CELE Geotechnical Engineering — Shear Strength of SoilsCheat Sheet
One-page cheat sheet for CELE Geotechnical Engineering — Shear Strength of Soils. 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. Shear Strength of Soils lands at position 7th 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.
Shear Strength of Soils - Cheat Sheet
Your 30-minute exam companion for shear strength fundamentals, test types, failure criteria, and drained vs. undrained behavior. Master the Mohr-Coulomb framework and laboratory testing protocols.
Sections
Formulas
Formula
τf = c + σ tan φ (total stress)
Meaning
τf = shear failure stress (kPa); c = cohesion (kPa); σ = normal total stress (kPa); φ = angle of internal friction (°)
Watch Out
Use TOTAL stress (σ), not effective stress. If pore pressure exists, convert to effective stress first (σ' = σ − u).
When To Use
Any soil where you have normal stress and need failure shear stress; most general form.
Formula
τf = c' + σ' tan φ' (effective stress)
Meaning
c' = effective cohesion (kPa); σ' = effective normal stress (kPa); φ' = effective friction angle (°)
Watch Out
ALWAYS use effective stress for drained behavior. σ' = σ − u, where u is pore pressure.
When To Use
Drained analysis, long-term stability, or when you know pore pressures. This is the rigorous form for saturated soils.
Formula
sin φ = (σ₁ − σ₃) / (σ₁ + σ₃) [when c = 0]
Meaning
σ₁ = major principal stress at failure (kPa); σ₃ = minor principal stress (kPa); φ = friction angle
Watch Out
Only valid when c = 0. Do NOT use this for cohesive soils; use the general Mohr-Coulomb form instead.
When To Use
For sands (c ≈ 0) or frictional soils in triaxial tests; derives φ directly from principal stresses.
Formula
σ₁ = σ₃ tan²(45° + φ/2) + 2c tan(45° + φ/2)
Meaning
Principal stress relationship at failure for cohesive-frictional soils (c > 0, φ > 0).
Watch Out
Angle is (45° + φ/2), not 45°. Memorize: tan²(45° + φ/2) = (1 + sin φ)/(1 − sin φ).
When To Use
Triaxial or theoretical analysis; relates confining stress to failure axial stress.
Section Title
Mohr-Coulomb Failure Criterion (Core Framework)
Important Facts
- Sand failure is frictional (c ≈ 0); shear strength increases linearly with normal stress.
- Saturated clay under undrained loading (φ_u = 0) is purely cohesive (c_u only); failure envelope is horizontal.
- Drained behavior uses effective stresses (c', φ'); undrained uses total stress (c_u, φ_u ≈ 0).
- Friction angle φ is roughly independent of normal stress (it is a material property).
- Cohesion can be zero (sands) or significant (clays); never negative.
- The failure envelope is generally straight in the τ–σ plane but may curve at very high stresses.
Key Definitions
Term
Cohesion (c)
Example
Clay has c ≈ 20–50 kPa; sand has c ≈ 0 kPa.
Definition
Shear strength intercept; resistance to shearing when normal stress is zero; represents inter-particle bonding.
Term
Angle of Internal Friction (φ)
Example
Sand φ ≈ 30–40°; clay φ ≈ 20–30°; increases with density and angularity.
Definition
Slope of the Mohr-Coulomb envelope; represents frictional resistance as a function of normal stress.
Term
Shear Failure Plane
Example
In triaxial compression, failure plane inclines ~60° to horizontal when φ = 30°.
Definition
Plane within soil where shear stress reaches τf and soil shears; typically at ~45° + φ/2 to horizontal in compression.
Term
Mohr Circle
Example
Failure occurs when circle is tangent to the Mohr-Coulomb line τf = c + σ tan φ.
Definition
Graphical representation of stress state; radius = (σ₁ − σ₃)/2, center at (σ₁ + σ₃)/2; tangent to failure envelope at failure.
Diagrams To Know
- Mohr circle at failure: circle tangent to Mohr-Coulomb envelope (τ = c + σ tan φ).
- Failure plane orientation: θ_f ≈ 45° + φ/2 to the major principal stress direction.
- τ vs. σ plot: straight line with intercept c and slope tan φ.
Formulas
Formula
c_u = q_u / 2
Meaning
c_u = undrained shear strength (kPa); q_u = unconfined compressive strength (kPa)
Watch Out
HALF of q_u, not q_u itself. q_u is the stress at failure; c_u is shear strength assuming φ_u = 0.
