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Predicting the chemical and mechanical properties of gypseous soils using different simulation technics

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Gypseous soils are soils that contain sufficient quantities of gypsum that are considered collapsible soil. The present study's objective is to predict the shear strength parameters (c, ϕ), collapse potential (CP), and compression index (Cc) from the gypseous soils' physical properties using a wide range of 220 collected data from various published articles. The linear and nonlinear approaches were used in this study, and the outcomes of the models were compared with artificial neural network (ANN) performance. The developed models predicted the shear parameters, compression index, gypsum content, and collapse potential as a function of accessible laboratories measurable such as specific gravity, moisture content, density, and Atterberg limits with acceptable accuracy. The soils' gypsum content (Gc) was also correlated well based on the total soluble salts (TSS), sulfate (SO3), and pH values using the nonlinear Vipulanandan correlation model. Based on the adjusted (R2), mean absolute error (MAE), and the root-mean-square error (RMSE), the linear and nonlinear models predicted the shear strength parameters, compression index, and collapse potential of the gypseous soils very well. The regression model predictions were comparable to the outcomes from the ANN model predicting.
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RESEARCH PAPER
Predicting the chemical and mechanical properties of gypseous soils
using different simulation technics
Ahmed Mohammed
1
Rizgar Ali Hummadi
2
Yousif Ismael Mawlood
2
Received: 27 March 2021 / Accepted: 30 June 2021
ÓThe Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
Abstract
Gypseous soils are soils that contain sufficient quantities of gypsum that are considered collapsible soil. The present study’s
objective is to predict the shear strength parameters (c,/), collapse potential (CP), and compression index (Cc) from the
gypseous soils’ physical properties using a wide range of 220 collected data from various published articles. The linear and
nonlinear approaches were used in this study, and the outcomes of the models were compared with artificial neural network
(ANN) performance. The developed models predicted the shear parameters, compression index, gypsum content, and
collapse potential as a function of accessible laboratories measurable such as specific gravity, moisture content, density,
and Atterberg limits with acceptable accuracy. The soils’ gypsum content (Gc) was also correlated well based on the total
soluble salts (TSS), sulfate (SO
3
), and pH values using the nonlinear Vipulanandan correlation model. Based on the
adjusted (R
2
), mean absolute error (MAE), and the root-mean-square error (RMSE), the linear and nonlinear models
predicted the shear strength parameters, compression index, and collapse potential of the gypseous soils very well. The
regression model predictions were comparable to the outcomes from the ANN model predicting.
Keywords Artificial neural network Collapse potential Gypseous soils Linear and nonlinear approaches
Sensitivity analysis Shear strength parameters
1 Introduction
Collapsible soils are unsaturated soils that are subjected to
a considerable volume change upon wetting with or with-
out loading. Generally, gypseous soils are very stiff when
they are dry. However, most of this stiffness is lost upon
wetting and becomes more compressible [61,64]. Gyps-
eous soils (hydrated calcium sulfate; CaSO
4
.2H
2
O) are
soils usually accompanying problems for construction that
cause collapse risk for foundations, pavements, and earth
structures when the soil is saturated with water [32,36,66].
The strength, collapsibility, and compressibility behav-
ior of gypseous soils were studied by several researchers
[9,18,22,27,33,39,43,58,59,65,80].
The hydro-mechanical behavior of partially saturated
gypseous soil. They observed a significant drop in the
cohesion and angle of internal friction, with an increase
in the soaking period and the density for a chosen
compaction effort—the hydro-mechanical behavior of
partially saturated sandy soil [30,55]. With an increase
in gypsum content, optimum moisture content and dry
density decreased. A decrease in friction angle and
effective stress parameter was also noted with an
increase in gypsum content. The character of variation
in the porosity and strength of the soils is a function of
initial gypsum content and found out that in the sandy
loam, the porosity increases with increasing initial
gypsum content. More brittle crystals, the mutual coa-
lescence of which gives rise to the appearance of low
cohesion, are found with increasing gypsum content. It
&Ahmed Mohammed
ahmed.mohammed@univsul.edu.iq
Rizgar Ali Hummadi
rizgar.hummadi@su.edu.krd
Yousif Ismael Mawlood
yousif.mawlood@su.edu.krd
1
Civil Engineering Department, College of Engineering,
University of Sulaimani, Sulaymaniyah, Kurdistan, Iraq
2
Civil Engineering Department, College of Engineering,
Salahaddin University-Erbil, Erbil, Kurdistan, Iraq
123
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is necessary to study the properties of such soils due to
the damage caused by these soils to building on or in
them. Seepage through sandy gypseous soil causes
serious damage to the foundation built on such type of
soil. Gypsification offers a variety of serious geotech-
nical hazards. Such a problem causes serious danger in
the Al-Mosul dam foundation (the largest dam located
in northern Iraq) which is built on highly gypseous soil.
The seepage through the soil under the foundation
causes leaching and dissolution to the gypsum, which
brought the dam to the danger of collapse, which could
kill hundreds of thousands of people
[31,34,44,57,81].
