ANALYSIS OF STATIC AND DYNAMIC HORIZONTAL LOAD TESTS ONSTEEL PIPE PILES
Pastsakorn Kitiyodom, Kanazawa University, Kanazawa, Japan
Tatsunori Matsumoto, Kanazawa University, Kanazawa, Japan
Eiji Kojima, Japan Pile Corporation, Tokyo, Japan
Hiromichi Kumagai, Japan Pile Corporation, Tokyo, Japan
Kouichi Tomisawa, Civil Engineering Research Institute of Hokkaido, Hokkaido, Japan

In order to estimate the deformation and load distribution of a single
pile subjected to dynamic horizontal load as well as vertical load, asimplified method of three-dimensional numerical analysis,
KWaveHybrid program, is developed using a hybrid model. In the
hybrid model, the pile is modelled as elastic beams, and the soil at
each pile node is treated as springs and dashpots in both verticaland horizontal directions. KWaveHybrid is also able to analyse thestatic response of the pile. Validity of the newly developed programis examined through comparisons with theoretical values andhorizontal dynamic and static pile load test results

INTRODUCTION

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 theseismic design of the pile foundation. Several
computer programs for analysing the onedimensional wave propagation in a pile havebeen developed, such as Smith method (Smith,1960), CAPWAP (Rausche et al., 1972),
WEAP (Goble & Raushe, 1976), TNOWAVE(TNO, 1977), KWave (Matsumoto & Takei,
1991) and KWaveFD (Wakisaka et al., 2004).
However, all of these programs can be applied
to the problem in vertical direction only.

It has been believed that the static load test is
the most reliable method to obtain the loaddisplacement relation of a pile. Most static load
tests are conducted using reaction piles as thereaction system. In the work of Kitiyodom et al.
(2004), it is suggested that the influence of thereaction piles on the measured loaddisplacement relation may not be neglected,
and that an interpretation of the measured
data is required to obtain a true loaddisplacement relation of the pile.

In this study, a computer program
KWaveHybrid has been developed based on a
hybrid model. In KWaveHybrid, the horizontal
resistance of the piles is incorporated into thehybrid model so as to be able to analyse thedeformation and load distribution of a single
pile subjected to horizontal load as well as
vertical load. The program can be also used to
calculate the static load-displacement relationof the pile in both horizontal and verticaldirections.

For axial compressive pile load test, thedynamic load testing or the rapid load testingis widely used because of the fact that thesemethods are unsusceptible to reaction piles,
and require less time and cost compared withthe conventional static load test wherereaction piles are employed. The dynamic load
testing and the rapid load testing, however,require interpretation of the measured signals
to derive a corresponding static loaddisplacement relation. Especially, for dynamic
load test in which wave propagation
phenomena in the pile cannot be neglected,
wave matching analysis is indispensable.

In order to examine the validity of the newly
developed program, verification analyses arecarried out first. Then the program is applied to690

The slider value is equal to the static
maximum shaft resistance in the verticaldirection and is equal to the limit horizontalpressure in the horizontal direction.

the static and dynamic horizontal load tests ofactual steel pipe piles.
METHOD OF ANALYSISThe total dynamic friction in vertical direction,
total, is generally taken as a non-linear functionof velocity, according to

Fig. 1 illustrates the hybrid modelling of thepile and the soil used in this study. The pile ismodelled as beam elements with masses andthe soil is treated as springs and dashpots.

total

Fig. 2 shows the dynamic shaft soil resistancemodel incorporated into KWaveHybrid. The
values of the vertical spring, k, the horizontalxysprings, k and k , the vertical radiation
damping, c, and the horizontal radiationxydamping, c and c , per unit shaft area areapproximated by means of Eqs. 1 and 2,
based on the work of Novak et al. (1978).
k

2.75Gs
, kx
d

ky

c

Gs
, cx
Vs

4.5Gs
Vs

cy

4Gs
d

max
static1where v0 is a reference velocity and v is therelative velocity between the pile and theadjacent soil. Non-linear viscous laws similar
to Eq. 3 have been proposed by Gibson &Coyle (1968), Heerema (1979), and Litkouhi &Poskitt (1980), all of whom suggest a value ofclose to 0.2, with the parametervaryingfrom about 0.1 for sand, to unity for clay soils(Randolph & Deek, 1992). The relation in Eq.
3 was introduced into the viscous damping in
Fig. 2 for vertical shaft resistance model.

