### Understanding Geotechnical Uncertainties in Performance-Based Earthquake Engineering ###

1. Geotechnical Uncertainties for PBEE

2. 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)

3. 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

4. Context 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

5. 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

6. Site Response Uncertainty • IM pdf from attenuation • IM dispersion is dependent on site condition • Estimated empirically

7. 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 Ref: Toro et al., 1997

8. 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)

9. 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

10. 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

11. 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

12. 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)

13. One-Dimensional Site Response 3 m Hydraulic fill 6 m 3% ground slope Ref: Jones et al. 2001

14. Monte Carlo Results Ref: Jones et al. 2001