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66 Is based on well-established rock mass and soil properties; Considering that the p-y method is currently being used Is verified against rigorous theory, for elastic range; and extensively by most state DOTs, effort should be made to Provides shear and moment distribution for structural address its present limitation by research aimed at better es- design. tablishing methods to specify appropriate p-y curves in rock. Full-scale field load testing with instrumentation is the only Limitations include: known method to verify p-y curves. Research conducted for this purpose would provide an opportunity to evaluate and Requires numerical (computer) solution, not currently calibrate other proposed analytical methods; for example, available commercially; those of Carter and Kulhawy (1992) and Zhang et al. (2000) Requires a larger number of rock mass material para- and for development of new models. Recommendations for meters; research are discussed further in chapter five. The research Currently is limited to two layers (one soil and one rock programs sponsored by the North Carolina and Ohio DOTs mass layer, or two rock mass layers); and illustrate the type of approach that is useful for advancing all Nonlinear MEI behavior of reinforced-concrete shaft of the available methods of analysis. In addition to providing is not accounted for explicitly; requires iterative analy- improved criteria for p-y curve modeling, the load test results ses with modified values of EI. reported by Gabr et al. (2002) and Liang and Yang (2006) can be used to evaluate each other's models and the SW and The most rigorous analytical methods based on a continuum continuum models described in this chapter. approach are FEM. When implemented by competent users, FEM analysis can account for the shaft, soil, and rock mass In summary, a range of analytical tools are available to behaviors more rigorously than the approximate methods de- foundation designers to consider rock sockets under lateral scribed herein, but FEM analyses are not suitable for routine and moment loading. These include simple, closed-form design of foundations in most cases. First, the results are only equations requiring a small number of material properties as reliable as the input parameters. In most cases the material (Carter and Kulhawy 1992). A more rigorous model that properties of the rock mass are not known with sufficient reli- predicts the complete nonlinear response but requires more ability to warrant the more sophisticated analysis. Second, the material properties is also available (Zhang et al. 2000). design engineer should have the appropriate level of knowledge Highly sophisticated numerical models requiring extensive of the mathematical techniques incorporated into the FEM material properties and appropriate expertise (FEM analysis) analyses. Finally, the time, effort, and expense required for exist and may be appropriate for larger projects. The p-y conducting FEM analyses are often not warranted. For very method of analysis is attractive to designers, as evidenced by large or critical bridge structures, sophisticated FEMs may be its wide use; however, considerable judgment is required in warranted and the agency might benefit from the investment selection of p-y curve parameters. All of the currently avail- required in computer codes, personnel training, and field and able methods suffer from a lack of field data for verification laboratory testing needed to take advantage of such techniques. and are best applied in conjunction with local and agency ex- perience, thorough knowledge of the geologic environment, Subgrade reaction methods, as implemented through the and field load testing. p-y curve method of analysis, offer some practical advantages for design. These include: STRUCTURAL ISSUES Predicts the full, nonlinear lateral load-deformation response; Twenty of the questionnaire responses indicated that struc- Can incorporate multiple layers of soil and/or rock; tural design of drilled shaft foundations is carried out by en- Accounts for nonlinear MEI behavior of reinforced- gineers in the Bridge Design or Structures Division of their concrete shaft; state DOTs. Three states indicated that structural design is a Provides structural analysis (shear, moment, rotation, joint effort between the Geotechnical and Structural/Bridge and displacement) of the drilled shaft; Divisions. One DOT indicated that structural design is done Accounts for the effects of axial compression load on by the Geotechnical Branch. All of the states responding to the structural behavior of the shaft; and the structural design portion of the questionnaire stated that Can be implemented easily on a desktop computer with the AASHTO LRFD Bridge Design Specifications are fol- available software. lowed for structural design of drilled shafts. Three states also cited the ACI Building Code Requirements for Structural The principal limitations are: Concrete. Lack of a strong theoretical basis for p-y curves and Barker et al. (1991) discussed the structural design of Requires back analysis of instrumented load tests to reinforced-concrete shafts and have several design examples verify and validate p-y curves; such verification is cur- illustrating the basic concepts. O'Neill and Reese (1999) also rently lacking or limited to a few cases. covered the general aspects of reinforced-concrete design for

