Keywords

1 Introduction

Cement-based grouting material is a kind of building material prepared in a professional factory, which has the characteristics of early strength, high strength, self-levelling and micro-expansion after mixing with water in a prescribed proportion at using sites. With the rapid advance of infrastructure construction, cement-based grouting materials have been widely used in the fields of bolt anchorage, reinforcement and reconstruction of concrete, and prefabricated construction projects. At the same time, higher requirements are placed on the performance of cement-based grouting materials.

Cement-based grouting material should adopt low water-binder ratio to obtain excellent later strength, but it will lead to slow early hydration of cement and insufficient early strength [1]. Early strength agent is often added to dry powder system to satisfy the early strength requirements of cement-based grouting materials in practical engineering applications. Calcium formate has been widely used in dry powder system as early strength agent due to its excellent coagulation promotion ability and solubility. Calcium formate solution is weakly acidic, and it improves the hydration rates of \({\mathrm{C}}_{2}S\) and \({\mathrm{C}}_{3}S\). And the ionized \({Ca}^{2+}\) accelerate the crystallization of AFT owing to ion effect, it promotes the early strength development [2,3,4]. However, the incorporation of calcium formate will lead to the loss of fluidity, and it is harmful to working performance [5, 6]. As a surfactant, defoaming agent can promote the rupture of bubbles in slurry, reduce the porosity, and effectively improve the strength of cement-based grouting materials [7, 8].

Response surface methodology (RSM) is an analytical method to establish an accurate prediction model with limited experimental data which is obtained from standard tests. RSM uses second-order standard polynomial to fit the response value and different factors, and can draw response surfaces that intuitively reflects the influence of factors on the response value. RSM has been widely used in the process formulation design of grain, oil and food, chemical engineering, and biological engineering [9], but it is rarely used in the related fields of construction and civil engineering [10,11,12].

There are few reports on the influence of calcium formate and defoaming agent on the mechanical properties of cement-based grouting materials with low water binder ratio. In this paper, calcium formate content, water-binder ratio and defoaming agent content were selected as experimental factors, and the compressive strength of 1d, 3d and 28d were response values. Box-Behnken design (BBD) was used to design the compressive strength test of cement-based grouting materials with low water-binder ratio, and the functional relationships between the response values and the factors were established to analyse the influence of various factors and their interactions on the compressive strength, so as to optimize the mix proportion. And the mechanism of agents was analysed of action combined with macroscopic mechanical microscopic morphology.

2 Experiment

2.1 Materials and Instruments

P · II 52.5R portland cement (PC), II fly ash (FA) and S95 slag powder (SL) were used as cementitious materials, and the chemical composition is shown in Table 1.

Table 1. The chemical composition of cementitious materials
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Concrete admixtures used in the experiment included industrial grade calcium formate (purity > 95%), P803 powder defoaming agent, low alkali u-type expansive agent, QH-100 plastic expansive agent, QS-8020 polycarboxylate superplasticizer. Other materials included water and ISO standard sand.

The compressive strength test adopted NELD-CH2000 electro-hydraulic servo pressure testing machine (Beijing Nierde Intelligent Technology Co., Ltd), structural equation model (SEM) analysis adopted Gemini300 scanning electron microscope (Carl Zeiss AG, German).

2.2 Compressive Strength Test Design

According to preliminary test results, the basic mix proportion is shown in Table 2.

Table 2. The basic mix proportion
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BBD method was used in the experimental design and data analysis would be completed. Calcium formate ratio, water-binder ratio and defoaming agent ratio were expressed as \({x}_{1}\), \({x}_{2}\) and \({x}_{3}\), respectively. Each independent variables was set at low level, central point and high level, which were encoded as −1, 0 and +1, respectively. The level of each factor and the corresponding coding value are shown in the Table 3.

Table 3. Coding and level of independent variables
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2.3 Specimen Forming and Test Method

The dry powder was weighed according to the proportion during the molding process of the specimen. After mixing evenly, water was added in proportion and stirred at a low speed for 2 min, stopped for 15 s, and stirred at high speed for 2 min. The mortar was poured into the triple mold, demoulded after curing for 24 h, and maintained to the target age. The loading speed of compressive strength test was controlled at 2.4 ± 0.2 k N/s. The blocks with particle size less than 5 mm were taken on the new section in SEM analysis, and the microstructure of hydration products was observed after drying, spraying gold, fixing and vacuuming.

