Permeability test of geotextile-soil system under different sand filling heights

2.1. Test device

In this test, a self-made permeameter was used to investigate the changes in the permeability characteristics of geotextile-soil systems under different sand-filling heights by varying the sand-filling height. The actual device and schematic diagram of the test setup are shown in Fig. 1 and Fig. 2, respectively. The device is a constant-head permeameter capable of providing unidirectional water flow and consists primarily of a permeameter and a water head supply system. The permeameter is composed of two cylindrical tubes: the upper tube has a diameter of 200 mm and a height of 300 mm, while the lower tube has a diameter of 200 mm and a height of 100 mm. The upper tube and lower tube are connected using a flanges and screws. Foam adhesive tape is applied at the flange connection to ensure tight contact between the fabric and the cylinder, preventing air ingress and water leakage at the device's connection points. The water head supply system consists of a water storage chamber and an overflow chamber to ensure the proper operation of the constant-head test.

Fig. 1Physical drawing of test device

Fig. 2Diagram of test device

2.2. Test materials

2.2.2. Soil sample

The soil sample used in this test was quartz sand. The mass distribution ratios of particles with various grain sizes are detailed in Table 2, and the corresponding particle size distribution curve is shown in Fig. 3.

Table 2Mass proportion of particles with different grain sizes

Particle size / mm	≤ 0.03	0.03-0.075	0.075-0.15	0.15-0.3	0.3-0.6	0.6-1.18
Mass proportion	0 %	10 %	10 %	10 %	40 %	30 %

Fig. 3Grain size distribution curve of the filling sand

2.3. Test process

The test apparatus and materials were prepared to conduct a constant head permeability test using a unidirectional head permeability apparatus, ensuring that the water head height remains constant. The specific steps of the test are as follows:

(1) The geotextile was cut into a diameter of 200 mm using a soldering iron (compared to traditional cutting machines, the soldering iron provides smooth cuts and minimizes damage to the geotextile).

(2) The cylinders were wiped with alcohol and then cleaned with a dry, clean cloth.

(3) Foam tape was applied to the top and bottom edges of the upper cylinder, and screws were used to connect the upper and lower cylinders while fixing the geotextile between them.

(4) The pre-weighed sand was poured into the upper cylinder and gently leveled with a brush. The inlet valve was then opened slightly to allow a small flow of water into the apparatus until the required water level was reached. The glass cover was placed on top, and the two side holes were connected to the pressure measurement tubes using soft pipes.

(5) The apparatus, which had been soaked for 24 hours, was manually deaerated to remove air bubbles. Valve B was connected to the water head supply device via a rubber tube, while inlet D was connected to the water supply system. A constant water flow was maintained, and water exiting the outlet was collected in a bucket. The flow rate over two minutes was recorded, and the readings from the pressure tubes were noted until the flow rate stabilized. The permeability coefficient corresponding to each time interval was calculated;

(6) Different geotextiles were replaced, or the sand fill height was adjusted, and the above test steps were repeated.

3.1. Test result

Derivation of the formula for the permeability coefficient $k$:

According to Darcy’s law:

where $v$ represents the water flow velocity.

Where the hydraulic gradient is:

where $H$ represents the hydraulic head difference, and $L$ represents the seepage path.

From Eqs. (1) and (2), we get:

Under constant head conditions, tests were conducted on three types of geotextiles with different mass per unit area to investigate the effect of different sand filling heights (specific parameters are shown in Table 3) on the permeability coefficient $k$ of each geotextile.

