prediction of ultimate capacity of axially loaded drilled ... · rocks to support the enormous...

When constructing huge structures, large diameter drilled shafts are most commonly socketed into

rocks to support the enormous load. Unconfined compressive strength is mostly used to calculate the

capacity of drilled shaft socketed in rock; many empirical correlational equations of the sort were

introduced worldwide as well. This paper employs the 23 cases of drilled shafts embedded in the

Songdo area to verify the most suitable method, then moves on to suggest a new empirical formula.

In the case where it is difficult to collect the undisturbed core of weathered rocks, the traditional

capacity computing equations are not useable due to the problems in defining the unconfined

compressive strength. Thus, the paper employs the RQD, the deformation modulus and the elastic

modulus from a pressuremeter test to deduct an empirical capacity equation.

In addition, the paper analyzes the aspect ratio which affects capacity as well. Finally, this paper

has been found that the most accurate result in both the side shear resistance and the end bearing

resistance.

Prediction of Ultimate Capacity of Axially Loaded Drilled Shafts Socketed in Weak Rock

권순재3) 김성헌4)김연정1) 조흥재2)

1. Introduction

2. Background Theory

3. Database

4. Result

5. Summary & Conclusions

6. Reference

1) 전무·토질 및 기초기술사·공학박사([email protected])2) 이사·토질 및 기초기술사([email protected])

3) 차장·토질 및 기초기술사([email protected])4) 사원([email protected])

www�yooshin�co�kr_ 177

+12-Prediction177-191.ps 2011.12.17 1:51 PM 페이지177

▲⃝유신기술회보 _기술자료

178_제18호

1. Introduction

The recent economical growth has

created a boom in the large-sized

structural construction business as well.

Especially, developmental efforts in the

coastal area(e.g. Inchon Songdo area) has

increased due to rise in demand for

skyscrapers, bridges, airports, and harbors.

This resulted an upheaval in the use of

large-diameter drilled shafts because

naturally coastal areas have soft soil.

During and after the mid 1970’s, the

defining method for ultimate capacity of

drilled shafts has been actively researched,

and many researchers have suggested

empirical prediction methods using the

capacity results of load tests.

However, the ultimate capacity predic-

tion methods for previous drilled shafts

socketed in rock were created with low

strength and/or high quality rocks. Thus,

in the cases for high strength and/or low

quality rocks, the prediction methods have

high error margins when compared with

actual load test results. As a result it is

harder to apply the prediction methods to

domestic rocks such as the granite and

gneiss variety among the weathered and

soft; those have high strength but large

amounts of discontinuity.

This paper includes a database from 15

cases of drilled shafts socketed in rock in

the Song-Do area, 8 cases from the Inchon

Bridge link road and land bridge; totalling

23 cases from load tests, load-transfer

measured data, and subsurface exploration

data. The paper predicts the behavior of

pile socketed in rock by analyzing the

correlation between the behavioral support

of a rock section developed from assaying

results from a pile load test, and the

property of a rock condition obtained by a

geotechnical investigation. Also, it

contains information of the feasibility of

previous capacity prediction methods on

domestic rocks.

2. Background Theory

The most common assumption is that

drilled shafts socketed in rock either

supports the load by the sum of the side

shear resistance and the end bearing

resistance or by either one of these.

To calculate the axial capacity of pile

foundation socketed in rock, we must first

measure the side shear resistance and the

end bearing resistance of the socketed part

of the shaft. In addition, we must

apprehend the load transfer mechanism



and the various factors that affect this

effort to evaluate the general resistance of

the socketed part.

2.1 Side shear resistance of drilled shaftusing unconfined compressive strength

Load tests of the socketed shaft shows

that the resistance of the rock layer takes

up most of the total resistance. The side

shear resistance of sand, clay, and fill layer

above the weathered rock stratum occupies

only a small portion of the whole. Thus, it

is general practice to measure only the side

shear resistance of the rock when design-

ing the drilled shaft socketed in rock.

The mechanism where shear strength

occurs is complicated. It relies on the

friction and the strength of attachment of

the contact surface between concrete and

rock: that is, the direct relationship with

the normal stress resulting from the

dilatancy of the contact surface. Dilatancy

can be addressed to the sliding effect of the

contact surface.

