-
Issues in Evaluating Capacity of Rock Socket Foundations
F. H. Kulhawy School of Civil and Environmental Engineering,
Cornell University, Ithaca, NY, USA [email protected]
W. A. Prakoso Department of Civil Engineering, University of
Indonesia, Depok, Indonesia [email protected]
Abstract: Drilled foundations often are socketed into rock to
increase the capacity. However, procedures to quantify the socket
side and tip resistance vary considerably. This paper reviews
methods to predict socket capacity and critically assesses them.
One method for side resistance is recommended, and several
approaches are suggested to assess tip resistance, depending on the
degree of geologic data available. Statistics for the methods are
given, where available, and design and construction implications
are noted.
1 INTRODUCTION
Drilled shafts (bored piles) are a common foundation selection
for all types of structures. When the structure loads are
relatively large or where the soil is of relatively poor quality,
the shafts often are drilled through the soil to the underlying
rock mass. These shafts could be founded or seated on the rock mass
surface, or they could be drilled into the rock mass to form a rock
socket, as shown in Fig. 1. The applied butt load or stress is
supported by the socket through both tip and side resistances,
assuming for illustration that the soil is non-contributory. How
the loads are distributed between the tip and side is a function of
the loading magnitude, problem geometry, properties of the rock
mass and shaft concrete, ultimate bearing capacity of the tip, side
resistance of the socket, and butt displacement. Discussion of all
of these issues is well beyond the scope of this paper.
Herein, the basics of socket capacity are addressed. Key rock
mass property issues are discussed first. Then methods are given to
calculate the socket capacity. The side resistance can be
quan-tified well, and various approaches are described to assess
the tip resistance. Some simple observations are made regarding
dis-placement limits. The paper concludes with general observations
on construction and field acceptance criteria.
Fig. 1. Illustrative rock socket.
2 ROCK MASS ENGINEERING PROPERTIES
The capacity of foundations in rock is a function of the rock
mass strength, which often is estimated, at least partially, from
the intact rock strength, which in turn often is estimated from the
intact rock index properties. However, several key issues need to
be addressed during property evaluation, as described below. If
these testing issues are not addressed properly, then the
subse-quent capacity predictions are likely to be in error.
2.1 Intact Rock: Effect of Testing Parameters
Fig. 2 illustrates a very important testing issue, which is the
influence of sample diameter on the resulting uniaxial compres-sive
strength (qu). Most standards specify a sample diameter on the
order of 50 to 54 mm. As can be seen, non-standard samples tend to
give strengths that decrease with increasing sample diameter.
Similar trends were noted with other strength measures as well
(Prakoso 2002). Note that, in this figure and others herein, a wide
variety of igneous, sedimentary, and metamorphic (primarily
non-foliated) rock types are included. These data were collected
from the lit-erature but were included only if both high-quality
foundation load tests and physical property tests were conducted.
In Fig. 2, the solid line represents the regression for the entire
data population. When these data were examined by separate rock
type family, it was found that each rock type gave results that
were very similar to the entire population. For example, the dashed
line represents the results for all carbonate rock types. As can be
seen, the results are very similar. Fig. 3 illustrates the
importance of testing at the field water content. As can be seen,
the saturated qu is only about 0.79 of the dry value. Although not
shown, comparable data for the point load index (IS) give a value
of 0.84, while data for the Brazilian tensile strength
(qt-Brazilian) give a value of 0.89. Therefore, testing samples
that have been allowed to dry clearly will overestimate the actual
in-situ strength.
-
0 50 100 150 200
Diameter, Bsample (mm)
0.0
0.5
1.0
1.5
2.0St
reng
th R
atio
, SR
qu
SRqu = [50 / Bsample] 0.25
I. IntrusiveI. PyroclasticS. ClasticS. ChemicalM.
Non-Foliated
Fig. 2. Effect of sample size on uniaxial compressive strength
qu(Kulhawy & Prakoso 2001).
0 100 200 300
Mean qu-dry (MPa)
0
100
200
300
Mea
n q u
-sat
urat
ed (M
Pa)
I. IntrusiveI. ExtrusiveS. ClasticS. ChemicalM. Non-Foliated
qu-sat = 0.79 qu-drym = 67, r2 = 0.92S.D. / pa = 165
Fig. 3. Effect of water content on qu (Kulhawy & Prakoso
2001).
2.2 Intact Rock: Index Property and Strength Correlations
For small projects, and for general correlation studies, various
quick and simple index tests have been used to estimate the intact
rock uniaxial compressive strength (qu), including the Schmidt
L-hammer rebound hardness (R), Shore scleroscope hardness (Sh), and
point load index (IS). Many correlations among these parameters
have been proposed. Fig. 4 shows our relationship between qu and R,
as normalized by the atmospheric stress, pa. Although not shown,
the Sh and IS correlations are as follows: qu (MPa) = 7.57 exp
(0.064 Sh) [m = 30, r2 = 0.77] and qu = 23.3 IS [m = 43, r2 =
0.77]. Other useful correlations are summarized by Prakoso (2002).
It should be noted that these correlations are not deterministic;
there is always a transformation uncertainty associated with them.
Using any of these correlations implies that the COV of qu will be
larger than that of R, Sh, or IS.
0 20 40 60 8
Mean R
00
1000
2000
3000
4000
Mea
n q u
/ p a
I. IntrusiveI. ExtrusiveI. PyroclasticS. ClasticS. ChemicalM.
FoliatedM. Non-Foliated
qu / pa = 143.1 exp (0.048 R)m = 78, r2 = 0.57
Fig. 4. Relationship between qu and R for Bsample = 50 - 58 mm
(Kulhawy & Prakoso 2003; Prakoso & Kulhawy 2004b).