Fig. 4Variation of the permeability coefficient with time for each geotextile-soil system at different sand filling heights

a) W100

b) W120

c) W150

Fig. 4 shows the variation of the permeability coefficient over time for the W100, W120, and W150 geotextile-soil systems. As shown in Fig. 4(a), under different sand filling heights, the permeability coefficient of the W100 geotextile-soil system exhibits a consistent trend over time, initially decreasing and then stabilizing. This phenomenon can be attributed to the following: under the scouring action of unidirectional water flow, fine particles in the quartz sand migrate downward. However, some fine particles that would otherwise be lost are intercepted by the geotextile, gradually leading to clogging above the geotextile and the formation of a structurally stable filtration system, eventually resulting in a stable permeability coefficient. It can also be observed that once the permeability coefficient of the W100 geotextile-soil system stabilizes, its stable value increases with the height of the sand filling. Since the permeability coefficient of the geotextile-soil system is determined by both the geotextile and the quartz sand, and the geotextile specifications and the grain size distribution of the quartz sand remain constant, the only factor influencing the permeability coefficient of the W100 geotextile-soil system is the sand filling height. The trends shown in Figs. 4(b) and 4(c) are consistent with those in Fig. 4(a). Therefore, the following analysis focuses on the impact of sand filling height on the permeability characteristics of the geotextile-soil system.

3.2. The influence of sand filling height on the permeability characteristics of geotextile-soil systems

Fig. 5 presents the relationship between sand filling height and the permeability coefficient of the geotextile-soil system. It can be observed from the figure that as the sand filling height increases, the permeability coefficients of the three geotextile-soil systems also increase. However, the rate of increase gradually slows down, specifically showing a larger rate of increase when the sand filling height is less than 5 cm and a smaller rate of increase when it exceeds 5 cm. In comparison to the permeability characteristics of pure sand, the permeability coefficient curves of the geotextile-soil systems approach the straight-line permeability coefficient of the pure sand system from below as the sand filling height increases. This phenomenon can be preliminarily explained as follows: under the action of unidirectional water flow, the geotextile obstructs the movement of sand particles, thereby influencing the permeability performance of the filled sand. The interaction between the geotextile and the sand forms a filtration structure, ultimately resulting in the permeability coefficient of the geotextile-soil system being lower than that of pure sand. However, since the geotextile has a limited ability to affect the permeability performance of pure sand, its influence is more pronounced on the sand within 5 cm above the geotextile, while the effect on sand beyond 5 cm is relatively smaller.

Fig. 5Variation of the permeability coefficient of the geotextile-soil system with sand filling height

To explore the reasons behind the reduction in the permeability of the geotextile-soil system caused by an increase in the unit mass of geotextiles, a hypothesis was proposed: the water permeability of geotextiles may significantly influence their permeability characteristics, and water permeability is closely related to porosity and permeability rate [30-31]. To verify this hypothesis, Matlab software was used to perform image processing on W100, W120, and W150 geotextiles, each with dimensions of 250 cm×250 cm, for a qualitative analysis of their water permeability. The results are shown in Fig. 6.

From Fig. 6, it can be observed that the pore distribution of geotextiles exhibits significant non-uniformity, with some areas appearing dense and completely pore-free. This phenomenon is primarily attributed to two factors: first, limitations in production processes affecting the uniformity of pore distribution in the fabric; second, compression that may occur during transportation and storage, causing non-directional displacement of woven threads, which further exacerbates the non-uniformity of pore distribution. When the image resolution was set to 2500×2500 pixels and the corresponding program was executed, the results indicated that the porosity of the geotextiles decreased as their unit mass increased. Based on this, it can be inferred that the greater the unit mass of the geotextile, the lower its porosity, and consequently, its water permeability diminishes.

Fig. 6Geotextile samples of different specifications

a) W100Geotextile sample

b) W120Geotextile sample

c) W150Geotextile sample

To further verify the above inference, a variable head permeability test was conducted. By measuring the variation of the water head difference over time, the relationship curves shown in Fig. 7 were obtained, which were used to perform a quantitative analysis of the water permeability of the geotextiles. This experiment provided more compelling evidence for studying the permeability characteristics of geotextiles by quantifying their water permeability.

Fig. 7Fitted curve of the head difference versus time according to Eq. (14)

According to Darcy’s law:

where the hydraulic gradient is:

It can be obtained:

Decree:

where, $\phi$ is the water permeability.