Linear and nonlinear approaches are valuable techniques
for predicting geotechnical characteristics from physical
and chemical soil properties; to be used for geotechnical
engineering applications, this technique has been used
successfully in a wide domain, such as predicting the
bearing, compressibility capacity of foundations, shear
strength parameters, swelling potentials
[27,53,54,56,60,68,79]. Artificial neural networks
(ANNs) are a valuable technique and proposed to be used
for this purpose. Even today, this technique has been uti-
lized successfully in a wide field of geotechnical engi-
neering applications, for instance, predicting the bearing
capacity of shallow and deep foundations and their settle-
ments [35,46,47,49,72,73,63]. Najjar and Ali [62] used
the ANN in assessing the liquefaction potential of soils.
Also, ANN has been highly efficient in estimating com-
paction parameters [15,76]. Al-Ani et al. [3] used ANN to
correlate gypseous soils’ properties with the compress-
ibility of soils under different conditions of wetting and
washing. ANNs were used for modeling the settlement
ratio for the wetting process; it was revealed that ANNs
had well able to predict the compressibility characteristics
of gypseous soil due to the soaking and washing process
with a high degree of accuracy. Zhang et al. [82] studied a
novel data-driven extreme gradient boosting (XGBoost),
and random forest (RF) ensemble is learning methods for
capturing the relationships between the USS and various
basic soil parameters. Based on the soil data sets from
TC304 database, a general approach is developed to predict
the USS of soft clays using the two machine learning
methods above, where five feature variables including the
pre-consolidation stress (PS), effective vertical stress
(VES), liquid limit (LL), plastic limit (PL) and natural
water content (W) are adopted. The Bayesian optimization
method is applied to determine the appropriate model
hyper-parameters of XGBoost and RF to reduce the
dependence on the rule of thumb and inefficient brute-force
search. The developed models are comprehensively com-
pared with three comparison machine learning methods
and two transformation models concerning predictive
accuracy and robustness under fivefold cross-validation
(CV). It is shown that XGBoost-based and RF-based
methods outperform these approaches. Besides, the
XGBoost-based model provides feature importance ranks,
making it a promising tool in predicting geotechnical
parameters and enhancing the interpretability of the model
[29]. When gypsum content is the noticeable component of
the soil, many methods have been proposed to identify
these soils. Each technique, with its limitations, controls
the physical and mechanical behavior of the soils.
1.1 Objectives
The fundamental objectives of this study are to forecast
the cand ;, Cc, and CP of gypseous soils from the
physical properties using Linear (LR) and nonlinear
(NLR) models, and the results were compared with the
performance of the ANN model using a wide range of
the collected data from the literature. Statistical anal-
ysis of gypseous soils’ geotechnical and chemical
properties is based on the information collected from
different scientific research papers.
1. Correlate the gypsum content in the soils with total
soluble salts (TSS), sulfate (SO
3
), and pH values using
the Vipulanandan correlation model.
2. Developing models to predict the shear strength
parameters, collapse potential, and compression index
of the gypseous soils with a wide range of gypsum
content.
3. Evaluate the developed models with ANN models’
performance using statistical assessment tools such as
R
2
, MAE, and RMSE.
2 Methodology
2.1 Data collection
Two hundred and twenty data collected from different
scientific published research with a wide range of gyp-
sum content ranged between 0 to 77.5% were evaluated
and quantified using different model techniques. The
geotechnical and chemical properties of gypseous soils
were grouped according to the gypsum content (Gc) that
is given in Table 1; the physical, mechanical, and
chemical properties of the utilized gypseous soil samples
from these studies were tested according to ASTM
standards.
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Table 1 Summary of gypseous soils properties reviewed for modeling
Variable Gc (%) Gc
(%)
C
(kPa)
/°CP
(%)
LL
(%)
PI
(%)
Gs e
o
MC
(%)
ctkN=m3
ðÞcdkN=m3
ðÞ
Cc
(%)
SO
3
