## 2 Materials and Methods
### The Average Height of the Water Front  
Capillary absorption [22] is the prime mechanism in moisture transport when the material is only partially wetted, and is usually described by the Lucas-Washburn equation [23]  
\[\mathrm{h}\ =\ \mathrm{k}\sqrt{\mathrm{t}}, \tag{2}\]  
where h is the average height of the water front (mm), t is the wetting time (min) and k is the capillary coefficient (mm min\({}^{-1/2}\)). The capillarity coefficient covers the relationship between the solid and liquid phases, as well as the pore structure inside the solid phase, and should be determined experimentally [24].  
The water front average heights of the seven samples at different times are shown in Figure 14. The hollow dots in Figure 14 represent the data obtained from the neutron imaging experiment (see Section 2 for the method), and the straight line is obtained by using the experimental data to fit the Lucas-Washburn equation. The equation result, a straight line, is also given in Figure 14. The value of R\({}^{2}\) is all above 0.99 for the seven samples. Consequently, at least the first 4 hours of water absorption, the Lucas-Washburn equation fits well. This is evidence that capillary absorption is the main mechanism when the sample is not saturated.  
The capillary coefficients for the seven samples are listed in Table 2. The capillary coefficient difference between our sample PC04 and the P42 sample in [25] (the composition is exactly the same, the water-cement ratio w/c is 0.42 and 0.4, respectively) is less than 10%, which supports our experimental results. Table 2 reflects the difference in water absorption of the seven samples, which can be ranked as follows: MP20 > MP10 > MP30 > PC04 > FA10 > FA30 > FA60. Therefore, the water absorption in cement paste is enhanced with the addition of marble powder, while it is reduced with the addition of fly ash. This may be an experimental example of the fly ash effect [26].  
Figure 14: The average height of the water front as a function of the square root of time for the seven samples using neutron imaging.  
We can also obtain the rising speed of the water front as a function of time shown in Figure 15. The same pattern appears in the seven samples: water absorption is rapid in the first hour and then gradually slows down. The differences in water absorption in the seven samples can also be obtained from Figure 15.  
It is worth mentioning that the Lucas-Washburn equation can be applied to the water uptake at the beginning and yet not be reasonable for long-term uptake. This anomaly has already been noticed by [PERSON] et al. [27; 28], which is explained by a new hydration. The new hydration takes place in the presence of water and causes an increase in effective grain size and tends to block the micropores. There are also some recent studies. [PERSON] et al. [29] proposed a theoretical model wherein the capillary absorption coefficient is linear with \(\lx@math@degree 0.25\), and pointed out that the main reasons for the deviation from \(\lx@math@degree 0.5\) are the hygroscopicity of calcium silicate hydrate and the swelling effect in the process. [PERSON] et al. [30] gave the physical evidence of swelling as the cause of anomalous capillary water uptake by cement-based materials. [PERSON] et al. [31] proposed a model in which the effective capillary diffusion coefficient depends on the instantaneous pore size distribution. In [32], long-term water uptake measurements were performed, revealing the primary and secondary periods of capillary uptake, which are well described by a bilinear relationship with the fourth root of time. In the future, we will conduct a longer water absorption experiment to study the deviation from the Lucas-Washburn equation.