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The buildings and structures of major infrastructure projects are required to be analysed for the various static loads such as self-weight, superimposed dead load, finish loads, etc., as well as dynamic loads including wind load, seismic loads, moving loads, blast loads, impact loads, etc., in accordance with the prevalent codes and standards. In order to analyse the structures for dynamic loads, dynamic soil parameters would be essential for carrying out the soil structure interaction (SSI) analysis. The spatial variations of the soil properties for any given site cannot generally be characterised if limited sub-soil investigations have been carried out. Therefore, the uncertainties in the dynamic properties, for example, shear wave velocity, dynamic Poisson's ratio, dynamic Young's modulus, dynamic modulus of rigidity, dynamic bulk modulus, etc. have to be incorporated in the SSI analysis. The uncertainties in data might be broadly classified as aleatory or epistemic (Tung & Yen, 2005; Coleman & Steele, 2009; Modarres et al., 2010). The aleatory uncertainty is associated with the natural randomness of the process or physical phenomenon and therefore cannot be reduced (Lombardi, 2017; Dauji, 2019). The epistemic uncertainty arises from the deficiencies in information, lack of scientific understanding and inaccuracy in modelling of the physical process and therefore can be reduced with more data and better knowledge of the process (Lombardi, 2017; Dauji, 2019). Rather than classification of uncertainties involved in an analysis, the engineering approach is targeted towards estimation of the uncertainty and incorporating the same into the analysis and safe design of the structure. When sufficient data is available, probabilistic tools are available for characterising the uncertainties (Ayyub & Gupta, 1998; Coleman & Steele, 2009) and this approach is the preferred option for handling geotechnical uncertainty as well (ASCE, 2000; AERB, 2009). Handling uncertainties in case of limited availability of data would require different approach and might be conducted with statistical tools such as re-sampling, Monte Carlo (MC) simulation, and Bayesian estimation or artificial intelligence (AI) tools such as neural network and fuzzy logic (Ayyub & Gupta, 1998; Hofer, 2018; Shaw, 2017).
The uncertainties in soil properties could arise from measurements, inherent spatial variability of soil properties – in both plan and along depth, employed empirical expressions, or the calculation models, among others. The geotechnical uncertainties have been categorised by Phoon & Kulwahy (1999a; 1999b) as: inherent variability that is aleatory; measurement errors and transformation uncertainty, which are epistemic. They provided some estimates of the variability in the form of coefficients of variation, for these various cases. Shear wave velocity is extremely useful for various applications such as site classification, seismic site response, liquefaction analysis, SSI, etc., and uncertainty associated with this variable has received particular attention in literature (Moss, 2008). The variability of shear wave velocity has been estimated to be between 1% and 6% for direct measurements, and between 20% and 35% for indirect estimates from correlation equations. This uncertainty could be compounded when the weighted average shear wave velocity is calculated for building analysis purposes. Incorporation of soil uncertainty into geotechnical analysis is discussed in literature (Phoon & Tang, 2019). However, specific estimation of the uncertainty in weighted average shear wave velocity due to the uncertainty in individual estimates (as indicated by Moss, 2008) is scarce in literature. Owing to the fact that the variability in sub-soil properties are much more compared to the engineering materials of construction such as concrete or steel, addressing the uncertainty associated with foundation parameters has remained an area of active research. Simple implementation schemes for addressing this issue would be useful for the foundation designers, particularly for cases with limited available sub-soil data.