for the respective *t *= 1 s and *t *= 1000 s responses

Sealant A

Sealant B

0.2

of sealant A, and *E *= 330 kPa and *E *= 170 kPa for

d/w = 0.5

d/w = 0.5

the 1 s and 1000 s responses of sealant B. The

0

analyses were conducted to allow comparison of

predictions of eq 7 with the more realistic nu-

0.2

merical results. The general nonlinearity of the

1 s Response

0.4

1000 s Response

finite element predictions and the effect that the

depth-to-width ratio has on the behavior are in-

0.4

deed captured by the eq 7 approximation. For

Sealant A

Sealant B

d/w = 1

d/w = 1

0.2

compressive strains the differences between the

predictions in Figure 5 are typically less than 10%.

0

For extensive strains, however, the eq 7 relation

0.2

predicts considerably stiffer responses than the

finite element analyses. As indicated in Figure 5,

0.4

the eq 7 predictions are closest to the numerical

0.6

results for the *d/w *= 0.5 and *d/w *= 1 seals. In this *d/*

Sealant A

Sealant B

0.4

d/w = 2

d/w = 2

parisons indicate that the Payne/Gent and Lindley

0

equation would provide conservative estimates

of the average bond stress that are roughly 20

0.4

30% high.

The small and large deformation relations of

0.8

eq 5 and 7 indicate that butt joint seals with large

0.2 0.1

0

0.2

0.1

0.2 0.1

0

0.1

0.2

e

e

depth-to-width ratios should be avoided. It should

be noted that, for asphalt pavement crack seals,

these relations provide a structural analysis-based

argument for preparing a joint at a crack rather

ample for an asphalt pavement crack seal design,

illustrating the use of eq 5 and 7, is presented in

Appendix A.

vided by the elastic modulus *E*, which is a func-

tion of the depth-to-width ratio. Predictions for

Equation 4 gives the normal stress distribution

compressions and extensions up to 0.25 are de-

at the interfaces between the seal and the joint for

picted. In the latter figure, predictions are shown

small deformations. The corresponding tangen-

for three depth-to-width ratios: 2, 1, and 0.5. The

tial stress distribution *t*y (*y*) is found, as suggested

curves in both figures demonstrate the nonlinear

stressstrain response predicted by the Payne/

by Gent et al. (1974), from the pressure distribu-

Gent and Lindley expression, and the curves in

tion *p*(*y*) according to

Figure 5 further demonstrate the effect of increas-

ing *d/w *values on the average bond stress acting

2* y*

on a seal.

Figure 5 also includes results from large defor-

(8)

= -2

mation numerical analyses of butt joint seals.

These analyses were finite element analyses, us-

Expressions like eq 4 and 8 for bonded rubber

ing the commercially available software ABAQUS

cylinders have been derived and validated by

(Hibbitt, Karlsson, and Sorenson, Inc. 1993), that

experiment by Gent et al. (1974).

incorporated strain energy constitutive models of

two silicone sealants at 0C for 1 s and 1000 s

The normal and tangential stress distributions

are illustrated in Figure 6 for the *d/w *values 4, 2, 1,

relaxation times (Ketcham et al. 1996). The seal-

and 0.5. The stresses, per unit nominal strain, are

ants are designated "sealant A" and "sealant B"

shown in a nondimensional form divided by the

in Figure 5. The measured Young's moduli of the

sealants at 0C were *E *= 540 kPa and *E *= 350 kPa

elastic modulus *E *as a function of the position *y/d*

5