Abstract
Spatial variability in soil properties is still in the exploratory stage and, despite of an increase in probabilistic and statistical analysis, many challenges remain in using spatial variability of soil properties in practical designs. This chapter addresses the problem of how to incorporate spatial variability of soil properties by using Geostatistics. Existing researches in variability analysis tend to focus on the distribution of the soil properties, reliability based design and simulation of random fields. However, there is limited evidence that researchers have approached the issue of spatial variability in soil properties. Consequently, the aim of this chapter is to develop a framework for incorporating spatial variability in soil properties in prediction analysis and how it could be applied to infrastructure design. The developed framework is validated by performing spatial variability analysis of soil strength parameters evaluated from the piezocone penetration test data.
TopIntroduction
Soils are inherently heterogeneous in nature. The constrained soil investigation works on heterogeneous soils leads to uncertainty and variability in soil properties. Several statistical studies have been conducted to evaluate the uncertainty present in geotechnical studies (Spry et al., 1988; Soulie et al, 1990; Phoon et al., 1995). In the recent decade, the reliability-based design (RBD) method has been established as the most powerful technique to account for uncertainties associated with soil properties, however, the spatial variability of soil parameters hasn’t gained sufficient attention in either practice or theoretical research. One recurring criticism of geotechnical RBD is that there is no particular motivation to use it because it seems to produce either designs comparable to existing practice (Phoon & Ching, 2012) or impractical probabilities of failure (Christian & Baecher, 2011). Geotechnical researchers often attribute this inconformity to the spatial variability of soil properties (Phoon & Ching, 2012; Christian & Baecher, 2011).
The uncertainties associated with soil parameters are divided into three sources: inherent spatial variability, measurement errors and transformation uncertainty (Vanmarcke, 1977; Baecher, 1982; Baecher and Christian, 2003; Kulhawy et al., 1992; Phoon et al., 1999). Inherent soil variability is due to complex process of geomaterials formation such as sedimentation, weathering, stress history and time (Kulhawy, 1992; Phoon and Kulhawy, 1999; Phoon & Ching, 2012). Measurement error resulted from equipment, procedural-operator and field effects (Lumb, 1974; Orchant et al., 1988; Phoon and Kulhawy, 1999; Phoon & Ching, 2012), while transformation errors occur when fields or laboratory measurements are transformed to design soil properties with empirical or other correlation models (Phoon and Kulhawy, 1999; Phoon & Ching, 2012). The spatial variability is referred as the inherent variability and measurement error associated with the testing method.
Earlier studies on uncertainty and variabilities associated with soil properties using conventional statistics (Hammah and Curran, 2006) do not offer any inferential information on the correlation structure of soil parameters. The lack of incorporating spatial variability of the soil properties in the analysis brings inevitable uncertainties in the geotechnical designs (Einstein et al., 1982; Lacasse et al., 1996).
Key Terms in this Chapter
Kriging: A best linear unbiased estimator for interpolation at unsampled locations based on available observations. All estimates at unsampled locations are assumed as linear combination of observations assigned with different weighting factors.
Weak Stationarity: Mean of a dataset is constant and covariance just depends on distance between observations, but no coordinates. It is a basic assumption in Geostatistics. Fundamentally stationarity is equivalent to statistical homogeneity.
Geostatistics: A spatial interpolation method based on spatial variability analysis.
Range: The distance at which the semivariogram reaches this plateau. It is a key parameter to describe spatial variability characteristics. The longer range value suggests greater spatial continuity.
Piezocone Penetration Testing: A modern advanced in situ testing method. It involves pushing a probe with built-in sensors into subsurface and nearly continuously recording the resistance at cone tip, friction along the sleeve, and pore water response at the filter. The resistance is thought to represent failure strength of subsoil.
Cross Validation: A validation technique to assess efficacy of the models developed using statistics. In geostatistics, cross validation refers to assessing and evaluating the estimation methods used for prediction analysis.
Variogram: One-half of the average squared differences between the x and y coordinates of each pair of points. A mathematical function for description of self-similarity between observations. It increases as the autocorrelation decreases.