Numerical modeling for crack self-healing concrete by microbial calcium carbonate
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], [2], [3], [4], [5], [6]. However, concrete is 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].
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], [10], [11], [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], [16], [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], [25], [26], [27], [28], [29], [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 byAliko-Benítez, 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).
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.
Section snippets
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
Verification of the predicted Crack-Healing results
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°33′52.4″N 103°39′16.3″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
Nodal urea distribution
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 coefficient 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
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
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
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