Novel application of machine learning for estimation of pullout coefficient of geogrid

Geosynthetics International, 2022, 29, No. 4

Novel application of machine learning for estimation
of pullout coefficient of geogrid

A. Pant1 and G.V. Ramana2

1Research Associate, Department of Civil Engineering, Indian Institute of Technology Delhi, India,
E-mail: (corresponding author)
2Professor, Department of Civil Engineering, Indian Institute of Technology Delhi, India,
E-mail:

Received 02 June 2021, accepted 15 September 2021, published 09 March 2022

ABSTRACT: Pullout behaviour of geogrids is critical to understand for the design of mechanically
stabilized earth walls. The pullout coefficients are determined through laboratory testing on geogrids
embedded in structural fill. Random forest (RF) is a data-driven ensemble learning method that uses
decision trees for classification and regression tasks. In the present study, the use of the RF regression
technique for estimation of pullout coefficient of geogrid embedded in different structural fills and at
variable normal stress based on 198 test results has been investigated using five-fold cross-validation.
80% of the data has been trained on the model algorithm and the accuracy of the model is then tested on
20% of the remaining dataset. The performance of the model has been checked using statistical indices,
namely R2, mean square error, as well as external validation methods. The validity of the model has also
been checked against laboratory tests conducted on geogrid embedded in four different fills. The results
of the RF model have been compared to results obtained with three other regression models, namely,
Multivariate Adaptive Regression Splines, Multilayer Perceptron, and Decision Tree Regressor. The
results demonstrate the superiority of the RF-based regression model in predicting pullout coefficient
values of geogrid.

KEYWORDS: Geosynthetics, random forest, machine learning, pullout test

REFERENCE: Pant, A. and Ramana, G.V. (2022). Novel application of machine learning for
estimation of pullout coefficient of geogrid. Geosynthetics International, 29, No. 4, 342–355.
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1. INTRODUCTION system, strain rate and clamps, and other parameters are
already specified ASTM D6706-01. A number of
Mechanically stabilized earth walls are subject to external researchers have studied the pullout behaviour of geogrids
and internal modes of failure. According to FHWA embedded in different types of fills (Moraci and Recalcati
(2001), the primary modes of failure against internal 2006; Teixeira et al. 2007; Cardile et al. 2016; Prasad and
stability of a mechanically stabilized earth wall are pullout Ramana 2016a).
and tension failure of reinforcement. Thus, in its design,
the knowledge of soil-geosynthetic interaction behaviour Pullout test is a large-scale and time-consuming
is particularly important. The reinforcement length experiment. Thus analytical methods have been developed
depends mainly on the assumed pullout coefficient to estimate pullout coefficient geogrid using properties of
(FHWA, 2001). The pullout coefficient depends on soil and geogrid (Jewell 1990; Cardile et al. 2017). These
several factors such as type of soil (particle size distri- methods depend on the engineering properties of soil
bution, placement condition, and moisture), type of (angle of shearing resistance) as well as the skin friction
reinforcement (geometry and mechanical properties), angle between soil and geogrid corresponding to each
boundary conditions and loading conditions (Moraci normal stress, calculating which can be tedious. Huang
et al. 2014). and Bathurst (2009) developed statistical bi-linear and
non-linear models for prediction of pullout capacity of
Pullout coefficient is determined through pullout geosynthetics based on a large database of published test
testing done on reinforcement (geosynthetic or metallic results. The non-linear models demonstrated superiority
grid) while being embedded in a fill material at different to the approaches described by FHWA (2001). The
normal stresses. The specifications of a typical pullout models however were purely empirical and were trained
testing machine regarding box dimensions, loading and tested on the same dataset. This limitation can be

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Novel application of machine learning for estimation of pullout coefficient of geogrid 343

overcome by regression model based on machine learning 2. METHODOLOGICAL BACKGROUND
(ML).
2.1. RF
ML techniques are gaining momentum to make
accurate estimates in the field of geotechnical engineering. RF is a bagging technique-based statistical learning theory
The utility of ML has been explored by researchers to that uses the bootstrap resampling method. The RF
estimate basic geotechnical properties as well as those method was developed by Breiman (2001). It extracts
pertinent to site characterization (Kirts et al. 2018; multiple random samples from the original dataset and
Tsiaousi et al. 2018; Hu and Solanki 2021; Jalal et al. models the decision tree for each of the bootstrap samples.
2021; Mittal et al. 2021; Zhang et al. 2021). However, Each tree, trained using different bootstrap samples of the
relatively fewer studies have been reported on predicting training data, acts as a regression function on its own.
the behaviour of geosynthetic reinforced soil using ML. Subsequently the predictions of multiple decision trees are
Chou et al. (2015) estimated the tensile loads generated in combined and averaged to build the result. The RF method
geogrids used as reinforcement in geosynthetic-reinforced creates many decision trees and provides the opportunity to
soil structures using an evolutionary metaheuristic intelli- evaluate over the combination of these trees.
gence model that was an improvement of the firefly
algorithm. In the RF method, the structure where decision trees are
formed is called the forest. In the forest, each decision tree
Prasad and Ramana (2016b) analyzed experimental is created by selecting samples from the data set by
pullout test data to model and capture the influence of row-sampling with replacement technique and determin-
several geogrid parameters and structural fill properties ing the number of random variables determined from all
on pullout coefficient using an artificial neural network variables at each node.
(ANN). The authors stressed the need for a large database
for better prediction and analysis of results. Debnath RF regression involves construction of k number of
and Dey (2018) used simplified vector regression for trees {Tk (X ), m = 1, 2, …, k}. The p-dimensional vector
prediction of the bearing capacity of unreinforced X = {x1, x2, …, xp}, where p is the number of features in
sand bed and geogrid-reinforced sand bed resting over a the dataset, that forms the forest is considered as the input
group of stone columns floating in soft clay. Sharma et al. vector of the algorithm. This ensemble generates k outputs

