CELE Geotechnical Engineering — Lateral Earth Pressure and Retaining StructuresCheat Sheet
Cheat sheet for CELE Geotechnical Engineering — Lateral Earth Pressure and Retaining Structures. Compact, printable, and organised around the concepts Professional Regulation Commission (PRC) — Board of Civil Engineering tests most frequently in the CELE 2026. Perfect for the week before exam day.
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. Lateral Earth Pressure and Retaining Structures lands at position 8th 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.
Lateral Earth Pressure and Retaining Structures - Cheat Sheet
Your final 30-minute quick-reference for earth-pressure coefficients, thrust calculations, wall stability checks, and common exam pitfalls in retaining structure design.
Sections
Formulas
Formula
Ka = (1 − sin φ)/(1 + sin φ) = tan²(45° − φ/2)
Meaning
Ka = active earth-pressure coefficient; φ = soil friction angle (degrees); acts when wall moves away from soil
Watch Out
Use radians if computing tan²; active is ALWAYS the minimum coefficient. Do NOT confuse tan(45° − φ/2) with tan²(45° − φ/2)
When To Use
Wall deflects away (bends outward); backfill subsides; typical driving case for retaining walls
Formula
Kp = (1 + sin φ)/(1 − sin φ) = tan²(45° + φ/2)
Meaning
Kp = passive earth-pressure coefficient; mobilized when wall pushes INTO soil
Watch Out
Passive resistance is OFTEN NEGLECTED conservatively (assume zero) unless soil is confirmed reliable; Kp = 1/Ka
When To Use
Toe of wall resists sliding; embedded sheet piles; wall compression case
Formula
K₀ = 1 − sin φ
Meaning
K₀ = at-rest earth-pressure coefficient; occurs when wall has zero movement
Watch Out
K₀ lies between Ka and Kp; for φ = 30°, K₀ = 0.5 (not 0.333 or 3.0)
When To Use
Tied-back walls; basement walls with no deflection; initial/design state
Common Values
Value
28–32°
Symbol
φ
Quantity
Loose sand φ
Value
34–40°
Symbol
φ
Quantity
Dense sand φ
Value
26–34°
Symbol
φ
Quantity
Silt φ
Value
18–30°
Symbol
φ'
Quantity
Clay φ (effective stress)
Value
17–19 kN/m³
Symbol
γ
Quantity
Typical soil unit weight (dry)
Value
19–21 kN/m³
Symbol
γsat
Quantity
Saturated soil unit weight
Value
9–11 kN/m³
Symbol
γ' = γsat − γw
Quantity
Buoyant soil unit weight
Section Title
Earth-Pressure Coefficients (Rankine Theory)
Important Facts
- For cohesionless soils (c = 0): Ka < K₀ < Kp; always true for φ > 0°
- Active pressure DECREASES with higher φ; passive INCREASES (inverse relationship)
- Ranking: Ka = 0.333 (φ = 30°), K₀ = 0.5 (φ = 30°), Kp = 3.0 (φ = 30°)
- Rankine theory assumes smooth wall (δ = 0); use Coulomb for wall friction δ > 0
- At-rest state is reference condition; Ka occurs after small outward movement (typically 0.1% H); Kp needs large inward movement (1–4% H)
Key Definitions
Term
Active Earth Pressure
Example
Gravity wall leaning back; bowed basement wall deflecting outward.
Definition
Minimum lateral pressure state when retaining wall moves away from backfill (lowest resistance demand).
Term
Passive Earth Pressure
Example
Toe of cantilever wall resisting sliding; embedded sheet pile pushed forward by surcharge.
Definition
Maximum lateral pressure state when wall is pushed INTO the soil (highest resistance available).
Term
At-Rest Earth Pressure
Example
Fully-tied basement wall with no deflection; braced soldier-pile wall.
Definition
Intermediate pressure when wall experiences zero movement; occurs in rigid basement walls or braced excavations.
Term
Cohesion
Example
Clay with c = 15 kPa; develops tension crack at depth zc = 2c√Ka / (γ√Ka)
Definition
Shear strength component of soil independent of normal stress; reduces active pressure near surface.
