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CELE Geotechnical EngineeringStresses in Soil MassCheat Sheet

Stresses in Soil Mass cheat sheet — the reference card you wish you had on exam day. Condensed from the full study notes, this is the high-yield core of Stresses in Soil Mass for CELE Geotechnical Engineering. Download, print, revise.

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. Stresses in Soil Mass lands at position 4th 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.

Stresses in Soil Mass - Cheat Sheet

Your 30-minute emergency reference for effective stress, pore pressure, and stress increase calculations. Every formula, definition, and pitfall you need to ace geotechnical stress problems on the PRC exam.

Sections

Formulas

Formula

σ = σ' + u → σ' = σ − u

Meaning

σ = total stress (kPa); σ' = effective stress (kPa); u = pore water pressure (kPa)

Watch Out

Do NOT forget the minus sign. Pore pressure REDUCES effective stress. Below water table, u ≠ 0.

When To Use

EVERY soil problem — effective stress governs strength and settlement, not total stress

Formula

σ = Σ(γᵢ × zᵢ)

Meaning

Sum of (unit weight × layer thickness) for all layers above the point of interest

Watch Out

Use γ_sat (not γ_moist or γ_dry) BELOW the water table. Above WTM, use γ_moist or γ_nat.

When To Use

Build total stress profile — always stack layers from surface downward

Formula

u = γ_w × z_w (hydrostatic)

Meaning

γ_w = unit weight of water (9.81 kN/m³ or ≈ 10 kN/m³); z_w = depth below water table (m)

Watch Out

u = 0 above the water table. If seepage flow exists, add/subtract seepage pressure: u = γ_w(z_w ± i·z_seep).

When To Use

Standard pore pressure calculation when there is no seepage

Common Values

Value

γ_w = 9.81 kN/m³ (or use 10 kN/m³ in approximations)

Symbol

γ_w

Quantity

Unit weight of water

Value

γ_sat ≈ 19–21 kN/m³

Symbol

γ_sat

Quantity

Typical saturated unit weight (clay)

Value

γ_sat ≈ 19–20 kN/m³

Symbol

γ_sat

Quantity

Typical saturated unit weight (sand)

Value

γ_moist ≈ 16–18 kN/m³

Symbol

γ_moist

Quantity

Typical moist unit weight (above WTM)

Value

i_critical ≈ (γ_sat − γ_w) / γ_w ≈ 1.0–1.1

Symbol

i_critical

Quantity

Critical hydraulic gradient (quick condition)

Section Title

Effective Stress Principle (Terzaghi's Law)

Important Facts

  • Effective stress is INDEPENDENT of pore pressure path — only σ and u matter, not how water got there.
  • Below the water table, ALWAYS use γ_sat, not γ_moist. Saturated unit weight includes all water in voids.
  • Pore pressure u is ALWAYS non-negative below WTM (cannot be negative in hydrostatic conditions).
  • Effective stress can INCREASE even if total stress stays the same if pore pressure DECREASES (e.g., drainage).
  • In a two-layer system with different WTM in each layer, compute u separately for each layer.
  • Quick sand occurs when σ' = 0, typically i_critical ≈ 1.0 to 1.1 for most natural soils.
  • Effective stress principle applies to ALL soil types: sand, clay, silt — no exceptions.
  • Seepage pressure is additive: u_total = γ_w·z_w + i·γ_w·z_seep (upward flow) or u_total = γ_w·z_w − i·γ_w·z_seep (downward).

Key Definitions

Term

Total Stress (σ)

Example

At 5 m depth in a clay layer (γ_sat = 20 kN/m³), σ = 20 × 5 = 100 kPa (if from surface).

Definition

Combined stress from soil weight and all external loads; includes both solid skeleton and pore fluid.

Term

Effective Stress (σ')

Example

If σ = 100 kPa and u = 40 kPa, then σ' = 60 kPa — this is what the soil 'feels' and resists with.

Definition

Stress carried by the soil skeleton (grains); controls shear strength, compressibility, and bearing capacity.

Term

Pore Water Pressure (u)

Example

At 3 m below water table, u = 9.81 × 3 ≈ 29.4 kPa (purely hydrostatic, no seepage).

Definition

Hydrostatic or dynamic pressure in the void spaces; acts equally in all directions (isotropic).

Term

Water Table (WTM)

Example

If WTM is at 2 m depth, then at 4 m depth z_w = 2 m (not 4 m).

Definition

The depth at which pore pressure first becomes non-zero; u = 0 above, u > 0 below.

Term

Seepage Pressure (i·γ_w·z_seep)

Example

Upward seepage (i > 0) INCREASES u and DECREASES σ'; can cause 'quicksand' condition if i_critical is reached.

Definition

Additional pore pressure caused by upward or downward groundwater flow; i = hydraulic gradient.

Term

Quick Condition (Boiling Sand)

Example

i_critical ≈ (γ_sat − γ_w) / γ_w ≈ (20 − 9.81) / 9.81 ≈ 1.02 for typical saturated soil.

Definition

Occurs when upward seepage reduces σ' to zero; soil loses bearing strength suddenly.

Diagrams To Know

  • Total stress, pore pressure, and effective stress profiles (vertical plots) — σ vs depth, u vs depth, σ' vs depth.
  • Soil layer stacking diagram showing γ above and below WTM with σ and u calculations.
  • Seepage flow diagram with hydraulic gradient i and resulting pore pressure variation.
  • Quick condition diagram showing σ' approaching zero as i approaches i_critical.

Formulas

Formula

Δσ (point) = (3Q) / (2πz²) × [1 / (1 + (r/z)²)]^(5/2)

Meaning

Q = point load (kN); z = depth below load (m); r = horizontal distance from load axis (m); Δσ = vertical stress increase (kPa)

Watch Out

At r = 0 (directly below), formula simplifies to Δσ = 3Q / (2πz²). Do NOT forget the 3 or the 2π.

When To Use

Boussinesq solution for a concentrated point load on the surface; use when r = 0 for directly below.

Formula

Δσ (point, r=0) = 3Q / (2πz²)

Meaning

Simplified Boussinesq at depth z directly below point load Q; Δσ decreases as z increases.

Watch Out

This is an approximation; the full formula includes (r/z) ratio. Stress spreads at ~45° from point.

When To Use

Direct stress increase below a concentrated load (pile point, column base, line load at one axis).

Formula

Δσ (2:1 method) = Q / [(B + z)(L + z)]

Meaning

Q = total load (kN); B = footing width (m); L = footing length (m); z = depth below footing (m); Δσ in kPa

Watch Out

Load spreads to (B+z) × (L+z) at depth z, NOT B × L. Common mistake: using B × L area instead.

When To Use

Quick approximation for rectangular footing on surface; assumes load spreads at 45° (2 vertical : 1 horizontal).

Formula

Δσ (strip load) = (q × B / π) × [θ + sin(θ)cos(2ϕ)]

Meaning

q = uniform load per unit area (kPa); B = strip width (m); θ, ϕ = angles (radians); used for uniform loads.

Watch Out

Requires angle computations — use tables or Newmark's chart for practical problems.

When To Use

For long, narrow uniformly loaded areas (e.g., embankment, long footing); more accurate than 2:1.

Common Values

Value

3 / (2π) ≈ 0.477

Symbol

C_B

Quantity

Boussinesq coefficient (directly below point load)

Value

arctan(0.5) ≈ 26.57°

Symbol

θ

Quantity

Load spread angle (2:1 rule)

Value

I_z ≈ 0.5 to 1.0 (depends on B, L, z ratio)

Symbol

I_z

Quantity

Influence factor (footing center, shallow depth)

Value

r ≈ 2–3z (horizontal offset)

Symbol

r_neg

Quantity

Negligible stress increase distance

Section Title

Stress Increase from Surface Loads

Important Facts

  • Boussinesq solution assumes elastic, semi-infinite, homogeneous soil — reasonable for most practical depths (z < 3B).
  • Stress increase at depth z is proportional to Q and INVERSELY proportional to z² — spreads rapidly with depth.
  • 2:1 method is conservative for clayey soils and reasonable for sandy soils; overestimates for very deep foundations.
  • Stress increase from a point load becomes negligible beyond r ≈ 2–3z (horizontal offset 2–3 times the depth).
  • Newmark's chart is accurate for any loaded area shape and position — preferred for complex layouts.
  • For circular footings, stress increase is uniform over the loaded area (no edge effects for circular load).
  • Stress increase is CUMULATIVE — multiple loads or adjacent footings must be superposed (added).
  • Below the footing, Δσ is maximum at z = 0 (surface) and decreases with depth; no lateral spreading at z = 0.

Key Definitions

Term

Boussinesq Solution

Example

A 100 kN pile load at 2 m depth and 1 m offset causes Δσ ≈ 5.7 kPa (use full formula with r = 1, z = 2).

Definition

Closed-form solution for stress increase from a point load on a semi-infinite elastic medium; foundation for all load-spread methods.

Term

2:1 Approximation

Example

A 3×4 m footing carries 1200 kN; at 2 m depth, Δσ = 1200 / [(3+2)(4+2)] = 1200 / 30 = 40 kPa.

Definition

Practical engineering rule assuming loads spread at 2:1 (vertical:horizontal slope) with depth — NOT exact but fast for design.

Term

Influence Factor (Newmark)

Example

For a rectangular area corner, influence factor at depth z is lower than directly below center.

Definition

Dimensionless factor to multiply average load pressure; accounts for loaded area shape and position.

Term

Stress Bulb

Example

Directly below a footing, σ ≈ average load pressure at z = 0, then decreases in a bulb shape with depth.

Definition

Vertical cross-section showing contours of constant stress increase; looks like an onion bulb or teardrop.

Term

Pressure Distribution Angle

Example

At depth z = 2 m, a 2×2 m load spreads to (2+2)×(2+2) = 4×4 m area, spreading at ~27° from vertical.

Definition

The angle at which surface load spreads with depth; 2:1 rule assumes 26.57° (arctan 0.5) from vertical.

Diagrams To Know

  • Boussinesq stress distribution diagram showing Δσ vs r/z ratio for point load.
  • 2:1 load spread diagram showing (B+z) × (L+z) expansion with depth z.
  • Stress bulb diagram for surface footing — concentric contours of equal stress increase.
  • Newmark's chart showing influence factors for rectangular areas at various depths and positions.
  • Stress distribution from strip load (uniform pressure on infinite strip) — smooth decay with depth and lateral distance.

Formulas

Formula

u = γ_w × z_w (no seepage)

Meaning

Pure hydrostatic pore pressure; z_w = depth below static water table

Watch Out

If water table is NOT at surface, z_w is measured from water table, not from ground surface.

When To Use

Default pore pressure calculation when groundwater is static (no flow).

Formula

u = γ_w × (z_w + i × L) (upward seepage)

Meaning

i = hydraulic gradient; L = seepage path length; upward flow INCREASES pore pressure.

Watch Out

Upward seepage REDUCES effective stress and can trigger quick sand. i = Δh / L (head loss / path).

When To Use

When groundwater flows upward (e.g., artesian, pumping near a well, beneath an embankment).

Formula

u = γ_w × (z_w − i × L) (downward seepage)

Meaning

Downward flow DECREASES pore pressure from hydrostatic value.

Watch Out

Downward seepage INCREASES effective stress, improving stability but causing consolidation settlement.

When To Use

When groundwater flows downward (e.g., infiltration from surface, drainage below a cut).

Formula

i_critical = (γ_sat − γ_w) / γ_w ≈ (γ' / γ_w)

Meaning

Hydraulic gradient at which effective stress becomes zero (quick condition); γ' = buoyant unit weight

Watch Out

i_critical ≈ 1.0–1.1 for most soils. If i_actual > i_critical, soil loses bearing strength suddenly.

When To Use

Check if upward seepage will trigger quicksand condition; compare i_actual to i_critical.

Formula

σ'_critical = 0 → i_critical = (γ_sat − γ_w) / γ_w

Meaning

At quick condition, effective stress is zero; soil behaves as liquid, no shear strength.

Watch Out

Quick sand is a limit state — once triggered, boiling/piping occurs; prevent by reducing i or increasing γ'.

When To Use

Design checks for embankments, excavations, and pumping situations with upward seepage.

Common Values

Value

γ_w = 9.81 kN/m³

Symbol

γ_w

Quantity

Unit weight of water

Value

γ' ≈ 9–11 kN/m³

Symbol

γ'

Quantity

Typical buoyant unit weight (sand)

Value

γ' ≈ 9–12 kN/m³

Symbol

γ'

Quantity

Typical buoyant unit weight (clay)

Value

i_critical ≈ 1.0–1.1

Symbol

i_c

Quantity

Critical hydraulic gradient (typical soil)

Section Title

Pore Pressure and Seepage

Important Facts

  • Pore pressure is ALWAYS zero or positive in saturated soil (cannot go negative in hydrostatic conditions).
  • Effective stress is REDUCED by upward seepage — can cause settlement, boiling, or piping.
  • Downward seepage IMPROVES stability by increasing effective stress but may cause internal erosion if too steep.
  • Critical hydraulic gradient i_critical ≈ 1.0 to 1.1 for most natural soils — depends on γ_sat and γ_w.
  • Quick sand occurs when σ' = 0; at this point, shear strength τ = c' ≈ 0 (no friction, no cohesion).
  • Seepage pressure follows the direction of flow — adds to u for upward flow, subtracts for downward flow.
  • Water table can fluctuate seasonally — design must account for both high and low water table positions.
  • In multi-layer soil, pore pressure profile can have kinks if permeability changes or flow direction changes.

Key Definitions

Term

Hydrostatic Pore Pressure

Example

At 4 m below water table with γ_w = 9.81 kN/m³, u = 39.24 kPa (purely from weight of water column).

Definition

Pore pressure in soil with no groundwater flow; u = γ_w × z_w below static water table.

Term

Seepage Pressure

Example

Upward flow with i = 0.5 over 2 m path adds 0.5 × 9.81 × 2 ≈ 9.81 kPa to hydrostatic pressure.

Definition

Additional pore pressure (positive or negative) caused by groundwater flow through soil.

Term

Hydraulic Gradient (i)

Example

If water level drops 1 m over a 2 m soil layer, i = 1 / 2 = 0.5 (downward seepage).

Definition

Ratio of head loss to seepage path length; i = Δh / L; dimensionless and always positive.

Term

Buoyant Unit Weight (γ')

Example

If γ_sat = 20 kN/m³ and γ_w = 9.81 kN/m³, then γ' ≈ 10.19 kN/m³.

Definition

Submerged unit weight; γ' = γ_sat − γ_w; accounts for buoyancy of soil grains in water.

Term

Quick Condition (Boiling, Piping)

Example

Sand deposit with i_critical = 1.02; if upward seepage i reaches 1.02, effective stress → 0, piping starts.

Definition

State where upward seepage reduces σ' to zero and soil behaves as liquid; occurs at i ≥ i_critical.

Term

Artesian Pressure

Example

Water rising above ground level in a well — indicates positive artesian pressure; can cause uplift on foundations.

Definition

Pore pressure in a confined aquifer above the static water table at the surface; can cause uplift.

Diagrams To Know

  • Pore pressure vs depth diagram showing hydrostatic profile, upward seepage, and downward seepage cases.
  • Effective stress reduction diagram showing σ' → 0 as i approaches i_critical (quick condition).
  • Seepage flow diagram in soil with hydraulic gradient, water table, and pore pressure variation.
  • Artesian well diagram showing confined aquifer with pore pressure above static water table.
  • Boiling/piping diagram showing soil particles lifting during quick condition with zero effective stress.

Formulas

Formula

Profile at depth z: σ(z) = Σ[γᵢ × Δzᵢ] + Δσ_external

Meaning

Layer-by-layer summation of stress; external loads (footing, embankment) add Δσ to geostatic stress.

Watch Out

Layer boundaries can have discontinuities in σ if γ changes. Always use γ_sat below water table.

When To Use

Build complete stress profiles combining initial (geostatic) stress with load-induced stress.

Formula

Geostatic stress: σ_v(z) = Σ(γᵢ × Δzᵢ) (no external load)

Meaning

Initial vertical stress from soil weight only; baseline before any footing or fill load.

Watch Out

Must account for water table change with depth — use γ_sat, not γ_moist below WTM.

When To Use

Starting point for all stress profiles; called 'in situ' or 'initial' stress.

Formula

Total stress increase from rectangular footing: Δσ_avg = Q / (B × L) (average, not point stress)

Meaning

Average vertical stress just below the footing contact area; not the same as point stress at depth.

Watch Out

This is NOT the vertical stress profile — it is only the average at z = 0. Use Boussinesq or 2:1 for depth z > 0.

When To Use

Quick first estimate of stress increase at footing level (z ≈ 0); used in bearing capacity.

Common Values

Value

dσ/dz = γ (typically 16–21 kN/m³)

Symbol

γ

Quantity

Geostatic stress gradient in uniform soil

Value

z ≈ 3B to 4B (footing width B)

Symbol

z_eff

Quantity

Depth of significant stress increase influence

Value

Δσ ≈ 0 when r > 2–3z

Symbol

r_lim

Quantity

Stress increase falloff with lateral distance

Section Title

Stress Profiles and Calculations

Important Facts

  • Geostatic stress increases linearly with depth in a uniform layer; slope = γ.
  • Stress profile changes slope at layer boundaries if γ changes (unit weight discontinuity).
  • Below the water table, use γ_sat in stress profile; above WTM, use γ_moist or γ_nat.
  • Load-induced stress (Δσ) decreases with depth; at great depth, Δσ becomes negligible (typically z > 3B).
  • Effective stress profile typically has a kink at the water table if γ_moist ≠ γ_sat.
  • Stress increase from load spreads laterally and vertically; use Boussinesq or 2:1 for any depth and offset.
  • Multiple loads superpose: if 2 footings load the same point, their Δσ values ADD.
  • Stress profile is always increasing with depth in the same layer (σ cannot decrease downward in hydrostatic case).

Key Definitions

Term

Geostatic Stress (Initial Stress)

Example

At 5 m depth in uniform soil (γ = 18 kN/m³), geostatic σ_v = 18 × 5 = 90 kPa.

Definition

Vertical stress from weight of soil above a point; no external load; baseline for all calculations.

Term

Stress Profile

Example

A stress profile above the water table is linear (straight line); below WTM, it bends if γ_sat ≠ γ above.

Definition

Plot of σ, u, or σ' vs depth; shows how stress changes with depth in a soil deposit.

Term

Load-Induced Stress (Δσ)

Example

A footing causes Δσ = 50 kPa at some depth; if geostatic σ = 100 kPa, total σ = 150 kPa.

Definition

Vertical stress increase from external loads (footing, embankment, pile); added to geostatic stress.

Term

Superposition

Example

Two adjacent footings each cause Δσ = 30 kPa at a point; combined effect Δσ = 60 kPa (superposed).

Definition

Linear principle: total stress from multiple loads = sum of individual load stresses; valid for elastic soil.

