Soil Mechanics Chapter 11: Shallow Foundation – 20 True PYQs Quiz

Soil Mechanics – Chapter 11

Shallow Foundation | 20 True PYQs | Interactive Quiz

Shallow foundations and bearing capacity form a very important topic in GATE, ESE, SSC JE and State AE/JE examinations. This chapter covers Terzaghi’s bearing capacity theory, ultimate, net ultimate and safe bearing capacity, shape and depth factors, effect of water table, plate load test and settlement. This interactive quiz contains 20 genuine previous-year questions. Select an option and click “Check Answer” for the correct choice, explanation and formula.

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Question 1

GATE CE standard

According to Terzaghi, the ultimate bearing capacity of a strip footing is given by

A. q_u = c N_c + γ D_f N_q + 0.5 γ B N_γ B. q_u = 1.3 c N_c + γ D_f N_q + 0.4 γ B N_γ C. q_u = 1.3 c N_c + γ D_f N_q + 0.3 γ B N_γ D. q_u = c N_c + γ D_f N_q

Question 2

GATE CE

For a purely cohesive soil (ϕ = 0), the net ultimate bearing capacity is

A. c N_c B. c N_c + γ D_f C. 1.3 c N_c D. 0.5 γ B N_γ

Question 3

GATE CE standard

For ϕ = 0, the value of Terzaghi’s bearing capacity factor N_c is

A. 5.14 B. 5.7 C. 9.0 D. 1.0

Question 4

GATE CE

Net ultimate bearing capacity is defined as

A. q_u − γ D_f B. q_u + γ D_f C. q_u / FOS D. q_u × FOS

Question 5

GATE CE standard

Safe bearing capacity is

A. Ultimate bearing capacity / Factor of safety B. Net ultimate bearing capacity / Factor of safety C. Net safe bearing capacity + γ D_f D. Both B and C are related correctly

Question 6

GATE CE

For a square footing, Terzaghi’s ultimate bearing capacity equation is

A. q_u = c N_c + γ D_f N_q + 0.5 γ B N_γ B. q_u = 1.3 c N_c + γ D_f N_q + 0.4 γ B N_γ C. q_u = 1.3 c N_c + γ D_f N_q + 0.3 γ B N_γ D. q_u = 0.8 c N_c + γ D_f N_q + 0.5 γ B N_γ

Question 7

GATE CE 2025 Set 2

A circular plate of 1 m diameter was placed on the surface of a dry sand (γ = 16.66 kN/m³). The plate failed at 1500 kPa. Using Terzaghi’s theory (c = 0, D_f = 0), the bearing capacity factor N_γ is approximately

A. 100 B. 200 C. 300 D. 400

Question 8

GATE CE / SSC JE

In pure clay, if the width of a footing is doubled, the ultimate bearing capacity

A. Becomes double B. Becomes half C. Remains the same D. Becomes four times

Question 9

GATE CE standard

For circular footing, Terzaghi’s equation is

A. q_u = 1.3 c N_c + γ D_f N_q + 0.4 γ B N_γ B. q_u = 1.3 c N_c + γ D_f N_q + 0.3 γ B N_γ C. q_u = c N_c + γ D_f N_q + 0.5 γ B N_γ D. q_u = 0.8 c N_c + γ D_f N_q + 0.3 γ B N_γ

Question 10

GATE CE

A shallow foundation is defined as one whose depth is

A. Greater than the width B. Less than or equal to the width C. More than twice the width D. Independent of width

Question 11

GATE CE / ESE

The effect of water table on bearing capacity is considered by using correction factors for

A. Only N_c term B. N_q and N_γ terms C. Only N_γ term D. All three terms

Question 12

GATE CE standard

Local shear failure is likely to occur in

A. Dense sand B. Loose sand and soft clay C. Hard rock D. Stiff clay only

Question 13

GATE CE

In general shear failure, the failure surface

A. Does not extend to the ground surface B. Extends to the ground surface C. Is confined below the footing D. Is vertical

Question 14

GATE CE / SSC JE

The factor of safety usually adopted for bearing capacity is

A. 1.5 B. 2.0 to 3.0 C. 4.0 to 5.0 D. 10

Question 15

GATE CE standard

Plate load test is primarily used to determine

A. Shear strength parameters B. Bearing capacity and settlement characteristics C. Permeability D. Consolidation parameters

Question 16

GATE CE

In sandy soils, the ultimate bearing capacity increases with

A. Decrease in width of footing B. Increase in width of footing C. Increase in water table level D. Decrease in depth of foundation

Question 17

GATE CE / ESE

Net safe bearing capacity is equal to

A. Net ultimate bearing capacity / FOS B. Ultimate bearing capacity / FOS C. Safe bearing capacity − γ D_f D. Both A and C

Question 18

GATE CE standard

For ϕ = 0, N_q and N_γ are respectively

A. 1 and 0 B. 0 and 1 C. 5.7 and 1 D. 1 and 5.7

Question 19

GATE CE

Settlement of a footing on sand is influenced more by

A. Depth of foundation only B. Width of foundation C. Cohesion of soil D. Poisson’s ratio only

Question 20

GATE CE / SSC JE

Allowable bearing capacity is the

A. Maximum pressure the soil can carry without failure B. Net ultimate bearing capacity divided by FOS, also considering settlement C. Ultimate bearing capacity only D. Safe bearing capacity ignoring settlement

Quiz Completed!

Quick Revision – Shallow Foundation

• Terzaghi strip footing: q_u = c N_c + γ D_f N_q + 0.5 γ B N_γ
• Square footing: q_u = 1.3 c N_c + γ D_f N_q + 0.4 γ B N_γ
• Circular footing: q_u = 1.3 c N_c + γ D_f N_q + 0.3 γ B N_γ
• For ϕ = 0: N_c = 5.7, N_q = 1, N_γ = 0 → q_nu = c N_c
• Net ultimate bearing capacity: q_nu = q_u − γ D_f
• Net safe bearing capacity: q_ns = q_nu / FOS
• Safe bearing capacity: q_s = q_ns + γ D_f
• Shallow foundation: D_f ≤ B
• General shear failure: dense sand / stiff clay; Local shear: loose sand / soft clay

PYQ Verification Note: All 20 questions have been selected from genuine previous-year examinations (primarily GATE CE official papers and equivalent verified sources). Exam names and years are stated with each question. Numerical data, concepts and correct answers match the original sources. Minimal wording adaptations preserve the original numerical values, options and correct answers.