Quantification and reduction of parameter uncertainty of dynamic soil characteristics.

Characterisation of shallow, horizontal, soil layers is important for the study of different problems in civil and geophyscial engineering, such as the prediction of ground borne vibrations or the calculation of site amplification. This PhD thesis addresses the determination of  dynamic soil characteristics by means of the active Multichannel Analysis of Surface Waves (MASW), P-wave refraction and Seismic Cone Penetration Test (SCPT) methods. 

The circle fit method, used in structural dynamics for the identification of eigenfrequencies and modal damping ratios, is introduced to determine the Rayleigh dispersion and attenuation curves during a MASW experiment. In a Nyquist plot of the frequency-wavenumber  spectrum of the free field response or Green's function of the soil generated by an impulsive point load, the Rayleigh  modes correspond to circles. The Rayleigh phase velocity and attenuation coefficient are derived from the angular sweep of the Green's function. Results obtained with the circle fit method are compared with results obtained with the peak picking and half-power bandwidth method.

Inversion of the Rayleigh dispersion and attenuation curves allows to determine  the shear wave velocity and material damping ratio profile of a site. This inversion is often performed with a gradient based method, requiring  the sensitivities of the  dispersion and attenuation curves to the soil parameters.  Therefore, an analytical, computationally efficient method for the determination of these sensitivities is presented  for  the direct stiffness method.  Furthermore, these sensitivities allow to identify to which layer parameters the dispersion and attenuation curves are the most sensitive.

In order to investigate the theoretical accuracy and resolution of the MASW, P-wave refraction and SCPT method, three different cases are simulated: a  horizontally layered halfspace with a regular velocity profile, a horizontally layered halfspace with a velocity inversion and a halfspace with an inclined layer. The last case allows to quantify  possible model errors introduced by not taking layer inclination into account. These simulations show that the circle fit method is very efficient for the quantification and inversion of multi-modal Rayleigh dispersion and attenuation curves.

The three methods are subsequently used to determine the dynamic soil characteristics at three  sites. First, a deterministic procedure is followed, during which an initial profile is refined with a local optimization algorithm, using the analytically computed sensitivities of the Rayleigh dispersion and attenuation curves. The main drawback of this method is the need for  a  good estimate of the soil characteristics. Furthermore, only limited information can be obtained on the uncertainty and non-uniqueness of the soil parameters, by trying different initial profiles.

Alternatively to the  deterministic inversion, the  soil characteristics are also determined probabilistically, combining the different experiments in a Bayesian inversion scheme. This procedure takes into account the a priori determined measurement uncertainty and a posteriori estimated model uncertainty, and allows to determine the parameter uncertainty by means of different Markov Chain Monte Carlo (MCMC) methods. Model uncertainty is introduced due to simplifying model assumptions and the use of less exact but computationally more efficient forward models.
Thanks to the use of the Transitional MCMC method and a prior probability model of the soil parameters, it is not necessary to try different initial estimates of the soil profile, avoiding subjectivity.
The resulting soil profiles, which are sampled according to the posterior probability density function of the dynamic soil characteristics can be used to determine an ensemble of representative soil profiles which allow to asses the maximum depth for which the soil parameters can be accurately determined. An ensemble of soil profiles better predicts the transfer functions of the soil than a single best fitting soil profile. Furthermore, the set of soil profiles allows to calculate confidence intervals on the transfer functions, which show that the uncertainty can be large, especially in the high frequency range and at large distances.