A Novel Mathematical Model for Repairing Rough Cracks Using the Microbially Induced Carbonate Precipitation (MICP)
Round 1
Reviewer 1 Report
1- The abstract provides a good overall summary of the study. However, it is dense with information and may benefit from some simplification to improve readability. Some technical terms could be replaced with more general terms to broaden its appeal. The abstract would benefit from a clarification of the research gap that this work fills and the specific improvements this novel model brings over existing solutions.
2- Introduction
2-1- Consider providing a brief explanation or definition of MICP at its first mention for the benefit of readers who may not be familiar with the technique.
2-2- The introduction could be more explicit in outlining the research gap that this study seeks to address.
2-3- There are several grammatical errors that need to be corrected for clarity.
3- New Mathematical Model
3-1- Some of the terms and symbols used in the mathematical models could be better explained. While it's possible that these are well-known in the field, a brief explanation or definition for each would make the paper more accessible to a wider audience.
3-2- The authors have made a number of assumptions in the development of their model (e.g., water flow not affected by isolated biomass, biofilm develops smoothly on rough surface, etc.). While it's understood that these are necessary simplifications, the potential impact of these assumptions on the model's accuracy should be discussed.
3-3- The authors should include more information on how this model can be applied in real-world situations.
3-4- It's unclear how this model differs from or improves upon existing models. The authors should provide a comparison with other mathematical models, demonstrating the advantages of their approach.
4- Crack Repair by MICP Technique
4-1- More detail is needed regarding how the specific gravity, modulus of fineness, constant of uniformity, and constant of curvature of the fine aggregate, as well as the grain size of the basalt stone, influenced the results. Furthermore, the significance of using Portland cement with P.O of 43 should be explained.
4-2- Please justify the specific selection of Sporosarcina pasteurii (ATCC 11859) as the ureolytic bacteria for the study. Why was this species chosen over others?
4-3- It would be beneficial to see data for a control without microbial treatment for comparison. This would help to ascertain the benefits of using the MICP technique over conventional methods or the natural self-healing process of concrete.
4-4- More information is required regarding the "special pump". How was the speed of 4 mL/min chosen and how does it affect the results?
4-5- The use of the crew apparatus should be clarified further. Specifically, how does it prevent "the sufficient retention and fast passing of mixed solution in concrete cracks"?
5- Modified Cubic Law for Rough Cracks
Please provide additional explanation or a brief summary of the modified cubic law, the experimental method by Barton [50], and how it contributes to your study.
6- Determination of Suspended Biomass Concentrations
More explanation on the importance of measuring biomass concentration and how it affects crack repair would be helpful.
7- Productive Rates for CaCO3
More detail should be provided regarding how the productive rates of CaCO3 were calculated. Also, how do these rates influence the efficacy of the MICP technique?
8- Sonic Time Values
The reasoning behind the selection of these specific measuring points should be clarified. How do these heights contribute to the understanding of the efficacy of the MICP method?
9- Suspended Biomass Concentrations
9-1- The authors could clarify the details of the experiment setup. For example, what are the 4# crack, 6# crack and 10# crack referring to? What is the exact difference among them? Are they crack width, depth, or crack pattern related?
9-2- Also, the authors could provide more information about how they calculated absorbance and what the unit of the suspended biomass concentration is. The precision and reliability of the measurement methods should also be discussed.
9-3- Comparison with previous studies is nicely done, but citation to Sun et al. could include a little more detail about their findings for the readers who are not familiar with the referenced work.
9-4- For better readability, consider using clearer and more concise language. The sentence structure is occasionally complex, which may distract from the intended point.
9-5- The authors should also provide a more comprehensive discussion on how the model can better align with the experimental results.
10- Biofilm Evolution
10-1- The authors should describe the methods used to determine biofilm volume fractions and explain why the biofilm volume fractions would differ based on the crack surface roughness profiles.
10-2- The conclusions derived from Fig. 4 are generally well-explained. However, the manuscript would benefit from a clearer explanation of the specific observations from Fig. 4(c) and 4(d), as they seem to be important for understanding the overall results.
10-3- The explanation of biofilm formation is lacking experimental verification, which weakens the credibility of this section. An experiment investigating biofilm formation would strengthen this part of the paper.
11- Solutes Concentrations
11-1- This section is well-written, but the authors could improve the clarity by explaining more about the units of urea concentrations and what are the expected range of urea concentrations based on the literature.
11-2- The assumptions regarding urea consumption for CaCO3 production could be better elaborated. What other reactions could possibly happen? And what effect would these reactions have on the final results?
11-3 The description of results is very detailed, which is good. However, the authors should provide more comparative and analytical statements instead of mainly descriptive ones.
12- Productive Rates for CaCO3
12-1- The acid pickling technique should be explained more comprehensively. What is the rationale behind this technique, and why is it used here?
12-2- The explanations derived from Fig. 6 and Fig. 7 are quite detailed. Still, authors could consider simplifying these discussions and focusing more on the key findings that are relevant to the main objective of the paper.
12-3- The authors should discuss more on why the model results are not as good for larger cracks and how they might improve the model in this respect.
13- Sonic Time Values
This section is incomplete, so it's hard to provide a comprehensive review. Nonetheless, a more detailed explanation about the sonic time, how it's calculated and how it's related to concrete repair should be included in the final version.
Minor editing of English language required.
Author Response
Dear Editor and Reviewer:
We are very grateful to your kind consideration of our revised manuscript submitted to Sustainability journal (Manuscript ID: sustainability-2553867R1). Many thanks are also given to the reviewers and editor for their constructive criticisms and valuable comments, which have obviously improved the quality of our manuscript.
