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Implementation of multi-expression programming (MEP), artificial neural network (ANN), and M5P-tree to forecast the compression strength cement-based mortar modified by calcium hydroxide at different mix proportions and curing ages



In this study, four different modeling techniques, nonlinear regression (NLR), artificial neural network (ANN), M5P-tree, and multi-expression programming (MEP), are used for developing reliable models to predict the compressive strength of cement-based mortar modified with various calcium hydroxide (CH) content up to 45% (wt% dry cement). The developed accurate models are essential in the construction fields since the material properties prediction from the model is time-saving and cost-effective. The dataset for model development contained data from previous literature related to calcium hydroxide cement blended cement-mortar. The water/cement ratio (w/c) was ranged from 0.3 to 0.74, and the testing age of the sample was varied between 1 and 28 days. Nevertheless, the MEP model was better than other models based on statistical tool assessments. The M5P-tree model is the second-best technique for compressive strength prediction of cement-based mortar modified with calcium hydroxide. Based on the collected data, the compressive strength of the cement mortar decreases as the addition of calcium hydroxide increases.
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Innovative Infrastructure Solutions (2022) 7:153
Implementation ofmulti‑expression programming (MEP), artificial
neural network (ANN), andM5P‑tree toforecast thecompression
strength cement‑based mortar modified bycalcium hydroxide
atdifferent mix proportions andcuring ages
AsoAbdalla1· AhmedSalih1
Received: 11 December 2021 / Accepted: 31 January 2022
© Springer Nature Switzerland AG 2022
In this study, four different modeling techniques, nonlinear regression (NLR), artificial neural network (ANN), M5P-tree,
and multi-expression programming (MEP), are used for developing reliable models to predict the compressive strength of
cement-based mortar modified with various calcium hydroxide (CH) content up to 45% (wt% dry cement). The developed
accurate models are essential in the construction fields since the material properties prediction from the model is time-saving
and cost-effective. The dataset for model development contained data from previous literature related to calcium hydroxide
cement blended cement-mortar. The water/cement ratio (w/c) was ranged from 0.3 to 0.74, and the testing age of the sam-
ple was varied between 1 and 28days. Nevertheless, the MEP model was better than other models based on statistical tool
assessments. The M5P-tree model is the second-best technique for compressive strength prediction of cement-based mortar
modified with calcium hydroxide. Based on the collected data, the compressive strength of the cement mortar decreases as
the addition of calcium hydroxide increases.
Keywords Calcium hydroxide· Compressive strength· Modeling· Sensitivity analysis
Nowadays, many environmental issues are raised from
cement production and other pollutions, such as global
warming caused by carbon dioxide (CO2) emissions into the
atmosphere and landfilling by-products of factories. It is
believed that using those waste can solve many environmen-
tal problems while producing a sustainable material for con-
struction. Mineral admixture addition is one of the solutions.
By-products of silicon industries and power plants include
silica fume, calcium hydroxide, and fly ash; several studies
have been conducted on the use of these wastes in cement-
based concrete and mortars, exhibiting better mechanical
performance qualities and composite durability [1, 2]. Many
studies have been done on the influence of calcium hydrox-
ide powder on the mechanical characteristics of cement-
based mortar by replacing some Portland cement with cal-
cium hydroxide powder and changing the fresh and hardened
properties of cement mortar [35]. For many decades, con-
crete has been widely used as an essential material for con-
structing various infrastructures, including residential and
commercial buildings and civil engineering structures. It is
also used for the new generation of gravity-defying sky-
scrapers. It provides an opportunity for creativity and unlim-
ited engineering potential. Therefore, concrete is responsible
for many of the global construction industries. Aggregate
constitutes the major percent of the concrete which has a
high impact on its properties, as it typically constitutes
60–80% of the concrete volume. These aggregates directly
affect the fresh and mechanical performance of the concrete
[6]. Despite the global acceptance of concrete as a key con-
struction material, it has some shortcomings that usually
affect its quality and general performance. For instance, rela-
tively high density, brittleness, weak tensile strength, low
* Ahmed Salih
Aso Abdalla
1 Civil Engineering Department, College ofEngineering,
University ofSulaimani, Kurdistan Sulaimani - Kirkuk Rd,
Sulaymaniyah46001, Iraq
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resistance to chemical attacks, etc. For these reasons,
research is continuously conducted to seek alternative
sources of concrete ingredients that are technically satisfac-
tory, cost effective, environmentally friendly, and materials
that resist an aggressive environment. Concrete materials,
including cement mortar, sand, and coarse aggregates, are
becoming expensive and sometimes not commonly found in
some locations. The need to find another source of construc-
tion materials is desirable. More durable and recyclable
materials are needed, utilization of waste and natural or agri-
cultural by-products. This may reduce the exploitation of
natural resources and reduce the effect of environmental pol-
lution. The utilization of recycled aggregate and natural
resources as coarse aggregate in concrete production mini-
mizes landfill waste. Many research on the properties of
concrete has been conducted [6, 7]. It was shown from the
literature that minerals recycled and agricultural by-products
are paved as alternative substitutes to aggregates. Ferro-
chrome slag replaced a certain amount of fine aggregate and
yielded a promising result for concrete production. Maxi-
mum strength was achieved when incorporated with 75%
steel slag as coarse aggregate. Incorporating copper waste
slag at 10–100% replacement as coarse aggregate enhanced
the mechanical performance of self-compacting concrete by
26–29%. Nowadays, machine learning has been used by the
researcher in civil engineering fields which includes fitness
monitoring of structural engineering system, mechanical
properties of concrete, the interface of composite members,
fire resistance of reinforced concrete elements, residual
properties of concrete subjected to fire [7]. Support vector
regression (SVR) is a type of machine learning technique
that works based on the rule of structural risk minimization.
The SVR can be used in regression and classification. The
behavior of high- and ultra-high-performance concrete
beams was estimated by developing an SVR-based model.