(1)

(2)
Fig. 3 shows the dynamic vertical pile baseresistance model. The values of the soil springat the pile base, kb, the damping, cb, and the
lumped soil mass, mb, per unit base area canbe estimated as follows (Deek & Randolph,
1995):

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

kh0
m0
c0

ch0

k0
(Kp)1

kb

8Gs
d (1 s )(4)cb

3.4 Gs(1 s ) Vs(5)mb

16ro s

kh1
m1

c1
k1

ch1
(Kp)2

c2 (Kp)3(Kp) nThe equation of motion of the pile isexpressed as

K w

chn
cb

(6)

s)

ch2

cn

kn

4
s

in which s and s are the Poisson’s ratio andthe density of the soil respectively.

khn

mn

0.1
(1

kh2
m2

k2

(v 0 = 1 m/s) (3)v / v0

C w

M w

F

(7)

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

cb

kb
mb

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

691

The static horizontal shaft soil spring values at
each pile node are estimated based on
Mindlin’s solution (Mindlin, 1936) which issimilar to the solution of the integral equation
method used by Poulos and Davis (1980). The
equations become

Pile node
Slidermax
staticDashpot cv(viscous)or qhSoil adjacent to pilex
kstatic

Dashpot c(radiation)

Spring k

Es l

(10)

pd / uEs(11)

where p is the horizontal distributed force
acting uniformly over the pile element and u isthe corresponding horizontal displacement at
each pile node calculated using the integral
equation method.

Soil far from pile (fixed)

Fig. 2. Vertical and horizontal shaft resistancemodel.

Note that the shear resistance at the pile basehas not been incorporated in the present
program. More details of the static analysis
method can be found in Kitiyodom &Matsumoto (2002, 2003).

Pile node
Dashpot cb

Slider qb

ykstatic

ACCURACY OF THE PROPOSED METHOD
Impacts on pile without soil resistanceSpring kb
Dashpot cb

Lumpedmass Mb

Vertical impacts on a homogeneous pile and a
non-homogeneous pile without soil resistanceare calculated by the program KWaveHybrid,and the calculated results are compared withthe theoretical values. Table 1 shows the
specifications of a homogeneous pile to beanalysed here.

Fig. 3. Vertical base resistance model.
When the stress at a pile-soil interface nodal
point reaches the soil yield stress, the soil
spring stiffness and the dashpot value at thatpoint are set to 0. In order to consider also thenonlinearity of the soil spring stiffness, Eq. 7 isrewritten in incremental form as:
F t

K t

w t

t

Ct w tt

Mt w tF tttFig. 4 shows the vertical impact force applied
to the pile head. Fig. 5 shows the calculated
and theoretical distributions of axial forcesalong the pile. Theoretically, the front ofcompression 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 pile head as the tension force and reaches
the pile head at t = 4 ms. The calculated
results are in good agreements with these
theoretical solutions. Fig. 6 shows the time vspile displacement at the middle point (z = 5 m).
A good agreement between the theoreticaland calculated values can be seen again.

(8)

Eq. 8 can be solved for the pile settlements,
deflections and rotations from which the axial
forces, the shear forces and the bending
moments can be obtained. Note that
Newmark’s
method (NewMark, 1959) isused for solving Eq. 8.
In the analysis of static pile load test, the static
vertical shaft soil spring, kstatic, is estimated bymeans of Eqs. 9 and 10 following Randolph
and Wroth (1978).
kstatic(2 / 2.75 ) k ,ln[5.0(1sTable 1. Specifications of a homogeneous pile.
Length (m)Diameter (mm)2
Cross-sectional area (m )2Young's modulus (kN/m )Bar wave velocity (m/s)
3
Density (ton/m )Mass (ton))l / d ] (9)where l is the pile embedment length.

