Correlations to predict friction angle of Soil using SPT-N Value

1. 1
Proceedings of the 8th International Symposium on
Advances in Civil and Environmental Engineering
Practices for Sustainable Development
ACEPS - 2021
Establishment of Correlations Between SPT-N Value and Friction
Angle of Soil
A.I. Liyanage1, N.H. Priyankara2
1 Irrigation Department, SRI LANKA
2 University of Ruhuna, Galle, SRI LANKA
A R T I C L E I N F O A B S T R A C T
Article history:
Received 31 July 2021
Revised 23 October 2021
Accepted 11 November 2021
Available online 15 December 2021
Keywords:
SPT N
Friction Angle
Correlations
Local Context
SPSS
The Standard Penetration Test (SPT) N value is the main parameter use in empirical
equations to predict the shear strength parameter of soil. These empirical equations
are generalized based on the selected published data/tests from different sources
having inconsistency of test material, test procedure and data interpretation. Hence
it is very difficult to predict the outcomes of those relations without justifying them
for local condition. In this research, it has aim to establish a correlation between SPT-
N value and internal friction angle for local context. For this study, 25 number of
soil samples were collected and followed by laboratory testing and classified the soil
type, determine the shear strength parameters, moisture content, bulk density, dry
density etc. Laboratory test results and relevant SPT-N values were modelled using
SPSS software under multi variable regression analysis. In the results square root
SPT- N value, dry density and friction angle shows highest meaningful relationship
and developed equation was assessed using bivariate correlation coefficient named
Kendall’s tau_b, Spearman’s rho, and Pearson correlation coefficients and
correlation values were 0.833,0.924 and 0.924 respectively. Reliability index value
was 0.857 for proposed equation. Finally proposed equation were compared with
previously proposed empirical equations and results shows a less standard error
and less standard deviation value for current study.
1. INTRODUCTION
1
Soil sampling associated with laboratory
2
testing is the most reliable way to determine
3
soil characteristics. Sometimes due to limited
4
budgets, tight schedules, or lack of concern,
5
projects do not receive proper laboratory
6
recommendations and tendency to avoid the
7
laboratory tests. However, in many cases,
8
subsoil investigation data, such as SPT- N
9
value (Standard Penetration Test Blow Count)
10
along with soil type available to judge the
11
subsurface soil characteristics. Therefore,
12
when laboratory data are not available it is a
13
common practice to estimate the soil
14
properties from the in- situ tests such as SPT
15
results. Many empirical correlations have been
16
developed to predict the shear strength
17
characteristics and bearing capacity in terms of
18
the SPT- N value. SPT - N value is an index for
19
quick prediction of shear strength
20
characteristic of soil due to its simplicity. These
21
empirical correlations have been extensively
22
used in the present when laboratory
23
experiments are not available for estimation of
24
shear strength characteristics. However, these
25
empirical correlations are based on the selected
26
published data/tests from different sources
27
having inconsistency of testing material,
28
procedures, data interpretation and
29
heterogeneity of soil. Hence, it is very difficult
30
to predict the outcomes of those relations
31
without justifying them for local condition.
32
Further, all these empirical correlations were
33
developed in other countries under seasoning
34
climate conditions. As such Sri Lanka as a
35
tropical country, applicability of such
36
empirical correlations developed by other
37
countries is questionable. Hence the local soil
38
may follow previous correlations with slight
39
deviation or may not follow the trend at all.
40

2. 2
2. LITERATURE REVIEW
1
The literature presents the portfolio of research
2
regarding application of SPT -N value and
3
internal friction angle of soil in terms of
4
empirical equations.
5
Development of Correlations Between
6
Angle of Friction and SPT-N value
7
Several studies have been done based on SPT -
8
N value and shear strength properties of soil
9
using different approaches. An early attempt
10
made by Peck in 1953 (Hatanka and Uchida,
11
1996) based on SPT-N value to predict the
12
friction angle for sandy soil. Here after
13
Dunham in 1954, derived three different
14
correlations for three different shapes of the
15
grain of soil particles to predict the internal
16
friction angle of soil based on SPT- N value.
