A new prediction method for the rheological behavior of grout with bottom ash for jet grouting columns

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Soils and Foundations 57 (2017) 384–396
www.elsevier.com/locate/sandf
A new prediction method for the rheological behavior of grout
with bottom ash for jet grouting columns
Hamza Güllü ⇑
Department of Civil Engineering, University of Gaziantep, 27310 Gaziantep, Turkey
Received 18 December 2015; received in revised form 4 October 2016; accepted 4 February 2017
Available online 16 May 2017
Abstract
Among the many variables involved in jet grout technology, dealing with the complex phenomena of grout flow, specifically related to
the pumping pressure (shear stress), the pumping rate (shear rate) and the viscosity, mostly becomes a difficult task for grouting in practice. Thus, this study presents the capability of a new methodology in soft computing techniques, called gene expression programming
(GEP), to predict the rheological behavior (i.e., the shear stress versus the shear rate and the viscosity versus the shear rate) of grout with
bottom ash for jet grouting columns, as an alternative approach to traditional methods. For this purpose, shear stress and viscosity formulas, including the main input variables of the shear rate and bottom ash proportion, are derived using GEP modeling through the
stages of production and testing. Then, the performances of the GEP formulas are compared with the measured data and the regression
and conventional rheological models (De Kee and Robertson-Stiff) for use in practice. The results indicate that the GEP formulas are
able to yield estimations with good precision resulting in better predictions (R 0.96) compared to the regression model. A successful
description of the pseudoplastic response of rheological behavior is given, and a response consistent with conventional rheological models is obtained. Moreover, the measured data (shear stress and viscosity) generally follow the GEP modeling well, but the level of satisfaction is more favorable at high proportions of bottom ash. In conclusion, the study reveals that the derived GEP formulas are
relatively promising for estimating the pumping pressure, the viscosity and the pumping rate of grout with bottom ash for jet grouting
columns, at least in assisting conventional methods for preliminary designs.
Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Jet grouting column; Grout; Bottom ash; Rheological behavior; Gene expression programming
1. Introduction
The jet grouting technique is one of the most popular
ground-improvement methods that offers relatively good
soil quality for the engineering characteristics (i.e., bearing
capacity, settlement, permeability, etc.) in a variety of
applications (i.e., foundation reinforcement, retaining
structures, impermeable barriers, etc.) for solving possible
ground problems. The resulting product is a cemented-
Peer review under responsibility of The Japanese Geotechnical Society.
⇑ Fax: +90 342 360 1107.
E-mail address: [email protected]
soil body called the jet column appropriately arranged in
the subsoil (Croce and Flora, 2000). In brief, in this technique (Fig. 1), the grout (cement-based fluid mixture) is
injected into the ground at the treatment depth at a very
high flow (200–400 L/min) with a very high velocity of
energy through small-diameter injection nozzles (1–
10 mm) placed on a grout pipe or rod. The jet grout propagates radially with respect to the treatment axis from the
borehole at a constant rate of rotation due to the road
speed by separating the soil particles. The particles are then
mixed and cemented with the jet grout. Then, the rod is
slowly withdrawn toward the ground surface resulting in
a homogeneous mass of a high-strength soil-cement body
http://dx.doi.org/10.1016/j.sandf.2017.05.006
0038-0806/Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
H. Güllü / Soils and Foundations 57 (2017) 384–396
Fig. 1. Brief representation of jet grouting (Shen et al., 2013).
(jet column) due to the solidification of the injected cementbased grout (Croce and Flora, 2000; Modoni et al., 2006;
Nikbakhtan et al., 2010). Most jet grouting applications
have been based on the subjective rules of thumb firstly
by means of trial and error at the site for jet grouting.
The grout is ejected from the small nozzles with at very
high speeds, but the experimental determination of the
velocity mechanism is very difficult. Thus, at the design
stage of the jet grout columns, there still appears a relative
degree of uncertainty coming from the grout variables (the
grout composition, binder content, particle size, particle
shape, particle distribution, temperature, mixing, etc.) that
play a significant role in grout rheology. The uncertainty
during the injection process is also a major problem. Thus,
it is necessary to adjust the operational injection parameters (Croce and Flora, 2000; Modoni et al., 2006, 2016;
Ochmański et al., 2015; Ribeiro and Cardoso, 2016). Relevant to the velocity considerations of grout are the uncertainty related to the pumping pressure (shear stress), the
pumping rate (shear rate) and the viscosity of the grout
involved with rheological behavior (i.e., flow behavior) that
significantly affect the hardened properties of the grout
(Warner, 2004). This issue encourages engineers to develop
more satisfactory design methods from the viewpoint of the
prediction of rheological behavior in jet grouting.