When To Use
Unconfined compression (UC) test on clay; quick field or lab estimate of undrained strength.
Formula
q_u = 2c_u
Meaning
Unconfined compressive strength equals twice the undrained shear strength.
Watch Out
This assumes φ_u = 0 (undrained, saturated clay); does not apply to sand or drained conditions.
When To Use
Reverse calculation: given c_u, estimate q_u for lab reporting.
Formula
τ = (N sin α) / A
Meaning
τ = shear stress in direct shear (kPa); N = normal force (N); A = shear area (mm²); α = failure plane angle.
Watch Out
Normal stress σ = (P cos α) / A; do NOT confuse shear and normal components of the applied force.
When To Use
Direct shear test; calculate shear stress on the shearing plane.
Section Title
Laboratory Tests for Shear Strength
Important Facts
- UU test → short-term clay stability (no drainage time); φ_u ≈ 0 (total stress), c_u governs.
- CU test with pore-pressure measurement → most practical; gives both total and effective parameters; common in PRC exams.
- CD test → long-term drained behavior; slow shearing ensures no excess pore pressures; c', φ' are true drained parameters.
- Unconfined compression is a rapid, field-friendly proxy for c_u; c_u = q_u/2 is a standard approximation for saturated clay.
- Direct shear test is simpler but fixes failure plane; triaxial allows failure along natural plane; triaxial is more realistic.
- Pore-pressure measurement in CU test is critical; difference u from hydrostatic reveals excess pore pressure generation during shear.
- Sands typically show drained behavior in all tests (φ changes little); clays show strong undrained (c_u, φ_u ≈ 0) vs. drained (c', φ') difference.
Key Definitions
Term
Unconsolidated-Undrained (UU) Test
Example
Load applied quickly; no pore-pressure measurement; used for short-term (immediate) stability of embankments.
Definition
Triaxial test on saturated clay; soil cannot drain during loading; total-stress strength c_u with φ_u ≈ 0.
Term
Consolidated-Undrained (CU) Test
Example
CU test on clay can give c_u, φ_u (total) and c', φ' (effective); more realistic than UU.
Definition
Triaxial test: sample first consolidated under confining pressure, then sheared undrained with pore-pressure measurement; yields both total and effective parameters.
Term
Consolidated-Drained (CD) Test
Example
Slow shearing (hours per stage) ensures pore pressures remain hydrostatic; most rigorous for drained behavior.
Definition
Triaxial test: sample consolidated, then sheared slowly with full drainage; yields effective-stress parameters c', φ'.
Term
Unconfined Compression (UC) Test
Example
Quick field or lab test on clay core samples; q_u and c_u = q_u/2 used for immediate slope/bearing capacity checks.
Definition
Special UU triaxial with confining pressure σ₃ = 0; sample sheared to failure in unconfined state; q_u measured.
Term
Direct Shear Test
Example
Drained or undrained variants; simple, but failure plane is predetermined (not at natural angle); suitable for sands and residual soils.
Definition
Sample in split box sheared along a horizontal plane under normal load; plots τ vs. σ to derive c and φ.
Diagrams To Know
- Direct shear apparatus: top platen shears bottom platen on horizontal plane under normal load.
- Triaxial cell: cylindrical sample under confining pressure σ₃; axial load (deviator stress Δσ = σ₁ − σ₃) applied; pore-pressure transducer (CU/CD).
- UC test: unconfined specimen; compressive stress vs. strain curve; q_u at peak.
- Shear strength vs. normal stress plots: linear τ vs. σ envelope for each test type.
Section Title
Drained vs. Undrained Behavior
Important Facts
- Saturated clay under undrained loading has φ_u ≈ 0 because pore water (incompressible) resists volume change; shear strength = c_u only.
- Undrained strength c_u is INDEPENDENT of confining pressure σ₃ (for saturated clays at same OCR and initial state).
- Drained strength uses effective stresses; c' and φ' are typically SMALLER than c_u and φ_u (for clays).
- Sands are always effectively drained (high permeability); undrained vs. drained distinction is mainly for clays.
- Short-term stability (immediate after loading) uses undrained parameters (c_u); long-term (design life) uses drained (c', φ').
- Excess pore pressure dissipates over time (consolidation); fast shear → undrained; slow shear → drained.
- In triaxial CU test, pore-pressure measurement u allows separation: total-stress envelope and effective-stress envelope.
