Dynamic Interaction of Machine Foundations

Abstract

The design of machine foundations involves the prediction of vibration magnitude. Very slight (of the order of a hundredth of a centimeter) vibration magnitude may cause harm to the function of the machine and may even terrify people or threaten the safety of surrounding structures, so the codes and manufacturers of the machines limit the amplitudes of the vibrations of machine foundation to certain values depending on their frequencies and types. In most designs, the interaction of nearby machine foundations is ignored, with the assumption of being far apart to minimize their cross effects. With no reliable analysis of machine foundation interaction, ignorance of interaction may lead to unsatisfactory results. In this research, the cross-interaction of machine foundations is investigated using the finite element method (FEM). The soil is modeled as a visco-elastic half space. The complex response method is adopted and the analysis is implemented in the frequency domain. A model of two square footings using three-dimensional finite elements, loaded with vertical harmonic forces is analyzed to study the following factors: 1. The effect of loading parameters (angular velocity, amplitude and phase difference) and spacing on the interaction of surface footings. 2. The effect of the footing embedment for the case of embedded-surface footings and the case of embedded-embedded footings. The loading parameters are also considered for the two cases. 3. The effect of the soil depth to the underlain rock stratum on the interaction of adjacent footings. 4. The use of trenches to reduce the effect of adjacent footings' interaction. Dimensionless curves have been developed for a mass ratio of 5.0 to account for the interaction of machine footings. The results show the importance of the interaction to get a satisfactory serviceability of machine foundations. The study also shows the effect of the loading characteristics, spacing, and depth of compressible layer on the dynamic behaviour of adjacent footings. The following results were obtained: 1. The vibrations of surface footings may double in magnitude due to the interaction in case of applying forces with equal angular frequencies. 2. The load-vibration relation is linear in case of equal angular frequencies and non-linear for other cases. 3. The maximum out-of-phase vibration amplitudes are greater than the in-phase vibration amplitudes by a slight difference. 4. The vertical and the rocking vibrations are no longer uncoupled when considering the dynamic interaction of adjacent footing. 5. The embedment of the footings reduces the vibration if the two footings are equally embedded and may increase the vibration in the case of surface-embedded footings. The vibration amplitudes decrease for cases of shallow depths of soil underlain by rock. At the same time, the dynamic response of the footings is not affected by the angular speed of the applied dynamic forces. 7. Trenches can be used to reduce the effect of machine foundation interaction with a width greater than O.lB, depth greater than 2B, and length greater than 3B, where B is the footing width. From the results of this study, the interaction of machine foundations must be considered in the design. Vibration reduction methods such as embedment and trenches, are investigated to obtain the optimum values of the parameters of each method.