(%)
TSS
(%)
pH References
N10 32 12 12 3 25 25 32 17 8 8 17 1 15 16 18 [1,2226,69,77]
Minimum 0 0 17.8 6 0 0 2.49 0.348 3.65 9.7 8.57 0.12 0.43 0.02 7.21
Maximum 10 260 37.9 7.7 47 20 2.689 2.07 21.6 20.26 17.992 0.12 22.33 37 8.3
Mean 3.326 68.3 27.67 6.9 27.7 7.01 2.6434 0.839 15.57 15.43 14.714 0.12 9.68 5.38 7.9789
N10 \Gc B20 32 9 9 13 22 22 32 20 14 14 20 1 19 10 11 [19,48,65]
Minimum 12 3 18.8 0.32 0 0 2.48 0.4085 1.13 10.7 9.57 0.24 0.39 6 7.43
Maximum 20 99 54.5 8.57 46 24 2.71 1.668 17.4 20.63 18.1 0.24 20 66.2 8.8
Mean 15.647 28.2 36.14 2.467 9.09 3.59 2.5907 0.6229 9.99 17.222 15.669 0.24 7.83 19.65 8.065
N20 \Gc B30 32 12 13 13 27 27 32 21 17 16 21 2 19 12 14 [34,39,44,45,52,
70,74,80]
Minimum 20.55 0 23.8 0.19 0 0 2.41 0.4 0.73 11.736 11.651 0.077 1.43 11.9 7.8
Maximum 30 140 40 9 46 14.4 2.66 1.098 21.1 20.29 17.8 0.91 30 31 8.5
Mean 27.973 42.3 33.31 4.04 11.46 2.719 2.5363 0.6211 8.54 16.506 14.984 0.493 16.2 20.08 8.1671
N30 \Gc B40 23 10 10 9 18 18 23 10 8 8 10 1 12 15 5 [6,9,10,21,41,42,
50,66,67,75]
Minimum 30.27 1 9.5 2.7 0 0 2.3 0.54 0.49 12 10.26 0.17 15.57 7.3 7.7
Maximum 40 54 38 17.74 38 14 2.62 1.389 30 18.54 16.179 0.17 46.5 80.7 8.1
Range 34.687 23.93 30.82 9.45 22.59 2.61 2.5004 0.8108 10.82 15.381 13.604 0.17 20.08 36.53 7.978
N40 \Gc B50 22 11 11 6 18 18 22 12 8 8 13 1 14 12 8 [4,7,8,29,31,
37,44,45]
Minimum 41.1 0 6.5 1.76 0 0 2.32 0.429 0.82 11.31 8.678 0.149 19.8 2.7 6.8
Maximum 50 185 43.6 20.39 56 28.7 2.663 1.728 30 16.8 17.17 0.149 58.8 80.7 9
Mean 45.667 52.7 28.74 8.8 25.61 5.89 2.466 0.948 12.07 14.2 13.356 0.149 27.81 35.88 8.091
N50 \Gc B60 31 11 12 12 29 29 31 21 15 14 21 2 21 12 14 [5,16,33,38,51,61,71]
Minimum 50.48 5.1 10 0.31 0 0 2.34 0.28 1.25 11.5 8.79 0.1716 10.81 3.6 6.9
Maximum 60 170 41.2 7.25 48 27 2.59 1.706 30.8 19.27 16.9 0.26 33.1 62 8.26
Mean 54.441 50.3 32.43 3.833 15.18 3.92 2.4095 0.6461 12.5 15.838 13.922 0.2158 25.549 40.65 7.805
N60 \Gc B77.48 34 5 5 7 18 18 34 20 18 17 20 1 22 13 17 [2,11
14,17,20,28,40,68]
Minimum 60.5 0.5 11 0.5 0 0 2.28 0.43 0 10.349 10.256 0.055 9.43 9 6.8
Maximum 77.48 55 49 18.5 55 16 2.48 1.017 22 18.72 14.6 0.055 38 79.43 9
Mean 69.441 29.7 36.26 6.3 24.89 4.111 2.3855 0.7601 5 14.105 12.917 0.055 31.21 52.35 7.835
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2.2 Collapse tests
Collapse tests (CP) can be conducted by using the
oedometer device. The most widely used collapsible test is
the single oedometer test; by steps, the soil sample is
loaded until it reaches vertical stress of 200 kPa; vertical
deformations are recorded with load increments. Then, the
sample is submerged with water for 24 h. At 200 kPa
stress, the additional deformation is recorded due to the
wetting process. The test continues like the conventional
consolidation test regarding loading and unloading. The CP
is determined by using the following equation:
CP ¼De
1þeo
100 ð1Þ
where De= change in the void ratio of the sample resulting
from wetting; and, eo= initial void ratio. The test is similar
to the conventional consolidation test procedure. CP is
determined from the difference at any given soil pressure
between the two curves of (e -log rv) according to
(ASTM D5333 03).
2.3 Modeling
(1) Vipulanandan correlation model
It was observed that there is a significant correlation (Eq. 2)
between gypsum content (Gc %) of the soils with a range
of 0 to 75% (Fig. 1) and TSS (%) and between Gc with
SO
3
(%) of the and shown in Figs. 2and 3[60,78].
y¼yoþX
aþbX ð2Þ
where yo,a, and bare the Vipulanandan model parameters.
(2) Linear regression (LR) and nonlinear regression (NLR)
models
LR models (Eqs. 3and 4) were proposed to predict the c
(kPa) and ;(°) of the gypseous soils. Models of NLR were
also considered in the form of Eqs. 5, and 6that were
proposed to predict Cc, and CP for gypseous soils from Gc,
Gs, void ratio (eo), and dry density (cdÞ;
c¼aGc þbLL þdMC þectþfcdð3Þ
aGc þbLL þdMC þectþfcdð4Þ
Cc ¼aG
P1
sþbe
P2
oþdcP3
dþeGC
cd

P4
þfGc
Gs

P5
ð5Þ
CP ¼aG
p1
cþbG
p2
sþdep3
oþeGs
eo

p4
þfcp5
dð6Þ
where a,b,d,e,f,p
1
,p
2
,p
3
,p
4,
and p
5
are the model
parameters which were calculated using the least square
method. The Eqs. two to six are proposed equations to
predict the Gc, c,;,Cc
,
and CP of gypseous soils based on
the easy measurable soil properties such as liquid limit,
moisture content, total and dry unit weight, specific gravity,
total soluble salts, sulfate content, pH and gypseous
content.
