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Estimating Shear Strength Properties of Soils Using SPT Blow Counts: An Energy Balance Approach

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The subsurface exploration of a site is often the aspect of a project that gets overlooked during the design process. Many clients will get standard soil borings, but do not want to pay for a full laboratory analysis. Lack of data forces the designer to estimate important engineering properties of the soil. Very often the Standard Penetration Test (SPT) blow counts are used to estimate the shear strength properties of soil in foundation designs. Few correlations are widely used. However, no clear explanation is found to justify the selection most of these mathematical equations. This manuscript describes a new approach to estimate the shear strength parameters based on the SPT blow counts. In this method, the standard penetration test is treated analogous to driving a miniature pipe pile. The energy input to the soil is used to correlate the SPT blow count to the shear strength parameters of the soil at the depth of testing. Soil boring records from few different sites were analyzed and a statistical analysis revealed that the proposed method can provide a better estimation than the widely used existing correlations.
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ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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Estimating Shear Strength Properties of Soils Using SPT Blow Counts: An
Energy Balance Approach
Timothy Brown1 and Hiroshan Hettiarachchi2
1 Geotechnical Engineer, Commonwealth Assoc. Inc., 2700 West Argyle Street, Jackson, MI 49202;
tsbrown@cai-engr.com
2 Assistant Professor, Department of Civil Engineering, Lawrence Technological University, 21000
West Ten Mile Road, Southfield MI 48075; hiroshan@ltu.edu
ABSTRACT: The subsurface exploration of a site is often the aspect of a project that
gets overlooked during the design process. Many clients will get standard soil
borings, but do not want to pay for a full laboratory analysis. Lack of data forces the
designer to estimate important engineering properties of the soil. Very often the
Standard Penetration Test (SPT) blow counts are used to estimate the shear strength
properties of soil in foundation designs. Few correlations are widely used. However,
no clear explanation is found to justify the selection most of these mathematical
equations. This manuscript describes a new approach to estimate the shear strength
parameters based on the SPT blow counts. In this method, the standard penetration
test is treated analogous to driving a miniature pipe pile. The energy input to the soil
is used to correlate the SPT blow count to the shear strength parameters of the soil at
the depth of testing. Soil boring records from few different sites were analyzed and a
statistical analysis revealed that the proposed method can provide a better estimation
than the widely used existing correlations.
INTRODUCTION
A combination of soil borings and laboratory testing is the most reliable method
available to obtain accurate shear strength properties for subsurface soils. Many
projects, due to limited budgets, tight schedules, or lack of concern, do not usually
have the luxury of getting laboratory recommendations. In many cases, the only
subsurface exploration performed consists of soil borings with a log recording the soil
type and classification, depth of water table and SPT blow counts. Lack of lab data
forces the designer to estimate the properties of the soil.
When laboratory data is not available, it is a common practice to estimate the
shear parameters from the of the SPT results. There are many charts and tables
available to make direct correlations between the SPT blow count (N) and the angle
of internal friction (

) and undrained cohesion (cu). These estimations should be
made by individuals who have a thorough understanding of soil behaviors. It has
ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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been the authors experience that this is often times not the case. Engineers with little
or no experience in evaluating soil borings and estimating

and cu are sometimes
expected to design foundations. It is very common for an inexperienced designer to
use a design chart which is not fully understood. It is this practice that shows a strong
need for a reliable tool to assist in design when a complete laboratory analysis is
unavailable.
EXISTING N60 -

AND N60 - cu CORRELATIONS
A brief review of widely accepted correlations of N value to

and cu are
presented herein. The two most common types of SPT hammers used in the US are
safety and donut hammers. Energy studies have revealed that the efficiency of safety
and donut hammers are about 60% and 45% respectively. When SPT results are
presented it is customary to modify the blow counts to the 60% efficiency levels
(N60). Almost all the correlations are hence based on N60. It is important to note that
the factors such as borehole diameter, sampling method, and rod length are also
incorporated into this standardization process.
Early work on estimating

from the N60 value attempted to make direct
correlations. Meyerhof (1956) and Peck et al. (1974) tabulated recommended values
for estimating

