. A. Hashash, Neven Matasovic, Robert Pyke, Zhiliang Wang, and Zhaohui Yang, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 133, No. 11, November 1, ProShake: Ground Response Analysis Program, Version 1.1User s Manual, EduPro Civil Systems, Inc. Redmond, Washington. 22

23 More recent research into G/G max and D (Darendeli 2001, Menq 2003) see page 1 of Excel spreadsheet for actual G/G max and D values 23

24 Notation on previous page: OCR = Overconsolidation ratio (highest ever past effective vertical stress divided by the current vertical effective stress PI = Plasticity Index (PI = LL-PL), where LL = Liquid Limit and PL is Plastic limit 0 - Nonplastic (1-5)- Slightly plastic (5-10) - Low plasticity (10-20)- Medium plasticity (20-40)- High plasticity >40 Very high plasticity Frq = dominant stress-strain cyclic loading frequency of interest (e.g., 1 Hz or 2 Hz or so) Note: Damping is reported as a % (this is why, a 100 appears in the equation) 24

25 Menq s Equations (Sands and Gravels, developed in 2003) G max = P1 C e P2 u σ 1.3+ ( D 50 o ' P a / P5) P 6 Coefficients Suggested by Menq, 2003 P3 C Note: This equation will over-estimate G max for particles with D 50 greater than 10mm (or more generally, particles greater than 1 in in diameter (range of what Dr. Menq tested so far, personal communication) P 4 u Note: e = void ratio Coefficient of Uniformity: C u = D 60 /D 10 where, D 60 is the grain diameter at 60% passing, and D 10 is the grain diameter at 10% passing (by weight) P1 (ksf) 1400 P2-0.2 P P P5 20 P

26 A different way of writing this equation yields: Older versions (below) are shown in the spreadsheet G max = σ ' C o G 1 Pa n G x = ( D P6 50 / P5) 26

27 27

28 see page 2 of Excel spreadsheet (Menq, Personal communications. for actual G/G max and D values 28

29 Related to the Excel Spreadsheet (from: Menq, Farn-Yuh, Ph. D.): Note: Please consider using Darendeli s model if PI is greater than 0, and Menq s model if PI = 0. The first page of the spreadsheet is for Darendeli s model (2001). You can input the following values to obtain G/Gmax and Damping curves: frq(hz) PI OCR σo' (atm) The second page of spreadsheet is the equation of the Menq model (2003). G/Gmax and Damping curves for different soils with different Cu is presented in the following 4 spreadsheets. Note: Cu is the Uniformity Coefficient (measure of the particle size range) Cu is also known as the Hazen Coefficient Cu = D60/D10 Cu < Very Uniform Cu = Medium Uniformity Cu > Non-uniform Note: On the Menq (2003) page, if you change the the C u =2 to C u = 30 for instance, you will find the corresponding values of G/G max and D% in the page of C u =2. For instance if you change the C u =2 to C u = 30, in the G/G max or D summary pages, you will see the C u =2 now falls on the C u = 30 curve. Also note that some values in the Menq (2003) page only affect G max itself such as the void ratio e See also: (link to Dr. Menq s PhD Thesis) 29

30 In order to calculate equivalent linear properties from nonlinear shear stress strain behavior, consider the widely employed Hyperbolic stressstrain relationship: 30

31 The hyperbolic shear stress-strain relationship Equivalent Linear properties: Secant modulus Ref: Soil Behavior in Earthquake Geotechnics, K. Ishihara, Ch 3, pages Change in secant shear modulus with shear strain amplitude Change in Damping D with shear strain amplitude or in terms of G/G max At large shear strain, D eventually reaches a max of 2/π = (63.7% damping) 31

32 For numerical implementation of a nonlinear hyperbolic relationship, γ r may be selected based on the Menq or Darendeli Equations, and the Shear strength S u would then correspond to a shear strain γ max : Or, Using this γ r, G/G max and D can be calculated from the equations above marked with a (as implemented in the Hyperbolic Excel Spreadsheet) Notes: 1. In terms of γ max, γ r can be written as: 2. s u = c + p sin φ where c is cohesion (S u for c-soils), p is effective confinement, and φ is friction angle 32

