CHAPTER 11

GEOTECHNICAL DESIGN OF DRILLED

SHAFTS UNDER AXIAL LOADING

11.1 INTRODUCTION

The methods used to analyze and design drilled shafts under axial loading
have evolved since the 1960s, when drilled shafts came into wide use. The
design methods recommended for use today reflect the evolution of construc-
tion practices developed since that time.

11.2 PRESENTATION OF THE FHWA DESIGN PROCEDURE

11.2.1 Introduction
This chapter presents methods for computation of the capacity of drilled shafts
under axial loading. The methods for computation of axial capacity were
developed by O’Neill and Reese (1999).
The methods of analysis assume that excellent construction procedures
have been employed. It is further assume that the excavation remained stable,
and was completed with the proper dimensions, that the rebar was placed
properly, that a high-slump concrete was used, that the concrete was placed
in a correct manner, that the concrete was placed within 4 hours of the time
that the excavation was completed, and that any slurry that was used was
properly conditioned before the concrete was placed. Much additional infor-
mation on construction methods is given in O’Neill and Reese (1999). An-
other FHWA publication (LCPC, 1986), translated from French, also gives
much useful information.

323
324 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

While the design methods presented here have proved to be useful, they
are not perfect. Research continues on the performance of drilled shafts, and
improved methods for design are expected in the future. An appropriate factor
of safety must be employed to determine a safe working load. The engineer
may elect to employ a factor of safety that will lead to a conservative as-
sessment of capacity if the job is small. A load test to develop design param-
eters or to prove the design is strongly recommended for a job of any
significance.

11.3 STRENGTH AND SERVICEABILITY REQUIREMENTS

11.3.1 General Requirements

Two methods are available for determining the factored moments, shears, and
thrusts for designing structures by the strength design method: the single-load
factor method and a method based on the American Concrete Institute Build-
ing Code (ACI 318).
In addition to satisfying strength and serviceability requirements, many
structures must satisfy stability requirements under various loading and foun-
dation conditions.

11.3.2 Stability Analysis

The stability analysis of structures such as retaining walls must be performed
using unfactored loads. The unfactored loads and the resulting reactions are
then used to determine the unfactored moments, shears, and thrusts at critical
sections of the structure. The unfactored moments, shears, and thrusts are
then multiplied by the appropriate load factors, and the hydraulic load factor
when appropriate, to determine the required strengths used to establish the
required section properties.
The single-load factor method must be used when the loads on the struc-
tural component being analyzed include reactions from a soil–structure in-
teraction stability analysis, such as footings for walls. For simplicity and ease
of application, this method should generally be used for all elements of such
structures. The load factor method based on the ACI 318 Building Code may
be used for some elements of the structure, but must be used with caution to
ensure that the load combinations do not produce unconservative results.

11.3.3 Strength Requirements

Strength requirements are based on loads resulting from dead and live loads,
hydraulic loading, and seismic loading.
 11.5 GENERAL COMPUTATIONS FOR AXIAL CAPACITY OF INDIVIDUAL DRILLED SHAFTS 325

11.4 DESIGN CRITERIA

11.4.1 Applicability and Deviations

The design criteria for drilled shafts generally follow the recommendations
for structures founded on driven piles for loading conditions and design fac-
tors of safety.

11.4.2 Loading Conditions

Loading conditions are generally divided into cases of usual, unusual, and
extreme conditions.

11.4.3 Allowable Stresses

No current design standard contains limitations on allowable stresses in con-
crete or steel used in drilled shafts. However, the recommendations of ACI
318-02, Section A.3 may be used as a guide for design. These recommen-
dations are summarized in Table 11.1.
In cases where a drilled shaft is fully embedded in clays, silts, or sands,
the structural capacity of the drilled shaft is usually limited by the allowable
moment capacity. In the case of drilled shafts socketed into rock, the structural
capacity of the drilled shaft may be limited by the allowable stress in the
shaft. Maximum shear force usually occurs below the top of rock.

11.5 GENERAL COMPUTATIONS FOR AXIAL CAPACITY

OF INDIVIDUAL DRILLED SHAFTS

The axial capacity of drilled shafts should be computed by engineers who are
thoroughly familiar with the limitations of construction methods, any special
requirements for design, and the soil conditions at the site.

TABLE 11.1 Permissible Service Load Stresses Recommended by ACI 318-95,

Section A.3
Case Stress Level*
Flexure—extreme fiber stress in compression 0.45 ƒ⬘c
Shear—shear carried by concrete 1.1兹ƒ⬘c
Shear—maximum shear carried by concrete plus shear reinforcement vc  4.4兹ƒc⬘
Tensile stress—Grade 40 or 50 reinforcement 20,000 psi
Tensile stress—Grade 60 reinforcement 24,000 psi
* vc  permissible shear stress carried by concrete, psi, ƒ⬘c  compressive strength of concrete,
psi.
326 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

The axial capacity of a drilled shaft may be computed by the following

formulas:

Qult  Qs  Qb (11.1)

Qs  ƒs As (11.2)

Qb  qmax Ab (11.3)

where

Qult 
axial capacity of the drilled shaft,
Qs 
axial capacity in skin friction,
Qb 
axial capacity in end bearing,
ƒs 
average unit side resistance,
As 
surface area of the shaft in contact with the soil along the side of
the shaft,
qmax  unit end-bearing capacity, and
Ab  area of the base of the shaft in contact with the soil.

11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION

AND IN UPLIFT

11.6.1 Description of Soil and Rock for Axial Capacity Computations

The following six subsections present the design equations for axial capacity
in compression and in uplift. The first five subsections present the design
equations in side resistance and end bearing for clay, sand, clay shales, grav-
els, and rock. The last section presents a discussion of a statistical study of
the performance of the design equations in clays and sands.
O’Neill and Reese (1999) introduced the descriptive terms used in this
book to describe soil and rock for axial capacity computations. Collectively,
all types of soil and rock are described as geomaterials. The basic distinction
between soil and rock types is the characteristic of cohesiveness. All soil and
rock types include the descriptive terms cohesive or cohesionless.

11.6.2 Design for Axial Capacity in Cohesive Soils

Side Resistance in Cohesive Soils The basic method used for computing
the unit load transfer in side resistance (i.e., in skin friction) for drilled shafts
in cohesive soils is the alpha (␣) method. The profile of undrained shear
strength cu of the clay versus depth is found from unconsolidated-undrained
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 327

triaxial tests, and the following equation is employed to compute the ultimate
value of unit load transfer at a depth z below the ground surface:

ƒs  ␣ cu (11.4)

where

ƒs  ultimate load transfer in side resistance at depth z,

cu  undrained shear strength at depth z, and
␣  empirical factor that can vary with the magnitude of undrained shear
strength, which varies with depth z.

The value of ␣ includes the effects of sampling disturbance on the soil’s

shear strength, migration of water from the fluid concrete into the soil, and
other factors that might affect axial capacity in side resistance.
The total load Qs in side resistance is computed by multiplying the unit
side resistance by the peripheral area of the shaft. This quantity is expressed
by

Qs  冕zbot

ztop
ƒszdA (11.5)

where

dA  differential area of perimeter along sides of drilled shaft over pen-

etration depth,
L  penetration of drilled shaft below ground surface,
ztop  depth to top of zone considered for side resistance, and
zbot  depth to bottom of zone considered for side resistance.

The peripheral areas over which side resistance in clay is computed are
shown in Figure 11.1. The upper portion of the shaft is excluded for both
compression and uplift to account for soil shrinkage in the zone of seasonal
moisture change. In areas where the depth of seasonal moisture change is
greater than 5 ft (1.5 m) or when substantial groundline deflection results
from lateral loading, the upper exclusion zone should be extended to deeper
depths. The lower portion of the shaft is excluded when the shaft is loaded
in compression because downward movement of the base will generate tensile
stresses in the soil that will be relieved by cracking of soil, and porewater
suction will be relieved by inward movement of groundwater. If a shaft is
loaded in uplift, the exclusion of the lower zone for straight-sided shafts
should not be used because these effects do not occur during uplift loading.
The value of ␣ is the same for loading in both compression and uplift.
328

Top Five Feet (1.5 Meters) Top Five Feet (1.5 Meters)
Noncontributing for Both Noncontributing for Both
Compression and Uplift Compression and Uplift

Two Base Diameters

Bottom One Shaft Diameter
Above Base
of Stem Noncontributing
Noncontributing

Bottom One Diameter Periphery of Bell

Noncontributing in Noncontributing
Compression Loading
Belled Shaft in Compression Belled Shaft in Uplift

(a) Straight Shafts (b) Belled Shafts

Figure 11.1 Portions of drilled shaft not considered in computing side resistance in clay.
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 329

If the shaft is constructed with an enlarged base (also called an underream

or a bell), the exclusion zones for side resistance at the bottom of the shaft
differ for loading in compression and uplift, as shown in Figure 11.1b. If the
shaft is loaded in compression, the lower exclusion zone includes the upper
surface of the bell and the lower one diameter of the shaft above the bell.
When a belled shaft is loaded in uplift, the lower exclusion zone for side
resistance extends two base diameters above the base. If the lower exclusion
zone overlaps the upper exclusion zone, then no side resistance is considered
in the computations of axial capacity in uplift.
Equation 11.4 indicates that the unit load transfer in side resistance at depth
z is a product of ␣ and undrained shear strength at depth z. Research on the
results of load tests of instrumented drilled shafts has found that ␣ is not a
constant and that it varies with the magnitude of the undrained shear strength
of cohesive soils. O’Neill and Reese (1999) recommend using

cu
␣  0.55 for ⱕ 1.5 (11.6a)
pa

and

␣  0.55  0.1 冉 cu
pa
 1.5 冊 for 1.5 ⱕ
cu
pa
ⱕ 2.5 (11.6b)

where pa  atmospheric pressure  101.3 kPa  2116 psf. (Note that 1.5 pa
 152 kPa or 3,170 psf and 2.5 pa  253 kPa or 5290 psf.)
For cases where cu /pa exceeds 2.5, side resistance should be computed
using the methods for cohesive intermediate geomaterials, discussed later in
this chapter.
Some experimental measurements of ␣ obtained from load tests are shown
in Figure 11.2. The relationship for ␣ as a function of cu /pa defined by Eq.
11.6 is also shown in this figure. For values of cu /pa greater than 2.5, side
resistance should be computed using the recommendations for cohesive in-
termediate geomaterials, discussed later in this chapter.
When an excavation is open prior to the placement of concrete, the lateral
effective stresses at the sides of the drilled hole are zero if the excavation is
drilled in the dry or small if there is drilling fluid in the excavation. Lateral
stresses will then be imposed on the sides of the excavation because of the
fluid pressure of the fresh concrete. At the ground surface, the lateral stresses
from the concrete will be zero or close to zero. It can be expected that the
lateral stress from the concrete will increase almost linearly with depth, as-
suming that the concrete has a relatively high slump. Experiments conducted
by Bernal and Reese (1983) found that the assumption of a linear increase in
the lateral stress from fluid concrete for depths of concrete of 3.0 m (10 ft)
or more is correct. For depths greater than 3.0 m, the lateral stress is strongly
330 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

Figure 11.2 Correlation between ␣ and cu / pa.

dependent on the character of the fresh concrete. From available experimental

evidence, it follows that a rational recommendation for ␣ is that ␣ should
vary perhaps linearly with depth, starting at zero at the groundline, to its
ultimate value at some critical depth below the groundline. However, insuf-
ficient data are available for making such a detailed recommendation. The
recommendations for design in Eq. 11.6 generally lead to a reasonable cor-
relation between experimental measurements and computed results.
With regard to the depth over which ␣ is assumed to be zero, consideration
must be given to those cases where there are seasonal changes in the moisture
content of the soil. It is conceivable, perhaps likely, that clay near the ground
surface will shrink away from the drilled shaft so that the load transfer is
reduced to zero in dry weather over the full depth of the seasonal moisture
change. There may also be other instances where the engineer may wish to
deviate from the recommendations of Eq. 11.6 because of special circum-
stances at a particular site. A drilled shaft subjected to a large lateral load is
an example of such a circumstance; if the lateral deflection at the groundline
is enough to open a gap between the shaft and soil, the portion of the drilled
shaft above the first point of zero deflection should be excluded from side
resistance.