. Peck et al. (1974) published a graphical representation which was
later approximated by the following equation by Wolff (1989).
2
6060 00054.03.01.27 NN
(1)
Results from a laboratory research by Gibbs and Holtz (1957) showed that
overburden pressure could significantly affect the SPT blow count. Schmertmann
(1975) considered overburden pressure to develop a relationship between N60 and

.
This correlation can be mathematically approximated as follows (Kulhawy and
Mayne, 1990) where
is the effective overburden pressure and pa is the
atmospheric pressure.
34.0
60
13.202.12/tan
a
p
N
(2)
Despite the research shown above, there have been few other attempts to correlate

directly to N60 without considering overburden pressure (Peck et al., 1953, and
Japan Road Assoc., 1990). Hatanaka and Uchida (1996) tested high quality,
undisturbed frozen samples from few sites in a standard triaxial apparatus and the
friction angles were compared against the corresponding N60. They proposed the
following equation to estimate

where CN is a factor to correct N60 to a standard
overburden pressure (100 kPa).
2020 60
NCN
(3)
ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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Correlating cu to N60 has been attempted many times. Efforts have been made to
find a general relationship for all clay types. The following equation presented by
Terzaghi and Peck (1967) is one of the more commonly used methods of estimating
cu for all clay types.
60
06.0 Npc au
(4)
Some believe it is unlikely a generally accepted relationship between cu and N60
will be found and a realistic correlation between cu and N60 may be possible for clays
within the same geology. The following equation by Hara et al. (1974) is an example
for one such effort.
 
72.0
60
29.0 Npc au
(5)
PROPOSED METHOD BASED ON ENERGY BALANCE
Modified version of Mohr-Coulomb failure criterion is typically used to estimate
the shear resistance between soil and pile material such as steel, concrete, etc.
Therefore, the shear resistance (
f) between soil and the SPT sampler is modeled by
the following equation where ca and
are adhesion and angle of friction between soil
and the sampler. K is defined as the coefficient of lateral earth pressure.
tan
Kcaf
(6)
Driving the sampler is analogous to driving a pipe pile. Assuming no plug
formation, the resisting force is the
f multiplied by the surface area of the sampler
both inner and outer. The work done by the sampler to overcome the
f of the soil
(E1) can be estimated by resisting force times the distance traveled (d).
 
 
dKcAKcAE innerainnerouteraouter )tantan
1
(7)
It is assumed that the lateral pressure on the inside of the sampler is zero. Inside
surface area of a standard sampler is approximately 70% of the outside. Therefore,
equation 7 can be simplified to:
 
 
 
tan7.17.0tan
1
KcdAdcAKcAE aouteraouterouteraouter
(8)
The energy transferred by the hammer to the soil (E2) is the total work done by
the hammer times the hammer efficiency (
). However, it is convenient to use
standardized N60 instead of the field N which results in the following equation where
W is the hammer weight and h is the drop height.
 
WhNNWhE 6026.0
(9)
ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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Assuming that there is no other energy lost to the system, equation 8 and 9 can be
set equal to each other to find N60 as a function of shear strength parameters. D is the
outer diameter of the sampler. Shear strength parameters are made non-dimensional
by dividing them by pa.
)tan7.1(
6.0
)tan7.1(
6.0
2
60
aa
aa
a
outer p
K
p
c
Wh
pDd
Kc
Wh
dA
N
(10)
The parameters pa, D, d, W, and h are constants and hence can be replaced by a
constant (B) to form a general equation.
)tan7.1(
60
aa
ap
K
p
c
BN
(11)
 
 
0.5
in30lb 1406.0 in
lb
144
2000
in12in2
6.0
2
2
2
Wh
pDd
Ba
(12)
PROPOSED N60 -

CORRELATION FOR COHESIONLESS SOILS
For granular soils, adhesion (ca) is zero. Angle of friction between soil and pile
material (steel in this case) is typically assumed to be proportional to soil friction i.e.,
=

where
is the constant of proportionality. Reese et al. (2006) proposed to use
K=0.8 for open ended pipe piles which are driven unplugged. Therefore, when the
soil is granular the general equation can be deduced to the following.
     
