CELE Geotechnical Engineering — Shear Strength of SoilsMemory Anchors
Memory anchors for Shear Strength of Soils — mnemonic devices, acronyms, and tricks that make the CELE Geotechnical Engineering syllabus stick. Use these when a concept just will not stay in your head.
Exam context
For the Civil Engineer Licensure Examination, Professional Regulation Commission (PRC) — Board of Civil Engineering tests Geotechnical Engineering under a "Core" label, with Shear Strength of Soils in the 7th 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.
Shear Strength of Soils - Memory Anchors
Memory anchors work by connecting unfamiliar technical information to vivid, emotionally-charged, or story-driven mental images that your brain already knows how to store. Research in cognitive science shows that spaced repetition + memorable associations can boost long-term recall by up to 400% compared to re-reading notes. For the PRC Civil Engineer Licensure Examination, where Geotechnical Engineering questions are frequently numerical and concept-heavy, these anchors give you instant access to formulas, classifications, and procedures under exam pressure. Use each anchor as a mental 'hook' — when you see a problem, the hook fires automatically, pulling the right formula or concept into working memory. The anchors in this set cover every major concept in Shear Strength of Soils: Mohr-Coulomb criterion, triaxial test types, drainage conditions, and principal stress relationships.
Anchors
Tags
- formula
- definition
- shear strength
Topic
Mohr-Coulomb Failure Criterion
Concept
Mohr-Coulomb Failure Criterion: τ_f = c + σ·tan(φ)
Anchor Id
A1
Difficulty
easy
Memory Aid
Think of a bangus (milkfish) sliding on a banana leaf. The banana leaf has a natural stickiness (that's cohesion 'c') AND roughness (that's friction angle 'φ'). The heavier the fish (normal stress σ), the more friction resists sliding. The total resistance to sliding = stickiness + (weight × roughness). That IS the Mohr-Coulomb equation. τ_f = c + σ·tan(φ): cohesion + normal stress × tangent of friction angle.
Anchor Type
analogy
Why It Works
The analogy maps each variable to a sensory, everyday object. The bangus is familiar to every Filipino student. Stickiness → c, roughness → tan(φ), fish weight → σ.
Example Usage
Exam problem: c = 20 kPa, φ = 30°, σ' = 150 kPa. Trigger: bangus on leaf → τ_f = c + σ'tan(φ) = 20 + 150·tan30° = 20 + 86.6 = 106.6 kPa.
Recall Trigger
Picture a bangus sliding on a banana leaf.
Tags
- classification
- definition
- cohesion
- friction
Topic
Soil Classification by Shear Behavior
Concept
Cohesion c vs. Friction angle φ — which soil has which
Anchor Id
A2
Difficulty
easy
Memory Aid
Use the phrase: 'Sand is Silly — it has Zero Cohesion.' → Sand ≈ c = 0 (purely frictional, φ > 0). Then: 'Clay is Clingy — it Clings with Cohesion.' → Saturated clay under undrained loading: φ = 0, strength comes purely from c_u. Acronym: SC-ZC-CC → Sand = c=0; Clay (undrained) = c_u only.
Anchor Type
acronym
Why It Works
Alliteration and contrasting character descriptions (silly vs. clingy) create a strong dual-coding effect — verbal + personality image.
Example Usage
Board exam asks: 'A saturated clay is loaded quickly. What are the shear strength parameters?' → Clay is Clingy → φ = 0, strength = c_u. Use τ = c_u.
Recall Trigger
Sand is Silly (zero c), Clay is Clingy (c_u only).
Tags
- formula
- UC test
- undrained shear strength
Topic
Unconfined Compression Test
Concept
Undrained shear strength from UC test: c_u = q_u / 2
Anchor Id
A3
Difficulty
easy
Memory Aid
Chant this: 'q_u divided by two, that's what c_u is due!' Unconfined compressive strength (q_u) is TWICE the undrained shear strength. So always halve it: c_u = q_u ÷ 2. Think of cutting a bibingka (rice cake) exactly in half — the undrained strength is just one half of the unconfined strength.
Anchor Type
rhyme
Why It Works
Rhyme encodes the formula in phonological memory (auditory loop), which is highly robust under stress. The bibingka image reinforces the 'half' concept visually.
Example Usage
Problem: q_u = 120 kPa. → Chant the rhyme → c_u = 120/2 = 60 kPa. Common pitfall: do NOT use q_u directly as c_u — always divide by 2.
Recall Trigger
Chant 'q_u divided by two' OR picture cutting bibingka in half.