(2019) studied the application of ANN and genetic corresponding to k number of trees and yˆm, m = 1, 2, …, k
programming methods in predicting the dynamic is denoted as the output of each tree (note: yˆm = Tk (X )).
response of geogrid reinforced machine foundation beds. The average of the output of each tree is considered as the
Ghani et al. (2021) studied the response of strip footing result of the algorithm.
resting on prestressed geotextile–reinforced industrial
waste using ANN and extreme learning machine. Raja In the RF algorithm, a new training dataset (bootstrap
and Shukla (2021) studied the settlement of shallow samples) is selected by replacing the original training dataset
reinforced soil foundations using five different types of for each regression tree structure. This leads to several
ML algorithms. training data sets being omitted from the sample, which can
be reused. These omitted data are known as out-of-bag
ML applicability studies in geotechnical engineering (OOB) samples and constitute one-third of new training
have primarily used a single sophisticated algorithm for samples. The other two-thirds of the data is used to derive
prediction (Sharma et al. 2019; Mittal et al. 2021; Raja the regression function. Thus, a randomly drawn training
and Shukla 2021). Due to the complex behaviour of soil, sample from the original training set is selected for creating a
geosynthetics, and their interaction, utilization of ensem- decision tree each time, and one of the samples outside the
ble methods must be explored to model such behaviour. bag is used for accuracy testing developing a generalized RF
Ensemble learning combines multiple algorithms that model. The total learning error is denoted by yˆe and is given
process several learner hypotheses in order to generate a in Equations 1 and 2, respectively as:
generalized hypothesis that gives better predictions
(Zhang et al. 2021). 1 Xk
yiXiị ẳ k mẳ1 y m ð1Þ
In this paper an ensemble learning based method,
namely random forest (RF), has been used to develop a yˆe ¼ 1 Xn 2
regression model to predict the pullout coefficient of ðyˆi À yiÞ ð2Þ
geogrid embedded in soil. A robust dataset comprising n i¼1
soil properties, geogrid parameters and pullout coefficient
from 198 published pullout test results has been compiled. where yˆi, yi and n represent the prediction of each tree
ML models have then been trained using five-fold cross- created by using OOB samples, the true output, and the
validation on randomly selected 80% of this data and then total number of OOB samples, respectively. This error
tested on the remaining 20% of the set. Laboratory shows the prediction performance of the RF algorithm.

pullout tests have then been conducted on four different Figure 1 illustrates the schematic view of flowchart of the
fill materials, the results of which have been compared RF algorithm.
with predictions from ML models. In order to demon-
strate the superiority of the ensemble learning method, 2.2. Multivariate adaptive regression splines (MARS)
ML models have also been developed using three other model
widely used regression models.
The MARS algorithm is a nonparametric regression
method utilized for solving non-linear functions. It

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344 Pant and Ramana

Training data error minimizes. In the backward pass, the large overfit
n observations, m predictors model is pruned by removing the least effective terms from
the model. If X = X, …, XR is the input vector of R
Bootstrapping Sample 1 Sample 2 ... Sample k number of training points and y is the output variable,
then y can be defined mathematically as in Equation 3:

InBag 1 OOB 1 InBag 2 OOB 2 InBag k OOB k y ¼ f X ị ỵ e ð3Þ
(2/3) (1/3) (2/3) (1/3) (2/3) (1/3)

where e is the distribution of error. The function f is

Tree 1 Tree 2 Tree k estimated by using basic functions, BF(X ). Thus, complex

... relations from high dimensional datasets can be extracted.

Prediction 1 Prediction 2 Prediction k Equation 4 demonstrates the approximation functioning

of MARS, considering the linear piecewise segments

Average of all predicted values which take the form of max(0, x − c) with a knot at

Figure 1. Architecture of RF model point c:

( x À c; if x ! c

max0; x cị ẳ 0; otherwise ð4Þ

estimates the relationships between the input dimensions By applying a linear combination of several BFs and
and the output variable by dividing the training dataset their interactions, the function f (X ) is defined as in
into a series of piecewise segments (splines) of varying Equation 5:
slope. The splines are polynomials which can be linear or
non-linear (Raja and Shukla 2021). The MARS model- X N
ling method thus analyses the multivariate data and finds f X ị ẳ o ỵ nBF X Þ ð5Þ
the influence of features in the form of basic functions
(BF) for simulation of the target variable. The terminal n¼1
point of each spline is known as the knot at which data
splits into two domains. The splitting produces BFs, where βo is a constant and βn is the BF, which can either
which provide MARS with the freedom to adapt for be an individual spline function or the product of
bends, thresholds, and departure from linear regression. two spline functions in the model. The backward
Figure 2 illustrates the schematic view of the MARS algorithm that is used to prevent overfitting removes
algorithm flowchart. insignificant BFs. A generalized cross-validation (GCV) is
employed to eliminate the unimportant BFs based upon
BFs are selected using a stepwise search together with a Equation 6:
selection of knot locations through adaptive recursive
regression methods. Thus, the MARS model consists of GCV ¼ RMSE ð6Þ

forward and backward passes wherein in the forward pass,
potential knots and functions are added until residual ẵ1 NF ỵ dNF ị=Rị2

Construction phase where RMSE is the root mean square error for
(input data and number of the training dataset, NF is the number of BFs, d is the
penalty factor, and R is the number of data points.
BFs) In-depth details and mathematical derivation of the
MARS algorithm have been discussed by Friedman and
Roosen (1995).

