Transcript Document

P
E
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Geotechnical Uncertainties for PBEE
Jonathan P. Stewart
University of California, Los Angeles
May 22, 2002
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
 DV    G DV | DM | dG DM | EDP dG EDP | IM | d ( IM ) |
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
V = 530 - 760 m/s
V = 310-530 m/s
V = 180 - 310 m/s
– IM dispersion is
dependent on site
condition
– Estimated empirically
Sadigh et al.
Boore et al.
0.7
m 6.5
0.5
m 7.5
0.4
}
}
Standard Error, s
0.6
Fa
0.3
PHA
0.01
0.1
Fv
1
Period (s)
10
Site Response Uncertainty
• IM pdf from site-specific
analysis
0
– Uncertainty in nonlinear
properties (G/Gmax, D)
– Vs
• Aleatory from spatial variability
- e.g. Savannah River (Toro,
Silva)
• Epistemic from measurement
error, incomplete site testing
40
80
Depth (m)
• Epistemic from sample
disturbance effects
• PEER Lifelines–developing
models for depth, PI, % fines
effects
Site Specific
Std. Dev. (s)
Corr. Coeff. (r )
120
160
200
0
0.2
0.4
0.6
ln(V) - m/s
Ref: Toro et al., 1997
0.8
1
Site Response Uncertainty
– Input motions
0.9
s (ln units)
• 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)
0.6
sRRS from 1-D
ground response
0.3
0
0.01
0.1
1
Period (s)
10
EDP|IM: Liquefaction
• Triggering:
– Liq|(pene. resistance, IM)
__ _ Seed et al., (1984)
__ _ Yoshimi et al. (1994)
• 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
Mw=7.5 sv' =1300 psf
0.5
PL
80% 20%
95% 50% 5%
0.4
0.3
CSR
0.2
0.1
0
0
10
20
N1,60,cs
30
40
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
0.60
Surface foundations with Quaternary
Shallowly embedded with Quaternary
Surface foundations with Tertiary and older
ka = 0.017 + 5.0E-04 Vs (m/s)
0.40
s = 0.57
ka
90% Confidence intervals
0.20
• Soil-Foundation Interaction
– Epistemic from model
formulation (spring, continuum
models from FE, FD)
– Aleatory from material
parameters
0.00
0
200
400
Vs (m/s)
600
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)
One-Dimensional Site Response
3m
Hydraulic
fill
6m
3% ground slope
Ref: Jones et al. 2001
Monte Carlo Results
Ref: Jones et al. 2001