**2.2. Theory of normal permeability on laminar geotextile composites**

Nonwoven geotextiles are a kind of materials with high porosity and have the three-dimen‐ sional structure with different fiber orientations. It is assumed that the pore shapes of geotex‐ tiles are very narrow and tube typed, and therefore, the permeability of geotextiles depends on the pore-size distribution. The structural model of laminar geotextile composites is considered as an assembly of narrow tubes, which join each other with different fiber-packing densities. Figure 17 shows the two schematic diagrams of laminar geotextile composites and the assembly to have the different fiber-packing densities. From Darcy's law, water permea‐ bility of laminar geotextile systems could be written as follows:

$$\frac{\mathbf{Q}}{A} = \frac{h}{\frac{T\_1 \cdot K\_2 + T\_2 \cdot K\_1}{K\_1 \cdot K\_2}}\tag{1}$$

where *Q* = quantity of flow, mm3

*A* = cross-sectional area of geotextile, mm2 The coefficient of cross-plane permeability of laminar geotextile composites, *K*, could be calculated

*A* = cross-sectional area of geotextile, mm<sup>2</sup>

*h* = head of water on the geotextile, mm by:

*T* = the thickness of geotextile, mm

*K*1, *K*2 = the coefficient of cross-plane permeability of upper- and lower-layer geotextiles, respectively, cm/sec *T T <sup>K</sup>*

The coefficient of cross-plane permeability of laminar geotextile composites, *K*, could be calculated by: 1 2 12 21 1 2 *TK TK K K* (2)

**Figure 17.** Schematic diagrams of (a) laminar geotextile composites and (b) structural model of tubes with different fiber-packing densities.

Nanotechnology Formulations and Modeling of Hydraulic Permeability Improvement for Nonwoven Geotextiles http://dx.doi.org/10.5772/61997 311

Permittivity, Ψ, could be written as

12 21 1 2

*K*1, *K*2 = the coefficient of cross-plane permeability of upper- and lower-layer geotextiles,

The coefficient of cross-plane permeability of laminar geotextile composites, *K*, could be calculated

The coefficient of cross-plane permeability of laminar geotextile composites, *K*, could be

1 2 12 21 1 2

×

(a)

(b)

**Figure 17.** Schematic diagrams of (a) laminar geotextile composites and (b) structural model of tubes with different

*T T <sup>K</sup> TK TK K K*

<sup>+</sup> <sup>=</sup> × +×

(1)

(2)

×

*K*1, *K*2 = the coefficient of cross-plane permeability of upper- and lower-layer geotextiles,

*Q h A TK TK K K* <sup>=</sup> × +×

where *Q* = quantity of flow, mm3

*A* = cross-sectional area of geotextile, mm2

 *A* = cross-sectional area of geotextile, mm<sup>2</sup> *h* = head of water on the geotextile, mm *T* = the thickness of geotextile, mm

respectively, cm/sec

(2)

*h* = head of water on the geotextile, mm

*T* = the thickness of geotextile, mm

respectively, cm/sec

*T T <sup>K</sup> TK TK K K*

12 21 1 2

1 2

fiber-packing densities.

calculated by:

by:

310 Non-woven Fabrics

$$\frac{1}{\Psi} = \frac{\Psi\_1 + \Psi\_2}{\Psi\_1 \cdot \Psi\_2} \tag{3}$$

where Ψ1, Ψ2 = permittivity of the upper/the lower geotextile

If the loss rate of hydraulic pressure, *fi* , is considered at the interface between geotextiles, permittivity, Ψ', could be calculated as follows:

$$\frac{1}{\Psi'} = \frac{1}{\Psi\_1} + \frac{1}{(1 - f\_i) \cdot \Psi\_2} \tag{4}$$

For convenience, equation (4) could be rewritten as:

$$f\_i = 1 - \frac{1}{\Psi\_2 \cdot (\frac{1}{\Psi'} - \frac{1}{\Psi\_1})} \tag{5}$$

#### **2.3. Experimental**

#### *2.3.1. Sample preparation*

To fabricate laminar geotextile composites, fiber-packing densities of geotextiles were discri‐ minated respectively. Six types of fibers were used to manufacture the laminar geotextile composites. The characteristics of these specimens are shown in Table 3.


**Table 3.** Characteristics of specimens for manufacturing laminar geotextile composites.

#### *2.3.2. Manufacturing of laminar geotextile composites*

Laminar geotextile composites having different fiber-packing densities were manufactured by needle-punching process. The fiber-packing densities of upper parts were smallerthan those of lower parts, and specifications of six laminar geotextile composites are represented in Table 4.


**Table 4.** Specifications of laminar geotextile composites.

#### *2.3.3. Water permeability test*

The hydraulic conductivity of laminar geotextile composites was determined in terms of permittivity under the constant head method and falling head method in accordance with ASTM D 4491 test method. The permeability coefficient was determined by multiplication of permittivity and thickness of geotextile. (*Fluet Jr, J. E., 1985; ASTM D 35 Committee, 2015*)