We have considered the all comments carefully and revised the manuscript according to these suggestions. We corrected English language of our manuscript from MDPI language correction department. We checked the model accuracy and provided missing data. Enclosed, please find the responses to the comments from reviewers and editor. All the changings are highlighted as blue lines in the main manuscript.
Thank you very much for your kind reconsideration. We hope that the revised paper will be considered for publication in your prestigious journal.
Yours Sincerely,
Zulkifl Ahmed
E-mail: [email protected]
Phone: +923335894688
School of Resource and Civil Engineering, Northeastern University, Shenyang 110819, China
Review 1:
We are very grateful for this reviewer for his/her encouragement regarding our work and for valuable suggestions to improve the quality of the manuscript. We tried our best and incorporated all the comments raised by this reviewer. The detail response of each comment is given below:
Comment: 1. The abstract provides a good overall summary of the study. However, it is dense with information and may benefit from some simplification to improve readability. Some technical terms could be replaced with more general terms to broaden its appeal. The abstract would benefit from a clarification of the research gap that this work fills and the specific improvements this novel model brings over existing solutions.
Response: We are very grateful for this reviewer for his/her encouragement regarding Abstract and for valuable suggestions to improve the quality of the Abstract. We replaced technical terms with general terms and provided research gap (Page #1 and line #9-26).
2- Introduction
Comment 2-1. Consider providing a brief explanation or definition of MICP at its first mention for the benefit of readers who may not be familiar with the technique.
Response: Thank you very much for your nice suggestions. We provided the detail of MICP for readers in Introduction (Page #2 and line #40-45).
MICP: Recently, the precipitation of MICP has been comprehensively researched for the repair of concrete cracks. Microbiologically induced calcium carbonate precipitation (MICP) is a bio-geochemical process that induces calcium carbonate precipitation by selected microorganisms within the material matrix through different pathways, considered as a potential plugging agent in many environmental and engineered applications (Liu et al. 2023).
Comment 2-2. The introduction could be more explicit in outlining the research gap that this study seeks to address.
Response: We polished the Introduction and outlined the research gape Thank you very much for your nice suggestions. We provided the detail of MICP for readers in Introduction (Page #2 and line #69-75).
Research gap: Exiting studies on crack repair did not considered the crack roughness, which could be filled only with the MICP technique. Furthermore, many studies on concrete crack repair only conducted by using qualitative examination, which is not appropriate in practical engineering. In reality, theoretical quantification for rough crack repair with the MICP technique cannot be ignored and it is of great importance to develop a new mathematical model for MICP rough crack repair. Also, control on repair period and microbial metabolism by the mathematical model could allow biomineralization, biofilm growth, on-demand adjustment and successive bioremediation of building materials.
Comment 2-3. There are several grammatical errors that need to be corrected for clarity.
Response: We corrected the grammatical issues and polished the whole manuscript as suggested by you. Our manuscript is corrected by MDPI language correction department. Language proofread certificate is submitted.
3- New Mathematical Model
Comment 3-1. Some of the terms and symbols used in the mathematical models could be better explained. While it's possible that these are well-known in the field, a brief explanation or definition for each would make the paper more accessible to a wider audience.
Response: Thank you very much for valuable suggestion. We corrected the grammatical issues and polished the whole manuscript as suggested by you. Track changes file of proof read from native speaker is submitted (Page #3-6 and line #119-203).
Terms and symbols: Aw (m2) is area of water phase, Af (m2) is the area of biofilm in concrete cracks, V0 (m3) is crack initial volume ignoring biofilm and calcite. εc is calcite volume fraction, εw is volume fraction of water and εf is biofilm volume fraction. Cm (kg/m3) is the average concentration of solutes. q (m/s) is Darcy rate of water flow. Dw (m2/s) is water dispersion coefficient and Df (m2/s) is biofilm dispersion coefficient. Dw and Df are the constants relating the slope of the average concentration to the fluctuating part of the flux. These constants depend on the dispersivity factor and flow rate, which can be determined by the texture and structure of the crack surface. V0Rm is relative bio-reaction, Rm (kg/m3.min) is the reaction rate of solutes in bio-reaction, w is the crack width and d is the crack thickness, μ represents the growth rate constant, Y is empirical constant, ρf (kg/m3) denotes the density of biofilm and Cbio (kg/m3) shows the average concentration of suspended biomass in the concrete cracks. F is the mass of oxygen.
Comment 3-2. The authors have made a number of assumptions in the development of their model (e.g., water flow not affected by isolated biomass, biofilm develops smoothly on rough surface, etc.). While it's understood that these are necessary simplifications, the potential impact of these assumptions on the model's accuracy should be discussed.
Response: Thank you very much for asking about the impact of assumptions. In this study, different assumptions are made to develop a new mathematical model by MICP. These assumptions do not affect the accuracy of the model. We checked the accuracy of the model as suggested by reviewer. The different equations are derived for the concentrations of solutes, for the concentrations of suspended biomass, for the biofilm growth, and for the CaCO3 precipitation. These equations are derived under the four assumptions (Page #3-6 and line #119-203).
Comment 3-3. The authors should include more information on how this model can be applied in real-world situations.
Response: Thank you very much for asking about the practical applications of this model and technique. We included the information about the model practical use. In the current research, a novel mathematical model was proposed by considering biofilm growth, the transport of solutes, geochemistry, CaCO3 precipitation, the transport of suspended biomass and ureolysis. By using this model, the productive rates of CaCO3, concentrations of biomass, concentrations of solutes and biofilm volume fractions were estimated via Python. The accuracy of the proposed model is judged by coefficient of determination (R2). Additionally, numerous rough concrete cracks were repaired through the MICP technique in the experiments to validate the usefulness and applicability of the proposed model. New model based on MICP has a wide range of applications in the field of concrete and building material repairs. One area of research involves using MICP to deposit layers of CaCO3 on surfaces to reduce water adsorption, fill cracks, or produce self-healing concrete (Page #17, 18 and line #528-536).
