Laterally constrained uniaxial tensile tests were performed on polyester continuous filament needle-punched geotextiles with different specifications. The mass per unit area of the geotextiles was 101 g/m² and 365 g/m², respectively referred to as NW101 and NW365. The main properties of these geotextiles are shown in Table 1.

Li et al. (2024) invented an instrument capable of applying uniaxial tensile and laterally constrained uniaxial tensile on geotextiles, as shown in Figure 1a. The device consists of a pair of upper and lower clamping devices, with two smooth rods extending vertically from the top through pre-cut holes on clamping device and linear slide. Lateral constraint of the geotextile was achieved by adjusting the quick clamps fixed on the linear slide. Subsequent application in tests on nonwoven geotextile revealed insufficient clamping force, leading to slippage, which prompted modifications to the instrument in this study. Additionally, based on the demand for collection of data on the relationship between lateral constrained force and vertical strain, corresponding improvements were made to the instrument, as shown in Figure 1b.

Five clamps were uniformly distributed between the upper and lower clamping devices, securing the geotextile on both sides with bolts. Moreover, these clamps were equipped with force sensors, allowing for the synchronous measurement of lateral constrained forces. In the geotextile lateral tensile test, a 250 mm wide and 300 mm high geotextile specimen was tested, as per T/ZWEIA 001-2023. The specimens were clamped 50 mm on the upper and lower sides, and 25 mm on each of the left and right sides, with a geotextile section of 200 mm wide and 200 mm high subjected to tension, as shown in Figure 1b. To ensure consistency with previous studies and based on strain levels reported in the literature (Rowe and Myleville, 1990; Schimelfenyg et al., 1990; Won and Kim, 2007; Izadi et al., 2018; Palmeira et al., 2019), a strain loading rate of 20 mm/min was applied during testing. The geotextiles were stretched to four strain levels: 5%, 10%, 15%, and 20%. After reaching the specified strain, a self-made acrylic clamping ring with an inner diameter of 70 mm was used to secure the geotextile, preventing it from rebounding (Figure 1b), for subsequent pore size characteristic testing.

According to the relevant specifications released by the American Society for Testing and Materials (ASTM), dry sieving test (ASTM D4751-20, 2020) and bubble point test (ASTM D6767-12, 2012) are the two most used methods for measuring the pore characteristics of geotextiles. However, due to factors such as electrostatic effects, particle shape, and sieving equipment, the repeatability of dry sieving results is poor and the errors are significant (Bhatia and Smith, 1994; Blond et al., 2015). Palmeira and Trejos Galvis (2018) tested a steel wire mesh with known pore sizes using the BBP test, and the difference between the actual pore size and the BBP result was less than 5%, indicating that the measurement accuracy of this method can meet the purpose of this study. Moreover, the currently available instruments for this test can achieve fully automatic measurement, thereby reducing the corresponding operational errors.

Therefore, the pore size distribution and characteristic pore size (O _n) of nonwoven geotextile samples under specified tensile strain conditions were measured using the BBP test, as per ASTM D6767. Here, O _n represents the n percentage of pores smaller than that size (Palmeira et al., 2019; Li et al., 2023). The experimental apparatus used was the BSD-PB bubble pressure method membrane pore size analyzer produced by Bester Instrument Co., Ltd. The geotextile samples were first completely wetted with anhydrous ethanol (surface tension at 20°C is 21.90 mN/m), and then air was used to squeeze the infiltrating liquid in the sample pores. As the airflow velocity gradually increased, the pressure in the air increased, and the infiltrated liquid in the largest pores was first pushed out. Then, as the pressure increased, the pore size decreased, and the infiltrating liquid in the pores was successively pushed out. By testing the relationship between gas pressure and flow rate, pore size distribution data can be obtained according to the Washburn equation (Washburn, 1921).

Figure 2 shows the variation of pore size distribution curves on specimens of geotextile NW100 and NW350 under lateral constrained uniaxial tensile strains ranging from 0% to 20%. The PSD curves for two geotextiles all exhibited an overall shift to the right under tensile strain, indicating an enlargement of all pores. The shapes of the PSD curves also demonstrated insignificant changes, suggesting a relatively uniform change in all pores.

However, for NW100 under 5% strain, the PSD curve corresponding to the cumulative frequency below 50% was located on the far right side of the other curves, indicating larger pore sizes than under other strains. Additionally, for NW350, the PSD curve under 20% strain was located on the left side of the curve under 15% strain for the cumulative frequency below 60%, indicating smaller pore sizes than under 15% strain. Therefore, the effect of lateral constrained tensile strain on the pore size characteristics of the geotextiles cannot be analyzed merely by observing the pore size distribution curves. The characteristic pore sizes were determined in this study using the PSD curve to quantify variations in pore size.

