STOCHASTIC METHODS FOR THE ESTIMATION OF POTENTIAL SEISMIC DAMAGE

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STOCHASTIC METHODS FOR THE ESTIMATION OF POTENTIAL SEISMIC DAMAGE Powered By Docstoc
					 STOCHASTIC METHODS FOR THE
ESTIMATION OF POTENTIAL SEISMIC
            DAMAGE



                 by Ayşegül Askan
  CONTENTS OF THE PRESENTATION

• Introduction

• Damage Probability Matrices
• Reliability-Based Model
• Discriminant Analysis
• Comparison and Discussion of Results
• Conclusions
                   INTRODUCTION
  Turkey is a country located in a seismically very
  active zone:
  • 95% of the population
  • 91% of the total area are under earthquake threat.

  Rapid urbanization along with poor construction
  control resulted in severe structural damage to the
  existing reinforced concrete building group, during the
  recent major earthquakes


Development of Seismic Vulnerability Assessment Methodologies
    1. DAMAGE PROBABILITY MATRICES (DPM’S)

A DPM GIVES THE DISCRETE PROBABILITY DISTRIBUTIONS
OF VARIOUS LEVELS OF DAMAGE THAT WILL RESULT FROM
EARTHQUAKES OF VARIOUS INTENSITIES.



  Each DPM applies to :

    •A PARTICULAR TYPE OF BUILDING
    • A PARTICULAR DESIGN STRATEGY
  DAMAGE STATE       CDR(%) MODIFIED MERCALLI INTENSITY(MMI)
      (DS)                      V      VI    VII   VIII   IX

NO DAMAGE                0

LIGHT DAMAGE             5          DAMAGE STATE
MODERATE DAMAGE         30      PROBABILITIES, P(DS,I)
SEVERE DAMAGE           70

COLLAPSE                100


  CDR: central damage ratio
Types of DPM’s:
1. Empirical DPM’s: based on damage
   databases of past earthquakes.
2. Subjective DPM’s: based on expert
   opinion.
3. Theoretical DPM’s: based on seismic
   structural analysis.


In this study, combination of the first and second types
is utilized.
             SOURCES TO FORM DPM’S

                                                           damage
1) Damage assessment records of past EQs
                                                           database
                     Structure types
   •data                   # of storeys

                      AC/ NAC


    Pr (DS, I) = n (DS, I) / n(I)
n(DS,I)= number of buildings in DS level, during an EQ of MMI, I

n (I) = total number of buildings subjected to an EQ of MMI, I.
        EMPIRICAL DPM CONSTRUCTED IN THIS STUDY

Damage       CDR    1.10.1995          17.08.1999      12.11.1999
                      Dinar            Adapazari         Düzce
State (DS)   (%)
                    MMI=VIII            MMI=IX          MMI=IX

                    AC          NAC
None          0    0.23         0.24      0.04            0.17
Light         5    0.31         0.24      0.34            0.16
Moderate     30    0.38         0.41      0.27            0.28
Heavy        70    0.04         0.05     0.175            0.19
Collapse     100   0.04         0.06     0.175            0.20
Number of                  39          79458 flats   31800 flats+119
Buildings                                               buildings
MDR(%)             19.75        23        39.6            42.5
2) Expert Opinion on the damage state probabilities
corresponding to certain levels of earthquakes.



  BEST ESTIMATE DPM’S:
 ARE FORMED BY COMBINING EXPERT OPINION AND
 EMPIRICAL DATA FOR EACH SEISMIC ZONE.
           Best Estimate DPM for Seismic Zone 1
Damage     CDR
                 MMI=V MMI=VI MMI=VII MMI=VIII MMI=IX
State (DS) (%)
                 AC NAC AC NAC AC NAC AC NAC AC NAC
None        0    1    0.95 0.95 0.58 0.70 0.46 0.50 0.28 0.30 0.07
Light       5    0    0.05 0.05 0.29 0.20 0.34 0.20 0.39 0.30 0.27
Moderate    30   0     0    0   0.11 0.10 0.14 0.20 0.20 0.20 0.30
Heavy       70   0     0    0   0.02   0   0.05 0.10 0.07 0.20 0.19
Collapse   100   0     0    0    0     0   0.01   0    0.06   0   0.17
MDR(%)           0    0.25 0.25 6.2    4   10.4   14   18.9 21.5 40.7



