Dear all

I have FEM analysis results for vibration foundation response that rested either on saturated salt-encrusted flat soil (case-1) or on finite cemented sand overlie saturated salt-encrusted flat soil (case-2) as shown in Fig. 1. I want an interpretation to increase the displacement amplitude of the foundation with increasing frequency for case-2. The problem’s condition, results, and suggest interpretation as the following;

Problem’s condition

the diameter of foundation (D) and amplitude loading (Q0) was 5.0 m, and 10 kN respectively. The stiffness of the cemented sand is larger than salt-encrusted flat soil by five times, the horizontal and vertical dimensions of cemented 1.5 D and 0.24 D, respectively. the foundation subjected to vertical vibration with several frequencies of 5, 10, 20, 40, and 80 Hz.

Results

For case-1, time displacement (vertical) history is no steady-state due to stiffness low of the subsoil, the displacement amplitude of frequency of 40 Hz is higher than of frequency of 20 Hz as shown in Fig. 2. In other words, for frequency less than natural frequency, the operation frequency leads to an increase in the displacement amplitude.

For case-2, the time displacement amplitude history is steady-state. The displacement amplitude decreases with increasing operating frequency, as shown in Fig.3.

Suggest interpretation for the results of case-2

It may be to the reflected wave (reflected energy) that comes back from the edge boundary of the cemented layer. The reflected wave may resist the foundation’s displacement and increase the damping ratio of structure-soil interaction.