Seismic Loading Pierre Yves Bard Alert Geomaterials by liaoqinmei

VIEWS: 2 PAGES: 31

									                   22nd ALERT Doctoral School
        Prevention and protection against hazard :
       some issues on seismic and gravitational risk

                          Aussois, 6-8/10/2011




           Seismic Loading
                       Pierre-Yves Bard


            Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                Outline
Introduction

Quantitative characterization of ground motion
Background physics
     Effects of magnitude, distance, and site conditions

EC8 regulatory motion
     zonation
     Importance classes
     spectra




            Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                       1
                     Physical phenomena at play
    Ground shaking / Wave propagation
            source effects : wave radiation
            regional effects : deep propagation in the Earth's crust
            local effects
              • surface topography
              • alluvial deposits
              • urban effects




10 km




                 Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




        Source : Rupture
             history

Finite duration
        Finite rupture velo-
        city
         • (2.5 – 3 km/s)
        Local slip function
         • (0.1 – 50 s)
Spatial heterogeneity
        Slip amplitude
        Slip direction


         Landers earthquake, 1992
                 Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                            2
             Earthquake Source Complexity
SOURCE effects:
• heterogeneity in the slip distributions                                        From Mai, 2006
• variability in rupture-propagation velocity
• variability in slip duration and slip function




                Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                          Source scaling laws

Geometrical similarity
   W/L       c1      0.5 (except strike slip events)
        c1     0.5


"Kinematic" similarity
   Stability of stress drop                        = C μ D0 / Lc
   D0/Lc c2
          c1      5. 10-5 to 10-4,                3 MPa


"Dynamic" similarity
         c3 L/Vr                           soit            Vr/L        c3
          c3      0.2

                Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                  3
                            Seismic moment
 Definition : M0 = μ S D0
        μ = shear modulus of the Earth's crust (3. 1010 Pa)
        S = surface of the ruptured area on the fault
        D0 = average slip on the ruptured area
           Highly representative of earthquake size and energy

 Moment of the equivalent double couple M0
        Waves emitted from the rupture front at point ,
         amplitude proportional to / t [ u( , ; t)]
         thus to / t [m( , ; t)].
       Summation on the fault area (d , d )
         amplitude proportional to         / t [M0 (t)]
       Corresponds to the very low frequency contents of earthquake
       ground motion

 Moment Magnitude Mw
         • Mw = 2/3 log(M0) - 6
         • (Back to "standard" magnitude values)


              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




Consequences of scaling laws on source parameters :




              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                         4
   From magnitude to main source parameters




                                                    200 km




          Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




Scaling laws and magnitude dependence of Fourier spectra




          Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                     5
    Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




Source + Crustal propagation + Site




    Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                               6
                    Crustal propagation :




        Complex wavefield
                 direct body waves, surface waves
                 reflexions, refractions
                 diffraction, scattering
                 geometrical spreading + damping
           Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




Empirical ground motion prediction equations

      GMA = F(magnitude M, distance R, Site conditions, ….)



                                               A        M+1
                         A
                                                          M




                R

  M                                                                                   d




      Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                          7
    A simple estimation method based on available
  recordings: the "attenuation relationship" (or GMPE)



    log(PSA( f ) ) = a ( f ) M + b( f ) R log( R ) + c(i, f ) +



  Source                               Magnitude

  Propagation                         Distance


  Site                                 Soil characteristics (? Vs30 ?)

   Scattering / uncertainties :                               0.3          factor 2
         Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                More general formulation
Y = b0 . f1(M) . f2 (R) . f3(M,R) . f4 (Pi) .

     Y = ground motion parameter
     M = magnitude (ML, Ms, Mb, Mw, …)
     R = distance metrics (Rep, Rh, Rf, …)

     f1(M) = exp (b1.M)
     f2(R) = exp(-b2.R) . [R + b4]-b3/2                               (0.5 < b3 < 1)
     f3(M,R) : b4= b5. exp(b6 . M)
     f4(Pi) : correction factors
         • site conditions (most frequently)
         • fault type (inverse / strike slip / normal)
         • Directivity …
         : standard deviation : factor 2 : NEVER FORGET !