3 Results and Analysis of Compressive Strength Test

3.1 Results and Fitting Models

The test results of 1d, 3d, 28d compressive strength are shown in Table 4. A total of 17 groups were set up, of which 5 groups were at the central point of each factor values, repeated to evaluate the test deviation.

Table 4. Design and results of Box-behnken test
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The second-order standard polynomials fitting of Table 4 test data were carried out by RSM. The simulation models of 1d compressive strength \({(S}_{1})\), 3d compressive strength \({(S}_{2})\) and 28 d compressive strength \({(S}_{3})\) are Eq. (1)–(3).

$$\begin{gathered} S_{1} = - 2.77 + 15.46x_{1} + 232.46x_{2} + 13.84x_{3} + 7.5x_{1} x_{2} - 0.25x_{1} x_{3} + 79.50x_{2} x_{3} \\ \bowtie - 11.84x_{1}^{2} - 461.50x_{2}^{2} + 29.62x_{3}^{2} \\ \end{gathered}$$
(1)
$$\begin{gathered} S_{2} = + 0.38 + 12.08x_{1} + 467.41x_{2} + 47.14x_{3} + 6.50x_{1} x_{2} - 3.45x_{1} x_{3} + 86.50x_{2} x_{3} \\ \bowtie - 10.52x_{1}^{2} - 1165.70x_{2}^{2} - 133.42x_{3}^{2} \\ \end{gathered}$$
(2)
$$\begin{gathered} S_{3} = + 41.35 + 6.05x_{1} + 347.89x_{2} + 25.05x_{3} + 4.60x_{1} x_{2} + 0.60x_{1} x_{3} + 234.50x_{2} x_{3} \\ \bowtie - 6.59x_{1}^{2} - 1005.50x_{2}^{2} - 159.38x_{3}^{2} \\ \end{gathered}$$
(3)

Table 5 shows variance analysis of regression models. F-value represents the test index of obviousness and P-value represents the probability, in which the smaller the P-value is, the stronger the significance of the model is and the higher the simulation accuracy is. The P-value of lack of fit reflects the significant degree that the experimental data is not related to the model. If the value is less than 0.05, the item is significant. and when the value is less than 0.05, the item is highly significant. The P-values of \({S}_{1}\), \({S}_{2}\) and \({S}_{3}\) are 0.0004, 0.0005 and 0.0010, respectively, which are not greater than 0.01, indicating that the simulation models are highly significant. As for lack of fit, the P-values of each model are 0.2141, 0.2347 and 0.4019, which are greater than 0.05, indicating that the mismatch term is not significant and the errors of simulation models are small. The fitting equation is highly consistent with the actual.

Table 5. Variance analysis and of regression models
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It can be seen from Table 6 that \(\mathrm{P}\left({x}_{1}\right)>\mathrm{P}\left({x}_{2}\right)>\mathrm{P}\left({x}_{3}\right)\) for the 1d compressive strength model \({S}_{1}\). It indicates that the water-binder ratio, the amount of calcium formate and the amount of defoaming agent all have a significant effect on the 1d compressive strength of the cement-based grouting material, and the main factor is calcium formate.

For the 3d compressive strength model \({S}_{2}\),\(\mathrm{P}({x}_{2})<P({x}_{1})<P({x}_{3})<0.01\). The influence of water-binder ratio, calcium formate and defoaming agent on the 3d compressive strength of the cement-based grouting material is highly significant. The influence order is \({x}_{2}>{x}_{1}>{x}_{3}\), and water-binder ratio is main factor.

The order of influence on the 28d compressive strength model \({S}_{3}\) is \({x}_{2}>{x}_{2}>{x}_{1}\), where the P-value of \({x}_{1}\) is greater than 0.05. The influence of water-binder ratio and defoaming agent on 28d compressive strength of grouting material is highly significant, among which water-binder ratio is still the most important factor, but calcium formate will not have a significant impact.

In summary, the incorporation of calcium formate plays a significant role in the early strength development of low water-binder ratio cement-based grouting materials, but contributes less to the later strength. The effects of water-binder ratio and defoaming agent on the compressive strength of cement-based grouting materials with low water-binder ratio at all ages cannot be ignored, especially for the strength contribution in the middle and late stages.

The closeness of \({\mathrm{R}}^{2}\) and Adj \({\mathrm{R}}^{2}\) can be used to verify the fitting degree of the simulation models, and the smaller the C.V is, the Adeq Precisior is greater than 4, indicating that the reliability and accuracy of the test are higher. It can be seen from Table 6 that the C.V of each model are 1.97%, 3.57% and 1.45%, respectively, and the Adeq Precisior of each model are 7.527, 9.524 and 6.199, respectively, indicating that the simulation models has high reliability and accuracy.

