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Statistical Analysis of Dynamic Bearing Capacity of Driven Pile Ardy Arsyad 1, a , Suyadi 1,b and Lawalenna Samang 1,c 1 Department of Civil Engineering, Faculty of Engineering, Hasanuddin University, P. Kemerdekaan Km. 10 Makassar 90254 Indonesia a [email protected], b [email protected], b [email protected] Keywords: Dynamic Formulas, Pile Bearing Capacity, Normal Distribution, Probabilistics. Abstract. This paper presents the use of statistical-probabilistic method in determining pile bearing capacities over a number of driven piles. Four dynamic formulas were employed to estimate pile bearing capacity including modified ENR, Hiley, Navy McKay and Danish. We investigated the final setting data of 47 concrete piles with 600 mm diameter in the construction projects of New Naval Engineering Building Hasanuddin University. Based on the data, pile bearing capacity were computed and then analyzed statistically. Goodness of fit with Kolmogorov-Smirnov and Shapiro- Wilk were used to fit the probability distribution function (PDF) of the pile bearing capacity data to the PDF model. It was found that the pile bearing capacity estimated using ENR is more uniform with 506 tons average pile capacity and 6.4% COV, while that with Hiley and Danish are less various with 252 tons and 346 tons average pile capacity, and 14.7% and 16.6% COV respectively. Navy-McKay was found to have 465.8 tons average pile capacity with higher variability of 44.08%. A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times the lower bound of pile capacity measured by pile driving analyzer (PDA). In comparison, 90% probability estimated by Danish is 420 tons or 0.93 times and 0.92 of the upper and lower bound of pile capacity measured by PDA, respectively. The Navy-McKay seeems to be overestimated whereas Hiley is underestimated. Introduction In recent years, there is a new approach in structural and geotechnical building inh relation to deal with uncertainties facts in designing process. This approach is the use of reliability based design by using statistics and probabilistic analysis. Most of pile foundation design formulas take account factors of safety, as empirical value, in order to prevent failure of design and to anticipate unexpected condition of design in the process of construction. Griffith et al. [1] suggested that factors of safety in specifically geotechnical engineering could be approached in two ways. the factor of safety obtained from allowable load for design (Terzaghi’s load capacity), as estimated ultimate load. This approach is for pile load capacity cases. Phoon et al. [3] stated that, in general, 3the application of factor of safety is most uncertain element. Factor of safety is determined by the experience and the judgement of the geotechnical engineer. Therefore, it is commonly that engineers use different safety factor for different location or even for the same location [2]. Due to uncertainty of safety factor, the determination of pile bearing capacity is also uncertain. Different methods used in determing pile bearing capacity will lead to different results and generally engineers consider the lowest result indicating preference of conservative design rather than optimum design . This will be a part of engineering judgement driven by limited data obtained in geotechnical survey. To overcome uncertainty in pile design, statistic-probabilistic could be used. Therefore, this study aims to investigate the pile bearing capacity which is determined based on dynamic formula with statistic-probabilistical approach.
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Statistical Analysis of Dynamic Bearing Capacity of Driven ... · A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times

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Page 1: Statistical Analysis of Dynamic Bearing Capacity of Driven ... · A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times

Statistical Analysis of Dynamic Bearing Capacity of Driven Pile

Ardy Arsyad1, a, Suyadi1,b and Lawalenna Samang1,c

1Department of Civil Engineering, Faculty of Engineering, Hasanuddin University, P. Kemerdekaan Km. 10 Makassar 90254 Indonesia

[email protected], [email protected], [email protected]

Keywords: Dynamic Formulas, Pile Bearing Capacity, Normal Distribution, Probabilistics.