Diagrams To Know
- Triangular active pressure distribution (zero at surface, maximum γKa H at base)
- Pressure envelopes showing Ka, K₀, Kp relationship vs. depth
- Wall movement states: rigid (K₀), active (Ka), passive (Kp)
Formulas
Formula
Pa = ½ Ka γ H²
Meaning
Pa = total active thrust (horizontal component); γ = unit weight; H = wall height
Watch Out
Result is H² (quadratic), NOT linear; doubling height quadruples the thrust. Units: if γ in kN/m³, H in m, then Pa in kN/m
When To Use
Cohesionless dry backfill with no surcharge; gives magnitude in kN/m (per meter length of wall)
Formula
Pp = ½ Kp γ H²
Meaning
Pp = total passive thrust; usually applied only at toe below dredge line or reliably-confined soil
Watch Out
Conservative design OFTEN IGNORES Pp entirely (set to zero) unless passive soil is confirmed and confined
When To Use
Resistance to sliding at toe of cantilever wall; embedded sheet piles
Formula
z̄a = H/3 (location of Pa)
Meaning
Active thrust acts at H/3 above base for triangular pressure distribution
Watch Out
Common error: using H/2 (that is for rectangular/surcharge part only). Triangular = H/3 from base = 2H/3 from top
When To Use
All cohesionless active-pressure cases; creates overturning moment about toe
Formula
Pa(surcharge) = Ka q H
Meaning
Additional active thrust from uniform surcharge q (kPa); distributed uniformly over height
Watch Out
Surcharge portion acts at H/2 (rectangular), NOT H/3. Total moment = (triangular part)×(H/3) + (surcharge part)×(H/2)
When To Use
Surcharge (traffic, building, live load) on backfill surface
Formula
Pa(cohesion-reduced) = Ka γ z − 2c√Ka
Meaning
Active pressure at depth z reduced by cohesion; c = cohesion (kPa)
Watch Out
Pressure can go negative (tension); crack depth zc = 2c√Ka / γ. Above zc, ignore pressure or use Ka q as minimum
When To Use
Cohesive soil (clay) or c-φ soil; identifies tension crack zone near surface
Section Title
Lateral Thrust and Point of Application
Important Facts
- Active thrust Pa increases with H² and γ, decreases with higher φ (larger Ka)
- For dry cohesionless soil: Pa ∝ γ H²/tan²(45° + φ/2) (inverse Ka relationship)
- Water table behind wall adds FULL HYDROSTATIC force (γw h²/2), acting at h/3 below water table; use γ' = γsat − γw for submerged soil
- Surcharge adds linear component Ka q H (acts at H/2); total moment includes both triangular and rectangular parts
- Below tension crack: pressure = Ka(γz − 2c√Ka); above crack (0 < z < zc): pressure = 0 or Ka q (if surcharge)
Key Definitions
Term
Resultant Thrust
Example
5 m wall with γ = 18 kN/m³, φ = 30° ⟹ Pa = 75 kN/m at 1.67 m above base.
Definition
Total lateral force per unit length of wall from soil pressure; acts at H/3 for active case, creates overturning moment.
Term
Tension Crack
Example
Clay with c = 20 kPa, φ = 20°, γ = 18 kN/m³ ⟹ zc ≈ 1.1 m; assume no pressure above this depth.
Definition
Zone near soil surface where cohesion reduces active pressure to zero; backfill is relieved of pressure.
Term
Hydrostatic Pressure
Example
Water table at depth d below crest; water adds ½ γw (H−d)² at H/3 of the submerged portion.
Definition
Water pressure acting on wall below water table; full pressure γw h (not affected by soil friction).