In terms of jet-soil interaction, the jet-grout column can
be reasonably considered through the typical features of
the seepage and erosion. These features can be useful for
modeling gravelly soils, and sandy and clayey soils, respectively (Modoni et al., 2006; Shen et al., 2013), where the
rheology plays a significant role in their modeling. Through
the mechanisms of jet grouting (Dabbagh et al., 2002) a
bellshaped crater is formed at the soil-jet interface with a
cutting front advancing at a progressively slower rate with
the increased rate from the nozzle. For jet grouting of very
pervious soils (gravels and sandy gravels), the seepage
385
velocity is very large near the nozzle. However, it decreases
sharply as the grout penetrates further into the soil
(Modoni et al., 2006). From the viewpoint of grout rheology, it may be inferred that the injected flow propagates in
the jet column under turbulent conditions in the inner
region and under laminar conditions in the outer region.
The diameter of jet grout column increases considerably
with the soil permeability through the mechanism of seepage in the case of very pervious materials (i.e., gravelly
soils). On the other hand, decreases in the column diameter
obtained for sands and clays depends upon the shear
strength of the soil. When the injected grout impacts the
soils with lower permeability compared to gravel, the grout
seepage is largely inhibited. Then, it turns back dragging
the soil aside from its initial position through the erosion
mechanism. This erosion mechanism of the flow results in
the growth of the jet columns together with the replacement of the soil particles by the grout. The column diameter, involved with the flow behavior, can be simulated on
the basis of the erosive action of the injected flow which
depends upon the resistive action of the soil (Modoni
et al., 2006, 2016). The extension of jet erosion for the jet
grouting column results from the balance between the soil
resistance and the jet cutting energy (Flora et al., 2013). It
has been reported that the dependence of the column diameters for all soil types during the grouting process can generally be attributed to the parameters that include the
diameter of the distance from the nozzle, the number of
nozzles, the lifting speed of the monitor, the velocity along
the cross-sectional profile, the kinematic viscosity of the
grout and the flow rate of the grout or the fluid velocity
(Modoni et al., 2006; Flora et al., 2013). Regarding clayey
soils, jet grouting is found effective only when the performance is improved by high flow rates and low monitor
withdrawal speeds. However, the increase in volume of
the injected fluid for an appropriate flow rate could
increase the amount of spoil. This results in a reduction
in the economical efficiency of the ground improvement
(Modoni et al., 2006). One of the existing methods for estimating the column diameter through the design stage of jet
grouting is the empirical approach (Shen et al., 2013). In
the proposed formulations for the empirical approach
(Shibazaki, 2003; Mihalis et al., 2004), it is observed that
the variables of jetting pressure and the flow rate of the
grout play primary roles compared to the other variables
(the number of passes of the jet, the velocity of the nozzle,
the withdrawal rate of the rod) (Shen et al., 2013). It has
been reported that any adverse effect due to the interactions
with the variables during the jet grouting process may
cause detrimental effects to the foundations of buildings
or utilities as well as to the anticipated displacements in
the subsoil and ground surface (Wang et al., 2013). When
the jet grouting involves the injection of large volumes of
grout that could need high pumping pressure, a considerable lateral movement of the soil with significant ground
improvement can be expected. This could have a possible
impact involving the hydraulic fracturing of the ground
386
H. Güllü / Soils and Foundations 57 (2017) 384–396
(Shen et al., 2008; Wang et al., 2013). Regarding the composition of the injected grout, a recent study (Modoni
et al., 2016) has shown that denser and less viscous grouts
allow columns with larger dimensions to be reached. In
practice, most of the operational parameters for jet grouting are assigned based on previous experiences with experimentally verified field trials for their effectiveness (Flora
et al., 2013; Shen et al., 2013). Nonetheless, more reliable
estimations of the shear stress (pumping pressure), the
shear rate (pumping rate) and the grout viscosity at the
design stage of jet grouting columns are of utmost importance. This is due to the rheology of these grout variables
that significantly interacts with other variables, such as
the rate of penetration of the fluid jet in the soil, the rotation speed, the duration of jetting action and the withdrawal rate for the final desired quality (i.e., the
hardened state of the grout).
The rheology of grout (i.e., cement-based mixtures) can
be represented by the flow behavior of the shear stress versus the shear rate. Depending upon the mixture proportions and the considered range of shear rates, the flow
behavior due to the cement-based grout for jet grouting
mostly results in the nonlinear responses of the pseudoplastic (shear thinning) or dilatant (shear thickening). While
the pseudoplastic response exhibits viscosity (apparent viscosity) that decreases with the increasing shear rate, the
dilatant response exhibits viscosity that increases with the
increasing shear rate (Roussel et al., 2010; Kazemian
et al., 2012; Güllü, 2015, 2016) (Fig. 2). While the pseudoplastic response could provide some interesting effects for
fresh grout, it has been reported (Ma et al., 2016) that
the dilatant response is strongly undesired for grout mixtures in the process of mixing or pumping. The dilatant
response may even lead to the damaging of the grouting
equipment, even though it is hard to avoid for grout. It
is important to note that the grouting process during the
production, mixing, transportation and pumping could
result in changes in the shear rate that causes an obvious
change in the rheological behavior. Thus, the grouting
pressure, the flow rate, the viscosity and the time become
the main focus in the design of grouting. To ensure an adequate flow of the grout for jet grouting, it is essential to
assure good fresh grout properties from the viewpoint of
rheology (Yahia, 2011; Ma et al., 2016). It should be noted
that the pumping pressure due to the grout behavior during
pumping will depend on the pumping rate and the mixture
proportion of the binder composition (Roussel et al.,
2010). The fundamental parameter, known as the viscosity
due to the rheological behavior of grout, depends not only
on the shear rate applied to the mixture, but also on the
duration under which the grout mixture has been subjected
to shearing during pumping. The yield stress (i.e., shear
stress at a zero shear rate) is also of importance such that
elastic deformation occurs when shear stress is applied that
is lower than the yield value. A continuous flow is obtained
when the shear stress exceeds the yield stress or the internal
network force resists structural breakage (Bras et al., 2013).
