Geotechnical and Geophysical Site Characterization – Huang & Mayne (eds) © 2008Taylor & Francis Group, London, ISBN 978-0-415-46936-4 Statistical analysis of geotechnical data M. Uzielli Georisk Engineering, Florence, Italy ABSTRACT: This paper attempts to provide an overview of the main domains of application of statistical-based techniques to geotechnical data. Examples and references to literature contributions are provided. 1 INTRODUCTION 1.1 Uncertainty, variability and determinism The geotechnical engineer processes testing data to obtain parameters for characterization and design. In practice, information is never sufficient in quan- tity, nor entirely precise and accurate. Geomaterials, moreover, are naturally complex and variable at all scales, ranging from the microstructure to regional scale. The competent engineer must account for this lack of uniformity and information while parame- terizing and modeling the physical world. The level of explicitness with which this occurs depends upon the selected approach. In deterministic approaches, variability is not addressed explicitly as in uncertainty- based approaches. In the technical literature – and geotechnical engineering is no exception – the terms variability and uncertainty are often employed interchangeably. Strictly speaking, this is not correct. Variability is an observable manifestation of heterogeneity of one or more physical parameters and/or processes. Uncer- tainty pertains to the modeler’s state of knowledge and strategy, and reflects the decision to recognize and address the observed variability in a qualitative or quantitative manner. Deterministic methods lie at the basis of virtually every technological science, and geotechnical engi- neering is no exception. However, the importance of explicitly modeling and assessing the variability of geotechnical parameters (i.e. quantifying, processing and reporting the associated uncertainty) is increas- ingly recognized in geotechnical design and charac- terization. Most evolutionary design codes operate in an uncertainty-based perspective, requiring explicit quantification not only of most suitable values (usu- ally termed ‘characteristic’ or ‘nominal’), but also of the level of uncertainty and confidence in the selection of such values. The progressive shift towards an uncertainty-based perspective may be motivated by the fact that this may be, on the whole more convenient in terms of safety, performance and costs. The explicit parameterization of uncertainty allows to provide more complete and realistic information regarding the level of risk asso- ciated with design. Addressing uncertainty does not per se increase the level of safety, but allows the engi- neer to rationally calibrate his decisions on a desired or required reliability or performance level of a geotech- nical system. Being able to select the performance level and reduce undesired conservatism, in turn, is generally beneficial in the economic sense. Among the main trade-offs for the positive aspects of uncertainty-based approaches, which hinder a more rapid diffusion among geotechnical practitioners, are the necessity to rely on specialized mathematical techniques and, not infrequently, large computational expense. While ever-increasing computational power is constantly reducing the relevance of the latter, a cor- rect implementation of uncertainty-based techniques requires at least some degree of comprehension on the side of the engineer. The results of uncertainty-based analyses can be used confidently for engineering pur- poses only if preceded, accompanied and followed by geotechnical expertise and judgment. 1.2 Rationale and scope of the paper Among mathematical disciplines which allow consis- tent modeling, processing, evaluation and assessment of uncertainty, statistical theory (usually employed jointly and iteratively with probability theory) provides a well developed, widely understood and accepted framework. Statistical theory encompasses a broad range of topics. A notable advantage of statistics over other uncertainty-addressing techniques such (e.g. fuzzy logic) is – at present – the vast bulk of statistical software packages which are available. 173