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Rock-Socketed Shafts for Highway Structure Foundations (2006)

Chapter: Chapter Three - Design for Axial Loading

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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
×
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Suggested Citation:"Chapter Three - Design for Axial Loading." National Academies of Sciences, Engineering, and Medicine. 2006. Rock-Socketed Shafts for Highway Structure Foundations. Washington, DC: The National Academies Press. doi: 10.17226/13975.
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33 SCOPE A rock-socketed drilled shaft foundation must be designed so that the factored axial resistance is not less than the effects of the factored axial loads. At the strength limit state, side and base resistances of the socketed shaft are taken into account. Design for the service limit state accounts for tolerable movements of the structure and requires analysis of the axial load-deformation response of the shaft. In this chapter, cur- rent understanding of rock socket response to axial loading is summarized, based on a literature review. Analysis methods for predicting axial load capacity and axial load- displacement response of shafts in rock and IGM are then reviewed and evaluated for their applicability to highway bridge practice. RELATIONSHIP TO GEOMATERIAL CHARACTERIZATION Design for axial loading requires reliable site and geoma- terial characterization. Accurate geometric information, especially depth to rock and thickness of weathered and unweathered rock layers, is essential for correct analysis of axial resistance. This information is determined using the tools and methods outlined in the previous chapter, princi- pally core drilling supplemented by geophysical methods. Rock mass characterization using the Geomechanics System (Bieniawski 1989) provides a general framework for assess- ing the overall quality of the rock mass and its suitability as a foundation material. Engineering properties of the intact rock and the rock mass are used directly in the analysis methods described in this chapter. For example, empirical relation- ships have been derived between rock-socket unit-side resis- tance and uniaxial strength of intact rock. Base capacity, analyzed as a bearing capacity problem, may require uniax- ial compressive strength of intact rock, shear strength of discontinuities, or the Hoek–Brown strength parameters of fractured rock mass, depending upon the occurrence, orien- tation, and condition of joint surfaces in the rock mass below the base. For analysis of axial load-displacement response, the rock mass modulus is required. Modulus may be deter- mined from in situ testing, such as pressuremeter or borehole jack tests, or estimated from rock mass classification param- eters as summarized in Table 12. Engineering properties of rock mass used in conjunction with LRFD methods should be mean values, not minimum values sometimes used in geo- technical practice. Several methods proposed in recent years for analysis of both axial and lateral load response of rock sockets require, as an input parameter, the GSI proposed by Hoek et al. (1995, 2002). GSI is also correlated to the parameters that establish the Hoek–Brown strength criterion for fractured rock masses. Although GSI is not widely used in foundation engineering practice at the present time, it likely will become a standard rock mass characteristic for rock-socket design. LOAD TRANSFER BEHAVIOR OF ROCK SOCKETS Compression Loading A compressive force applied to the top (head) of a rock- socketed drilled shaft is transferred to the ground through (1) shearing stress that develops at the concrete–rock inter- face along the sides of the shaft and (2) the compressive nor- mal stress that develops at the horizontal interface between the base of the shaft and the underlying rock. A conceptual model of the load transfer can be illustrated by considering a generalized axial load versus displacement curve as shown in Figure 19 (Carter and Kulhawy 1988). Upon initial loading, shearing stress develops along the vertical shaft–rock inter- face. For a relatively small load, displacement is small and the stress–strain behavior at the shaft–rock interfaces is linear (line OA). There is no relative displacement (“slip”) between the concrete shaft and surrounding rock and the sys- tem may be modeled as being linearly elastic. With increas- ing load, the shear strength along some portion of the shaft sidewall is exceeded, initiating rupture of the “bond” and rel- ative slip at the shaft–rock interface. The load-displacement curve becomes nonlinear as rupture, and slip progress and a greater proportion of the applied load is transferred to the base (line AB). At some point, the full side resistance is mobilized, and there is slip along the entire surface (“full slip” condition), and a greater proportion of the applied load is transferred to the shaft base (beyond point B in Figure 19). If loading is continued to a displacement sufficient to cause failure of the rock mass beneath the base, a peak compressive load may be reached. In practice, design of drilled shafts in rock requires consideration of (1) deformation limits and (2) geotechnical and structural capacity (strength limit states). Geotechnical capacity in compression is evaluated in terms of limiting side and base resistances. Load transfer in uplift involves the same mechanisms of side resistance mobilization as described previously for compression. CHAPTER THREE DESIGN FOR AXIAL LOADING

A rigorous model for the behavior of a rock-socketed drilled shaft under axial compression would provide a pre- diction of the complete load-displacement curve. In reality, the mechanisms of side and base load transfer are complex and can only be modeled accurately through the use of so- phisticated numerical methods, such as finite-element or boundary-element methods. Input parameters required for accurate modeling are not normally available for design. In recent years, several researchers have presented simplified methods of analysis that provide bounds on the expected and observed behaviors for shafts that fall within the range of conditions typically encountered in practice. Methods most relevant to rock-socketed bridge foundations are presented in this chapter. Some of the more important behavioral aspects pertaining to side and base resistance and their mobilization are described first. Side Resistance Mechanisms The conditions of the sidewall interface determine the strength and load transfer in side resistance. Side resistance often exhibits a “bond” component that may exist physically as a result of the cementation between the concrete and rock and from mechanical interlocking between asperities along the interface. If the shearing strength of the interface is mod- eled as a Mohr–Coulomb material, the bond component can be considered as the interface adhesion, c. If displacements are sufficient, the interface bond is ruptured and the cohesion component of resistance may be diminished. The second mechanism of resistance is frictional. Physically, the fric- tional resistance can have two components. The first is the sliding friction angle of the interface, φ. The second is mechanical dilatancy, which can be described as an increase in the interface normal stress in response to the normal displacement (dilation) required to accommodate shear dis- placement of a rough surface. For mathematical simplicity, dilatancy can be quantified in terms of the angle of dilation (ψ), where ψ corresponds to the average angle of triangular 34 asperities from the direction of shear displacement. The in- terface shear strength (τ) is then given by τ = c + σn tan (φ + ψ) (18) in which σn = interface normal stress. Physically, all three components of strength (c, φ, ψ) may vary with displace- ment. The initial shear strength may have both cohesive and frictional components. Following rupture, the cohesion is probably decreased and dilation is mobilized. With further displacement, dilation may cease and resistance may be purely frictional and correspond to the residual friction angle. In addition, field conditions of construction can significantly affect the nature of the sidewall interface and, in practice, will determine the relative contributions of cohesion, fric- tion, and dilatancy to shearing resistance. For example, the bond (adhesion) may be partially or completely prevented by the presence of drilling slurry, or by “smearing,” which occurs in some argillaceous rocks or in rocks that are sensi- tive to property changes in the presence of water. Dilatancy is a function of interface roughness and shear strength of the intact rock forming the asperities. Sidewall roughness is determined in part by rock type and texture, but can also be affected by construction tools and practices. Practices that result in a “smooth” sidewall will reduce dilatancy compared with practices that provide a “rough” sidewall (Williams and Pells 1981; Horvath et al. 1983). Johnston and Lam (1989) made detailed investigations of the rock–concrete interface with the goal of better under- standing the factors that determine interface roughness and its influence on side-load transfer. Figure 20a shows an ide- alized section of a rock socket following construction. An initial normal force exists between the rock and concrete. When the shaft is loaded vertically, the shearing resistance develops and the rock mass will deform elastically until slip occurs. Figure 20a and b show the positions of the shaft before and after slip displacement. These two conditions are represented by 2-D models in Figure 20c and d, respectively. Figure 20d illustrates the dilation that occurs as a result of geo- metrical constraints. Dilation occurs against the surrounding rock mass, which must deform to compensate for the increase in socket diameter, resulting in an increase in the interface normal stress. The average normal stress increase (Δσn) can be approximated using the theoretical solution that describes expansion of an infinite cylindrical cavity, as follows: (19) where EM and ν are the rock mass modulus and Poisson’s ra- tio, respectively; Δr is the dilation, and r is the original shaft radius. A normal stiffness K can be defined as the ratio of normal stress increase to dilation, as follows: (20)K r E r n M = = +( ) Δ Δ σ ν1 Δ Δσ ν n ME r r = +1 Settlement, wc Lo ad , Q c B Linear elastic Progressive slip Full slip O A FIGURE 19 Idealized load-displacement behavior.

