This study establishes a correlation between Standard Penetration Test N-values (SPT-N) and internal friction angles for soils in Sri Lanka. 25 soil samples were collected and tested in a laboratory to determine soil types, shear strength parameters, moisture content, density, etc. Correlations between SPT-N values and friction angles were developed using regression analysis in SPSS. The analysis found the highest correlation with the square root of SPT-N. The proposed correlation equation had high reliability and was within the range of existing correlations, indicating its accuracy for estimating friction angles using SPT-N values in the local context of Sri Lanka.

1. 1
CORRELATION BETWEEN SPT-N VALUE
AND FRICTION ANGLE
FOR THE SRI LANKAN CONTEXT
Liyanage A.I1
and Priyankara N.H2
1
Irrigation Department, Sri Lanka
2
Department of Civil and Environmental Engineering, Faculty of Engineering,
University of Ruhuna, Sri Lanka
liyanageamal@ymail.com
Abstract
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. This research has the aim to establish a correlation between SPT-N value and
internal friction angle for the local context. For this study, 25 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 regression analysis.
Square root SPT- N value and friction angle show the highest meaningful relationship.
For the developed correlation, the Reliability index value was 0.857, Kendall’s tau_b,
Spearman’s rho, and Pearson correlation values were 0.833,0.924 and 0.924 respectively.
Comparison results show proposed correlation is in the range of existing predictors
indicating its accuracy. Hence, the proposed correlation will give a quick and easy
approach to determine the internal friction angle in local context.
Keywords: SPT N, Friction Angle, Correlations, Local Context, SPSS
1. INTRODUCTION
Soil sampling associated with laboratory testing is the most reliable way to determine soil
characteristics. Sometimes due to limited budgets, tight schedules, or lack of concern,
projects do not receive proper laboratory recommendations and tendency to avoid the
laboratory tests. However, in many cases, SPT- N value (Standard Penetration Test Blow
Count) along with soil type is available to judge the subsurface soil characteristics. SPT -
N value is an index for quick prediction of shear strength characteristic of soil due to its
simplicity. However, it is very difficult to predict the outcomes of those relations without
justifying them for local condition. As such Sri Lanka is a tropical country, the
applicability of such empirical correlations developed by other countries is questionable.
Hence the local soil may follow previous correlations with slight deviation or may not
follow the trend at all. Several studies have been done based on SPT - N value and shear

2. 2
strength properties of soil using different approaches. An early attempt was made by Peck
in 1953 based on SPT-N value to predict the friction angle for sandy soil 1
. Dunham in
1954, derived three different correlations for three different shapes of the grain of soil
particles to predict the internal friction angle of soil based on SPT- N value 1
. In 1957,
Meyerhof proposed an empirical equation relating the SPT- N, effective overburden
pressure, 𝜎𝑣
,
and the relative density of sandy soils, 𝐷𝑟.
1
Peck, Hanson and Thornburn,
1974 proposed an empirical equation between friction angle and SPT-N60.
2
Shioi and
Fukui,1982 proposed empirical relationships between friction angle and energy corrected
SPT- N70. 2
Hettiarachchi and Brown established a correlation between friction angle and
SPT- N60 using energy balance approaches. 3
2. METHODOLOGY
2.1 Sample Collection and Laboratory Investigation
Sample collection was achieved from obtaining SPT- N known soil samples, covering
different locations of the country. Samples were classified according to the Unified Soil
Classification System (USCS). Further, shear strength parameters and soil index
properties were determined. All laboratory tests were conducted in the geotechnical
laboratory at the Faculty of Engineering, University of Ruhuna, Sri Lanka.
2.2 Data Analysis
SPSS (Statistical Package for Social Science) software was used for analysis. Identify the
significance between laboratory determined soil properties and SPT –N values. The
significance was evaluated based on Pearson Correlations Coefficient. Variables were
internal friction angle, SPT- N , log SPT, ℓn SPT, √𝑆𝑃𝑇 𝑁 , moisture content, bulk
density, and dry density. Correlation equations are generalized using two variable and
multivariable linear regression analysis.
2.3 Equation for In-Situ Applications
Reliability index value (R2
) was used for selection of the best-fit equation. A total of 12
equations were developed and selected best-fit equation was developed for in-situ
application. Following statistical hypotheses were considered for evaluating model
meaningful using Fisher test under 95% confidence level. Pearson correlation coefficient,
Kendall’s tau_b and Spearman’s rho correlation coefficient were evaluated.
.
H0: β=0, The model is not meaningful
H1: β≠0, The model is meaningful
Sig. (ρ –value) > α=0.05→H0 acceptable
Sig. (ρ –value) < α=0.05→H1 acceptable

