Article 3

Construction and Building Materials 189 (2018) 816–824
Contents lists available at ScienceDirect
Construction and Building Materials
journal homepage: www.elsevier.com/locate/conbuildmat
Numerical modeling for crack self-healing concrete by microbial calcium
carbonate
Hassan Amer Algaifi a,⇑, Suhaimi Abu Bakar a, Abdul Rahman Mohd. Sam b, Ahmad Razin Zainal Abidin a,
Shafinaz Shahir c, Wahid Ali Hamood AL-Towayti c
a
Department of Structure and Materials, School of Civil Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, Johor, Malaysia
UTM Construction Research Centre, Institute for Smart Infrastructure and Innovative Construction, School of Civil Engineering, Faculty of Engineering, Universiti Teknologi
Malaysia, Johor, Malaysia
c
Department of Biosciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, Malaysia
b
h i g h l i g h t s
The developed model is able to predict the bioconcrete crack-healing relatively well.
A crack width of 0.4 mm was healed at 70 days compared to 60 days in the model.
With the increasing of urea hydrolysis, more calcium carbonate could be formed.
The hydrolysis of urea induces the diffusive transport mechanism to the boundary.
a r t i c l e
i n f o
Article history:
Received 3 March 2018
Received in revised form 30 August 2018
Accepted 31 August 2018
Available online 18 September 2018
Keywords:
Crack-healing concrete
Crack-healing modeling
Bacteria-based healing
a b s t r a c t
The inevitable existence of microcracks in concrete matrix can create interconnected flow paths due to
external load, which will then provide easy access to harmful substances, and thus yielding to corrosion
of reinforcement. Consequently, this affects the durability of the structure. Recent researches are devoted
in crack self-healing concrete, which mimics the natural remarkable biological system of wounds healing.
Despite that, the issue revolving around the efficiency of crack self-healing technique remains important.
Microbial calcium carbonate offers an attractive biotechnique to fill pores volume as well as both micro
and macrocracks in the affected cementitious material, resulting in barriers to inhibit water or aggressive
chemical flow. However, results of this approach have only been demonstrated at laboratory scale and
theoretical information is still limited. The present study describes a theoretical model to simulate the
kinetics of calcite precipitation induced in response to the hydrolysis of urea in concrete crack. In addition, a second-order partial differential equation in time and space to model the healing process, rationally based on physic-bio-chemical issues, was developed. Both finite element and finite difference were
implemented to solve this equation. SEM images were conducted to verify the predicted crack-healing
results through artificial cracked mortar specimens incorporating indigenous Lysinibacillus sphaericus.
As such, it could be concluded that a prediction of the healing process of the affected cementitious materials can be provided via the developed model.
Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction
Inevitable microcracks remain to be a challenge to civil engineers as they are considered as a threat to the durability of structures. Such microcracks, porosity and interconnectivity of pores
volume create an easy pathway for harmful substances to enter
and cause reinforcement corrosion [1–6]. However, concrete is
⇑ Corresponding author.
E-mail address: enghas78@gmail.com (H.A. Algaifi).
https://doi.org/10.1016/j.conbuildmat.2018.08.218
0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
capable of plugging these microcracks themselves, which is well
known as autogenous healing. Nonetheless, the ability is still limited to crack width that is less than 0.06 mm [7]. Various manual
cracks repairing techniques are available to extend the life of structures. However, several drawbacks have been detected such as
short period of time (10–15 years), high cost, difficult-to-access
locations and the fact that most traditional repair techniques are
polymer based that lead to hazards associated with the environment and health [8].