33 Examples of User-friendly Computer Programs 33

34 DEEPSOIL (For XP and Windows 7) This slide contributed by Professor Youssef Hashash 34

35 DEEPSOIL SUMMARY Non-linear analysis Hyperbolic hysteretic pressure dependent soil model Flexible sub-incrementation scheme to allow for accurate & efficient analysis Advanced damping formulations to reduce numerically introduced artificial damping Equivalent Linear Analysis (a.k.a. SHAKE method) Unlimited number of soil layers of varying material properties Unlimited number of input motion data points Two types of complex shear modulus Improved numerical accuracy This slide contributed by Professor Youssef Hashash 35

36 DEEPSOIL DEEPSOIL Frequency Domain Time Domain Linear Equivalent Linear Linear Non Linear Total Stress Effective Stress Std. Hyperbolic Model (MR, MRD, MD) New Hyperbolic Model (MRDF) PWP Model Sand PWP Model Clay This slide contributed by Professor Youssef Hashash 36

37 Prof. Ellen M. Rathje, Ph.D., P.E. Strata Developed by Albert Kottke and Ellen Rathje Strata performs one-dimensional linear-elastic and equivalent-linear (SHAKE-type) site response analyses using time series or random vibration theory ground motions. Strata allows for stochastic variation of the site properties, including the shear-wave velocity, layer thicknesses, depth to bedrock, and shear modulus reduction and material damping curves.the program can be installed as a desktop application or run within the NEES cyberinfrastructure platform, NEEShub. Strata can be downloaded from the NEEShub at Strata. SigmaSpectra Developed by Albert Kottke and Ellen Rathje SigmaSpectra is a computer program that selects suites of of earthquake ground motions from a library of ground motions such that the median of the suite matches a target response spectrum at all defined periods. The program also scales the suite such that the standard deviation fits the target standard deviation.the program can be installed as a desktop application or run within the NEES cyberinfrastructure platform, NEEShub. SigmaSpectra can be downloaded from the NEEShub atsigmaspectra. 37

38 SLAMMER Developed by Randall Jibson, Ellen Rathje, Matthew Jibson, and Yong-Woo Lee SLAMMER performs a variety of sliding-block analyses to evaluate seismic slope performance. Functionalities include both rigorous and simplified analyses of rigid sliding blocks (i.e. Newmark analysis) and flexible sliding blocks (i.e. decoupled and fully coupled approaches). Rigorous analyses calculate displacement based on user-specified ground motions, while simplified analyses use empirical regression relationships to predict displacement based on ground motion parameters (e.g., peak ground acceleration). The nonlinear response of the soil within the flexible sliding blocks can be taken account through the equivalent-linear approximation. A large database of recorded ground motions from the PEER Ground Motion Database are included with the program or users can import their own ground motion for analysis. The program can be installed as a desktop application or run within the NEES cyberinfrastructure platform, NEEShub. Slammer can be downloaded from the USGS at SLAMMER (download) or accessed on the NEEShub at SLAMMER (NEEShub). 38

39 GeoMotions Suite ( SHAKE2000 D-MOD2000 RspMatchEDT Equivalent-Linear Total Stress Analysis Fully Nonlinear Effective- Stress w/ PWP Dissipation Development of Design Motions by Spectral Matching The GeoMotions Suite2000 is an essential toolkit for anyone practicing in the field of Geotechnical Earthquake Engineering (Jonathan D. Bray) Copyright 2009 GeoMotions, LLC This slide contributed by Dr. Neven Matasovic 39

40 Pre-Processing (Target Spectra, Design Motions, Soil Profile, ) Copyright 2009 GeoMotions, LLC This slide contributed by Dr. Neven Matasovic 40

41 Analysis (Total-Stress, Effective Stress, Liquefaction, ) Copyright 2009 GeoMotions, LLC This slide contributed by Dr. Neven Matasovic 41

42 Post-Processing (Newmark-type analysis, Animations, ) This slide contributed by Dr. Neven Matasovic 42

43 PM4Sand Stress-Strain Model PM4Sand (Boulanger 2010, Boulanger & Ziotopoulou 2012) builds on the Dafalias & Manzari (2004) model. Modified & calibrated at equation level to improve consistency with body of experimental data & design correlations Added fabric history, including cumulative fabric term Plastic modulus (K p ), elastic modulus (G), and dilatancy (D) depend on fabric and fabric history D constrained by Bolton's (1986) dilatancy relationship Recast in terms of relative state parameter index (ξ R ) Modified logic for updating initial back-stress ratio Neglects Lode Angle dependence Implemented as a user-defined material model in FLAC (Itasca 2011) and posted on-line. This slide contributed by Professor Ross Boulanger 43

