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

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

3. Site Response Analysis
May 4th, 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

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

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

6. Site Information The geological formation of the Fraser Delta
May 4th, 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)

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

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

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

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

11. May 4th, 2015
Geotechnical Data
Vs data, 300m Borehole from Richmond

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

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

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

15. May 4th, 2015
Geotechnical Data
Combining the Measured Vs profiles and Empirical Vs-depth relationship

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

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

18. May 4th, 2015
Analysis Results
Example 1: to demonstrate the influence of the uncertainty in a critical parameter, Vs
Input Variables to Monte Carlo
Material property
Mean value
Standard Deviation
Vs (above 30m)
Varies (from SCPT data)
25m/s or 75m/s
Vs (below 30m)
Varies (Empirical equation)
Nkt 14 2 φ
38° 2° γ
19kN/m3
0.5kN/m3

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

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

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

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

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

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

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

26. May 4th, 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 Vs went from 25m/s to 75m/s

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