Practical Probabilistic Approach Using Spreadsheet

B. K. Low 

School of Civil and Environmental Engineering, Nanyang Technological University (NTU), Singapore

The conventional factor of safety as used in geotechnical engineering does not reflect the degree of uncertainty of the relevant parameters. A better approach is to compute a reliability index which reflects not only the mean values of the parameters but also their uncertainties.

A practical method for calculating the second moment reliability index using the optimization tool of a spreadsheet software is proposed. The method is based on the perspective of an ellipsoid that just touches the failure surface in the original space of the variables. This perspective is mathematically equivalent to the widely adopted perspective of a sphere in the space of reduced variates, but provides perhaps a more intuitive definition of Hasofer and Lind’s reliability index. The ellipsoid approach via spreadsheet is applied to an example problem on consolidation settlement. It yields results identical to those of Lagrange multiplier method and Rackwitz’s iterative procedure, but is much simpler to implement because no partial derivatives are involved on the user’s part. By freeing the engineer from tedious mathematical calculations, the ellipsoid approach may reduce the risk of the engineer’s not seeing the wood for the trees. It may also remove one major disincentive for the use of probability concepts. 

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