End Bearing in Cohesive Soils The computation of load transfer in end

bearing for deep foundations in clays is subject to much less uncertainty than
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 331

is the computation of load transfer in side resistance. Skempton (1951) and

other investigators have developed consistent formulas for the computation of
end bearing. In addition, the accuracy of Skempton’s work has been confirmed
by results from instrumented drilled shafts where general base failure was
observed. Equation 11.7 is employed for computing the ultimate unit end
bearing qmax for drilled shafts in saturated clay:

qmax  N*c
c u (11.7)

where cu is an average undrained shear strength of the clay computed over a

depth of two diameters below the base, but judgment must be used if the
shear strength varies strongly with depth.
The bearing capacity factor N*c is computed using

N*c  1.33(ln兩Ir兩  1) (11.8)

where Ir is the rigidity index of the soil, which for a saturated, undrained
material (␾  0) soil is expressed by

Es
Ir  (11.9)
3cu

where Es is Young’s modulus of the soil undrained loading. Es should be

measured in laboratory triaxial tests or in-situ by pressuremeter tests to apply
the above equations. For cases in which measurements of Es are not available,
Ir can be estimated by interpolation using Table 11.2.
When L/B is less than 3.0, qmax should be reduced to account for the effect
of the presence of the ground surface by using

冋
qmax  0.667 1  0.1667
L
B册N*c
c u (11.10)

where:

TABLE 11.2 Ir and N*

c Values for Cohesive Soil

cu Ir N*
c

24 kPa (500 psf) 50 6.55

48 kPa (1000 psf) 150 8.01
96 kPa (2000 psf) 250 8.69
192 kPa (4000 psf) 300 8.94
332 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

L  length of the shaft, and

B  diameter of the base of the shaft.

Uplift Resistance of Straight-Sided Shafts in Cohesive Soil Base resis-

tance for uplift loading on straight-sided shafts should be assumed to be zero
unless confirmed by load testing.

Uplift Resistance of Belled Shafts in Cohesive Soil Unit base resistance

for belled shafts can be computed from

qmax (uplift)  su Nu (11.11)

where

Nu  bearing capacity factor for uplift, and

su  average undrained shear strength between the base of the bell and 2
Bb above the base.

Nu can be computed from

Db
Nu  3.5 ⱕ9 for unfissured clay (11.12)
Bb

or from

Db
Nu  0.7 ⱕ9 for fissured clay (11.13)
Bb

In the expressions above, Db is the depth of the base of the bell below the
top of the soil stratum that contains the bell, but not counting any depth within
the zone of seasonal moisture change.
The unit uplift resistance should be applied over the projected area of the
bell, Au. The projected area is computed from

␲ 2
Au  (B  B2) (11.14)
4 b

Example Problem 1—Shaft in Cohesive Soil This is an example of a

shaft drilled into clay. It is based on a case history, referred to as ‘‘Pile A,’’
reported by Whitaker and Cooke (1966).

Soil Profile. The soil profile is shown in Figure 11.3. The clay is overcon-
solidated. The depth to the water table was not given and is not needed in
making capacity calculations. However, the range of depth of the water table
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 333

Undrained Shear Strength (tsf)

Depth, ft 0.0 0.4 0.8 1.2 1.6

0.0 0.0

20
Depth, ft

Clay 40

60

80
Figure 11.3 General soil description of Example Problem 1.

should be determined and always reported in the construction documents for

construction considerations.

Soil Properties. Values of undrained shear strength obtained from laboratory

tests are included in Figure 11.3.

Construction. High-quality construction, good specifications, and excellent

inspection are assumed.

Loadings. The working axial load is 230 tons. No downdrag acting on the
shaft is expected, and vertical movement of the soil due to expansive clay is
not a problem. Effects due to lateral loading are also thought to be negligible.
The depth to the zone of seasonal moisture change is judged to be about 10
ft.

Factor of Safety. It is assumed that a load test has been performed in the
area, that the design parameters have been proven, and that the soil conditions
across the site are relatively uniform; therefore, an overall factor of safety of
2 was selected.

Ultimate Load. Using a factor of safety of 2, the ultimate axial load was
computed to be 460 tons.

Geometry of the Drilled Shaft. An underreamed shaft was designed to pen-

etrate a total of 40 ft into the clay. The height of the bell is 4 ft, making the
334 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

length of the straight-sided portion 36 ft. The diameter of the straight-sided

portion of the shaft is 2.58 ft, and the diameter of the bell is 5.5 ft.

Computations
SIDE RESISTANCE. For ease of hand computations, a constant value of ␣z equal
to 0.55 and an average cu of 2280 psf are assumed. However, the computer
program interpolates linearly the top and bottom values of cu with depth. The
hand computations are as follows:

Depth Interval, ft ⌬A, ft2 Avg. Effective Stress, tsf ␣Z ⌬Qs, tons
0–5 0 0
5–33.4 230.4 1.14 0.55 144.4
33.4–40 0 0
Qs  144.4

BASE RESISTANCE. The average undrained shear strength over two base di-
ameters below the base is 1.48 tsf, and the area of the base is 23.76 ft2.
By interpolation between the values of N* c shown in Table 11.2, N* c 
8.81.

qmax  N*
c cu  (8.81) (1.48 tsf)  13.04 tsf
Ab  23.76 ft2
Qb  (12.92 tsf) (23.76 ft2)  309.8 tons

TOTAL RESISTANCE

QT  144.3  307  454 tons

11.6.3 Design for Axial Capacity in Cohesionless Soils

Side Resistance in Cohesionless Soils The shear strength of sands and
other cohesionless soils is characterized by an angle of internal friction that
ranges from about 30⬚ up, depending on the kinds of grains and their packing.
The cohesion of such soils is assumed to be zero. The friction angle at the
interface between the concrete and the soil may be different from that of the
soil itself. The unit side resistance, as the drilled shaft is pushed downward,
is equal to the normal effective stress at the interface times the tangent of the
interface friction angle.
Unsupported shaft excavations are prone to collapse, so excavations in
cohesionless soil are made using drilling slurry to stabilize the borehole, and
the normal stress at the face of the completed drilled shaft depends on the
construction method. The fluid stress from the fresh concrete will impose a
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 335

normal stress that is dependent on the characteristics of the concrete. Exper-

iments have found that concrete with a moderate slump (up to 6 in., 150 mm)
acts hydrostatically over a depth of 10 to 15 ft (3 to 4.6 m) and that there is
a leveling off in the lateral stress at greater depths, probably due to arching
(Bernal and Reese, 1983). Concrete with a high slump (about 9 in., 230 mm)
acts hydrostatically to a depth of 32 ft (10 m) or more. Thus, the construction
procedures and the nature of the concrete will have a strong influence on the
magnitude of the lateral stress at the concrete–soil interface. Furthermore, the
angle of internal friction of the soil near the interface will be affected by
the details of construction.
In view of the above discussion, the method of computing the unit load
transfer in side resistance must depend on the results from field experiments
as well as on theory. The following equations are recommended for design.
The form of the equations is based on theory, but the values of the parameters
that are suggested for design are based principally on the results of field
experiments.

ƒsz  K␴z⬘ tan ␾c (11.15)

Qs  冕L

0
K␴⬘z tan ␾c dA (11.16)

where

ƒsz  ultimate unit side resistance in sand at depth z,

K  a parameter that combines the lateral pressure coefficient and a cor-
relation factor,
␴⬘z  vertical effective stress in soil at depth z,
␾c  friction angle at the interface of concrete and soil,
L  depth of embedment of the drilled shaft, and
dA  differential area of the perimeter along sides of drilled shaft over the
penetration depth.

Equations 11.15 and 11.16 can be used in the computations of side resis-
tance in sand, but simpler expressions can be developed if the terms for K
and tan ␾c are combined. The resulting expressions are shown in Eqs. 11.17
through 11.20.

ƒsz  ␤ ␴z⬘ ⱕ 2.1 tsf (200 kPa) (11.17)

Qs  冕L

0
␤␴⬘z dA (11.18)
336 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

␤  1.5  0.135兹z (ft) or (11.19a)

␤  1.5  0.245兹z (m); 0.25 ⱕ ␤ ⱕ 1.20

where z  depth below the ground surface, in feet or meters, as indicated.

When the uncorrected SPT resistance, N60, is less than or equal to 15
blows/ft, ␤ is computed using

N60
␤ (1.5  0.135兹z (ft)) or
15 (11.19b)
N60
␤ (1.5  .245兹z (m)) for N60 ⱕ 15
15

Note that for sands

␤  0.25 when z  85.73 ft or 26.14 m (11.20)

For very gravelly sands or gravels

␤  2.0  0.0615 [z (ft)]0.75 or (11.21)

␤  2.0  0.15 [z (m)] 0.75
; 0.25 ⱕ ␤ ⱕ 1.8

For gravelly sands or gravels

␤  0.25 when z  86.61 ft or 26.46 m (11.22)

The design equations for drilled shafts in sand use SPT N60-values uncor-
rected for overburden stress. The majority of the load tests on which the
design equations are based were performed in the Texas Gulf Coast region
and the Los Angeles Basin in California. The N60-values for these load tests
were obtained using donut hammers with a rope-and-pulley hammer release
system. If a designer has N-values that were measured with other systems or
were corrected for level of overburden stress and rod energy, it will be nec-
essary to adjust the corrected N-values to the uncorrected N60 form for donut
hammers with rope-and-pulley hammer release systems before use in the de-
sign expressions of Eq. 11.19b and Table 11.4. Guidance for methods used
to correct SPT penetration resistances is presented in Chapter 3 of EM 1110-
1-1905.
The parameter ␤ combines the influence of the coefficient of lateral earth
pressure and the tangent of the friction angle. The parameter also takes into
account the fact that the stress at the interface due to the fluid pressure of the
concrete may be greater than that from the soil itself. In connection with the
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 337

lateral stress at the interface of the soil and the concrete, the assumption
implicit in Eq. 11.17 is that good construction procedures are employed. See
Chapter 5 for further construction information. Among other factors, the
slump of the concrete should be 6 in. or more and drilling slurry, if employed,
should not cause a weak layer of bentonite to develop at the wall of the
excavation. The reader is referred to O’Neill and Reese (1999) for further
details on methods of construction.
The limiting value of side resistance shown in Eq. 11.17 is not a theoretical
limit but is the largest value that has been measured (Owens and Reese, 1982).
Use of higher values can be justified by results from a load test.
A comparison of ␤ values computed from Eq. 11.19 and ␤ values derived
from loading tests in sand on fully instrumented drilled shafts is presented in
Figure 11.4. As can be seen, the recommended expression for ␤ yields values
that are in reasonable agreement with experimental values.
Equation 11.17 has been employed in computations of fsz, and the results
are shown in Figure 11.5. Three values of ␤ were selected; two of these are
in the range of values of ␤ for submerged sand, and the third is an approxi-
mate value of ␤ for dry sand. The curves are cut off at a depth below 60 ft
(18 m) because only a small amount of data has been gathered from instru-
mented drilled shafts in sand with deep penetrations. Field load tests are
indicated if drilled shafts in sand are to be built with penetrations of over 70
ft (21 m).
It can be argued that Eqs. 11.17 and 11.18 are too elementary and that the
angle of internal friction, for example, should be treated explicitly. However,
the drilling process has an influence on in situ shearing properties, so the true
friction angle at the interface cannot be determined from a field investigation
that was conducted before the shaft was constructed. Furthermore, Eqs. 11.17
and 11.18 appear to yield an satisfactory correlation with results from full-
scale load tests.
The comparisons of results from computations with those from experi-
ments, using the above equations for sand, show that virtually every computed
value is conservative (i.e., the computed capacity is less than the experimen-
tally measured capacity). However, it is of interest that most of the tests in
sand are at locations where the sand was somewhat cemented. Therefore,
caution should be observed in using the design equations for sand if the sand
is clean, loose, and uncemented.
Either Eq. 11.15 or Eq. 11.17 can be used to compute the side resistance
in sand. The angle of internal friction of the sand is generally used in Eq.
11.15 in place of the friction angle interface at the interface of the concrete
and soil if no information is available. In some cases, only SPT resistance
data are available. In such cases, the engineer can convert the SPT penetration
resistance to the equivalent internal friction angle by using Table 11.3 as a
guide.
338 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