35 Assuming the deformation Δr is small compared with r, and EM and v can be considered to be constant for the stress range considered, it follows that the behavior of the rock–concrete interface is governed by CNS conditions. This concept forms the basis of the CNS direct shear test, in which the normal force is applied through a spring (Johnston et al. 1987; Ooi and Carter 1987). Shaft Geometry and Relative Rigidity Load transfer in a rock socket depends on the geometry, expressed by the embedment ratio (depth/diameter), and the stiffness of the concrete shaft relative to stiffness of the sur- rounding rock mass. Figure 21, based on finite-element analysis, illustrates this behavior for the initial (no slip) part of the load-displacement curve. In Figure 21, L = socket length, D = shaft diameter, Ep = modulus of the shaft, Er = modulus of rock mass above the base, Eb = modulus of rock mass below the base, Qb = load transmitted to the base, and Qt = load applied to the head of the shaft. The portion of ap- plied axial compressive load that is transferred to the base is shown as a function of embedment ratio and modulus ratio. With increasing embedment ratio, the relative base load transfer decreases. For embedment ratios of 10, less than 10% of the applied load is transferred to the base. The effect of modulus ratio is more significant at lower embedment ratios and, in general, base load transfer increases with in- creasing modulus ratio. Cases that result in the most base load transfer correspond to low embedment ratio with high modulus ratio (shaft is rigid compared to rock mass); whereas the smallest base load transfer occurs at higher em- bedment ratios and low modulus ratio (stiff rock mass). The proportion of load transferred to the base will also vary with the stiffness of the rock mass beneath the base of the shaft relative to the stiffness of the rock along the side. In many situations, a rock socket is constructed so that the base elevation corresponds to relatively “sound” or “intact” rock, and it may be necessary to excavate through weathered or fractured rock to reach the base elevation. In that case, the modulus of the rock mass below the base may be greater than that of the rock along the sidewall of the socket. Osterberg and Gill (1973) demonstrate the difference in load transfer in side and base resistances for two conditions, one in which the base modulus is twice that of the sidewall rock modulus and one where the base rock has a much lower modulus than that of the rock surrounding the shaft side. Their results show that base load transfer increases as the ratio Eb/Er increases (Figure 22). Load transfer is affected significantly by the roughness of the sidewall interface. Fundamentally, this can be explained by the higher load transfer in side shear reducing the propor- tion of load transferred to the base. Because side resistance increases with interface roughness, rock sockets with higher interface roughness will transfer a higher proportion of load in side resistance than smooth sockets. The complex interre- lationships between load transfer, interface roughness, mod- ulus ratio, and embedment ratio have been studied by several researchers, and the reader is referred to Pells et al. (1980), Williams et al. (1980), Rowe and Armitage (1987a), and Seidel and Collingwood (2001) for more detailed discus- sions. Six state DOTs indicated the use of grooving tools or other methods to artificially roughen the sidewalls of rock- socketed shafts. FIGURE 20 Idealized rock–concrete interface under axial loading (Johnston and Lam 1989). FIGURE 21 Theoretical base load transfer (Rowe and Armitage 1987b).

Base Condition In many cases encountered in practice there is uncertainty about conditions at the base of the shaft. Most transporta- tion agencies include, in their drilled shaft specifications, limits on the amount of drill cuttings, water, or slurry that is permissible at the base before concrete placement (Survey Question 34). However, compliance is not always verified and in some cases there is a perception that it is not practical to clean or inspect the base of the socket. In these cases, the designer may assume that base resistance will not develop without large downward displacement and for this reason base resistance is sometimes neglected for design purposes. Ten states indicated in their responses to Question 14 of the survey that rock-socketed shafts are sometimes designed under the assumption of side resistance only. The draft Interim 2006 AASHTO LRFD Bridge Design Specifications state that “Design based on side-wall shear alone should be considered for cases in which the drilled hole cannot be cleaned and inspected or where it is determined that large movements of the shaft would be required to mobilize resistance in end bearing.” Table 16 lists the most common reasons cited by foundation designers for neglecting base resistance in design, along with actions that can be taken to address the concern. Crapps and Schmertmann (2002) suggest that accounting for base resistance in design and using appropriate construc- 36 tion and inspection techniques to ensure quality base condi- tions is a better approach than neglecting base resistance. The authors support their recommendations with field load test results in which load transferred to the base was measured. The database consisted of 50 Osterberg load cell (O-cell) tests and 22 compression tests in which the load was applied to the top of the shaft. Of those, 30 of the O-cell tests and 4 of the top load tests were conducted on rock-socketed shafts. Eight of the O-cell tests (27%) showed evidence of bottom disturbance in the O-cell load-displacement curves. Results from the 34 tests are plotted in Figure 23 in terms of base load ratio (Qb = base load, Qt = actual top load or top load inferred from the O-cell test) versus socket-effective depth-to-diameter ratio (L/B). For some of the shafts, multiple measurements are included at different values of load and displacement. However, all of the base load ratio values correspond to downward displacements at the top of the shaft that range from 2.5 mm to 25.4 mm, with most in the range of from 3 to 15 mm. These values are within the service limit state for most bridge foundations. Additional details regarding the test shafts, subsurface profiles, and load test interpretation are given in Crapps and Schmertmann (2002). Several important observations arise from the data shown in Figure 23. First, base resistance mobilization represents a sig- nificant contribution to overall shaft resistance at downward displacements corresponding to typical service loads. Second, the magnitude of base resistance is generally greater than pre- dicted by elasticity-based numerical solutions (e.g., compare with Figure 21). The dashed lines in Figure 23 represent ap- proximate upper and lower bounds to the data from top load tests and O-cell tests without bottom disturbance. For the most part, O-cell tests that exhibited bottom disturbance fall below the lower-bound curve. Although the data are not sufficient to provide design values of base load transfer in advance for a given situation, they provide compelling evidence that shaft design in rock should account properly for base resistance, and that quality construction and inspection aimed at minimizing base disturbance can provide performance benefits. Time Dependency Time-dependent changes in load transfer may occur in rock- socketed shafts under service load conditions. Ladanyi (1977) reported a case in which the bearing stress at the base of an in- strumented rock socket increased, at a steadily decreasing rate, over a period of 4 years; although the total applied head FIGURE 22 Effect of rock mass modulus at base on axial load transfer (Wyllie 1999, based on Osterberg and Gill 1973). Reason Cited for Neglecting Base Resistance Correction Settled slurry suspension Utilize available construction and inspection methods Reluctance to inspect bottom Utilize available construction and inspection methods Concern for underlying cavities Additional inspection below base Unknown or uncertain base resistance Load testing TABLE 16 REASONS FOR NEGLECTING BASE RESISTANCE AND CORRECTIVE ACTIONS (after Crapps and Schmertmann 2002)

37 load remained essentially constant. However, the percentage of total load carried by the base after this period was still less than 10% of the applied load and agreed quite well with pre- dictions based on elastic theory. Tang et al. (1994) described a similar monitoring program on a shaft socketed into karstic dolomite supporting a building on the University of Ten- nessee campus. Some change in load transfer occurred fol- lowing the end of construction; however, most of the change was from side resistance in the overlying soil (decreased) to side resistance in the rock socket (increased). Neither case would suggest changes in design of rock sockets to account for the time dependency of load transfer mechanisms. CAPACITY UNDER AXIAL LOADING The factored axial resistance of a drilled shaft in compres- sion is the sum of the factored side resistance and the fac- tored base resistance. The factored resistances are calcu- lated by multiplying appropriate resistance factors by the nominal resistances, which are generally taken as the ulti- mate values. One approach to the design process depicted in Figure 3 of chapter one is to size the foundation initially to achieve a factored resistance that exceeds the factored loads. The trial design is then analyzed to predict load- displacement response. If necessary, revised trial dimen- sions can then be analyzed until all of the design criteria are satisfied, including the movement criteria associated with the service limit state. In the case of axial loading, the ultimate side and base resistances are required to establish the initial trial design. Side Resistance The ultimate side resistance of a rock socket is the summa- tion of peak shearing stress acting over the surface of the socket, expressed mathematically by (21) in which Qs = total side resistance (force), fsu = unit side resis- tance (stress), A = surface area along the side of the socket, B = socket diameter, and L = socket length. In practice, socket side resistance capacity is calculated by assuming that a single av- erage value of unit side resistance acts along the concrete–rock interface, for each rock layer. This value of f is multiplied by the area of the interface to obtain total side resistance Qs, or (22) Methods for predicting socket side resistance are, therefore, focused on the parameter fsu. The interaction between a rock mass and drilled shaft that determines side resistance is complex. The principal factors controlling this interaction include: • Rock material strength; • Rock mass structure (discontinuities); • Modulus of the concrete relative to modulus of the rock mass; • Shear strength mobilized by dilatancy; • Confining stress; and • Construction-related factors, including roughness of shaft–rock interface. Geomechanical models that account for these factors (to varying degrees) are described in the literature (e.g., Rowe and Pells 1980); however, the methods required to obtain the necessary input parameters normally fall outside the scope of a typical investigation conducted for the design of highway bridge foundations. More realistically, methods based on the strength of intact rock, in some cases with modifications to account for one or more of the other factors, have been used successfully and are more rational than some of the strictly empirical methods or presumptive values. This approach rep- resents a practical compromise between oversimplified em- pirical methods and more sophisticated numerical methods that might be warranted only on larger projects. The methods are summarized here. Methods Based on Rock Compressive Strength A practical approach to evaluating average unit side resis- tance is to relate fsu to the strength of the intact rock material. The rock material strength parameter most often measured is the uniaxial compressive strength (qu). In this approach, val- ues of fsu are determined from full-scale field load tests in which ultimate side resistance (Qs) has been determined. This value is divided by the socket side area (As) to obtain an average value of unit side resistance at failure: fsu = Qs/As (23) Q f BLs su= × π Q f dA B fdzs su L= =∫ ∫surface π 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 9 10 L/B Q b /Q t O-cell, good base O-cell, base disturbed top load test FIGURE 23 Base load transfer interpreted from load tests (data from Crapps and Schmertmann 2002).