(3) Artificial neural network (ANN)
ANN includes the input layer, the hidden layer (one or more
layers), and the output layer. The hidden layer is related by
weight, transfer function, and bias to the other layers; a
multi-layer feed-forward network with a Gc, LL, x, den-
sities, void ratio, Gs, TSS, SO
3
, and pH as inputs, and c,/,
Cc, CP, and Gc of the gypsum soils as the output has been
configured. There is no standard technique available for
constructing an ANN system design. Depending on the
lowest average RMSE and MAE values and highest R
2
, the
maximum number of HL and number of neurons was
chosen. There is no standard method for designing or
selecting a network architecture. Therefore, the trial and
error test’s maximum number of hidden layers and neurons
was calculated based on the lowest average square error
criterion. The second step of the optimal network design
process was to choose the optimum number of epochs
during the training that gave the minimum MAE and
RMSE and high R-value. The same preliminarily designed
networks with hyperbolic tangent transfer functions were
used to see the effect of several epochs on reducing the
MAE and RMSE. After creating the optimum architecture,
the available data set (Fig. 4). Several transfer functions
and ANN structures with a varied number of hidden layers
and neurons were tested to design the optimal network
structure to predict the gypseous soil properties. One hid-
den layer with seven neurons and a hyperbolic tangent
transfer function was chosen among the networks due to
having the minimum mean absolute error (MAE). Model
performance adjusted (R
2
), MAE, and RMSE values were
7260483624120
35
30
25
20
15
10
5
0
Gypsum Content, Gc (%)
Frequency
No. of Data=220
Max.=77.5 Min.= 0,
Median=15.575,
StDev=23.06,
Variance=541.428,
A-Squared=10.71,
Skewness=0.61
Fig. 1 Histogram for gypsum content of Gypseous soils used in this
study
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used to predict the modeling mentioned above methods.
The three most common statistical measures: R, MAE, and
RMSE, were used as performance evaluation efficiency of
regression approaches. Numerous trials were performed to
find the optimal value of the key parameters. Higher R
2
values (Eq. 7) and lower MAE values (Eq. 8), RMSE
(Eq. 9) indicate the best precision of the model.
R2¼Pixi
xðÞyi
yðÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pixi
xðÞ
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Piyi
yðÞ
2
q
0
B
@1
C
A
2
ð7Þ
0
10
20
30
40
50
60
70
80
0 102030405060708090
Gypsum Content, Gc (%)
Total Dissolved Salt, TSS (%)
No. of Data=197
Data for Literature
Vipulanandan Correlation Model
-40
-30
-20
-10
0
10
20
30
40
50
0 25 50 75 100 125 150 175 200
Residual Error, Gc (%)
Data set Number
Vipulanandan Correlation Model
Predicted=Measured line
a
b
= . + . + .
Fig. 2 aRelationship between TSS and gypsum content using Vipulanandan correlation model, and bresidual errors
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MAE ¼Pn
i¼1yixi
ðÞ
jj
Nð8Þ
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pn
i¼1yixi
ðÞ
2
N
sð9Þ
y
i
= tested data; x
i
= predicted data;
y= mean value of y
i
;
and Nis the number of datasets.
3 Results and discussion
3.1 Statistical analysis
The performance of any statistical model is significantly
dependent on the size of the database; thus, the database
must integrate all soil variables that influence the
geotechnical characteristics of soils to determine
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35 40 45
Gypsum Content, Gc (%)
Sulfur Trioxide, SO
3
(%)
No. of Data= 197
Data from the literature
Vipulanandan Correlation Model
-40
-30
-20
-10
0
10
20
30
0 25 50 75 100 125 150 175 200
Residual Error, SO
3
(%)
Data set Number
Vipulanandan Correla on Model
Predicted=Measured line
a
b
= . + . + .
Fig. 3 aRelationship between SO
3
and gypsum contents using Vipulanandan correlation models, and bresidual errors
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mathematical formulas suitable for different gypseous soils
at any conditions [54]. The input variables for statistical
analysis including the liquid limit, plasticity index, water
content, total and dry unit weight, cohesion, angle of
internal friction, total soluble salts, sulfate, pH, and gyps-
eous content were integrated; obtained dataset with a wide
range of gypseous content ranged between 0 and 77.5%.
Relationships of regression analysis models were deter-
mined based on maximum adjusted R-squared and mini-
mum MAE and RMSE using Minitab 18.1 and checked by
STATGRAPHICS Centurion 18.1, based on the collected
dataset with powerful features for organizing the
correlations such as statistical charts. Data can be modeled
using a toolbox of nonlinear and linear regression models.
The summary of the statistical analysis is presented in
Table 2.
3.2 Gypseous soil properties
(a) Gypsum content (Gc)
According to a total of 220 data, the gypsum content was
ranged between 0 and 77.5 with a median of 15.575, a
standard deviation of 23.269, and a variance of 541.428.
The skewness of 0.6148 and A-squared of 10.71.
