SOIL MECHANICS – CHAPTER 7
CONSOLIDATION OF SOIL (TERZAGHI THEORY)
(SSC JE | RRB JE | OSSC JE – NUMERICAL-DOMINANT & HIGH WEIGHTAGE)
👉 3–4 questions every exam
👉 Direct numericals (Cv, settlement, time factor)
👉 One of the MOST scoring chapters
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🔹 1. ONE-PAGE PRECISE ONE-LINER NOTES (EXAM FOCUSED)
🔸 Consolidation
- Time-dependent reduction in volume of saturated soil
- Occurs due to expulsion of pore water under sustained load
- Mostly significant in clay soils
🔸 Terzaghi’s One-Dimensional Consolidation Theory
✔ Soil is homogeneous & fully saturated
✔ Compression is one-dimensional (vertical)
✔ Darcy’s law is valid
✔ Load increment is instantaneous
✔ Permeability & compressibility are constant
🔸 Types of Consolidation
1️⃣ Primary consolidation → due to pore water expulsion
2️⃣ Secondary consolidation → due to creep of soil skeleton
🔸 Effective Stress Concept
Where:
- σ = total stress
- σ′ = effective stress
- u = pore water pressure
👉 During consolidation:
- u ↓ with time
- σ′ ↑ with time
🔹 2. CONSOLIDATION CURVE (VERY IMPORTANT)
- Plot of Settlement vs Time
- Initial → Immediate settlement
- Curved portion → Primary consolidation
- Straight line (log t) → Secondary consolidation
🔹 3. OEDOMETER (CONSOLIDATION) TEST
Purpose:
✔ Determine Cv, Cc, mv
✔ Predict settlement & time
🔸 Drainage Conditions
| Condition | Drainage Path (Hdr) |
| Double drainage | H/2 |
| Single drainage | H |
⚠️ Time ∝ (Hdr)² → VERY IMPORTANT
🔹 4. IMPORTANT CONSOLIDATION PARAMETERS
🔸 Coefficient of Consolidation (Cv)
Units: m²/s
🔸 Compression Index (Cc)
🔸 Coefficient of Volume Compressibility (mv)
🔸 Time Factor (Tv)
🔸 Degree of Consolidation (U)
| U (%) | Tv |
| 50 | 0.197 |
| 90 | 0.848 |
| 95 | 1.129 |
🔹 5. SETTLEMENT FORMULAS (MOST REPEATED)
🔸 Normally Consolidated Clay
🔸 Over-Consolidated Clay
🔹 6. IMPORTANT NUMERICAL EXAMPLES (SSC JE LEVEL)
🔢 Example 1 (Easy – Time Factor)
Cv = 2×10⁻⁴ m²/s
Hdr = 2 m
t = 2000 s
🔢 Example 2 (Moderate – Time of Consolidation)
Given:
Cv = 1×10⁻³ m²/s
Hdr = 1 m
U = 50% → Tv = 0.197
🔢 Example 3 (Primary Settlement – NC Clay)
Cc = 0.3
H = 4 m
e₀ = 0.8
σ₀′ = 100 kN/m²
Δσ = 50 kN/m²
🔢 Example 4 (Drainage Path Trap)
If thickness doubles →
✔ Hdr doubles → time increases by 4 times
🔢 Example 5 (Conceptual)
Clay with OCR > 1 is:
👉 Over-consolidated clay
🔹 7. 50 EXAM-LEVEL MCQs
(25 THEORY + 25 NUMERICAL)
🟢 THEORY MCQs (1–25)
Q1. Consolidation occurs due to:
- Expulsion of air
B. Compression of grains
C. Expulsion of water from voids ✅
D. Increase in void ratio
Q2. Consolidation is significant in:
- Sand
B. Gravel
C. Silt
D. Clay ✅
Q3. Effective stress during consolidation:
- Decreases
B. Remains same
C. Increases with time ✅
D. Becomes zero
Q4. Oedometer test is used to determine:
- Shear strength
B. Permeability only
C. Consolidation parameters ✅
D. Atterberg limits
Q5. Secondary consolidation is due to:
- Pore pressure dissipation
B. Air expulsion
C. Creep of soil skeleton ✅
D. Recompression
🟡 NUMERICAL MCQs (26–50)
Q26. Cv = 5×10⁻⁴ m²/s, Hdr = 1 m, t = 400 s.