In this study, we just developed a new model to solve the problem that how and how much the calcium carbonate is produced, and the test can verify the model. This paper is about the development of theoretical model, and it is verified, and the application will be in the next work. Some practical use of this model are:
Fig. (10) shows the self-healing effects on concrete rough cracks after 28 days of water curing. Fig. (10) is the result of image processing method. It could be seen that the reference cases had mostly been repaired, while a few white powders appeared on the surface of the samples and the cracks were almost completely repaired. Some areas of more rough crack did not heal completely as compare to less rough cracks as shown in Fig. 10(a). Because the unprotected bacteria had limited survival time to move easily in more rough cracks and cement-based materials, resulted in the poor repair effect, which indicates that the proposed model is more effective to repair crack of less rough surface. The area repair rate of specimens was estimated by using the method presented by Zheng and Qian (Zheng and Qian 2020). The results showed that the cracks of more rough surface were less repaired, and the area repair rate of this group was 91%, while the area repair rate of less rough crack was 98%, as clearly observed from Fig. 10(b-d).
Accuracy of new method
To judge the accuracy of the new method, determination coefficient R2 has been generally used and is well famous today also. The R2 value defines the goodness of method, that is an arithmetical approach for observing the accuracy of a technique in forecasting the real data sets. Determination coefficient R2 was used to evaluate the performance of proposed reduction method. Larger value of R2 indicates that the forecasting precision of the method is high.
A comparison of targeted and output vale is presented in Fig. (2) at the calculated and experimental stage. The constant of determination (R2) between the measured and predicted values shows a good determination capacity of the proposed method. There is almost not any remarkable dissimilarity between the calculated and experimental results (Fig. 2). Results showed that the developed mathematical model is an appropriate tool to repair concrete cracks of rough surface.
Figure 9. Accuracy of the proposed model: (a) at calculated results (b) at experimental results.
Comment: 3-4. It's unclear how this model differs from or improves upon existing models. The authors should provide a comparison with other mathematical models, demonstrating the advantages of their approach.
Response: Thank you very much for your nice suggestions. For repairing concrete cracks, the MICP technique has been widely analyzed in recent times for crack of smooth surface; however, no research has been conducted to deeply investigate the repair effects of MICP on concrete cracks with a rough surface using a theoretical model. So, there is no model or method already exist for rough cracks repair. Therefore, we cannot compare it with previous studies. We compared the results with experimental research and determine the accuracy by coefficient of determination.
4- Crack Repair by MICP Technique
Comment: 4-1. More detail is needed regarding how the specific gravity, modulus of fineness, constant of uniformity, and constant of curvature of the fine aggregate, as well as the grain size of the basalt stone, influenced the results. Furthermore, the significance of using Portland cement with P.O of 43 should be explained.
Response: Very nice comment. Actually, the effects of these constants was ignored in this particular research, because these properties are not directly related MICP technique. The specific gravity, modulus of fineness, constant of uniformity, and constant of curvature are here the properties of the fine aggregate, and basalt stone is for coarse aggregate, that are used to make concrete sample. The effects of these parameters on concrete strength have been deeply investigated previously. Some reference paper are:
- DOI: https://doi.org/10.1016/j.proeng.2016.07.263
- DOI: https://doi.org/10.1016/j.promfg.2018.03.060
- DOI: https://doi.org/10.24321/2456.9925.202201
Comment: 4-2. Please justify the specific selection of Sporosarcina pasteurii (ATCC 11859) as the ureolytic bacteria for the study. Why was this species chosen over others?
Response: We justify the section of Sporosarcina pasteurii by latest related citation. Also, mentioned its importance over others. The ureolytic bacterium Sporosarcina pasteurii is well-known today for its capability of microbially induced calcite precipitation (MICP), representing a great potential in constructional engineering and material applications. Also, it produces the high amount of CaCO3 than bacteria (Ma et al. 2020). (Page #7 and line #226-230).
Comment: 4-3. It would be beneficial to see data for a control without microbial treatment for comparison. This would help to ascertain the benefits of using the MICP technique over conventional methods or the natural self-healing process of concrete.
Response: Thank you very much for your nice suggestion. Needful in revised version. Previously, a lot of research have been conducted to compare different crack repair techniques, some are:
- https://doi.org/10.1016/j.clet.2021.100188
- https://doi.org/10.1016/j.conbuildmat.2005.01.011
- https://doi.org/10.1016/j.conbuildmat.2021.124227
- https://doi.org/10.1080/19648189.2023.2194942
Results of previous publications suggest that MICP technique is more beneficial. We conducted the comparison between calculated results and experimental results. More recently, many scholars have made a great effort to repair larger cracks through the MICP technique (Castro-Alonso et al. 2019; Rauf et al. 2020; Reshma et al. 2023). Based on the MICP method, the precipitation of CaCO3 can seal cracks without any addition. On the other hand, repairing cracks through the precipitation of CaCO3 is not beneficial for larger cracks, and this is why a few scholars have explored other chemicals to seal large cracks (Hu et al. 2019). For example, Zhang et al. (Zhang et al. 2023) and Sun et al. (Sun et al. 2019a) suggested the use of polyvinyl alcohol (PVA) fibers and aluminum oxide to repair cracks 0.5 to 2.0 mm in size through microbially induced carbonate precipitation. Existing studies on crack repair did not consider the crack roughness (Page #2 and line #64-71).