Early studies relating fsu to qu include those by Rosenberg and Journeaux (1976) and Horvath (1978, 1982). Other re- searchers have continued to expand the available database and propose equations relating unit side resistance to rock strength on the basis of statistical best-fit analyses. Notable studies include those of Williams and Pells (1981), Rowe and Armitage (1984, 1987b), Bloomquist and Townsend (1991), McVay et al. (1992), and Kulhawy and Phoon (1993). These studies, including the proposed equations relating unit side resistance to rock strength are reviewed briefly. Horvath and Kenney (1979) proposed the following cor- relation between side resistance and compressive strength: (24) in which fsu = ultimate unit side resistance, qu = compressive strength of the weaker material (rock or concrete), and where b ranges from 0.2 (smooth) to 0.3 (rough). Both fsu and qu in Eq. 24 are in units of MPa. Eq. 24 can be expressed in nor- malized form by dividing both unit side resistance and com- pressive strength by atmospheric pressure (pa = 0.1013 MPa). This results in the following expression, which is equivalent to Eq. 24 with b = 0.2: (25) A modified relationship was recommended by Horvath et al. (1983) to account for shafts with artificially roughened (grooved) sockets. The suggested relationship is given by (26) (27) in which RF = roughness factor, Δrh = average height of as- perities, rs = nominal socket radius, Ls = nominal socket length, and Lt = total travel distance along the socket wall profile. A device (caliper) was used to measure field rough- ness for determination of the parameters needed in Eq. 27, as described by Horvath et al. (1993). The FHWA Drilled Shaft Manual (O’Neill and Reese 1999) and the draft 2006 Interim AASHTO LRFD Bridge Design Specifications have adopted Eqs. 24 to 27 as a recommended method for selection of design side resistance for shafts in rock. RF r r L L h s t s = Δ f RF qsu u= [ ] ×0 8 0 45. . f p q p su a u a = 0 65. f b qsu u= 38 AASHTO refers to this as the Horvath & Kenney method. A socket that is not specified to be artificially roughened by grooving is considered “smooth” and side resistance is gov- erned by Eq. 25. If the socket is artificially roughened, Eq. 26 is recommended; however, this requires estimation or mea- surement of roughness as defined by Eq. 27. Rowe and Armitage (1987b) summarized the available data on side resistance of rock sockets, including the data- bases used by Williams et al. (1980), Williams and Pells (1981), and Horvath (1982). The suggested correlation for regular clean sockets, defined as roughness classes R1, R2, and R3 in Table 17, is given as (28) To account for rough sockets, defined as category R4, side resistance is increased and the following is recommended: (29) The correlation suggested by Horvath and Kenney (1979) as given by Eq. 25 represents a lower bound to the data used by Rowe and Armitage (1987b) Kulhawy and Phoon (1993) incorporated the database compiled by Rowe and Armitage, which included more than 80 load tests from more than 20 sites, and the data reported by Bloomquist and Townsend (1991) and McVay et al. (1992) consisting of 47 load tests to failure from 23 different Florida limestone sites. Linear regression was conducted on two sets of data, one consisting of all data points and the other using data that were averaged on a per-site basis. Av- eraging eliminates the bias associated with multiple load tests conducted at many of the sites. All stresses are normal- ized by atmospheric pressure, pa (0.1013 MN/m2) and nor- malized values of one-half of the uniaxial compressive strength were plotted against normalized values of average unit side resistance on a log–log plot as shown in Figure 24 (shown previously as Figure 17). The following exponential expression provides a best-fit to the available data for rock: (30)f p C q p su a u a = × 2 f qsu u= 0 6. f qsu u= 0 45. Roughness Class Description R1 Straight, smooth-sided socket; grooves or indentations less than 1 mm deep R2 Grooves 1–4 mm deep, >2 mm wide, spacing 50–200 mm R3 Grooves 4–10 mm deep, >5 mm wide, spacing 50–200 mm R4 Grooves or undulations >10 mm deep, >10 mm wide, spacing 50–200 mm TABLE 17 SHAFT ROUGHNESS CLASSIFICATION (after Pells et al. 1980)

39 where values of the coefficient C = 1 represents a reasonable lower bound, C = 2 represents the mean behavior, and C = 3 corresponds to an upper bound for artificially roughened sockets. Kulhawy and Phoon (1993) noted that the expres- sions and variations are consistent with those reported by Rowe and Armitage (1987b). Values of fsu obtained using Eq. 30 with C = 2 (mean) are identical to the values obtained using Eq. 28 (Rowe and Armitage) corresponding to the mean trend for smooth sockets. The expression of Rowe and Ar- mitage for rough sockets (Eq. 29) corresponds to Eq. 30 with C = 2.7. Kulhawy et al. (2005) recently reexamined the data avail- able and attempted to evaluate them in a more consistent manner. Only data showing load-displacement curves to fail- ure were incorporated into the analysis, so that the “inter- preted failure load” could be established in a consistent man- ner. Based on the updated analysis, the authors recommend the use of Eq. 30 with C = 1 for predicting side resistance of normal rock sockets for drilled shafts. The authors also note the importance of using compressive strength values (qu) obtained from laboratory uniaxial compression tests, not from point load tests. In summary, Eq. 30 with C = 1 provides a conservative estimate of design ultimate side resistance, based on the most up-to-date analysis of the available data. Use of C values greater than 1 for design should be verified by previous ex- perience or load testing. Load test results that exhibit values of C in the range of 2.7 to 3 demonstrate the potential in- crease in side resistance that is possible if the sidewalls of the socket are roughened. These upper-bound values of fsu should only be considered when they can be validated by field load testing. The methods described rely on empirical relationships between side resistance and a single parameter, uniaxial com- pressive strength, to represent the rock mass. There is signif- icant scatter in the database because the relationships do not capture all of the mechanisms affecting unit side resistance and because the database incorporates load test results for many different rock types. Use of these empirical correla- tions for design should therefore be conservative (i.e., C = 1) unless a site-specific correlation has been developed that jus- tifies higher values. Research on development of methods that account for these additional factors affecting peak side resistance is summarized here. Methods Based on Additional Rock Mass Parameters Williams et al. (1980) and Rowe and Armitage (1987a) point out that unit side resistance determined strictly by empirical correlations with uniaxial compressive strength does not ac- count explicitly for the degree of jointing in the rock mass. Figure 25 shows the potential influence on average side re- sistance (denoted by τ in the figure) of jointing in terms of the ratio of rock mass modulus to modulus of intact rock. Both theoretical and experimental curves show substantially reduced side resistance for rock that may have high intact strength and stiffness but low mass modulus. The draft Interim 2006 AASHTO LRFD Bridge Design Specifications adopt the Horvath and Kenney method de- scribed earlier (Eqs. 25–27), with the following modification as recommended O’Neill and Reese (1999). Values of unit side resistance calculated by either Eq. 25 or Eq. 26 are mod- ified to account for rock mass behavior in terms of RQD, modulus ratio (EM/ER), and joint condition using the factor α as defined in Table 18. In Table 18, fdes is the reduced unit FIGURE 24 Unit side resistance versus strength (Kulhawy and Phoon 1993). FIGURE 25 Effect of rock mass modulus on average unit side resistance (Rowe and Armitage 1987a).

side resistance recommended for design. The modulus re- duction ratio (EM/ER) is given in Table 13, in chapter two, based on RQD. However, application of the α-factor may be questionable because the RQD and rock mass modulus were not accounted for explicitly in the original correlation analy- sis by Horvath and Kenney (1979). Because the load test data included sites with RQD less than 100 and modulus ratio val- ues less than one, it would appear that these factors affected the load test results and are therefore already incorporated into the resulting correlation equations. Interface roughness is identified by all researchers as hav- ing a significant effect on peak side resistance. Pells et al. (1980) proposed the roughness classification that assigns a rock socket to one of the categories R1 through R4 as defined in Table 17. The criteria are based on observations of sock- ets drilled in Sydney sandstone and the classification report- edly forms the basis for current practice in that city (Seidel and Collingwood 2001). The Rowe and Armitage (1987b) correlation equations were developed by distinguishing be- tween roughness classes R1–R3 (Eq. 28) and roughness class R4 (Eq. 29). Horvath et al. (1983) proposed the roughness factor (RF) defined in Eqs. 26 and 27 as presented earlier. Despite these efforts, selection of side resistance for rock- socket design in the United States is done mostly without considering interface roughness explicitly. Seidel and Haberfield (1994) developed a theoretical model of interface roughness that accounts for the behavior and char- acteristics of socket interfaces under CNS conditions. Rough- ness is modeled using a quasi-probabilistic approach that involves fractal geometry to predict the distribution and char- acteristics of asperities. Results of the interface model and laboratory CNS testing are incorporated into the computer pro- gram ROCKET that predicts the axial load-displacement curve, including post-peak behavior. Extending this work, Seidel and Collingwood (2001) proposed a nondimensional parameter defined as the shaft resistance coefficient (SRC) to account for the factors that influence side resistance, as follows: (31) fsu = (SRC) qu (32) SRC = + η ν c s n r d1 Δ 40 in which ηc = construction method reduction factor, as de- fined in Table 19; n = ratio of rock mass modulus to uniaxial compressive strength of intact rock (EM/qu); v = Poisson’s ratio; Δr = mean roughness height; and ds = socket diameter. Implementation of the SRC in design requires an estimate of socket roughness in terms of Δr. As noted by the authors, reliable measurements of roughness are not undertaken in routine design. However, the SRC factor incorporates many of the significant parameters that influence side resistance, including rock mass modulus, Poisson’s ratio, and intact rock strength, and provides a framework for taking into account socket roughness and construction effects. The SRC method represents the type of approach that holds promise for improved methods for selecting design side resistance. Although more detailed guidance is required for determination of socket roughness and construction effects, improvements in reliability of design equations are possible only if the relevant factors controlling side resistance are in- corporated properly. Advancement of the SRC or other robust methods can be facilitated by promoting the awareness of engineers involved in field load testing of the importance of collecting appropriate data on rock mass characteristics. Docu- mentation of RMS and modulus along with careful observation and documentation of construction procedures would allow these methods to be evaluated against load test results. The key parameter that is currently missing from the database is socket roughness. O’Neill et al. (1996) point out that roughness can be quantified approximately by making electronic or mechanical caliper logs of the borehole, and that such borehole calipers are available commercially. Seidel and Collingwood (2001) de- scribe a device called the Socket-Pro that is operated remotely and records sidewall roughness to depths of 60 m. Geomaterial-Specific Correlations Correlations between unit side resistance and intact rock strength that are based on a global database (e.g., Figure 24, Eq. 30) exhibit scatter and uncertainty because the results reflect the variations in interface shear strength of different rock types, interface roughness, and other factors that control side resistance. For this reason, selection of design side re- sistance values based on such correlations should be consid- ered as first-order estimates and the philosophy underlying their use for design is that a lower-bound, conservative rela- tionship should be used (e.g., C = 1 in Eq. 30). Alternatively, correlations have been developed for specific geomaterials. Correlations identified by the literature review and the survey are summarized here. Florida Limestone Limestone formations in Florida are characterized by highly variable strength profiles, the pres- ence of cavities that may be filled with soil, and interbedding of limestone with sand and marine clay layers (Crapps 1986). Locally, geotechnical engineers distinguish between “lime- TABLE 18 SIDE RESISTANCE REDUCTION BASED ON MODULUS REDUCTION (O’Neill and Reese 1999) EM/ER α = fdes/fsu 1.0 1.0 0.5 0.8 0.3 0.7 0.1 0.55 0.05 0.45