Abstract. This paper presents the use of statistical-probabilistic method in determining pile bearing

capacities over a number of driven piles. Four dynamic formulas were employed to estimate pile

bearing capacity including modified ENR, Hiley, Navy – McKay and Danish. We investigated the

final setting data of 47 concrete piles with 600 mm diameter in the construction projects of New

Naval Engineering Building Hasanuddin University. Based on the data, pile bearing capacity were

computed and then analyzed statistically. Goodness of fit with Kolmogorov-Smirnov and Shapiro-

Wilk were used to fit the probability distribution function (PDF) of the pile bearing capacity data to

the PDF model. It was found that the pile bearing capacity estimated using ENR is more uniform

with 506 tons average pile capacity and 6.4% COV, while that with Hiley and Danish are less

various with 252 tons and 346 tons average pile capacity, and 14.7% and 16.6% COV respectively.

Navy-McKay was found to have 465.8 tons average pile capacity with higher variability of 44.08%.

A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper

bound, and 1.4 times the lower bound of pile capacity measured by pile driving analyzer (PDA). In

comparison, 90% probability estimated by Danish is 420 tons or 0.93 times and 0.92 of the upper

and lower bound of pile capacity measured by PDA, respectively. The Navy-McKay seeems to be

overestimated whereas Hiley is underestimated.

Introduction

In recent years, there is a new approach in structural and geotechnical building inh relation to

deal with uncertainties facts in designing process. This approach is the use of reliability based

design by using statistics and probabilistic analysis. Most of pile foundation design formulas take

account factors of safety, as empirical value, in order to prevent failure of design and to anticipate

unexpected condition of design in the process of construction. Griffith et al. [1] suggested that

factors of safety in specifically geotechnical engineering could be approached in two ways. the

factor of safety obtained from allowable load for design (Terzaghi’s load capacity), as estimated

ultimate load. This approach is for pile load capacity cases. Phoon et al. [3] stated that, in general,

3the application of factor of safety is most uncertain element. Factor of safety is determined by the

experience and the judgement of the geotechnical engineer. Therefore, it is commonly that

engineers use different safety factor for different location or even for the same location [2]. Due to

uncertainty of safety factor, the determination of pile bearing capacity is also uncertain. Different

methods used in determing pile bearing capacity will lead to different results and generally

engineers consider the lowest result indicating preference of conservative design rather than

optimum design . This will be a part of engineering judgement driven by limited data obtained in

geotechnical survey. To overcome uncertainty in pile design, statistic-probabilistic could be used.

Therefore, this study aims to investigate the pile bearing capacity which is determined based on

dynamic formula with statistic-probabilistical approach.

Page 2: Statistical Analysis of Dynamic Bearing Capacity of Driven ... · A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times

Case Study

The project of Engineering Faculty New Campus, Hasanuddin University is located about 19 km southeast of Makassar, the capital of South of Sulawesi. The project has been constructing several buildings over the area of 630×330 m

2, including Faculty, Center of Technology, Civil Engineering,

Architecture, Electrical Engineering, Mechanical Engineering, Geology Engineering, and Naval Engineering Buildings. The object of the study is Naval Engineering Building A with 2364.48 m

2.

During the construction, 109 pre-cast concrete piles were driven for foundations of the building, in which 47 piles with 0.6 m and 62 piles with 0.5 m diameters. The concrete compressive strength of the pile is 52 Mpa. Hammer used in the driving is diesel hammer with 6.3 ton weight. To determine pile bearing capacity, dynamic methods were employed including Hiley (Eq. 1), ENR (Eq. 2), Navy-McKay (Eq. 3) and Danish (Eq. 4).

Formula Hiley.

𝑄𝑢 =𝑒ℎ . 𝑊𝑟 . h

𝑠+1/2(𝑘1+𝑘2+𝑘3)𝑥𝑊𝑟 + 𝑛2 . 𝑊𝑝

𝑊𝑟 + 𝑊𝑝 (1)

Modified New ENR.

𝑄𝑢 =𝑒ℎ . 𝐸ℎ

𝑠+𝑐 𝑥𝑊𝑟 + 𝑛2 . 𝑊𝑝

𝑊𝑟 + 𝑊𝑝 ( 2 )

Navy-Mc.Kay.

