Machine Foundations

Chapter 2. Block Foundation

Chapter 2
2.1 Description of Block Foundation?2.2 Dynamic Impedance Models2.3 Richart-Whitman Model2.4 Veletsos Model2.5 Veletsos Model Calculator2.6 Examples

2.2 Dynamic Foundation Impedance Models

Figure 2.2.1 Equivalent Radius of Rectangular Foundation and Degrees of Freedom

In the literature, there are many models to calculate the impedance of block foundation. Among these models, we will only introduce two models, Richart-Whitman and Veletsos Models. Each model has its advantages and disadvantages that makes it suitable for some certain situations. The degrees of freedom are illustrated in Figure 2.2.1

Both of the models that will be introduced to calculate the impedance of block foundation is based on a circular foundation disc. However, a rectangular foundation shape can be converted to an equivalent circular shape using the following formulas,

DirectionRadiusEquation
Translation
R=abπ R = \sqrt{\frac{ab}{\pi}}
(2-1)
Rocking about X
Rψa=ab33π4 R_{\psi_a} = \sqrt[4]{\frac{ab^3}{3 \pi}}
(2-2)
Rocking about Z
Rψb=a3b3π4 R_{\psi_b} = \sqrt[4]{\frac{a^3 b}{3 \pi}}
(2-3)
Torsion about Y
Rη=ab(a2+b2)6π4 R_{\eta} = \sqrt[4]{\frac{ab(a^2 + b^2)}{6 \pi}}
(2-4)

Observations

If the foundation that is being analyzed is circular, then the radius can be used directly to calculate the impedance as it will be shown in the next aections. However, if the footing shape is rectangle, then the equations listed in the table above must be used to obtain the equivalent radius that can then be used in the equations.