RESEARCH PAPER

Applicability of CPT-based methods in predicting toe bearingcapacities of driven piles in sand

Le Chi Hung1 • Tien Dung Nguyen1 • Ju-Hyung Lee2 • Sung-Ryul Kim1

Received: 22 January 2014 / Accepted: 27 May 2015

� Springer-Verlag Berlin Heidelberg 2015

Abstract This paper presents a study on applicability of

predicting toe bearing capacities from cone penetration test

(CPT) for PHC (pretensioned spun high-strength concrete)

driven piles into deep sandy deposits in the Nakdong River

deltaic area west of Busan City in South Korea. Using toe

bearing capacities obtained from pile driving analyzer

(PDA) tests as reference values, which were reliably cali-

brated by on-site O-cell tests, the applicability of the CPT-

based methods was evaluated using a statistical rank index

(RI). A total of 82 piezocone penetration test soundings and

190 PDA test piles were used for reliability analysis in this

study. Three correction steps were applied to obtain reli-

able PDA and CPT data sets before ranking is carried out.

The RI index is combined from four criteria: (1) the best-fit

line, (2) the arithmetic mean and standard deviation, (3) the

cumulative probabilities, and (4) the log-normal and his-

togram distributions. Based on these criteria the perfor-

mance of some SPT-based methods in the literature is

evaluated.

Keywords Cone penetration test � Driven piles � Piledriving analyzer Statistical analysis � Toe bearing capacity

1 Introduction

The cone penetration test (CPT) has been widely used to

characterize soils and has been directly applied in

geotechnical engineering, including the determination of

pile bearing capacity. Cones and piles possess a similar

working mechanism; thus, several CPT-based methods

related to unit shaft and toe resistances have been proposed

to evaluate pile bearing capacity using CPT data (e.g., qcand fs). Most of the methods have been proposed to

determine the ultimate bearing capacity of driven piles

(e.g., [2, 15]), whereas some have been suggested for both

driven and cast in situ piles (e.g., [8, 26]) and base-grouted

cast in situ piles in sand (e.g., [31]).

Each CPT-based method has been developed based on

static load test (SLT) results obtained from specific regions

and geologies. In addition, the failure criteria used to define

the bearing capacity of a test pile (e.g., [11]) can differ

depending on author preference and the recommendation

for the region. Some methods exhibit large scatter of the

predicted bearing capacities of piles [23]. Thus, the appli-

cability of CPT-based methods in new geological areas

(e.g., for Louisiana state area [1], Florida state area [6],

Jiangsu province of eastern China [9], or a combined

database from different countries [29]) must be evaluated.

Pretensioned spun high-strength concrete (PHC) piles

were developed in Japan in the early 1970s and introduced

to Korea in the early 1990s. The PHC pile has been used as

the foundation of a residential complex project only

recently in the Nakdong River delta west of Busan City in

South Korea. Several studies have been conducted on the

bearing capacities of the PHC piles used in the project;

these works include the determination of true resistance in

an instrumented PHC driven pile [16], a comparative study

among different design methods for the bearing capacity of

& Sung-Ryul Kim

sungryul@dau.ac.kr

1 Civil Engineering Department, Dong-A University, 840

Hadan2-dong, Saha-gu, Pusan 604-714, Korea

2 Geotechnical Engineering Research Institute, Korea Institute

of Civil Engineering and Building Technology, 283

Goyangdae-Ro, Ilsanseo-Gu, Goyang-Si, Gyeonggi-Do

411-712, Korea

123

Acta Geotechnica

DOI 10.1007/s11440-015-0398-4

driven piles [12], and an investigation into the residual load

distribution in instrumented PHC piles [16].

The SLT most reliably verifies pile bearing capacity;

however, conducting the required representative SLTs for

this project, which mobilizes thousands of PHC piles dri-

ven into deep sands, is very costly and time-consuming.

The dynamic method, which combines the pile driving

analyzer (PDA) test with the case pile wave analysis pro-

gram (CAPWAP) to predict pile bearing capacity, was

therefore selected to enhance the design and to calibrate

pile capacity using CPT-based methods.