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67 drilled shafts, for axial compression loading and flexure, P P citing as primary references the 1994 AASHTO LRFD Bridge Design Specifications (1st edition) and the 1995 ACI Building M M Code Requirements for Structural Concrete (ACI 318-94). V V Both the AASHTO and ACI codes have since been revised (AASHTO in 2004 and ACI in 2002); however, there are no Top of Column y y major differences that would change the structural design of drilled shafts. According to the survey, all of the states are designing in accordance with the AASHTO LRFD Bridge Design Specifications. At the time of this writing, Section 10 (Foundations) of the draft 2006 Interim AASHTO LRFD Equivalent Bridge Design Specifications was available for reference. Fixed-end Deep However, the other sections of the 2006 Interim specifica- Column Foundation tions were not available and so comments pertaining to Sec- tion 5 are referenced to the 2004 edition. Only issues of struc- depth of fixity tural design pertaining specifically to rock-socketed drilled shafts are addressed here. FIGURE 47 Depth of fixity for equivalent fixed-end column. General Issues Section 10.8.3.9 ("Shaft Structural Resistance") of the 2006 depth of fixity based on the depth of the foundation and a Interim AASHTO LRFD Bridge Design Specifications states relative stiffness factor that depends on the flexural rigidity that of the pile and the subgrade modulus of the soil or rock. In- terviews with state DOT engineers indicated that different The structural design of drilled shafts shall be in accordance with criteria for establishing depth of fixity are being applied. One the provisions of Section 5 for the design of reinforced concrete. state DOT defines fixity as the depth at which LPILE analy- sis shows the maximum moment, whereas another defines This language makes it clear that drilled shaft structural fixity as the depth at which LPILE shows zero lateral deflec- design is subject to the same provisions as other reinforced- tion. In Section 12 of Bridge Design Aids (1990), the Massa- concrete members. The designer must then determine chusetts Highway Department) describes a rigorous ap- whether the shaft is a compression member or a member sub- proach involving use of the program LPILE (or other p-y jected to compression and flexure (beam column). Article analysis) to establish a depth of fixity as defined in Figure 47. 10.8.3.9.3 states the following: For the given soil/rock profile, approximate service loads are applied to the "Top of Column" (Figure 47). Shear and Where the potential for lateral loading is insignificant, drilled shafts may be reinforced for axial loads only. Those portions of moment are applied as separate load cases and the resulting drilled shafts that are not supported laterally shall be designed as lateral deflections and rotations at the top of the column are reinforced-concrete columns in accordance with Article 5.7.4. designated as follows: Reinforcing steel shall extend a minimum of 10 ft below the plane where the soil provides fixity. V = deflection due to shear (V) M = deflection due to moment (M) The commentary accompanying Article 10.8.3.9.3 states fur- V = rotation due to shear (V) ther that: M = rotation due to moment (M). A shaft may be considered laterally supported: below the zone of liquefaction or seismic loads, in rock, or 5.0 ft below the Equivalent column lengths are then calculated using the ground surface or the lowest anticipated scour elevation. . . . . following analytical expressions for each loading case. The Laterally supported does not mean fixed. Fixity would occur four resulting values of L should be approximately equal and somewhere below this location and depends on the stiffness of the supporting soil. the average value can be taken as a reasonable approxima- tion of the equivalent fixed-end column length. Depth of fix- The language in this provision could be improved by pro- ity corresponds to the portion of the fixed-end column below viding a definition of "fixity." Fixity is defined by Davisson groundline. (1970) for piles under lateral loading as the depth below 3V ( EI ) 1 3 groundline corresponding to the fixed base of an equivalent LV = (136) free-standing column; that is, a column for which the top V deflection and rotation would be the same as that of a column 2 M ( EI ) 1 2 supported by the embedded deep foundation (Figure 47). LM = (137) Approximate equations are given by Davisson for establishing M

