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CELE Geotechnical Engineering — Lateral Earth Pressure and Retaining StructuresMemory Anchors

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Mnemonics for Lateral Earth Pressure and Retaining Structures in the CELE 2026. Every one of these anchors has been designed to help you recall the concept under the pressure of Professional Regulation Commission (PRC) — Board of Civil Engineering's CELE Geotechnical Engineering exam conditions.

Exam context

For the Civil Engineer Licensure Examination, Professional Regulation Commission (PRC) — Board of Civil Engineering tests Geotechnical Engineering under a "Core" label, with Lateral Earth Pressure and Retaining Structures in the 8th 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.

Lateral Earth Pressure and Retaining Structures - Memory Anchors

Memory anchors are cognitive shortcuts that hijack your brain's natural tendency to remember vivid, emotional, and story-driven information. Instead of re-reading formulas passively, you attach each key formula or concept to a funny story, a Filipino pop-culture reference, or an absurd image — and suddenly, your brain files it under 'memorable' rather than 'forgettable textbook text.' Research shows that multi-modal encoding (combining words + images + stories + emotion) can boost long-term recall by 400–600% compared to rote repetition. For the PRC Civil Engineer board exam, where Geotechnical Engineering can account for 15–20% of the total score, mastering these anchors means the difference between guessing and confidently computing Ka, Kp, and checking sliding stability under exam pressure. Use these anchors during your review sessions: read the concept once, then close your eyes and replay the story or image. Test yourself with the recall triggers. Play the revision game with a barkada. Your goal is to make these formulas feel like old friends — not strangers.

Anchors

Topic

Earth Pressure States

Concept

Three states of lateral earth pressure: At-rest (K0), Active (Ka), Passive (Kp)

Anchor Id

Difficulty

easy

Memory Aid

Remember the order with: 'A – AP' = At-rest, Active, Passive. Better yet, picture a JEEPNEY DRIVER: (1) At-REST — the jeepney is parked, engine off, not moving. (2) ACTIVE — the driver reverses away from a barrier; the barrier 'relaxes' (soil expands). (3) PASSIVE — the driver floors it forward INTO the barrier; the barrier is compressed. The sequence Always goes: K0 > Ka is WRONG — actually Ka < K0 < Kp. So the jeepney: Ka (smallest) → K0 (middle) → Kp (largest). Think: 'Active workers get the LEAST pay (smallest K), passive investors get the MOST (largest K).'

Anchor Type

acronym

Why It Works

The jeepney analogy ties an abstract soil mechanics concept to a familiar Filipino daily experience, and the pay analogy creates an emotional hook (money) that aids encoding.

Example Usage

Exam question: 'Arrange Ka, K0, Kp from smallest to largest.' Recall: Active worker (least) → At-rest (middle) → Passive investor (most). Answer: Ka < K0 < Kp.

Recall Trigger

Think: 'Which K is biggest?' → Passive investor = most money = Kp largest.

Topic

Active Earth Pressure Coefficient

Concept

Ka formula: Ka = tan²(45 − φ/2)

Anchor Id

Difficulty

easy

Memory Aid

The formula for ACTIVE pressure: 'ACTIVE goes DOWN from 45.' The angle inside the tangent SUBTRACTS φ/2 from 45°. Think: 'When you're ACTIVE (running away from something), you SUBTRACT — you're losing ground.' Memory phrase: 'Active = 45 MINUS half-phi, all squared.' Finger trick: for Active, make a minus sign (−) with your left index finger.

Anchor Type

mnemonic

Why It Works

Spatial (minus = subtracting, going down) combined with a physical finger gesture creates muscle memory for which formula gets the minus sign.

Example Usage

φ = 30°: Ka = tan²(45 − 15°) = tan²(30°) = (0.577)² = 0.333. Confirm: smaller than 1, which is correct for active.

Recall Trigger

Active = minus sign = 45 − φ/2.

Topic

Passive Earth Pressure Coefficient

Concept

Kp formula: Kp = tan²(45 + φ/2) = 1/Ka

Anchor Id

Difficulty

easy

Memory Aid

PASSIVE goes UP from 45. 'When you're PASSIVE (pushing FORWARD, like a sumo wrestler), you ADD — you're gaining ground.' Finger trick: for Passive, make a plus sign (+) with both index fingers. Also: 'Passive = 1 over Active' — they are RECIPROCALS. Remember: 'KP and KA are like fractions — they multiply to 1 (KaKp = 1).'

