3.1 Effect of polycarboxylic acid on bacterial growth
Figure 2 (a), the bacteria growth curves under various polycarboxylic acid addition levels are presented. Notably, bacterial growth was rapid between 14 to 20 hours, reaching its peak concentration around 30 hours. The logistic model represented by Eq. (2) [14] was employed to fit the bacteria growth curve. Based on this model, the maximum bacteria growth rate, minimum doubling time, and maximum growth concentration were calculated, as depicted in Eq. (3)-(5). The fitting results and calculation outcomes are summarized in Table 4.
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)
In the Eq. (2)-(5), N(t) represents the number of bacteria in the culture medium at time t, N0 denotes the initial population in the culture medium, K indicates the carrying capacity of the environment, and r is the growth rate constant. The variables \(\mu\)max, tdmin and Gcmax signify the growth of bacteria, representing the maximum specific growth rate, minimum doubling time, and maximum growth concentration, respectively.
According to the fitting results, the addition of polycarboxylic acid exhibited almost no impact on the maximum specific growth rate and minimum doubling time of bacteria. However, after the addition of polycarboxylic acid, the carrying capacity decreased to some extent, with no significant difference observed between the carrying capacity and the addition of polycarboxylic acid. To quantitatively analyze whether polycarboxylic acid had an effect on bacterial growth, a statistical analysis was conducted.
Table 4
Results of bacterial growth curve fitting and growth parameters under different dosage of polycarboxylic acid
Addcon
|
K
|
r
|
R2
|
\(\varvec{\mu }\)max
107 cells/ml/h
|
tdmin
h
|
Gcmax
107cells/ml
|
0
|
141.26
|
0.27
|
0.96
|
4.77
|
0.15
|
141.26
|
0.01
|
133.39
|
0.28
|
0.97
|
4.67
|
0.15
|
133.39
|
0.02
|
126.73
|
0.28
|
0.99
|
4.44
|
0.16
|
126.73
|
0.03
|
130.35
|
0.27
|
0.97
|
4.40
|
0.16
|
130.35
|
0.04
|
129.24
|
0.29
|
0.96
|
4.68
|
0.15
|
129.24
|
0.05
|
132.75
|
0.28
|
0.99
|
4.65
|
0.15
|
132.75
|
Multivariate analysis of variance[41] was employed to examine the correlation between polycarboxylic acid addition as the independent variable and maximum growth rate, minimum doubling time, and maximum growth concentration as dependent variables. The analysis results are presented in Table 5. The significance level is obviously greater than 0.05, which suggests that there is no significant correlation between the addition of polycarboxylic acid and the growth parameters. These findings indicate that there is no significant correlation between the maximum growth rate, minimum doubling time, and maximum growth concentration and the quantity of polycarboxylic acid added at the test concentration. This illustrates that polycarboxylic acid does not adversely affect the growth of S. pasteurii.
Table 5
Correlation analysis between polycarboxylic acid addition and basic growth parameters of bacteria.
multivariate linear model
|
Test Statistics
|
Value
|
Num DF
|
Den DF
|
F Value
|
Pr>F
|
Wilks’ lamda
|
Intercept
|
0.0000
|
3.0000
|
2.0000
|
26030.4705
|
0.0000
|
Addcon
|
0.3877
|
3.0000
|
2.0000
|
0.9684
|
0.0000
|
Pillai’s trace
|
Intercept
|
1.0000
|
3.0000
|
2.0000
|
26030.4705
|
0.0064
|
Addcon
|
0.6123
|
3.0000
|
2.0000
|
0.9684
|
0.0000
|
Hotelling-Lawley trace
|
Intercept
|
39045.7057
|
3.0000
|
1.0000
|
13015.2352
|
0.5209
|
Addcon
|
1.5792
|
3.0000
|
1.0000
|
0.4842
|
0.5209
|
Roy’s greatest root
|
Intercept
|
39045.7057
|
3.0000
|
2.0000
|
26030.4705
|
0.7381
|
Addcon
|
1.5792
|
3.0000
|
2.0000
|
0.9684
|
0.5209
|
In Fig. 2 (b), the changes in urease activity per unit bacterial concentration over time are illustrated under various polycarboxylic acid addition amounts. It is evident that the trend of urease activity per unit bacterial concentration over time remains consistent across different dosages of polycarboxylic acid.