The O ₉₅ is widely used in current application standards for geotextiles to evaluate and design geotextile filters. Additionally, the importance of other characteristic pore sizes representing different-sized pores has gradually been recognized by scholars (Wu and Hong, 2016; Palmeira et al., 2019; Li et al., 2024a). Therefore, different characteristic pore sizes O _n (with n = 10%, 30%, 50%, 80%, and 98%) were determined as shown in Figure 3.

It can be noted that with the increase of tensile strain, the five characteristic pore sizes show a relatively stable increasing trend. When the tensile strain increased from 0% to 20%, the O ₉₅, O ₈₀, O ₅₀, O ₃₀, and O ₁₀ of NW100 increased by 9.30%, 14.58%, 17.03%, 20.72%, and 26.38%, respectively, while the corresponding characteristic pore sizes of NW350 increased by 18.05%, 27.21%, 13.43%, 28.02%, and 22.21%, respectively.

With respect to an unstrained specimen, for a tensile strain of 5%, the characteristic pore sizes of NW100 and NW350 exhibited opposite trends. The characteristic pore sizes of NW100 increased sharply under a tensile strain of 5% and then gradually increased with further strain (O ₉₅, O ₈₀, O ₁₀) or first decreased and then increase (O ₅₀, O ₃₀). In contrast, the characteristic pore sizes of NW350 steadily increased or even first decreased and then increased under tensile strain. For example, O ₃₀ value decreased by 5.45% when the tensile strain increased from 0% to 5% and then increased by 13.16% when the tensile strain increased from 5% to 10%.

It should be noted that in the previous study of Li et al. (2024c), experimental investigations and numerical simulations were conducted on the pore size characteristic changes of nonwoven geotextiles under uniaxial tensile strain, with results showing certain similarities to the lateral constrained uniaxial tensile test findings in this study.

The uniaxial tensile tests revealed that the equivalent pore size of nonwoven geotextiles exhibited an initial decrease followed by an increase or a continuous increase within the 0%–20% tensile strain range, with the transition point occurring in the 0%–10% strain interval. Similarly, fluctuations in equivalent pore size were observed in the early stages of lateral constrained uniaxial tensile tests (e.g., an initial increase followed by a decrease or vice versa), while a general increasing trend with strain was noted in later stages. This phenomenon may be explained by the pore size characteristic variation model proposed by Li et al. (2024c): under small strain conditions, fiber reorientation leads to adjustments in pore shape, resulting in either an increase or decrease in pore size. As the confined uniaxial tensile strain further increases, the overall pore shape of the nonwoven geotextiles undergoes minimal changes, with pore enlargement becoming dominant and thus leading to an increasing trend in pore size in subsequent stages.

Regarding the inconsistency between lateral constrained uniaxial and uniaxial tensile tests in the early stages, as well as the fluctuation in equivalent pore size for both NW100 and NW350 nonwoven geotextiles when lateral constrained uniaxial tensile strain exceeds 15%, this may be attributed to the necking effect in tensile specimens. As the stretching process progresses, localized deformation induces stress concentration, prompting fiber rearrangement and consequently altering the equivalent pore size. This observation aligns with the findings of Palmeira et al. (2019) on the plane strain behavior of nonwoven geotextiles. It can be noted that when uniaxial tensile strain exceeds 10%, the equivalent pore size begins to significantly deviate from results obtained under lateral constraint-free conditions, attributing this discrepancy to the necking effect.

Combining the stochastic and geometrical probability approaches, the cumulative probability of a particle with diameter r passing through the layers of unstrained nonwoven geotextiles F r is shown in the following Equations 1–5 (Rawal, 2010; Rawal and Agrahari, 2011): F r = 1 − 1 + ω r + ω 2 r 2 2 e − ω r N (1) ω = 4 V f K α π d f (2) V f = μ g ρ f T g (3) K α = ∫ − π 2 π 2 cos ⁡ φ χ φ d φ (4) N = T g d f (5) where ω is the coverage parameter; N is the number of layers; V f is the volume fraction; K α is the directional parameter indicating when the average distance between the two bonds in projected on planar direction ( α ; d f is the diameter of the fiber; ρ f is the density of the fiber; χ φ is the distribution function of initial fiber orientation angle φ . The details of the parameters can be found in the literature (Rawal, 2010; Rawal and Agrahari, 2011).