Diagrams To Know

  • Complete geostatic stress profile (σ vs depth) for a multilayer soil with water table.
  • Pore pressure profile (u vs depth) showing hydrostatic distribution and changes at WTM.
  • Effective stress profile (σ' vs depth) showing variation above and below water table.
  • Load-induced stress profile (Δσ vs depth) from footing — decays with depth using 2:1 or Boussinesq.
  • Combined total stress profile (σ_geostatic + Δσ_load) showing effect of external load on depth.
  • Stress path diagram (σ_v vs σ_h) used in advanced soil mechanics.
  • Mohr's circle diagram showing stress state at a point in soil.

Must Remember

  • σ' = σ − u ALWAYS — effective stress is what matters for strength and settlement, NOT total stress. Below water table, pore pressure u REDUCES effective stress.
  • Use γ_sat BELOW the water table, γ_moist ABOVE — this is the #1 source of student errors in stress profiles. Saturated soil is heavier.
  • Boussinesq point load directly below: Δσ = 3Q / (2πz²) — not Q / (2πz²). The coefficient 3/(2π) ≈ 0.477 is critical.
  • 2:1 method spreads load to (B+z) × (L+z) at depth z — NOT B × L. This is a 45° angle spread (2 vertical : 1 horizontal).
  • Quick condition occurs when σ' = 0 during upward seepage — i_critical ≈ (γ_sat − γ_w) / γ_w ≈ 1.0 to 1.1. Prevent piping.
  • Pore pressure u is measured from the WATER TABLE, not from the ground surface — if WTM is at 3 m depth, then at 5 m depth, z_w = 2 m (not 5 m).
  • Upward seepage INCREASES pore pressure, DECREASES effective stress, reduces stability. Downward seepage DECREASES pore pressure, INCREASES effective stress, improves stability.
  • Stress increase (Δσ) from loads DECREASES with depth and lateral distance — becomes negligible at z > 3–4 times the footing width B.
  • Superposition principle: multiple loads' Δσ values ADD together at a point. If 2 footings both load a location, their stress increases combine.
  • Layer boundaries in stress profiles show KINKS in the σ vs depth plot when γ changes — not smooth curves. Always mark these when drawing profiles.

Last Minute Tips

  • ALWAYS CHECK THE WATER TABLE POSITION FIRST — this determines whether to use γ_moist or γ_sat, and where u = 0 starts becoming u > 0. A wrong water table depth ruins the entire stress profile.
  • For any Boussinesq or 2:1 calculation, SKETCH the geometry (footing, load, point of interest) before calculating. This prevents sign errors and wrong assumptions about depth z and offset r.
  • When building a stress profile in a multi-layer system with different WTM, STOP at the water table, recalculate u, and restart — do NOT assume linear continuation across WTM.
  • If an exam problem mentions 'seepage,' 'piping,' 'boiling,' or 'artesian,' immediately CHECK whether i_critical is exceeded. If i_actual > i_critical, the answer is 'quick condition' or 'boiling' — σ' = 0.
  • In comparative problems (e.g., 'compare effective stress before and after water table rise'), draw both profiles side by side. The difference in σ' is always u_difference — often the entire exam point hangs on recognizing this.

Comparison Tables

Rows

Values

  • Sum of soil skeleton + water pressure
  • Stress carried by soil grains only
  • Water pressure in soil voids

Property

What it is

Values

  • Initial calculation (not used for strength)
  • Strength, settlement, consolidation
  • Water flow, pore pressure dissipation

Property

Controls

Values

  • σ = Σ(γᵢ × zᵢ)
  • σ' = σ − u
  • u = γ_w × z_w (+ seepage)

Property

Formula

Values

  • σ = γ_moist × z
  • σ' = σ − u_capillary (if present)
  • u ≈ 0 (or negative if capillary)

Property

Above water table

Values

  • σ = γ_sat × z (from WTM down)
  • σ' = σ − γ_w × z_w
  • u = γ_w × z_w (hydrostatic)