Key Definitions
Term
Undrained (φ_u ≈ 0) Condition
Example
Clay embankment loading after construction (days to weeks); pore pressures have not yet dissipated; use c_u for stability check.
Definition
Shear applied faster than pore water can drain; excess pore pressure builds; shear strength is c_u only; governs SHORT-TERM stability.
Term
Drained (c', φ') Condition
Example
Same clay embankment after years of consolidation; pore pressures have normalized; use c', φ' for design.
Definition
Shear applied slowly enough for pore pressure to dissipate; excess pore pressure ≈ 0; true effective-stress parameters c', φ' govern; LONG-TERM stability.
Term
Pore Pressure Ratio (r_u)
Example
r_u → 1 for quick undrained loading (clay); r_u → 0 for slow drained loading (sand, or clay after consolidation).
Definition
r_u = u / σ; ratio of excess pore pressure to total normal stress; 0 (drained) to ~1 (undrained).
Diagrams To Know
- Effective stress concept: σ' = σ − u; three phases (solid, water, air) shown schematically.
- Time-dependent pore pressure: excess u decays exponentially during consolidation; affects shear strength evolution.
- Undrained vs. drained envelopes: undrained typically higher c_u but φ_u ≈ 0; drained lower c' but higher φ'.
Formulas
Formula
σ₁ − σ₃ = deviator stress (Δσ)
Meaning
σ₁ = major principal stress; σ₃ = minor principal stress; difference is the applied differential stress.
Watch Out
Deviator stress is NOT the same as σ₁; σ₁ = σ₃ + deviator stress.
When To Use
Triaxial test reporting; deviator stress increases until failure.
Formula
sin φ = (σ₁ − σ₃) / (σ₁ + σ₃) [c = 0]
Meaning
Derives friction angle from principal stresses at failure; valid only for c = 0 soils.
Watch Out
Numerator is DIFFERENCE, denominator is SUM. Do not reverse. Only for c = 0.
When To Use
Sand or frictional soils; triaxial or theoretical stress analysis.
Formula
Failure plane angle = 45° + φ/2 (to major principal stress)
Meaning
Angle at which the failure plane forms with respect to the direction of σ₁.
Watch Out
Angle is 45° + φ/2, NOT 45°. If φ = 30°, failure plane is at 45° + 15° = 60° to σ₁ direction.
When To Use
Predicting shear plane orientation in compression tests or foundation problems.
Section Title
Principal Stresses & Failure Orientation
Important Facts
- Failure plane orientation depends on φ, not on the magnitude of stress.
- For φ = 30°, failure plane is ~60° to σ₁; for φ = 45°, plane is 67.5°.
- Mohr circle radius = (σ₁ − σ₃)/2; at failure, the circle is tangent to the Mohr-Coulomb envelope.
- On a horizontal shear plane (like in direct shear), both normal and shear stresses act; τ = c + σ tan φ governs failure.
- In a natural slope, the failure plane often is NOT horizontal but at the angle of maximum shear stress to the boundary.
- The principal stress path (plot of (σ₁+σ₃)/2 vs. (σ₁−σ₃)/2) helps visualize stress evolution during triaxial loading.
Key Definitions
Term
Major Principal Stress (σ₁)
Example
In triaxial compression, σ₁ is the axial stress (σ₃ + deviator stress).
Definition
Largest normal stress acting on the soil element; acts perpendicular to a principal plane with zero shear stress.
Term
Minor Principal Stress (σ₃)
Example
In triaxial test, σ₃ = 100 kPa (confining pressure).
Definition
Smallest normal stress; in triaxial cell, it is the confining pressure.
Term
Intermediate Principal Stress (σ₂)
Example
True triaxial apparatus can control σ₂; standard triaxial ignores σ₂ for simplicity.
Definition
Middle principal stress; typically not directly measured in triaxial tests (assumed = σ₃ in conventional triaxial).
Diagrams To Know
- Mohr circle: center at (σ₁+σ₃)/2 on normal stress axis, radius (σ₁−σ₃)/2.
- Failure plane on element: inclines at 45° + φ/2 to the σ₁ axis.
- Principal stress orientation within a slope: σ₁ roughly parallel to slope surface, σ₃ normal to surface.