0 1000 2000 3000 4000 5000
Mean qu / pa
0
500
1000
1500
2000
Mea
n E t
-50
/ pa
Et-50 / pa = 5280 (qu / pa)0.62
m = 100, r2 = 0.57
I. IntrusiveI. ExtrusiveI. PyroclasticS. ClasticS. ChemicalM.
FoliatedM. Non-Foliated
0.5106
1.0 106
1.5106
2.0106
Fig. 5. Relationship between Et-50 and qu.
2.3 Intact Rock: Strength and Modulus Correlation
The intact rock Youngs modulus often is represented by the
tan-gent Youngs modulus at 50% of the uniaxial compressive strength
(Et-50). This value commonly is estimated from the uni-axial
compressive strength (qu), as shown in Fig. 5. The regres-sion
equation in Fig. 5 is comparable to, and a bit less than, the
typical modulus correlation for concrete, which is given by E =
5000 (fc in MPa)0.5. Note that Et-50 / qu varies from about 500 or
more at low strength to about 200 at very high strength.
2.4 Intact Rock: Weathering
The deleterious effect of weathering on intact rock properties
is well-recognized, but quantifying this effect is more difficult.
Fig. 6 shows various mean correlations between the properties of
unweathered rock and rock weathered to varying degrees. These
-
Weathering Conditions
0.0
0.2
0.4
0.6
0.8
1.0
Mea
n Pr
oper
ty R
atio
(Wea
ther
ed /
Unw
eath
ered
)
Rquqt-BrazilianIsEt-50
Slight Moderate High
Fig. 6. Effect of weathering on rock properties (Kulhawy &
Prakoso 2001, 2003). degrees are somewhat subjective, as given by
the source authors. This database is dominated by igneous intrusive
rocks, followed by igneous extrusive and sedimentary clastic rocks.
However, the general rock type is not expected to have a
significant effect on the overall results.
All properties decrease with increasing weathering. The unit
weight () decreases only a modest amount, to about 90% of the
unweathered value. However, all other properties decrease
sub-stantially, with the R value decreasing to about 40% of the
unweathered value. The strength and modulus values decrease even
more, to about 15 to 25% of the unweathered values. These decreases
should be addressed in engineering evaluations.
Furthermore, these decreases are not deterministic; there is
always some uncertainty in the data. The standard deviation (S.D.)
for is about 0.04 for all degrees of weathering, but the S.D. of
the other properties is about 0.11. Therefore, the coeffi-cient of
variation (COV = S.D. / mean) increases substantially as the
weathering increases, from about 15% for slightly weathered to 50%
or more for highly weathered. These substantial varia-tions need to
be addressed cautiously.
2.5 Rock Mass: Strength of Artificial Rock Blocks
In bearing capacity calculations, it is necessary to estimate
the rock mass strength, which is difficult to do because of the
need to assess the in-situ rock mass structure. Instead,
researchers have conducted artificial rock block tests to estimate
the effect of rock mass structure on its strength (e.g., Brown
1970; Brown & Trol-lope 1970; Ladanyi & Archambault 1972;
Einstein & Hirschfeld 1973; Kulatilake et al. 1997; Yang et al.
1998). Herein, these test results were compiled and re-analyzed to
evaluate the rock mass strength relative to the intact rock
strength and to estimate the variability of the rock mass
strength.
In general, the rock mass strength is dependent on the primary
discontinuity orientation. However, the results of artificial block
tests are not always in agreement with theoretical solutions.
Therefore, a simplified approach was adopted in evaluating the
effect of discontinuity angle relative to a horizontal plane () on
the strength. This effect is represented by a strength ratio
(SRblock), which is given by:
SRblock = (1-3)f-block / (1-3)f-intact (1) in which (1-3)f-block
and (1-3)f-intact = deviator stresses at failure of the rock mass
and intact rock, respectively. The results from several sets of
tests, with typical confining stress (3) for foundations (3 < 1
MPa), are plotted versus in Fig. 7, and they can be fitted by the
following: < 40 SRblock = - 0.02 + 0.9 (2a) 40 < < 60
SRblock = 0.1 (2b) > 60 SRblock = 0.02 - 1.1 (2c) The S.D. of
Eqs. 2a and 2b is 0.09, while that of Eq. 2c is 0.10. It can be
inferred that the variability of rock mass strength, as
rep-resented by the COV, is maximum for between 40 and 60.
The effect of number of discontinuities, typically assessed by
using different block sizes, also was evaluated using the strength
ratio (SRblock) approach. The results from blocks with three
dif-ferent discontinuity orientations (vertical only, horizontal
only, and vertical and horizontal) were considered. Only three
numbers of discontinuities were available for evaluation. As shown
in Fig. 8, SRblock decreases only slightly with increasing number
of dis-continuities. However, the variability of SRblock appears to
in-crease with increasing number of discontinuities. In addition,
for vertical and horizontal discontinuities, the effect of
discontinuity orientation appears to be minimal. These test results
also were used to estimate the variability of rock mass strength,
which is defined as the deviator stress at fail-ure [(1-3)f]. The
results were separated based on the disconti-nuity angles ( = 0-25
and 70-90, and = 25-70) to consider the effect of on the strength.
The results are plotted versus the confining stress (3) in Fig. 9
and show that the COV of (1-3)f
0 30 60
Discontinuity Angle to Horizontal Plane, 90
0.0
0.2
0.4
0.6
0.8
1.0
SRbl
ock
= (
1 -
3)f-b
lock
/ ( 1
- 3
) f-in
tact 1: SRblock = -0.02 + 0.9; S.D. = 0.092: SRblock = 0.1; S.D.
= 0.093: SRblock = 0.02 - 1.1; S.D. = 0.10
*
*
1
2
3
Einstein et al. (1969, 1973), 3 = 0Ladanyi & Archambault
(1972), 3 = 0.35 MPaLadanyi & Archambault (1972), 3 = 0.70
MPaKulatilake et al. (1997), 3 = 0, symm.Kulatilake et al. (1997),
3 = 0, asymm.Yang et al. (1998), 3 = 0
o o o
Fig. 7. Effect of discontinuity angle on rock block strength
(Prakoso & Kulhawy 2004b).
