Stresses in Soil Mass - Memory Anchors
For the PRC Civil Engineer Licensure Exam, where a single formula forgotten under pressure can cost you a question, having a vivid mental 'hook' for every concept is not a luxury — it's a strategy. This set of memory anchors transforms abstract soil-stress equations into unforgettable mental images, culturally familiar stories, and crisp recall triggers. Work through each anchor once, visualize it fully, and your brain will store it in long-term memory rather than short-term clutter. Remember: the weirder and more vivid the image, the stronger the memory trace.
Memory anchors
Terzaghi's Effective Stress Principle: σ' = σ − u
Memory aid
Imagine a packed MRT train (total stress σ). The passengers are so tightly packed that some are literally floating on the crowd — they're not touching the floor (that's the pore water pressure u). Only the passengers whose feet are firmly on the floor are actually pressing down on the train structure. Those floor-touching passengers represent the effective stress σ'. The formula: σ' = σ − u means 'total crowd minus the floating passengers = the real load on the floor.'
Why it works
The MRT analogy is instantly familiar to Filipino students who commute daily. It converts an abstract principle into a visceral, everyday experience — making it emotionally memorable and conceptually accurate.
Example usage
Board question: 'A saturated clay has total stress 90 kPa and pore pressure 30 kPa. Find σ'.' Trigger: MRT — floor passengers only → σ' = 90 − 30 = 60 kPa.
Recall trigger
Think: MRT train. Who is actually pressing on the floor?
Total stress σ = Σγᵢzᵢ (sum of unit weight × thickness for each layer)
Memory aid
Remember 'LAYER CAKE': each layer of the cake has a specific weight (γ) and thickness (z). To find the total weight pressing down at the bottom of the cake, you MULTIPLY each layer's weight density by its thickness and ADD them all up. Stress = Σ(γ × z) — just like adding up the weight of each cake layer from top to bottom.
Why it works
The layer cake image is multi-sensory (visual, tactile, even taste). The act of stacking layers mirrors the mathematical summation, making the formula intuitive rather than memorized.
Example usage
For a 3 m dry layer (γ = 18 kN/m³) over a 2 m saturated layer (γ_sat = 20 kN/m³): σ = 18×3 + 20×2 = 54 + 40 = 94 kPa. Layer cake — add each layer's contribution.
Recall trigger
Think: stacking bibingka layers — each layer adds weight.
Pore water pressure u = γ_w × z_w (hydrostatic, z_w = depth below water table)
Memory aid
Think of the water table as the surface of Laguna de Bay. The deeper a fish dives below the surface, the more water pressure it feels on its body. That pressure is u = 9.81 × z_w. The fish doesn't care about the soil above the water table — only about how deep below the lake surface it is. So: u only starts counting BELOW the water table.
Why it works
Laguna de Bay is a familiar Philippine landmark. The fish-diver image makes it clear that pore pressure is purely a function of depth below the water surface — a common exam confusion point.
Example usage
Water table at 3 m depth; find u at 5 m: z_w = 5 − 3 = 2 m. u = 9.81 × 2 = 19.62 kPa. Fish is 2 m below the lake surface.
Recall trigger
Think: fish diving below Laguna de Bay surface — only depth below water counts.
Use γ_sat (not γ_moist) below the water table when computing total stress
Memory aid
Engineer Mando made this classic mistake on his first board exam. He was computing the total stress at 5 m depth, with the water table at 2 m. He used the moist unit weight (17 kN/m³) for the saturated layer below — and got the wrong answer. The examiner's comment? 'Below the water table, the soil is WET — use γ_sat, not γ_moist.' Mando never forgot: SATURATED SOIL = γ_sat. He passed the next exam with flying colors.
Why it works
A cautionary micro-story with a named character creates emotional engagement. The 'mistake-and-correction' narrative activates the brain's error-detection circuits, making the correct rule memorable.
Example usage
Layer below water table: use γ_sat = 20 kN/m³ (not γ_moist = 17 kN/m³) in σ = Σγᵢzᵢ.
Recall trigger
Think: Mando's mistake — wet soil below water table always uses γ_sat.
