DEVELOPMENT OF A NEW COMPUTER PROGRAM FOR
DYNAMIC AND STATIC PILE LOAD TESTS
T. Wakisaka i), T. Matsumoto ii), E. Kojima iii) & S. Kuwayama iii)
ABSTRACT It has been believed that the static load test is the most reliable method to obtain theload-settlement relation of a pile. Most static load tests are conducted using reaction piles as thereaction system. However, some researches point out that the influence of the reaction piles on themeasured load-settlement relation may not be neglected, and that an analysis of the measured data isrequired to obtain a true load-settlement of the. From this point of view, the dynamic load testing or the
rapid load testing may not be necessarily inferior to the static load test, considering cost and time
performance of the dynamic load test as well. In this study, a new computer program for analysing thestress-wave propagation phenomena in pile driving was developed using a finite difference scheme andrational soil resistance models. Verification analyses of the proposed method are conducted first, and thenthe developed method is applied to the dynamic and static load tests on an end-bearing concrete pile.
Keywords: pile driving analysis, static analysis, finite difference, wave-propagation equation,

1. INTRODUCTION
To obtain the load-settlement relation of a pile, it
has been believed that the static axial load test is
the most reliable method. Most static load tests

are conducted using reaction piles as thereaction system. However, Latozle et al. (1997),
Poulos (1998) and Kitiyodom, Matsumoto &Kanefusa (2004) suggest that the influence of thereaction piles on the measured load-settlement
relation may not be neglected, and that an analysisof the measured data is required to obtain a trueload-settlement of the pile.
The dynamic load testing and the rapid load
testing are unsusceptible to reaction piles. The
dynamic load testing requires less time and costcompared to the rapid load testing. Thus, thedynamic load testing can be applied to many piles
in a construction site to determine the distributionof pile capacity that could be used in reliability
design of the pile foundation (Hayashi, Matsumoto& Suzuki 2000).
Several computer programs for analysing the
one-dimensional wave propagation in a pile havebeen developed, such as Smith method (Smith
1960), WEAP (Goble & Rausche 1976), CAPWAP(Rausche et al. 1972), TNOWAVE (TNO 1977),
KWAVE (Matsumoto & Takei 1991) and others.
Recently, analytical methods based on thecharacteristic solutions of the one-dimensional

wave equation without skin friction may beprevailing. The characteristic method treats skinfrictions as discrete concentrated forces, and deals
with them as external forces acting along the pile
shaft. In the authors' experience, the calculation
using the characteristic method tends to oscillate
or diverge when very large values of the soil
stiffness or the damping are encountered. Recently
in Japan, impact force applied to a test pilesometimes reaches the point that near the yieldstress of the pile. In such pile driving,
non-linearity of the pile material, especially forconcrete piles, would be taken into account in the
wave propagation analysis.
In this study, a numerical method for the
one-dimensional wave equation in which the shaft
resistance of the pile is explicitly considered wasdeveloped using finite difference scheme. The
proposed method is incorporated in a computer
program KWAVEFD. The program can consider
changes in the pile section and non-linearity of thepile material. Furthermore, the program can bealso used to calculate the static load-settlement
relation of a pile.
In order to examine the validity of the newly
developed program, verification analyses wereconducted, and responses of the incorporated soilmodels are demonstrated first. Then the program isapplied to the static and dynamic load tests of an
end-bearing concrete pile.

i) Graduate student, Graduate School of Kanazawa University, Kanazawa, Japanii) Professor, Department of Civil Engineering, Kanazawa University, Kanazawa, Japaniii) Geotop Corporation, Tokyo, Japanwhere G and Vs are the shear modulus and theshear wave velocity of the surrounding soil
respectively.
The dynamic friction, τd, is generally taken as a
non-linear function of velocity, according to

2. THEORETICAL BASIS
2.1 Finite difference approximation of wave
equationIn the proposed method, the differential equation(Eq. (1)) for the one-dimensional wave
propagation in a pile is solved by means of a finite
difference scheme.
2
12
∂2w
2 ∂ w
+ Hτ , H = −
c
=
2
2
ρr
∂x
∂t

β

 ∆v  τ d = τ max 1 + α   
 v0  where τmax is the static maximum shaft friction, v0
is a reference velocity (taken for convenience as 1m/s), and ∆v is the relative velocity between thepile and the adjacent soil. Non-linear viscous laws
similar to Eq. (4) have been proposed by Gibson
and Coyle (1968), Heerema (1979) and Litkouhi
and Poskitt (1980), all of whom suggest a value ofβ close to 0.2, with the parameter α varying fromabout 0.1 for sand, to unity for clay soils (after
Randolph & Deeks 1992). The relation of Eq. (4)was introduced into the viscous damping in Fig. 2.