Fig. 2. Typical nonlinear rheological behaviors of cement-based grout for
jet grouting (modified from Kazemian et al., 2012).
In other words, the yield stress of the grout mixture during
grouting should be overcome to initiate the flow from rest.
The grout flow stops during casting below the yield stress
(Roussel et al., 2010). All these concerns can clearly be
overcome by referring to the impact of the rheological
behavior of the grout that needs to be investigated for
obtaining reliable prediction methods. The rheological
behavior of grout is closely associated with its fresh properties that should be understood and controlled well in
order for the correct pumping and flowing of the grout
inside the ground soil to be injected for improvement.
The rheological behavior of grout mixtures (Fig. 2)
could be described by rheological models (Bingham, modified Bingham, Casson, De Kee, Herschel-Bulkley, and
Robertson-Stiff, etc.) that offer mathematical equations
for the shear stress versus the shear rate, reported in many
past studies (Yahia and Khayat, 2001, 2003; Nehdi and
Rahman, 2004; Banfill, 2006; Kazemian et al., 2012;
Güllü, 2016). It has been observed that the mathematical
equations for the rheological models are mostly based on
a derivation using the curve fitting method that gives the
empirical relationships for the shear stress versus the shear
rate curves. It was proposed in the previous study (Güllü,
2016) that while the Casson model is unfavorable for the
case of jet grouting, the Bingham, modified Bingham,
Herschel-Bulkley, De Kee and Robertson-Stiff models
could be acceptable through the ranking from low to high
H. Güllü / Soils and Foundations 57 (2017) 384–396
levels, respectively. It can be said that the time-dependent
behavior of the rheological models limitedly allows for
the fitting of the shear stress, the shear rate and the viscosity data to their empirical equations, since none of them is
free from statistical errors (Nehdi and Rahman, 2004).
Thus, as well as the need to choose an appropriate model,
the rheology of the mathematically derived model deserves
to be investigated by more attempts that depend upon on
the power for precise predictions with the fewest errors.
If relationships could be established on the basis of more
reliable methods alternatively, the rheological behavior of
grout mixtures mostly involved with the interactions of
the shear stress, the shear rate and the viscosity could be
understood well in practice for jet grouting applications.
Through the development of soft computing techniques
in recent decades (Tinoco et al., 2014; Ochmański et al.,
2015), a new prediction approach to artificial intelligence,
called gene expression programming (GEP), has been proposed for function finding (i.e., mathematical equations)
for more precise estimations of desired models, compared
to the conventional curve-fitting methods. GEP is as an
extended algorithm of the biological evolutionary-based-c
omputational technique that was first proposed by
Ferreira (2001). As for a comparison with previous
genetic-based-methods (i.e., genetic algorithm (Goldberg,
1989) and genetic programming (Koza, 1992)), it has been
reported (Ferreira, 2001; Baykasoglu et al., 2008; Güllü,
2012) that the GEP technique offers superior algorithms
for solving the complex relationships between model
parameters. Its algorithms have the ability to produce relationships between the data of input variables (i.e., independent variables) and the corresponding output variables
(i.e., dependent variables) resulting in the derivation of
mathematical formulations through an efficient evolutionary process in a wide range of flexible operations applicable
to experimental data. This facility of flexible operations
provides the derivation of formulations that considerably
reduce the errors between predicted and measured outputs.
Moreover, this GEP facility has been found to be relatively
beneficial particularly for the most complex behaviors
(such as the rheological behavior of grout addressed in this
study) between input and output parameters.
Using the GEP for the field of civil engineering has been
found successful for solving several issues and for the
derivation of predictive models for a wide range of applications (Baykasoglu et al., 2008; Cevik and Sonebi, 2008;
Sonebi and Cevik, 2009; Saridemir, 2010; Alkroosh and
Nikraz, 2011; Güllü, 2012). However, as attempts to use
GEP for the prediction of the rheological behavior of grout
mixtures for jet grouting are insufficient, they still need to
be extensively studied. More importantly, according to
the author’s knowledge of surveying and predictions of
rheological behavior for jet grouting purposes via the
GEP method, cement-based-grout mixtures that specifically include waste material (i.e., bottom ash in this study)
have not been researched up to now. Bottom ash (an industrial waste material or byproduct) is a pozzolanic material
387
that could be useful for improving the flow properties of
grout mixtures (Güllü, 2015), most likely due to the interparticle repulsive forces developed through pozzolanic
reactions from the viewpoint of physicochemical effects
(Roussel et al., 2010; Yahia, 2011). The reuse of bottom
ash in grout mixtures as a recyclable material would bring
about economical and environmental benefits.