tan4tan8.05tan
60 aaa ppp
KBN
(13)
a
p
N60
125.0tan
1
(14)
Results from 36 standard penetration tests conducted at 24 different boreholes in
Oconto and Marinette County, WI, in 2005 were used to estimate
parameter in Eq.
14. Details of these tests and the laboratory evaluated friction angles of soils obtained
at the same locations are reported in Brown (2007). These data produced an average
value of 1/
=0.3818 with a 0.018 standard deviation. Low standard deviation
indicates a reliable value for
.
PROPOSED N60
cu CORRELATION FOR COHESIVE SOILS
For cohesive soils

is zero. Adhesion between soil and pile material (steel in this
case) is typically assumed to be proportional to undrained cohesion i.e., ca=
cu where
is the constant of proportionality.
ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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a
u
a
u
a
ap
c
p
c
p
c
BN
5.87.15)7.1(
60
(15)
60
5.8
1N
p
ca
u
(16)
Results from 14 standard penetration tests conducted at 9 different boreholes in
St. Clair, MI, in 1973 were used for
estimation (Eq. 16). Details of these tests and
the laboratory evaluated undrained cohesion values obtained at the same locations
can be found in Brown (2007). These data resulted an average value of 1/
=0.3535
with a 0.162 standard deviation. High standard deviation suggests that this
value
may not support a strong prediction from equation 16.
VERIFICATION AND DISCUSSION
The estimated
and
values were used to analyze 2 sets of data to verify the
usefulness of the proposed 2 equations. Data used for this verification are presented
in Tables 1 and 2.
The laboratory values of

were compared to those predicted by Equation 14 in
Figure 1. Predictions by equations 1, 2, and 3 were also included in Figure 1 for
comparison. Overburden pressure correction proposed by Liao and Whitman (1986)
was used with Hatanaka and Uchida (1996) method. Performance of all equations
was compared by the distribution of error which was defined as the percent deviation
of the calculated friction angle from the measured. This comparison is presented in
Table 3. With the lowest average and standard deviation in error, statistically, the
proposed equation does a better estimation than other equations. It is also noticed that
for the given set of data, the proposed equation generates more conservative results
(slightly underestimate), while other methods overestimate