Diagrams To Know
- Pressure distribution diagram: active case (triangular), with surcharge (triangular + rectangular)
Formulas
Formula
FS(overturn) = ΣMR / ΣMO ≥ 1.5 to 2.0
Meaning
FS(OT) = factor of safety against overturning; ΣMR = resisting moments (weight, passive), ΣMO = overturning moments (active thrust)
Watch Out
Moments taken about toe (pivot point); passive toe resistance often excluded conservatively; overturning is FIRST check
When To Use
Check all gravity and cantilever walls; typical FOS = 1.5–2.0 per NSCP 2015 guidelines
Formula
FS(slide) = [μ ΣW + Pp] / Pa,H ≥ 1.5
Meaning
FS(slide) = factor of safety against sliding; μ = base friction coefficient; ΣW = total weight; Pa,H = horizontal component of active thrust; Pp = passive toe resistance
Watch Out
Pp (passive toe) often set to ZERO (conservative); ΣW includes wall weight + backfill surcharge only within failure wedge
When To Use
Sliding check at base of wall; μ = tan φb (friction angle at wall-base interface) or 0.5–0.7 for concrete on soil
Formula
FS(bearing) → ensure resultant within middle third (B/6 from toe and heel)
Meaning
Prevent tension at heel; eccentricity e = (ΣMR − ΣMO) / ΣW must satisfy e ≤ B/6
Watch Out
If e > B/6, toe pressure becomes negative (tension), indicating bearing failure or need for prestress/anchors
When To Use
All walls; keep resultant in middle third to avoid tension crack under base
Formula
σtoe = (ΣW/B)(1 + 6e/B), σheel = (ΣW/B)(1 − 6e/B)
Meaning
Bearing stresses at toe and heel; e = eccentricity of resultant from base centroid
Watch Out
Toe stress MUST NOT exceed bearing capacity qa of foundation soil; heel stress must be ≥ 0 (no tension)
When To Use
Detailed bearing-capacity check; stress limits set by φ and c of foundation soil
Formula
Failure wedge angle ≈ (45° + φ/2) from horizontal
Meaning
Active-failure plane inclination; wedge bounded by wall and failure plane
Watch Out
Wedge weight and friction angle change with backfill slope; Coulomb angle assumes worst case
When To Use
Coulomb analysis; identifying which portion of backfill contributes to active pressure
Common Values
Value
1.5–2.0
Symbol
FOS(OT)
Quantity
Typical FOS overturning
Value
1.5
Symbol
FOS(slide)
Quantity
Typical FOS sliding
Value
0.5–0.7
Symbol
μ
Quantity
Concrete-on-soil friction coefficient
Value
0.4–0.6 H = 2.0–3.0 m
Symbol
B
Quantity
Typical base width (cantilever wall, H = 5 m)
Section Title
Retaining-Wall Stability Analysis
Important Facts
- Overturning is checked FIRST (governs wall geometry); sliding is second; bearing is final
- Overturning moment = Pa × (H/3) for triangular pressure; surcharge adds Ka q H × (H/2)
- Resisting moments = wall weight × (horizontal distance from toe) + backfill weight (within wedge) × centroid distance
- Sliding check assumes base interface friction only; cohesion at base can ADD to resistance but often neglected (conservative)
- Passive toe resistance (Pp) is RARELY used in design (too conservative to exclude); if included, requires confinement (dredge limit, other structure)
Key Definitions
Term
Factor of Safety Against Overturning
Example
Wall base moment 300 kN·m/m, active moment 125 kN·m/m ⟹ FOS = 2.4 (safe).
Definition
Ratio of resisting moments to overturning moments about the toe; typical FOS = 1.5–2.0.
Term
Factor of Safety Against Sliding
Example
Wall weight 250 kN/m, μ = 0.5, active thrust horizontal = 80 kN/m ⟹ FOS = (250 × 0.5)/80 = 1.56 (marginal).
Definition
Ratio of shear resistance (friction + passive toe) to horizontal active thrust; typical FOS = 1.5.
Term
Eccentricity
Example
Base B = 3 m, e = 0.4 m ⟹ e/B = 0.133 > 0.167 (B/6), so wall is overstressed at heel.
Definition
Distance of resultant from base centroid; must stay within B/6 (middle third) to ensure no tension.
Term
Friction Coefficient (μ)
Example
Concrete on sand: μ ≈ 2/3; concrete on clay: μ ≈ 0.4–0.5 (cohesion adds separately).
Definition
Ratio of shear to normal stress at wall base; typically μ = tan φb ≈ 0.5–0.7 for soil-concrete interface.