41 rock” and “limestone”; the former defined informally as material with qu less than approximately 13.8 MN/m2 (2,000 psi). McVay et al. (1992) conducted a study of design meth- ods used to predict unit side resistance of drilled shafts in Florida limestone. Based on a parametric finite-element study and a database of 14 case histories consisting of full- scale load tests and field pullout tests, the following expres- sion was found to provide a reasonable estimate of ultimate unit side resistance: (33) In which qu = uniaxial compressive strength and qt = split ten- sile strength. To account for the effect of material strength variability on side resistance, the authors recommend a min- imum of 10 (preferably more) core samples be tested in un- confined compression and splitting tensile tests. The mean values of qu and qt are used in Eq. 33. The standard error of the mean from the laboratory strength tests can be used to estimate the expected variation from the mean side resis- tance, for a specified confidence level. According to Lai (1998), design practice by the Florida DOT is based on a modified version of the McVay et al. relationship in which spatial variations in rock quality are incorporated by multiplying the unit side resistance, accord- ing to Eq. 33, by the average percent recovery (REC) of rock core expressed as a decimal, or: (34) Lai (1998) also recommends using larger diameter double- tube core barrels (61 mm to 101.6 mm inner diameter) for ob- taining samples of sufficient quality for laboratory strength tests. Analysis of the laboratory strength data involves dis- carding all data points above or below one standard deviation about the mean, then using the mean of the remaining values as input to Eq. 34. Crapps (2001) recommends using RQD in place of REC in Eq. 34 and points out that values of qu and qt f q qsu u t( ) = ⎡⎣⎢ ⎤ ⎦⎥design REC(%) %100 1 2 f q qsu u t= 12 used for design should be limited to the design strength of the shaft concrete. Side resistance values in Florida limestone have also been evaluated using a small-scale field pullout test devised by Schmertmann (1977) for the Florida DOT and shown schematically in Figure 26. A grout plug is placed into a 140- mm-diameter cored hole at the bottom of a 165-mm-diameter hole drilled to the test depth in rock. Overburden soils are supported by a 200-mm-diameter casing. The grout plug is reinforced with a wire cage and a threaded high-strength steel bar extends from the bottom of the plug to the ground sur- face. A center hole jack is used to apply a pullout force to the bar. The grout plug is typically 610 mm (2 ft) in length, but other lengths are also used. The average unit side resistance is taken as the measured pullout force divided by the sidewall interface area of the plug (Eq. 23). Results of pullout tests were included in the database of McVay et al. (1992) that forms the basis of Eq. 33, and McVay et al. recommend the test as an alternative method for estimating side resistance for design. Cohesionless IGM The FHWA Drilled Shaft Manual (O’Neill and Reese 1999) recommends a procedure for cal- culating unit side resistance specifically for cohesionless IGM. These are granular materials exhibiting SPT N60-values between 50 and 100. The method follows the general approach for calculating side resistance of drilled shafts in granular soils, given by (35) in which fsu = ultimate unit side resistance, σv' = vertical effec- tive stress, Ko = in situ coefficient of lateral earth pressure, and φ' = effective stress friction angle of the IGM. The modifica- tions to account for cohesionless IGM behavior are incorpo- rated into empirical correlations with the N-value as follows: (36) (37)OCR p v = σ σ ' ' σ ' .p aN p= 0 2 60 f Ksu v o= σ φ' tan ' Construction Method ηc Construction without drilling fluid Best practice construction and high level of construction control (e.g., socket sidewalls free of smear and remolded rock) 1.0 Poor construction practice or low-quality construction control (e.g., smear or remolded rock present on rock sidewalls) 0.3–0.9 Construction under bentonite slurry Best practice construction and high level of construction control 0.7–0.9 Poor construction practice or low level of construction control 0.3–0.6 Construction under polymer slurry Best practice construction and high level of construction control 0.9–1.0 Poor construction practice or low level of construction control 0.8 TABLE 19 CONSTRUCTION METHOD REDUCTION FACTORS, ηc (Seidel and Collingwood 2001)

(38) (39) where σp' = preconsolidation stress, σ'v = average vertical effective stress over the layer, N60 = SPT N-value corre- sponding to 60% hammer efficiency, and OCR = overconsoli- dation ratio. O’Neill et al. (1996) reported good agreement with results of load tests on shafts in residual micaceous sands in the Piedmont province (Harris and Mayne 1994) and gran- ular glacial till in the northeastern United States. Soft Argillaceous Rock Side resistance in weak shales and claystones can be approximated for design using the relation- ships given previously for rock. Alternatively, a procedure for evaluating unit side resistance specifically in argillaceous (containing clay) cohesive IGMs is presented in the FHWA Drilled Shaft Manual (O’Neill and Reese 1999). The ulti- mate unit side resistance is given by fsu = αqu (40) where qu = compressive strength of intact rock and α = em- pirical factor given in Figure 27. In Figure 27, σn = fluid pres- sure exerted by the concrete at the time of the pour and σp = atmospheric pressure in the same units as σn. As indicated in Figure 27, the method is based on an assumed value of interface friction angle φrc = 30 degrees. If it is known that a Ko = −( sin ') sin '1 φ φOCR φ σ ' tan . . ' = + ⎛ ⎝⎜ ⎞ ⎠⎟ ⎡ ⎣ ⎢⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥⎥ −1 60 12 2 20 3 N p v a 0 34. 42 different value of interface friction applies, then the parame- ter α can be adjusted by (41) The method is based on work reported by Hassan et al. (1997) in which detailed modeling and field testing were conducted to study side resistance of shafts in clay–shales of Texas. O’Neill and Reese (1999) provide additional equa- tions for modifying side resistance for roughness, the pres- ence of soft seams, and other factors, and the reader is advised to consult their work for these additional details. Correlations with In Situ Tests The survey responses indicate that several states use mea- surements from field penetration tests to estimate unit side resistance in weak rock. As an example, consider the Texas cone penetration test (TCPT) described in chapter two. The Texas DOT Geotechnical Manual, which is accessible on- line (2005), presents graphs for estimating design values of allowable unit side and base resistances as a function of the penetration resistance (millimeters of penetration per 100 blows), for materials that exhibit TCPT blowcounts of greater than 100 blows per 300 mm. For materials exhibiting fewer than 100 blowcounts, separate graphs are provided for allowable values of unit side and base resistances. The Mis- souri DOT also reports using the TCPT to correlate allow- able side and base resistances in weak rock. Base Resistance Load transmitted to the base of a rock-socketed shaft, ex- pressed as a percentage of the axial compression load applied α α φ = 26 30 tan tan rc o 0.61 m grout plug w/ #9 wire cage drilled hole, 165 mm dia top of rock centerhole jack nut plate timber 200-mm dia casing 0.76 m cored hole, 140 mm dia steel bearing plate 35 mm dia threaded bar FIGURE 26 Small-scale pullout test used in Florida limestone (after Crapps 1986). FIGURE 27 Factor α for cohesive IGM (O’Neill et al. 1996).

