The main aim of this work was to develop methods to estimate quantitatively, and describe qualitatively, the non-linear behaviour of soft soil in intermediate-scale laboratory experiments. Previous works stated that non-linearity of the soil was found for environments involving a large impedance gradient in the near-surface, e.g., a shallow layer of soft, unconsolidated soil overlying a thick harder layer. It is believed that the micro-grains inside the soft soil, in combination with the geometry, caused the non-linearity, although other laboratory experiments found non-linear behaviour for core samples of different single materials.

The novelty of this thesis project lies in the introduction of a new method for investigating the shallow subsurface that has both the advantages of the laboratory environment (e.g., more control over the parameters and higher resolution measurements) and of the field experiments. Therefore, this new, intermediate-scale laboratory approach could be seen as a missing bridge between the experiments on core samples and the field experiments. To the best of our knowledge, this kind of experiment has not been done before and therefore there have not been any physical definitions or classifications of the observed phenomena, yet.

The research was developed in four experiments. The first two experiments verify the scaling, characterize the chosen analogue materials (Clay and Sand), and investigate the influence of the model boundaries. While, the last two experiments focused on the non-linearity behaviour of the soft soil analogues in response to large voltage (e.g., low 100s of Volts) swept-source signals. Overall, we believe we have observed in these experiments several non-linear behaviours for the constructed two layer model; both in terms of a non-linear dependence of the amplitudes on the voltage level as well as in the form of a slowing of the waves for increasing voltage. In addition, we quantify the non-linearity trough a new parameter called the ``Non-linearity parameter'', $\gamma$, and its magnitude describes the level of non-linearity of the soil. The larger $\gamma$, the more non-linearly the soil behaves, and vice-versa. A model linearized to first order was used to compare the data measured using an laser Doppler vibrometer with other observed data assuming the linear response. Thanks to that model, we could mathematically generalize the amplitude behaviour of the measured velocities of the soil as a function of $\gamma$ and visualize the threshold between the linear and non-linear regimes graphically. It appears it is the first time that such parameter is introduced to describe quantitatively the non-linearity.

The proposed methods for investigating the shallow surface by way of intermediate scale analogue models could breathe new life in the use of the physical modeling for near-surface Geophysics. Both the intermediate scale two layer model and the non-linearity parameter appear to be new in this field. The hope is to open a new path for future research keen in understanding better the non linearity behaviour of soft soils.