Boussinesq Point Load — vertical stress directly below load: Δσ = 3Q / (2πz²)
Memory aid
Acronym: '3 QUEENS in 2 PIE ZAP' → '3Q / (2π z²)'. Visualize 3 queens (3Q) trapped inside 2 pies (2π) getting zapped by lightning (z²) directly below them. When r = 0 (directly below), the formula simplifies to this clean expression.
Why it works
The nonsensical imagery (queens in pie getting zapped) is precisely what makes it stick — the brain flags unusual combinations as 'important to remember.' The phonetic mapping to each symbol is direct.
Example usage
Q = 100 kN, z = 2 m, r = 0: Δσ = 3(100) / (2π × 4) = 300 / 25.13 = 11.9 kPa. Recall the queens, the pies, the zap.
Recall trigger
Think: 3 Queens in 2 Pies getting Zapped. r = 0 case.
Full Boussinesq formula with r offset: Δσ = (3Q/2πz²) × [1/(1+(r/z)²)]^(5/2)
Memory aid
Chunk it in 3 parts: Part 1 = '3Q over 2πz²' (the vertical-only part — your '3 Queens Zapped'). Part 2 = 'the correction factor in square brackets: [1 / (1 + (r/z)²)]'. Part 3 = 'raise it to the power 5/2'. Memory phrase: 'QUEENS get CORRECTED to the FIVE-HALVES power when they move SIDEWAYS (r > 0).' Sideways movement always reduces the stress — the correction factor ≤ 1.
Why it works
Chunking breaks a complex formula into 3 digestible units. The mental rule 'sideways = reduced stress' also builds intuition, not just rote recall.
Example usage
Q = 200 kN, z = 3 m, r = 2 m: (r/z) = 0.667; 1+(0.667)² = 1.444; [1/1.444]^2.5 = (0.693)^2.5 = 0.399. Δσ = [3×200/(2π×9)] × 0.399 = 10.61 × 0.399 = 4.23 kPa.
Recall trigger
Queens Zapped → Corrected → Five-Halves. Sideways means smaller.
2:1 Stress Distribution Method: Δσ = Q / [(B+z)(L+z)]
Memory aid
Imagine a photographer's camera flash (the footing load Q). The flash of light spreads out as it travels deeper — for every 2 meters you go down, it spreads 1 meter sideways on each side (2:1 ratio). So a B×L footing becomes (B+z)×(L+z) at depth z. The same total light (load Q) now covers a BIGGER area — so the intensity (stress) drops. Δσ = Q ÷ bigger area.
Why it works
The camera flash spreading analogy makes the geometric concept of load spreading viscerally clear. It also explains WHY stress decreases with depth — the same load covers more area.
Example usage
2×2 m footing, Q = 800 kN, z = 3 m: Δσ = 800 / [(2+3)(2+3)] = 800/25 = 32 kPa. Flash spreads to 5×5 at depth 3 m.
Recall trigger
Think: camera flash spreading sideways. B becomes B+z, L becomes L+z.
Common pitfall: 2:1 formula uses (B+z)(L+z), NOT just B×L
Memory aid
During a board exam, Maria was in a rush and computed Δσ = Q / (B×L) — forgetting to add z to both dimensions. She got 800/(2×2) = 200 kPa instead of 32 kPa — more than 6× too high! She imagined the camera flash NOT spreading at all, staying the same tiny area all the way down. 'Of course the flash spreads!' she thought on the next exam, and never forgot to write (B+z) and (L+z).
Why it works
The vivid numerical contrast (200 vs 32 kPa — a 6× error) creates a strong 'danger signal' in memory. The story format attaches personal stakes to the correct procedure.
Example usage
Never write Q/(B·L). Always: Q/[(B+z)(L+z)]. The '+z' accounts for load spreading with depth.
Recall trigger
Maria's 6× error — always add z to B and L.
Water table at surface → u = γ_w × full depth; raises pore pressure, lowers σ'
Memory aid
Picture the famous flood photos from Ondoy (Typhoon Ketsana, 2009) — water completely covering Metro Manila streets. When the water table rises to the surface, EVERY point in the soil has pore pressure equal to γ_w × z (full depth). Total stress σ = γ_sat × z (using γ_sat since all soil is now saturated). Effective stress σ' = (γ_sat − γ_w) × z = γ' × z, where γ' is the submerged (buoyant) unit weight. Ondoy = submerged weight only.