Figure 11.4 Plot of experimental values of ␤.

 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 339

Figure 11.5 Variation of ƒsz with depth (z) for values of ␥.

Side Resistance in Cohesionless Soils—Uplift Loading For uplift load-

ing in granular materials, the side resistance developed under drained, uplift
conditions is reduced due to the Poisson effect, lowering the normal stress at
the side of the shaft. Based on analytical modeling and centrifuge research
reported by de Nicola (1996), side resistance in uplift may be computed using

ƒmax (uplift)  ⌿ ƒmax (compression) (11.23)

The factor ⌿ is computed using

340 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

TABLE 11.3 Relationship Between N, ␾, and Dr

N ␾, deg. Dr, % ␾, deg. Dr, % ␾, deg. Dr, %
2 32 45
4 34 55
6 36 65 30 37
10 38 75 32 46 31 40
15 42 90 34 57 32 48
20 45 100 36 65 34 55
25 37 72 35 60
30 39 77 36 65
35 40 82 36 67
40 41 86 37 72
45 42 90 38 75
50 44 95 39 77
55 45 100 39 80
60 40 83
65 41 86
70 42 90
75 42 92
80 43 95
85 44 97
90 44 99
Source: After Gibbs and Holtz (1957).

冉 冊冉 冊
␩  vp tan ␦
L
B
Gavg
Ep
(11.24)

⌿ 再1  0.2 log10 冏 冏冎
100
(L/B)
(1  8␩  25␩2) (11.25)

where

Ep  Young’s modulus of the shaft, and

Gavg  average shear modulus of the soil along the length of the shaft,
estimated as the average Young’s modulus of soil divided by 2.6.

O’Neill and Reese (1999) examined Eq. 11.25 and concluded that typical
values of ⌿ fall into the range 0.74 to 0.85 for L/B ratios of 5 to 20. They
noted that Eq. 11.25 appears to overestimate ⌿ for L/B ratios larger than 20.
The value ⌿ can be taken conservatively to be 0.75 for design purposes.

End Bearing in Cohesionless Soils Because of the relief of stress when

an excavation is drilled into sand, the sand tends to loosen slightly at the
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 341

bottom of the excavation. Also, there appears to be some densification of the

sand beneath the base of a drilled shaft as settlement occurs. A similar phe-
nomenon has also been observed in model tests on spread footings founded
in sand by Vesić (1973). The load-settlement curves for the base of drilled
shafts that have been obtained from load tests on instrumented test shafts are
consistent with these concepts. In many load tests, the base load continued
to increase to a settlement of more that 15% of the diameter of the base. Such
a large settlement cannot be tolerated for most structures; therefore, it was
decided to formulate the design equations for end bearing to limit values of
end bearing for drilled shafts in granular soil to those that are expected to
occur at a downward movement of 5% of the diameter of the base (O’Neill
and Reese, 1999).
Values of qb are tabulated as a function of N60 (standardized for hammer
energy but uncorrected for overburden stress) in Table 11.4. The computation
of tip capacity is based directly on the penetration resistance from the SPT
near the tip of the drilled shaft.
The values in Table 11.4 can be expressed in equation form as follows:

If L ⱖ 10 m: qb  57.5 NSPT ⱕ 2.9 MPa (11.26)

L L
If L  10 m: qb  57.5 NSPT ⱕ 2.9 MPa (11.27)
10 m 10 m

or in U.S. Customary Units

If L ⱖ 32.8 ft: qb  0.60 NSPT ⱕ 30 tsf (11.28)

L L
If L  32.8 ft: qb  0.60 NSPT ⱕ 30 tsf (11.29)
32.8 ft 32.8 ft

where L is the shaft length in meters or feet as required.

These values are similar to those recommended by Quiros and Reese
(1977). These authors recommended no unit end bearing for loose sand

TABLE 11.4 Recommended Values of Unit End Bearing for Shafts in

Cohesionless Soils with Settlements Less Than 5% of the Base Diameter
Range of Value on N60 Value of qb, tons / ft2 Value of qb, MPa
0 to 50 blows / ft 0.60 N60 0.0575 N60
Upper limit 30 tsf 2.9 MPa
Note: For shafts with penetrations of less than 10 base diameters, it is recommended that qb be
varied linearly from zero at the groundline to the value computed at 10 diameters using Table
11.4.
342 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

(␾ ⱕ 30⬚), a value of 16 tons/ft2 (1.53 MPa) for medium-dense sand (30⬚ 

␾ ⱕ 36⬚), and a value of 40 tons/ft2 (3.83 MPa) for very dense sand (36⬚ 
␾ ⱕ 41⬚).
Neither of the sets of recommendations involves the stress in the soil out-
side the tip of the drilled shaft. This concept is consistent with the work of
Meyerhof (1976) and others. Furthermore, the values in Table 11.4 are based
predominantly on experimental results for shaft settlements of less than 5%
of the base diameter where the drilled shafts had various penetrations. How-
ever, implicit in the values of qb that are given is that the penetration of the
drilled shaft must be at least 10 diameters below the ground surface. For
penetration of less than 10 diameters, it is recommended that qb be varied
linearly from zero at the groundline to the value computed at 10 diameters
using Table 11.4.
Table 11.4 sets the limiting value of load transfer in end bearing at 30 tsf
(2.9 MPa) at a settlement equal to 5% of the base diameter. However, higher
unit end-bearing values are routinely used when validated by load tests. For
example, a value of 58 tsf (5.6 MPa) was measured at a settlement of 4% of
the diameter of the base at a site in Florida (Owens and Reese, 1982).

Example Problem 2—Shaft in Cohesionless Soil This is an example of

a shaft drilled into sand. The example has been studied in the referenced
literature of Reese and O’Neill (1988). It is also modeled after load tests in
sand (Owens and Reese, 1982).

Soil Profile. The soil profile is shown in Figure 11.6. The water table is at a
depth of 4 ft below the ground surface.

Soil Properties. N60-values (blow counts per foot) from the SPT are included
in Figure 11.6.

Construction. High-quality construction is assumed. The contractor will have

all the required equipment in good order, and experienced personnel will be
on the job.

Loadings. The working axial load is 170 tons, the lateral load is negligible,
and no downdrag is expected.

Factor of Safety. It is assumed that a load test has been performed nearby,
but considering the possible variation in the soil properties over the site and
other factors, an overall factor of safety of 2.5 is selected. The diameter will
be sufficiently small so that reduced end bearing will not be required. Con-
sequently, the global factor of safety can be applied to both components of
resistance.

Ultimate Load. The ultimate axial load is thus established as 2.5 170 tons
 425 tons, since a global factor of safety (of 2.5) is used.
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 343

N60-Values

Depth, ft 0 10 20 30 40 50
0

20

Sand

40

60
Sand w/
Some
Limerock

80
Figure 11.6 General soil description of Example Problem 2.

Geometry of the Drilled Shaft. A straight-sided drilled shaft is selected with

a diameter of 3 ft and a penetration of 60 ft.

Computations
SIDE RESISTANCE. Computations are performed assuming a total unit weight
of sand equal to 115 pcf. The hand computations are as follows:

Depths, ft ⌬ A, ft2 Avg. Effective Stress, tsf ␤ ⌬Qs, tons

0–4 37.7 0.115 1.200 5.2
4–30 245.0 0.572 0.943 132.1
30–60 282.7 1.308 0.594 219.7
Qs  357.0 tons

BASE RESISTANCE. Computations for base resistance are performed using the
soil at the base of the shaft. At the 60-ft location, NSPT  21.

qb  0.60NSPT ⱕ 30 tsf
qb  (0.6) (21)  12.6 tsf
344 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

Ab  7.07 ft2
Qb  (7.07 ft2) (12.6 tsf)  89.1 tons

TOTAL RESISTANCE

QT  357  89.1  446.1 tons

Example Problem 3—Shaft in Mixed Profile This is an example of a shaft

drilled into a soil of a mixed profile with layers of clay and sand. It is modeled
after load tests performed and reported by Touma and Reese (1972) at the
G1 site.

Soil Profile. The soil profile is shown in Figure 11.7. The water table is at a
depth of 17 ft below the ground surface.

Soil Properties. Values of undrained shear strength obtained from laboratory

tests and N60-values (blow counts per foot) from the SPT are included in
Figure 11.7.

Construction. High-quality construction, good specifications, and excellent

inspection are assumed.

Loadings. The working axial load is 150 tons, no downdrag is expected, and
lateral loading is negligible. The depth to the zone of seasonal moisture
change is judged to be about 10 ft.

Undrained Shear Strength (tsf)

Depth, ft 0 0.2 0.4 0.6 0.8 1.0
0 0

Silty Clay
20

32
N = 20
40

N = 25
Sand
60

N = 50
80 80
Figure 11.7 General soil description of Example Problem 3.
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 345

Factor of Safety. Soil conditions across the site are variable, and the foun-
dation is for a major and complex structure. An overall factor of safety of 3
was selected.

Ultimate Load. Using the factor of safety of 3, the ultimate axial load is
computed to be 450 tons.

Geometry of the Drilled Shaft. A straight-sided shaft is selected, with a di-

ameter of 3 ft and a penetration of 59 ft.