Anchor Type

mnemonic

Why It Works

The plus/minus contrast between Passive and Active creates a paired-encoding effect — learning one cues the other automatically.

Example Usage

φ = 30°: Kp = tan²(45 + 15°) = tan²(60°) = (1.732)² = 3.0. Check: 3.0 = 1/0.333 ✓.

Recall Trigger

Passive = plus sign = 45 + φ/2. And Kp = 1/Ka.

Topic

At-Rest Earth Pressure Coefficient

Concept

K0 formula: K0 = 1 − sin φ

Anchor Id

Difficulty

easy

Memory Aid

Sing to the tune of a simple counting song: 'K-zero equals ONE minus SINE PHI, one minus sine phi, one minus sine phi — K-zero for at-rest, no movement, no lie!' Short version: 'K-nought = 1 − sin φ' — the 'nought' (zero) rhymes with 'nought' as in nothing moves, so you SUBTRACT sin φ from 1 (perfect rest state, no extremes).

Anchor Type

rhyme

Why It Works

Rhyming and melody exploit the brain's phonological loop, creating a verbal rhythm that makes the formula easier to retrieve under exam stress.

Example Usage

φ = 30°: K0 = 1 − sin 30° = 1 − 0.5 = 0.50. This is between Ka = 0.333 and Kp = 3.0 ✓.

Recall Trigger

Hum the jingle: 'K-zero = 1 minus sine phi.'

Topic

Active Thrust Magnitude and Location

Concept

Active thrust resultant Pa = ½ Ka γ H² acts at H/3 from the base

Anchor Id

Difficulty

medium

Memory Aid

Think of the TRIANGULAR pressure diagram as a PIZZA SLICE standing on its tip. The slice is widest at the bottom (maximum pressure at depth H) and tapers to zero at the top. The CENTER OF GRAVITY of a triangle is at 1/3 of its height from the base. So the resultant force — the 'weight' of the pizza slice — acts at H/3 from the base. Formula Pa = ½ K γ H² is just the AREA of the triangle: base × height / 2 = (Ka γ H) × H / 2.

Anchor Type

analogy

Why It Works

Pizza is universally loved by Filipino students. Connecting the triangular pressure diagram to a tangible 2D food shape makes the geometry intuitive and unforgettable.

Example Usage

H = 5 m: Pa = ½(0.333)(18)(25) = 75 kN/m, acting at 5/3 = 1.67 m above the base.

Recall Trigger

Triangular pressure diagram = pizza slice on its tip → centroid at H/3 from base.

Topic

Surcharge Effect on Active Pressure

Concept

Surcharge q adds a UNIFORM (rectangular) pressure Ka·q over the full height

Anchor Id

Difficulty

medium

Memory Aid

Imagine placing a HEAVY BALIKBAYAN BOX uniformly on top of the backfill. That box pushes down everywhere equally — so the extra lateral pressure from the surcharge is the SAME at every depth: Ka × q. This creates a RECTANGLE in the pressure diagram (not a triangle). The resultant of that rectangle acts at H/2 from the base (midpoint of a rectangle), not H/3.

Anchor Type

analogy

Why It Works

The balikbayan box is a culturally resonant symbol of uniform load. Contrasting rectangle (uniform surcharge) vs. triangle (soil self-weight) helps students avoid mixing up the moment arms.

Example Usage

q = 10 kPa, H = 6 m, Ka = 0.307: Surcharge force = Ka·q·H = 0.307 × 10 × 6 = 18.4 kN/m acting at 3 m above base.

Recall Trigger

Balikbayan box on top = rectangle = H/2 moment arm.

Topic

Active Thrust Formula

Concept

Doubling the wall height QUADRUPLES the active thrust (Pa ∝ H²)

Anchor Id

Difficulty

medium

Memory Aid

Engineer Manny designs a retaining wall for a 3 m embankment. His boss suddenly says: 'Double the height to 6 m!' Manny casually says 'OK, twice the force.' His boss slams the table: 'WRONG! It's FOUR times the force! Pa = ½ Ka γ H² — H is SQUARED! You just quadrupled the overturning moment!' Manny now tattoos 'H²' on his forearm. The moral: height squared — NEVER forget the square.

Anchor Type

micro_story

Why It Works

The dramatic story (boss slamming table, tattoo) creates an emotional memory trace. The exaggerated consequence (tattoo) signals that this is an exam trap.

Example Usage

Common trap: If H doubles, Pa increases by 2² = 4 times. If H triples, Pa increases by 3² = 9 times.

