ANALYSIS OF PILE DRIVING IN VERTICAL AND HORIZONTAL DIRECTIONSUSING A HYBRID MODELTATSUNORI MATSUMOTOi) PASTSAKORN KITIYODOMii) EIJI KOJIMAiii) HIROMICHI KUMAGAIiv)SATOSHI NISHIMOTOv) and KOUICHI TOMISAWAvi)
ABSTRACT
In order to estimate the deformation and load distribution of a single pile subjected to dynamic horizontal load aswell as vertical load, a simplified method of three-dimensional numerical analysis, KWaveHybrid program, isdeveloped using a hybrid model. In the hybrid model, the pile is modelled as elastic beams, and the soil at each pilenode is treated as springs and dashpots in both vertical and horizontal directions. KWaveHybrid is also able toanalyse the static response of the pile. Validity of the newly developed program is examined through comparisonswith theoretical values and horizontal dynamic and static pile load test results.
Key Words : Pile load test, Pile driving analysis, Hybrid model, Horizontal loading, Vertical loading, Case study
pile have been developed, such as Smith method2),
CAPWAP3), WEAP4), TNOWAVE5), KWave6) andKWaveFD7). However, all of these programs can beapplied to the problem in vertical direction only.
In this study, a computer program KWaveHybrid
has been developed based on a hybrid model. In
KWaveHybrid, the horizontal resistance of the piles isincorporated into the hybrid model so as to be able toanalyse the deformation and load distribution of asingle pile subjected to horizontal load as well as
vertical load. The program can be also used to calculate
the static load-displacement relation of the pile in bothhorizontal and vertical directions.
In order to examine the validity of the newly
developed program, verification analyses are carriedout first. Then the program is applied to the static anddynamic horizontal load tests of actual steel pipe piles.

1. INTRODUCTION
It has been believed that the static load test is themost reliable method to obtain the load-displacement
relation of a pile. Most static load tests are conductedusing reaction piles as the reaction system. In the workof Kitiyodom et al.1), it is suggested that the influenceof the reaction piles on the measured load-displacement
relation may not be neglected, and that an interpretationof the measured data is required to obtain a trueload-displacement relation of the pile.
For axial compressive pile load test, the dynamic
load testing or the rapid load testing is widely usedbecause of the fact that these methods are unsusceptible
to reaction piles, and require less time and costcompared with the conventional static load test wherereaction piles are employed. The dynamic load testing
and the rapid load testing, however, requireinterpretation of the measured signals to derive a
corresponding static load-displacement relation.
Especially, for dynamic load test in which wave
propagation phenomena in the pile cannot be neglected,
wave matching analysis is indispensable.
In a seismic area such as Japan, application of the
dynamic or rapid pile load test to horizontal pile load
testing would be very useful in the seismic design ofthe pile foundation. Several computer programs foranalysing the one-dimensional wave propagation in a

2 METHOD OF ANALYSIS
Figure 1 illustrates the hybrid modelling of the pileand the soil used in this study. The pile is modelled asbeam elements with masses and the soil is treated as
springs and dashpots.
Figure 2 shows the dynamic shaft soil resistancemodel incorporated into KWaveHybrid. The values ofthe vertical spring, k, the horizontal springs, kx and ky,
the vertical radiation damping, c, and the horizontal

I)

Professor, Graduate School of Natural Science and Technology, Kanazawa University, Kodatsuno 2-40-20, Kanazawa, 920-8667, Japan.
Research Associate, Graduate School of Natural Science and Technology, Kanazawa University, Kodatsuno 2-40-20, Kanazawa, 920-8667, Japan.
Japan Pile Corporation, Shinkawa 1-16-3, Chuo-ku, Tokyo, 104-0033, Japan
iv)
Japan Pile Corporation, Shinkawa 1-16-3, Chuo-ku, Tokyo, 104-0033, Japanv)
Civil Engineering Research Institute of Hokkaido, Hiragishi 1-3-1-34, Toyohira-ku, Sapporo, 062-8602, Japanvi)
Civil Engineering Research Institute of Hokkaido, Hiragishi 1-3-1-34, Toyohira-ku, Sapporo, 062-8602, Japan
Manuscript was received for review on May 9, 2005.
ii)

iii)

1

503

MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA

radiation damping, cx and cy, per unit shaft area areapproximated by means of Equations (1) and (2), basedon the work of Novak et al.8).
k2.75Gs x
4Gs, k ky
d
d
Gs x
4.5
G
s
c
, c cyVs
Vs