Comment: 4-4. More information is required regarding the "special pump". How was the speed of 4 mL/min chosen and how does it affect the results?
Response: A special pump (hydraulically powered mortar mixer pump) was used to add the mixed cementation solution and bacterial suspension to the cracks (Fig. 2). This is a multipurpose and capable pump that can mix, dump, and pump heavy and light bodied restoration mortars. It consists of a hydraulically powered 7 cubic foot horizontal shaft and a reversible rotor. Controls for the mixer, pump, and dump functions are located directly on the unit. A segregation free speed of 4 mL/min is chosen from American Association of State Highway and Transportation Officials (AASHTO) standard (Page #7 and line #237-243).
Comment: 4-5. The use of the crew apparatus should be clarified further. Specifically, how does it prevent "the sufficient retention and fast passing of mixed solution in concrete cracks"?
Response: The sufficient retention and fast passing of mixed solution in concrete cracks controlled by collective device. With the help of knob/button the movement of solution can be control easily. A collection device with a special valve was put beneath the concrete samples to prevent mixed solution from passing through the cracks fast, and to ensure an adequate retention in the cracks. By closing the valves, the samples were kept in contact for approximately 23.5 h.
5- Modified Cubic Law for Rough Cracks
Comment: Please provide additional explanation or a brief summary of the modified cubic law, the experimental method by Barton [50], and how it contributes to your study.
Response: We provided the more details about modified cubic law as suggested by reviewer.
Modified Cubic Law for Rough Cracks
In 1965, Snow (Snow 1969) derived the cubic law of fluid flow in ideal single fracture through the Navier-Stocks formula. Since then, the cubic law has become the basis for the study of fluid flow in rock-mass fracture.
Since ideal slab cracks do not exist in nature and all natural fracture surfaces are rough surfaces, Barton conducted a lot of tests in 1985 to consider the effect of rough fluctuation of fracture surfaces on fluid flow in rock cracks, and proposed to describe fracture roughness with JRC (Joint Roughness Coefficient). Ten typical fracture contour curves are summarized, and the empirical relationship between equivalent hydraulic gap width, mechanical gap width and JRC is proposed, and the influence of fracture roughness on flow passing capacity is considered from the perspective of JRC. The modified cubic principle has been widely applied to precisely forecast the seepage behavior and water flow in small cracks (Li et al. 2023; Qin et al. 2021). Considering the roughness of repaired cracks, the cubic law needs to be modified. Barton adopted an experimental method (Barton and Choubey 1977) and compared the relationship between a mechanical crack and an equivalent hydraulic crack to correct the joint roughness constant (JRC). In the Barton formula, the equivalent hydraulic crack is taken as the crack width:
Three particular rough cracks with the relevant roughness profiles were chosen to represent the specific JRC values as presented in Table 2. Table 2 also gives a description of the three surfaces and area of cracks (S0). The 4# crack has the rough and tectonic surface, and #6 crack has rough and undulating surface, and 10# crack has rough and irregular surface.
Table 2. Barton standard joint profile and JRC values, from Barton and Choubey (Barton and Choubey 1977) (Page #8 and line #260-288).
6- Determination of Suspended Biomass Concentrations
Comment: More explanation on the importance of measuring biomass concentration and how it affects crack repair would be helpful.
Response: We provided the more explanation about biomass concentration in revised paper. In this study, the leachate was collected by opening the valve during the addition of the mixed solution. The plate colony counting technique was applied to measure the concentration (cell/mL) of viable cells in the leachate. The possible relationship between the absorbance values and viable cell count was analyzed, and the number of viable bacterial cells was assessed by considering the reliable effects of the absorbance measurement for each condition. Equations 6 ~ 8 were used in the mathematical model to determine the growth of biofilm and the transport of biomass. The suspended biomass concentration significantly changed along the cracks due to biofilm growth (Page #8 and line #276-282).
7- Productive Rates for CaCO3
Comment: More detail should be provided regarding how the productive rates of CaCO3 were calculated. Also, how do these rates influence the efficacy of the MICP technique?
Response: We are very thankful for this suggestion, which will obviously increase the readability of our paper. We provided more detail about the production rates of CaCO3.
HCL (0.1 mol/L) was used to wash all samples, which were then weighed after drying. The decrease in the weight (dry weight) of the samples was used as the precipitated value of calcium carbonate. With the help of C × V × Mc, the mass of calcium carbonate was calculated, where C is the calcium ion concentration, V represents the volume of urea Ca(CH3COO)2 solution and Mc is the molar mass of calcium carbonate (100.088 g/mol). The relation of the produced calcium carbonate to the mass of calcium carbonate shows the productive amounts of calcium carbonate. In the mathematical model, the distribution of CaCO3 may be affected by the movement of the suspended biomass and the transport of solutes (Page #9 and line #293-307).
8- Sonic Time Values
Comment: The reasoning behind the selection of these specific measuring points should be clarified. How do these heights contribute to the understanding of the efficacy of the MICP method?
Response: The values of sonic time are a suitable indicator to assess the influences of repair (Castro-Alonso et al. 2019; Rauf et al. 2020; Reshma et al. 2023). Four points equal interval are selected for more accuracy. Also, the variation in sonic speed between the unrepaired parts and repaired parts is large, therefore we divided sample into four parts. A location perpendicular to the concrete cracks was adopted to determine the values of sonic time, as shown in Fig. 2. Four different measuring points situated at heights of 12 mm, 36 mm, 60 mm and 84 mm from the bottom of the samples were selected to measure sonic time. The values of sonic time (TS) can be obtained using the volume of CaCO3 (V0εc), as shown in Eq. (26) (Page #9 and line #309-314).
