Permeability of Soil - Complete Notes for Loksewa 7th Level
Permeability is one of the most important chapters in Geotechnical Engineering, and it carries extra weight in Paper II because of seepage analysis, flow nets, and seepage control design. This post covers the full syllabus for this chapter in simple language, with diagrams, formulas, solved logic, and practice MCQs, so you can revise everything from one place.
According to the Loksewa syllabus, this chapter includes:
- Permeability of soils
- Factors affecting permeability
- Coefficient of permeability
- Laboratory methods
- Field methods
In Paper II, it further includes:
- Darcy's Law
- Flow net
- Seepage analysis
- Quicksand condition
- Sheet piles
- Earthen dams
- Filter design
- Seepage control techniques
- Explain permeability in simple words.
- State and apply Darcy's Law.
- Calculate the coefficient of permeability (k).
- Differentiate permeability and seepage velocity.
- Solve constant-head and falling-head numerical problems.
- Draw and interpret flow nets.
- Explain quicksand and piping.
- Design basic seepage control measures.
1. What is Permeability?
Definition: Permeability is the property of soil that allows water to flow through its interconnected voids. In simple words, it tells us how easily water can pass through the soil.
Sand: Imagine pouring water onto beach sand. The water disappears almost immediately. Reason: sand has high permeability.
Clay: Now pour water onto clay. Water remains on the surface for a long time. Reason: clay has very low permeability.
Engineering importance: permeability is important in foundation engineering, earth dams, retaining walls, drainage systems, groundwater flow, seepage analysis, slope stability, pavement drainage, and landfills.
A. Clay B. Silt C. Sand D. Peat
Answer: C
2. Why Does Water Flow?
Water flows because of a difference in hydraulic head. Water always moves from higher total head to lower total head. Just as electricity flows from higher potential to lower potential, water flows from higher head to lower head.
3. Hydraulic Head
Total Head (H) consists of:
Where z is the elevation head and u / gamma_w is the pressure head. Velocity head is usually neglected in soil because seepage velocities are very small.
4. Darcy's Law
Definition: Darcy (1856) established that the rate of flow through saturated soil is directly proportional to the hydraulic gradient. This law is the foundation of seepage analysis.
Q = Discharge (m3/s), k = Coefficient of permeability (m/s), i = Hydraulic gradient, A = Cross-sectional area
Hydraulic gradient: i = h / L, where h is head loss and L is the length of the seepage path. A higher hydraulic gradient means a greater driving force for water flow.
Engineering meaning of k: the coefficient of permeability (k) indicates how easily water moves through soil. Higher k means faster flow, lower k means slower flow.
Typical range of permeability by soil type. Note the values span several orders of magnitude between clay and gravel.
Validity of Darcy's Law
Darcy's Law is valid only for laminar flow conditions, which is the case for almost all seepage through soil because the flow velocities are very small and the pore channels are narrow. Validity is normally checked using the Reynolds number (Re):
- Darcy's Law holds well when Re is less than about 1, and remains reasonably valid up to about 1 to 10.
- At very high velocities, such as flow through coarse gravel or rockfill, the flow can become turbulent and Darcy's Law is no longer valid.
5. Seepage Velocity vs Discharge Velocity
This distinction is frequently tested and often confused.
- Discharge velocity (v): the velocity calculated using Darcy's Law directly, v = k i, assuming flow occurs across the entire cross-sectional area of the soil, including the solid particles. This is a fictitious or average velocity used for calculation convenience.
- Seepage velocity (vs): the actual, higher velocity at which water moves through the interconnected voids only, since water can only travel through the pore space and not through the solid particles.
Since porosity n is always less than 1, seepage velocity is always greater than discharge velocity.
6. Factors Affecting Permeability
1. Particle Size
Larger particles create larger pores, which gives higher permeability.
2. Void Ratio
A higher void ratio means larger flow channels, which gives higher permeability.
3. Soil Structure
- Flocculated structure gives higher permeability.
- Dispersed structure gives lower permeability.
4. Degree of Saturation
Air blocks flow paths. Fully saturated soil generally allows more continuous water flow.
5. Water Temperature
Higher temperature decreases water viscosity, which increases permeability.
6. Mineral Composition
Clay minerals such as montmorillonite have much lower permeability than sandy soils because of very small pores and adsorbed water layers around the particles.
7. Laboratory Determination of Permeability
Constant head test setup (left) and falling head test setup (right).
A. Constant Head Test
Used for coarse-grained soils such as gravel and sand, because water flows rapidly through them.
