Keywords: modal harmonic analysis, pile-soil-pile interaction with three-dimensional finite elements, vibrating machinery foundation.

Modal harmonic analysis for vibrating machinery foundation design has been performed satisfactorily in the past. Design guidelines [1] provide appropriate analysis procedures to compute the dynamic response of piled foundations. Normally the pile cap on which the machine is mounted can be considered as rigid, and the impedance function for the pile-soil-pile interaction can be determined from established theories [2,3] or derived from finite element modelling [4]. The problem is simplified to a six degree of freedom spring-mass-damper system for computation in the frequency or time domain. In the past, modelling pile-soil-pile interaction using three-dimensional finite elements to represent the soil domain was computationally expensive [5]. That is why the impedance function was developed. However, in situations where the impedance function is impossible to determine, using the three-dimensional finite element approach is the only method available.

This paper presents the case study for an unusual foundation where a booster assembly was mounted on a flexible steel platform supported by steel piles around the perimeter. A central caisson was buried as deep as the pile toes. Its close proximity to the piles and its complex connection arrangement meant the impedance function could not be determined. Therefore, the pile foundation system was modelled with three-dimensional solid elements for the soil and with shell elements for the steel structure. By carefully selecting the mesh density and using tie-contacts for efficient mesh transition, the problem was discretised with 44,522 solid finite elements. The appropriate soil properties and pile-soil separation depth were used to investigate two ground conditions. The machine unbalanced force under normal operating condition was applied. The eigenvalue and modal harmonic analyses were performed using ABAQUS. Up to 364 eigenvalues and modes were extracted. The harmonic analysis used eigenmodes that were within ±20% of the operating frequency. The analyses were performed using two Intel Xeon X5482 processors, which took 29.5 minutes to complete.

The case study demonstrated that modal harmonic analysis of a pile foundation using three-dimensional finite element model can be successfully performed using personal computer in reasonable elapsed time. The results showed the foundation responded in a sway mode with minor twisting about the vertical. The peak velocity of the platform was assessed against the performance criteria. A small amount of soil was mobilised and the strains were very small such that the shear modulus did not need to be degraded. This suggested that the soil stiffness, and possibly damping, for this foundation was independent of the machine operating frequency.

Further research such as a mesh convergence study, boundary effects and the element types may be investigated. A sensitivity study using different soil shear moduli and damping values may also be performed.

1

American Concrete Institute (ACI), "Foundations for Dynamic Equipment", ACI 351.3R-04, 2011.

2

R. Taherzadeh, D. Clouteau, R. Cottereau, "Simple formulas for the Dynamic Stiffness of Pile Groups", Earthquake Engineering and Structural Dynamics, John Wiley & Sons Ltd, 2002.

3

M. Novak, "Dynamic Stiffness and Damping of Piles", Canadian Geotechnical Journal, 11(4), 574-598, 1974. doi:10.1139/t74-059

4

M. Gohnert, I. Luker, C. Morris, "Designing Foundations with Piles for Vibrating Machinery", The Open Construction and Building Technology Journal, 2, 306-312, 2009. doi:10.2174/1874836800802010306

5

J. Howell, "Design of Deep Foundations", in P.J. Moore, (Editor), "Analysis and Design of Foundations For Vibrations", A.A. Balkema, 1985.

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