Bayesian assessment of site-specific performance of geotechnical design charts with unknown model uncertainty

Soil properties are indispensable input parameters in geotechnical design and analysis. In engineering practice, particularly for projects with relatively small or medium sizes, soil properties are often not measured directly, but estimated from geotechnical design charts using results of some commonly used laboratory or in situ tests. For example, effective friction angle ϕ′ of soil is frequently estimated using standard penetration test (SPT) N values and design charts relating SPT N values to ϕ′. Note that directly measured ϕ′ data are generally not available when (and probably why) the use of design charts is needed. Because design charts are usually developed from past observation data, on either empirical or semi-theoretical basis, uncertainty is unavoidably involved in the design charts. This situation leads to two important questions in engineering practice: how good or reliable are the soil properties estimated in a specific site when using the design charts? (or how to measure the performance of the design charts in a specific site?); and how to incorporate rationally the model uncertainty when estimating soil properties using the design charts? This paper aims to address these two questions by developing a Bayesian statistical approach. In this paper, the second question is firstly addressed (i.e., soil properties are probabilistically characterized by rationally incorporating the model uncertainty in the design chart). Then, based on the characterization results obtained, an index is proposed to evaluate the site-specific performance of design charts (i.e., to address the first question). Equations are derived for the proposed approach, and the proposed approach is illustrated using both real and simulated SPT data.