uniten iccbt 08 soil parameters and bearing capacity derived from responses of

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ICCBT 2008 - E - (32) pp391-402

ICCBT2008

Soil Parameters and Bearing Capacity Derived from Responses of

Drilled Shaft Socketed into Rock

I.S.H. Harahap*,Universiti Teknologi PETRONAS,MALAYSIA

C.W. Wong, Universiti Teknologi PETRONAS,MALAYSIA

ABSTRACT

Pile load test is commonly conducted during design and construction stages. The objective of

pile load test conducted during design stage is to obtain the actual soil parameter and

ultimate load in-situ for the purpose of design. For the test conducted during construction

stage, the objective is to provide a quality control measure to prove that the actual pile

capacity conforms to the design objectives. This paper presents probabilistic interpretation of

proof pile test to obtain the ultimate pile capacity. As the first step, the actual field

parameters are back calculated using ultimate pile capacity from proof pile load tests. The

probabilistic inverse method is used for back calculation of parameters. Soil parametersobtained from back calculation are then sampled using Monte Carlo simulation technique, to

generate histogram of ultimate pile capacity. From the synthetic histogram, other statistical

metrics such as mean, standard deviation and cumulative probability density of ultimate pile

capacity can be obtained.

Keywords: Socketed drilled shaft, Monte Carlo simulation, probabilistic inverse analysis,

proof pile load test

*Correspondence Author: Assoc. Prof. Dr. Indra S. Harahap, Universiti Teknologi PETRONAS, Malaysia. Tel:

+6053687340, Fax: +6053656716. E-mail: [email protected]
http://www.uniten.edu.my/newhome/content_list.asp?contentid=4017


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Soil Parameters Derived from Responses of Drilled Shaft Socketed into Rock

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1. INTRODUCTIONDuring construction proof test to verify pile design are conducted. Specification usually calls

for the amount of absolute and permanent pile displacement during proof test to be less than a

specified amount. The number of pile subjected to proof test is proportional to total number ofpile being constructed and the number of pile that failed relative to the number of proof test

should not exceed a certain prescribed number. Load applied for proof test is usually twice the

design load at constant loading rate using one or two load cycles.

In this paper, attempt has been made to interpret pile proof test for obtaining soil parameters

(soil and rock unit skin resistance as well as base resistance). The method used is probabilistic

inverse analysis as given in [1].to obtain actual soil parameters in the form of its joint

probability density. Parameters obtained are then utilized to generate histogram of ultimate

pile load capacity using Monte Carlo simulation technique. This paper is arranged as follow:

Section 2 will outline geotechnical aspects of the drilled shaft particularly its designmethodology and interpretation of pile-load-test results at project site near Kuala Lumpur.

The soil condition and pile-load-test results at project site near Kuala Lumpur are explained in

Section 3. In Section 4 the salient features of the probabilistic inverse method are given,

followed by its application to interpret pile-load-test results in Section 5. Section 6 will

conclude results from this work.

2. GEOTECHNICAL ASPECTS2.1 Design of Socketed Drilled ShaftThe ultimate capacity of socketed drilled shaft can be determined using the followingequation:

bbRRSSu

bufuu

AqCfCfQ

QQQ

++=

+=

)(

(1)

where uQ is ultimate pile capacity, fuQ is ultimate shaft capacity, buQ is ultimate base

capacity. The ultimate skin resistance consist of contribution from soil part ( )Sf and rockpart )( Rf where Sf and Rf are unit shaft resistance, SC and RC are circumferential area of

pile embedded in each layer (soil and rock). bq is unit base resistance for the bearing layer

(rock) and bA pile base area. Figure 1 shows components of ultimate capacity of drilled shaft

socketed into rock.

The unit skin resistance of cohesionless material usually has the form of tanosR Kf =

where sK is coefficient of lateral pressure, o is vertical overburden pressure and is

friction angle [2]. For cohesive material the unit skin resistance is commonly taken as

proportional to the undrained shear strength as uR Sf = where is proportional coefficient

and uS is undrained shear strength [3]. For rock, the unit skin resistance is empirically

determined from rock unconfined compressive strength, uq [4], orRock Quality Designation,

RQD. Table 1 shows available empirical correlation to determine Rf from uq and Table 2 to

determine Rf fromRQD. However, the unit skin resistance has a limiting value depends on


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I.S.H. Harahap and C.W. Wong

ICCBT 2008 - E - (32) pp391-402 393

the unconfined compressive strength of the rock [5]. The empirical correlations proposed is

either has linear relation with uq or power-curve relation to uq . Evaluation by [6] indicated

that the SPT N-value may not a good indicator of Rf due to its sampling rate because it is too

infrequent and suffers too much variability. From evaluation of pile load test results [7], there

is a significant difference of load-settlement behaviour among sedimentary, granitic anddecomposed rock, and hence the range of uq for these rocks. Generally granitic rock has a

softer response compared to sedimentary rock. The ultimate unit resistance range between 6

to 50 MPa for granitic rock compared to between 1 to 16 MPa for sedimentary rock.