Tags
- classification
- triaxial test
- drainage
- sequence
Topic
Triaxial Test Types
Concept
Triaxial Test Types: UU, CU, CD — what they mean
Anchor Id
A4
Difficulty
medium
Memory Aid
Remember the three barangay officials at a meeting: Uncle Ulysses (UU = Unconsolidated-Undrained), Cousin Umberto (CU = Consolidated-Undrained), and Chief Doming (CD = Consolidated-Drained). Each level of drainage = more time for water to leave = more realistic long-term behavior. Uncle (UU) rushed in without preparing; Cousin (CU) prepared but did not drain; Chief (CD) was fully prepared AND drained — the most realistic for long-term.
Anchor Type
acronym
Why It Works
Narrative + character personalities make the sequence memorable. Filipino students relate to barangay community structures.
Example Usage
Board question: 'Which triaxial test gives effective parameters c' and φ'?' → Chief CD (fully drained) → CD test gives effective c', φ'.
Recall Trigger
Three barangay officials: Uncle UU, Cousin CU, Chief CD.
Tags
- UU test
- undrained
- short-term
- clay
Topic
Drainage Conditions — Short Term vs. Long Term
Concept
UU test → short-term (undrained) parameters: φ = 0, c = c_u
Anchor Id
A5
Difficulty
medium
Memory Aid
It's the first day of a big typhoon in Manila. A contractor needs to build an emergency embankment on soft clay RIGHT NOW — no time to wait for pore pressures to dissipate. The soil engineer shouts: 'Use UU! The clay has NO time to drain — φ is ZERO, use only c_u!' The typhoon = emergency loading = short-term = UU. Every time you see 'short-term stability of clay,' picture that typhoon scene.
Anchor Type
micro_story
Why It Works
Emotional context (typhoon emergency, urgency) dramatically increases encoding strength. Filipino students have direct experience with typhoons, making this highly relatable.
Example Usage
Exam: 'What test is used for short-term stability of a newly constructed clay embankment?' → Typhoon = urgent = UU → answer: UU test, φ = 0.
Recall Trigger
Typhoon emergency → no time to drain → UU → φ = 0, c_u.
Tags
- CD test
- drained
- long-term
- effective stress
Topic
Drainage Conditions — Long Term
Concept
CD test → long-term (drained) parameters: c', φ' (effective)
Anchor Id
A6
Difficulty
medium
Memory Aid
Years after the typhoon, the embankment has been standing for a long time. The pore water has fully drained, the soil is consolidated. The old engineer checks stability using c' and φ' — effective parameters from the CD test. Long time passing = pore pressure gone = drained = CD = effective stress parameters. Picture a dried-out bangus under the sun after many years — fully drained, fully consolidated.
Anchor Type
micro_story
Why It Works
Contrast with A5 (typhoon = short term) creates a paired memory. The dried bangus image completes the story arc from wet to dry, reinforcing drainage concept.
Example Usage
Problem asks for long-term slope stability analysis → use c', φ' from CD test. Paired with UU (short-term) for comparison.
Recall Trigger
Dried bangus under the sun = long-term = CD = c', φ' effective.
Tags
- formula
- Mohr circle
- principal stress
- friction angle
Topic
Principal Stresses at Failure
Concept
Principal stress relationship at failure (c = 0 sand): sin φ = (σ₁ - σ₃)/(σ₁ + σ₃)
Anchor Id
A7
Difficulty
hard
Memory Aid
Visualize a Mohr circle drawn on a whiteboard. The circle has DIAMETER = (σ₁ - σ₃) and CENTER at (σ₁ + σ₃)/2 from the origin. The sine of the friction angle = opposite over hypotenuse = RADIUS over DISTANCE-FROM-ORIGIN = [(σ₁-σ₃)/2] / [(σ₁+σ₃)/2] = (σ₁-σ₃)/(σ₁+σ₃). Picture a basketball (Mohr circle) where sin φ is simply the ratio of half-diameter to half-span. Every time you see a Mohr circle, recall: sin φ = difference ÷ sum.
Anchor Type
visual_association
Why It Works
Geometric visualization of the Mohr circle is the CORRECT mathematical basis of the formula. This anchor teaches the formula by deriving it visually, making forgetting almost impossible.
Example Usage
Triaxial test: σ₃ = 100 kPa, σ₁ = 300 kPa. → sin φ = (300-100)/(300+100) = 200/400 = 0.5 → φ = 30°.
Recall Trigger
Mohr circle on whiteboard → sin φ = difference over sum.