              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                         8
                                                               pga, g           Parkfield 2004
  Example variability for
     a (M-D) couple

Very simple, BUT

Large variability
       From event to event
       From site to site within the same event



pga, cm/s2                                                                  Fault distance, km




                                                                          pgv, cm/s
            Kobe 1995

                                                                           Niigata 2004
                    Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                     Dealing with uncertainties
 Epistemic :
        Controling them with more
        instruments / metadata / research

 Aleatory
        big issue at long return periods




                                                                  2


                                                                            3.5



                    Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                 9
             ? Do GMPE uncertainties reduce with increased data set ?




                                                                                       (Courtesy of John Douglas)
                              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                 Example : PGV
                    Strike-slip




               10

                                                                               M7       Europe + USA
(cm/s) PGV
   GM




                1
                                     CB06, Vs=760 m/s
                                     This study - Stiff
                                     This study - Rock
                                                                               M5
                        (c)
              0.1
                    1                          10                          100

                                     Distance (km)                                             (Akkar & Bommer, 2006)
                              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                                        10
  pga decay with distance for different soil types
                  (magnitude 6)




        Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011
                                                                                   Lussou et al., 2000




                 Source + Path + Site

                                                                               Site




Source                                    Path = crustal
                                          propagation


   Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                         11
                                Site effects
Direct - ground shaking - site effects
     Wave propagation effects, resulting in localized amplifications,
     (or deamplifications), highly variable with frequency, reaching
     up very high levels (> 10)
          – Surface topography
          – "Soft" surface deposits

Induced site effects
     Soil damage resulting in localized soil failures
           – Liquefaction of water saturated sandy deposits,
             settlements
           – Slope instabilities (slides, falls, debris flows, …)

Surface ruptures (fault trace)
Tsunamis local effects (bathymetry / topography)

            Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                             170 cm/s

                                                                T ~ 2s


                                                                         35 cm/s
      MEXICO 1985
                                                                             T ~ 2s


                        150 cm/s




                                                Ground motion decay
                                                with distance

                                                                       Amplification in the
                                                                       lake-bed zone


                                                                         (Mouroux,
        Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011          1999)




                                                                                                  12
     Sa (g)
                                                           T ~ N/10
                              0.75g



                                                                       MEXICO 1985


                                               x 7.7
                                                                                           SCT
                                                                     Rock

        0.15g
x5
        0.035g

                                                                       T (s)
                                                                               (Mouroux,
              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011     1999)




                                  Collapsed and severely damage buildings
         Damage
       distribution




Damaged controled by
- the shallow subsoil ("lake bed zone")
- building height
              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                   13
                  2 floor building: no damage




   MEXICO 1985
         Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




Hospital, 10 to
   20 story




                          Crédit photo: Cdt Fabre-Avignon
         Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                    14
            Ground shaking site effects
Repeated examples during (almost) all recent earthquakes
     Caracas 1967, Lima 1974, Mexico 1985, San Francisco 1989,
     Northridge 1994, Kobe 1995, Armenia 1999, Izmit 1999, Athens
     1999, Gujarat 2001, Bam 2003,…

Amplification factors
     Intensity increment : I = 1 to 2 very common
     Spectral domain (Fourier) : 5 common, 10 not exceptional
          (10 : corresponds to M = 2)
     Relatively stable (10 =2)

Control, at least partially, sometimes totally, the damage
  distribution
Easier (less uneasy) to predict than source effects
         Very interesting for mitigation
            Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




            Sites prone to amplification




                                (illustrations from "guide PPR Risques sismiques 2002"
                                                              – source Laurence Barret)
            Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                          15
 Amplification on
   tops of hills

 (still poorly understood
    and accounted for)