Consequently, an attempt has been made in this paper
to model the flow phenomena due to the rheology of grout
mixtures with bottom ash via the GEP approach for jet
grouting columns. Considering the complexity of the flow
characteristics, the prediction has been restricted to
approximations of the shear stress (i.e., pumping pressure)
versus the shear rate (i.e., pumping velocity) and the viscosity (apparent viscosity) versus the shear rate.
2. GEP methodology
The GEP algorithm simply presented in Fig. 3 has been
employed in this study for the derivation of the mathematical formulations due to the generation of models through
the evolutionary process. In this process, the GEP modeling starts with the random generation of chromosomes of
the initial population (see Ferreira (2001) for algorithm
details). The GEP methodology is based on the evolution
of computer programs (chromosomes or individuals) that
are encoded linearly in the chromosomes of a fixed length.
Fig. 3. Flow chart of GEP algorithm used for this study (modified from
Ferreira (2001)).
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H. Güllü / Soils and Foundations 57 (2017) 384–396
Expression tree (ETs) (Fig. 4), which are the main power of
GEP for the formula derivation, have been used to represent the chromosomes of different sizes and shapes. During
the expressions of the GEP models, the gene (one-ormultiple) encoded in a smaller sub-program has been constructed by the chromosomes. Linking functions are used
to connect multiple genes. The computations of the GEP
algorithm (Fig. 3) for the model generations and the function finding use biologically evolutionary operators, which
include mutation, inversion, transposition and recombination (crossover) operators (Ferreira, 2001; Baykasoglu
et al., 2008; Alkroosh and Nikraz, 2011).
The mathematical derivations of the models, by means
of the GEP algorithm (Fig. 3), are obtained through a procedure that generally includes the following main components: (i) the terminal set (i.e., the model variables, such
as a, b, c and d, and the constants, such as 1, 2, 3 and 4),
(ii) the function set (i.e., the arithmetical and mathematical
operators used in the model, such as +, , *, /, Sqrt, Exp,
Ln, Sin, Cos, etc., or Boolean functions, such as AND,
OR, IF, etc.), (iii) the fitness function (i.e., the function
used for the GEP modeling to provide an optimal solution
for the expression of the formulation (i.e., the derivation of
the mathematical equation) within an accepted error or
correlation coefficient), (iv) the stop condition (i.e., a stopping criterion met for the developmental process and
repeated due to the individuals of the new generation based
on an error tolerance on the fitness or a predefined number
of generations) (Ferreira, 2001; Saridemir, 2010).
The fitness function of the GEP algorithm (Fig. 3) is
mathematically expressed by the error Eq. (1), principally
the absolute error (Eq. (1a)) or the relative error (Eq.
(1b)), as follows (Ferreira, 2001):
Fitnessi ¼
Ct
X
ðM jC ði;jÞ T ðjÞ jÞ
j¼1
ð1aÞ
Ct X
C ði;jÞ T ðjÞ
M 100
Fitnessi ¼
T
ðjÞ
j¼1
ð1bÞ
where ‘‘M” is the range of selection, ‘‘C(i, j)” is the value
returned by the individual chromosome ‘‘i” for fitness case
‘‘j”, ‘‘Ct” is the total number of fitness cases and ‘‘Tj” is the
target value for fitness case ‘‘j”. It is noted that the GEP
system in this form of fitness function is able to find the
optimal solution for itself. The GEP running for the model
generations could be stopped when the fitness values vary
within the tolerable limits required for the model
derivation.
Through the fitness evaluations Eq. (1) of the GEP algorithm (Fig. 3), the three statistical measures given by Eq. 2
were employed for a performance assessment of the generated GEP models in this study, namely, the mean absolute
error (MAE), the root-mean-squared error (RMSE) and
the correlation coefficient (R), as follows:
MAE ¼
N
1X
jX m X p j
N i¼1
PN
RMSE ¼
R¼
i¼1 ðX m X p Þ
N
ð2aÞ
2
!1=2
PN
2
N
X
ðX m X p Þ
2
ðX m Þ i¼1
PN
2
i¼1
i¼1 ðX m Þ
ð2bÞ
!0:5
ð2cÞ
where N is the number of samples, and Xm and Xp are the
measured and predicted output values, respectively. The
aim is to produce GEP models that are capable of fewer
errors with a higher correlation using the performance
measures.
For the derivation of GEP-based empirical models of
the rheological behavior (i.e., Fig. 2), by means of the grout
mixture for jet grouting in this study, a free evaluation of
the GEP software, called GeneXproTools (www.gepsoft.com) and developed by Ferreira (2001), has been run
for the employed GEP algorithm (Fig. 3). This tool has
been employed successfully in the past works (Alkroosh
and Nikraz, 2011; Güllü, 2012) for engineering problems.
3. Data used and development of GEP model
Fig. 4. Typical example of expression tree with one gene.