Common Values
Value
35–40°
Symbol
φ'
Quantity
Dense sand φ (drained)
Value
28–32°
Symbol
φ'
Quantity
Loose sand φ (drained)
Value
25–30°
Symbol
φ'
Quantity
Stiff clay φ' (drained)
Value
10–25 kPa
Symbol
c_u
Quantity
Soft clay c_u (undrained)
Value
50–100 kPa
Symbol
c_u
Quantity
Stiff clay c_u (undrained)
Value
30–35°
Symbol
φ'
Quantity
Silt φ' (typical)
Value
≈ 0° (or 1–3°)
Symbol
φ_u
Quantity
Normally consolidated clay φ_u
Value
≈ 0 kPa
Symbol
c'
Quantity
Normally consolidated clay c' (typical)
Section Title
Soil Classification & Typical Shear Strength Values
Important Facts
- Sand shear strength increases with density and effective stress; φ increases ~2–3° per 10% density increase.
- Clay undrained strength c_u depends on consolidation history (OCR), remolding, and clay mineralogy.
- Normally consolidated (NC) clay: φ_u ≈ 0, c_u ≈ 0.2–0.3 σ_vc (vertical effective stress); c' ≈ 0.
- Overconsolidated (OC) clay: φ_u may be 5–10°; c_u higher; c' may exist due to desiccation or unloading.
- Silt often behaves as sand (frictional) but can have some cohesion; typical φ ≈ 30–35°, c ≈ 5–15 kPa.
- Effective friction angle φ' is largely independent of stress level (constant ~25–35° for most clays).
- Remolded clay has zero cohesion (c = 0) but retains residual friction φ_res ≈ 0.5–0.7 φ_peak.
Key Definitions
Term
Cohesionless Soil (Sand, Gravel)
Example
Dense sand: c ≈ 0 kPa, φ ≈ 35–40°; loose sand: c ≈ 0 kPa, φ ≈ 28–32°.
Definition
Soil with negligible cohesion (c ≈ 0); shear strength entirely from friction and interlocking.
Term
Cohesive Soil (Clay)
Example
Stiff clay: c' ≈ 20 kPa, φ' ≈ 25°; very soft clay: c_u ≈ 10 kPa, φ_u ≈ 0.
Definition
Soil with significant cohesion (c > 0); includes both particle bonding and interparticle attraction (clay minerals).
Term
Residual Soil
Example
Residual clay in Philippines from tropical weathering; φ' ≈ 30–35°, variable c'.
Definition
Soil formed by in-situ weathering of rock; may retain some bonding; often high friction angle.
Diagrams To Know
- Soil type vs. φ, c scatter plot: sand cluster (c ≈ 0, φ high); clay cluster (c significant, φ moderate).
- Clay sensitivity: peak strength vs. residual strength vs. remolded strength on a τ vs. σ plot.
- Overconsolidation ratio (OCR) vs. undrained strength: c_u increases with OCR (higher than NC).
Formulas
Formula
Deviator stress q = σ₁ − σ₃
Meaning
q = deviator stress (kPa); represents the difference between major and minor principal stresses.
Watch Out
q is NOT the same as σ₁. Remember: σ₁ = q + σ₃.
When To Use
Triaxial test plotting; stress path diagrams (q vs. p); failure criterion often expressed as q_f.
Formula
Mean stress p = (σ₁ + σ₃) / 2 or p = (σ_x + σ_y + σ_z) / 3
Meaning
p = mean (or average) principal stress (kPa); also called hydrostatic or isotropic stress.
Watch Out
p is the arithmetic average of all three principal stresses, not just (σ₁ + σ₃)/2 in 3D; for plane strain or axisymmetric triaxial, p = (σ₁ + 2σ₃)/3.
When To Use
Stress path diagrams; some failure criteria (e.g., Cam clay) use p–q space.
Formula
Stress ratio at failure: (σ₁/σ₃)_f = tan²(45° + φ/2) + 2c tan(45° + φ/2) / σ₃
Meaning
For given σ₃, the stress ratio σ₁/σ₃ at failure is a function of c and φ.
Watch Out
This is derived from the Mohr-Coulomb criterion. For c = 0, it simplifies to σ₁/σ₃ = tan²(45° + φ/2).
When To Use
Triaxial test design; predicting failure axial stress from confining pressure.
Section Title
Stress Paths & Triaxial Interpretation
Important Facts
- UU test stress path is typically vertical (p constant, q increases) because confining pressure is fixed.
- CU test stress path depends on the soil's pore-pressure generation during shear; can slope up or down.
- CD test stress path is generally linear from the initial to final stress state (elastic + plastic compression + shear).
- Normally consolidated clay plots below overconsolidated clay on the q–p plane at the same initial p.