Recall Trigger

Boss slamming table = H is SQUARED in Pa formula.

Topic

Effect of Cohesion on Active Pressure

Concept

Cohesion REDUCES active pressure; tension crack forms near the top

Anchor Id

Difficulty

hard

Memory Aid

Think of cohesion as the SOIL'S OWN GLUE. In cohesive soils (clay), the soil tries to stick together and 'hold itself up,' so it pushes LESS against the wall. The formula σa = Ka γ z − 2c√Ka has a MINUS for the cohesion term — the glue subtracts from the pressure. But near the surface where z is small, the pressure goes NEGATIVE (tension). Since soil cannot truly pull on the wall, a TENSION CRACK forms — like when glue is pulled apart and splits. The depth of the crack: zc = 2c / (γ√Ka).

Anchor Type

analogy

Why It Works

The 'soil glue' analogy makes the abstract cohesion term physically meaningful, and 'crack in the glue' is a vivid image for where tension occurs.

Example Usage

c = 15 kPa, γ = 18 kN/m³, φ = 20°, Ka = 0.490: zc = 2(15)/(18 × √0.490) = 30/(18 × 0.700) = 2.38 m.

Recall Trigger

Clay = soil glue = minus term in active pressure = tension crack at top.

Topic

Water Table Effect on Earth Pressure

Concept

Water table behind the wall: use γ' for soil below WT, add full hydrostatic pressure

Anchor Id

Difficulty

hard

Memory Aid

Engr. Ana designs a wall and forgets the water table. During the rainy season, the backfill becomes saturated. She used γ = 18 kN/m³ everywhere. But BELOW the water table, she should have used γ' = γsat − γw ≈ 8–9 kN/m³. AND she forgot to add the water pressure u = γw × hw. Her wall rotates and fails — she now draws a cartoon of a wall wearing a scuba mask to remind her: 'Below water = buoyant weight + water pressure SEPARATELY.'

Anchor Type

micro_story

Why It Works

The failure story creates a negative consequence memory (wall collapses), and the scuba mask cartoon is an absurd, humorous image that sticks.

Example Usage

Water table at mid-height of a 6 m wall: Upper 3 m uses γ = 18; lower 3 m uses γ' ≈ 9 kN/m³ for soil term plus γw = 9.81 kN/m³ for water pressure separately.

Recall Trigger

Scuba mask on the wall = below WT: use γ' for soil + γw for water — two separate forces.

Topic

Overturning Stability Check

Concept

Overturning stability: FS_OT = ΣMR / ΣMO ≥ 1.5 to 2.0

Anchor Id

A10

Difficulty

medium

Memory Aid

Visualize a SEESAW (tilaog/balances) at a Filipino playground. The RESISTING moments are kids sitting on the STABLE side (heavy, many kids = large ΣMR). The OVERTURNING moment is one bully pushing on the other side (ΣMO = Pa × H/3). For the wall to be SAFE, the stable side must outweigh the bully by a factor of 1.5 to 2.0. If the bully is too strong (FS < 1.5), the seesaw — and the wall — tips over.

Anchor Type

visual_association

Why It Works

The seesaw is a universal childhood experience. Mapping ΣMR and ΣMO to the two sides of a seesaw makes the moment balance equation feel natural and physical.

Example Usage

ΣMR = 300 kN·m/m, ΣMO = 125 kN·m/m: FS = 300/125 = 2.4 ≥ 2.0 ✓ Safe.

Recall Trigger

Seesaw: ΣMR (stable side) / ΣMO (bully side) ≥ 1.5–2.0.

Topic

Sliding Stability Check

Concept

Sliding stability: FS_slide = μΣW / Pa,H ≥ 1.5

Anchor Id

A11

Difficulty

medium

Memory Aid

Picture a REFRIGERATOR on a tiled floor. The FRICTION force holding it in place = μ × Weight (your muscles pushing the ref down × the friction coefficient). The FORCE pushing the ref sideways = Pa,H (the horizontal earth pressure). For the wall not to slide, friction must beat the horizontal push by at least 1.5 times. Formula: FS_slide = μΣW / Pa,H ≥ 1.5. If you add a rubber mat (passive resistance Pp at the toe), the ref becomes even harder to slide.

Anchor Type

analogy

Why It Works

Everyone has tried to slide a heavy appliance across a floor. Mapping sliding stability to this experience makes the formula viscerally relatable.

