Prediction of Geotechnical Parameters Using Machine Learning Techniques

Abstract

Machine Learning (ML) is a science dealing with the study and development of computational models of learning and discovery process, alongwith building learning programs for specific applications. In the present study, ML techniques have been used to develop correlations for predicting geotechnical parameters for Civil Engineering design. For the determination of design values, strength and compressibility tests need to be carried out on undisturbed samples of soil. It is difficult to obtain an undisturbed sample every time, due to handling, transportation, the release of overburden pressure and poor laboratory conditions. ML techniques can predict fairly accurate values of various geotechnical parameters like in-situ density, compression index (Cc) and shear strength parameters (c and ϕ), if accurate datasets of laboratory and field results are used to develop the models. Several ML techniques like Linear Regression (LR), Artificial Neural Network (ANN), Support Vector Machine (SVM), Random Forest (RF) and M5 tree (M5P) have been used for the analysis. In the present study, relationships between in-place density using SPT N-value, compression index (Cc) using liquid limit (LL) and void ratio (e), and cohesion (c) and angle of internal friction (ϕ) using SPT N-value have been developed. Geotechnical data up to a depth of 50 m from 1053 borehole locations covering almost every district in the state of Haryana have been considered to develop models and statistical correlations. A general trend has been recorded in the observed data and accordingly, the outliers have been excluded. Several models have been developed to establish functional correlations. These correlations have been ranked on the basis their coefficient of determination (R2) value and mean absolute error (MAE). Subsequently, the model with the highest R2 value and minimum mean absolute error has been considered for the development of correlations. Sensitivity analysis has also been carried out for all the developed correlations to assess their individual performance. For this purpose, all the developed models have been evaluated by fitting a straight line between observed and modelled values, and in all the cases, a good value of R2 has been observed. The R2 values obtained for all the models range from 0.798 to 0.988. On comparison, it has been observed that the values of geotechnical parameters obtained are in close agreement with the existing work.

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Procedia Computer Science 125 (2018) 509–517
1877-0509 © 2018 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the scientific committee of the 6th International Conference on Smart Computing and Communications
10.1016/j.procs.2017.12.066
10.1016/j.procs.2017.12.066 1877-0509
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510 Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517
2 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
1. Introduction
In Geotechnical Engineering, empirical correlations are frequently used to evaluate various engineering properties
of soils. Correlations are generally derived with the help of statistical methods using data from extensive laboratory
or field testing. Linear Regression (LR) Analysis, Artificial Neural Network (ANN), Support Vector Machine
(SVM), Random Forest (RF) and M5 model trees (M5P) are some of the types of machine learning techniques.
These techniques learn from data cases presented to them to capture the functional relationship among the data even
if the fundamental relationships are unknown or the physical meaning is tough to explain. This contrasts with most
traditional empirical and statistical methods, which need prior information about the nature of the relationships
among the data. ML is thus well suited to model the complex performance of most Geotechnical Engineering
materials, which, by their very nature, exhibit extreme erraticism. This modeling capability, as well as the ability to
learn from experience, has given ML techniques superiority over most traditional modeling approaches since there is
no need for making assumptions about what could be the primary rules that govern the problem in hand. These
techniques are being widely used to solve various civil engineering problems[1-10].
Geotechnical parameters like in-place density, compression index (Cc), coefficient of consolidation (Cv), strength
characteristics (c, ϕ) are extensively used for the design of earthen dams, embankments, pavements, landfill liners
and foundation of various Civil Engineering structures. Most of these parameters are determined in the laboratory
and some are estimated on the field. Their calculation requires a specific laboratory equipment, an experienced
geotechnical engineer with a team of skilled technicians. Thus, determination of these parameters is costly and time
consuming. Also, soil is a highly erratic material as its performance is based on the processes due to which it is
formed. Hence, correlations developed for one region may not be applicable for the other. This ascertains the need to
develop region-based correlations to predict geotechnical properties.
In the present study, engineering parameters like in-place density, compression index (Cc), strength
characteristics, namely cohesion (c) and angle of internal friction (ϕ) have been correlated with soil parameters
determined in laboratory and in field. For this purpose, machine learning techniques like Linear Regression (LR)
Analysis, Artificial Neural Network (ANN), Support Vector Machine (SVM), Random Forest (RF) and M5 Tree
(M5P) have been used. Geotechnical data have been collected from various government and private organizations
across Haryana and optimized for development of more accurate models. The results indicate that developed models
are very accurate and provide a viable tool to site engineers and consultants for predicting missing data, and for cross
checking the observed values.
2. Study Area, Data Collection and Methodology
Haryana is a non-coastal state in North India with its capital at Chandigarh. It is a moderate sized state having an
area of 44,212 km2, which is 40 times the area of Delhi. It ranks 19th in terms of area in the country. It is surrounded
by the states of Uttarakhand, Himachal Pradesh and Shiwalik hills on the North, Uttar Pradesh on the East, Punjab
on the West and Delhi, Rajasthan and Aravali hills on the South. It lies between 27°39' to 30°35' N latitude and
74°28' and 77°36' E longitude. The country’s capital Delhi is surrounded by Haryana from three sides, forming the
northern, western and southern borders of Delhi. Consequently, a large area of Haryana is included in the National
Capital Region (NCR) for the purposes of planning for development. Haryana is a leading state in the country on
both the industrial and agricultural front. The state has invested in the development of world class infrastructure
facilities such as special economic zones (SEZs), Kundli-Manesar-Palwal (KMP) global corridor and Delhi-Mumbai
industrial corridor (DMIC) [11].
Geotechnical data collected from Public Works Department (PWD), Delhi Metro Rail Corporation (DMRC),
Northern Railways (NR), Haryana Urban Development Authority (HUDA), Nuclear Power Corporation of India
Limited (NPCIL), Rail Vikas Nigam Limited (RVNL) and several geotechnical consultants have been used in the
study. The developed geotechnical database has information for 1053 distinct locations in the State of Haryana
covering almost each district up to a depth of 50 m.