Pruning phase (determination 2.3. Multilayer perceptron (MLP)
of GCV and deleting
redundant BFs) MLP is a supervised learning algorithm that is a
feed-forward ANN, and generates results using back-
Final Mars Model and check propagation function on the training dataset (Singh et al.
for performance 2012). Back-propagation reduces the error between pre-
dicted and true output value. MLP has a three-layered
Use MARS Yes Check if No Change number architecture, comprising an input layer consisting of n
R2 ~ 1 of BFs input nodes, and an output layer consisting of m output
model nodes. The single or multi hidden layer converts the input
command to output using optimizer functions as shown
Predict pullout in Figure 3. The training process of the MLP regression
coefficient comprises two stages: (i) calculate the output value using
forward propagation of the input values through the
Figure 2. Architecture of MARS model hidden layers, and estimate the error between the
predicted and true value, and (ii) minimize the error by
adjusting the connection weights and estimation of output
with revised weights.

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Novel application of machine learning for estimation of pullout coefficient of geogrid 345

Input layer Hidden layer Output layer design of pullout apparatus as an input parameter for
model development.
Input 1 Output
Input 2 Pullout force is directly proportional to normal stress
Input 3 (Farrag et al. 1993; Lee and Bobet 2005). Increase in
Input 4 normal stress reduces soil dilatancy, thus leading to an
Input 5 increase in passive soil resistance. The rate of increase of
Input 6 pullout force decreases with increasing normal stress
(Alfaro et al. 1995). Thus, normal stress is a key input
Figure 3. MLP architecture employed in this study parameter to be considered for prediction of the pullout
interaction factor. Amongst the properties of soil, fines
2.4. Decision tree regressor (DTR) content and average particle size of fill (D50) of soil have
been considered as input parameters. Pullout resistance
Decision tree regression is a non-parametric supervised depends on the ratio between the geogrid opening size and
ML method that uses binary rules to calculate a target D50 (Jewell et al. 1984; Lopes and Lopes 1999). Pullout
value. The DTR algorithm is based on recursive parti- resistance decreases with an increase in percentage of fines
tioning of input parameters to classify the data where it in fill (Pant et al. 2019e).
splits the dataset by data entropy and performs a local
linear regression on the new subsets of data (Wei et al. Length of geogrid, spacing between longitudinal and
2019). Multiple iterations are run on the dataset to give transverse members, and ultimate tensile strength of
different decisions and the best fit is determined by the set geogrid have been considered as input parameters for
of decisions that lead to least entropy. The algorithm has a development of prediction models. Teixeira et al. (2007)
recursive tree like structure of decision calls each of which observed that an increase in geosynthetic specimen length
contributes to a change in entropy. On every decision call, leads to an increase of pullout resistance, stiffness and
the set of input parameters is split into two or more displacement at peak pullout resistance. Pullout resistance

subsets. The recursive splitting continues over each subset increases linearly with geogrid specimen length. Moraci
until the terminal nodes are reached. The number of and Recalcati (2006) investigated the influence of geogrid
subsets doubles every time the data splits which leads to specimen length on the pullout behaviour of geogrids and
increasing depth of the decision tree. The accuracy of reported that for longer geogrids (L = 1.5 m) under higher
DTR is calculated from the mean square error value normal stresses pullout resistance increases progressively
between predicted and actual values. with increase in displacement. On the other hand, under
low normal stress, both short (L = 0.4 m) and long
3. EXPERIMENTAL DATABASE geogrid specimens (L = 1.5 m) show a progressive
COLLECTION decrease of pullout resistance after the peak with further
displacement.
3.1. Model inputs and outputs
Palmeira and Milligan (1989) indicated that a decrease
Input parameters play the most significant role in training in spacing between transverse members causes a reduction
a data-driven model. Thus, it is critical to select in peak pullout resistance due to increasing interference
parameters that impact the output variable. The factors between transverse members. Teixeira et al. (2007)
that influence pullout test results can be classified into reported that there is an optimum spacing (43 mm)
three categories: influence of design of pullout apparatus, between transverse ribs that maximizes pullout resistance.
influence of geosynthetic reinforcement, and influence of Similarly, Calvarano et al. (2012) reported that a peak
fill material. Several researchers have assessed the influ- pullout resistance is obtained at a spacing of 86.7 mm
ence of these factors on pullout behaviour of geosyn- between transverse members. A spacing less than or more
thetics. While using ML for development of a data driven than optimum spacing affects pullout resistance value.
predictive model, it is important to incorporate critical Thus, spacing between transverse members has been
input parameters for the development of a robust and shown to be a critical factor that influences pullout test
generalized model. In order to develop a comprehensive results and has been considered as an input parameter for
model and reduce its complexity it is also important to development of the data-driven predictive models.
limit the number of input parameters without compromis-
ing the model’s accuracy. Thus, in this study, published Aperture size of geogrids has also shown a considerable
pullout test results that complied with the apparatus effect on pullout interaction coefficient (Bernal et al.
guidelines of ASTM D6706-01 (2013) have been used 1997). An increase in pullout interaction coefficient is
which allowed the authors to remove the influence of observed with decreasing aperture size. Chen et al. (2013)

concluded that geogrid aperture size plays a more
significant role than tensile strength or thickness of
geogrid ribs. Therefore, to consider the influence of
aperture size of the geogrid, spacing between longitudinal
members has been used as an input parameter in this
study.