-
0 2 4 6 8
Number of Discontinuities
100.0
0.5
1.0
1.5SR
bloc
k =
( 1 -
3) f-
bloc
k / (
1 -
3)f-i
ntac
t
No. Discontinuity = 2: Mean = 0.98; S.D. = 0.12No. Discontinuity
= 4: Mean = 0.92; S.D. = 0.10No. Discontinuity = 8: Mean = 0.92;
S.D. = 0.17
Vertical DiscontinuitiesHorizontal DiscontinuitiesVertical &
Horizontal Discontinuities
Fig. 8. Effect of number of discontinuities on rock block
strength (Prakoso & Kulhawy 2004b). decreases with increasing 3
but, for typical 3 values for founda-tions (3 < 1 MPa), the COV
range still is wide, from 10 to 75%. In addition, the prior group
of discontinuity angles ( = 0-25 and 70-90) tends to yield a lower
COV of (1-3)f.
2.6 Rock Mass: Modulus
A realistic rock mass Youngs modulus (Em) is required in any
foundation displacement analysis, but typically it is obtained by
conducting field load tests, which are rather expensive.
Alterna-tively, Em can be estimated from the intact rock uniaxial
compres-sive strength (qu) or the intact rock modulus (Et-50). A
modulus ratio can be defined as follows:
Modulus Ratio = Em / qu (3)
Using mainly the data base developed by Rowe and Armitage
(1984), this ratio is plotted versus qu in Fig. 10. Note that the
exclusion of some data in Fig. 10 was based on a further detailed
statistical analysis (Prakoso 2002). Em also can be estimated from
Et-50 using a modulus reduction factor defined as follows:
E = Em / Et-50 (4)
In this form, E is a lumped parameter that includes the intact
rock properties and the discontinuity frequencies and properties.
Using the data base developed by Heuze (1980), the distribution of
E is shown in Fig. 11.
In addition, geomechanical models have been proposed to estimate
Em. The orthogonal model proposed by Kulhawy (1978) incorporates
key physical properties of the intact rock and the rock
discontinuities, as well as the mean discontinuity spacing, as
given by:
111
+=
njrm KSE
E
(5)
0 4 8 12
Confining Stress, 3 (MPa)16
0
20
40
60
80
CO
V of
(1
- 3)
f (%
) Einstein & Hirschfeld (1973)Brown & Trollope (1970),
Brown (1970)Ladanyi & Archambault (1972)
0o - 25o 25o-70o70o - 90o
Discontinuity Angle to Horizontal Plane,
Fig. 9. Effect of confining stress on COV of rock block strength
(Prakoso & Kulhawy 2004b).
1 10 100
Uniaxial Compressive Strength, qu / pa
10001
10
100
1000
10000
Mod
ulus
Rat
io, E
m /
q u
log10(Em / qu) = 2.73 - 0.49 log10(qu / pa)m = 71, r2 = 0.48,
S.D. log(Em / qu) = 0.26
MudstoneShaleSandstoneOthers
Fig. 10. Rock Mass Youngs Modulus from Load Tests (Filled
symbols excluded from statistical analysis).
0.0 0.2 0.4 0.6 0.8 1.0
E = Em / Et-50
0
2
4
6
8
10
No.
Obs
erva
tions
Mean =S.D. =
m =
0.320.2627
Log-NormalDistribution
0
Fig. 11. Distribution of E from plate bearing tests.
-
00.2
0.4
0.6
0.8
0 20 40 60 80 1
Mean RQD (%)
000
0.2
0.4
0.6
0.8Mea
n E
Simulation Results Negative Exponential Log-Normal (COV = 50%)
Log-Normal (COV = 100%)Kulhawy (1978)
Simulation Results Negative Exponential Log-Normal (COV = 100%)
Kulhawy (1978)
Er / Kn (m) = 0.5
Er / Kn (m) = 0.1
Er / Kn (m) = 1.0
Fig. 12. Relationship between Rock Mass Modulus and RQD. in
which Er = intact rock modulus (typically given by Et-50), Sj =
discontinuity spacing, and Kn = discontinuity normal stiffness.
This Em also can be correlated to Er = Et-50, as in Eq. 4, to
define the modulus reduction factor E. The discontinuity spacing
(Sj) is not obtained routinely in foundation practice, but the Rock
Quality Designation (RQD) is used commonly to characterize the rock
mass. Kulhawy (1978) used a simple geometric model to relate Si to
RQD; others have used statistical or random number-generated
relationships. In any case, as shown in Fig.12, the effect of
different Sj-RQD relation-ships is minor, compared to that of the
properties of the rock and discontinuities.
3 ROCK SOCKET CAPACITY
3.1 Generalized Socket Behavior
Fig. 13 depicts the generalized load-displacement behavior of
drilled shafts under axial load. This general pattern holds in both
soil (Hirany & Kulhawy 1988) and rock (Carter & Kulhawy
1988), as shown in many load tests that were carefully conducted
and well-documented. There is essentially a linear response from
the origin to L1, followed by a nonlinear transition region to L2,
after which there is a final linear region. In rock masses, these
regions correspond to initial linear elastic behavior, followed by
bond breakage and progressive slip, and then full frictional slip
with dilation. The same general pattern holds for both compres-sion
and uplift tests, although the relative sizes and importance of the
regions differ somewhat. In all cases, the occurrence of a clearly
defined peak to the curve is infrequent. With nonlinear curves such
as these, there is always a major question about how to define the
foundation "capacity" for sub-sequent design use. Examination of
the literature (Hirany & Kulhawy 1988) reveals at least 41
different methods used for the interpretation of axial load tests,
including displacement limits
Displacement
Load
Final linear region
Initial linear region
Transition region
QL2
QL1
Fig. 13. Generalized load-displacement behavior.