Empirical correlation by [8] in Table 2 is the lower bound for sedimentary rock [7]. The rock

unit skin resistance, Rf and RQDrelationship as in Table 2 is commonly used in Malaysia to

design drilled shaft socketed into rock [9]. Other note, the unit resistance for uplift load

should be adjusted due to contraction of pile under uplift load, and hence reducing

confinement stress [10].

The design approach for socketed drilled shaft varies from place to place [11], for example

the ultimate capacity could be determined by considering all resistances (from soil and rock

skin resistance, and from base), or omitting the based resistance due to the fact that less

displacement is required to fully mobilize skin resistance compared to the displacement that

required to fully mobilize base resistance. On the practical side, the length of socket and

hence total pile length is determined based on observed rock condition, i.e. RQD at that

particular location during construction.

Discussions on various construction method and constructability issues of drilled shaft can be

found in Ref [12], and the effect of construction method on skin and base resistance in Ref

[13,14]. However, from pull out test results [6], drilled shaft construction method has no

significant effect on ultimate resistance.

Figure 1 Ultimate capacity of socketed drilled shaft

2.2 Pile Load TestPile-load-test generally serves two purposes. When conducted during design stage, it helps to

establish parameters to be used in design, and when conducted during construction stage, it

proves working assumptions during design. To obtain the actual soil parameters for design

purpose, the pile test is instrumented [4] and parameters are back calculated from data

qb

fS

fR LR

LS

D


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obtained during testing. The number of this type of test is limited due to its cost; therefore site

variability of pile ultimate capacity cannot be established.

The load settlement curves do not always show a sign of failure as specified by various

methods, for example Davissons, Terzaghis, Chins methods and others. As such, it is

difficult to ascertain the validity of design assumption, i.e. the ultimate skin resistance, basedon informations obtained from this test. Other elaborate method to interpret pile load test in

sand and clay can be found in [15,16]. A new and novel approach that utilizes a data base of

pile load tests is recently proposed by [17]. In their method design parameters are extracted

from the data base using Bayesian neural network that intelligently update its knowledge

when a new information is added to the data base.

Table 1. Empirical value of unit skin resistance for socketed drilled shaft determine from rock

unconfined compressive strength and SPTN-value. Complete references are given in [6]

No Empirical Correlation Reference

1 fR(tsf) = 1.842 qu0.367 Williams et al. (1980)

2fR(tsf) = 1.45 uq for clean sockets, and

fR(tsf) = 1.94 uq for rough sockets.

Rowe and Armitage (1987)

3fR(tsf) = 0.67 uq .

Horvath and Kenney (1979):

4fR(tsf) = 0.63 uq .

Carter and Kulhawy (1988)

5 fR(tsf) = 0.3(qu). Reynolds and Kaderabek (1980):

6 fR(tsf) = 0.2(qu). Gupton and Logan (1984)

7 fR(tsf) = 0.15(qu). Reese and O'Neill (1987)

8 fR= 0.017V (tsf), or

fR= -5.54 + 0.4N(tsf).

Crapps (1986)

9 N-value = {10,15,20,25,30,>30};

fR(tsf) = {0.36,0.77,1.1,1.8,2.6,2.6}

Hobbs and Healy (1979)

10 N-range= 10 - 20, 20 - 50, 50 - 50/3 in., >50/3 in.;

fR(tsf) = 1.5,2.5,3.8,5.

McMahan (1988)

Table 2. Empirical value of unit skin resistance for socketed drilled shaft determine from

RQD Ratio

RQD Ratio % Working Rock Socket Resistance Rf (kPa)

Below 25 300

25 - 70 600

Above 70 1000

Other than instrumented pile as previously cited, [18] proposed method to derive soil

parameters from load settlement curve from pile-load-test. Using the approach, the ultimate

capacity is obtained from projected load settlement curve. The projected load settlement

curve is an analytical function for load settlement relations with parameters of the function are


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obtained from regression of the actual load settlement curve. For this purpose, failure is

defined as correspond to a settlement of 10% of pile diameter.

