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stress. Shear capacity of concrete is increased at higher field. However, the ability of analytical methods to account
confining stress and deep foundations are subjected to sig- properly for rock mass response and rockstructure interac-
nificant confinement, especially when they are embedded tion has not developed to the same level as methods used for
in rock. This is a topic that warrants research but has yet to deep foundations in soil.
be investigated in a meaningful way that can be applied to
foundation design. The survey shows that most state DOTs use the program
COM624 or its commercial version LPILE for design of
rock-socketed shafts. Review of the p-y curve criteria cur-
Axial rently built into these programs for modeling rock mass re-
sponse shows that they should be considered as "interim" and
When lateral loading is not significant, structural design of
that research is needed to develop improved criteria. Some of
concrete shafts must account for axial compression or ten-
this work is underway and research by North Carolina (Gabr
sion (e.g., uplift) capacity. For shafts designed for signifi-
et al. 2002), Ohio (Liang and Yang 2006), Florida (McVay
cant load transfer at the base, compression capacity of the
and Niraula 2004), and Ashour et al. (2001) is described. All
reinforced-concrete shaft could be less than that of the rock
of these criteria are in various stages of development and are
bearing capacity. In high-strength intact rock, compressive
not being applied extensively.
strength of the shaft may be the limiting factor. For design of
reinforced-concrete columns for axial compression, the
Models based on elastic continuum theory and developed
AASHTO-factored axial resistance is given by
specifically for rock-socketed shafts have been published.
Pr = 0.85 [ 0.85 f c
' ( Ag - Ast ) + f y Ast ]
Two methods reviewed in this chapter are the models of
(147)
Carter and Kulhawy (1992) and Zhang et al. (2000). Advan-
tages and disadvantages of each are discussed and compared
in which Pr = factored axial resistance, with or without flex-
with p-y methods of analysis. These models are most useful
ure; = resistance factor (0.75 for columns with spiral trans-
as first-order approximations of shaft lateral displacements
verse reinforcement, 0.70 for tied transverse reinforcement);
for cases where the subsurface profile can be approximated
fc' = strength of concrete at 28 days; Ag = gross area of the
as consisting of one or two homogeneous layers. For exam-
section; Ast = total area of longitudinal reinforcement; and
ple, when a preliminary analysis is needed to develop trial
fy = specified yield strength of reinforcement. One source of
designs that will satisfy service limit state deflection criteria,
uncertainty is that the design equations given here are for
the method of Carter and Kulhawy can provide convenient
unconfined reinforced-concrete columns. The effect of con-
solutions that can be executed by means of spreadsheet
finement provided by rock on the concrete strength is not
analysis. A disadvantage of these methods is that they do not
easy to quantify, but increases the strength compared with
directly provide solutions to maximum shear and moment,
zero confinement, and warrants further investigation.
parameters needed for structural design, and they do not in-
corporate directly the nonlinear properties of the reinforced-
SUMMARY concrete shaft.
Lateral loading is a major design consideration for trans- Structural issues associated with rock-socketed shafts are
portation structures and in many cases governs the design of reviewed. The concept of depth of fixity is shown to be a use-
rock-socketed drilled shafts. Design for lateral loading must ful analytical tool providing a link between geotechnical and
satisfy performance criteria with respect to (1) structural re- structural analysis of drilled shafts. A method for establish-
sistance of the reinforced-concrete shaft for the strength limit ing depth of fixity is presented and its use in the design
state and (2) deflection criteria for the service limit state. process is described. Other issues identified by the survey,
Analytical methods that provide structural analysis of deep including high shear in short sockets subjected to high
foundations while accounting for soilstructure interaction moment loading and its implications for reinforced-concrete
have, therefore, found wide application in the transportation design, are addressed.