(absolute and percent of diameter), graphical constructions, and
mathematical functions. These also reflect a mix of what actually
are both ultimate limit state and serviceability limit state
criteria.
Our detailed studies (e.g., Hirany & Kulhawy 1988; Prakoso
2002) indicate that a consistent and reasonable method for defining
the "interpreted failure load" is to use QL2, which is the load at
L2. Similarly, QL1 is the load at L1, which represents the "elastic
limit". The L1 and L2 points are determined graphically from a plot
at a scale similar to that of Fig. 13. As can be seen, QL2 always
follows the nonlinearity, sometimes represents the actual curve
peak where there is little or no dilation, and can be evaluated
from virtually all quality test data.
Once the "capacity" is defined, then the tip and side
resis-tances can be evaluated based on measurements made in
com-pression tests of full sockets. In uplift tests, and in
compression tests with a void or frangible material beneath the
tip, the evalua-tion is straightforward and only requires
consideration of the shaft weight.
Most often, the tip and side resistances then are compared to
one of the simpler rock material indices, such as the uniaxial
compressive strength (qu). The qu tests should all be done in
accordance with proper test procedures, such as those given by
ASTM, ISRM , or others. Estimating qu from simpler tests such as
the point load index, Schmidt hammer, or others, may be
inap-propriate, as shown by the variability in the correlations
shown previously. Strictly speaking, any comparison also should be
with the average qu over the depth of the socket.
Most studies conducted to date have not met these criteria,
based on the documentation presented or stated. This statement is
not intended to fault the authors, who undoubtedly presented the
best information they could. It is intended to point out that we
are frequently dealing with imperfect and sometimes poor data, and
therefore our expectations should be tempered accordingly.
3.2 Calculation Model
In general, foundation capacity is a function of the tip
resistance (Qt), side resistance (Qs), and foundation weight (W).
By force equilibrium, the compression capacity (Qc) is given by: Qc
= Qtc + Qsc W (6)
-
in which the subscript c refers to compression. The uplift
capac-ity (Qu) is given by: Qu = Qtu + Qsu + W (7) in which the
subscript u refers to uplift. In most design cases, only limited
information is available on the rock mass properties and in-situ
conditions, and consequently the use of theoretical solutions is
difficult. More often, the only rock strength property available is
the intact rock uniaxial com-pressive strength (qu), and therefore
the foundation resistances typically are related to qu. In
simplified fashion, the tip (or base) resistances of circular
footings and drilled shafts in compression can be estimated by:
Qtc = 0.25 B2 Nc* qu (8) in which B = foundation diameter and
Nc* = empirical tip resis-tance factor. Information on the tip
resistance in uplift is very limited, so this resistance is not
discussed herein. The side resistance of drilled shaft foundations
socketed in rock involves a complex interaction among the adhesion,
friction, dilatancy, and normal stress effects along the socket
wall. These effects are difficult to measure or estimate, and
therefore they often are lumped into an average unit side
resistance (f). Using this simplification, the side resistance (Qs)
can be estimated by: Qs = B D f (9) in which B = foundation
diameter and D = foundation socket depth. It is assumed commonly
that f can be related directly to the intact rock uniaxial
compressive strength (qu), and therefore the side resistance is
given by: Qs = B D r qu (10) in which r = empirical side resistance
factor = f / qu.
3.3 Tip Resistance
The tip resistance for tests conducted on the socket tip and on
complete sockets was evaluated to assess the range of the tip
resistance factor (Nc*). The data base developed for this study
included 9 sites with 14 field load tests conducted in several rock
types, mainly in fine-grained sedimentary rocks, and 2 centrifuge
laboratory tests. All of the load tests had qu, and all were
con-ducted on straight-sided rock sockets. Axial compressive
loading was applied in all cases, with 7 tests performed on socket
tips and 7 tests performed on complete sockets. For the complete
sockets, the tip resistance was determined from the reported tip
and side resistance load distribution. The tip resistance factor
(Nc*) was evaluated using Eq. 8, and these values are plotted
versus the corresponding socket diameter (B) in Fig. 14, in which
Nc* appears to be independent of B. The mean of the tip resistance
factor (mNc*) and its COV (COVNc*) are given by mNc* = 3.38 and
COVNc* = 35.4%. The distribution of Nc* is shown in Fig. 15, and it
resembles a log-normal prob-ability distribution with the same mNc*
and COVNc*. Furthermore, Nc* appears to be independent of the rock
type.
3.4 Side Resistance
Carter & Kulhawy (1988) reviewed the Rowe & Armitage
(1984)
0.4 0.6 0.8 1.0 1.2
Socket Diameter, B (m)
0
2
4
6
8
10
Bear
ing
Cap
acity
Fac
tor,
Nc*
Nc* = 3.38, S.D. = 1.20
0
Fig. 14. Drilled socket tip resistance factor (Prakoso &
Kulhawy 2002).
0 1 2 3 4 5 6
Tip Resistance Factor, Nc*
0
2
4
6
8
No.
Obs
erva
tions
Mean =COV =
m =
3.3835.4%14
0
Log-NormalDistribution
Fig. 15. Distribution of drilled socket tip resistance factor
(Prakoso & Kulhawy 2002). data and noted that there is an
approximate lower bound to side resistance that is given by: f / pa
= 0.63 (qu / pa)0.50 (11) in which f = average unit side
resistance. To link the f / pa format with the r format, the
equations are given by: log10 r = A B log10 (qu / pa) (12a) f / pa
= 10A (qu / pa)B (12b) After examination of these data, they also
made two important design check recommendations. First, values of f
in excess of 0.15 qu, over the full range of expected values,
should be used only when they are demonstrated to be reasonable by
a load test, local experience, or adequate in-situ testing. And
second, after obtaining the design value of f, typically from Eq.
9, and apply-ing a factor of safety to this value, a check should
be made against the concrete bond value of 0.05 f'c. The lower
value should be used unless load test data show otherwise.