17
(Hatanka and Uchida, 1996). In 1957,
18
Meyerhof proposed an empirical equation
19
relate the SPT- N, effective over burden
20
pressure, 𝜎𝑣
,
and the relative density of sandy
21
soils, 𝐷𝑟(Hatanka and Uchida, 1996). Peck,
22
Hanson and Thornburn, 1974 proposed an
23
empirical equation between friction angle and
24
SPT-N60 (Shooshpasha et al,2014). Shioi and
25
Fukui proposed empirical relationships
26
between friction angle and energy corrected
27
SPT- N70 (Shooshpasha et al,2014). Hettiarachi
28
and Brown established correlation between
29
friction angle and SPT- N60 using energy
30
balance approaches (Hettiarachchi and Brown,
31
2009). The previously published antecedent
32
correlations and their limitations are discussed
33
in the following sectors.
34
2.1.1. Peck Study, 1953
35
Peck, 1953 introduced empirical corelation Eq.
36
(1) to predict the internal friction angle for
37
sandy soil using SPT-N value.
38
39
𝜑𝑑 = √0.3𝑁 + 15 (1)
40
41
Where,𝜑𝑑 is drained internal friction angle
42
and N is filed SPT N value.
43
2.1.2. Dunham Study, 1954
44
Dunham,1954 introduced three different
45
correlations to find the friction angle based on
46
field SPT- N values. The categorization of these
47
equations was based on the shape and grading
48
of soil particles as shown in Eq. (2) to (4).
49
50
For angular and well graded soil particles
51
52
53
54
For round and uniform grained soil particles
55
56
57
For round and well grained soil particles
58
59
60
61
2.1.3. Shioi and Fukui’s Study, 1982
62
Shioi and Fukui, 1982 introduced three
63
different equations for determining internal
64
friction angle using raw SPT - N value. These
65
equations were based on the type of structure.
66
Eq. (5) is defined for road structures where Eq.
67
(6) and (7) is used for bridges and buildings
68
respectively
69
70
𝜑 = √18𝑁70 + 15 (5)
71
72
𝜑 = 0.36𝑁70 + 27 (6)
73
74
𝜑 = 4.5𝑁70 + 20 (7)
75
76
Where, N70 is energy corrected SPT -N value.
77
2.1.4. Japan Road Association Equation and
78
Wolff Equations
79
In Japan, an empirical equation is used to
80
determine the internal friction angle of soil.
81
This equation has introduced by the Japan
82
Road association in 1990. The equation is only
83
valid at SPT - N value range between 5 and 45.
84
(5 < N ≤ 45) as shown in Eq. (8).
85
86
𝜑 = √15𝑁 + 15 (5 < 𝑁 ≤ 45) (8)
87
88
Wolff,1986 introduced an equation to
89
determine the internal friction angle of soil
90
using the SPT- N value. This Eq.(9) is
91
applicable only for sand.
92
93
𝜑 = 27.1 + 0.3𝑁60 - 0.00054𝑁60
2
(9)
94
95
𝜑 = √12𝑁 + 25 (2)
𝜑 = √12𝑁 + 15 (3)
𝜑 = √12𝑁 + 20 (4)

3. 3
3. METHODOLOGY
1
This research was aim to establish a corelation
2
between SPT-N value and internal friction
3
angle for local context. To achieve aim of the
4
research three objectives were established.
5
Identify previously proposed empirical
6
equations between SPT- N and shear strength
7
parameter of soil was the first objective and it
8
has achieved from the literature reviews.
9
Second objective of the research is
10
establishment of correlation between friction
11
angle and SPT- N values, moisture content,
12
density. Final objective was to select the most
13
reliable equation to predict the friction angle
14
using SPT -N value and compare with the
15
existing correlations. To achieve the second
16
and final objectives different approaches were
17
carried out and most practicable method were
18
implemented in the research.
