 ### Test - 2

 Description: Test - 2 Number of Questions: 20 Created by: Yashbeer Singh Tags: Test - 2 Soil Mechanics Civil Engineering - CE
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The vertical stress at some depth below the corner of a 2 m x 3 m rectangular footing due to a certain load intensity is 100 kN/m2. What is the vertical stress in kN/m2 below the centre of a 4 m x 6 m rectangular footing at the same depth and same load intensity?

1. 25

2. 100

3. 200

4. 400

Correct Option: D
Explanation: A field vane shear testing instrument (shown alongside) was inserted completely into a deposit of soft, saturated silty clay with the vane rod vertical such that the top of the blades were 500 mm below the ground surface. Upon application of a rapidly increasing torque about the vane rod, the soil was found to fail when the torque reached 4.6 Nm. Assuming mobilisation of undrained shear strength on all failure surfaces to be uniform and the resistance mobilised on the surface of the vane rod to be negligible, what would be the peak undrained shear strength (rounded off to the nearest integer value of kPa) of the soil? 1. 5 kPa

2. 10 kPa

3. 15 kPa

4. 20 kPa

Correct Option: B
Explanation: In an aquifer extending over 150 hectares, the water table was 21 m below ground level. Over a period of time, the water table dropped to 23 m below the ground level. If the porosity of aquifer is 0.40 and the specific retention is 0.15, what is the change in ground water storage of the aquifer?

1. 67.5 ha-m

2. 112.5 ha-m

3. 180.0 ha-m

4. 450.0 ha-m

Correct Option: B
Explanation: Identical surcharges are placed at ground surface at sites X and Y, with soil conditions shown alongside and water table at ground surface. The silty clay layers at X and Y are identical. The thin sand layer at Y is continuous and free-draining with a very large discharge capacity. If primary consolidation at X is estimated to complete in 36 months, what would be the corresponding time for completion of primary consolidation at Y? 1. 2.25 months

2. 4.5 months

3. 9 months

4. 36 months

Correct Option: C
Explanation: A sand layer found at sea floor under 20 m water depth is characterised with relative density = 40%, maximum void ratio = 1.0, minimum void ratio = 0.5 and specific gravity of soil solids = 2.67. Assume the specific gravity of sea water to be 1.03 and the unit weight of fresh water to be 9.81 kN/m3.

What would be the effective stress (rounded off to the nearest integer value of kPa) at 30 m depth into the sand layer?

1. 77 kPa

2. 273 kPa

3. 268 kPa

4. 281 kPa

Correct Option: D
Explanation: A sand layer found at sea floor under 20 m water depth is characterised with relative density = 40%, maximum void ratio = 1.0, minimum void ratio = 0.5 and specific gravity of soil solids = 2.67. Assume the specific gravity of sea water to be 1.03 and the unit weight of fresh water to be 9.81 kN/m3.

What would be the change in the effective stress (rounded off to the nearest integer value of kPa) at 30 m depth into the sand layer if the sea water level permanently rises by 2 m?

1. 19 kPa

2. 0 kPa

3. 21 kPa

4. 22 kPa

Correct Option: B
Explanation:

Effective stress is basically stress developed in between soil particles, hence changing water level would not cause any change in effective stress.

$$\triangle\sigma_1 = 0$$

The vertical stress at point P1 due to the point load Q on the ground surface as shown in figure is s2. According to Boussinesq’s equation, the vertical stress at point P2 shown in the figure will be 1. $\frac{\sigma_z}{2}$

2. $\sigma_z$

3. $2 \sigma_z$

4. $4 \sigma_z$

Correct Option: D
Explanation: An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having coefficient of permeability of 10−2m/ s. The barrel stands on a saturated bed of gravel. The time required for the water level in the barrel to drop by 0.75 m is

1. 58.9 s

2. 75 s

3. 100 s

4. 150 s

Correct Option: B
Explanation:

$k = 10^{-2}m/s \\ \text{time required for water level drop by 0.75} \\ = \frac{0.75m}{10^{-2}m/s} = 75 s.$

Direction: The unconfined compressive strength of a saturated clay sample is 54 kPa.

The value of cohesion for the clay is

1. zero

2. 13.5 kPa

3. 27 kPa

4. 54 kPa

Correct Option: C
Explanation:

$q_u = 54 KPa, C_u' = \frac{q_u}{2} = \frac{54}{2} = 27 KPa$

Direction: The unconfined compressive strength of a saturated clay sample is 54 kPa.