Tv =
A. 0.1
B. 0.2 ✅
C. 0.4
D. 0.5
Q27. Degree of consolidation corresponding to Tv = 0.848 is:
- 50%
B. 75%
C. 90% ✅
D. 95%
Q28. If drainage is changed from double to single, time required will:
- Reduce to half
B. Become same
C. Double
D. Increase 4 times ✅
Q29. Compression index is obtained from:
- e–t curve
B. σ–t curve
C. e–logσ′ curve ✅
D. S–t curve
Q30. Consolidation settlement depends on:
- Load only
B. Soil type only
C. Time only
D. Load, soil & drainage path ✅
🔥 EXAM TRICKS & SHORTCUTS
✔ Time ∝ (Hdr)² (MOST COMMON TRAP)
✔ Cv has unit m²/s
✔ Clay → consolidation, Sand → compaction
✔ U = 50% → Tv = 0.197
✔ Double drainage → time ↓ 4 times
CONSOLIDATION OF SOIL – TERZAGHI THEORY
(SSC JE | RRB JE | OSSC JE)
Focused strictly on settlement traps, OCR concepts, Cv numericals, and drainage-condition MCQs — exactly exam-pattern.
(Q31–Q50 include: settlement traps, OCR concepts, Cv numericals, drainage condition MCQs)
🟡 NUMERICAL & CONCEPTUAL MCQs (31–50)
Q31. A clay layer is said to be normally consolidated if:
- OCR < 1
B. OCR = 1 ✅
C. OCR > 1
D. OCR = 0
Explanation:
For NC clay → σ′p = σ′0
Q32. If preconsolidation pressure is greater than existing overburden pressure, soil is:
- Normally consolidated
B. Under-consolidated
C. Over-consolidated ✅
D. Sensitive clay
Q33. OCR value of an over-consolidated clay is:
- < 1
B. = 1
C. > 1 ✅
D. = 0
Q34. Consolidation settlement in over-consolidated clay is:
- Greater than NC clay
B. Same as NC clay
C. Less than NC clay for same load increment ✅
D. Independent of load
Q35. Which index is used for recompression of OC clay?
- Compression index (Cc)
B. Swelling index (Cs)
C. Recompression index (Cr) ✅
D. Void ratio index
Q36. Given:
Cv = 4×10⁻⁴ m²/s,
Hdr = 2 m,
t = 1000 s.
Time factor Tv equals:
A. 0.05
B. 0.10 ✅
C. 0.20
D. 0.40
Solution:
Q37. If drainage condition changes from double to single, time required for same degree of consolidation will:
- Reduce to half
B. Become same
C. Double
D. Increase four times ✅
Explanation:
Q38. For a clay layer of thickness 6 m with double drainage, drainage path is:
- 6 m
B. 3 m ✅
C. 12 m
D. 1.5 m
Q39. Degree of consolidation corresponding to is:
- 25%
B. 40%
C. 50% ✅
D. 90%
Q40. If coefficient of consolidation doubles, time required for consolidation will:
- Double
B. Reduce to half ✅
C. Increase four times
D. Remain unchanged
Q41. Primary consolidation settlement depends mainly on:
- Time only
B. Pore water pressure
C. Load increment and compressibility ✅
D. Creep of soil
Q42. Secondary consolidation is significant in:
- Sand
B. Gravel
C. Normally consolidated clay
D. Organic clay ✅
Q43. The slope of the e–log σ′ curve in virgin compression range gives:
- mv
B. Cv
C. Cc ✅
D. Cr
Q44. If void ratio change is zero, consolidation settlement will be:
- Maximum
B. Finite
C. Zero ✅
D. Infinite
Q45. Settlement of clay layer is directly proportional to:
- Thickness of layer ✅
B. Square of thickness
C. Width of footing
D. Permeability only
Q46. Which parameter has unit of m²/s?
- mv
B. Cv ✅
C. Cc
D. OCR
Q47. Which settlement occurs instantaneously?
- Primary consolidation
B. Secondary consolidation
C. Immediate settlement ✅
D. Creep settlement
Q48. Under-consolidated clay means:
- σ′p < σ′0
B. σ′p > σ′0
C. Excess pore pressure still exists ✅
D. OCR > 1
Q49. Consolidation settlement calculation for normally consolidated clay uses:
- Cr only
B. Cs only
C. Cc only ✅
D. Cv only
Q50. Which statement is TRUE?
- Cv depends on drainage path
B. Time for consolidation is independent of thickness
C. Consolidation occurs due to expulsion of air
D. Effective stress increases during consolidation ✅
🔥 QUICK EXAM RECAP (MUST REMEMBER)
✔ OCR = 1 → Normally Consolidated
✔ OCR > 1 → Over-Consolidated
✔ Time ∝ (Hdr)² (most repeated trap)
✔ Cv ↑ ⇒ time ↓
✔ Cc → NC clay, Cr → OC clay
✔ Double drainage = safest assumption