The observed values of geotechnical properties for 1053 borehole locations have been considered for
development of various models and statistical correlations. Sorting of relevant data has been carried out by
observing a recurring trend and thus deleting the outliers from the data sets. The models were then ranked based on
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 3
their coefficient of determination (R2) and Mean Absolute Error (MAE). Analysis has been carried out by plotting
the observed and modeled values on ordinate and abscissa respectively [12] for all the models to assess their
individual performance. Figure 1 shows typical performance analysis of SVM model for predicting angle of internal
friction of soil (ϕ) using SPT N-value.
Fig. 1 Performance analysis of SVM model for predicting angle of internal friction of soil (ϕ) using SPT N-value
3. Results and Discussions
3.1 In-Situ Density
Prediction capabilities of all the developed models have been evaluated by fitting a straight line between
observed and modeled values. High value of R2 ranging from 0.84 to 0.97 has been observed between modeled and
observed densities for all the models.Observed error estimates for the models developed for predicting in-place
density using SPT N-value are presented in Table 1. All the 20 models have been ranked based on their overall
performance including their prediction capability, R2 value of the correlation and MAE of the correlation. For coarse
grained soils, models developed using M5P and linear regression have shown maximum accuracy in estimation of
bulk density (ρb) and dry density (ρd) respectively. In the case of fine grained soils, M5P and ANN models have
shown maximum accuracy in the estimation of bulk and dry density respectively. Consequently, best models, model
number 17 (R2 value of 0.95) and number 2 (R2 value of 0.96) have been adopted for determination of bulk and dry
density for coarse grained soils respectively. Model number 19 (R2 value of 0.97) and number 8 (R2 value of 0.9)
have been adopted for determination of bulk and dry density of fine grained soils respectively. The proposed
correlations established have been reported in Table 2.
Table 1. Observed error estimate of models for in-place density and SPT N-value
Model
No. Technique Soil Type Soil
Property (R2)
Mean
Absolute
Error
(g/cm3)
Root
Mean
Squared
Error
(g/cm3)
Relative
Absolute
Error (%)
Root
Relative
Squared
Error (%)
1 Regression Coarse Bulk Density 0.91 0.05 0.06 41.65% 40.65 %

Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517 511
2 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
1. Introduction
In Geotechnical Engineering, empirical correlations are frequently used to evaluate various engineering properties
of soils. Correlations are generally derived with the help of statistical methods using data from extensive laboratory
or field testing. Linear Regression (LR) Analysis, Artificial Neural Network (ANN), Support Vector Machine
(SVM), Random Forest (RF) and M5 model trees (M5P) are some of the types of machine learning techniques.
These techniques learn from data cases presented to them to capture the functional relationship among the data even
if the fundamental relationships are unknown or the physical meaning is tough to explain. This contrasts with most
traditional empirical and statistical methods, which need prior information about the nature of the relationships
among the data. ML is thus well suited to model the complex performance of most Geotechnical Engineering
materials, which, by their very nature, exhibit extreme erraticism. This modeling capability, as well as the ability to
learn from experience, has given ML techniques superiority over most traditional modeling approaches since there is
no need for making assumptions about what could be the primary rules that govern the problem in hand. These
techniques are being widely used to solve various civil engineering problems[1-10].
Geotechnical parameters like in-place density, compression index (Cc), coefficient of consolidation (Cv), strength
characteristics (c, ϕ) are extensively used for the design of earthen dams, embankments, pavements, landfill liners
and foundation of various Civil Engineering structures. Most of these parameters are determined in the laboratory
and some are estimated on the field. Their calculation requires a specific laboratory equipment, an experienced
geotechnical engineer with a team of skilled technicians. Thus, determination of these parameters is costly and time
consuming. Also, soil is a highly erratic material as its performance is based on the processes due to which it is
formed. Hence, correlations developed for one region may not be applicable for the other. This ascertains the need to
develop region-based correlations to predict geotechnical properties.
In the present study, engineering parameters like in-place density, compression index (Cc), strength
characteristics, namely cohesion (c) and angle of internal friction (ϕ) have been correlated with soil parameters
determined in laboratory and in field. For this purpose, machine learning techniques like Linear Regression (LR)
Analysis, Artificial Neural Network (ANN), Support Vector Machine (SVM), Random Forest (RF) and M5 Tree
(M5P) have been used. Geotechnical data have been collected from various government and private organizations
across Haryana and optimized for development of more accurate models. The results indicate that developed models
are very accurate and provide a viable tool to site engineers and consultants for predicting missing data, and for cross
checking the observed values.
2. Study Area, Data Collection and Methodology
Haryana is a non-coastal state in North India with its capital at Chandigarh. It is a moderate sized state having an
area of 44,212 km2, which is 40 times the area of Delhi. It ranks 19th in terms of area in the country. It is surrounded
by the states of Uttarakhand, Himachal Pradesh and Shiwalik hills on the North, Uttar Pradesh on the East, Punjab
on the West and Delhi, Rajasthan and Aravali hills on the South. It lies between 27°39' to 30°35' N latitude and
74°28' and 77°36' E longitude. The country’s capital Delhi is surrounded by Haryana from three sides, forming the
northern, western and southern borders of Delhi. Consequently, a large area of Haryana is included in the National
Capital Region (NCR) for the purposes of planning for development. Haryana is a leading state in the country on
both the industrial and agricultural front. The state has invested in the development of world class infrastructure
facilities such as special economic zones (SEZs), Kundli-Manesar-Palwal (KMP) global corridor and Delhi-Mumbai
industrial corridor (DMIC) [11].