𝑄𝑢 =𝑒ℎ . 𝑤𝑟 . ℎ

𝑠(1+0.3𝐶1) ( 3 )

𝑐1 =𝑤𝑟

𝑊𝑝

Danish.

𝑄𝑢 =𝑒ℎ . 𝐸ℎ

𝑠 + 𝐶2 ( 4 )

𝑐2 = 𝑒ℎ .𝐸ℎ . 𝐿

2 . 𝐴 . 𝐸

where

eh is hammer efficiency Eh is hammer energy s is average penetration in the last 20 blows n is restitution coefficient wr is weight of hammer wp is weight of pile c is empirical coefficient of energy loss during driving K1 is elastic compression of capbox and pilecap, K2 for elastic compression for pile and K3 for elastic compression of soil A is Area of pile section

Page 3: Statistical Analysis of Dynamic Bearing Capacity of Driven ... · A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times

Ep is elastic modulus of pile h is drop height of ram L is length of pile Qu is ultimate bearing capacity

Determination of bearing capacity using Dynamic Formula During construction from November 2011 – February 2012, the contractor collected driving data

of the piles, including final setting of pile. Final setting data over 47 piles with 600 diameter is shown in Table 1. The depth peneration of the pile for the final blow of hammer during driving and rebound were also obtained. The length of pile driven into the ground varies from 6 m to 10 m. The pile bearing capacity was determined by using the dynamic methods. Hammer energy can be obtained from multiplication of hammer weight and drop its height, whereas hammer efficiency is 0.85 based on the type of hammer as diesel hammer. Restitution coefficient was selected as 0.5 due to the pile is concrete pile with wooden cushion [4]. Ultimate bearing capacity (Qu) was estimated by using dynamic formulas. The safety factor of ENR formula is 6, while that of Danish, Hiley and Navy-McKay are 3. It can be seen in Figure 1, the bearing capacity of pile estimated by dynamic formulae varies. For example, Navy-McKay has fluctuated pile bearing capacity, while ENR seems to be more uniform. Danish and Hiley perform little variability, but not as uniform as ENR does.

Statistic-Probabilistic Method

Pile bearing capacities were analyzed statistically by generating their histogram and quantifying

their probabilities. Once the histogram was obtained, the probability distribution function (PDF) can

be generated and a goodness of fit with Kolmogrov-smirnov and Shapiro-Wilk test was used to

examine the fitnes of the PDF of the data to PDF model. It was found that the pile bearing capacity

data with Danish, ENR, and Hiley show a normal distribution, while that with Navy-McKay is less

significant to match with normal distribution (Figure 2). The statistical parameters can be

determined, shown in Table 2. Average pile bearing capacity estimated with Danish is accounted

for 345.9 tons with the COV of 16.6%, while ENR is accounted for 506 tons with a 6.4% COV.

Navy-McKay based estimation is 465 tons average pile bearing capacity with very wide values with

a 44.08% COV. Hiley estimation resulted in the lowest value, 252 tons with 14.7% COV

Cumulative probability of those dynamic methods are presented by Figure 3. Fifty percent and 90%

of cumulative probability (P50 and P90) for Danish are 320 and 420 tons. On the other hand, P50 and

P90 of the pile bearing capacity estimated by ENR are 490 and 535 tons. the Navy-McKay and Hiley

were found to be 280 and 780 tons, and 280 and 290 tons. To examine reliability of the statistical

results, their results were compared to the bearing capacities which is obtained from Pile Driving

Analyzer (PDA) test. Two PDA tests were commenced by contractors during pile driving, with two

ranges of bearing capacity. They are 343 tons - 455 tons, and 353 tons - 449 tons. It can be seen that

average bearing capacity with Danish formula is very close to PDA result, while that with ENR

over estimate the lower bound of PDA result. Navy-McKay and Hiley results are out of range of

PDA test results. However, these findings require more data of PDA tests and static load tests to

confirm the reliability of statistical results of pile bearing capacity and this will become future

research.