Example Usage

ΣW = 250 kN/m, μ = 0.5, Pa,H = 80 kN/m: FS = 0.5 × 250/80 = 1.56 ≥ 1.5 ✓ Safe.

Recall Trigger

Refrigerator on tiled floor = friction (μΣW) vs. earth push (Pa,H).

Topic

Bearing Pressure and Middle Third Rule

Concept

Bearing pressure check: keep resultant in the MIDDLE THIRD of the base (no tension under footing)

Anchor Id

A12

Difficulty

medium

Memory Aid

Divide the base of the wall into THREE equal zones like a traffic light: GREEN (middle third) = safe, resultant lands here, no tension. YELLOW (outer third near toe) = caution, eccentric. RED (outside the base) = danger, tension develops, wall lifts off. Memory image: 'The result is a picky dinner guest — it will only sit at the CENTER TABLE (middle third). If it's forced to sit at the edge, it falls off the chair (tension/bearing failure).'

Anchor Type

visual_association

Why It Works

Traffic light color coding (green/yellow/red) is a well-established visual heuristic that makes the three zones immediately recognizable.

Example Usage

If eccentricity e = B/6, resultant is at edge of middle third. If e > B/6, tension develops under the toe — design must be revised.

Recall Trigger

Traffic light: Green = middle third = safe. Red = outside base = failure.

Topic

Rankine vs. Coulomb Theory

Concept

Rankine vs. Coulomb: Rankine assumes smooth vertical wall + horizontal backfill; Coulomb adds wall friction and sloped backfill

Anchor Id

A13

Difficulty

medium

Memory Aid

Think of RANKINE as a BASIC CELLPHONE (Nokia 3310) — simple, clean, no frills: smooth wall, horizontal backfill, no friction. COULOMB is a SMARTPHONE with all the extras: wall friction (δ), sloped backfill (β), sloped wall back (α). Rankine = simple and conservative. Coulomb = more accurate but more complex. For most board exam problems, Rankine is used unless friction angle δ is given.

Anchor Type

analogy

Why It Works

Technology analogy maps directly onto the concept of simple vs. complex models. Filipino students are very familiar with the Nokia 3310 as a 'basic but reliable' icon.

Example Usage

If exam gives smooth vertical wall, horizontal backfill, no δ: use Rankine. If wall friction δ is given: use Coulomb.

Recall Trigger

Rankine = Nokia 3310 (basic). Coulomb = smartphone (complex with friction and slopes).

Topic

Passive Resistance at Toe

Concept

Passive resistance at the toe is often NEGLECTED (conservative approach)

Anchor Id

A14

Difficulty

medium

Memory Aid

Engr. Ben calculates sliding stability and boosts his FS by including Kp at the toe. His professor crosses it out with a red pen: 'NEVER rely on passive resistance you can't guarantee! The soil in front of the toe may be disturbed, eroded, or excavated in the future. Neglect it unless the problem specifically says to include it.' Ben now writes in his notebook: 'Passive at toe = bonus — don't count your chickens before they hatch.'

Anchor Type

micro_story

Why It Works

The red pen correction creates a fear-based memory (getting marked wrong on an exam). The Filipino idiom equivalent anchors the conservatism rule culturally.

Example Usage

In sliding check: FS = μΣW / Pa,H (without Pp). If Pp is given and you're told to include it: FS = (μΣW + Pp) / Pa,H.

Recall Trigger

Red pen crossing out Kp at toe = passive is a bonus, not a guarantee. Neglect it conservatively.

Topic

Relationship Between Ka and Kp

Concept

Relationship: Ka × Kp = 1 (they are reciprocals)

Anchor Id

A15

Difficulty

easy

Memory Aid

Short rhyme: 'Ka times Kp equals ONE — active and passive, together they're done! Ka goes down, Kp goes up — flip the fraction, fill the cup!' This reminds you: Ka = tan²(45−φ/2) and Kp = tan²(45+φ/2) = 1/Ka. They are mirror images around 45°, and their product is always 1.

Anchor Type

rhyme

Why It Works

The fill-the-cup image (flip = reciprocal) is a concrete visual metaphor. Rhyme makes it musical and easy to recall in silence during an exam.

Example Usage

φ = 34°: Ka = tan²(28°) = 0.280. Kp = 1/0.280 = 3.57. Check: 0.280 × 3.57 ≈ 1.0 ✓.

Recall Trigger

'Ka times Kp = 1' — flip the fraction.