19
Sample Collection
20
Sample collection part of this research were
21
achieved from obtaining SPT- N known soil
22
samples from well-established geotechnical
23
company in Sri Lanka. 25 number of soil
24
samples were collected covering different
25
locations of the country as shown in Table 1.
26
Laboratory Investigation
27
Collected soil samples were subjected to a
28
different laboratory tests. Soil, were classified
29
according to Unified Soil Classification System
30
(USCS). Further shear strength parameters and
31
soil index properties were determined. All
32
laboratory tests were conducted in the
33
geotechnical laboratory at Faculty of
34
Engineering, University of Ruhuna, Sri Lanka.
35
36
3.2.1. Soil Classification
37
Soil classification were conducted according to
38
Unified Soil Classification (USCS) and sieve
39
analysis test were performed to all 25 soil
40
samples according to the ASTMD-2487
41
42
3.2.2. Direct Shear Test
43
Based to the results obtained from soil
44
classification ,12 number of soil samples were
45
subjected to the direct shear test and test was
46
performed according to BS 1377: Part 2.
47
48
49
Table 1- Collected Soil Sample Data
50
51
Data Analysis
52
Data analysis of the research was conducted to
53
establish correlations between Standard
54
Penetration Test - N value and soil properties.
55
For the analysis SPSS (Statistical Package for
56
Social Science) software was used. The
57
application of SPSS software was launched
58
under different criteria.
59
3.3.1. Criteria One
60
Criteria one was proposed to identify the
61
meaningful correlation coefficient between soil
62
properties and SPT –N values. The significance
63
of variables was evaluated based on bivariate
64
statics Pearson Correlations Coefficient.
65
Pearson correlation coefficient was evaluated
66
under two-tailed distribution at 90% and 95%
67
Sample
No
Location
Depth(m)
SPT-N
Soil
Type
(USCS)
1 - 0.50 3 SM/SC
2 - 4.50 29 SW
3 - 16.50 - -
4 Matara 1.50 10 SM/SC
5
Highway
Extension
13.50 - -
6 Wellawaththa 1.50 - -
7 Wellawaththa 0.50 19 SW
8 Kerawalapitiya 3.50 28 SW
9 Mahabage 1.50 5 SM/SC
10 Kerawalapitiya 1.50 25 SP
11 Mahabage - 2 SP
12 Wallawaththa 7.50 63 SP
13 Bagathale 1.50 5 SM/SC
14 Colombo-04 1.50 7 SP
15 Homagama 2.50 2 SM/SC
16 Colombo -05 2.50 7 SP
17 Colombo-04 4.50 24 SP
18 Rajagiriya 1.50 3 SP
19 Polonaruwa 2.50 41 SP
20 Colombo-04 1.50 7 SP
21 Colombo-12 1.50 2 SM/SC
22 Matara 3.50 22 SW
23 Hibutana 19.50 50 SP
24 Colombo-04 4.50 50 SP
25 Matara 29.00 50 SP

4. 4
confidence levels. To determine the
1
meaningful correlations, 12 soil sample's data
2
were used. There internal friction angle,
3
relevant SPT- N values, log SPT, ℓn SPT,
4
Square root of SPT- N, moisture content of
5
samples, bulk density, and dry density were
6
used as data parameters on SPSS.
7
3.3.2. Criteria Two
8
Criteria two established correlations based on
9
two variable methods using linear regression
10
analysis. Under criteria two, friction angle was
11
used as a dependent variable while SPT- N was
12
an independent variable. Different format of
13
SPT was used as independent variable. Eg: log
14
SPT - N, ℓn SPT- N, Square root SPT- N.
15
3.3.3. Criteria Three
16
Criteria three was enclosed with generalized
17
equations using multi-variable linear
18
regression analysis. As the independent
19
variable use the SPT- N value with the format
20
of the log, antilog, and the square root of raw
21
SPT- N and dry density, bulk density. Friction
22
angle was used as dependent variables.
23
Different models were established changing
24
the independent variables.
