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.' 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.
Memory anchors
Three states of lateral earth pressure: At-rest (K0), Active (Ka), Passive (Kp)
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).'
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.
Ka formula: Ka = tan²(45 − φ/2)
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.
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.
Kp formula: Kp = tan²(45 + φ/2) = 1/Ka
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).'
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.
K0 formula: K0 = 1 − sin φ
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).
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.'
Active thrust resultant Pa = ½ Ka γ H² acts at H/3 from the base
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.
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.
Surcharge q adds a UNIFORM (rectangular) pressure Ka·q over the full height
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.
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.
Doubling the wall height QUADRUPLES the active thrust (Pa ∝ H²)
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.
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.
Cohesion REDUCES active pressure; tension crack forms near the top
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).
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.
Water table behind the wall: use γ' for soil below WT, add full hydrostatic pressure
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.'
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.
Overturning stability: FS_OT = ΣMR / ΣMO ≥ 1.5 to 2.0
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.
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.
Sliding stability: FS_slide = μΣW / Pa,H ≥ 1.5
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.
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).
Bearing pressure check: keep resultant in the MIDDLE THIRD of the base (no tension under footing)
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).'
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.
Rankine vs. Coulomb: Rankine assumes smooth vertical wall + horizontal backfill; Coulomb adds wall friction and sloped backfill
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.
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).
Passive resistance at the toe is often NEGLECTED (conservative approach)
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.'
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.
Relationship: Ka × Kp = 1 (they are reciprocals)
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.
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.
Point of application of Pa for combined triangle + rectangle (soil + surcharge): two separate resultants, NOT combined at H/3
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.
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.
Wall movement required: Active << Passive (passive needs 10× more displacement to mobilize)
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.
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).
Tension crack depth: zc = 2c / (γ√Ka) in cohesive soils
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.
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.
FS for overturning ≥ 1.5–2.0; FS for sliding ≥ 1.5 (standard minimum values)
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.
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.
Wall types: Gravity wall (own weight), Cantilever wall (reinforced stem + heel/toe), Sheet pile (embedded in soil)
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.
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
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?
Answer
Ka — Active Earth Pressure Coefficient [Ka = tan²(45 − φ/2)]
Memory link
A2 — Active SUBTRACTS from 45°; A1 — Active worker earns the least pay.
Double the wall height. By what factor does the active thrust Pa increase?
Answer
4 times (Pa ∝ H² — height is squared, so doubling H multiplies Pa by 2² = 4)
Memory link
A7 — Boss slams table: 'H is SQUARED!'
I am the Filipino construction material whose acronym stands for the three external stability checks of a retaining wall. What are those three checks?
Answer
OSB Plywood → Overturning, Sliding, Bearing
Memory link
Quick Recall Chain 2 — 'OSB: Oh Shall Be safe!'
In cohesive soil, I am the zone near the top of the wall where the active pressure is NEGATIVE. What is my depth?
Answer
Tension crack depth: zc = 2c / (γ√Ka)
Memory link
A18 — Cracked wall tile at the top; A8 — Soil glue analogy.
A retaining wall has ΣMR = 240 kN·m/m and ΣMO = 120 kN·m/m. Compute FS against overturning. Is it safe?
Answer
FS_OT = 240/120 = 2.0 ≥ 2.0 ✓ Just barely safe (preferred minimum is 2.0)
Memory link
A10 — Seesaw analogy: stable side / bully side ≥ 1.5–2.0.
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?
Answer
Red pen crossing out Kp — 'Passive is a bonus, don't count your chickens.' Neglect Pp unless explicitly stated.
Memory link
A14 — Engr. Ben's professor with the red pen.
For a retaining wall with dry cohesionless backfill (φ=30°, γ=18 kN/m³, H=5 m), compute Pa and state where it acts.
Answer
Ka = tan²(30°) = 0.333; Pa = ½(0.333)(18)(25) = 75 kN/m; acts at H/3 = 1.67 m above base.