H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
Therefore, researchers have devoted considerable efforts to
mimic natural biohealing by incorporating bacteria in cementitious material in recent years. The direct use of bacteria with their
nutrients in fresh concrete mix without human intervention was
first proposed by Jonkers and colleagues [9–12]. The potential ability of bacteria to seal cracks through the formation of calcium carbonate was investigated through different mechanisms such as
sulfate reduction bacteria [13,14], oxidation of organic acids [15–
17], nitrate reduction bacteria [18,19] and ureolytic bacteria
[20,21]. 0.46 mm of concrete crack-width was completely healed
after 100 days via Bacillus alkalinitrilicus, while ureolytic bacterial
has proven its ability to heal crack widths of up to 0.97 mm in
8 weeks of water submission [22,23]. In the same context, nitrate
reducing bacteria also showed its capability to heal crack widths
of 0.46 mm in 56 days [18]. However, most of these studies have
only focused primarily on both laboratory and experimental work
and they are still suffering from the lack of numerical simulation to
accurately predict experimental behaviour, which can result in the
decrease of cost. Examples of mathematics researches of polymer
self-healing are available in the previous studies [24–30].
On the other hand, computational research into self-healing
concrete is still in its infancy stage and there are only a few numerical modelling involving the healing process of affected cementitious material. Autogenous crack-healing in cementitious
material through further hydration was mathematically simulated
using water transport theory, ion diffusion model and thermodynamics model [31]. The results showed that the rate of healing processing speed increased according to the amount of water available
that was assumed to be in a capsule. Further modelling study was
focused on the interaction between the crack and embedded
micro-capsule in cementitious material [32]. In addition, autogenous self-healing concrete by calcium carbonate due to the carbonation of dissolved calcium hydroxide was also developed byAlikoBenítez, Doblaré [33]. Moving from Autogenous self-healing model
to bacteria-based self-healing, a numerical model was developed
to describe the healing process of cracks in concrete using bacteria,
which relies on the oxidation of organic acids [34]. The diffusion of
the healing agent over the crack is governed by diffusion equation
which is solved using Galerkin finite element, while the evolution
of moving boundary due to calcite precipitation is solved using
level set method.
In this study, indigenous ureolytic bacteria was utilised to
induce microbial calcium carbonate by releasing urease enzyme,
which in turn stimulated the urea degradation to carbonate and
ammonium under appropriate condition as expressed in Eq. (1)
[35]. At the same time, the formation of calcite would develop
due to the reaction between the carbonate and calcium ions on
the cell wall of the bacteria since it is negatively charged,
which was specifically considered as bacterial aggregate as shown
in Eq. (2).
urease
817
COðNH2 Þ2 þ 2H2 O ! 2NHþ4 þ CO2
3
ð1Þ
Ca þ CO2
3 ! CaCO3
ð2Þ
The evolution of bacterial aggregate was predicted by developing a numerical model. In the said model, urea, calcium, nutrient
and bacteria were pre-mixed in the concrete matrix and distributed homogeneously. In addition, urea was assumed to be
stored in capsules, which would break if they were intersected
by a crack. On the contrary, bacteria, nutrient and calcium were
assumed to exist in the crack domain. Consequently, with water
and nutrients, the spores of the bacteria would germinate and
reproduce, and thus limestone would develop in the crack as
shown in Fig. 1. In other words, both the urea and calcium (artificial blood platelet) would be recruited to the damage area to block
the water filled crack. This mechanism was inspired by the idea of
blood clotting in skin wounds via platelet, which exists in the
blood, and ultimately, stops the bleeding. Specifically, the said process was mathematically simulated using a system of equations
including first-order ordinary differential equation and second
order partial differential equation, in which both finite difference
and finite element methods were used to solve the said form of
bio-chemical-diffusive model.
2. Mathematical development of the model
2.1. Model description
In this study, the model is schematically shown in Fig. 2. A
macro-crack with the size of 20 mm (length) 0.4 mm
(width) 20 mm (depth) was supposed to pass through a capsule.
In addition, the crack domain was also assumed to be filled with
water instantaneously. The model was developed rationally, relying on the physics, biology and chemistry of the healing process
respectively.
Firstly, urea was recruited to the damage area due to the flux
(F). In our model, flux denoted that the ion species are allowed to
diffuse as a consequence of a natural movement from a high concentration area to a low concentration area inside the cracks developed in the concrete cover. The mechanism of diffusive was
governed by Fick’s first law for ion species as shown in Eq. (3),
where c is the concentration of species in mol/m3, D is the diffusion
coefficient in unit of m2/day and flux F is in units of mol/m2 day.