Tags
- formula
- principal stress
- chunking
- triaxial
Topic
Principal Stress at Failure — General Formula
Concept
σ₁ at failure in terms of σ₃: σ₁ = σ₃·tan²(45 + φ/2) + 2c·tan(45 + φ/2)
Anchor Id
A8
Difficulty
hard
Memory Aid
Break the formula into two CHUNKS. CHUNK 1: σ₃·tan²(45 + φ/2) — this is the CONFINEMENT contribution. CHUNK 2: 2c·tan(45 + φ/2) — this is the COHESION contribution. Memory phrase: 'Confinement SQUARED, Cohesion DOUBLED — both times N.' Where N = tan(45 + φ/2) is the flow number (Rankine's coefficient Nφ). So: σ₁ = σ₃·N² + 2c·N. Two chunks: confinement × N², cohesion × 2N.
Anchor Type
chunking
Why It Works
Chunking reduces cognitive load by grouping the complex formula into two meaningful parts with a shared factor N. Once N is memorized, both terms are easy to reconstruct.
Example Usage
Given: c = 20 kPa, φ = 30°, σ₃ = 100 kPa. N = tan(60°) = 1.732. σ₁ = 100·(1.732)² + 2·20·1.732 = 100·3 + 69.28 = 300 + 69.28 = 369.28 kPa.
Recall Trigger
Confinement (σ₃·N²) + Cohesion (2c·N) = σ₁. Where N = tan(45 + φ/2).
Tags
- direct shear test
- laboratory test
- cohesion
- friction
Topic
Direct Shear Test
Concept
Direct shear test — plots τ_f vs σ to get c and φ
Anchor Id
A9
Difficulty
easy
Memory Aid
Think of the direct shear test as the pandesal-cutting test. You have a stack of pandesal (soil sample). You push down on top (normal load σ), then push horizontally from the side (shear force T) until the bread splits on a horizontal plane. Plot how much sideways force you needed (τ_f) for each different downward force (σ). The graph gives you a straight line — the y-intercept is cohesion c, and the slope angle is φ. Simple, direct, on a predetermined failure plane.
Anchor Type
analogy
Why It Works
Pandesal is iconic Filipino bread. The physical cutting action directly mirrors the mechanics of the direct shear apparatus — horizontal splitting plane, normal force, shear force.
Example Usage
Exam: 'What does a direct shear test plot look like?' → Pandesal image → τ vs σ plot → y-intercept = c, slope = tan(φ).
Recall Trigger
Pandesal-cutting test: push down (σ), push sideways (τ), plot the line → c and φ.
Tags
- formula
- deviator stress
- triaxial
- pitfall
Topic
Triaxial Test — Deviator Stress
Concept
Deviator stress vs. major principal stress: σ₁ = σ₃ + Δσ (deviator)
Anchor Id
A10
Difficulty
medium
Memory Aid
Remember: 'DEVIATE from confinement to reach the peak.' The deviator stress (Δσ) is the EXTRA axial load beyond the confining pressure σ₃. Think of σ₁ as the total vertical push = base confinement (σ₃) + extra deviator kick (Δσ). Board exam pitfall: if the problem gives you 'deviator stress = 200 kPa' and σ₃ = 100 kPa, then σ₁ = 100 + 200 = 300 kPa — do NOT use 200 as σ₁ directly!
Anchor Type
mnemonic
Why It Works
The word 'deviate' is phonetically and semantically linked to 'deviator stress.' The warning about the common mistake makes the anchor doubly useful — it prevents the #1 board exam error.
Example Usage
Problem: σ₃ = 80 kPa, deviator = 180 kPa. → σ₁ = 80 + 180 = 260 kPa. Then sin φ = (260-80)/(260+80) = 180/340 = 0.529 → φ ≈ 32°.
Recall Trigger
DEVIATE = extra push above σ₃. σ₁ = σ₃ + deviator. Never use deviator as σ₁.
Tags
- CU test
- total stress
- effective stress
- pore pressure
Topic
CU Triaxial Test
Concept
CU test — gives BOTH total stress and effective stress parameters
Anchor Id
A11
Difficulty
medium
Memory Aid
Meet Cousin Umberto (CU). He consolidates first (waits for drainage during consolidation), but during shearing, he plugs his ears and refuses to drain. However, his friends measure BOTH his emotional reaction (total stress envelope) AND his true feelings (effective stress with pore pressure measured). CU test is the 'middle child' — partially drained during consolidation, undrained during shear, but with pore pressure measurement, you get both total (c, φ) and effective (c', φ') parameters.
Anchor Type
micro_story
Why It Works
Character narrative (Cousin Umberto) from the A4 anchor extends the story, building a connected memory palace. The 'middle child' analogy clarifies the intermediate nature of CU.