The slider value is equal to the static maximum shaft
max
resistance, static, in the vertical direction and is equal to
the limit horizontal pressure, qh, in the horizontal
direction.
The total dynamic friction in vertical direction, total,
is generally taken as a non-linear function of velocity,
according to

(1)
(2)

total

where Gs and Vs are the shear modulus and the shear
wave velocity of the surrounding soil respectively, andd is the outer diameter of the pile.

m0
c0

ch0
(Kp)1

kh1

m1
c1

k1

ch1

(Kp)2

kh2

m2
c2 (Kp)3

k2

kb

ch2

(Kp) n

cb

khn

mn
chn

kb

cb

cb

K w

mb

or qh

Dashpot cv(viscous)

8Gs
d(1 s )
3.4 Gs(1 s ) Vs
0.1
(1

(4)
(5)
4
s

(6)

s)

C w

M w

F

Pile node

Soil adjacent to pile

Spring k(3)(7)

where [K], [C] and [M] are the stiffness matrix, thedamping matrix and the mass matrix respectively. { F}is the external force vector. The stiffness matrix isformed from the pile stiffness matrix and the soil
stiffness matrix. The damping matrix is equal to the soil
damping matrix. The mass matrix is formed from thepile mass matrix and the lumped soil mass at the pile
base.

Pile nodemax
static(v0 = 1 m/s)

in which s and s are the Poisson s ratio and thedensity of the soil respectively.
The equation of motion of the pile is expressed as

Fig. 1. Hybrid modelling of the pile and the soil.

Sliderv / v0mb 16ro s

cn

kn

1

where v0 is a reference velocity and v is the relative
velocity between the pile and the adjacent soil.
Non-linear viscous laws similar to Equation (3) havebeen proposed by Gibson and Coyle9), Heerema10), andLitkouhi and Poskitt11), all of whom suggest a value ofclose to 0.2, with the parameter varying from about
0.1 for sand, to unity for clay soils12). The relation in
Equation (3) was introduced into the viscous damping
in Figure 2 for vertical shaft resistance model.
Figure 3 shows the dynamic vertical pile baseresistance model. The values of the soil spring at thepile base, kb, the damping, cb, and the lumped soil mass,
mb, per unit base area can be estimated as follows13):

kh0

k0

max
staticSlider qb

Dashpot c(radiation)

Spring kb

Soil far from pile (fixed)

Fig. 2. Vertical and horizontal shaft resistance model.

2504

Dashpot cb

LumpedDashpot cb mass Mb

Fig. 3. Vertical base resistance model.

Mass (ton)
1.51
Figure 4 shows the vertical impact force applied tothe pile head. Figure 5 shows the calculated andtheoretical distributions of axial forces along the pile.
Theoretically, the front of compression force reaches
the pile base at t = 2 ms because the bar wave velocity
is 5000 m/s. The compression force is reflected at thepile base, and the reflected force goes back to the pilehead as the tension force and reaches the pile head at t
= 4 ms. The calculated results are in good agreementswith these theoretical solutions. Figure 6 shows thetime vs pile displacement at the middle point (z = 5 m).
A good agreement between the theoretical andcalculated values can be seen again.

When the stress at a pile-soil interface nodal point
reaches the soil yield stress, the soil spring stiffness andthe dashpot value at that point are set to 0. In order toconsider also the nonlinearity of the soil spring stiffness,
Equation (7) is rewritten in incremental form as:
F t

Kt

wt

t

Ct wt

M t wt

t

t

F t

t

(8)

Equation (8) can be solved for the pile settlements,
deflections and rotations from which the axial forces,
the shear forces and the bending moments can beobtained. Note that Newmark s method14) is used forsolving Equation (8).
In the analysis of static pile load test, the static
vertical shaft soil spring, kstatic, is estimated by means ofEquations (9) and (10) following Randolph andWroth15).

1200
Force (kN)1000

kstatic (2 / 2.75 ) k ,ln[5.0(1 s )l / d](9)where l is the pile embedment length.
The static horizontal shaft soil spring values at eachpile node are estimated based on Mindlin s solution16)
which is similar to the solution of the integral equation
method used by Poulos and Davis17). The equations
becomekystatick

Es l

pd / uEs

200

(10)

1200

(11)

800

0

1

2
3
Time (ms)45Calculated (t = 2 ms)
Calculated (t = 4 ms)
Theoretical (t = 2 ms)
Theoretical (t = 4 ms)

400
0
-400

t = 2 mst = 4 ms

-800
-1200

0

2

4
6
Pile distance (m)810Pile displacement (mm)Fig. 5. Distribution of axial force along the pile.