(1)

in which, t is the time, x the coordinate along thepile axis, c the wave velocity, τ skin friction, andw, r, ρ are the displacement, the radius and thedensity of the pile, respectively. In Eq. (1), theinfluence of skin friction (or end resistance) is
explicitly considered, unlike the characteristic
solutions of the wave equation.
Finite difference approximation for Eq. (1) isexpressed by Eq. (2) to take into account a change
in pile section properties shown in Fig. 1.

Pile nodewi , j +1 = 2wi , j − wi , j −1

dashpot cv(viscous)slider τmax2
 ∆t   ×( Ai ρi + Ai +1 ρi +1 )  ∆x 
2

+

(4)

Soil adjacent to pile

( Ai +1 Ei +1 wi +1, j − Ai Ei wi , j − Ai +1 Ei +1wi , j + Ai Ei wi −1, j )−U i + U i +1(∆t ) 2τ i , j
Ai ρi + Ai +1 ρi +1(2)

spring ks

where ∆t is the time increment, A is the cross-sectionalarea, E the Young's modulus, U the circumferential
length of a pile element having a length of ∆x.
Subscripts 'i' and 'j' denote node number and time step,
respectively.
i-1

i
Ai

ρi

Ei
Ui

i+1
Ai+1

ρi+1

τi

Ei+1
Ui+1

x

Figure 1. Notations used
2.2 Soil models

Figure 2 shows the shaft resistance model
incorporated into KWAVEFD. The values of the
shaft spring, ks, and the radiation damping, cr, perunite area are approximately obtained from thework of Novak et al. (1978) as follows:

ks =
2

2.75G
G
, cr =
2π r
Vs

Soil far from pile (fixed)

Figure 2. Shaft resistance model(after Randolph & Simons, 1986)

Figure 3 shows the pile base resistance model.
The value of the soil spring, kb, the damping, cb(cb1= cb2), and the lumped soil mass, mb, per unit
base area can be estimated as follows (Deeks &Randolph 1993):

kb =

∆x

(3)

dashpot cr(radiation)

4G
3.4 G
, cb =,
π r (1 − ν )π (1 − ν ) Vs

(5)
0. 1 − ν 4
mb = 16r
ρs
π (1 − ν )where ν and ρs are the Poisson's ratio and thedensity of the soil respectively.
Non-linear response of the soil spring at the pilebase can be taken into account, based on an
empirical relation of Eq. (6) (Chow 1986).

q
kb = 1 − Rf  kb 0
qb 


(6)

Spring kb

Dashpot cb1

Lumpedmass mb

Figure 3. Pile base resistance model(after Deeks & Randolph, 1995)
In Eq. (6), Rf is the reduction coefficient, q is
the static base stress (stress in the spring), qb is thestatic ultimate base resistance, and kb0 is the initialspring stiffness.
The typical response of the non-linear soil
spring is illustrated in Figure 4. The soil spring
response in unloading and reloading stages ismodelled as linear having the stiffness of kb0.
The program KWAVEFD can be used for
estimating the pile and soil behaviours subjected
to static, rapid and dynamic loading.
τstatic

or q

Table 1. Specifications of homogeneous pile
Length (m)10Diameter (mm)400
Cross-sectional area (m2)0.126
2Young's modulus (kN/m )3.0×107
Wave velocity (m/s)
5000
Density (ton/m3)
1.2
Mass (ton)1.51
2Dashpot cb2

Slider qb

velocity is 5000 m/s. The compression stress isreflected at the pile base, and it goes back to thepile head as the tension stress and reaches the pilehead at t = 4 ms. The calculated results are in good
agreements with these theoretical solutions. Figure
7 shows the time vs. pile displacement at the
middle point (x = 5 m). A good agreement between
the theoretical and calculated values can be seen
again.

