Gazetas

Gazetas equations for shallow foundation stiffness as summarized in ATC-40

Stiffness

Equation Surface Stiffness

Vertical Translation

Horizontal Translation (toward long side)

GL 

  B   K  Z  ' = 0.73 + 1.54  1 − v    L 

0 .75

  

GL 

0 .85

  

GL 

0 .85

 GL     B   + 0.11 −   0.75 − v     L 

  B   K Y  ' = 2 + 2.5  2 − v    L 

Horizontal Translation (toward short side)

  B   K  X  ' = 2 + 2.5  2 − v    L 

Rotation about x-axis

 B    L     K θ  x ' =  I  X     2.4 + 0.5   L  1− v   B       L  0.15  G 0.75  K θ  y ' =  I Y  3   1− v    B  

Rotation about y-axis

G

0 .25

0.75

Stiffness Embedment Factors Embedment Factor, Vertical Translation

Embedment Factor, Horizontal Translation (toward long side)

Embedment Factor, Horizontal Translation (toward short side)

Embedment Factor, Rotation about x axis

Embedment Factor, Rotation about y axis

0.67  D f      B     2 L + 2 B    e Z  = 1 + 0.095  H   1 + 1.3  1 + 0.2  B    L       LB     0.4        H   0.5    D f  − 2 16( L + B ) H     2 D f            1 + 0.52    eY  = 1 + 0.15 2  B  BL                 0.4        H   0.5  ( )  D  L  B  H  − + 16    f  2      2 D f              1 + 0.52 e X  = 1 + 0.15  LB 2        L              2 H    d    −0.2  B 0.5   H          eθ  X  = 1 + 2.52 1+        B  B   D f      L      −0.60 0.60   1.9      H   2 H     2 H      eθ Y  = 1 + 0.92 1.5 +       D f       L       L        

Where, K i = Uncoupled Total Surface Stiffness for a rigid plate on a semi-infinite homogeneous elastic half-space, ei = Stiffness Embedment Factor for a rigid plate on a semi-infinite homogeneous elastic half space, L = foundation length, B = foundation width, D f  = depth of embedment, H = foundation thickness, G = Shearing Modulus, υ = Poisson’s ratio.