Topic

Point of Application of Combined Thrust

Concept

Point of application of Pa for combined triangle + rectangle (soil + surcharge): two separate resultants, NOT combined at H/3

Anchor Id

A16

Difficulty

hard

Memory Aid

Think of a buffet line: the RICE (triangular pressure from soil weight) is served from a triangular tray — it sits at H/3 from the base. The EXTRA VIAND (surcharge rectangle) is served from a rectangular container — it sits at H/2. You CANNOT mix them into one dish at a single height. You must compute EACH moment separately about the base, then add. Students who combine them at H/3 get the overturning moment WRONG — and the board exam will catch them.

Anchor Type

micro_story

Why It Works

Buffet/food analogy resonates with Filipino culture around communal eating. The message about 'not mixing' the two components is memorable through the food metaphor.

Example Usage

Pa_soil acts at H/3, Pa_surcharge acts at H/2. ΣMO = Pa_soil × H/3 + Pa_surcharge × H/2.

Recall Trigger

Buffet: rice at H/3 (triangle), viand at H/2 (rectangle) — don't mix the trays.

Topic

Mobilization of Active vs. Passive Pressure

Concept

Wall movement required: Active << Passive (passive needs 10× more displacement to mobilize)

Anchor Id

A17

Difficulty

medium

Memory Aid

ACTIVE pressure mobilizes with TINY wall movement — like tapping a sleeping cat: it wakes up instantly (small movement, big response). PASSIVE pressure needs MASSIVE wall movement — like pushing a stubborn carabao: you have to push hard and far before it gives way. This is why passive is often neglected: the wall would have to deflect enormously before passive pressure fully develops, which is structurally unacceptable.

Anchor Type

analogy

Why It Works

The carabao (water buffalo) is a quintessentially Filipino agricultural symbol — stubborn and powerful — making passive pressure unforgettable.

Example Usage

Explains why in retaining wall design, we rely on active pressure (easily mobilized) and are conservative about passive pressure at the toe.

Recall Trigger

Active = tapping a cat (small movement). Passive = pushing a carabao (huge movement needed).

Topic

Tension Crack in Cohesive Soils

Concept

Tension crack depth: zc = 2c / (γ√Ka) in cohesive soils

Anchor Id

A18

Difficulty

hard

Memory Aid

Visualize the ACTIVE PRESSURE DIAGRAM for clay. Near the top, the pressure is NEGATIVE (tension zone). Draw a dotted line where pressure = 0 — that is the tension crack depth zc. Below zc, the wall feels soil pressure. Above zc, nothing (crack = air gap). Image: a CRACKED WALL TILE near the top with nothing pushing on the upper portion. The tension crack 'erases' the top of the pressure diagram.

Anchor Type

visual_association

Why It Works

The cracked tile is a common construction defect familiar to Filipino engineering students who have seen it in buildings. The visual 'erasing' of the pressure diagram above zc is a clear geometric memory cue.

Example Usage

c = 15 kPa, γ = 18 kN/m³, Ka = 0.490 (φ=20°): zc = 2(15)/(18√0.490) = 30/12.6 = 2.38 m from top.

Recall Trigger

Cracked tile at top of wall = tension crack. Below crack: normal pressure. Above crack: zero.

Topic

Minimum Factor of Safety

Concept

FS for overturning ≥ 1.5–2.0; FS for sliding ≥ 1.5 (standard minimum values)

Anchor Id

A19

Difficulty

easy

Memory Aid

Chunk the FS requirements as '1.5 – 2.0 – 1.5': OVERTURNING lower bound = 1.5, OVERTURNING preferred = 2.0, SLIDING = 1.5. Say it rhythmically: 'one-five, two-oh, one-five' — clap on each number. Overturning is STRICTER (preferred FS = 2.0) because if the wall tips over, it's catastrophic and sudden. Sliding can sometimes be stopped; overturning cannot.

Anchor Type

chunking

Why It Works

Rhythmic chunking (1.5-2.0-1.5) makes the three numbers feel like a phone number — easy to memorize. The clapping adds kinesthetic encoding.

Example Usage

Computed FS_OT = 1.7: acceptable (≥1.5) but aim for 2.0. Computed FS_slide = 1.4: UNSAFE, must redesign.

Recall Trigger

Clap: 'one-five, two-oh, one-five' = FS_OT ≥ 1.5–2.0; FS_slide ≥ 1.5.