Geotechnical data collected from Public Works Department (PWD), Delhi Metro Rail Corporation (DMRC),
Northern Railways (NR), Haryana Urban Development Authority (HUDA), Nuclear Power Corporation of India
Limited (NPCIL), Rail Vikas Nigam Limited (RVNL) and several geotechnical consultants have been used in the
study. The developed geotechnical database has information for 1053 distinct locations in the State of Haryana
covering almost each district up to a depth of 50 m.
The observed values of geotechnical properties for 1053 borehole locations have been considered for
development of various models and statistical correlations. Sorting of relevant data has been carried out by
observing a recurring trend and thus deleting the outliers from the data sets. The models were then ranked based on
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 3
their coefficient of determination (R2) and Mean Absolute Error (MAE). Analysis has been carried out by plotting
the observed and modeled values on ordinate and abscissa respectively [12] for all the models to assess their
individual performance. Figure 1 shows typical performance analysis of SVM model for predicting angle of internal
friction of soil (ϕ) using SPT N-value.
Fig. 1 Performance analysis of SVM model for predicting angle of internal friction of soil (ϕ) using SPT N-value
3. Results and Discussions
3.1 In-Situ Density
Prediction capabilities of all the developed models have been evaluated by fitting a straight line between
observed and modeled values. High value of R2 ranging from 0.84 to 0.97 has been observed between modeled and
observed densities for all the models.Observed error estimates for the models developed for predicting in-place
density using SPT N-value are presented in Table 1. All the 20 models have been ranked based on their overall
performance including their prediction capability, R2 value of the correlation and MAE of the correlation. For coarse
grained soils, models developed using M5P and linear regression have shown maximum accuracy in estimation of
bulk density (ρb) and dry density (ρd) respectively. In the case of fine grained soils, M5P and ANN models have
shown maximum accuracy in the estimation of bulk and dry density respectively. Consequently, best models, model
number 17 (R2 value of 0.95) and number 2 (R2 value of 0.96) have been adopted for determination of bulk and dry
density for coarse grained soils respectively. Model number 19 (R2 value of 0.97) and number 8 (R2 value of 0.9)
have been adopted for determination of bulk and dry density of fine grained soils respectively. The proposed
correlations established have been reported in Table 2.
Table 1. Observed error estimate of models for in-place density and SPT N-value
Model
No. Technique Soil Type Soil
Property (R2)
Mean
Absolute
Error
(g/cm3)
Root
Mean
Squared
Error
(g/cm3)
Relative
Absolute
Error (%)
Root
Relative
Squared
Error (%)
1 Regression Coarse Bulk Density 0.91 0.05 0.06 41.65% 40.65 %

512 Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517
4 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
Table 2. Proposed correlations between in-place density and SPT N-value
3.2 Compression Index of Soil
2 Analysis Coarse Dry Density 0.96 0.01 0.02 23.65 % 25. 65 %
3 Fine Bulk Density 0.97 0.01 0.02 19.50 % 23.39 %
4 Fine Dry Density 0.90 0.04 0.06 41.35 % 42.55 %
5
Artificial
Neural
Network
Coarse Bulk Density 0.90 0.05 0.06 45.57 % 44.46%
6 Coarse Dry Density 0.95 0.02 0.02 30.04 % 32.52%
7 Fine Bulk Density 0.97 0.02 0.03 21.98 % 25.31 %
8 Fine Dry Density 0.90 0.04 0.05 39.34 % 38.13 %
9
Support Vector
Machine
Coarse Bulk Density 0.91 0.04 0.06 39.45 % 43.94 %
10 Coarse Dry Density 0.94 0.02 0.03 28.40% 34.52%
11 Fine Bulk Density 0.96 0.01 0.02 19.5 % 23.39 %
12 Fine Dry Density 0.89 0.04 0.05 39.34 % 38.13 %
13
Random Forest
Coarse Bulk Density 0.92 0.04 0.06 37.34 % 39.24 %
14 Coarse Dry Density 0.96 0.01 0.02 24.79% 26.95 %
15 Fine Bulk Density 0.95 0.02 0.02 25.93 % 30.67 %
16 Fine Dry Density 0.84 0.05 0.072 50.90 % 55.02 %
17
M5 Model Tree
Coarse Bulk Density 0.95 0.02 0.03 22.83 % 25.24 %
18 Coarse Dry Density 0.94 0.02 0.02 29.01 % 32.87 %
19 Fine Bulk Density 0.97 0.01 0.02 19.54 % 23.62 %
20 Fine Dry Density 0.90 0.04 0.06 41.35 % 42.55 %
Eq. No. Soil Type Soil Property Correlation Unit N Value Technique R2
1. (a)
Coarse Grained Bulk density (ρb) ρb = 0.0096 * N + 1.5001 g/cm3 1-39 M5P 0.95
1. (b) Coarse Grained Bulk density (ρ
b
) ρ
b
= 0.0141 * N + 1.3726 g/cm3 40-50 M5P 0.95
2. Coarse Grained Dry Density (ρd) ρd = 0.0068 * N + 1.5554 g/cm3 1-50 LR 0.96
3. Fine Grained Bulk Density (ρb) ρb = 0.0080 * N + 1.7202 g/cm3 1-50 M5P 0.97
4. Fine Grained Dry Density (ρd) ρd = 0.0114 * N + 1.2488 g/cm3 1-50 ANN 0.90
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 5
A total of 10 models have been developed and their prediction capabilities have been evaluated by fitting a
straight line between observed and modeled values. The proximity of scatter graphs (with R2 ranging from 0.86 to
0.92) obtained between observed and modeled values proves high efficiency of the developed correlations. Models
have been ranked based on their overall performance. For estimation of Cc using liquid limit and void ratio, models
developed using M5P technique (model 5 and 10 respectively) have shown maximum accuracy, with R2 value of
0.92 for determining Cc using liquid limit and R2 value of 0.96 for determining Cc using void ratio as reported in
Tables 3-4. The established correlations are reported in Table 5. This study also concludes that machine learning
techniques offer distinct advantages over conventional hand calculations and laboratory tests. The developed
correlations for the determination of Cc from liquid limit have been compared with the correlations developed by
Skempton [13] and Terzaghi & Peck [14] as shown in the Figure 2. It has been observed, that the modeled values of
Ccare on the lower side of the Terzaghi & Peck [14] and in close agreement with Skempton [13]. The correlations
developed for the determination of Cc with the value of void ratio have been compared with the correlations
developed by Cozzolino [15], Azzouz et al. [16] and Kalantary and Kordnaeij [17]. It has been observed that the
calculated values of Cc using present study are on the higher side of the values obtained by Azzouz et al. [16], but
closer to the values obtained by Cozzolino [15]. For the values calculated using Kalantary and Kordnaeij [17], it has
been observed that there is a proximity in Cc value with the present study when void ratio is less than 0.8, beyond a
void ratio of 0.8; values modeled by present study are on the higher side, as shown in Figure 3.