Why it works
Typhoon Ondoy is a powerful cultural-historical memory anchor for Filipino students. Connecting the engineering scenario to a lived national experience creates an emotional memory trace that is nearly impossible to forget.
Example usage
WT at surface; γ_sat = 20 kN/m³; z = 5 m: σ = 20×5 = 100 kPa; u = 9.81×5 = 49.05 kPa; σ' = 100 − 49.05 = 50.95 kPa. Alternatively: σ' = (20−9.81)×5 = 10.19×5 = 50.95 kPa. ✓
Recall trigger
Think: Ondoy flood — water table at surface → use γ' = γ_sat − γ_w for σ'.
Upward seepage increases u, decreases σ', and can cause the 'quick condition' (σ' → 0)
Memory aid
Imagine a construction site in Pasig — workers excavate a deep pit, and suddenly water starts flowing UPWARD from the bottom (artesian pressure). The site engineer shouts: 'Quick condition! Everyone out!' The upward water flow acts like extra pore pressure, reducing the effective stress toward zero. When σ' reaches zero, the soil has no strength — it liquefies like quicksand. The site engineer's shout is your trigger: UPWARD SEEPAGE = QUICK CONDITION DANGER.
Why it works
The dramatic construction-site story with the engineer's shout creates a vivid scene. The term 'quick condition' is also directly related to 'quicksand,' providing an additional semantic hook.
Example usage
Upward seepage pressure per unit area = i × γ_w × z (where i = hydraulic gradient). This ADDS to pore pressure u. If total u ≥ σ, then σ' = 0 → quick condition.
Recall trigger
Think: Pasig construction pit, engineer shouts — upward seepage → σ' → 0 → quick!
Stress DECREASES with depth for surface loads (Boussinesq and 2:1)
Memory aid
Think of dropping a stone into calm water at Burnham Park Lake (Baguio). The ripples (stress wave) are strongest right at the impact point and spread outward and downward, getting weaker as they travel further. A surface load is like that stone — maximum stress increase right below the footing at shallow depth, decreasing as you go deeper. The stress 'ripples' outward and fades.
Why it works
The ripple analogy is visually compelling and physically intuitive. It correctly conveys both the spatial decay of stress with depth AND the lateral spreading — two ideas in one image.
Example usage
2×2 footing, Q=800 kN: at z=3 m → Δσ=32 kPa; at z=5 m → Δσ = 800/[(2+5)(2+5)] = 800/49 = 16.3 kPa. Deeper = smaller. Ripple fades.
Recall trigger
Think: Burnham Park ripples — stress ripples fade with depth and distance.
Effective stress controls strength and settlement — total stress does NOT
Memory aid
Imagine two wrestlers — one is dry (effective stress fighter) and one is floating in a swimming pool (total stress). The pool wrestler can't grip the floor, can't push off, and has zero fighting strength. The dry wrestler uses all his weight to generate friction and strength. Strength in soil works the same way — only the grain-to-grain contact force (effective stress σ') generates friction, cohesion, and resistance. Total stress without considering u is like counting the pool wrestler as full strength.
Why it works
The wrestler analogy ties physical strength (grip, friction) to grain-to-grain contact, making Terzaghi's principle intuitively clear. The pool image vividly shows why total stress alone misleads.
Example usage
Exam question: 'Which stress parameter controls shear strength in Mohr-Coulomb criterion?' Answer: Effective normal stress σ' (not total stress σ). Pool wrestler = no strength.
Recall trigger
Think: wrestler floating in pool — total stress alone is meaningless for strength.
Boussinesq assumes soil is homogeneous, isotropic, semi-infinite elastic solid
Memory aid
Acronym: HIS — Homogeneous, Isotropic, Semi-infinite. 'Boussinesq wants HIS soil perfect.' Every time you apply Boussinesq, remember HIS three assumptions. Real soil violates all three — but for exam purposes, Boussinesq is the standard theoretical approach. Remember: 'HIS perfect soil' — Homogeneous (same everywhere), Isotropic (same in all directions), Semi-infinite (extends infinitely deep and wide).
Why it works
Three-letter acronyms are among the most effective mnemonic devices. The possessive phrase 'HIS perfect soil' adds a mini-narrative that makes the acronym easier to retrieve.
