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16-Civ-A4 Geotechnical Materials and Analysis · December 2014

Question 3 of 6: Seepage and the stability of a homogeneous earth dam

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Examinations (Engineers Canada / PEO), 98-Civ-A4 Geotechnical Materials and Analysis, December 2014. Closed book, 3 hours, 100 marks. Six questions — answer all. Charts and equations supplied at the back of the paper.

Reference texts: Das & Sobhan, Principles of Geotechnical Engineering (9th ed.), Cengage; Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering (2nd ed.), Pearson; Craig’s Soil Mechanics (Knappett & Craig, 8th ed.), CRC Press.

Check: The label inside Figure 3 prints “$k = 2.0 \times 10^{5}$ m/s”, which is physically impossible (200 km/s). The text of Question 5(b) prints $k = 2.0 \times 10^{-5}$ m/s, so the figure label has lost its minus sign and $2.0 \times 10^{-5}$ m/s is used throughout Question 5.

Question 3: Seepage and the stability of a homogeneous earth dam (10 marks)

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.

Homogeneous silty-sand dam: seepage and its controlfoundationreservoircrestseepage force j = γw ihomogeneous silty sandchimney filter (graded)blanket drainrock toe bermphreatic line with filter drainwithout drain: exits on thedownstream face (u high, i → i_cr)
Figure Q3. Without drainage the phreatic line (red) exits on the downstream face, where pore pressure is high and the exit gradient approaches i_cr. A graded chimney filter feeding a blanket drain (blue) draws the phreatic line down inside the embankment, and a rock toe berm adds weight and protects the toe.

How seepage attacks stability. When the reservoir fills, water percolates through the silty-sand embankment along a phreatic (top flow) line that emerges on the downstream slope. Three linked effects reduce stability:

1. Reduced effective stress and shear strength. Below the phreatic line the soil is saturated and carries a positive pore-water pressure $u$. Since $\sigma' = \sigma - u$ and the available shear strength is $\tau_f = c' + \sigma'\tan\phi'$ (with $c'\approx 0$ for a silty sand), every rise in $u$ directly lowers $\sigma'$ and therefore the frictional strength on any potential slip surface. The wetted downstream embankment zone is the weakest zone.

2. Seepage force. Flowing water exerts a drag on the soil skeleton equal to $j = \gamma_w\,i$ per unit volume, acting in the direction of flow. On the downstream slope this seepage force has a component directed out of the face and downslope, which adds to the destabilising (driving) forces on the slip mass.

3. Piping / internal erosion. Where the flow exits the downstream toe the upward exit gradient can approach the critical hydraulic gradient $i_{cr} = \gamma'/\gamma_w \approx 1$. If the local gradient reaches $i_{cr}$ the effective stress at the surface falls to zero, particles are floated away, and a pipe erodes backwards into the dam (a “boil” that can unravel the whole embankment). Silty sands are especially vulnerable because they are cohesionless yet fine enough to be transported.

Two remedial measures.

(a) Internal filter drainage — a chimney (inclined) filter connected to a horizontal blanket / toe drain. A properly graded sand–gravel filter intercepts the seepage and pulls the phreatic line down so that it discharges into the drain inside the dam rather than on the downstream face. This keeps the downstream embankment zone unsaturated (high $\sigma'$, full strength), eliminates the outward exit gradient, and — because the filter is designed to the retention/permeability criteria — prevents migration of the silty-sand particles, stopping piping. This is the single most effective control and is shown in the sketch.

(b) Flatten the downstream slope and add a rock toe berm. A flatter slope lengthens the potential failure surface and reduces the driving moment, while a free-draining rock berm at the toe adds stabilising weight, provides drainage, and armours the exit against erosion. (An equally valid alternative is an upstream impervious blanket or a central clay core to cut the quantity of seepage and lower the phreatic line at source.)