The characteristic parameters include fracture energy, ulti-
mate load, and so forth. SVR-and ANN-based models have
been developed and applied to predict the concrete behavior
based on mix design using experimental data. The compres-
sive strength was successfully predicted with high accuracy
based on SVR models [5, 6]. Another interesting block-
oriented model, which includes linear dynamic blocks and
non-memory blocks, is useful in nonlinear system modeling
responsible for simple block-oriented structures and efficient
structural ensemble. Hammerstein–Wiener model consists
of two static nonlinear blocks confining dynamic linear
blocks are generally employed for a nonlinear system. The
Hammerstein–Wiener model can describe or approximate
the complicated nonlinear industrial process than the Ham-
merstein model or Wiener model [7]. The statistical tech-
niques and machine learning algorithms are very strong tools
that are commonly used in engineering design. These tech-
niques are specifically used in complex engineering systems,
including composite materials and structures, and solved
technically. Therefore, this study has paid attention to pre-
dicting the compressive strength of concrete modified with
jujube seed as a partial substitute to coarse aggregate by
employing SVM and HWM models. The durability of con-
crete structures is essential [3]; thus, concrete must be ade-
quately compacted during the casting of fresh concrete to
achieve durable concrete leading to SCC development.
Improved segregation resistance translates aggregate parti-
cles’ distribution in the concrete mixtures relatively at all
locations and different levels [6]. Most importantly, SCC can
easily be poured into the formwork of congested reinforced
structures with no vibration, reducing construction time,
feasible design work, and enhancing product and working
environment quality. Therefore, contractors are motivated to
utilize industrial by-products and construction waste such as
recycled concrete aggregates that can be used as a partial
replacement for aggregates in concrete [4]. Calcium carbide
waste (CCW) is a by-product of the acetylene gas (C2H2)
production process. CCW is obtained through a chemical
reaction between water and calcium carbide. CCW is highly
alkaline (pH > 12) and contains a high proportion of
Ca(OH)2, which is about 92% of its mass fraction [6]. There-
fore, when it is combined with other pozzolanic materials,
the Ca(OH)2 will react with the silicon oxide or silicon and
aluminum oxides present in pozzolans to yield more calcium
silicate hydrates (C–S–H) responsible for strength develop-
ment [6]. Adamu etal. [7] also replaced fly ash with CCW
at 0, 10, 20, and 30% levels in alkali-activated fly ash sus-
tainable material using sodium hydroxide and sodium sili-
cate as activators. Their findings showed that the setting time
of mortar decreases, while the
CaC2 + 2H2O C2H2 + Ca(OH)2 compressive strength and
shear bond strengths increase with increment in CCW con-
tent. CCW also densified the microstructure of the mortar
and increased the peaks of calcium hydroxide and calcium
silicate hydrates, leading to the strength increment. Haruna
etal. [6] used a hybrid of CCW and silica fume via a new
combustion technique to produce a new supplementary
cementitious material (SCM) in concrete, where they
replaced 5% cement with the new SCM. The findings
showed that the new SCM prolonged the hydration process
of the concrete, thereby increasing the setting times,
improved the compressive strength at later ages (45days),
and lower drying shrinkage value at the same age compared
to reference concrete. Adamu etal. [7] reported the effect of
RHA and Al2O3 nanoparticles on concrete’s mechanical and
durability properties. They replaced 10% cement with RHA,
and 1, 2, 3, and 4% cement with Al2O3 nanoparticles. Their
results showed that replacing 10% cement with RHA identi-
fied the concrete microstructure and increased the compres-
sive strength, flexural strength, tensile strength, and durabil-
ity properties in terms of resistance to hydrochloric acid and
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acid attack of the concrete. They further reported that replac-
ing cement with Al2O3 further densified the concrete micro-
structure and increased its strength and durability [8, 9].
Modeling the properties of materials can be performed in
various ways, including computational modeling, statistical
techniques, and newly created tools like regression analysis,
M5P-tree, and artificial neural networks (ANN) [1018].
Also, Armaghani and Asteris [19] investigated the applica-
tion of ANN and adaptive neuro-fuzzy inference system
(ANFIS) models to predict the compressive strength of
cement mortar with or without metakaolin concluded that
ANFIS performed better than ANN. Moreover, Suba etal.
[20] employed ANN for mechanical properties prediction
and compared the result with linear regression, the forecast
of the ANN model was pretty close to actual work. Multi-
expression programming (MEP) was used to estimate the
mechanical properties of concrete and provide acceptable
results as implemented by Shah etal. [21]. The parametric
study revealed the accuracy of the MEP model, with a high
correlation coefficient (R). As a result, several techniques
were used in the literature to forecast the mechanical proper-
ties of cement-based mortar, but MEP has not been used for
that purpose.
Problem statement
i. There is no comprehensive study in the previous
research studies on the cement mortar modified with
the calcium hydroxide evaluating and quantifying the
effect of a wide range of mix proportions on the long-
term compressive strength of cement mortar.
ii. From now towards the researchers and the construc-
tion industry can use the developed models in this
study with high accuracy (low RMSE and high R val-
ues) to predict the compressive strength of the cement
mortar withoutany costand would save time for the
experimental lab work.
iii. Several new ideas were used in this study as follows:
iv. Collecting 215 tested data, statistical analysis to disci-
pline concerns the collection, organization, analysis,
interpretation, and presentation of data.
v. Long-term compressive strength prediction for the
cement mortar.
Objectives ofthis study
This study aims to determine the compressive strength of
cement mortar modified with calcium hydroxide (CH) with
various water to cement ratios and curing time using differ-
ent multiscale models. The models were subjected to sen-
sitivity analysis utilizing statistical evaluation tools. As a
consequence, experimental data from other research papers
were gathered and evaluated using a variety of statistical
modeling techniques to accomplish the following goals: (i)
To perform a statistical analysis and determine the impact of
mixture compositions of cement mortar (ii) To determine the
influence of calcium hydroxide on the compressive strength
of cement mortar (iii) Using statistical analysis, compare
and determine the most trustworthy model for measuring
the compressive strength of cement mortar modified with
calcium hydroxide.
Figure1 presents the steps that have been followed during
this study.
Data collection
A comprehensive 215 data on compressive strength and 41
data on flexural strength of cement-based mortar modified
with calcium hydroxide were collected from different pre-
vious studies [24, 11, 17, 2229, 4851]. The dataset was
divided into three groups (training, testing, and validating)
randomly using the rand function in Microsoft Excel. The
largest group included 70% of the dataset (151 data), and
each of the other two groups included 15% of the dataset
(32 data). The training data is used to develop the model, an
algorithm is feeded with the training data and continually
evaluated to learn from the data and make a future predic-
tion while validating and testing data is provided to test the
developed model against unseen data and overfitting of the
developed model can be minimized [26]. The summary of
statistical analysis on the input and output parameters with
detail of the collected data is shown in Table1.