Example usage
Exam: 'State the assumptions of Boussinesq's theory.' Answer: The soil is Homogeneous, Isotropic, and forms a Semi-infinite elastic half-space (HIS). Also: linear elastic behavior under small strains.
Recall trigger
Boussinesq = HIS soil (Homogeneous, Isotropic, Semi-infinite).
Effective stress profile: build it layer by layer, switching unit weights at the water table
Memory aid
Use your body as the soil profile. Your HEAD is the ground surface (zero stress). Your SHOULDERS represent the depth where the water table is — this is where you switch from γ_moist to γ_sat, and where pore pressure (u) starts. Your WAIST is the point of interest — you've added two layer contributions to σ, and subtracted u. Your FEET are the deepest point. Walk through your body top to bottom every time you compute an effective stress profile: HEAD (surface) → SHOULDERS (water table, switch γ) → WAIST (target depth) → compute σ, u, σ'.
Why it works
Method of loci (memory palace) uses the body as a familiar spatial anchor. The physical walk-through creates a procedural memory that is more reliable than formula recall alone.
Example usage
Head: σ=0. Shoulders (3 m, WT): σ = 18×3 = 54 kPa, u starts. Waist (5 m, 2 m below WT): σ = 54 + 20×2 = 94 kPa; u = 9.81×2 = 19.62 kPa; σ' = 74.4 kPa.
Recall trigger
Body scan: Head → Shoulders → Waist → compute σ, u, σ'.
Newmark's influence chart is used for stress under irregular or large loaded areas
Memory aid
Imagine Newmark's chart as a giant dartboard. The bullseye is the point directly under the center of the footing. Each annular ring on the dartboard represents an influence zone — the more rings your loaded area covers, the more stress it contributes at the target depth. The influence value I = N × 0.005 where N = number of rings covered. Dartboard → count rings → multiply by 0.005 × q.
Why it works
The dartboard is a universally recognizable visual. The 'counting rings' action creates a procedural image that mirrors the actual use of Newmark's chart, making the method memorable.
Example usage
Scale drawing so depth z = radius of innermost ring. Count N blocks inside loaded area. Δσ = 0.005 × N × q. More rings covered = larger stress increase.
Recall trigger
Think: Newmark dartboard — count influence zones (rings), multiply by 0.005.
Boussinesq vs. 2:1 method — Boussinesq is more accurate but more complex; 2:1 is quick estimate
Memory aid
Boussinesq is the SCIENTIFIC CALCULATOR — precise, takes more steps, gives theoretically correct results. The 2:1 method is the SOLAR CALCULATOR — quick, simple, good enough for a fast estimate. For the board exam, know BOTH: Boussinesq for theory questions, 2:1 for quick footing problems. 'When in a hurry, use the solar calc (2:1). When precision is needed, use the scientific calc (Boussinesq).'
Why it works
The calculator analogy is immediately relatable for engineering students. It also correctly conveys the trade-off between precision and speed, which is the practical engineering judgment being tested.
Example usage
Exam: 'Estimate Δσ at 3 m below a 2×2 footing with Q=800 kN.' → Use 2:1 (solar calc) → 32 kPa. For theory or point loads → use Boussinesq (scientific calc).
Recall trigger
Scientific calc = Boussinesq (precise). Solar calc = 2:1 (quick estimate).
Submerged (buoyant) unit weight γ' = γ_sat − γ_w
Memory aid
Rhyme: 'Saturated minus water, that's the buoyant daughter — γ' = γ_sat minus γ_w, she carries the effective load for you!' The 'buoyant daughter' is γ' — she's lighter than γ_sat because water is holding part of her weight up (buoyancy). Typical values: γ' ≈ 20 − 9.81 ≈ 10.2 kN/m³ for saturated soil.
Why it works
Rhymes engage the brain's phonological memory system, which is separate from semantic memory — meaning two independent memory systems store the same concept, improving recall reliability.
Example usage
When WT is at surface: σ' at depth z = γ' × z = (γ_sat − γ_w) × z. E.g., γ_sat = 19 kN/m³: γ' = 19 − 9.81 = 9.19 kN/m³; at z = 4 m: σ' = 9.19 × 4 = 36.8 kPa.
Recall trigger
Buoyant daughter — γ_sat minus γ_w = γ'.