Fig. 4 Optimal artificial neural network structure acohesion (c), bangle of internal friction (/), ccompression index (Cc), dcollapse potential
(CP), and egypsum content
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(b) Liquid limit (LL)
The 78 data from the literature were used in this analysis.
The LL data ranged from non-plastic (NP) to 59%, with a
median of 24.50, StDev of 23.372, skewness of 0.198, and
A-squared of 7.67.
(c) Plasticity index (PI)
The 78 data from the literature were used in this analysis.
The PI data ranged from non-plastic (NP) to 35%, with a
median of 24, StDev. of 7.293, skewness of -1.555, and
A-squared of 3.03.
(d) Water content (MC)
Depending on the total of 78 data, the MC of the soils was
ranged between 4 and 31% with a median of 21.32%, the
StDev. of 6.338%, variance 40.175, and skewness is
0.8330, and A-squared is 4.45.
(e) Dry density (c
d
)
Based on the total of 78 c
d
data for soils, the data varied
from 13 to 17 kN/m
3
with a median of 16.3 kN/m
3
, the
StDev. of 0.948 kN/m
3
, variance 0.898, and Skewness is –
1.268, and A-squared is 4.20.
(f) Wet density (c
t
)
Based on the total of 78 c
t
data for soils, the data varied
from 13 to 20 kN/m
3
with a median of 18.363 kN/m
3
, the
StDev. of 1.281 kN/m
3
, variance 1.641, and skewness is –
1.831, and A-squared is 5.76.
(g) Cohesion (c)
According to a total of 78 data, the c ranged from 2.5 to
185 kPa with a median of 35.414 kPa, a standard deviation
of 38.841 kPa, and variance of 1508.6, skewness of 1.371,
and A-squared of 5.64.
(h) Angle of internal friction (;)
According to a total of 78 data, the c ranged from 2.5°to
49°with a median of 22.92°, a standard deviation of
15.370°, and a variance of 236.23, skewness of -0.339,
and an A-squared of 8.23.
(i) Collapse potential (CP)
Collapse potential was ranged between 0.31 and 20.4%,
with a median of 4.72%, a standard deviation of 4.695%,
and a variance of 22.05. The skewness of 1.380 and A-
squared of 1.99.
(j) Specific gravity (Gs)
According to a total of 220 data, the Gs ranged from 2.26 to
2.71 with a median of 2.57, a standard deviation of
0.1233 kPa, and a variance of 0.015, skewness of -0.587,
and an A-squared of 9.79.
3.3 Relationships between gypsum content
and TSS, and SO
3
contents
The Vipulanandan relationships between gypsum content
Gc (%), TSS (%), and SO
3
(%) contents are presented in
Eqs. 2 and 10 &11, respectively. Based on the R
2
and
RMSE, the Vipulanandan correlation model predicted the
gypsum content as a function of TSS and SO
3
.
Table 2 The descriptive statistic details for each dataset
Variable NMean StDev CoefVar Min Max Mean Mode Skewness
Total Non-missing Missing
Gc (%) 220 220 0 33.58 23.06 68.68 0 77.48 77.48 55 0.16
LL (%) 220 170 50 21.35 19.35 90.63 0 72 72 0 0.16
PI (%) 220 170 50 5.708 8.326 145.86 0 31 31 0 1.42
Gs 220 220 0 2.5177 0.1121 4.45 2.28 2.71 0.43 2.54 0.05
eo220 134 86 0.7339 0.3097 42.2 0.28 2.07 1.79 0.408, 0.427, 0.436 1.57
x(%) 220 101 119 11.572 8.692 75.11 0 30.8 30.8 10 0.63
ckN=m3
ðÞ
220 98 122 16.017 2.603 16.25 9.7 20.63 10.93 14.98 -0.15
cdkN=m3
ðÞ
220 135 85 14.343 2.167 15.11 8.57 18.1 9.53 14.6 -0.36
Cc 220 20 200 0.2121 0.1733 81.7 0.055 0.91 0.855 0.16 3.72
c (kPa) 220 79 141 44.72 48.15 107.66 0 260 260 41 2.34
;o220 81 139 29.03 12.05 41.51 3 54.5 51.5 31, 33, 40 -0.75
CP (%) 220 63 157 5.29 4.527 85.58 0.19 20.387 20.197 0.31, 0.72, 1.13, 1.55 1.29
SO
3
% 197 197 0 8.269 11.28 136.39 0.009 39.550 39.541 0.015 1.30
TSS (%) 197 197 0 13.23 19.15 144.76 0.01 79.43 79.42 0.045 1.81
pH 197 175 22 7.7309 0.297 3.85 6.800 9.0 2.2000 7.6 0.67
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Gc %ðÞ¼0:4975 þTSS
0:908 þ0:0019TSS
No. data ¼197;R2¼0:864;and RMSE ¼7:383%

ð10Þ
Gc %ðÞ¼0:30 þSO3
0:502 þ0:0017SO3
ðNo. data ¼197;R2¼0:901;and RMSE ¼6:703%Þ
ð11Þ
From the residual error (Figs. 2b, 3b), more than 50% of
the Vipulanandan correlation model data were matched
with experimental data.