F ¼ D
@c
@x
ð3Þ
Secondly, calcium ions would stick and gather on the bacteria
cells that release urease enzyme to catalyse the decomposition of
urea to carbonate ions. These bacteria cells exist in all boundaries
of the crack with different numbers since cell growth cannot repro-
Fig. 1. The evolution of a crack closing in different stages.
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H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
Fig. 2. Schematic diagram of evolving bacteria aggregate.
duce in the absence of oxygen such as in the deeper parts of the
cracks. In other words, if higher bacterial cells concentration (a)
is achieved, more urea hydrolysis can be formed, which was taken
into account in the proposed model [36]. The initial cell concentration was taken as 105 cell/cm3 at deeper part of the crack according
to Zemskov, Jonkers [34],while the bacterial cells were considered
as the optimum cell concentration 108 cell/cm3 at the crack mouth
(cracks surface). According to mass action law and stoichiometry,
urea hydrolysis can be formalised mathematically. Dynamical system was utilised to model the concentration of urea species over
time using ordinary differential equation and a first order rate
reaction was proposed as shown in Eq. (4). It should be mentioned
that the urea species COðNH2 Þ2 and calcite species ½CaCO3 (concentration is denoted by brackets) are treated as dynamic species
which consume and accumulate with time, respectively.
@ CO ðNH2 Þ2 @c
¼
¼ k1 a c
@t
@t ureolysis
ureolysis
concentration at each node and
1
day
Thirdly, the formation of calcium carbonate would start to precipitate according to Eq. (2), which states that the microbial calcium carbonate is the product of the chemical reaction between
calcium and carbonate ions. This carbonate ion is in equimolar
with urea hydrolysis according to Eq. (1). In the proposed model,
the evolution of urea hydrolysis was the main sole parameter to
affect the productivity of calcite since sufficient amount of calcium
was assumed to be available in the damaged area, similar to bacterial nutrient. Therefore, the evolution of calcite with time was
taken into account as pseudo first-order reaction and is as
expressed in Eq. (5), according to mass balance and stoichiometry.
h
i
@ ½CaCO3 @c
¼ þk2 CO2
¼
þk
2
3
@t
@t ureolysis
which k2 ¼ calcium carbonate precipitation rate
ð5Þ
M ðCaCO3 Þ:h
qCaCO3
Eq. (3) is analogous to the one-dimensional stress/strain law for
the stress analysis problem which is rx ¼ E @u
. The minus sign
@x
indicates that the species flow from regions of higher concentration to regions of lower concentration. Moreover, it states that
the flux in the x direction is proportional to the gradient of concentration in the x direction. Similarly, the concentration gradient at
x þ dx is evaluated
F xþdx ¼ D
1
day
ð6Þ
The calculations were automatically stopped if the healing ratio
was S ¼ VVh 1. As such, if S = 1, the volume of the crack could be said
@c @xxþdx
ð7Þ
In the present model, the diffusion flux and concentration gradient of species at a particular point in a crack domain varied with
time, with a net depletion of the diffusing species that can be
depicted by a control volume as shown in Fig. 3. This could be
expressed mathematically as shown in Eq. (8).
Flux in = Flux out + accumulation rate + consumption (losses by
bacteria)
F x F xþdx ¼
@ci
@ci dx þ
dx
@t
@t
depletion
ð8Þ
Eq. (8) denotes that the flux in of the species urea minus the flux
out is equal to the amount of accumulation rate into this volume
element plus the depletion of species due to the reaction. This is
discussed in detail in the following section. Using a two-term of
Taylor series to expand the flux out F xþdx , the equation could be
expressed as:
@c
@t
)
Once the calcite concentration was calculated, the volume of
calcite precipitates (healed volume) inside the crack domain is as
expressed in Eq. (6), whereV is the volume of crack, V h is the crack
healed volume, qCaCO3 ¼ 2:711 cmg 3 ; the molar mass of calcite is
g M ðCaCO3 Þ ¼ 100:0869 mole and h is the amount of calcite precipitation (mole).