Stress increase directly below a point load is MAXIMUM; it decreases as you move sideways (r > 0)
Memory aid
Picture a spotlight shining straight down on a stage (the point load Q). The beam is BRIGHTEST directly below the lamp (r = 0, maximum Δσ). As you move sideways along the stage floor away from the center, the light intensity drops. Move far enough sideways and the stage is barely lit. The Boussinesq correction factor [1/(1+(r/z)²)]^(5/2) is exactly this 'spotlight dimming function' — it equals 1.0 at r=0 and approaches 0 as r increases.
Why it works
The spotlight image is a perfect physical analog for the Boussinesq stress distribution. It creates a spatial mental map that helps students visualize why the correction factor must be ≤ 1.0.
Example usage
At r=0: correction factor = [1/(1+0)]^2.5 = 1.0. At r=z: correction factor = [1/(1+1)]^2.5 = (0.5)^2.5 = 0.177. Stress drops to 17.7% of the direct-below value when you move one z-distance sideways.
Recall trigger
Think: stage spotlight — brightest below (r=0), dims sideways (r increases).
The 2:1 method formula for stress increase: Δσ = Q / [(B+z)(L+z)]
Memory aid
Chunk it as 'LOAD over SPREAD AREA'. Load = Q (total load on footing, in kN). Spread area = the footing dimensions PLUS the depth on each side: (B+z)(L+z). Memory phrase: 'Q over the GROWN-UP footing.' The footing 'grows up' from B×L to (B+z)×(L+z) as you go deeper — like a teenager getting bigger. The same load Q now covers a bigger area, so stress = Q ÷ big area.
Why it works
The 'growing-up footing' metaphor creates a dynamic, dimensional memory. It also reinforces the conceptual reason for the formula — stress spreads and decreases — rather than just memorizing symbols.
Example usage
3×4 m footing, Q = 1500 kN, z = 2 m: Grown-up area = (3+2)(4+2) = 5×6 = 30 m². Δσ = 1500/30 = 50 kPa. At z = 5 m: (3+5)(4+5) = 8×9 = 72 m². Δσ = 1500/72 = 20.8 kPa.
Recall trigger
Think: 'Q over the GROWN-UP footing' → Q / [(B+z)(L+z)].
Order of computation: Total stress σ first, pore pressure u second, effective stress σ' last
Memory aid
Acronym: 'TUE' — Total, U (pore pressure), Effective. 'Always compute in TUEsday order: Total first, U (pore pressure) second, Effective last.' Like scheduling: you can't compute σ' without first knowing σ and u. TUE = σ, u, σ'. Never skip ahead to σ' without doing the TUE sequence.
Why it works
TUE is a one-syllable word that maps to a familiar calendar day, creating a double anchor. The sequential logic (you can't skip steps) is reinforced by the idea of 'scheduling' — a process that must follow order.
Example usage
Step 1 (Total): σ = 18(3) + 20(2) = 94 kPa. Step 2 (U): u = 9.81(2) = 19.62 kPa. Step 3 (Effective): σ' = 94 − 19.62 = 74.4 kPa. TUE complete.
Recall trigger
TUEsday: Total → U (pore pressure) → Effective. Always in that order.
Revision game
A 3×3 m footing carries 900 kN. I am the stress increase at 3 m below the footing base. The formula uses a 'grown-up footing.' What is my value in kPa?
Answer
Δσ = 900 / [(3+3)(3+3)] = 900/36 = 25 kPa
Memory link
A7 — Camera flash spreading; A19 — Q over grown-up footing.
I am the three assumptions Boussinesq makes about soil. If soil were perfectly me, his formula would be exact. My acronym is a pronoun that usually means 'belonging to him.' What is my acronym?
Answer
HIS — Homogeneous, Isotropic, Semi-infinite
Memory link
A13 — Boussinesq wants HIS perfect soil.
A site is flooded like during Ondoy — water table at the surface. The soil below has γ_sat = 19.5 kN/m³. I am the effective stress at 4 m depth. Use the shortcut with buoyant unit weight. What am I?
Answer
γ' = 19.5 − 9.81 = 9.69 kN/m³; σ' = 9.69 × 4 = 38.76 kPa
Memory link
A9 — Ondoy anchor; A17 — Buoyant daughter rhyme.