Computations
SIDE RESISTANCE. Computations are performed assuming a total unit weight
of clay equal to 125 pcf and a total unit weight of sand equal to 115 pcf. For
ease of hand computations, an average value of ␤ was selected for the sand
layer. The computations are as follows:

Avg. cu or
Soil Depth Interval, Effective Stress,
Type ft ⌬ A, ft2 tsf ␣Z or ␤ ⌬Qs, tons
Clay 0–5 — (Cased) 0 0
Clay 5–32 254.5 0.81 0.55 113.4
Sand 32–59 254.5 1.887 0.589 282.9
Qs  396.3 tons

BASE RESISTANCE. Computations for base resistance are performed using the
soil at the base of the shaft. At the 59-ft location, NSPT  25.

qb  (0.6) (25 tsf)  15.0 tsf

Ab  7.07 ft2
Qb  (7.07 ft2) (15.0 tsf)  106.0 tons

TOTAL RESISTANCE

QT  396.3  106.0  502.3 tons

11.6.4 Design for Axial Capacity in Cohesive Intermediate

Geomaterials and Jointed Rock
Side Resistance in Cohesive Intermediate Geomaterials Weak rock is
the term for materials that some authors call intermediate geomaterials. In
general, the soil resistances and settlements computed by these criteria are
considered appropriate for weak rock with compressive strength in the range
346 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

of 0.5 to 5.0 MPa (73 to 725 psi). The following intermediate geomaterials
usually fall within this category: argillaceous geomaterials (such as heavily
overconsolidated clay, hard-cohesive soil, and weak rock such as claystones)
or calcareous rock (limestone and limerock, within the specified values of
compressive strength).
Drilled shafts are attractive as a reliable foundation system for use in in-
termediate geomaterials. These geomaterials are not difficult to excavate, and
provide good stability and excellent capacity.
Two procedures for computation of side resistance in cohesive intermediate
geomaterials are presented by O’Neill and Reese (1999). One procedure is a
simplified version of a more detailed procedure developed by O’Neill et al.
(1996). Both procedures are presented in the following sections.

Simplified Procedure for Side Resistance in Cohesive Intermediate Geo-

material. The first decision to be made by the designer is whether to classify
the borehole as smooth or rough. A borehole can be classified as rough only
if artificial means are used to roughen its sides and to remove any smeared
material from its sides. If conditions are otherwise, the borehole must be
classified as smooth for purposes of design.
The term smooth refers to a condition in which the borehole is cut naturally
with the drilling tool without leaving smeared material on the sides of the
borehole wall. To be classified as rough, a borehole must have keys cut into
its wall that are at least 76 mm (3 in.) high, 51 mm (2 in.) deep, and spaced
vertically every 0.46 m (1.5 ft) along the depth of shafts that are at least 0.61
m (24 in.) in diameter.
The peak side resistance for a smooth borehole in Layer i is computed
using

ƒmax,i  ␣␸qu,i (11.30)

where ␣ (not equal in value to the ␣ for cohesive soils) is obtained from
Figure 11.8. The terms in the figure are defined as follows. Em is Young’s
modulus of the rock (i.e., the rock mass modulus), qu is the unconfined
strength of the intact material, and wt is the settlement at the top of the rock
socket at which ␣ is developed. The rock mass modulus can be estimated
from measurements of Young’s modulus of intact rock cores using Table 11.6.
The curves in Figure 11.8 are based on the assumption that the interface
friction angle between the rock and concrete is 30⬚. If the interface friction
is different from 30⬚, it should be modified using

tan␾rc
␣  ␣␾rc30⬚
or tan 30⬚ (11.31)
␣  1.73␣␾rc30⬚ tan ␾rc
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 347

Figure 11.8 Definition of terms for surface roughness.

To use Figure 11.8, the designer must estimate the horizontal pressure of the
fluid concrete acting at the middle of Layer i, ␴n. If the concrete has a slump
of 175 mm (7 in.) or more and is placed at a rate of 12 m (40 ft) per hour,
then ␴n at a depth z*i below the cutoff elevation up to 12 m (40 ft) can be
estimated from

␴n  0.65␥c z*
i (11.32)

␸ is a joint effect factor that accounts for the presence of open joints that
are voided or filled with soft gouge material. The joint effect factor can be
estimated from Table 11.5.
qu,i is the design value for qu in Layer i. This is usually taken as the mean
value from intact cores larger than 50 mm (2 in.) in diameter. The possibility
of the presence of weaker material between the intact geomaterial that could
be sampled is considered through the joint effect factor, ␸.
For a smooth rock socket in cohesive intermediate geomaterial, the side
resistance is computed using

TABLE 11.5 Estimation of Em / Ei Based on RQD

RQD (%) Closed Joints Open Joints
100 1.00 0.60
70 0.70 0.10
50 0.15 0.10
20 0.05 0.05
348 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

ƒmax,i  0.65␸ pa 冪qp

u,i

a
(11.33)

If the rock socket has been roughened, the side resistance for a rough rock
socket in cohesive intermediate geomaterial is

ƒmax,i  0.8␸ 冉 冉 冊册
⌬r
r
L⬘
L
0.45

qu,i (11.34)

where

⌬r  depth of shear keys,

r radius of borehole,
L⬘  vertical spacing between the shear keys, and
L depth covered by the shear keys, as defined in Fig. 11.9.

Detailed Procedure for Side Resistance in Cohesive Intermediate Geoma-

terial. O’Neill et al. (1996) recommend methods for estimating side and base
resistances as well as settlement of drilled shafts under axial loads in this
type of geomaterial. Their primary method, called direct load-settlement sim-

Figure 11.9 Factor ␣ for smooth category 1 or 2 IGMs.

 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 349

ulation, is used to compute the axial capacity of drilled shafts socketed into
weak rock.
The direct simulation design model, based on an approximation of the
broad range of FEM solutions, is as follows:
Decide whether the socket of weak rock in which the drilled shaft is placed
requires subdivision into sublayers for analysis. If the weak rock is relatively
uniform, the behavior of axially loaded drilled shafts can probably be simu-
lated satisfactorily for design purposes using the simple procedure outlined
below. If there is significant layering of the weak rock in the depth range of
the socket, a load transfer function analysis should be modeled by a special
FEM, as recommended by O’Neill et al. (1996). Significant layering in this
respect will exist if the weak rock at the base of the shaft is considerably
stronger and stiffer than that surrounding the sides and/or if changes in the
stiffness and strength of the weak rock occur along the sides of the shaft.
Load transfer function analyses should also be conducted if sockets exceed
about 7.6 m (25 ft) in length.
Obtain representative values of the compressive strength qc of the weak
rock. It is recognized in practice that qu is often used to represent compressive
strength. Accordingly, qu will be used to symbolize qc in this criteria. When-
ever possible, the weak rock cores should be consolidated to the mean effec-
tive stress in the ground and then subjected to undrained loading to establish
the value of qu. This solution is valid for soft rocks with 0.5  qu  5.0 MPa
(73  qu  725 psi). The method also assumes that high-quality samples,
such as those obtained using triple-walled core barrels, have been recovered.
Determine the percentage of core recovery. If core recovery using high-
quality sampling techniques is less than 50%, this method does not apply,
and field loading tests are recommended to establish the design parameters.
Determine or estimate the mass modulus of elasticity of the weak rock,
Em. If Young’s modulus of the material in the softer seams within the harder
weak rock, Es, can be estimated, and if Young’s modulus of the recovered,
intact core material, Ei, is measured or estimated, then the following expres-
sion, can be used:

Em Lc

冘t 冘t
(11.35)
Ei ei
seams  intact core segments
Es

In Eq. 11.32, Lc is the length of the core and 兺tseams is the summation of
the thickness of all of the seams in the core, which can be assumed to be
(1  rc) Lc, where rc is the core recovery ratio (percent recovery/100%) and
can be assumed equal to rc Lc. If the weak rock is uniform and without
significant soft seams or voids, it is usually conservative to take Em  115
qu. If the core recovery is less than 100%, it is recommended that appropriate
in situ tests be conducted to determine Em. If the core recovery is at least
350 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

50%, the recovered weak rock is generally uniform and the seams are filled
with soft geomaterial, such as clay, but moduli of the seam material cannot
be determined. Table 11.6 can be used, with linear interpolation if necessary,
to estimate very approximately Em /Ei. Use of this table is not recommended
unless it is impossible to secure better data.
The designer must decide whether the walls in the socket can be classified
as rough. If experience indicates that the excavation will produce a borehole
that is rough according to the following definition, then the drilled shaft may
be designed according to the method for the rough borehole. If not, or if the
designer cannot predict the roughness, the drilled shaft should be designed
according to the method for the smooth borehole.
A borehole can be considered rough if the roughness factor Rƒ will reliably
exceed 0.15. The roughness factor is defined by

Rƒ  冋 冉 冊册
⌬r
r
Lt
Ls
(11.36)

where the terms in this equation are defined in Figure 11.9.

Estimate whether the soft rock is likely to smear when drilled with the
construction equipment that is expected on the job site. Smear in this sense
refers to the softening of the wall of the borehole due to drilling disturbance
and/or exposure of the borehole to free water. If the thickness of the smear
zone is expected to exceed about 0.1 times the mean asperity height, the
drilled shaft should be designed as if it were smooth.
The effects of roughness and smear on both resistance and settlement are
very significant, as will be demonstrated in the design examples. As part of
the site exploration process for major projects, full-sized drilled shaft exca-
vations should be made so that the engineer can quantify these factors, either
by entering the borehole or by using appropriate down-hole testing tools such
as calipers and sidewall probes. Rough borehole conditions can be assured if
the sides of the borehole are artificially roughened by cutting devices on the
drilling tools immediately prior to placing concrete such that Rƒ  0.15 is
attained.
Estimate ƒa, the apparent maximum average unit side shear at infinite dis-
placement. Note that ƒa is not equal to ƒmax, which is defined as a displace-
ment defined by the user of this method.

TABLE 11.6 Estimation of Em / Ei Based on RQD

RQD (%) Closed Joints Open Joints
100 1.00 0.60
70 0.70 0.10
50 0.15 0.10
20 0.05 0.05
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 351

For weak rock with a rough borehole, use

qu
ƒa  (11.37)
2

For weak rock with a smooth borehole, use

ƒa  ␣ qu where ␣ ⱕ 0.5 (11.38)

where ␣ is a constant of proportionality that is determined from Figure 11.9

based on the finite element simulations. The factor ␴p in Figure 11.9 is the
value of atmospheric pressure in the units employed by the designer. The
maximum value of ␣ that is permitted is 0.5. The parameter ␾rc in Figure
11.9 represents the angle of internal friction at the interface of the weak rock
and concrete. The curves of Figure 11.9 are based on the use of ␾rc  30⬚,
a value measured at a test site in clay-shale that is believed to be typical of
clay-shales and mudstones in the United States. If evidence indicates that ␾rc
differs from 30⬚, then ␣ should be adjusted using Eq. 11.39:

tan ␾rc
␣  ␣Figure  1.73 (␣Figure ) tan ␾rc (11.39)
11.8
tan 30⬚ 11.8

If Em /Ei  1, adjust ƒa for the presence of soft geomaterial within the soft
rock matrix using Table 11.7. Define the adjusted value of ƒa as ƒaa. Em can
be estimated from the Em /Ei ratios based on RQD of the cores. In cases where
RQD is less than 50%, it is advisable to make direct measurements of Em in
situ using plate loading tests, borehole jacks, large-scale pressuremeter test,
or by back-calculating Em from field load tests of drilled shafts. The corre-
lations shown in Table 11.7 become less accurate with decreasing values of
RQD.
Estimate ␴n, the normal stress between the concrete and borehole wall at
the time of loading. This stress is evaluated when the concrete is fluid. If no
other information is available, general guidance on the selection of ␴n can be

TABLE 11.7 Adjustment of ƒa for the Presence of

Soft Seams
Em / Ei ƒaa / ƒa
1 1.0
0.5 0.8
0.3 0.7
0.1 0.55
0.05 0.45
0.02 0.3
352 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

obtained from Eq. 11.40, which is based on measurements made by Bernal

and Reese (1983):

␴n  M ␥c zc (11.40)

where

␥c  unit weight of the concrete,

zc  distance from the top of the completed column of concrete to the
point in the borehole at which ␴n is desired, usually the middle of
the socket, and
M  an empirical factor which depends upon the fluidity of the concrete,
as indexed by the concrete slump (obtained from Figure 11.10).

