Geostatistics for modeling of soil spatial variability in Adapazari, Turkey

Transkript

1 1 Geostatistics for modeling of soil spatial variability in Adapazari, Turkey Jack W. Baker Michael H. Faber (IBK) ETH - Zürich 2 Practical evaluation of liquefaction occurrence Obtained from empirical observations (from Seed et al.) Useful for practical evaluations Applied only at single locations An approach is proposed here for incorporating spatial dependence of soil properties to evaluate the potential spatial extent of liquefaction 1

2 3 Proposed procedure for evaluating liquefaction extent Note that soil property values may be available for a few locations 4 A demonstration site in Adapazari, Turkey 2

3 5 Sampled N 1,60 values near the demonstration site in Adapazari, Turkey Test site Sampled soil values 6 Sampled N 1,60 values near the demonstration site in Adapazari, Turkey ρ( h) = exp( h 5000) 3

4 7 Simulation of N 1,60 values, conditional on observations (Sequential Gaussian Simulation) 1 1. Transform data so that it is normally distributed: z =Φ ( F( y) ) Empirical CDF of N 1,60 values Standard normal CDF 8 Simulation of N 1,60 values, conditional on observations (Sequential Gaussian Simulation) 2. Estimate spatial dependence of soil properties ρ( h) = exp( h 5000) 4

5 9 Simulation of N 1,60 values, conditional on observations (Sequential Gaussian Simulation) 2. Estimate spatial dependence of soil properties ρ( h) = exp( h 5000) 3. Simulate one additional point (Z 1 ), conditional upon observed values Z N, Σ orig Z 0 Σ Σ ( ) ( 1 Z 1 1 Zorig = z N Σ12 Σ22 z, 1Σ12 Σ22 Σ21) 10 Simulation of N 1,60 values, conditional on observations (Sequential Gaussian Simulation) 2. Estimate spatial dependence of soil properties ρ( h) = exp( h 5000) 3. Simulate one additional point (Z 1 ), conditional upon observed values Z N, Σ orig Z 0 Σ Σ ( ) ( 1 Z 1 1 Zorig = z N Σ12 Σ22 z, 1Σ12 Σ22 Σ21) 4. Repeat step 3 for each location, treating previously simulated points as fixed 5

6 11 Simulation of N 1,60 values, conditional on observations (Sequential Gaussian Simulation) 2. Estimate spatial dependence of soil properties ρ( h) = exp( h 5000) 3. Simulate one additional point (Z 1 ), conditional upon observed values Z N, Σ orig Z 0 Σ Σ ( ) ( 1 Z 1 1 Zorig = z N Σ12 Σ22 z, 1Σ12 Σ22 Σ21) 4. Repeat step 3 for each location, treating previously simulated points as fixed 5. Transform the simulated Gaussian variables back to the original distribution 12 Conditional simulations of N 1,60 6

7 13 Mean and coefficient of variation of conditional N 1,60 simulations Mean CoV 14 Comments on Sequential Gaussian Simulation Common in petroleum engineering and mining Requires jointly Gaussian random variables Partially achieved using the normal score transform This numerical transform is applicable for any probability distribution Can also be used for vectors of dependent parameters (e.g., SPT blow count and fines content) It is not necessary to condition on all previous points when simulating 7

8 15 Procedure for evaluating liquefaction extent 16 A probabilistic liquefaction criterion (Cetin et al., 2004) σ g( Xu, ) = N1,60 ( FC) 13.32ln CSReq 29.53ln M 3.70ln FC ε L P ' v a PGA σ v CSReq = 0.65 r ' d g σ v * amax Mw V s,12m 1 + * 0.341( d Vs,12 m ) e rd = + ε * rd amax Mw V s,12m 1 + * 0.341(0.0785Vs,12 m ) e σ ε 0.85 d if d 12m r d = if d>12m 8

9 17 A probabilistic liquefaction criterion (Cetin et al., 2004) σ g( Xu, ) = N1,60 ( FC) 13.32ln CSReq 29.53ln M 3.70ln FC ε L P ' v a PGA σ v CSReq = 0.65 r ' d g σ v * amax Mw V s,12m 1 + * 0.341( d Vs,12 m ) e rd = + ε * rd amax Mw V s,12m 1 + * 0.341(0.0785Vs,12 m ) e σ ε 0.85 d if d 12m r d = if d>12m 18 A probabilistic liquefaction criterion (Cetin et al., 2004) σ g( Xu, ) = N1,60 ( FC) 13.32ln CSReq 29.53ln M 3.70ln FC ε L P ' v a PGA σ v CSReq = 0.65 r ' d g σ v * amax Mw V s,12m 1 + * 0.341( d Vs,12 m ) e rd = + ε * rd amax Mw V s,12m 1 + * 0.341(0.0785Vs,12 m ) e σ ε 0.85 d if d 12m r d = if d>12m 9

10 19 Realizations of liquefaction extent 20 Probabilistic evaluation of consequences, given a M=7 earthquake causing a PGA of 0.3g ( ( )) P( Y > y pga, m) = I h g( η pga, m) > y f ( e) de η η 10

11 21 Probability of liquefaction at the study site, given a M=7.4 earthquake causing a PGA of 0.3g 22 The previously computed result for a deterministic loading case can be combined with stochastic loading obtained from probabilistic seismic hazard analysis (PSHA) (see Baker and Faber, 2006) 11

12 23 Comments The procedure is useful for organizing the many pieces of relevant engineering data, but the inputs need careful consideration Soil random field models are challenging to characterize Soil layering? Unidentified local soil lenses? Homogeneity/Ergodicity assumptions? Modeling post-liquefaction behavior is a challenge Geotechnical data often comes from several sources of varying quality 24 Conclusions A framework has been proposed for modeling the spatial extent of liquefaction Accounts for spatial dependence of soil properties Incorporates known values of soil properties at sampled locations Complex functions of the spatial extent of liquefaction can be evaluated Probabilistic seismic hazard analysis can be used to incorporate all possible ground motion intensities Avoids the use of a scenario load intensity with unknown recurrence rate Provides an explicit estimate of annual occurrence probabilities This approach potentially allows for the design of projects with uniform levels of reliability 12