Memory link
A5 — Pizza slice (triangle): centroid at H/3; A2 — Active formula Ka = tan²(45−φ/2).
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?
Answer
Rankine (basic/Nokia 3310) vs. Coulomb (advanced/smartphone with wall friction δ and slope β)
Memory link
A13 — Nokia 3310 vs. smartphone analogy.
Formula mnemonics
Ka = (1 − sin φ)/(1 + sin φ) = tan²(45 − φ/2)
Mnemonic
ACTIVE SUBTRACTS: 'A for Active, A for Away (wall moves away), A for minus (−). Top minus, bottom plus = Ka.' Finger: point finger DOWN (away from wall) = Active = minus sign in angle.
When to use
Use for dry cohesionless backfill, smooth vertical wall (Rankine). Active state: wall moves away from backfill. Gives the MINIMUM lateral pressure.
What each part means
Ka = active earth pressure coefficient (dimensionless); φ = internal friction angle of soil (degrees); tan²(45 − φ/2) = Rankine active; the fraction form: numerator (1 − sin φ) < denominator (1 + sin φ), so Ka < 1 always.
Kp = (1 + sin φ)/(1 − sin φ) = tan²(45 + φ/2) = 1/Ka
Mnemonic
PASSIVE ADDS: 'P for Passive, P for Push (wall pushes into soil), P for Plus (+). Top plus, bottom minus = Kp.' Reciprocal of Ka — flip the fraction.
When to use
Use at the passive (compression) side: wall toe, anchor blocks, or any surface where the wall presses into the soil. Passive pressure RESISTS movement.
What each part means
Kp = passive earth pressure coefficient; always Kp > 1 (in fact Kp >> 1 for typical φ); it is the MAXIMUM lateral pressure the soil can exert when compressed; Kp = 1/Ka.
K0 = 1 − sin φ
Mnemonic
'K-nought = 1 minus sine phi, standing still, no reason why.' Simple and exact for normally consolidated soils (NC). For OCR soils: K0,OC = K0,NC × OCR^(sin φ) — but board exams rarely ask this.
When to use
Use for rigid walls with no movement (basement walls, braced excavations). K0 is the in-situ horizontal stress state before any wall movement occurs.
What each part means
K0 = at-rest lateral earth pressure coefficient; applies when there is ZERO wall movement; 1 − sin φ is between Ka and Kp for all valid φ.
Pa = ½ Ka γ H² (active thrust, dry cohesionless, per unit length of wall)
Mnemonic
'HALF K-ALPHA GAMMA H-SQUARED' — say it like a chant. The ½ is because the pressure diagram is triangular (area of triangle = ½ base × height). The H² warns you: HEIGHT IS SQUARED — double the height, quadruple the force.
When to use
Dry cohesionless backfill, no water table, no surcharge, uniform γ. Foundation for all other variations.
What each part means
Pa = total active thrust (kN/m); ½ = triangular area factor; Ka = active coefficient; γ = unit weight of soil (kN/m³); H² = wall height squared (m²). Acts at H/3 from the base.
σa = Ka γ z − 2c√Ka (active pressure at depth z, c-φ soil)
Mnemonic
'Sigma-active = Ka gamma z MINUS two-c root-Ka.' The minus sign = cohesion SUBTRACTS pressure. Think: 'c helps the soil hold itself — MINUS from the wall's burden.' Negative σa = tension = crack.
When to use
Any clay or c-φ soil backfill. Find tension crack depth by setting σa = 0: zc = 2c/(γ√Ka).
What each part means
σa = active lateral pressure at depth z (kPa); Ka γ z = frictional component (increases with depth); 2c√Ka = cohesion component (constant, subtracted); negative result means tension — physical crack forms.
