Shallow Foundation MCQ Quiz - Objective Question with Answer for Shallow Foundation - Download Free PDF

Explanation:

A fully compensated raft foundation (also called buoyant raft) is designed so that the weight of the soil excavated for the foundation equals the weight of the building and the foundation combined.

• This compensation reduces the net increase in stress on the soil, minimizing settlement.

• It is especially useful in soft or compressible soils where minimizing settlement is critical.

• The idea is that the removal of soil weight balances the load, so the foundation does not cause additional stress on the soil below.

Additional InformationRaft Foundation (or mat foundation) is a large, continuous slab supporting multiple columns and walls, spreading the load over a wide area. It is used when soil bearing capacity is low or loads are heavy.

Types of Raft Foundations

• Rigid Raft: Assumes the raft acts as a stiff plate, distributing loads uniformly.

• Flexible Raft: Assumes the raft bends and deflects under loads, distributing unevenly.

• Fully Compensated Raft: Designed so that the weight of the soil excavated equals the weight of the building and foundation.

Fully Compensated Raft Foundation

• Also known as buoyant foundation or compensated foundation.

• The purpose is to neutralize the additional load on the soil by removing an equivalent weight of soil during excavation.

• Reduces settlement by minimizing changes in stress on the underlying soil.

• Commonly used in soft, compressible soils or areas with high water tables.

• Helps prevent excessive consolidation and uneven settlement.

Explanation:

1. A raft foundation is a large slab that supports the building and spreads the load across the entire foundation area. This helps in evenly distributing the weight across the soil.

2. It is particularly useful when the soil is weak or highly variable in terms of load-bearing capacity, as it minimizes differential settlement.

3. By spreading the load, it ensures uniform settlement, reducing the risk of cracks or structural issues in the building.

Additional InformationPile Foundations:

1. Deep Foundation
   A pile foundation is a type of deep foundation that transfers the load of a structure to deeper, more stable soil or bedrock, often used when the surface soil is not strong enough to support the load.

2. Types of Piles
   Piles can be pre-cast concrete, steel, or timber and can either be driven (hammered into the ground) or bored (drilled and filled with concrete).

3. Used in Weak Soils
   Pile foundations are commonly used in areas with weak or compressible surface soils, such as swamps, soft clay, or loose sands, to provide stability to buildings and structures.

4. Load Distribution
   Piles transmit the load of the structure through weak soil layers and into stronger soil or rock beneath. This helps in resisting both vertical loads and lateral forces such as wind or seismic activity.

5. Types of Pile Foundations
   There are different types of pile foundations based on the method of installation: friction piles (rely on friction between the pile surface and surrounding soil) and end-bearing piles (transfer load to a firm rock or soil layer at the pile tip).

Explanation:

Based on the Assumptions, Terzaghi’s Theory is applicable for shallow foundation because side shear resistance and stressing of soil above the foundation is ignored whereas,

Meyerhoff considered stress zone extended up to G.L. Hence Meyershoff's theory is applicable for deep footing also.

Hence, both statements are correct.

Concept:

Variation of contact pressure and settlement of footing on different types of soil is as follows:

1. Flexible footing:

Case-I: Resting on Sand

• Settlement: Maximum at edges and minimum at the center
• Contact Pressure: Uniform

Case-II: Resting on Clay

• Settlement: Minimum at edges and maximum at the center
• Contact Pressure: Uniform​

2. Rigid footing:

Case-I: Resting on Sand

• Settlement: Uniform
• Contact Pressure: Zero at edges and maximum at the center

Case-II: Resting on Clay

• Settlement: Uniform
• Contact Pressure: maximum at edges and minimum at the center

Concept;

Dilatancy correction:

It is to be applied when N_o obtained after overburden correction, exceeds 15 in saturated fine sands and silts. IS: 2131-1981 incorporates the Terzaghi and Peck recommended dilatancy correction (when N_o > 15) using the equation

