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NBSIR 88-3765

Effect of Blow Count on Energy

Transfer in SPT

Felix Y. Yokel

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

00 DEPARTMENT OF COMMERCE

56 0NAL BUREAU OF STANDARDS

88-3765

988

.2 I

NBSIR 88-3765

Jteaearch Information Center

(National bureau of Standards

Gaithersburg, Maryland 20899

effect of blow count on energy

TRANSFER IN SPT

m -37teC

\m

C.7K

Felix Y. Yokel

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Gaithersburg, MD 20899

July 1988

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
: : . •• •< -i '

•••i • • ''
ABSTRACT

A rigid-hammer model is used to investigate the effect of the

blow count in Standard Penetration Tests on the energy

transmission characteristics of the tests. It is shown that the

percentage of the impact energy used to advance the sampler

decreases with an increase in blow count and could increase

somewhat with increasing drill rod size, and that for low blow

counts several penetration cycles are required to transmit the

energy to the sampler. The effect of the blow count on the

energy loss associated with short drill rod lengths is also

investigated. It is shown that the energy loss associated with

the short-rod effect is less than that predicted when total

energy rather than useable energy is considered, and that the

energy loss decreases with an increase in blow count.

Keywords: Boring? energy transfer? field tests? in-situ

soil sampling? Standard Penetration Test? wave equation.

testing?

iii
.

.

IV
TABLE OF CONTENTS

ABSTRACT iii

NOTATION iv

INTRODUCTION 1

FORCES AND PARTICLE VELOCITIES IN THE DRILL ROD 1

ENERGY AVAILABLE FOR PENETRATION 3

BLOW COUNT VS. RESISTANCE AND ENERGY EFFICIENCY 6

LIMITATIONS OF THE MODEL USED 11

SHORT DRILL RODS 12

COCLUSIONS 16

REFERENCES 16

V
NOTATION

The

a =

c =

E

rl

E

P

"

E

s =

Ers=

ERp=

ERS = Frd=

E

ru

=

F

s =

t = Mh

= N =

s =

t = t* = Vv

' =

0 = V

<5

p

following symbols are used in this paper.

cross section area of drill rod in m

3

stress wave propagation velocity in steel in m/s

= energy transfered to a long rod in N-m

energy used for sampler penetration in N-m

energy used for sampler displacement in N-m

energy transfered to a short rod in N-m

energy fraction used for sampler penetration

energy fraction used for total sampler displacement

force transmitted through rod by downward moving stress

wave in N

force transmitted through rod by upward moving stress

wave in N

force exerted by soil on sampler in N

length of drill rod in m

mass of hammer in Kg

blow count in SPT in blows/ft (blows/ . 3048m)

distance of sampler penetration in m

time in s time at which soil penetration ceases in s impact velocity of hammer in m/s

effect of v0

' below anvil in m/s

particle velocity in m/s

elastic soil compression in mm

mass density of steel in kg/m3

Subscripts

d = downward direction

(n)= penetration cycle number

p = subscript for soil penetration (velocity)

u = upward direction
INTRODUCTION

Part of the energy transmitted in the Standard Penetration Test

(SPT) from the hammer to the drill rod advances the sampler into

the soil, and thus is responsible for the "blow count" (N) . Another part of the energy remains in the drill rod as strain

energy of deformation and kinetic energy associated with the

travelling stress wave and does not contribute to the penetration

of the sampler into the soil. A rigid-hammer model is used to

study the effect of the blow count on the energy transfer

mechanism, the efficiency of energy transmission, and the time

required for energy transfer. The model has been previously used

to study drill rod length effects (4), and it has been

demonstrated in that case that the simplifying assumptions

associated with the rigid hammer model did not significantly

affect the results. The model does not deal with energy losses

associated with the hammer/anvil geometry, nor does it consider

energy loss by damping in the drill rod, for which no data are

presently available.

FORCES AND PARTICLE VELOCITIES IN THE DRILL ROD

It has been shown (3) that a compressive-stress wave, imparted to

a fixed-ended prismatic rod is reflected from the fixed end,

where the stress is twice the stress of the arriving stress wave.

