**5. Effective moisture transport factor**

In order to measure the resistance to capillary suction, Smeplass and Skjølsvold [6] have suggested calculating the time, *t cap*, and the corresponding absorption value, *Qcap*, that the water front reaches the top surface of the specimen with the height "*h*" (see **Figure 7**). The mass storage is usually registered in the following order during capillary suction test:

• 10 and 30 min,

hydrophobed surface is more than 90°, the pressure sign will be positive, thus the smaller the pore radius, the larger the repellency effect if these small pores are hydrophobed. The pore structure of hcp is more complicated than a capillary tube with connections between the pores. In addition, the hydrophobic agents may not cover all the pore surface areas. One may generally assume that the pore structure of hcps with lower w/c is finer than the higher w/c, simply by comparing the volumetric fraction of gel pores. Consequently, it is expected that water-repellant admixtures will be more effective in lower w/c if these smaller pores are the main part of the pore system that is impregnated. This effect is observed in the current

**Figure 5.** Pore protection factor (PF) for reference (Ref) sample and the samples containing rapeseed oil (Oil), alkyl

**Figure 4.** Pore distribution of different mixes with the w/c of 0.58 for reference (Ref) samples and the samples containing

1% rapeseed oil (Oil), 1% alkyl alkoxysilane (Si), and 20% silica fume (SF).

*<sup>P</sup>* <sup>=</sup> (−2*<sup>σ</sup>* cos*θ*) \_\_\_\_\_\_\_\_\_ *<sup>r</sup>* (1)

example as an increase in εps by using hydrophobic agents (**Figure 6**).

alkoxysilane (Si), and silica fume (SF).

70 Cement Based Materials


**Figure 7.** Regression analysis for calculating the resistance number (*m*) and the capillary number (*k*).

A regression analysis is then carried out based on the data points from 10 min to 6 h for the first/left linear part, and the rest of the points (from 1 to 4 days or alternatively 5 days) for the second/right linear part. Then, the resistance number, *m*, and the capillary number, *k*, will be calculated using the following equations:

$$m = \frac{t\_{eq}}{h^2} \tag{2}$$

The resistance number and the capillary number reflect the fineness of the pore system. In cementitious composites, the capillary number indicates the amount of the binder in the material by neglecting water sorption of the other composite components. However, these values cannot be properly calculated to give a good reflection of the material behavior under capillary suction in the current SF and Oil samples. The reason is high resistance of these

Thus, another method for characterization of these samples is desired which can give a proper comparison between ordinary materials and the modified ones. *EMT* factor will be defined in

**Figure 8** presents the water absorption versus the square root of time for specimens with w/c = 0.36. As seen in the figure, although silica fume does not have a high effect on PF, it reduces capillary suction compared to reference and silane samples. The reason can be described as the finer pore structure as well as less connection between the pores (less percolated), but since it does not repel water or block the pores, the pores will more easily be filled with water than hydrophobized samples in case of submersion. Moreover, the Ref samples have a higher absorption than the other samples since they have less resistance to water transport in the pores. On the other hand, although the rate of mass transport (the slope of the lines in **Figure 8**) in SF and Oil samples is similar in this case, but the absorption in SF samples is larger than Oil samples. This is probably due to the initial moisture content of SF samples. In other words, SF and Oil samples have shown similar resistance to water suction according to **Figure 8**, but since the SF samples had a higher moisture content after drying at 50°C, the moisture content is higher for SF samples after the water suction test. Since the samples have been dried in the oven for 2 weeks at 50°C, it can be judged that the moisture content after this drying period is not very active in water transport during capillary suction test. Therefore, by considering the initial moisture as mass content with low mobility, we can define the mobile capillary suction porosity (*εmcsuc*) as the weight gain after capillary suction excluding initial moisture (**Table 2**). This can be a more realistic estimation of the part of the pore structure which is involved in capillary suction compared to the value obtained after severe drying at

The slope of the line obtained from the first 6 h of suction curve, *K″*, can be an indication of the rate of mass transport in the material. Furthermore, the final mass storage after water suction test could be different for the samples with the same *K″* due to different gradients in the curves after the first 6 h. In other words, *εmcsuc* can be different for the samples with the same *K″* due to different pore structure or pore chemistry. Thus, both *εmcsuc* and *K″* are indications of moisture transport in the material in the abovementioned capillary test. A general experience with capillary suction testing of cement-based materials is that the capillary nick points become less clear at reducing w/b, when adding pozzolana, increasing the initial moisture content and in hydrophobed samples. In such cases, the resistance number and the capillary number are not useful, and therefore a different parameter is proposed here: "effective moisture transport (*EMT*)" factor. *EMT* can be defined as a criterion for the effective mass

\_\_\_\_\_\_\_\_\_

*εmcsuc* × *K''* (4)

*cap* and *Qcap*.