3. 3
3. RESULTS AND DISCUSSION
3..1 Laboratory Results
Summary of laboratory test results have been tabulated in Table 1 with relevant SPT-N
values.
Table 1: Laboratory Results
3.2. Results in Meaningful Variables
The highest meaningfulness indicated between √𝑆𝑃𝑇 𝑁 and friction angle showing 0.779
Pearson correlation Value.
3.3 Generalized Equations Using Linear Regression Analysis
Using regression analysis 12 correlations were developed and the best fit correlation was
selected comparing the Reliability index (R2
). Best fit correlation was observed from Eq.
(01). (R2
= 0.710)
𝜑 = 2.038 √𝑁 − 12.260𝛾 + 52.030 (01)
Sample
No
SPT-N
Bulk
Density
(g/cm3
)
Friction Angle-
(Based on Direct
Shear Test) ˚
Moisture
Content
10 25 1.57 46.51 14.07
11 2 2.13 32.21 22.1
12 63 1.63 42.83 8.65
14 7 1.91 29.07 0.68
16 7 2.18 25.36 14.3
17 24 2.01 35.94 15.46
18 3 2.04 30.88 10.86
19 41 1.96 48.09 9.72
20 7 1.91 36.42 0.31
23 50 2.07 41.31 11.27
24 50 2.20 39.76 15.52
25 50 1.90 42.95 16.27

4. 4
Where, 𝜑 is the friction angle, √𝑁 is square root value of field SPT -N, 𝛾 is bulk density
(g/cm3
)
3.4 Proposed Equation for In-Situ Applications
Laboratory determined bulk density values of SP soil samples with the corresponding
SPT- N values were applied in Eq. (01) and calculate the friction angle. These results were
model considering the Polynomial graph pattern. Fisher test indicated meaningfulness of
model and R2
was 0.857. Spearman’s rho Correlation Coefficient was 0.924, Pearson
Correlation Coefficient results 0.924 and Correlation -Kendall’s tau_b was 0.833.
𝜑 = −0.093𝑁 + 3.2√𝑁 + 25.09 (02)
Table 2:ANOVA table for studying the meaningfulness of the model
ANOVA
Equation (02)
Sum of
Squares
df
Mean
Square
F Sig
Between People 377.874 11 34.352
Within
People
Between Items 6495.118 1 6495.118 839.363 .000
Residual 85.120 11 7.738
Total 6580.238 12 548.353
Total 6958.111 23 302.527
Grand Mean = 21.1625
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
Figure 1: Developed Polynomial Graph

5. 5
3.5 Comparison of Proposed Correlation Equation and Existing Correlations
The comparison was done based on the current study and Dunham’s equation for well-
graded soil, Japan road association equation (1990), Equation Proposed by Wolff (1982)
and Shioi and Fuki’s equation developed for buildings. Graphically comparison is
illustrated in Figure 2. It can be clearly seen that proposed equation is in the range of
existing predictors indicating the accuracy of the proposed equation.
4. CONCLUSIONS
Deriving empirical equations among various geotechnical parameters such as SPT -N
value and friction angle of soil is very important in different areas. It produces a fast and
simple approach compared to a laboratory approach. The correlation proposed in this
research to estimate internal friction angle (𝜑) using SPSS software are based on the
laboratory test data taken from 25 soil samples. Samples were classified using USCS and
12 samples were classified as SP soil. Thus, established equations are valid for Poorly
Graded Sand (SP). Equation (2) was selected as the applicable correlation for Poorly
Graded sand in order to determine friction angle using raw SPT-N. It will give a quick and
easy approach to determine the internal friction angle in the local context.
REFERENCES
1. Hatanka, M. & Uchida, A., 1996, “Empirical Correlation between Penetration
Resistance and Internal Friction Angle of Sandy Soils’’ Soil and Foundation, Vol 36,
No. 4, pp.1-9
2. Shooshpasha et al, 2015, ‘An investigation of friction angle correlation with
geotechnical properties for granular soils using GMDH type neural network, Scientia
Iranica, May ,157-164
3. Hettiarachchi H. & Brown, T., 2009, “Use of SPT Blow Counts to Estimate Shear
Strength Properties of Soils: Energy Balance Approach', Journal of Geotechnical and
Geoenvironmental Engineering, June, 830- 834
0
20
40
0 10 20 30 40 50 60 70
Friction
Angle
(φ)˚
SPT N
Dunham Equation for Angular and Well Grained Soil
Particles
Japan Road Association Equation (1990)
Equation by Wolff (1982)
Shioi and Fuki's Equation for Buildings
Proposed Equation (Eq:02)
Figure 2-Graphically Comparison