9- Suspended Biomass Concentrations
Comment: 9-1. The authors could clarify the details of the experiment setup. For example, what are the 4# crack, 6# crack and 10# crack referring to? What is the exact difference among them? Are they crack width, depth, or crack pattern related?
Response: Thank you very much for asking more detail about experiment and cracks. We provided more detail about experiment and 4# crack, 6# crack and 10# crack in revised manuscript. Three particular rough cracks with the relevant roughness profiles were chosen to represent the specific JRC values as presented in Table 2. Table 2 also gives a description of the three surfaces. The 4# crack has the rough and tectonic surface, and #6 crack has rough and undulating surface, and 10# crack has rough and irregular surface (Table 2).
Comment: 9-2. Also, the authors could provide more information about how they calculated absorbance and what the unit of the suspended biomass concentration is. The precision and reliability of the measurement methods should also be discussed.
Response: We provided the detail about the method to calculate the absorbance. Unit of suspended biomass concentration is kg/m3. Also we checked the precision of measurement method by R2.
Comment: 9-3. Comparison with previous studies is nicely done, but citation to Sun et al. could include a little more detail about their findings for the readers who are not familiar with the referenced work.
Response: Nice suggestion. Needful done in revised paper. Sun et al. (Sun et al. 2019b) reported that a reduction in pH is important for bacterial growth in concrete cracks and also leads to higher productivities of microbial utilization. The suspended biomass concentration did not show a unique decline with respect to the calculated results, which is not in agreement with the experimental results. The precipitation of calcium carbonate, biofilm growth and attachment of biomass affect the suspended biomass concentrations in the proposed mathematical model (Page #9 and line #334-339).
Comment: 9-4. For better readability, consider using clearer and more concise language. The sentence structure is occasionally complex, which may distract from the intended point.
Response: We corrected the language from MDPI English correction department.
Comments: 9-5. The authors should also provide a more comprehensive discussion on how the model can better align with the experimental results.
Response: We discussed this aspect in subsection 4.1. (Concentrations of Suspended Biomass), 4.2. Biofilm Evolution, 4.3. Concentrations of Solutes, 4.4. Productive Rates of CaCO3, and 4.5. Sonic Time Values. (Table 3).
10- Biofilm Evolution
Comment: 10-1. The authors should describe the methods used to determine biofilm volume fractions and explain why the biofilm volume fractions would differ based on the crack surface roughness profiles.
Response: Eq. (1) and Eq. (2) are used to determine biofilm volume fraction (εf). Initially its value kept zero.
Comment: 10-2. The conclusions derived from Fig. 4 are generally well-explained. However, the manuscript would benefit from a clearer explanation of the specific observations from Fig. 4(c) and 4(d), as they seem to be important for understanding the overall results.
Response: Needful done. After 21 days, the biofilm volume fractions were smaller in the samples with cracks 4# and 6#. Similarly, a clear increase in the volume of the biofilm fractions was observed after increasing the crack surface roughness and decreasing the distance from the inlet. Additionally, due to the boundary conditions, there was an obvious recovery at the crack outlet in the proposed mathematical model (Fig. 4d). As compared to the 14th day and 7th day, the recovery was clearer on the 21st day (Page #11 and line #383-397).
Comments 10-3. The explanation of biofilm formation is lacking experimental verification, which weakens the credibility of this section. An experiment investigating biofilm formation would strengthen this part of the paper.
Response: The biofilm content cannot be straightforwardly measured, and there is a considerable shortage of harmony among the variety of methods adopted to study and grow biofilms (Kumar et al. 2023; Sportelli et al. 2022). The formation of biofilm was not investigated in the experiment. However, the growth of biofilm affected the precipitation of CaCO3 and suspended biomass concentrations in the proposed model. The comparison of the productive rates of CaCO3 and the suspended biomass concentrations between the experimental and calculated outcomes indirectly confirmed the accuracy of the biofilm model and the existence of a biofilm.
11- Solutes Concentrations
Comment 11-1: This section is well-written, but the authors could improve the clarity by explaining more about the units of urea concentrations and what are the expected range of urea concentrations based on the literature.
Response: Thank you very much for appreciation. The unit of urea concentration is kg/m3, and its range was 30 kg/m3.
Comment 11-2. The assumptions regarding urea consumption for CaCO3 production could be better elaborated. What other reactions could possibly happen? And what effect would these reactions have on the final results?
Response: We elaborated the assumption regarding CaCO3 as suggested. The production of the urea concentrations was the same as that of the calcium ion concentrations. According to Fig. 5(a), as the distance from the inlet increased, the initial concentrations of urea decreased after injection considering the dispersion of solutes and advection. In addition, the pressure change between the outlet and inlet was higher for cracks 4# and 6# due to the greater influences of the dispersive and advective fluxes. No any other reaction is observed during experiment (Page #12 and line #416-421).
Comment 11-3. The description of results is very detailed, which is good. However, the authors should provide more comparative and analytical statements instead of mainly descriptive ones.
Response: We try our best to provide more analytical statements in revised manuscript.
12- Productive Rates for CaCO3
Comment 12-1. The acid pickling technique should be explained more comprehensively. What is the rationale behind this technique, and why is it used here?
Response: Acid could also be used to degrade the levels of cement slurry, meaning that the outcomes could be misinterpreted. However, the use of HCL in concrete is an acceptable technique to quantify CaCO3 produced through MICP (Bagga et al. 2022; Sidhu et al. 2023; Sun et al. 2021). Thus, the acid pickling technique was utilized for comparison in the current research (Page #14 and line #457-462).
Comment 12-2. The explanations derived from Fig. 6 and Fig. 7 are quite detailed. Still, authors could consider simplifying these discussions and focusing more on the key findings that are relevant to the main objective of the paper.