73

Water Sorption of Hardened Cement Pastes http://dx.doi.org/10.5772/intechopen.76378

specimens to water suction which does not give a clear nick point for calculating *t*

105°C which highly affects the pore structure of the material as well.

transport in the material where we have problems of defining a nick point:

*EMT* = √

this part for this purpose.

$$k = \frac{Q\_{op}}{\sqrt{l\_{op}^{r}}} \tag{3}$$

**Figure 8.** Water absorption versus the square root of time of different mixes with the w/c ratio of 0.36 for reference (Ref) samples and the sample containing 1% rapeseed oil (Oil), 1% alkyl alkoxysilane (Si), and 20% silica fume (SF) (w/b = 0.30).

The resistance number and the capillary number reflect the fineness of the pore system. In cementitious composites, the capillary number indicates the amount of the binder in the material by neglecting water sorption of the other composite components. However, these values cannot be properly calculated to give a good reflection of the material behavior under capillary suction in the current SF and Oil samples. The reason is high resistance of these specimens to water suction which does not give a clear nick point for calculating *t cap* and *Qcap*. Thus, another method for characterization of these samples is desired which can give a proper comparison between ordinary materials and the modified ones. *EMT* factor will be defined in this part for this purpose.

**Figure 8** presents the water absorption versus the square root of time for specimens with w/c = 0.36. As seen in the figure, although silica fume does not have a high effect on PF, it reduces capillary suction compared to reference and silane samples. The reason can be described as the finer pore structure as well as less connection between the pores (less percolated), but since it does not repel water or block the pores, the pores will more easily be filled with water than hydrophobized samples in case of submersion. Moreover, the Ref samples have a higher absorption than the other samples since they have less resistance to water transport in the pores. On the other hand, although the rate of mass transport (the slope of the lines in **Figure 8**) in SF and Oil samples is similar in this case, but the absorption in SF samples is larger than Oil samples. This is probably due to the initial moisture content of SF samples. In other words, SF and Oil samples have shown similar resistance to water suction according to **Figure 8**, but since the SF samples had a higher moisture content after drying at 50°C, the moisture content is higher for SF samples after the water suction test. Since the samples have been dried in the oven for 2 weeks at 50°C, it can be judged that the moisture content after this drying period is not very active in water transport during capillary suction test. Therefore, by considering the initial moisture as mass content with low mobility, we can define the mobile capillary suction porosity (*εmcsuc*) as the weight gain after capillary suction excluding initial moisture (**Table 2**). This can be a more realistic estimation of the part of the pore structure which is involved in capillary suction compared to the value obtained after severe drying at 105°C which highly affects the pore structure of the material as well.

The slope of the line obtained from the first 6 h of suction curve, *K″*, can be an indication of the rate of mass transport in the material. Furthermore, the final mass storage after water suction test could be different for the samples with the same *K″* due to different gradients in the curves after the first 6 h. In other words, *εmcsuc* can be different for the samples with the same *K″* due to different pore structure or pore chemistry. Thus, both *εmcsuc* and *K″* are indications of moisture transport in the material in the abovementioned capillary test. A general experience with capillary suction testing of cement-based materials is that the capillary nick points become less clear at reducing w/b, when adding pozzolana, increasing the initial moisture content and in hydrophobed samples. In such cases, the resistance number and the capillary number are not useful, and therefore a different parameter is proposed here: "effective moisture transport (*EMT*)" factor. *EMT* can be defined as a criterion for the effective mass transport in the material where we have problems of defining a nick point:

**Figure 8.** Water absorption versus the square root of time of different mixes with the w/c ratio of 0.36 for reference (Ref) samples and the sample containing 1% rapeseed oil (Oil), 1% alkyl alkoxysilane (Si), and 20% silica fume (SF)

A regression analysis is then carried out based on the data points from 10 min to 6 h for the first/left linear part, and the rest of the points (from 1 to 4 days or alternatively 5 days) for the second/right linear part. Then, the resistance number, *m*, and the capillary number, *k*, will be

**Figure 7.** Regression analysis for calculating the resistance number (*m*) and the capillary number (*k*).

*cap* \_\_\_

√ \_\_\_ *t cap*

*<sup>h</sup>*<sup>2</sup> (2)

(3)

calculated using the following equations:

72 Cement Based Materials

*<sup>m</sup>* <sup>=</sup> *<sup>t</sup>*

*<sup>k</sup>* <sup>=</sup> *Qcap* \_\_\_\_

(w/b = 0.30).