The values shown in Fig. 11.10 represent the distance from the top of the
completed column of concrete to the point in the borehole at which ␴n is
desired. Figure 11.10 may be assumed valid if the rate of placement of con-
crete in the borehole exceeds 12 m/hr and if the ratio of the maximum coarse
aggregate size to the borehole diameter is less than 0.02. Note that ␴n for
slump outside the range of 125 to 225 mm (5 to 9 in.) is not evaluated. Unless
there is information to support larger values of ␴n, the maximum value of zc
should be taken as 12 m (40 ft) in these calculations. This statement is pred-
icated on the assumption that arching and partial setting will become signif-
icant after the concrete has been placed in the borehole for more than 1 hour.

Figure 11.10 Factor M versus slump of concrete.

 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 353

Note that Em increases with increasing qu, and the Poisson effect in the
shaft causes an increase in the lateral normal interface stresses as Em increases,
producing higher values of side load transfer at the frictional interface.
Determine the characteristic parameter n, which is a fitting factor for the
load-settlement syntheses produced by the finite element analyses. If the weak
rock socket is rough:

␴n
n (11.41)
qu

If the weak rock socket is smooth, estimate n from Figure 11.11. Note that
n was determined in Figure 11.11 for ␾rc  30⬚. It is not sensitive to the
value of ␾rc. However, ␣ is sensitive to ␾rc, as indicated in Eq. 11.31.
If the socket has the following conditions—relatively uniform, and the soft
rock beneath the base of the socket has a consistency equivalent to that of
the soft rock along the sides of the shaft, 2  L/D 20, D  0.5 m, and 10
 Ec /Em  500—then compute the load-settlement relation for the weak rock
socket as follows. Under the same general conditions, if the socket is highly
stratified and/or if the geomaterial beneath the base of the socket has a con-
sistency considerably different from that along the sides of the socket, use
the unit load transfer function version of this method described later.
Compute Qt (load still in the shaft at the top of the socket) versus wt
(settlement at the top of the socket) from Eq. 11.42 or Eq. 11.43, depending
on the value of n. These equations apply to both rough and smooth sockets.

Figure 11.11 Factor n for smooth sockets for various combinations of parameters.
354 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

␲D2
If Hƒ ⱕ n: Qt  ␲DLHƒƒaa  q (11.42)
4 b
␲D2
If Hƒ  n: Qt  ␲DLKƒƒaa  q (11.43)
4 b

Equation 11.42 applies in the elastic range before any slippage has oc-
curred at the shaft–weak rock interface, and an elastic base response, as rep-
resented by the last expression on the right-hand side of the equation, also
occurs. Equation 11.43 applies during interface slippage (nonlinear response).
To evaluate Qt, a value of wt is selected, and Hƒ, which is a function of wt,
is evaluated before deciding which equation to use. If Hƒ  n, evaluate Kƒ
and use Eq. 11.43; otherwise, use Eq. 11.42. Equations 11.44 and 11.45 are
used to evaluate Hƒ and Kƒ, respectively.

Em⍀
Hƒ  w (11.44)
␲L⌫ƒaa t

(Hƒ  n)(1  n)
Kƒ  n  ⱕ1 (11.45)
Hƒ  2n  1

where

⍀  1.14 冉冊
L
D
0.5

 0.05 冋冉 冊 册 冏 冏
L
D
0.5

 1 log10
Ec
Em
 0.44 (11.46)

with D  1.53 m and

⌫  0.37 冉冊
L
D
0.5

 0.15 冋冉 冊 册 冏 冏
L
D
0.5

 1 log10
Ec
Em
 0.13 (11.47)

Finally,

qb  ⌳ w0.67
t (11.48)

where

⌳  0.0134Em 冉 L/D
L/D  1 冊冋 200(兹L/D  ⍀)(1  L/D)
␲ L⌫ 册 (11.49)

Check the values computed for qb. If core recovery in the weak rock sur-
rounding the base is 100%, qb should not exceed qmax  2.5 qu. At working
loads, qb should not exceed 0.4 qmax.
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 355

Graph the load-settlement curve resulting from the computations. Select

ultimate and service limit resistances based on settlements. For example, the
ultimate resistance might be selected as the load Qt corresponding to a set-
tlement wt of 25 mm (1 in.), while the service limit resistance might be
selected as the load Qt corresponding to a value of wt  25 mm (wt  1 in.).

Example Problem 4—Shaft in Cohesive Intermediate Geomaterial

This is an example of a drilled shaft in weak rock.

Description of the Problem—Rough Socket. Consider the shaft and soil pro-
file shown in Figure 11.12. The user is asked to compute the load-settlement
relation for the socket and to estimate the ultimate resistance at a settlement
of wt  25 mm. The socket is assumed to be rough. The RQD for the sample
is 100%.

Computations

1. Since the core recovery and RQD are high, assume that Em  115 qu.
Note that Ec /Em  100%.
2. ƒaa  ƒa  2.4/2  1.2 MPa, or 1200 kPa.
3. zc  6.1 m (depth from the top of the concrete to the middle of the
socket). Considering concrete placement specifications:

␴n  0.92 ␥c zc from Figure 11.12 or

␴n  0.92 (20.4) (6.1)  114.5 kPa  1.13 ␴p.

4. n  115 kPa/2400 kPa  0.0477.

5. L/D  6.1/0.61  10.

Overburden Layer
3.05 m (discounted)

Intermediate Geomaterial:
qu = 2.4 MPa, %Rec. = 100%
Interface: Rough, Unsmeared
Total Unit Weight = 20.4 kN/m
6.10 m Drilled Shaft:
Ec = 27.8 MPa
Unit Weight = 20.4 kN/m
Slump > 175 mm
Placement Rate > 12 m/hr

Figure 11.12 General soil description of Example Problem 4.

356 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

6. ⍀  1.14兹10  0.05⎣兹10  1⎦log兩100兩  0.44  2.949.

7. ⌫  0.37兹10  0.15⎣兹10  1⎦log兩100兩  0.13 or ⌫  0.651.
8. Hƒ  {[115 (2400) 2.94)]/[3.14 (6100 mm)(0.651) 1200]}wi
Hƒ  0.0541 wt
9. Kƒ  0.0477  (0.0541wt  0.0477) (1  0.0477)/(0.0541wt 
0.096  1)
Kƒ  0.0477  (0.0541wt  0.0477) (0.952)/(0.0541wt  0.904)
10. At the end of the elastic stage, ⌰ƒ  n (implied by Eq. 3.44).
Therefore,

wte  n/ ⌰  0.0477/0.0541  0.882 mm

where wte signifies wt at the end of the elastic stage. (Note that the
elastic response occurs only up to a very small settlement in this
example.)
11. qb  ⌳w0.67
t (Eqs. 3.50 and 3.51)
qb  {[(115) (2400) (10/11)} {[200 (100.5  2.949) (11)]/[3.14 (6100)
0.651]}0.67 w0.67
t

qb  373.4 wt (mm)0.67 (kPa). Note that ⌳  373.4.

12. ␲ DL  11.69 m2; ␲ D2 /4  0.2922 m2.
13. Compute Qt corresponding to wte, signified by Qte:

Qte  11.69 (0.0541)(0.882)(1200)  (0.2922)(373.4)(0.881)0.67

Qte  669  100  769 kN (Eq. 3.44).

Note that at this point, 670 kN is transferred to the weak rock in

side resistance and 103 kN is transferred in base resistance. (Qte, wte)
is a point on the load-settlement curve, and a straight line can be drawn
from (Qt  0, wt  0) to this point.
14. Compute the values of Qt for selected values of wt on the nonlinear
portion of the load-settlement curve. Numerical evaluations are made
in the following table.

Rough Socket
wt, mm Hƒ Kƒ Qs, kN qb, kPa Qb, kN Qt, kN
1 0.0541 0.0540 758.2 373.4 109.1 867.3
2 0.1082 0.1046 1466.9 594.2 173.6 1640.5
3 0.1623 0.1500 2103.7 779.7 227.9 2331.6
4 0.2164 0.1910 2679.1 945.4 276.3 2955.4
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 357

5 0.2705 0.2282 3201.5 1097.8 320.8 3522.3

6 0.3245 0.2622 3677.9 1240.5 362.5 4040.5
7 0.3786 0.2933 4114.2 1375.5 402.0 4516.2
8 0.4327 0.3219 4515.2 1504.2 439.6 4954.8
9 0.4868 0.3482 4885.0 1627.7 475.7 5360.7
10 0.5409 0.3726 5227.1 1746.8 510.5 5737.6
11 0.5950 0.3953 5544.5 1861.9 544.1 6088.7
12 0.6491 0.4163 5839.9 1973.7 576.8 6416.7
13 0.7032 0.4359 6115.3 2082.4 608.6 6723.9
14 0.7573 0.4543 6372.9 2188.5 639.6 7012.5
15 0.8114 0.4715 6614.2 2292.0 669.8 7284.0
16 0.8654 0.4877 6840.7 2393.3 699.4 7540.2
17 0.9195 0.5028 7053.9 2492.5 728.4 7782.3
18 0.9736 0.5172 7254.7 2589.8 756.9 8011.6
19 1.0277 0.5307 7444.3 2685.3 784.8 8229.1
20 1.0818 0.5435 7623.6 2779.2 812.2 8435.8
21 1.1359 0.5556 7793.3 2871.6 938.2 8632.5
22 1.1900 0.5670 7954.3 2962.5 865.8 8820.1
23 1.2441 0.5779 8107.2 3052.0 891.9 8999.2
24 1.2982 0.5883 8252.6 3140.3 917.7 9170.4
25 1.3523 0.5982 8391.0 3227.4 943.2 9334.2

Note that

qb (at wt  25 mm)  3.23 MPa  1.34 qu  qmax  2.5 qu

which is acceptable for the definition of ultimate resistance. Based on

base resistance, the working load should be limited to qb  qu or wt
should be limited to about 12 mm at the working load. Note also that
the compressive stress in the shaft at wt  15 mm is 24,900 kPa (7284
kN/cross-sectional area), which may be approaching the structural fail-
ure load in the drilled shaft.
15. The numerical values from Steps 13 and 14 are graphed in Figure
11.13. Also shown in the figure is the case with a smooth socket for
the same problem. Hand computations for the case of a smooth socket
are included in the next section.
The physical significance of the parameters Qƒ and Kƒ is evident
from the numerical solution. Qƒ is a constant of proportionality for
elastic resistance for side shear, and Kƒ is a proportionality parameter
for actual side shear, including elastic, plastic, and interface slip
effects.

Description of the Problem—Smooth Socket. Consider the same example

as before (shaft and soil profile shown in Figure 11.12). The rock socket is
now assumed to be smooth. Estimate that ␾rc  30⬚. The user is asked to
358 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

Figure 11.13 Computed axial load versus settlement for Example Problem 4.

compute the load-settlement relation for the socket and to estimate the ulti-
mate resistance at a settlement of wt  25 mm.