The data (i.e., the shear stress versus the shear rate due
to the cement-based grout mixture with bottom ash additions) used for the GEP modeling in this study was
obtained from the experimental study conducted in the previous work (Güllü, 2015). The viscosity used for the modeling in this study is the apparent viscosity (i.e., the ratio
between instantaneous shear stress and shear rate) that
was calculated from the data. Readers interested in a
detailed description of the experimental study are asked
to refer to the corresponding work. In summary, the experimental study consists of conducting rheometer (or viscometer) tests for obtaining the shear stress-shear rate
data due to the cement-based grout mixtures with added
H. Güllü / Soils and Foundations 57 (2017) 384–396
bottom ash for jet grouting purposes. The grout mixtures
include the binders of cement (PC)+bottom ash (BA),
where the bottom ash additions are at the stabilizer proportions of 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%,
90% and 100%, by dry weight of the binder, employing
the water/binder ratio of 1/1. The experimental apparatus
of the rheometer used for the testing is a rotational rheometer with a smooth-walled concentric cylinder (Brookfield
DV-II + Pro). The shear stresses are measured at the shear
rates of 0.17, 0.34, 0.85, 1.70, 3.40, 6.8, 17 and 34 s1. The
principal of the operation by the DV-II + Pro type
rheometer is to drive a spindle (immersed in the test fluid)
through a calibrated spring. The spring deflection, measured with a rotary transducer, is used to measure the viscous drag of the fluid against the spindle. The measurement
range of the rheometer is determined by the rotational
speed, the size and the shape of the spindle, the container
and the calibrated spring. The data used for the GEP modeling in this study have been illustrated in Fig. 5. Table 1
summarizes the variables included in the GEP models,
the number of samples and the range of variables.
As for the development of the GEP models, their input
and output variables for the derivation of the mathematical
formulas due the rheological behavior have been presented
in Table 2. The GEP models are produced in terms of function formulations that include the terminal set (i.e., variables) given by Eq. 3, as follows:
s ¼ f ð_c; BAÞ
ð3aÞ
s ¼ f ð_c; g; BAÞ
ð3bÞ
g ¼ f ð_c; BAÞ
ð3cÞ
g ¼ f ðs; c_ ; BAÞ
ð3dÞ
In order for the data division to generate the GEP models in this study, the data are randomly divided into two
subsets (i) a training set for model calibration and (ii) a
testing test for model generalization or verification, following the recommendations in the previous studies
(Baykasoglu et al., 2008; Alkroosh and Nikraz, 2011;
Güllü, 2012). As a result, 56 data samples (71%) of the
available 79 data samples are used for the training set,
389
Table 1
Data used in the study: the variables, the number of samples and the
range.
Variables
Number of samples
Range
Shear stress (s), Pa
Viscosity (g), Pa s
Shear rate (_c), 1/s
Bottom Ash (BA) addition, %
79
79
79
79
0.09–21.4
0.03–13.5
0.17–34
0–100
s = shear stress (Pa), g = viscosity (Pa s), c_ = shear rate (1/s), BA = Bottom Ash (%).
Table 2
Inputs and outputs of the GEP models.
Model name
Model input
Model output
s
s
g
g
c_ ,
c_ ,
c_ ,
s,
s
s
g
g
BA
g, BA
BA
c_ Z, BA
and 23 data samples (29%) are used for the testing set.
Here, it should be noted that the GEP models are mostly
able to predict within the ranges of data used, since the
GEP performs best in interpolation rather than extrapolation, like all empirical models.
For building the formulations, the settings (i.e., the fitness function, the number of chromosomes, the head size,
the linking functions, the GEP operators, the function set
and the number of generations) used for the GEP models
are presented in Table 3. As shown in this table, the fitness
function of the error type (MAE) is used for the fitness of
the models through the performance measures (Eq. 2)
given earlier. The sizes of the general GEP settings (i.e.,
the number of chromosomes, the head size, the number
of genes and the linking functions of the genes) were fixed
after many trials to obtain high fitness. The settings of the
biologically evolutionary GEP operators (i.e., mutation,
inversion, transposition and recombination) for the model
generations were selected from the values suggested in past
studies (Ferreira, 2001; Baykasoglu et al., 2008; Güllü,
2012). The function set includes some arithmetical and
Fig. 5. Data used for the GEP modeling in the study. BA: Bottom Ash.
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H. Güllü / Soils and Foundations 57 (2017) 384–396
0
Table 3
Parameter settings for the GEP models.
B
s ¼ f ð_c; g; BAÞ ¼ @
Parameter
Setting
Fitness function error type
Number of chromosomes
Head size
Number of genes
Linking function
Mutation rate
Inversion rate
IS transposition rate
RIS transposition rate
One-point recombination rate
Two-point recombination rate
Gene recombination rate
Gene transposition rate
Function set
MAE
30
6 and 7
2 and 3
Addition, Multiplication
0.044
0.1
0.1
0.1
0.3
0.3
0.1
0.1
+, , *, /, Pow10, Sqrt, Exp,
Ln, x2, x3, x4, 3Rt, 4Rt
6177, 3882, 10628, 2943
Number of generations
mathematical operators, such as ‘‘+, , *, /, power
(Pow10), square root (Sqrt), exponential (Exp), natural
logarithm (Ln), x2 (x2), x3 (x3), x4 (x4), x5 and cube root
(3Rt) and quartic root (4Rt)”. The number of model generations falls in the range of 2943–10,628. Usually, several
runs (or many trials) are required for best fitness. The formulations due to the GEP modeling that propose the best
responses in the performances of MAE, RMSE and R are
presented and discussed next.
