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)

One-Dimensional Site Response

Hydraulic fill

3 m

6 m

3% ground slope Ref: Jones et al. 2001

Monte Carlo Results

Ref: Jones et al. 2001