$$EMT = \sqrt{\varepsilon\_{msw} \times K}^{\cdot \cdot} \tag{4}$$

analysis of the slopes were more than 0.93. Since the slopes of the lines for both SF and Oil have been similar during the first 6 h and the rest of the capillary suction test (**Figure 8**), a similar *EMT* value has been obtained for these samples. Furthermore, the difference between the resistance of SF to water suction compared to Si and Ref samples is clearer in **Figure 9**. Moreover, the figure shows that using 1% rapeseed oil has a reduced *EMT* of the hcp with w/c = 0.58 to a level even lower than the reference material with w/c = 0.36. Using 30% SF was as effective as using 1% rapeseed oil in samples with w/c = 0.44. It is worth noting that adding silica fume is more effective in resistance to mass transport than reducing w/c ratio. This is shown in **Figure 10** in which the effect of adding 10, 20, and 30% silica fume in reducing *EMT* is compared to the Ref and Oil samples as a function of water to binder ratio (w/b). However, 1% oil is found to be more effective than using SF.

Water Sorption of Hardened Cement Pastes http://dx.doi.org/10.5772/intechopen.76378 75

Factors affecting the water sorption of hcps such as w/c, pozzolanic materials, and internal hydrophobation were described in this chapter. The hcps with lower w/c have a less total porosity which results in a less water sorption. The amount of pores filled with water under capillary suction (*εcsuc*) was near to total porosity (*εtot*) for plain hcps (Ref samples). In addition, silica fume as pozzolanic material increases resistance to water transport in hcps due to a reduction in the pore size and the connectivity between the pores, but it is not effective in

A minor effect on water sorption was observed using alkyl alkoxysilane showing that this agent which is developed for surface treatment is not suitable for internal hydrophobation. However, rapeseed oil as a hydrophobic agent resulted in an obvious reduction in the water suction of hcps. Pore blocking by oil droplets and denser pore structure can be the other possible reasons for less PF values in some samples. However, the effect of a denser pore structure is not comparable to the water repellency effect of the oil. The behavior of hcps under water suction can be different from cement-based composites due to the effect of ITZ in the

Due to the lack of clear capillary nick points, for the determination of resistance number and capillary number, an alternative parameter "effective moisture transport (*EMT*)" factor was proposed instead in this chapter. The *EMT* factor can be a more comparative measure for denser or hydrophobed samples, especially when the samples are dried at lower temperatures to reduce the effect of drying on pore structure and composition of the material components.

The author gratefully appreciates the Norwegian University of Science and Technology (NTNU) for project funding, professor emeritus Per Jostein Hovde, professor Stefan Jacobsen, and adjunct professor Roar Myrdal at NTNU for their advices as well as the help given by

composite materials and the formation of micro-cracks in hcps during drying.

**6. Conclusions**

reducing the total water suction of hcps.

**Acknowledgements**

engineer Ove Edvard Loraas in the NTNU laboratory.

**Figure 9.** Effective moisture transport factor (*EMT*) for reference (Ref) samples and the sample containing 1% rapeseed oil (Oil), 1% alkyl alkoxysilane (Si), and silica fume (SF).

**Figure 10.** Effective moisture transport factor (*EMT*) for reference (Ref) samples and the sample containing 1% rapeseed oil (Oil) and 10, 20, and 30% silica fume(SF) as a function of water to binder (w/b) ratio.

where *εmcsuc* is the mobile capillary suction porosity and *K″* is the slope of the line obtained from the first 6 h of suction curve. Both *εmcsuc* and *K″* depend on the fineness, connectivity, chemistry, and volume of the mobile capillary suction pores in the material but from different perspectives; thus, a square root of multiplication of these two values can be a criterion for effective mass transport in the material.

**Figure 9** shows *EMT* for different w/c ratios of the mixes. The effect of fine pore structure is shown for both adding the same amount of silica fume to different w/c ratios and increasing the dosage of silica fume for a constant w/c ratio. All correlation coefficients from the regression analysis of the slopes were more than 0.93. Since the slopes of the lines for both SF and Oil have been similar during the first 6 h and the rest of the capillary suction test (**Figure 8**), a similar *EMT* value has been obtained for these samples. Furthermore, the difference between the resistance of SF to water suction compared to Si and Ref samples is clearer in **Figure 9**. Moreover, the figure shows that using 1% rapeseed oil has a reduced *EMT* of the hcp with w/c = 0.58 to a level even lower than the reference material with w/c = 0.36. Using 30% SF was as effective as using 1% rapeseed oil in samples with w/c = 0.44. It is worth noting that adding silica fume is more effective in resistance to mass transport than reducing w/c ratio. This is shown in **Figure 10** in which the effect of adding 10, 20, and 30% silica fume in reducing *EMT* is compared to the Ref and Oil samples as a function of water to binder ratio (w/b). However, 1% oil is found to be more effective than using SF.