FS_OT = ΣMR / ΣMO ≥ 1.5–2.0
Mnemonic
'FACTOR of SAFETY against Overturn = Resisting over Overturning.' FS = R/O. Remember: 'R is for Reliable (resisting), O is for Oh no! (overturning).' R must beat O by 1.5 to 2.0 times.
When to use
External stability check for ALL retaining walls. Moments computed about the TOE of the wall.
What each part means
ΣMR = sum of moments of all forces resisting overturning about the toe (kN·m/m) = weight of wall + soil on heel; ΣMO = moment of active thrust about toe = Pa × (H/3); FS ≥ 1.5 minimum, ≥ 2.0 preferred.
FS_slide = μΣW / Pa,H ≥ 1.5 (with passive: add Pp to numerator)
Mnemonic
'MU-SIGMA-W over Pa-horizontal.' Think: 'MU is friction, SIGMA-W is total weight, Pa,H is the wall's enemy (horizontal push).' Mu × Weight = friction resistance. FS ≥ 1.5 to not slide.
When to use
External stability check for sliding. The horizontal component Pa,H is the driving force; friction is the resistance.
What each part means
μ = coefficient of friction between base of wall and foundation soil (tan δ ≈ tan(⅔φ) ≈ 0.4–0.6); ΣW = total vertical load per unit length; Pa,H = horizontal component of active thrust; Pp = passive resistance at toe (add if reliable).
zc = 2c / (γ√Ka) — depth of tension crack
Mnemonic
'z-crack = 2c over gamma root-Ka.' Memory: 'Two-c / gamma root-Ka — where the crack appears, the wall hears nothing.' The tension crack depth is where active pressure = 0. Below it: positive pressure. Above it: crack (no contact).
When to use
For cohesive (c-φ or pure clay) backfill. Important for computing EFFECTIVE active thrust (use only the pressure below zc) in temporary cuts and earth pressure on wall.
What each part means
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.
Quick recall chains
Three Earth Pressure States in Correct Order (Smallest to Largest K)
Recall test
Quick: Which K is smallest? Largest? What is the correct order? Expected: Ka < K0 < Kp.
Memory chain
Use the 'PAY SCALE' story: The ACTIVE worker earns the LEAST pay (Ka = smallest). The AT-REST employee on retainer earns MIDDLE pay (K0 = middle). The PASSIVE investor collects the MOST income (Kp = largest). Always: Ka < K0 < Kp. Chant: 'Active-less, Rest-mid, Passive-most.'
Items to remember
- Ka (Active, smallest)
- K0 (At-rest, middle)
- Kp (Passive, largest)
Retaining Wall Stability Checks (Three External Modes)
Recall test
Name the 3 external stability checks for a retaining wall and their minimum FS values. Expected: Overturning (1.5–2.0), Sliding (1.5), Bearing (middle third rule).
Memory chain
Acronym: 'OSB — Oh Shall Be safe!' O = Overturning, S = Sliding, B = Bearing. Think of OSB PLYWOOD (a common construction material in the Philippines) — your wall must be as solid as OSB plywood: it must not OVERTURN, SLIDE, or BEAR too much pressure. Every stability analysis: check O, then S, then B.
Items to remember
- Overturning (FS ≥ 1.5–2.0, about toe)
- Sliding (FS ≥ 1.5, friction vs. Pa,H)
- Bearing (resultant in middle third, toe pressure ≤ qa)
Active Pressure with Surcharge — Components and Moment Arms
Recall test
A wall H = 6 m has soil (γ=18, Ka=0.307) and surcharge q=10 kPa. What are the two force components and where do they act? Expected: Pa_soil = ½(0.307)(18)(36) = 99.5 kN/m at 2 m; Pa_surch = 0.307(10)(6) = 18.4 kN/m at 3 m.
Memory chain
Remember the BUFFET TRAY system: Tray 1 = TRIANGULAR RICE DISH (soil weight): sits at H/3. Tray 2 = RECTANGULAR VIAND (surcharge): sits at H/2. Never mix trays. For overturning moment: MO = (½ Ka γ H²)(H/3) + (Ka q H)(H/2).
