# Monitoring of the Variation in Pore Sizes of Woven Geotextiles with Uniaxial Tensile Strain
## 5 Variation in Pore Size Distribution  
The design pore size distribution encloses a scope of guided pore sizes for retention and permeability under tensioning. In order to identify the effect of different pore sizes on the pore size variation with uniaxial tensile strain, the pore size distribution frequency and pore size distribution scale are supposed to be specified. Therefore, the experimental pore sizes of geotextile W120c are analyzed. Figure 9 illustrates the distributions of unstrained pore sizes and pore sizes under the uniaxial tensile strain of 9%. The \(x\)-axis indicates the values of pore-opening sizes. The left \(y\)-axis illustrates the frequency distribution of pore sizes and the right \(y\)-axis shows the cumulative frequency of pore-opening sizes. The \(x\) values ranging from 0 to 1 mm are divided into 20 groups on average. The number of pore sizes in each group is counted to calculate the frequency distribution of geotextile W120c. As shown in Figure 9, the light orange histogram and light orange curve show that unstrained pore-opening sizes have a Gaussian distribution which is a symmetrical bell-shaped curve. The dark orange curve demonstrates the cumulative frequency of unstrained pore-opening sizes. The characteristic pore-opening sizes O950, O500, and O100, obtained by using image analysis, describe the pore diameters for which 95%, 50%, and 10% of the remaining pore diameters are smaller for unstrained W120c. The characteristic pore size O500 has the approximately largest distribution proportion among all pore-opening sizes of unstrained geotextile W120c. The dark green curve describes the cumulative frequency of pore-opening sizes which are subjected to the uniaxial tensile strain of 9%. The characteristic pore-opening sizes O\({}_{95}\)\({}^{\text{\%}}\), O\({}_{95}\)\({}^{\text{\%}}\), and O\({}_{10}\)\({}^{\text{\%}}\), demonstrate the pore diameters for which 95%, 50%, and 10% of the remaining pore diameters are smaller for geotextile W120\({}^{\text{c}}\) under the tensile strain of 9%. Figure 9 illustrates the pore size-frequency distribution under the uniaxial tensile strain of 9% by the light green histogram and light green curve. The pore-opening sizes subjected to the tensile strain of 9%, exhibit a bell-shaped Gaussian distribution curve which is similar to the unstrained Gaussian distribution curve. For geotextile W120\({}^{\text{c}}\), the characteristic pore size O\({}_{50}\)\({}^{\text{\%}}\) has the largest distribution proportion among all pore sizes subjected to the uniaxial tensile strain of 9%. There is a good consistency with pore-opening size Gaussian distribution of woven geotextile W120\({}^{\text{c}}\) and pore size distributions of the other tested geotextiles. The bell-shaped Gaussian distribution curves of unstrained pore-opening sizes and strained pore-opening sizes of woven geotextiles can be expressed by the Equation (1):  
\[y=\left[y_{0}+\frac{A}{w\cdot\sqrt{\frac{\pi}{4\ln(2)}}}\cdot e^{\frac{-4\ln (2)(x-x_{c})^{2}}{w^{2}}}\right]\times 100\% \tag{1}\]  
where \(y\) is the frequency of various pore-opening sizes; \(y_{0}\) is the frequency distribution of pore sizes ranging from 0 to 0.1 mm; \(x\) is the pore-opening size; \(x_{c}\) is the expected pore size value of the maximum frequency distribution; \(A\) is the amplitude of the frequency distribution and \(w\) is the variance of Gaussian distribution curves. Table 2 suggests that uniaxial tensile strains can influence the Gaussian distribution curve parameters of geotextile W120\({}^{\text{c}}\). \(x_{c}\) is almost the same as the value of medium pore size of woven geotextiles, which has a larger value in the late period of tensile strain. However, the value of \(x_{c}\) has a slight fluctuation under the low tensile deformation. Meanwhile, the largest distribution frequency \(y\) of \(x_{c}\) suggests that the medium pore size has the largest distribution proportion among all pore sizes. The distribution frequency of medium pore size increases as uniaxial tensile strain increases.