Q = collected water volume, L = length of specimen, A = cross-sectional area, h = constant head difference, t = time
B. Falling Head Test
Used for fine-grained soils such as silt and clay, because water flows slowly through them.
a = area of standpipe, A = area of specimen, h1 and h2 = initial and final heads
8. Field Methods
These are used for large-scale field investigations where laboratory samples may not represent in-situ conditions:
- Pumping-out test
- Pumping-in test
- Packer test (used in rock)
- Auger-hole test
9. Flow Nets
A flow net is a graphical method used to solve two-dimensional seepage problems, such as seepage under a sheet pile wall, below a dam, or through an earth embankment. It consists of two sets of curves:
- Flow lines: the paths that water particles follow as they seep through the soil.
- Equipotential lines: lines joining points of equal total head. These are drawn so that they intersect the flow lines at right angles, forming approximate squares.
A flow net around a sheet pile wall. Flow lines (blue) and equipotential lines (red, dashed) intersect at right angles.
Rules for sketching a flow net:
- Flow lines and equipotential lines must always intersect at 90 degrees.
- The figures formed between the lines should be approximately square (curvilinear squares).
- The boundary of the impervious soil layer and the surface of the structure act as flow lines.
- The upstream and downstream ground surfaces act as equipotential lines.
Seepage quantity from a flow net:
q = seepage quantity per unit length, k = coefficient of permeability, H = total head loss, Nf = number of flow channels, Nd = number of equipotential drops
10. Seepage Through Earthen Dams
In an earthen dam, water seeps from the reservoir through the body of the dam. The uppermost flow line, above which the soil is unsaturated and below which the soil is saturated, is called the phreatic line (or seepage line). Its shape is normally close to a parabola.
The phreatic line marks the top of the saturated seepage zone within the dam. A toe filter safely collects seeping water and prevents piping at the downstream face.
Key points for earthen dam seepage:
- If the phreatic line exits on the unprotected downstream slope, it can cause sloughing and slope failure.
- A toe filter or drainage blanket is provided to intercept seepage and bring the phreatic line down safely within the body of the dam.
- As noted in the compaction chapter, the impervious core of a dam is often compacted slightly wet of optimum to reduce permeability and control seepage.
11. Quicksand Condition
Quicksand is not a special type of soil. It is a condition that can occur in any cohesionless soil (like fine sand) when the upward seepage force becomes equal to the submerged weight of the soil particles. At this point, the effective stress in the soil becomes zero, the soil loses all its shear strength, and it behaves like a heavy liquid. This condition is also linked to piping failure.
icr = (Gs - 1) / (1 + e)
Gs = specific gravity of soil solids, e = void ratio
For most sands, Gs is about 2.65 and e is about 0.6 to 0.7, which gives a critical hydraulic gradient close to 1. Quicksand conditions typically occur when the actual exit hydraulic gradient approaches or exceeds this critical value.
12. Sheet Piles
Sheet piles are thin, interlocking structural sections (steel, concrete, or timber) driven into the ground to form a continuous wall. In seepage problems, they are commonly used as cutoff walls below dams, cofferdams, and excavation support systems.
- Driving a sheet pile deeper into the ground increases the length of the seepage path, which reduces the hydraulic gradient and the seepage quantity.
- Flow nets are used to analyze seepage below and around sheet piles, and to check the exit gradient on the downstream side against the critical hydraulic gradient, to guard against piping.
- Sheet piles are also used to control seepage into excavations and to prevent undermining of foundations.
13. Filter Design
A filter is a layer of granular material placed to allow water to pass freely while preventing the migration of fine soil particles from the base soil. Poorly designed filters can lead to piping and internal erosion. The most widely used guidelines are Terzaghi's filter criteria:
Permeability criterion: D15 (filter) / D15 (base soil) is greater than 4, so the filter is coarse enough to allow water to drain freely.
Here D15 and D85 refer to the particle sizes at which 15 percent and 85 percent, respectively, of the material by weight is finer.
14. Seepage Control Techniques
Common measures used in practice to control seepage and prevent piping include:
- Cutoff walls: sheet piles, concrete diaphragm walls, or grout curtains extending into an impervious layer to reduce seepage under a structure.
- Grouting: injecting cement or chemical grout into the soil or rock to fill voids and reduce permeability.
- Filters and drainage blankets: graded granular layers placed to safely collect and discharge seepage water while holding back fine particles.
- Relief wells: vertical wells on the downstream side of a dam that relieve uplift pressure and safely release seepage water.
- Impervious blankets: low-permeability layers placed on the upstream face or reservoir floor to lengthen the seepage path and reduce seepage quantity.
