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52 presented in the draft 2006 Interim AASHTO LRFD Bridge deformation. Research published over the past 25 years has Design Specifications are not the same as those originally resulted in methods for predicting ultimate side resistance of proposed by Horvath and Kenney (1979) and by Carter and shafts in rock that can be selected by a designer on the basis Kulhawy (1988), but are nonetheless attributed to those stud- of commonly measured geomaterial properties and that ac- ies. Furthermore, both studies have been superseded by more count for levels of uncertainty associated with the project. recent research. In future calibration studies for LRFD For example, Eq. 30 with C taken equal to 1.0 provides a con- applications and for updates of AASHTO specifications, servative estimate of side resistance for preliminary design consideration of alternative design equations for side resis- or for final design of small structures or at sites where no tance should be considered and the most up-to-date research additional testing is planned. If laboratory CNS testing is should be referenced. conducted to measure rockconcrete interface strength, higher values of side resistance can be justified for design. If The draft 2006 Interim AASHTO LRFD Bridge Design field load tests are conducted, they normally result in higher Specifications allow the use of methods other than those side resistance values than given by Eq. 30 (with C = 1.0) and given in Table 20, especially if the method is "locally recog- higher resistance factors are allowed by AASHTO for results nized and considered suitable for regional conditions . . . based on load tests. If field load testing demonstrates that a if resistance factors are developed in a manner that is consis- particular construction technique; for example, artificial tent with the development of the resistance factors for the roughening the walls of a socket, can increase side resistance, method(s) provided in these Specifications." then it may be possible to justify the use of Eq. 30 with val- ues of C higher than 1.0. AASHTO specifies resistance factors for base resistance based on the two methods given by the Canadian Geotechni- Rational methods are available for estimating ultimate cal Society (Canadian Foundation Engineering Manual base resistance of rock sockets. A first order approximation 1985). The first is according to Eqs. 6365 and is a straight- based on strength of intact rock is given by Zhang and forward method to apply, provided the rock satisfies the cri- Einstein (1998) (see Figure 33). For fractured rock, a rea- teria of being horizontally jointed and the appropriate para- sonable estimate can be made if the GSI (or RMR) is evalu- meters can be determined. Standard logging procedures for ated (see Figures 31 and 32). Although most states surveyed rock core would normally provide the required information. do not currently use GSI and RMR, the parameters required The second method is based on PMT and is given by Eq. 66. for its implementation can be obtained during the course of As noted in chapter two, only a few states reported using the standard core logging procedures. The method recom- PMT in rock. The third method for base resistance is O'Neill mended by CGS and adopted by AASHTO is applicable to and Reese (1999) and the two equations given by AASHTO moderately jointed sedimentary rocks, which is the most correspond to Eq. 43 of this report for massive rock and Eq. commonly encountered rock type for rock-socketed founda- 57 of this report for highly fractured rock. tions. A method based on PMT provides another practical approach for calculating base resistance. AASHTO also allows higher resistance factors on both side and base resistances when they are determined from a A source of uncertainty in rock-socket design stems from field load test. The cost benefits achieved by using a load test attempting to combine side and base resistances at a specific as the basis for design can help to offset the costs of con- value of downward displacement; for example, at the speci- ducting load tests. This issue is considered further in chapter fied limiting value of settlement or at the strength limit state. five. Finally, AASHTO recommends that all of the resistance A relatively straightforward analysis based on elastic contin- factors given in Table 20 be reduced by 20% when used for uum theory, as given by Carter and Kulhawy (1988), is pre- the design of nonredundant shafts; for example, a single shaft sented in the form of closed-form expressions that predict supporting a bridge pier. axial load-deformation and base load transfer for typical conditions encountered in practice. Similar analytical ap- SUMMARY proaches for IGMs are given by O'Neill and Reese (1999). These equations are easily implemented in spreadsheet or The principal factors controlling the behavior of rock-socketed other convenient form and allow designers to make rational foundations under axial loading are identified and discussed. estimates of load carried by both side and base at specified It is concluded from this study that sufficient tools are cur- displacements. The survey questionnaire shows that this rently available for transportation agency personnel to design method is used by some state DOTs. The approach should be rock-socketed shafts for axial loading conditions that provide evaluated further against field load test measurements and, if adequate load carrying capacity without being overly con- verified, used more widely. Alternatively, the design charts servative. given in Rowe and Armitage (1987a,b) provide a rational means of estimating axial load-displacement behavior and The principal performance design criteria for axial load- base load transfer. The charts are based on rigorous numeri- ing are (1) adequate capacity and (2) ability to limit vertical cal modeling and are the benchmark against which the Carter

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53 and Kulhawy closed-form expressions were evaluated. How- Methods for calculating nominal (ultimate) unit side and ever, the charts are more cumbersome to use. A computer base resistances and associated resistance factors according program that models the full load-displacement curve, to the Interim 2006 AASHTO LRFD Bridge Design Specifi- ROCKET, is available, but requires input parameters that cations are summarized in Table 20. Considering the infor- normally are not determined by transportation agencies, such mation identified by the literature review, in particular recent as triaxial strength properties and socket roughness param- studies on correlation equations for unit side resistance, a eters. However, for agencies interested in obtaining the suggested improvement in future specifications would be to required material properties, this program offers an effective consider design methods recommended by the more recent method for axial load-deformation analysis. studies for inclusion and calibration to LRFD.