ACCURACY OF THE PROPOSED METHOD

3.1 Impacts on pile without soil resistances
Vertical impacts on a homogeneous pile and a
non-homogeneous pile without soil resistance arecalculated by the program KWaveHybrid, and thecalculated results are compared with the theoreticalvalues.
Table 1 shows the specifications of a homogeneous
pile to be analysed here.

4
Calculated
Theoretical

3
2
1
0

z=5m

0

2

4
6
Time (ms)810Fig. 6. Time vs pile displacement
Table 2. Specifications of a non-homogeneous pile

Table 1. Specifications of a homogeneous pile
Length (m)Diameter (mm)Cross-sectional area (m2)Young's modulus (kN/m2)
Bar wave velocity (m/s)
Density (ton/m3)

400

Fig. 4. Pile head force.

where p is the horizontal distributed force acting
uniformly over the pile element and u is thecorresponding horizontal displacement at each pilenode calculated using the integral equation method.
Note that the shear resistance at the pile base has notbeen incorporated in the present program. More detailsof the static analysis method can be found in
References 18) and 19).
3

600

0

Force (kN)xstatic

800

10
400
0.126
3.0×107
5000
1.2

Length (m)Diameter (mm)Cross section area (m2)Young's modulus (kN/m2)
Bar wave velocity (m/s)
Density (ton/m3)

3

505

Upper
5
100
7.85×10-3
3.0×107
5000
1.2

Lower
5
141.4
15.7×10-3
3.0×1075000
1.2

MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA

A non-homogeneous pile with no soil resistanceshown in Table 2 was also analysed using the proposed
method. The pile consists of two sections having thesame material but different cross-sectional areas. The
cross-sectional area of the lower section is twice that of
the upper section. The impact force shown in Figure 4
was applied to the pile head.
Figures 7 and 8 show time vs velocity and time vspile head displacement, respectively. Good agreements
between the calculated and theoretical values can beseen in both the velocity and displacement.

M = 1.51 ton
K = 2.51×104 kN/m

Pile displacement (mm)Fig. 9. Single mass system.

3.2 Friction pile with elastic soil response
A perfect friction pile with elastic friction response
is analysed, and the calculated results are comparedwith the theoretical solutions of the single mass system
shown in Figure 9.
Specifications of the pile to be analysed here are thesame as those shown in Table 1. The values of thevertical shaft spring stiffness, k, and the verticalradiation damping, c, were set as k = 2.0×103 kN/m3 andc = 5.0 kNs/m3 along the pile shaft uniformly forconvenience. The corresponding values of the total
vertical spring stiffness, K, and the total vertical damping,C, in the single mass system are shown in Figure 9.
Figures 10 and 11 show time vs displacement of the
middle point of the pile without damping (c = 0) and with
damping, respectively. Overall, the calculated results arein good agreement with the theoretical solutions in bothcases. Periodical oscillations can be seen in the calculated
results. These oscillations in the calculation results reflect
the wave propagation phenomena in the pile, which cannot
be simulated using the single mass system.

Velocity (m/s)

Pile displacement (mm)4Calculated
Theoretical2

4
6Time (ms)Pile head disp. (mm)

0
-4
-8
-12

Calculated
Theoritical
50
100
150
Time (ms)012Peaks from solution
with damping

8
4
0
-4
-8
-12

Calculated
Theoritical

z=5m
0

50

100
Time (ms)150

CASE STUDY

The test piling on two steel pipe piles was
performed. Figure 12 shows the profiles of soil layer
and the SPT N-values at the test site. Two test piles,
designated as P1 and P2, were installed by preboring.
So there is no soil plug inside the piles. The test pile
specifications are summarised in Table 3. The distance
between the centres of the two piles is 3.5 m.

8

10

Fig. 7. Time vs pile head velocity

Table 3. Specifications of test steel piles

60
50

Calculated
Theoretical

40

Length (m)Embedment length (m)Outer diameter (mm)
Inner diameter (mm)Cross-sectional area (cm2)Young's modulus (kN/m2)
Shear wave velocity (m/s)
Density (ton/m3)
Pile mass (ton)

30
20
10
0

4

4.1 Test description

0
0

z=5m

8

Fig. 11. Time vs pile displacement (with damping).

