Integral bridges - Computational Analysis and Design of Bridge Structures - page 501

n is the shape parameter
y is the lateral displacement of the pile
y u is the ultimate lateral displacement

Alternatively, the guidelines by the American Petroleum Institute (API)
(1993) are used to develop the P-y curves, which represent the stiffness for
the nonlinear springs substituting the soil around the piles. The P-y rela-
tionship is a hyperbolic tangent curve defined as follows:

kz
AP y

P = A P tanh

(16.5a) u

u

where:
P u is the ultimate bearing capacity
k is the parameter defined by φ angle of internal friction
z is the depth in the soil
y is the lateral displacement of the pile
A is the parameter that varies with soil depth in case of static loading
according to Equation 16.5a

X
D

A 3 0 0 8 . . 0 9 .

= − ≥ (16.5b)

where:
X is the soil depth
D is the average pile length

16.3.2.2 Soil behind the abutment
The soil-structure interaction is modeled by attaching linear springs at the
selected nodes of the abutment and piles. The springs simulate the effect of
the abutment fill on the bridge. As shown in Figure 16.9, the number of soil
springs behind the abutment depends on the size of the tributary area each
spring represents.
Using the design curves by National Cooperative Highway Research
Program (NCHRP, Barker 1991), passive and active earth pressure effects
behind the abutment can be modeled for the soil with the corresponding
unit weight and φ angle of internal friction.

16.3.2.3 Soil around piles
Figure 16.10 shows the soil-pile interaction where the soil is idealized by
three sets of springs: lateral springs k h , vertical springs k v , and a point spring k q .
Table 16.1 lists the parameters for soil spring (Greimann and Wolde-Tinsae
1988).