Nayeri and Fakharian (2009) indicated that structural
stiffness of the geogrid has a direct influence on pullout
resistance at different normal stresses. Abdel-Rahman

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346 Pant and Ramana

et al. (2007), Prasad and Ramana (2016b) and samples available, mean is the average value of any feature
Wilson-Fahmy et al. (1994) indicated that pullout resist- under consideration, std is the standard deviation of the
ance increases non-linearly with an increase in the feature, min is the minimum value of the feature in the
ultimate tensile strength of the geogrid. Hence, ultimate dataset, 25%, and 75% refers to the percentile value of
tensile strength has also been considered as an input the feature, and max refers to its maximum value.
parameter to develop a robust model for prediction of
pullout interaction coefficient. The developed ensemble learning models have also
been verified on new data obtained from conducting
It has been demonstrated in the literature that other laboratory pullout tests on geogrids embedded in four
factors such as fill material properties (for instance, angle types of granular materials. It must be pointed that these
of shearing resistance of soil, relative density of soil), and test results were not a part of the database used to develop
mechanical and physical properties of geogrid (like width the ML models. Pullout tests were carried out on an
of geogrid, shape of aperture) also influence the pullout apparatus with inner dimensions of 900 mm × 600 mm ×

capacity of geogrids. The factors were however not 600 mm (length × width × height). Air-dried material was
considered as input variables for model development, filled in the test box in four layers of 150 mm in height and
primarily due to the lack of data of these parameters thereafter compacted to achieve a relative density of 80%.
in much of the published literature used as a database in Geogrid was fastened between clamps using countersunk
this study. Moreover, it has been reported in the literature bolts and positioned within the compacted fill material at
that soil properties such as angle of shearing resistance 300 mm in height. An airbag was used to apply uniformly
depend significantly on the normal stress, fines content distributed pressure over the fill surface. The applied load
and D50 of soil that have been included as input and the displacements were monitored for a pullout
parameters for model development (Wang et al. 2009; displacement of 100 mm. The pullout tests were per-
Phan et al. 2016). formed at three different normal stresses (20, 40, and
80 kPa).
Normal stress, D50, fines content (per unit weight),
length of geogrid specimen (L), spacing between the 4. MODEL CONSTRUCTION AND
longitudinal members (sL), spacing between the transverse IMPLEMENTATION
members of geogrid (sT) and ultimate tensile strength of
the geogrid (Tult) have thus been used as the input For prediction of pullout coefficient values, four data-
parameters which affect the pullout coefficient of the driven regression-based models, – that is, RF, MARS,
geogrid. In the models developed, these parameters have MLP, and DTR, were constructed and implemented. The
been used as input variables to predict pullout coefficient analysis and coding of algorithms in this study has been
of geogrid embedded in granular fill. conducted on Python 3.8.5. The dataset of 198 samples
was randomly divided into training and test datasets in
3.2. Database description 80 : 20 ratio. While each algorithm was trained on the
training dataset (158 randomly picked pullout test
The size of the dataset plays the most critical role in results), the predictability of the model was checked on
development of a reliable prediction model in ML. In test set (remaining 40 pullout test results). Five-fold cross
order to develop the models, published laboratory pullout validation was used on the training dataset for optimiz-
test results on geogrids embedded in different types of fill ation of regression models. Each dataset was randomly
materials were retrieved and compiled to develop a divided into five folds, four of which were utilized for
robust database of 198 samples (Goodhue et al. 2001; training purposes while the model was tested on the
Duszýnska and Bolt 2004; Moraci and Recalcati 2006; remaining fifth fold. The procedure was repeated over five

Abdel-Rahman et al. 2007; Teixeira et al. 2007; Vieira runs. Due to the unavailability of a large dataset, the
et al. 2016; Prasad and Ramana 2016a, 2016b; Abdi and number of folds was restricted to five only.
Mirzaeifar 2017; Wang et al. 2018; Mirzaalimohammadi
et al. 2019; Pant et al. 2019a, 2019b 2019c, 2019e). Table 1 The optimized RF model was created using the RF
lists the statistical properties of the dataset summarizing Regressor algorithm within the Scikit-learn library of
the central tendency, dispersion, and shape of the dataset
distribution. Count refers to the number of individual

Table 1. Statistics of the dataset used in the study

Normal stress (MPa) D50 (mm) Fines L (m) sL (m) sT (m) Tult (kN/mm) Pullout coeff

Count 198 198 198 198 198 198 198 198
Mean 0.038 0.527 0.141 0.828 0.020 0.182 0.086 0.797
Std 0.031 0.985 0.241 0.266 0.010 0.125 0.027 0.417
Min 0.005 0.024 0.000 0.280 0.012 0.013 0.030 0.090
25% 0.013 0.213 0.020 0.600 0.015 0.032 0.066 0.473
Median 0.025 0.220 0.027 0.900 0.015 0.220 0.080 0.710
75% 0.050 0.750 0.190 1.000 0.027 0.230 0.099 1.030
Max 0.200 8.000 0.941 1.500 0.081 0.600 0.200 1.840

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Novel application of machine learning for estimation of pullout coefficient of geogrid 347

Python 3.8.5. The critical hyperparameters to tune when 4.1. Correlation analysis
using the algorithm are number of trees in the forest and
the size of the random subsets of features to consider The correlation coefficient between any two variables

when splitting a node. In this study a RF model with helps in the preliminary investigation of the strength of
600 trees was constructed that considered all the interdependency between two parameters. The
seven input features for node split. The influence Spearman’s rank correlation coefficient (rs) exhibiting
of limiting the maximum tree depth (total number of the correlations between each pairwise feature is shown in
splitting nodes) was assessed over a range of 1 to the heatmap in Figure 4. The maximum value of rs is
the maximum possible number of nodes. The tree limited to 1 and runs diagonally along Figure 4. The
depth was not constrained because the model accuracy higher the rs value, the higher the correlation between the
did not decrease with increasing tree depth. The two features. The sign of correlation signifies proportion-
importance of the predictor was calculated as the ality, where positive value indicates the pair being directly
percentage increase in model mean squared error when proportional and negative refers to an inverse relation
the predictor was permuted. However, irrespective of the between the features. Table 2 summarizes the correlation
predictor importance the model was fit using all the of all parameters according to the absolute value of rs.
seven predictors. Normal stress plays the most significant role in estimation
of pullout coefficient.
The MARS model was constructed using pyearth
library in Python 3.8.5. A maximum of three degrees 4.2. Check for outliers
were generated by forward pass in the optimized MARS
model developed in this study. The maximum degree of Outliers are the values of target variable that are either
the terms was restricted to three as increasing it increased very small or very large compared to the average values
the non-linearity of the model which led to overfitting as and may bring bias to the model developed. Figure 5
well as increase in computation time. The value of the shows a box plot of pullout coefficient values. It contains
penalty parameter used in the model was three. The the upper limit, lower limit, median, as well as the upper
penalty parameter is used to calculate generalized cross quartile (Q3) and lower quartile (Q1) of the available
validation. It is used during the pruning pass and aids in pullout coefficient data. The Q1 and Q3 values are the 25
determination of addition of a hinge or linear basis percentile and 75 percentile values of pullout coefficient as
function during the forward pass. The number of extreme mentioned in Table 1. The upper limit and the lower limit
data values of each feature not eligible as knot locations
was determined to be five. Default values of other 1.0
hyperparameters were used in the development of the Normal stress
optimized MARS model.