Panel data analysis[33] was employed to investigate the impact of polycarboxylic acid addition on the urease activity of bacteria at unit concentration over time, considering the amount and culture time of polycarboxylic acid as independent variables. The analysis results are presented in Table 6. The significance level is obviously greater than 0.05, which suggests that the addition of polycarboxylic acid has no effect to the urease activity of bacteria per unit concentration.
Table 6
Correlation analysis of polycarboxylic acid addition amount and bacterial activity per unit concentration.
OLS Regression Results
|
Dep.V: Normalizedact
|
Coef
|
Std err
|
t
|
p>| t |
|
[0.025
|
0.975]
|
|
Const
|
0.339
|
0.030
|
11.133
|
0.000
|
0.278
|
0.400
|
|
Addcon
|
0.0094
|
0.007
|
1.299
|
0.199
|
-0.005
|
0.024
|
|
Time
|
-0.0039
|
0.001
|
-6.054
|
0.000
|
-0.005
|
-0.003
|
|
3.2 Effect of polycarboxylic acid on the precipitation of calcium carbonate
Figure 3 (a) illustrates the real-time reaction diagram of reaction systems with different amounts of polycarboxylic acids over the experiment. The diagram clearly shows that as the quantity of polycarboxylic acids added to the system increases, the time of calcium carbonate precipitation in the system significantly delays. In Fig. 3 (b), the change in calcium ion conversion rate with time in reaction systems with varying polycarboxylic acid additions is depicted. The figure indicates that the calcium ion conversion rate initially increases and then decreases at 24 hours with the rise in polycarboxylic acid concentration. When the amount of polycarboxylic acid is 3%, the precipitation rate of calcium ions reaches 100% within 24 hours.
As explained earlier, polycarboxylic acids can form complexes with calcium ions in solution reactions[1, 2, 18, 38, 46], resulting in a delayed precipitation formation time. When the amount of polycarboxylic acid is small, such as 1%, the inhibition effect is limited, leading to faster precipitation production. In cases where the amount of polycarboxylic acid is moderate, like 3%, the formation time of calcium carbonate can be delayed by the complexation of polycarboxylic acid and calcium ions. Additionally, the complexation of polycarboxylic acid and calcium ions allows the polycarboxylic acid to substitute for bacteria, serving as a condensation nucleus during the crystallization of calcium carbonate. This extension of the action time of bacteria contributes to a higher 24-hour conversion rate of calcium ions. However, when the amount of polycarboxylic acid is excessive, such as 5%, the inhibitory effect on the crystallization of calcium carbonate becomes more pronounced. As a result, the precipitation formation time is significantly delayed. By the time the reaction reaches 24 hours, the calcium ion conversion rate is still low.
In Fig. 4, the alterations in supernatant pH in the reaction system with varying amounts of added polycarboxylic acids are depicted. The figure reveals that the lowest pH value among all of the reaction systems is about 5.5, and the change in pH of the solution during the reaction process with different amounts of polycarboxylic acid is relatively minor, most of the time remaining stable between 6–7. This observation further suggests that the inhibition of calcium carbonate precipitation by polycarboxylic acid is attributed to the complexation between carboxylic acid groups and calcium ions, rather than a reduction in the pH of the reaction system.