Table 6. Model reliability test analysis
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3.2 Response Surface Interaction Analysis

The response surface diagrams of 1d, 3d and 28d compressive strength were established as shown in Fig. 1, 2 and 3. The response surface reflects the effect of the interaction of two factors on the compressive strength of each age when the other factor is at the central point.

Figure 1 shows the 1d compressive strength had a process of first increasing and then decreasing with the increase of calcium formate ratio and water-binder ratio from −1 level and the increase of defoaming agent ratio promoted the continuous growth of 1d compressive strength, but the growth was limited under high ratio. Maximum 1d compressive strength was attained at around 0.72% calcium formate, 0.23 water-binder ratio and 0.30% defoaming agent. Table 6 shows that the P-values of the interaction of two factors in the 1d compressive strength model are 0.6572, 0.9762 and 0.3587, respectively, which are greater than 0.05. It indicates that the interaction of any two factors does not contribute significantly to the 1d compressive strength.

Fig. 1.
figure 1

Effect of two-factor interaction on 1d compressive strength

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The compressive strength of 3d and 28d increased first and then decreased significantly with the increase of calcium formate ratio, water-binder ratio and defoaming agent ratio, as is shown in Fig. 2 and Fig. 3. Maximum 3d compressive strength was attained at around 0.60% calcium formate, 0.21 water-binder ratio and 0.24% defoaming agent, while Maximum 28d compressive strength was attained at around 0.54% calcium formate, 0.20 water-binder ratio and 0.23% defoaming agent. The compressive strength decreased slightly with the increase of the dosage, after the defoaming agent ratio reached the optimal solution, but the decrease was limited. Plot of Table 6 reveals the P-values of the interaction of the two factors in the 3d compressive strength model are 0.7128, 0.6961 and 0.3414, respectively, which are greater than 0.05, indicating that the interaction of any two factors has a low contribution to the 3d compressive strength. While, the P-value of the interaction of defoaming agent ratio and water-binder ratio in the 28d compressive strength model is 0.0427, which is less than 0.05, indicating that there is a strong dependence of 28d compressive strength on the interactive pattern between defoaming agent and water-binder ratio.

Fig. 2.
figure 2

Effect of two-factor interaction on 3d compressive strength

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Fig. 3.
figure 3

Effect of two-factor interaction on 28d compressive strength

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With the increase of calcium formate ratio, water-binder ratio and defoaming agent ratio, the compressive strength of each age generally had a process of first increasing and then decreasing. The proper calcium formate ratio promotes the hydration of \({C}_{3}S\), \({C}_{2}S\) and the formation of CSH gel, which is helpful for the early hydration of slurry. However, the high content leads to excessive loss of fluidity, which is not conducive to the formation of dense structure, and it causes the reduction of compressive strength [13]. Higher water consumption contributes to the early hydration reaction of cement particles, but the residual free water inside the slurry evaporates to form pores with the increase of age. The pores will increase with the increase of water-binder ratio, resulting in strength loss. With the increase of defoaming agent ratio, the compressive strength of 3d and 28d first increased and then decreased, and the compressive strength of 1d continued to increase, which was consistent with the early research [14]. The defoaming agent weakens the effect of water reducing agent, especially in the case of high dosage, resulting in the loss of fluidity. It is not conducive to the formation of dense structure, and it induce the decrease of strength.

3.3 Parameter Optimization and Verification

Taking the compressive strength of each age as the optimization object, the mix proportion of cement-based grouting material was optimized, and the optimized mix proportion scheme was obtained as follows: 0.64% calcium formate, 0.21 water-binder ratio and 0.26% defoaming agent. The predicted values and test values of the regression model were compared, and the relative error was used for characterization. The results are shown in Table 7.

Table 7. Comparison of predicted value and test value after parameter optimization
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The experimental results show that the compressive strength of cement-based grouting material prepared by optimized mix ratio is Relatively high, and the relative error between predicted value and test value is small. It is reliable and accurate to optimize the mix proportion of cement-based grouting materials by response surface method.

4 Analysis of the Action Mechanism of Additives

Calcium formate and defoaming agent are additives widely used in cement-based grouting materials. In order to analyse the mechanism of action of the two, five groups of samples were taken to observe the type, morphology and quantity of hydration products of cement-based grouting materials by scanning electron microscope. The typical morphology diagrams are shown in Fig. 4.