However, since these factors are in

reality hard to consider, and most of the

experimental data from field and

laboratory tests result in unit side shear

resistance τ, it is general practice to use τ

for designing purposes. Also, the experien-

tial prediction methods to estimate the unit

side shear resistance τwere suggested

worldwide. Most of the methods point to

either a exponential or a constant propor-

tional relationship between unconfined

compressive strength and unit side shear

resistance.

2.2 End bearing resistance of drilled shaftusing unconfined compressivestrength

From the mid 1970’s, research was

actively undertaken to define the ultimate

bearing capacity of drilled shafts via

unconfined compressive strength of rock.

But the unconfined compressive strength

of rock cannot represent the total rock

strength. Thus, the unconfined compre-

ssive strength of rock core gained from

laboratory tests must be reduced to the

representative average strength value of

the field rock for it to be used to calculate

end bearing resistance. This decision to

reduce the strength must be based on

experience concerning the regionality, the

discontinuity degree and property of the

rock.

Since end bearing resistance is also

related to unit end bearing resistance qu

derived from the experiential data of field

and laboratory tests, it is general practice




180_제18호

to use qu for designing purposes. Also, the

experiential prediction methods to

estimate the unit end bearing resistance qu

were proposed widely.

2.3 Resistance of drilled shaft using otherproperties

When given directly representative

values of the strength of a rock to

deformation modulus and elastic modulus

from pressuremeter test, properties from

field test can be assumed to have a close

relationship to the end bearing resistance.

Also, RQD, an index concerning the crack

of a rock core, differs in value consequent

to the degree of weathering; its space of

discontinuity surface can be easily

classified, and can be closely associated

with the resistance of the rock as well.

According to the study of Hoek(1983), the

strength of a rock is strongly affected by

the number and the interval between

discontinuity surfaces; also, the research

done by Kwon et al.(2008), which points to

the fact that the end bearing resistance and

the side shear resistance have a strong

correlation with the deformation modulus:

the elastic modulus: and the RQD.

3. Database

As previously mentioned, to analyze the

behavioral support of the drilled shaft

socketed in a soft rock representative

domestically, the paper uses a load test

report of the large diameter drilled shaft

installed in the Incheon free economic zone

(Incheon City, Yeonsu-Gu, Dongchun-

Dong area), Inchon bridge link road and

land bridge. Drilled shafts totalling 23

cases were used ranging in diameter

1.2~2.85 m, in length 33~70 m, and in

socketed depth 7~35 m. Also, the bedrocks

used were metamorphic rock and biotite

granite.

The method for the drilled shaft

construction is the RCD(Reverse Circula-

tion Drill) method, and bi-directional load

tests are naturally used. As for the use of

field property, the paper adapted the soil

property of the relevant section when

calculating the side shear resistance; and in

the case where the property of the

concerned segment was non-existent. The

paper used the average property of the

borehole. When calculating the end

bearing resistance, the paper used the

property of the pile tip depth that has 1D

or less of the overall shaft. (Peck at al.

1974)




4. Result

Among the properties of a rock, the

following shows the relationship between

unconfined compressive strength: defor-

mation modulus and elastic modulus

using a pressuremeter test: RQD: aspect

ratio: and unit side shear resistance and

unit end bearing resistance of drilled shaft.

4.1 Unconfined compressive strength ofrock vs. Side shear resistance

Below is the plotted Log-Log chart

showing the relationship between the unit

side shear resistance of a drilled shaft from

the load test, and the unconfined

compressive strength. The regression

curve was gained from a exponential

function, and the deducted empirical

formula is as below. The Table 1. shows

the average of the bias factor, standard

deviation, and the covariance calculated

by the 16 capacity prediction methods

whereas the graph shows the 2 prediction

methods that produced the closed results

with the measured data. The bias factor in

the chart, is capacity divided by predicted

capacity. It can be said that the empirical

formula is conservative when the average

of the bias factor is higher than 1. Also the

smaller the covariance, the smaller the

deviation between the measured data and

the predicted data. By analyzing the

statistical property of the bias factor, one

can see that the method suggested by

Williams et al. (1980), Rosenberg and

Journeaux (1976) produces results that are

the closest with the measured data.

Here, the line is the regression of mea-

sured data, and the dotted line represents

the predicted data produced from the

previously suggested formula.

Evaluated the correctiveness of the

approximation formulas by comparing the

RMSE result of the suggested formula

with the three most correct prediction

formulas. Although there is only a slight

difference, one can see that the suggested

formula has the least deviation.