I am the sequence you must ALWAYS follow when computing effective stress. I am named after a day of the week. What is my name, and what are my three steps?
Answer
TUE — Total stress (σ), then U (pore pressure u), then Effective stress (σ')
Memory link
A20 — TUEsday morning routine anchor.
Engineer Mando used γ_moist = 17 kN/m³ for the saturated layer below the water table. I am the correct unit weight he should have used. What am I called, and why?
Answer
γ_sat (saturated unit weight) — below the water table, all voids are filled with water, so the saturated unit weight (typically 19–21 kN/m³) must be used, not moist unit weight.
Memory link
A4 — Mando's cautionary micro-story.
A concentration load Q = 200 kN acts at the surface. I am the vertical stress increase DIRECTLY BELOW it at z = 2 m. Three queens, two pies, zapped. What am I in kPa?
Answer
Δσ = 3(200) / (2π × 2²) = 600 / 25.13 = 23.87 kPa
Memory link
A5 — '3 Queens in 2 Pies getting Zapped' mnemonic.
I happen in a construction pit when upward seepage pressure equals the total overburden stress — effective stress reaches zero and the soil acts like a liquid. I am named after a type of moving sand. What am I called in geotechnical engineering?
Answer
Quick condition (also: quicksand condition, heave, or hydraulic uplift failure) — occurs when σ' = 0 due to upward seepage
Memory link
A10 — Pasig construction pit micro-story.
Formula mnemonics
σ' = σ − u
Mnemonic
MRT Train: Total passengers (σ) minus floating ones (u) = real floor load (σ'). Or simply: 'EFFECTIVE = TOTAL minus UGLY pore pressure.' E-T-U → rearrange: σ' = σ − u.
When to use
ALWAYS when computing shear strength, consolidation settlement, or any geotechnical behavior. Anytime you see 'effective stress' or 'stress carried by soil grains' in a problem.
What each part means
σ = total vertical stress at a point (kPa); u = pore water pressure at that point (kPa); σ' = effective stress — the stress carried by the soil skeleton (kPa). This is Terzaghi's effective stress principle.
σ = Σ(γᵢ × zᵢ)
Mnemonic
LAYER CAKE: sum up each layer's γ × z contribution from top down to the point of interest. 'Gamma-Z for each layer, add them all — that's your sigma.'
When to use
Computing total vertical stress at any depth in a layered soil profile. Always the FIRST step in the TUE sequence (Total → U → Effective).
What each part means
γᵢ = unit weight of layer i (kN/m³) — use γ_moist above WT, γ_sat below WT; zᵢ = thickness of layer i (m); Σ = sum all layers from surface down to the depth of interest.
u = γ_w × z_w
Mnemonic
FISH IN LAGUNA: u = 9.81 × (depth below water table). The fish feels pressure only for how deep it swims BELOW the lake surface. z_w = depth below the water table, NOT total depth.
When to use
Computing hydrostatic pore pressure in any problem where a water table is present. For seepage problems, add seepage pressure ±i·γ_w·z to the hydrostatic u.
What each part means
γ_w = unit weight of water = 9.81 kN/m³ (use 9.81 unless problem states otherwise); z_w = depth below the phreatic surface / water table (m). Note: u = 0 above the water table (hydrostatic case, no capillary).
Δσ = 3Q / (2πz²) [Boussinesq, r = 0]
Mnemonic
'3 Queens in 2 Pies, Zapped Twice' → 3Q / (2π × z²). Only works directly BELOW the load (r = 0). The 'zap' (z²) in the denominator means stress drops fast — proportional to 1/z² directly below.
When to use
When a concentrated surface load (point load Q) is applied, and you need stress increase DIRECTLY BELOW it (r = 0). For offset points, use the full formula with the correction factor.
What each part means
Q = point load at surface (kN); z = depth below the surface (m); r = horizontal distance from load = 0 for this simplified form; the factor 3/(2π) ≈ 0.477 is the Boussinesq influence coefficient at r=0.
Δσ = (3Q/2πz²) × [1/(1+(r/z)²)]^(5/2) [Boussinesq, general]
Mnemonic
Queens-Zapped × Spotlight-Dimmer^(5/2). Part 1: '3Q/2πz²' (queens zapped). Part 2: '[1/(1+(r/z)²)]^(5/2)' is the spotlight dimmer — equals 1 at r=0, shrinks as r grows. Five-halves power = 2.5.
