Soil Mechanics Chapter 6: Compressibility and Compression – 20 True PYQs Quiz

Soil Mechanics – Chapter 6

Compressibility and Compression of Soil | 20 True PYQs | Interactive Quiz

Chapter 6: Compressibility and Compression
This quiz covers compression index, coefficient of compressibility, coefficient of volume compressibility, consolidation settlement, coefficient of consolidation, drainage conditions, compression curve, consolidation time and settlement calculations.

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Quiz Instructions: Each question carries 1 mark. Select one option and click Check Answer. Your score and percentage will be displayed automatically after all 20 questions.

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GATE 2003

1. A double-draining clay layer, 6 m thick, settles by 30 mm in three years. Its final consolidation settlement is estimated as 120 mm. If a thin sand layer of negligible thickness is introduced at a depth of 1.5 m below the top surface, the final consolidation settlement will be:

A) 60 mm B) 120 mm C) 240 mm D) None of these

Answer: B) 120 mm
Introducing an intermediate drainage layer changes the rate of consolidation, but it does not change the ultimate consolidation settlement.

GATE 2005

2. The root-time method is used to determine:

A) Time factor B) Coefficient of consolidation C) Coefficient of compressibility D) Coefficient of volume compressibility

Answer: B) Coefficient of consolidation
Taylor's square-root-of-time method is used to determine Cv from consolidation-test data.

GATE 2010

3. The e-log p curve shown for a soil is representative of:

A) Normally consolidated clay B) Over-consolidated clay C) Under-consolidated clay D) Normally consolidated clayey sand

Answer: B) Over-consolidated clay
The characteristic e-log p curve shown in the GATE question represents an over-consolidated clay.

GATE 2011

4. Identical surcharges are applied at sites X and Y. The clay layers are identical, but site Y contains a continuous, free-draining sand layer at mid-depth. If primary consolidation at X takes 36 months, the corresponding time at Y is:

A) 2.25 months B) 4.5 months C) 9 months D) 36 months

Answer: C) 9 months
The intermediate sand layer reduces the maximum drainage path. Since t is proportional to drainage-path squared, the consolidation time reduces.

GATE 2012

5. A 1 m thick normally consolidated saturated silty clay layer is subjected to a pressure increment of 20 kPa. Given G = 2.7, natural water content = 45%, compression index = 0.45 and initial average effective stress = 100 kPa. The primary consolidation settlement is approximately:

A) 2 mm B) 9 mm C) 14 mm D) 16 mm

Answer: D) 16 mm
For normally consolidated clay: S = [Cc H/(1+e0)] log10(σ'f/σ'0), which gives approximately 16 mm.

GATE 2014

6. For a laboratory clay sample: σ'0 = 175 kPa, e0 = 1.1, σ'0 + Δσ' = 300 kPa, and final void ratio e = 0.9. If the specimen thickness is 25 mm, the coefficient of volume compressibility is approximately:

A) 2.0 × 10^-4 m²/kN B) 4.0 × 10^-4 m²/kN C) 6.0 × 10^-4 m²/kN D) 7.6 × 10^-4 m²/kN

Answer: D) 7.6 × 10^-4 m²/kN
m_v = Δe / [(1+e₀)Δσ']. For the given data, m_v ≈ 7.62 × 10^-4 m²/kN.

GATE 2015

7. A 4 m thick layer of normally consolidated clay has average void ratio 1.30 and compression index 0.6. If the increase in vertical pressure due to the foundation load is equal to the existing effective overburden pressure, the change in thickness of the clay layer is:

A) 157 mm B) 214 mm C) 278 mm D) 314 mm

Answer: D) 314 mm
For σ'f = 2σ'0: S = [Cc H/(1+e0)] log10(2), giving approximately 314 mm.

GATE 2017

8. A 3 m thick clay layer has one-way drainage, coefficient of consolidation C_v = 3.0 mm²/min and T_v = 0.85 for 90% consolidation. The time required for 90% consolidation is approximately:

A) 365 days B) 885 days C) 1325 days D) 1771 days

Answer: D) 1771 days
Using T_v = C_vt/H_d² with one-way drainage: t ≈ 1771 days.

GATE 2018 Set 2

9. The compression curve of a clay is a straight line on a semi-log plot. It passes through (e = 1.2, σ' = 50 kPa) and (e = 0.6, σ' = 800 kPa). The compression index is:

A) 0.25 B) 0.50 C) 0.75 D) 1.20

Answer: B) 0.50
C_c = (1.2 − 0.6) / log₁₀(800/50) = 0.6/log₁₀(16) ≈ 0.498 ≈ 0.50.

