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70 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.