Example Usage
Exam: 'Which test gives both total and effective shear parameters?' → Cousin Umberto (CU) → CU test with pore pressure measurement.
Recall Trigger
Cousin CU: consolidates yes, drains during shear NO, measures pore pressure YES → both total and effective parameters.
Tags
- effective stress
- pore pressure
- drained
- formula
Topic
Effective Stress Principle
Concept
Effective vs. total stress: use σ' = σ - u for drained analyses
Anchor Id
A12
Difficulty
medium
Memory Aid
Total stress is like your gross salary — what you earn on paper. Pore water pressure u is like tax. Effective stress σ' is your NET take-home pay — what actually controls your buying power (shear strength). τ_f (effective) = c' + σ'·tan(φ'). Always subtract the 'tax' (pore pressure) before calculating real shear strength in drained analyses.
Anchor Type
analogy
Why It Works
Salary-tax-net pay is a universal analogy that every working professional immediately understands. It correctly maps the mathematical relationship σ' = σ - u.
Example Usage
Problem: σ = 200 kPa, u = 50 kPa, c' = 10 kPa, φ' = 28°. σ' = 200 - 50 = 150 kPa. τ_f = 10 + 150·tan28° = 10 + 79.7 = 89.7 kPa.
Recall Trigger
Gross salary (σ) minus tax (u) = net pay (σ'). Use net pay for drained shear strength.
Tags
- UC test
- UU test
- unconfined
- cohesive soil
Topic
Unconfined Compression Test
Concept
Unconfined compression test (UC): σ₃ = 0, special case of UU
Anchor Id
A13
Difficulty
easy
Memory Aid
Picture a clay cylinder standing ALONE on a table — no chamber, no confining pressure, nothing squeezing it from the sides. It's naked (σ₃ = 0). You just push down on top until it fails. That's the UC test. It's the 'cheapest triaxial' — UU test with zero confinement. The sample stands on its own because clay has cohesion; sand would fall apart immediately (no c). This also explains why UC test ONLY works for cohesive soils.
Anchor Type
visual_association
Why It Works
The visual image of a naked, unconfined cylinder is striking and unique. The 'cheapest triaxial' label correctly positions the UC test in the hierarchy of shear tests.
Example Usage
Exam: 'Why can't you perform UC test on sand?' → Naked cylinder → sand has no c → it collapses without confinement → UC only for cohesive soils.
Recall Trigger
Naked clay cylinder on a table — no confinement, σ₃ = 0 = UC test.
Tags
- failure plane
- Mohr circle
- geometry
- formula
Topic
Failure Plane Orientation
Concept
Failure plane orientation: 45 + φ/2 degrees from major principal plane
Anchor Id
A14
Difficulty
medium
Memory Aid
Remember: '45 PLUS HALF the friction.' The failure plane in soil is NOT at 45° like pure shear — it tilts by an extra φ/2 due to friction. So it's steeper than 45°. Think of it as: 'Friction adds a lean — half of φ beyond 45.' For φ = 30°: failure plane = 45 + 15 = 60° from the σ₃ plane (or equivalently, 30° from the σ₁ plane).
Anchor Type
mnemonic
Why It Works
The phrase '45 PLUS HALF' is a clean verbal chunk that encodes both the base angle and the modifier. It also immediately alerts students to the common error of using 45° alone.
Example Usage
Exam: φ = 30°. Failure plane angle from horizontal = 45 + 30/2 = 45 + 15 = 60° from the minor principal plane.
Recall Trigger
Failure plane = 45 + φ/2. Friction adds a lean.
Tags
- pitfall
- UC test
- c_u
- formula
Topic
UC Test — Common Pitfall
Concept
Board exam pitfall: c_u = q_u/2, NOT q_u
Anchor Id
A15
Difficulty
easy
Memory Aid
A student named Carlo memorized 'c_u equals q_u' and used q_u = 120 kPa directly. He got 120 kPa as c_u — and failed that board question. His classmate Maria remembered 'cut the bibingka in half' and wrote c_u = 60 kPa. Maria passed. Every board review group in Manila tells Carlo's story: 'Don't be a Carlo — always HALVE the q_u.'
Anchor Type
micro_story
Why It Works
Social consequences (passing vs. failing) create emotional stakes that dramatically improve memory encoding. Named characters make the story personal. The 'Don't be a Carlo' warning is quotable and repeatable.
Example Usage
q_u = 90 kPa → Don't be Carlo → c_u = 90/2 = 45 kPa. Never use 90 kPa directly as c_u.