0.8
Based on the iterations on number of hidden layers to D50
be used for the development of the MLP model, a model
with three hidden layers and 50 to 100 hidden units was 0.6
created using the MLP Regressor algorithm within the
Scikit-learn library of Python 3.8.5. The rectified linear Fines content
unit function was used to activate the hidden layers. A 0.4
default stochastic gradient-based optimizer was used as
weight optimization function for the layers. The weight L
optimization function was iterated until it converged (i.e. 0.2
tolerance for optimization reached within 1e−4), or 5000
iterations, after which training of data was stopped. An sL
initial learning rate of 0.01 was used as a step-size 0
controlling parameter for updating weights. Standard
values of other hyperparameters were used in the devel- sT
opment of the MLP model. –0.2

The DTR model was constructed using the DTR Tult
algorithm within the Scikit-learn library of Python –0.4
3.8.5. A decision tree with large depth leads to the
construction of a complex model that has more splits and Pull coeff
thereby can gather more information on the training data –0.6
leading to overfitting. Thus, the maximum depth of
decision trees was restricted to ten in the present study. Normal stress D50 Fines L sL sT Tult Pull coeff
Friedman mean square error was used as the criterion
to measure the quality of split. The decision trees were content
made five-deep. A minimum of two samples were specified
to be at each leaf node for a split point at any depth of Figure 4. Correlation coefficient matrix heatmap of feature
decision tree to be considered for splitting an internal variables and label
node.

Table 2. rs value interpretation

rs Level Parameters

0–0.10 Very weak Pullout coeff vs D50,
Pullout coeff vs sT,
0.1–0.2 Weak Pullout coeff vs Tult
0.2–0.5 Moderate Pullout coeff vs L,
0.5–0.7 Strong Pullout coeff vs sL
Pullout coeff vs Fines
Pullout coeff vs Normal Stress

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348 Pant and Ramana

2.00 Upper Lt. (ii) mean square error (MSE); and (iii) mean absolute
1.75 percentage deviation (MAPD). The mathematical rep-
resentation of the criteria has been summarized in Table 3.
1.55 Fp,i and Fo,i are the predicted and observed values of
pullout coefficient values, respectively.
1.25
The values of the statistical parameters for the training
Value 1.00 Q3 and testing datasets have been tabulated in Tables 4 and 5,
respectively. The statistical metrics of each model is
0.75 Median calculated for both training and testing dataset individu-
ally. A model that gives better values of performance
0.55 Q1 evaluation indicators in the training dataset compared to

the testing dataset indicates that the model exhibits low
0.25 Lower Lt. bias and high variance. In other words, the model gives
0 less error in predictions made on training dataset than on
1 testing dataset. Such a model is referred to as an overfit
Pullout coeff model and is not considered as a robust model for making
predictions (difference between R2 values of DTR in
Figure 5. Pullout coefficient values boxplot for identification of training and testing dataset).
outliers
Ranks were given to the models for each criterion,
have been calculated using Equations 7 and 8: where larger rank corresponds to better performance
against the criterion under study. The total score of ranks
Upper Lt: ẳ Q3 ỵ 1:5Q3 Q1ị ð7Þ is the sum of ranking score of a model for each statistical
parameter. Based on the total score, the final rankings of
Lower Lt: ẳ Q3 1:5Q3 Q1ị ð8Þ all the models were determined.

The maximum and minimum values of the upper and From the results reported in Tables 4 and 5 of training
lower limit values are limited to the maximum and and testing datasets, it can be observed that the perform-
minimum values of pullout coefficient used in this study ance of the four models varied greatly, but the RF model
as mentioned in Table 1. As can be observed from significantly outperformed MARS, MLP, and DTR for
Figure 5, no data point lies outside the lower and upper both training and testing data. The R2 value of the RF
limit of pullout coefficient values, indicating that the model was found to be 0.97 for training dataset and 0.83
entire dataset is representative of true pullout coefficient for testing dataset, which demonstrated that it had
values with no outliers. satisfactory estimative capabilities for predicting the
pullout coefficient of geogrids. In addition, the lower
5. PERFORMANCE EVALUATION error indices (MSE and MAPD) for the RF model
METRICS indicate unbiased estimations and less difference
between observed and predicted response of geogrids.
5.1. Training and testing performance Thus, amongst the four models used in this study, the
highest R2 and lowest error indices were obtained in the
The statistical analysis between the observed and pre- training dataset of the RF model, indicating that the RF

dicted values of the pullout coefficient was conducted to model has excellent training ability. Irrespective of the fact
assess the accuracy of all the models. Three widely used that the R2 and error indices for the testing dataset of the
statistical performance criteria have been used as per- RF model showed a decrease of estimation accuracy
formance indicators of the data-driven models (Raja and compared with the training dataset, they are still higher
Shukla 2021), namely: (i) coefficient of correlation (R2); than other data-driven models used in his study. These
observations signify that the RF model outperforms
MARS, DTR and MLP models in predicting pullout
coefficient of geogrids.