Statistical analysis
Water tocement ratio (w/c)
According to the statistical evaluation on the collected
data, w/c was ranged between 0.3 and 0.74, with mean and
median, standard deviation (SD), variance (Var), skew-
ness (Skew), and kurtosis (Kur) of 0.5, 0.08, 0.01, 0.67,
3.29, respectively (Table2). The relation between w/c and
compressive strength and the histogram for w/c is shown
in Fig.2.
Calcium hydroxide content (CH) (%)
Based on the collected data from previous literature, the
percentage of cement replacement with calcium hydroxide
was 45% maximum. With a median, SD, Var, Skew, and Kur
of 12, 10.83, 117.27, 0.82, 0.42, respectively (Table2). The
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variation of compressive strength with the percentage of the
replacement of calcium hydroxide content and histogram for
CH content is displayed in Fig.3.
Curing time (t) (days)
The collected dataset contained experimental results from
previous research; curing time ranged from 1 to 28days,
with a median of 7days, SD, Var, Skew, and Kur of 12days,
143.45 0.5, and −1.67, respectively (Table2). The histo-
gram for curing time and variation of compressive strength
with curing time are presented in Fig.4.
Compressive strength (CS)
Compressive strength of cement-based mortar modified
with calcium hydroxide up to 28days was ranged from 3
to 75MPa, with a median of 28.85MPa, SD, Var, Skew,
and Kur of 13.5MPa, 182.36, 0.41, −0.34 (Table2). The
histogram of compressive strength of cement-based mortar
modified with calcium hydroxide and Weibull distribution
function is shown in Fig.4.
•Considering w/c, curing time, calcium hydroxide content as
independent variable (predictors) and compressive strength as a
target for the models.
•Data collection from previous researches related to modification of
cement mortar with calcium hydroxide.
•Statistical analysis, presentation of the data , and finding possible
correlation between independent and dependent variables.
•Data splitting randomly ,70% of the data for training the models,
the remaining 30% for validation and testing the developed models.
•Modeling using MEP, NLR, ANN, and M5P- tree models.
•Evaluation of the developed models based on R2, RMSE, MAE, SI,
and OBJ.
•Performing sensitivity analysis to find out the most influential
parameter in predicting the compressive strength of cement mortar
modified with calcium hydroxide.
Fig. 1 Flowchart of the methodology of the current study
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The correlation matrix (Fig.5) shows that the correlation
coefficients (R) of CS with w/c, curing time, and calcium
hydroxide concentration are −0.516, 0.676, and −0.149,
respectively, indicating that there is no direct relationship
between cement-based-mortar compositions and compres-
sive strength. The correlation matrix (Fig.5) shows that the
correlation coefficients (R) of CS with w/c, curing time, and
calcium hydroxide concentration are −0.516, 0.676, and
−0.149, respectively, indicating that there is no direct rela-
tionship between cement-based-mortar compositions and
compressive strength.
Multi‑expression programing (MEP model)
Genetic algorithm (GA) was first introduced by Holland
[30], which was motivated through evolution theory, simi-
lar to that genetic programming (GP) proposed by Cramer
[3032]. Several linear variations of GP have already been
proposed to deal with some difficulties (such as bloat)
caused by tree representations of GP. A few examples are
Cartesian genetic programming, grammatical evolution
(GE), linear GP, MEP, and gene expression programming
[33, 34]. Multiple solutions are stored in a separate chro-
mosome in MEP individuals. The most acceptable option is
usually chosen when it comes to fitness assignments. This is
Table 1 Summary of
model input parameters for
compressive strength prediction
and correlation between
compressive and flexural
References Water to cement ratio (w/c) Curing time, t (days) Calcium
hydroxide con-
tent, CH (%)
CS (MPa)
[23] 0.6 3, 7, and 28 0–20 3–33
[24] 0.43 3, 7, and 28 0 and 30 46–65
[25] 0.5 2, 7, and 28 0–15 9–55
[26] 0.3–0.5 7 and 28 0–45 18–65
[27] 0.5 1,3, 7, and 28 0–20 13.6–70
[28] 0.74 7 and 28 0–30 5–32
[29] 0.5 1 and 28 0–35 14–47.5
[48] 0.33 1, 3, 7, and 28 0–10 29–64
[49] 0.5 2, 7, and 28 0 and 30 16–60
[50] 0.5 3 and 28 0 and 30 17–60
[51] 0.5 2 and 28 0–35 6.7–62
[52] 0.5 3, 7, and 28 0–30 18–54
Remarks Ranged from 0.3 to 0.74 1, 3, 7, and 28days Varied between
0 and 45%
from 3 to
Table 2 Summary of statistical
analysis Statistical parameters Independent variables Dependent variables
Water to
Cement ratio,
time, t
Calcium hydrox-
ide content, CH
strength, FS
No of data 215 215 215 215 41
Max 0.74 28 45 70 12
Min 0.3 1 0 3 4
Median 0.5 7 12 28.854 7.2
Mean 0.5 12 12.96 29.32 7.51
SD 0.085 12 10.83 13.5 1.934
Var 0.007 143.45 117.266 182.364 3.739
Skew 0.671 0.497 0.818 0.407 0.414
Kur 3.287 −1.674 0.424 −0.342 −0.244
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known as strong implicit parallelism, and it is a distinctive
characteristic of MEP [35, 36]. This feature does not make
MEP more complex when compared with GE and GEP. The
MEP model incorporates different fitting factors to generate
a generalized relationship. Math operators were employed
to generate simple expressions in this investigation, and a
trial and error procedure was used to determine the fitting
parameters [37].
Nonlinear regression model (NLR)
The following formula (Eq.1) can be considered as a gen-
eral form for developing a nonlinear regression model [26,
27] to determine the compressive strength of the standard
cement mortar component and modified cement mortar,
Eq.1 represents the interrelationship between the independ-
ent variables,
CS, w/c, t, and L are compressive strength, water to
cement ratio, curing time, and calcium hydroxide content,
and a, b, c, d, e, f, and g are model parameters.
ANN model
The artificial neural network (ANN) is a computing system
that resembles the human brain and its information analy-
sis. In addition, this model is a machine learning system
employed in construction engineering for various numerical
forecasts and difficulties [1, 12, 13]. ANN consists of three
layers input, hidden, and output layer; these layers are con-
nected through biases and weights (Fig.6). The behavior of
an ANN network is influenced by the pattern of neurons’
connections, which also determines the network’s class.