Response: Thank you very much for your kind suggestion. We simplified and focused on key findings. The distribution of the CaCO3 productive rates after the 21-day repair is clearly displayed in Fig. 7. By increasing the distance from the crack inlet, the productive rates of CaCO3 decreased (Fig. 7). Additionally, the productive rates of CaCO3 were lower for crack 10#; however, the amount of decrease was also higher. (Page #16 and Table 3).
Comment 12-3. The authors should discuss more on why the model results are not as good for larger cracks and how they might improve the model in this respect.
Response: Very nice and logical question by reviewer. Actually, we did not consider crack size in this study. We considered three cracks of various rough surfaces with similar width and length. In next study we will considered crack size.
The productive rate of CaCO3 with the proposed model was 95% at the inlet of crack 4#, which was greater than the experimental result due to the ideal calculation conditions. At the outlet, the calculated CaCO3 amount was about 72% for crack 4# (Table 3). From Table 3, the average productive rates of CaCO3 were 72%, 73% and 79% for the samples with rough cracks 4#, 6# and 10#, respectively. More bacterial cells remained in the case of cracks 4# and 6#; therefore, the typical productive rates of calcium carbonate were increased by reducing the roughness of the cracks (Page #15 and line #483-490).
13- Sonic Time Values
Comment: This section is incomplete, so it's hard to provide a comprehensive review. Nonetheless, a more detailed explanation about the sonic time, how it's calculated and how it's related to concrete repair should be included in the final version.
Response: Thank you very much for your patience. We provided more detail about sonic time. The values of sonic time (TS) can be obtained using the volume of CaCO3 (V0εc), as shown in Eq. (26). The reason is that the variation in sonic speed between the unrepaired parts and repaired parts is large. (Page #9,10 and line #325-334).
References
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Barton, N. & Choubey, V. 1977. The shear strength of rock joints in theory and practice. Rock mechanics, 10, 1-54.
Castro-Alonso, M.J., Montañez-Hernandez, L.E., Sanchez-Muñoz, M.A., Macias Franco, M.R., Narayanasamy, R. & Balagurusamy, N. 2019. Microbially induced calcium carbonate precipitation (MICP) and its potential in bioconcrete: microbiological and molecular concepts. Frontiers in Materials, 6, 126.
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Liu, N., Haugen, M., Benali, B., Landa-Marbán, D. & Fernø, M.A. 2023. Pore-scale spatiotemporal dynamics of microbial-induced calcium carbonate growth and distribution in porous media. International Journal of Greenhouse Gas Control, 125, 103885.
Ma, L., Pang, A.-P., Luo, Y., Lu, X. & Lin, F. 2020. Beneficial factors for biomineralization by ureolytic bacterium Sporosarcina pasteurii. Microbial cell factories, 19, 1-12.
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Author Response File: 
Author Response.docx
Reviewer 2 Report
The present work deals with preparing a Novel Mathematical Model for Rough Cracks Repairing by 2 Using the method of microbially Induced Carbonate 3 Precipitation (MICP). The repair effect was taken as the main outcome of 87 MICP in the tests. In the experiments, the sonic time values, CaCO3 productive rates and 88 absorbance leachate were attained and matched by calculated outcomes. However, some points throughout the article in terms of scientific content do not meet the required standard of the journal. Therefore, the following recommendation should be made for the article to be published in Sustainability.
1- The English of this paper should be improved for better understanding of the paper.
2- There are disconnections between paragraphs in the introduction. It should be revised (https://doi.org/10.1080/03067319.2021.1884240 and https://doi.org/10.1016/j.scitotenv.2022.157170)
3- Properties of CaCO3 used should be given.
4- The authors do not well cover the practical implication of this study. It should be reviewed again.
The present work deals with preparing a Novel Mathematical Model for Rough Cracks Repairing by 2 Using the method of microbially Induced Carbonate 3 Precipitation (MICP). The repair effect was taken as the main outcome of 87 MICP in the tests. In the experiments, the sonic time values, CaCO3 productive rates and 88 absorbance leachate were attained and matched by calculated outcomes. However, some points throughout the article in terms of scientific content do not meet the required standard of the journal. Therefore, the following recommendation should be made for the article to be published in Sustainability.
1- The English of this paper should be improved for better understanding of the paper.
2- There are disconnections between paragraphs in the introduction. It should be revised (https://doi.org/10.1080/03067319.2021.1884240 and https://doi.org/10.1016/j.scitotenv.2022.157170)
3- Properties of CaCO3 used should be given.
4- The authors do not well cover the practical implication of this study. It should be reviewed again.
Author Response
Dear Editor and Reviewer:
We are very grateful to your kind consideration of our revised manuscript submitted to Sustainability journal (Manuscript ID: sustainability-2553867R1). Many thanks are also given to the reviewers and editor for their constructive criticisms and valuable comments, which have obviously improved the quality of our manuscript.
We have considered the all comments carefully and revised the manuscript according to these suggestions. We corrected English language of our manuscript from MDPI language correction department. We checked the model accuracy and provided missing data. Enclosed, please find the responses to the comments from reviewers and editor. All the changings are highlighted as blue lines in the main manuscript.
Thank you very much for your kind reconsideration. We hope that the revised paper will be considered for publication in your prestigious journal.