V h ¼ V CaCO3 ¼
2.2. hydrolysis-diffusion equation
ð4Þ
In which a ¼ aami , am is optimum cells concentration, ai is cells
k1 ¼ ureolysis rate constant
to have been filled with calcite, which would result in maximum
healing capacity. On the contrary, the healing product has yet to
start precipitate if S = 0.
2
@ c
¼ D @x
2 @c
@t
@c
@t ureolysis
@ c
¼ D @x
2 k1 a c
2
ð9Þ
Once the boundary and initial conditions were prescribed for
the species, the model was then completely defined through one
ordinary differential Eq. (5) and a second-order partial differential
Eq. (9).
2.3. Numerical implementation
Eq. (9) represents the consumption –diffusion differential equation, which can be solved using the finite element method by
dividing the problem domain into finite length, one dimensional
element and discretising the distribution of urea concentration
within each element as shown in the following equation.
cðx; t Þ ¼¼ N1 ðxÞc1 ðtÞ þ N2 ðxÞc2 ðtÞ
ð10Þ
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H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
Fig. 3. Control volume for one dimensional diffusion with depletion.
where a two-node linear element (shape function Ni ) were used similar to the displacement function of truss equation as shown below:
3. Verification of the predicted Crack-Healing results
x
N1 ðxÞ ¼ 1 ;
L
For the purpose of verification of the predicted crack healing
results, experimental work was carried out to support the proposed model. Accordingly, indigenous Lysinibacillus sphaericus
was isolated from 10 cm of the ground surface located in Universiti
Teknologi Malaysia (1°330 52.400 N 103°390 16.300 E). It was tested for
its capability to survive in a harsh environment, such as concrete
and induce calcium carbonate, in response to hydrolysis of urea.
It demonstrated a positive result, which was consistent with previous studies[37,38]. Subsequently, the partial sequencing of the
bacterial genetic code 16S rRNA was deposited in the gene bank
database under the accession number of MG928532. In addition,
it was stored as glycerol stock at 80 °C for future use[17].
N 2 ð xÞ ¼
x
L
By applying Galerkin’s finite element method to Eq. (9), the following is obtained:
Z
L
N i ð xÞ
0
!
@c
@2c
D 2 þ k1 ac Adx ¼ 0
@t
@x
i ¼ 1; 2
ð11Þ
Subsequently, using the integration by parts to the second term
and integration to the first and third terms of Eq. (11), it becomes:
LA 2 1
6 1 2
c_ 1
c_ 2
þ
AD 1 1
L 1 1
c1
c2
þ
Aak1 L 2 1 c1
¼
6
1 2 c2
F1
F2
ð12Þ
For simplicity, Eq. (12) could be expressed as:
½mfc_ g þ ½kfcg þ kg fcg ¼ ff g
ð13Þ
Eq. (13) represents a first-order differential equations in time.
Element nodes were assigned to the global nodes and the element
matrix was added to the appropriate global matrix, and thus yielding the global equation as the following.
n o
½M C_ þ ½K fC g þ K g fC g ¼ fF g
ð14Þ
The forward finite difference method was used as a simple
approach to obtain the solution to both Eqs. (5) and (14). To apply
the concept of Euler’s method, which is known as a forward finite
difference, the time derivative approximation of the nodal concentration matrix took place as:
fC iþ1 g fC i g
C_ ffi
Dt
ð15Þ
½M fC i gg þ ½K fC g þ K g fC g ¼ fF 0 g
) fC iþ1 g ¼ fC i g þ Dt½M 1 fF 0 g ½K fC i g K g fC i g
ð16Þ
while Eq. (5) becomes
) fPiþ1 g ¼ fPi g þ Dt k2 K g fC i g
Ureolytic activity and calcium carbonate formation screening
were conducted to determine the rate of urea hydrolysis and calcium carbonate precipitation respectively. 20 ml of tap water supplemented with 5.0 mM urea and 2.5 mM calcium was inoculated
with a given bacterial cell concentration species 107 cell/ml in a
flask. The test ran for 7 days with static incubation at 30 °C and
pH 9 to simulate the real condition of concrete crack [39,40].