As a proof test, in practice, pile-load-test results are interpreted based on criteria establishes to

achieve the design objectives and elucidated in the technical specification. As an example, thesettlement of the pile tested should not exceeding specified settlement at working load and

permanent settlement should not exceed settlement at twice of the working load. The pile is

considered pass if both criteria are satisfied. The number of pile tested for proof test are

prescribed based on total length of pile constructed, as such more that one proof pile-load-

tests are conducted within one project. Furthermore, it is common that proof pile-load-test is

fail to reach failure, in other words the applied load is less than ultimate capacity of the pile.

While the interpretation of proof test based on settlement criteria lay out in the technical

specification is sufficient for practical purposes, there are also attempts to further exploit

informations from proof pile-load-test. For example, from pile-load-test that reaches failure,

informations can be obtained to update the reliability of pile [19-22]. For pile-load-test that

fails to reach failure, informations can be obtained to update the probability distribution of

pile capacity [23]. These approaches follow trend of migration of geotechnical analysis from

factor of safety based to reliability based [24]. It is worth to note that, besides ultimate load

limit state approach previously cited, serviceability limit state for drilled shaft to establish

probability of failure and reliability index from load settlement curve of pile load test also

have been attempted by [25,26]. In their approach, the pile load settlement curves are

calculated using t-z approach and finite difference method. Probabilistic load-settlement

curves are developed using Monte Carlo simulation. From the histogram generated, the

probability of failure and reliability index can be determined.

For this work, the probability density of soil parameters are calculated from ultimate pilecapacity, deduced from pile-load-test, using probabilistic inverse method. The histogram of

pile capacity is then generated using Monte Carlo simulation technique. The probability of

ultimate pile capacity, or the reliability index, can be obtained from cumulative density of pile

capacity.

3. DESCRIPTION OF THE PROJECT3.1 Site ConditionA total of 12 bore holes were carried out for soil investigation during design stage. The soilinvestigations were mainly carried out by using Standard Penetration Test (SPT) as well as

standard soil index and physical properties test.The site condition was mainly formed by 3

types of soil, which were silt, clay and sand. Silt was found on the top of the soil layer while

very stiff or hard sandy silt were encountered on the next layer which range from Reference

Level(RL) 70 m toRL50 m. Generally, high organic content was observed for the upper layer

materials. TheRQDfor the site ranged from 10% to 30%, with average of 25%

3.2 Pile LoadingThere were three types of pile being used at the site consisting of a 450 mm, 600 mm and 900

mm diameter bored pile with design load of 1500 kN, 4000 kNand 9000 kNrespectively. Out


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of a total of 19 proof pile-load-tests conducted, only two gave ultimate pile capacity based on

Davissons criteria. The calculated ultimate pile capacity is 8900 kNand 3900 kNfor 900 mm

and 600 mm diameter piles, respectively. Figure 2 shows load deflection curves and ultimate

load determination using Davissons method for 600 m and 900 mm piles, and Table 3 shows

the schedule of all pile-load-test.

Figure 2. Load settlement curve for proof pile-load-test. Davissons ultimate load can be

obtained only in two out of nineteen tests.

Table 3. Attributes of pile proof test result

Pile LocationEstimate of

uQ (kN)Pile Length

(m)

Pile Diameter

(mm)

Socket Length

(m)

FF1- P28 Not fail 6.000 900 4.5

FF1- P67 8900 10.245 900 4.5

FF2 - P184 Not fail 6.000 900 4.5

FF2 - P472 Not fail 11.000 900 4.5

FF3 - P234 Not fail 11.075 900 4.5

FF4 - P236 Not fail 12.325 450 1.5

FF4 - P275 Not fail 14.625 450 1.5

FF5 - P33 Not fail 12.425 600 3.0

FF5 - P85 Not fail 22.125 600 3.0

FSK 1,5 - P47 Not fail 14.000 900 4.5

FSK 1,5 - P44 Not fail 8.200 450 1.5

FSK 2,3,4 - P200 Not fail 8.800 900 4.5

FSK 2,3,4 -P387 Not fail 18.000 900 4.5

FSK 6 - P 74 Not fail 2.600 900 2.6

FSK 6 - P 307 Not fail 5.700 600 3.0

FSK 7 - P40 Not fail 21.025 600 3.0

FSK 7 - P370 Not fail 7.330 600 3.0

PSB - P138 Not fail 19.500 600 3.0

PSB- P183 3900 10.775 600 3.0


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4. PROBABILISTIC INVERSE METHODSuppose that we have function f that map parameters into theoretical quantity such that

)(md f= where },..,{ NDi dd=d and },..,{ NMi mm=m , the objective of inverse analysis isto determine m given d . In the context of pile-load-test, to determine