3.3 Effect of polycarboxylic acid on the MICP cementation
In Fig. 5 (a), the unconfined compressive strength of the sand column under different reinforcement times with varying amounts of added polycarboxylic acid is presented. Notably, when polycarboxylic acid is not added, the sand column made by one-phase injection experienced serious blockage at the top, and the bottom cannot be cemented. Consequently, the strength of this group of sand columns is not shown in the figure. The test results indicate a noticeable increase in the strength of the sand column with an increase in reinforcement times. With the same reinforcement time, the strength of the sand column initially rises and then decreases with an increase in polycarboxylic acid ratio. This trend aligns with the change in calcium ion conversion observed in the tube test, suggesting a high correlation between the strength of the sand column and the content of calcium carbonate. After 5 rounds of treatment, the unconfined compressive strength of the sand column can reach up to 2.76 MPa. For reinforcement times of 1 and 3, the strength of the sand column with 1% addition is slightly higher than that with 5% addition. However, when the reinforcement time reaches 5, the strength of the sand column with a 5% addition is significantly higher than that of the 1% group. This may be attributed to the fact that the calcium carbonate content has a greater influence on strength at low reinforcement times, while the uniformity of calcium carbonate distribution has a more pronounced impact on the strength of the sand column at higher reinforcement times.
In Fig. 5 (b), the typical stress-strain curves and failure modes of sand columns, reinforced five times by adding three dosages of polycarboxylic acids, are presented. During the unconfined compression process, the sample undergone the compaction stage, followed by the elastic stage where the stiffness differences among samples were minimal. The elastic stage concludes upon reaching the peak stress. The 3% polycarboxylic acid group exhibits a longer elastic stage and higher peak stress, potentially attributed to the higher calcium carbonate content and more uniform distribution. Cracks appeared after reaching the peak stress, and these cracks continued to expand until the specimen was completely destroyed. The failure modes of all sand columns are brittle failure. The 1% addition amount experienced failure primarily at the bottom of the sample due to its lower calcium carbonate content. In contrast, the failure of the 3% and 5% addition amounts was attributed to splitting, indicative of a relatively uniform distribution of calcium carbonate.
Figure 5 (c) illustrates the distribution of calcium carbonate along the depth of the sand column under different reinforcement conditions. It is evident that the addition of polycarboxylic acid significantly improves the uniformity of calcium carbonate distribution in the specimen. When polycarboxylic acid was absent, calcium carbonate was primarily concentrated in the upper part of the sample, and the uneven distribution became more apparent with an increase in reinforcement times. Throughout the entire strengthening process, the calcium carbonate content at the bottom of the sample remains consistently low, explaining the failure of sample formation without the addition of polycarboxylic acid. At 1% addition and 5 reinforcement times, there is a slight uneven distribution of calcium carbonate. However, at concentrations of 3% and 5%, there is no obvious non-uniformity. The increase in calcium carbonate content from the third to the fifth grouting is not as substantial as from the first to the third, possibly due to previously generated calcium carbonate occupying part of the pore space, resulting in a decrease in the volume of reinforcement solution that can be injected.
Figure 5 (d) presents the data on calcium carbonate content and strength of the sand column measured in this experiment and relative studies. It is observed that the calcium carbonate content in the sand column in this study exhibits an exponential relationship with the strength of the sand column. Comparing the relationship between calcium carbonate content and the strength of the sand column in this study with other studies, it is noted that the strength in this study is higher under the same calcium carbonate content. This difference may be attributed to the more even distribution of calcium carbonate.
3.4 Microscopic analysis
In Fig. 6, the XRD results of calcium carbonate produced with varying amounts of polycarboxylic acid are presented. The findings reveal that the crystal morphology of the generated calcium carbonate in each group is predominantly calcite and vaterite. No significant differences are observed among these groups.
Figure 7 shows the SEM results of sand columns treated five times with polycarboxylic acid dosages of 0%, 1%, 3%, and 5%. The SEM images demonstrate that when 1% and 3% polycarboxylic acid is added, the calcium carbonate generated appears as distinct spheroids, with larger particle sizes and higher content compared to other groups. Particularly at 3%, the calcium carbonate crystals are noticeably larger, representing one possible reason for the higher strength of the sand column with 3% polycarboxylic acid addition.
Figure 8 displays the infrared spectra of polycarboxylic acids and the precipitates generated under different polycarboxylic acid dosages. The results indicate the presence of an absorption peak of the C-O bond of the carboxylic acid group in the calcium carbonate precipitates[17]. This absorption peak becomes more pronounced with an increase in the addition of polycarboxylic acid, suggesting that polycarboxylic acid co-precipitates with the generated calcium carbonate and plays a role in the nucleation process of calcium carbonate.