Table 3. Developed models and their performance indices for compression index (Cc) and liquid limit (LL)
Table 4. Developed models and their performance indices for compression index (Cc) and void ratio (e)
Table 5. Proposed correlations for compression
Model
Number
Technique Coefficient of
Determination
(R2)
Mean
Absolute
Error
Root Mean
Squared Error
Relative Absolute
Error (%)
Root Relative
Squared Error
(%)
1 Linear Regression 0.86 0.012 0.015 49.78 % 51.50 %
2 Artificial Neural Network 0.81 0.014 0.177 59.56 % 60.57 %
3 Support Vector Machine 0.86 0.012 0.015 49.73 % 51.29 %
4 Random Forest 0.91 0.009 0.012 37.29 % 39.78 %
5 M5 Tree 0.92 0.009 0.012 38.62 % 40.54 %
Model
Number
Technique Coefficient of
Determination
(R2)
Mean
Absolute
Error
Root Mean
Squared Error
Relative
Absolute Error
(%)
Root Relative
Squared Error
(%)
6 Linear Regression 0.92 0.014 0.018 35.27 % 39.03 %
7 Artificial Neural Network 0.92 0.014 0.019 36.52 % 39.74 %
8 Support Vector Machine 0.92 0.013 0.021 34.29 % 45.62 %
9 Random Forest 0.94 0.010 0.016 24.83 % 33.26 %
10 M5 Tree 0.95 0.011 0.014 22.44 % 30.21 %
Index
Property
Equation
Number
Correlations Coefficient of
Determination
(R2)
Technique Remarks
Liquid
Limit (LL)
1 Cc = (0.0092 * LL) - 0.1091 0.92 M5P LL ≤ 29.25
2 Cc = (0.0017 * LL) + 0.1235 29.25 < LL < 37.35
3 Cc = (0.0064 * LL) - 0.05237 LL ≥ 37.35
Void Ratio
(e)
4 Cc = (0.2945 * e) - 0.0774 0.95 M5P e ≤ 0.495
5 Cc = (0.2534 * e) - 0.052 0.495 < e < 0.615
6 Cc = (0.7071 * e) - 0.3471 e ≥ 0.615

Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517 513
4 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
Table 2. Proposed correlations between in-place density and SPT N-value
3.2 Compression Index of Soil
2 Analysis Coarse Dry Density 0.96 0.01 0.02 23.65 % 25. 65 %
3 Fine Bulk Density 0.97 0.01 0.02 19.50 % 23.39 %
4 Fine Dry Density 0.90 0.04 0.06 41.35 % 42.55 %
5
Artificial
Neural
Network
Coarse Bulk Density 0.90 0.05 0.06 45.57 % 44.46%
6 Coarse Dry Density 0.95 0.02 0.02 30.04 % 32.52%
7 Fine Bulk Density 0.97 0.02 0.03 21.98 % 25.31 %
8 Fine Dry Density 0.90 0.04 0.05 39.34 % 38.13 %
9
Support Vector
Machine
Coarse Bulk Density 0.91 0.04 0.06 39.45 % 43.94 %
10 Coarse Dry Density 0.94 0.02 0.03 28.40% 34.52%
11 Fine Bulk Density 0.96 0.01 0.02 19.5 % 23.39 %
12 Fine Dry Density 0.89 0.04 0.05 39.34 % 38.13 %
13
Random Forest
Coarse Bulk Density 0.92 0.04 0.06 37.34 % 39.24 %
14 Coarse Dry Density 0.96 0.01 0.02 24.79% 26.95 %
15 Fine Bulk Density 0.95 0.02 0.02 25.93 % 30.67 %
16 Fine Dry Density 0.84 0.05 0.072 50.90 % 55.02 %
17
M5 Model Tree
Coarse Bulk Density 0.95 0.02 0.03 22.83 % 25.24 %
18 Coarse Dry Density 0.94 0.02 0.02 29.01 % 32.87 %
19 Fine Bulk Density 0.97 0.01 0.02 19.54 % 23.62 %
20 Fine Dry Density 0.90 0.04 0.06 41.35 % 42.55 %
Eq. No. Soil Type Soil Property Correlation Unit N Value Technique R2
1. (a)
Coarse Grained Bulk density (ρb) ρb = 0.0096 * N + 1.5001 g/cm3 1-39 M5P 0.95
1. (b) Coarse Grained Bulk density (ρ
b
) ρ
b
= 0.0141 * N + 1.3726 g/cm3 40-50 M5P 0.95
2. Coarse Grained Dry Density (ρd) ρd = 0.0068 * N + 1.5554 g/cm3 1-50 LR 0.96
3. Fine Grained Bulk Density (ρb) ρb = 0.0080 * N + 1.7202 g/cm3 1-50 M5P 0.97
4. Fine Grained Dry Density (ρd) ρd = 0.0114 * N + 1.2488 g/cm3 1-50 ANN 0.90
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 5
A total of 10 models have been developed and their prediction capabilities have been evaluated by fitting a
straight line between observed and modeled values. The proximity of scatter graphs (with R2 ranging from 0.86 to
0.92) obtained between observed and modeled values proves high efficiency of the developed correlations. Models
have been ranked based on their overall performance. For estimation of Cc using liquid limit and void ratio, models
developed using M5P technique (model 5 and 10 respectively) have shown maximum accuracy, with R2 value of
0.92 for determining Cc using liquid limit and R2 value of 0.96 for determining Cc using void ratio as reported in
Tables 3-4. The established correlations are reported in Table 5. This study also concludes that machine learning
techniques offer distinct advantages over conventional hand calculations and laboratory tests. The developed
correlations for the determination of Cc from liquid limit have been compared with the correlations developed by
Skempton [13] and Terzaghi & Peck [14] as shown in the Figure 2. It has been observed, that the modeled values of
Ccare on the lower side of the Terzaghi & Peck [14] and in close agreement with Skempton [13]. The correlations
developed for the determination of Cc with the value of void ratio have been compared with the correlations
developed by Cozzolino [15], Azzouz et al. [16] and Kalantary and Kordnaeij [17]. It has been observed that the
calculated values of Cc using present study are on the higher side of the values obtained by Azzouz et al. [16], but
closer to the values obtained by Cozzolino [15]. For the values calculated using Kalantary and Kordnaeij [17], it has
been observed that there is a proximity in Cc value with the present study when void ratio is less than 0.8, beyond a
void ratio of 0.8; values modeled by present study are on the higher side, as shown in Figure 3.