. However, it has to be
tested with more sets of data to see if it is a general trend.
Figure 2 compares the laboratory measured cu to those predicted by Equation 16.
Predictions by Terzaghi and Peck (1967) equation are also included in Figure 2. Hara
et al. (1974) equation was not considered in the analysis as the geological history of
the soil was not known to make a fair comparison. Statistical distribution of percent
errors by both proposed and Terzaghi and Peck (1967) equations are also presented in
Table 3. High standard deviation in percent error indicates a less reliable correlation.
However, the proposed equation (Eq. 16) still does a better estimation than Terzaghi
and Peck (1967) method. In addition, the prediction by the proposed equation is
conservative (slightly underestimates).
When
in equation 16 is replaced by the estimated value, it produces
cu=0.04paN60 which is different from Terzaghi and Peck (1967) only by the
proportionality constant (0.04 instead of 0.06). In a way the proposed method
supports what Terzaghi and Peck (1967) suggested, i.e. N60 is directly proportional to
cu. However, the high standard deviation indicates that both methods perhaps lack
details specific to cohesive soils such as overconsoldated ratio and in-situ moisture
content.
ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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Table 1. Data Used for Verification of Eq. 14
Borehole
No.
N60
Depth
(ft)
(psf)
Lab
Eq.14
Borehole
No.
N60
Depth
(ft)
(psf)
Lab
Eq.14
SB-8
5
5
525
30
29.84
23
27
28
2900
30
29.74
SB-8
11
13
1525
31
28.45
32
11
6
660
30
31.76
SB-8
25
20
1998
35
30.90
32
11
14
1100
30
30.05
SB-22
8
8
880
30
29.63
32
26
23
1640
32
31.62
SB-22
9
13
1455
30
27.53
44
24
8
960
35
32.62
12
16
5
550
30
32.87
44
31
45
3240
30
29.86
12
13
8
715
32
31.97
44
45
50
3565
35
30.93
12
23
13
1015
30
32.44
49
11
13
1080
32
30.13
12
69
50
3420
35
32.21
49
23
17
1340
30
31.83
Note: Data from Commonwealth Associates Inc., Jackson, MI. Logs SB8 and SB22; Drilling by Braun
Intertec Corporation, in 2006, Circle Pines, MN, 75% efficiency assumed for automatic hammer. Logs
12, 23, 32, 44, 49; Drilling by American Engineering Testing Inc. in 2005, Farmington, MN, hammer
efficiency 60-65%.
Table 2. Data Used for Verification of Eq. 16
Borehole
No.
N60
Depth
(ft)
cu -lab
(psf)
cu -Eq.16
(psf)
Borehole
No.
N60
Depth
(ft)
cu -lab
(psf)
cu -Eq.16
(psf)
1
11
9
750
915
49
7
3
750
582
1
6
13
500
499
49
12
43
2000
998
2
7
2
500
582
49
10
48
1000
832
2
6
4.5
500
499
49
16
53
1500
1331
12
7
2.5
750
582
4066
10
4.5
750
832
12
12
26
1125
998
4066
17
7
1250
1414
32
9
4
1125
749
4066
31
10
2000
2579
44
16
4
1000
1331
4066
35
35
3000
2911
Note: Data from Commonwealth Associates Inc., Jackson, MI. Drilling by American Engineering
Testing Inc., logs 1 and 2 in 2001, Empire, MN, other logs in 2005, Farmington, MN, hammer
efficiency 60-65%.
Table 3. Statistical Comparison of Methods
Method
Average error (%)
Standard deviation of error (%)
Proposed (Eq. 14)
1.94
6.50
Wolff (1989)
-5.30
9.83
Kulhawy and Mayne (1990)
-37.62
13.43
Hatanaka and Uchida (1996)
-31.02
12.85
Proposed (Eq. 16)
2.90
23.12
Terzaghi and Peck (1967)
-40.08
33.35
It should be emphasized that the validity of a correlation depends highly on the
quality of data used. A close inspection of Figures 1 and 2 reveals that the laboratory
values tend to follow rounded off number pattern. Most of the friction angles are
either 300, 320, or 350 and the undrained cohesion values are either 500, 1000, or
2000 psf. It is unclear if it was a coincidence or a biased interpretation. Personal
ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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communications with the drilling companies revealed that they have conducted some
direct shear tests and unconfined compressive strength tests. However, details of the
laboratory testing were not available with the borehole records.
25
30
35
40
45
50
25 30 35 40 45 50
Friction Angle_measured
Friction Angle_calculated
Proposed
Wolff (1989)
Kulhawy and Mayne (1990)
Hatanaka & Uchida (1996)
FIG. 1. Comparison of calculated friction angle with the measured.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0500 1000 1500 2000 2500 3000 3500 4000 4500
Cu_measured (psf)
Cu_calculated (psf)
Proposed
Terzaghi & Peck (1967)
FIG. 2. Comparison of calculated undrained cohesion with the measured.
ASCE Geotechnical Special Publication No. 179, ISBN 978-0-7844-0972-5
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CONCLUSIONS
The equations proposed to estimate shear strength properties in this manuscript
use a principle based on energy balance. SPT was treated analogous to driving a
miniature pipe pile. The energy input to the soil was used to correlate the SPT blow
count to the skin resistance which is a function of shear strength properties of the soil
at the depth of testing. Logical reasoning behind the proposed method makes it a
stronger prediction technique. A statistical analysis revealed that the proposed
method does a better estimation than the existing equations in predicting

from SPT
data. Undrained cohesion prediction for the set of data analyzed was not as strong as
the