44 PM4SAND: Example Cyclic undrained loading Fabric damage terms in PM4Sand enable accumulation of shear strains: Shear stress ratio, τ/σ' vc D R = 35% σ' vo = 100 kpa Shear strain γ (%) 0.4 α = τ / σ' vo = 0.0 Shear stress ratio, τ/σ' vc Vertical Effective Stress, σ' v / σ' vc Shear stress ratio, τ/σ' vc D R = 55% σ' vo = 100 kpa α = τ / σ' vo = Shear strain γ (%) Vertical Effective Stress, σ' v / σ' vc Shear stress ratio, τ/σ' vc This slide contributed by Professor Ross Boulanger 44

45 PM4SAND Manual and documentation Element responses illustrated for: D R = 35, 55, 75% σ v of ¼, 1, 4, 16, & 64 atm Drained & undrained Simple shear & planestrain loading Monotonic, cyclic, and post-cyclic. Purpose: know what you model can, and cannot, do well. This slide contributed by Professor Ross Boulanger 45

46 OpenSees at UC Berkeley 46

47 OpenSees PEER Center, UC Berkeley, Prof. Gregory Fenves Open-source platform Solid Node Fluid Node Solid-Fluid Fully Coupled Element for Saturated Soil Beam Element for Pile 47

48 Nonlinear hysteretic Model Note: Also available with Tension Cut-off for interface between structure and soil 48

49 Soil Constitutive Model Multi-yield surface plasticity model (based on Prevost 1985) Incorporating dilatancy and cyclic mobility effects Conical yield surfaces for granular soils (Prevost 1985; Elgamal et al. 2003; Yang and Elgamal 2008) Shear stress-strain and effective stress path under undrained shear loading condition (Parra 1996, Yang 2000, Yang and Elgamal 2002) 49

50 Yang, Z., Elgamal, A. and Parra, E., "Computational Model for Liquefaction and Associated Shear Deformation," J. Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 129, No. 12, σ 2 1 Soil Stress-Strain Model: Multi-surface Plasticity σ 1 p 0 σ 2 σ 3 Principal effective stress space p 3 σ Deviatoric plane 3 σ 50

51 OpenSeesPL Graphical User Interface 51

52 OpenSeesPL: 52

53 OpenSeesPL: 53

54 Shallow Foundation Caisson Ground Modification Soil-structure Interface 54

55 Ongoing Research 55

56 OpenSeesPL OpenSeesPL 56

57 Ground Modification - Gravel Drain/Stone column - Pile Pinning Schematic view of stone column or pile-pinning layout 10 m depth Sand Layer (or Silt Layer) Mild Infinite Slope (4 degrees) 57

58 58

59 BridgePBEE: PBEE Analysis Framework For Bridge-Abutment-Ground Systems (2-Span Bridge) Ahmed Elgamal and Jinchi Lu University of California, San Diego Kevin Mackie University of Central Florida 59

60 BridgePBEE: PBEE Analysis Framework For Bridge-Abutment-Ground Systems (2-Span Bridge) What is BridgePBEE BridgePBEE* ( BridgePBEE is a PC-based graphical pre- and post-processor (user-interface) for conducting Performance-Based Earthquake Engineering (PBEE) studies for bridge-ground systems (2-span single column). The three-dimensional (3D) finite element computations are conducted using OpenSees developed by the Pacific Earthquake Engineering Research Center (PEER). The analysis options available in BridgePBEE include (SI units in current version): 1) Pushover Analysis, 2) Base Input Acceleration Analysis, and 3) Full Performance-Based Earthquake Engineering (PBEE) Analysis. *Lu, J., Mackie, K.R., and Elgamal, A. (2011). BridgePBEE: OpenSees 3D Pushover and Earthquake Analysis of Single-Column 2-span Bridges, User Manual, Beta