Table 3. Performance evaluation indicators

Indicator Mathematical formulation Best performance criteria
R2 =1
MSE Àn i¼1 Pn F p;i Fo;i À i¼1 Pn F p;i i¼1 Pn Fo;i Á2 =0
MAPD (%)  Pn À Á2 ÀPn Á2 Pn À Á2 ÀPn Á2 =0
n i¼1 F p;i À i¼1 F p;i n i¼1 Fo;i À i¼1 Fo;i

1 Xn À Fo;i À F p;i Á2

n i¼1

1 Xn F o;i À F p;i  100
n i¼1 Fo;i

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Novel application of machine learning for estimation of pullout coefficient of geogrid 349

Table 4. Statistical parameters for the training dataset Rank

Proposed model Network results in training dataset Ranking the predicted models Total ranking score 1
4
MSE R2 MAPD MSE R2 MAPD 12 3
3 2
RF 0.004 0.97 6.9 4 4 4 6
MARS 9
MLP 0.023 0.86 20.2 1 1 1
DTR
0.019 0.88 15.1 2 2 2

0.007 0.95 9.6 3 3 3

Table 5. Statistical parameters for the testing dataset

Proposed model Network results in testing dataset Ranking the predicted models Total ranking score Rank

MSE R2 MAPD MSE R2 MAPD 12 1
9 2
RF 0.036 0.83 18.6 4 4 4 4 4
MARS 5 3
MLP 0.047 0.78 25.7 3 3 3
DTR
0.058 0.73 27.0 1 1 2

0.054 0.75 28.7 2 2 1

The RF model understands the complex nonlinear and datasets, the results of which have not been plotted as the
hierarchical soil-geosynthetic interaction behaviour. It reliability of a model depends on its accurate prediction of

also resists overfitting by demonstrating insensitivity to test datasets. It can be noted that the values of pullout
noise in input data and has an unbiased error rate coefficient greater than 1 are normally under- or over-
measurement compared with other estimation methods, predicted by the models. This may be attributed to the
resulting in higher estimation accuracy by the model restrained dilatancy effect that is exhibited by structural
(Breiman 2001). fill during shearing at low normal stresses, thereby
increasing the actual normal stress at the soil-geogrid
Tables 6 shows the combined performance of all interface which remains unaccounted for in the models
the models applied in the prediction of pullout coefficient developed in this study (Pant et al. 2019a).
value. In this table, considering the individual ranks
obtained by each model according to the statistical indices 5.2. External model validation
(R2, MSE and MAPD in Tables 4 and 5), a total rank was
provided to each model based on either the train or test External validation is the process of comparing observed
total score, whichever was lower. The ranking showed that and predicted results using a certain set of statistical
the RF model achieved the highest predictive accuracy criteria. Golbraikh and Tropsha (2002) developed an
(total score = 12). The DTR model obtained the external model validation method that evaluates the
second-best accuracy (total score = 5). Furthermore, reliability of model predictions based on model perform-
MLP (total score = 4) and MARS (total score = 3) ance on test dataset. The method is designed to ensure
models showed lower accuracy in predicting the pullout model reliability even for a small dataset through rigorous
coefficient value of the geogrid in comparison to RF. statistical penalties. For a model to be considered
acceptable, it is mandatory for it to meet certain criteria
The scatter plots of real and predicted values of pullout that have been discussed below.
coefficient values of test dataset obtained through the ML
models can be seen in Figures 6a–6d. According to the For a model to be called 100% accurate, its ideal value
comparisons, it can be observed that the RF-based model of correlation coefficient – that is, R2 must be 1. This
maintained a high prediction accuracy in the testing sets. means that one of the regression line gradients – that is,
Similar observations have been made on the training predicted versus observed values, or vice versa, passing

Table 6. Ranking of ML models based on training and testing scores

Proposed model Training dataset Testing dataset Rank

MSE R2 MAPD MSE R2 MAPD 12
3
RF 4 4 4 4 4 4 4
MARS 3 5
MLP 1 1 1 1 3 3
DTR 2
2 2 2 1 2

3 3 3 2 1

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350 2.0 Pant and Ramana
Lab results
2.0 Lab results
1.6 RF MARS
1.6

Pullout coefficient 1.2 1.2

0.8 0.8

0.4 0.4

0 0
0
10 20 30 40 0 10 20 30 40

2.0
(a) (b)
1.6
2.0 Lab results
Lab results DTR

MLP
1.6

Pullout coefficient 1.2 1.2

0.8 0.8

0.4 0.4

0 0

0 10 20 30 40 0 10 20 30 40

Count Count
(c) (d)

Figure 6. Scatter plot between the observed and the predicted values for testing datasets using (a) RF; (b) MARS; (c) MLP; and (d) DTR
models

through the origin should approximate to 1. Thus, of the predicted versus the observed values and of the

i¼1 Pn F p;iFo;i observed versus the predicted values, respectively. Rs,

k ¼ Pn 2 ð9Þ referred to as a stabilization criterion, can be calculated

i¼1 F p;i
using Equation 13:

i¼1 Pn F p;iFo;i  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k′ ¼ Pn 2 R2s ¼ R2 1 À R2 À R2 ð13Þ
ð10Þ
i¼1 Fo;i o

where k and k′ are the slopes of regression lines through According to the external validation method, any
model is reliable if it meets at least two of the following
the origin for fits to experimental and predicted data, conditions: (1) R2 ≥ 0.6; (2) 0.85 ≤ k ≤ 1.15 or 0.85 ≤
k′ ≤ 1.15; (3) R02 or R0′2 close to R2 – that is, the ratio of
respectively. The correlation coefficients passing through absolute difference of R2 from R0′2 (or R0′2) to R2 must be
less than 0.1; and (4) Rs2 ≥ 0.5. A model is considered fully
the origin can be defined as Equations 11 and 12: acceptable if it meets all four conditions discussed.