The applicability of the ten CPT-based methods in

evaluating the toe bearing capacities of PHC piles driven

into deep sand in the Nakdong River delta is examined in

the present study. A total of 190 PDA test piles measuring

500 and 600 mm diameters and 82 piezocone penetration

test (CPTu) soundings were conducted at the construction

site. The reliability of the PDA-based toe bearing capacity

from the end of initial driving (EOID) is first verified by

two on-site O-cell tests. Thereafter, the applicability of the

ten CPT-based methods in determining the toe bearing

capacities (Qp) is investigated using the PDA-based toe

bearing capacities (determined from CAPWAP analysis)

that have been calibrated as reference values (Qm). The

correlation between Qp and Qm is investigated based on the

rank index (RI), which consists of four criteria, namely: (1)

the best-fit line, (2) arithmetic mean and standard devia-

tion, (3) cumulative probabilities, and (4) log-normal and

histogram distributions. This paper focuses on the toe

bearing capacity rather than the total capacity because the

shaft and toe resistances obtained from restrike test were

unsatisfactory due to significant shaft resistance gains from

soil setup effects. These effects were in turn caused by the

thick clay layer at the site. Using a high-energy hammer

was not feasible given pile integrity. The PDA-based toe

bearing capacity obtained from the EOID data using

CAPWAP analysis is therefore analyzed.

2 Field tests

2.1 Location of study site

The study site is the Myeongji residential complex situated

at the coastline of the Nakdong River deltaic area west of

Busan City in South Korea (Fig. 1). An approximately

5-m-thick landfill was constructed and finally completed in

the late 1990s. Tall apartment buildings were built at the

site only a few years ago. The total area of the study site

was approximately 1.0 km 9 1.4 km, and the site was

divided into four main blocks, namely MA (upper left),

MB (lower left), MC (lower right), and MD (upper right),

as shown in Fig. 2. Each main block was divided further

into sub-blocks (e.g., MA1–MA4) to facilitate site inves-

tigation and construction management. The CPTus and

PDA test piles were conducted on blocks MA and MC, and

the results are used in the analysis.

2.2 Piezocone penetration test

The CPTus were conducted extensively at specific loca-

tions under the planned apartment buildings where driven

PHC piles were to be installed. The tests were conducted

using 15 cm2 Geomil cone (area ratio = 0.6) driven by a

track-mounted CPT machine with 20-t capacity. The

electrical-type cone had a 60� apex, and a porous element

Fig. 1 Location of the study site in the Nakdong River delta (Google maps)

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123

(filter) was mounted behind the cone shoulder to measure

induced pore water pressure (u2). The average CPTu pen-

etration rate was 20 mm/s [4].

Figure 3 shows typical soil profiles observed during the

CPTus at blocks MA and MC in which soil parameters

[i.e., effective friction angle ð/0Þ; relative density (Dr), and

overconsolidated ratio (OCR)] were obtained from com-

monly recommended equations given by Mayne [22]. Site

ground conditions based on CPT data are briefly described

as follows. A loose silty sand (shallow sand) layer 5–15 m

depth is found under the fill layer. A soft-to-medium silty

clay layer is subsequently located at depths of 15–33 m,

followed by a loose-to-dense (deep sand) layer 33–58 m

deep and sandy gravel on bed rock. A thin clayey silt layer

is prominently sandwiched between the sand in the deep

sand layer. Groundwater level at the site was approxi-

mately located at 2.5 m below the ground surface. As

shown in Fig. 2, the deep sand layer varies from loose to

very dense (Dr = 20–80) and is characterized as lightly

overconsolidated deposit, the over consolidation ratio of

which typically varies from 1.5 to 1.8. Samples of this

layer as retrieved from the standard penetration test sam-

pler indicated that over 90 % of sand particles have

diameter of\1.0 mm and that almost 100 % of the parti-

cles passed sieve number 4 (aperture size = 4.75 mm).

Singh and Chung [30] provided additional details on the

physical and strength properties of the deep sand layer.

2.3 Pile driving and PDA tests

The PDA test piles used were closed-end, prestressed

concrete cylinder embedded with 24 steel rebars of

9.2 mm diameter (yield strength of 1300 MPa), which

were anchored to a donut-shaped steel plate at each seg-

ment ends. The test piles were cast in 5–15-m-long seg-

ments. The piles had outer diameters of 500 and 600 mm,

with the wall thicknesses measuring 80 and 90 mm,

respectively. Net prestress was approximately 8 MPa. The

concrete composed of Portland cement, and the concrete

aggregates were crushed granite. Nominal cube strength

was 80 MPa.