Diagrams To Know
- Free-body diagram of wall showing Pa, weight W, reactions at base (normal, friction, passive)
- Moment diagram about toe showing overturning (Pa × H/3) and resisting moments (W × horizontal distance)
Formulas
Formula
Ka (Coulomb) with δ ≠ 0, β ≠ 0 (wall friction δ, backfill slope β)
Meaning
Active coefficient modified for non-vertical wall and sloping backfill; more complex than Rankine; generally Ka(Coulomb) < Ka(Rankine) for typical cases
Watch Out
Coulomb requires iterative or graphical solution; for board exams, often given or assumed Rankine unless explicitly stated otherwise
When To Use
Battered walls (δ > 0 toward backfill reduces Ka); inclined backfill (increases Ka if slope rises away from wall)
Formula
δ = wall-soil friction angle; typical 0 ≤ δ ≤ φ (often δ ≈ 2φ/3 for design)
Meaning
Friction at wall-soil interface; battered (inward) wall improves stability (reduces Ka)
Watch Out
δ = 0 is conservative (Rankine); δ > 0 requires detailed Coulomb analysis or tables; most exam problems use δ = 0
When To Use
Battered walls (outward slope) or rough walls; increases effective wall friction
Common Values
Value
δ ≈ 20–25° (rough wall)
Symbol
δ
Quantity
Wall friction for concrete on sand
Value
δ ≈ 15–20°
Symbol
δ
Quantity
Wall friction for concrete on clay
Value
δ = 0°
Symbol
δ
Quantity
Vertical wall (Rankine)
Section Title
Coulomb Theory (Wall Friction & Sloping Backfill)
Important Facts
- Rankine (δ = 0, β = 0) is most common board-exam case; Coulomb is more general but rarely assigned without tables
- Battered walls (δ > 0) reduce Ka; sloping backfill (β > 0) increase Ka; effects partially offset in practice
- For typical φ = 30–35°: assume δ ≈ 15–20° if battered; δ = 0 if vertical (Rankine is default)
Key Definitions
Term
Wall Friction (δ)
Example
Battered cantilever wall: δ = 15°; Rankine wall (vertical): δ = 0°.
Definition
Angle between soil-wall interface shear and normal; reduces active pressure if wall leans into soil.
Term
Backfill Slope (β)
Example
Sloping backfill β = 20° requires higher thrust than horizontal (β = 0°).
Definition
Angle of backfill surface above horizontal; inclined surface increases active pressure (higher Ka).
Diagrams To Know
- Coulomb failure wedge with inclined backfill and wall friction
Formulas
Formula
σ'a = Ka γ' z − 2c√Ka (effective stress, cohesion-reduced)
Meaning
Active pressure in cohesive soil; c = cohesion; γ' = γsat − γw below water table; σ'a goes to zero at tension crack depth
Watch Out
Tension can develop; assume zero pressure above zc = 2c√Ka / γ. Resultant thrust is REDUCED by cohesion
When To Use
Clay or c-φ backfill; identifies tension crack zone near surface
Formula
zc = 2c√Ka / γ (depth of tension crack)
Meaning
Depth from surface where active pressure becomes zero due to cohesion
Watch Out
If zc > H, no crack develops (cohesion holds entire backfill); if zc << H, crack is shallow but significant for stability
When To Use
Clay backfill; determines height of unsupported (cracked) zone at top of wall
Formula
Pw = ½ γw (H − hw)² (hydrostatic force from water table at depth hw)
Meaning
Pw = water pressure force; acts at (H − hw)/3 below water table; γw = 9.81 kN/m³
Watch Out
Water is INDEPENDENT of soil friction (no Ka needed); add Pw and Pa separately. Use γ' (buoyant weight) for soil below water table
When To Use
Seepage behind wall, phreatic surface, or saturated backfill; water pressure ADDS to active soil pressure
Formula
γ' = γsat − γw ≈ (γ − γw) = specific weight submerged (buoyant unit weight)
Meaning
Effective soil weight below water table; typically γ' ≈ 9–11 kN/m³ (less than dry weight)
Watch Out