If a square footing of size 4 m x 4 m is resting on the surface of a deposit of the above clay, the ultimate bearing capacity of the footing (as per Terzaghi’s equation) is

1. 1600 kPa

2. 316 kPa

3. 200 kPa

4. 100 kPh

Correct Option: C
Explanation: The laboratory test results of a soil sample are given below:
Percentage finer than 4.75 mm = 60
Percentage finer than 0.075 mm = 30
Liquid Limit = 35%
Plastic Limit = 27%
The soil classification is

1. GM

2. SM

3. GC

4. ML-MI

Correct Option: B
Explanation: Direction: Examine the test arrangement and the soil properties given below. The maximum resistance offered by the soil through skin friction while pulling out the pile from the ground is

1. 104.9 kN

2. 209.8 kN

3. 236 kN

4. 472 kN

Correct Option: A
Explanation: A wall of diameter 20 cm fully penetrates a confined aquifer. After a long period of pumping at a rate of 2720 litres per minute, the observations of drawdown taken at 10 m and 100 m distances from the centre of the wall are found to be 3 m and 0.5 m respectively. The transmissivity of the aquifer is

1. 676m2 /day

2. 576 m2 /day

3. 526 m2 /day

4. 249 m2 /day

Correct Option: B
Explanation: A plate load test is carried out on a 300 mm x 300 mm plate placed at 2 m below the ground level to determine the bearing capacity of a 2 m x 2 m footing placed at same depth of 2 m on a homogeneous sand deposit extending 10 m below ground. The ground water table is 3 m below the ground level. Which of the following factors does not require a correction to the bearing capacity determined based on the load test?

1. Absence of the overburden pressure during the test

2. Size of the plate is much smaller than the footing size

3. Influence of the ground water table

4. Settlement is recorded only over a limited period of one or two days

Correct Option: C
Explanation: Direction: Examine the test arrangement and the soil properties given below. The maximum pressure that can be applied with a factor of safety of 3 through the concrete block, ensuring no bearing capacity failure in soil using Terzaghi’s bearing capacity equation without considering the shape factor, depth factor and inclination factor is

1. 26.67 kPa

2. 60 kPa

3. 90 kPa

4. 120 kPa

Correct Option: A
Explanation: A saturated undisturbed sample from a clay strata has moisture content of 22.22% and specific weight of 2.7. Assuming $y_\omega$ = 10 kN/m3, the void ratio and the saturated unit weight of the clay, respectively are

1. 0.6 and 16.875 kN/m3

2. 0.3 and 20.625 kN/m3

3. 0.6 and 20.625 kN/m3

4. 0.3 and 16.975 kN/m3

Correct Option: C
Explanation: The ultimate load capacity of a 10 m long concrete pile of square cross-section 500 mm x 500 mm driven into a homogeneous clay layer having undrained cohesion value of 40 kPa is 700 kN. If the cross-section of the pile is reduced to 250 mm x 250 mm and the length of the pile is increased to 20 m, the ultimate load capacity will be

1. 350 kN

2. 632.5 kN

3. 722.5 kN

4. 1400 kN

Correct Option: B
Explanation: The liquid limit (LL), plastic limit (PL) and shrinkage limit (SL) of a cohesive soil satisfy the relation

1. LL>PL<SL

2. LL>PL>SL

3. LL<PL<SL

4. LL<PL>SL

Correct Option: B
Explanation: Using the properties of the clay layer derived from the above question, the consolidation settlement of the same clay layer under a square footing (neglecting its self weight) with additional data shown in the figure below (assume the stress distribution as 1H : 2V from the edge of the footing and$y_{\omega}$= 10kN/m3) is 1. 32.78 mm

2. 61.75 mm

3. 79.5 mm

4. 131.13 mm

Correct Option: B
Explanation: A singly under-reamed, 8-m long, RCC pile (shown in the adjoining figure) weighing 20 kN with 350 mm shaft diameter and 750 mm under-ream diameter is installed within stiff, saturated silty clay (undrained shear strength is 50 kPa, adhesion factor is 0.3 and the applicable bearing capacity factor is 9.0 to counteract the impact of soil swelling on a structure constructed above. Neglecting suction and the contribution of the under-ream to the adhesive shaft capacity, what would be the estimated ultimate tensile capacity (rounded off to the nearest integer value of kN) of the pile? 1. 132 kN

2. 156 kN

3. 287 kN

4. 301 kN

Correct Option: B
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