The PHC piles in the field were driven by hydraulic

impact hammers with the maximum potential energy of

24 tf 9 m. The segments were spliced by welding the end

plates together, making one splice at a time. The final

penetration depths varied from 31.5 to almost 54 m

depending on ground conditions. The PDA tests were

conducted in the test piles throughout the pile driving

process according to procedures described in Ref. [3]. Pile

driving and PDA monitoring were performed by the

company Piletech Ltd., under the supervision of a

geotechnical group from Dong-A University. Table 1 lists

the numbers of test piles with corresponding penetration-

depth ranges. The distance between the locations of the

CPTu and adjacent PDA test piles was\40 m.

Fig. 2 Schematic plan view of blocks with field tests at the study site

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123

2.4 O-cell tests

Two PHC test piles that included O-cells at the pile toe

elevations were installed and were then bidirectionally

loaded at the MA1 and MA3 blocks to verify the reliability

of the PDA-based toe bearing capacity at the site. The piles

were labeled as MA1-101 and MA3-203, as shown in

Fig. 4a.

Figure 4b illustrates some steps in the O-cell pile

installation procedure, which is briefly described as follows.

A T-shaped shoe with a total height of 300 mm, a diameter

of 600 mm, and a 30-mm-thick base plate was first fitted

into the pile toe (Fig. 4b, upper left). The pile segment was

then driven and spliced consecutively until the target depth

was reached (Fig. 4b, lower left). A PDA test was con-

ducted similarly as in other test piles during driving. An

O-cell (diameter = 330 mm, height = 400 mm) was wel-

ded to a reinforced cage at one end and settled on top of the

shoe when the system was lowered into the hollow of the

pile (Fig. 4b, upper right). Seven pairs of strain gauges

(Geokon model 4911 series) were attached oppositely along

the cage, as schematically shown in Fig. 4a to measure the

shear stress along the pile after pile installation and during

load testing. Finally, the hollow space framed by the O-cell

and reinforced cage was filled with cement paste up to

ground surface level (Fig. 4b, lower right). All technical

work related to the O-cell setup and installation was carried

out by technicians from LOADTEST Korea Ltd., and

LOADTEST Asia Ltd. (based in Singapore), under the

supervision of the geotechnical group from Dong-A

University. The use of O-cells in the PHC piles in this study

was highlighted as a typical case study by Bullock [7] as

well as in project profiles of LOADTEST Company [20].

The MA1-101 and MA3-203 piles were bidirectionally

loaded after monitoring the strains that accumulated in the

piles for 49 and 45 days, respectively. Then, 30 and 43

equal loading increments at 51.71 MPa (7500 psi) and

74.12 MPa (10,750 psi) were applied to MA1-101 and

MA3-203, respectively, using the quick load test method

for individual piles provided in Ref. [5] until the ultimate

resistances were reached.

3 Toe bearing capacity

3.1 Reliability of PDA-based toe bearing capacity

The reliability of the PDA-based pile bearing capacity has

been confirmed in extensive studies (e.g., [19]). However,

reliability of individual toe bearing capacity is seldom

Table 1 Characteristics of the investigated piles

Pile outer diameter,

D (mm)

Penetration depth,

L (m)

Number of PDA

test

500 35 6

32–35 63

35–40 42

40–54 37

600 32–35 25

35–54 17

Fig. 3 Typical CPT profiles and soil properties at the study site. Notes on parameters: /0 = tan-1[0.1 ? 0.38log(qt/r0v0)]; OCR =

0.101pa0.102G0

0.478r0�0:580

v0 ; where G0 = q[277qt0.13r

0:27

v0 ]2; Dr = 100 [0.268ln[(qt/pa)/(r0v0=pa)

0.5] - 0.675]. All equations are given by Mayne [22]

Acta Geotechnica

123

discussed. Thus, the reliability of the PDA-based pile

bearing capacity is verified by comparing its toe bearing

capacities with those obtained from O-cell tests before the

applicability of the CPT-based methods is investigated.