Items to remember
- Soil triangle: force = ½ Ka γ H², arm = H/3
- Surcharge rectangle: force = Ka q H, arm = H/2
- Add moments separately about toe for ΣMO
Steps to Check Overturning of a Retaining Wall
Recall test
In sequence, what are the 5 steps to compute FS against overturning for a gravity retaining wall? Expected: Ka → Pa → ΣMO → ΣMR → FS = ΣMR/ΣMO.
Memory chain
Acronym: 'KPAMF' — 'Ka-Pa-Mo-Mr-FS.' Or say: 'K finds the Pressure, P makes the Moment (overturning), M resists, F checks the Factor.' Walk through it like a checklist: K → P → MO → MR → FS.
Items to remember
- Step 1: Compute Ka from φ
- Step 2: Compute Pa (and location H/3)
- Step 3: Compute ΣMO = Pa × H/3 (about toe)
- Step 4: Compute ΣMR = Σ(Wi × xi) about toe
- Step 5: FS = ΣMR / ΣMO ≥ 1.5–2.0
Effect of Parameters on Active Thrust Pa
Recall test
How does each of the following affect Pa? (a) Double H → ×4 Pa. (b) Add surcharge → +Ka q H rectangle. (c) Add cohesion → reduces Pa, tension crack. (d) Higher φ → smaller Ka → smaller Pa.
Memory chain
Use the 'HQGCC' chain: 'Happy Quiet Goats Can Climb' — H (height, squared), Q (surcharge q, adds rectangle), G (gamma, linear), C (cohesion, subtracts), C (phi angle, reduces Ka). Each factor has its own rule. Visualize a wall with each factor as a dial you turn up or down.
Items to remember
- 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)
Diagrams
Lateral Earth Pressure — Master Concept Map
A comprehensive mind map showing the three earth pressure states (Active, At-Rest, Passive), the thrust formulas, modifying factors (surcharge, cohesion, water), stability checks (OSB: Overturning, Sliding, Bearing), and wall types. Use this as a pre-study orientator and post-study recall check.
Retaining Wall Stability Check — Step-by-Step Decision Flowchart
A complete decision flowchart for the three external stability checks of a retaining wall: Overturning (FS ≥ 1.5–2.0), Sliding (FS ≥ 1.5), and Bearing (middle third rule, e ≤ B/6). Follow the arrows step-by-step during problem solving. Any failed check routes back to 'Redesign Wall.'
Active Pressure Diagram: Dry vs. Surcharge vs. Cohesive vs. Water Table
A decision flowchart helping students choose the correct active pressure model based on backfill conditions: (1) simple triangle for dry cohesionless soil, (2) triangle + rectangle when surcharge is present, (3) modified diagram with tension crack for cohesive soils, (4) split-zone approach when a water table is present. Each path leads to computing separate moment arms before summing.
Typical Distribution of Active Thrust Components (Example: H=6m, q=10kPa, γ=18, φ=32°)
For a 6 m wall with γ=18 kN/m³, φ=32° (Ka=0.307), and q=10 kPa: Pa_soil = ½(0.307)(18)(36) = 99.5 kN/m and Pa_surcharge = (0.307)(10)(6) = 18.4 kN/m. Total ≈ 118 kN/m. The soil self-weight triangle dominates (81%) while the surcharge adds 19%. This shows why the soil weight term is always the primary concern, and the surcharge is additive but secondary.
State Transitions of Lateral Earth Pressure with Wall Movement
A state diagram showing how lateral earth pressure transitions between states depending on wall movement direction and magnitude. The At-Rest state is the initial condition. Active state is reached with small outward movement. Passive state requires large inward movement (roughly 10× more than active). This diagram directly supports the 'cat vs. carabao' analogy in A17.