As previously mentioned, it is possible to train a network
to enhance network performance. In more technical terms,
the network’s topology and connection weights change
Fig. 2 a Scatter plot of compressive strength and water to cement
ratio and b histogram of water to cement ratio
Fig. 3 a Scatter plot of compressive strength and calcium hydroxide
content and b histogram for calcium hydroxide content
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repeatedly such that the error at each output layer node is
minimized [19]. In this study, a multi-layer feed-forward
network was designed with mortar composition (w/c, t, CH)
as input and CS as output, and a sigmoid activation function
is used in the output layer.
where j is the number of input variables, xj is the input num-
ber j, and bias is the threshold for sigmoid activation func-
tion. The typical process of the result of ANN is illustrated
in Fig.7.
M5P‑tree model
Quinlan [38] first devised the M5 algorithm, which was
developed into the M5P-tree algorithm [39]. One of the
most significant advantages of model trees is their ability to
efficiently solve problems, dealing with many data sets with
a substantial number of attributes and dimensions. They are
also noted for being powerful while dealing with missing
data. The M5P-tree approach establishes a linear regression
at the terminal node by classifying or partitioning diverse
data areas into numerous separate spaces. It fits on each sub-
location in a multivariate linear regression model. The error
is estimated based on the default variance value inserted
into the node. The general formula for the M5P-tree model
is shown in Fig.8.
Performance criteria formodel evaluation
The developed models are evaluated based on different
assessment tools to choose the best model to predict the
CS of the mortar; the following are efficacy measurements
for the models. The evaluation formulas are illustrated in
Analysis ofoutputs
Relation betweenpredicted andmeasured
compressive strength
MEP model
Comparison of measured with the predicted value of CS
using the MEP model is presented in Fig.9a. The model
had a good performance with R2 of 0.87, 0.87, and 0.897
for training, testing, and validating, respectively. Figure9a
contained −25 and + 25% error lines in the training, testing,
and validating datasets.
Fig. 4 a Scatter plot for compressive strength and curing time and b
histogram for compressive strength of cement mortar modified with
calcium hydroxide from 1 to 28days of curing
Fig. 5 Correlation matrix for independent variables and dependent
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Fig. 6 Typical procedure for
output of ANN network in a
single node
Fig. 7 Optimal ANN network structures, a two hidden layers and 4 hidden neurons, b two hidden layers and 5 hidden neurons, and c two hidden
layers and 7 hidden neurons
Fig. 8 Pruned M5P-tree model
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NLR model
The variation of predicted compressive strength with meas-
ured compressive strength is displayed in Fig.9b. From the
modeling result, it is clear w/c and curing time are affect the
CS more than calcium hydroxide content. In comparison, the
effect of w/c is more significant on the compression strength
of cement-mortar. The model is developed, and the model
parameters are determined using the least square method
and solver technique [4047]. The NLR model is presented
in Table4. Figure9a contained −25 and + 25% error lines
in the training, testing and validating datasets similar to the
MEP model.
ANN model
Figure8 shows the optimal ANN network structures, the
best network structure (Fig.8b) selected containing two hid-
den layers and five hidden neurons, with momentum, learn-
ing rate, learning time of 0.1, 0.2, and 2000, respectively.
Figure9c shows variation in predicted CS with measured
CS using the training, testing, and validating datasets and
error line −25 to + 25%, indicating the measurements and
predictions are in this limit with R2, RMSE of 0.901 and
M5P‑tree model
Figure8 shows the division of the input space by the algo-
rithm of the M5P-tree model into two linear regression func-
tions named LM 1 and LM 2. The relationship of predicted
and measured CS of the M5P-tree model showed in Fig.9d,
with R2 and RMSE of 0.81 and 5.219MPa. With error lines
of −20 to 25% for the training data set and −25 to 25% for
testing and validating datasets.
The error lines for the relationship between measured
compressive strength and the prediction using all the mod-
els were ranged between + 25 and − 25%, as shown in
Fig.10a. Also, the minimum and maximum values of the
ratio between the predicted compressive strength value and
the measured values range between 0.5 and 4.5 with the best
prediction of ANN and MEP models (Fig.10b).
Model evaluations
The MAE for MEP models is less than NLR and M5P-tree
by 15.6 and 15%, while greater than the ANN model by
12%. However, the MAE values of the MEP model for test-
ing and validating datasets are less than NLR, ANN, and
M5P-tree model. The OBJ values for the proposed models
are also evaluated; the OBJ for the MEP model is less than
Table 3 The criteria for measuring the efficiency of the developed models
where R2, RMSE, MAE, MBE, SI, OBJ, t test, U95, and ρ are coefficient of determination, root mean squared error, mean absolute error, an aver-
age of errors, scatter index, objective, t test, 95% confidence uncertainty, and performance index, respectively. yp, ye, and
are predicted com-
pressive strength, measured compressive strength, and an average of measured compressive strength, respectively. n, tr, te, val are several data
in the training, testing, and validating dataset. For all of the assessment parameters, the ideal value is zero, while the best value for R2 is one.
Corresponding to SI, the performance of the model is excellent, good, fair, and poor if the SI<0.1, 0.1<SI<0.2, 0.2<SI<0.3, and SI>0.3,
respectively [46]
Formula Equation number Best value
(3) 1
R2(4) 1
(5) 0
(6) 0
(7) 0
RMSEval+MAEva l
(8) 0
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NLR, and M5P-tree models by 15 and 17%; in addition, the
OBJ of ANN is 6% less MEP model’s OBJ as displayed in
Fig.11. Also, the performance index for the MEP model was
less than other developed models for testing and validating
data which specifies better performance of the MEP model
over NLR, ANN, and M5P-tree models for unseen data
(Fig.11c). Summary of model evaluation for R2, RMSE,
and MAE of the developed models is presented in Table4.
Distinct soft computing techniques can be utilized to con-
struct useful and time-saving models; in this study, four dif-
ferent approaches were employed to develop a trustworthy
model for the prediction of compressive strength of calcium
hydroxide-modified cement mortar; the following are the
primary conclusions:
Fig. 9 Variation of CS Predicted with CS Measured using, a MEP model, b NLR model, c ANN model, and d M5P-tree model
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1. Based on the collected data from literature maximum
percentage of calcium hydroxide is 45%, w/c was ranged
from 0.3 to 0.74. The addition of calcium hydroxide to
cement mortar decreases the compressive strength for
the same mixture and w/c.