3.4 The LR between calculated and measured
cohesion (c) of the gypseous soils
The relationships between measured and calculated c val-
ues of the gypseous soils are shown in Fig. 5and Eq. 12.
All the research training dataset contains a±35% error
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Cohesion, c (kPa) (Predicted)
Cohesion, c (kPa) (Measured)
LR model
ANN model
Y=X line
LR model (Eq.12), No. Data =78, =0.823,
RMSE= 14.21 kPa
γ
d
-60
-40
-20
0
20
40
60
0 1020304050607080
Residual Error, c (kPa)
Data set Number
LR model
ANN model
Predicted=Measured line
a
b
Fig. 5 aMeasured and predicted the cohesion of the gypseous soils using LR and ANN models, and bresidual errors
Acta Geotechnica
123
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line, indicating that most checked results are in ±35%
error lines.
c¼0:58Gc þ1:21LL 14:20MC þ98:6ct99:76cd
ð12Þ
From model parameters in Eq. 12, No. of the training
dataset is 78, R
2
= 0.823, RMSE = 14.21 kPa. It can be
concluded that the cthas the highest factor (98.6) effect on
increasing the c value of the gypseous soils compared with
other physical properties. Equation 12 predicted cwell
with an error line in the range of ±35% (Fig. 5b). The
residual error (predicted-measured) for the cfor more than
85% of the datasets with a residual error of less than ±
20 kPa. However, about 15% of the dataset has a residual
error in the maximum between ±20 to ±35 kPa
(Fig. 5b). The LR performance was close to the ANN
model performance, and the residual errors were ranged
between ±40 kPa as shown in Fig. 5.
3.5 The LR between calculated and measured ;
of the gypseous soils
The relationships between measured and calculated ;
gypseous soils are shown in Fig. 6a. The research training
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45
Angle of Internal Friction,
φ
(
o
) (Predicted)
Angle of Internal Friction, f (o) (Measured)
LR model
ANN model
Y=X line
LR model (Eq.13), No. Data =78,
= 0.969, RMSE= 2.577
o
γ
d
a
-15
-5
5
15
0 1020304050607080
Residual Error,
φ
(o)
Data set Number
LR model
ANN model
Predicted=Measured line
b
Fig. 6 aMeasured and predicted the angle of internal friction (/) of the gypseous soils using LR and ANN models, and bresidual errors
Acta Geotechnica
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dataset contains a±20% error line, indicating that
experimental data results are in ±20% error lines.
0:17Gc 0:39LL þ3:63MC 29:48ctþ32:31cd
ð13Þ
From model parameters in Eq. 13, No. of the dataset is
78, R
2
= 0.969, RMSE = 2.577°; it can be concluded that
the cdhas the highest effect (factor = 32.31) on increasing
/gypseous soils comparing with other geotechnical
properties. Equation 13 predicted ;very well using LR and
ANN models with an error line of ranged between ±5°
(Fig. 6).
3.6 The NLR relation between calculated
and measured Cc of the gypseous soils
The relationship between Cc with Gs,eo,cd, and Gc has
also been investigated. Since the Cc is influenced by the
specific gravity, void ratio, dry unit weight (kN/m
3
), and
gypsum content (Gc%), the models were analyzed using
nonlinear regressions (Eq. 14).
Cc ¼0:591G0:439
sþ0:20e1
o0:276c1:05
d
0:015 Gc
cd

2:58
þ0:0003 Gc
Gs

2:409
ð14Þ
0
0.05
0.1
0.15
0.2
0.25
0.000 0.050 0.100 0.150 0.200 0.250
Compression Index, Cc (Predicted)
Compression Index, Cc (Measured)
NLR model
ANN
Y=X line
NLR model (Eq.14), No. Data =82,
=0.816, RMSE= 0.0208
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0 1020304050607080
Residual Error, Cc
Data set Number
NLR model
ANN model
Predicted=Measured line
a
b
Fig. 7 aMeasured and predicted the compression index (Cc) of the gypseous soils using NLR and ANN models, and bresidual errors
Acta Geotechnica
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Content courtesy of Springer Nature, terms of use apply. Rights reserved.
(No. of training data = 82, R
2
= 0.816,
RMSE = 0.0208).
Moreover, from model parameters in Eq. 14, it can be
concluded that the specific gravity (Gs) to the dry density
of the gypseous soils had the highest impact on decreasing
the Cc than other geotechnical properties (Fig. 7a). The
model performance (Eq. 14) has compared with the actual
dataset, and the residual error (predicted-measured) for the
Cc for the dataset was in the range of ±0.04 using ANN
and NLR models (Fig. 7b).
3.7 The NLR relation between calculated
and measured CP of the gypseous soils
The relationship between CP with Gs,eo, and Gc has also
been investigated. Since the CP is influenced by the
specific gravity, void ratio, and gypsum content (Gc%), the
models were analyzed using nonlinear regressions
(Eq. 15).
0
2
4
6
8
10
12
14
16
18
0 2 4 6 8 10 12 14 16 18
Collapse Potentioal, CP (%) (Predicted)
Collapse Potentioal, CP (%) (Measured)
NLR model
ANN
Y=X line
NLR model (Eq.15), No. Data =46, =0.817,
RMSE= 1.696%
= .