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68 Moment Transfer 2V ( EI ) 1 2 LV = (138) Rock sockets subjected to high lateral and/or moment loading V require a minimum depth of embedment to transfer moment M ( EI ) to the rock mass and to satisfy minimum development length LM = (139) requirements for reinforcing steel. The mechanism of moment M transfer from a column to the rock is through the lateral The principal use of depth of fixity is to establish the resistance developed between the concrete shaft and the rock. elevation of equivalent fixed-end columns supporting the The resistance depends on many of the factors identified superstructure, thus enabling structural designers to uncou- previously, primarily strength and stiffness of the rock mass ple the foundations from the superstructure for the purpose of and flexural rigidity of the shaft. When the strength and mod- structural analysis and design of the bridge or other structure. ulus of the rock mass are greater than that of the concrete Structural modeling of the superstructure with equivalent shaft, the question may arise, why excavate such high qual- fixed-end columns is also used to establish the column loads. ity rock and replace it with lower strength concrete? The only These column loads are then used to analyze the drilled shaft means to transfer moment into the rock mass is through a foundations by applying them to the top of the actual col- properly designed shaft with the dimensions, strength, and umn, which is continuous with the foundation (left side of stiffness to transmit the design moment by the assumed Figure 47) using p-y analysis. As described at the beginning mechanisms of lateral resistance. In some situations where of this chapter, these analyses may be done by either the GD high strength rock mass is close to the ground surface, shaft or Bridge offices, but the soil and rock parameters are pro- size may be governed by structural considerations rather than vided by GD. The p-y analysis gives the maximum moment by geotechnical capacity. and shear that are used in the reinforced-concrete design. Use of software such as LPILE, COM624, or other programs For some relatively short, stubby shafts in hard rock, is thus seen to be an integral tool in both the geotechnical socket length could be governed by the required develop- and structural design of drilled shafts for bridges or other ment length of longitudinal reinforcing bars. Article 5.11 of transportation structures. As noted previously, AASHTO the AASHTO LRFD Bridge Design Specifications (2004) specifications define the strength limit state for lateral load- specifies basic tension development lengths for various bar ing only in terms of foundation structural resistance. Lateral sizes as a function of steel and concrete strengths. Because deflections as predicted by p-y analyses are used as a design the bars will be stressed to their maximum values at the tool to satisfy service limit state criteria. points where maximum moments occur, the distance between the point of maximum moment and the bottom of the socket The concept of fixity also has implications for reinforcing must be at least equal to the required development length. steel requirements of drilled shafts. According to Article As an example, for No. 18 bars, assuming fy = 414 MPa 10.8.3.9.3, as cited earlier, if a drilled shaft designed for axial (60 ksi) and fc' = 27.6 MPa (4 ksi), basic development length compression extends through soil for a distance of at least is 267 cm (105 in. or 8.75 ft). Although this is not often the 3 m (10 ft) beyond fixity before entering into rock, the rock- governing factor for socket length, it should be checked. socketed portion of the shaft does not require reinforcement. This provision would also limit the need for compression steel in rock sockets to a maximum depth of 3 m below fix- Shear ity. Exceptions to this are shafts in Seismic Zones 3 and 4, for which Article 5.13.4.6.3d states that "for cast-in-place Some designers commented on cases where p-y analysis of piles, longitudinal steel shall be provided for the full length laterally loaded rock-socketed shafts resulted in unexpectedly of the pile." high values of shear and whether the results were realistic. In particular, when a rock socket in relatively strong rock is Some state DOTs use permanent steel casing in the top por- subjected to a lateral load and moment at its head, values of tion of drilled shafts or, in many cases, down to the top of rock. shear near the top of the socket may be much higher than the Permanent casing is not mentioned in the 2006 Interim speci- applied lateral load. This result would be expected given the fications, but the 2004 specifications included the following mechanism of moment load transfer. When the lateral load statement: "Where permanent steel casing is used and the shell has a high moment arm, such as occurs in an elevated struc- is smooth pipe greater than 0.12 in. thick, it may be considered ture, the lateral load transmitted to the top of the drilled shaft to be load-carrying. Allowance should be made for corrosion." may be small or modest, but the moment may be relatively large. The principal mechanism of moment transfer from the A few states indicated that questions arise in connection shaft to the rock mass is through the mobilized lateral resis- with relatively short sockets in very hard rock. The questions tance. If a large moment is transferred over a relatively short pertain to moment transfer, development length of steel re- depth, the lateral resistance is also concentrated over a rela- inforcing, and apparently high shear loads resulting from tively short length of the shaft and results in shear loading high moment loading. that may be higher in magnitude than that of the lateral load.