                                                  ROGNES 1909 : I = 2 (VII - IX)

       Castillon 1887 : x 10
                   Top
                             Church


                                                               Top                     Church




            Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




      Evidence from insurance claims
   San Simeon 2003 (see McCrink et al. 2009)




Yellow : insurance claim
                                               (McCrink et al., 2009; Courtesy C. Real)
Black dot : insured house
            Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                16
   Surface topography effects: knowledge status

Main characteristics
      Top amplification (convex part) + foothill deamplification (concave)
       (for identical soil conditions)
      Frequency dependence
       Maximum effects for        = c/f    mountain width
      Largest effects on Horizontal components
       • T > L >> V
      Possible range
       • from 2 to above 10

Origin : not completely captured yet !
      Focusing / defocusing
      Reflexion coefficients on side slopes (oblique incidence)
      ??? Fracturation / decompression in summit areas

Accounting for them
      Codes : nothing in general; a few exceptions however (PS92, EC8,
      Maximum amplification = 1.4, no frequency dependence)
      Specific studies: numerical approach possible, but instrumental
      approach MANDATORY
              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




          Resonance effects in sediments

Wave field in surface deposits
      Refraction, diffraction, focusing
      Wave Trapping
       • vertical reverberations
       • lateral reverberations                          ! + soil non-linearities !
Consequences
      constructive interferences: amplification
      trapping : prolongation
      resonance at specific frequencies




              Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                         17
    Resonance 1 layer

                                          ,
h                                     1        1,    1




                   2    ,   2,   2



Transfer function (Fourier)
         H(f) = 2 C / [C . cos (2 fh/ 1) + i. sin(2 fh/ 1)

Resonance frequencies
                 Fundamental mode: f0 =                  1/4h
                 Harmonics fn = (2n+1) f0                                                  C=    2 2/ 1 1
Amplification
                 Elastic case
                  A0 = H(f0)/2 = C =           2. 2/ 1. 1
                 With damping        1:
                       C / (1 Loading 1 C ) ALERT Doctoral School, Aussois, 0ctober 6-8, 2011
                  A0 =Seismic+ 0,5    - 22nd




                                                    Typical values
        Frequency f0 =                        1/4h
                                                                      Amplification
                   Depends only on surface layer                            A0 = C / (1 + 0,5  1 C ),
                   characteristics                                          C = 2. 2/ 1. 1
                                                                            Also depends on bedrock !
             1
                   50        100     200            400     800       Density conrast
    h                                                                                           2/ 1
                                                                                     1.8
        5          2.5       5.0     10.0           20.         40.
        10        1.25       2.5          5.        10.         20.   Velocity contrast          2/ 1
                                                                                 2 up to 2.5 km/s
        20        0.62 1.25           2.5            5.         10.
                                                                                 1 up to 50 m/s
        50        0.25       0.5      1.0           2.5         4.       usual values 2/         1  : 3-4
    100             -       0.25      0.5           1.0         2.       Extreme values           2/ 1 : 10-15
    200             -            -   0.25           0.5         1.    Damping        1
    500             -            -        -      0.25           0.4              1   from 1% to 20%
                                                                         No (anti-) correlation         1   /   1
                            ! Weathered rock!
                                                                      Resulting values for A0
                                                                            10
                        Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                                    18
                                                                                 Soft layers


                                                                          Kobe 1995 : "damage belt"
                                                                            and basin-edge effects




  Mexico City 1985 :
damage only in lake bed
        area,
very large amplification
                Non-Linear issue

                                                                                         (Pitarka
                         Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011   & Irikura, 1998)




                                           From 1D to 2-3 D
                1) 1D : vertical reverberations                                  2) 2D / 3D : lateral
                                                                                 reverberations

                                                ,
                h                           1       1,   1




                         2   ,    2,   2




                                 fo=Vs/4H                                          fo
amplification




                                                               amplification




                                                                                   fréquence
                        fréquence - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011
                          Seismic Loading