− .
+ .
− .
+ .
.
a
-5
-4
-3
-2
-1
0
1
2
3
4
5
0 5 10 15 20 25 30 35 40 45
Residual Error, CP (%)
Data set Number
NLR model
ANN model
Predicted=Measured line
b
Fig. 8 aMeasured and predicted the collapse potential (CP) of the gypseous soils using NLR and ANN models, and bresidual errors
Acta Geotechnica
123
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CP ¼0:3Gc18:3513 þ2:5Gs29:9þ9:23e7:97
o
62:5Gs
eo

1:82
173:82276:47
dð15Þ
(No. of training data = 46, R
2
= 0.817,
RMSE = 1.696%).
Moreover, from model parameters in Eq. 15, it can be
concluded that the specific gravity GsðÞhas a significant
effect on increasing the CP of the soils compared with
other geotechnical properties (Fig. 8a). Based on the R
2
and RMSE, Eq. 15 predicted the measured data and the
data collected from the published papers well with an error
line of ±35%. The model performance (Eq. 15) was
compared with the actual dataset, and the residual error for
the CP for the dataset was in the range of ±3 using NLR
and ANN models (Fig. 8b).
3.8 The NLR relation between calculated
and measured gypsum content
The relationship between Gc with Gs,SO
3, TSS and pH has
also been quantified using NLR and ANN models (Eq. 16).
0
2
4
6
8
10
12
14
16
18
024681012141618
Collapse Potentioal, CP (%) (Predicted)
Collapse Potentioal, CP (%) (Measured)
NLR model
ANN
Y=X line
NLR model (Eq.15), No. Data =46, =0.817,
RMSE= 1.696%
= .
− .
+ .
− .
+ .
.
-30
-20
-10
0
10
20
30
0 20 40 60 80 100 120 140 160 180 200
Residual Error, Gc
Data set Number
NLR model
ANN model
Predicted=Measured line
a
b
Fig. 9 aMeasured and predicted the gypsum content (Gc) of the gypseous soils using NLR and ANN models, and bresidual errors
Acta Geotechnica
123
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Gc ¼739:64
Gs2:511 þ0:184SO1:49
354:89
TSS0:018 2:9pH
0:3ð16Þ
(No. of training data = 175, R
2
= 0.914,
RMSE = 6.587%).
From model parameters in Eq. 16, it can be concluded
that the specific gravity (Gs) also had the highest effect on
decreasing the Gc of the soils compared with other
chemical compositions (Fig. 9a). Equation 16 predicted the
experiential dataset very well, and the outcome of the NLR
model was compared with results from the ANN model
with a residual error of ?10 and -20% (Fig. 9b).
3.9 The sensitivity analysis
Sensitivity comparison of the models on the dataset was
performed to investigate the most important explanatory
variable when calculating the cohesion, angle of internal
friction, and collapse potential for gypseous soils. Based on
R
2
, MAE, and RMSE, the results obtained by LR, NLR,
and ANN models are appropriate to predict the c,;, and CP
of the soils using Eqs. 12,13, and 14, respectively. The
comparison of the highest R
2
, lowest RMSE, and MAE for
the LR models is given in Tables 3,4and 5for the c,;and
CP, respectively.
Results obtained from Tables 3,4and 5indicate that the
liquid limit has the lowest adjusted R-squared and highest
MAE, and RMSE and moisture content are the most
influencing parameter for predicting cohesion, using
Eq. 12, in Table 3. Moreover, the liquid limit has the
lowest adjusted R-squared. And the highest MAE and
RMSE and dry unit weight had a higher influence on
estimating the angle of internal friction compared to
Gc;MC;and total unit weight using Eq. 13, in Table 4.
Furthermore, the ratio of gypsum content to specific gravity
has the lowest adjusted R-squared, and the highest MAE
and RMSE had the highest impact on predicting the com-
pression index when compared to PI;LL,eoand cdusing
Eq. 14, in Table 5.
4 Conclusions
Based on the data collected from many research studies,
based on ANN, linear and nonlinear regression modeling,
the following conclusions are conducted:
1. Based on the statistical assessment of R
2
, MAE, and
RMSE, the shear strength parameters (cohesion and
angle of internal) of the soils were quantified accu-
rately as a component of gypsum content, liquid limit,
moisture content, total and dry unit weight. The
variability of shear strength parameters of gypseous
soils showed a good association between cohesion and
angle of internal with simple measured geotechnical
properties of gypseous soils.
2. The compression index and collapsible potential of the
gypseous soils were quantified accurately as a compo-
nent of specific gravity, void ratio, dry unit weight, and
gypsum content. The properties of compression index
and collapse potential parameters of gypseous soils
showed a good association between compression index
and collapsible potential with easy measurable physical
properties of gypseous soils.
3. Based on the statistical assessment of the highest
adjusted R-squared, and lowest MAE, and RMSE, the
gypsum content of gypseous soils can be predicted in
terms of total soluble salts or sulphate content, using
the nonlinear Vipulanandan correlation model. The
Table 3 Sensitivity analysis using linear relationship model for
cohesion (c) training dataset using Eq. 12
Sr.