Two PHC piles MA1-101 and MA3-203, which

included O-cells at the pile toe elevations, were installed

and tested to verify the reliability of the PDA-based toe

bearing capacity at the site. Typical force and velocity

records obtained from the PDA tests at final blows for

these two piles are shown in Fig. 5. The wave speed

c values were calculated as 4000 m/s for both piles based

on the time 2L/c (L is the distance from PDA strain gages

to the pile toe), which are indicated in Fig. 5. In addition,

there was a large separation between the force and

velocity curves after the time 2L/c, and the force was

raised up significantly. It means that there was large soil

resistance at the pile toe. The pile toe reached the

designed bearing stratum. Similar trends of force and

(a) (b)

Fill

Silty clay

Silty sand

sand

Sand & Gravel

10.0

20.0

30.0

40.0

50.0

60.0

0.0 Original GL(±) 0.0

Silty sand &

5.0

14.0

33.0

58.0

Straingauges

A

Dep

th (m

)

Cross-sections A-A, B-B

Sister bar &Strain gauge

Pre-tensedsteel bar

Cement

2.5 Excavated layer

A B B

O-cells

MA1-101 MA3-203

34.536.5

Fig. 4 Test piles with O-cells at the toes. a Soil profile and schematic configurations of two piles, b images illustrating the installation process

(a) (b)

Fig. 5 Force and velocity records for CAPWAP analysis. a Pile MA1-101, b pile MA3-203

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velocity records were observed in the work of Lee et al.

[17]. From these force and velocity records, the toe

bearing capacities (Qm,PDA) for these piles were obtained

by using CAPWAP analysis, as presented in Fig. 6.

The downward movements of the O-cells are depicted

in Fig. 6. Table 2 presents some basic parameters from

the PDA tests. As shown in Fig. 6, the Qm,PDA values

obtained from the PDA tests are slightly smaller than

those determined from the O-cell tests (Qm,O-cell). Both

piles produced a similar Qm,O-cell/Qm,PDA ratio of 1.15.

The smaller values of the PDA tests resulted at the EOID

were actually unaffected by soil setup, which often

enhances pile bearing capacity over time. Rausche et al.

[27] extensively reviewed long-term pile capacity pre-

diction based on EOID. They stated that no single for-

mula or factor can suggest the possibility that long-term

capacity varies from 50 to 1000 % of the EOID value.

However, the average setup factors recommended for silty

sand and sand are 1.2 and 1.0, respectively. The same

factors are also given in Hannigan et al. [14]. The Qm,O-

cell/Qm,PDA ratio of 1.15 in the two piles is between 1.0

and 1.2 because the deep sand layer mostly consists of

silty sand and sand. This setup factor is relatively small

but conservative. The toe bearing capacity obtained from

the PDA test used in this study is therefore reliable and

could be used as a reference value to evaluate the

applicability of the CPT-based methods.

3.2 CPT-based methods

In this study, ten common CPT-based methods were

selected for evaluating their applicability in predicting

the toe bearing capacities of PHC driven piles. The

equations for estimating toe bearing capacity from each

method are summarized in Table 3. Pile toe bearing

capacity is controlled by the following three key aspects:

influence zone above and below the pile toe,

average cone resistance mechanism, and correction

factors.

4 Applicability analysis

4.1 Data selection

A total of 82 CPTus and 190 PDA test piles were con-

ducted for pile foundation design at the project. The PDA

test piles closest to each CPTu were used to evaluate the

applicability of the ten CPT-based methods in this study.

However, the soil profiles of the CPTu and PDA test pile

locations differed significantly as a result of the change in

ground surface level during construction and the variation

of the soil layers. To optimize the soil profiles of these

locations before analysis, three data selection steps were

performed as follows.

Fig. 6 Downward movement curves obtained from the O-cell tests. a Pile MA1-101, b pile MA3-203

Table 2 PDA-based toe bearing capacity

Pile number Stage Length (m) Seta (mm/blow) EMX (t 9 m) CSX (MPa) TSX (MPa) Toe BC (MN) Shaft BC (MN)

MA1-101 EOID 32.0 9.0 10.41 28.40 2.80 2.48 0.91

MA3-203 EOID 34.0 3.0 9.46 28.70 6.10 3.54 0.35

a The permanent penetration obtained at the final blow

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Step 1 Correction of CPTu penetration depth

The cone rod was inclined at a maximum angle of

10�–15� compared with the vertical axis, as shown in

Fig. 7. Thus, the recorded CPTu depth did not

accurately reflect the real depth of the soil profile at

the construction site. The cone used in this study was

equipped with a single-axis inclinometer; thus, the

following equation was applied to obtain corrected

penetration depth:

L ¼Xn

i¼1

cos ai � Li ð1Þ

where L is the total corrected penetration depth, Li is the ith

recorded depth increment during penetration, and ai is theinclination angle between vertical axis and the cone at the

ith increment.

