Characterisation of shear wave velocity profiles of non-uniform bi-layer soil deposits: Analytical evaluation and experimental validation

• .Closed-form solution for low-strain stiffness of bi-layered inhomogeneous deposits
• Simplified closed-form relationships for applications in design codes.
• Validation of numerical results using data from experimental shaking table tests.

A crucial aspect of physical geotechnical model tests (under both 1-g and n-g conditions) is the evaluation of the initial (low-strain) stiffness of the soil layers of the sample test deposit, especially in the case of coarse materials. While for uniform soil deposits this issue can be addressed in a straightforward manner, e.g. by determining the fundamental frequency through the transfer function of an applied white-noise excitation, the problem becomes cumbersome for multi-layered deposits. After reviewing a number of available theoretical solutions, this paper illustrates a simplified yet reliable analytical procedure for determining the shear wave velocity profile (Vs) in a single or bi-layer deposit, taking into account the inhomogeneity of the individual soil layers, under the hypothesis of vanishing shear modulus at ground surface. The fundamental natural frequency of the inhomogeneous bi-layer deposit is analysed using the Rayleigh quotient procedure. The associated shape function is evaluated by considering the equilibrium of the soil column under a pseudo-static lateral inertial excitation imposed at its base, accounting for both layering and inhomogeneity. A validation of the proposed method is provided by comparing numerical results obtained from both time- and frequency- domain analyses against experimental data on Leighton Buzzard sand, from a recently-completed research project conducted on the shaking table facility at BLADE Laboratory, University of Bristol (UK).