There are various methods of analysis for machine foundation. They include:
- Empirical methods
- Elastic half space method
- Lumped parameter method
- Barkan’s method
Among these methods lumped parameter method and barkan’s method are most popular widely used.
Empirical methods: – The empirical methods suggested by Tschebotarioff and Alpan can be used for preliminary design purpose for the different soil types. However, these methods can be used only to check the occurrence of resonance which in itself is not adequate for a satisfactory design.
Elastic Half Space Method:- In his method the soil is considered as semi-infinity isotropic elastic solid. The foundation is assumed to have a circular base of radius r0. For vertical vibration the method suggested by Richart is popular. The soil properties used in this method include shear modulus G, Poisson’s ratio µ and unit weight áµž. The theory predicts amplitude of motion resulting from a periodic force. In this theory two types of exciting force are considered. In one type amplitude exciting force is constant and in the other amplitude is dependent on exciting force. The theory makes use of certain mathematical simplification which are not quite realistic. However it serves as useful guide for a rational guide of evaluation the spring and damping constants which are utilized in Lumped Parameter Method.
Lumped Parameter Method:- In this approach mass of machine and mass of soil is taken a the lumped mass. Typical equivalent lumped parameter are given in figure 1 below.
This approach was developed by Lysmer (1965) and Lysmer and Richart (1966). Lysmer’s theory for the vertical response of a rigid circular foundation on the elastic half-space is expresses as: