CELE Geotechnical Engineering — Permeability and SeepageCheat Sheet
One-page cheat sheet for CELE Geotechnical Engineering — Permeability and Seepage. Every formula, definition, and key fact you need for this chapter, condensed to a single printable page. Designed for the final review session before the CELE 2026.
Exam context
On the CELE 2026, the Geotechnical Engineering subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Permeability and Seepage lands at position 3rd out of 11 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Geotechnical Engineering on a typical CELE paper.
Permeability and Seepage - Cheat Sheet
Your last-minute revision companion for Permeability and Seepage. Master Darcy's law, flow nets, layered soils, and quick conditions in 30 minutes. All formulas, definitions, and exam traps covered.
Sections
Formulas
Formula
v = k × i
Meaning
v = discharge velocity (m/s); k = coefficient of permeability (m/s); i = hydraulic gradient (dimensionless)
Watch Out
This is DISCHARGE velocity, not seepage velocity. Divide by porosity n to get v_s = v/n (actual pore velocity is higher).
When To Use
Any seepage problem with laminar flow through soil; i = h/L
Formula
Q = k × i × A
Meaning
Q = discharge (m³/s); A = gross cross-sectional area perpendicular to flow (m²)
Watch Out
A is the total area INCLUDING voids. Common error: forgetting that i = h/L must be calculated first.
When To Use
Calculate total flow rate under a head gradient across a soil sample or foundation
Formula
i = h / L
Meaning
h = total head loss (m); L = length of flow path (m)
Watch Out
h and L must be in same units. Ensure L is measured along actual flow direction, not horizontal distance.
When To Use
Convert given head loss into dimensionless hydraulic gradient for use in Darcy's law
Formula
v_s = v / n
Meaning
v_s = seepage (actual pore) velocity (m/s); n = porosity (e/(1+e))
Watch Out
Porosity n = e/(1+e), NOT void ratio e. Many students confuse these. If given e, convert to n first.
When To Use
Find the true velocity of water moving through soil pores (faster than discharge velocity)
Common Values
Value
10⁻² to 10⁻⁴ m/s
Symbol
k
Quantity
Permeability of sand
Value
10⁻⁵ to 10⁻⁷ m/s
Symbol
k
Quantity
Permeability of silt
Value
10⁻⁷ to 10⁻⁹ m/s
Symbol
k
Quantity
Permeability of clay
Section Title
Darcy's Law & Basic Seepage
Important Facts
- Darcy's law: v = ki is LINEAR relationship; valid for Re < 1
- Discharge velocity v always < seepage velocity v_s by factor of porosity n
- Permeability k is independent of hydraulic gradient (in laminar regime) and depends ONLY on soil type & structure
- Finer soils (clay) have lower k; coarser soils (sand) have higher k
- Water travels faster through pores than the average (discharge) velocity suggests
Key Definitions
Term
Permeability (k)
Example
Sand k ≈ 10⁻² to 10⁻⁴ m/s; clay k ≈ 10⁻⁷ to 10⁻⁹ m/s
Definition
Measure of ease with which soil transmits water under a hydraulic gradient; units m/s.
Term
Hydraulic Gradient (i)
Example
If 2 m head loss over 5 m path, then i = 0.4
Definition
Ratio of head loss to length of flow path; dimensionless; measure of driving force for seepage.
Term
Discharge Velocity (v)
Example
Lower than actual pore velocity because water only flows through voids
Definition
Average seepage velocity assuming flow occurs over entire cross-sectional area; v = Q/A.
Term
Seepage Velocity (v_s)
Example
Always greater than discharge velocity by factor of 1/n
Definition
True velocity of water moving through soil pores; v_s = v/n or v_s = Q/(A × n).
Term
Laminar Flow
Example
Most natural soil seepage is laminar; turbulent flow rare except in gravel/fractures
Definition
Condition where Darcy's law applies; Re < 1 (typically); common in most soil seepage.
Diagrams To Know
- Soil element with flow lines showing head gradient h over length L
- Darcy's law flow regime graph: discharge velocity vs hydraulic gradient (linear, laminar region)
- Cross-section of porous medium: voids vs solid grains (explains why v_s > v)
Formulas
Formula
k = (V × L) / (A × h × t)
Meaning
V = volume collected (m³); L = sample length (m); A = sample area (m²); h = constant head (m); t = time (s)
Watch Out
All units must be consistent (mm or m throughout). If V in cm³, must convert. Time t must be in seconds. Watch for head in different units than L.
When To Use
CONSTANT-HEAD TEST for coarse-grained soils (sand, gravel); head remains constant during test
Formula
k = (2.303 × a × L) / (A × t) × log₁₀(h₁/h₂)
Meaning
a = standpipe cross-sectional area (m²); L = sample length (m); A = sample area (m²); h₁, h₂ = initial & final heads (m); t = time elapsed (s)
Watch Out
Factor 2.303 = ln(10); use LOG BASE 10, not natural log. a and A must be in same units. h₁ > h₂ always (head falls). Time t is elapsed time for head to drop from h₁ to h₂.
When To Use
FALLING-HEAD TEST for fine-grained soils (silt, clay); head drops during test as water drains
Section Title
Laboratory Permeability Tests
Important Facts
- Constant-head: suitable for sand, gravel (k > 10⁻⁵ m/s); higher flow rate makes measurement practical
- Falling-head: suitable for silt, clay (k < 10⁻⁵ m/s); low flow requires longer observation times
- Both tests assume laminar flow and use Darcy's law
- Result k is independent of which test used (if done correctly)
- Temperature affects k; must correct to standard 20°C if conditions vary
Key Definitions
Term
Constant-Head Test
Example
Sand sample: maintain 30 cm head, measure volume of water collected in time t
Definition
Permeability test in which head across sample is maintained constant by adding water; used for high-k soils.
Term
Falling-Head Test
Example
Clay sample: measure time for head to drop from 50 cm to 20 cm through small standpipe
Definition
Permeability test in which water drains from standpipe, head decreases over time; used for low-k soils.
Diagrams To Know
- Constant-head apparatus: soil cell with inlet/outlet, constant water head tank, collecting cylinder
- Falling-head apparatus: standpipe connected to soil sample, water drains and head drops over time
- Graph of head vs time for falling-head test (should show exponential decay curve)
Formulas
Formula
k_eq(parallel) = (Σ k_i × H_i) / (Σ H_i)
Meaning
Flow parallel to layers; each layer i has permeability k_i and thickness H_i
Watch Out
This is a WEIGHTED AVERAGE; larger k dominates. If one layer has k much higher, k_eq ≈ that layer's k. DO NOT use harmonic mean.
When To Use
Water flows horizontally through stratified soil (parallel to bedding planes); horizontal seepage under dam
Formula
k_eq(perpendicular) = (Σ H_i) / (Σ H_i/k_i)
Meaning
Flow perpendicular to layers; same notation as parallel case
Watch Out
This is a HARMONIC MEAN; smallest k dominates (controls flow). If one layer has low k, flow is throttled by that layer. DO NOT use arithmetic mean.
When To Use
Water flows vertically through stratified soil (perpendicular to bedding); vertical seepage/consolidation
Section Title
Layered Soils & Equivalent Permeability
Important Facts
- Parallel flow: k_eq is ALWAYS between max and min layer k, closer to higher k values
- Perpendicular flow: k_eq is ALWAYS between max and min layer k, but closer to lower k values
- Parallel: arithmetic-type weighted average (high k wins)
- Perpendicular: harmonic-type formula (low k wins)
- If only two layers, perpendicular k_eq ≈ 2k₁k₂/(k₁+k₂) for equal thicknesses
- Direction of flow (parallel vs perpendicular) is critical—wrong choice = wrong answer
Key Definitions
Term
Equivalent Permeability (k_eq)
Example
Three layers with k₁=10⁻³, k₂=10⁻⁵, k₃=10⁻⁴ m/s; direction matters which formula to use
Definition
Single permeability value that represents flow through a multi-layered soil stack as if it were homogeneous.
Term
Flow Parallel to Layers
Example
Horizontal seepage through alternating sand and silt layers under a dam
Definition
Water travels horizontally; each layer contributes to total flow independently; high-k paths dominate.
Term
Flow Perpendicular to Layers
Example
Vertical drainage/consolidation through clay and sand layers; consolidation time governed by least permeable layer
Definition
Water travels vertically; all water must pass through every layer; low-k layers restrict flow.
Diagrams To Know
- Stratified soil with 3+ horizontal layers; arrow showing horizontal (parallel) flow through stack
- Same stratified soil with vertical (perpendicular) flow arrow; visual contrast of flow paths
- Flow-resistance analogy: parallel = resistors in parallel (high conductance wins); perpendicular = resistors in series (low conductance bottleneck)
Formulas
Formula
Q = k × H × (N_f / N_d)
Meaning
H = total head across the flow net (m); N_f = number of flow channels; N_d = number of equipotential drops; Q per unit width (m³/s per m)
Watch Out
N_f and N_d are COUNTS of flow tubes and equipotential lines, not lengths. Ratio N_f/N_d is dimensionless. Per-unit-width result; multiply by dam length for total Q.
When To Use
Calculate seepage under dams, sheet piles, or embankments from a hand-drawn or computer flow net
Section Title
Flow Nets & Seepage Analysis
Important Facts
- Flow net is solution to 2D Laplace equation: ∇²h = 0 (h = piezometric head)
- Flow lines and equipotentials intersect at right angles (90°) everywhere
- Hand-drawn flow nets: iterative refinement to make squares or near-squares in each grid cell
- Each flow channel carries same discharge; each equipotential drop has same head loss
- Q = k × H × (N_f/N_d) is per UNIT WIDTH perpendicular to the page
- For total seepage multiply Q by width/length of dam perpendicular to 2D section
- Flow net method assumes: homogeneous, isotropic soil; steady-state flow; no wells/sources/sinks
Key Definitions
Term
Flow Net
Example
Underneath a sheet pile, flow lines curve around pile tip, equipotentials are perpendicular
Definition
Grid of flow lines and equipotential lines that solves Laplace equation for 2D seepage; allows graphical calculation of Q.
Term
Flow Line
Example
Lines that start at upstream surface and end at downstream surface; show direction of seepage
Definition
Path along which water particle travels; always perpendicular to equipotential lines; tangent to velocity vector.
Term
Equipotential Line
Example
Vertical line upstream = equipotential; horizontal line in flow field = another equipotential
Definition
Locus of points at same total head; perpendicular to flow lines; no flow occurs along equipotential.
Term
Flow Channel (Tube)
Example
If 4 flow channels, each carries 25% of total discharge
Definition
Region between two adjacent flow lines; same flow rate passes through each channel (Q_channel = Q_total / N_f).
Term
Equipotential Drop
Example
If total head = 10 m and 5 drops, each drop = 2 m head loss
Definition
Head loss between two adjacent equipotential lines; ΔH_drop = H_total / N_d.
Diagrams To Know
- Simple flow net under a dam: flow lines curve downward and around, equipotentials perpendicular
- Flow net grid showing near-square cells (properly drawn net has aspect ratio ≈ 1:1 in each cell)
- Counting diagram: identify N_f flow channels by counting parallel flow lines; count N_d drops between left and right equipotentials
Reactions Or Equations
Note
Flow nets are graphical solutions to this PDE. Equipotentials and flow lines are orthogonal coordinates.
Equation
Laplace Equation: ∂²h/∂x² + ∂²h/∂y² = 0
Conditions
2D steady-state seepage through homogeneous isotropic soil; h = total head
Formulas
Formula
i_cr = (G_s − 1) / (1 + e)
Meaning
G_s = specific gravity of solids; e = void ratio at critical condition
Watch Out
This assumes saturated soil with upward seepage. e may be different from initial void ratio if soil has undergone compression. Use e at critical state, not initial e.
When To Use
Find the critical hydraulic gradient at which soil 'boils' (liquefies); upward seepage makes effective stress zero
Formula
i_cr = γ' / γ_w
Meaning
γ' = effective unit weight of soil (N/m³); γ_w = unit weight of water (≈ 9.81 kN/m³)
Watch Out
γ' must be effective weight (saturated weight minus buoyancy), not total or dry weight.
When To Use
Alternative expression for critical gradient; directly relates to when σ' = 0
Formula
FS_piping = i_cr / i_exit
Meaning
i_exit = hydraulic gradient at soil exit point (toe of dam or sheet pile); FS = factor of safety against piping
Watch Out
FS > 1.0 is safe; FS < 1.0 means piping will occur. i_exit must be calculated at the actual exit location from flow net or seepage analysis.
When To Use
Assess stability against piping/boiling failure at exit point of seepage
Common Values
Value
0.9 to 1.0
Symbol
i_cr
Quantity
Critical gradient (typical sand)
Value
0.7 to 0.85
Symbol
i_cr
Quantity
Critical gradient (loose sand)
Value
1.0 to 1.2
Symbol
i_cr
Quantity
Critical gradient (dense sand)
Value
9.81 kN/m³ (or 1000 kg/m³)
Symbol
γ_w
Quantity
Unit weight of water
Section Title
Quick Condition & Piping Failure
Important Facts
- Quick sand forms when i_exit ≥ i_cr; person/object sinks because soil has no shear strength
- For typical sand: G_s ≈ 2.65, e ≈ 0.6–0.8, so i_cr ≈ 0.9–1.0
- Upward seepage reduces effective stress: σ' = σ − u; if i = i_cr, u = σ and σ' = 0
- FS_piping = 1.5 to 2.0 typical design target for dam toe or under sheet pile
- Piping can develop suddenly; once i_exit > i_cr, erosion accelerates (positive feedback)
- Exit gradient highest near tip of sheet pile or toe of dam (streamlines converge)
- Control measures: filter design, cutoffs, berms, or drainage to reduce i_exit
Key Definitions
Term
Quick Condition (Boiling)
Example
Beneath a dam with upward seepage, soil at exit point 'boils' if gradient exceeds i_cr
Definition
State when upward seepage gradient equals critical gradient; effective stress becomes zero; soil liquefies and loses bearing capacity.
Term
Critical Gradient (i_cr)
Example
For typical sandy soil: i_cr ≈ 0.9 to 1.0; for loose sand i_cr lower; for dense sand i_cr higher
Definition
Minimum upward hydraulic gradient at which effective stress = 0 and soil loses all shear strength.
Term
Piping
Example
Water tunnels through soil (like pipes), removing particles; void enlarges until collapse
Definition
Progressive erosion and internal collapse of soil caused by uncontrolled seepage; begins at i_exit > i_cr.
Term
Exit Gradient
Example
Read from flow net at exit point; largest drops occur near exit where flow lines converge
Definition
Hydraulic gradient at point where seepage emerges from soil (e.g., toe of dam); governs piping risk.
Diagrams To Know
- Effective stress diagram showing σ, u, and σ' before and after piping condition
- Dam cross-section with flow net, highlighting high gradient zone at toe (exit point)
- Piping failure progression: initial seepage → erosion cone → internal pipe → collapse
Reactions Or Equations
Note
At critical gradient, u = σ, so σ' = 0; this is quicksand state.
Equation
Effective stress with seepage: σ' = σ − u = σ − γ_w × h_w
Conditions
h_w = piezometric head at depth; upward seepage increases u and reduces σ'
Note
All forms equivalent; choose based on given soil parameters.
Equation
i_cr = (γ_sat − γ_w) / γ_w = (γ_d(1+w)−γ_w) / γ_w
Conditions
Alternative: use water content w and dry unit weight γ_d if void ratio not given
Formulas
Formula
n = e / (1 + e)
Meaning
e = void ratio; n = porosity (fraction of voids in total volume)
Watch Out
Porosity n is NOT the same as void ratio e. n ranges 0–1; e ranges 0–∞. For n = 0.5, e = 1; for n = 0.33, e = 0.5.
When To Use
Convert void ratio to porosity for seepage velocity calculation or flow net analysis
Formula
γ' = γ_sat − γ_w = (γ_d × G_s + γ_w) / (1 + e) − γ_w
Meaning
γ' = effective unit weight (buoyant weight); γ_sat = saturated unit weight; γ_d = dry unit weight; G_s = specific gravity
Watch Out
γ' is different from γ_sat (which includes water weight) and γ_d (which is without water). Must use saturated condition for i_cr.
When To Use
Calculate effective unit weight for critical gradient formula: i_cr = γ' / γ_w
Formula
γ_sat = (G_s × γ_w + γ_w × e) / (1 + e)
Meaning
Compute saturated unit weight from specific gravity, water weight, and void ratio
Watch Out
Assumes saturated soil (all voids filled with water). If partially saturated, use degree of saturation S.
