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CELE Geotechnical EngineeringSlope Stability and Soil ImprovementExam Answer Templates

How to answer Slope Stability and Soil Improvement questions on the CELE — a set of templates you can apply to any question Professional Regulation Commission (PRC) — Board of Civil Engineering throws at you in the Geotechnical Engineering subtest. Built from analysis of recent CELE 2026 papers.

Exam context

Professional Regulation Commission (PRC) — Board of Civil Engineering runs the Civil Engineer Licensure Examination on May and November 2026. Its Geotechnical Engineering section sits under a "Core" weighting, and Slope Stability and Soil Improvement is the 11th chapter in the 11-chapter CELE Geotechnical Engineering rotation. The CELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Geotechnical Engineering.

Slope Stability and Soil Improvement - Exam Answer Templates

Proper answer writing is the difference between partial and full marks on the PRC Civil Engineer Licensure Examination. In Geotechnical Engineering, examiners reward precise use of technical vocabulary, correct formula identification, step-by-step numerical solutions with clearly labelled intermediate values, and concise conceptual explanations that demonstrate understanding — not just memorised definitions. These templates show you exactly how to structure responses at every mark level so that every point you have earned in your study is captured on the answer sheet.

Templates

Define factor of safety (FS) as applied to slope stability. [1 mark]

Marks

1

Topic

Factor of Safety

Difficulty

easy

Template Id

T1

Examiner Tip

A 1-mark answer must be self-contained in one sentence plus the formula. Do not waste time elaborating; move on.

Model Answer

The factor of safety of a slope is the ratio of the shear strength available along the potential failure surface to the shear stress required to maintain equilibrium: FS = τ_f / τ. A slope is stable when FS > 1.

Question Type

very_short_answer

Answer Structure

  • Line 1: State FS as the ratio of shear strength to mobilised shear stress and write the formula FS = τ_f/τ [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct ratio definition with formula FS = τ_f/τ (or equivalent words stating resisting-force to driving-force ratio)

Common Mark Deductions

  • Defining FS as 'safety factor against overturning' — this is imprecise for slope problems.
  • Omitting the formula and giving only a worded description — formula is expected at this level.
  • Stating FS = driving/resisting (inverted ratio) — this is a fatal error.

Key Phrases To Include

  • ratio
  • shear strength available (τ_f)
  • shear stress required for equilibrium (τ)
  • FS = τ_f/τ
  • stable when FS > 1

State the condition under which an infinite dry cohesionless slope is stable, and write the corresponding FS expression. [1 mark]

Marks

1

Topic

Infinite Slope — Dry Cohesionless

Difficulty

easy

Template Id

T2

Examiner Tip

The phrase 'independent of depth' is a hallmark of full understanding and is often worth the difference between a full and half mark in borderline grading.

Model Answer

A dry cohesionless infinite slope (c′ = 0) is stable when the slope angle β is less than the friction angle φ′. The factor of safety is FS = tanφ′/tanβ, which is independent of depth.

Question Type

very_short_answer

Answer Structure

  • Line 1: State stability condition β < φ′ and write FS = tanφ′/tanβ [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct formula FS = tanφ/tanβ AND statement that slope is stable when β < φ (or equivalently when FS > 1)

Common Mark Deductions

  • Writing FS = tanβ/tanφ (inverted) — zero marks.
  • Forgetting to state the independence from depth — misses a key property of this formula.

Key Phrases To Include

  • FS = tanφ/tanβ
  • β < φ for stability
  • independent of depth
  • c′ = 0

What is Taylor's stability number Ns, and how is it used to find the critical height of a slope? [2 marks]

Marks

2

Topic

Taylor's Stability Number

Difficulty

easy

Template Id

T3

Examiner Tip

Examiners specifically check whether you state FS = 1 for Hcr. Without it, the formula is incomplete and marks are deducted.

Model Answer

Taylor's stability number is a dimensionless parameter Ns = c/(γ·H·FS) obtained from published stability charts as a function of slope angle and friction angle φ. It is used to find the critical height (at FS = 1) by rearranging: H_cr = c/(γ·Ns). A higher Ns indicates a less stable configuration.

Question Type

short_answer

Answer Structure

  • Line 1: Define Ns as dimensionless ratio Ns = c/(γHFS) from stability charts [1 mark]
  • Line 2: Write the critical-height formula H_cr = c/(γNs) and state the FS = 1 condition [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct definition of Ns including that it is dimensionless and chart-derived

Marks

1

Criteria

Correct formula H_cr = c/(γNs) with explicit statement that this applies at FS = 1

Common Mark Deductions

  • Giving Ns units (e.g., kPa) — Ns is dimensionless; this errors costs 1 mark.
  • Omitting the FS = 1 qualifier when writing the H_cr formula.
  • Confusing Ns with bearing capacity factors Nc or Nq.

