Bearing Capacity of Soils - Memory Anchors
For PRC board exam preparation, where you must recall dozens of formulas and correction factors under exam pressure, anchoring abstract geotechnical concepts to vivid stories, acronyms, and visual images is a game-changer. Instead of memorizing 'q_u = cN_c + qN_q + 0.5γBN_γ' as a string of symbols, you will attach each term to a concrete mental image — so that even at 2 PM on exam day, your brain retrieves the formula automatically. This collection uses mnemonics, analogies from Filipino everyday life, micro-stories, and Mermaid visual maps to make every concept in Bearing Capacity of Soils truly UNFORGETTABLE.
Memory anchors
Terzaghi's Three-Term Bearing Capacity Equation: q_u = cN_c + qN_q + 0.5γBN_γ
Memory aid
Remember the three terms with the acronym CQG: 'C' for Cohesion (cN_c), 'Q' for overburden surcharge (qN_q), 'G' for Gamma-width or ground width (0.5γBN_γ). Think: 'CQG = Can Quit Gravity?' — No, you can NEVER quit gravity in foundation design! Each letter is one term, each term has its own N-factor. Say it aloud: 'Cohesion, overburden surcharge, weight-of-soil.' C–Q–G.
Why it works
Acronyms compress multi-part information into a single retrievable token. The humorous question 'Can Quit Gravity?' adds an emotional hook, making it stickier.
Example usage
Board exam: 'Find q_u for a strip footing.' Mentally fire CQG → write c·N_c + q·N_q + 0.5γBN_γ → substitute given values.
Recall trigger
Think 'CQG' every time you see a footing problem.
Shape Factors: Strip = 1.0/0.5, Square = 1.3/0.4, Circular = 1.3/0.3 on the cN_c and γBN_γ terms
Memory aid
Use the phrase 'Strip is Straight, Square and Circle Share 1.3, but differ on B.' For the γBN_γ coefficient: Strip=0.5, Square=0.4, Circle=0.3. Remember these as '5-4-3 counting DOWN' (5 for strip, 4 for square, 3 for circle). Filipino shortcut: think of billiard balls going into pockets — you shoot the STRIP shot first (0.5), then SQUARE up (0.4), then roll it in a CIRCLE (0.3). For the cN_c multiplier: Strip=1.0, Square=1.3, Circle=1.3 — the two 'rounded' shapes (square and circle) both get the bonus 1.3.
Why it works
The countdown 5-4-3 is a natural numerical pattern that the brain encodes as a sequence, not three separate facts. The billiard analogy is culturally familiar.
Example usage
Square footing problem: 1.3·c·N_c + q·N_q + 0.4·γ·B·N_γ. Circular: same 1.3 on cohesion, but 0.3 on the width term.
Recall trigger
Picture a billiards table with three ball paths: straight, square-corner, circular.
Surcharge Term: q = γD_f (overburden pressure at footing base)
Memory aid
Imagine burying a balikbayan box (pasalubong box) at depth D_f underground. The weight of all the soil pressing DOWN on that box is exactly γ × D_f — that is the surcharge 'q'. The deeper you bury it (larger D_f), the heavier the press, the higher the surcharge. The soil above the footing is essentially a surcharge load on the bearing stratum below.
Why it works
The balikbayan box is a strong cultural image for Filipino students. Connecting a physical weight concept to γD_f makes the formula intuitive rather than arbitrary.
Example usage
Given γ=18 kN/m³, D_f=1.5 m → q = 18×1.5 = 27 kPa. This q multiplies N_q in Terzaghi's equation.
Recall trigger
Visualize a balikbayan box buried at depth D_f with soil piled on top.
ϕ=0 (Pure Clay) Special Values: N_c=5.7, N_q=1, N_γ=0
Memory aid
Chunk the three numbers as a phone area code: '5-7-1-0' — read it as '57, 1, 0' where 57 is N_c (Terzaghi), 1 is N_q, and 0 is N_γ. The rhyme: 'When phi is ZERO, clay is the hero — N_c is 5.7, N_q is one, and N_gamma is done (zero)!' The width term vanishes because loose clay has no frictional wedge to mobilize.
Why it works
Chunking numbers into familiar patterns (like a phone number) reduces cognitive load. The rhyme adds rhythm-based encoding.
Example usage
Clay footing, ϕ=0: q_u = 1.3·c·5.7 + q·1 + 0 = 7.41c + γD_f (for square footing).