DO NOT apply Ka to water pressure; water pressure is ALWAYS hydrostatic (full), independent of φ or c
When To Use
Any retaining wall with water table; reduces active pressure in saturated zone but adds separate water force
Common Values
Value
zc = 2c√Ka / γ ≈ 0.5–2.0 m (typical)
Symbol
zc
Quantity
Tension crack depth (clay)
Value
9.81 kN/m³ (use 9.8 or 10 in exams)
Symbol
γw
Quantity
Water unit weight
Value
≈ 9–10 kN/m³
Symbol
γ'
Quantity
Buoyant unit weight (sand)
Value
15–25 kPa
Symbol
c
Quantity
Cohesion (stiff clay)
Value
5–10 kPa
Symbol
c
Quantity
Cohesion (soft clay)
Section Title
Water and Cohesion Effects
Important Facts
- Cohesion REDUCES active pressure; water table INCREASES total pressure (separate hydrostatic component)
- Tension crack in cohesive backfill means top portion is unloaded; assume zero pressure above zc for thrust calculation
- Water pressure adds independently: total lateral force = (soil active) + (water hydrostatic); act at different depths
- Submerged soil unit weight γ' ≈ 9–11 kN/m³; much less than dry 17–19 kN/m³; reduces Ka γ' term but water adds Pw
- Design for both cases: (1) dry cohesionless (worst Ka), (2) saturated with water table (worst Pw + reduced γ')
Key Definitions
Term
Cohesion
Example
Clay c = 20 kPa, φ = 20°, γ = 18 kN/m³ ⟹ zc ≈ 1.1 m (no pressure in top 1.1 m if wall is tall).
Definition
Shear strength independent of normal stress; reduces active pressure by 2c√Ka per unit depth; creates tension crack zone.
Term
Phreatic Surface
Example
Water table 2 m below crest of 8 m wall; upper 2 m uses γdry, lower 6 m uses γ' plus separate water force.
Definition
Water table boundary; soil above is vadose (partially saturated or dry), below is saturated.
Term
Effective Stress
Example
At depth z in saturated soil: σ'v = γ'z (not γz).
Definition
Stress carried by soil skeleton; σ' = σ − u (total minus pore water pressure); controls friction angle φ.
Diagrams To Know
- Pressure diagram showing tension crack zone (zero pressure above zc) in cohesive backfill
- Combined soil + water pressure diagram with water table
Common Values
Value
0.4–0.7 H
Symbol
B
Quantity
Gravity wall base width
Value
H/12 to H/10
Symbol
t
Quantity
Cantilever stem thickness
Value
0.4–0.6 H
Symbol
B
Quantity
Cantilever base width
Value
0.3–0.5 × free height
Symbol
d
Quantity
Sheet pile embedment
Section Title
Retaining-Wall Types & Design Features
Important Facts
- Gravity wall: FS(OT) and FS(slide) both critical; passive toe resistance often contributes significantly
- Cantilever wall: stem bending governs design; base must be wide and strong; heel backfill weight is crucial for OT stability
- Sheet piles: embed depth determined by passive resistance and moment; no backfill weight; high lateral stiffness
- Soldier piles: lagging can be thin (reduces excavation disturbance); anchors/braces reduce moment at pile cap
- All walls: check bearing capacity of foundation soil; ensure resultant in middle third; factor of safety ≥ 1.5–2.0
Key Definitions
Term
Gravity Wall
Example
Stone or unreinforced concrete masonry wall; 2–4 m tall; wide base (0.4–0.7 H).
Definition
Wall stabilized by its own weight (no reinforcement); passive resistance from backfill pressure; simple, massive.
Term
Cantilever Wall
Example
T-shaped or L-shaped reinforced concrete wall; stem thickness ≈ H/12 to H/10; base width ≈ 0.4–0.6 H.
Definition
Reinforced concrete wall with toe and heel; thin stem; economical for 4–8 m heights.
Term
Sheet Pile Wall
Example
Steel or vinyl sheet piles for cofferdams, temporary excavation support, waterfront structures.
Definition
Interlocking metal or reinforced concrete piles; flexible, high lateral stiffness; used in wet or confined sites.