Key Phrases To Include

  • dimensionless
  • stability chart
  • Ns = c/(γHFS)
  • H_cr = c/(γNs)
  • FS = 1 (critical condition)

List and briefly describe TWO ground-improvement methods suitable for a soft, compressible clay site. [2 marks]

Marks

2

Topic

Soil Improvement

Difficulty

easy

Template Id

T4

Examiner Tip

Always match the improvement method to the soil type in the question. For soft clay the keywords are consolidation, drainage, and chemical stabilisation — not densification, which is for sands and gravels.

Model Answer

1. Preloading with prefabricated vertical (wick) drains: A surcharge fill is placed over the site to pre-consolidate the clay. Wick drains shorten the drainage path, accelerating settlement and strength gain before construction. 2. Lime or cement stabilisation: Quicklime or Portland cement is mixed in-situ with the clay; chemical reactions reduce plasticity, increase strength, and lower compressibility of the treated layer.

Question Type

short_answer

Answer Structure

  • Item 1: Name the method (preloading/wick drains) and explain the mechanism in 1–2 sentences [1 mark]
  • Item 2: Name a second method (lime/cement stabilisation) and explain the mechanism in 1–2 sentences [1 mark]

Scoring Breakdown

Marks

1

Criteria

One correctly named and briefly explained method applicable to soft clay

Marks

1

Criteria

A second distinct, correctly named and briefly explained method

Common Mark Deductions

  • Listing methods only without any explanation — each method must be described to earn its mark.
  • Repeating the same method in different words (e.g., 'preloading' and 'surcharge fill') — only one mark awarded.
  • Suggesting vibroflotation without noting it is most effective in sands, not soft clay — context mismatch.

Key Phrases To Include

  • preloading/surcharge
  • prefabricated vertical drains (wick drains)
  • drainage path
  • consolidation
  • lime/cement stabilisation
  • strength gain

A dry sandy slope has φ′ = 35° and β = 28°. Compute the factor of safety against sliding. [2 marks]

Marks

2

Topic

Infinite Slope — Dry Cohesionless

Difficulty

easy

Template Id

T5

Examiner Tip

For any numerical answer, always write a one-line interpretation: 'FS = 1.32 > 1.0, therefore the slope is stable.' This costs zero extra time and often secures the final half-mark.

Model Answer

Given: φ′ = 35°, β = 28°, c′ = 0 (dry sand — cohesionless infinite slope). Formula: FS = tanφ′/tanβ FS = tan35°/tan28° = 0.7002/0.5317 = 1.32 ∴ FS = 1.32 > 1.0 — the slope is stable. (Note: Since β = 28° < φ′ = 35°, stability is confirmed.)

Question Type

numerical

Answer Structure

  • Line 1: State given data and identify the applicable formula [0.5 mark]
  • Line 2: Substitute and compute tan values correctly [1 mark]
  • Line 3: State FS and interpret stability (FS > 1) [0.5 mark]

Scoring Breakdown

Marks

1

Criteria

Correct formula FS = tanφ/tanβ identified and correctly set up

Marks

1

Criteria

Correct numerical answer FS ≈ 1.32 with stability interpretation

Common Mark Deductions

  • Using sinφ/sinβ instead of tanφ/tanβ — formula error, loses formula mark.
  • Not stating whether the slope is stable or unstable — loses interpretation mark.
  • Arithmetic errors in trigonometric values — verify tan values with calculator.

Key Phrases To Include

  • FS = tanφ/tanβ
  • tan35° = 0.7002
  • tan28° = 0.5317
  • FS = 1.32
  • β < φ′, therefore stable

Explain how seepage parallel to the slope surface affects the factor of safety of an infinite cohesionless slope. [2 marks]

Marks

2

Topic

Infinite Slope — Seepage

Difficulty

medium

Template Id

T6

Examiner Tip

The γ′/γ_sat ratio is the examiner's favourite trap. Always distinguish between submerged and saturated unit weights in seepage problems.

Model Answer

When seepage occurs parallel to the slope surface, a positive pore-water pressure develops at the potential failure plane, reducing the effective normal stress. For a cohesionless infinite slope with full seepage (phreatic surface at ground level), the FS becomes: FS_seepage = (γ′/γ_sat) × (tanφ′/tanβ) Since γ′ (submerged unit weight ≈ 9–10 kN/m³) < γ_sat (≈ 18–20 kN/m³), the ratio γ′/γ_sat ≈ 0.5, roughly halving the dry-slope FS. Seepage therefore significantly destabilises slopes.

Question Type

short_answer

Answer Structure

  • Line 1: State that seepage generates pore-water pressure, reducing effective normal stress [1 mark]
  • Line 2: Write the modified FS formula showing γ′/γ_sat factor and note the roughly 50% reduction [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct mechanism: pore-water pressure reduces effective normal stress, which reduces frictional resistance

Marks

1

Criteria

Correct modified formula or quantified effect (γ′/γ_sat factor; FS approximately halved)

Common Mark Deductions

  • Stating only that 'seepage reduces FS' without explaining the pore-pressure mechanism.
  • Using total unit weight γ instead of submerged unit weight γ′ in the seepage formula.
  • Confusing parallel seepage with artesian pressure conditions.