Recall trigger
Hear 'phi = 0' and immediately think '5.7 – 1 – 0'.
Factor of Safety: q_a = q_u / FS, with FS = 2.5 to 3
Memory aid
Think of FS as a Helmet Law analogy: The NSCP and Philippine traffic laws require helmets on motorcycles for safety. You never ride AT the failure load (skull crack = soil failure). The FS=3 is your three-layer helmet — the outer shell (1×), the foam (2×), the inner liner (3×). You work at only 1/3 of the 'skull-crack' load. FS=2.5 is the minimum required — a two-and-a-half-layer helmet is the legal minimum for non-highway riding.
Why it works
Safety factor concepts are intuitive when tied to personal safety. The helmet layers make '3 layers = FS 3' a physical image.
Example usage
q_u = 756 kPa, FS=3 → q_a = 756/3 = 252 kPa. Don't apply the full ultimate load!
Recall trigger
Think of a helmet with three layers every time you divide by FS.
Net vs Gross Allowable Bearing Capacity: q_a,net = (q_u − γD_f) / FS
Memory aid
Story: Engineer Nico designs a footing in Pasig. His boss says 'We already paid for the excavation — the soil we removed is not a NEW load!' The removed soil (γD_f) was already there — it isn't 'added' load from the structure. So NET capacity = only the EXTRA pressure the structure adds, not the overburden that was already there. Subtract γD_f from q_u FIRST, then divide by FS. The gross capacity includes the overburden; the net strips it away first.
Why it works
The narrative of 'already paid for' creates a logical reason to subtract, making the formula feel like common sense rather than a rule to memorize.
Example usage
q_u = 388.5 kPa, γD_f = 18 kPa → q_u,net = 370.5 kPa → q_a,net = 370.5/3 = 123.5 kPa.
Recall trigger
Think: 'the excavation was already paid for — don't count it again.'
Water Table Correction: Use γ' (submerged unit weight) when WT is at or above footing base
Memory aid
Think of a fishpond (isda sa palayan) — when the pond is flooded, the soil under the water 'feels lighter' because water buoys it up. The submerged unit weight γ' = γ_sat − γ_w ≈ 9–10 kN/m³ instead of the full γ ≈ 18–20 kN/m³. When the water table RISES to the footing base, you must use the 'buoyed' γ' in the width term (0.5γBN_γ). The soil under the footing is swimming — it's only half as heavy!
Why it works
The fishpond image is vivid and culturally relevant in the Philippines. Buoyancy is a concrete physical concept most students understand well.
Example usage
WT at footing base: replace γ with γ' = γ_sat − 9.81 in the γBN_γ term. If γ_sat=20, γ'=10.19 kN/m³.
Recall trigger
Visualize the footing sitting in a flooded fishpond.
Local/Punching Shear (Loose Soil): Reduce c and tanϕ by factor 2/3
Memory aid
Remember '2/3 Rule for Loose Losers.' When soil is LOOSE (punching/local shear governs), both c and tanϕ are LOSERS — they lose 1/3 of their value. Use c* = (2/3)c and tanϕ* = (2/3)tanϕ. The 2/3 is like getting a 'Needs Improvement' grade (67%) on your board exam — you pass but not fully. Dense soil gets full marks (general shear); loose soil gets the 2/3 penalty.
Why it works
The grade analogy ties the reduction to a familiar academic experience. 'Loose Losers' is a humorous alliterative hook.
Example usage
ϕ=28° (loose sand): compute ϕ*=arctan(2/3·tan28°), use modified N-factors for local shear q_u.
Recall trigger
Think '2/3 Needs Improvement' when you see loose soil or punching shear.
Three Modes of Bearing Failure: General, Local, Punching Shear
Memory aid
Story of three boxers: GENERAL Shear is the champion — he delivers a clean, full knockout with a well-defined failure surface (like a classic bulge on both sides of the footing). LOCAL Shear is the semi-pro — partial failure, the surface only shows on one side, soil is moderately loose. PUNCHING Shear is the street brawler — no visible technique, the footing just sinks straight down through very loose soil or deep footings, no side bulge at all. Dense=General, Moderate=Local, Loose=Punching.
Why it works
Personifying failure modes as fighters creates a narrative with clear personality differences, making classification intuitive.
