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CHAPTER THREE
DESIGN FOR AXIAL LOADING
SCOPE Several methods proposed in recent years for analysis of
both axial and lateral load response of rock sockets require, as
A rock-socketed drilled shaft foundation must be designed so an input parameter, the GSI proposed by Hoek et al. (1995,
that the factored axial resistance is not less than the effects of 2002). GSI is also correlated to the parameters that establish
the factored axial loads. At the strength limit state, side and the HoekBrown strength criterion for fractured rock masses.
base resistances of the socketed shaft are taken into account. Although GSI is not widely used in foundation engineering
Design for the service limit state accounts for tolerable practice at the present time, it likely will become a standard
movements of the structure and requires analysis of the axial rock mass characteristic for rock-socket design.
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 LOAD TRANSFER BEHAVIOR
methods for predicting axial load capacity and axial load- OF ROCK SOCKETS
displacement response of shafts in rock and IGM are then Compression Loading
reviewed and evaluated for their applicability to highway
bridge practice. 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 concreterock inter-
RELATIONSHIP TO GEOMATERIAL
CHARACTERIZATION face along the sides of the shaft and (2) the compressive nor-
mal stress that develops at the horizontal interface between
Design for axial loading requires reliable site and geoma- the base of the shaft and the underlying rock. A conceptual
terial characterization. Accurate geometric information, model of the load transfer can be illustrated by considering a
especially depth to rock and thickness of weathered and generalized axial load versus displacement curve as shown in
unweathered rock layers, is essential for correct analysis of Figure 19 (Carter and Kulhawy 1988). Upon initial loading,
axial resistance. This information is determined using the shearing stress develops along the vertical shaftrock inter-
tools and methods outlined in the previous chapter, princi- face. For a relatively small load, displacement is small and
pally core drilling supplemented by geophysical methods. the stressstrain behavior at the shaftrock interfaces is
Rock mass characterization using the Geomechanics System linear (line OA). There is no relative displacement ("slip")
(Bieniawski 1989) provides a general framework for assess- between the concrete shaft and surrounding rock and the sys-
ing the overall quality of the rock mass and its suitability as a tem may be modeled as being linearly elastic. With increas-
foundation material. Engineering properties of the intact rock ing load, the shear strength along some portion of the shaft
and the rock mass are used directly in the analysis methods sidewall is exceeded, initiating rupture of the "bond" and rel-
described in this chapter. For example, empirical relation- ative slip at the shaftrock interface. The load-displacement
ships have been derived between rock-socket unit-side resis- curve becomes nonlinear as rupture, and slip progress and a
tance and uniaxial strength of intact rock. Base capacity, greater proportion of the applied load is transferred to the
analyzed as a bearing capacity problem, may require uniax- base (line AB). At some point, the full side resistance is
ial compressive strength of intact rock, shear strength of mobilized, and there is slip along the entire surface ("full
discontinuities, or the HoekBrown strength parameters of slip" condition), and a greater proportion of the applied load
fractured rock mass, depending upon the occurrence, orien- is transferred to the shaft base (beyond point B in Figure 19).
tation, and condition of joint surfaces in the rock mass below If loading is continued to a displacement sufficient to cause
the base. For analysis of axial load-displacement response, failure of the rock mass beneath the base, a peak compressive
the rock mass modulus is required. Modulus may be deter- load may be reached. In practice, design of drilled shafts
mined from in situ testing, such as pressuremeter or borehole in rock requires consideration of (1) deformation limits and
jack tests, or estimated from rock mass classification param- (2) geotechnical and structural capacity (strength limit
eters as summarized in Table 12. Engineering properties of states). Geotechnical capacity in compression is evaluated in
rock mass used in conjunction with LRFD methods should terms of limiting side and base resistances. Load transfer
be mean values, not minimum values sometimes used in geo- in uplift involves the same mechanisms of side resistance
technical practice. mobilization as described previously for compression.
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asperities from the direction of shear displacement. The in-
terface shear strength () is then given by
= c + n tan ( + ) (18)
Full slip
Load, Qc
in which n = interface normal stress. Physically, all three
B components of strength (c, , ) may vary with displace-
Progressive slip ment. The initial shear strength may have both cohesive and
A frictional components. Following rupture, the cohesion is
probably decreased and dilation is mobilized. With further
displacement, dilation may cease and resistance may be
Linear elastic purely frictional and correspond to the residual friction angle.