Stress (MN/m )Pile node

20
15
10
5
0
0

static123Time (ms)

4

5

20

2

Stress (MN/m )Figure 5. Pile head stress

3. VERIFICATION ANALYSES
3.1 Comparison to theoretical values

The wave equation free from the skin friction has
the theoretical solutions. Therefore, impacts on ahomogeneous pile and a non-homogeneous pile
without soil resistance are calculated by the
program KWAVEFD, and the calculated results
are compared with the theoretical values in below.
3.1.1 Homogeneous pile

Table 1 shows the specifications of ahomogeneous pile to be analysed here.
Figure 5 shows the impact stress applied to thepile head. Figure 6 shows the calculated andtheoretical distributions of axial stresses along thepile. Theoretically, the front of compression stressreaches the pile base at t = 2 ms because the wave
3

10

t = 2 ms

0
-10
-20
0

t = 4 ms

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

2
4
6
8
Pile distance (m)10Figure 6. Distributions of the stresses in the pile

Pile displacement (mm)

Soil displacement
Figure 4. Non-linear soil model10
Calculated
Theoretical

8
6
4
2
0
0

x=5m

2

4
6
Time (ms)8

Figure 7. Time vs. pile displacement103.1.2. Non-homogeneous pileMh = 1.51 ton

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 the same material but different
cross-sectional areas; the cross-sectional area ofthe lower section is twice the upper section. The
impact stress shown in Figure 5 was used in thisanalysis again.
Figures 8 and 9 show time vs. velocity and timevs. displacement at the pile head, respectively.
Good agreements between the calculated andtheoretical results can be seen in both the velocity
and displacement.

Calculated
Theoretical

2

4

6

8

10

Pile head disp (mm)Figure 8. Time vs. pile head velocity
10
Calculated
Theoretical

8
6
4

x=5m
Vibration
solution

5
0
-5
Cal.

-10
0

50

100

150

Time (ms)2

Figure 11. Time vs. pile disp. (without damping)
2

4

6

8

10

Time (ms)Figure 9. Time vs. pile head displacement
3.2 Friction pile with elastic soil response

It is known that the one-dimensional wave
equation considering skin friction has no
theoretical solutions. Hence, a perfect friction pile
without base resistance with elastic firction
response is analysed, and the calculated results arecompared with the theoretical solutions of thesingle mass system shown in Figure 10.
4Specifications of the pile to be analysed here are
the same as Table 1. The values of the shaft spring
stiffness, ks, and the radiation damping, cr, wereset as ks = 2.0×103 kN/m3 and cr = 5.0 kN・s/m3
along the pile shaft uniformly for convenience.
The corresponding values of the total spring
stiffness, Ks, and the total damping, Cr, in the
single mass system are shown in Fig. 10.
Figures 11 and 12 show time vs. displacementof the middle point of the pile without damping (cr= 0) and with damping, respectively. Overall, thecalculated results are in good agreements with thetheoretical solutions in both cases. Periodical
oscillations having a period of 2L/c can be seen in
the calculated results, which are never seen in thetheoretical solutions. It is interesting to note thatthese oscillations in the calculation results reflect
the wave propagation phenomena in the pile,which cannot be simulated using the single mass
system.
10

Time (ms)00Figure 10. Single mass system

Pile disp. (mm)

10
8
6
4
2
0
-2
-4
0

Cr = 62.8 kN・s/m

Pile disp. (mm)Velocity (m/s)

Table 2. Specifications of non-homogeneous pile
Upper
Lower
Length (m)55Diameter (mm)
100
141.4
Cross section area (m2)
7.85×10-3 15.7×10-3
2
Young's modulus (kN/m )3.0×107
3.0×107
Wave velocity (m/s)
5000
5000
Density (ton/m3)
1.2
1.2

Ks = 2.51×104 kN/m

10
5

Peaks from solution
with damping

x=5m0
Calculated

-5

-10
0

Theoretical solution
with damping

50

100

150

Time (ms)Figure 12. Time vs. pile disp. (with damping)3.3 Responses of soil resistance models