When To Use
Find γ_sat if not given directly; need for critical gradient or stress calculations
Common Values
Value
2.65 (quartz sand standard)
Symbol
G_s
Quantity
Specific gravity of mineral soil solids
Value
9.81 kN/m³ (1000 kg/m³)
Symbol
γ_w
Quantity
Unit weight of water at 4°C
Value
0.4–0.8
Symbol
e
Quantity
Void ratio (sand)
Value
0.5–1.0
Symbol
e
Quantity
Void ratio (silt)
Value
0.6–1.5
Symbol
e
Quantity
Void ratio (clay)
Value
0.3–0.5
Symbol
n
Quantity
Porosity (sand)
Value
0.4–0.6
Symbol
n
Quantity
Porosity (clay)
Section Title
Soil Properties & Formulas Used in Seepage
Important Facts
- Porosity n = e/(1+e): if e = 1, then n = 0.5; larger e means more voids and higher n
- Seepage velocity uses porosity: v_s = v/n; if porosity is low, pores are narrow and v_s is much higher than v
- Effective unit weight γ' is ALWAYS less than saturated γ_sat by exactly γ_w in submerged condition
- Critical gradient i_cr = γ'/γ_w; for sand i_cr ≈ 1.0 because γ_sat ≈ 2 × γ_w, so γ' ≈ γ_w
- Void ratio changes with consolidation; must use final e (not initial) for piping calculations if consolidation has occurred
Key Definitions
Term
Void Ratio (e)
Example
e = 0.8 means for every 1 m³ of solids, there are 0.8 m³ of voids
Definition
Ratio of volume of voids to volume of solids; V_v / V_s; typically 0.4–1.0 for soils.
Term
Porosity (n)
Example
n = 0.5 means 50% of soil volume is voids, 50% is solid grains
Definition
Fraction of total volume that is voids; V_v / V_total; ranges 0 to 1.
Term
Effective Unit Weight (γ')
Example
For saturated sand, γ' ≈ 10 kN/m³; for clay γ' ≈ 8 kN/m³
Definition
Weight of soil solids per unit volume, accounting for buoyancy of water; controls shear strength and stability.
Term
Saturated Unit Weight (γ_sat)
Example
γ_sat ≈ 18–20 kN/m³ for most soils; includes weight of pore water
Definition
Total weight per unit volume of saturated soil (solids + water).
Diagrams To Know
- Soil element showing solids, water, and voids; labeled volumes for e and n derivation
- Relationship graph: e vs n (hyperbola); show typical ranges for sand, silt, clay
Must Remember
- 1. DARCY'S LAW: v = ki; Q = kiA. Discharge velocity v is NOT the same as seepage velocity v_s = v/n (pore velocity is faster).
- 2. CONSTANT-HEAD TEST FORMULA: k = VL/(Aht). All units must match (mm or m). Test used for sand/gravel (high k).
- 3. FALLING-HEAD TEST FORMULA: k = 2.303 × aL/(At) × log₁₀(h₁/h₂). Remember factor 2.303 = ln(10) and use LOG BASE 10, not ln.
- 4. LAYERED SOILS PARALLEL: k_eq = Σ(k_i × H_i) / Σ H_i. High k dominates. Used for horizontal seepage under dams.
- 5. LAYERED SOILS PERPENDICULAR: k_eq = Σ H_i / Σ(H_i/k_i). Low k dominates (bottleneck). Used for vertical consolidation.
- 6. FLOW NET SEEPAGE: Q = k × H × (N_f/N_d). N_f = number of flow channels; N_d = number of equipotential drops. Result is PER UNIT WIDTH.
- 7. CRITICAL GRADIENT: i_cr = (G_s−1)/(1+e) OR i_cr = γ'/γ_w. At this gradient, soil 'boils' (σ' = 0). For sand, i_cr ≈ 0.9–1.0.
- 8. PIPING SAFETY: FS = i_cr / i_exit. If i_exit > i_cr, piping occurs. Design target FS ≥ 1.5 under dams and sheet piles.
- 9. POROSITY VS VOID RATIO: n = e/(1+e). NOT the same thing. Porosity n for seepage velocity; void ratio e for critical gradient.
- 10. FLOW NET RULES: Flow lines ⊥ equipotentials. Each flow channel carries same Q. Each equipotential drop has same head loss ΔH = H_total/N_d.
Last Minute Tips
- CHECK UNITS FIRST: Constant-head and falling-head test formulas are unit-sensitive. If V is in cm³, L and A in mm, convert to m or mm consistently before plugging in. One wrong unit = wrong order of magnitude in k.
- PARALLEL vs PERPENDICULAR INSTINCT: Think of water choosing paths (parallel, high k wins ➜ arithmetic mean) vs water squeezing through all layers (perpendicular, low k throttles ➜ harmonic mean). Never swap formulas.
- FLOW NET SHORTCUT: Always identify N_f and N_d by visual inspection FIRST, count carefully, then plug into Q = kH(N_f/N_d). Most errors are miscounting flow tubes or drops, not the formula itself.