When to use
For Boussinesq stress at any point not directly below the load. Compute r/z ratio first, then evaluate the correction bracket, raise to 2.5 power, multiply by the direct-below value.
What each part means
Q = point load (kN); z = depth (m); r = horizontal offset from load (m); (r/z) = dimensionless ratio; [1/(1+(r/z)²)]^2.5 = influence factor (always ≤ 1.0, equals 1.0 only when r=0).
Δσ = Q / [(B+z)(L+z)] [2:1 method]
Mnemonic
'Q over the GROWN-UP FOOTING.' The footing dimensions B and L each grow by z. Total load Q is spread over this grown-up area. 'Load stays, area grows, stress shrinks.'
When to use
Quick estimate of stress increase under a rectangular footing at depth z below the footing base. Use for preliminary settlement calculations. NOT for stress at offset locations — only directly below the footing center.
What each part means
Q = total load on footing (kN); B = footing width (m); L = footing length (m); z = depth below footing base (m); (B+z) and (L+z) = effective spread dimensions at depth z (m). Result Δσ in kPa.
γ' = γ_sat − γ_w
Mnemonic
'Buoyant daughter = saturated mom minus water.' γ_sat = ~18-22 kN/m³; γ_w = 9.81 kN/m³; γ' ≈ 8-12 kN/m³ typically. When WT is at surface, use γ' instead of (γ_sat − γ_w) directly in σ' = γ' × z.
When to use
When the water table is at or above the surface. Instead of computing σ then subtracting u, directly use σ' = γ' × z for fully submerged uniform layers. Saves computation steps.
What each part means
γ' = buoyant (submerged) unit weight (kN/m³); γ_sat = saturated unit weight of soil (kN/m³); γ_w = 9.81 kN/m³. The buoyant unit weight represents the net downward unit weight of saturated soil when submerged — gravity minus buoyancy.
Quick recall chains
TUE Chain — Computing Effective Stress at a Point
Recall test
Without looking: what are the 3 steps in TUE order for computing effective stress? Can you write the formula for each step?
Memory chain
TUEsday morning routine: T = wake up and TOTAL your stress for the day. U = take a cold shower (pore WATER pressure — refreshing!). E = feel EFFECTIVE after your TUE routine. You cannot feel effective without completing T and U first — the sequence is locked. TUE: Total → U (pore pressure) → Effective. Every single time.
Items to remember
- Step 1: Compute Total stress σ = Σ(γᵢ × zᵢ) — use γ_moist above WT, γ_sat below WT
- Step 2: Compute pore pressure u = γ_w × z_w (z_w = depth below water table)
- Step 3: Compute Effective stress σ' = σ − u
Layer Stress Profile Chain — Building σ from Top to Bottom
Recall test
A site has 2 m dry (γ=17), then 4 m saturated (γ_sat=19.5), WT at 2 m depth. Without a calculator, write the expression for σ and u at 4 m depth.
Memory chain
Story: 'Top to Bottom Cooking' — You're layering a kare-kare (Filipino stew). Each ingredient layer has a weight (γ) and thickness (z). Above the water level in the pot: dry ingredients (γ_moist). Below the water level: wet ingredients (γ_sat). The deeper you go, the more pore pressure (liquid) builds up. At each depth, tally: What dry ingredients are above the water? What wet ingredients are below? How deep is this point below the water line? Cook layer by layer, then combine — that's your σ.
Items to remember
- Identify all soil layers and their thicknesses
- Identify position of water table
- Above WT: use γ_moist (or γ_dry); Below WT: switch to γ_sat
- Multiply each layer's γ by its thickness z
- Sum all contributions: σ = Σ(γᵢ × zᵢ)
- Pore pressure starts at zero at WT and increases as γ_w × z_w below
Boussinesq Formula Sequence — Step-by-Step for General Case
Recall test
Q=150 kN, z=4 m, r=3 m. Write out all 6 steps with numbers (do not skip the r/z ratio step). What is Δσ?