[Figure 1] The relationship between the unconfinedcompressive strength and the unit side shearresistance

τmax = 0.32σc0.50 (R2 = 0.57)



182_제18호

4.2 Unconfined compressive strength ofrock vs. End bearing resistance

The follow is the plotted Log-Log graph

showing the relationship between the unit

end bearing resistance of a drilled shaft,

and the unconfined compressive strength.

The regression curve was gained from an

exponential function, and the deducted

empirical formula is as below.

The Table 2. shows the average of the

bias factor, standard deviation, and the

covariance calculated by 8 of the 11

previously mentioned capacity prediction

methods; whereas the graph shows the 2

prediction methods that produced the

closed results with the measured data. In

methods Carter and Kulhawy(1988) and

Canadian Foundation Engineering Manual

(2006), there were a few instances where

[Figure 2] The predicted relationship between unconfinedcompressive strength of rock and side shearresistance using Williams et al. (1980) methodand Rosenberg and Journeaux (1976) method

[Figure 3] Assessment of the correctiveness of theapproximation formulas by comparing theRMSE (Side shear resistance)

qmax = 6.1σc0.35 (R2 = 0.39)

[Figure 4] The relationship between unit end bearingresistance and unconfined compressivestrength




values of g(aperture of the discontinuities)

and s(spacing of the discontinuities) could

not be obtained; and in Hoek(1983),

AASHTO(1989) the deviation was too

large to interpret the result. By analyzing

the statistical property of the bias factor,

one can see that the method suggested by

ARGEMA (1992), Zhang & Einstein (1988)

produces results that are the closest with

the measured data.

Here, the line is the regression of

measured data, and the dotted line

represents the predicted data produced

from the previously suggested formula.

Evaluated the correctiveness of the

approximation formulas by comparing

the RMSE result of the suggested formula

with the two most correct prediction

formulas. One can see that the suggested

formula has the least deviation.

4.3 Pressuremeter Test vs. Side ShearResistance

The following graph showing the

relationship between the unit side shear

resistance of a drilled shaft, and the

deformation modulus D and elastic

modulus E from pressuremeter test. The

empirical function, deducted from the

linear regression, is as below. One can see

[Figure 5] The predicted relationship between unconfinedcompressive strength of rock and end bearingresistance using ARGEMA (1992) method andZhang & Einstein (1988) method

[Figure 6] Assessment of the correctiveness of theapproximation formulas by comparing theRMSE (End bearing resistance)



184_제18호

that the correlation coefficient of side

shear resistance and the property of

pressuremeter test is much higher than

the other properties.

[Table 1] The empirically predicted values of the statistical property of bias factor using the unconfined compressivestrength of rock (Side shear resistance)

1. Design Code of Highway Bridge (2008), AASHTO (1996) 1.54 0.69 0.44

2. Structural Foundation design criteria (2003), NAVFAC DM 7-2 1.87 0.83 0.44

3. Korea Expressway Corporation (2002), CFEM (2006) 2.66 1.87 0.70

4. AASHTO (2007), Horvath and Kenney (1979) 3.75 1.72 0.46

5. Railroad design criteria (1999), AASHTO LRFD (2004) 1.70 0.75 0.44

6. Horvath and Kenney (1979) 1.70 0.75 0.44

7. Carter and Kulhawy (1988) 1.79 0.79 0.44

8. Williams et al.(1980) 1.12 0.54 0.48

9. Rowe and Armitage (1984) 0.77 0.34 0.44

10. Rosenberg and Journeaux(1976) 1.03 0.45 0.44

11. Reynolds and Kaderabek (1980) 0.44 0.31 0.70

12. Gupton and Logan (1984) 0.66 0.47 0.70

13. Reese and O’Neill (1987) 0.89 0.62 0.70

14. Toh at al. (1989) 0.53 0.37 0.70

15. Meigh and Wolshi(1979) 1.30 0.59 0.45

16. Horvath (1982) 1.79 0.79 0.44

MethodBias factor

Mean Stdev COV

1. Design Code of Highway Bridge (2008) 3.46 1.48 0.43

2. Structural Foundation design criteria (2003) 5.86 4.60 0.79

3. NAVFAC DM 7-2 4.90 2.86 0.58

4. Coates (1967) 0.39 0.31 0.79

5. Rowe and Armitage (1987b) 0.43 0.34 0.79

6. ARGEMA (1992) 1.89 0.72 0.38

7. Zhang & Einstein (1988) 0.86 0.34 0.39

8. Teng (1962) 0.23 0.18 0.79

Bias factor

Mean Stdev COV

[Table 2] The statistical property of the empirical prediction values using the unconfined compressive strength ofrock(End bearing resistance)

