Stochastic Modeling of the Spatial Variability of Soil

Abstract

Disparate sources of uncertainties contribute to the variability in geotechnical properties. Inherent variability in soil property, error in measurement and uncertainty in transformation models are the three major sources of geotechnical uncertainties. This paper mainly focusses on inherent soil variability; while the rest are beyond the scope. The inherent variability in soil originates mainly from the natural geological phenomena that result in the origination and the continual modification of the in situ or residual soil mass. Inherent soil variability is generally modelled as a random field. Simulating geotechnical variability as random process incorporates significant statistical results to be inferred from field test data and helps in including such variability in reliability analysis of geotechnical design. In this study, a stochastic model for inherent soil variability in terms of SPT-N value is developed for IIT Guwahati campus (26.1903ο N, 91.6920ο E) situated in Guwahati city of state Assam in India. Total 146 borehole SPT-N profile of the campus are used for developing the model. SPT-N value is observed to have an increasing trend with depth i.e. the data is nonstationary. In this model, the original data is first detrended and the trend function can be treated as deterministic in nature. The trend function is then evaluated using linear regression; a linear model is found to be good enough for present data. The residual part (error) is modelled as a one-dimensional random field. The squared exponential correlation structure is found to be best fitted in this case. The scale of fluctuation of the random field characterizing the error has been estimated from the fitted autocorrelation structure. The errors can be simulated easily once the correlation structure is known and added to the deterministic part to generate desire number of N profiles for further geotechnical analyses of the site.