   MDR ( I )   Pr( DS , I )  CDR( DS )
                 DS
          45

          40

          35                                         Zone I (AC)
          30
                                                     Zone II (AC)
 MDR(%)




          25
                                                     Zone III (AC)
          20
                                                     Zone IV (AC)
          15

          10                                         All Zones
                                                     (NAC)
          5

          0
               V   VI     VII       VIII      IX
                           MMI




• NAC buildings have the same MDR’s irrespective of the zone,
• MDR’s for AC buildings increase as seismicity decreases.
        2. RELIABILITY-BASED MODEL
Damage Rate= f ( Ground Motion Intensity, Building Vulnerability)

• Ground Motion Intensity: expressed in terms of PGA or MMI,
represented with EQ force index CS


• Building vulnerability: expressed in terms of base shear
coefficient (Shiga, 1968), represented with seismic resistance index
CR


• Damage Rate: expressed in terms of probability of seismic
demand exceeding seismic capacity under a certain level of
damage, evaluated in the classical reliability framework.
• EQ Force Index: f (local soil conditions, period effects,
damping, PGA or I)
                   A max
   CS  S(T)  γ 
                    g


• Seismic Resistance Index: An estimate of the base shear
coefficient derived on the basis of the nominal shear stress on
buildings, derived using Düzce 1999 EQ damage database.


       25  A W  18  A C
  CR 
         (1300  ΣA f )
• Damage State Definition: (α) derived on the basis of energy
conservation rule and the ratio of plastic capacity to elastic
capacity:
             1
   
          (2  d  1)

• Evaluation of Damage State Probabilities:

  Pr( failure )  Pr(C R    C S )
 Pr( failure )  1  (  )            where β is the reliability index


          R                     1R 
                                      2
      ln(                        1 2 
             )  ln   0.5  ln       
          S                         S 
 
            ( ln( 1   R )  (1   S ))
                        2            2
                         1.00
                         0.90
Cumulative Damage Rate




                         0.80
                         0.70                                                    Light
                         0.60
                                                                                 Moderate
                         0.50
                         0.40
                                                                                 Severe
                         0.30
                         0.20
                         0.10
                         0.00
                                6          7         8         9         10
                                                         MMI




                                    Fragility Curves for Düzce Damage Database
Damage State     CDR(%)     VI     VII    VIII      IX      X
None               0       0.97    0.87   0.61     0.30    0.08
Light              5       0.03    0.11   0.29     0.38    0.28
Moderate           30        -     0.01   0.08     0.21    0.30
Severe             85        -     0.01   0.02     0.11    0.34
MDR(%)                     0.15    1.7    5.55     17.55   39.3
               DPM derived for Erzincan Damage Database

Damage State     CDR(%)     VI     VII    VIII      IX      X
None               0       0.97    0.81   0.41     0.10    0.01
Light              5       0.03    0.17   0.44     0.40    0.13
Moderate           30        -     0.01   0.13     0.35    0.33
Severe             85        -     0.01   0.02     0.15    0.53
MDR(%)                     0.15     2     7.8      25.25   55.6
           DPM derived for Dinar Damage Database

Damage State     CDR(%)    VI     VII     VIII      IX      X
None               0      0.99    0.88    0.60     0.23    0.05
Light              5      0.01    0.10    0.32     0.44    0.25
Moderate           30       -     0.01    0.06     0.24    0.35
Severe             85       -     0.01    0.02     0.09    0.35
MDR(%)                    0.05    1.65    5.1      17.1    41.5
           DPM derived for Düzce Damage Database
             3. DISCRIMINANT ANALYSIS TECHNIQUE
used for classification of the damage databases to
obtain damage state probabilities