Obtained:

From the integral relationship:

where:

Substituting into Eq. (8) obtained:

Integrating Eq. (11) obtained:

Eliminating the constant of integration obtained:

Simplifying obtained:

where:

Subsequently, the data in Fig. 7 were fitted using Eq. (14), resulting in the permeability rate relationship graph for the three geotextiles shown in Fig. 8. The results indicate that the permeability rate of W100 is significantly higher than that of W120, while the permeability rate of W120 is higher than that of W150. This trend clearly demonstrates that, under a constant sand fill height, the lower the unit mass of the geotextile, the higher its porosity and permeability rate, leading to better permeability performance and stronger seepage characteristics. Therefore, it can be concluded that the pore structure of the geotextile plays a crucial role in its own permeability and the permeability of the geotextile-soil system. These research results validate, both qualitatively and quantitatively, that the water permeability of the geotextile has a significant impact on the permeability of both the geotextile itself and the geotextile-soil system.

Fig. 8Permeability relationship diagram for each geotextile

3.3. Research on the influence of geotextiles on the permeability characteristics of geotextile-soil systems

Considering that the movement of sand particles under the action of water flow can affect the permeability coefficient $k$, further investigation into the movement pattern of sand particles was conducted. A formula was derived, and the permeability coefficient of each sand layer was calculated (Fig. 9). The layers are defined as follows: from bottom to top, the ranges 0-1 cm, 1-3 cm, 3-5 cm, 5-7 cm, 7-9 cm, and 9-11 cm are designated as layers A, B, C, D, E, and F, respectively.

Derivation of the permeability coefficient formula for each sand layer.

According to Darcy’s law:

where $v_1$ represents the flow velocity corresponding to the water passing through layer A; $k_A$ represents the permeability coefficient of layer A; $j_1$ represents the hydraulic gradient corresponding to layer A:

where $v_2$ represents the flow velocity corresponding to the water passing through layer B; $k_B$ represents the permeability coefficient of layer B; $j_2$ represents the hydraulic gradient corresponding to layer B.

Where the hydraulic gradient is:

where $H_1$ represents the head difference corresponding to layer A; $L_1$ represents the seepage path corresponding to layer A:

where $H_2$ represents the head difference corresponding to layer B; $L_2$ represents the seepage path corresponding to layer B.

Because:

From Eqs. (16) and (18), we get:

Additionally, since:

Substituting Eqs. (19), (22), (23), and (24) into Eq. (17) yields:

Similarly, the permeability coefficients of layers C, D, E, and F can also be determined.

Fig. 9 shows the relationship between the permeability coefficients of the sand-filled layers for each geotextile. It can be observed from the figure that the permeability coefficients of the sand-filled layers initially increase, then decrease, and eventually stabilize. The permeability coefficient reaches its maximum in layer C, while the coefficients in layers A, B, D, E, and F are relatively smaller. The occurrence of this phenomenon can be explained as follows: Under the influence of water flow, the sand samples near the geotextile (layer A) are affected by the presence of geotextile pores. The fine particles in layer A are subjected to a downward net force, causing the fine particles to either pass through the geotextile or become trapped in its pores. Once a certain amount of fine particles in layer A are lost, a channel of fine particles gradually forms in this layer, leading to the migration of fine particles from layer B into layer A under the influence of water flow. These fine particles further clog the fine particle channels in layer A and the pores of the geotextile. When the fine particles in layer B are lost to a certain extent and form a similar particle channel to that in layer A, the fine particles in layer C begin to move downward. These particles also block the fine particle channels in layers B and A, as well as the geotextile pores. As the degree of particle clogging increases, the flow velocity of water gradually decreases, reducing the force exerted by the water flow on the fine particles. When the downward movement of fine particles in layer C reaches a certain stage, the force of the water flow is insufficient to mobilize the fine particles in layer D downward, resulting in the inability of layer D’s fine particles to fill the fine particle channels in layer C. At this stage, the movement of fine particles within the sand samples tends to reach equilibrium. Fine particle loss from layers D, E, and F is minimal. The fine particle channels in layer A and the pores of the geotextile are filled with fine particles from layers B and C, which results in layer A having the smallest permeability coefficient, while layer C has the largest permeability coefficient, and layer B’s coefficient lies in between. In contrast, the fine particle loss in layers D, E, and F is relatively minor, leading to permeability coefficients in these layers being lower than those of layers A and B but higher than that of layer C. However, under the influence of water flow, a small amount of fine particles in layers D, E, and F inevitably begins to migrate downward, starting from layer D. As the number of layers increases, the amount of fine particle loss decreases progressively, causing the permeability coefficients of layers D, E, and F to decrease. This leads to the observed pattern where the permeability coefficient initially increases, then decreases, and finally stabilizes.