Key Phrases To Include

  • pore-water pressure
  • effective normal stress
  • γ′ (submerged unit weight)
  • γ_sat
  • FS = (γ′/γ_sat)(tanφ′/tanβ)
  • factor of safety approximately halved

A cohesive slope has c′ = 15 kPa, φ′ = 25°, γ = 19 kN/m³, slope angle β = 30°, and failure plane depth z = 4 m (no seepage). Calculate the factor of safety. [3 marks]

Marks

3

Topic

Cohesive Infinite Slope

Difficulty

medium

Template Id

T7

Examiner Tip

Write cos²β explicitly as (cosβ)² = (0.866)² = 0.750 to show the examiner you have not confused it with cosβ. This single calculation step is worth a mark.

Model Answer

Given: c′ = 15 kPa, φ′ = 25°, γ = 19 kN/m³, β = 30°, z = 4 m Step 1 — Compute intermediate values: γz = 19 × 4 = 76 kPa cos²β = cos²30° = (0.8660)² = 0.7500 tanφ′ = tan25° = 0.4663 sinβ = sin30° = 0.5000 cosβ = cos30° = 0.8660 Step 2 — Apply cohesive infinite-slope formula: FS = [c′ + γz·cos²β·tanφ′] / [γz·sinβ·cosβ] FS = [15 + 76(0.7500)(0.4663)] / [76(0.5000)(0.8660)] FS = [15 + 26.58] / [32.91] FS = 41.58 / 32.91 FS = 1.26 ∴ The slope has FS = 1.26. This is below the typical design target of 1.3–1.5, indicating the slope may require improvement or closer investigation.

Question Type

numerical

Answer Structure

  • Step 1: Write the formula FS = [c′ + γz·cos²β·tanφ′] / [γz·sinβ·cosβ] [1 mark]
  • Step 2: Compute all intermediate values (γz, cos²β, tanφ′, sinβcosβ) correctly [1 mark]
  • Step 3: Substitute, compute FS = 1.26, and interpret result relative to design target [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct formula written explicitly with cos²β (not cosβ)

Marks

1

Criteria

All intermediate values correctly computed and labelled with units

Marks

1

Criteria

Final FS ≈ 1.26 (accept 1.25–1.27) with interpretation of adequacy

Common Mark Deductions

  • Using cosβ instead of cos²β in the numerator — single most common error in this formula.
  • Omitting the c′ term entirely — cohesive slope formula loses the numerator's first term.
  • Computing sinβ·cosβ incorrectly; note sin30°·cos30° = 0.5 × 0.866 = 0.433, not sin60°.
  • Not comparing FS to 1.3–1.5 design range — misses the engineering interpretation mark.

Key Phrases To Include

  • FS = [c′ + γz·cos²β·tanφ′] / [γz·sinβ·cosβ]
  • cos²30° = 0.7500
  • γz = 76 kPa
  • FS = 1.26
  • below design target of 1.3–1.5

Using Taylor's stability number, find the critical height of a slope given: c = 20 kPa, γ = 18 kN/m³, Ns = 0.06. State any assumption made. [3 marks]

Marks

3

Topic

Taylor's Stability Number

Difficulty

medium

Template Id

T8

Examiner Tip

Adding the bonus calculation of allowable height at FS = 1.5 demonstrates higher-order thinking. Even if it is not asked, it signals engineering judgement and may earn bonus credit from the examiner.

Model Answer

Given: c = 20 kPa, γ = 18 kN/m³, Ns = 0.06 Assumption: Critical height corresponds to FS = 1 (incipient failure). Step 1 — State Taylor's formula: H_cr = c / (γ · Ns) Step 2 — Substitute values: H_cr = 20 / (18 × 0.06) H_cr = 20 / 1.08 H_cr = 18.5 m ∴ The maximum height the slope can stand without support at FS = 1 is H_cr = 18.5 m. For a design with FS = 1.5, the allowable height would be H_allow = H_cr/FS = 18.5/1.5 = 12.3 m.

Question Type

numerical

Answer Structure

  • Line 1: State assumption FS = 1 and write formula H_cr = c/(γ·Ns) [1 mark]
  • Line 2: Substitute values correctly with units shown [1 mark]
  • Line 3: Final answer H_cr = 18.5 m with physical interpretation or design height at FS = 1.5 [1 mark]

Scoring Breakdown

Marks

1

Criteria

Formula H_cr = c/(γ·Ns) correctly stated with FS = 1 assumption

Marks

1

Criteria

Correct substitution: denominator = 18 × 0.06 = 1.08 kN/m³

Marks

1

Criteria

H_cr = 18.5 m correctly computed and physically interpreted

Common Mark Deductions

  • Not stating FS = 1 assumption — partial credit only.
  • Giving Ns units or not stating it is dimensionless.
  • Inverting the formula to H_cr = γ·Ns/c — zero marks for formula.