Topic

Types of Retaining Walls

Concept

Wall types: Gravity wall (own weight), Cantilever wall (reinforced stem + heel/toe), Sheet pile (embedded in soil)

Anchor Id

A20

Difficulty

easy

Memory Aid

Three Filipino characters resist the lateral earth: (1) LOLO (GRAVITY WALL) — a heavy, old man who resists by sheer body mass. No tricks, just weight. (2) MANONG ENGINEER (CANTILEVER WALL) — a lean but strong man using LEVERAGE — slender stem with a wide footing that uses the soil weight on the heel as an ally. (3) SHEET PILE — a thin but deeply embedded warrior stuck into the ground like a BOLO knife, relying on embedment depth and passive resistance below the dredge line.

Anchor Type

analogy

Why It Works

Filipino character archetypes (lolo, manong) create personality-driven memory hooks. Each character's physical trait maps to the wall's structural mechanism.

Example Usage

Exam: 'Which wall type resists by self-weight?' → Lolo = gravity wall. 'Which relies on stem-footing action?' → Manong = cantilever.

Recall Trigger

Lolo = gravity (heavy). Manong = cantilever (leverage). Bolo in ground = sheet pile (embedment).

Revision Game

Ka — Active Earth Pressure Coefficient [Ka = tan²(45 − φ/2)]

Clue

I am the SMALLEST of the three K values. I happen when the wall leans AWAY from the soil. My formula subtracts phi/2 from 45°. Who am I?

Memory Link

A2 — Active SUBTRACTS from 45°; A1 — Active worker earns the least pay.

4 times (Pa ∝ H² — height is squared, so doubling H multiplies Pa by 2² = 4)

Clue

Double the wall height. By what factor does the active thrust Pa increase?

Memory Link

A7 — Boss slams table: 'H is SQUARED!'

OSB Plywood → Overturning, Sliding, Bearing

Clue

I am the Filipino construction material whose acronym stands for the three external stability checks of a retaining wall. What are those three checks?

Memory Link

Quick Recall Chain 2 — 'OSB: Oh Shall Be safe!'

Tension crack depth: zc = 2c / (γ√Ka)

Clue

In cohesive soil, I am the zone near the top of the wall where the active pressure is NEGATIVE. What is my depth?

Memory Link

A18 — Cracked wall tile at the top; A8 — Soil glue analogy.

FS_OT = 240/120 = 2.0 ≥ 2.0 ✓ Just barely safe (preferred minimum is 2.0)

Clue

A retaining wall has ΣMR = 240 kN·m/m and ΣMO = 120 kN·m/m. Compute FS against overturning. Is it safe?

Memory Link

A10 — Seesaw analogy: stable side / bully side ≥ 1.5–2.0.

Red pen crossing out Kp — 'Passive is a bonus, don't count your chickens.' Neglect Pp unless explicitly stated.

Clue

I am the memory aid that tells you PASSIVE resistance at the toe should NOT be counted in a conservative sliding analysis. What is the mnemonic?

Memory Link

A14 — Engr. Ben's professor with the red pen.

Ka = tan²(30°) = 0.333; Pa = ½(0.333)(18)(25) = 75 kN/m; acts at H/3 = 1.67 m above base.

Clue

For a retaining wall with dry cohesionless backfill (φ=30°, γ=18 kN/m³, H=5 m), compute Pa and state where it acts.

Memory Link

A5 — Pizza slice (triangle): centroid at H/3; A2 — Active formula Ka = tan²(45−φ/2).

Rankine (basic/Nokia 3310) vs. Coulomb (advanced/smartphone with wall friction δ and slope β)

Clue

I am the Rankine theory simplified: smooth vertical wall, horizontal backfill, no friction. My 'upgraded' counterpart (which includes wall friction δ and sloped backfill β) is named after whom?

Memory Link

A13 — Nokia 3310 vs. smartphone analogy.

zc = tension crack depth from top of backfill (m); 2c = twice the cohesion; γ = unit weight of soil; √Ka = square root of active coefficient. This is found by setting σa = 0 in the active pressure equation.

Increasing φ: Ka decreases → Pa decreases (friction helps soil hold itself)
Increasing H: Pa increases by H² (quadratic!)
Increasing γ: Pa increases linearly
Adding surcharge q: adds Ka q H (rectangle)
Adding cohesion c: REDUCES Pa (tension crack near top)

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Bearing Capacity of Soils

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CELE Geotechnical Engineering — Lateral Earth Pressure and Retaining StructuresMemory Anchors

Exam context

Lateral Earth Pressure and Retaining Structures - Memory Anchors

Anchors

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