The presence of the reaction force needed to reflect the

compressive-stress wave is a necessary and sufficient condition

for end fixity. Therefore, the drill rod in the SPT will act

like a "fixed ended" rod from the instant when the force

1
imparted to the sampler by the arriving stress wave is one-half

the force required to advance the sampler into the soil. The

energy of the stress wave arriving at the sampler after this

instant does not contribute to further sampler penetration.

Thus, the amount of energy which is used to advance the sampler

decreases with increasing soil resistance.

At the instant sampler penetration ceases:

F

s = ^ F rd (1)

in which: F

g = Force exerted by the soil on the sampler, and

F rd = Force transmitted to the sampler by the arriving

stress wave.

The time variation of the force arriving at the sampler is (4)

:

F rd (t) = av 0 'cp exp[ (-ac p/Mh

) t] (2)

in which: Mh = mass of hammer (63.5 kg standard)

v

0

'= hammer impact velocity

a = hammer contact area (assumed equal to cross

section area of rod)

c = stress wave propagation velocity ["bar

velocity" (3)] in steel=5047m/s

p = mass density of steel = 7850 kg/m3

t = time elapsed from the arrival of the front of the

stress wave at the sampler

The resultant force F(t) acting on any cross section of the drill

rod at any given instance is:

F (t ) = F rd + F ru (3)

in which: F rd = the force attributable to a downward moving

stress wave

F ru

= f° rce attributable to an upward moving

(reflected) stress wave

The particle velocity in the drill rod at any cross section can

be calculated from the forces attributable to the downward and

upward moving stress waves as follows (3)

:

v = vd

- v u = (1/ac P ) (F rd - F ru ) (4)

2
in which: v = resultant particle velocity

vd and v u are particle velocities that would result if

F rd or F ru respectively were acting alone.

In equations 3 and 4 compressive stresses and downward particle

velocities are taken as positive, tensile stresses and upward

particle velocities are taken as negative.

ENERGY AVAILABLE FOR SOIL PENETRATION

If it is assumed that before the onset of sampler penetration the

soil compresses elastically and that during sampler penetration

the soil deformation is plastic and thus the force exerted by the

soil on the sampler is reasonably uniform (an elasto-plast ic

model) , then:

F

s = 1/s (E s - F

s 6 /2) (5)

in which: E

g = Total energy used to advance the sampler

(including elastically stored energy)

,

s = Distance of sampler penetration, and

6 = Downward displacement of the sampler caused by

elastic soil compression prior to penetration.

If a rigid-plastic model for soil resistance is used (the elastic

soil deformation prior to sampler penetration is assumed to be

zero) the energy used for sampler penetration can be calculated

as follows:

At the sampler, the soil resistance during the penetration must

be F g# To maintain this reaction force, a force equal to F

g -

F rd is reflected from the end of the rod and propagates upward.

If F

g - F rd is negative this latter force is a tensile force.

Thus at the sampler:

v

p

= vd-v u = (l/acp)[F rd - (F

s -F rd )] = (1/acp ) (2F rd-Fg

) . . (6)

in which: Vp = velocity of soil penetration.

As noted above, soil penetration will continue until F

g = 2F rd . The time from the arrival of the compression wave at the sampler

3
at which this condition occurs is designated as time t*. After

time t* penetration will cease (or cease temporarily as explained

later) . Thus the energy used for sampler penetration,

t* t*

E

s = J

F s Vp dt = —-- j

|

2av 0 cp exp[-(acp /Mh

)t] - F

s |dt =

in which:

= F

s/acp

|

2M^v0 [1-exp (-acpt*/Mh ) ] - F s t*j (7)

t* = (Mh/acp) [ln(2F0/F s

) ] [from (1) and (2)]

F

o

= av Q cp

v Q is v 0

* adjusted for the anvil effect.

F

s = 2F rd = 2av 0 cpexp(-acpt*/Mh ) Equation 7 accounts for the part of the energy contained in the

initial downward moving stress wave which is utilized for soil

penetration and thus dissipated. The rest of the energy is

contained in the stress wave reflected upward from the end of the

drill rod. The magnitude of this reflected stress at any time

is: F ru = F s - F r £. If this quantity is negative, the reflected

stress (F ru ) is tensile. This tensile stress propagates to the

top of the rod , and if the arriving tensile stress exceeds the

stress exerted by the hammer on the upper end of the drill rod it

separates the rod from the hammer (this would be the case for the

range of rod lengths and blow counts which are of practical

interest) . After hammer separation, the resulting reaction force

at the top of the drill rod is zero, and therefore the upward

moving stress wave is reflected and propagated down as a stress

wave of equal magnitude and opposite sign. Thus the tensile

stress wave initially reflected from the sampler returns to the

sampler as a compressive-stress wave. This second cycle of

compressive stress will further advance the sampler if the

compressive stress propagated downward exceeds F

g/2. If the soil

resistance is low (the blowcount is low) , there are several

penetration cycles until the entire energy available for soil

penetration has been utilized.

