Contributions to semi-analytical and numerical modeling of vibration pressure compaction

Vibro-compaction represents a soil improvement method for deep compaction of cohesionless granular soils, which has been used successfully for several decades. The soil around to the vibrator is primarily excited horizontally. This leads to a reduction in pore ratio and consequently to an increase in soil density. The excitation generated by deep vibro-compaction is based on an eccentrically arranged mass, so-called imbalance, which rotates around the vertical axis of the vibrator at a constant angular velocity. Due to the compaction control, which up to now has only been possible after the compaction process and also only selectively by means of probing, the compaction success essentially depends on the experience of the machine operator. The methods for quality control of the compaction works are largely empirical in nature and therefore often unreliable. There is currently no approved method for a reliable continuous compaction control for this ground improvement technique available. For this reason, a work-integrated testing tool is required. That means, the vibrator should not just serve as a compaction device but at the same time as a measurement tool, too.

Despite the compaction process itself, a compaction state is assumed in this master's thesis. As a consequence, the vibration response on the surface due to excitation by the vibrator at a certain depth is investigated. The quite complex behavior of the soil in close proximity to the vibro-compaction device is neglected completely. Furthermore, the subsoil is considered as an isotropic linearly elastic homogeneous half-space. In this work three modelling approaches of the current problem are chosen comprising semi-analytical as well as numerical models. On the one hand these semi-analytical models use numerical solutions of analytical solutions of the dynamic half-space problem documented in the literature. On the other hand, a commercial toolbox based on similar analytical solutions is used. Plausibility checks and sensitivity studies have shown that the semi-analytical approach mentioned first cannot be applied effectively. Furthermore, the numerical model represents a three-dimensional finite element model. This work only observes the acceleration response on the surface of the half-space because in previous field tests the surface response was recorded.

In a first step, the excitation representing the vibrator is idealized as a horizontally periodic single force. A decrease of the maximum amplitude in the time domain of the acceleration response is observed with increasing distance to the vibrator, depending on the shear modulus. The decay of the acceleration on the surface predicted by the semi-analytical and the numerical model is in good agreement with respect to shape and quantitative values as the shear modulus increases.

To model the rotational movement of the deep vibrator more realistically, two horizontal, orthogonally positioned, periodic single forces are superposed. The two horizontal soil accelerations resulting at the surface are superimposed in each point, and the area within these so called Lissajous curves is plotted with increasing distance to the idealized vibrator. It is shown that the circle in the center of the model (i.e. origin of the Cartesian coordinate system) degenerates to a rotated ellipse due to the change in phase shift with increasing distance from the origin. The results of the semi-analytical and numerical model are both qualitatively and quantitatively in good agreement. Furthermore, the depth of the idealized vibrator as well as the shear modulus have an impact on the superposition figures.



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