61 Select PBEE Terminology IM - Intensity Measure for a given earthquake motion For any input earthquake motion, the Intensity Measures calculated by BridgePBEE include: PGA (Peak Ground Acceleration) PGV (Peak Ground Velocity) PGD (Peak Ground Displacement) D 5-95 (Strong Motion Duration) CAV (Cumulative Absolute Velocity) Arias Intensity SA (Spectral Acceleration; assuming 1 second period) SV (Spectral Velocity), SD (Spectral Displacement) PSA (Pseudo-spectral Acceleration) PSV (Pseudo-spectral Velocity) 61

62 The BridgePBEE Framework Define Bridge-abutment-ground geometry and material properties Select/Define ensembles of input earthquake ground acceleration (e.g., 100 different ground motions spanning a wide range of Intensities as defined by IM quantities such as Peak ground acceleration (PGA) or Peak Ground Velocity (PGV) Conduct individual earthquake shaking simulations for all input motions and View output in terms of Decision Variables (DVs) such as peak column drift and other similar parameters of interest displayed against any desired IM for each employed earthquake input motion. View detailed time histories of all responses of interest for any of the individual earthquake simulations (including animations of the deformed mesh, ). Use the DVs (clustered into Performance groups or PGs) variation against the IM to compute repair cost and repair time (based on pre-defined relationships that related the level of each DV to a Damage State (DS) and these Damage states associated with different levels of repair (predefined by repair quantities and associated repair times). See contribution to cost for each repair quantity, or for each Performance group as a function of the level od shaking (represented by the IM parameter). Compute total cost and repair time shown as a function of level of IM (such as PGV) For the bridge geographic location, define the expected seismic hazard. Use expected seismic hazard and define expected repair cost and time for this bridge For any possible level of shaking, see % contribution of the various performance groups (the DVs) or the Repair quantities to the overall cost or time. 62

63 BridgePBEE Main Window 63

64 Appendix: Illustrative Examples of Large Scale Numerical Analyses 64

65 Numerical Analysis of Embankment Dynamic Response Adalier, K., A. -W. Elgamal, and G. R. Martin, "Foundation Liquefaction Countermeasures for Earth Embankments," Journal of Geotechnical and Geo-environmental Engineering, ASCE, Vol. 124, No. 6, , June, Elgamal, Ahmed, Ender Parra, Zhaohui Yang, and Korhan Adalier, Numerical Analysis of Embankment Foundation Liquefaction Countermeasures, Journal of Earthquake Engineering, Vol. 6, No. 4, pp , Yang, Zhaohui, Ahmed Elgamal, Korhan Adalier, and Michael Sharp, "Earth Dam on Liquefiable Foundation: Numerical Prediction of Centrifuge Experiments," Journal of Engineering Mechanics, ASCE, Volume 130, Issue 10, October

66 OpenSees 3D FE Model Three-Dimensional Seismic Response of Humboldt Bay Bridge-Foundation-Ground System, A. Elgamal; L. Yan; Z. Yang; and J. P. Conte, Journal of Structural Engineering, Vol. 134, No. 7, July 1, ,237 nodes 1,140/280 linear/nonlinear beam-column elements 81 linear shell elements 23,556 solid brick elements 1,806 zero-length elements Transverse and Longitudinal Response 3D Spatial Configuration Abutments Pile Foundations Ground 66

67 Three-Dimensional Seismic Response of Humboldt Bay Bridge-Foundation-Ground System, A. Elgamal; L. Yan; Z. Yang; and J. P. Conte, Journal of Structural Engineering, Vol. 134, No. 7, July 1,

68 Elevation and plan view of residual deformation (Scale factor = 50) Three-Dimensional Seismic Response of Humboldt Bay Bridge-Foundation-Ground System, A. Elgamal; L. Yan; Z. Yang; and J. P. Conte, Journal of Structural Engineering, Vol. 134, No. 7, July 1,

69 Permanent Deformation of Bridge, Foundations, and Abutments Original position Final position with residual deformation Left abutment #1 Pier & pile group #2 Pier & pile group #3 Pier & pile group #4 Pier & pile group #5 Pier & pile group #6 Pier & pile group #7 Pier & pile group #8 Pier & pile group Right abutment (a) Elevation view (exaggerated scale by a factor of 50) Final position with residual deformation Original position (b) Plan view (exaggerated scale by a factor of 150) 69

70 3D Slice of Wharf supported on pile foundation Contour lines show the longitudinal displacement in meters (factor of 30) Work by Elgamal and Lu Close-up of Final Deformed Mesh Case W3N-F 70