Term
Soldier Pile (Tangent/Secant Pile) Wall
Example
Soldier piles spaced 1.5–2.0 m; lagging is timber or shotcrete; used in urban areas (minimal noise).
Definition
Vertical drilled or driven piles with lagging between; high bending stiffness; economical for deep excavations.
Term
Tieback Wall
Example
Diaphragm wall or soldier piles with grouted cables at depth; typical for basements.
Definition
Thin wall anchored to stable ground behind; resists thrust by tension anchors; used when space is limited.
Diagrams To Know
- Gravity wall cross-section (massive, trapezoidal, centered weight)
- Cantilever wall T-section (thin stem, toe, heel, reinforcement pattern)
- Sheet pile and soldier pile elevation (embedment, spacing, lagging)
Section Title
Practical Board-Exam Workflow
Important Facts
- Step 1: Identify soil type (cohesionless, cohesive, c-φ) and water table location
- Step 2: Calculate Ka (and Kp if relevant) using φ; identify tension crack depth if c > 0
- Step 3: Compute active thrust Pa = ½ Ka γ H² and surcharge Pa,surcharge = Ka q H; locate at H/3 and H/2 respectively
- Step 4: Add water force Pw = ½ γw (H−hw)² if water table exists; separate from soil pressure
- Step 5: Estimate wall geometry (usually given); calculate weight ΣW and location of centroid
- Step 6: Check overturning (FS(OT) ≥ 1.5–2.0): ΣMR / ΣMO
- Step 7: Check sliding (FS(slide) ≥ 1.5): [μ ΣW ± Pp] / Pa,H
- Step 8: Check bearing (resultant in middle third): e = (ΣMR − ΣMO) / ΣW ≤ B/6
- Step 9: If failing, increase base width B, add heel backfill, or add anchors; iterate
Must Remember
- Ka = tan²(45° − φ/2) is ALWAYS the minimum; Kp = tan²(45° + φ/2) is ALWAYS the maximum; K₀ = 1 − sin φ is between them.
- Active thrust Pa = ½ Ka γ H² acts at H/3 above base; surcharge adds Ka q H (acts at H/2); do NOT mix locations.
- Overturning check FS(OT) = ΣMR / ΣMO ≥ 1.5–2.0 is typically FIRST check; governs wall height and base width.
- Sliding check FS(slide) = [μ ΣW (+ Pp)] / Pa,H ≥ 1.5; passive toe (Pp) often set to ZERO for conservatism.
- Bearing/eccentric check: keep resultant within middle third of base (e ≤ B/6) to avoid tension at heel.
- Cohesion REDUCES active pressure by 2c√Ka; creates tension crack at depth zc = 2c√Ka / γ; assume zero pressure above zc.
- Water table adds INDEPENDENT hydrostatic force Pw = ½ γw h² (acts at h/3 below water table), NOT affected by Ka or c.
- Use γ' = γsat − γw ≈ 9–11 kN/m³ for submerged soil; γ' is much smaller than dry γ, reducing active pressure but water adds Pw.
- Rankine (smooth wall, horizontal backfill, δ = 0, β = 0) is most common exam case; Coulomb required only if stated.
- Conservative design ignores passive toe resistance (Pp = 0); include Pp only if passive soil is verified confined (rare).
Last Minute Tips
- Always START with Ka, K₀, Kp using φ; these three values govern EVERYTHING. Memorize: Ka < K₀ < Kp.
- For thrust calculation, remember Pa = ½ Ka γ H² (quadratic in H); doubling height means 4× the thrust. Surcharge is LINEAR (Ka q H).
- Moment arms: active thrust at H/3 from base; surcharge at H/2; weight of wall at its center of gravity. Use toe as pivot point.
- If wall fails OVERTURNING: increase base width B (add heel backfill weight). If wall fails SLIDING: increase friction μ (roughen base or use pins/anchors).
- DO NOT forget water table: if water is present, use γ' for submerged soil PLUS a separate water force Pw = ½ γw (H−hw)². They act independently with different moment arms.