2. Based on SI, the performance of MEP and ANN mod-
els are nearly the same, while the SI of MEP model for
validating data is 5% smaller than the SI value for the
ANN model. The objective value for the MEP model
is less than NLR and M5P-tree models by 17 and 16%.
95% Uncertainty value for MEP is smaller than other
developed models.
3. According to the statistical evaluation tools, the MEP
model is better than NLR and M5P-tree models for com-
pressive strength prediction after the ANN model.
4. Using several evaluation criteria, including the root
mean square error (RMSE), the coefficientof determi-
nation(R2), the OBJ, the SI, and the mean absolute error
(MAE). The sequence of models was ANN and M5P-
tree, suggesting that the ANN was the best model pro-
vided in this research based on data acquired from the
literature and producing a higher R2 and lower MAE and
RMSE. The most effective technique for the prediction
of CS of cement mortar is ANN, though the less com-
plicated model can be developed using multi-expression
5. The sensitivity analysis test was performed in order to
check the most effective dependent variables on inde-
pendent variables’ output performance. The results
indicated that the most effective parameters causing the
output result were curing time and CH content.
Table 4 Summary of developed models
Model Formula Eq. no R2RMSE (MPa) No. of data
(9a) 0.87 4.857 215
(t)0.334 +19.63
(10) 0.84 5.39 215
=27.38 15.67
=76.68 92.69
0.85 5.21 215
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Fig. 10 Comparison of
developed model based on, a
variation between measured and
predicted CS values for testing
data and b Ratio of predicted
compressive strength to meas-
ured compressive strength
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Page 13 of 15 153
Scater Index, SI
Training Te stingValidating
Excele nt
Mean Absolute Error, MAE (MPa)
Training Te stingValidating
Fig. 11 Comparing developed models based on, a SI, b MAE, c OBJ value
Conflict of interest The authors declare that they have no known com-
peting financial interests or personal relationships that could have ap-
peared to influence the work reported in this paper.
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... AmiR 75 used MEP to obtain robust predictive models for computing the tangent elastic modulus of normal and high strength concrete. Abdalla 76 incorporated four different techniques to predict the CS of cement-based mortar modified with calcium hydroxide and found that MEP outperformed all the other models based on statistical assessment. Ilyas 77 utilized the MEP to estimate CS of carbon fiber reinforced polymers (CFRP) confined concrete and concluded that developed model is trained enough to accurately predict the strength of CFRP wrapped structural members. ...
This study investigates the resistance of concrete to Rapid Chloride ions Penetration (RCP) as an indirect measure of the concrete’s durability. The RCP resistance of concrete is modelled in multi-expression programming approach using different input variables, such as, age of concrete, amount of binder, fine aggregate, coarse aggregate, water to binder ratio, metakaolin content and the compressive strength (CS) of concrete. The parametric investigation was carried out by varying the hyperparameters, i.e., number of subpopulations N sub , subpopulation size S size , crossover probability C prob , mutation probability M prob , tournament size T size , code length C leng , and number of generations N gener to get an optimum model. The performance of all the 29 number of trained models were assessed by comparing mean absolute error (MAE) values. The optimum model was obtained for N sub = 50, S size = 100, C prob = 0.9, M prob = 0.01, T size = 9, C leng = 100, and N gener = 300 with MAE of 279.17 in case of training (TR) phase, whereas 301.66 for testing (TS) phase. The regression slope analysis revealed that the predicted values are in good agreement with the experimental values, as evident from their higher R and R ² values equaling 0.96 and 0.93 (for the TR phase), and 0.92 and 0.90 (for the TS phase), respectively. Similarly, parametric and sensitivity analyses revealed that the RCP resistance is governed by the age of concrete, amount of binder, concrete CS, and aggregate quantity in the concrete mix. Among all the input variables, the RCP resistance sharply increased within the first 28 days age of the concrete specimen and similarly plummeted with increasing the quantity of fine aggregate, thus validating the model results.
... They found curing time to be the most important input parameter in estimating the CS of mortars. Similarly, Abdalla and Salih [18] compared M5P trees, GP and ANN metamodels. ...
Full-text available
Predicting the mechanical properties of cement-based mortars is essential in understanding the life and functioning of structures. Machine learning (ML) algorithms in this regard can be especially useful in prediction scenarios. In this paper, a comprehensive comparison of nine ML algorithms, i.e., linear regression (LR), random forest regression (RFR), support vector regression (SVR), AdaBoost regression (ABR), multi-layer perceptron (MLP), gradient boosting regression (GBR), decision tree regression (DT), hist gradient boosting regression (hGBR) and XGBoost regression (XGB), is carried out. A multi-attribute decision making method called TOPSIS (technique for order of preference by similarity to ideal solution) is used to select the best ML metamodel. A large dataset on cement-based mortars consisting of 424 sample points is used. The compressive strength of cement-based mortars is predicted based on six input parameters, i.e., the age of specimen (AS), the cement grade (CG), the metakaolin-to-total-binder ratio (MK/B), the water-to-binder ratio (W/B), the superplasticizer-to-binder ratio (SP) and the binder-to-sand ratio (B/S). XGBoost regression is found to be the best ML metamodel while simple metamodels like linear regression (LR) are found to be insufficient in handling the non-linearity in the process. This mapping of the compressive strength of mortars using ML techniques will be helpful for practitioners and researchers in identifying suitable mortar mixes.
... Except mixture amounts heating degree was used as an input. Rest of the studies used ANN to predict compressive strength by using common inputs can be addressed in the literature [24][25][26][27][28] In the last decade, the basic developments were observed, especially in prediction parameters and metaheuristic models. Split tension, flexural strength, modulus of elasticity, rebar pull-off [29], and fresh properties [30,31], are a few examples. ...