Example usage
Exam asks: 'Which failure mode applies to dense sand?' → General Shear → use full c and ϕ values.
Recall trigger
Three boxers: Champion (General), Semi-Pro (Local), Street Brawler (Punching).
Bearing Capacity Factors N_c, N_q, N_γ increase with ϕ
Memory aid
Visualize a STAIRCASE going UP from left to right. The x-axis is ϕ (friction angle), and the staircase steps are N_c, N_q, N_γ. At ϕ=0: steps are at 5.7, 1, 0 (very low ground floor). As ϕ increases to 40°+, the staircase shoots up dramatically — N_c can exceed 75, N_q over 64, N_γ over 93. The staircase is STEEPER for N_γ than for N_q, and N_c is always the tallest step. Remember: ALL N-factors ALWAYS go UP with ϕ — they never decrease.
Why it works
The staircase is a spatial image that encodes the monotonic increasing relationship. Students can literally 'see' N-values climbing as ϕ increases.
Example usage
ϕ=25°: N_c=25.13, N_q=12.72, N_γ=8.34. ϕ=30°: N_c=37.16, N_q=22.46, N_γ=19.13. Higher ϕ = bigger N.
Recall trigger
See a staircase climbing from ϕ=0 upward.
Settlement Often Governs Over Shear Failure
Memory aid
Think of the LEANING TOWER of Pisa. It didn't collapse from shear bearing failure — it just SETTLED unevenly. In practice, a soil can have a high q_u (won't shear) but still be 'unsafe' if it settles too much. The real enemy is often the carpenter's rule: 'A wall that leans is worse than a wall that falls.' For most real projects in the Philippines (especially Manila's soft alluvium), settlement controls the design, not shear failure. Always check BOTH — q_u and settlement.
Why it works
The Leaning Tower is a globally recognized example that creates a concrete memorable case. The dual-check reminder is embedded in the story.
Example usage
Even if q_a = 150 kPa is safe for shear, check if the footing will settle > 25 mm (typical allowable limit) under that load.
Recall trigger
Picture the Leaning Tower of Pisa every time you finish a q_u calculation.
Formula for Allowable Column Load: Q_a = q_a,net × A
Memory aid
QA = Quality Assurance. In factory quality control, Q_a is the 'approved output quantity.' Here, Q_a (allowable load) = the unit allowable pressure (q_a,net) multiplied by the 'factory floor area' (A = B² for square, B×L for rectangular). Think: the soil factory can process q_a,net kPa per unit area — multiply by the floor area to get total approved capacity (kN).
Why it works
The QA factory metaphor reframes the formula as a production capacity problem, making the multiplication logical.
Example usage
q_a,net=123.5 kPa, A=2×2=4 m² → Q_a=123.5×4=494 kN.
Recall trigger
Think 'QA Factory: unit rate × floor area = total output'.
Terzaghi Shallow Footing Condition: D_f ≤ B (shallow foundation criterion)
Memory aid
Rhyme: 'If Depth is less than Width, Terzaghi's your myth — er, your method! Shallow and light, Terzaghi's right. Deeper than wide? Another equation — set Terzaghi aside.' The shallow footing assumption (D_f ≤ B) is what validates Terzaghi's original equation. Deeper footings (like piles) need different approaches — Meyerhof, Hansen, or Vesic for inclined/eccentric loads.
Why it works
Rhyme creates a phonological loop memory trace. The 'depth less than width' rule is embedded in a rhythmic couplet.
Example usage
B=2m, D_f=1m → D_f < B → Terzaghi applies. B=2m, D_f=5m → not strictly shallow → consider Meyerhof.
Recall trigger
Recite the rhyme when checking whether Terzaghi applies.
Common Board Pitfall: Forgetting the N_q (Surcharge) Term
Memory aid
Story: Student Mika was halfway through the board exam when she computed q_u = cN_c + 0.5γBN_γ and got a very low answer. She forgot qN_q! She imagined the soil ABOVE the footing whispering 'Hey! What about ME? I'm also pushing down!' The overburden is always present — D_f is never zero in a real footing. After the exam, she put a sticky note on her review book: 'q = γD_f is NEVER zero unless told so — don't ghost the surcharge term!'
Why it works
The narrative of a common mistake creates an emotional warning. Students are motivated by the fear of repeating someone else's error.
Example usage
Before writing q_u, always confirm you have THREE terms: cN_c, qN_q, 0.5γBN_γ. If any is missing, ask why.