692

10
400
0.126
7
3.0×10
5000
1.2
1.51

1200

theoretical values can be seen in both thevelocity and displacement.

Force (kN)

1000
800

Friction pile with elastic soil response

600
400

A perfect friction pile with elastic friction
response is analysed, and the calculated
results are compared with the theoreticalsolutions of the single mass system shown in
Fig. 9.

200
0

0

1

2
3
Time (ms)45Fig. 4. Pile head force.
1200

Calculated (t = 2 ms)
Calculated (t = 4 ms)
Theoretical (t = 2 ms)
Theoretical (t = 4 ms)

Force (kN)

800
400

Specifications of the pile to be analysed here
are the same as those shown in Table 1. The
values of the vertical shaft spring stiffness, k,
and the vertical radiation damping, c, were set
3
3
3
as k = 2.0×10 kN/m and c = 5.0 kNs/malong the pile shaft uniformly for convenience.
The corresponding values of the total verticalspring stiffness, K, and the total vertical
damping, C, in the single mass system areshown in Fig. 9.

t = 2 ms

0-400

t = 4 ms

-800
-1200

0

2

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

Figs. 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 are in good agreementwith the theoretical solutions in both cases.
Periodical oscillations can be seen in thecalculated results. These oscillations in thecalculation
resultsreflect
thewave
propagation phenomena in the pile, whichcannot be simulated using the single mass
system.

4
Calculated
Theoretical

3
2
1

z=5m
0

0

2

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

60

Lower
5
141.4
-3
15.7×107
3.0×105000
1.2

Calculated
Theoretical

40
20
0
-20

0

2

4
6
Time (ms)810Fig. 7. Time vs pile head velocity.
Pile head disp. (mm)Length (m)Diameter (mm)2
Cross section area (m )2Young's modulus (kN/m )Bar wave velocity (m/s)
3
Density (ton/m )

Upper
5
100
-3
7.85×107
3.0×105000
1.2

Velocity (m/s)

Table 2. Specifications of a non-homogeneouspile.

A non-homogeneous pile with no soil
resistance shown in Table 2 was also
analysed using the proposed method. The pileconsists of two sections having the samematerial but different cross-sectional areas.
The cross-sectional area of the lower sectionis twice that of the upper section. The impact
force shown in Fig. 4 was applied to the pile
head.

60
50

Calculated
Theoretical

40
30
20
10
0

0

2

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

Figs. 7 and 8 show time vs velocity and timevs pile head displacement, respectively. Goodagreements between the calculated and693

measured at the same level of the hit pointwith a sampling rate of 15 ms.

M = 1.51 ton
K = 2.51×104 kN/m

C = 62.8 kNs/m

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
method (JSSMFE, 1983) was conducted first.
Load step sequence for the step loading isshown in Fig. 13, following JSF T32-8320). In
vertical pile load test standard JGS 1811200221),
twoloading
methodsarerecommended 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 the continuous
loading method was also conducted. The load
step sequence of continuous loading is also
shown in Fig. 13. The static horizontal load
was applied at the same loading point as the
dynamic horizontal pile load test. The
horizontal displacement of the pile and theapplied force were monitored throughout thestatic pile load tests.

Pile displacement (mm)Fig. 9. Single mass system.
12
z=5m

8
4
0
-4
-8
-12

Calculated
Theoritical
50
100
150
Time (ms)0Pile displacement (mm)Fig. 10. Time vs pile displacement (without
damping).

