Estimating vibrations induced by dynamic compaction using the finite element method

Dynamic compaction is a soil improvement method in which a heavy tamper is repeatedly dropped onto the ground. When the tamper hits the ground, it induces strong vibrations that may be harmful to nearby structures. The research aim is to numerically simulate the impact of the tamper and replicate the amount of vibration caused by the dynamic compaction at a distance. However, a key challenge arises: the recorded acceleration signal from the tamper (see Shpata, 2024) cannot be used directly in Plaxis software, which does not accommodate initial velocity and deceleration. To overcome this, we derived velocity and displacement signals from the measured acceleration to serve as input for the simulations (Fig. 1) (Shpata et al., 2025). This raises the central research question: which of these derived signals provides the most reliable prediction of ground vibrations?

In addition to defining the input, accurately modelling the soil response was essential. We developed a custom constitutive model for soil that accounts for shear strain–dependent stiffness degradation at small strains and implemented it in PLAXIS 2D. The model requires only two parameters (Shpata, 2024) and is coupled with Rayleigh damping, with damping ratios adjusted based on an empirical curve linking the damping ratio to the shear strain (Darendeli, 2001).

The two input signals, velocity and displacement, produced different outputs in terms of particle velocity (Fig. 2) and vertical acceleration (Fig. 3). Comparison with field tests revealed that neither signal was universally superior: the velocity input provided a better prediction of peak vertical acceleration, while the displacement input yielded more accurate estimates of peak particle velocity. These results raise questions about which approach should be trusted, highlighting the importance of engineering judgment. Moreover, we now explore alternative numerical methods, such as the Material Point Method, which may offer a more robust solution for simulating the impact process.