Yours Sincerely,
Zulkifl Ahmed
E-mail: [email protected]
Phone: +923335894688
School of Resource and Civil Engineering, Northeastern University, Shenyang 110819, China
Reviewer 2:
The present work deals with preparing a Novel Mathematical Model for Rough Cracks Repairing by 2 Using the method of microbially Induced Carbonate 3 Precipitation (MICP). The repair effect was taken as the main outcome of MICP in the tests. In the experiments, the sonic time values, CaCO3 productive rates and absorbance leachate were attained and matched by calculated outcomes. However, some points throughout the article in terms of scientific content do not meet the required standard of the journal. Therefore, the following recommendation should be made for the article to be published in Sustainability.
Response: We are very thankful for this reviewer for his/her valuable comments on our paper, which increased the quality of paper.
Comment 1. The English of this paper should be improved for better understanding of the paper.
Response: Our English is now proofread from MDPI English correction department. Certificate is submitted.
Comment 2. There are disconnections between paragraphs in the introduction. It should be revised (https://doi.org/10.1080/03067319.2021.1884240 and https://doi.org/10.1016/j.scitotenv.2022.157170)
Response: We revised the introduction part as suggested by reviewer (Page #23 and line #721).
Comment 3. Properties of CaCO3 used should be given.
Response: We provided the properties of all material used in this research as APENDIX A.
Parameter in the MICP model for crack repair
|
Parameter |
Value |
|
Yield coefficient Y |
0.5 |
|
The mass of oxygen consumed per unit mass of nutrient F |
0.5 |
|
Biofilm density |
2.0 g/L |
|
Maximum substrate utilization rate |
4.1667×10-5 1/s |
|
Half saturation constant of oxygen |
2.0×10-5 g/L |
|
Half saturation constant of nutrient |
7.99×10-4 g/L |
|
Empirical parameter |
6.15×10-10 |
|
Endogenous decay rate |
3.18×10-7 g/L |
|
Decay rate due to calcite precipitation |
1.0 |
|
Biomass attachment rate |
6.15×10-7 mm/s |
|
Biofilm detachment 1 |
3.0×10-9 mm/Pa s |
|
Biofilm detachment 2 |
0.0 dm/Pa |
|
Urea growth rate |
0.7067 mol/g s |
|
Urease content in biofilm |
0.001 |
|
Half saturation constant of urea |
0.355 mol/ kgw |
|
Calcite precipitation 1 |
8.9×10-7 mol/mm2 s |
|
Calcite precipitation 2 |
5.01×10-10 mol/mm2 s |
|
Calcite precipitation 3 |
6.6×10-13 mol/mm2 s |
|
Component diffusivity |
1.0×10-3 mm2/s |
|
Calcite density |
2710 g/L |
|
Molecular weight of calcite |
100.09 g/mol |
|
Exponent for calcite precipitation rate |
1.0 |
|
Constant coefficient |
0.1 |
|
Temperature |
25°C |
Initial conditions
|
Initial conditions |
Value |
|
Nutrient concentration |
0 kg/m3 |
|
Oxygen concentration |
0 kg/m3 |
|
Biomass concentration |
0 kg/m3 |
|
Biofilm volume fraction |
0 |
|
Calcite volume fraction |
0.0 |
|
pH |
8.2 |
|
Total carbon CT |
1.318×10-5 mol/L |
|
Total nitrogen NT |
0.187 mol/L |
|
Total calcium CaT |
0.0 mol/L |
Inlet boundary conditions
|
Inlet boundary conditions |
Value |
|
Nutrient concentration |
3.0 kg/m3 |
|
Oxygen concentration |
8.0×10-3 kg/m3 |
|
Biomass concentration |
7.44×10-8 kg/m3 |
|
Urea concentration |
30 kg/m3 |
|
Calcium concentration |
20 kg/m3 |
|
Total carbon CT |
1.318×10-5 mol/L |
|
Total nitrogen NT |
0.187 mol/L |
|
Total calcium CaT |
0.0 mol/L |
|
Injection speed |
4 ml/min |
Comment 4. The authors do not well cover the practical implication of this study. It should be reviewed again.
Response: We provided the practical implication of this study. Fig. (10) shows the self-healing effects on concrete rough cracks after 28 days of water curing. Fig. (10) is the result of image processing method. It could be seen that the reference cases had mostly been repaired, while a few white powders appeared on the surface of the samples and the cracks were almost completely repaired. Some areas of more rough crack did not heal completely as compare to less rough cracks as shown in Fig. 10(a). Because the unprotected bacteria had limited survival time to move easily in more rough cracks and cement-based materials, resulted in the poor repair effect, which indicates that the proposed model is more effective to repair crack of less rough surface. The area repair rate of specimens was estimated by using the method presented by Zheng and Qian (Zheng and Qian 2020). The results showed that the cracks of more rough surface were less repaired, and the area repair rate of this group was 91%, while the area repair rate of less rough crack was 98%, as clearly observed from Fig. 10(b-d).
Fig. 10. Surface binarization images of rough cracked samples before and after 28 days incubation.
References
Zheng, T. & Qian, C. 2020. Self-healing of later-age cracks in cement-based materials by encapsulation-based bacteria. Journal of Materials in Civil Engineering, 32, 04020341.
Author Response File: Author Response.docx
Reviewer 3 Report
1. Microbially Induced Carbonate Precipitation method has been explained clearly before going into experimental work. Poor presentation on the survey of literatures
2. Novelty is not clearly portrayed.
3. How equations 1-9 were framed or developed? On which basis or references, was it formed. What is the contribution of this manuscript authors in developing these equations? Justify
4. Validation of the mathematical model should be presented
5. Conclusion has to be more comprehensive and clear.
Moderate editing of English language required
Author Response
Dear Editor and Reviewer:
We are very grateful to your kind consideration of our revised manuscript submitted to Sustainability journal (Manuscript ID: sustainability-2553867R1). Many thanks are also given to the reviewers and editor for their constructive criticisms and valuable comments, which have obviously improved the quality of our manuscript.
