6.1 Dewatering System Design & Well Drawdown

6.1 Dewatering System Design & Well Drawdown

Subsurface Dewatering Objectives & System Selection

Construction dewatering is the intentional lowering of the water table or piezometric surface to permit excavation and foundation construction in stable, dry conditions. Controlling groundwater is critical for preventing base heave, controlling slope instabilities, avoiding quicksand (piping) conditions, and reducing lateral earth pressures on temporary support structures. Selecting an appropriate dewatering methodology depends primarily on soil permeability ($k$), required drawdown depth ($s_w$), excavation dimensions, and environmental constraints such as adjacent structure settlement.

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Aquifer Hydraulics & Steady-State Radial Flow

Analytic calculations for well drawdown rely on potential flow theory applied to radial symmetry around fully penetrating vertical wells. Aquifers are classified as either confined (overlain by an impermeable aquiclude, piezometric head above aquifer top) or unconfined (phreatic water table surface open to atmospheric pressure).

   UNCONFINED AQUIFER RADIAL FLOW               CONFINED AQUIFER RADIAL FLOW
      
      Ground Surface                               Ground Surface
    |----------------|                           |----------------|
    |   Original W.T. \                     |   Piezometric Level 
  - - - - - - - - - -  - -                      - - - - - - - - - -  - -
    |         drawdown cone                      |       | drawdown cone  
    |                 |                          |=======|================== Impervious Top
    |                 |                          |         | Confined Layer 
    |   Aquifer      \|                          |        \| Thickness b    
    |==============|=== Impervious Bed           |========|================ Impervious Base

1. Confined Aquifer Hydraulics (Thiem Equation)

In a confined aquifer of uniform saturated thickness $b$, flow remains horizontal and horizontal cross-sectional area decreases linearly with radius ($A = 2\pi r b$). Applying Darcy's Law ($q = k A \frac{dh}{dr}$):

$$q = 2\pi k b r \frac{dh}{dr}$$

Integrating between the well casing radius $r_w$ (where hydraulic head is $h_w$) and distance of influence $R$ (where head is uninfluenced initial piezometric level $H$):

$$\int_{r_w}^{R} \frac{dr}{r} = \frac{2\pi k b}{q} \int_{h_w}^{H} dh$$ $$\ln\left(\frac{R}{r_w}\right) = \frac{2\pi k b (H - h_w)}{q}$$

Solving for total steady-state discharge rate $q$:

$$q = \frac{2\pi k b (H - h_w)}{\ln(R/r_w)} = \frac{2\pi k b (h_2 - h_1)}{\ln(r_2/r_1)}$$

Where $h_1$ and $h_2$ are measured piezometric heads at observation well radii $r_1$ and $r_2$.

2. Unconfined Aquifer Hydraulics (Dupuit-Forchheimer Equation)

In an unconfined aquifer, the water table forms the upper flow boundary. Under Dupuit's assumptions (horizontal flow lines across vertical sections and hydraulic gradient equal to free surface slope $dh/dr$), the flow area at radius $r$ is $A = 2\pi r h$:

$$q = 2\pi k r h \frac{dh}{dr}$$

Integrating from well radius $r_w$ to radius of influence $R$:

$$\int_{r_w}^{R} \frac{dr}{r} = \frac{2\pi k}{q} \int_{h_w}^{H} h dh$$ $$\ln\left(\frac{R}{r_w}\right) = \frac{\pi k (H^2 - h_w^2)}{q}$$

Solving for unconfined steady-state discharge $q$:

$$q = \frac{\pi k (H^2 - h_w^2)}{\ln(R/r_w)} = \frac{\pi k (h_2^2 - h_1^2)}{\ln(r_2/r_1)}$$

The height of the phreatic surface $h(r)$ at any intermediate radius $r$ is calculated by:

$$h(r) = \sqrt{H^2 - \frac{H^2 - h_w^2}{\ln(R/r_w)} \ln\left(\frac{R}{r}\right)}$$

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Radius of Influence ($R$) & Well Group Superposition

The radius of influence $R$ represents the distance from the well center at which drawdown becomes negligible ($s \approx 0$). While $R$ can be measured via field pumping tests, standard engineering practice estimates $R$ using Sichardt's empirical formula:

$$R = 3000 \cdot s_w \cdot \sqrt{k} \quad \text{(SI units: } s_w \text{ in meters, } k \text{ in m/s)}$$