No.
Input
combination
Removed
parameter
R
2
MAE
(kPa)
RMSE
(kPa)
Ranking
1 Gc, LL,
MC,ct;cd
0.952 8.89 14.21 6
2 LL,
MC,ct;cd
Gc 0.897 9.39 14.88 5
3Gc,
MC,ct;cd
LL 0.814 14.28 20.04 1
4 Gc, LL,
ct,cd
MC 0.862 10.14 17.26 2
5 Gc, LL,
MC,cd
ct0.868 9.92 16.87 3
6 Gc, LL,
MC,ct;
cd0.690 9.90 16.81 4
The bold values mean that this Sr. No has the highest impact
Table 4 Sensitivity analysis using linear relationship model for /
training dataset using Eq. 13
Sr.
No.
Input
combination
Removed
parameter
R
2
MAE
(
o
)
RMSE
(
o
)
Ranking
1 Gc, LL,
MC,ct;cd
0.990 2.15 2.58 6
2 LL,
MC,ct;cd
Gc 0.987 2.35 2.89 5
3Gc,
MC,ct;cd
LL 0.958 4.23 5.28 1
4 Gc, LL,
ct,cd
MC 0.981 2.81 3.59 4
5 Gc, LL,
MC,cd
ct0.979 2.92 3.74 3
6 Gc, LL,
MC,ct;
cd0.978 3.01 3.88 2
The bold values mean that this Sr. No has the highest impact
Acta Geotechnica
123
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gypsum content of gypseous soils also can be well
predicted in terms of specific gravity, total soluble
salts, sulphate content, and pH, using NLR models
4. By using the linear and nonlinear regression-based
models, sensitivity analysis indicated that the liquid
limit (has lowest adjusted R-squared and lowest MAE,
and RMSE) and moisture content are the most
influencing parameters for the prediction of cohesion,
while for the angle of internal friction, the more
significant physical parameter is the liquid limit and
dry unit weight of the gypseous soils. However, for
predicting compression index, the ratio of gypsum
content to specific gravity is the highest physical soil
parameter of the soil.
5. ANN model with LR and NLR performance was very
close to predicting the main gypseous soil properties as
a function of the physical properties of gypsum soils.
Data availability No data, models, or codes were generated or used
during the study.
Declarations
Conflict of interest The authors declare no conflicts of interest.
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Compaction is simple ground improvement technique where the soil is densified through external compactive effort. The important parameters of compaction are Optimum Moisture Content (OMC) and Maximum Dry Density (MDD) which depends on the index properties of soil. Compaction increases the density of soil thereby, increasing shear strength and bearing capacity. These above parameters which are determined from laboratory tests are laborious and time consuming. However index soil properties test is relatively inexpensive, simple and can be performed within less time with utmost accuracy. In this research work, an attempt has been made to predict the compaction parameters from index properties of the soil in terms of Liquid Limit, Plasticity Index, soil particles finer than 75microns and greater than 75microns size. A feed forward neural network model is developed to predict the compaction parameters of the soil using index properties of the soil and the analysis is done by using Artificial Neural Network (ANN) methodology. Using this model, compaction parameters can be easily predicted by performing simple index properties tests in the laboratory. The R 2 values of OMC of ANN model for training and testing dataset were found to be 0.8526 and 0.7568 respectively. The R 2 values of MDD of ANN model for training and testing dataset were found to be 0.8801 and 0.8071 respectively. The R 2 values of OMC and MDD for simulation dataset for this parameter are 0.9463 and 0.9478 respectively. Hence, it was proved that the developed neural network model can predict OMC and MDD with reasonable degree of accuracy.
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The focus of this research is to develop models for predicting the unconfined compressive strength and compression index (Cc) of clay soils according to Atterberg limits, natural water content, dry density, void ratio, and fine content. The soil unconfined compressive strength (UCS) ranged from 24 to 340 kPa and has been quantified with great precision using tested data and data collected from published research studies. The soil compression index ranged from 0.014 to 0.831 which is also correlated by the easily measurable soil properties of Atterberg limits, natural moisture content, density, void ratio, and fine contents (passes no. 200 sieves). A wide experimental test results (a total of 253 tested soils) were combined with more than 350 data collected from different academic research studies, and total data were statistically analyzed and modeled using a linear regression model (LR). According to the correlation determination (R2), mean absolute error (MAE), and the root mean square error (RMSE), the unconfined compressive strength and compression index of soil can be well predicted in terms of liquid limit (LL), plasticity index (PI), moisture content (MC), dry density (γd), void ratio, and percentage passing no. 200 sieve using linear simulation techniques. The performance of the LR models was compared using artificial neural networks (ANN) models with different hidden layers and input layers. Based on the statistical assessments such as R2, RMSE, and MAE the LR models were close to the ANN model to predict the UCS and Cc of the soils. The sensitivity study concludes that the dry density and void ratio are the most influential parameter in determining the unconfined compressive strength and compression index with the training dataset.