25
3.3.4. Selection of Best Fit Equation
26
Reliability index value (R2) was used for
27
selection of more reliable and best-fit equation
28
among the proposed equations. A total of 12
29
number of equations were developed under
30
criteria two and three. For these 12 numbers of
31
equations, reliability indices were determined
32
using SPSS under 95% confidence interval.
33
3.3.5. Prescribed Method of Generating an
34
Equation for In-Site Applications
35
Based on the results under criteria two and
36
three, an equation was developed for in-site
37
application. Main purpose of introducing such
38
equation is to quick and easy approach to
39
determine the friction angle. Tabulated values
40
were used to generate the quick and easy
41
approachable equation to calculate friction
42
angle by considering one independent variable
43
(square root value of the raw value of SPT-N).
44
Method for selecting best-fit equation, linear
45
model and polynomial model graph were
46
asses and best-fit graph pattern were selected
47
based on Reliability Index (R2) value. The
48
equation that would be more closed to 1.00 was
49
selected as the proposed equation. The selected
50
graph pattern was subjected to analysis
51
through curve estimation in regression
52
analysis in SPSS and compare the results, as
53
well as calculate the correlation based on the
54
bivariate statics. In correlation coefficient
55
calculation, three different coefficients, namely
56
Pearson correlation coefficient, Kendall’s
57
tau_b coefficient and Spearman’s rho
58
correlation coefficient were used. In bivariate
59
statics and curve regression conduct under
60
two-variable methods, the independent
61
variable was the square root value of SPT- N
62
and the dependent variable was the calculated
63
friction angle values.
64
Statistical Hypotheses
65
Other than the studying meaningfulness of the
66
proposed equation model using different
67
correlation coefficients, following statistical
68
hypotheses were considered.
69
70
H0: β=0, The model is not meaningful
71
72
H1: β≠0, The model is meaningful
73
74
Sig. (ρ –value) > α=0.05→H0 acceptable
75
Sig. (ρ –value) < α=0.05→H1 acceptable
76
77
Sig ((ρ –value) were obtained from Fisher Test
78
using reliability analysis in SPSS, and
79
modelling were conducted under 95%
80
confidence level.
81
Method of Comparison of Previously
82
Proposed Equation and Current Study
83
Objective three of this research was to compare
84
the correlations developed under this research
85
study with the previously established
86
correlations. To achieve this objective,
87
previously published equations were selected
88
from the literature review. Compare these
89
equations with the newly proposed equations
90
using graphical analysing approach. Statistical
91
analysis was used as another analysing
92
technique. The standard error and standard
93
deviation of the existing and proposed
94
equations were evaluated.
95

5. 5
4. RESULTS AND DISCUSSION
1
Laboratory Test Results
2
As described in methodology, collected 25
3
numbers of soil samples were subjected to
4
sieve analysis and classified according to USCS
5
(Table 1). After classification of soil samples, it
6
was identified that most of soil samples were
7
classified as Poorly Graded Sand (SP). Hence,
8
direct shear test was used to determine the
9
shear strength parameters of those samples. In
10
addition, tests were carried out to determine
11
moisture content and bulk density. Summary
12
of laboratory test results have been tabulated
13
in Table 2. The typical variation of particle size
14
distribution and shear stress vs shear strain
15
graphs of sample No 16 is illustrated Figure 1
16
and Figure 2 respectively.
17
18
Table 2: Laboratory Test Results
19
Sample
No
Bulk
Density
(g/cm
3
)
Friction
Angle-
(Based
on
Direct
Shear
Test)
˚
Moisture
Content
10 1.57 46.51 14.07
11 2.13 32.21 22.1
12 1.63 42.83 8.65
14 1.91 29.07 0.68
16 2.18 25.36 14.3
17 2.01 35.94 15.46
18 2.04 30.88 10.86
19 1.96 48.09 9.72
20 1.91 36.42 0.31
23 2.07 41.31 11.27
24 2.20 39.76 15.52
25 1.90 42.95 16.27
20
21
22
23
24
25
26
27
Figure 1: Practical size distribution Curve
28
(Sample No 16)
29
Figure 2: Variation of Shear Stress vs Shear
30
Strain (Sample No -16)
31
SPSS Analysis Results
32
The Pearson correlation coefficients were
33
determined to find the meaningful
34
correlations. SPT -N value, friction angle,
35
moisture content, bulk density, dry density
36
were used as variables to the SPSS and
37
determined Person Correlation values as
38
shown in Table 3.