Figure 4a shows that a large number of needle-like AFT crystals were formed on the surface of cement, mineral powder and fly ash particles after hydration for 1 day, and the network structure was constructed by alternating AFT, with 1% calcium formate and 0.3% defoaming agent. Increased magnification factor from 10k to 30k, Fig. 4b shows that there was a small amount of CSH gel in the network structure, forming a relatively stable hydration structure, but the overall hydration degree of the slurry was low and the structure was loose. It can be seen from Fig. 4c that when the slurry was hydrated to 3 days, the AFT crystallization was more robust, and the constructed network structure was obviously filled with a large number of flocculent CSH gels. The lamellar \(\mathrm{Ca}{\left(OH\right)}_{2}\) crystals were obviously observed on the surface of cement, mineral powder and fly ash particles, and the hydration degree was significantly improved. The overall structure was more stable than that of 1 day, forming a relatively dense hydration structure. When the slurry is hydrated to 28 days, the microstructure is shown in Fig. 4f. The network structure constructed by AFT crystallization was basically filled and compacted by hydration products, and a stable structure formed between cement, mineral powder and fly ash particles. At this time, the hydration reaction has been basically completed and the microstructure was dense.

Comparing Fig. 4c (3d, 0.1% calcium formate) with Fig. 4d (3d, 0% calcium formate), the sample without calcium formate still had a network structure formed by alternating overlap of AFT, but the CSH gel was significantly reduced compared with the calcium formate group. There are no lamellar \(\mathrm{Ca}{\left(OH\right)}_{2}\) crystals were observed, and the hydration structure was loose. The above phenomenon shows that the incorporation of calcium formate into cement-based grouting materials helps the slurry to form.

Fig. 4.
figure 4

SEM diagrams of hydration products

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Fig. 5.
figure 5

Section of test block

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\(\mathrm{Ca}{\left(OH\right)}_{2}\) crystallization and CSH gel in the early stage, thereby improving the early compressive strength.

It can be seen from Fig. 4c (3d, 0.3% defoaming agent) and Fig. 4e (3d, 0.1% defoaming agent), that when the ratio of defoaming agent decreased from 0.3% to 0.1%, a large number of flocculent CSH gels are still filled into the network structure constructed by AFT crystallization, and a large number of flake \(\mathbf{C}\mathbf{a}{\left({\varvec{O}}{\varvec{H}}\right)}_{2}\) crystals are precipitated as well, and there was no obvious increase in the gap between particles. Therefore, it indicated that the significant influence of defoaming agent is not based on changing the microstructure of hydration products to improve compressive strength. Compared with Fig. 5a (3d, 0.3% defoaming agent) and Fig. 5b (3d, 0.1% defoaming agent), when the dosage of defoaming agent ratio was 0.1%, there were a large number of visible pores on the cross section of the sample. With the increase of the dosage to 0.3%, the pores on the cross section decreased significantly and the structure was denser. The above phenomena show that the defoaming agent can improve the compressive strength of cement-based grouting materials, because it can promote the bubble rupture in the slurry and reduce the macro pores, rather than having no significant influence on the microstructure of hydration products.

5 Conclusion

The effects of calcium formate and defoamer on the mechanical properties of cement-based grouting materials were studied through compressive strength test and microstructure analysis. The results show that:

  1. (1)

    The models established by RSM can accurately predict the results, providing a reliable method for the optimization design of the mix proportion of cement-based grouting materials.

  2. (2)

    The water-binder ratio and the defoaming ratio have significant effects on the compressive strength of cement-based grouting materials at different ages, but it is more significant in the middle and later stages. While the dosage of calcium formate only has significant effects on the compressive strength of 1d and 3d. The 28d compressive strength was significantly affected by the interaction of water binder ratio and defoaming agent.

  3. (3)

    Comprehensively considering the compressive strength of each age, the optimal mix proportion of cement-based grouting materials with low water-binder ratio was obtained by response surface method, namely, the calcium formate content was 0.64%, the water-binder ratio was 0.21, and the defoamer content was 0.26%.

  4. (4)

    Calcium formate is beneficial to the formation of CSH gel and \(\mathrm{Ca}{\left(OH\right)}_{2}\) crystallization in the early slurry, which is beneficial to the rapid formation of dense hydration structure. The defoamer mainly acts on reducing macro pores and has no significant effect on the microstructure.