4
In each successive increment of sampler advance the force in the

compressive-stress wave arriving at the sampler is reduced by F_.

The following equations can be written for the energy utilized in

any one penetration cycle:

E s(n) = F s/acp j 2Mhv 0 [l-exp(-acp t (n) /Hh ) ]-F s (2n-l)t (n) ! (8)

t(n) =(Mh/acp ) [ln(F0/F (n) )] (9)

F(n) = F s (n-0 .5) (10)

in which: t( n )=the time elapsed between the arrival of the

reflected compressive stress wave at the sampler

and the cessation of sampler penetration in the

nth penetration cycle. In the first (n = 1)

penetration cycle t^

n ^=t*.

The advance of the sampler in each penetration cycle, S( n ), can

also be calculated. For the rigid-plastic model examined:

s (n) =Es (n)/F s =1/ ac P {2Mh

v o[ 1 - exP(-ac Pt (n)/MhU-Fs (2n-l)t (n) )

• ••• \ ± ± ) The total advance of the sampler per blow, s, and the blow count,

N, are calculated as follows:

n

s = V S (n) (12); N = 0 .3048 (m) / s (12)

n=l

The energy efficiency of the soil penetration, which is the

percentage of the energy passing through the rod below the anvil

actually used to advance the sampler, can be calculated as

follows

:

n

ERs =

( ^

]

E s(n))/E thru

n=l

in which E

t ^ ru is the energy passing through the rod below the

anvil. The fraction of the potential energy of the hammer

utilized for soil penetration can similarly be calculated if the

energy loss in the hammer/anvil system is known.

5
BLOW COUNT VS. SOIL RESISTANCE AND ENERGY EFFICIENCY

The relationship between the blow count (N) and the soil

resistance, F

s , and the fraction of E t ^ru used for soil

penetration, ERS , were calculated for a rigid-plastic soil

penetration model and an A, as well as an NW rod. The following

quantities were used in the calculations, in addition to those

noted in Eq. (2)

:

Drill rods: A rod ap = 5.97 kg/m

NW rod ap = 8.18 kg/m

Energy/velocity: E thru = °- 64 E (free fall) = 304.2 N-m

v Q

= 0.8v (free fall) = 3.095 m/s

Force in drill rod: A rod F

Q

= 93,261 N

NW rod F

q

= 127,785 N

The results of the calculation are shown in figures 1 through 4.

Figure 1 shows plots of F

r ^(t) for the A and NW rods. The plots

were calculated for a rigid-hammer model using Eq(2). Note that

the initial force in the NW rod is larger than that in the A rod.

Because the total energy is the same for both rods, the force in

the NW rod decays faster with time than that in the A rod.

Figure 2 shows a plot of ERS as a function of the blow count, N,

calculated for an A rod and a rigid-plastic soil resistance

function. ERS is given as a percentage of E t ^ ru . The upper curve

in figure 2 shows the total percentage of energy utilized for

soil penetration. It is obvious that the energy utilized

decreases with increasing blow counts, because the force in the

downward moving compression wave at which penetration ceases

increases with the blow count. The dashed curves in the figure

show the cumulative percentage of energy utilized in successive

penetration cycles. Note that the energy utilized in the first

cycle reaches a maximum at an approximate blow count of 60. At

this blow count the energy content of the reflected stress wave

is the least. At smaller blow counts the amount of energy

6
TIME, ms

Figure Is Force propagated down in the drill rod as a function of

time for A and NW rods.

7
120

100

80

60

Jjc:

LL

40

20

0

Figure 2s Energy Fraction Used For Soil Penetration as a Function of Blow Count Calculated For a Rigid Plastic

Soil Resistance Function and an A rod (no damping)

8
140

120

100

80

60

40

20

0

N, blows per ft.