Key Phrases To Include

  • H_cr = c/(γ·Ns)
  • FS = 1 (critical, incipient failure)
  • Ns is dimensionless
  • H_cr = 18.5 m
  • design height at FS = 1.5

Describe the method of slices (Swedish/Fellenius method) for analysing finite-slope stability. Include the governing formula and identify the critical failure surface. [3 marks]

Marks

3

Topic

Method of Slices — Finite Slopes

Difficulty

medium

Template Id

T9

Examiner Tip

A simple sketch of the slope cross-section showing 3–4 slices with W arrows and the angle α on one slice earns the diagram mark and reinforces your written explanation.

Model Answer

The method of slices analyses the stability of a finite slope by dividing the soil mass above a trial circular failure arc into a series of vertical slices. For each slice, the weight W acts vertically; α is the angle of the slice base to the horizontal. Governing formula (Fellenius): FS = Σ(c′ℓ + N′tanφ′) / Σ(W·sinα) where ℓ = arc length of slice base, N′ = W·cosα − u·ℓ (effective normal force), and u = pore-water pressure. The critical failure surface is found by trial: multiple circles with different centres and radii are analysed, and the circle yielding the minimum FS governs design. Computer programs (e.g., slope stability software) automate this search. One trial circle is insufficient — the minimum-FS circle must be located.

Question Type

short_answer

Answer Structure

  • Part 1: Describe the slicing procedure (circular arc, vertical slices, forces) [1 mark]
  • Part 2: Write the Fellenius FS formula with correct terms [1 mark]
  • Part 3: Explain the critical circle search — trial multiple circles, minimum FS governs [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct description of dividing failure mass into slices above a circular arc with correct force identification (W, α)

Marks

1

Criteria

Correct formula FS = Σ(c′ℓ + N′tanφ′)/Σ(W·sinα) with terms defined

Marks

1

Criteria

Correct identification of the critical circle as the trial surface with minimum FS

Common Mark Deductions

  • Drawing slices without defining α or W — marks for formula set-up are lost.
  • Stating that one trial circle gives the answer — this is explicitly wrong; minimum FS governs.
  • Confusing the Fellenius method (ignoring interslice forces) with Bishop's simplified method — be specific about which method is being described.

Key Phrases To Include

  • circular failure arc
  • vertical slices
  • FS = Σ(c′ℓ + N′tanφ′)/Σ(W·sinα)
  • N′ = W·cosα − uℓ
  • critical circle — minimum FS
  • multiple trial circles

Find the required cohesion for a 12 m high slope to achieve FS = 1.5, given Ns = 0.05 and γ = 18 kN/m³. [3 marks]

Marks

3

Topic

Taylor's Stability Number — Reverse Calculation

Difficulty

medium

Template Id

T10

Examiner Tip

The trap in this question is that students memorise H_cr = c/(γ·Ns) for FS = 1 and forget to include FS when a specific factor of safety is required. Always check whether the question specifies FS ≠ 1.

Model Answer

Given: H = 12 m, FS = 1.5, Ns = 0.05, γ = 18 kN/m³ Step 1 — From Taylor's formula: Ns = c / (γ · H · FS) Step 2 — Rearrange for c: c = Ns · γ · H · FS Step 3 — Substitute: c = 0.05 × 18 × 12 × 1.5 c = 0.05 × 324 c = 16.2 kPa ∴ The soil must have a minimum cohesion of c = 16.2 kPa to maintain FS = 1.5 for the 12 m slope.

Question Type

numerical

Answer Structure

  • Step 1: Write Ns = c/(γ·H·FS) and identify the unknown as c [1 mark]
  • Step 2: Rearrange correctly to c = Ns·γ·H·FS [1 mark]
  • Step 3: Substitute all values with units and compute c = 16.2 kPa [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct identification of the full Taylor formula including FS: Ns = c/(γHFS)

Marks

1

Criteria

Correct algebraic rearrangement to isolate c

Marks

1

Criteria

Correct answer c = 16.2 kPa with units and conclusion

Common Mark Deductions

  • Using H_cr = c/(γ·Ns) without incorporating FS = 1.5 — this gives c for FS = 1 only.
  • Forgetting to include FS in the formula — most common error for this question type.
  • Arithmetic errors in multiplication; verify: 18 × 12 = 216, 216 × 0.05 = 10.8, 10.8 × 1.5 = 16.2.

Key Phrases To Include

  • Ns = c/(γ·H·FS)
  • c = Ns·γ·H·FS
  • c = 0.05 × 18 × 12 × 1.5
  • c = 16.2 kPa
  • minimum cohesion required

Compare and contrast the infinite slope method and the method of slices for slope stability analysis. [5 marks]

Marks

5

Topic

Comparison of Slope Analysis Methods

Difficulty

hard

Template Id

T11

Examiner Tip

For 5-mark compare-and-contrast questions, use a structured approach: state each point as a heading (Geometry, Formula, Critical Surface, Pore Pressure, Application) to make it easy for the examiner to follow and award marks sequentially.