0.5 ml of the solution was taken from the reaction flask every
day to examine the evolution of urea and calcium carbonate concentration prior to centrifuging to remove the cells of bacteria
and any suspended precipitation. For the examination of the former, the Nessler method was utilised to measure the ammonium
concentration NH4+ in the solution via DR5000 UV-Vis Spectrophotometer at 425 nm [41]. As indicated earlier, NH4+ is produced by
1 mol of urea. Thus, the measured NH4+ could be converted to calculate the urea hydrolysis as expressed in Eq. (18).
urea decomposed ðmg=LÞ ¼
Substituting Eq. (15) into Eq. (14), the Equation becomes
1
ffC iþ1 g
Dt
3.1. Chemical analyses
ð17Þ
where P is Limestone precipitation
2.4. Procedure
1) Initialise the nodal variables with initial condition ct¼0 ¼ 0,
external flux F 0 ¼ 0 and the concentration of urea on the left
side of the crack is c = 333 mol/m3.
2) Solve system of Eqs. (16) and (17) at t = 1
3) Repeat the second step to obtain the C 2;3;4:::: and P2;3;4 for
all other time steps until crack width fully filled with Limestone at S = 1.
NH4ðmg=LÞ 60ðg=molÞ
2 18ðg=molÞ
ð18Þ
In the latter, the evolution of the microbial calcium carbonate
was linked to the amount of insoluble calcium concentration to
monitor the productivity rate. As such, the soluble calcium
strength was first measured using an inductively coupled plasma
atomic emission spectroscopy (Agilent 700 ICP-OES). Later, the
insoluble calcium was calculated by subtracting the total calcium
from the soluble calcium strength. A logistic curve fitting was used
to obtain the rate of urea hydrolysis and calcium carbonate precipitation as shown in Eq. (19) [36].
y¼
a
1 þ ekðtbÞ
ð19Þ
where a is maximum capacity of y, it is time, b is the time at maximum y variation (dy/dx) and k is the rate constant (1/d) which was
calculated from regression analysis.
In addition, an experimental test was also conducted to confirm
that the precipitation of the microbial calcium carbonate was
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H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
dependent on the amount of urea hydrolysis in the proposed
model. 50 ml of water supplemented with different urea concentration (5, 10, 15, 20, 30 g/L) was inoculated with bacteria in a flask.
Calcium concentration was kept constant at 5 g/L, while yeast
extract and peptone were added for bacterial growth. The solution
was incubated under shaking (150 rpm) at 30 °C for 7 days. Subsequently, the calcium carbonate precipitation product was filtered
through filter paper, which was then dried in the oven at 60 °C
and weighed [42]. Finally, the smart lab x rays diffractometer
(Rigoku) was used to analyse and identify the microbial product
powder since XRD and 16 s rRNA sequence are considered as fingerprint techniques to identify solid material and bacteria strain,
respectively. It was operated at 40 kV and 30 mA with Cu anode
to produce intensive x rays spectra (CuKa radiation = 1.5418 Å),
while, the diffracted patterns was collected using D/teX Ultra 250
detector over Bragg angle (2 theta3-100), 8.2551 deg/min,
0.0200 deg /step as continuous scans for 10 min.
nied by nutrient (yeast extract 0.2%) for bacterial growth [43]. In
addition, the bacterial cell concentration was kept at 107 cell/ml
of mixing water prior to mortar mixing [44]. Next, 0.4 mm standard cracks were formed in the specimens after mixing by introducing a copper plate up to 20 mm deep, which was removed
during the demolding of specimens [45]. Later, all specimens were
cured in water and examined every two weeks to monitor the healing process. It is important to note that all specimens were
assessed in triplicate.