Step 2 Matching of soil profiles between CPTu and PDA

test locations

The recorded CPTu depths differed with those of

the PDA test piles due to the change of the ground

surface level during construction, as shown in

Fig. 8a, because the CPTus were conducted on

natural ground surface, whereas the piles were

driven after ground surface excavation. In addition,

the RMX resistance profiles (mobilized static resis-

tance based on CASE method) obtained from the

PDA tests and the cone resistance determined in the

CPTus should be similar if the soil profiles of the

test locations do not vary significantly. Therefore,

similar CPTu and RMX profiles were reviewed and

used to match the recorded depths. CPTu profile

depths were then justified gradually until the

resistances of the RMX and CPTu profiles fitted

each other, as shown in Fig. 8b. A total of 137

PDA test piles remained after matching.

Table 3 Toe bearing capacity equations from ten CPT-based methods

Method qp (unit toe bearing

capacity

Note

Aoki and De Alencar [2] qp = qca/Fb

(qp B 15 MPa)

qca = arithmetic mean of qc values in 8D above and 4D below the pile toe; Fb = correction

factor according to pile type, Fb = 1.75 for driven piles

Bustamante and

Gianeselli [8] (LCPC)

qp = kbqeq qeq = equivalent mean of qc values in 1.5D above and 1.5D below the pile toe;

kb = 0.15–0.6 depending on soil type and pile installation method and kb = 0.4 for driven

pile in sand–gravel

Jardine et al. [15] (ICP-

05)

qp = [1 - 0.5log(D/

Dcpt)]qca

qca = qeq in LCPC method; qp = 0.3qc for D[ 0.90 m; D = pile diameter; Dcpt = cone

diameter

Meyerhof [24] qp = C1C2qca qca = arithmetic mean of qc values in 1D below and 4D above the pile toe; C1,

C2 = correction factors for scale effect and penetration into dense stratum, respectively

Clisby et al. [10]

(Penpile)

qp = 0.125qca qca = arithmetic mean of three qc values near the pile toe

Philipponnat [25] qp = kbqca qca = arithmetic mean of qc values in 3D above and 3D below the pile toe; kb = bearing

factor depending on soil type, kb = 0.4 and 0.3 for sand and gravel, respectively

Schmertmann [28] qp = (qc1 ? qc2)/2

(qp B 15 MPa)

qc1 = average qc by minimum path method in 0.7–4D below the pile toe; qc2 = mean qc by

minimum path method within 8D above the pile toe

Lehane et al. [18]

(UWA-05)

qp = 0.6qca qca = arithmetic mean of qc value 1.5D above and 1.5D below the pile toe

Zhou et al. [32] qp = aqca qca = arithmetic mean of qc values 4D above and 4D below the pile toe; a = factor

according to soil type

Eslami and Fellenius

[13]

qp = CtqEg qEg = geometric mean qE (= qt - u2) values in 8D above and 4D below the pile toe;

Ct = toe adjustment factor, Ct = 1.0 for D B 0.4 m, Ct = 1/(3D) for D[ 0.4 m

The summary intentionally covers only for closed-end driven piles in sandy soils

Fig. 7 CPTu depth correction. a Examples of cone inclination angle,

b a schematic configuration of depth correction

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Step 3 Statistical screening

The Qm values obtained from the PDA tests and the

Qp values predicted from the CPT-based methods may

differ greatly because of unknown factors, such as the

high variation in sandy soil layers that results in soft

soil portions, or the thickness variation in soil layers

within the influence zone. To evaluate the applicabil-

ity of the CPT-based methods, the data sets that

deviate greatly from the measured values must be

eliminated using the following procedures.

First, the Qm values at each depth were obtained from the

remaining test piles at Step 2. Second, the Qp values corre-

sponding to themeasuredQm depthwere calculated based on

the ten CPT-based methods using data from the 82 CPTus.

