Loosely deposited granular soils can be strengthened through cyclic loading, with vibrocompaction being a widely used and effective method. However, the lack of rational design methods stems from the complex interaction between soil and vibrator, as well as the inaccurate description of plastic accumulation caused by small strains in soil regions distant from the vibrator. In this work, we investigate Osinov's hypothesis which suggests that the soil densification primarily results from numerous cycles of small-amplitude strains rather than wave propagation effects (including reflection and dispersion). In this way, the complex dynamic interaction between vibrator and soil (contact forces, large deformations around the vibrator, high frequency waves emanating from the vibrator, resonance effects, soil flow, etc.) is replaced by the effect of the vibrator on the soil: cyclic deformations applied repeatedly to the soil, with amplitudes varying both spatially and temporally. Quasi static finite element simulations using a combined hypoplastic and high cyclic accumulation model, with a prescribed field of strain amplitudes, show that the proposed simplified approach is able to qualitatively capture in-situ observations. The impact of different factors such as probe spacing, insertion depth, probe movement, and even the sequence in which the probe are driven can be reproduced by the model. The model's predictions may complement on-line compaction control methods.

Experimental evidence indicates that multidimensional cyclic loading of soils causes larger accumulation of deformations than equivalent one-dimensional loading. The response of sand to high-cyclic loading with 10,000 cycles and up to four-dimensional stress paths (i.e., four independent oscillating components) is examined in 120 triaxial and hollow cylinder tests in this work to extend these findings. With increasing number of oscillating stress components, the accumulation of permanent strains tends to increase. It is demonstrated that the definition of the multidimensional strain amplitude incorporated in the high-cycle accumulation (HCA) model can account for this. The validation of the HCA model for complex cyclic loading is complemented by the simulation of model tests on monopile foundations of offshore wind turbines subjected to multidirectional cyclic loading, for which the consideration of spatially variable cyclic loading with nonconstant load amplitudes in the HCA model is discussed. For this purpose, an extension of the HCA model considering multiple strain amplitudes is presented.