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

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.

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