More recently, Prakoso (2002) re-examined the data available and
attempted to evaluate them in a more consistent manner.
-
First, the only data used were those that had load-displacement
curves to failure so that the "interpreted failure load" could be
determined for all the data and therefore the "capacities" were
evaluated in a consistent manner. However, it was not possible to
reevaluate the qu data to ensure consistency in test conduct and
averaging over the shaft depth. An initial assessment of
addi-tional Asia data (e.g., Ng et al. 2001) indicates that they
fall in the data range as above.
Fig. 16 shows the results for all of the data, including
multiple tests at the same site and results for (a) shafts in
natural and man-made rocks, (b) grouted piles in natural rocks, and
(c) rock an-chors in natural rocks. The regression line is given
by: f / pa = 2.00 (qu / pa)0.69 (13)
Fig. 17 shows the results of the data averaged per test site.
The regression line is given by: f / pa = 1.74 (qu / pa)0.67
(14)
Careful examination of these results indicates that the rock
an-chor data are clustered in the lower portions of the figure,
espe-cially in the lower right. Setting these data aside gives the
results for drilled shafts and grouted piles as shown in Fig. 18 by
the solid line. The regression line corresponds to: f / pa = 0.98
(qu / pa)0.50 (15)
which can be conveniently rounded to
f / pa = (qu / pa)0.50 (16)
The lower bound 10A value of 0.63 that was cited previously
actually represents the lower bound for 90% of the data in Fig. 18.
To capture 100% of the data, the absolute lower bound would be
about 0.5. It should be noted in Fig. 18 that the regression is
altered significantly when the rock anchor data are included.
Clearly these data constitute a separate population.
In addition to the general relationships described above, there
have been a number of studies that have focused exclusively on
1 10 100 1000 10000
Uniaxial Compressive Strength, qu / pa
0
0
0
0
1
Side
Res
ista
nce
Fact
or,
r
log10 r = 0.30 - 0.69 log10(qu / pa)m = 104, r2 = 0.72, S.D. =
0.29
0.0001
0.001
0.01
0.1
I. IntrusiveI. ExtrusiveI. PyroclasticS. Clastic (fine)
S. Clastic (coarse)S. ChemicalM. Non-FoliatedMan-Made
Fig. 16. Non-roughened side resistance of drilled foundations
(Kulhawy et al. 2005).
1 10 100 1000 10000
Uniaxial Compressive Strength, qu / pa
0
0
0
0
1
Side
Res
ista
nce
Fact
or,
r
log10 r = 0.24 - 0.67 log10(qu / pa)m = 52, r2 = 0.69, S.D. =
0.30
0.0001
0.001
0.01
0.1
I. IntrusiveI. ExtrusiveI. PyroclasticS. Clastic (fine)
S. Clastic (coarse)S. ChemicalM. Non-FoliatedMan-Made
Fig. 17. r vs. qu for all data, averaged per site (Kulhawy et
al. 2005).
1 10 100 1000 10000
Uniaxial Compressive Strength, qu / pa
0
0
0
0
1
Side
Res
ista
nce
Fact
or,
r
0.0001
0.001
0.01
0.1
log10 r = - 0.01 - 0.50 log10(qu / pa)m = 41, r2 = 0.51, S.D. =
0.31
I. IntrusiveI. ExtrusiveI. PyroclasticS. Clastic (fine)
S. Clastic (coarse)S. ChemicalM. Non-FoliatedMan-Made
Regression Line for Data with Rock Anchors
Fig. 18. r vs. qu for drilled shafts and grouted piles, averaged
per site (Kulhawy et al. 2005).
localized rock units, such as the chalks of southern England and
the limerocks of Florida. These studies are of local importance and
are too specialized to be discussed herein. When these are
addressed, they should be considered within the broad framework
described above.
3.5 Effect of Socket Roughening
The values of r for roughened drilled foundations are plotted
versus their corresponding qu/pa in Fig. 19. The r decreases with
increasing qu/pa, and the regression equation is given by:
f / pa = 1.91 (qu / pa)0.46 (17)
The side resistance factor (r) differs with socket
roughening.
-
1 10 100 1000 10000
Uniaxial Compressive Strength, qu / pa
0
0
1Si
de R
esis
tanc
e Fa
ctor
, r
log10 r = 0.28 - 0.46 log10(qu / pa)m = 43, r2 = 0.67, S.D. =
0.16 S. Clastic S. Chemical Man-Made
0.01
0.04
0.1
0.4
Fig. 19. Roughened side resistance of drilled foundations.
For non-roughened sockets, r is lower than that for roughened
sockets. The overall trend of both data sets and the regression
lines is similar. Both regression lines are close for lower qu,
sug-gesting that the nominal side resistances are about the
same.
3.6 Rock Socket Side Resistance and Concrete Bond Strength
Carter & Kulhawy (1988) recommended a design check to
com-pare the allowable side resistance of the rock socket (f / FS)
to the concrete bond strength, given by 0.05 f'c. The lower value
would control, unless field testing showed otherwise. By using
typical safety factors of 2 and 3, the ultimate side resistance can
be compared with the factored concrete bond strength, as given in
Fig. 20. Typical ranges of concrete strength, f'c / pa = 200 - 400,
were used for comparison.
Fig. 20 shows that most side resistances are below the lower
concrete strength and factor of safety. All of these cases showed
acceptable behavior when the bond strength of the concrete was
exceeded. Clearly the concrete behaves better when it is confined
in a socket and reinforced than when it is unconfined and
unre-inforced. The percentages are given in Table 1, which shows
that there are more cases of sockets exceeding the concrete bond
strength with lower concrete strength and factor of safety. Again,
all of these cases showed acceptable behavior when the bond
strength of the concrete was exceeded.