Computations

1. ƒa  ƒaa  ␣qu.
2. Referring to Figure 11.13, for ␴n / ␴p  1.13 and qu  2.4 MPa, we
have ␣  0.12.
3. ƒa  ƒaa  0.12(2400)  288 kPa.
4. qu / ␴p  2400/101.3  23.7 and Em / ␴n  115 (2.4) (1000)/114.5 
2411.
5. From Figure 11.13, n  0.11.
6. ⍀  2.949 (unchanged); ⌫  0.651 (unchanged).
7. Hƒ  {[l15(2400) 2.949)]/[3.14 (6100 mm)(0.651) 288]}wt
 0.226 wt.
8. Kƒ  0.11  [(0.226 wt  0.11)(1  0.11)]/[0.226 wt  2(0.11)  1]
 0.11  (0.226 wt  0.11)(0.89)/(0.226 wt  0.78).
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 359

9. At Hƒ  n, wte  0.11/0.226  0.486 mm.

10. qb  373.4 (wt)0.67, where wt is in millimeters and qb is in kPa.
11. Qte  11.69 (0.226)(0.486)(288)  (0.2922)(373.4)(0.486)0.67 Qte 
370  67.3  437 kN (Eq. 3.44).
12. Qte  437 kN, wte  0.486 mm is the point at the end of the linear
portion of the load settlement curve.
13. Compute the values of Qt for selected values of wt on the nonlinear
portion of the load-settlement curve. Numerical evaluations are made
below.

Smooth Socket
wt qb Qb Qs Qt
mm Hƒ Kƒ  kPa kN kN kN
1 0.23 0.213 373 109.1 717 826
2 0.45 0.357 594 173.6 1203 1377
3 0.68 0.457 780 227.9 1539 1767
4 0.91 0.530 945 276.3 1785 2061
5 1.13 0.586 1098 320.8 1972 2293
6 1.36 0.630 1240 362.5 2120 2482
7 1.58 0.665 1375 402.0 2239 2641
8 1.81 0.694 1504 439.6 2337 2777
9 2.04 0.719 1628 475.7 2420 2896
10 2.26 0.740 1747 510.5 2491 3001
11 2.49 0.758 1862 544.1 2551 3095
12 2.72 0.773 1974 576.8 2604 3181
13 2.94 0.787 2082 608.6 2650 3259
14 3.17 0.799 2188 639.6 2691 3331
15 3.40 0.810 2292 669.8 2728 3398
16 3.62 0.820 2393 699.4 2761 3460
17 3.85 0.829 2492 728.4 2791 3519
18 4.08 0.837 2590 756.9 2817 3574
19 4.30 0.844 2685 784.8 2842 3627
20 4.53 0.851 2779 812.2 2864 3676
21 4.75 0.857 2872 839.2 2885 3724
22 4.98 0.862 2692 865.8 2904 3770
23 5.21 0.868 3052 891.9 2921 3813
24 5.43 0.873 3140 917.7 2937 3855
25 5.66 0.877 3227 943.2 2953 3896

14. The numerical values for a smooth socket are graphed in Figure 11.13
in comparison with the values from a rough socket to illustrate the
effect of borehole roughness in this problem. Note again that qb  2.5
qu.

Side Resistance in Cohesive Intermediate Geomaterials—Uplift

Loading Side resistance in uplift loading for cohesive intermediate geo-
360 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

materials is identical to that developed in compressive loading, provided that

the shaft borehole is rough. If the shaft borehole is smooth, Poisson’s effect
reduces shaft resistance because the normal stress at the side of the borehole
is reduced.
When the borehole is smooth, fmax should be reduced from the value com-
puted for compressive loading by a factor ⌿:

ƒmax (uplift)  ⌿ ƒmax (compression) (11.50)

The value of ⌿ is taken to be 1.0 when (Ec /Em) (B/D)2 ⱖ 4, or 0.7 when
(Ec /Em) (B/D)2  4, unless field loading tests are performed. Ec and Em are
the composite Young’s modulus of the shaft’s cross section and rock mass,
respectively, B is the socket diameter, and D is the socket length.

End Bearing in Cohesive Intermediate Geomaterials Several procedures

are available for estimating the undrained unit end bearing in jointed rock.
The procedures of Carter and Kulhawy (1988) and of the Canadian Foun-
dation Engineering Manual (Canadian Geotechnical Society, 1992) are pre-
sented.
The method developed by Carter and Kulhawy (1988) can be used to
estimate a lower bound for end bearing on randomly jointed rock. The same
solution is used either for a shaft base bearing on the surface of the rock or
for a base socketed into rock. It is assumed that

• the joints are drained,

• the rock between the joints is undrained,
• the shearing stresses in the rock mass are nonlinearly dependent on the
normal stresses at failure,
• the joints are not necessarily oriented in a preferential direction,
• the joints may be open or closed, and
• the joints may be filled with weathered geomaterial (gouge).

End-bearing resistance is computed by

冉
qmax  兹s  兹m兹s  s qu 冊 (11.51)

The parameters s and m for the cohesive intermediate geomaterial are

roughly equivalent to c⬘ and ␾⬘ for soil. The term in parentheses is analogous
to the parameter Nc for clay soils. Values of s and m for cohesive intermediate
geomaterial are obtained from Tables 11.8 and 11.9.
The second method for computing resistance in end bearing for drilled
shafts in jointed, sedimentary rock, where the joints are primarily horizontal,
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 361

TABLE 11.8 Descriptions of Rock Types for Use in Table 11.9

Rock Type Rock Description
A Carbonate rocks with well-developed crystal cleavage (dolostone,
limestone, marble)
B Lithified argillaceous rocks (mudstone, siltstone, shale, slate)
C Arenaceous rocks (sandstone, quartz)
D Fine-grained igneous rocks (andesite, dolerite, diabase, rhyolite)
E Coarse-grained igneous and metamorphic crystalline rocks
(amphibolite, gabbro, gneiss, granite, norite, quartzdirorite)

is the method of the Canadian Foundation Engineering Manual (Canadian

Geotechnical Society, 1992):

qmax  3Ksp d qu (11.52)

Ds
d  1  0.4 ⱕ 3.4 (11.53)
B

3  cs /Bb
Ksp  (11.54)
10兹1  300 ␦ /cs

where

TABLE 11.9 Values of s and m Based on Rock Classification

Value of m as a Function of Rock Type
(A–E) from Table 11.8
Rock Joint Description
Quality and Spacing s A B C D E
Excellent Intact (closed); spacing 1 7 10 15 17 25
3 m
Very good Interlocking spacing of 0.1 3.5 5 7.5 8.5 12.5
1 to 3 m
Good Slightly weathered; 0.04 0.7 1 1.5 1.7 2.5
spacing of 1 to 3 m
Fair Moderately weathered; 104 0.14 0.2 0.3 0.34 0.5
spacing of 0.3 to 1 m
Poor Weathered with gouge 105 0.04 0.05 0.08 0.09 0.13
(soft material);
spacing of 30 to 300
mm
Very poor Heavily weathered; 0 0.007 0.01 0.015 0.017 0.025
spacing of less than
50 mm
362 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

qmax  unit end-bearing capacity,

Ksp  empirical coefficient that depends on the spacing of discontinuities,
qu  average unconfined compressive strength of the rock cores,
cs  spacing of discontinuities,
␦ thickness of individual discontinuities,
Ds  depth of the socket measured from the top of rock (not the ground
surface), and
Bb  diameter of the socket.

The above equations are valid for a rock mass with spacing of disconti-
nuities greater than 12 in. (0.3 m) and thickness of discontinuities less than
0.2 in. (5 mm) (or less than l in. [25 mm] if filled with soil or rock debris)
and for a foundation with a width greater than 12 in. (305 mm). For sedi-
mentary or foliated rocks, the strata must be level or nearly so. Note that Eq.
11.52 is different in form from that presented in the Canadian Foundation
Engineering Manual in that a factor of 3 has been added to remove the
implicit factor of safety of 3 contained in the original form. Further, note that
the form of Eq. 11.53 differs from that in the first edition of the Manual.

11.6.5 Design for Axial Capacity in Cohesionless Intermediate

Geomaterials
Cohesionless intermediate geomaterials are residual or transported materials
that exhibit N60-values of more than 50 blows per foot. It is common practice
to treat these materials as undrained because they may contain enough fine-
grained material to significantly lower permeability.
The following design equations are based on the original work of Mayne
and Harris (1993) and modifications by O’Neill et al. (1996). The theory was
proposed for gravelly soils, either transported or residual, with penetration
resistances (from the SPT) between 50 and 100. The method has been used
by Mayne and Harris to predict and verify the behavior of full-scale drilled
shafts in residual micaceous sands from the Piedmont province in the eastern
United States. Further verification tests were reported by O’Neill et al. for
granular glacial till in the northeastern United States.

Side Resistance in Cohesionless Intermediate Geomaterial The max-

imum load transfer in side resistance in Layer i can be estimated from

ƒmax,i  ␴vi⬘ K0i tan ␾⬘i (11.55)

where ␴⬘vi is the vertical effective stress at the middle of Layer i. The earth
pressure coefficient K0i and effective angle of internal friction of the gravel
␾⬘ can be estimated from field or laboratory testing or from
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 363

K0i  (1  sin ␾⬘i ) 冉

0.2N60,i
␴⬘vi /pa 冊 sin␾⬘i

(11.56)

␾⬘i  tan1 再冋 N60,i

12.2  20.3(␴v⬘ /pa) 册 冎0.34

(11.57)

where N60,i is the SPT penetration resistance, in blows per foot (or blows per
300 mm), for the condition in which the energy transferred to the top of the
drive string is 60% of the drop energy of the SPT hammer, uncorrected for
the effects of overburden stress; and pa is the atmospheric pressure in the
selected system of units (usually 1 atmosphere, which converts to 101.4 kPa
or 14.7 psi).

Side Resistance in Cohesionless Intermediate Geomaterial—Uplift

Loading The equations for side resistance in uplift for cohesionless soils
can be used for cohesionless intermediate geomaterials. The pertinent equa-
tions are Eqs. 11.23, 11.24, and 11.25.

End Bearing in Cohesionless Geomaterial Mayne and Harris (1993) de-

veloped the following expression for unit end-bearing capacity for cohesion-
less intermediate geomaterials:

qmax  0.59 N60冋 冉 冊册pa

␴⬘vb
0.8

␴⬘vb (11.58)

where N60 is the blow count immediately below the base of the shaft.
The value of qmax should be reduced when the diameter of the shaft Bb is
more than 1.27 m (50 in.). If the diameter of the shaft is between 1.27 and
1.9 m (50 to 75 in.), qmax,r is computed using

1.27
qmax,r  q (11.59)
Bb (m) max

and if the shaft diameter is more than 1.9 m:

qmax,r  qmax 冋 2.5

aBb (m)  2.5b 册 (11.60)

where
364 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

L
a  0.28Bb (m)  0.083 (11.61)
Bb

b  0.065兹sub (kPa) (11.62)

where

L  depth of base below the ground surface or the top of the bearing
layer if the bearing layer is significantly stronger than the overlying
soils, and
sub  average undrained shear strength of the soil or rock between the
elevation of the base and 2Bb below the base. If the bearing layer is
rock, sub can be taken as qu /2.

The above equations are based on load tests of large-diameter underreamed

drilled shafts in very stiff clay and soft clay-shale. These equations were
developed assuming qmax,r to be the net bearing stress at a base settlement of
2.5 in. (64 mm) (O’Neill and Sheikh, 1985; Sheikh et al., 1985). When one-
half or more of the design load is carried in end bearing and a global factor
of safety is applied, the global factor of safety should not be less than 2.5,
even if soil conditions are well defined, unless one or more site-specific load
tests are performed.