Recall Trigger
Don't be Carlo — always halve q_u. c_u = q_u/2.
Tags
- undrained
- phi = 0
- saturated clay
- UU test
Topic
φ = 0 Concept for Saturated Undrained Clay
Concept
Saturated clay undrained behavior: φ_u = 0 (φ = 0 concept)
Anchor Id
A16
Difficulty
medium
Memory Aid
Saturated clay under fast (undrained) loading is like a water balloon. No matter how much you squeeze it (increase confining pressure), the water inside transfers the load — the effective stress barely changes. Shear strength does NOT increase with more confinement. It's like all Mohr circles for UU tests have the same diameter — they all touch the same horizontal failure envelope (φ = 0, a flat line at height c_u). The balloon can't get 'firmer' — it just redistributes water.
Anchor Type
analogy
Why It Works
The water balloon is a tactile, sensory analogy. Students can feel the concept. The visual of same-diameter Mohr circles all touching a horizontal line is a powerful geometric memory.
Example Usage
UU triaxial tests on saturated clay at σ₃ = 50, 100, 200 kPa all give same failure stress difference → Mohr circles same size → φ_u = 0 → c_u = constant.
Recall Trigger
Saturated clay = water balloon. More pressure = same strength. φ_u = 0, horizontal envelope at c_u.
Tags
- sand
- cohesion
- friction
- frictional soil
Topic
Sand Shear Behavior
Concept
Sand behavior: purely frictional, c = 0, φ typically 28°–45°
Anchor Id
A17
Difficulty
easy
Memory Aid
Pour sugar on a plate — it forms a cone (the angle of repose). Sugar grains don't stick together (c = 0); they just pile up based on friction (φ). Dry sand behaves exactly like sugar: no cohesion, pure friction. If you remove the confining stress, the pile collapses. This is why σ₃ > 0 in triaxial tests matters for sand — without confinement, strength drops to zero for c = 0 soils.
Anchor Type
analogy
Why It Works
Sugar and sand are physically similar granular materials. Students can picture pouring sugar and see the angle of repose forming. The sugar analogy makes c = 0 intuitive.
Example Usage
Triaxial on sand with σ₃ = 0: σ₁ = σ₃·tan²(45+φ/2) = 0 → sand has zero strength with zero confinement, confirming c = 0.
Recall Trigger
Sand = sugar pile: c = 0, pure friction, strength depends on confinement.
Tags
- CU test
- total stress
- effective stress
- visual
- long-term
Topic
CU Test Envelopes
Concept
CU test: total stress parameters vs. effective stress parameters
Anchor Id
A18
Difficulty
hard
Memory Aid
In a CU test with pore pressure measurement, imagine drawing TWO Mohr-Coulomb envelopes on the same graph: a YELLOW line (total stress, using σ) and a GREEN line (effective stress, using σ' = σ - u). The green line (c', φ') is steeper and shifted right — it shows TRUE soil behavior. The yellow line (c_T, φ_T) is the apparent envelope. Board exams often ask which one to use for long-term → always GREEN (effective). For immediate loading → can use YELLOW (total).
Anchor Type
visual_association
Why It Works
Color-coding two lines on one graph creates a distinctive visual memory. The GREEN = go (long-term, effective) mnemonic adds a traffic-light anchor.
Example Usage
Exam: CU test data with pore pressure. Long-term analysis → use GREEN line parameters c', φ'. Short-term → use YELLOW (total) c, φ.
Recall Trigger
Two lines on CU plot: YELLOW (total) vs. GREEN (effective). Go green for long-term.
Tags
- CU test
- CD test
- consolidation
- drainage
- sequence
Topic
CU vs. CD Test Procedure
Concept
Sequence: Consolidation then Shearing in CU and CD tests
Anchor Id
A19
Difficulty
medium
Memory Aid
Place yourself in a Filipino wet market (palengke). STALL 1 (Consolidation): The soil is squeezed under the confining pressure — like pressing water out of a wet towel at the first stall. STALL 2 (Shearing): The sample is now sheared — like slicing through the pressed towel at the second stall. In CU — you squeeze at Stall 1 (drain open), then slice at Stall 2 (drain CLOSED). In CD — you squeeze at Stall 1, then slice at Stall 2 with drain STILL OPEN. The difference is just whether the drain valve stays open during slicing.
Anchor Type
method_of_loci
Why It Works
Method of loci (memory palace) using a familiar Philippine setting. Each stall represents a test phase. The wet towel gives a tangible feel for consolidation and drainage.