Figure 13 shows the mobilisations of the shaft
resistance at the middle point of the pile (x = 5 m)
calculated from Types F1, F2 and F3. It can beseen that the separation of the pile and the adjacentsoil and re-join of them are well simulated. It isalso seen that the effects of the radiation damping,cr, and the dependency of the dynamic shaft
resistance on the relative velocity between the pileand the adjacent soil after yielding (i.e. effects of
α and β) are well simulated.
Figure 14 shows the time vs. pile displacement
calculated from Type F3. The displacements of thepile and the soil are calculated separately after theyielding. The rebound of the pile as well as thesoil are simulated well.
Figure 15 shows the mobilisations of the baseresistance calculated from Types B1, B2 and B3. It
is seen that the effects of the radiation damping(cb1) and the lumped soil mass (cb2 and Mb) are
well simulated and that these effects are very large
in pile driving.
5

τ (kPa)

40
20
0

-20

x=5m

-40

0

1

2

3

4

5

Pile disp. (mm)Type F1 (ks alone)
Type F2 (ks, cr)
Type F3 (ks, cr, α, β)Figure 13. Mobilisation of the shaft resistance

Displacement (mm)Table 3. Soil resistance parameters
G (kN/m2)
5000
νs
0.5
Soil
ρs (ton/m3)
1.8
τs (kN/m2)
30
Shaft resistanceks (kN/m3)
10942(in perfect friction cr (kN⋅s/m3)
94.9
pile)
α
1.0
β
0.2
2
qb (kN/m )600
Base resistancekb (kN/m3)
6.35×104(in perfectcb (kN⋅s/m3)
205.3
end-bearing pile)Mb (ton)
0.017

60

5
4
3

Pile disp.
Adjacent soil disp.

2
1
0

x=5m

-1
0

10

20

30

40

50

Time (ms)Figure 14. Time vs displacements
1600
1200

σb (kPa)To demonstrate the responses of the soil models(Figures 2 and 3), analyses of pile driving on aperfect friction pile and a perfect end-bearing pile
were carried out separately. The specifications of
the pile are the same as Table 1. The soil
parameters and the corresponding values of thesoil resistance models are summarised in Table 3.
The bi-linear response (Rf = 0) was assumed forthe soil springs. The impact stress shown in Fig. 5
was applied to the top of both piles.
Three types of pile driving analysis wereconducted for each pile. In the analyses of theperfect friction pile, ks alone was considered in
Type F1, ks and cr in Type F2, and ks, cr, α and β inType F3, in order to demonstrate the effect of eachcomponent. In the analyses of the perfect
end-bearing pile, kb alone was considered in TypeB1, kb and cb1 in Type B2, and kb, cb1 and cb2 (i.e.
Mb) in Type B3.

800
400
0
-400
0

5

10

15

20

25

Pile tip disp. (mm)Type B1 (kb alone)
Type B2 (kb, cb1)
TYpe B3 (kb, cb1, cb2, Mb)

Figure 15. Mobilisation of the pile base resistance
4. APPLICATION TO AN ACTUAL
END-BEARING CONCRETE PILE

The newly developed program KWAVEFD wasapplied to the static and dynamic load tests of an
actual end-bearing pile carried out by Kojima &Kuwayama (2003).

Table 4. Specifications of the test pile
Length (m)8Outer diameter (mm)400
Inner diameter (mm)2702Cross-sectional area (cm )684.1
Young's modulus (kN/m2) 3.92×107
Wave velocity (m/s)
4636
Density (ton/m3)
1.825
Pile mass (ton)1.0
xm = 900 mm

Measuringpoint

Ground8m
Steelcasing

600 mm
400 mmRubberplate

Figure 16. Illustration of the set pile
6

Pile head load (kN)

The test pile was a concrete pile, 8 m long and 400
mm diameter. The specifications of the test pile
are shown in Table 4. The test pile was inserted ina pre-installed steel pile casing having an innerdiameter of 580 mm (Fig. 16). A rubber membrane,
40 mm thickness, was placed beneath the pile base,making the test pile a perfect end-bearing pile.
Below the rubber membrane was a relatively hardsoil having the SPT blow count, N, of 15.
The static load test of the pile was carried out
prior to the dynamic load tests. The relationshipbetween the load and the pile base displacement isshown in Fig. 17. A linear relationship between
them was observed until the pile head load of 30
kN. From this result, the value of kb was estimated,
and the corresponding values of the shear modulus,
G, of the ground (the rubber membrane in thisparticular test) and cb were calculated using therelations in Eq. (4) with assumptions of the
Poisson's ratio ν = 0.3 and the soil density ρs = 1.8
ton/m3 for the first approximations to be used in
the wave matching analysis (Table 5).
In the dynamic load tests, the pile was driven byfalling a hammer mass of 0.3 ton onto the pilehead. Strains and accelerations were measured at
xm = 0.9 m below the pile head with a sampling
rate of 15 µs.

