Skip to main content
Memory AnchorsCELE · Geotechnical EngineeringReal content

CELE Geotechnical EngineeringStresses in Soil MassMemory Anchors

Quick-recall memory tricks for CELE Geotechnical Engineering — Stresses in Soil Mass. Acronyms, rhymes, visual hooks, and association techniques that turn rote memorisation into reliable recall. Built specifically for the concepts Professional Regulation Commission (PRC) — Board of Civil Engineering tests most often.

Exam context

For the Civil Engineer Licensure Examination, Professional Regulation Commission (PRC) — Board of Civil Engineering tests Geotechnical Engineering under a "Core" label, with Stresses in Soil Mass in the 4th slot across 11 chapters. CELE candidates must clear the 70% weighted average, no sub-test below 50% cut on the 2026 paper, which draws about a meaningful share of Geotechnical Engineering questions. Date to watch: May and November 2026.

Stresses in Soil Mass - Memory Anchors

Memory techniques — mnemonics, analogies, micro-stories, and visual associations — can boost recall by up to 400% compared to rote reading. 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.

Anchors

Tags

  • formula
  • definition
  • principle

Topic

Effective Stress Principle

Concept

Terzaghi's Effective Stress Principle: σ' = σ − u

Anchor Id

A1

Difficulty

easy

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.'

Anchor Type

analogy

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?

Tags

  • formula
  • definition
  • sequence

Topic

Total Vertical Stress

Concept

Total stress σ = Σγᵢzᵢ (sum of unit weight × thickness for each layer)

Anchor Id

A2

Difficulty

easy

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.

Anchor Type

mnemonic

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.

Tags

  • formula
  • definition

Topic

Pore Water Pressure

Concept

Pore water pressure u = γ_w × z_w (hydrostatic, z_w = depth below water table)

Anchor Id

A3

Difficulty

easy

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.

Anchor Type

analogy

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.

Tags

  • common mistake
  • definition
  • pitfall

Topic

Unit Weight Selection

Concept

Use γ_sat (not γ_moist) below the water table when computing total stress

Anchor Id

A4

Difficulty

medium

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.

Anchor Type

micro_story

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.

Tags

  • formula
  • Boussinesq
  • point load

Topic

Boussinesq Point Load Stress

Concept

Boussinesq Point Load — vertical stress directly below load: Δσ = 3Q / (2πz²)

Anchor Id

A5

Difficulty

medium

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.

Anchor Type

mnemonic

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.

Tags

  • formula
  • Boussinesq
  • point load
  • offset

Topic

Boussinesq Point Load Stress (General)

Concept

Full Boussinesq formula with r offset: Δσ = (3Q/2πz²) × [1/(1+(r/z)²)]^(5/2)

Anchor Id

A6

Difficulty

hard

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.

Anchor Type

chunking

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.

Tags

  • formula
  • 2:1 method
  • footing
  • stress increase

Topic

2:1 Stress Distribution Method

Concept

2:1 Stress Distribution Method: Δσ = Q / [(B+z)(L+z)]

Anchor Id

A7

Difficulty

easy

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.

Anchor Type

analogy

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.

Tags

  • pitfall
  • formula
  • 2:1 method

Topic

2:1 Method — Common Pitfall

Concept

Common pitfall: 2:1 formula uses (B+z)(L+z), NOT just B×L

Anchor Id

A8

Difficulty

easy

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).

Anchor Type

micro_story

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.

Tags

  • effective stress
  • water table
  • buoyant unit weight

Topic

Water Table at Surface — Effective Stress

Concept

Water table at surface → u = γ_w × full depth; raises pore pressure, lowers σ'

Anchor Id

A9

Difficulty

medium

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.

Anchor Type

visual_association

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'.

Tags

  • seepage
  • quick condition
  • effective stress
  • danger

Topic

Seepage and Effective Stress

Concept

Upward seepage increases u, decreases σ', and can cause the 'quick condition' (σ' → 0)

Anchor Id

A10

Difficulty

hard

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.

Anchor Type

micro_story

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!

Tags

  • concept
  • stress distribution
  • depth

Topic

Stress Distribution with Depth

Concept

Stress DECREASES with depth for surface loads (Boussinesq and 2:1)

Anchor Id

A11

Difficulty

easy

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.

Anchor Type

analogy

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.

Tags

  • concept
  • effective stress
  • shear strength
  • settlement

Topic

Why Effective Stress Matters

Concept

Effective stress controls strength and settlement — total stress does NOT

Anchor Id

A12

Difficulty

medium

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.