39
Table 3: Summery of Person Correlation
40
Values
41
Variable
01
Variable
02
Pearson
Correlation
Sig.
(ρ
Value)
SPT- N
Friction
Angle
0.747 0.005
√𝑆𝑃𝑇 𝑁
Friction
Angle
0.779 0.003
Log
(SPT-
N)
Friction
Angle
0.770 0.003
ℓn (SPT-
N)
Friction
Angle
0.771 0.003
Bulk
density
Dry
density
0.823 0.001
Dry
density
Friction
Angle
0.591 0.043
0
10
20
30
40
50
60
70
0 2 4 6 8 10
Shear
Stress
(kPa)
Shear Strain (%)
Normal Stress =27.78 kPa
Normal Stress = 55.56kPa
Normal Stress =83.33 kPa

6. 6
Generalized Equation Using Liner
1
Regression Analysis
2
Correlations were generalized using a
3
different format of models. SPT- N value with
4
its different formats and bulk density, dry
5
density, moisture content were used as
6
independent variables. Friction angle was used
7
as a dependent variable. Equations were
8
modelled using two variable and
9
multivariable regression analyses in SPSS. The
10
best correlation was selected comparing
11
Reliability index (R2). According to the
12
reliability index values, best fit correlation
13
were observed from following Eq. (10). It was
14
found that R2 of this equation is 0.710.
15
16
𝜑 = 2.038 √𝑁 − 12.260𝛾 + 52.030 (10)
17
18
Where, 𝜑 is the friction angle, √𝑁 is square root
19
value of field SPT -N, 𝛾 is bulk density (g/cm3)
20
Proposed Equation for In-Situ
21
Applications
22
To determine friction angle using proposed Eq.
23
(10) requires bulk density value of soil in a
24
particular location. To determine the bulk
25
density, it is needed to carry- out laboratory
26
tests and it is time consuming. Hence, a quick
27
and easy applicable correlation is developed
28
(Eq.11) based on the results obtained from Eq.
29
(10). Using the laboratory determined bulk
30
density values of SP categorised soil samples
31
through this research study with
32
corresponding SPT-N values were applied in
33
Eq. (10) to calculate the friction angle.
34
Calculated friction angle is used as dependant
35
variable, relevant square root SPT-N values
36
were considered as independent variables, and
37
values are presented in Table 4. Correlations
38
were modelled considering Linear and
39
Polynomial graph patterns. Reliability index
40
values were determined using SPSS software
41
and results are shown in Figure 3. The highest
42
reliability index value was shown in
43
polynomial graph pattern as shown in Figure4.
44
Hence, Eq. (11) is proposed for in-situ
45
applications as a quick approach to determine
46
friction angle for SP soils in local context.
47
48
𝜑 = −0.093𝑁 + 3.2√𝑁 + 25.09 (11)
49
50
Where, 𝜑 is friction angle, N is field SPT -N
51
value.
52
Table 4: Data Values Used to Developed Eq. (11)
53
54
Figure 3: Reliability Index Values for
55
Proposed Eq. (11)
56
Comparison of Proposed Equation with
57
Existing Equations
58
Proposed Correlation Eq. (11) is introduced to
59
determine friction angle in local context for SP
60
soil type. Equation shows 0.857 reliability
61
index value and it shows best corelation. In
62
Sample
No
SPT-
N
Square
Root
SPT-N
(√𝑁 )
Bulk
Density
(g/cm3)
Calculated
Friction
Angle- 𝜑°
(Based on
Eq:10)
10 25 5.00 1.57 42.97
11 2 1.41 2.13 28.80
12 63 7.94 1.63 48.22
14 7 2.65 1.91 34.01
16 7 2.65 2.18 30.70
17 24 4.90 2.01 37.37
18 3 1.73 2.04 30.55
19 41 6.40 1.96 41.05
20 7 2.65 1.91 34.01
23 50 7.07 2.07 41.06
24 50 7.07 2.20 39.47
25 50 7.07 1.90 43.15
Figure 4: Developed Polynomial graph to
generate Eq. (11)
y = -0.0934x2 + 3.2009x + 25.091
R² = 0.8572
0
10
20
30
40
50
60
0.00 2.00 4.00 6.00 8.00 10.00
Friction
Angle
(φ)˚
Square Root SPT- N

7. 7
addition, three different correlation
1
coefficients were evaluated. For the proposed
2
equation, Spearman’s rho Correlation
3
Coefficient was 0.924, Pearson Correlation
4
Coefficient Results 0.924 and Correlation -
5
Kendall’s tau_b was 0.833.