20

-20

12

Fig. 10. Time vs pile displacement (without damping).

60
40

C = 62.8 kNs/m

0

2

4
6
Time (ms)810Fig. 8. Time vs pile head displacement

4

506

P1
6.5
5.4
600
582
167.1
2.06×108
3187
7.8
0.9

P2
10.0
8.9
500
482
138.8
2.06×108
3187
7.8
1.1

60

30
20
10
0

10

20

30 40 50
Time (ms)

60

70

80

Horizontal Disp., u (mm)2(m/s )
Acceleration,

Clayed
Sand
Sandy
Clay

20
Measured
Calculated

15
10
5
0
-5

0

10

20

30 40 50
Time (ms)

60

70

80

400
300
200
100
0
-100
-200

0

10

20

30 40 50
Time (ms)

60

70

80

90

70

80

90

1.2

P1

Sand

8 Silt
P2

10
Clay

0.9
0.6
0.3
0.0
-0.3
-0.6

0

10

20

30 40 50
Time (ms)60(d) Velocity (integrate of acceleration by time)100

Fig. 14. Dynamic pile load test signals of P1.

Force, Fsta (kN)

Fig. 12. Profiles of soil layers and SPT N-values.
Step loading (JSF T32-83)
Cont. loading

4.2 Measured static and dynamic test signals

60

The dynamic test signals of P1 and P2 are shown in
Figures 14 and 15, respectively. The measured forces
increase and decrease rapidly with time and have a peakof about 50 kN. The loading duration is about 50 ms.
Figures 16 and 17 show the measured static anddynamic horizontal load-horizontal displacement
relations of P1 and P2, respectively. It can be seen fromthe figures that there are good agreements between themeasured load displacement relations from the static

40
20
0

0

90

(c) Measured acceleration

14

80

90

(b) Measured and estimated horizontal displacement

Clay

6 Fine1240(a) Measured force

Velocity, v (m/s)

Depth from G.L. (m)

4

50

0

SPT N-value
0 5 10 15 20

02Force, Fdyn (kN)

Both static and dynamic horizontal load tests werecarried out on each pile. The dynamic pile load test was
carried out prior to the static pile load tests. In the
dynamic pile load test, the pile was hit horizontally by ahammer mass of 0.96 ton at the point z = 0.25 m below
the pile head. Applied force, horizontal displacements
and accelerations were measured at the same level ofthe hit point with a sampling rate of 15 s.
After the dynamic pile load test, two static
horizontal pile load tests with different loading methods
were conducted on each pile. Static horizontal pile load
test with step loading method20) was conducted first.
Load step sequence for the step loading is shown in
Figure 13, following JSF T32-8320). In vertical pile load
test standard JGS 1811-200221), two loading methods
are recommended which are the step loading method
and the continuous loading methods. However, in JSF
T32-83, only the step loading method is prescribed. In
this study, the static horizontal pile load test with thecontinuous loading method was also conducted. The
load step sequence of continuous loading is also shownin Figure 13. The static horizontal load was applied at
the same loading point as the dynamic horizontal pileload test. The horizontal displacement of the pile andthe applied force were monitored throughout the static
pile load tests.

50

100
150
Time (min)200

Fig. 13. Load step sequence of static pile load tests.

5507

MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA

100

load tests with continuous loading and that from thestatic load tests with step loading. On the other hand,
the measured load displacement relations from the
dynamic load tests are totally different from themeasured static load displacement relations. Therefore,
in order to obtain the static load displacement relationof the pile from the measured signals of the dynamic
load test, wave matching analysis of the measured
dynamic signals was carried out using KWaveHybrid.

Force, F (kN)80

Force, Fdyn (kN)

60
50

20

0

10

20

30 40 50
Time (ms)

60

70

80

100

90

80

20

Force, F (kN)Horizontal Disp., u (mm)(a) Measured force
Measured
Calculated

15
10
5
0
0

10

20

30 40 50
Time (ms)

60

70

80

2

(m/s )
Acceleration,

60
40
20
0 5 10 15 20 25 30
Horizontal displacement, u (mm)Fig. 17. Measured load-displacement relations of P2.