prediction. However, the proposed prediction method suggests that the N60
should be directly proportional to undrained cohesion supporting Terzaghi and Peck
(1967).
REFERENCES
Brown, T.S. (2007). “Estimating shear strength properties of soils using SPT results,”
Graduate Project Report, Department of Civil Engineering, Lawrence
Technological University, Southfield MI.
Gibbs, H.J. and Holtz, W.G. (1957). "Research on determining the density of sand by
spoon penetration test," Proc. 4th ICSMFE, Vol. 1, pp. 35-39.
Hara, A., Ohta, T., Niwa, M., Tanaka, S., and Banno, T., (1974). “Shear Modulus and
Shear Strength of Cohesive Soils,” Soils and Foundations, Vol.14, No.3, pp.1-12.
Hatanka, M. and Uchida, A. (1996). “Empirical correlation between penetration
resistance and internal friction angle of sandy soils,” Soils and Foundations, Vol.
36, No. 4, pp. 1-9.
Japan Road Association (1990). Specifications for highway bridges, Part IV.
Kulhawy, F.H. and Mayne, P.W. (1990). Manual on estimating soil properties for
foundation design, Electric Power Research Institute, Palo Alto, CA.
Liao, S.S.C. and Whitman, R.V. (1986). Overburden correction factors for SPT in
sand,” J. of Geotechnical Engineering, ASCE, Vol. 112, No. 3, pp. 373-377.
Meyerhof, G.G. (1956). “Penetration tests and bearing capacity of cohesionless
soils, J. of Soil Mech. and Foundations Div., ASCE, Vol.82, No.SM1, pp.1-19.
Peck, R.B., Hanson, W.E., and Thornburn, T.H. (1953). Foundation Engineering,
John Wiley and Sons, pp. 222.
Peck, R.B., Hanson, W.E., and Thornburn, T.H.,(1974). Foundation Engineering, 2nd
ed., John Wiley and Sons, New York, NY.
Reese, L.C., Isenhower, W.M., and Wand, S.T. (2006). Analysis and Designing of
Shallow and Deep Foundations, John Wiley and Sons, pp.574.
Schmertmann, J.H. (1975). Measurement of In-Situ Shear Strength", Proc., ASCE
Specialty Conference on In-Situ Measurement of Soil Properties, Vol. 2, Raleigh,
SC, pp. 57-138.
Terzaghi, K. and Peck, R.B. (1976). Soil Mechanics in Engineering Practice, 2nd ed.,
John Wiley and Sons, New York, pp. 729.
Wolff, T.F. (1989). “Pile capacity prediction using parameter functions,” ASCE
Geotechnical Special Publication No. 23, pp. 96-107.
... When laboratory data is not available, it is a common practice to estimate the shear parameters from the SPT results. There are many charts, tables and empirical relationships are available in the literature between the SPT N value and the angle of internal friction ( and undrained cohesion (c u ) by different researchers like [9][10][11][12][13]. ...
... Gibbs and Holtz (1957) showed that overburden pressure could significantly affect the SPT blow count. Schmertmann (1975) considered overburden pressure to develop a relationship between GSJ: Volume 7, Issue 11, November 2019 ISSN 2320-9186 1186 GSJ© 2019 www.globalscientificjournal.com N 60 and internal friction angle ( ) .This correlation can be mathematically approximated as follows (Kulhawy and Mayne, 1990) where is the effective overburden pressure and P a is the atmospheric pressure [10,11]. ...
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In foundation designs, standard penetration test (SPT) blow counts are typically used to estimate shear strength properties of soils. Few correlations are widely in use to make such estimations. However, the selection of these correlation equations are not often justified or explained. This manuscript describes a new approach to estimate the shear strength properties based on the SPT blow counts. The proposed method treats SPT analogous to driving a miniature open-ended pipe pile. During SPT, part of the energy is transferred into the soil. This energy is dissipated at the soil-sampler interface to overcome skin and point resistance to penetrate a sampler into the soil. Energy balance was used to correlate the SPT blow count to the shear strength properties of the soil at the depth of testing. Two separate equations were derived: one to estimate the friction angle (phi(')) of sand and the other to estimate the undrained shear strength (c(u)) of clay. SPT results from two sites were used to calibrate the proposed equations, and then two other sets of data were used to verify them. With a low average standard deviation in the calibration process, the proposed N-60-phi(') equation demonstrated a strong correlation. The proposed N-60-c(u) equation did not provide as strong a correlation as the N-60-phi(') equation. However, a statistical analysis revealed that for the data used in this research, both equations could estimate shear strength properties better than the commonly used, other existing correlations. The proposed equations may not work in very stiff clay or very dense sand and should not be used to analyze SPT results with poor recovery.
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This manual focuses on the needs of engineers involved in the geotechnical design of foundations for transmission line structures. It also will serve as a useful reference for other geotechnical problems. In all foundation design, it is necessary to know the pertinent parameters controlling the soil behavior. When it is not feasible to measure the necessary soil parameters directly, estimates will have to be made from other available data, such as the results of laboratory index tests and in-situ tests. Numerous correlations between these types of tests and the necessary soil parameters exist in the literature, but they have not been synthesized previously into readily form in a collective work. This manual summarizes the most pertinent of these available correlations for estimating soil parameters. In many cases, the existing correlations have been updated with new data, and new correlations have been developed where sufficient data have been available. For each soil parameter, representative correlations commonly are presented in chronological order to illustrate the evolutionary development of the particular correlation. The emphasis is on relatively common laboratory and in-situ tests and correlations, including those tests that are seeing increased use in practice.