\(\rm N= 15 + \frac{1}{2}\left( {N_0-\;15} \right)\)

N₀ - SPT value after overburden correction

Calculation:

Given: N₀ = 21

\(\rm N= 15 + \frac{1}{2}\left( {21-\;15} \right)\)

⇒ N = 18

Ultimate bearing capacity for a strip footing is

\({q_u} = C{N_c} + \gamma {D_f}{N_q} + 0.5\gamma B{N_\gamma }\)

For pure clay, N_c = 5.14, N_q = 1 and Nγ = 0 (∵ assuming smooth footing)

Footing is on the ground surface i.e. D = 0

q_u = c_uN_c

qu = 5.14 c_u

Concept:

According to Tarzaghi,

Ultimate bearing capacity of circular footing, 

\({q_u} = 1.3C{N_c} + q{N_q} + 0.3Dγ {N_γ }\)

Ultimate bearing capacity of strip footing, 

\({q_u} = C{N_c} + q{N_q} + 0.5Bγ {N_γ }\)

For square footing, ultimate bearing capacity,

qu = 1.3 CNc + γDfNq + 0.4 γBNγ

Where,

C = cohesion 

Nc, Nq, Nγ = Bearing capacity factors

q = overburden pressure = γDf

Df = depth of the footing, B = width of footing, D = diameter of circular footing

γ = unit weight of soil

Calculation:

Given,

D = B

Surface footing ⇒ Df = 0 ⇒ q = 0

Purely cohesionless ⇒ C = 0

\(Ratio = \frac{{{q_{u,circular}}}}{{{q_{u,strip}}}} = \frac{{0.3D\gamma {N_\gamma }}}{{0.5B\gamma {N_\gamma }}} = 0.60\)

Concept:

Plate Load Test:

It is a field test to determine the ultimate bearing capacity of soil and the portable settlement under a given loading.

Bearing Capacity Calculation for Clayey Soils

\(Ultimate\: bearing\: capacity\:[q_u(f)] = Ultimate\: load\: for\: plate\:[q_u(p)]\)

Bearing Capacity Calculation for Sandy Soils

\(Ultimate\: bearing\: capacity\:[q_u(f)] = {Width\: of\: pit (Bf) \over Size\: of\: Plate (Bp)}\times q_u(p)\)

Settlement of plate in clayey soil:

\(​\dfrac{S_P}{S_F} = \dfrac{B_P}{B_F}\)

Settlement of plate in sandy soil:

\(\dfrac{S_P}{S_F} = \left(\dfrac{B_P(B_F + 0.3)}{B_F(B_P + 0.3)}\right)^2\)

Where

Sf = settlement of foundation

Sp = settlement of plate

Bf = width of footing/foundation

Bp = width of plate

Calculation:

Given data,

Width of plate(Bp) = 35 cm, S_P = 2 cm

Width of footing(Bf) = 85 cm

Settlement of footing(S_F) in clayey soil:

\(​\dfrac{S_P}{S_F} = \dfrac{B_P}{B_F}\)

\(​\dfrac{2}{S_F} = \dfrac{35}{85}\)

S_F = 4.85 cm

Concept;

Dilatancy correction:

It is to be applied when N_o obtained after overburden correction, exceeds 15 in saturated fine sands and silts. IS: 2131-1981 incorporates the Terzaghi and Peck recommended dilatancy correction (when N_o > 15) using the equation

\(\rm N= 15 + \frac{1}{2}\left( {N_0-\;15} \right)\)

N₀ - SPT value after overburden correction

Calculation:

Given: N₀ = 21

\(\rm N= 15 + \frac{1}{2}\left( {21-\;15} \right)\)

⇒ N = 18

Explanation:

SPT test can be conducted to determine:

a) Relative Density of sands

b) Angle of internal friction

c) Unconfined compressive strength of clays

d) Ultimate bearing capacity on the basis of shear criteria

e) Allowable bearing pressure on the basis of settlement criteria

In this test, the split spoon sampler is driven by dynamic mechanism of hammer. This test is conducted either at every 2 to 5 meter interval or at the change of stratum.