4. Results and discussions
In this study, the GEP approach was employed to derive
the mathematical formulas due to the GEP modeling to
predict the flow behavior (rheological behavior) of the
grout mixture with bottom ash for jet grouting. The
obtained models that result in the best performances in
MAE, RMSE and R are first illustrated by the expression
trees of the GEP approach, given in Fig. 6. Then, from
the expression trees of GEP (Fig. 6), the rheological formulas are derived for discussion. From the ETs of the GEP
models (Fig. 6), it is seen that two genes (Fig. 6a and c)
and three genes (Fig. 6b and d) were used for the derivation. The genes were linked by the linking functions of
‘‘multiplication” (Fig. 6a–c) or ‘‘addition” (Fig. 6d), mentioned in Table 3.
The derived GEP formulations from the expression trees
(Fig. 6), in accordance with the terminal set (Eq. 3) with (i)
s dependent upon c_ and BA (Eq. (3a) and Fig. 6a), (ii) s
dependent upon c_ , g and BA (Eq. (3b) and Fig. 6b), (iii)
g dependent upon c_ and BA (Eq. (3c) and Fig. 6c) and
(iv) g dependent upon s, c_ and BA (Eq. (3d) and
Fig. 6d), are given through Eq. 4, as follows:
s ¼ f ð_c;BAÞ ¼ ð6:945099ð_c0:5 BAÞ
0:67
10:333
Þ þ ðBA2 þ 10ð4:923218BAÞ Þ
ð4aÞ
c_
9:998017
c_
8:051544
C
0:5 A
2 0:333
ðBA3 Þ ð9:324859 þ ðg þ ðln gÞ Þ
Þ
3:585449
g ¼ f ð_c; BAÞ ¼ ð2BA4 Þ 0:25
10lnðð0:036þ_cÞ Þ
ðs2 Þ
s
g ¼ f ðs; c_ ; BAÞ ¼ ð105:185699ðe sþBAÞ Þ þ
c_
þ ð105:185699ðlnðs
2 Þþ5:185699þBAÞ
Þ
ð4bÞ
ð4cÞ
ð4dÞ
Predictions using the GEP formulas (Eq. 4) are compared with the measured experimental data by the graphical representation of the perfect fit (i.e., y = x) in the
scattering plot, for the results of the testing phases of the
GEP models (Fig. 7). It is seen from the scattering of data
in Fig. 7 that the predictions are relatively precise in view of
their deviations. As shown in Fig. 7, despite the highly nonlinear responses (i.e., shear stress and viscosity) due to the
rheological behavior of grout mixtures, the GEP approach
employed in this study is clearly able to derive formulations
for s and g that appear to have good prediction potential
with the measured data and with high accuracy.
Performances (MAE, RMSE and R) of the derived formulations using the GEP models (Eq. 4 and Fig. 6) from
the results of the training and testing phases are presented
in Table 4 and compared to the performances from the
conventional prediction method of nonlinear regression.
For the regression analysis, the SPSS statistical analysis
software program (Ver.15.0, 2006) was run in this study.
It can be noted that the nonlinear regression has the ability
to produce nonlinear models with arbitrary relationships
between the dependent and the independent parameters
using the iterative estimation algorithms, in comparison
with the linear models estimated by the ordinary linear
regression (Walpole et al., 2007). Thus, within the conventional regressions of curve-fitting methods, a comparison
with the nonlinear regression is considered plausible specifically for the rheological behavior of jet grout mixtures that
highly represent nonlinear behavior. The model performances (Table 4) due to the GEP and the regression methods could be evaluated using a previous guide (Smith,
1986), where it is suggested that the correlation (R) between
the predicted and the measured values: (i) become weak if
jRj < 0.2, (ii) exist (likely to be moderate) if 0.2 < jRj < 0.8
and (iii) become strong if jRj 0.8. Since a verification of
the training performances is conducted during the testing
phase, the testing performances (i.e., testing MAE, RMSE
and R) have been taken into consideration for the predictive ability of the GEP models. It is shown in Table 4 that
the performances of the GEP models are obtained in a
more superior way than those of the regression. It can be
said that the formulations from the GEP models become
more satisfactory for all responses (s and g) resulting in
an acceptable degree of accuracy in errors (MAE and
H. Güllü / Soils and Foundations 57 (2017) 384–396
391
Fig. 6. Expression trees for the formulas: (a) d0 = c_ , d1 = BA, c0 = 6.945099 (Gene 1), c0 = 3.923218 (Gene 2): (Eq. (3a)) (b) d0 = c_ , d1 = g, d2 = BA,
c0 = 9.998017 (Gene 1), c1 = 8.051544 (Gene 1), c0 = 9.324859 (Gene 3): (Eq. (3b)); (c) d0 = c_ , d1 = BA, c1 = 0.00177 (Gene 1), c0 = 3.585449
(Gene 2), c1 = -3.327789 (Gene 2): (Eq. (3c)) (d) d0 = s, d1 = c_ , d2 = BA, c1 = 5.185699 (Gene 1), c1 = -5.185699 (Gene 3): (Eq. (3d)).