                                                                                                                       19
                          The Grenoble example

                                                           Glacial valley
                                                                     Recent deposits (post
                                                                     glacial : < 25 000 years)
                                                                     Thick lacustrine clay
                                                                        • Rather stiff
                                                                        • h > 900 m
                                                                     2D / 3D geometry: deeply
                                                                     embanked
                                                                     Very hard bedrock


                                                           Example : local M4 event




                     Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




Example valley effects : Recordings of
 the Laffrey event (M4, 11/01/1999)




                                                                        Campus


                                                              Sud Parc Mistral
Vitesse (mm/s)




                                                        Cimetière Saint-Roch


                                                            Musée Dauphinois


                                                                  Pont-de-Claix

                 F
                 F

                     Seismic Loading Temps (s) Doctoral School, Aussois, 0ctober 6-8, 2011
                                     - 22nd ALERT




                                                                                                 20
      Soil non - linearities

                                                                             pga = 0,7 m/s




                             sand
 weak event:                 clay
soil / rock = 3,5            sand, gravel

                             clay




                                                                            pga = 0,2 m/s


                                                                                  (Cotton, 2001)
               Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                             Soil non-linearities

                                                                            pga = 4,3 m/s


                                                                            acc. maxi = 0,7 m/s




        sand

        clay
                                                                             strong event:

        sand, gravel                                                        soil / rock = 1,2
        clay




                                                                           pga = 3.7 m/s



                                                                                    (Cotton, 2001)
               Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                     21
Non-linear behavior
Origin: Soil degradation under
large deformation
      decrease of shear modulus
      Increase of damping


           Consequences

Fundamental frequency f0
   f0 =   1/4h,   1=   (G1/ 1)0.5

      Decrease of f0

Amplification A0
   A0 = C / (1 + 0,5           1   C)
   C = 2. 2/ 1. 1 ,        1

      Decrease of A0

           Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                   Consequences



                                                        Peak acceleration




      Transfer functions



           Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                      22
   Pga Observations (Taiwan, SMART1)

   Horizontal component                              Vertical component




      Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                               Engineering practice




                                                       After 1990
       0.13 g




Before 1985



                                                                                 0.4 g


      Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                         23
                       Regulatory spectra
                                                     EC8 : Hz Spectra
     PS92 : Hz Spectra


NL




         Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




     Non-linear
 degradation curves:

      evolution with
           time




         Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                    24
Non-linear degradation
curves




  Vucetic & Dobry:


  mainly controlled by
  plasticity index




          Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




          Seismic loading in building code

  Design level
                             F       ag . S a(T, ) / Qs,
    ag = ag,R . I, "anchoring" acceleration, depending on
      • Seismicity zone (regional hazard) : Zonation : ag,R
      • de la classe d'importance : I

    S a(T, ) = normalized spectral shape: Spectra
      • Takes into account the magnitude of "representative" earthquakes
      • Varies with varying site conditions,

    Qs (behavior coefficient) = reduction factor accounting for the
    structure post-elastic behavior (ductility)
      • Ductility of constructions materials and structural elements
      • Varies from 1 - 1.5 (for brittle structures: unreinforced masonry) up to
        8 (highly ductile steel structures).


                 Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                            25
    Example seismic
       zonation

Derived from probabilistic
  analysis
     exceedance probability =
     10 % over 50 years
     T = 475 years




             Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




      Example probabilistic hazard curves



                                                                                                  1.6 m/s2
                                  1.1   m/s2




          0.4 m/s2

                                                                                               0.7 m/s2
                            T = 475 years




             Journée d'étude : "Le risque sismique dans la construction" - Paris, 28/03/2011




                                                                                                             26
                  Relation
     Importance category / Return period
Usually accepted asumption : power law relationship with
  exponent y=-3)