Figure 3: Energy Fraction Used For Soil Penetration as a

Function of Blow Count Calculated For a Rigid Plastic

Soil Resistance Function and an NW rod (no damping)

.

9
100

80

60

2

JSC

CO 40 LL

20

0

Figure 4s Effect of Drill Rod Size on the Energy Fraction Used

for Penetration and the Soil Resistance,

10
utilized in the first penetration cycle decreases, but additional

energy is utilized in successive penetration cycles. The smaller

the blow count, the more penetration cycles are needed to utilize

the energy available for soil penetration. Figure 2 also shows

the soil resistance force F

g

. it is obvious that this latter

force increases with increasing blow counts.

Figure 3 is a plot of ERS versus N for the NW rod, and figure 4

shows a comparison between results for A and NW rods. Note that

more energy is utilized for soil penetration when an NW rod is

used. However a comparison of soil resistances F

g associated

with particular blow counts indicates that the effect of the rod

size on the blow count decreases with decreasing blow counts.

The effect seems insignificant for blow counts smaller than 40.

LIMITATIONS OF THE MODEL USED

When interpreting the results shown in figures 1 through 4 it is

important to recognize the limitations of the model used. Some

of these limitations are:

1. A rigid hammer model was used to calculate the force imput

.

While a comparison of published results in refs. (2) and (4)

indicates that results obtained by a more accurate theoretical

representation of actual hammer characteristics do not

significantly differ from those obtained with a rigid hammer

model, force versus time signatures obtained in field

measurements (1) are more complex and irregular than those in

figure 1.

2. In the absence of measured attenuation data it was assumed

that the stress wave propagating up and down the drill rod,

sometimes for large cumulative distances, does not decay as it

travels along the rod. Consideration of damping in the drill rod

would result in reduced energy utilization for lower blow counts.

11
and thus tend to reduce the difference in energy utilization

between high and low, blow counts. It would also eliminate some

of the penetration cycles at lower blow counts.

3. The hammer contact area could differ from the drill rod cross

section, resulting in a different force in the rod, and perhaps

altering or eliminating the drill rod size effect shown in Fig. 4.

4. The rigid-plastic soil penetration model does not consider the

energy tied up in elastic soil compression. Since this energy. is

not independent of soil type, it is difficult to generalize its

effect. Figure 5 shows a comparison between the results obtained

from a rigid plastic and an elasto plastic soil resistance model

for an NW rod. An elastic soil compression of 2 mm was assumed

for all blow counts in the elasto-plast ic model. Inherent in

this assumption, which is similar to assumptions made in pile

analysis, is the concept that soil stiffness is proportional to

the blow count. Note that the effect of elastic soil compression

increases with increasing blow counts. For large rod lengths the

soil could de-compress between successive compression cycles.

This would tend to increase the relative effect of soil

compression with decreasing blow counts, since some energy would

be used for elastic re-compression.

SHORT DRILL RODS

The effect of the blow count on the energy loss when short drill

rods are used is also of interest. This effect is caused by the

premature cutoff of the energy transfer from the hammer to the

drill rod when the reflected tensile-stress wave reaches the

hammer/anvil interface at time t = 2t /c, in which l = length of

drill rod. If the energy transferred before the return of the

tension wave to the hammer equals or exceeds the energy that can

be utilized for soil penetration the rod length will have no

effect on the blow count. If all of the usable energy is not

12
100

80

60

40

20

0

Figure 5: Comparison of Energy Fractions Used For Soil

Penetration and Soil Resistance as a Function of

Blowcount Calculated for a Rigid-Plastic Soil

Resistance Function and an Elasto—Plastic Function With

an Elastic Soil Displacement of 2 mm at Penetration.

13

F

s

, kN
transferred, the rod length should be taken into consideration.

Since the energy that can be utilized increases with decreasing

blow count, the short-rod effect will increase with decreasing

blow count.