Fig. 9Permeability relationship diagram for each geotextile

3.4. The migration pattern of particles within the apparatus

To investigate the changes in permeability coefficients of each sand layer, W120 was taken as an example. The sand from each layer was extracted and tested for its gradation after the test, following the specific testing process below: After completing the permeability test, the water in the apparatus was drained completely, and the setup was left to stand for 12 hours, allowing the sand to settle. The height of the sand layer was measured using a right-angle ruler, and sand samples were extracted proportionally based on the measured layer heights. During the layering process, the right-angle ruler was consistently used to ensure that the height of each layer was measured with millimeter-level precision. For sampling, ring knives of consistent diameter were used to take three-point samples from each sand layer, ensuring that the sampling locations were evenly and reasonably distributed. After sampling, the samples were labeled and placed in an oven for drying. Once dried, the samples were weighed to determine their mass. Subsequently, sieves with different mesh sizes were used to separate the sand particles by size range. For particles trapped in the sieve mesh, a soft brush was used to gently remove them, and they were placed in the corresponding location. After sieving, the sand samples were weighed again, and the gradation of each layer was calculated based on the weighing results. During the sieving process, operations were conducted as slowly as possible, and the sieve cover was kept tightly sealed to prevent fine particles from escaping and affecting the accuracy of the experimental results. A high-precision electronic balance was used for weighing to ensure the reliability and accuracy of the data. The test results are shown in Fig. 10, which shows the particle size distribution curves of sand layers from A to F. From the figure, observed that after the test, fine sand particles in each layer moved downward, while the proportion of coarse sand remained largely unchanged. Compared to the initial gradation, the proportion of fine sand was the lowest and that of coarse sand was the highest in layer C, resulting in the highest permeability coefficient for layer C. In contrast, layer A had the highest proportion of fine sand, leading to clogging and thus the lowest permeability coefficient. The proportion of fine sand in layer B was slightly lower than that in layer A. For layers D, E, and F, a proportion of the fine sand was lost compared to the initial gradation, but the amount of loss was less than that of layer C, while the proportions of other sand sizes remained largely unchanged. Therefore, the results align with the reasoning proposed by the author.

Fig. 10Permeability relationship diagram for each geotextile

A series of empirical formulas for the permeability coefficient $k$ have been derived based on previous research, including the Hazen formula [7] $k=C{d}_{10}^2$ (where $C$ is a dimensionless coefficient), the Zhu Chonghui formula [11] $k=Re{C}_u{C}_c{d}_{10}^2$ (where $Re$ is a dimensionless coefficient), and the Man Xiaolei formula [24]$k=P{d}_{50}^2{C}_c/C_u$ (where $P$ is a dimensionless coefficient). These formulas were used for theoretical calculations (specific parameters are shown in Table 4 and Table 5), and the resulting empirical values were compared with experimental values in the curve shown in Fig. 11. As observed in the figure, regardless of which formula was used, the results exhibited a trend of initially increasing and then decreasing, which aligns closely with the experimental results. This consistency also verifies the accuracy of the testing method.

Fig. 11Comparison of permeability coefficient test values and empirical values for each sand layer