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

2.3 Richart-Whitman Model

Figure 2.2.1 Equivalent Radius of Rectangular Foundation and Degrees of Freedom

Richart and Whitman 1967 introduced a model to calculate the soil empidance parameters with simple frequency-independent formulas for both circular and rectangular footings.

Stiffness Constants

Richart and Whitman 1967 introduced the equations to calculate the spring constants and damping for a rigid circular and rectangular footings, these values are shown in Table 2.3.1.

Table 2.3.1 Richart Model Stiffness Constants

DOFCircularRectangular
Vertical kv k_v
41−νGR \frac{4}{1- \nu} GR
G1−νβvab \frac{G}{1- \nu} \beta_v \sqrt{ab}
Horizontal ku k_u
32(1−ν)(7−8ν)GR \frac{32(1-\nu)}{(7- 8 \nu)} GR
2(1+ν)Gβuab 2(1 + \nu ) G \beta_u \sqrt{ab}
Rocking kψ k_{\psi}
83(1−ν)GRψ3 \frac{8}{3(1- \nu)} GR^3_{\psi}
G(1−ν)βψba2 \frac{G}{(1- \nu)} \beta_{\psi} b a^2
Torsion kη k_{\eta}
163GRη3 \frac{16}{3} GR^3_{\eta}

In Table 2.3.1, G G is the dynamic shear modulus of the soil, psi (MPa), ν \nu is Poisson's ratio of the soil, R R is the radius of the circular footing, and a,b a, b are the horizontal dimensions of the retangular footing.

The values of the parametrs βi \beta_i in Table 2.3.1 was introduced by Richart in a graphical form as a function of the footing aspect ratio L/B.

βi \beta_i Calculator

The values of the parametrs βi \beta_i in Table 2.3.1 can be calculated with the convienient calculator below.

Input the values for the rectangular footing horizontal dimensions:
Results:

L/B= L/B = 1.00

βu(Horizontal)= \beta_{u} \text{(Horizontal)}= 1.0

βv(Vertical)= \beta_{v} \text{(Vertical)} = 2.1

βψ(Rocking)= \beta_{\psi} \text{(Rocking)} = 0.5

Observations

Richart-Whitman Model has limited applications in practice, so we will not discuss it in further detail.