Anchor Type

analogy

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.

Tags

  • definition
  • assumptions
  • Boussinesq

Topic

Boussinesq Theory — Assumptions

Concept

Boussinesq assumes soil is homogeneous, isotropic, semi-infinite elastic solid

Anchor Id

A13

Difficulty

medium

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).

Anchor Type

acronym

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).

Tags

  • process
  • sequence
  • effective stress
  • layered soil

Topic

Effective Stress Profile Computation

Concept

Effective stress profile: build it layer by layer, switching unit weights at the water table

Anchor Id

A14

Difficulty

medium

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'.

Anchor Type

method_of_loci

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'.

Tags

  • method
  • Newmark
  • influence chart
  • stress increase

Topic

Newmark Influence Chart

Concept

Newmark's influence chart is used for stress under irregular or large loaded areas

Anchor Id

A15

Difficulty

hard

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.

Anchor Type

visual_association

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.

Tags

  • comparison
  • concept
  • method selection

Topic

Boussinesq vs. 2:1 Method

Concept

Boussinesq vs. 2:1 method — Boussinesq is more accurate but more complex; 2:1 is quick estimate

Anchor Id

A16

Difficulty

medium

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).'

Anchor Type

analogy

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).

Tags

  • formula
  • definition
  • buoyant weight

Topic

Buoyant Unit Weight

Concept

Submerged (buoyant) unit weight γ' = γ_sat − γ_w

Anchor Id

A17

Difficulty

easy

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.

Anchor Type

rhyme

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'.

Tags

  • concept
  • Boussinesq
  • radial stress
  • visualization

Topic

Boussinesq Stress Distribution — Radial Variation

Concept

Stress increase directly below a point load is MAXIMUM; it decreases as you move sideways (r > 0)

Anchor Id

A18

Difficulty

hard

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.

Anchor Type

visual_association

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).

Tags

  • formula
  • 2:1 method
  • chunking

Topic

2:1 Stress Distribution — Formula Recall

Concept

The 2:1 method formula for stress increase: Δσ = Q / [(B+z)(L+z)]

Anchor Id

A19

Difficulty

easy

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.

Anchor Type

chunking

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)].

Tags

  • process
  • sequence
  • acronym
  • computation order

Topic

Effective Stress Computation Sequence

Concept

Order of computation: Total stress σ first, pore pressure u second, effective stress σ' last

Anchor Id

A20

Difficulty

easy

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.

Anchor Type

acronym

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

Effective stress (σ' = σ − u)

Clue

I am the stress that actually controls soil strength and settlement. Total stress minus me equals zero... wait, I AM the one after subtracting pore pressure. What am I?

Memory Link

A1 — MRT Train anchor: I am the passengers whose feet touch the floor.

Δσ = 900 / [(3+3)(3+3)] = 900/36 = 25 kPa

Clue

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?

Memory Link

A7 — Camera flash spreading; A19 — Q over grown-up footing.

HIS — Homogeneous, Isotropic, Semi-infinite

Clue

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?

Memory Link

A13 — Boussinesq wants HIS perfect soil.

γ' = 19.5 − 9.81 = 9.69 kN/m³; σ' = 9.69 × 4 = 38.76 kPa

Clue

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?

Memory Link

A9 — Ondoy anchor; A17 — Buoyant daughter rhyme.

TUE — Total stress (σ), then U (pore pressure u), then Effective stress (σ')

Clue

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?

Memory Link

A20 — TUEsday morning routine anchor.

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.

Clue

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?

Memory Link

A4 — Mando's cautionary micro-story.

Δσ = 3(200) / (2π × 2²) = 600 / 25.13 = 23.87 kPa

Clue

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?

Memory Link

A5 — '3 Queens in 2 Pies getting Zapped' mnemonic.

Quick condition (also: quicksand condition, heave, or hydraulic uplift failure) — occurs when σ' = 0 due to upward seepage

Clue

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?

Memory Link

A10 — Pasig construction pit micro-story.

Formula Mnemonics

Formula

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.

Formula

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.

Formula

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).

Formula

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.

Formula

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).

Formula

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.

Formula

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

Chain Title

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

Chain Title

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

Chain Title

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

Chain Title

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'

Chain Title

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)
Loading diagram…
Loading diagram…
Loading diagram…
Loading diagram…

Ready to practise for the CELE 2026?

Super Tutor's AI review plan adapts to your weak areas and builds a weekly practice schedule around your target CELE exam date.