Method




4.4 Pressuremeter Test vs. BearingResistance

Below is the graph showing the

relationship between the unit end bearing

resistance of a drilled shaft, and the

deformation modulus and elastic modul-

us. The empirical function, deducted from

the linear regression, is as below. One can

see that the relationship of the deforma-

tion modulus and the elastic modulus

with the end bearing resistance has a

much lower correlation coefficient than

that of the side shear resistance. Although

the deformation modulus and the elastic

modulus of rock is high, settlement of

shaft could occurred excessively during

the earlier stage of loading. This led to the

presence of several cases of shafts with

conservatively evaluated ultimate

capacity. This factor is thought to be the

cause of the phenomenon. Also, in a case

[Figure 7] The relationship between unit side shearresistance, and deformation, elastic modulusof PMT

τmax = 0.0014D + 0.51 (R2 = 0.68)

τmax = 0.00082E + 0.45 (R2 = 0.69)

[Figure 8] The relationship between unit end bearingresistance and deformation, elastic modulus ofPMT

qmax = 0.0025D + 13.2 (R2 = 0.20)

qmax = 0.00088E + 15.1 (R2 = 0.043)



186_제18호

where the pile tip is positioned at the

boundary of weathered rock and soft

rock, or at the boundary of soft and hard

rock, the capacity of the end bearing is

more difficult to predict than that of the

side shear because the capacity and the

settlement can differ in variance with the

ground investigation. Thus, the prediction

of the pile tip resistance has to be made

with great caution.

4.5 Rock Quality Designation (RQD) vs.Resistance

The follow is the graph showing the


resistance and the unit end bearing

resistance of a drilled shaft, and the RQD.

Although an upfront prediction of the

capacity using only the RQD value is

unprobable, the empirical formula below

is deducted from an approximate linear

regression.

The correlation between the RQD and

the side shear resistance is higher than

that of the end bearing resistance. This is

also because the settlement of shaft

occurred excessively during the earlier

stage of loading. This led to the presence

of several cases of shafts with

conservatively evaluated ultimate

capacity. This factor is thought to be the

cause of the phenomenon. The correlation

is considered to be low because when the

RQD is high while the rock strength is low

or vice versa, it is hard to calculate the

capacity using only the RQD.

4.6 Aspect Ratio vs. Resistance

Below is the graph showing the


resistance and the unit end bearing

[Figure 9] Relationship between RQD and unit side shearresistance, unit end bearing resistance

τmax = 0.026RQD + 0.59 (R2 = 0.34)

qmax = 0.028RQD + 17.8 (R2 = 0.0091)




resistance of a drilled shaft from a load

test, the aspect ratio of the shafts.

Although an upfront prediction of the

capacity using only the aspect ratio is

unprobable, the graph shows an

approximate linear regression. The L/B,

D/B shown below represents aspect ratio

and length of socketed part over shaft

diameter respectively. One can see that

the unit side shear resistance is negatively

correlated with the aspect ratio, while the

unit end bearing resistance is positively

correlated.

4.7 Appraisal for the empirical formulaeof unconfined compres sive strength

Analyzing the statistical properties of

the bias factor concerning the side shear

resistance while referring to the table 1,

showed results that when the average of

the bias factors is close to 1 and the

covariance is small, the prediction method

has a smaller deviation with the measured

data. Also, when the average of the bias

[Figure 10] The relationship between the aspect ratio, theratio of diameter to length of socketed part,and the side shear resistance

[Figure 11] The relationship between the aspect ratio, theratio of diameter to length of socketed part,and the end bearing resistance



188_제18호

factors is much larger than 1 the

prediction method is conservative; while

when the average was much smaller than

1 the prediction method overestimates.

The covariance of the methods here, that

have an average close to 1, are distributed

around the 0.4 mark.

The following 3 methods have the most

accurate predictions.

8. Williams et al.(1980)

τ= 0.44σc0.36 (MPa)

10. Rosenberg and Journeaux(1976)

τ= 0.34σc0.51 (MPa)

15. Meigh and Wolshi(1979)

τ= 0.22σc0.6 (MPa)

The methods No. 1, 2, 3, 4, 5, 6, 7, 16

have comparatively conservative

predictions. And the methods No. 9, 11,

12, 13, 14 overestimate the capacity.