40
30
20
10
0
0

2

4

6

8

Pile base displacement (mm)Figure 17. Result of the static load test
Table 5. Soil parameters (initial values)
Spring stiffness, kb (kN/m3)
5.12×104
2
Shear modulus, G (kN/m )9.42×103
Damping, cb (kN⋅s/m3)
201.4
Added mass, mb (ton/m2)
0.31
Maximum base resistance, qb (kN/m2)
1200
4.2 Matching analyses of dynamic load tests

In the first pile driving test, the falling height of
the hammer was 1.1 m. The impact force on thepile head is shown in Figure 18. The impact force,
F(0, t), was obtained from the downward andupward travelling forces, Fd and Fu, measured at
the measuring point of xm = 0.9 m.

x 
x 


F (0, t ) = Fd  xm , t − m  + Fu  xm , t + m  (7)
c 
c 


The impact force in Fig. 18 was used as theboundary condition at the pile head in the piledriving analysis.
Figure 19 shows the results of the initialmatching analysis of the first driving. The soil
resistance parameters listed in Table 5 were usedin this analysis. Although periodic changes in thecalculated force and velocity correspond to themeasured results, their amplitudes overestimate
the measured results of force and velocity due tounderestimation of the radiation damping, cb.

Pile head force (kN)

4.1 Test description

700
600
500
400
300
200
100
0
-100
0

10

20

30

40

50

Time (ms)Figure 18. Measured pile head force in the 1st
drivingForce (kN)

800

Calculated
Measured

600
400
200
0

-200
-400
0

10

20

30

40

50

Time (ms)

4.3 Prediction analysis(a) Force at measuring point

Velocity (m/s)

2.0
1.6
1.2
0.8
0.4
0.0
-0.4
-0.8
0

Calculated
Measured

10

20

30

40

Hence, matching analysis was proceededchanging the cb value alone. The results of final
matching analysis are shown in Fig. 20. In thisanalysis, cb = 415 kN ⋅ s/m3 was assumed.
Remarkable agreements between the calculated
and measured results in both of force and velocity
were obtained. A larger value of the identified cb
compared to the initial assumption (cb = 201.4 kN⋅s/m3) may be attributed to the fact that the rubber
membrane beneath the pile base was underlain by
the hard soil as mentioned earlier.

50

The falling height of the hammer was reduced to
0.9 m in the second driving. The measured impact
force in this driving is shown in Fig. 21. The stressat the measuring point was predicted using thesame soil parameters identified in the final
matching analysis of the first driving.
The predicted and measured forces at themeasuring point are shown in Fig. 22. There is agood agreement between them, indicating thevalidity of the soil resistance parameters identified
in the matching analysis of the first driving.

Time (ms)800

Calculated
Measured

Force (kN)

600
400
200
0
-200
-400
0

Force (kN)(b) Velocity at measuring point
Figure 19. Results of initial matching analysis

700
600
500
400
300
200
100
0
-100
0

10

20

30

40

50

Time (ms)40

50

Figure 21. Measured pile head force in the 2nd
drivingCalculated
Measured

Force (kN)

Velocity (m/s)

30

800

Calculated
Measured

600
400
200
0

-200
-400
10

10

20

30

40

50

Time (ms)((b) Velocity at measuring point
Figure 20. Results of final matching analysis
720Time (ms)(a) Force at measuring point
2.0
1.6
1.2
0.8
0.4
0.0
-0.4
-0.8
0

10

20

30

40

50

Time (ms)Figure 22. Comparison of calculated and measured
forces at the measuring point in the prediction
analysis

4.4 Static analysis

KWAVEFD can be applied to not only the
dynamic load test but also the static load test. In
the static analysis, only loading rate on the pilehead is decreased to an acceptable level so that the
dynamic effects including wave propagation
phenomena and soil damping can be negligible.
The load-pile head settlement relation of the test
pile was calculated using KWAVEFD and iscompared with the measured one in Fig. 23. Goodagreement was obtained as expected.

