Integral bridges - Computational Analysis and Design of Bridge Structures - page 500

bridge deck, abutment walls, girders, and cross members at the piers are
idealized using four-node shell elements, piles and remaining cross mem-
bers are modeled as beam elements. The soil backfill and the piles, fixed at
their base, support the abutments.

16.3.2.1 Soil spring and p - y curve
To allow the stiffness of the deck-girder connection to be varied, spring
tied elements are employed at their interface. Nonlinear spring elements
model the soil backfill as well as the soil around the piles. A set of p - y
curves may be generated using the modified Ramberg-Osgood model as
shown in Figure 16.8 for different types of soil, particularly very stiff clay,
loose sand, and dense sand. Similar curves for f - z (load-slip) and q - z (pile
tip load-settlement) are also generated using the same modified Ramberg-
Osgood model. Based on Greimann and Wolde-Tinsae (1988), the modified
Ramberg-Osgood model can be used to approximate the p-y , f-z , and q-z
soil displacement-resistance curves as follows:

k y

h

P (16.4a)

=

n

1 + y y

n

u

where:

P
k

u
h

(16.4b)

y =

u

where:
k h is the initial lateral stiffness
P is the generalized soil resistance
P u is the ultimate lateral soil resistance

P u

k h

Modified Ramberg-Osgood

P

Elastic-perfectly plastic

y u

y

Figure 16.8 The modified Ramberg-Osgood curve for a typical P - y curve.