Table 3. Specifications of test steel piles

12
Peaks from solution
with damping

8
4

Length (m)Embedment length (m)Outer diameter (mm)
Inner diameter (mm)2
Cross-sectional area (cm )2Young's modulus (kN/m )Shear wave velocity (m/s)
3
Density (ton/m )Pile mass (ton)

0
-4
-8
-12

Calculated
Theoritical

z=5m
0

50

100

150

Time (ms)Fig. 11 Time vs pile displacement (withdamping).
CASE STUDY
Test description

Depth from G.L. (m)2Both static and dynamic horizontal load tests
were carried 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 a hammer massof 0.96 ton at the point z = 0.25 m below the
pile
head.
Appliedforce,
horizontal
displacements
andaccelerations
were

P2
10.0
8.9
500
482
138.8
8
2.06×10
3187
7.8
1.1

SPT N-value
0 5 10 15 20

0

The test piling on two steel pipe piles was
performed. Fig. 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.

P1
6.5
5.4
600
582
167.1
8
2.06×10
3187
7.8
0.9

Clay
ClayedSand

4 Sandy
Clay

6 Fine

Sand

8

P1

Silt

P2

10
Clay

12
14
Fig. 12. Profiles of soil layers and SPT Nvalues.

694

KWaveHybrid during the loading andunloading states are the same. It can be seenfrom the measured results (Figs. 16 and 17)that the values of the soil spring during theloading and unloading states should be
different. These extensions are left for future
work.

Step loading (JSF T32-83)
Cont. loading

80
60
40
20
0

0

50

100
150
Time (min)200
60
Force, Fdyn (kN)

Force, Fsta (kN)

100

Fig. 13. Load step sequence of static pile load
tests.
Measured static and dynamic test signals

50
40
30
20
10
0

The dynamic test signals of P1 and P2 areshown in Figs. 14 and 15, respectively. The
measured forces increase and decrease
rapidly with time and have a peak of about 50
kN. The loading duration is about 50 ms.

0

10

20

30 40 50
Time (ms)

60

70

80

90

Horizontal Disp., u (mm)(a) Measured force

The measured static and dynamic horizontal
load-horizontal displacement relations of P1
and P2 are shown in Figs. 16 and 17,
respectively. It can be seen from the figuresthat there are good agreements between themeasured load displacement relations fromthe static load tests with continuous loading
and that from the static load tests with step
loading. On the other hand, the measured load
displacement relations from the dynamic load
tests are totally different from the measured
static load displacement relations. Therefore,
in order to obtain the static load displacement
relation of the pile from the measured signalsof the dynamic load test, wave matching
analysis of the measured dynamic signals was
carried out using KWaveHybrid.

20
Measured
Calculated

15
10
5
0
-5

0

10

20

30 40 50
Time (ms)

60

70

80

90

400

Acceleration,2(m/s )(b) Measured and estimated displacement

Wave matching analysis results
Matching analysis was repeated with assumed
values for the maximum shaft limit horizontalpressure, 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 and themeasured pile displacement was obtained.
Soil parameters used in the final matching of
P1 are listed in Table 4. Fig. 14(b) and Fig. 18
show the displacement vs time and load
displacement relation of P1 in the final
matching analysis, compared with themeasured values.

300
200
100
0
-100
-200

0

10

20

30 40 50
Time (ms)

60

70

80

90

80

90

(c) Measured acceleration

Velocity, v (m/s)

1.2
0.9
0.6
0.3
0.0
-0.3
-0.6

0

10

20

30 40 50
Time (ms)6070(d) Velocity (integrate of acceleration by time)
It can be seen that the calculated dynamic pile
displacement underestimated the measured
values after the peak displacement. This isthought to be due to the soil spring model. At
the present, the value of the soil springs in

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

695

Force, Fdyn (kN)60

The same analysis procedures as P1 werecarried out for P2. Soil parameters used in the
final matching of P2 are listed in Table 5. Fig.
15(b) and Fig. 20 show the displacement vstime and load displacement of P2 in the final
matching analysis, compared with themeasured values.

