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Allowing for Uncertainty in Site Response Analysis Dr Jason Dowling Dept of Civil Engineering The University of British Columbia The 5 th Tongji-UBC Symposium on Earthquake Engineering Facing Earthquake Challenges Together May 4-8 2015, Tongji University Shanghai, China

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Overview -Site Information & Motivation for the Study -Geotechnical Data -Variation of Input Properties -Site Response Analysis Allowing For Uncertainty -Analysis Results May 4 th, 2015 2/27

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May 4 th, 2015 Site Response Analysis The propagation of seismic waves as they travel through the local soil stratigraphy to the surface The key components: Input Motions and Soil Properties 3/27

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May 4 th, 2015 Site Information Three schools sites in Richmond, BC British Columbia 4/27

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May 4 th, 2015 Site Information Three schools sites in Richmond, BC 5/27

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May 4 th, 2015 Site Information The geological formation of the Fraser Delta As a result, there can be a considerable depth to bedrock in areas of the delta Source: Clague et al. (1998) 6/27

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May 4 th, 2015 Site Information Geological cross-section from Burrard Inlet, BC to Bellingham, WN 7/27

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8/27 May 4 th, 2015 Site Information Geological cross-section from Burrard Inlet, BC to Bellingham, WN

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May 4 th, 2015 Site Information Geological cross-section from Burrard Inlet, BC to Bellingham, WN Source: Clague et al. (1998) 9/27

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May 4 th, 2015 Geotechnical Data Example of data available >300m Borehole from Richmond Source: Clague et al. (1998) 10/27

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May 4 th, 2015 Geotechnical Data V s data, 300m Borehole from Richmond 11/27

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May 4 th, 2015 Geotechnical Data Richmond V s data V s (to depths of 3.5km) derived from seismic reflection data Source: Clague et al. (1998) 12/27

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May 4 th, 2015 Geotechnical Data Richmond V s data Empirical relationship Source: Clague et al. (1998) 13/27

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May 4 th, 2015 Geotechnical Data Borings were performed at the three school sites, giving V s profiles (top 30m only) 14/27

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May 4 th, 2015 Geotechnical Data Combining the Measured V s profiles and Empirical V s -depth relationship 15/27

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May 4 th, 2015 Variation of Input Properties Monte Carlo Distributions 16/27

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May 4 th, 2015 17/27 Site Response Analysis Allowing For Uncertainty 1,000s of randomly simulated sets of soil properties are analysed subject to the same input motions

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May 4 th, 2015 Analysis Results Example 1: to demonstrate the influence of the uncertainty in a critical parameter, V s Input Variables to Monte Carlo Material propertyMean valueStandard Deviation V s (above 30m)Varies (from SCPT data)25m/s or 75m/s V s (below 30m)Varies (Empirical equation)25m/s or 75m/s N kt 142 382 19kN/m 3 0.5kN/m 3 18/27

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May 4 th, 2015 Analysis Results Example 1: to demonstrate the influence of the uncertainty in a critical parameter, V s The standard deviation used in the input in 25m/s here 19/27

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May 4 th, 2015 Analysis Results Example 1: to demonstrate the influence of the uncertainty in a critical parameter, V s Spread of Input parameters, V s (standard deviation = 25m/s) 20/27

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May 4 th, 2015 Analysis Results Example 1: to demonstrate the influence of the uncertainty in a critical parameter, V s The standard deviation is increased to 75m/s here 21/27

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May 4 th, 2015 Analysis Results Example 1: to demonstrate the influence of the uncertainty in a critical parameter, V s Comparing the 25m/s and 75m/s standard deviation results 22/27

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May 4 th, 2015 Analysis Results Full Stochastic Analysis: 30 input motions, 150 variations of soil properties for each motion, 4,500 simulations in total 23/27

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May 4 th, 2015 Analysis Results Full Stochastic Analysis: 30 input motions, 150 variations of soil properties for each motion, 4,500 simulations in total 24/27

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May 4 th, 2015 Analysis Results Full Stochastic Analysis: 30 input motions, 150 variations of soil properties for each motion, 4,500 simulations in total 25/27

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May 4 th, 2015 Conclusions -Stochastic Monte Carlo simulation was used in the site response analyses of three deep (300m) school sites located in Richmond, BC to estimate amplification factors for seismic retrofit designs -It was found to be an effective method of coping with the effects of uncertainty in the soil properties used in nonlinear 1D site response analyses -The simulations resulted in stable mean values of spectral accelerations -The mean spectral response in the period range of interest for retrofit design of 1-2seconds, increased by 15% as the standard deviation in V s went from 25m/s to 75m/s 26/27

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We would like to express our gratitude to some organisations and industry partners who contributed to our travel expenses 27/27