6
4.5.1. Comparison with Dunham's equations
7
Present study was compared with Dunham’s
8
equation and it is graphically presented in
9
Figure 5. It can be noted that proposed
10
equation is lying in average zone of Dunham’s
11
results.
12
4.5.2. Comparison With Shioi and Fuki’s
13
Study.
14
Comparison of current study with Shioi and
15
Fuki’s study is graphically presented in
16
Figure 6. Based on graphical interpretation, it
17
can be seen that, proposed equation is over
18
predicted the friction angle when the SPT-N
19
value is less than 40 when compared with that
20
of Shioi and Fuki’s method. However,
21
proposed equation is well agreed with Shioi
22
and Fuki’s method when SPT-N value is
23
greater than 40.
24
Figure 6: Comparison of Proposed Equation
25
with Shioi and Fuki's Study
26
4.5.3. Comparison with FHWA
27
Recommended Values
28
Peck et al. (1974) study, and Meyerhof's (1956)
29
studies have been used to illustrate the FHWA
30
recommendations (Salari et al, 2015).
31
Comparison of FHWA recommendations with
32
present study is illustrated in Table 5. Column
33
(a) and (b) in the Table 5 depict the FHWA
34
recommended values where as column (c)
35
illustrated in values predicted by present
36
study. According to the comparison, it shows
37
current study results are bounded within the
38
range of FHWAS recommended values
39
Table 5: Comparison of Proposed Equation
40
with FHWA Recommended Values
41
SPT-N (a) (b) (c)
0 to 4 <28 <30 25.09-31.11
4 to 10 28-30 30 to 35 31-34.28
10 to 30 30 to 36 35 to 40 34.28-39.83
30 to 50 36 to 41 40 to 45 39.83-43.06
>50 >41 >45 >43.06
4.5.4. Summary of comparison
42
Summary of comparison were done based on
43
the current study and Dunham’s equation for
44
well graded soil, Japan road association
45
equation (1990), Equation Proposed by Wolff
46
(1982) and Shioi and Fuki’s equation
47
developed for buildings. The variation of
48
friction angle over SPT-N values in above
49
methods together with proposed equation is
50
illustrated in Figure 7. It can be clearly seen
51
that proposed equation is in the range of
52
existing predictors indicating the accuracy of
53
proposed equation.
54
Figure7: Summery of Comparison
55
Figure 5: Comparison of Proposed Equation
with Dunham's Study
0
10
20
30
40
50
0 20 40 60
Friction
Angle
(φ)˚
SPT N
Proposed Equation
Equation for Roads (5)
Equation for Bridges (6)
Equation for general conditions (7)
10
20
30
40
50
0 20 40 60
Friction
Angle
(φ)˚
SPT N
Dunham Equation (2)
Dunham Equation (3)
Dunham Equation (4)
Proposed Equation
0
5
10
15
20
25
30
35
40
45
50
55
0 10 20 30 40 50 60 70
Friction
Angle
(φ)
˚
SPT N
Dunham Equation (1) (1954)
Japan Road Association Equation (1990)
Equation by Wolff (1982)
Shioi and Fukui Equation for Buildings
Proposed Equation

8. 8
4.5.5. Statistical Comparison
1
Statistical comparison was done between
2
proposed equation and selected empirical
3
equations as shown in Table 6. SPSS
4
descriptive statics use for the evaluation.