50
40
30
20
10
0

0

10

20

30 40 50
Time (ms)

60

70

80

90

Fig. 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 themeasured results.

20
Measured
Calculated

15

100

10
5

80
Force, F (kN)Horizontal Disp., u (mm)(a) Measured force

0
-5

0

10

20

30 40 50
Time (ms)

60

70

80

90

2

(m/s )(b) Measured and estimated displacement

40

400

0

300

0
5 10 15 20 25 30
Horizontal Displacement, u (mm)100

Fig. 16. Measured load-displacement of P1

0
-100
-200

100
0

10

20

30 40 50
Time (ms)

60

70

80

90

80
Force, F (kN)

Acceleration,

60

20

200

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

Dynamic
Static (Step)
Static (Cont.)

0.9
0.6

Dynamic
Static (Step)
Static (Cont.)

60
40
20

0.3
0.0

0

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

-0.3
-0.6

0

10

20

30 40 50
Time (ms)

60

70

80

90

Fig. 17. Measured load-displacement of P2
Table 4. Parameters for final matching of P1.

(d) Velocity (integrate of acceleration by time)

Depth (m)0 to 1>1

Fig. 15. Dynamic pile load test signals of P2.
Using the same soil parameters as shown in
Table 4, the static load displacement relationof P1 was estimated using KWaveHybrid. Fig.
19 shows the comparison of the estimatedstatic load displacement relation of P1 with themeasured value. It can be seen that theestimated result matches very well with themeasured one.

Gs (kPa)
1083
1083

s

0.3
0.3

qh (kPa)
1
Elastic range

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

696

Gs (kPa)
1539
1539

s

0.3
0.3

qh (kPa)
5
Elastic range

60

Fig. 22 shows the predicted displacement vstime and the predicted dynamic load
displacement relation of P1, compared withthe measured values.

Force, Fdyn (kN)50
40

Fig. 23 shows the predicted static load
displacement relation of P1, compared withthe measurement. It can be seen from thefiguresthat
althoughthepredicted
displacements overestimate the measured
values, there are reasonable agreements
between the predicted and the measured
values.

30
20
10
0

Calculated
Measured

0
3
6
9
12 15
Horizontal displacement, u (mm)100

Fig. 18. Dynamic pile load test results of P1

Force, Fsta (kN)

Force, Fsta (kN)

100
80
60
40
20
0

40

0

Estimated
Measured0 5 10 15 20 25 30
Horizontal displacement, u (mm)Horizontal Disp., u (mm)Fig. 21. Static pile load test results of P1.

Fig. 19. Static pile load test results of P1.
60
Force, Fdyn (kN)

60

20

0 5 10 15 20 25 30
Horizontal displacement, u (mm)50

Estimated
Measured80

Calculated
Measured40
30

20
Predicted
Measured

15
10
5
0
-5

0

10

20

30 40 50
Time (ms)

60

70

80

90

20

(a) Measured and predicted displacement.

10

60

0

0
3
6
9
12 15
Horizontal displacement, u (mm)Force, Fdyn (kN)50

Fig. 20. Dynamic pile load test results of P2.
Prediction analysis
In actual construction site, it would be very
useful to estimate the static load displacement
relation of the actual 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.

40
30
20
10
0

Predicted
Measured

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

697

Force, Fsta (kN)

100

Heerema, E. P., 1979. Relationships between
wall friction displacement, velocity andhorizontal stress in clay and in sand for piledriveability analysis. Ground Engineering,12(1).

80
60

Japanese
GeotechnicalSociety,
2002.
Standards of Japanese Geotechnical Society
for vertical load tests of piles. Japanese
Geotechnical Society, Tokyo.

40
20
0

Predicted
MeasuredJapanese Society of Soil Mechanics andFoundation Engineering, 1983. JSSMFE
standard method for lateral loading test for apile. Japanese Society of Soil Mechanics andFoundation Engineering, Tokyo.