Note:

The weight of the hammer is 63.5 kg.

The height of free fall is 750 mm or 75 cm.

The inner and outer diameter of the sampler is 35 mm and 50.5 mm respectively.

Concept:

The area of footing (A_f) is given by

\(\rm A_f = \rm\frac{{Total~ load}}{{{Safe ~bearing ~capacity}}}\)

Calculation:

Given:

Total load = 1750 kN, Safe bearing capacity = 200 kN/m²

\(\rm A_f = \rm\frac{{Total~ load}}{{{Safe ~bearing ~capacity}}}\)

\(A_f = \frac{{1760}}{{200}} = 8.8\;{m^2} \approx9 m^2\)

Explanation:

IS code specification for permissible settlement:

(i) Total Permissible settlement:

• For isolated footing on clay = 65 mm
• For isolated footing on sand = 40 mm
• For raft footing on clay = 65-100 mm
• For raft footing on sand = 40-65 mm

(ii) Permissible Differential settlement:

• For isolated footing on clay = 40 mm
• For isolated footing on sand = 25 mm

(iii) Permissible angular settlement:

• For high framed structure < 1/500
• To prevent all type of minor damage < 1/1000

Note: For multi-storeyed buildings having isolated foundations on sand, the maximum permissible settlement is 60 mm [ For multistorey buildings having isolated foundations take the higher load as compare to single storey buildings having isolated foundations. So that deflection caused by multistorey building having isolated foundation higher than 40 mm (from the safer side)]

Explanation:
Types of footings and their characteristics:

Concept:

Rankine's formula provides guidance on the minimum depth of foundation based on the bearing capacity of the soil.

\(q_u={\gamma } {D_f}\left( {\frac{{1 +\sin \varphi }}{{1 - \sin \varphi }}} \right)^2\)​

Therefore the depth of the foundation can be expressed as,

\(D_f = \frac{q_u}{\gamma }\left( {\frac{{1 - \sin ϕ }}{{1 + \sin ϕ }}} \right)^2\)​

Where Df = Minimum depth of foundation, qu = Ultimate bearing capacity of the soil

Calculation:

Intensity of loading (qu) =180 kN/m2,

Unit weight = 20 kN/m3 and angle of internal friction (ϕ) = 30°

Depth of foundation = \(D_f = \frac{180}{20 }\left( {\frac{{1 - \sin 30° }}{{1 + \sin 30° }}} \right)^2\)

Depth of foundation (Df) = 1.0 m

Hence, According to Rankine's formula, the minimum depth of foundation is 1.0 m.

Explanation:

NOTE: We have to find the incorrect statement from the given statements.

Standard Penetration Test: Standard penetration test can be used to determine:

• Relative density of sand
• Angle of internal friction (ϕ)
• Unconfined compressive strength of clay
• Ultimate bearing capacity on the basis of shear criteria
• Allowable bearing pressure on the basis of settlement criteria
• Load carrying capacity of pile
   

For standard penetration test:

(i) It is performed as a guideline in IS: 2131-1981 in the clean hole of 55 to 150 mm in diameter.

(ii) A thick wall split-tube sampler, 50.8 mm outer diameter and 35 mm inner diameter, is driven into the undisturbed soil at the bottom of the hole under the blows of a 65 kg drive weight with 75 cm free fall.

(iii) The minimum open length of the sampler should be 60 cm. It is first driven through 15 cm as a seating drive and is further driven through 30 cm or until 100 blows have been applied.

(iv) The number of blows required to drive the sampler 30 cm beyond the seating drive, is termed the penetration resistance N or SPT number.

The final SPT number is related to friction angle and relative density. which is given in the table