GATE 2019

10. A building on clay was completed in January 2010. In January 2014, the average consolidation settlement was 10 mm. The ultimate settlement was estimated as 40 mm. Assuming double drainage, the expected consolidation settlement in January 2019 is:

A) 10 mm B) 12 mm C) 15 mm D) 25 mm

Answer: C) 15 mm
The first observation corresponds to U = 10/40 = 25%. Using the time-factor relationship for the later time gives U ≈ 37.5%, hence settlement ≈ 15 mm.

GATE 2020

11. A 19 mm thick clay specimen is tested in a one-dimensional consolidation test. The oedometer reading just before unloading is 2.1 mm and the void ratio at that stage is 0.62. The initial void ratio is:

A) 0.82 B) 0.72 C) 0.62 D) 0.52

Answer: A) 0.82
Using ΔH/H = Δe/(1+e), the initial void ratio is approximately 0.82.

SSC JE 2004

12. The unit of coefficient of consolidation C_v is:

A) cm²/gm B) cm²/sec C) gm/cm²/sec D) gm-cm/sec

Answer: B) cm²/sec
C_v has dimensions of length²/time.

SSC JE 2007

13. The consolidation time of soils:

A) Increases with increasing compressibility B) Decreases with increasing permeability C) Is independent of the stress change D) All of the above

Answer: D) All of the above
This is the answer reported for the SSC JE 2007 PYQ.

SSC JE 2008

14. For a routine consolidation test in the laboratory, the specimen thickness is:

A) 10 mm B) 20 mm C) 40 mm D) 60 mm

Answer: B) 20 mm
The standard routine consolidation-test specimen thickness is approximately 20 mm.

SSC JE 2009

15. The rate of consolidation:

A) Increases with decrease in temperature B) Increases with increase in temperature C) Is independent of temperature D) All of the above

Answer: C) Is independent of temperature
This is the answer reported for the SSC JE 2009 PYQ.

SSC JE 2012

16. The unit of coefficient of consolidation C_v is:

A) gm/cm²/sec B) cm²/sec C) gm-cm/sec D) cm³/sec

Answer: B) cm²/sec
C_v is a coefficient having dimensions of area per unit time.

SSC JE 04 March 2017 – Afternoon

17. The coefficient of compressibility of soil is the ratio of:

A) Stress to strain B) Strain to stress C) Stress to settlement D) Rate of loading to rate of settlement

Answer: B) Strain to stress
Coefficient of compressibility represents change in strain/void ratio per unit increase in effective stress, depending on the convention used.

SSC JE 29 January 2018 – Morning

18. A clay deposit is 10 cm thick with an initial void ratio of 0.5. After settlement, the final void ratio is 0.2. The settlement of the layer is:

A) 1.0 cm B) 1.5 cm C) 2.0 cm D) 2.5 cm

Answer: C) 2.0 cm
Settlement: ΔH = H₀(e₀ − e₁)/(1 + e₀) = 10(0.5 − 0.2)/1.5 = 2 cm.

SSC JE 29 January 2018 – Morning

19. In a consolidometer test, the pore-water pressure in the soil sample is maximum at:

A) Bottom B) Center C) Top D) It is minimum at the center

Answer: B) Center
For a normally loaded specimen with drainage from both sides, the excess pore-water pressure distribution is maximum at the center.

SSC JE 29 October 2020 – Morning

20. In a consolidation test, the load is changed from 50 kN/m² to 100 kN/m² and the void ratio changes from 0.80 to 0.60. The coefficient of compressibility is:

A) 0.002 m²/kN B) 0.003 m²/kN C) 0.001 m²/kN D) 0.004 m²/kN

Answer: D) 0.004 m²/kN
a_v = Δe/Δσ' = (0.80 − 0.60)/(100 − 50) = 0.004 m²/kN.

🎯 Quiz Complete!

Quick Revision – Compressibility and Compression

Compressibility: Property of soil due to which its volume decreases under applied stress.

Compression Index: C_c = Δe / Δlog₁₀σ'
Coefficient of Compressibility: a_v = Δe / Δσ'
Coefficient of Volume Compressibility: m_v = a_v/(1+e₀)
Coefficient of Consolidation: C_v = k/(m_vγ_w)
Time Factor: T_v = C_vt/H_d²
Normally Consolidated Clay: S = [C_cH/(1+e₀)] log₁₀(σ'₂/σ'₁)
50% Consolidation: T_v ≈ 0.197
Drainage: For double drainage, H_d = H/2.
Important: Increasing drainage capacity increases the rate of consolidation, but does not change the ultimate consolidation settlement.