43 at the head, can vary over a wide range at typical working loads. Several authors suggest a typical range of 10% to 20% of the head load (Williams et al. 1980; Carter and Kulhawy 1988), and some authors suggest that base resistance should be neglected entirely for rock-socket design (Amir 1986). Elasticity solutions show that base load transfer depends on the embedment ratio (L/B) and the modulus ratio (Ec/Er). The ratio of base load to applied load (Qb/Qc) decreases with in- creasing L/B (see Figure 21) and increases with increasing modular ratio. As discussed previously, there is ample evi- dence that base resistance should not be discounted in most cases (Figure 23), and that construction and inspection meth- ods are available to control base quality. Load tests, described in chapter five, provide a means to determine the effects of construction on base load transfer. The ultimate base resistance of a rock-socketed drilled shaft, Qb, is the product of the limiting normal stress, or bear- ing capacity, qult, at the base and the cross-sectional area of the shaft base (Ab): Qb = qult Ab = qult [1/4 πB2] (42) Analytical solutions for bearing capacity of rock are based on the general bearing capacity equation developed for soil, with appropriate modifications to account for rock mass characteristics such as spacing and orientation of discontinu- ities, condition of the discontinuities, and strength of the rock mass. Typical failure modes for foundations bearing on rock are shown in Figure 28. The failure modes depicted were in- tended to address shallow foundations bearing on rock (Sow- ers 1976); however, the general concepts should be applica- ble to bearing capacity of deep foundations. The cases shown can be placed into four categories: massive, jointed, layered, and fractured rock. Massive Rock For this case, the ultimate bearing capacity will be limited to the bearing stress that causes fracturing in the rock. An intact rock mass can be defined, for purposes of bearing capacity analysis, as one for which the effects of discontinuities are insignificant. Practically, if joint spacing is more than four to five times the shaft diameter, the rock is massive. If the base is embedded in rock to a depth of at least one diame- ter, the failure mode is expected to be by punching shear (Figure 28, mode a). In this case, Rowe and Armitage (1987b) stated that rock fracturing can be expected to occur when the bearing stress is approximately 2.7 times the rock uniaxial compressive strength. For design, the following is recommended: qult = 2.5 qu (43) Other conditions that must be verified are that the rock to a depth of at least one diameter below the base of the socket is either intact or tightly jointed (no compressible or gouge- filled seams) and there are no solution cavities or voids below the base of the pier. O’Neill and Reese (1999) recommend limiting base resistance to 2qu if the embedment into rock is less than one diameter. In rock with high compressive strength, the designer also must determine the structural ca- pacity of the shaft, which may govern the allowable normal stress at the base. Jointed Rock Mass When discontinuities are vertical or nearly vertical (α > 70°), and open joints are present with a spacing less than the socket diameter (S < B, Figure 28, mode c), failure can occur (theo- retically) by unconfined compression of the poorly con- strained columns (Sowers 1979). Bearing capacity can be estimated from qult = qu = 2c tan (45° + 1⁄2 φ) (44) where qu = uniaxial compressive strength and c and φ are Mohr–Coulomb strength properties of the rock mass. If the nearly vertical joints are closed (Figure 28, mode d), a gen- Rock Mass Conditions Failure Joint Dip Angle, from horizontal Joint Spacing Illustration Mode Bearing Capacity Equation No. (a) Brittle Rock: Local shear failure caused by localized brittle fracture Eq. 43 IN TA C T / M AS SI V E N/A S>>B (b) Ductile Rock: General shear failure along well-defined shear surfaces Eq. 43 (c) Open Joints: Compression failure of individual rock columns Eq. 44 S < B (d) Closed Joints General shear failure along well defined failure surfaces; near vertical joints Eqs. 45–52 ST EE PL Y D IP PI N G JO IN TS 70 ° < α < 90 ° S > B (e) Open or Closed Joints: Failure initiated by splitting leading to general shear failure; near vertical joints Eqs. 53–54 JO IN TE D 20 ° < α < 70 ° S < B or S > B if failure we dge can de ve lop along joints (f) General shear failure with potential for failure along joints; moderately dipping joint sets. Eqs. 45–52 (g) Rigid layer over weak compressible layer: Failure is initiated by tensile failure caused by flexure of rigid upper layer N/A L AY ER ED 0 < α < 20 ° Limiting va lue of H w/re to B is dependent upon material properties (h) Thin rigid layer over weak compressible layer: Failure is by punching shear through upper layer N/A FR A C TU R ED N/A S << B (g) General shear failure with irregular failure surface through fractured rock mass; two or more closely spaced joint sets Eq. 57 s α s B s H rigid weak, compressible weak, compressible H rigid FIGURE 28 Bearing capacity failure modes in rock (after Rock Foundations 1994).

eral wedge failure mode may develop and the bearing ca- pacity can be approximated using Bell’s solution for plane strain conditions: (45) in which B = socket diameter; γ = effective unit weight of the rock mass; D = foundation depth; Nc, Nγ, and Nq are bearing capacity factors; and sc, sγ, and sq are shape factors to account for the circular cross section. The bearing capacity factors and shape factors are given by: (46) (47) (48) (49) (50) sγ = 0.6 (51) sq = 1 + tan φ (52) In these equations (46–52), the values of c and φ are RMS properties, which may be difficult to determine accurately for rock mass beneath the base of drilled shafts. If joint spacing S is greater than the socket diameter (Figure 28, mode e), failure occurs by splitting, leading eventually to general shear failure. This problem has been evaluated by Bishnoi (1968) and developed further by Kulhawy and Goodman (1980). The solution can be expressed by: qult = J c Ncr (53) in which J = a correction factor that depends on the ratio of horizontal discontinuity spacing to socket diameter (H/B) as shown in Figure 29, c = rock mass cohesion, and Ncr = a bear- ing capacity factor given by (54) where Nφ is given by Eq. 49. If the actual RMS properties are not evaluated, Kulhawy and Carter (1992a) suggest that rock mass cohesion in Eq. 53 can be approximated as 0.1qu, where qu = uniaxial compressive strength of intact rock. Rock mass cohesion can also be estimated from the Hoek–Brown strength properties using Eq. 17 given in chapter two. For the case of moderately dipping joint sets (Figure 28, mode f, 20° < α < 70°), the failure surface is likely to de- N N N S B N N Ncr = + ( ) −⎛⎝⎜ ⎞ ⎠⎟ − ( ) + 2 1 1 1 2φ φ φ φφ φ 2 cot cot φ s N Nc q c = +1 Nφ φ = + ⎛⎝⎜ ⎞⎠⎟tan2 45 2ο N Nq = φ2 N N Nγ φ φ= −( )2 1 N N Nc = +( )2 1φ φ q cN s B N s DN sult c c q q= + +2 γ γγ γ 44 velop along the discontinuity planes. Eq. 45 can be used, but with strength parameters representative of the joints. Rock Foundations (1994) recommends neglecting the first term in Eq. 45 based on the assumption that the cohesion component of strength along the joint surfaces is highly uncertain. Layered Rocks Sedimentary rock formations often consist of alternating hard and soft layers. For example, soft layers of shale in- terbedded with hard layers of sandstone. Assuming the base of the shaft is bearing on the more rigid layer, which is un- derlain by a soft layer, failure can occur either by flexure if the rigid layer is relatively thick or by punching shear if the rigid layer is thin (Figure 28, modes g and h). Both modes are controlled fundamentally by the tensile strength of the intact rock, which can be approximated as being on the order of 5% to 10% of the uniaxial compressive strength. According to Sowers (1979) neither case has been studied adequately and no analytical solution proposed. The failure modes de- picted in Figure 28 merely suggest possible methods for analysis. Fractured Rock Mass A rational approach for calculating ultimate bearing capac- ity of rock masses that include significant discontinuities (Figure 28, mode g) is to apply Eq. 45 with appropriate RMS properties, c' and φ'. However, determination of c' and φ' for highly fractured rock mass is not straightforward because the failure envelope is nonlinear and there is no stan- FIGURE 29 Correction factor for discontinuity spacing (Kulhawy and Carter 1992a).

45 dard test method for direct measurement. One possible ap- proach is to employ the Hoek–Brown strength criterion described in chapter two. The criterion is attractive because (1) it captures the nonlinearity in the strength envelope that is observed in jointed rock masses and (2) the required para- meters can be estimated empirically using correlations to GSI and RMR, also described in chapter two. To use this approach, it is necessary to relate the Hoek–Brown strength parameters (mb, s, and a) to Mohr–Coulomb strength pa- rameters (c' and φ'); for example, using Eqs. 16 and 17 in chapter two. Alternatively, several authors (Carter and Kulhawy 1988; Wyllie 1999) have shown that a conservative, lower-bound estimate of bearing capacity can be made directly in terms of Hoek–Brown strength parameters by assuming a failure mode approximated by active and passive wedges; that is, the Bell solution for plane strain. The failure mass beneath the foundation is idealized as consisting of two zones, as shown in Figure 30. The active zone (Zone 1) is subjected to a major principal stress (σ1') coinciding at failure with the ultimate bearing capacity (qult) and a minor principal stress (σ3') that satisfies equilibrium with the horizontal stress in the adjacent passive failure zone (Zone 2). In Zone 2, the minor principal stress is vertical and conservatively as- sumed to be zero, whereas the major principal stress, acting in the horizontal direction, is the ultimate strength accord- ing to the Hoek–Brown criterion. From chapter two, the strength criterion is given by (55) where σ1' and σ3' = major and minor principal effective stresses, respectively; qu = uniaxial compressive strength of intact rock; and mb, s, and a are empirically determined strength parameters for the rock mass. For Zone 2, setting the vertical stress σ3' = 0 and solving Eq. 55 for σ1' yields (56)σ σ' '1 = =H u aq s σ σ σ ' ' ' 1 3 3 = + + ⎛ ⎝⎜ ⎞ ⎠⎟q m q su b u a where σH' = horizontal stress in Zone 2. To satisfy equilibrium, the horizontal stress given by Eq. 56 is set equal to σ3' in Zone 1. Substituting σ3' = qu s0.5 into Eq. 55 and considering that σ1' = qult yields (57) The assumption of zero vertical stress at the bearing ele- vation may be overly conservative for many rock sockets. A similar derivation can be carried out with the overburden stress taken into account, resulting in the following. Let (58) where σ'v,b = vertical effective stress at the socket bearing elevation, which is also the minor principal stress in Zone 2. Then (59) A limitation of Eqs. 57–59 is that they are based on the assumption of plane strain conditions, corresponding to a strip footing. Kulhawy and Carter (1992a) noted that for a circular foundation the horizontal stress between the two assumed failure zones may be greater than for the plane strain case, resulting in higher bearing capacity. The analy- sis is therefore conservative for the case of drilled shafts. Eqs. 57–59 require determination of a single rock strength property (qu) along with an approximation of the Hoek–Brown strength parameters. In chapter two, the Hoek–Brown strength parameters are correlated to GSI by Eqs. 12–15. This allows a correlation to be made between the GSI of a rock mass; the value of the coefficient mi for intact rock as given in Table 11 (chapter two), and the bearing capacity ratio qult/qu by Eq. 57. The resulting relationship is shown graphically in Figure 31. The bearing capacity ratio is limited by an upper-bound value of 2.5, corresponding to the recommendation of Rowe and Armitage (Eq. 43). q A q m A q sult u b u a = + ⎛ ⎝⎜ ⎞ ⎠⎟ + ⎡ ⎣⎢ ⎤ ⎦⎥ A q m q sv b u b v b u a = + ( ) + ⎡ ⎣⎢ ⎤ ⎦⎥σ σ ' ' , , q q s m s sult u a b a a = + +( )⎡⎣ ⎤⎦ Qult Zone 1 (active wedge) Zone 2 (passive wedge) qult qusa Zone 2 (passive wedge) FIGURE 30 Bearing capacity analysis. 0.0 0.5 1.0 1.5 2.0 2.5 10 20 30 40 50 60 70 80 90 100 Geological Strength Index (GSI) q u lt/q u 4 10 1520 m i = 33 25 maximum qult/qu = 2.5 FIGURE 31 Bearing capacity ratio versus GSI.

