Page 172 - Civil Engineering Formulas

PILES AND PILING FORMULAS 109

thickness of the consolidating soil layers penetrated by the piles, and their
undrained shear strength, respectively. Such forces as Q gd could only be
approached for the case of piles driven to rock through heavily surcharged,
highly compressible subsoils.
Design of rock sockets is conventionally based on

2
Q d
d s L s f R d s q a (4.13)
4
where Q allowable design load on rock socket, psi (MPa)
d
d socket diameter, ft (m)
s
L socket length, ft (m)
s
f allowable concrete-rock bond stress, psi (MPa)
R
2
q allowable bearing pressure on rock, tons/ft (MPa)
a
Load-distribution measurements show, however, that much less of the load
goes to the base than is indicated by Eq. (4.6). This behavior is demonstrated
by the data in Table 4.1, where L /d is the ratio of the shaft length to shaft
s
s
diameter and E /E is the ratio of rock modulus to shaft modulus. The finite-
r
p
element solution summarized in Table 4.1 probably reflects a realistic trend if
the average socket-wall shearing resistance does not exceed the ultimate f R
value; that is, slip along the socket side-wall does not occur.
A simplified design approach, taking into account approximately the compati-
bility of the socket and base resistance, is applied as follows:
1. Proportion the rock socket for design load Q with Eq. (4.6) on the assump-
d
tion that the end-bearing stress is less than q [say q /4, which is equivalent to
a
a
2
assuming that the base load Q b (
/4) d s q a /4].
2. Calculate Q RQ , where R is the base-load ratio interpreted from Table 4.1.
b
d
3. If RQ does not equal the assumed Q , repeat the procedure with a new q a
b
d
value until an approximate convergence is achieved and q q a .
The final design should be checked against the established settlement tolerance
of the drilled shaft.
Following the recommendations of Rosenberg and Journeaux, a more realis-
tic solution by the previous method is obtained if f Ru is substituted for f . Ideally,
R
f Ru should be determined from load tests. If this parameter is selected from data
that are not site specific, a safety factor of at least 1.5 should be applied to f Ru in
recognition of the uncertainties associated with the UC strength correlations.*
FOUNDATION-STABILITY ANALYSIS
The maximum load that can be sustained by shallow foundation elements at
incipient failure (bearing capacity) is a function of the cohesion and friction
angle of bearing soils as well as the width B and shape of the foundation.
*Rosenberg, P. and Journeaux, N. L., “Friction and End-Bearing Tests on Bedrock for High-
Capacity Socket Design,” Canadian Geotechnical Journal, 13(3).