The service life performance of conventional and modified concrete subjected to harsh climatic condition environment is directly related to durability properties of concrete like abrasion, freezing and thawing cycles. These properties are critical issues that should be predicted before performing experimental test. On this basis, the basic purpose of this paper is to predict the abrasion loss, freezing and thawing properties of concrete modified with silica fume (SF) and steel fiber (SFb) by using mix design and additional properties. From this point of view, a conducted experimental study was selected as a case study. In the control concrete (CC) mixtures, Portland cement, crushed stone aggregate, and superplasticizer (SP) were used in the selected experimental study. SP in concrete mixtures was used in the amounts of 1.0%, 1.5%, and 2.0% by weight of cement, and so modified concrete was produced with and without SFb according to the target strength of C25. Furthermore, SF and SFb were used in different amounts to modify the concrete. The SF was replaced with cement in the amounts of 7.5%, 10.0%, and 15.0%. In total, 16 different mix designs were prepared with different SP and SF ratios. In addition, SFb was added to all mixtures of designed concrete at a constant amount of 65 kg/m3. Additionally, a 16-mix design was prepared with SFb. Cumulatively, 32 different mix designs were prepared for the experimental study. Tests on the fresh, hardened, and life-cycle performance properties of the concrete were conducted. As for the metaheuristic part of this study, on the basis of the available experimental data, life-cycle performance parameters of the concrete modified with SF and SFb are predicted by using single and hybrid generalized extreme learning machine methods. Eight different data sets were generated with gradually extended input data. Two different outputs were considered: abrasion resistance (AL) and freezing/thawing (FT). Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) algorithms were used to produce binary and ternary hybrid methods. Four different models were proposed as listed: single use of Generalized Extreme Learning Machine (GRELM), binary use of GRELM-PSO, and GRELM-GWO. Finally, PSO and GWO were hybridized and integrated into GRELM. Two quality indicators, namely Root Mean Square Error (RMSE) and correlation of determination (R²), were considered to see the performance of the prediction. The results showed that the proposed ternary prediction model composed of GRELM-PSO-GWO provided more accurate results in all sets from 74% to 91% by extending input parameters, even if complicated parameters are inserted in as an input to the data set.
... MEP individuals are strings of genes encoding complex computer programs; when MEPs package expressions for conceptual regression issues, they comparably represent them to how processors convert C or Pascal expressions into machine code [34][35][36]. Simple math operators were employed to generate simple expressions in this investigation, and a trial-and-error procedure was used to determine the fitting parameters [37]. Population number, subpopulation size, code length, crossover probability, mutation probability, tournament size, functions and variables probability, and number of generations of 40, 100, 100, 1, 0.01, 4, 0.5, 0.5, 3000, respectively. ...
Cement kilns are used for the pyroprocessing stage of the manufacture of Portland and other types of hydraulic cement. Calcium carbonate reacts with silica-bearing minerals to form a mixture of calcium silicates. Over a billion tons of cement are made per year, and cement kilns are the heart of this production process: their capacity usually defines the capacity of the cement plant. As the main energy-consuming and greenhouse-gas–emitting stage of cement manufacture, improving kiln dust efficiency has been the central concern of cement manufacturing technology. Emissions from cement kilns are a significant source of greenhouse gas emissions, accounting for around 2.5% of non-natural carbon emissions worldwide. This study evaluated the effect of the primary two components of CKD, such as SiO2 and CaO, on the long-term compressive strength of cement-based mortar up to 360 days of curing. For that purpose, 167 data of cement-based mortar samples modified with CKD were collected from literature and analyzed. Water to binder ratio (w) ranged from 0.34 to 0.76, CKD content ranged from 0 to 50% (dry weight of cement), different CaO and SiO2 of CKD and cement ranged from 17.64 to 25.45%, and 51.45 to 65.57%, respectively. Several soft computing models were used to predict the compressive strength of the cement-mortar modified with CKD. It was revealed from the modeling results that are increasing both SiO2 and CaO contents (%) resulted in increasing the compressive strength of the mortar. Based on the sensitivity analysis, the curing time is the most influential parameter in the compressive strength prediction of cement-based mortar modified with CKD
Abstract In order to predict the compressive strength (σc) of Ultra-high performance fiber reinforced concrete (UHPFRC), developing a reliable and precise technique based on all main concrete components is a cost-effective and time-consuming process. To predict the UHPFRC compressive strength, four different soft computing techniques were developed, including the nonlinear- relationship (NLR), pure quadratic, M5P-tree (M5P), and artificial neural network (ANN) models. Thus, 274 data were collected from previous studies and analyzed to evaluate the effect of 11 variables that impact the compressive strength, including curing temperature. The performance of the predicted models was evaluated using several statistical assessment tools. According to the findings, ANN results performed more suitable than other models with the lowest root mean square error (RMSE) and highest coefficient of determination (R2) value. According to the sensitivity analysis, the most variables that affect the compressive strength prediction of UHPFRC are a curing temperature with a percentage of 17.36%, the fiber content of 17.13%, and curing time of 15.13%.
Full-text available
Abstract A variety of ashes used as the binder in geopolymer concrete such as fly ash (FA), ground granulated blast furnace slag (GGBS), rice husk ash (RHA), metakaolin (MK), palm oil fuel ash (POFA), and so on, among of them the FA was commonly used to produce geopolymer concrete. However, one of the drawbacks of using FA as a main binder in geopolymer concrete is that it needs heat curing to cure the concrete specimens, which lead to restriction of using geopolymer concrete in site projects; therefore, GGBS was used as a replacement for FA with different percentages to tackle this problem. In this study, Artificial Neural Network (ANN), M5P-Tree (M5P), Linear Regression (LR), and Multi-logistic regression (MLR) models were used to develop the predictive models for predicting the compressive strength of blended ground granulated blast furnace slag and fly ash based-geopolymer concrete (GGBS/FA-GPC). A comprehensive dataset consists of 220 samples collected in several academic research studies and analyzed to develop the models. In the modeling process, for the first time, eleven effective variable parameters on the compressive strength of the GGBS/FA-GPC, including the Activated alkaline solution to binder ratio (l/b), FA content, SiO2/Al2O3 (Si/Al) of FA, GGBS content, SiO2/CaO (Si/Ca) of GGBS, fine (F) and coarse (C) aggregate content, sodium hydroxide (SH) content, sodium silicate (SS) content, (SS/SH) and molarity (M) were considered as the modeling input parameters. Various statistical assessments such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Scatter Index (SI), OBJ value, and the Coefficient of determination (R2) were used to evaluate the efficiency of the developed models. The results indicated that the ANN model better predicted the compressive strength of GGBS/FA-GPC mixtures compared to the other models. Moreover, the sensitivity analysis demonstrated that the alkaline liquid to binder ratio, fly ash content, molarity, and sodium silicate content are the most affecting parameter for estimating the compressive strength of the GGBS/FA-GPC.