For English units ($s_w$ in ft, $k$ in ft/s):

$$R = 3000 \cdot s_w \cdot \sqrt{k_{ft/s}}$$

Dewatering Excavation Pits: Equivalent Well Radius Method

When dewatering large rectangular construction pits of width $B$ and length $L$ using a ring of wellpoints or perimeter deep wells, the individual well array can be modeled as a single equivalent circular well of radius $r_e$:

$$r_e = \sqrt{\frac{B \cdot L}{\pi}} \quad \text{or} \quad r_e = \frac{B + L}{\pi}$$

The total flow rate $Q_{total}$ required to depress the water table to target height $h_w$ inside the excavation enclosure is evaluated by substituting $r_e$ into Dupuit's or Thiem's formula in place of $r_w$:

$$Q_{total} = \frac{\pi k (H^2 - h_w^2)}{\ln(R/r_e)}$$

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Groundwater Drawdown and Consolidation Settlement Risk

Lowering the water table reduces pore water pressure ($u$) throughout the affected soil deposit within the radius of influence $R$. According to Terzaghi's effective stress principle ($\sigma' = \sigma - u$), a drop in water table $\Delta h$ induces an effective vertical stress increase $\Delta \sigma'$ equal to:

$$\Delta \sigma'(z) = \gamma_w \cdot \Delta h(z)$$

If compressible clay or organic soil strata lie within this zone of influence, the increase in effective stress causes primary consolidation settlement. The settlement $S_c$ of a clay layer of thickness $H_c$ is calculated as:

$$S_c = \frac{C_c \cdot H_c}{1 + e_0} \log_{10}\left(\frac{\sigma'_{0} + \Delta \sigma'}{\sigma'_{0}}\right)$$

Where $\sigma'_{0}$ is the pre-dewatering effective stress at mid-layer, $C_c$ is the compression index, and $e_0$ is the initial void ratio. Nearby structures, utilities, and pavement supported on soft clay strata must be monitored for differential settlement during dewatering operations. Recharge wells or perimeter cutoff walls (e.g., slurry walls, sheet piles) are routinely deployed to limit drawdown outside the work site.

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Worked Numerical Examples

Worked Example 1: Unconfined Aquifer Dewatering Discharge

Problem Statement: An excavation requires lowering the water table in an unconfined sand aquifer from an initial thickness $H = 15.0\text{ m}$ to $h_w = 9.0\text{ m}$ (target drawdown $s_w = 6.0\text{ m}$) inside an equivalent well radius $r_e = 12.0\text{ m}$. The hydraulic conductivity of the sand is $k = 4.0 \times 10^{-4}\text{ m/s}$. Estimate the radius of influence $R$ using Sichardt's equation, and calculate the total required steady-state pumping flow rate $Q_{total}$ in liters per second (L/s).

Solution:

1. Calculate Sichardt's radius of influence $R$:

   $$R = 3000 \cdot s_w \cdot \sqrt{k} = 3000 \times (6.0\text{ m}) \times \sqrt{4.0 \times 10^{-4}\text{ m/s}} = 18,000 \times 0.020 = 360\text{ m}$$

2. Apply the Dupuit formula for equivalent unconfined well flow:

   $$Q_{total} = \frac{\pi k (H^2 - h_w^2)}{\ln(R/r_e)} = \frac{\pi \times (4.0 \times 10^{-4}\text{ m/s}) \times (15.0^2 - 9.0^2)}{\ln(360 / 12.0)}$$ $$H^2 - h_w^2 = 225 - 81 = 144\text{ m}^2$$ $$\ln(360 / 12.0) = \ln(30.0) = 3.4012$$ $$Q_{total} = \frac{\pi \times 4.0 \times 10^{-4} \times 144}{3.4012} = \frac{0.180956\text{ m}^3/\text{s}}{3.4012} = 0.05320\text{ m}^3/\text{s}$$

3. Convert flow rate to L/s ($1\text{ m}^3/\text{s} = 1000\text{ L/s}$):

   $$Q_{total} = 0.05320 \times 1000 = 53.20\text{ L/s}$$