Page 4: Statistical Analysis of Dynamic Bearing Capacity of Driven ... · A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times

Summary

1. ENR formula generates a uniform pile beearing capacity with a 506 tons average and 6.4%

COV.

2. Hiley and Danish generate 252 tons and 346 tons average pile capacity with 14.7% and

16.6% COV, respectively.

3. Navy-McKay yields a 465 tons average pile capacity with higher variability, 44.08%.

4. Compared to the PDA results, 90% Probability of pile bearing capacity estimated by Danish

is very close, 0.93 times and 0.92 of the upper and lower bound of pile capacity measured by

PDA, respectively. In comparison, 90% probability estimated by ENR is 1.17 times and 1.4

times the upper and lower bound of pile capacity measured by PDA, respectively.

References

[1] Griffiths, D.V., Fenton, G.A. and Manoharan, N., (2002). "Bearing capacity of a rough rigid

strip footing on cohesive soil: A probabilistic study," ASCE J. Geotech. Geoenv. Eng., 128(9), 743-

-755.

[2] Gobel, G.G. (1999): Geotechnical related development and implementation of load and

resistance factor design (LRFD) methods, Synthesis of Highway Practice, NCHR syntesis276,

TRB, NRC

[3] Phoon, K. K., and Kulhawy, F. H. (1999). "Evaluation of geotechnical property variability."

Can. Geotech. J., 36(4), 625-639.

[4] Chellis, R.D., (1951). Pile foundation, McGraw Hill Book Company, 704p.

[5] Hiley, A., (1925). A rational pile driving formula and its application in piling practice explained.

Engineering(London), 119, Pp. 657-721.

Figure 1. Pile bearing capacity estimated by Danish, ENR, Navy-McKay, Hiley.

0

100

200

300

400

500

600

700

800

900

1000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47

Allo

wab

le P

ile B

ear

ing

Cap

acit

y (t

on

s)

No. Pile

Danish

ENR

Navy-McKay

Hilley

Page 5: Statistical Analysis of Dynamic Bearing Capacity of Driven ... · A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times

Table 1. Data of final setting of piles during construction.

Table 2. Statistical parameters of dynamic methods.

Descriptive Statistics

Formula N Range Minimum Maximum Sum Mean Std. Deviation COV (%)

Statistic Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Statistic

Danish 47 241.26 227.50 468.76 16261.88 345.9974 8.37647 57.42616 16.58

ENR 47 148.43 419.91 568.34 23796.70 506.3128 4.73653 32.47201 6.4

Navy - McKay 47 712.86 168.20 881.06 21891.90 465.7851 30.03579 205.91500 44.08

Hiley 47 147.91 163.98 311.89 11855.65 252.2478 5.40682 37.06731 14.7

Page 6: Statistical Analysis of Dynamic Bearing Capacity of Driven ... · A 90% Probability of pile bearing capacity estimated by ENR is 535 tons, or 1.17 times the upper bound, and 1.4 times

`Figure 2. Normal distribution of pile bearing capacities based on dynamic methods.

(a) (b)

(c) (d)

Figure 3. Cumulative probability of pile bearing capacity estimated by (a) Danish, (b) ENR, (c)

Navy-McKay, (d) Hiley

Table 3. Evaluation of the performance of dynamic methods

Formula

Statistics Cumulative probability

Mean Sd Rank P50 P90 P90/

lower

PDA

P90/upper

PDA

Rank

ENR 506.3 6.4 1 490 535 1.42 1.17 2

Hiley 252.4 14.7 2 280 290 0.81 0.63 3

Danish 345.9 16.6 3 320 420 0.93 0.92 1

Navy-McKay 465.8 44.08 4 280 780 0.81 1.71 4

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%)

Allowable Pile Bearing Capacity (tons)

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400 450 500 550 600Cu

mu

lati

ve P

rob

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%)

Allowable Pile Bearing Capacity (tons)

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