The effect of the drill rod length and the blow count on energy

transmission by short drill rods is shown in Fig. 6. It has been

shown (4) that the fraction of the impact energy transmitted to

the drill rod during time t = 2 l /c can be calculated by the

following equation:

E

rs/E r i = 1 - exp(-4M r/Mh ) (14)

in which E

rs is the energy transfered to the short rod, E r y is

the energy that would be transfered to a long drill rod, M r =a 'p = mass of drill rod. Equation (14) accounts for the fraction of

the total energy which is transmitted to the drill rod. However

part of the energy that is not transmitted would not have

contributed to sampler penetration. In Fig. 6, Eq. (14) for an

NW rod is compared with the fraction of the energy that can

actually be used for various blow counts, which is transmitted by

the short rod. This energy fraction was calculated by

substituting 2 i/

c

for in Eq.8 whenever 2i/z is smaller than

t (n)r and dividing the result by Eq.8. Note that the energy

fraction is plotted against blow counts that would have resulted

if a long rod were used (the actual result of the unutilized

energy would be to increase the short-rod blow count for the same

soil resistance) . It can be seen from Fig. 6 that the energy

loss associated with the short-rod effect is less than that

predicted when total energy, rather than usable energy is

considered and that the energy loss decreases with an icrease in

blow count.

14
PERCENT OF LONG-ROD ENERGY

Figure

0 20 40 60 80 100

6: Effect of Drill Rod Length on Energy Transmission

15
CONCLUSIONS

The energy transfer during sampler penetration in the SPT is

studied using a closed-form solution for a rigid-hammer model and

a rigid-plastic soil resistance function. It is shown that the

energy utilized for soil penetration decreases with increasing

blow counts, and that several penetration cycles are required to

transfer the energy at low blow counts. It is also shown that the

energy utilization for an NW rod is somewhat more efficient than

that for an A rod, but that more penetration cycles are required

to transfer the energy from an NW rod and that the rod size would

not have a significant effect on the blow count for blow counts

less than 40. The energy utilization has also been determined

for one particular elasto-plastic soil resistance function and an

NW rod. Damping has not been considered because of lack of

available data. It is reasoned that in actual field conditions

the energy transfer efficiency is reduced for low blow counts and

some of the penetration cycles are eliminated. The effect of

energy loss caused by using short drill rods is also examined. It

is shown that the energy loss associated with the short-rod

effect is less than that predicted when total energy, rather than

usable energy is considered and that the energy loss decreases

with an icrease in blow count.

REFERENCES

(1) Kovacs, W. D., Salomone, L. A. and Yokel, F. Y., "Energy

Measurement in the Standard Penetration Test," NBS Building

Science Series 135, Washington, D.C., Aug., 1981.

(2) Palacios, A., "The Theory and Measurement of Energy Transfer

During Standard Penetration Test Sampling," thesis presented

to the University of Florida, Gainsville, FL., 1977.

(3) Timoshenko, S. and Goodier, T. N., Theory of Elasticity . 3rd

ed. , Chapter 14, Sections 168 and 169, McGraw-Hill

Publishing Co., Inc., New York, NY, 1970, pp. 496 and 499.

(4) Yokel, F. Y., "Energy Transfer in the Standard Penetration

Test, Journal of the Geotechnical Engineering Division , ASCE, Vol . 108, No. GT9 , Sept., 1982, pp. 1197-1202.

16
NBS-114A (rev. 2 - 8 C) 1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

NBSIR 88-3765 JULY 1988

U.s. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions) 4. TITLE AND SUBTITLE

Effect of Blow Count on Energy Transfer in the SPT

5. AUTHOR(S)

Felix Y. Yokel

6 . PERFORMING ORGANIZATION (If joint or other than N BS, see instructions)

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8 . Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gn i fi cant

bi bliography or literature survey, mention it here)

A rigid-hammer model is used to investigate the effect of the blow count in

Standard Penetration Tests on the energy transmission characteristics of the tests.

It is shown that the percentage of the impact energy used to advance the sampler

decreases with an increase in blow count and could increase somewhat with increasing

drill rod size, and that for low blow counts several penetration cycles are required

to transmit the energy to the sampler. The effect of the blow count on the energy

loss associated with short drill rod lengths is also investigated. It is shown that

the energy loss associated with the short-rod effect is less than that predicted when

total energy rather than useable energy is considered, and that the energy loss

decreases with an increase in blow count.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) boring; energy transfer; field tests; in-situ tests; soil-sampling;

Standard Penetration Test; wave equation

13. AVAILABILITY

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