Alternatively, the bearing capacity ratio can be related ap- proximately to the rock mass description based on RMR (Table 9) using an earlier correlation given by Hoek and Brown (1988). The resulting Hoek–Brown strength parame- ters (m, a, and s) are substituted into Eq. 57 to obtain the bear- ing capacity ratio as a function of RMR. This relationship is shown graphically in Figure 32. Both figures are for the case of zero overburden stress at the bearing elevation. To ac- count for the depth of embedment and resulting surcharge stress, Eqs. 58 and 59 can be used. Method Based on Field Load Tests Zhang and Einstein (1998) compiled and analyzed a database of 39 load tests to derive an empirical relationship between ultimate unit base resistance (qult) and uniaxial compressive strength of intact rock (qu). Reported values of uniaxial com- pressive strength ranged from 0.52 MPa to 55 MPa, although most were in the range of relatively low strength. The authors relied on the interpretation methods of the original references to determine ultimate base capacity and acknowledge that some uncertainties and variabilities are likely to be incorpo- rated into the database as a result. The results are shown on a log–log plot in Figure 33. The linear relationship recommended by Rowe and Armitage (1987a) is shown for comparison. Based on statistical analysis of the data, the fol- lowing recommendations are given by the authors: Lower bound: (60) Upper bound: (61) Mean: (62) Eqs. 60–62 provide a reasonably good fit to the available data and can be used for estimating ultimate base resistance, q qult u= 4 8. q qult u= 6 6. q qult u= 3 0. 46 with due consideration of the limitations associated with pre- dicting a rock mass behavior on the basis of a single strength parameter for intact rock. Rock mass discontinuities are not accounted for explicitly, yet they clearly must affect bearing capacity. By taking this empirical approach, however, rock mass behavior is accounted for implicitly because the load tests on which the method is based were affected by the char- acteristics of the rock masses. Additional limitations to the approach given by Zhang and Einstein are noted in a discus- sion of their paper by Kulhawy and Prakoso (1999). None of the analytical bearing capacity models described above by Eqs. 44 through 59 and depicted in Figure 28 have been evaluated and verified against results of full-scale field load tests on rock-socketed drilled shafts. The primary rea- son for this is a lack of load test data accompanied by suffi- cient information on rock mass properties needed to apply the models. Canadian Geotechnical Society Method The Canadian Foundation Engineering Manual [Canadian Geotechnical Society (CGS) 1985] presents a method to es- timate ultimate unit base resistance of piles or shafts bearing on rock. The CGS method is described as being applicable to sedimentary rocks with primarily horizontal discontinuities, where discontinuity spacing is at least 0.3 m (1 ft) and dis- continuity aperture does not exceed 6 mm (0.25 in.). The method is given by the following: (63) in which (64)K s B t s sp v d v = + + 3 10 1 300 q q K dult u sp= 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 q u lt/q u E D C B A VE RY P O O R PO O R FA IR G O O D VE RY G O O D maximum qult/qu = 2.5 IN TA CT A. Carbonate rocks with well-developed cleavage: dolomite, limestone, marble. B. Lithified argillaceous rocks: mudstone, siltstone, shale, and slate. C. Arenaceous rocks with strong crystals and poorly developed crystal cleavage: sandstone and quartzite. D. Fine-grained polyminerallic igneous crystalline rocks: andesite, dolerite, diabase, and rhyolite. E. Coarse-grained polyminerallic igneous and metamorphic crystalline rocks: amphibolite, gabbro, gneiss, quartz, norite, quartz-diorite. FIGURE 32 Bearing capacity ratio as a function of rock type and RMR classification (see Table 9). 1 10 100 1000 0.1 1 10 100 Uniaxial Compressive Strength qu (MPa) Ul tim at e Un it Ba se R es is ta nc e, q u lt (M Pa ) qmax = 2.5 a = 6.6 4.8 3.0 qult = a (qu)0.5 FIGURE 33 Unit base resistance versus intact rock strength (derived from Zhang and Einstein 1998).

47 (65) where sv = vertical spacing between discontinuities, td = aperture (thickness) of discontinuities, B = socket diameter, and Ls = depth of socket (rock) embedment. A method to calculate ultimate unit base resistance from PMT is also given by CGS as follows: (66) where p1 = limit pressure determined from PMT tests averaged over a depth of two diameters above and below socket base elevation, po = at-rest total horizontal stress measured at base elevation, σv = total vertical stress at base elevation; and Kb = socket depth factor given as follows: H/D 0 1 2 3 5 7 Kb 0.8 2.8 3.6 4.2 4.9 5.2 The two CGS methods described earlier are adopted in the draft 20006 Interim AASHTO LRFD Bridge Design Specifi- cations (2006). AXIAL LOAD-DISPLACEMENT BEHAVIOR Analysis of the load-displacement behavior of a drilled shaft is an essential step in a rational design. Design of most sock- ets is governed by the requirement to limit settlement to a specified allowable value. The problem of predicting verti- cal displacement at the top of a rock socket has been studied through theoretical and numerical analyses along with lim- ited results from full-scale field load testing. Methods that appear to have the most application to design of highway bridge foundations are summarized in this section. The basic problem is depicted in Figure 34 and involves predicting the relationship between an axial compression load (Qc) applied to the top of a socketed shaft and the resulting axial displacement at the top of the socket (wc). The concrete shaft is modeled as an elastic cylindrical inclusion embedded within an elastic rock mass. The cylinder of depth L and diameter B has Young’s modulus Ec and Poisson’s ratio vc. The rock mass surrounding the cylinder is homoge- neous with Young’s modulus Er and Poisson’s ratio vc, whereas the rock mass beneath the base of the shaft has Young’s modulus Eb and Poisson’s ratio vb. (Note: some authors use Er to denote modulus of rock in elasticity solu- tions; elsewhere in this report, Er denotes modulus of intact rock and EM is the rock mass modulus of deformation.) The q K p pult b o v= −( ) +1 σ d L B s = +1 0 4. shaft is subjected to a vertical compressive force Qc as- sumed to be uniformly distributed over the cross-sectional area of the shaft resulting in an average axial stress σb = 4Q/(πB2). Early solutions to the problem of a single compressible pile in an elastic continuum were used primarily to study the response of deep foundations in soil (e.g., Mattes and Poulos 1969; Butterfield and Banerjee 1971; Randolph and Wroth 1978). In most cases, the solutions were not directly applicable to rock sockets because they did not cover the typical ranges of modulus ratio (Ec/Er) or embedment ratio (L/B) of rock sockets, but they did provide the basic methodology for analysis of the problem. Osterberg and Gill (1973) used an elastic finite-element formulation to an- alyze rock sockets with D/B ranging from zero to 4 and the modulus ratios ranging from 0.25 to 4. Their analysis also considered differences between the modulus of the rock be- neath the base (Eb) and that along the shaft (Er). Results showed the influence of these parameters on load transfer, in particular the relative portion of load carried in side re- sistance and transmitted to the base, but did not provide a method for predicting load-displacement behavior for de- sign. Pells and Turner (1979) and Donald et al. (1980) con- ducted finite-element analyses assuming elastic and elasto- plastic behaviors. Their numerical results were used to determine values of the dimensionless influence factor (Iρ) that can be used to predict elastic deformation using the general equation (67)w QE B Ic c r = ρ B L Qc Er,ν r Eb, ν b Ec,ν c FIGURE 34 Axially loaded rock socket, elastic analysis.

Values of the influence factor were presented in the form of charts for a range of modulus and embedment ratios com- mon for rock sockets. Graphs are also provided showing the ratio of applied load transferred to the base (Qb/Qc). These studies provided the first practical methods for predicting the load-displacement response of rock sockets. Their principal limitation lies in the assumption of a full bond between the shaft and the rock; that is, no slip. Observations from load tests; for example, Horvath et al. (1983), show that peak side resistance may be reached at displacements on the order of 5 mm. Rupture of the interface bond begins at this point, re- sulting in relative displacement (slip) between the shaft and surrounding rock. Under service load conditions, most rock sockets will undergo displacements that reach or exceed the full slip condition and should be designed accordingly. Analyses that account for both fully bonded conditions and full slip conditions provide a more realistic model of load- displacement response. Rowe and Pells (1980) conducted a theoretical study based on finite-element analyses of rock-socketed shafts that accounts for the possibility of slip at the shaft–rock interface. The analysis treats the shaft and rock as elastic materials, but provides for plastic failure within the rock or the concrete shaft and for slip at the cohesive-frictional and dilatant rock– shaft interface. At small loads, the shaft, rock, and interface are linearly elastic and the shaft is fully bonded to the rock. Slip is assumed to occur when the mobilized shear stress reaches the interface strength, assumed to be governed by a Mohr–Coulomb failure criterion: τ = cpeak + σn tanφpeak (68) where cpeak = peak interface adhesion, σn = interface normal stress, and φpeak = peak interface friction angle. Once slip oc- curs, it is assumed that c and φ degrade linearly with relative displacement between the two sides of the ruptured interface from the peak values to residual values (cresidual, φresidual) at a relative displacement δr. Roughness of the interface is mod- eled in terms of a dilatancy angle ψ and a maximum dilation, and strain softening of the interface is considered. Modeling of the interface in this way provides a good mechanistic rep- resentation of the load-displacement behavior of a rock- socketed shaft, as described in the beginning of this chapter (Figure 19). From these studies, Rowe and Armitage (1987a,b) pre- pared design charts that enable construction of a theoretical load-displacement curve in terms of (1) the influence factor Iρ used to calculate axial displacement by Eq. 67 and (2) the ratio of load Qb/Qt transmitted to the socket base, where Qb = base load and Qt = total load applied to the top of the shaft. Figure 35 is an example of the chart solution for a complete socket. The charts offer a straightforward means of calculat- ing load-displacement curves and have been used by practi- tioners for the design of bridge foundations. The Rowe and 48 Armitage solutions represent a standard against which approximate methods can be compared and verified. Rowe and Armitage (1987a,b) developed design charts for two contact conditions at the base of the socket: (1) a “com- plete socket,” for which full contact is assumed between the base of the concrete shaft and the underlying rock; and (2) a shear socket, for which a void is assumed to exist beneath the base. These conditions are intended to model the socket arrangements and methods of loading used in field load test- ing. When clean base conditions during construction can be verified and instrumentation is provided for measuring base load, a complete socket is assumed. Frequently, however, base resistance is eliminated by casting the socket above the base of the drilled socket, in which case the test shaft is modeled as a shear socket. The boundary condition at the base of a shear socket under axial compression is one of zero stress. The charts given in Rowe and Armitage (1987a,b) provide a rigorous method for analyzing rock-socket load-displacement behavior. Closed Form Solutions An approximate method given by Kulhawy and Carter (1992b) provides simple, closed-form expressions that are at- tractive for design purposes and yield results that compare well with those of Rowe and Armitage. For axial compres- sion loading, the two cases of complete socket and shear socket are treated. Solutions were derived for two portions of the load-displacement curve depicted in Figure 19; the initial linear elastic response (OA) and the full slip condition (re- FIGURE 35 Design chart for shaft displacement and base load transfer, complete socket (Rowe and Armitage 1987a).