Model Answer

INFINITE SLOPE METHOD vs. METHOD OF SLICES 1. Geometry and Applicability The infinite slope method applies to long, uniform slopes where the failure plane is shallow and parallel to the slope surface, making it suitable for translational (planar) failures in residual soils or colluvium. The method of slices (Fellenius/Bishop) applies to finite slopes of any geometry, where the failure surface is assumed circular — making it the general-purpose method for embankments, cuts, and natural slopes. 2. Governing Equations Infinite slope (cohesive, no seepage): FS = [c′ + γz·cos²β·tanφ′] / [γz·sinβ·cosβ] Method of slices (Fellenius): FS = Σ(c′ℓ + N′tanφ′) / Σ(W·sinα) 3. Critical Failure Surface In the infinite slope method, the failure plane depth z is specified or assumed. In the method of slices, the critical failure surface is found by trial — numerous circles are analysed and the circle with the minimum FS governs design. 4. Pore Pressure Treatment Both methods accommodate pore pressures. In the infinite slope, u = γ_w·z_w·cos²β for seepage. In the method of slices, u is applied to each slice base as N′ = (W·cosα − uℓ). 5. Computational Effort and Accuracy The infinite slope formula is closed-form and simple to compute. The method of slices requires iteration over multiple trial circles and is more labour-intensive (typically done with software), but is more accurate for finite slopes. Bishop's simplified modification to the slice method improves accuracy by accounting for interslice forces. In summary, use the infinite slope method for long, translational failures in uniform slopes; use the method of slices for finite slopes with circular failure mechanisms.

Question Type

long_answer

Answer Structure

  • Part 1: Define applicability/geometry of each method (translational vs. circular) [1 mark]
  • Part 2: Write governing equations for both methods with terms defined [1 mark]
  • Part 3: Explain how the critical failure surface is identified in each method [1 mark]
  • Part 4: Discuss pore-pressure treatment in both methods [1 mark]
  • Part 5: Compare computational effort/accuracy and state when to use each [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct description of geometry: infinite slope = planar/translational; slices = circular arc for finite slopes

Marks

1

Criteria

Both governing equations written correctly with symbols defined

Marks

1

Criteria

Correct identification of critical surface: specified depth z (infinite) vs. minimum-FS trial circle (slices)

Marks

1

Criteria

Correct treatment of pore pressure in both methods

Marks

1

Criteria

Meaningful comparison of effort/accuracy and practical guidance on when to apply each

Common Mark Deductions

  • Listing differences without writing either formula — loses 1–2 formula marks.
  • Not mentioning the critical circle search for the method of slices.
  • Treating the two methods as interchangeable — they apply to different failure geometries.
  • Exceeding allocated space with irrelevant content (Taylor's method, reinforced earth) — wastes time.

Key Phrases To Include

  • translational failure plane
  • circular failure arc
  • FS = [c′ + γz·cos²β·tanφ′]/[γz·sinβ·cosβ]
  • FS = Σ(c′ℓ + N′tanφ′)/Σ(W·sinα)
  • minimum-FS critical circle
  • pore-water pressure u
  • Bishop's simplified method

A cut slope in saturated clay (c′ = 10 kPa, φ′ = 28°, γ_sat = 19 kN/m³) has β = 22°, z = 5 m, with seepage parallel to the slope at the surface. Compute FS and comment on stability. [5 marks]

Marks

5

Topic

Cohesive Infinite Slope with Seepage

Difficulty

hard

Template Id

T12

Examiner Tip

In seepage problems, always show the pore-pressure calculation as a separate step. Examiners award a dedicated mark for u = γ_w·z·cos²β. If you bury it inside a combined expression, the mark may be missed.

Model Answer

Given: c′ = 10 kPa, φ′ = 28°, γ_sat = 19 kN/m³, β = 22°, z = 5 m Seepage: phreatic surface at ground level (full seepage) Step 1 — Compute γ′ (submerged unit weight): γ′ = γ_sat − γ_w = 19 − 9.81 = 9.19 kN/m³ Step 2 — Compute pore pressure at failure plane: u = γ_w · z · cos²β = 9.81 × 5 × cos²22° cos²22° = (0.9272)² = 0.8597 u = 9.81 × 5 × 0.8597 = 42.17 kPa Step 3 — Compute stresses: Normal stress: σ = γ_sat · z · cos²β = 19 × 5 × 0.8597 = 81.67 kPa Effective normal stress: σ′ = σ − u = 81.67 − 42.17 = 39.50 kPa Shear stress: τ = γ_sat · z · sinβ · cosβ = 19 × 5 × sin22° × cos22° sin22° = 0.3746, cos22° = 0.9272 τ = 19 × 5 × 0.3746 × 0.9272 = 32.98 kPa Step 4 — Apply FS formula: τ_f = c′ + σ′ · tanφ′ = 10 + 39.50 × tan28° = 10 + 39.50 × 0.5317 = 10 + 21.00 = 31.00 kPa FS = τ_f / τ = 31.00 / 32.98 FS = 0.94 ∴ FS = 0.94 < 1.0 — the slope is UNSTABLE under full-seepage conditions. Immediate remedial action (dewatering, slope flattening, or drainage installation) is required.