Memory chain
Acronym: 'QZR — RISE 5/2 — FRONT × CORRECT'. Read it as a battle cry: 'I know Q, Z, R — I RISE to the 5/2 power — then FRONT times CORRECT!' Step 1: Q, Z, R (identify variables). Step 2: r/z ratio. Step 3: bracket [1/(1+(r/z)²)]. Step 4: RISE to 5/2. Step 5: FRONT = 3Q/2πz². Step 6: FRONT × CORRECTION. Six steps, one battle cry.
Items to remember
- Identify Q, z (depth), and r (horizontal offset)
- Compute r/z ratio (dimensionless)
- Compute [1/(1 + (r/z)²)]
- Raise this to the power 5/2 (= 2.5)
- Compute the front factor 3Q/(2πz²)
- Multiply front factor × correction factor
Pitfall Prevention Chain — 5 Must-Avoid Errors in Soil Stress Problems
Recall test
List all 5 MWBLE pitfalls without looking. Which one is most likely to cause the largest numerical error?
Memory chain
The '5 Deadly Sins of Soil Stress' — remembered as 'MWBLE': Moisture (use sat below WT), Water level (measure from WT, not surface), Big area (add z to B and L), Loss of U (never ignore pore pressure), Extra seepage (upward flow increases u). If you commit any of these MWBLE sins, expect to get the wrong answer. Confess them in your exam solution steps to avoid them.
Items to remember
- Pitfall 1: Using γ_moist below the water table (must use γ_sat)
- Pitfall 2: Measuring z_w from the surface (must measure from the water table)
- Pitfall 3: Using B×L instead of (B+z)(L+z) in the 2:1 formula
- Pitfall 4: Ignoring pore pressure (computing strength from total stress)
- Pitfall 5: Forgetting upward seepage adds to u and reduces σ'
Stress Method Selection Chain — When to Use Which Formula
Recall test
A board exam problem gives a 3×5 m footing with 2000 kN. Which formula do you use? What if it asks for stress at a point 2 m to the side of the footing?
Memory chain
Decision tree mnemonic: 'PROBE the problem — Point-load? Rectangle? Offset? Big-area? Edge-case?' P = Point load below → simplified Boussinesq. R = Rectangular footing → 2:1 method (quick). O = Offset point → full Boussinesq. B = Big/irregular area → Newmark chart. E = Edge/line load → Boussinesq line-load variant. PROBE: choose your weapon before computing.
Items to remember
- Point load, directly below (r=0): use Δσ = 3Q/2πz² (Boussinesq simplified)
- Point load, offset (r>0): use full Boussinesq with correction factor
- Rectangular footing, quick estimate: use 2:1 method Δσ = Q/[(B+z)(L+z)]
- Irregular or large loaded area, accurate: use Newmark influence chart
- Line load or strip footing: use Boussinesq line-load formula (separate equation)
Diagrams
Stresses in Soil Mass — Complete Concept Map
A comprehensive mind map showing all major topics in Stresses in Soil Mass: the effective stress principle and its components, water table effects including the quick condition, the three major methods for computing stress increase from loads (Boussinesq, 2:1, Newmark), and the five key pitfalls. Use this as a visual checklist during review.
TUE Flowchart — Step-by-Step Effective Stress Computation
A decision-tree flowchart illustrating the TUE sequence for computing effective stress. The flowchart handles multi-layer profiles, the water table decision (above or below), proper unit weight selection (γ_moist vs γ_sat), pore pressure computation (u = γ_w × z_w only below WT), and the final effective stress formula σ' = σ − u. Follow this chart step-by-step in any board exam problem involving effective stress.
PROBE Chart — Selecting the Right Stress Increase Formula
A decision-tree flowchart for selecting the correct stress-increase formula in any board exam problem. The PROBE chart branches by load type (point, rectangular footing, irregular area, strip load), then by specific conditions (offset or not, accuracy required). Each branch leads to the appropriate formula. Use this as a mental decision map before computing Δσ in any geotechnical problem.
Effective Stress States — From Dry to Quick Condition
A state diagram showing the progression of effective stress states in soil: from the dry zone above the water table (u=0), through normal saturated conditions (hydrostatic u), to reduced effective stress under upward seepage, and finally the critical quick condition where σ'=0 and the soil loses all shear strength. This diagram maps the 'danger escalation' from normal soil behavior to the catastrophic quick condition, making the seepage-pore pressure-effective stress relationship unforgettable.