Table 3. Developed models and their performance indices for compression index (Cc) and liquid limit (LL)
Table 4. Developed models and their performance indices for compression index (Cc) and void ratio (e)
Table 5. Proposed correlations for compression
Model
Number
Technique Coefficient of
Determination
(R2)
Mean
Absolute
Error
Root Mean
Squared Error
Relative Absolute
Error (%)
Root Relative
Squared Error
(%)
1 Linear Regression 0.86 0.012 0.015 49.78 % 51.50 %
2 Artificial Neural Network 0.81 0.014 0.177 59.56 % 60.57 %
3 Support Vector Machine 0.86 0.012 0.015 49.73 % 51.29 %
4 Random Forest 0.91 0.009 0.012 37.29 % 39.78 %
5 M5 Tree 0.92 0.009 0.012 38.62 % 40.54 %
Model
Number
Technique Coefficient of
Determination
(R2)
Mean
Absolute
Error
Root Mean
Squared Error
Relative
Absolute Error
(%)
Root Relative
Squared Error
(%)
6 Linear Regression 0.92 0.014 0.018 35.27 % 39.03 %
7 Artificial Neural Network 0.92 0.014 0.019 36.52 % 39.74 %
8 Support Vector Machine 0.92 0.013 0.021 34.29 % 45.62 %
9 Random Forest 0.94 0.010 0.016 24.83 % 33.26 %
10 M5 Tree 0.95 0.011 0.014 22.44 % 30.21 %
Index
Property
Equation
Number
Correlations Coefficient of
Determination
(R2)
Technique Remarks
Liquid
Limit (LL)
1 Cc = (0.0092 * LL) - 0.1091 0.92 M5P LL ≤ 29.25
2 Cc = (0.0017 * LL) + 0.1235 29.25 < LL < 37.35
3 Cc = (0.0064 * LL) - 0.05237 LL ≥ 37.35
Void Ratio
(e)
4 Cc = (0.2945 * e) - 0.0774 0.95 M5P e ≤ 0.495
5 Cc = (0.2534 * e) - 0.052 0.495 < e < 0.615
6 Cc = (0.7071 * e) - 0.3471 e ≥ 0.615

514 Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517
6 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
3.3 Strength Parameters of Soil
The overall performance of all the 10 developed models has been assessed based on their R2 values, MAE and
performance analysis. High value of R2 ranging from 0.8 to 0.99 has been observed for the estimation of cohesion
and angle of internal friction value for all the models in performance analysis. For the estimation of the angle of
internal friction by SPT N-value, SVM technique has been observed to be more useful with a R
2 value of 0.98
(model number 3) (Tables 6). For the estimation of cohesion using SPT N-value, model developed using M5P
technique has shown maximum accuracy, with a R2 value of 0.93 (model number 10) (Tables 7). The established
correlations are reported in Table 8. Also, a comparison has been done for the model number 3 predicting cohesion
value with the studies carried out by Terzaghi & Peck [18] and Kumar et al. [19], as show in the Figure 4. It has
been observed that value of cohesion obtained in the present study is on the lower side of the other studies.
Figure 2. Comparison between prediction models for compression indices (Cc) using liquid limit (LL)
Figure 3. Comparison between prediction models for compression indices (Cc) using void ratio (e)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Compression Index (Cc)
Void Ratio (e)
Present Stud
y
Cozzolino
(
1961
)
Azzouz
(
1976
)
Kalantar
y
et al
(
2012
)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
10 15 20 25 30 35 40 45 50 55 60
Compression Index (Cc)
Liquid Limit (%)
Present
S
tud
y
S
kem
p
ton
(
1944
)
Terzha
g
i and Peck
(
1967
)
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 7
Table 6. Developed models and their performance indices for angle of internal friction (ϕ) and SPT N-value
Similarly, a comparison between model number 10 and studies carried out by Shioi & Fukui [20] and Wolff [21] has
been done. It has been observed that the value of angle of internal friction obtained in the present study is in close
proximity to both, as shown in the Figure 5.
Table 7. Developed models and their performance indices for cohesion (c) and SPT N-value
Figure 4. Comparison between prediction models for cohesion (c) using SPT N-value.