Recall trigger
Hear the soil above the footing say 'What about me?'
Net Ultimate Bearing Capacity: q_u,net = q_u − γD_f
Memory aid
Visualize a CASH REGISTER receipt. The GROSS amount (q_u) includes a line item for 'soil already there' (γD_f). The NET amount after deducting that pre-existing load is q_u,net. Think of γD_f as the 'existing mortgage' on the soil — the structure only adds NEW load on top of it. The net ultimate capacity is the maximum NEW load the soil can take beyond what it was already carrying.
Why it works
Financial metaphors of gross vs net income are universally understood and map perfectly to the gross vs net pressure concept.
Example usage
q_u=388.5 kPa, γD_f=18 kPa → q_u,net=370.5 kPa. This net value is used for net allowable capacity.
Recall trigger
Picture a cash register: GROSS minus DEDUCTION (γD_f) = NET.
Water Table Depth Zones: WT at/above base vs within B below vs deeper than B
Memory aid
Walk through a building: GROUND FLOOR (WT at or above footing base) → use γ' everywhere in the width term. FIRST FLOOR (WT between base and depth B below) → interpolate — partial reduction. SECOND FLOOR (WT deeper than B below footing) → no correction needed, full γ applies. Each 'floor' of the building is a different water table zone, and as you go UP (WT gets deeper), the correction gets LESS severe — until it disappears on the second floor.
Why it works
The method of loci (memory palace) uses spatial navigation to encode a multi-case rule. Each floor = one zone = one correction level.
Example usage
WT at footing base → ground floor → γ'=γ_sat−9.81 in width term. WT at 0.5B below → first floor → interpolate γ_effective.
Recall trigger
Mentally 'walk up the building' and check which floor the water table is on.
Bearing Capacity Factors Table for ϕ=25°: N_c=25.13, N_q=12.72, N_γ=8.34
Memory aid
For ϕ=25° (a very common exam value), chunk the factors as '25-12-8' — round numbers close to the actual values (25.13, 12.72, 8.34). Think of it as a sports jersey numbering: #25 (N_c), #12 (N_q), #8 (N_γ). Player 25 is the captain (biggest N), Player 12 is the vice-captain, and Player 8 is the playmaker (smallest but still important). Team '25° Phi' scores 25-12-8.
Why it works
Sports jersey numbers are memorable cultural references. Chunking three values as a team set reduces three separate memories to one.
Example usage
ϕ=25°: N_c≈25.13, N_q≈12.72, N_γ≈8.34. Quick board exam check before substituting.
Recall trigger
Visualize three basketball jerseys: #25, #12, #8.
Bearing Capacity Factors for ϕ=30°: N_c=37.16, N_q=22.46, N_γ=19.13
Memory aid
For ϕ=30° (another extremely common board value), remember '37-22-19' as a birth year sequence: 'Born in 1937, married in 1922, retired in 1919 — wait, that's backwards!' The absurdity (retiring before marrying) makes it memorable. Or think: 37 > 22 > 19 — they count DOWN but all start near 20-40. Better hook: '37 (N_c) is your father's age, 22 (N_q) is yours, 19 (N_γ) is your younger sibling's.'
Why it works
Family age relationships create an emotionally resonant ordering that is easy to reconstruct from a memorable anchor.
Example usage
ϕ=30°: q_u (strip) = c(37.16) + γD_f(22.46) + 0.5γB(19.13).
Recall trigger
Three family members: father=37, you=22, sibling=19.
The Three N-Factors are Always Positive and Dimensionless
Memory aid
Mnemonic: 'N is Never Negative.' All bearing capacity factors (N_c, N_q, N_γ) are always positive numbers greater than or equal to zero. N_γ=0 only when ϕ=0 (pure clay). If you ever calculate a negative N in an exam, you made an error. Think of N as the soil's 'enthusiasm' — soil can be less enthusiastic (ϕ=0, N_γ=0) but never depressed (never negative).
Why it works
A simple rule ('never negative') with an anthropomorphic explanation removes a common error source.
Example usage
Check: ϕ=25° → N_c=25.13 ✓, N_q=12.72 ✓, N_γ=8.34 ✓. All positive. If any were negative, error detected.
Recall trigger
'N is Never Negative' — if you get a negative N, recheck your ϕ or table lookup.