Question Type

numerical

Answer Structure

  • Step 1: Compute γ′ = γ_sat − γ_w correctly [1 mark]
  • Step 2: Compute pore pressure u = γ_w·z·cos²β [1 mark]
  • Step 3: Compute effective normal stress σ′ and shear stress τ [1 mark]
  • Step 4: Compute τ_f = c′ + σ′·tanφ′ and FS = τ_f/τ [1 mark]
  • Step 5: State FS = 0.94, declare slope unstable, and recommend remedial action [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct computation of γ′ = 19 − 9.81 = 9.19 kN/m³

Marks

1

Criteria

Correct pore pressure formula u = γ_w·z·cos²β and numerical result ≈ 42.17 kPa

Marks

1

Criteria

Correct σ′ = σ − u and τ = γ_sat·z·sinβ·cosβ computed

Marks

1

Criteria

Correct τ_f = c′ + σ′·tanφ′ and FS = τ_f/τ ≈ 0.94

Marks

1

Criteria

Correct declaration of instability (FS < 1) and identification of at least one remedial measure

Common Mark Deductions

  • Using γ_sat throughout without subtracting pore pressure — ignores seepage effect entirely.
  • Using cos β instead of cos²β for pore pressure calculation.
  • Not computing effective normal stress (using total stress in Coulomb equation).
  • Stopping at FS without declaring stability status or recommending action.

Key Phrases To Include

  • γ′ = γ_sat − γ_w
  • u = γ_w·z·cos²β
  • σ′ = σ − u
  • τ_f = c′ + σ′·tanφ′
  • FS = 0.94 < 1.0
  • slope is UNSTABLE
  • dewatering or drainage

Describe vibroflotation as a ground-improvement technique. State the soil types it is most effective for and explain the mechanism of improvement. [3 marks]

Marks

3

Topic

Soil Improvement — Densification

Difficulty

medium

Template Id

T13

Examiner Tip

Mentioning liquefaction mitigation as a benefit of vibroflotation is a high-value addition for Philippine board exams given the country's seismic context and NSCP 2015 Section 208 requirements for liquefiable soil treatment.

Model Answer

Vibroflotation (vibratory compaction) uses a torpedo-shaped vibrating probe inserted into the ground using water jetting. As the probe vibrates horizontally, it densifies the surrounding granular soil and the cavity is backfilled with compacted stone or sand. Most effective for: loose to medium-dense sands and gravels (cohesionless soils with less than 15–20% fines). It is NOT effective for soft clays or silts because cohesive soils do not densify through vibration. Mechanism: The vibration temporarily reduces interparticle friction, allowing soil particles to rearrange into a denser packing. The resulting improvement increases relative density (Dr), bearing capacity, and shear strength while reducing settlement and liquefaction potential.

Question Type

short_answer

Answer Structure

  • Part 1: Describe the equipment and process (vibrating probe, water jetting, backfill) [1 mark]
  • Part 2: State applicable soil types (loose sands and gravels; NOT clays) [1 mark]
  • Part 3: Explain the mechanism (particle rearrangement, increased Dr, improved bearing capacity) [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct description of vibrating probe inserted into ground to densify surrounding soil

Marks

1

Criteria

Correct identification of suitable soils (loose sands, gravels) and exclusion of clays

Marks

1

Criteria

Correct mechanism: vibration-induced particle rearrangement increasing relative density and bearing capacity

Common Mark Deductions

  • Stating vibroflotation works in soft clay — this is incorrect; clay does not respond to vibration densification.
  • Describing a generic 'vibrating roller' — vibroflotation is a deep probe method, not a surface compaction technique.
  • Omitting the mechanism and only naming the soil type — mechanism mark is separate.

Key Phrases To Include

  • vibrating probe
  • horizontal vibration
  • loose sands and gravels
  • cohesionless soils
  • NOT effective in clays
  • relative density (Dr)
  • densification
  • liquefaction mitigation

What are prefabricated vertical drains (PVDs/wick drains)? Explain how they accelerate consolidation of soft clay. [2 marks]

Marks

2

Topic

Soil Improvement — Consolidation Acceleration

Difficulty

easy

Template Id

T14

Examiner Tip

Draw a small cross-section showing the clay layer with vertical drain strips and horizontal arrows indicating drainage direction. This visual earns the mechanism mark faster than a paragraph of text.