Model
Number
Technique Coefficient of
Determination
(R2)
Mean Absolute
Error
Root Mean
Squared Error
Relative
Absolute
Error (%)
Root Relative
Squared
Error (%)
6 Linear Regression 0.93 0.237 0.311 44.72% 37.64 %
7 Artificial Neural Network 0.89 0.283 0.375 53.27 % 45.38 %
8 Support Vector Machine 0.92 0.176 0.315 33.20 % 48.56 %
9 Random Forest 0.91 0.209 0.345 39.29 % 41.72 %
10 M5 Tree 0.93 0.171 0.312 32.75 % 37.73 %
Model
Number
Technique Coefficient of
Determination
(R2)
Mean
Absolute
Error
Root Mean
Squared Error
Relative
Absolute
Error (%)
Root Relative
Squared Error
(%)
1 Linear Regression 0.98 0.495 0.664 16.12 % 17.87 %
2 Artificial Neural Network 0.98 0.596 0.784 19.40 % 21.01 %
3 Support Vector Machine 0.98 0.246 0.454 7.99 % 12.01 %
4 Random Forest 0.98 0.481 0.683 15.65 % 18.36 %
5 M5 Tree 0.98 0.319 0.494 10.37 % 13.30 %
0
0.5
1
1.5
2
2.5
3
3.5
0 10 20 30 40 50
Cohesion (kg/cm2)
Observed SPT N-Value
Present Study Terzhagi and Peck (1982) Choudhury et al (2016)
Kumar et al. (2016)

Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517 515
6 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
3.3 Strength Parameters of Soil
The overall performance of all the 10 developed models has been assessed based on their R2 values, MAE and
performance analysis. High value of R2 ranging from 0.8 to 0.99 has been observed for the estimation of cohesion
and angle of internal friction value for all the models in performance analysis. For the estimation of the angle of
internal friction by SPT N-value, SVM technique has been observed to be more useful with a R
2 value of 0.98
(model number 3) (Tables 6). For the estimation of cohesion using SPT N-value, model developed using M5P
technique has shown maximum accuracy, with a R2 value of 0.93 (model number 10) (Tables 7). The established
correlations are reported in Table 8. Also, a comparison has been done for the model number 3 predicting cohesion
value with the studies carried out by Terzaghi & Peck [18] and Kumar et al. [19], as show in the Figure 4. It has
been observed that value of cohesion obtained in the present study is on the lower side of the other studies.
Figure 2. Comparison between prediction models for compression indices (Cc) using liquid limit (LL)
Figure 3. Comparison between prediction models for compression indices (Cc) using void ratio (e)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Compression Index (Cc)
Void Ratio (e)
Present Stud
y
Cozzolino
(
1961
)
Azzouz
(
1976
)
Kalantar
y
et al
(
2012
)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
10 15 20 25 30 35 40 45 50 55 60
Compression Index (Cc)
Liquid Limit (%)
Present
S
tud
y
S
kem
p
ton
(
1944
)
Terzha
g
i and Peck
(
1967
)
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 7
Table 6. Developed models and their performance indices for angle of internal friction (ϕ) and SPT N-value
Similarly, a comparison between model number 10 and studies carried out by Shioi & Fukui [20] and Wolff [21] has
been done. It has been observed that the value of angle of internal friction obtained in the present study is in close
proximity to both, as shown in the Figure 5.
Table 7. Developed models and their performance indices for cohesion (c) and SPT N-value
Figure 4. Comparison between prediction models for cohesion (c) using SPT N-value.
Model
Number
Technique Coefficient of
Determination
(R2)
Mean Absolute
Error
Root Mean
Squared Error
Relative
Absolute
Error (%)
Root Relative
Squared
Error (%)
6 Linear Regression 0.93 0.237 0.311 44.72% 37.64 %
7 Artificial Neural Network 0.89 0.283 0.375 53.27 % 45.38 %
8 Support Vector Machine 0.92 0.176 0.315 33.20 % 48.56 %
9 Random Forest 0.91 0.209 0.345 39.29 % 41.72 %
10 M5 Tree 0.93 0.171 0.312 32.75 % 37.73 %
Model
Number
Technique Coefficient of
Determination
(R2)
Mean
Absolute
Error
Root Mean
Squared Error
Relative
Absolute
Error (%)
Root Relative
Squared Error
(%)
1 Linear Regression 0.98 0.495 0.664 16.12 % 17.87 %
2 Artificial Neural Network 0.98 0.596 0.784 19.40 % 21.01 %
3 Support Vector Machine 0.98 0.246 0.454 7.99 % 12.01 %
4 Random Forest 0.98 0.481 0.683 15.65 % 18.36 %
5 M5 Tree 0.98 0.319 0.494 10.37 % 13.30 %
0
0.5
1
1.5
2
2.5
3
3.5
0 10 20 30 40 50
Cohesion (kg/cm2)
Observed SPT N-Value
Present Study Terzhagi and Peck (1982) Choudhury et al (2016)
Kumar et al. (2016)

516 Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517
8 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
Figure 5. Comparison between prediction models for angle of internal friction (ϕ) using SPT N-value
Table 8. Proposed correlations for cohesion (c) and angle of internal friction (ϕ) using SPT N-value
4. Conclusion
An attempt has been made to develop several statistical correlations relating various geotechnical parameters of
soil using different machine learning techniques. Most of the correlations developed in this study are quite
comparable with the existing studies and have shown a proximity in trend and prediction as well. These correlations
based on geotechnical data measured in-situ are very accurate and can help in reducing errors associated with their
assumption in geotechnical engineering problems. Given the general potential of these techniques, we have barely
started to use them in solving problems. Many published studies referenced in the present work point to many
opportunities. It can be concluded that these techniques can be materialized into practical systems if the application
process is executed carefully and it can help to solve various problems very efficiently and precisely. The results of
this study can be used for crosschecking the values determined in laboratory or can also be used directly for design
purpose, where equipment and expertise are not available. The correlations presented in this study are region
specific and hence should only be used for sites falling in state of Haryana and nearby areas.