One PDA test pile may have several Qm values at different

depths; therefore, a total number of 154 Qm values were

determined from 137 PDA test piles. Third, Qp/Qm ratios

were calculated for all CPT-based methods. The statistical

empirical rule (Eqs. 2–4) was then adapted to eliminate the

data sets that deviate greatly. The rule with approximately

95.45 % of the Qp/Qm values lied within two standard

deviations of the mean was applied, as shown in Eq. 4. The

empirical rule equations used in this study are as follows:

l ¼ 1

n

Xn

i¼1

xi ð2Þ

r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xn

i¼1

ðxi � lÞ2s

ð3Þ

l� 2r� xi � lþ 2r ð4Þ

where l is arithmetic mean of variable, xi = Qp/Qm

denotes the variable, r is the standard deviation, and n is

the number of variable xi.

The Qp/Qm values ranged from 144 to 154 data sets

depending on the CPT-based methods after empirical rule

was carried out.

4.2 Definition of rank criteria

The RI proposed by Abu-Farsakh and Titi [1] was adapted

to evaluate the applicability of the CPT-based methods

used in this study. Equation (5) expresses RI as the sum of

four different rank criteria (i.e., R1, R2, R3, and R4). A low

RI value indicates the effective applicability of the CPT-

based method, and a detailed discussion of each criterion is

provided in the work of Abu-Farsakh and Titi [1].

RI ¼ R1þ R2þ R3þ R4 ð5Þ

Each criterion (R1–R4) is briefly defined as follows.

The R1 criterion is determined by plotting Qp versus Qm.

A regression analysis calculates the slope of the best-fit line

Qfit/Qm and the corresponding correlation coefficient (r2).

Sub-ranks A and B for the Qfit/Qm slope and the corre-

sponding r2 are then assigned, respectively, for each CPT-

based method. Low sub-ranks are obtained as the Qfit/Qm

slope, and r2 values approach unity. The R1 criterion is

calculated as the average value of A and B.

The R2 criterion is obtained using the arithmetic mean land the standard deviation r for the Qp/Qm ratios, as shown

in Eqs. 2 and 3. Sub-ranks C and D are set for l and r,respectively, in each CPT-based method. Low C and

D sub-ranks are defined when the l value approaches unity

with the r value that nears zero. The R2 criterion is defined

as the average value of C and D.

The Qp/Qm ratios for each CPT-based method are first

sorted in an ascending order (i.e., 1; 2; 3; . . .; i. . .; n).

Thereafter, the 50 % (P50) and 90 % (P90) cumulative

probabilities of this Qp/Qm order are calculated as sug-

gested by Long and Wysockey [21] using Eq. 6. Two Qp/

Qm ratios are obtained at P50 and P90, and these ratios

indicate the overestimation (Qp[Qm) or underestimation

(Qp\Qm) tendencies of the CPT-based method. Sub-ranks

E and F are then evaluated in terms of P50 and P90,

respectively. Low sub-ranks are obtained as the P50 and

P90 values approach unity. The R3 criterion is calculated

as the average values of E and F.

P ¼ i

ðnþ 1Þ ð6Þ

where i is the order number of each Qp/Qm ratio, and n is

the total number of Qp/Qm ratios.

The R4 criterion is determined by plotting the histogram

and log-normal distributions of the Qp/Qm values. The log-

normal distribution is defined by using Eq. 7. A ±20 %

accuracy range of Qp/Qm (0.8 B Qp/Qm B 1.2) is first

limited on the histogram and log-normal distribution plots.

Fig. 8 Correction of pile penetration depth by comparing the

resistance of RMX and CPTu profiles. a Before depth matching,

b after depth matching

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Fig. 9 Best-fit line of Qp versus Qm for different CPT-based methods

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123

The areas within this range are then examined. Sub-ranks G

and H are obtained for areas of histogram and log-normal

distributions, respectively. Low sub-ranks are defined for

the high ±20 % accuracy areas. The R4 criterion is cal-

culated as the average of G and H.

f ðx; l; rÞ ¼ 1ffiffiffiffiffiffi2p

pxirln

e

� lnðxiÞ�lln½ �22r2

ln ð7Þ

where lln is mean of ln(Qp/Qm) and rln is standard devi-

ation of ln(Qp/Qm).