•tests group (Damage States) differences

• due to several dependent variables (Damage
Inducing Parameters) simultaneously

• with the investigation of a number of cases
(buildings)
MAIN STEPS:
1. Discrimination of the cases with respect to groups
   (through discriminant functions)
2. Classification based on discriminant functions
   Discriminant Functions: (for Düzce Damage Database)
Performance                  Standardized Discriminant Function(s)
Level
LSPL              0.748.n-0.158.SRSSI-0.413.rs-0.089.ss+0.049.drs+0.305.oh
IOPL              0.691.n-0.136.SRSSI-0.247.rs+0.183.ss+0.313.drs-0.133.oh
CDS Func. #1 -0.731.n+0.393.SRSSI+0.069.rs+0.085.ss-0.020.drs+0.211.oh
        Func. #2 0.163.n+0.362.SRSSI-0.456.rs+0.356.ss+0.458.drs+0.288.oh
        Func #3   -0.214.n+0.563.SRSSI+0.333.rs+0.126.ss+0.546.drs-0.785.oh



   • For any performance level number of stories is the most
   significant parameter. (others are SRSSI, redundancy score,
   and density ratio score)
   • Significance tests also indicate these parameters are
   dominant variables.
 Classification Results: (for Düzce Damage Database)
                                          Predicted Group Membership     Total
                                          1        2       3       4
                               1         25       10       5       1      41
Original Group                 2         10       33       9       15     67
Membership     Count
                               3         2         8       5       6      21
                               4         1          4      4      14      23
                              1        61.0        24.4   12.2    2.4    100.0
                      %       2        14.9        49.3   13.4    22.4   100.0
                              3         9.5        38.1   23.8    28.6   100.0
                              4         4.3        17.4   17.4    60.9   100.0
50.7% of original grouped cases correctly classified




    Based on the classification results, damage rate profile is
    obtained by using relative frequency analysis on the
    predicted group memberships.
    Damage State Probabilities: (for Düzce Damage Database)

        Performance      Damage States      Damage Ratio
           Level
                            N+L+M               0.69
           LSPL
                               S                0.31
                             N+L                0.63
           IOPL
                             M+S                0.37
                              N                 0.25
                               L                0.36
           CDS
                              M                 0.15
                               S                0.24



Based on the damage state probabilities, Mean Damage Ratios (MDR’s)
are computed for each damage database.
COMPARISON OF RESULTS OF THE THREE STOCHASTIC
                          METHODOLOGIES


             Stochastic Method                       MMI
                                           VI    VII   VIII     IX
   DPM/ AC Buildings (1st Seismic Zone)    0.3   4     14      21.5
   DPM/ NAC Buildings (1st Seismic Zone) 6.2     10.4   18.9   40.7
   Reliability (1992 Erzincan)             0.2   1.7    5.6    17.6
   Reliability (1995 Dinar)                0.2    2     7.8    25.3
   Reliability (1999 Düzce)                0.1   1.7    5.1    17.1
   Discriminant Analysis (1992 Erzincan)    -     -     20.7    -
   Discriminant Anaysis (1995 Dinar)        -     -     16.9    -
   Discriminant Analysis (1999 Düzce)       -     -      -     26.7
                    CONCLUSIONS

• At any intensity level, discriminant analysis and DPM
gave quite close results whereas reliability-based model
underestimated the MDR’s since it utilized the mean
conversion between PGA and MMI instead of the actual
PGA values.

• When actual PGA values are utilized in the
reliability-based model, the MDR values become close
to those of DPM for NAC buildings, which prove the
fact that many of the buildings in the damage
databases are NOT constructed according to the
Code.
•Empirical methods are quite sensitive to any bias
in the databases towards any damage state.

• Amount of wall areas and number of stories are
found to be the most critical parameters affecting
damage for the building databases under
consideration.

• Seismic damage prediction should be carried out
based on probabilistic terms. The methods introduced
in this study are consistent among themselves and
appear to be valid methods for probabilistic damage
estimation.
  RECOMMENDATIONS FOR FUTURE STUDIES AND
                      RESEARCH
• Complete and random earthquake damage data to
avoid bias.

• Minimizing the subjectivity in seismic assessment in the
aftermath of earthquakes.

• Construction date of all buildings should be included
in damage assessment forms.

• Additional damage parameters may be developed to be
included in discriminant analysis.

• The proposed methods should be applied on the other
damage databases to investigate their validity.
               Acknowledgments

• Prof. Semih Yucemen, Middle East Technical University,
Ankara, Turkey.
•Prof. Jacobo Bielak, Carnegie Mellon University, Dept. of Civil
and Env. Eng.
•CERRA for the graduate student fellowship.
• ICASP-9 Conference organization

				
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