In addition, field conditions of construction can significantly
O
affect the nature of the sidewall interface and, in practice,
Settlement, wc will determine the relative contributions of cohesion, fric-
FIGURE 19 Idealized load-displacement behavior. 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-
A rigorous model for the behavior of a rock-socketed
tive to property changes in the presence of water. Dilatancy
drilled shaft under axial compression would provide a pre-
is a function of interface roughness and shear strength of
diction of the complete load-displacement curve. In reality,
the intact rock forming the asperities. Sidewall roughness is
the mechanisms of side and base load transfer are complex
determined in part by rock type and texture, but can also be
and can only be modeled accurately through the use of so-
affected by construction tools and practices. Practices that
phisticated numerical methods, such as finite-element or result in a "smooth" sidewall will reduce dilatancy compared
boundary-element methods. Input parameters required for with practices that provide a "rough" sidewall (Williams and
accurate modeling are not normally available for design. In Pells 1981; Horvath et al. 1983).
recent years, several researchers have presented simplified
methods of analysis that provide bounds on the expected and Johnston and Lam (1989) made detailed investigations of
observed behaviors for shafts that fall within the range of the rockconcrete interface with the goal of better under-
conditions typically encountered in practice. Methods most standing the factors that determine interface roughness and
relevant to rock-socketed bridge foundations are presented in its influence on side-load transfer. Figure 20a shows an ide-
this chapter. Some of the more important behavioral aspects alized section of a rock socket following construction. An
pertaining to side and base resistance and their mobilization initial normal force exists between the rock and concrete.
are described first. When the shaft is loaded vertically, the shearing resistance
develops and the rock mass will deform elastically until slip
Side Resistance Mechanisms occurs. Figure 20a and b show the positions of the shaft
before and after slip displacement. These two conditions are
The conditions of the sidewall interface determine the represented by 2-D models in Figure 20c and d, respectively.
strength and load transfer in side resistance. Side resistance Figure 20d illustrates the dilation that occurs as a result of geo-
often exhibits a "bond" component that may exist physically metrical constraints. Dilation occurs against the surrounding
as a result of the cementation between the concrete and rock rock mass, which must deform to compensate for the increase
and from mechanical interlocking between asperities along in socket diameter, resulting in an increase in the interface
the interface. If the shearing strength of the interface is mod- normal stress. The average normal stress increase (n) can be
eled as a MohrCoulomb material, the bond component can approximated using the theoretical solution that describes
be considered as the interface adhesion, c. If displacements expansion of an infinite cylindrical cavity, as follows:
are sufficient, the interface bond is ruptured and the cohesion
component of resistance may be diminished. The second EM r
n = (19)
mechanism of resistance is frictional. Physically, the fric- 1+ r
tional resistance can have two components. The first is the
sliding friction angle of the interface, . The second is where EM and are the rock mass modulus and Poisson's ra-
mechanical dilatancy, which can be described as an increase tio, respectively; r is the dilation, and r is the original shaft
in the interface normal stress in response to the normal radius. A normal stiffness K can be defined as the ratio of
displacement (dilation) required to accommodate shear dis- normal stress increase to dilation, as follows:
placement of a rough surface. For mathematical simplicity,
dilatancy can be quantified in terms of the angle of dilation n EM
K= =
r r (1 + )
(), where corresponds to the average angle of triangular (20)
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FIGURE 21 Theoretical base load transfer (Rowe and
Armitage 1987b).
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
FIGURE 20 Idealized rockconcrete interface under axial the shaft relative to the stiffness of the rock along the side. In
loading (Johnston and Lam 1989).
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
Assuming the deformation r is small compared with r, and fractured rock to reach the base elevation. In that case, the
EM and v can be considered to be constant for the stress range modulus of the rock mass below the base may be greater than
considered, it follows that the behavior of the rockconcrete that of the rock along the sidewall of the socket. Osterberg
interface is governed by CNS conditions. This concept forms and Gill (1973) demonstrate the difference in load transfer in
the basis of the CNS direct shear test, in which the normal side and base resistances for two conditions, one in which the
force is applied through a spring (Johnston et al. 1987; Ooi base modulus is twice that of the sidewall rock modulus and
and Carter 1987). 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
Shaft Geometry and Relative Rigidity (Figure 22).