5 Analysis results

Figure 9 shows the Qp versus Qm plots and the regression

analysis results for the R1 criterion. The Aoki and De

Alencar [2] method is ranked first with a slope of Qfit/

Qm = 0.98 and r2 = 0.62. These values correspond to the

sub-ranks A = 1 and B = 1, respectively, and approach

R1 = 1. The LCPC [8] method has a slope of Qfit/

Qm = 0.92 and r2 = 0.58, thus denoting sub-ranks A = 2

and B = 3. The R1 criterion for this method is 2.5. The

ICP-05 [15] methods rank third with the R1 = 4. The

Meyerhof [24] method is least effective with R1 = 9.5

because it significantly overestimates the PDA-based toe

bearing capacity, with a large difference of 65 %. The R1

of the other methods is similarly calculated and presented

in Fig. 9 and Table 4.

The R2 results for each method are displayed in Table 4.

The Aoki and De Alencar [2] method ranks first with

l = 0.99 and r = 0.22. It is followed by the ICP-05 [15],

Philipponnat [25], Zhow et al. [32], and LCPC [8] methods

with l = 0.96 and r = 0.27, l = 0.84 and r = 0.19,

l = 0.69 and r = 0.13, and l = 0.91 and r = 0.27,

respectively. The Meyerhof [24] method is ranked last.

The R3 results are presented in Fig. 10 and Table 4. The

Aoki and De Alencar [2] method is still ranked first with

R3 = 3, followed by the ICP-05 [15], Zhou et al. [32],

LCPC [8], Philliponnat [25], Schmertman [28], Penpile

[10], UWA-05 [18], Eslami and Fellenius [13], and

Table 4 Rank index of CPT-based methods in predicting toe bearing capacities of the driven PHC piles

Method Best-fit line of Qp versus Qm Arithmetic calculations of Qp/Qm

Qfit/Qm r2 A B R1 l r C D R2

Aoki and De Alencar [2] 0.98 0.62 1 1 1.0 0.99 0.22 1 5 3.0

LCPC [8] 0.92 0.58 2 3 2.5 0.91 0.27 4 6 5.0

ICP-05 [15] 0.91 0.52 3 5 4.0 0.96 0.27 2 6 4.0

Philipponnat [25] 0.82 0.58 6 3 4.5 0.84 0.19 6 3 4.5

Schemrtmann [28] 0.90 0.37 4 7 5.5 0.94 0.30 3 8 5.5

Zhou et al. [32] 0.66 0.62 7 1 4.0 0.69 0.13 7 2 4.5

Eslami and Fellenius [13] 0.84 0.27 5 9 7.0 0.88 0.36 5 9 7.0

UWA-05 [18] 0.56 0.31 8 8 8.0 0.57 0.20 9 4 6.5

Penpile [10] 0.31 0.52 10 5 7.5 0.31 0.10 10 1 5.5

Meyerhof [24] 1.65 0.21 9 10 9.5 1.40 0.72 8 10 9.0

Method Cumulative probability of Qp/Qm ±20 % accuracy of Qp/Qm RI Rank

At P50 At P90 E F R3 Log-normal Histogram G H R4

Aoki and De Alencar [2] 0.98 1.28 1 5 3.0 65.92 66.83 1 1 1.0 8.0 1

LCPC [8] 0.87 1.22 4 4 4.0 51.30 51.10 2 2 2.0 13.5 2

ICP-05 [15] 0.93 1.30 2 6 4.0 50.86 47.52 3 4 3.5 15.5 3

Philipponnat [25] 0.82 1.12 6 1 3.5 48.75 54.21 4 3 3.5 16.0 4

Schemrtmann [28] 0.90 1.40 3 7 5.0 44.28 44.30 5 5 5.0 21.0 5

Zhou et al. [32] 0.68 0.86 7 2 4.5 18.98 17.50 8 8 8.0 21.0 5

Eslami and Fellenius [13] 0.85 1.40 5 7 6.0 33.22 35.00 6 6 6.0 26.0 7

UWA-05 [18] 0.55 0.83 9 3 6.0 12.40 12.50 9 9 9.0 29.5 8

Penpile [10] 0.30 0.45 10 9 9.5 0.16 0.00 10 10 10.0 32.5 9

Meyerhof [24] 1.43 2.41 9 10 9.5 29.92 18.80 7 7 7.0 35.0 10

RI = R1 ? R2 ? R3 ? R4, R1 = (A ? B)/2, R2 = (C ? D)/2, R3 = (E ? F)/2, R4 = (G ? H)/2, r2 = correlation coefficient between Qp

and Qm, l = arithmetic mean of Qp/Qm, r = standard deviation of Qp/Qm, P50 = cumulative probability of Qp/Qm at 50 %, P90 = cumulative

probability of Qp/Qm at 90 %

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Fig. 10 Cumulative probabilities of Qp/Qm for different CPT-based methods

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Fig. 11 Log-normal and histogram distributions of Qp/Qm for different CPT-based methods

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Meyerhof [24] methods. The Aoki and De Alencar [2]

method slightly underpredicts Qm compared with the other

methods, which extremely underpredict Qm. However, the

Meyerhof [24] method overpredicts Qm.

