Topic 1: Measurement and uncertainties 1.2 – Uncertainties and errors
PEER Jonathan P. Stewart University of California, Los Angeles May 22, 2002 Geotechnical...
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Transcript of PEER Jonathan P. Stewart University of California, Los Angeles May 22, 2002 Geotechnical...
May 22, 2002
PPEEEERR
Jonathan P. StewartUniversity of California, Los Angeles
Geotechnical Uncertainties for PBEE
Definitions of Uncertainty
• Epistemic: uncertainty associated with incomplete or imperfect knowledge– Lack of information, e.g., insufficient soil sampling
– Shortcomings in measurement, e.g., soil disturbance effects on modulus reduction/damping curves
– Shortcoming of calculation, e.g., limitations of 1-D ground response model
– Can be reduced with research (development of additional data, better models)
Definitions of Uncertainty
• Aleatory: uncertainty inherent to a physical process or property– Spatial variability of soil properties
– Dispersion of IM from source/path effects at high frequencies
– Cannot be reduced with additional data/knowledge
Context
|)(||||| IMdIMEDPdGEDPDMdGDMDVGDV
Where geotechnical uncertainty matters:• Site response – IM
• EDP|IM for EDPs related to ground failure– Liquefaction and its effects (ground movement, instability)
– Slope failure
– Volume change in unsaturated soils
• Soil-structure interaction– Seismic demand imparted to structure from free-field
– Flexibility/damping of foundation-soil interaction
Information Resource
• Jones/Kramer/Arduino PEER report 2001/03
• “Estimation of uncertainty in geotechnical properties for performance based earthquake engineering”
• Parameter variability from field/lab tests subdivided according to:– Inherent variabilty
– Measurement variability
– Spatial correlation
Site Response Uncertainty
• IM pdf from attenuation– IM dispersion is
dependent on site condition
– Estimated empirically
0.01 0.1 1 10P e rio d (s)
0.3
0.4
0.5
0.6
0.7
Sta
nda
rd E
rro
r,
V = 530 - 760 m /sV = 310-530 m /sV = 180 - 310 m /sSadigh et a l.
Boore et a l.
m 7.5
m 6.5
PH A
}
F a
}
F v
Site Response Uncertainty
• IM pdf from site-specific analysis– Uncertainty in nonlinear
properties (G/Gmax, D)• Epistemic from sample
disturbance effects• PEER Lifelines–developing
models for depth, PI, % fines effects
– Vs
• Aleatory from spatial variability - e.g. Savannah River (Toro, Silva)
• Epistemic from measurement error, incomplete site testing
0 0.2 0.4 0.6 0.8 1ln(V ) - m /s
200
160
120
80
40
0
De
pth
(m
)
S ite Sp e cificS td. D ev. (s )
Corr. C oeff. (r )
Ref: Toro et al., 1997
Site Response Uncertainty
– Input motions • Epistemic uncertainty in IM
hazard results (target spectrum for ground motion scaling)
• Aleatory from phasing of input time histories
• Result: large uncertainty in calculated soil response – especially at short periods (e.g., T < 1 s) 0.01 0.1 1 10
P e rio d (s)
0
0.3
0.6
0.9
(l
n u
nits
)
RR S from 1-D ground response
EDP|IM: Liquefaction
• Triggering: – Liq|(pene. resistance, IM)
• Epistemic from model minimized with recent PEER work (Seed et al.)
• Modest aleatory
– Still large uncertainty in penetration resistance
• COV 50% (sand N-values); Ref. Phoon and Kulhawy, 1999
• Effect on liquefaction can be of similar order to that of IM uncertainty 0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40N1,60,cs
CSR
50% 5%Mw=7.5 v' =1300 psf
__ _ Seed et al., (1984)
__ _ Yoshimi et al. (1994)
95%20%80%
P L
Liquefaction Effects
• Ground/structure settlement– Correct form of model
unknown
– Epistemic from inadequate data
– Aleatory uncertainty not quantified
• Undrained residual strength
• Lateral spread displacement
Opportunity for PEER impact
Soil-Structure Interaction
• Seismic demand – kinematic interaction– Rigorous analysis with
incoherent wave field vs. simplified model with incoherence parameter
– Epistemic model uncertainty– Aleatory uncertainty on
incoherence parameters
• Soil-Foundation Interaction– Epistemic from model
formulation (spring, continuum models from FE, FD)
– Aleatory from material parameters
90% C onfidence in terva ls
0 200 400 600
V s (m /s)
0.00
0.20
0.40
0.60
a
Surface foundations w ith Q uaternaryShallow ly em bedded w ith Q uaternarySurface foundations w ith Tertiary and older
= 0 .57
a= 0.017 + 5.0E-04 V s (m /s)
Propagation of Uncertainties
• Evaluation of ground response effects on IMs – hazard analysis– Category-specific dispersion in PSHA– 1-D response analysis procedures for randomized soil
properties and input (RASCAL)– Must quantify epistemic uncertainty using logic trees– Methodology challenge: propagation of epistemic
uncertainty through the framing equation
• Opensees simulations for dG[EDP|IM]d(IM)– Monte Carlo methods– Repeat for different IMs (epistemic)