49 gion beyond point B). The closed-form expressions cannot predict the load-displacement response between the occur- rence of first slip and full slip of the shaft (AB). However, the nonlinear finite-element results indicate that the progression of slip along the socket takes place over a relatively small interval of displacement. Comparisons of the bilinear curve given by the closed-form expressions with results of Rowe and Armitage (1987b) indicated that this simplification is reasonably accurate for the range of rock-socket conditions encountered in practice. The closed-form expressions for approximating the load- displacement curves for complete and shear socket are given here. For a full description of the assumptions and deriva- tions the reader is referred to Carter and Kulhawy (1988) and Kulhawy and Carter (1992b). 1. For the linearly elastic portion of the load-displace- ment curve. (a) Shear socket (zero stress at the base): (69) in which wc = downward vertical displacement at the butt (top) of the shaft and where μ is defined by: (70) ζ = ln [5(1 − vr)L/B] (71) λ = Ec/Gr (72) Gr = Er / [2(1 + vr] (73) where Gr = elastic shear modulus of rock mass. (b) Complete socket: (74) where ξ = Gr /Gb (75) Gb = Eb/ [2(1 + vb] (76) The magnitude of load transferred to the base of the shaft (Qb) is given by (77)QQ Lb c b = − ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞ ⎠⎟ [ ] ⎛ ⎝⎜ ⎞ ⎠⎟ − 4 1 1 1 4 1 ν ξ μ ν cosh b L B L L ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞ ⎠⎟ + ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛⎝ ⎞⎠ [ ]1 2 2 ξ π ζ μ μ tanh⎛ ⎝⎜ ⎞ ⎠⎟ G Bw Q L Br c c b 2 1 4 1 1 2 = + − ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞ ⎠⎟ ⎛⎝ ⎞⎠ν πλξ tanh μ μ ν ξ π ζ L L b [ ]⎛ ⎝⎜ ⎞ ⎠⎟ − ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞ ⎠⎟ + ⎛ ⎝⎜ ⎞ ⎠⎟ 4 1 1 2 2L B L L ⎛⎝ ⎞⎠ [ ]⎛⎝⎜ ⎞ ⎠⎟ tanh μ μ μ ζλL L B ( ) = ⎛⎝⎜ ⎞ ⎠⎟ ⎛⎝ ⎞⎠2 222 E Bw Q B E E Lr c c r c2 1 2 = ⎛⎝ ⎞⎠ ⎛⎝⎜ ⎞ ⎠⎟ ⎛⎝⎜ ⎞⎠⎟ [ ] π μ μcosh sinh μL[ ] ⎛ ⎝⎜ ⎞ ⎠⎟ 2. For the full slip portion of the load-displacement curve. (a) Shear socket: (78) in which F1 = a1(λ2BC2 − λ1BC1) – 4a3 (79) (80) C1,2 = exp[λ2,1L]/(exp[λ2L] − exp[λ1L]) (81) (82) (83) (84) a1 = (1 + vr)ζ + a2 (85) (86) (87) (b) Complete socket: (88) in which F3 = a1(λ1BC3 − λ2BC4) – 4a3 (89) (90) (91) (92) The magnitude of load transferred to the base of the shaft (Qb) is given by (93) in which P3 = a1(λ1 − λ2) B exp[(λ1 + λ2)L]/(D4 – D3) (94) P4 = a2(exp[λ2D] − exp[λ1L])/(D4 – D3) (95) The solutions given previously (Eqs. 69–95) are easily implemented by spreadsheet, thus providing designers with Q Q P P B c Q b c c = + ⎛⎝⎜ ⎞⎠⎟3 4 2π D E E a a Bb r b 3 4 2 3 1 2 11 4, , ex= −( )⎛⎝⎜ ⎞⎠⎟ + +⎡⎣⎢ ⎤ ⎦⎥π ν λ p ,λ2 1L[ ] C D D D3 4 3 4 4 3 , , = − F a D D B a c Er 4 1 1 2 4 3 21= − − − ⎛⎝⎜ ⎞⎠⎟⎡⎣⎢ ⎤ ⎦⎥ ⎛⎝⎜ ⎞⎠⎟ λ λ w F Q E B F Bc c r = ⎛⎝⎜ ⎞⎠⎟ −3 4π a E E c r c 3 2 = ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛⎝⎜ ⎞⎠⎟ ν ψtan a E Ec r c r2 1 1 1 2 = −( )⎛⎝⎜ ⎞ ⎠⎟ + +( ) ⎡ ⎣⎢ ⎤ ⎦⎥ ⎛ ν ν φ ψtan tan⎝⎜ ⎞ ⎠⎟ β = ⎛⎝⎜ ⎞⎠⎟a E E Bc r 3 α = ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞⎠⎟a E E Bc r 1 2 4 λ β β α α 1 2 2 124 2, = − ± +( ) F a c Er 2 2= ⎛⎝⎜ ⎞⎠⎟ w F Q E B F Bc c r = ⎛⎝⎜ ⎞⎠⎟ −1 2π

a simple analytical tool for assessing the likely ranges of be- havior for trial designs. A spreadsheet solution provides the opportunity to easily evaluate the effects of various input pa- rameters on load-displacement response. When combined with appropriate judgment and experience, this approach represents a reasonable analysis of rock-socketed drilled shafts. The method of Carter and Kulhawy presented herein is also adopted in the FHWA Drilled Shaft Manual (O’Neill and Reese 1999) for analysis of load-displacement response of single drilled shafts in rock (see Appendix C of the Man- ual). Reese and O’Neill also present methods for predicting load-displacement response of shafts in cohesive IGMs and cohesionless IGMs. The equations are not reproduced here, but are given as closed-form expressions that can be imple- mented easily using a spreadsheet. Other Methods A computer program that models the axial load-displacement behavior of a rock-socketed shaft, based on the methods de- scribed by Seidel and Haberfield (1994) and described briefly earlier, has been developed. The program ROCKET requires the following input parameters: • Drained shear strength parameters of the intact rock, • Rock mass modulus and Poisson’s ratio, • Foundation diameter, • Initial normal stress, and • Mean socket asperity length and mean socket asperity angle. Although some of these parameters are determined on a routine basis for the design of rock-socketed foundations, asperity characteristics are not typically evaluated. Drained triaxial tests are also not considered routine by most trans- portation agencies in the United States. However, this ap- proach is promising because it provides a theoretical basis for predicting rock-socket behavior that encompasses more of the important parameters than the empirical approaches now available to predict side resistance. Combining Side and Base Resistances A fundamental aspect of drilled shaft response to axial com- pression loading is that side and base resistances are mobilized at different downward displacements. Side resistance typi- cally reaches a maximum at relatively small displacement, in the range of 5 to 10 mm. Beyond this level, side resis- tance may remain constant or decrease, depending on the stress–strain properties of the shaft-rock interface. Ductile behavior describes side resistance that remains constant or decreases slightly with increasing displacement. If the inter- face is brittle, side resistance may decrease rapidly and significantly with further downward displacement. One question facing the designer is how much side resistance is 50 mobilized at the strength limit state. As stated by O’Neill and Reese (1999), “the issue of whether ultimate side resistance should be added directly to the ultimate base resistance to ob- tain an ultimate value of resistance is a matter of engineering judgment.” Responses to Question 20 of the survey (Appen- dix A) show a wide range in the way that side and base resistances are combined for design of rock sockets. Several states indicated that they follow the guidelines given by O’Neill and Reese in the FHWA Drilled Shaft Manual (1999). Three possible approaches are described here. The first applies to the case where load testing or laboratory shear strength tests prove that the rock is ductile. In this case, the ultimate values of side and base resistance are added directly. If no field or lab tests are conducted, a “fully reduced fric- tional shearing resistance at the interface” is used to compute side resistance and this value is added to the ultimate base re- sistance. The fully reduced strength is taken as the residual shear strength of the rock = σ'htanφrc, where σ'h = horizontal effective stress normal to the interface and φrc = residual angle of interface friction between rock and concrete. A value of 25 degrees is recommended in the absence of mea- surements and σ'h is assumed to be equal to the vertical effective stress σ'v. A second approach is recommended for cases in which base resistance is neglected in design. In this case, the ultimate side resistance is recommended for design at the strength limit state, unless “progressive side shear fail- ure could occur,” in which case the resistance should be reduced “according to the judgment of the geotechnical engineer.” Several states indicate in their response to Question 20 that load testing, especially using the Osterberg load cell, is one of the ways in which the issue is addressed. Load tests that provide independent measurements of side and base resistance as a function of displacement and that are carried to large displacements provide the best available data for es- tablishing resistance values. When testing is not conducted, the major uncertainty (i.e., judgment) is associated with the question of whether or not side shear behavior will exhibit significant strain softening. Research is needed to provide guidance on what conditions are likely to produce a “brittle” response of the side resistance. Most load test data in which side resistance is measured independently do not exhibit a se- vere decrease in side resistance with large displacement. A study with the objective of identifying the factors that con- trol stress–strain behavior at the shaft–rock interface at large displacement is needed. A large amount of data have been produced in recent years from load tests using the Osterberg cell (O-cell) and such data would be useful for a study of post-peak interface behavior. The results would be most useful to practitioners if guidance could be provided on spe- cific rock types, drilling methods, construction practices, and ranges of confining stress that are likely to cause strain softening at the interface. These factors could then be used as indicators of cases for which further field or laboratory testing is warranted.