- Failure locus in q–p space is often curved for clays (not perfectly linear), especially at low p.
- The slope of the stress path (dq/dp) helps diagnose pore-pressure behavior: steep slope → high pore-pressure generation (undrained); shallow → low (drained).
- Peak stress (q_f) and critical state stress (q_crit) are often different for overconsolidated soil; peak is higher.
Key Definitions
Term
Stress Path (q–p plot)
Example
UU test on clay: horizontal stress path (p constant if confining pressure fixed); q increases to failure.
Definition
Graph of deviator stress q (y-axis) vs. mean stress p (x-axis) during loading; shows how stress state evolves.
Term
Failure Envelope (in q–p space)
Example
Effective stress envelope: q_f = c' + p' tan(3φ') (approximate form in q–p space).
Definition
Curve or line representing all stress states at failure; for Mohr-Coulomb, it is linear: q = c tan(some angle) + p tan(some angle).
Term
Critical State
Example
Overconsolidated clay may peak, then strain-soften toward a lower critical stress state.
Definition
Final shear state at which strain continues without change in stress (or stress ratio); occurs after peak in some soils.
Diagrams To Know
- q–p stress path diagram: plot of triaxial test from initial to failure state.
- Failure envelope in q–p space: line or curve tangent to the stress path at failure.
- Three test types overlaid: UU path (vertical), CU path (sloped), CD path (linear from initial consolidation to shear).
Section Title
Common Exam Pitfalls & Problem-Solving Strategy
Important Facts
- Do NOT confuse c_u (undrained total-stress strength) with c' (drained effective-stress cohesion); they are different.
- c_u = q_u / 2 ONLY; half of the unconfined compressive strength, not the full value.
- Always check whether the problem asks for total-stress (φ = 0, c = c_u) or effective-stress (c = c', φ = φ') parameters.
- The failure plane angle is 45° + φ/2, NOT 45°.
- In triaxial: σ₁ = σ₃ + deviator stress; do not mix up the terms.
- Pore pressure u is positive (or zero); never negative in practical problems.
- For normally consolidated clay, c' ≈ 0 kPa; cohesion intercept arises only if overconsolidated or if sample is bonded.
- Sand shear strength increases with confining pressure (normal stress); clay undrained strength does NOT.
- Effective stress principle: σ' = σ − u; if u is not given, assume u = 0 (dry or drained condition).
- Friction angle φ does not depend on confining pressure (it is a material property); higher φ for denser, coarser sand.
Key Definitions
Term
Overconsolidation Ratio (OCR)
Example
Clay previously buried 50 m deep but now at surface 20 m deep; OCR = 50/20 = 2.5.
Definition
OCR = σ_vc / σ'_v0; ratio of maximum past effective vertical stress to current effective vertical stress; OCR > 1 = overconsolidated.
Must Remember
- 1. THE MOHR-COULOMB CRITERION: τ_f = c + σ tan φ (total stress) OR τ_f = c' + σ' tan φ' (effective stress) — this is the foundation of all shear strength analysis.
- 2. c_u = q_u / 2 — Half the unconfined compressive strength; common exam trap to use q_u directly.
- 3. UNDRAINED (φ_u ≈ 0) governs SHORT-TERM stability; DRAINED (c', φ') governs LONG-TERM stability — choose the correct approach based on time scale.
- 4. SIN φ = (σ₁ − σ₃) / (σ₁ + σ₃) when c = 0 — For sand/frictional soils; derives friction angle from triaxial principal stresses.
- 5. FAILURE PLANE ANGLE = 45° + φ/2 to the major principal stress — Not 45°; depends on friction angle.
- 6. EFFECTIVE STRESS PRINCIPLE: σ' = σ − u — Must subtract pore pressure to get effective stress for drained analysis.
- 7. UU TEST: Fast, c_u only, φ_u ≈ 0 for saturated clay. CU TEST: Pore pressure measured, gives both total & effective parameters. CD TEST: Slow, true drained c' and φ'.
- 8. SAND IS ALWAYS EFFECTIVELY DRAINED — φ changes little; c ≈ 0; UU and CD tests yield same φ. Avoid confusing sand with clay behavior.
- 9. NORMALLY CONSOLIDATED CLAY: c' ≈ 0, φ_u ≈ 0. OVERCONSOLIDATED CLAY: c' > 0, φ_u may be 5–10°; peak strength higher than NC.