Considering the Poisson effect, the dimensions of the geotextile will change under lateral constrained uniaxial tensile strain ε , as shown in Figure 4. Therefore, a ε = a (6) b ε = b 1 + ε (7) T g ε = T g 1 − ν ε 1 − ν (8) where a and a ε are the width of the nonwoven geotextile before and after stretching (Equation 6), b and b ε are the length of the nonwoven geotextile before and after stretching (Equation 7), T g ε is the thickness of the geotextile under the lateral constrained uniaxial tensile strain (Equation 8), and ν is the Poisson’s ratio.

Hence, the mass per unit area of geotextile μ g ε , the volume fraction V f ε , and the number of layers N ε under tensile strain can be modified to the following Equations 9–11. μ g ε = μ g · a b a ε b ε = μ g 1 + ε (9) V f ε = μ g ε ρ f T g ε (10) N ε = T g ε d f (11)

Consider a fiber oriented at an initial orientation angel φ , with respect to the loading direction and reorientated to φ ε under lateral constrained uniaxial tensile loading based the affine deformation of fiber, as shown in Figure 5. ε = x s (12)   φ ε = A B O A ′ = s · ⁡ tan ⁡ φ x + s (13)

Diving Equation 13 by s from Equation 12, the fiber orientation can be expressed as Equation 14   φ ε = tan − 1 tan ⁡ φ 1 + ε (14)

Therefore, the directional parameter K α ε can be updated based the reorientation of fibers during the application of tensile loading as Equation 15: K α ε = ∫ − π 2 − α π 2 − α cos ⁡   φ ε χ   φ ε d   φ ε (15)

The coverage parameter ω ε under tensile strain can also be updated as Equation 16: ω ε = 4 V f ε K α ε π d f (16)

Finally, the cumulative probability of a particle with diameter r passing through the layers of strained nonwoven geotextiles F r ε can be expressed: F r ε = 1 − 1 + ω ε r + ω ε 2 r 2 2 e − ω ε r N ε (17)

The parameters contained in Equation 17 were recorded in Tables 1, 2. The in-plane fiber orientation distributions of geotextiles were obtained utilizing the two-dimensional digital analysis and calculated using Equation 4 (Li et al., 2023; 2024b). The fiber diameter and Poisson’s ratio were measured and recorded in Table 2 (Li et al., 2024b). Based on these parameters, the theoretical PSD curves of geotextiles were calculated according to Equation 17.

Figure 6 presents the variation of theoretical PSD curves with lateral constrained uniaxial tensile strain. As the tensile strain increases, the PSD curves of both geotextiles steadily shift towards the larger direction, and the shape of the curves remains consistent. This trend is generally consistent with the experimental results. Moreover, since it is a theoretical model, the PSD curves obtained were very smooth, with consistent shapes and intervals of change with strain, in contrast to the uncertainties present in the actual experimental process.

Figure 7 compares the theoretical results for the O _n (with n = 10%, 30%, 50%, 80%, and 95%) values of NW100 and NW350 under lateral constrained uniaxial tensile strains of 0%, 5%, 10%, 15%, and 20% with the results of the BBP tests.

For NW100, the theoretical values of the five characteristic pore sizes all show an increasing trend with strain. Within the 0%–20% strain range, the theoretical values of characteristic pore sizes O ₁₀, O ₃₀, O ₅₀, and O ₈₀ were all smaller than the BBP-based values. For O ₉₅, the theoretical and BBP-based values were very close, with an error within 12.04%. Moreover, the theoretical model can accurately predict the variations in the experimental O ₉₅, the correlation coefficient between the two is 0.90.

For NW350, the theoretical values of the five characteristic pore sizes also show an increasing trend. Within the 0%–20% strain range, the theoretical values of the five characteristic pore sizes are all smaller than BBP-based values. For O ₉₅, the error between the two is within 31.76%. However, the theoretical model can also accurately predict the trend of the experimental O ₉₅, with a correlation coefficient of 0.9962.

O ₉₅ was widely used in engineering, but the theoretical O ₉₅ values obtained cannot completely match the experimental values. Tang et al. (2020) measured the initial O ₉₅ value of the unstrained geotextiles and used the difference between this experimental value and the theoretical value to correct the theoretical O ₉₅ error. Therefore, the model proposed in this study is effective, as it can accurately predict the trend of O ₉₅ with increasing lateral constrained uniaxial tensile strain, providing a reference for filter design under engineering strain.