51 A promising technique for improving base load- displacement response of drilled shafts involves post-grouting at the base (base grouting). The technique involves casting drilled shafts with a grout delivery system incorporated into the reinforcing cage capable of placing high pressure grout at the base of the shaft, after the shaft concrete has cured. The effect is to compress debris left by the drilling process, thus facilitating mobilization of base resistance within service or displacement limits. According to Mullins et al. (2006), base grouting is used widely internationally, but its use in North America has been limited. An additional potential advantage is that the grouting procedure allows a proof test to be con- ducted on the shaft. Base grouting warrants further consider- ation as both a quality construction technique and a testing tool for rock-socketed shafts. For evaluation of service limit states, both side and base resistances should be included in the analysis. Analytical methods that can provide reasonable predictions of axial load-deformation response, for example the Carter and Kul- hawy method described in this chapter or similar methods given by O’Neill and Reese (1999), provide practical tools for this type of analysis. All of these methods require evalu- ation of rock mass modulus. CURRENT AASHTO PRACTICE The draft 2006 Interim AASHTO LRFD Bridge Design Specifications recommends specific methods and associated resistance factors for evaluating side and base resistance of rock-socketed shafts under axial load. These are summarized in Table 20. The resistance factors are based on a calibration study conducted by Paikowsky et al. (2004a) and additional recommendations given by Allen (2005). Rock mass proper- ties used with LRFD resistance factors should be based on average values, not minimum values. Three methods are cited for predicting ultimate unit side resistance in rock. The first is identified as Horvath and Ken- ney (1979). However, the equation given in the AASHTO Specifications is actually the original Horvath and Kenney recommendation (Eq. 25), but with unit side resistance mod- ified to account for RQD. A reduction factor, α, is applied, as determined by Table 13 and Table 18 of this report. This approach was recommended by O’Neill and Reese (1999). The second method is identified as Carter and Kulhawy (1988). The draft 2006 Interim AASHTO LRFD Bridge De- sign Specifications does not state explicitly the equation to be used in connection with the Carter and Kulhawy method. However, in the calibration study by Paikowsky et al. (2004a) the expression used for all evaluations attributed to Carter and Kulhawy is fsu = 0.15 qu (96) in which qu = uniaxial compressive strength of rock. In their original work, Carter and Kulhawy (1988) proposed the use of 0.15 qu as a design check, whereas the AASHTO Specifi- cations treat it as a design recommendation. This unintended usage is inappropriate and does not adequately represent the most up-to-date research based on regression analysis of the available data on socket-side resistance. The third method given by AASHTO is O’Neill and Reese (1999). It is not clear how this differs from the Horvath and Kenney (1979) method because the equations given by AASHTO are all taken directly from O’Neill and Reese (1999). The equations Method/Condition Resistance Factor Nominal Axial Compressive Resistance of Single-Drilled Shafts Side resistance in rock Tip resistance in rock Side resistance, IGMs Tip resistance, IGMs Static load test Compression, all materials 1. Horvath and Kenney (1979) 2. Carter and Kulhawy (1988) 3. OíNeill and Reese (1999) 1. Canadian Geotechnical Society (1985) 2. PMT Method (Canadian Geotechnical Society 1985) 3. O’Neill and Reese (1999) 1. O’Neill and Reese (1999) 1. O’Neill and Reese (1999) 0.55 0.50 0.55 0.50 0.50 0.50 0.60 0.55 <0.70* Nominal Uplift Resistance of Single-Drilled Shaft Rock Horvath and Kenney (1979) Carter and Kulhawy (1988) Load Test 0.40 0.40 0.60 *Depends on the number of load tests and site variability. AASHTO LRFD Bridge Design Specifications, 2006 Interim. TABLE 20 SUMMARY OF CURRENT AASHTO METHODS AND RESISTANCE FACTORS

presented in the draft 2006 Interim AASHTO LRFD Bridge Design Specifications are not the same as those originally proposed by Horvath and Kenney (1979) and by Carter and Kulhawy (1988), but are nonetheless attributed to those stud- ies. Furthermore, both studies have been superseded by more recent research. In future calibration studies for LRFD applications and for updates of AASHTO specifications, consideration of alternative design equations for side resis- tance should be considered and the most up-to-date research should be referenced. The draft 2006 Interim AASHTO LRFD Bridge Design Specifications allow the use of methods other than those given in Table 20, especially if the method is “locally recog- nized and considered suitable for regional conditions . . . if resistance factors are developed in a manner that is consis- tent with the development of the resistance factors for the method(s) provided in these Specifications.” AASHTO specifies resistance factors for base resistance based on the two methods given by the Canadian Geotechni- cal Society (Canadian Foundation Engineering Manual 1985). The first is according to Eqs. 63–65 and is a straight- forward method to apply, provided the rock satisfies the cri- teria of being horizontally jointed and the appropriate para- meters can be determined. Standard logging procedures for rock core would normally provide the required information. The second method is based on PMT and is given by Eq. 66. As noted in chapter two, only a few states reported using the PMT in rock. The third method for base resistance is O’Neill and Reese (1999) and the two equations given by AASHTO correspond to Eq. 43 of this report for massive rock and Eq. 57 of this report for highly fractured rock. AASHTO also allows higher resistance factors on both side and base resistances when they are determined from a field load test. The cost benefits achieved by using a load test as the basis for design can help to offset the costs of con- ducting load tests. This issue is considered further in chapter five. Finally, AASHTO recommends that all of the resistance factors given in Table 20 be reduced by 20% when used for the design of nonredundant shafts; for example, a single shaft supporting a bridge pier. SUMMARY The principal factors controlling the behavior of rock-socketed foundations under axial loading are identified and discussed. It is concluded from this study that sufficient tools are cur- rently available for transportation agency personnel to design rock-socketed shafts for axial loading conditions that provide adequate load carrying capacity without being overly con- servative. The principal performance design criteria for axial load- ing are (1) adequate capacity and (2) ability to limit vertical 52 deformation. Research published over the past 25 years has resulted in methods for predicting ultimate side resistance of shafts in rock that can be selected by a designer on the basis of commonly measured geomaterial properties and that ac- count for levels of uncertainty associated with the project. For example, Eq. 30 with C taken equal to 1.0 provides a con- servative estimate of side resistance for preliminary design or for final design of small structures or at sites where no additional testing is planned. If laboratory CNS testing is conducted to measure rock–concrete interface strength, higher values of side resistance can be justified for design. If field load tests are conducted, they normally result in higher side resistance values than given by Eq. 30 (with C = 1.0) and higher resistance factors are allowed by AASHTO for results based on load tests. If field load testing demonstrates that a particular construction technique; for example, artificial roughening the walls of a socket, can increase side resistance, then it may be possible to justify the use of Eq. 30 with val- ues of C higher than 1.0. Rational methods are available for estimating ultimate base resistance of rock sockets. A first order approximation based on strength of intact rock is given by Zhang and Einstein (1998) (see Figure 33). For fractured rock, a rea- sonable estimate can be made if the GSI (or RMR) is evalu- ated (see Figures 31 and 32). Although most states surveyed do not currently use GSI and RMR, the parameters required for its implementation can be obtained during the course of standard core logging procedures. The method recom- mended by CGS and adopted by AASHTO is applicable to moderately jointed sedimentary rocks, which is the most commonly encountered rock type for rock-socketed founda- tions. A method based on PMT provides another practical approach for calculating base resistance. A source of uncertainty in rock-socket design stems from attempting to combine side and base resistances at a specific value of downward displacement; for example, at the speci- fied limiting value of settlement or at the strength limit state. A relatively straightforward analysis based on elastic contin- uum theory, as given by Carter and Kulhawy (1988), is pre- sented in the form of closed-form expressions that predict axial load-deformation and base load transfer for typical conditions encountered in practice. Similar analytical ap- proaches for IGMs are given by O’Neill and Reese (1999). These equations are easily implemented in spreadsheet or other convenient form and allow designers to make rational estimates of load carried by both side and base at specified displacements. The survey questionnaire shows that this method is used by some state DOTs. The approach should be evaluated further against field load test measurements and, if verified, used more widely. Alternatively, the design charts given in Rowe and Armitage (1987a,b) provide a rational means of estimating axial load-displacement behavior and base load transfer. The charts are based on rigorous numeri- cal modeling and are the benchmark against which the Carter

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

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TRB’s National Cooperative Highway Research Program (NCHRP) Synthesis 360: Rock-Socketed Shafts for Highway Structure Foundations explores current practices pertaining to each step of the design process, along with the limitations; identifies emerging and promising technologies; examines the principal challenges in advancing the state of the practice; and investigates future developments and potential improvements in the use and design of rock-socketed shafts.

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