4 ROCK MASS CONDITIONS & ROCK FOUNDATION BEARING CAPACITY:
THEORETICAL RELATIONSHIPS
Prakoso & Kulhawy (2004a) proposed a lower bound bearing
capacity model, coupled with a simple discontinuity strength model,
for strip footings on jointed rock masses. The strength of both the
rock material (r and cr) and the discontinuities (j and cj), and
the number and orientation of the discontinuity sets (1n), are
considered explicitly in the model. The lower bound bearing
capacity factor (Ncs) for strip footings on rock masses with a
single discontinuity set is given in Figs. 21 through 24. The
uniaxial compressive strength (qu) of the rock material,
nor-malized by cr, also is given. In all figures, Ncs is related to
the discontinuity orientation angle (1). The effect of friction
angle
1 10 100 1000 10000
Uniaxial Compressive Strength, qu / pa
0
20
40
60
80
100
Side
Res
ista
nce,
f / p
a I. IntrusiveI. ExtrusiveI. PyroclasticS. Clastic (fine)
S. Clastic (coarse)S. ChemicalM. Non-FoliatedMan-Made
0.05 FSlim (fc' / pa)
fc' / pa = 200
fc' / pa = 400
FSlim = 3
2
32
Fig. 20. Socket side resistance versus concrete bond strength
(Kulhawy et al. 2005). Table 1. Comparison of Side Resistance and
Concrete Bond Strength (Kulhawy et al. 2005). Rock Socket % socket
fallow > 0.05 f'c FSlim = 2 FSlim = 3 Non-Roughened f'c / pa =
200 16% 4% f'c / pa = 400 2% 0% Roughened
f'c / pa = 200 40% 14% f'c / pa = 400 9% 0% Concrete bond
strength = 0.05 FSlim (f'c / pa) variation (r = j) on Ncs is shown
in Fig. 21. As r increases, the maximum and minimum Ncs increase, 1
for the minimum Ncs decreases, and the ratio of maximum to minimum
Ncs increases slightly. Also, the range of 1 affecting Ncs
decreases, and the shape of the line of Ncs changes with increasing
r.
The effect of discontinuity cohesion, given by cj / cr, is shown
in Fig. 22. As cj / cr increases, the minimum Ncs increases, and
the range of 1 affecting Ncs decreases. The effect of discontinuity
friction angle (r j) is shown in Fig. 23. As j increases, the
minimum Ncs increases, and 1 for the minimum Ncs changes. Also, the
range of 1 affecting Ncs decreases, and the shape of the line of
Ncs changes significantly with increasing j.
Ncs for rock masses with two discontinuity sets is given in Fig.
24. As shown, Ncs is influenced significantly by 1 and the angle
between the discontinuity sets (). The minimum Ncs and 1 for this
minimum differ for different values. Also, the range of 1 affecting
Ncs varies, and the shape of the line of Ncs changes sig-nificantly
with different values. The results for both one and two
discontinuity sets suggest that the strength of both the rock
material and the discontinuities, and the number and orientation of
the discontinuity sets, all have significant effects on Ncs.
Prakoso & Kulhawy (2006) provide an update of the Kulhawy
& Goodman model for foundations on rock with vertical
discon-tinuities. For a rock mass with open vertical
discontinuities, where the discontinuity spacing (Sj) is less than
or equal to the foundation width (B), the likely failure mode is
uniaxial com-pression of rock columns. The ultimate capacity based
on the Mohr-Coulomb failure criterion then is given by:
qult = qu = 2 c tan (45 + / 2) (18)
in which qu = uniaxial compressive strength, c = cohesion, and =
friction angle. The qu, c, and are rock mass properties.
-
0 30 60
Discontinuity Angle to Horizontal Plane, 1 (o)
900
10
20
30
40
50
60
Bear
ing
Cap
acity
Fac
tor,
Ncs
cj / cr = 0.3
1
r = j = 30o
50o
45o
40o
35o
Fig. 21. Lower bound bearing capacity of strip footings on
jointed rock masses - one discontinuity set (Prakoso & Kulhawy
2004a).
0 30 60
Discontinuity Angle to Horizontal Plane, 1 (o)
900
10
20
30
Bear
ing
Cap
acity
Fac
tor,
Ncs
cj / cr = 0.1
1r = j = 40o
0.9
0.7
0.5
0.3
qu /cr
Fig. 22. Effect of discontinuity cohesion on lower bound bearing
capacity (Prakoso & Kulhawy 2004a).
For a rock mass with vertical discontinuities spaced wider than
the foundation width (B), the likely failure mode is splitting of
the rock mass. Bishnoi (1968) proposed the following format to
evaluate this failure mode:
qult J c Ncr (19) in which J = correction factor, c = intact
rock cohesion, and Ncr = bearing capacity factor. The J factor is
later. The bearing capacity factor (Ncr) is given by Goodman
(1980):
( )
=
11
2 1150 Nj.
cr BS
NN
NN (20)
0 30 60
Discontinuity Angle to Horizontal Plane, 1 (o)
900
10
20
30
Bear
ing
Cap
acity
Fac
tor,
Ncs
j = 20o
1
r = 40o; cj / cr = 0.3
40o
35o
30o
25o qu /cr
Fig. 23. Effect of discontinuity friction angle on lower bound
bearing capacity (Prakoso & Kulhawy 2004a).