RMSE) and relatively strong correlations (R 0.96). As
for the regression, while it produces a moderate level of
correlations for g (R = 0.65 and R = 0.68), the performances for s are obtained in the strong level (R = 0.81
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H. Güllü / Soils and Foundations 57 (2017) 384–396
Fig. 7. Comparison of the predictions due to the GEP formulas with the measured data.
Table 4
Performances of GEP models compared to regression.
Formula or model
GEP
Regression
Train
s-Eq. (4a)-Fig. 6a
s-Eq. (4b)-Fig. 6b
g-Eq. (4c)-Fig. 6c
g-Eq. (4d)-Fig. 6d
Test
MAE
RMSE
R
MAE
RMSE
R
MAE
RMSE
R
0.642
0.687
0.567
0.0002
0.854
0.939
0.319
0.0002
0.98
0.98
0.98
0.99
0.763
0.766
0.489
0.0001
1
1.047
0.843
0.0002
0.97
0.96
0.96
0.99
2.233
2.201
1.411
1.414
2.783
2.686
2.001
1.934
0.81
0.83
0.65
0.68
and R = 0.83), but still less than GEP. However, it is obvious that the accuracy of the performances in the errors
(MAE and RMSE) due to the regression could be considered far from the adequate for the predictions of s and g
in both, despite the existence of correlations. As a consequence of the performance results (Table 4), it is found that
the performances are less improved by the regression
method than by the GEP. Thus, it is concluded that in predicting the rheological behavior of grout mixtures, the use
of the GEP approach is thought to be more favorable than
the regression method.
The GEP technique can be applied by comparing it to
some common conventional rheological models particularly for the GEP formulation of s versus c_ (Eq. (4a))
regarding the inclusion rates. The conventional models
(Table 5) that are found more favorable for a description
of the nonlinear behavior of grout for jet grouting than
others (i.e., Casson, Bingham, modified Bingham and
Herschel-Bulkley) in the previous study (Güllü, 2016) have
been used for the comparison. The applicability of GEP
was primarily tested for Eq. (4a), because the conventional
rheological models in current practice are mostly modeled
in the functional form s versus c_ , as presented in Table 5.
Readers are recommended to check elsewhere (Yahia and
Khayat, 2001, 2003) for more information on rheological
models (Table 5 and the others), as these details are out
of the scope of the present work. Comparisons are shown
in Fig. 8 in the s versus c_ plots. It is seen in Fig. 8 that
the GEP formulation is relatively consistent with the conventional rheological models for the usual representation
of the shear stress versus shear rate curve due to the pseudoplastic (shear-thinning) response (see Fig. 2a). It generally seems to have a good modeling potential for all
dosage rates (except for native cement) due to the high level
of correlations (R 0.96). However, the GEP formulation
appears to favorably follow well the measured data with
mostly high dosage rates (i.e., >40%BA) compared to the
conventional models (R 0.89). Thus, it can be said that
the prediction trend of the GEP is better with increased
BA proportions. This finding for GEP modeling could be
H. Güllü / Soils and Foundations 57 (2017) 384–396
Table 5
Some conventional rheological models employed for comparison (Yahia
and Khayat, 2001, 2003; Güllü, 2016).
Model name
Mathematical formulation
De Kee (DK)
Robertson-Stiff (RS)
1
s ¼ s0 þ l_c ea_
c
n
s ¼ Að_c þ BÞ
s: shear stress (Pa), c_ : shear rate (s1), s0: yield stress (Pa), l: viscosity
(plastic viscosity) (Pa s), a: time-dependent parameter, A and B: adjustable
parameters, n: flow behavior index or rate index.
useful for understanding the nonlinearity of rheology
specifically due to the high BA rates for jet grouting. Here,
it should be emphasized that for the native cement only
393
(i.e., 0%BA), the GEP modeling was not able to fit the prediction of s, since in the GEP formulation (Eq. (4a)) a zero
inclusion rate of BA unfortunately causes zero shear stress.
This issue most likely needs to be fixed by using a large
dataset that includes a sufficient number of samples of
native cement (i.e., 0% rate of stabilizer) for the model calibration during the training phase and the model generalization during the testing phase. However, this is a
separate investigation for future study. As a result of the
comparisons (Fig. 8), it can be concluded that the GEP
technique used in this study is potentially considered a
good candidate for modeling the rheological curves (shear
stress-shear rate) due to the grout with bottom ash for jet
grouting.
Fig. 8. Comparison of GEP model (Eq. (4a)) with the conventional rheological models (DK = De Kee = ; RS = Robertson-Stiff).