Acknowledgements
We acknowledge the help and assistance given by DST, India for the study under INSPIRE Fellowship scheme.
Authors would also like thank Mr. Madan Mohan Puri, Senior Section Engineer, Ministry of Railways, Delhi, India
for providing geotechnical reports of several construction projects located in State of Haryana without which this
study would not have been possible.
25.0
27.0
29.0
31.0
33.0
35.0
37.0
39.0
41.0
43.0
0 5 10 15 20 25 30 35 40 45 50
Angle of Internal Friction (ϕ) in degrees
Observed SPT N-Value
Present Study Shioi and Fukui (1982) Wolff (1989)
Soil Property Equation
Number
Correlations Coefficient of
Determination (R2)
Technique Units N-Value
Cohesion (c) 1 c = 0.0464 * N + 0.0075 0.93 M5P kg/cm2 1-25
2 c = 0.0702 * N – 0.5453 kg/cm2 26-52
Angle of Internal
Friction (ϕ)
3 ϕ= 0.3125 * N + 26.1261 0.99 SVM degree 1-52
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 9
References
[1] A.T.C Goh(1995). “Neural networks for evaluating CPT calibration chamber test data”.International Journal of Microcomputers in Civil
Engineering10(2): 47-51.
[2] B. Saini, V.K. Sehgal, M.L. Gambhir (2007). “Least-cost design of singly and doubly reinforced concrete beam using genetic algorithm
optimized artificial neural network based on Levenberg–Marquardt and quasi-Newton backpropagation learning techniques”. Structural and
Multidisciplinary Optimization 34 (3): 243-260.
[3] R. Siddique, P. Aggarwal and Y. Aggarwal (2011). “Prediction of compressive strength of self-compacting concrete containing bottom ash
using artificial neural networks”. Advances in Engineering Software42(10):780-786.
[4] M. Pal, N.K. Singh and N.K.Tiwari (2012).“M5 model tree for pier scour prediction using field dataset”.KSCE Journal of Civil
Engineering16(6): 107-124.
[5] N. Puri and A. Jain (2015).“Correlation between california bearing ratio and index properties of silt and clay of low compressibility”. Proc.
Fifth Indian Young Geotechnical Engineers Conference, Vadodara.
[6] G. Singh, S.N. Sachdeva and M. Pal (2016). “M5 model tree based predictive modeling of road accidents on non-urban sections of
highways in India”. Accident; analysis and prevention96:108-117.
[7] P. Anbazhagan, A. Uday, S.S.R. Moustafa, and S.N.A. Nassir (2016). “Correlation of densities with shear wave velocities and SPT N
values”. J. Geophys. Engg.13(3): 320–341.
[8] H.D. Prasad, N. Puri and A. Jain (2017). “Prediction of in-place density of soil using SPT N-value”. Proc. National Conference on Recent
Advances in Mechanical Engineering, Roorkee.
[9] B. Singh, P. Sihag and K. Singh (2017). “Modelling of impact of water quality on infiltration rate of soil by random forest regression”.
Modeling Earth Systems and Environment3(3): 999-1004.
[10] H.D. Prasad, N. Puri and A. Jain (2017). “Prediction of compression index of clays using machine learning techniques” Proc. National
Conference on Numerical Modeling in Geomechanics, Kurukshetra.
[11] https://www.ibef.org/states/haryana.aspx, Accessed on 30-10-2017.
[12] G. Pin
͂eiro, S. Perelman, J.P. Guerschman and J. M. Paruelo (2008). “How to evaluate models: observed vs. predicted or predicted vs.
observed?”. Ecological Modelling 216: 316-322.
[13] A.W. Skempton (1944). “Notes on the compressibility of clays”. Quarterly J. Geological Soc.100(1-4): 119-135.
[14] K. Terzaghi and R.B. Peck, 2nd Edition: Soil Mechanics in Engineering Practice, John Wiley and Sons, New York, 1967.
[15] V.M. Cozzolino (1961). “Statistical Forecasting of Compression Index”. Proc. 5th Int. Conf. Soil Mech. Foundation Engg, Paris.
[16] A.S. Azzouz, R.J. Krizek, and R.B. Corotis (1976). “Regression Analysis of Soil Compressibility”.Soils and Foundations16(2): 19-29.
[17] F. Kalantary and A. Kordnaeij (2012). “Prediction of compression index using artificial neural network”. Scientific Research and
Essays7(31): 2835-2848.
[18] J.E. Bowles,3rd Edition, Foundation Analysis and Design, McGraw-Hill, Inc., New York, 1982.
[19] R. Kumar, K. Bhargava and D. Choudhury (2016). “Estimation of Engineering Properties of Soils from Field SPT Using Random Number
Generation”. INAE Lett1(3-4): 77-84.
[20] Y. Shioi and J. Fukui (1982). “Application of N-Value to Design of Foundation in Japan”. 2nd ESOPT 1: 40-93.
[21] T.F. Wolff(1989). “Pile capacity prediction using parameter function”. Proc. InPredicted and Observed Axial Behavior of Piles, Results of a
PilePrediction Symposium, sponsored by Geotechnical EngineeringDivision, ASCE, Evanston, Ill., June 1989, ASCE GeotechnicalSpecial
Publication No. 23, 96-106.

Nitish Puri et al. / Procedia Computer Science 125 (2018) 509–517 517
8 Nitish Puri / Procedia Computer Science 00 (2018) 000–000
Figure 5. Comparison between prediction models for angle of internal friction (ϕ) using SPT N-value
Table 8. Proposed correlations for cohesion (c) and angle of internal friction (ϕ) using SPT N-value
4. Conclusion
An attempt has been made to develop several statistical correlations relating various geotechnical parameters of
soil using different machine learning techniques. Most of the correlations developed in this study are quite
comparable with the existing studies and have shown a proximity in trend and prediction as well. These correlations
based on geotechnical data measured in-situ are very accurate and can help in reducing errors associated with their
assumption in geotechnical engineering problems. Given the general potential of these techniques, we have barely
started to use them in solving problems. Many published studies referenced in the present work point to many
opportunities. It can be concluded that these techniques can be materialized into practical systems if the application
process is executed carefully and it can help to solve various problems very efficiently and precisely. The results of
this study can be used for crosschecking the values determined in laboratory or can also be used directly for design
purpose, where equipment and expertise are not available. The correlations presented in this study are region
specific and hence should only be used for sites falling in state of Haryana and nearby areas.