400
300

4.3 Wave matching analysis results

200

Matching analysis was repeated with assumed
values for the maximum shaft limit horizontal pressure,qh, and the soil shear modulus, Gs, using the measured
Fdyn as the force boundary condition at the loading
point, until a good matching between the calculated andthe measured pile displacement was obtained. Soilparameters used in the final matching of P1 are listed inTable 4. Figure 14(b) and Figure 18 show thedisplacement vs time and load displacement relation of
P1 in the final matching analysis, compared with themeasured values.
It can be seen that the calculated dynamic pile
displacement underestimated the measured values after
the peak displacement. This is thought to be due to thesoil spring model. At the present, the value of the soil
springs in KWaveHybrid during the loading andunloading states are the same. It can be seen from themeasured results (Figures 16 and 17) that the values ofthe soil spring during the loading and unloading statesshould be different. These extensions are left for future
work.

100
0
-100
0

10

20

30 40 50
Time (ms)

60

70

80

90

70

80

90

(c) Measured acceleration
1.2
Velocity, v (m/s)

Dynamic
Static (Step)
Static (Cont.)

090(b) Measured and estimated horizontal displacement

0.9
0.6
0.3
0.0
-0.3
-0.6

20

Fig. 16. Measured load-displacement relations of P1.

10

-200

40

0 5 10 15 20 25 30
Horizontal Displacement, u (mm)

30

-5

60

0

40

0

Dynamic
Static (Step)
Static (Cont.)

0

10

20

30 40 50
Time (ms)60(d) Velocity (integrate of acceleration by time)

Fig. 15. Dynamic pile load test signals of P2.

6
508

60

Table 4. Soil parameters for final matching of P1.
Gs (kPa)
1083
1083

s

0.3
0.3

qh (kPa)
1
Elastic range

Force, Fdyn (kN)

Depth (m)0 to 1>1

Table 5. Soil parameters for final matching of P2.
Depth (m)0 to 1>1

Gs (kPa)
1539
1539

s

0.3
0.3

qh (kPa)
5
Elastic range

Fig. 20. Dynamic pile load test results of P2.

Force, Fsta (kN)

100

Force, Fdyn (kN)

Estimated
Measured60
40
20
0 5 10 15 20 25 30
Horizontal displacement, u (mm)Fig. 21 Static pile load test results of P1.
4.4 Prediction analysis
In actual construction site, it would be very useful toestimate the static load displacement relation of theactual pile from the dynamic load test of another pile
having smaller diameter. In this work, the soil
parameters of P2 (Table 5), which has a smaller
diameter than P1, were employed to predict the load
displacement relation of P1.
Figure 22 shows the predicted displacement vs time
and the predicted dynamic load displacement relation of
P1, compared with the measured values.
Figure 23 shows the predicted static load
displacement relation of P1, compared with themeasurement. It can be seen from the figures that
although the predicted displacements overestimate themeasured values, there are reasonable agreements
between the predicted and the measured values.

30
20
Calculated
Measured

0
3
6
9
12 15
Horizontal displacement, u (mm)Fig. 18. Dynamic pile load test results of P1.
100
Force, Fsta (kN)

80

0

40

80
60

5

40

0

20

0
3
6
9
12 15
Horizontal displacement, u (mm)

50

20

30

0

60

0

40

10

Using the same soil parameters as shown in Table 4,
the static load displacement relation of P1 wasestimated using KWaveHybrid. Figure 19 shows thecomparison of the estimated static load displacement
relation of P1 with the measured value. It can be seenthat the estimated result matches very well with themeasured one.
The same analysis procedures as P1 were carried out
for P2. Soil parameters used in the final matching of P2
are listed in Table 5. Figure 15(b) and Figure 20 show
the displacement vs time and load displacement of P2
in the final matching analysis, compared with themeasured values.
Figure 21 shows the comparison of the estimatedstatic load displacement relation of P2 with themeasured value. Again there is a good agreement
between the estimated and the measured results.

10

Calculated
Measured50

CONCLUSIONS

A new numerical program KWaveHybrid foranalysing pile driving as well as static load test invertical and horizontal directions has been developed inthis study. Performance of the program was verified
through comparisons with theoretical solutions
The developed program was then applied to the
dynamic and static horizontal load tests on two steel
pipe piles. A good matching between the calculated andEstimated
Measured0 5 10 15 20 25 30
Horizontal displacement, u (mm)Fig. 19 Static pile load test results of P1.