15. Common Loksewa MCQs
1. Darcy's Law is applicable to:
A. Turbulent flow B. Laminar flow C. Both laminar and turbulent flow D. Compressible flow
Answer: B
2. Which test is suitable for coarse-grained soils?
A. Falling-head test B. Constant-head test C. Plate load test D. Direct shear test
Answer: B
3. Which soil generally has the lowest permeability?
A. Gravel B. Sand C. Silt D. Clay
Answer: D
4. Hydraulic gradient is:
A. L / h B. A / Q C. h / L D. Q / A
Answer: C
5. Permeability generally increases with:
A. Increasing clay content B. Decreasing void ratio C. Increasing particle size D. Increasing plasticity
Answer: C
6. Quicksand condition occurs when the hydraulic gradient:
A. Becomes zero B. Equals the critical hydraulic gradient C. Is negative D. Equals the void ratio
Answer: B
7. In a flow net, flow lines and equipotential lines intersect at:
A. 45 degrees B. 60 degrees C. 90 degrees D. 180 degrees
Answer: C
16. Interview / Descriptive Questions
- Why is Darcy's Law valid only for laminar flow?
- Why is the constant-head test unsuitable for clay?
- How does temperature affect permeability?
- Why does gravel have much higher permeability than clay?
- What is the difference between laboratory and field permeability?
- Why is seepage velocity always greater than discharge velocity?
- How does increasing the depth of a sheet pile reduce seepage and exit gradient?
- Why must a filter satisfy both the piping criterion and the permeability criterion?
17. Previous Loksewa Exam Questions
A note on this section for transparency: a searchable public archive of every past Loksewa paper does not exist, so only a limited number of genuine past questions on this exact chapter could be verified from published sources. Below, the confirmed real question is marked clearly, followed by a set of practice questions written in the same style and difficulty as recent Loksewa 7th level papers, covering the parts of the syllabus that past papers have been shown to test. Treat the practice set as strong revision material, not as verified past-paper text.
Confirmed Past Question
Source: Pradesh Lok Sewa Aayog, Civil Engineering, 7th Level, written exam (Technical Subject paper).
Question [5 Marks]: Discuss the factors affecting the effective stress in soils and explain the phenomenon of capillary rise and quick sand condition.
Model Answer:
Effective stress (sigma') is the stress carried by the soil skeleton and is given by sigma' = sigma - u, where sigma is total stress and u is pore water pressure. It is affected mainly by:
- Changes in total stress, such as additional structural loads or removal of overburden.
- Changes in pore water pressure, caused by a rising or falling water table, seepage, or external loading on saturated soil before drainage occurs.
- Capillary rise, which develops negative pore water pressure (suction) above the water table and therefore increases effective stress in the capillary zone.
- Seepage direction: downward seepage increases effective stress, while upward seepage decreases it.
Capillary rise occurs because surface tension pulls water upward through the fine pore channels of the soil above the free water table, similar to water rising in a thin glass tube. The height of capillary rise is greater in fine-grained soils (small pore size) than in coarse-grained soils. This capillary water is held under negative pressure, which pulls soil particles together and adds apparent effective stress, temporarily increasing soil strength (this is why moist sand near a beach feels firmer than dry or fully submerged sand).
Quicksand condition is explained in detail in Section 11 above: when upward seepage pressure equals the submerged weight of soil particles, effective stress drops to zero, and the soil loses all shear strength, behaving like a liquid. It is governed by the critical hydraulic gradient, icr = (Gs - 1) / (1 + e).
Practice Questions in Loksewa Exam Style
Q1 [Paper II, 10 Marks]: State Darcy's Law and derive the expression for the coefficient of permeability from a constant head permeability test. A constant head test on a sand sample of length 20 cm and cross-sectional area 75 cm2 gave a discharge of 350 cm3 in 5 minutes under a constant head of 40 cm. Determine the coefficient of permeability.
Answer: Darcy's Law: Q = k i A, where i = h / L.
Here Q = 350 cm3 / 300 s = 1.1667 cm3/s, L = 20 cm, A = 75 cm2, h = 40 cm.
k = QL / (Aht) is the constant head formula (using total volume and time directly): k = (350 x 20) / (75 x 40 x 300) = 7000 / 900000 = 0.00778 cm/s (approximately 7.8 x 10^-3 cm/s).
This value falls in the typical range for sand, which confirms the calculation is reasonable.
Q2 [Paper II, 10 Marks]: Explain, with a neat sketch, how a flow net is used to estimate seepage loss below a concrete dam. What is meant by the number of flow channels (Nf) and the number of equipotential drops (Nd)?