Foundation Design Goal: Applied Pressure < Allowable Bearing Capacity, AND Settlement < Allowable Settlement
Memory aid
Think of foundation design as passing TWO subjects in school (like passing both Theory and Lab in Engineering Chemistry). You must pass BOTH to pass the course: (1) Applied stress ≤ q_a (pass the 'Shear Failure' subject), AND (2) Settlement ≤ δ_allow (pass the 'Deformation' subject). Failing either one means redesign. A footing that passes shear but fails settlement is like a student who passes the lecture exam but fails the laboratory — still failed!
Why it works
The dual-subject analogy is immediately relatable to students who have experienced failing one component of a course. It reinforces the dual-check requirement.
Example usage
Compute q_a → check applied load ≤ q_a × A. Then compute expected settlement → check ≤ 25 mm (typical) or project spec.
Recall trigger
Two passing grades needed: Shear AND Settlement.
Revision game
I am the 'password' to enter Terzaghi's equation. I equal unit weight times depth. Who am I?
Answer
Surcharge q = γD_f
Memory link
A3 — the balikbayan box buried at depth D_f, with all the soil weight pressing down.
I am the three magic numbers for a soil with zero friction angle. Recite me in order!
Answer
N_c = 5.7, N_q = 1, N_γ = 0
Memory link
A4 — the phone pattern '57-1-0' for pure clay (ϕ=0).
I am the 'width-term' shape factor countdown. From strip to circle, name my three values.
Answer
Strip = 0.5, Square = 0.4, Circle = 0.3
Memory link
A2 — the billiards countdown 5-4-3: Strip, Square, Circle.
When the water table rises to the footing base, I replace the full unit weight in the width term. What am I called?
Answer
Submerged (effective) unit weight γ' = γ_sat − γ_w
Memory link
A7 — the flooded fishpond where soil feels half as heavy.
I am the two-thirds champion. When soil is loose, both cohesion and friction must multiply by me. State the formula.
Answer
c* = (2/3)c and tan ϕ* = (2/3) tan ϕ for local/punching shear
Memory link
A8 — the '2/3 Needs Improvement' grade for loose soil.
I am the safety multiplier that separates failure from allowable. My range for foundations is what?
Answer
Factor of Safety FS = 2.5 to 3.0
Memory link
A5 — the three-layer helmet analogy.
Complete the sentence: 'Net allowable = (q_u minus ____) divided by FS.' What fills the blank?
Answer
γD_f (the overburden pressure — the 'already paid mortgage')
Memory link
A6 — the excavation already paid for, plus Anchor A15 cash register analogy.
Name the three failure modes in order from dense to loose soil.
Answer
General Shear (dense) → Local Shear (medium) → Punching Shear (loose)
Memory link
A9 — the three boxers: Champion, Semi-Pro, Street Brawler.
Formula mnemonics
q_u = cN_c + qN_q + 0.5γBN_γ (Strip Footing)
Mnemonic
CQG Strip: 'Cohesion Quirky Gamma — Strip uses half-gamma.' The three terms are C (cohesion), Q (surcharge), G (gamma-width). For strip, the G-term uses coefficient 0.5 (half). Remember: 'STRIP = HALF-GAMMA.'
When to use
Strip (continuous) footings under walls, when footing length L >> B. Use the coefficient 0.5 on the γBN_γ term.
What each part means
c=cohesion (kPa), N_c=cohesion factor; q=γD_f=surcharge at footing base (kPa), N_q=surcharge factor; γ=unit weight of soil (kN/m³), B=footing width (m), N_γ=weight factor. All N's are dimensionless functions of ϕ.
q_u = 1.3cN_c + qN_q + 0.4γBN_γ (Square Footing)
Mnemonic
'Square gets a bonus on cohesion (1.3) and a penalty on width (0.4 < 0.5).' The 1.3 multiplier on cohesion is the 'square bonus' — the 2D corner confinement boosts cohesion resistance. The 0.4 on the width term is the 'square penalty' compared to strip. Think: '1.3 up, 0.4 down.'
When to use
Square isolated column footings (B=L). Most common footing shape in PRC board problems.