Acknowledgements
We acknowledge the help and assistance given by DST, India for the study under INSPIRE Fellowship scheme.
Authors would also like thank Mr. Madan Mohan Puri, Senior Section Engineer, Ministry of Railways, Delhi, India
for providing geotechnical reports of several construction projects located in State of Haryana without which this
study would not have been possible.
25.0
27.0
29.0
31.0
33.0
35.0
37.0
39.0
41.0
43.0
0 5 10 15 20 25 30 35 40 45 50
Angle of Internal Friction (ϕ) in degrees
Observed SPT N-Value
Present Study Shioi and Fukui (1982) Wolff (1989)
Soil Property Equation
Number
Correlations Coefficient of
Determination (R2)
Technique Units N-Value
Cohesion (c) 1 c = 0.0464 * N + 0.0075 0.93 M5P kg/cm2 1-25
2 c = 0.0702 * N – 0.5453 kg/cm2 26-52
Angle of Internal
Friction (ϕ)
3 ϕ= 0.3125 * N + 26.1261 0.99 SVM degree 1-52
Nitish Puri / Procedia Computer Science 00 (2018) 000–000 9
References
[1] A.T.C Goh(1995). “Neural networks for evaluating CPT calibration chamber test data”.International Journal of Microcomputers in Civil
Engineering10(2): 47-51.
[2] B. Saini, V.K. Sehgal, M.L. Gambhir (2007). “Least-cost design of singly and doubly reinforced concrete beam using genetic algorithm
optimized artificial neural network based on Levenberg–Marquardt and quasi-Newton backpropagation learning techniques”. Structural and
Multidisciplinary Optimization 34 (3): 243-260.
[3] R. Siddique, P. Aggarwal and Y. Aggarwal (2011). “Prediction of compressive strength of self-compacting concrete containing bottom ash
using artificial neural networks”. Advances in Engineering Software42(10):780-786.
[4] M. Pal, N.K. Singh and N.K.Tiwari (2012).“M5 model tree for pier scour prediction using field dataset”.KSCE Journal of Civil
Engineering16(6): 107-124.
[5] N. Puri and A. Jain (2015).“Correlation between california bearing ratio and index properties of silt and clay of low compressibility”. Proc.
Fifth Indian Young Geotechnical Engineers Conference, Vadodara.
[6] G. Singh, S.N. Sachdeva and M. Pal (2016). “M5 model tree based predictive modeling of road accidents on non-urban sections of
highways in India”. Accident; analysis and prevention96:108-117.
[7] P. Anbazhagan, A. Uday, S.S.R. Moustafa, and S.N.A. Nassir (2016). “Correlation of densities with shear wave velocities and SPT N
values”. J. Geophys. Engg.13(3): 320–341.
[8] H.D. Prasad, N. Puri and A. Jain (2017). “Prediction of in-place density of soil using SPT N-value”. Proc. National Conference on Recent
Advances in Mechanical Engineering, Roorkee.
[9] B. Singh, P. Sihag and K. Singh (2017). “Modelling of impact of water quality on infiltration rate of soil by random forest regression”.
Modeling Earth Systems and Environment3(3): 999-1004.
[10] H.D. Prasad, N. Puri and A. Jain (2017). “Prediction of compression index of clays using machine learning techniques” Proc. National
Conference on Numerical Modeling in Geomechanics, Kurukshetra.
[11] https://www.ibef.org/states/haryana.aspx, Accessed on 30-10-2017.
[12] G. Pin
͂eiro, S. Perelman, J.P. Guerschman and J. M. Paruelo (2008). “How to evaluate models: observed vs. predicted or predicted vs.
observed?”. Ecological Modelling 216: 316-322.
[13] A.W. Skempton (1944). “Notes on the compressibility of clays”. Quarterly J. Geological Soc.100(1-4): 119-135.
[14] K. Terzaghi and R.B. Peck, 2nd Edition: Soil Mechanics in Engineering Practice, John Wiley and Sons, New York, 1967.
[15] V.M. Cozzolino (1961). “Statistical Forecasting of Compression Index”. Proc. 5th Int. Conf. Soil Mech. Foundation Engg, Paris.
[16] A.S. Azzouz, R.J. Krizek, and R.B. Corotis (1976). “Regression Analysis of Soil Compressibility”.Soils and Foundations16(2): 19-29.
[17] F. Kalantary and A. Kordnaeij (2012). “Prediction of compression index using artificial neural network”. Scientific Research and
Essays7(31): 2835-2848.
[18] J.E. Bowles,3rd Edition, Foundation Analysis and Design, McGraw-Hill, Inc., New York, 1982.
[19] R. Kumar, K. Bhargava and D. Choudhury (2016). “Estimation of Engineering Properties of Soils from Field SPT Using Random Number
Generation”. INAE Lett1(3-4): 77-84.
[20] Y. Shioi and J. Fukui (1982). “Application of N-Value to Design of Foundation in Japan”. 2nd ESOPT 1: 40-93.
[21] T.F. Wolff(1989). “Pile capacity prediction using parameter function”. Proc. InPredicted and Observed Axial Behavior of Piles, Results of a
PilePrediction Symposium, sponsored by Geotechnical EngineeringDivision, ASCE, Evanston, Ill., June 1989, ASCE GeotechnicalSpecial
Publication No. 23, 96-106.