A square footing of 2 {m} sides rests on the surface of a homogeneous soil bed having the properties: cohesion {c}=24 {kPa}, angle of internal friction \phi=25^{\circ}, and unit weight \gamma=18 {kN} {/} {m}^{3}. Terzaghi's bearing capacity factor ϕ=25^{\circ} are {N}_{ {c}}=25.1, {N}_{ {q}}=12.7, {N}_{\gamma}=9.7, {N}{'} {c}= 14.8, {N}{'} {q}=5.6, and {N}{'} \gamma=3. The ultimate bearing capacity of the foundation (in {kPa}, round off to 2 decimal places) is __________

GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 49 of 65

Marks: +1, -0

A square footing of

2 {m}

sides rests on the surface of a homogeneous soil bed having the properties: cohesion

{c}=24 {kPa}

, angle of internal friction

φ=25^{∘}

, and unit weight

γ=18

{kN} {/} {m}^{3}

. Terzaghi's bearing capacity factor

ϕ=25^{∘}

are

{N}_{ {c}}=25.1, {N}_{ {q}}=12.7, {N}_{γ}=9.7, {N}{'} {c}=

14.8,

{N}{'} {q}=5.6

and

{N}{'} γ=3

. The ultimate bearing capacity of the foundation (in

{kPa}

, round off to 2 decimal places) is __________

Solution:

Q_{\;\text "ultimate"\;}=1.3 c'N_{c}^{'}+q N_{q}'+0.4 B_{γ} N_{γ}'

=1.3 ×(\;{2}/{3} × 24) × 14.8+0+0.4 × 2 × 18 × 3.2

=353.92 {kPa}

Here,

ϕ<29^{∘}

Footing rests on the ground
Hence,

{q}=0

c'=\;{2}/{3} c

use

{N}_{q}' {N}_{ {c}}' {N}_{r}'

accordingly.

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