- CRITICAL GRADIENT IS NOT UNIQUE: i_cr depends on soil properties (G_s, e), not on the dam or seepage geometry. But i_exit DOES depend on geometry. FS = i_cr/i_exit—keep them separate in your head.
- SEEPAGE VELOCITY TRAP: If asked 'how fast does water move,' think: is it asking discharge (v) or true pore (v_s)? Discharge v uses entire area; seepage v_s = v/n uses only voids. Problem context tells you which.
Comparison Tables
Rows
Values
- Coarse soils (sand, gravel)
- Fine soils (silt, clay)
Property
Best for
Values
- k > 10⁻⁵ m/s
- k < 10⁻⁵ m/s
Property
Permeability range
Values
- Held constant by water supply tank
- Decreases over time as water drains
Property
Head condition
Values
- k = VL/(Aht)
- k = (2.303 × aL / At) × log₁₀(h₁/h₂)
Property
Formula
Values
- Collect volume V in time t
- Measure time t for head to drop from h₁ to h₂
Property
Measurement
Values
- Soil cell + constant-head tank + collection cylinder
- Soil cell + small-diameter standpipe
Property
Apparatus
Values
- Short (minutes)
- Long (hours to days)
Property
Test duration
Values
- Simple, fast, direct measurement
- Works for very low k without long wait times
Property
Main advantage
Values
- Inconsistent units for V, L, A, h, t
- Using natural log instead of log₁₀; forgetting 2.303 factor
Property
Common error
Columns
- Feature
- Constant-Head Test
- Falling-Head Test
Table Title
Constant-Head vs Falling-Head Permeability Tests
Rows
Values
- Horizontal (along bedding planes)
- Vertical (across bedding planes)
Property
Flow direction
Values
- k_eq = (Σ k_i × H_i) / (Σ H_i)
- k_eq = (Σ H_i) / (Σ H_i/k_i)
Property
Formula
Values
- Weighted arithmetic mean (HIGHER k dominates)
- Harmonic mean (LOWER k dominates)
Property
Type of average
Values
- k_eq ≈ k_max (if any layer has very high k)
- k_eq ≈ k_min (if any layer has very low k)
Property
k_eq relative to layer values
Values
- Water chooses path of least resistance (high-k layers)
- All water must pass through all layers (low-k layer throttles flow)
Property
Physical reason
Values
- Resistors in parallel (high conductance wins)
- Resistors in series (low conductance bottleneck)
Property
Analogy
Values
- Horizontal seepage under a dam or foundation
- Vertical consolidation/drainage through layered strata
Property
Exam typical scenario
Values
- Using harmonic formula (wrong type of average)
- Using arithmetic formula (wrong type of average)
Property
Common mistake
Columns
- Aspect
- Flow Parallel to Layers
- Flow Perpendicular to Layers
Table Title
Layered Soil Permeability: Parallel vs Perpendicular Flow
Rows
Values
- 10⁻² to 10⁻³
- Very high
- Constant-head
Property
Gravel/Coarse sand
Values
- 10⁻³ to 10⁻⁴
- High
- Constant-head
Property
Medium sand
Values
- 10⁻⁴ to 10⁻⁵
- Moderate to low
- Constant-head or falling-head
Property
Fine sand
Values
- 10⁻⁵ to 10⁻⁷
- Low
- Falling-head
Property
Silt
Values
- 10⁻⁷ to 10⁻⁹
- Very low
- Falling-head
Property
Clay
Columns
- Soil Type
- k (m/s)
- Drainage Class
- Lab Test
Table Title
Permeability by Soil Type (Typical Ranges)
Rows
Values
- i_cr = (G_s − 1)/(1 + e)
- Dimensionless
- ≈ 0.9–1.0 (sand)
Property
Critical gradient
Values
- i_cr = γ' / γ_w
- Dimensionless
- Same as above
Property
Critical gradient (alternative)
Values
- i_exit = ΔH_exit / L_exit (read from net)
- Dimensionless
- Depends on dam geometry
Property
Exit gradient from flow net
Values
- FS = i_cr / i_exit
- Dimensionless
- FS > 1.5 safe; FS < 1.0 piping
Property
Safety factor
Values
- σ' = 0 (soil loses strength)
- Pressure units
- —
Property
Effective stress at critical
Columns
- Quantity
- Formula/Expression
- Units
- Typical Value
Table Title
Quick Condition: Key Comparisons
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