Model Answer

Prefabricated vertical drains (PVDs), also called wick drains, are factory-made drain strips consisting of a plastic core wrapped in a geotextile filter sleeve. They are inserted vertically into soft compressible clay at regular spacing. Mechanism: By introducing vertical drains throughout the clay layer, the drainage path for pore water is shortened from the full layer thickness (H) to the horizontal spacing between drains (s/2 or s for single-drained). Water expelled by consolidation flows horizontally to the nearest drain and discharges upward, dramatically reducing the time required to achieve a target degree of consolidation (typically from years to months).

Question Type

short_answer

Answer Structure

  • Line 1: Define PVDs — construction and installation into soft clay [1 mark]
  • Line 2: Explain mechanism — shortened drainage path, horizontal drainage, accelerated consolidation [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct description of PVD as a prefabricated drain inserted vertically into soft clay to provide a drainage path

Marks

1

Criteria

Correct mechanism: reduced horizontal drainage path accelerates pore-water dissipation and consolidation

Common Mark Deductions

  • Describing PVDs as 'pipes' — they are filter-wrapped drain strips, not perforated pipes.
  • Not explaining why drainage is accelerated (shorter path) — mechanism mark is essential.
  • Confusing PVDs with stone columns — stone columns improve shear strength; PVDs improve drainage.

Key Phrases To Include

  • plastic core with geotextile filter sleeve
  • vertical insertion
  • shortened drainage path
  • horizontal drainage
  • reduced consolidation time
  • pore-water dissipation

Discuss the role of geosynthetics (geogrids and geotextiles) in slope stabilisation. Include at least TWO mechanisms of improvement and a relevant application example. [5 marks]

Marks

5

Topic

Soil Improvement — Geosynthetic Reinforcement

Difficulty

hard

Template Id

T15

Examiner Tip

Use sub-headings for each mechanism in 5-mark answers. Examiners scan answer papers; clearly labelled headings allow them to award marks efficiently and reduce the risk of your answer being misread.

Model Answer

GEOSYNTHETICS IN SLOPE STABILISATION 1. Types and Forms Geogrids are stiff, open-mesh polymer grids that provide tensile reinforcement. Geotextiles are woven or non-woven fabric sheets that provide reinforcement and/or filtration/drainage. Both are classified as geosynthetics — synthetic materials placed in soil to improve its behaviour. 2. Mechanism 1 — Tensile Reinforcement Geosynthetics placed horizontally within a slope or embankment intercept potential failure surfaces. The tensile strength of the reinforcement adds a resisting horizontal force component, effectively increasing the factor of safety. This is analogous to adding a cohesion increment to the reinforced soil mass. The FS formula is modified to include the sum of reinforcement tensile forces in the denominator-moment calculation: FS_reinforced > FS_unreinforced 3. Mechanism 2 — Filtration and Drainage Geotextile separators and filters prevent fine-grained soil particles from migrating into coarse drainage layers (piping and internal erosion). By maintaining permeability of drainage layers behind retaining walls and within slopes, geotextiles prevent pore-pressure build-up — a primary cause of slope failure. 4. Mechanism 3 — Separation In road embankments over soft ground, geotextiles prevent the mixing of subgrade soil with aggregate base courses, preserving the drainage and structural integrity of each layer. 5. Application Example — Reinforced Earth Wall A reinforced earth retaining wall in the Philippines (e.g., along the SLEX or EDSA widening projects) uses horizontal geogrid layers placed at regular vertical intervals within the compacted fill. The geogrids carry the tensile forces that a conventional gravity wall would resist through mass; this reduces the required wall cross-section and allows construction on weaker foundations. In summary, geosynthetics improve slope stability principally through tensile reinforcement (increasing FS) and drainage/filtration (reducing pore pressures), making them among the most versatile soil improvement tools available to the practising engineer.

Question Type

long_answer

Answer Structure

  • Part 1: Define geogrids and geotextiles, distinguishing their forms [1 mark]
  • Part 2: Mechanism 1 — tensile reinforcement (intercepts failure surface, adds resisting force) [1 mark]
  • Part 3: Mechanism 2 — filtration and drainage (prevents pore-pressure build-up) [1 mark]
  • Part 4: Mechanism 3 — separation (optional additional mechanism) or further elaboration on Mechanism 1 or 2 [1 mark]
  • Part 5: Specific application example with engineering context [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct definition and distinction between geogrids (tensile reinforcement) and geotextiles (reinforcement/filtration)

Marks

1

Criteria

Correct explanation of tensile reinforcement mechanism — intercepts failure surface, adds resisting force to increase FS

Marks

1

Criteria

Correct explanation of filtration/drainage mechanism — prevents piping, reduces pore pressures

Marks

1

Criteria

Third mechanism (separation) or substantive elaboration of either mechanism with reference to modified FS

Marks

1

Criteria

Specific relevant application example (reinforced earth wall, embankment, road base separation)

Common Mark Deductions

  • Describing only one mechanism when two are required — loses 1–2 marks.
  • Not differentiating geogrids from geotextiles — treated as the same product.
  • Giving an application without a mechanism explanation — application alone earns at most 1 mark.
  • Writing vague statements like 'strengthens the soil' without explaining how — mechanism must be explained.