       = 1.2           T = 820 years
       = 1.4           T = 1300 years

                Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




    Anchoring (rock) accelerations for EC8 (agr)

   Depend on 2 factors
         Seismic hazard = seismic zone
         Importance class = return period



           EC8                            Classe

               Zone             II            III            IV
               Z1               -              -              -
               Z2            [0.7]          0.84            1.0
               Z3             1.1           1.32           1.54
               Z4             1.6           1.92           2.24
               Z5             3.0            3.6            4.2

                Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                           27
       "Generic" acounting for site conditions: site
             classes and associated spectra
Spectral shapes : control
parameters
       S : high-frequency amplification                                                  EC8 Type II Spectra
       R : plateau level
       TB, TC : position and plateau width                                10
       TD : long period level                                              9




                                                    Acceleration (m/s )
                                                                           8
? Dependency on site conditions                                            7
                                                                           6
                                                                                                                    EC8_TypeII_A
                                                                           5
                                                                           4                                        EC8_TypeII_D
                                                                           3
                                                                           2
                                                                           1
                                                                           0
                                                                            0,01   0,1                1        10
                                                                                         Period (s)




                      Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




       "Generic" acounting for site conditions: site
             classes and associated spectra
Spectral shapes : control
parameters
       S : high-frequency amplification                                                  EC8 Type II Spectra
       R : plateau level
       TB, TC : position and plateau width                                10
       TD : long period level                                              9
                                                    Acceleration (m/s )




                                                                           8
? Dependency on site conditions                                            7
       Depends on site classes                                             6
                                                                                                                    EC8_TypeII_A
                                                                           5
       Today : VS30                                                                                                 EC8_TypeII_D
                                                                           4
                                                                           3
      A : VS30 > 800 m/s
                                                                           2
      B : VS30 [360, 800 m/s]
                                                                           1
      C : VS30 [180, 360 m/s]
                                                                           0
      D : VS30 [100, 180 m/s]
                                                                            0,01   0,1                1        10
      E : formation peu rigide peu
      épaisse (h < 20 m) sur substratum                                                  Period (s)
      rigide



                      Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                                                                   28
                         EC8 site categories
Based on Vs30 (!!!...)




                Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                    Special sites

  S1 = Sites with deposits at least 10 m thick consisting of
    soft, high plasticity (PI > 40) silts or clays with high
    water contents
        ? VS < 100 m/s (indicative)
        Low damping
        Weak non-linearity

  S2
        Liquefiable soils or sensitive clays
        All sites not entering the A-E and S1 classes


               Need for specific studies of site response

                  Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                             29
              Simple site characterization
What for ?
        Design : accounting for site effects in building codes /
        microzonation studies
        Strong motion site characterization
         • GMPE : need for accurate and quantitative site conditions
         • Shake maps …

How ?
        Today : Standard = VS30
         • Sometimes measured, often inferred (SPT, …)
         • To be considered as a regional proxy to more physical parameters
           (Impedance contrast, soil thickness)
         • Should be adapted regionally
         • Often discussed, but no other fully achieved alternative proposal

        Should combine simplicity, cost effectiveness, and physical
        relevance

               Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




           EC8 recommendations : 2 types
     Type 1 (high seismicity)                                   Type 2 (weak seismicity)




   Broad spectra, including                                      Very narrow spectra
           on rock
                                                             higher site amplification




                 Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                            30
          Final comment : ? safety margins

Loading / Design
                               F      ag . S a(T, ) / Qs

History
     F     5 -10% W (                 ag = 0.05 – 0.1 g)

Seismological measurements
     very large amount of high quality data
     clear trend to increase : no safety margins
         • (examples : Japan NPPs, Lorca 2011, L'Aquila, Parkfield, …)

Results in design costs perceived as prohibitive
     ? Actual margins in structural design
     ? More measurements within structures ?

               Seismic Loading - 22nd ALERT Doctoral School, Aussois, 0ctober 6-8, 2011




                                                                                          31

								
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