What each part means
1.3 = shape factor on cohesion for square; 0.4 = shape factor on width term for square. All other symbols identical to strip formula.
q_u = 1.3cN_c + qN_q + 0.3γBN_γ (Circular Footing)
Mnemonic
'Circle shares the 1.3 bonus with Square but gets the smallest width factor (0.3).' Circle and Square both use 1.3 on cohesion. For the width term: Circle=0.3 (lowest), Square=0.4, Strip=0.5. Circle is the most 'penalized' on width. Memory: '3-4-5: Circle-Square-Strip on the width term (counting up from 3).'
When to use
Circular footings (tanks, columns with circular cross-section). Less common in PRC exams but appears in tricky problems.
What each part means
0.3 = shape factor on γBN_γ for circular footing. B = diameter of circular footing.
q = γD_f
Mnemonic
'Depth makes Pressure.' q (surcharge) = unit weight (γ) times depth (D_f). The deeper the footing, the higher the surcharge. Think: γ × D_f = γD_f — just two variables multiplied. No fancy factors needed.
When to use
Always — compute q first before substituting into Terzaghi's equation.
What each part means
γ = bulk unit weight of soil above footing base (kN/m³); D_f = depth of footing below ground surface (m); q = resulting overburden pressure at footing level (kPa).
q_a = q_u / FS (Gross Allowable Bearing Capacity)
Mnemonic
'Divide by Safety.' FS=2.5 to 3. The gross q_a includes the overburden. Think: 'Gross = Divide the whole thing.' Quick: if FS=3 and q_u=750 kPa, q_a=250 kPa.
When to use
When gross pressure from structure plus soil weight above footing is compared to q_a.
What each part means
q_u = ultimate bearing capacity (kPa); FS = factor of safety (dimensionless, typically 2.5–3); q_a = allowable gross bearing pressure (kPa).
q_a,net = (q_u − γD_f) / FS (Net Allowable Bearing Capacity)
Mnemonic
'Net = Subtract first, then Divide.' Subtract the overburden γD_f from q_u to get net ultimate, then divide by FS. Think: 'NET = (Total − Overburden) ÷ Safety.' It's like net income: gross minus existing obligations divided by risk factor.
When to use
When applying load from structure only (excluding existing soil weight) — most conservative and commonly tested.
What each part means
γD_f = overburden stress already present before construction (kPa); (q_u − γD_f) = net ultimate capacity; FS = safety factor.
Q_a = q_a,net × A (Allowable Column Load)
Mnemonic
'Pressure times Area gives Force.' Unit pressure (kPa = kN/m²) × area (m²) = force (kN). This is just unit conversion — pressure times area always yields load. Think: 'kPa × m² = kN always.'
When to use
Final step: once q_a,net is known, multiply by footing area to get maximum allowable structural load.
What each part means
q_a,net = net allowable bearing pressure (kPa); A = footing area (m²); Q_a = allowable column load (kN).
c* = (2/3)c; tan ϕ* = (2/3) tan ϕ (Local/Punching Shear Reduction)
Mnemonic
'Loose soil gets Two-Thirds.' Reduce both cohesion and friction to 2/3 of their lab values for loose soil. Think: 'Loose = 2/3 grade.' The reduced values give modified N-factors for local/punching shear q_u calculation.
When to use
When soil is loose (low relative density), or when problem explicitly states 'local shear' or 'punching shear' failure mode.
What each part means
c* = modified cohesion for local shear; tanϕ* = modified friction for local shear; 2/3 = Terzaghi's empirical reduction factor for non-general shear conditions.
Quick recall chains
Terzaghi's Three Terms in Order
Recall test
Without looking: write the three terms of Terzaghi's strip footing formula in order. What letter represents each term in CQG?
Memory chain
CQG Chain: 'COHESION starts the party (cN_c), the QUEUE of soil above joins (qN_q), and GRAVITY wraps it up (γBN_γ).' Three guests, three terms, always in this order: C → Q → G. At any party (footing), the host is cohesion, the line-up is surcharge, and gravity is the last to arrive but never forgotten.
Items to remember
- Cohesion term: cN_c
- Surcharge term: qN_q
- Width/Weight term: 0.5γBN_γ (strip)
Shape Factor Coefficients (Width Term): Strip → Square → Circle
Recall test
What is the coefficient of γBN_γ for: (a) strip, (b) square, (c) circular footing? Say '5-4-3' and assign.
Memory chain
Countdown 5-4-3: 'FIVE, FOUR, THREE — Strip, Square, Circle agrees!' Like a basketball countdown before tipoff: Strip (0.5) shoots first, Square (0.4) passes, Circle (0.3) dunks last. Counting DOWN: 5→4→3 as you go from Strip to Square to Circle.