S

f ,R

f andbu

q knowing uQ obtained from pile-load-test and f is the relationship inEq. (1).4.1 Data SpaceSuppose that we have observed data values obsd , the probability density model to describeexperimental uncertainty, such as Gaussian model, can be written as follow

= )()(

2

1exp)( 1 obsD

TobsD ddCddkd (2)

where DC is the covariance matrix. If the uncertainties are uncorrelated and follow Gaussiandistribution, it can be written as

=

2

2

1exp)(

i

iobs

i

D

ddk

d (3)

4.2Model SpaceIn a typical problem we have model parameters that have a complex probability distributionover the model space. The probability density is denoted as )(mM . Suppose that we know

joint probability density function ),( dm and )(md f= , then the conditional probabilitydensity function, ( ))(|)( )(| mdmm md fMM == can be obtained as follow [1].

)(

2/12/1

2/1

..detdet

)det())(,()(

md f

DM

FDgTFMg

DM

D

T

MMgggg

FgFgmfmkm

=

= (4)

For constant )(mMg and )(dDg , and linear or weak linearity problem [1],Eq.(4)reduces to

)()(

)()()(

mdd

dmm

fD

DMM k

=

=

(5)

where )(dD is homogenous probability density function.

5. INTERPRETATION OF PILE LOAD TESTThe simplistic model of bearing capacity of socketed drilled shaft is given by Eq. (1).Assuming known pile geometry, the model space is then ),,( bRS qff=m . The probabilitydensity model to describe experimental uncertainty (Eq. 3) is formed using the theoreticalmodel )(md f= as in Eq. (1), and observed pile ultimate capacity as obsd . The joint

probability density is then ),,()( bRSMM qff =m . Prior knowledge can be incorporated in),,()( bRSMM qff =m particularly knowledge on those parameters specific for the rock

type and its locality. The effect of prior knowledge on unit skin resistance in rock isinvestigated using log normal distribution with various mean values. It should be noted that,

by usingEq. (1), it is implicitly neglected the effect of the shape of the interface between the

shaft and surrounding rock (undulating or smooth) as numerically observed by in Ref [27,


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28]. In this work, only the effect of unit skin and base resistances are considered, and the joint

probability density is obtained fromEq (5)as

= SbRSMbRM dfqffqf ),,(),( (6)

Analytical form of Eq. (6) is difficult to obtain, and even if successfully integrated very

difficult to interpret. Figure 3 shows joint probability density plotted in material space, which

is numerically integrated fromEq. (6). Prior distribution of unit skin resistance in rock, Rf is

assumed to have log normal distribution (Figure 2). The mean value of the prior distribution is

300 kPa, which conform to an empirical value for unit skin resistance for rock with low RQD

(Table 2). This number somewhat lower than back calculated from pile load test in limestone

which range from 900 kPato 2300 kPa[29].

The shape of the joint probability is far from Gaussian, and skewed to the right. The three

dimensional plot of the joint probability has a peak value, as shown in Figure 2(c), that

theoretically can be obtained using function optimization. The cumulative distribution of theultimate pile capacity is also difficult to obtain analytically; therefore numerical method must

be used utilizing Monte Carlo simulation technique. Figure 4(a) shows randomly generated

sampling points along the range of Ruf and bq , and fulfilling Eq. (6). As it appears, the

sampling points are banded following the trend of the joint probability. The histogram of the

ultimate pile load is obtained usingEq. (1). No efforts have been made to obtain continuous

function to describe the histogram. However, discrete method can be used to obtain statistical

parameters such as mean value standard deviation as well as to generate the cumulative

distribution from the histogram.

6. CONCLUDING REMARKMethod to interpret pile-load-test to obtain probabilistic characteristics of ultimate load has

been presented. The first step is to obtain joint distribution of soil parameters in the material

(or parameter) space. The second step is to generate histogram of ultimate load using Monte

Carlo technique. Probabilistic characteristics of the ultimate load are then obtained from the

synthetic histogram using standard discrete method.

Acknowledgments

The authors acknowledge Universiti Teknologi PETRONAS for the support andencouragement to attend the conference.


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ICCBT 2008 - E - (32) pp391-402 399

Figure 2. Prior distribution of unit skin resistance of rock

(a) (b)

Figure 3. Joint probability in the material space is shown in (a) using prior distribution of rock

skin resistance, Ruf , following log normal distribution(Fig. 2) with mean equal to 300 kPa.

The 3D picture of the joint probability distribution is shown in (b)

(a) (b)

Figure 4. The distribution of ultimate loads shown in (b) are generated using sampling points

shown in (a)


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