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The traditional method to obtain optimum bitumen content and the relevant parameters of asphalt pavements entails time-consuming, complicated and expensive laboratory procedures and requires skilled personnel. This research study uses innovative and advanced machine learning techniques, i.e., Multi-Expression Programming (MEP), to develop empirical predictive models for the Marshall parameters, i.e., Marshall Stability (MS) and Marshall Flow (MF) for Asphalt Base Course (ABC) and Asphalt Wearing Course (AWC) of flexible pavements. A comprehensive, reliable and wide range of datasets from various road projects in Pakistan were produced. The collected datasets contain 253 and 343 results for ABC and AWC, respectively. Eight input parameters were considered for modeling MS and MF. The overall performance of the developed models was assessed using various statistical measures in conjunction with external validation. The relationship between input and output parameters was determined by performing parametric analysis, and the results of trends were found to be consistent with earlier research findings stating that the developed predicted models are well trained. The results revealed that developed models are superior and efficient in terms of prediction and generalization capability for output parameters, as evident by the correlation coefficient (R) (in this case >0.90) for both ABC and AWC.
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Abstract: Cement paste is the most common construction material being used in the construction industry. Nanomaterials are the hottest topic worldwide, which affect the mechanical properties of construction materials such as cement paste. Cement pastes containing carbon nanotubes (CNTs) are piezoresistive intelligent materials. The electrical resistivity of cementitious composites varies with the stress conditions under static and dynamic loads as carbon nanotubes are added to the cement paste. In cement paste, electrical resistivity is one of the most critical criteria for structural health control. Therefore, it is essential to develop a reliable mathematical model for predicting electrical resistivity. In this study, four different models—including the nonlinear regression model (NLR), linear regression model (LR), multilinear regression model (MLR), and artificial neural network model (ANN)—were proposed to predict the electrical resistivity of cement paste modified with carbon nanotube. Furthermore, the correlation between the compressive strength of cement paste and the electrical resistivity model has also been proposed in this study and compared with models in the literature. In this respect, 116 data points were gathered and examined to develop the models, and 56 data points were collected for the proposed correlation model. Most critical parameters influencing the electrical resistivity of cement paste were considered during the modeling process—i.e., water to cement ratio ranged from 0.2 to 0.485, carbon nanotube percentage varied from 0 to 1.5%, and curing time ranged from 1 to 180 days. The electrical resistivity of cement paste with a very large number ranging from 0.798–1252.23 Ω.m was reported in this study. Furthermore, various statistical assessments such as coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), scatter index (SI), and OBJ were used to investigate the performance of different models. Based on statistical assessments—such as SI, OBJ, and R2—the output results concluded that the artificial neural network ANN model performed better at predicting electrical resistivity for cement paste than the LR, NLR, and MLR models. In addition, the proposed correlation model gives better performance based on R2, RMSE, MAE, and SI for predicting compressive strength as a function of electrical resistivity compared to the models proposed in the literature.
Full-text available
The ultimate strength of composite columns is a significant factor for engineers and, therefore, finding a trustworthy and quick method to predict it with a good accuracy is very important. In the previous studies, the gene expression programming (GEP), as a new methodology, was trained and tested for a number of concrete-filled steel tube (CFST) samples and a GEP-based equation was proposed to estimate the ultimate bearing capacity of the CFST columns. In this study, however, the equation is considered to be validated for its results, and to ensure it is clearly capable of predicting the ultimate bearing capacity of the columns with high-strength concrete. Therefore, 32 samples with high-strength concrete were considered and they were modelled using the finite element method (FEM). The ultimate bearing capacity was obtained by FEM, and was compared with the results achieved from the GEP equation, and both were compared to the respective experimental results. It was evident from the results that the majority of values obtained from GEP were closer to the real experimental data than those obtained from FEM. This demonstrates the accuracy of the predictive equation obtained from GEP for these types of CFST column.
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The need for evaluation of compressive strength of a concrete is of utmost importance in civil and structural engineering as one of the factors that determine quality of concrete. In this paper, two artificial intelligence (AI) techniques, namely Hammerstein–Wiener model (HWM) and support vector machine (SVM) were used in the prediction of compressive strength (σ). The input variables including curing age (T), amount of coarse aggregate (cA), percentage replacement of aggregate (cAR), amount of Jujube seed (S) and slump (D) as the independent variables. Two evaluation metrics were used to determine the fitness between the computed and the predicted values of the σ namely, Correlation co-efficient (R) and determination co-efficient (R2), while two other metrics were employed to check the errors depicted by each model combination inform of mean square error (MSE) and root mean square error (RMSE). The result obtained from AI-based models revealed that both HWM and SVM showed higher prediction skills in prediction of σ. Overall, the comparative performance results proved that HWM-M4 indicated an outstanding performance of 0.9953 and 0.9982 in both the training and testing stages, respectively.
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Rock tensile strength (TS) is an essential parameter for designing structures in rock-based projects such as tunnels, dams, and foundations. During the preliminary phase of geotechnical projects, rock TS can be determined through laboratory works, i.e., Brazilian tensile strength (BTS) test. However, this approach is often restricted by laborious and costly procedures. Hence, this study attempts to estimate the BTS values of rock by employing three non-destructive rock index tests. BTS predictive models were developed using 127 granitic rock samples. Since the simple regression analysis did not yield a meaningful result, the development of models that integrate multiple input parameters were considered to improve the prediction accuracy. The effects of non-destructive rock index tests were examined through the use of multiple linear regression (MLR) and adaptive neuro-fuzzy inference system (ANFIS) approaches. Different strategies and scenarios were implemented during modelling of MLR and ANFIS approaches, where the focus was to consider the most important parameters of these techniques. As a result, and according to background and behaviour of the ANFIS (or neuro-fuzzy) model, the predicted values obtained by this intelligent methodology are closer to the actual BTS compared to MLR which works based on linear statistical rules. For instance, in terms of system error and a-20 index, values of (0.84 and 1.20) and (0.96 and 0.80) were obtained for evaluation parts of ANFIS and MLR techniques, which revealed that the ANFIS model outperforms the MLR in forecasting BTS values. In addition, the same results were obtained through ranking systems by the authors. The neuro-fuzzy developed in this study is a strong technique in terms of prediction capacity and it can be used in the other rock-based projects for solving relevant problems.
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Multi Expression Programming (MEP) is a new evolutionary paradigm intended for solving computationally difficult problems. MEP individuals are linear entities that encode complex computer programs. MEP chromosomes are represented in the same way as C or Pascal compilers translate mathematical expressions into machine code. MEP is used for solving some difficult problems like symbolic regression and game strategy discovering. MEP is compared with Gene Expression Programming (GEP) and Cartesian Genetic Programming (CGP) by using several well-known test problems. For the considered problems MEP outperforms GEP and CGP. For these examples MEP is two magnitude orders better than CGP.