Example Usage
Exam asks to distinguish CU from CD: → palengke image → CU closes drain valve at Stall 2 (no drainage during shear); CD keeps it open → pore pressures dissipate during shear in CD.
Recall Trigger
Palengke: Stall 1 = consolidate (squeeze), Stall 2 = shear (slice). CU: Stall 2 drain CLOSED; CD: Stall 2 drain OPEN.
Tags
- short-term
- long-term
- UU
- CD
- embankment
- clay
Topic
Short-term vs. Long-term Stability
Concept
Short-term vs. Long-term stability: which governs for clay embankments
Anchor Id
A20
Difficulty
medium
Memory Aid
Imagine two engineers, Ate Dina (short-term) and Kuya Ernesto (long-term). Ate Dina is worried about the day the embankment is built — pore pressures are high, no drainage yet — she uses UU parameters (c_u, φ=0). Kuya Ernesto checks back 5 years later — pore pressures have dissipated, soil is drained — he uses CD parameters (c', φ'). Both must be checked. In Philippine practice (DPWH embankment design), BOTH stability conditions are evaluated because each can govern depending on soil type.
Anchor Type
micro_story
Why It Works
Named Filipino characters with clear roles are memorable. The timeline (day of construction vs. 5 years later) gives a concrete temporal anchor. Professional practice context adds exam relevance.
Example Usage
Board question: 'Which stability condition governs just after construction of a clay embankment?' → Ate Dina (short-term) → UU → φ = 0, c_u controls.
Recall Trigger
Ate Dina (short-term, UU, c_u) vs. Kuya Ernesto (long-term, CD, c' φ').
Revision Game
Unconfined Compression (UC) Test — σ₃ = 0
Clue
I am the test where the soil cylinder stands completely naked — no jacket, no confining pressure, just being pushed from above until I fail. What test am I?
Memory Link
A13 — Naked clay cylinder on a table (visual association)
One-half (1/2) — c_u = q_u / 2
Clue
I am the fraction that converts the unconfined compressive strength into undrained shear strength. Say my value and the formula.
Memory Link
A3 — 'q_u divided by two, that's what c_u is due!' (rhyme) and A15 — Don't be Carlo!
σ₁ = 300 kPa; sin φ = (300-100)/(300+100) = 200/400 = 0.5; φ = 30°
Clue
In a triaxial test on sand, σ₃ = 100 kPa and the deviator stress = 200 kPa. What is φ? (Solve in your head using the SINE formula.)
Memory Link
A7 — Mohr circle on whiteboard: sin φ = difference over sum; A10 — DEVIATE: σ₁ = σ₃ + deviator
UU test parameters — c_u with φ_u = 0 (undrained, short-term)
Clue
A typhoon just hit and the contractor must check the clay embankment stability RIGHT NOW. Which test type parameters should the engineer use, and what is the friction angle value?
Memory Link
A5 — Typhoon emergency micro-story; A20 — Ate Dina (short-term, UU)
Chief Doming — the CD (Consolidated-Drained) test
Clue
I am the barangay official who is fully prepared, completely drained, and gives you the most realistic long-term effective parameters c' and φ'. Who am I?
Memory Link
A4 — Three barangay officials: Uncle UU, Cousin CU, Chief CD
τ_f = 15 + 200·tan(25°) = 15 + 200(0.4663) = 15 + 93.26 = 108.26 kPa
Clue
A soil has c = 15 kPa and φ = 25°. The normal stress on the failure plane is 200 kPa. What is the shear strength? (Use the bangus-on-banana-leaf formula.)
Memory Link
A1 — Bangus on banana leaf: stickiness (c) + weight × roughness (σ·tan φ)
σ' = 200 - 50 = 150 kPa. Use in τ_f = c' + σ'·tan(φ') for drained/long-term analysis.
Clue
My salary (total stress) is ₱200 kPa. I pay ₱50 kPa in tax (pore pressure). What is my take-home pay (effective stress), and how do I use it in the shear strength formula?
Memory Link
A12 — Salary-tax-net pay analogy for effective stress (σ' = σ - u)
Sand is Silly → c ≈ 0 (no cohesion), φ > 0 (frictional). Clay is Clingy (undrained) → c_u > 0, φ_u = 0 (purely cohesive in short-term).
Clue
Sand is Silly. Clay is Clingy. What do these phrases tell you about the shear parameters c and φ for each soil type?
Memory Link
A2 — SC-ZC-CC acronym and personality analogy
Formula Mnemonics
Formula
τ_f = c + σ·tan(φ)
Mnemonic
CST: Cohesion + Sigma Times tangent-phi. 'C plus STan-phi.' Think: Every COST has a fixed base (c) plus a variable rate (σ·tan φ). The shear strength COST = fixed cohesion + variable friction.