Commentary on the Direct Load-Settlement Method This method is

intended for use with relatively ductile weak rock, in which deformations
occur in asperities prior to shear. If the weak rock is friable or unusually
brittle, the method may be unconservative, and appropriate loading tests
should be conducted to ascertain the behavior of the drilled shaft for design
purposes. The method is also intended for use with drilled shafts in weak
rocks produced in the dry. If it is necessary to produce the shaft using water,
or with mineral or synthetic drilling slurries, the shaft should be treated as
smooth for design purposes unless it can be proved that rough conditions
apply. The method also assumes that the bearing surface at the base of the
socket is clean, such that the shaft concrete is in contact with undisturbed
weak rock. If base cleanliness cannot be verified during construction, base
resistance (qb) should be assumed to be zero.
The design examples did not consider the effect of a phreatic surface (water
table) above the base of the socket. This effect can be handled by computing
␴n, assuming that the unit weight of the concrete below the phreatic surface
is its buoyant unit weight:

␴n  M[␥c zw  ␥⬘c (zc  zw)] (11.63)

where
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 365

␥⬘c  buoyant unit weight of concrete,

M is obtained from Figure 11.7, and
zw  depth from top of concrete to elevation of water table.

11.6.6 Design for Axial Capacity in Massive Rock

Computation Procedures for Rock A broad view of the classification of
intact rock can be obtained by referring to Figure 11.14 (Deere, 1968, and

Figure 11.14 Engineering classification of intact rock (after Deere, 1968, by Horvath
and Kenney, 1979).
366 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

Peck, 1976, as presented by Horvath and Kenney, 1979). The figure shows
medium clay at the low range and gneiss at the high range. Concrete and
steel are also shown for reference. Several of the rock categories have com-
pressive strengths that are in the range of that for concrete or higher. As can
be expected, many of the design procedures for drilled shafts in rock are
directed at weak rock because strong rock could well be as strong as or
stronger than the concrete in the drilled shaft. In this situation, the drilled
shaft would fail structurally before any bearing capacity failure could occur.
Except for instances where drilled shafts were installed in weak rocks such
as shales or mudstones, there are virtually no occasions where loading has
resulted in failure of the drilled shaft foundation. An example of a field test
where failure of the drilled shaft was impossible is shown in Figures 11.15
and 11.16. The rock at the site was a vuggy limestone that was difficult to
core without fracture. Only after considerable trouble was it possible to obtain
the strength of the rock. Two compression tests were performed in the labo-
ratory, and in situ grout-plug tests were performed under the direction of
Schmertmann (1977).
The following procedure was used for the in situ grout-plug tests. A hole
was drilled into the limestone, followed by placement of a high-strength steel
bar into the excavation, casting of a grout plug over the lower end of the bar,
and pulling of the bar after the grout had cured. Five such tests were per-

Load

0 1 2 3 4 5 6 7 8 9
MN
200 400 600 800 1000
0 Tons

Test Shaft #1
2
0.1
Settlement

4 Test Shaft #2
0.2
6

0.3
8
mm

inches

Figure 11.15 Load-settlement curves for Test Shafts No. 1 and 2, Florida Keys.
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 367

Load

0 1 2 3 4 5 6 7 8 9
MN

200 400 600 800 1000

0 Tons
Penetration Into Limestone

2
10
Test Shaft #2
4
Test Shaft #1
6 20

8
30
10

12 40

14
50
Figure 11.16 Load-distribution curves for Test Shafts Nos. 1 and 2, Florida Keys.

formed over the top 10 ft of the rock. Side resistance ranged from 12.0 to
23.8 tons/ft2 (1.15 to 2.28 MPa), with an average of approximately 18.0 tons/
ft2 (1.72 MPa). The compressive strength of the rock was approximately 500
psi (3.45 MPa), putting the vuggy limestone in the lower ranges of the
strength of the chalk shown in Figure 11.14.
Two axial load tests were performed at the site on cylindrical drilled shafts
that were 36 in. (914 mm) in diameter (Reese and Nyman, 1978). Test Shaft
No. 1 penetrated 43.7 ft (13.3 m) into the limestone, and Test Shaft No. 2
penetrated 7.6 ft (2.32 m). Test Shaft No. 1 was loaded first, with the results
shown in Figures 11.15 and 11.16, and it was then decided to shorten the
penetration and construct Test Shaft No. 2. As may be seen in Figure 11.15,
the load-settlement curves for the two shafts are almost identical, with Test
Shaft No. 2 showing slightly more settlement at the 1000-ton (8.9-MN) load
(the limit of the loading system). The settlement of the two shafts under the
maximum load is quite small, and most of the settlement (about 0.10 in., 2.5
mm) was due to elastic shortening of the drilled shafts.
The distribution of load with depth, determined from internal instrumen-
tation in the drilled shafts, for the maximum load is shown in Figure 11.16.
As may be seen, no load reached the base of Test Shaft No. 1, and only about
368 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

60 tons (530 kN) reached the base of Test Shaft No. 2. The data allowed a
design for the foundations to be made at the site with confidence; however,
as indicated, it was impossible to find the ultimate values of load transfer in
side resistance and in end bearing because of the limitations of the loading
equipment in relation to the strength of the rock. The results are typical for
drilled shafts that are founded in rock that cannot develop the ultimate values
of load transfer.
A special program of subsurface exploration is frequently necessary to
obtain the in situ properties of the rock. Not only is it important to obtain the
compressive strength and stiffness of the sound rock, but it is necessary to
obtain detailed information on the nature and spacing of joints and cracks so
that the stiffness of the rock mass can be determined. The properties of the
rock mass will normally determine the amount of load that can be imposed
on a rock-socketed drilled shaft. The pressuremeter has been used to inves-
tigate the character of in situ rock, and design methods have been proposed
based on such results.
An example of the kind of detailed study that can be made concerns the
mudstone of Melbourne, Australia. The Geomechanics Group of Monash Uni-
versity in Melbourne has written an excellent set of papers on drilled shafts
that give recommendations in detail for subsurface investigations, determi-
nation of properties, design, and construction (Donald et al., 1980; Johnston
et al., 1980a, 1980b; Williams, 1980; Williams et al., 1980a, 1980b; Williams
and Erwin, 1980). These papers imply that the development of rational meth-
ods for the design of drilled shafts in a particular weak rock will require an
extensive study and, even so, some questions may remain unanswered. It is
clear, however, that a substantial expenditure for the development of design
methods for a specific site could be warranted if there is to be a significant
amount of construction at the site.
Williams et al. (1980b) discussed their design concept and stated: ‘‘A sat-
isfactory design cannot be arrived at without consideration of pile load tests,
field and laboratory parameter determinations and theoretical analyses; ini-
tially elastic, but later hopefully also elastoplastic. With the present state of
the art, and the major influence of field factors, particularly failure mecha-
nisms and rock defects, a design method must be based primarily on the
assessment of field tests.’’
Other reports on drilled shafts in rock confirm the above statements about
a computation method; therefore, the method presented here must be consid-
ered to be approximate. Detailed studies, including field tests, are often
needed to confirm a design.
The procedure recommended by Kulhawy (1983) presents a logical ap-
proach. The basic steps are as follows.

1. The penetration of the drilled shaft into the rock for the given axial
load is obtained by using an appropriate value of side resistance (see
the later recommendation).
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 369

2. If the full load is taken by the base of the drilled shaft, the settlement
of the drilled shaft in the rock is computed by adding the elastic short-
ening to the settlement required to develop end bearing. The stiffness
of the rock mass is needed for this computation.
3. If the computed settlement is less than about 0.4 in. (10 mm), the side
resistance will dominate and little load can be expected to reach the
base of the foundation.
4. If the computed settlement is more than about 0.4 in. (10 mm), the bond
in the socket may be broken and the tip resistance will be more
important.

Kulhawy (1983) presents curves that will give the approximate distribution
of the load for Steps 3 and 4; however, the procedure adopted here is to
assume that the load is carried entirely in side resistance or in end bearing,
depending on whether or not the computed settlement is less or more than
0.4 in.
The recommendations that follow are based on the concept that side resis-
tance and end bearing will not develop simultaneously. The concept is con-
servative, of course, but it is supported by the fact that the maximum load
transfer in side resistance in the rock will occur at the top of the rock, where
the relative settlement between the drilled shaft and the rock is greatest. If
the rock is brittle, which is a possibility, the bond at the top of the rock could
fail, with the result that additional stress is transferred downward. There could
then be a progressive failure in side resistance.
Note that the settlement will be small if the load is carried only in side
resistance. The settlement in end bearing could be considerable and must be
checked as an integral part of the analysis.
The following specific recommendations are made to implement the above
general procedure:

1. Horvath and Kenney (1979) did an extensive study of the load transfer
in side resistance for rock-socketed drilled shafts. The following equation is
in reasonable agreement with the best-fit curve that was obtained where no
unusual attempt was made to roughen the walls:

ƒs (psi)  2.5兹qu (psi) (11.64)

where

ƒs  ultimate side resistance in units of lb/in.2, and

qu  uniaxial compressive strength of the rock or concrete, whichever is
less in units of lb/in2.

(Note: Equation 11.61 is nonhomogeneous, and the value of qu must be

converted to English units, the equation solved for ƒs in English units, and ƒs
370 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

then converted to SI units before performing further computations with SI

units.)
Note that there was a large amount of scatter in the data gathered by
Horvath and Kenney (1979), but Eq. 11.64 can be used to compute the nec-
essary length of the socket. If the drilled shaft is installed in clay-shale, the
ultimate side resistance may be predicted more accurately by the procedures
described in the previous section for clay-shale rather than by using Eq. 11.64.
2. The shortening ␳c of the drilled shaft can be computed by elementary
mechanics, employing the dimensions of the shaft and the stiffness of the
concrete:

QST L
␳c  (11.65)
AEc

where

L  penetration of the socket,

QST  load at the top of the socket,
A  cross-sectional area of the socket, and
Ec  equivalent Young’s modulus of the concrete in the socket, consid-
ering the stiffening effects of any steel reinforcement.

3. The settlement of the base of the shaft can be obtained by assuming

that the rock will behave elastically. The following equation will give an
acceptable result:

QST I␳
w (11.66)
BbEm

where

w  settlement of the base of the drilled shaft,

I␳  influence coefficient,
Bb  diameter of drilled shaft, and
Em  modulus of the in situ rock, taking the joints and their spacing into
account.

4. The value of I␳ can be found by using Figure 11.17. The symbol Ec in

the figure refers to Young’s modulus of the concrete in the drilled shaft. The
value of Young’s modulus of the intact rock EL can be obtained by test or by
selecting an appropriate value from Figure 11.14. The value of the modulus
of the in situ rock can be found by test, or the intact modulus can be modified
in an approximate way. Figure 11.18 allows modification of the modulus of
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 371

1.1
1.0
0.9
0.8
Influence Factor Ip

0.7 Q
Settlement

0.6 L Econcrete
0.5
B Emass
0.4 10
0.3
0.2 50
100
0.1 5000

0 2 4 6 8 10 12 20
Embedment Ratio L/B
Figure 11.17 Elastic settlement influence factor as a function of embedment ratio
and modular ratio (after Donald et al., 1980).

