VIBRATION CONTROLS OF FOUNDATION

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Introduction of
DESIGN OF FOUNDATIONS FOR VIBRATION CONTROLS
Joseph E. Bowles, RE., S.E. 5th Edition
Consulting Engineer/Software Consultant
Engineering Computer Software
Peoria, Illinois

INTRODUCTION
Foundations supporting reciprocating engines, compressors, radar towers, punch presses, turbines, large electric motors and generators, etc. are subject to vibrations caused by unbalanced machine forces as well as the static weight of the machine. If these vibrations are excessive, they may damage the machine or cause it not to function properly. Further, the vibrations may adversely affect the building or persons working near the machinery unless the frequency and amplitude of the vibrations are controlled.

The design of foundations for control of vibrations was often on the basis of increasing the mass (or weight) of the foundation and/or strengthening the soil beneath the foundation base by using piles. This procedure generally works; however, the early designers recognized that this often resulted in considerable overdesign. Not until the 1950s did a few foundation engineers begin to use vibration analyses, usually based on a theory of a surface load on an elastic half-space. In the 1960s the lumped mass approach was introduced, the elastic half-space theory was refined, and both methods were validated.

The principal difficulty in vibration analysis now consists in determining the necessary soil values of shear modulus G' and Poisson's ratio JUL for input into the differential equation solution that describes vibratory motion. The general methods for design of foundations, both shallow and deep, that are subject to vibration (but not earthquakes) and for the determination of the required soil variables will be taken up in some detail in the following sections.

The piles provide additional spring and damping contributions to the system, so some means is necessary to incorporate the significant properties of the two materials into equivalent springs and damping factors. When we do this we can then use Eq. (20-4a) to obtain the solution (or the coupling concepts) for that vibration mode.
There are few theories and even fewer reported data from field performance studies on full scale dynamically loaded bases supported by pile foundations. For this reason the theories are substantially uncertain; however, rational estimates are better than simply guessing at the response.

It is generally accepted that using piles will:
1. Decrease geometric (or radiation) damping
2. Increase the resonant frequency fr and may also increase /„
3. Influence the amplitude near resonance
4. When laterally loaded, produce dynamic responses that are uncertain to estimate

EMBEDMENT EFFECTS ON DYNAMIC BASE RESPONSE

The previous methods of analysis considered the dynamic base on the ground surface. Most bases supporting machinery will be embedded some depth into the ground so as to be founded on more competent soil below the zone of seasonal volume change.

It is generally accepted from both a theoretical analysis and field measurements that placing the base into the ground affects the system response to excitation forces. It appears that embedment tends to increase the resonant frequency and may decrease the amplitude.

Several methods to account for vertical vibration exist, including those of Novak and Beredugo (1972), Dobry and Gazetas (1985), and as attributed to Whitman by Arya et al. (1979). Those of Novak and Beredugo and in Arya et al. are for round bases and will not be used here since rectangular base response is substantially different.

The Arya et al. (1979) reference is the only one the author located purporting to allow for rocking and sliding as well as vertical excitation. It is suggested, however, that rocking and sliding spring adjustments for depth should be used cautiously—if at all—for these reasons:

1. Rocking of the base into the side soil may produce a gap over time.
2. Sliding of the base into the side soil may produce gaps over time.
3. The space around the base would have to be carefully backfilled and compacted to provide
any appreciable side resistance unless the excavation was excavated and the base poured
without using concrete forms.
4. It is not uncommon, where wooden concrete forms are used, to leave them in place.
5. A slight adjustment for depth is automatically accounted for since the effective normal
stress at a depth is larger [see Eqs. (20-12) through (20-13)] so that G' is larger. This in
turn increases the computed soil springs.