6.4 Subsurface Drainage Systems & Filter Criteria

6.4 Subsurface Drainage Systems & Filter Criteria

Subsurface Drainage Purpose & System Elements

Subsurface drainage systems are designed to collect and convey groundwater away from structural foundations, earth retaining walls, slopes, and pavement subgrades. Effective drainage lowers excess hydrostatic pressures, prevents seepage-induced slope shear failures, eliminates frost heave, and safeguards against internal soil erosion (piping). A complete drainage system consists of three functional elements: Filter Layer (protects base soil from erosion), Drainage Layer (high-permeability conduit zone), and Collector Pipe Network (transports collected water to an outfall).

          TYPICAL SUBSURFACE TRENCH DRAIN CROSS-SECTION
          
          |===================================| Ground Surface
          |      Impervious Clay Cap          |
          |-----------------------------------| 
          |  |                             |  |
          |  |   Granular Filter Aggregate |  |
          |  |   Envelope (D15, D85)       |  | Trench Wall
          | G|                             | G| (Base Soil D15, D85)
          | E|         /=======\            | E|
          | O|        /  Slot   \           | O|
          | T|       | Perforated|         | T|
          | E|       | Collector |         | E|
          | X|        \    Pipe  /          | X|
          |  |         \=======/           |  |
          |===================================|

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Granular Filter Design Principles & Terzaghi Criteria

To perform effectively, a filter surrounding a base soil must satisfy two conflicting requirements: Retention (void spaces must be small enough to hold back base soil grains) and Permeability (void spaces must be large enough to allow water to pass without creating back-pressure).

Terzaghi & USACE Classic Filter Rules

Karl Terzaghi established criteria relating the grain size distribution of the filter material to the base soil, using grain diameters $D_{15}$ and $D_{85}$ (diameters corresponding to 15% and 85% passing by weight):

1. Retention / Piping Criterion: To prevent base soil particles from migrating into filter voids:

   $$\frac{D_{15,\text{filter}}}{D_{85,\text{base}}} \le 4 \text{ to } 5$$

2. Permeability / Free-Drainage Criterion: To ensure filter permeability is significantly higher than base soil permeability ($k_{\text{filter}} \approx 20-25 \times k_{\text{base}}$):

   $$\frac{D_{15,\text{filter}}}{D_{15,\text{base}}} \ge 4 \text{ to } 5$$

3. Segregation & Uniformity Criterion: To avoid aggregate segregation during placement, the filter material should be uniformly graded:

   $$C_u = \frac{D_{60,\text{filter}}}{D_{10,\text{filter}}} \le 20$$

4. Prevent Base Soil Gap-Grading: The grain size distribution curve of the filter should be roughly parallel to the grain size distribution curve of the protected base soil.

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Modern Refinements (USACE & NRCS Soil Categories)

The U.S. Army Corps of Engineers (USACE) and Natural Resources Conservation Service (NRCS) refined Terzaghi criteria by categorizing base soils according to percent passing the U.S. No. 200 sieve ($0.075\text{ mm}$):

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Perforated Collector Pipe Sizing

Perforated carrier pipes (corrugated HDPE or PVC underdrains) collect water from granular filter envelopes. Pipe perforations must be sized relative to the surrounding filter aggregate to prevent aggregate entry:

1. Slot Width Limit:

   $$\text{Slot Width} \le D_{85,\text{filter}}$$

2. Circular Hole Diameter Limit:

   $$\text{Hole Diameter} \le 1.2 \cdot D_{85,\text{filter}}$$

Pipe Flow Capacity (Manning's Equation):

Full-pipe volumetric discharge $Q_{pipe}$ is checked using Manning's equation:

$$Q_{pipe} = \frac{k_{n}}{n} \cdot A \cdot R_h^{2/3} \cdot S^{1/2}$$

Where $n$ is Manning's roughness coefficient ($n \approx 0.010-0.012$ for smooth PVC, $n \approx 0.015-0.020$ for corrugated HDPE), $A$ is pipe area, $R_h = D_{pipe}/4$ is hydraulic radius, $S$ is pipe slope, and $k_n = 1.0$ (SI units) or $1.486$ (English units).

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Geosynthetic Filters (Geotextiles)

Nonwoven needle-punched geotextiles frequently replace or augment aggregate filters due to lower installation costs and ease of construction. Geotextile design evaluates three critical criteria:

1. Geotextile Retention Criterion (Apparent Opening Size, $AOS / O_{95}$):

The Apparent Opening Size ($O_{95}$) represents the sieve opening size where 95% of geotextile pores are smaller.

• For steady flow in granular soils with $C_u \le 2$ or $C_u \ge 8$: $$O_{95,\text{geotextile}} \le D_{85,\text{base}}$$
• For soils with $2 < C_u < 8$: $$O_{95,\text{geotextile}} \le B \cdot D_{85,\text{base}} \quad \text{where } B = \frac{C_u}{2} \text{ to } 1.5$$

2. Geotextile Cross-Plane Permittivity Criterion ($\psi$):

Permittivity $\psi$ measures flow capacity perpendicular to the geotextile plane ($k_g / t_g$):

$$\psi = \frac{k_{g}}{t_g} \ge 10 \cdot \psi_{\text{soil}} = 10 \cdot \left(\frac{k_{\text{soil}}}{L_{\text{soil}}}\right)$$

3. Clogging Resistance:

To prevent fines from clogging geotextile pores, nonwoven geotextiles should have a percent open area $A_O \ge 4\%$, or satisfy Gradient Ratio test criteria ($GR \le 3.0$).

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Subsurface Drainage Configurations & Prefabricated Vertical Drains

• Chimney Drains: Inclined or vertical aggregate drainage layers placed inside earth dams to intercept embankment core seepage.
• Blanket Drains: Horizontal drainage layers beneath dam downstream toes, highway pavements, or building basements.
• French / Trench Drains: Deep narrow trenches filled with filter aggregate enclosing a perforated pipe.
• Prefabricated Vertical Drains (PVDs / Wick Drains): Flat plastic cores wrapped in nonwoven geotextile installed on $1.0-2.5\text{ m}$ grids into thick soft clay deposits. PVDs convert slow vertical 1D consolidation into rapid radial horizontal drainage, reducing primary consolidation time from years to months ($t \propto H_d^2$).

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Worked Numerical Examples

Worked Example 1: Granular Filter Design

Problem Statement: A base sand protecting an embankment core has the following grain size metrics: $D_{15,\text{base}} = 0.03\text{ mm}$ and $D_{85,\text{base}} = 0.24\text{ mm}$. Design the allowable $D_{15}$ grain size range for a granular filter aggregate according to classic Terzaghi criteria.

Solution:

1. Calculate Retention Limit ($D_{15,\text{filter}}$ upper bound):

   $$D_{15,\text{filter}} \le 5 \cdot D_{85,\text{base}} = 5 \times 0.24\text{ mm} = 1.20\text{ mm}$$

2. Calculate Permeability Limit ($D_{15,\text{filter}}$ lower bound):

   $$D_{15,\text{filter}} \ge 4 \text{ to } 5 \cdot D_{15,\text{base}} = 5 \times 0.03\text{ mm} = 0.15\text{ mm}$$

3. Specify Filter Envelope Range:

   $$0.15\text{ mm} \le D_{15,\text{filter}} \le 1.20\text{ mm}$$

   Any clean sand-gravel mixture with $D_{15}$ between $0.15\text{ mm}$ and $1.20\text{ mm}$ (and $C_u \le 20$) satisfies both retention and free drainage.