Items to remember
- Strip: 0.5 on γBN_γ
- Square: 0.4 on γBN_γ
- Circle: 0.3 on γBN_γ
ϕ=0 Special Values for N_c, N_q, N_γ
Recall test
For ϕ=0 saturated clay, state N_c, N_q, N_γ. Which term drops out of Terzaghi's equation entirely?
Memory chain
'571-Zero': When phi is ZERO, the N-factors go 5.7-1-0. Story: 'At zero degrees friction, the soil scores 5.7 on cohesion, 1 on surcharge, and ZERO on width — it completely ignores footing width!' The zero N_γ means the width term vanishes in pure clay. Remember as a phone pattern: '57-1-0'.
Items to remember
- N_c = 5.7
- N_q = 1
- N_γ = 0
Water Table Correction Zones (Shallow to Deep)
Recall test
The water table is 0.8B below the footing base. Which zone? What correction applies?
Memory chain
Three Floors: 'Ground Floor (Zone 1) is fully submerged — γ' only. First Floor (Zone 2) is half-wet — interpolate. Second Floor (Zone 3) is dry — full γ, no worries.' Walk UP from ground to second floor and the water correction DISAPPEARS as you go higher (water table goes deeper).
Items to remember
- Zone 1: WT at or above footing base → use γ' in width term
- Zone 2: WT within depth B below base → interpolate γ_eff
- Zone 3: WT deeper than B below base → no correction, use full γ
Steps to Solve a Terzaghi Bearing Capacity Problem
Recall test
Solve a square footing problem step by step using SQNWCDL. Which step is most commonly skipped by examinees?
Memory chain
SHAPE-Q-N-WATER-COMPUTE-DIVIDE-LOAD: 'Shape Quiz Never Waits — Compute, Divide, Load!' Seven steps in order: S(Shape) → Q(surcharge) → N(N-factors) → W(Water table) → C(Compute q_u) → D(Divide by FS) → L(Load = q_a × A). The acronym SQNWCDL sounds like 'Sequel CD Load' — imagine loading a sequel CD in proper order.
Items to remember
- Step 1: Identify footing shape (strip/square/circular)
- Step 2: Compute q = γD_f
- Step 3: Look up N_c, N_q, N_γ from ϕ
- Step 4: Check water table zone and adjust γ if needed
- Step 5: Apply shape factors and compute q_u
- Step 6: Divide by FS for q_a (or compute q_a,net)
- Step 7: Multiply by area for Q_a if required
Diagrams
Bearing Capacity of Soils — Complete Concept Map
A hierarchical mind map linking all major topics in Bearing Capacity of Soils. Use this to see how Terzaghi's equation, shape factors, N-factors, failure modes, water table, and allowable capacity all connect. Review before exam to activate all memory anchors simultaneously.
Step-by-Step Solution Flowchart for Terzaghi Bearing Capacity Problems
A decision-tree flowchart guiding students through every step of a Terzaghi bearing capacity calculation. Follow each branch based on the problem's given data. The flowchart enforces the correct sequence: shape → surcharge → N-factors → water table → q_u → allowable → load. The settlement reminder at the end references Anchor A11 and A20.
Bearing Failure Mode Selection Guide
A flowchart for classifying the bearing failure mode based on soil condition. Dense soils → general shear (full parameters). Medium → local shear. Loose → punching shear. Both local and punching shear require the 2/3 reduction to c and tanϕ before looking up N-factors. This directly supports memory anchors A8 and A9.
Distribution of qu Components — Typical Dense Sand Example
A pie chart showing the approximate percentage contribution of each Terzaghi term to the total q_u for a typical strip footing on dense sand (ϕ=25°, c=15 kPa, γ=18, B=2m, Df=1m). The surcharge term (qN_q) typically dominates in medium-depth footings. This reinforces Anchor A3 — never omit the surcharge term, as it contributes ~43% of total q_u in this case.
Footing Design State: From Ultimate to Allowable to Safe Design
A state diagram showing the complete progression from raw soil data to a safe foundation design. Each state represents a calculation stage, and the feedback loop (Redesign → back to ComputeQu) reinforces that both shear and settlement must be satisfied. This visual directly supports the dual-criterion analogy in Anchor A20 and the settlement warning in Anchor A11.