Wave Propagation under Vertically Excited Surface Foundation

Recently developed equipment allows measurement of the shear modulus of soil in situ as a function of level of strain. In these field experiments, the excitation is applied on the ground surface using large scale shakers, and the response of the soil deposit is recorded through embedded receivers. The focus of this paper is on the simulation of signals which would be recorded at the receiver locations in idealized conditions to provide guidelines on the interpretation of field measurements. Discrete and finite element methods are employed to model one dimensional and three dimensional geometries, respectively, under various lateral boundary conditions. When the first times of arrival are detected by receivers under the vertical impulse, they coincide with the arrival of the P wave, related to the constrained modulus of the material, regardless of lateral boundary conditions. If one considers, on the other hand, phase differences between the motions at two receivers the picture is far more complicated and one would obtain propagation velocities, function of frequency and depth, which do not correspond to either the constrained modulus or Young's modulus. It is thus necessary to apply some care when interpreting the data from field tests based on vertical steady state vibrations. The use of inverse analysis can be considered as a way of extracting the shear modulus of soil from the field test measurements.