Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 530

CG of superstructure

Rigid link to sot

Foundation node

Column elements
(number depends
on height)
Footing elements
Foundation springs
(if used)

Figure 17.12 Illustration of a spine model.

In either spine or grillage model, elements are defined with superstructure
simplified, substructure with ends released, fixed or directly modeled
through soil spring elements, and proper connectivity between super-
and substructures. A close-view illustration of such model is shown in
Figure 17.12. The superstructure is represented by a single line (spine
model) or multilines (grillage model) of 3D frame elements, which pass
through the center of gravity (CG) of the superstructure. Each of the col-
umns and the cap beam are represented by 3D frame elements, which pass
through the geometric centers and midheight, respectively. Rigid end zone
can be used to account for the offset between the centerline of the cap beam
and the soffit of the superstructure.

17.3.2 soil stiffness
Abutment may provide longitudinal stiffness K eff due to passive soil pres-
sure uniformly distributed over the height ( H w ) and width ( W w ) of the back-
wall or diaphragm.

P = p H W (17.21)

p p w w

For integral- or diaphragm-type abutments, equivalent linear secant stiff-
ness K eff is

P
F H

p

K

eff =

)

(17.22)

(

w w

where F w is a factor taken between 0.01 and 0.05 for soils ranging from
dense sand to compact clays.
The foundation modeling methods (FMMs) adopted are depending on
their SDC where FMM I is for SDCs B and C while FMM II is for SDC
D (Table 17.3). There are two ways to determine the foundation stiffness