Figure 11.18 Modulus reduction ratio as a function of RQD (from Bieniawski,

1984).
372 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

the intact rock by using the RQD. As may be seen, the scatter in the data is
great but the trend is unmistakable.
5. The bearing capacity of the rock can be computed by a method pro-
posed by the Canadian Geotechnical Society (1978):

qa  Ksp qu (11.67)

3  cs /Bb
Ksp  (11.68)
10兹1  300 ␦ /cs

where

qa  allowable bearing pressure,

Ksp  empirical coefficient that depends on the spacing of discontinuities
and includes a factor of safety of 3,
qu  average unconfined compressive strength of the rock cores,
cs  spacing of discontinuities,
␦  thickness of individual discontinuities, and
Bb  diameter of socket.

6. Equation 11.65 is valid for a rock mass with spacing of discontinuities

greater than 12 in. (305 mm) and thickness of discontinuities less than 0.2
in. (5 mm) (or less than l in. [25 mm] if filled with soil or rock debris), and
for a foundation with a width greater than 12 in. (305 mm). For sedimentary
or foliated rocks, the strata must be level or nearly so (Canadian Geotechnical
Society, 1978). Again, if the drilled shaft is seated on clay-shale, the proce-
dures described in the previous section should provide a better prediction.
7. If the rock is weak (compressive strength of less than 1000 psi), the
design should depend on load transfer in side resistance. The settlement
should be checked to see that it does not exceed 0.4 in.
8. If the rock is strong, the design should be based on end bearing. The
settlement under working load should be computed to see that it does not
exceed the allowable value as dictated by the superstructure.

For the equations for the design of drilled shafts in rock to be valid, the
construction must be carried out properly. Because the load-transfer values
are higher for rock, the construction requires perhaps more attention than does
construction in other materials. For example, for the load transfer in side
resistance to attain the allowable values, there must be a good bond between
the concrete and the natural rock. An excellent practice is to roughen the
sides of the excavation if this appears necessary. There may be occasions
when the drilling machine is underpowered and water is placed in the exca-
vation to facilitate drilling. In such a case, the sides of the excavation may
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 373

be ‘‘gun barrel’’ slick, with a layer of weak material. Roughening of the sides
of the excavation is imperative.
Any loose material at the bottom of the excavation should be removed
even though the design is based on side resistance.
Another matter of concern with regard to construction in rock is whether
or not the rock will react to the presence of water or drilling fluids. Some
shales will lose strength rapidly in the presence of water.

Example Problem 5—Shaft in Rock This is an example of a drilled shaft

into strong rock.

Soil Profile. The soil profile is shown in Figure 11.19. Only a small amount
of water was encountered at the site during the geotechnical investigation.

Soil Properties. The dolomite rock found at the site had a compressive
strength of 8000 psi, and the RQD was 100%. Young’s modulus of the intact
rock was estimated as 2.0 106 psi, and the modulus of the rock mass was
identical to this value. Assume that the spacing of discontinuities is about 7
ft and that the thickness of the discontinuities is negligible.

Construction. The excavation can be made dry. A socket can be drilled into
the strong rock and inspected carefully before concrete is poured.

Loading. The lateral load is negligible. The working axial load is 300 tons.
No downdrag or uplift is expected.

Depth, ft

Clay

Dolomite
No evident joints

Figure 11.19 General soil and rock description of Example Problem 5.

374 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

Factor of Safety. An overall factor of safety of 3 is selected.

Geometry of the Drilled Shaft. A diameter of 3.5 ft is selected, and a socket

of 3.5 ft into the dolomite is specified.

Hand Computations. Assuming that all load is transferred in end bearing and
using the method proposed by the Canadian Geotechnical Society (1978):

qa  Ksp qu
qa  (0.5)(8000)  4000 psi
QB  (4000)(␲ /4)(42)2  5.54 106 lb  2771 tons

Note: The value of end bearing includes a factor of safety of 3.

11.6.7 Addition of Side Resistance and End Bearing in Rock

The decision to add or not to add side resistance and end bearing in rock
must be made on a case-by-case basis using engineering judgment. A short
discussion of several commonly encountered cases follows.
If only compression loading is applied and massive rock exists, it may only
be necessary to penetrate the massive rock a short distance, large enough to
expose the sound rock. In this situation, only end bearing is counted on be-
cause the distance of penetration (usually just a few inches) is too short for
any significant side resistance to be developed.
In cases where a rock socket is formed to provide uplift resistance, the
decision on whether to add side and base resistance for establishing the ul-
timate bearing capacity in compression is a matter of engineering judgment
in which the nature of the rock must be considered. There are two possible
cases. If the rock is brittle, it is possible that the majority of side resistance
may be lost as settlement increases to the amount required to fully mobilize
end bearing. It would not be reasonable to add side and base resistances
together in this situation because they would not occur at large amounts of
settlement. If the rock is ductile in shear and deflection softening does not
occur, then side resistance and end bearing resistance can definitely be added
together.
In cases where end bearing is questionable because of poor rock quality,
the length of shafts is often extended in an effort to found the tip of the shaft
in good-quality rock. In such situations, the rock socket may become long
enough to develop substantial axial capacity in side resistance. In such situ-
ations, it is permissible to add side and base resistance together to obtain the
total axial capacity of the shaft. Often, questions about the nature of the rock
are best answered by conducting a well-planned load test on a full-size test
shaft using an Osterberg load cell. The results of such a load test can establish
the actual axial load capacity. If the actual axial capacity is sufficiently high,
 11.6 DESIGN EQUATIONS FOR AXIAL CAPACITY IN COMPRESSION AND IN UPLIFT 375

the results of the load test may be used to reduce the size of the foundation
shafts to obtain a more economically efficient design.

11.6.8 Commentary on Design for Axial Capacity in Karst

Design of drilled shaft foundations in karst presents the foundation designer
with dangerous situations not found elsewhere. In karst geology, the depth to
rock is uncertain (i.e., pinnacled rock), solution cavities may be present, nu-
merous seams of softer materials may be present in the rock, and rock ledges
and floaters may be encountered above the bearing strata.
These situations make it difficult for the designer to obtain accurate sub-
surface information from the field exploration program. The uncertain con-
ditions caused by karst make it difficult for the designing engineer to prepare
foundation plans and specifications. In such situations, it is mandatory that
the engineer recognize the following:

• The field exploration must be more extensive than usual.

• Any change in structure location, or increased loading, will require ex-
isting field data to be reviewed and additional field exploration to be
conducted to obtain the necessary information.
• Foundation plans and specifications should be written to anticipate the
likely changed conditions to be encountered.
• It may be necessary to provide a means in the specifications to set the
maximum length of drilled shafts based on side resistance alone when
poor end-bearing conditions are encountered during construction.
• It is mandatory to prepare the plans and specifications in a manner con-
sistent with existing purchasing regulations and in sufficient detail that
each bid proposal will cover an identical scope of work.

The above conditions make it difficult to estimate the cost of construction

accurately. In conditions with pinnacled rock, it may be necessary to drill
additional exploratory borings at the location of every drilled shaft to obtain
realistic estimates of foundation depths prior to the finalization of bid docu-
ments. In such situations, it is mandatory that the additional borings extend
to depths greater than the planned depths of the foundations to ensure that
no solution cavities exist below the foundations.
The issues discussed in the preceding paragraphs can only be resolved by
a thorough field investigation. In some situations with karst, it will be nec-
essary to conduct two or more phases of field boring programs to obtain the
necessary information on which to base bid documents.
In large projects with highly variable conditions, use of technique shafts
may be warranted prior to submission of bids for foundation construction.
Technique shafts are full-sized demonstration shafts that are drilled on site.
In this practice, all interested contractors are required to be on site to observe
376 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

the drilling of the technique shafts before they submit their bids for shaft
construction. Observation of the technique shafts allows the interested con-
tractors to observe the local conditions to determine the tools and equipment
required to complete the job successfully. Use of technique shafts has reduced
claims for changed conditions on many projects.

11.6.9 Comparison of Results from Theory and Experiment

Several studies have compared axial capacities computed using the static de-
sign methods to experimentally measured axial capacities. The results from
one study by Isenhower and Long (1997) are presented in Figure 11.20. The
data in this figure represent a database of axial load tests on drilled shafts
that was compiled independently of the database used by Reese and O’Neill
when developing the FHWA axial capacity methods.

Figure 11.20 Computed axial capacity versus measured axial capacity (from Isen-
hower and Long, 1997).
 PROBLEMS 377

PROBLEMS

P11.1. Compute the axial capacity of drilled sand in sand. The shaft di-
ameter is 3 ft and the length is 50 ft.
The soil profile is:

0–20 ft, average N60  11 blows/ft, ␥  115 pcf

20–50 ft, average N60  32 blows/ft, ␥  120 pcf
50–80 ft, average N60  35 blows/ft, ␥  123 pcf

The depth of the water table is 10 ft.

P11.2. What is the allowable axial capacity of the foundation in P11.1 if a
factor of safety of 3 is used?
P11.3. Develop a bearing graph for the shaft of P11.1. Plot axial capacity
on the horizontal axis and shaft length on the vertical axis. Include
shaft lengths from 10 ft to 50 ft, at 5 ft intervals.
P11.4. Develop a bearing graph for shafts in the soil profile of P11.1 for
shaft diameters of 2, 3, 4, 5, 6, 7, and 8 ft. Include shaft lengths
from 10 ft to 50 ft, at 5 ft intervals.
P11.5. Using the bearing graph of P11.4, estimate the cost of the shaft
dimensions that would have allowable capacities of 100 tons, using
a factor of safety of 3 and unit cost figures provided by your
instructor.
P11.6. Consider a deep layer of sand extending from the ground surface to
a depth of 40 meters. For this sand, ␥  18 kN/m3 and the water
table is at the ground surface. Calculate the axial capacity in side
resistance for a shaft with a 1 m diameter and a length of 32 m.
Perform the computations using a single layer, two equally thick
layers, and four equally thick layers. How does the thickness of the
layer affect the computed results?
P11.7. Compute the axial capacity of a drilled shaft in a cohesive soil pro-
file. The shaft diameter is 4 ft and the length is 65 ft.
The soil profile is:

0–15 ft, c  2200 psf, ␥  120 pcf

15–30 ft, c  2700 psf, ␥  123 pcf
30–55 ft, c  3250 psf, ␥  125 pcf
55–100 ft, c linearly varying with depth from 3250 to 4400 psf,
␥  130 pcf

The depth of the water table was 15 ft.

378 GEOTECHNICAL DESIGN OF DRILLED SHAFTS UNDER AXIAL LOADING

P11.8. What is the axial uplift capacity of the shaft of P11.7.

P11.9. Compute the axial capacity of the drilled shaft of P11.7 with a 3-m,
45 deg. Bell.
P11.10. What are the exclusion zones from side resistance for compression
loading for the shaft of P11.7?
P11.11. What are the exclusion zones from side resistance for uplift loading
for the shaft of P11.7?
P11.12. What are the exclusion zones from side resistance for compression
loading for the shaft of P11.9?
P11.13. What are the exclusion zones from side resistance for uplift loading
for the shaft of P11.9?
P11.14. Compute the axial capacity of a rock socket. The rock joints are
horizontal and closed. The uniaxial compressive strength is 12 MPa,
and the RQD  75%. The diameter of the socket is 1 m and the
depth is 3.5 m. Show the computations for side resistance and base
resistance.
P11.15. Discuss the situations when axial side resistance and end bearing can
be combined for rock sockets and when they cannot be combined.