Comparison Tables
Rows
Values
- Ka = tan²(45° − 15°) = tan²(30°)
- 0.333
- Wall moves away (active)
- Retaining wall driving force
Property
Ka
Values
- K₀ = 1 − sin 30°
- 0.5
- No wall movement (at-rest)
- Rigid basement, initial condition
Property
K₀
Values
- Kp = tan²(45° + 15°) = tan²(60°)
- 3.0
- Wall pushed into soil (passive)
- Toe resistance (often ignored)
Property
Kp
Columns
- Coefficient
- Formula
- Value
- When (State)
- Typical Use
Table Title
Earth-Pressure Coefficients for φ = 30°
Rows
Values
- Static (normal)
- 1.5–2.0
- Conservative; first check; governs geometry
Property
Overturning
Values
- Static (normal)
- 1.5
- Friction at base + passive toe (often Pp = 0)
Property
Sliding
Values
- Static (normal)
- qall / qactual ≥ 1.5–2.0
- Resultant must be in middle third; no tension at heel
Property
Bearing
Values
- Slope failure
- 1.3–1.5
- For walls on slopes; circular/wedge analysis
Property
Global stability
Columns
- Failure Mode
- Load Case
- Minimum FOS
- Comment
Table Title
Retaining-Wall Stability Factor of Safety Targets (NSCP 2015 Guidance)
Rows
Values
- Minimum (Ka = 0.333 for φ = 30°)
- Maximum (Kp = 3.0 for φ = 30°)
Property
Magnitude
Values
- Away from backfill (small outward displacement ~0.1% H)
- Into backfill (large inward displacement ~1–4% H)
Property
Wall Movement
Values
- Soil expands, shear stress decreases, friction mobilized away from wall
- Soil compressed, shear stress increases, friction mobilized into wall
Property
Soil State
Values
- Driving force (thrust on wall); worst case for stability checks
- Resisting force at toe or embedded depth; often conservatively ignored
Property
Design Use
Values
- Design against Pa; FS = 1.5–2.0
- Pp included only if verified to be mobilized (rare)
Property
Typical FOS
Columns
- Aspect
- Active (Ka)
- Passive (Kp)
Table Title
Active vs. Passive Earth Pressure Comparison
Rows
Values
- σa = Ka γ z (triangular)
- Pa = ½ Ka γ H² (at H/3)
- Baseline case; no reduction; maximum thrust for dry soil
Property
Dry cohesionless
Values
- σa = Ka γ z − 2c√Ka (with tension crack above zc = 2c√Ka / γ)
- Pa < ½ Ka γ H² (reduced; trapezoid not triangle if zc < H)
- Cohesion reduces thrust; tension crack in top zc zone
Property
Dry cohesive (c > 0)
Values
- σa = Ka γ' z (soil part) + γw (H − hw) (water part; separate)
- Pa,soil + Pw (sum independently, different moment arms)
- Use γ' in soil term; water adds FULL hydrostatic, no Ka factor
Property
Saturated (no cohesion)
Values
- σa = Ka γ' z − 2c√Ka + γw (water above water table)
- Complex; tension crack may be present; must account for both
- Worst case if water table is high; rare in exams (usually simplified)
Property
Saturated + cohesive
Columns
- Scenario
- Active Pressure Formula
- Resultant Magnitude
- Comment
Table Title
Effect of Cohesion and Water Table on Active Thrust
Rows
Values
- 28–32°
- 0.37–0.31
- 17–18
- High compressibility; use conservative (lower φ)
Property
Loose sand
Values
- 30–35°
- 0.33–0.27
- 18–19
- Average; Ka ≈ 0.3 is rule-of-thumb
Property
Medium sand
Values
- 35–40°
- 0.27–0.22
- 19–20
- High angle of repose; low Ka
Property
Dense sand
Values
- 26–34°
- 0.40–0.28
- 17–18
- Wide range; depends on compaction and cohesion
Property
Silt
Values
- 18–30°
- 0.53–0.33
- 18–20
- Use effective stress φ'; undrained φu ≈ 0 (total stress method)
Property
Clay (φ' effective)
Columns
- Soil Type
- Typical φ (degrees)
- Ka (approx.)
- Typical γ (kN/m³)
- Notes
Table Title
Common φ Values by Soil Type
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