The results for R4 are depicted in Fig. 11 and Table 2. It

can be seen that the Aoki and De Alencar [2] method ranks

first with the log-normal and histogram distributions of

65.92 and 66.83 %, respectively, given ±20 % accuracy,

as shown in Table 4. The LCPC [8] method ranks second

with log-normal and histogram distributions of ±20 %

accuracy at 51.30 and 51.10 %, respectively. The Penpile

[10] method ranks lowest with log-normal and histogram

distributions at the areas of ±20 % accuracy at 0.16 and

0.00 %, respectively.

The overall RI of the CPT-based methods used to

determine toe bearing capacities in this study is provided in

Table 4. The Aoki and De Alencar [2] method most

accurately calculates the toe bearing capacities of driven

PHC piles, followed by the LCPC [8], ICP-05 [15], and

Phillipponat [25] methods. The Meyerhof [24] method is

the least effective technique.

6 Conclusions

Statistical analyses were conducted to investigate the

applicability of the ten CPT-based methods in calculating

the toe bearing capacities of the PHC piles driven into deep

sand in the Nakdong river deltaic area west of Busan City

in South Korea. A total of 82 CPTus and 190 PDA test

piles were used. The following conclusions were drawn.

The reliability of the PDA-based toe bearing capacity

was verified by comparing its toe bearing capacities with

those obtained from O-cell tests before the applicability of

the CPT-based methods was to be investigated. It was

found that the Qm,PDA values obtained from the PDA test at

EOID were slightly smaller than the Qm,O-cell values

determined from the O-cell tests, with the Qm,O-cell/Qm,PDA

ratios of 1.15. Thus, this finding indicated the reliability of

the PDA-based toe bearing capacity, and it could be used

as a reference value to evaluate the applicability of the

CPT-based methods.

To determine optimum toe bearing capacities and soil

profiles, three primary selection steps were performed: (1)

correction of CPTu penetration depth, (2) matching of soil

profiles of the CPTus and PDA test locations, and (3)

statistical screening to consider unknown factors, such as

the high variation in sandy soil layers that results in soft

soil portions between sandy soil layers, and the thickness

variation in soil layers within the influence zone. In all, 137

PDA test piles with 144–154 toe bearing capacity data sets

were determined.

The applicability of the ten CPT-based methods used in

this study was investigated by using RI. The correlation

between Qp and Qm was evaluated, and four different cri-

teria were adapted, namely the best-fit line of Qp versus

Qm, the arithmetic mean and standard deviation of Qp/Qm,

the 50 and 90 % cumulative probabilities of Qp/Qm, and

the ±20 % accuracy of the histogram and log-normal

distributions of Qp/Qm. Based on the evaluation results, the

Aoki and De Alencar [2] method most accurately predicted

the toe bearing capacities, followed by the LCPC [8],

Philipponnat [25], ICP-05 [15], Schmertmann [28], Zhow

et al. [32], Eslami and Fellenius [13], UWA-05 [18],

Penpile [10], and Meyerhof [24] methods.

A specific CPT-based method might be the best

method or the worst method depending on local soil

conditions, pile characteristics, load test types used to

determine the bearing capacity, as well as type of bearing

capacity (i.e., ultimate bearing capacity, skin friction, or

toe bearing capacity). Therefore, the results obtained

from this study might be applied to other areas, which

have similar soil conditions, load test methods (i.e., PDA

with CAPWAP analysis) and type of driven piles (i.e.,

PHC pile).

Acknowledgments The research presented in this paper was con-

ducted with funding from the project entitled ‘‘Development of

Control System for Disaster of Urban Underground Collapse’’ at

Korea Institute of Civil Engineering and Building Technology. The

authors acknowledge the financial support from the institution.

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