5.4 Geosynthetics in Geotechnical Engineering

Fundamentals of Geosynthetics

Geosynthetics are planar, polymeric materials incorporated into geotechnical engineering systems to solve civil infrastructure challenges. They are manufactured from synthetic polymers including Polypropylene (PP), High-Density Polyethylene (HDPE), Polyester (PET), and Polyvinyl Chloride (PVC).

The Six Core Functions of Geosynthetics

1. Separation: Preventing the intermixing of two distinct soil layers (e.g., preventing soft subgrade clay from intruding up into clean aggregate base course).
2. Filtration: Allowing liquid to pass cross-plane perpendicular to the geotextile while retaining soil particles on the upstream side.
3. Drainage: Collecting and conveying liquid in-plane parallel within the thickness of the geosynthetic structure.
4. Reinforcement: Tensile strength mobilization through interface friction, interlock, or adhesion to increase composite system shear capacity.
5. Containment (Barrier): Serving as an impermeable fluid barrier to block gas or liquid migration (e.g., landfill liners, canal linings).
6. Protection: Cushioning geomembranes against localized puncture and abrasion from sharp aggregate backfill.

Geosynthetic Categories and Engineering Characteristics

1. Geotextiles

• Woven Geotextiles: Manufactured by weaving monofilament, multifilament, or slit-film yarns. Characterized by high tensile strength ($15-100\text{ kN/m}$), high initial modulus, low elongation ($< 20\%$), but lower hydraulic permittivity. Ideal for separation and unpaved road subgrade stabilization.
• Nonwoven Geotextiles: Manufactured by needle-punching or heat-bonding continuous polymer filaments. Characterized by high elongation ($> 50\%$), high cross-plane permeability, excellent three-dimensional pore structure, and high puncture resistance. Ideal for filtration, subsurface subsurface drainage, and geomembrane cushion protection.

2. Geogrids

Polymeric grid structures featuring open apertures ($10-50\text{ mm}$) that allow aggregate particles to interlock mechanically across the grid structure.

• Uniaxial Geogrids: High tensile strength in the longitudinal direction; used for MSE retaining walls and steep slope reinforcement.
• Biaxial & Multi-Axial (Triaxial) Geogrids: Equal or isotropic tensile stiffness in all planar directions; used for road base stabilization and subgrade reinforcement over soft soils.

3. Geomembranes & Geosynthetic Clay Liners (GCLs)

• Geomembranes: Impermeable polymer sheets ($1.0-2.5\text{ mm}$ thick) providing fluid containment. Hydraulic conductivity $k \approx 10^{-11} - 10^{-13}\text{ cm/s}$.
• Geosynthetic Clay Liners (GCLs): Factory-manufactured hydraulic barriers consisting of a layer of dry sodium bentonite clay ($5.0\text{ kg/m}^2$) encased between two geotextiles held together by needle-punching. When hydrated under confinement, bentonite swells, achieving an equivalent hydraulic conductivity of $k \le 1 \times 10^{-9}\text{ cm/s}$.

Geotextile Hydraulics & Filter Design Criteria

Geotextile filtration design requires balancing two conflicting requirements: the geotextile openings must be small enough to retain soil particles (piping constraint) while remaining large enough to pass water freely without clogging (permeability constraint).

Hydraulic Parameters

1. Permittivity ($\psi$): Cross-plane volumetric flow capacity per unit hydraulic head across the geotextile thickness:

   $$\psi = \frac{k_n}{t_g} \quad [\text{s}^{-1}]$$

   where $k_n$ is normal hydraulic conductivity and $t_g$ is geotextile thickness.

2. Transmissivity ($\theta$): In-plane volumetric flow capacity per unit width through the geotextile thickness:

   $$\theta = k_p \cdot t_g \quad [\text{m}^2/\text{s}]$$

   where $k_p$ is in-plane hydraulic conductivity.

