Question 5 of 5: Capillary Barriers, Wetting-Front Advance, DNAPL Remediation, and Landfill Siting

Question 5: Capillary Barriers, Wetting-Front Advance, DNAPL Remediation, and Landfill Siting (equal value)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — coarse-material capillary barriers around a waste vault. This proposal exploits exactly the capillary-barrier behaviour quantified in Question 4: a coarse material (gravel, coarse sand) has a very small air-entry (bubbling) pressure $P_d$, so under unsaturated conditions — the normal state of the vadose zone — its unsaturated hydraulic conductivity collapses almost immediately once suction exceeds that small $P_d$ (a steep Brooks-Corey $\lambda$ makes the drop-off even sharper, as the sand in Question 4 demonstrated: $S\approx0.10$, essentially residual, at a suction only about 11× its own $P_d$). A finer material above the coarse layer stays at a much higher suction before it would drain, so as long as the overlying suction never rises to the coarse layer's tiny entry value, water arriving from above is held in the fine material by capillarity and is diverted laterally along the fine/coarse interface rather than flowing straight down into (and through) the coarse layer and the vault it surrounds. Only if the fine material becomes saturated enough to develop a positive pore-water pressure exceeding the coarse layer's entry pressure does water actually break through into the coarse zone — a condition that ordinary infiltration rarely produces. The vault therefore stays comparatively dry not because the coarse material physically excludes water, but because its capillary properties make it hydraulically "invisible" to unsaturated flow until the fine cover is driven to near saturation.

Given. Initial saturation $S_i=0.15$, surface saturation after rainfall $S_0=0.84$, Brooks-Corey $P_d=0.2\ \text{m}$, $\lambda=3.0$, $S_{wr}=0.05$, $S_m=1.0$, porosity $n=0.4$, saturated hydraulic conductivity $K=10^{-3}\ \text{cm/s}$.

Find. Time for the wetting front to reach $L=1\ \text{m}$ depth, and the front's velocity at that time.

Approach. Use the Green-Ampt piston-flow model with an effective wetting-front suction head derived from the Brooks-Corey parameters (Brakensiek's relation), then solve the standard Green-Ampt time-of-advance equation for $t$ at $L=1\ \text{m}$ and differentiate to get the instantaneous front velocity.

1. Effective wetting-front suction head. The Brooks-Corey air-entry pressure translates to an effective Green-Ampt suction via $$\psi_f=P_d\cdot\frac{2+3\lambda}{1+3\lambda}=0.2\cdot\frac{2+9}{1+9}=0.2(1.1)=\boxed{0.220\ \text{m}}.$$
2. Moisture-content change across the front. $$\theta_i=nS_i=(0.4)(0.15)=0.060,\qquad \theta_s=nS_0=(0.4)(0.84)=0.336,\qquad \Delta\theta=\boxed{0.276}.$$
3. Time for the front to reach 1 m. Converting $K=10^{-3}\ \text{cm/s}=1.0\times10^{-5}\ \text{m/s}$, the Green-Ampt time-depth relation gives $$t=\frac{\Delta\theta}{K}\left[L-\psi_f\ln\!\left(1+\frac{L}{\psi_f}\right)\right]=\frac{0.276}{1.0\times10^{-5}}\left[1-0.220\ln\!\left(1+\frac{1}{0.220}\right)\right]=\boxed{1.72\times10^4\ \text{s}\ (4.78\ \text{hours})}.$$
4. Front velocity at $L=1\ \text{m}$. The Green-Ampt infiltration rate is $f=K(1+\psi_f/L)$, and since cumulative infiltration $F=L\,\Delta\theta$, the front velocity is $dL/dt=f/\Delta\theta$: $$\frac{dL}{dt}=\frac{K(1+\psi_f/L)}{\Delta\theta}=\frac{(1.0\times10^{-5})(1+0.220/1)}{0.276}=\boxed{4.42\times10^{-5}\ \text{m/s}}\ (3.82\ \text{m/day},\ 15.9\ \text{cm/hr}).$$ The front is still decelerating at this depth (velocity $\propto1+\psi_f/L$, falling toward the asymptotic rate $K/\Delta\theta$ as $L\to\infty$) — capillary suction ahead of the front is still meaningfully boosting the driving gradient beyond gravity alone at only 1 m of penetration.

Part (c) — remediation of DNAPL in fractured clay. Fractured clay is one of the hardest DNAPL settings to remediate, because most of the mass diffuses out of the fractures into the low-permeability clay matrix, where it becomes essentially inaccessible to any technology that only sweeps fluid through the fracture network. (1) Pump-and-treat / hydraulic containment. Advantage: straightforward to implement, provides immediate plume containment and some mass removal from the fractures. Disadvantage: matrix-diffused DNAPL back-diffuses into the fractures for years to decades after active pumping stops, producing severe concentration rebound and effectively unbounded cleanup timeframes — this technology addresses the fractures, not the matrix, which holds most of the mass. (2) In-situ chemical oxidation (ISCO) / enhanced bioremediation via fracture injection. Advantage: can destroy (not just relocate) DNAPL mass reachable via the fracture network, and enhanced anaerobic bioremediation can accelerate natural reductive dechlorination. Disadvantage: oxidant or amendment delivery is entirely controlled by fracture connectivity and can bypass large matrix volumes; oxidant demand from the clay matrix itself can be very high, and a poorly-controlled exothermic oxidation reaction near fractures can occasionally mobilize residual DNAPL further into un-impacted fractures. (3) Monitored natural attenuation (MNA) with institutional controls. Advantage: low cost, avoids the risk of an aggressive active remedy mobilizing DNAPL deeper into the fracture network, and is realistic given the very long timeframes any active technology would need anyway in this setting. Disadvantage: provides no active mass reduction, requires long-term monitoring and institutional controls (land-use restrictions) that must be maintained potentially for decades, and is only defensible where receptors are not currently threatened.

Part (d) — field-study variables for a municipal waste-disposal site. A site-suitability field study for a landfill must characterize every element of the future source-pathway-receptor system (Question 2(c)) before any waste is placed. Geology and stratigraphy — the sequence, thickness, and lateral continuity of natural attenuating layers (especially low-permeability clay units that could serve as a natural liner component), measured by continuous soil borings/coring with laboratory grain-size and Atterberg-limit testing, supplemented by geophysical surveys (electrical resistivity, seismic refraction) to map unit continuity between boreholes. Hydraulic conductivity and hydraulic gradient — controls how fast leachate could migrate if it escaped containment, measured via slug tests or pumping tests in monitoring wells, and via a network of piezometers read over time to establish the gradient and flow direction. Depth to and seasonal fluctuation of the water table — determines separation between the base of the landfill and groundwater and the risk of the water table intersecting the waste, measured by monitoring-well water-level readings over at least one full seasonal cycle. Groundwater and surface-water use downgradient (receptors) — identifies whether any drinking-water wells, wetlands, or streams could be affected, established through a water-well survey and surface-water inventory in the surrounding area. Background water quality — establishes a pre-development baseline against which any future leachate impact must be judged, measured by sampling and laboratory analysis of existing monitoring wells and surface water before construction. Climate/precipitation — drives the water balance and leachate generation rate, obtained from regional climate records and an on-site rain gauge. Each variable feeds directly into the same source-pathway-receptor logic as the conceptual site model: geology and hydraulic conductivity define the pathway, water-table depth and gradient define how fast a pathway could activate, and the receptor survey defines what is actually at risk if it does.