Answer: A flow net for seepage below a dam is drawn using two families of curves: flow lines, which trace the path of seeping water beneath the dam and around any cutoff walls, and equipotential lines, which join points of equal total head and are drawn perpendicular to the flow lines, forming curvilinear squares (see the flow net diagram in Section 9 above, which illustrates the same principle for a sheet pile). Nf is the number of flow channels formed between adjacent flow lines, and Nd is the number of equipotential drops, that is, the number of head-loss increments between the upstream and downstream water levels. Once the flow net is drawn, the seepage quantity per unit length of dam is calculated as q = k H (Nf / Nd), where H is the total head loss across the structure and k is the coefficient of permeability of the foundation soil. The same flow net can also be used to estimate uplift pressure at the base of the dam and to check the exit gradient on the downstream side against the critical hydraulic gradient, to guard against piping failure.
Q3 [Paper I, MCQ]: The falling head permeability test is more suitable than the constant head test for which type of soil, and why?
Answer: Fine-grained soils such as silt and clay. In these soils the flow rate is so slow that measuring a collected volume in a reasonable time (as the constant head test requires) is impractical, whereas the falling head test can track the small, slow drop of the water level in a narrow standpipe over a longer, measurable time interval.
Q4 [Paper II, 5 Marks]: A sand deposit has a specific gravity of 2.68 and a void ratio of 0.7. Determine the critical hydraulic gradient and comment on the safety of an excavation with an exit gradient of 0.9.
Answer: icr = (Gs - 1) / (1 + e) = (2.68 - 1) / (1 + 0.7) = 1.68 / 1.7 = 0.988, approximately 0.99.
Since the exit gradient (0.9) is close to but still less than the critical gradient (0.99), the condition is close to unsafe. Factor of safety = icr / iexit = 0.99 / 0.9 = 1.1, which is far below the generally recommended factor of safety of about 4 to 5 against piping, so this excavation would be considered unsafe in practice and would need seepage control measures such as a deeper cutoff, filters, or dewatering.
Q5 [Paper I, MCQ]: In Terzaghi's filter criteria, the ratio D15(filter) / D85(base soil) must be less than:
A. 2 B. 4 C. 5 D. 9
Answer: C
Q6 [Paper II, 10 Marks]: With the help of a sketch, explain the phreatic line in an earthen dam. Why is a downstream filter or drainage blanket necessary?
Answer: See Section 10 above for the full explanation and diagram. In brief, the phreatic line is the top flow line of seepage within the dam body, separating the saturated zone below from the unsaturated zone above, and it is approximately parabolic in shape. If left unmanaged, the phreatic line can exit on the unprotected downstream slope of the dam, causing softening, sloughing, and eventual slope failure. A downstream filter or drainage blanket intercepts the seepage, safely carries it out of the dam body, and forces the phreatic line down within the dam, keeping the downstream slope dry and stable while also providing protection against piping by satisfying Terzaghi's filter criteria.
18. Memory Box
- Permeability = Ability of soil to transmit water.
- Darcy's Law: Q = k i A
- Hydraulic Gradient: i = h / L
- Seepage velocity vs = v / n, always greater than discharge velocity.
- Constant-head test -> Coarse soils (sand, gravel)
- Falling-head test -> Fine soils (silt, clay)
- Permeability order: Gravel > Sand > Silt > Clay
- Darcy's Law is valid for laminar flow.
- Flow net: flow lines and equipotential lines cross at 90 degrees, forming curvilinear squares.
- Quicksand: icr = (Gs - 1) / (1 + e)
- Filter criteria: D15(filter)/D85(base) < 5 and D15(filter)/D15(base) > 4
19. Quick Revision Summary
| Concept | Key Point |
|---|---|
| Permeability | Ability of soil to transmit water through interconnected voids |
| Darcy's Law | Q = k i A, valid only for laminar flow |
| Constant Head Test | Coarse soils, k = QL/(Aht) |
| Falling Head Test | Fine soils, k = (aL/At) ln(h1/h2) |
| Flow Net | q = kH(Nf/Nd), 90 degree intersections |
| Phreatic Line | Top flow line in an earthen dam, roughly parabolic |
| Quicksand | icr = (Gs - 1)/(1 + e), effective stress becomes zero |
| Sheet Pile | Deeper embedment lengthens seepage path, lowers exit gradient |
| Filter Design | Must retain fines and stay permeable (Terzaghi's criteria) |
| Seepage Control | Cutoff walls, grouting, filters, relief wells, impervious blankets |
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