3.2. Preparation of cracked specimens
4. Results and discussion
Mortar specimens (U30, 50 mm) were casted using cement
(OPC) Type I, tap water and river sand with 2.6 specific gravity
according to BS EN 196-1:1995. The ratio of cement to sand was
1:3 by mass, while water cement ratio was 0.6. Urea and calcium
nitrate were added into the mixing water to obtain 0.333 M urea
and 0.15 M calcium for the urease enzyme activity and its function
in bacterial aggregate formation respectively. This was accompa-
4.1. Nodal urea distribution
3.3. Vp-sem-edx
VP-SEM-EDX (JEOL JSM-IT300LV Scanning Microscope) was utilised to verify the predicted crack-healing results [46]. Specifically,
SEM was used to visualise the crack filling area every two weeks,
while EDX analysis was conducted to better identify the filling
product.
When the capsule broke, urea was released into the water
filled-crack, which was treated as big pore. The diffusion of urea
through the pore path was not affected by any tortuosity or pore
size in the proposed model since the targeted crack width was
greater than 0.08 mm [47,48]. Consequently, the diffusion coeffi-
Fig. 4. Discretised model for crack in concrete.
Fig. 5. Nodal urea concentration in the crack domain without bacteria.
H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
cient of urea was obtained from previous studies [49]. The amount
of urea released into the crack domain from the crack’s left surface
was maintained at a constant concentration and the other perimeter of the discretised model was assumed to be insulated to prevent any losses of urea outside the crack domain as shown in
Fig. 4. Regardless of the size and shape of the capsule, only the
amount of urea was taken into account in the present study’s
model.
Fig. 5 shows the concentration of urea in the crack at different
times without bacteria. When there was no bacteria inside the
crack domain, it began to increase without any hindrance until
the equilibrium state was reached. As such, it could be said that
the nodal concentration on all boundaries sought to go towards
the boundary condition at node1. This state was known as the
steady state, which was detected at t = 400 day.
Moving on, Fig. 6 illustrates the nodal value of urea concentration in the cracks at different time with bacteria. According to Eqs.
(4), and (9) the amount of urea that diffused from node 1 towards
the rest of the boundary was depleted by the bacteria. The consumption by the bacteria induced the diffusive transport mechanism to the rest of the boundary. Thus, the urea consumption
was proportional to the available concentration on the nodes. This
mechanism continued until the equilibrium was achieved. The
equilibrium state denoted that the amount of material that flows
out is equal to the amount that is consumed. Fig. 6(c) shows that
steady state conditions were attained at about t = 100 day.
4.2. Model convergence
It should be demonstrated that the present study’s finite element model predicted a linear concentration distribution within
each node as was indicated by the straight lines connecting the
nodal urea concentration values. These nodal values were
increased; that is, the number of elements was increased to ensure
the accuracy and convergence of the solution as shown in Fig. 7. It
should also be noted that the solution became smother when
increasing the number of elements and four elements were taken
into account since the difference was less than 1%.
821
Fig. 7. convergence of urea concentration using the numerical method.
4.3. Hydrolysis of urea
Fig. 8(a) describes the dependence of the amount of urea
hydrolysis on the concentration of urea, which is as expressed in
Eq. (4). It shows that the amount of urea hydrolysis was significantly higher with 666 Mole/m3 urea compared to 333 Mole/m3.
In addition, it was also observed that the amount of limestone
was dependent on the amount of urea hydrolysis as show in
Fig. 8(b). Owing to that, as urea hydrolysis increased, the amount
of calcite (limestone) also increased. This predicted hypothesis
was clearly confirmed through the authors’ experimental test,
which was also consistent with the finding of previous studies
[40]. Fig. 8(c) shows that the amount of calcite was linearly proportional to the amount of urea hydrolysis. With the increasing of urea
concentration, more calcite could be formed. However, the mount
of calcium and nutrient were kept at constant 5 g/L and 3 g/L
respectively.
Fig. 6. Nodal urea concentration with bacteria.
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H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
Fig. 8. The dependence of Limestone on urea (a) Predicted urea hydrolysis (b) Predicted Limestone (c) Experimental data of produced Limestone with different concentration
of urea (d) Identification of the product (Limestone) through XRD.
Fig. 9. Comparison between actual and predicted crack healing ratio at 42 and 60 days (a and b) Predicted crack healing (b and c) Actual crack healing (e and f) Identification
of the filling product (Limestone) using EDX.