0 30 60
Discontinuity Angle to Horizontal Plane, 1 (o)
900
10
20
30
Bear
ing
Cap
acity
Fac
tor,
Ncs
1 2 = 1 +
r = j = 40o; cj / cr = 0.3
= 30o = 60o = 90o
qu /cr
Fig. 24. Lower bound bearing capacity of strip footings on
jointed rock masses - two discontinuity sets (Prakoso & Kulhawy
2004a).
in which Sj = spacing between vertical discontinuities and N =
bearing capacity factor given by: N = tan2 (45 + / 2) (21)
As the spacing between a pair of vertical discontinuities (Sj)
increases, the failure mode changes, from splitting of the rock
mass to general shear failure. For general shear, the modified
solution proposed by Bell (1915) can be used:
qult = c Nc cs cd + 0.5 B N s d + q Nq qs qd (22) in which c =
rock mass cohesion, B = foundation diameter or width, = rock mass
effective unit weight, q = D = overburden stress at tip, D =
foundation depth, and Nc, N, and Nq = bearing
-
capacity factors. The factors cs, cd, s, d, qs, and qd are
modifiers for square or circular foundations; the second subscript
s denotes the shape factor and the second subscript d denotes the
depth factor. For shallow foundations, D is very small, and the 0.5
B N term normally is very small compared to the c Nc term, and
therefore Eq. 22 often is simplified as: qult = c Nc cs (23a) qult
= 2 c [tan(45 + / 2) + tan3(45 + / 2)] cs (23b) The modifying
factor cs is given by: cs = 1 + N1.5 / [2 (N + 1)] (24) The results
of Eqs. 18-23 are shown in Fig. 25 for a range of rock mass
friction angles. Note that, as the results are given in terms of
Ncr, for the uniaxial compression failure mode, Ncr is given by:
Ncr = 2 tan (45 + / 2) (25) For the general wedge failure mode, Ncr
is given by: Ncr = Nc cs (26) The changes in failure modes in Fig.
25 are identified by the dashed lines.
The correction factor (J), based on Bishnoi (1968), also was
updated. Contrary to Bishnois suggestions, the results show no
apparent trend, as can be seen in Fig. 26. The mean and COV of J
are 1.14 and 33.3 percent, respectively.
5 DEFORMATION OF ROCK SOCKETS
Carter and Kulhawy (1988) suggested that the displacement of a
rigid shear socket under uplift loading can be evaluated by:
u
mu FDG
y
= 1
2 (27)
in which = ln[5 (1-) D/B], = rock mass Poissons ratio, Gm = rock
mass shear modulus, D = shaft depth, and Fu = applied uplift load.
This equation also is used for a single anchor in uplift.
Carter and Kulhawy (1988) also suggested that the elastic
dis-placement of a rigid complete socket can be evaluated by:
+
+
=11 2
DEBEFy
m
b
b
cc
(28) in which Fc = applied compressive load, Eb = rock mass
Youngs modulus below the tip, b = rock mass Poissons ratio below
the tip, and B = socket diameter. Note that, because the typical
val-ues of and b are low and Eb = Em is commonly assumed, Eq. 28
can be simplified as follows:
+
+
1
1 BDEFy mcc
(29)
0 1 10 100
Discontinuity Spacing, Sj / B
1
10
100
1000
Bear
ing
Cap
acity
Fac
tor,
Ncr
= 10o20o30o40o
50o
60o
0.1
Limit for Sj > B
Ncr Equation
Bell Solution
UniaxialCompression
Fig. 25. Capacity factor for vertical open discontinuities
(Prakoso & Kulhawy 2006).
0 5 10 15 20
Thickness of Rock Layer, H/B
0.0
0.5
1.0
1.5
2.0
Cor
rect
ion
Fact
or, J
Igneous IntrusiveSedimentary ChemicalConcrete
Fig. 26. Correction factor J (Prakoso & Kulhawy 2006). These
equations are valid up until L1, at which displacements typically
are on the order of 10-15 mm. Beyond L1, nonlinearity and load
transfer must be addressed.
6 CONSTRUCTION AND FIELD ACCEPTANCE CRITERIA
In general, when constructing a rock socket, it is necessary to
ensure that the rock mass is of sufficient quality to carry the
load without adverse behavior. To achieve this goal, it is common
to set exploration and/or construction criteria that must be
met.
First and foremost, there must be sufficient exploration data to
define the rock materials present and to delineate the rock mass
structure and discontinuities. These data should be of sufficient
depth beneath the tips of the rock sockets to define the rock mass
well enough so that the bearing capacity and settlement can be
computed with some confidence. In particular, it is necessary
to
-
define the layering and/or soft seams that can be present in
many types of stratified rock masses and the voids that can be
present in certain types of volcanic rocks and in the carbonate
rock fam-ily. If these features are not defined with some
confidence during exploration, then it usually will be necessary to
do so during con-struction.
Second, the socket must be constructed to give a nominally
"clean" socket. The tip should be cleaned out as best as possible
using conventional clean-out tools. Only in extraordinary cases
should any special procedures be used. If side resistance is being
considered in the design, then the sides of the socket must be
clean as well, again using conventional tools. There is no need to
resort to special procedures for removing any light drilling muds,
because they will be displaced by proper tremie placement of
high-slump concrete. However, in some softer or weathered rocks,
for example compaction clay-shales, softening of the socket side
may occur. Special clean-out procedures and socket roughening or
grooving may be considered in these cases.
Third is the issue of socket use and design. Where there is rock
surface uncertainty and therefore a need to ensure a quality
bearing surface, "seating" sockets can be considered. These types
of sockets minimally penetrate the rock surface, usually to a depth
less than one socket diameter, and provide little, if any, side
resistance. For these sockets, only tip clean-out is necessary.
When the sockets are deeper, they will be "load-carrying" sock-ets.
These sockets can be used and designed in several ways. If "tip
resistance only" sockets are designed, then there is no ration-ale
to prescribe acceptance criteria for the rock along the socket
sides. If "side resistance only" sockets are designed, then there
is no rationale to prescribe acceptance criteria for the rock
quality beneath the socket tips. However, if both side and tip
resistances are included in the design, then acceptance criteria
for both are appropriate. For the side, criteria sometimes are
suggested that relate to the percent of soil surface area or number
of seams pre-sent along the surface of the socket. These may or may
not be realistic, depending on the actual geologic details. For the
tip, criteria sometimes are suggested for probe holes drilled
beneath the tip to determine the frequency and thickness of soil
seams in the rock within a depth beneath the tip equal to a shaft
diameter or sometimes more. These types of criteria are based on
settle-ment limitations and must be evaluated as such, considering
stress distribution models for sockets in layered media.