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One-of-a-kind coverage on the fundamentals of foundation analysis and design Analysis and Design of Shallow and Deep Foundations is a significant new resource to the engineering principles used in the analysis and design of both shallow and deep, load-bearing foundations for a variety of building and structural types. Its unique presentation focuses on new developments in computer-aided analysis and soil-structure interaction, including foundations as deformable bodies. Written by the world's leading foundation engineers, Analysis and Design of Shallow and Deep Foundations covers everything from soil investigations and loading analysis to major types of foundations and construction methods. It also features: Coverage on computer-assisted analytical methods, balanced with standard methods such as site visits and the role of engineering geology. Methods for computing the capacity and settlement of both shallow and deep foundations. Field-testing methods and sample case studies, including projects where foundations have failed, supported with analyses of the failure. CD-ROM containing demonstration versions of analytical geotechnical software from Ensoft, Inc. tailored for use by students in the classroom.
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Several formulae and charts have been published for correcting the results of the standard penetration test (SPT) performed in sands for the effects of overburden pressure. However, depending on which published correction factor is used, very different interpretations may result. This paper attempts to clarify and resolve some of these differences, and proposes a simple correction factor as a tentative standard, contingent on data from future research.
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A series of drained triaxial compression tests were performed on high-quality undisturbed samples of sandy soils for the determination of the angle of internal friction (ϕd). The high-quality undisturbed samples were recovered by the in-situ freezing sampling method (FS sample). The angle of internal friction for the high-quality undisturbed samples (ϕd(fs)) was compared with calculations from the empirical equations proposed by many investigators previously using the N-value of the standard penetration test (SPT). It was found that the angle of internal friction for the high quality undisturbed sand samples was much higher than that estimated from the proposed empirical equations. In order to take into account the effects of the confining stress on the SPT N-value, the measured N-value was normalized at an effective overburden pressure of 98 kPa (1 kgf/ cm²) using the equation proposed by Liao and Whitman (1986). The normalized N-value, N1, was induced to relate the angle of internal friction for the high-quality undisturbed sand samples. A fairly good correlation between the N1 value and the ϕd(Fs) was established. Finally, based on the test results, a simple equation (ϕd(Fs) = (20N)°.5 + 20) was proposed to relate the N1 value and ϕd(Fs) of sandy soils in the range of N1 between 3.5 and 30, for this study. The relationship between the angle of internal friction for the high-quality undisturbed gravel samples (ϕd(gk)) and the penetration resistance was also discussed. A new parameter of NL1 was introduced in order to relate to ϕd(GV), where NL1 is the penetration resistance of the large scale penetration test (LPT) normalized at an effective overburden pressure of 98 kPa (1 kgf/cm²), using a similar equation to that proposed by Liao and Whitman (1986). Although data is limited, a correlation between NL1 and ϕd(GV) similar to that proposed in this study for sandy soils was found.
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The purpose of this paper is to evaluate the relation between initial shear modulus and shear strength of cohesive soils. The initial shear moduli were obtained from the results of the well-shooting tests by means of shear waves, while the shear strength could be obtained from the results of laboratory tests conducted on undisturbed soil samples collected at the same site as the well-shooting tests. Taking into consideration the fact that there have been a number of instances where the well-shooting test and the standard penetration test were conducted on the same sites, the authors conducted their research to seek some relationships between the initial shear modulus and the N-value of the standard penetration test, between the shear strength and the N-value, and between the initial shear modulus and the shear strength. The research works have finally led the authors to finding out several relations among initial shear modulus, shear strength and N-value.
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