AASHTO / FHWA Filter Design Rules

1. Retention Criterion (Piping Constraint)

To prevent soil piping, the Apparent Opening Size ($AOS$ or $O_{95}$) of the geotextile (the sieve opening where 95% of openings are smaller) must satisfy:

$$AOS (O_{95}) \le B \cdot D_{85,\text{soil}}$$

where:

• $B = 1.0$ for steady flow in sand/gravel ($C_u \le 2$)
• $B = 1.5 - 2.0$ for well-graded soils ($C_u > 4$)
• $B = 0.5 - 1.0$ for dynamic/cyclic flow conditions

2. Permeability Criterion

To prevent pore water pressure buildup behind the geotextile filter:

$$k_{\text{geotextile}} \ge 10 \cdot k_{\text{soil}} \quad \text{or} \quad \psi_{\text{geotextile}} \ge 0.5\text{ s}^{-1}$$

3. Clogging Resistance Criterion

• For Woven Geotextiles: Percent Open Area ($POA) \ge 4.0\%$.
• For Nonwoven Geotextiles: Porosity $n \ge 50 - 70\%$.
• Gradient Ratio Test (ASTM D5101): $GR \le 3.0$.

Unpaved Road Subgrade Stabilization (Giroud-Han Method)

When roads are constructed over soft subgrades ($CBR < 3.0, s_u < 90\text{ kPa}$), aggregate base rutting occurs rapidly under wheel loads. Incorporating a geotextile or geogrid at the subgrade-aggregate interface enhances bearing capacity factor $N_c$:

• Unreinforced Subgrade: $N_c = 3.14$ (undrained plastic punching shear failure limit).
• With Geotextile Separator: $N_c = 5.14$ (prevents subgrade intermixing and mobilizes full undrained shear strength).
• With Geogrid Reinforcement: $N_c = 6.00$ (provides lateral aggregate restraint, membrane tension, and stress distribution).

This increase in $N_c$ reduces required aggregate base thickness $T$ by 30% to 50%.

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Geosynthetic Categories and Design Summary

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Worked Engineering Calculation: Geotextile Hydraulics

Problem Statement

A nonwoven geotextile filter is specified for a subsurface edge drain wrapped around a perforated collector pipe. Soil lab testing indicates the surrounding subgrade sand has $k_{\text{soil}} = 2.0 \times 10^{-4}\text{ cm/s} = 2.0 \times 10^{-6}\text{ m/s}$ and $D_{85} = 0.18\text{ mm}$.

The candidate nonwoven geotextile has:

• Thickness under load $t_g = 2.0\text{ mm} = 0.0020\text{ m}$
• Cross-plane hydraulic conductivity $k_n = 3.5 \times 10^{-3}\text{ m/s}$
• Apparent Opening Size $AOS (O_{95}) = 0.15\text{ mm}$

Determine:

1. The geotextile permittivity $\psi$.
2. Evaluate whether the geotextile satisfies AASHTO retention ($AOS \le 1.0 \cdot D_{85}$) and permeability ($k_g \ge 10 \cdot k_s$) criteria.
3. Calculate the flow rate per unit area ($q/A$) through the geotextile under a hydraulic head loss $\Delta h = 0.10\text{ m}$.

Step-by-Step Solution

Step 1: Calculate Permittivity ($\psi$)

$$\psi = \frac{k_n}{t_g} = \frac{3.5 \times 10^{-3}\text{ m/s}}{0.0020\text{ m}} = 1.75\text{ s}^{-1}$$

Step 2: Evaluate AASHTO Criteria

• Retention Check:

  $$AOS = 0.15\text{ mm} \le 1.0 \times D_{85} = 1.0 \times 0.18\text{ mm} = 0.18\text{ mm} \quad \text{(Retention OK)}$$

• Permeability Check:

  $$k_n = 3.5 \times 10^{-3}\text{ m/s} \ge 10 \times k_{\text{soil}} = 10 \times (2.0 \times 10^{-6}\text{ m/s}) = 2.0 \times 10^{-5}\text{ m/s} \quad \text{(Permeability OK)}$$

Step 3: Calculate Flow Rate Per Unit Area ($q/A$)

Using Darcy's Law for geotextile cross-plane flow:

$$\frac{q}{A} = v = k_n \cdot i = k_n \left( \frac{\Delta h}{t_g} \right) = \psi \cdot \Delta h$$ $$\frac{q}{A} = (1.75\text{ s}^{-1}) \times (0.10\text{ m}) = 0.175\text{ m}^3/(\text{s}\cdot\text{m}^2) = 175.0\text{ L/s/m}^2$$

Conclusion

The proposed nonwoven geotextile satisfies both hydraulic filtration criteria and delivers a robust discharge capacity of $175\text{ L/s/m}^2$ under $0.10\text{ m}$ head.