Guide-lines are warranted to adjust these criteria if deepening is
needed because the acceptance criteria are not met. In this case,
more load is transferred through the socket side as the socket
deepens.
How the field acceptance criteria are implemented is an issue of
potentially significant economic concern, in the same category as
the evaluation of rock characteristics. If the rock
characteris-tics are defined well during the investigation, then
there should be few, if any, surprises during construction. If the
investigation is minimal, the opposite is likely. To minimize
surprises, some even note that probe holes be drilled prior to
construction at each shaft location to establish the final shaft
depth before construc-tion. This important economic issue needs to
be assessed care-fully and delineated clearly prior to
construction.
7 CONCLUDING COMMENTS
Drilled foundations often are socketed into rock to increase the
capacity. However, procedures to quantify the socket side and tip
resistance vary considerably. In this paper, a critical assessment
is made of some key aspects of rock socket behavior.
First, several methods are presented to estimate key rock
material and rock mass properties needed for socket design. Then
one method for evaluating side resistance is presented, after a
detailed evaluation. Several possible approaches are suggested to
assess the tip resistance, depending on the degree of geologic data
available. Where available, statistics are given for the properties
and the methods. Some design and construction implications are
noted as well. Detailed load-settlement-load transfer evaluations
are beyond the scope of this paper.
REFERENCES
Bell, A.L. 1915. Lateral Pressure & Resistance of Clay,
& Sup-porting Power of Clay Foundations. Minutes of Proc. of
In-stitution of Civil Engineers: 199: 233-336.
Bishnoi, B.L. 1968. Bearing Capacity of Closely Jointed Rock.
PhD Thesis. Atlanta: Georgia Institute of Technology.
Carter, J.P. & Kulhawy, F.H. 1988. Analysis & Design of
Drilled Shaft Foundations Socketed into Rock. Report EL-5918. Palo
Alto: Electric Power Research Institute.
Goodman, R.E. 1980. Introduction to Rock Mechanics. New York:
Wiley
Heuze, F.E. 1980. Scale Effects in Determination of Rock Mass
Strength & Deformability. Rock Mechanics, 12(3-4): 176-92.
Hirany, A. & Kulhawy, F.H. 1988. Conduct &
Interpretation of Load Tests on Drilled Shafts. Report EL-5915.
Palo Alto: Electric Power Research Institute.
Kulhawy, F.H. 1978. Geomechanical Model for Rock Founda-tion
Settlement. J. Geotech. Eng. Div., ASCE, 104(2): 211-27.
Kulhawy, F.H. & Prakoso, W.A. 2001. Foundations in Carbonate
Rocks & Karst. Foundations & Ground Improvement (GSP 113),
Ed. T.L.Brandon. Reston: ASCE: 1-15.
Kulhawy, F.H. & Prakoso, W.A. 2003. Variability of Rock
Index Properties. Proc. Soil & Rock America, Ed. P.J.Culligan
et al. Cambridge (MA): 2765-70.
Kulhawy, F.H., Prakoso, W.A., & Akbas, S.O. 2005. Evaluation
of Capacity of Rock Foundation Sockets. Proc. 40th U.S. Symp. Rock
Mechanics, Ed. G.Chen et al. Anchorage: paper 05-767 CDROM.
Ng, C.W.W., Yau, T.L., Li, J.H.M., & Tang, W.H. 2001. Side
Resistance of Large Diameter Bored Piles Socketed into De-composed
Rocks. J. Geotech. Eng., ASCE, 127(8): 642-57.
Prakoso, W.A. 2002. Reliability-Based Design of Foundations on
Rock for Transmission Line & Similar Structures. PhD Thesis.
Ithaca: Cornell University.
Prakoso, W.A. & Kulhawy, F.H. 2002. Uncertainty in Capacity
Models for Foundations in Rock. Proc. 5th North Amer. Rock
Mechanics Symp., Ed. R.Hammah et al. Toronto: 1241-48.
Prakoso, W.A. & Kulhawy, F.H. 2004a. Bearing Capacity of
Strip Footings on Jointed Rock Masses. J. Geotech. Eng., ASCE,
130(12): 1347-49.
Prakoso, W.A. & Kulhawy, F.H. 2004b. Variability of Rock
Mass Engineering Properties. Proc. 15th SE Asian Geotech. Conf.(1),
Ed. S.Sambhandharaksa et al. Bangkok: 97-100.
Prakoso, W.A. & Kulhawy, F.H. 2006. Capacity of Foundations
on Discontinuous Rock. Proc. 41st U.S. Symp. Rock Mechan-ics, Ed.
D.P.Yale et al. Golden: paper 06-972 CDROM.
Rowe, R.K. & Armitage, H.H. 1984. Design of Piles Socketed
into Weak Rock, Report GEOT-11-84, London: University of Western
Ontario.
1 INTRODUCTION2 ROCK MASS ENGINEERING PROPERTIES2.1 Intact Rock:
Effect of Testing Parameters2.2 Intact Rock: Index Property and
Strength Correlations2.3 Intact Rock: Strength and Modulus
Correlation2.4 Intact Rock: Weathering2.5 Rock Mass: Strength of
Artificial Rock Blocks2.6 Rock Mass: Modulus
3 ROCK SOCKET CAPACITY 3.1 Generalized Socket Behavior3.2
Calculation Model3.3 Tip Resistance3.4 Side Resistance3.5 Effect of
Socket Roughening3.6 Rock Socket Side Resistance and Concrete Bond
Strength
4 ROCK MASS CONDITIONS & ROCK FOUNDATION BEARING CAPACITY:
THEORETICAL RELATIONSHIPS5 DEFORMATION OF ROCK SOCKETS6
CONSTRUCTION AND FIELD ACCEPTANCE CRITERIA 7 CONCLUDING COMMENTS
REFERENCES