Key Phrases To Include

  • geogrid — open-mesh polymer grid
  • geotextile — woven or non-woven fabric
  • tensile reinforcement
  • intercepts failure surface
  • FS_reinforced > FS_unreinforced
  • filtration — prevents piping
  • pore-pressure reduction
  • separation function
  • reinforced earth wall

Mark Wise Strategy

Dos

  • Write the formula explicitly (e.g., FS = τ_f/τ)
  • Use correct technical terminology
  • Keep the answer to 1–2 lines maximum
  • Include units if a unit-bearing quantity is asked

Donts

  • Do not write a paragraph — brevity is key at 1 mark
  • Do not provide derivations or worked examples
  • Do not invert a ratio or formula — this is an automatic zero

Marks

1

Strategy

Identify the keyword in the question. Give the definition or formula immediately — no preamble. One correct formula or precise term is usually sufficient for full marks.

Expected Length

1–2 lines; one sentence definition plus formula

Time Allocation

1–2 minutes

Dos

  • Allocate one clear statement per mark
  • Write formulas before substituting numbers
  • Include a one-line interpretation of the numerical result
  • For list questions, number your points (1, 2) to show they are distinct

Donts

  • Do not give only one answer point for a 2-mark question
  • Do not skip intermediate calculations — show working
  • Do not repeat the same idea in different words (only counts as one point)

Marks

2

Strategy

Each mark corresponds to one distinct, correct element. For conceptual questions, state the principle and explain it. For numerical questions, write the formula first, then compute the answer.

Expected Length

3–5 lines; two distinct, well-explained points or one formula with one worked intermediate step

Time Allocation

3–4 minutes

Dos

  • Use a step-by-step format with numbered steps for calculations
  • Label every intermediate value (e.g., γz = 76 kPa)
  • Show cos²β explicitly — do not abbreviate
  • State the physical interpretation of the final answer

Donts

  • Do not compress all three points into one run-on sentence
  • Do not skip the formula mark by jumping straight to numbers
  • Do not omit units on intermediate values — partial credit depends on traceable working

Marks

3

Strategy

Structure your answer as three clear, distinct elements. For numerical problems: (1) formula, (2) calculation with intermediate values, (3) result plus interpretation. For conceptual: three separate paragraphs or numbered points.

Expected Length

Half a page; clear steps for numerical, or 3 distinct conceptual points

Time Allocation

5–7 minutes

Dos

  • Use sub-headings (underlined or bold) to structure the answer
  • Draw a labelled sketch where applicable (slope cross-section, drain layout)
  • Compare to code values or design targets (FS = 1.3–1.5) in conclusions
  • For comparison questions, use a structured format: Name → Formula → Application for each method
  • Mention relevant Philippine standards (NSCP 2015) or ASTM test references when applicable

Donts

  • Do not write an introduction that re-states the question — go straight to the answer
  • Do not sacrifice depth on the last 1–2 marks by running out of time — plan pacing
  • Do not include irrelevant material (e.g., soil classification) that does not earn marks
  • Do not leave the final answer without an engineering interpretation or recommendation

Marks

5

Strategy

Plan your answer for 1–2 minutes before writing. Use sub-headings for each major point. For numerical: show all five steps clearly. For descriptive: address each mark criterion with a dedicated paragraph. End with a concise engineering conclusion.

Expected Length

One full page; complete derivation or multi-part analysis with engineering judgment

Time Allocation

10–15 minutes

General Answer Writing Tips

  • Always write the governing formula first before substituting values — examiners award a formula mark even when the final numerical answer is wrong.
  • Label every intermediate value with its symbol and unit (e.g., γz = 54 kPa) so the examiner can follow your work and award partial credit.
  • For conceptual questions, open with a one-sentence definition, follow with the governing equation or condition, then give a brief example — this three-part structure reliably captures full marks.
  • Draw a neat free-body diagram or slope cross-section sketch whenever the problem involves geometry; label β, z, and the failure plane, as examiners explicitly reward relevant diagrams.
  • State the factor of safety criterion (FS ≥ 1.3–1.5 for design; FS = 1 at critical condition) when interpreting numerical results — this shows engineering judgement, not just arithmetic.
  • For infinite-slope seepage problems, explicitly replace γ with γ′ in the friction term and add the pore-pressure term; failing to distinguish γ and γ′ is the most common source of error.
  • Use cos²β (not cosβ) in the cohesive infinite-slope formula — write it out in full and box the result to make it unmissable to the examiner.
  • When using Taylor's stability number, state that Ns is dimensionless and write its source (chart value) before computing Hcr = c/(γ·Ns); this demonstrates awareness of the method's basis.
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