When To Use
Always, for any soil shear strength calculation. Use total stress (σ, c, φ) for total stress analysis (UU conditions). Use effective stress (σ', c', φ') for drained or long-term analysis (CD conditions).
What Each Part Means
τ_f = shear stress at failure (kPa); c = cohesion intercept (kPa), soil's inherent 'stickiness'; σ = normal stress on failure plane (kPa); tan(φ) = tangent of friction angle, the 'slope' of the failure envelope; φ = angle of internal friction (degrees).
Formula
c_u = q_u / 2
Mnemonic
HALF THE UCS. 'c_u = HALF of q_u.' Chant: 'Undrained strength is half the unconfined — always cut it in two, you'll be fine.' The bibingka rule: cut the unconfined strength in half.
When To Use
Only for saturated clay under undrained conditions (φ = 0) from unconfined compression test results. Do NOT use for drained conditions or for sands.
What Each Part Means
c_u = undrained shear strength (kPa); q_u = unconfined compressive strength (kPa) from UC test; the factor 1/2 arises because at failure in the UC test, the Mohr circle has diameter q_u and the shear stress at the top of the circle (representing the failure plane for φ = 0) is q_u/2.
Formula
sin(φ) = (σ₁ - σ₃) / (σ₁ + σ₃)
Mnemonic
SINE = DIFF over SUM. 'Sin phi — difference over sum.' Like a fraction: top = how far apart the principals are; bottom = how far they span total. Picture the Mohr circle: sin(φ) = radius / center-distance = [(σ₁-σ₃)/2] / [(σ₁+σ₃)/2].
When To Use
For sands (c = 0) in CD or drained triaxial tests. Also works for any c = 0 soil. NOT directly applicable when c ≠ 0 — must use graphical Mohr circle or the general tangent-line method.
What Each Part Means
φ = friction angle (degrees); σ₁ = major principal stress at failure (kPa); σ₃ = minor principal stress / confining pressure (kPa); (σ₁ - σ₃) = deviator stress at failure = diameter of Mohr circle; (σ₁ + σ₃) = twice the center location of Mohr circle from origin. Valid only when c = 0.
Formula
σ₁ = σ₃·tan²(45 + φ/2) + 2c·tan(45 + φ/2)
Mnemonic
SIGMA-ONE = CONFINEMENT-N-squared PLUS TWO-C-N. Where N = tan(45 + φ/2). 'Two chunks: σ₃·N² + 2c·N.' The confinement chunk uses N², the cohesion chunk uses 2N.
When To Use
When you know σ₃, c, and φ and need to find the major principal stress at failure. Common in triaxial test problems and bearing capacity checks. For c = 0 soils, the formula simplifies to σ₁ = σ₃·tan²(45 + φ/2).
What Each Part Means
σ₁ = major principal stress at failure (kPa); σ₃ = confining (minor principal) stress (kPa); c = cohesion (kPa); φ = friction angle (degrees); N = tan(45 + φ/2) = Rankine's passive pressure coefficient (√K_p) = flow factor. The term tan²(45 + φ/2) is sometimes written as K_p (passive coefficient) or N_φ².
Formula
θ_f = 45 + φ/2 (failure plane angle from minor principal plane)
Mnemonic
THETA = 45 PLUS HALF-PHI. 'Start at 45, add half the friction.' The failure plane is always tilted more than 45° from the σ₃ plane (horizontal in standard triaxial setup) by an extra φ/2.
When To Use
When locating the failure plane in a triaxial specimen or when drawing the Mohr-Coulomb envelope graphically. Essential for understanding why triaxial specimens fail at an angle rather than at 45°.
What Each Part Means
θ_f = angle of failure plane measured from the minor principal stress plane (degrees); 45° = base angle for pure shear; φ/2 = additional tilt due to internal friction. Note: measured from σ₃ plane. If measured from σ₁ plane, the angle is (45 - φ/2).
Formula
τ_f (effective) = c' + σ'·tan(φ') where σ' = σ - u
Mnemonic
EFFECTIVE STRENGTH = subtract the tax first. 'Take away pore pressure u (the tax), then apply Mohr-Coulomb.' c' and φ' are effective (true) soil parameters; σ' is net (take-home) stress.
When To Use
For all drained analyses (CD test, long-term stability, sand in any condition). The fundamental equation for realistic soil behavior. Always preferred over total stress when pore pressures are known.