Force (kN)40
30

Calculated
Measured

20
10
0
0

2

4

6

8

Pile head disp. (mm)Figure 23. Static load test analysis
5. CONCLUDING REMARKS

A new numerical program KWAVEFD for
analysing pile driving as well as static load test
was developed in this study, based on the finite
difference scheme. Rational soil resistance models
have been incorporated in the program.
Performance of the program was verified throughcomparisons with analytical solutions. Responsesof the soil models were numerically demonstrated.
The developed program was applied to the
dynamic and static load tests on a perfect
end-bearing concrete pile. A good matching
between the calculated and measured behaviour ofthe pile during driving was obtained. Then, theidentified soil resistance parameters were used in
prediction of the succeeding pile driving, and agood prediction was obtained. Furthermore,
KWAVEFD was applied to the analysis of thestatic load test successfully.
REFERENCES
Chow, YK (1986). Analysis of vertically loaded pilegroups. Int. Jour. for Numerical and Analytical
Methods in Geomech., 10: 59-72.

Deeks AJ & Randolph MF (1995). A simple model
for inelastic footing response to transientloading. Int. Jour. for Num. and Analytical

8

Methods in Geomech., 19: 307-329.
Gibson G & Coyle H.M (1968). Soil damping
onstant related to common soil properties in sandsand clays. Report No. 125-1, Texas Transport
Institute, Texas A & M University.
Goble G.G & 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.
Hayashi, M., Matsumoto, T. & Suzuki, M. (2000).
Dynamic load testing on 102 steel pipe piles forbridge foundations on mudstone. Proc. 6th Int.
Conf. on the Application of Stress-Wave Theory to
Piles, São Paulo, Brazil: 697 - 705.
Heerema E.P (1979). Relationships between wall
friction, displacemen, velocity and horizontal
stress in clay and in sand for pile driveability
analysis. Ground Engineering, 12(1).
Kitiyodom P, Matsumoto T & Kanefusa N (2004).
Influence of reaction piles on the behaviour of test
pile in static load testing. Canadian Geotechnical
Journal (to be published).
Kojima E & Kuwayama S (2003). Development of a
dynamic load test system on piles and its
verification in experiments. Proc. of the 48th
Goetechnical Symposium, JGS, Tokyo: 99-106.
Latotzke, J, König, D, and Jessberger, HL (1997).
Effects of reaction piles in axial pile tests. In
Proc. of the 14th ICSMFE, Hamburg, Germany,
2: 097-1101.
Litkouhi S & Poskitt TJ (1980). Damping constantfor pile driveability calculations. Geotechnique,30(1): 77-86.
Matsumoto, T & Takei, M. (1991). Effects of soil
plug on behaviour of driven pipe piles, Soil andFoundations 3(2): 14-34.
Novak M, Nogami T & Aboul-Ella F (1978).
Dynamic soil reactions for plane strain case. Jour.
of Mechanical Eng. Div., ASCE 104(EM4):
953-959.
Poulos HG (1998). Pile testing - From the designer's
viewpoint. Proc. of 2nd Int. Statnamic Seminar,
Tokyo, 1: 3-21.
Randolph MF & Deeks AJ (1992). Dynamic andstatic soil models for axial pile response. Proc. of
4th Int. Conf. on Application of Stress-Wave
Theory to Piles, The Hague: 3-14.
Randolph MF & Simons HA (1986). An improved
soil model for one-dimensional pile driving
analysis. Proc. of the 3rd Int. Conf. on Numerical
Methods in Offshore Piling: 1-17.
Rausche F, Moses F & Goble G.G (1972). Soil
resistance predictions from pile dynamics. Jour.
of the Soil Mech. and Found. Div., ASCE,
98(SM9).
Smith, E.A.L. (1960). Pile driving analysis of by thewave equation. J. Soil Mech. and Found. Div.,ASCE, 86(SM4): 35-61
TNO (1977). Dynamic pile testing. Report No.
BI-77-13