7509

MATSUMOTO, KITIYODOM, KOJIMA, KUMAGAI, NISHIMOTO AND TOMISAWA
3) Rausche, F., Moses, F. and Goble, G. G. (1972): Soil
resistance predictions from pile dynamics Journal of the Soil
Mechanics and Foundation Division ASCE, 98(SM9),
917-937.
4) Goble, G. G. and Rausche, F. (1976): Wave equation analysis
of pile driving-WEAP program, prepared for the U.S.
department of transportation, federal highway administration,
implementation division, office of research and development.
5) TNO (1977): Dynamic pile testing. Report No. BI-77-13.
6) Matsumoto, T. and Takei, M. (1991): Effects of soil plug on
behaviour of driven pipe piles. Soil and Foundations, 3(2),14-34.
7) Wakisaka, T., Matsumoto, T., Kojima, E. and Kuwayama S.
(2004): Development of a new computer program for
dynamic and static pile load tests. Proceedings of the 7thInternational Conference on the Application of Stresswave
Theory to Piles, Kuala Lumpur, 341-350.
8) Novak, M., Nogami, T. and Aboul-Ella F. (1978): Dynamic
soil reactions for plane strain case. Journal of MechanicalEngineering ASCE, 104(EM4), 953-959.
9) Gibson, G. and Coyle, H. M. (1968): Soil damping constantrelated to common soil properties in sands and clays. Report
No. 125-1, Texas Transport Institute, Texas A&M University.
10) Heerema, E. P. (1979): Relationships between wall friction
displacement, velocity and horizontal stress in clay and insand for pile driveability analysis. Ground Engineering,12(1).
11) Litkouhi, S. and Poskitt, T. J. (1980): Damping constant forpile driveability calculations. Géotechnique, 30(1), 77-86.
12) Randolph, M. F. and Deeks A. J. (1992): Dynamic and static
soil models for axial pile response. of the 4th International
Conference on the Application of Stresswave Theory to Piles,
The Hague, 3-14.
13) Deek, A. J. and Randolph, M. F. (1995): A simple model for
inelastic footing response to transient loading. International
Journal for Numerical and Analytical Methods inGeomechanics, 19, 307-329.
14) Newmark, N. M. (1959): A method of computation forstrucural dynamics. Journal of the Engineering Mechanics
Division ASCE, 85(EM3), 67-94.
15) Randolph, M. F. and Wroth, C. P. (1978): Analysis ofdeformation of vertically loaded piles. Journal of
Geotechnical Engineering ASCE, 104(12), 1468-1488.
16) Mindlin, R. D. (1936): Force at a point interior of asemi-infinite solid. Physics, 7, 195-202.
17) Poulos, H. G. and Davis E. H. (1980): Pile Foundation
Analysis and Design, Wiley, New York.
18) Kitiyodom, P. and Matsumoto, T. (2002): A simplified
analysis method for piled raft and pile group foundations
with batter piles. International Journal for Numerical andAnalytical Methods in Geomechanics, 26, 1349-1369.
19) Kitiyodom, P. and Matsumoto, T. (2003): A simplified
analysis method for piled raft foundations in
non-homogeneous soils. International Journal for Numericaland Analytical Methods in Geomechanics, 27, 85-109.
20) Japanese Society of Soil Mechanics and Foundation
Engineering. (1983): JSSMFE standard method for lateralloading test for a pile. Japanese Society of Soil Mechanics
and Foundation Engineering, Tokyo.
21) Japanese Geotechnical Society. (2002): Standards ofJapanese Geotechnical Society for vertical load tests of piles.
Japanese Geotechnical Society, Tokyo.

Horizontal Disp., u (mm)measured behaviours of the piles during driving andduring static load test was obtained.
The identified soil resistance parameters of thesmaller diameter pile were used to predict the
behaviours of the bigger pile, and a good prediction
was obtained.
20
Predicted
Measured

15
10
5
0
-5

0

10

20

30 40 50
Time (ms)

60

70

80

90

(a) Measured and predicted horizontal displacement
60
Force, Fdyn (kN)

50
40
30
20
10
0

Predicted
Measured

0
3
6
9
12 15
Horizontal displacement, u (mm)(b) Measured and predicted load-displacement relation
Fig. 22. Predicted dynamic results of P1.

Force, Fsta (kN)

100
80
60
40
20
0

Predicted
Measured0 5 10 15 20 25 30
Horizontal displacement, u (mm)Fig. 23. Predicted static load-displacement of P1.
REFERENCES
1) Kitiyodom, P., Matsumoto, T. and Kanefusa, N. (2004):
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2) Smith, E. A. L. (1960): Pile driving analysis by the wave
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