Analysis of the statistical properties of

the bias factor concerning the end bearing

resistance is referred to the table 2. The

covariance of the methods here, that have

an average close to 1, are distributed

below the 0.4 mark.

The following 2 methods have the most

accurate predictions.

6. ARGEMA (1992)

qu = 4.5σc < 10 (Mpa)

7. Zhang & Einstein (1988)

qu = 4.83σc0.51

The methods No. 1, 2, 3 have the most

conservative predictions. And the

methods No. 4, 5, 8 overestimate the

capacity.

5. Summary & Conclusions

Having analyzed the correlations

between the side shear resistance and the

end bearing resistance of drilled shafts

that have been casted in the Songdo area

and Incheon Bridge with properties of

rock, which is an indicator of the strength

and the weathered degree, a formula that

can be applied to both the domestic

weathered and soft rock has been

derived. Furthermore, the following

results have been inferred from the

comparison and analysis of previous

formulas that use unconfined

compressive strength.

1. As the following table shows, proposed




formulas that use properties for both

the side shear resistance and end

bearing resistance have been derived.

2. It has been observed that as the aspect

ratio of shaft and the length of socketed

part over shaft diameter in negatively

correlated with the unit side shear

resistance, while it is positively

correlated unit end bearing resistance.

3. After conducting an analysis of the

correlation and statistical properties of

the bias factor concerning the predicted

values deducted from the traditional

empirical prediction methods of

unconfined compressive strength, it has

been found that the proposed formula

shows the most accurate result in both

the side shear resistance and the end

bearing resistance. Other than the

proposed formula, the Williams et al.,

Rosenberg & Journeaux method shows

the closest result for side shear

resistance, and Zhang & Einstein and

ARGEMA formula shows the closest

result for end bearing resistance. And

the methods can be recommended,

when it comes to domestic weak rock.

4. As for the prediction methods for

unconfined compressive strength, 5 out

of 16 methods have a tendency to

overestimate the side shear resistance,

and 3 methods tend to overestimate the

end bearing resistance. The empirical

formulae that overestimate have a

slightly higher variance, ranging from

0.7 to 0.8.

6. Reference

ARGEMA (1992). Design Guides for

Offshore Structures: Offshore Piles

Design. Ed: P. L. Tirant, Editions Techniq,

Paris, France.

Coates, D. (1967). “Rock mechanics

principles.”Dept. of Energ., Mines and

Unit Side ShearResistance (Mpa)

τCorrelationCoefficient (R2)

σc

PMT D

PMT E

RQD

Unit End BearingResiatance(Mpa)

qu CorrelationCoefficient (R2)

σc

PMT D

PMT E0.043 (low

correlationship)

0.0091 (lowcorrelationship)

RQD

0.57

0.68

0.69

0.34

0.39

0.20

τmax = 0.32σc0.50

τmax = 0.0014D + 0.51

τmax = 0.00082E + 0.45

τmax = 0.026RQD + 0.59

qmax = 6.1σc0.35

qmax = 0.0025D + 13.2

qmax = 0.00088E + 15.1

qmax = 0.028E + 17.8



190_제18호

Resources.

Fellenius, B. “Discussion of Side resis-

tance in piles and drilled shafts’by M. W.

O-Neill.”J. Geotech. Geoenvir. Eng: 446-

448.

Fellenius, B. and A. Altaee (1996).

Critical depth: how it came into being and

why it does not exist, Elsevier.

Hoek, E. (1983). “Strength of jointed

rock masses.”Geotechnique 33: 187-223.

Horvath, R. G., Kenney, T. C. (1979).

Shaft resistance of rock-socketed drilled

piers. proc. American Society of Civil

Engineers Annual Convention, Atlanta,

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Reese, L. C., O-Neill, M. W., et al. (1976).

“Behavior of drilled piers under axial

loading.”Journal of the Geotechnical

Engineering Division 102(5): 493-510.

Rowe, R. and H. Armitage (1987). “A

design method for drilled piers in soft

rock.”Canadian Geotechnical Journal

24(1): 126-142.

Rowe, R. and H. Armitage(1987).

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Vesic, A. (1977). “Design of pile founda-

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Practice 42.

Zhang, L. (2004). Drilled Shafts in Rock:

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현장타설말뚝의 선단지지거동.”대한토목학회논

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