Approximate up-scaling of geo-spatial variables applied to deep foundation design

Abstract

We present a series of simple approximate methods for up-scaling the cumulative distribution function of spatially correlated variables by using an effective number n _e of independent variables. Methods are based on the property of distribution permanence of the gamma and inverse Gaussian distributions under averaging, bootstrap sampling and expansions about the normal and gamma distributions. A stochastic simulation study is used to validate each method, and simple parameters are defined to identify respective ranges of applicability. A practical example is presented where core sample rock strength data are up-scaled to shaft size for probabilistic (risk-based) deep foundation design. Supplemental material is available online.

Keywords:

• probability of failure
• reliability
• change of support
• geostatistics
• Edgeworth
• gamma expansion
• bootstrap
• inverse Gaussian

Acknowledgements

This research was partially funded by the Bahia State Research Foundation FAPESB (Brazil) under fellowship BOL 1072/2005, the Florida Department of Transportation under contract BD-545, RPWO # 76, and the Environmental Security Technology Certification Programme (ESTCP), US Department of Defense (DoD): Project Number ER-200831.