2 iẳ1 Pn F p2;i1 kị2 ð11Þ The results of the external model validation criteria for
i¼1 F p;i Ro ¼ 1 À Pn À À F p;meanÁ2 the test dataset have been summarized in Table 7. It may
be noted that for conditions 2 and 3, only one sub-criteria
Pn 2 2 needs to be satisfied. It is evident from the results that
iẳ1 Fo;i1 kị none of the four models met all the four conditions of the
Ro ¼ 1 À Pn À ′2 Á2 ð12Þ validation method including the stabilization criteria. RF
exhibited the best performance amongst the four models
i¼1 Fo;i À Fo;mean satisfying three of the four conditions, while the MARS,

where Fp,mean and Fo,mean are the mean values of the

predicted and real pullout coefficient value of geogrid,
respectively. R02 and R0′2 are the determination coefficients

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Novel application of machine learning for estimation of pullout coefficient of geogrid 351

Table 7. External validation for all the data-driven models according to the criteria suggested by Golbraikh and Tropsha (2002)

Model Criteria Cond. 1 Cond. 2 Cond. 3 Cond. 4 Cond.s met

RF R2 k k′ R02 R0′2 Rs
MARS
MLP 0.83 1.06 0.90 0.98 0.93 0.57 3 3 ✗ 3 3
DTR
0.78 1.01 0.92 0.99 0.96 0.45 3 3 ✗ ✗ 2

0.73 1.02 0.90 0.99 0.94 0.40 3 3 ✗ ✗ 2

0.70 1.03 0.89 0.99 0.93 0.36 3 3 ✗ ✗ 2

DTR and MLP models met only two conditions. Meeting 6.2. Laboratory test results
a minimum of two criteria shows that the developed
models could predict the response value with reasonable The pullout resistance versus displacement results of the
accuracy but amongst all modelling techniques, the geogrid embedded in the two different well compacted
ensemble learning method – that is, the RF model, was bottom ash samples, J_BA and D_BA under 20 kPa,
most accurate. 40 kPa and 80 kPa normal stress have been presented in
Figures 7a and 7b. The geogrid exhibited strain softening
6. COMPARISON OF MODEL behaviour, – that is, a gradual decrease of the pullout
PREDICTIONS WITH LABORATORY resistance after peak load, for both bottom ashes. Similar
EXPERIMENTS observations were made for geogrid embedded in fly ash

samples (Figures 8a and 8b. The pullout resistance offered
In order to verify the generalization ability of the by geogrid embedded in fly ash was almost 35–40% less
established pullout coefficient value prediction model, than that offered in J_BA and D_BA. This is due to a
laboratory pullout tests were conducted on geogrid higher percentage of fines in fly ash than in bottom ash
embedded in four different fill materials, the results of samples which leads to lower shear resistance mobilization
which were compared with the predictions of ML models in fly ash. Also, unlike bottom ash, fly ash samples
developed in the previous section. These experimental exhibited stick-slip oscillations in its pullout resistance
data were not present in the model development phase. curves (Pant et al. 2019d) at each normal stress.

6.1. Material used 6.3. Determination of pullout coefficient

Bottom ash and fly ash were separately collected from In order to interpret the pullout test, Moraci and Recalcati
Dadri thermal power plant (TPP) and Jhajjar TPP. The (2006) proposed Equation 14 to calculate the pullout
materials were air dried, and a detailed geotechnical coefficient (F ):
characterization of the materials was then conducted
following standard procedures. The geotechnical proper- F ¼ PR ð14Þ
ties of the four materials have been summarized in Table 8. 2Lσn
BA stands for bottom ash and FA stands for fly ash. J_BA
refers to bottom ash from Jhajjar TPP while D_BA refers where PR, peak pullout resistance per unit of width
to Dadri TPP. Fly ash was finer than bottom ash and (kN/m); L, Embedment length of the reinforcement (m);
contained a higher percentage of fines (particles less than σn, effective normal stress at the soil-reinforcement inter-
75 μm) and lower D50. face (kN/m2)

A uniaxial polyester (PET) geogrid was used as a The value of F ranged from 1.04 to 0.41 in BA samples,
reinforcement in this study. It was a polyvinyl coated PET and 0.7 to 0.28 in FA at the three normal stresses. For a
geogrid that consisted of knitted yarn fibers. The particular ash type, the value of F was observed to be
manufacturer provided ultimate tensile strength of the higher at lower normal stress of 20 kPa which decreased
geogrid was 80 kN/m in machine direction and 30 kN/m with an increase in normal stress. This behaviour in
in cross-machine direction. The aperture size of the granular soil is attributed to suppression of the soil
geogrid was 27 × 29 mm. dilatancy (Fannin and Raju 1993; Teixeira et al. 2007).