What Each Part Means
c' = effective cohesion (kPa) — true cohesion after drainage; φ' = effective friction angle (degrees) — true friction; σ = total normal stress (kPa); u = pore water pressure (kPa); σ' = effective normal stress = σ - u (kPa). This is Terzaghi's effective stress principle applied to shear strength.
Quick Recall Chains
Chain Title
Three Triaxial Test Types in Order of Drainage
Recall Test
Without looking, name the three triaxial test types from least-drained to fully-drained, and state what parameters each gives. Time yourself: 30 seconds.
Memory Chain
Three barangay officials at increasing levels of experience: UNCLE (UU) barged in with zero preparation and zero drainage. COUSIN (CU) prepared (consolidated) but panicked and closed the drain during shearing. CHIEF (CD) was calm, fully prepared, and kept everything open — the most experienced and most drained. Uncle → Cousin → Chief = UU → CU → CD. Each step adds MORE drainage.
Items To Remember
- UU — Unconsolidated-Undrained (no drainage at all)
- CU — Consolidated-Undrained (drain during consolidation, close during shear)
- CD — Consolidated-Drained (drain throughout — fully drained)
Chain Title
Steps to Solve a Triaxial Test Problem (c = 0 Sand)
Recall Test
A CD test on sand: σ₃ = 80 kPa, deviator stress = 180 kPa. Run through DAVETs and find φ. Answer: σ₁ = 260 kPa; sin φ = 180/340 = 0.529; φ ≈ 31.9°.
Memory Chain
DEVIATE to SUCCESS: Diagnose σ₃ → Add deviator to get σ₁ → Verify with SINE formula → Evaluate φ by arcsin → Take the answer. Short: DAVETs — Diagnose, Add, Verify, Evaluate, Take. Picture Dave taking a triaxial test step by step.
Items To Remember
- Step 1: Identify σ₃ (confining pressure)
- Step 2: Calculate σ₁ = σ₃ + deviator stress
- Step 3: Apply sin φ = (σ₁ - σ₃)/(σ₁ + σ₃)
- Step 4: Find φ = arcsin of result
- Step 5: Verify using τ_f = σ·tan φ if needed
Chain Title
Key Formulas for UC Test
Recall Test
A UC test on clay gives q_u = 150 kPa. What is c_u and φ? Answer: c_u = 75 kPa, φ = 0.
Memory Chain
NAKED CLAY HALF STRENGTH: Naked (σ₃=0) Clay (cohesive only) HAlves the strength to give c_u. N-C-H-S. Or: 'Naked Clay Halves Strength.' Picture a naked clay cylinder on a table being cut in half to reveal c_u.
Items To Remember
- UC test: σ₃ = 0 (no confinement)
- Failure load gives q_u (unconfined compressive strength)
- φ_u = 0 for saturated clay
- c_u = q_u / 2 (halve the UCS)
- Only valid for cohesive soils
Chain Title
Mohr-Coulomb Envelope — What the Graph Shows
Recall Test
Describe a Mohr-Coulomb plot: what are the axes, what does the y-intercept represent, what does the slope represent, and write the equation of the failure envelope.
Memory Chain
Graph story: 'I STAND on the NORMAL, I RISE with SHEAR. My starting height is C (cohesion), my rising angle is PHI (friction). The line I trace is Mohr-Coulomb.' Standing on x-axis (normal), rising on y-axis (shear), starting at c, rising at angle φ.
Items To Remember
- X-axis: Normal stress σ (or σ')
- Y-axis: Shear stress τ
- Y-intercept: Cohesion c
- Slope angle: Friction angle φ
- Equation of line: τ_f = c + σ·tan φ
- Points on/below envelope: stable; above: failure
Chain Title
Short-term vs. Long-term Stability — Which Test to Use
Recall Test
A clay slope is built during rainy season. Which parameters govern stability (a) on the day of construction and (b) after 10 years? Answer: (a) UU — c_u, φ=0; (b) CD — c', φ'.
Memory Chain
Timeline: TYPHOON DAY (UU) → CALM AFTER STORM (CU) → SUNNY YEARS LATER (CD). Typhoon = emergency short-term = UU = c_u. After storm = medium-term = CU. Sunny long-term = CD = c', φ'. Remember: Philippines has typhoon seasons (short-term) and dry seasons (long-term). Both must be designed for.
Items To Remember
- Short-term (just after construction): use UU test → c_u, φ = 0
- Intermediate: use CU test → total or effective parameters
- Long-term (years after construction): use CD test → c', φ'
- Sand: always drained → always use φ' (CD parameters)
- Saturated clay: check both short-term (UU) and long-term (CD)
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Lateral Earth Pressure and Retaining Structures
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