Load transfer in a rock socket depends on the geometry, Load transfer is affected significantly by the roughness of
expressed by the embedment ratio (depth/diameter), and the the sidewall interface. Fundamentally, this can be explained
stiffness of the concrete shaft relative to stiffness of the sur- by the higher load transfer in side shear reducing the propor-
rounding rock mass. Figure 21, based on finite-element tion of load transferred to the base. Because side resistance
analysis, illustrates this behavior for the initial (no slip) part increases with interface roughness, rock sockets with higher
of the load-displacement curve. In Figure 21, L = socket interface roughness will transfer a higher proportion of load
length, D = shaft diameter, Ep = modulus of the shaft, Er = in side resistance than smooth sockets. The complex interre-
modulus of rock mass above the base, Eb = modulus of rock lationships between load transfer, interface roughness, mod-
mass below the base, Qb = load transmitted to the base, and ulus ratio, and embedment ratio have been studied by several
Qt = load applied to the head of the shaft. The portion of ap- researchers, and the reader is referred to Pells et al. (1980),
plied axial compressive load that is transferred to the base is Williams et al. (1980), Rowe and Armitage (1987a), and
shown as a function of embedment ratio and modulus ratio. Seidel and Collingwood (2001) for more detailed discus-
With increasing embedment ratio, the relative base load sions. Six state DOTs indicated the use of grooving tools or
transfer decreases. For embedment ratios of 10, less than other methods to artificially roughen the sidewalls of rock-
10% of the applied load is transferred to the base. The effect socketed shafts.
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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
FIGURE 22 Effect of rock mass modulus at base on axial load from 2.5 mm to 25.4 mm, with most in the range of from 3
transfer (Wyllie 1999, based on Osterberg and Gill 1973). to 15 mm. These values are within the service limit state for
most bridge foundations. Additional details regarding the test
Base Condition shafts, subsurface profiles, and load test interpretation are
given in Crapps and Schmertmann (2002).
In many cases encountered in practice there is uncertainty
about conditions at the base of the shaft. Most transporta- Several important observations arise from the data shown in
tion agencies include, in their drilled shaft specifications, Figure 23. First, base resistance mobilization represents a sig-
limits on the amount of drill cuttings, water, or slurry that is nificant contribution to overall shaft resistance at downward
permissible at the base before concrete placement (Survey displacements corresponding to typical service loads. Second,
Question 34). However, compliance is not always verified the magnitude of base resistance is generally greater than pre-
and in some cases there is a perception that it is not practical dicted by elasticity-based numerical solutions (e.g., compare
to clean or inspect the base of the socket. In these cases, the with Figure 21). The dashed lines in Figure 23 represent ap-
designer may assume that base resistance will not develop proximate upper and lower bounds to the data from top load
without large downward displacement and for this reason tests and O-cell tests without bottom disturbance. For the most
base resistance is sometimes neglected for design purposes. part, O-cell tests that exhibited bottom disturbance fall below
Ten states indicated in their responses to Question 14 of the lower-bound curve. Although the data are not sufficient to
the survey that rock-socketed shafts are sometimes designed provide design values of base load transfer in advance for a
under the assumption of side resistance only. The draft given situation, they provide compelling evidence that shaft
Interim 2006 AASHTO LRFD Bridge Design Specifications design in rock should account properly for base resistance, and
state that "Design based on side-wall shear alone should that quality construction and inspection aimed at minimizing
be considered for cases in which the drilled hole cannot base disturbance can provide performance benefits.
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 Time Dependency
reasons cited by foundation designers for neglecting base
resistance in design, along with actions that can be taken to Time-dependent changes in load transfer may occur in rock-
address the concern. socketed shafts under service load conditions. Ladanyi (1977)
reported a case in which the bearing stress at the base of an in-
Crapps and Schmertmann (2002) suggest that accounting strumented rock socket increased, at a steadily decreasing
for base resistance in design and using appropriate construc- rate, over a period of 4 years; although the total applied head
TABLE 16
REASONS FOR NEGLECTING BASE RESISTANCE AND CORRECTIVE ACTIONS (after
Crapps and Schmertmann 2002)
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