H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
In addition, The microbial product powder was recognised and
identified as microbiological calcium carbonate precipitation by
comparing the component of targeted sample to diffraction references data through XRD analysis since all solid material have a
unique arrangement of atoms, similar to any living organism with
unique DNA sequence. At 2h = 31°, the strongest reflection was
achieved as shown in Fig. 8(d).
4.4. Calcite precipitation in the crack
The present model observed the self-healing capacity of the
artificial cracks in cementitous specimen. When the healing ratio
(S) is equal to 1, it demonstrates that the crack volume is completely sealed with calcite, and thus the calculation stopped as
shown in Equation 6. Fig. 9(a and b) illustrates the healing ratio
in different times. Specifically, the 0.4 mm crack width was completely healed at 60 days, while predicted crack healing was 58%
at time 42 days.
In the same context, the laboratory data had a relatively high
degree of similarity with the predicted results. This was obtained
by monitoring the top surface of the cracked specimens every
two weeks using VP-SEM images. It could be concluded that the
823
healing ratio increased with time and a crack width of 0.4 mm
could be completely healed after 70 days, compared to 60 days in
the model as shown in Fig. 9(c and d). The slight difference was
due to two reasons. Firstly, the decreasing of porosity and interconnectivity of pores volume in the concrete with time due to cement
hydration led to the difficulty of getting sufficient amount of oxygen, nutrient, nitrogen and calcium that is necessary for metabolic
activity. Secondly, the viability of bacteria was affected by the
increased age due to the continuing decreasing space, in which
the bacteria occupied. Moreover, the crystal formation in the crack
mouth was also identified as calcium carbonate due to the high
peaks of Ca, O and C through EDX analysis. These ions were evident
and their percentage was similar to the composition of calcium
carbonate as shown in Fig. 9(e and f).
At the same context, the verification of the proposed model was
also made on the basis of the relationship between the predicted
healing ratio and the actual filled area in the crack mouth. Both
revealed relatively similar results with correlation coefficient
(R = 0.99) as shown in Fig. 10. Correlation coefficient acted as a
statistics indicator to show the strength of the results and fitting
degree between the predicted output of the model and the experimental data.
Fig. 10. Experimental test of crack healing compared with those predicted by proposed model (a) Predicted and actual crack healing ratio as function of time (b) Correlation
of predicted and actual crack healing results.
Fig. 11. healing ratio with different crack lengths at t = 42 days.
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H.A. Algaifi et al. / Construction and Building Materials 189 (2018) 816–824
Furthermore, the effect of the crack length in x direction on selfhealing capacity was also observed. Fig. 11 shows that when the
crack length decreased, the crack healing increased.
5. Conclusion
The kinetics of calcite precipitation induced in response to the
hydrolysis of urea by indigenous Lysinibacillus sphaericus in artificial concrete cracks were investigated. The amount of calcite
depended on the amount of urea degradation, on the basis that
the concentration of nutrient and calcium were sufficient for the
bacterial activity. A mathematical model was developed based on
a biochemical-diffusive concept. An ordinary differential equation
and a second-order partial differential equation in time and space
were numerically solved using finite element and finite difference
method. The model was found to be applicable to highly reactive
systems such as those proposed for engineering applications of
MICP. Moreover, scanning electron microscopy (VP-SEM) with
energy dispersive X-ray analysis (EDX) was used to verify the predicted crack healing results. Both showed a relative high degree of
similarity with a correlation coefficient of R = 0.99.
Conflict of interest
None.
Acknowledgements
The authors acknowledge full gratitude to the Research University Grant (Tier 2 - Q.J130000.2622.15J43) for funding this
research. This research activities were also supported and funded
by the Ministry of Higher Education, Malaysia (MOHE) under the
FRGS grant R.J130000.7822.4F722 and Universiti Teknologi Malaysia under the UTM COE research grant Q.J130000.2409.04G00. The
authors would like to thank their support and cooperation in this
research. Finally, the authors also express their thanks to Biosensor
and Biomolecular Technology Laboratory (FS-UTM-Malaysia) for
allowing required permission to carry out the isolation and identification of the bacteria.
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