Table 8. Geotechnical characterization of materials used 6.4. Comparison of predicted and actual pullout
coefficient value
Material J_BA D_BA J_FA D_FA
From pullout coefficient predictions based upon training
Fines content (%) 7.3 23.0 79.1 82.0 and testing datasets, it has been shown that the RF model
0.22 0.15 0.032 0.036 yields higher prediction performance than other models
D50 (mm) SP SP-SM ML ML in terms of all performance indicators. The values of R2
USCS classification 13.8 9.4 13.9 13.7 and MAPD of the validation dataset have been summar-
γdmax (kN/m3) 24.9 20.4 19.2 19.1 ized in Table 9. It can be observed that with an MAPD
OMC (%) value of 7.7%, RF shows good predictive performance for
the dataset with reasonable accuracy. A similar obser-
vation can be made for the value of R2 where the slope of

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352 J_BA Pant and Ramana

50 20 kPa 50
40 40 kPa D_BA
30 80 kPa
40 20 kPa

Pullout resistance, kN/m Pullout resistance, kN/m 40 kPa

80 kPa
30

20 20

10 10

0 0

0 20 40 60 80 100 0 20 40 60 80 100

Horizontal displacement, mm Horizontal displacement, mm

(a) (b)

Figure 7. Pullout resistance of geogrid in well compacted (a) J_BA and (b) D_BA

50 50
J_FA D_FA

40 20 kPa 40 20 kPa

Pullout resistance, kN/m 40 kPa 40 kPa

80 kPa 80 kPa
30 30

20 20

10 10

0 0

0 20 40 60 80 100 0 20 40 60 80 100

Horizontal displacement, mm Horizontal displacement, mm

(a) (b)

Figure 8. Pullout resistance of geogrid in well compacted (a) J_FA and (b) D_FA

Table 9. Statistical parameters for the validation dataset can be concluded that the RF model is more estimative
than other models used in this study, and thus has been
Model R2 MAPD Rank ranked 1 amongst all the models studied. DTR performs
poorly for all the datasets as predictions of decision trees
RF 0.99 7.7 1 are neither smooth nor continuous, but piecewise constant
MARS approximations and hence lead to incorrect extrapolation.
MLP 0.98 16.1 3 The results therefore indicate the superiority of the RF
DTR model in prediction of pullout coefficient. The reliability
0.97 11.8 2 of RF in accurate and realistic predictions can also be
owing to the structure of the RF algorithm. The ensemble
0.94 12.7 4 of RFs that is based on drawing a random number of
samples with replacement from training dataset decreases
the linear fit using RF model is closest to 1, indicating that the variance of the error estimator. Individual decision
the data points are almost equally distributed around the trees lead to a high variance in the model and the model
diagonal line. These observations can also be confirmed thus tends to overfit on the training data. However, the
from the plot of true versus predicted pullout coefficient
values for the models as shown in Figure 9. Based on the
training dataset, testing dataset and validation dataset it

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Novel application of machine learning for estimation of pullout coefficient of geogrid 353

1.4 1.4 Lab results
MARS
Lab results

1.2 RF 1.2

Pullout coefficient 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 2 4 6 8 10 12 0 2 4 6 8 10 12

(a) (b)

1.4 1.4

Lab results Lab results
DTR
1.2 MLP 1.2

Pullout coefficient 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 2 4 6 8 10 12 0 2 4 6 8 10 12

Count Count
(c) (d)

Figure 9. Scatter plot between the observed and the predicted values for validation datasets using (a) RF, (b) MARS, (c) MLP and
(d) DTR models

randomness injected in the model during model develop- also compared with laboratory pullout test results con-
ment yields decision trees with decoupled errors in ducted on geogrid embedded in four different fill
predictions. On taking an average of such predictions, materials.
the error reduces. This leads to development of an overall
better regression model. From the point of view of Based on the statistical performance criterion and
developing a predictive model for pullout interaction external validation method results, the ensemble learning
coefficient, the value of which holds critical importance in method, namely the RF based regression model, demon-
the design of MSE walls, RF exhibits superiority above strated superior predictive ability compared to other
other data-driven regression models. modelling approaches. The RF model created in this
study exhibited good prediction accuracy (R2 = 0.97
7. CONCLUSION and MSE = 0.004 for training data, R2 = 0.83 and
MSE = 0.036 for testing data, and R2 = 0.99 and
This paper explored the utilization of the ensemble MAPD = 7.7% for validation data). In comparison to

learning method for predicting pullout coefficient value RF, the results of other data-driven regression models were
of geogrid embedded in granular structural fill under significantly less accurate.
variable normal stress. ML models based on RF
regression analysis were developed and checked for Thus, based on the results, the use of RF for prediction
accuracy of their prediction using statistical performance of pullout coefficient of geogrid embedded in well
criteria. The predictions of the RF model were compared compacted granular structural fill is recommended. The
with three other data-driven ML models, namely MARS, technique is well suited to this application because it can
MLP, and DTR. Predictions of ML models were be applied to multivariate datasets that include highly
skewed data, multicollinearity between predictors, non-
linear relationships between predictors and response
variables, and high-order interactions.

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354 Pant and Ramana

The limitation of the present study is that the analysis Tult ultimate tensile strength of the geogrid (N/m)
discussed here applies only to well compacted cohesionless X input variable in MARS (dimensionless)
granular fill materials. The models have not been trained y output of MARS model (varies)
for uncompacted or loosely placed fill material. The future yˆ output of each decision tree (varies)
study of this work considers generalization as well as yi OOB true output (varies)
improvisation of the models developed using optimization yˆ i prediction of each decision tree using OOB
algorithms together with regression models for more samples (varies)
accurate estimation of pullout coefficient value of geogrids. γdmax maximum dry unit weight (N/m3)
σn normal stress (N/m2)

DATA AVAILABILITY STATEMENT ABBREVIATIONS

Data used in this study for model development are ANN artificial neural network
available from the corresponding author on reasonable BF basic functions
request. Python codes for each model are available in the decision tree regressor
Supplemental Material for this paper. DTR generalized cross-validation
GCV mean absolute percentage deviation
NOTATION MAPD multivariate adaptive regression splines
MARS machine learning
Basic SI units are given in parentheses. multilayer perceptron
ML out-of-bag
D50 average particle size of fill (m) MLP polyester
d penalty factor (dimensionless) OOB random forest
F pullout coefficient (dimensionless) PET thermal power plant
original pullout coefficient value Unified Soil Classification System
Fo,i (dimensionless) RF
mean values of the real pullout coefficient value TPP
Fo,mean of geogrid (dimensionless) USCS
predicted pullout coefficient value
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