We have considered the all comments carefully and revised the manuscript according to these suggestions. We corrected English language of our manuscript from MDPI language correction department. We checked the model accuracy and provided missing data. Enclosed, please find the responses to the comments from reviewers and editor. All the changings are highlighted as blue lines in the main manuscript.
Thank you very much for your kind reconsideration. We hope that the revised paper will be considered for publication in your prestigious journal.
Yours Sincerely,
Zulkifl Ahmed
E-mail: [email protected]
Phone: +923335894688
School of Resource and Civil Engineering, Northeastern University, Shenyang 110819, China
Reviewer 3:
Comments and Suggestions for Authors
Comment 1. Microbially Induced Carbonate Precipitation method has been explained clearly before going into experimental work. Poor presentation on the survey of literatures
Response: We are very thankful for this reviewer for his/her valuable suggestions on our manuscript, which obviously increased the quality of the manuscript. We explain Microbially Induced Carbonate Precipitation method in revised paper, and strengthen introduction pat and literature review.
Recently, MICP has been comprehensively researched for repairing concrete cracks. Microbiologically induced calcium carbonate precipitation (MICP) is a bio-geochemical process that induces calcium carbonate precipitation via selected microorganisms within the material matrix through different pathways, considered as a potential plugging agent in many environmental and engineering applications (Liu et al. 2023) (Page #1,3 and line #38-100).
Comment 2. Novelty is not clearly portrayed.
Response: We presented novelty of work clearly. For repairing concrete cracks, the MICP technique has been widely analyzed in recent times; however, no research has been conducted to deeply investigate the repair effects of MICP on concrete cracks with a rough surface using a theoretical model. In the current research, MICP with a novel mathematical model was conducted considering the precipitation of calcium carbonate (CaCO3), ureolysis, suspended biomass, geochemistry, transport of solutes and biofilm growth. Furthermore, crack repair experiments were performed to assess the performance of the new mathematical model (Page #1 and line #70-77).
Furthermore, many studies on concrete crack repair only conducted qualitative examinations, which are not appropriate in practical engineering. In reality, theoretical quantification of rough crack repair with the MICP technique cannot be ignored, and it is of great importance to develop a new mathematical model for MICP rough crack repair. Also, control of the repair period and microbial metabolism using a mathematical model could allow for biomineralization, biofilm growth, on-demand adjustment and successive bioremediation of building materials (Page #2 and line #11-17).
Comment 3. How equations 1-9 were framed or developed? On which basis or references, was it formed. What is the contribution of this manuscript authors in developing these equations? Justify
Response: The equations 1-9 framed based on following techniques:
- Monod-type kinetics has the ability to accurately model solute consumption in biofilms (Algaifi et al. 2020; Landa-Marbán et al. 2021).
- Biomass growth rate constant (μ) adopted from Sun et al. (Sun et al. 2021).
- The source term for suspended biomass (Rbio) can be estimated using Eq. (7), as stated by Ebigbo et al. (Ebigbo et al. 2012).
- Decay rate coefficient (kdec,2) is the second (Ebigbo et al. 2012),
- The Michaelis–Menten kinetics technique has been used to study ureolysis kinetics (Lauchnor et al. 2015).
In this study, we first time develop new mathematical model by using the following Barton formula (Eq. 25) into Eq. 1 (solute transport) and Eq. 6 (transport of suspended biomass) to estimate CaCO3 precipitation and bio film growth in rough cracks.
Comment 4. Validation of the mathematical model should be presented.
Response: We provided the detail about the method to calculate the absorbance. Unit of suspended biomass concentration is kg/m3. Also we checked the precision of measurement method by R2.
Figure 9. Accuracy of the proposed model: (a) at calculated results (b) at experimental results.
Comment 5. Conclusion has to be more comprehensive and clear.
Response: We revised the conclusion section as suggested.
Comment 6. Comments on the Quality of English Language. Moderate editing of English language required.
Response: Our English language is now proofread.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper, as shown in revised paper. We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval. Once again, thank you very much for your comments and suggestions.
References
Algaifi, H.A., Bakar, S.A., Sam, A.R.M., Ismail, M., Abidin, A.R.Z., Shahir, S. & Altowayti, W.A.H. 2020. Insight into the role of microbial calcium carbonate and the factors involved in self-healing concrete. Construction and Building Materials, 254, 119258.
Ebigbo, A., Phillips, A., Gerlach, R., Helmig, R., Cunningham, A.B., Class, H. & Spangler, L.H. 2012. Darcy‐scale modeling of microbially induced carbonate mineral precipitation in sand columns. Water Resources Research, 48.
Landa-Marbán, D., Tveit, S., Kumar, K. & Gasda, S.E. 2021. Practical approaches to study microbially induced calcite precipitation at the field scale. International Journal of Greenhouse Gas Control, 106, 103256.
Lauchnor, E.G., Topp, D., Parker, A. & Gerlach, R. 2015. Whole cell kinetics of ureolysis by Sporosarcina pasteurii. Journal of applied microbiology, 118, 1321-1332.
Liu, N., Haugen, M., Benali, B., Landa-Marbán, D. & Fernø, M.A. 2023. Pore-scale spatiotemporal dynamics of microbial-induced calcium carbonate growth and distribution in porous media. International Journal of Greenhouse Gas Control, 125, 103885.
Sun, X., Miao, L., Wu, L. & Wang, H. 2021. Theoretical quantification for cracks repair based on microbially induced carbonate precipitation (MICP) method. Cement and Concrete Composites, 118, 103950.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Accept in present form
Accept in present form
Reviewer 3 Report
Now the manuscript can be accepted in present form