Property

Below water table

Values

  • σ = 18(3) + 20(2) = 94 kPa
  • σ' = 94 − 9.81(2) = 74.4 kPa
  • u = 9.81(2) = 19.62 kPa

Property

Example at 5 m depth (WTM at 3 m, γ_sat = 20 kN/m³)

Columns

  • Property
  • Total Stress (σ)
  • Effective Stress (σ')
  • Pore Pressure (u)

Table Title

Total Stress vs Effective Stress vs Pore Pressure

Rows

Values

  • Concentrated loads (pile, column point)
  • Δσ = (3Q/2πz²) × [1/(1+(r/z)²)]^2.5
  • High (elastic theory)
  • Single point or small loads at known location
  • Cannot easily superpose many loads; tedious for offsets

Property

Boussinesq Point Load

Values

  • Rectangular footings, quick design
  • Δσ = Q / [(B+z)(L+z)]
  • Moderate (engineering approximation)
  • Fast footing stress at any depth
  • Does not account for footing stiffness; conservative estimate

Property

2:1 Approximation

Values

  • Any loaded area shape and position
  • I_z = influence factor from chart
  • High (empirical-analytical)
  • Complex footing shapes, multiple areas, edge stresses
  • Requires chart or table lookup; graphical method has reading error

Property

Newmark's Chart

Columns

  • Method
  • Best For
  • Formula/Approach
  • Accuracy
  • When to Use
  • Limitation

Table Title

Boussinesq vs 2:1 Method vs Newmark's Chart

Rows

Values

  • u = γ_w × z_w
  • σ' = σ − γ_w × z_w (normal reduction)
  • Lake, pond, or calm groundwater
  • u increases linearly; σ' stable

Property

Static (no flow)

Values

  • u = γ_w × (z_w + i × L)
  • σ' DECREASES further; can reach 0 at i_critical
  • Below embankment, near pumping well, spring outlet
  • Check if i > i_critical; if yes, quick sand → boiling

Property

Upward seepage

Values

  • u = γ_w × (z_w − i × L)
  • σ' INCREASES; soil more stable
  • Drainage, infiltration, drying
  • u < hydrostatic; σ' improves but consolidation settlement

Property

Downward seepage

Values

  • u approaches γ_w × z_w + i_critical × γ_w × L
  • σ' → 0; soil loses all shear strength
  • Artesian flow, uncontrolled piping, embankment toe seepage
  • σ' = 0 → immediate stability failure; prevent by design

Property

Critical condition

Columns

  • Condition
  • Pore Pressure Formula
  • Effective Stress Impact
  • Example Scenario
  • Critical Check

Table Title

Hydrostatic vs Seepage Pore Pressure

Rows

Values

  • γ_d
  • 13–17
  • Laboratory consolidation, compaction (rarely in field stress profiles)
  • All void space is AIR; no water in voids

Property

Dry unit weight

Values

  • γ_nat or γ_moist
  • 16–19
  • ABOVE the water table in field profiles
  • Soil has some moisture; partially saturated

Property

Moist (natural) unit weight

Values

  • γ_sat
  • 19–21
  • BELOW the water table in field profiles — ALWAYS use below WTM
  • All voids filled with water; heaviest unit weight

Property

Saturated unit weight

Values

  • γ' = γ_sat − γ_w
  • 9–12
  • Effective stress calculations below water table; quick condition check
  • Net weight of soil particle in water; used in σ' analysis

Property

Submerged (buoyant) unit weight

Values

  • γ_w
  • 9.81 (≈10)
  • Pore pressure calculation; seepage pressure
  • Constant; use 9.81 kN/m³ or 10 kN/m³ approximation

Property

Water unit weight

Columns

  • Unit Weight
  • Symbol
  • Value Range (kN/m³)
  • When to Use
  • Remember

Table Title

Soil Unit Weights — When to Use Which

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