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In this study, the impact of two types of polymer on the stress-strain behavior, elastic modulus and toughness of cement paste, were investigated and quantified. The cement paste was modified with two types of polymer up to 0.06% (based on the dry weight of cement), and the samples were cured at different curing times (1, 3, 7, and 28 days) before testing. Polymers increased cement flowability by 7% to 26% and lowered the water/cement ratio (w/c) by 12% to 43%, based on the types of polymer and polymer content. The nonlinear Vipulanandan p-q model was used to predict the stress-strain behavior of modified cement, and the results were compared to the β model. The elastic modulus (E) at different strain levels and total toughness (TT) of the modified cement was determined by differentiating and integrating the Vipulanandan p-q model. When 0.06 % polymers were added to cement paste, the compressive strength increased by 107 to 257%. During the early curing age, the cement modified with polymer was able to withstand large deformations that mean increase the ductility of the materials, but with increasing curing, the cement modified with polymers become brittle and the strain at failure reduced. Adding polymers to the cement paste creates an amorphous gel that fills the spaces between cement particles with working fibers net or meshes covering the cement particles, which cause a reduction in the voids, porosity and increasing the density of the cement, subsequently the mechanical properties significantly increased.
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In the present research, the information on compressive strength of self-compacting concrete (SCC) containing rice husk ash (RHA) and calcium carbide waste (CCW) as an admixture cured for 28 days was provided. The research applied feedforward propagation neural network (FFNN), emotional neural network (EANN), and conventional linear regression (LR) in the prediction of compressive in which FFNN, EANN, and LR models were trained on the experimental data obtained from addition of 0%–10% RHA and 0%–20% CCW in the SCC mixtures. The results revealed that inclusion of CCW reduces the workability of SCC mixtures and increases in compressive strength at 28 days were observed for SCC mixture containing 10% RHA and 0% CCW against the reference mixtures. The results also indicated that all the AI models (FFNN, EANN, and LR) performed very well with R2-values higher than 0.8951 in both the testing and training stages. The results showed that EANN-M3, FFNN-M3, and LR-M3 combination has the highest performance evaluation criteria of R2 = 0.9733 and 0.9610, R2 = 0.9440 and 0.9454 and R2 = 0.9117 and 0.9205 in both training and testing stages, respectively. It indicates the proposed models' high accuracy in predicting the compressive strength σ of self-compacting concrete with rice husk ash as cement replacement and calcium carbide waste as supplementary materials. The result also suggested that other models, like emerging algorithms, hybrid models, and optimization methods, could enhance the models’ performance.
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Liquefaction has caused many catastrophes during earthquakes in the past. When an earthquake is occurring, saturated granular soils may be subjected to the liquefaction phenomenon that can result in significant hazards. Therefore, a valid and reliable prediction of soil liquefaction potential is of high importance, especially when designing civil engineering projects. This study developed the least squares support vector machine (LSSVM) and radial basis function neural network (RBFNN) in combination with the optimization algorithms, i.e., the grey wolves optimization (GWO), differential evolution (DE), and genetic algorithm (GA) to predict the soil liquefaction potential. Afterwards, statistical scores such as root mean square error were applied to evaluate the developed models. The computational results showed that the proposed RBFNN-GWO and LSSVM-GWO, with Coefficient of Determination (R²) = 1 and Root Mean Square Error (RMSE) = 0, produced better results than other models proposed previously in the literature for the prediction of the soil liquefaction potential. It is an efficient and effective alternative for the soil liquefaction potential prediction. Furthermore, the results of this study confirmed the effectiveness of the GWO algorithm in training the RBFNN and LSSVM models. According to sensitivity analysis results, the cyclic stress ratio was also found as the most effective parameter on the soil liquefaction in the studied case.
Employing ceramic wastes in lime mortars for the restoration of historic buildings has environmental, cultural, social, and economic benefits. This study deals with the possibility of recycling waste glass powder and brick dust in air-lime mortars for restoration purposes. The theatre of the city of Skikda in Algeria was chosen as a case study. To correctly perform the intervention, the main pathologies and the substrate properties were investigated. Different samples of mortars (structural, plaster, external, internal) were taken from the theatre. Their physical and mineralogical properties were determined. Eleven repair mortars were investigated and waste glass powder and brick dust were added to air lime at different substitution rates: 10, 15, 20, 25 and 30%. The local raw materials used and the mortars investigated, were characterised in the laboratory to obtain their mechanical and physical properties. The results were satisfactory and fulfilled the requirements for the application of these mortars for restoration of the theatre, especially concerning mechanical performance. The mortars that were made up by substituting 30% with the two wastes, presented the highest values with an augmentation of 68.7% for mortars with waste glass powder, and 50.5 % for mortars with brick dust. The compressive strength was augmented. Furthermore, it was found that the mortars can also be used for other historic buildings. The two wastes presented pozzolanic activity and improved the mechanical strength of the mortars. From an environmental standpoint, the use of these ceramic wastes offers many advantages, encouraging their re-utilisation and, consequently, reducing landfill disposal.
Tensile strength of rock plays a significant role in the design of tunnels and underground engineering projects. Due to the inefficiency of direct method in determining rock tensile strength, the use of non-destructive tests has become a new direction in predicting the Brazilian Tensile Strength (BTS) of the rock samples. Fuzzy Inference System (FIS), Artificial Neural Network (ANN), and Adaptive Neuro-Fuzzy Inference System (ANFIS) are three widely-used methods for BTS prediction. This study investigated the performance of these three intelligent models for BTS forecasting. In this regard, three non-destructive tests, namely Schmidt hammer, p-wave velocity, and density, were performed on 127 granitic rock samples, and their results were considered as input parameters. Then, the BTS tests were carried out on the samples and their results were considered as model output. Four measures of coefficient of determination (R²), Root mean square error (RMSE), Mean absolute error (MAE), and Scatter index (SI) were used for evaluation. The results showed that the ANFIS model, which is enjoying advantages of both ANN and FIS models, provides more accurate results in comparison with the proposed ANN and FIS models in predicting BTS values. R² values for ANFIS, ANN, and FIS models were 0.92, 0.88, and 0.87, respectively. Besides, the ANFIS model could yield the lowest RMSE value of 81.5%, whereas RMSEs for FIS and ANN were 89.5% and 87.5%, respectively.