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69 There is some question, however, whether high values of where Avs = area of shear reinforcement, s = longitudinal (ver- shear predicted by p-y methods of analysis for such cases tical) spacing of the ties or pitch of the spiral, and d = effective exist in reality or are artifacts of the analysis. One designer sug- shear depth. For a circular cross section this can be taken as gested that the structural model of the shaft does not account properly for shear deformation, resulting in unrealistically high B B d 0.9 + ls shear values. The topic requires further investigation. 2 (146) In some cases, the magnitude of shear must be addressed The need for additional transverse reinforcement, beyond in the reinforced-concrete design, primarily in the use of that required for compression, can be determined by Eq. 141. transverse reinforcement. According to AASHTO LRFD For the majority of rock-socketed shafts, the transverse rein- Bridge Design Specifications (2004), the minimum amount forcement required to satisfy compression criteria (Eq. 140) of spiral reinforcement to satisfy the requirements for com- combined with the shear resistance provided by the concrete pression is governed by (Eq. 142) will be adequate to resist the factored shear load- ing without the need for additional transverse reinforcement. Ag f ' However, in cases where high lateral load or moment are to s = 0.45 - 1 c (140) Ac f y be distributed to the ground over a relatively small distance; for example, a short stubby socket in high-strength rock, in which s = ratio of spiral reinforcement to total volume of factored shear forces may be high and the shaft dimensions concrete core, measured out-to-out of spirals; Ag = gross and reinforcement may be governed by shear. In these cases, (nominal) cross-sectional area of concrete; and Ac = cross- the designer is challenged to provide a design that provides sectional area of concrete inside the spiral steel. When shear adequate shear resistance without increasing the costs exces- occurs in addition to axial compression, the section is then sively or adversely affecting constructability by constricting checked by comparing the factored shear loading with the the flow of concrete. factored shear resistance, given by To handle high shear loading in the reinforced-concrete Vr = Vn = (Vc + Vs ) (141) shaft, the designer has several options: (1) increase the shaft diameter, thus increasing the area of shear-resisting concrete; in which Vr = factored shear resistance, Vn = nominal shear (2) increase the shear strength of the concrete; or (3) increase resistance, Vc = nominal shear resistance provided by the the amount of transverse reinforcing, either spiral or ties, to concrete, Vs = nominal shear resistance provided by the trans- carry the additional shear. Each option has advantages and verse steel, and = resistance factor = 0.90 for shear. The disadvantages. nominal shear strength provided by the concrete is given (in U.S. customary units) by: Two variables that can be adjusted to increase shear re- sistance are concrete 28-day compressive strength, f c ' , and Pu shaft diameter, B. Increasing the concrete strength can be a Vc = 2 1 + fc ' Av (142) 2, 000 Ag cost-effective means of increasing shear strength. For exam- ple, increasing fc' from 27.6 MPa to 34.5 MPa (4000 psi to or, when axial load is zero, 5000 psi) yields a 12% increase in shearing resistance. In- creasing the diameter of a rock socket can add considerably Vc = 2 f c ' Av (143) to the cost, depending on rock type, drillability, socket depth, etc. Rock of higher strength, which is likely to coincide with the case when shear is critical, can be some of the most ex- where Pu = factored axial load and Av = area of concrete in the pensive rock to drill. However, increasing the diameter can cross section that is effective in resisting shear. For a circular provide other benefits that may offset additional costs, such section this can be taken as as reducing the congestion of reinforcement steel (improved constructability), increasing axial and bending capacity, and B B Av = 0.9 B + ls (144) further limiting displacements. 2 Shear strength of the shaft can also be increased by in which B = shaft diameter and Bls = diameter of a circle providing additional transverse reinforcement in the form of passing through the center of the longitudinal reinforcement. either spiral or ties. From Eq. 145, this can be achieved by in- creasing the size of transverse reinforcement or by decreas- The nominal shear strength provided by transverse rein- ing the pitch(s). Constructability can be affected when bar forcement is given by spacings are too small to allow adequate flow of concrete. Avs f y d One aspect of reinforced-concrete behavior in shear that Vs = (145) s is not taken into account in any building code is confining