0 5 10 15 20 25 30
Horizontal displacement, u (mm)Fig. 23. Predicted static load-displacement of
P1.

Kitiyodom, P. and Matsumoto, T., 2002. A
simplified analysis method for piled raft andpile group foundations with batter piles.
International Journal for Numerical andAnalytical Methods in Geomechanics, 26,
1349-1369.

CONCLUSIONS
A new numerical program KWaveHybrid foranalysing pile driving as well as static load test
in vertical and horizontal directions has beendeveloped in this study. Performance of the
program was verified through comparisonswith theoretical solutions

Kitiyodom, P. and Matsumoto, T., 2003. A
simplified analysis method for piled raftfoundations in non-homogeneous soils.
International Journal for Numerical andAnalytical Methods in Geomechanics, 27, 85109.

The developed program was then applied tothe dynamic and static horizontal load tests on
two steel pipe piles. A good matching between
the calculated and measured behaviours of
the piles during driving and during static load
test was obtained.

Kitiyodom, P., Matsumoto, T. and Kanefusa,N., 2004. Influence of reaction piles on the
behaviour of test pile in static load testing.
Canadian Geotechnical Journal, 41(3), 408420.

The identified soil resistance parameters of thesmaller diameter pile were used to predict the
behaviours of the bigger pile, and a goodprediction was obtained.

Litkouhi, S. and Poskitt, T. J., 1980. Damping
constant for pile driveability calculations.
Géotechnique, 30(1), 77-86.

REFERENCES
Matsumoto, T. and Takei, M., 1991. Effects ofsoil plug on behaviour of driven pipe piles. Soiland Foundations, 3(2), 14-34.

Deek, A. J. and Randolph, M. F., 1995. A
simple model for inelastic footing response totransient loading. International Journal for
Numerical and Analytical Methods inGeomechanics, 19, 307-329.

Mindlin, R. D., 1936. Force at a point interior ofa semi-infinite solid. Physics, 7, 195-202.
Newmark, N. M., 1959. A method ofcomputation for strucural dynamics. Journal of
the Engineering Mechanics Division ASCE,
85(EM3), 67-94.

Gibson, G. and Coyle, H. M., 1968. Soil
damping constant related to common soil
properties in sands and clays. Report No. 1251, Texas Transport Institute, Texas A&M
University.

Novak, M., Nogami, T. and Aboul-Ella F., 1978.
Dynamic soil reactions for plane strain case.
Journal of Mechanical Engineering ASCE,
104(EM4), 953-959.

Goble, G. G. and Rausche, F., 1976. Wave
equation analysis of pile driving-WEAP
program, prepared for the U.S. department oftransportation, federal highway administration,
implementation division, office of research anddevelopment.

698

Poulos, H. G. and Davis E. H., 1980. Pile
Foundation Analysis and Design, Wiley, NewYork.
Randolph, M. F. and Deeks A. J., 1992.
Dynamic and static soil models for axial pile
response. Proceedings of the 4th International
Conference on the Application of Stresswave
Theory to Piles, The Hague, 3-14.
Randolph, M. F. and Wroth, C. P., 1978.
Analysis of deformation of vertically loaded
piles. Journal of Geotechnical Engineering
ASCE, 104(12), 1468-1488.
Rausche, F., Moses, F. and Goble, G. G.,
1972. Soil resistance predictions from pile
dynamics Journal of the Soil Mechanics andFoundation Division ASCE, 98(SM9), 917-937.
Smith, E. A. L., 1960. Pile driving analysis by
the wave equation. Journal of the Soil
Mechanics and Foundation Division ASCE,
86(SM4), 35-61.
TNO, 1977. Dynamic pile testing. Report No.
BI-77-13.
Wakisaka, T., Matsumoto, T., Kojima, E. andKuwayama S., 2004. Development of a newcomputer program for dynamic and static pilethload tests. Proceedings of the 7 International
Conference on the Application of Stresswave
Theory to Piles, Kuala Lumpur, 341-350.

699