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H. Güllü / Soils and Foundations 57 (2017) 384–396
The GEP technique has also been performed through
comparisons using the GEP formulation of g versus c_
(Eq. (4c)) particularly for high inclusion rates (Fig. 9). It
is observed from the comparisons (Fig. 9) that the GEP
formulation (Eq. (4c)) becomes relatively satisfactory for
the usual description of the viscosity versus shear rate curve
due to the pseudoplastic behavior (see Fig. 2a). This GEP
formulation also follows the measured data and conventional rheological models well resulting in a fitting trend
with strong correlations (R 0.93). Thus, it can be concluded (Fig. 9) that the GEP technique can also be a good
candidate for offering viscosity versus shear rate predictions. Overall, from the successful comparisons
(Figs. 8 and 9) using the GEP formulations (Eqs. (4a)
and (4c)), it can be said that the GEP technique could be
beneficial for predicting rheology due to the grout with bottom ash as an alternative to the conventional rheological
models.
Based on the effort given to the ability of the GEP technique presented in this paper, it is understood that the GEP
modelings (Fig. 6) are able to derive the mathematical formulas (Eq. 4) for the rheological behavior. They are not
only capable of producing the mathematical formulas
(Eq. 4) during the training stage, but they can also general-
ize the formulas during the testing stage for the potential
use in practice through a verification of their precision
(Fig. 7 and Table 4). Compared to the nonlinear regressions, the GEP formulations are found to achieve better
predictions in strong correlations and fewer errors resulting
in high accuracy (Table 4). For their applicability in practice, as compared to the measured data (s, g) and the conventional rheological models (Table 5), it is shown that the
GEP modeling could be assessed as a powerful tool for
describing the rheological behavior (i.e., shear stress versus
shear rate and viscosity versus shear rate) due to the grout
with bottom ash in good quality predictions (Figs. 8 and 9).
Hence, all the findings obtained in this study are relatively
promising for the application of the GEP technique for
prediction of the flow behavior or the rheological behavior
of grout with bottom ash for jet grouting, as an alternative
to curve-fitting methods (the nonlinear regression or conventional rheological models). Even though the mathematical functions evolved from the GEP technique are
complex, the successful results offer significant advantages
over the conventional solutions.
Consequently, the derived GEP formulas (Eq. 4) could
be proposed to estimate the pumping pressure (shear stress
s) and the viscosity (g) of grout with bottom ash under an
Fig. 9. Comparison of GEP model due to the GEP formulation of g versus c_ (Eq. (4c)) with the conventional rheological models.
H. Güllü / Soils and Foundations 57 (2017) 384–396
applied pumping rate (shear rate c_ ) for jet grouting columns, at least to assist with the conventional rheological
models resulting in even more satisfactory predictions.
Moreover, the GEP formulations could present some contributions for querying the interactions between the pumping pressure and the pumping rate of grout. However, it
should be emphasized that the proposed GEP formulations
are more able to predict within the range of data used in
this study. Thus, supplying more data that covers new
ranges in future experimental works will extend the current
limitation of the proposed GEP models. The attempt to use
GEP to predict the rheological behavior of grout, specifically including bottom ash, is newly proposed in this study.
Hence, the findings obtained due to the GEP could be better offered for a preliminary design of jet grouting in practice. As a final remark, the benefits of including GEP
predictions in engineering judgments should not be underestimated for final decisions made during the design stage.
5. Conclusions
For the prediction of rheological behavior (i.e., the shear
stress versus the shear rate and the viscosity versus the
shear rate), using grout with bottom ash for jet grouting
has been investigated and the ability of a new prediction
technique called GEP has been presented in this research
as an alternative method. Based on the findings obtained
from the GEP modeling in the study, the following conclusive remarks can be drawn for the prediction of the rheological behavior of grout with bottom ash for jet grouting:
(1) The rheological formulations (Eq. 4) due to the GEP
models (Fig. 6) are relatively able to produce estimations with good precision (Fig. 7).
(2) Compared to the nonlinear regression (R 0.65), the
GEP obtains better predictions with fewer errors and
strong correlations (R 0.96) for accurate
predictions.
(3) The rheological formulas due the GEP (Eqs. (4a) and
(4c)) are found consistent with the conventional rheological models (De Kee and Robertson-Stiff) for a
successful description of the pseudoplastic behavior
(i.e., the shear stress-shear rate and the viscosity versus shear rate) of grout with bottom ash (Figs. 8 and
9). The estimations due to the GEP formulations
(Eqs. (4a) and (4c)) generally follow the measured
data well. However, they are obtained better specifically at high BA proportions.
(4) The GEP technique is relatively promising for predictions of the rheological behavior of grout with bottom ash as an alternative to the conventional
rheological models. Thus, the derived GEP formulas
could be beneficial for adjusting the pumping pressure, the viscosity and the pumping rate of grout mixtures with bottom ash for jet grouting columns, at
least to assist the conventional solutions.
395
Acknowledgements
The author would like to express his gratitude to the
anonymous reviewers for their valuable comments and suggestions on how to improve the quality of this article during the revision of the manuscript.
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