5
According to the analysis, it can be noted that
6
standard error and standard deviation of the
7
proposed equation are 1.524 and 5.498
8
respectively. When compared with existing
9
correlations, the proposed equation shows the
10
smallest standard error and standard
11
deviation indicating the accuracy of the
12
proposed equation.
13
Table 6: Statistical Comparison
14
15
5. CONCLUSIONS
16
Deriving empirical equations among various
17
geotechnical parameters such as SPT -N value
18
and friction angle of soil is very important in
19
different areas. It produces a fast and simple
20
approach compared to a laboratory approach.
21
The equations proposed in this research to
22
estimate internal friction angle (𝜑) using SPSS
23
software are based on the laboratory test data
24
taken from 25 soil samples. Samples were
25
classified using USCS and 12 samples were
26
classified as SP soil. Thus, established
27
equations are valid for poorly graded sand
28
(SP). Using regression analysis in statistical
29
based platform analysis has been used to
30
established the equations. Among the
31
established equations, Equation (11) was
32
selected as the applicable equation for Poorly
33
Graded sand in order to determine friction
34
angle using raw SPT- N value. It will give
35
quick and easy approach to determine internal
36
friction angle in local context.
37
6. ACKNOWLEDGMENTS
38
The authors express their sincere thanks to
39
GEOTEC (Pvt) LTD for providing the soil
40
samples.
41
7. REFERENCES
42
1. Hatanka, M. & Uchida, A., 1996,
43
“Empirical Correlation between
44
Penetration Resistance and Internal
45
Friction Angle of Sandy Soils’’ Soil and
46
Foundation, Vol 36, No. 4, pp.1-9
47
2. Hettiarachchi H. & Brown, T., 2009,
48
“Use of SPT Blow Counts to Estimate
49
Shear Strength Properties of Soils:
50
Energy Balance Approach', Journal of
51
Geotechnical and Geoenvironmental
52
Engineering, June, 830- 834
53
3. Peck, R.B., Hanson, W.E., &
54
Thornburn, T.H., 1974, Foundation
55
Engineering, 2nd Edn: 1, John Wiley
56
and Sons, Inc
57
4. Shioi, Y. & Fukui, J., 1982,
58
“Application of N-Value to Design of
59
Foundation in Japan.’’, 2nd ESOPT, Vol
60
1, 40-93.
61
5. Shooshpasha et al, 2015, ‘An
62
investigation of friction angle
63
correlation with geotechnical
64
properties for granular soils using
65
GMDH type neural network, Scientia
66
Iranica, May ,157-164
67
6. Salari et al, 2015, ‘Presentation of
68
Empirical Equations for Estimating
69
Internal Friction Angle of SP and SC
70
Soil in Mashhdad, Iran Using
71
Standard Penetration and Direct Shear
72
Test and Comparison with Previous
73
Equations’, International Journal of
74
Geography and Geology,4(5), 89-95.
75
7. Salari et al, 2015, ‘Presentation of
76
Empirical Equations for Estimating
77
Internal Friction Angle of GW and GC
78
Soil in Mashhdad, Iran using Standard
79
Penetration and Direct Shear Test and
80
Comparison with previous
81
Equations’, International Journal of
82
Geography and Geology,2015(5), 231-
83
238.
84
8. Zinan A, & Ansari, M.A., 2017 ‘’
85
Interpreation of geotechnical
86
parameters from CPT and SPT for
87
reclaimed areas of Dhaka, Bangladesh,
88
research gate, November.
89
Equation
Std:
Error
Std:
Deviation
Dunham Eq. (2) 2.163 7.798
Dunham Eq. (3) 2.163 7.798
Wolff Eq. (9) 1.446 5.214
Shioi and Fuki-
Eq. (7)
2.430 8.762
Japan Road
Association
Eq. (8)
1.931 5.795
Proposed
Equation
Eq. (11)
1.524 5.498