- 10. TRIAXIAL STRESS STATE: σ₁ = σ₃ + (deviator stress); do not mix up terms; p = (σ₁ + σ₃)/2 is the mean stress.
Last Minute Tips
- In ANY direct shear or triaxial problem, FIRST identify whether it is asking for drained (use c', φ') or undrained (use c_u, φ_u ≈ 0) parameters. This single decision eliminates half the common mistakes.
- For an unconfined compression test, remember c_u = q_u / 2, NOT q_u. This formula appears in almost every PRC exam; students routinely miss it by using q_u directly.
- When plotting Mohr-Coulomb envelope (τ vs. σ plot), the INTERCEPT on the τ-axis is c, and the SLOPE is tan φ. A common error is reading the intercept as zero for sand when it truly is zero (c = 0); draw the line through the origin for pure friction.
- In a stress path (q–p plot), remember that UU tests give a VERTICAL path (p constant, q increases to failure), while CD tests give a more LINEAR path. The shape of the path reveals the test type and pore-pressure generation.
- Check the SIGN of pore pressure. In a saturated saturated soil under positive confining pressure, excess pore pressure u is typically positive (adds to hydrostatic). Always use σ' = σ − u correctly; if u > 0, then σ' < σ.
Comparison Tables
Rows
Values
- None
- Fast (minutes–hours)
- No
- c_u, φ_u ≈ 0
- Not directly obtained
- Short-term clay stability (embankments, cuts, foundations)
Property
UU (Unconsolidated-Undrained)
Values
- Partial (pre-consolidation only)
- Moderate (hours)
- Yes (critical)
- c_u, φ_u (may be nonzero)
- c', φ' (from effective stress analysis)
- Most practical; both short & long-term behavior
Property
CU (Consolidated-Undrained)
Values
- Full (throughout shear)
- Very slow (days per stage)
- No (u ≈ hydrostatic)
- Not typically reported
- c', φ' (rigorous drained parameters)
- Long-term stability, design; ultimate bearing capacity
Property
CD (Consolidated-Drained)
Columns
- Test Type
- Drainage
- Speed
- Pore Pressure Measured?
- Total-Stress Parameters
- Effective-Stress Parameters
- Primary Use
Table Title
Triaxial Test Types & Key Parameters
Rows
Values
- τ_f = c + σ tan φ
- τ_f = c' + σ' tan φ' where σ' = σ − u
Property
Formula
Values
- σ (total normal stress, includes pore pressure effect)
- σ' = σ − u (excludes pore pressure; effective stress only)
Property
Stresses Used
Values
- Short-term (undrained, φ ≈ 0); quick lab tests
- Long-term (drained); rigorous design; any drainage condition
Property
When to Use
Values
- c_u for undrained clay; varies with stress history
- c' for drained clay; often ≈ 0 for NC clay but nonzero for OC or bonded soil
Property
Cohesion Value
Values
- c ≈ 0, φ ≈ same as φ' (sand is always drained)
- c' ≈ 0, φ' ≈ 30–40° (density-dependent)
Property
Sand Behavior
Columns
- Aspect
- Total Stress Approach
- Effective Stress Approach
Table Title
Mohr-Coulomb vs. Effective-Stress Principle
Rows
Values
- ≈ 0 kPa
- c_u > 0 (undrained); c' ≈ 0 or > 0 (drained, depends on OCR)
Property
Cohesion (c or c')
Values
- φ' ≈ 30–40° (denser = higher)
- φ' ≈ 20–30° (drained); φ_u ≈ 0° (undrained, NC clay)
Property
Friction Angle (φ or φ')
Values
- Always drained (high permeability); UU/CD tests give same φ
- Undrained (short-term) or drained (long-term); UU vs. CD very different
Property
Drainage Behavior
Values
- Linear increase: τ increases with σ (or σ')
- UU test: c_u independent of σ₃; CD test: τ increases with σ'
Property
Strength vs. Confining Pressure
Values
- CD triaxial or direct shear; can also do UU (same result)
- CU or UU (undrained); CD (drained); UC test for quick c_u check
Property
Typical Lab Test
Values
- Always use c' = 0, φ' (effective-stress)
- Short-term: c_u, φ_u ≈ 0; Long-term: c', φ' (effective-stress)
Property
Design Approach
Columns
- Property
- Sand (Cohesionless)
- Clay (Cohesive)
Table Title
Sand vs. Clay Shear Strength Characteristics
Previous chapter
Consolidation and Settlement
Next chapter
Lateral Earth Pressure and Retaining Structures
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