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Question

A bridge of 40×10 m is to be founded on the river bed at a depth of 6 meters. The soil is clay having shear strength of 15 tonnes/m2. The wall cohesive on the sides of pier could be taken as half of shear strength and the saturated density of 2 gm/cc. The rectangular pier is expected to carry a total load of 25,000 tonnes including its own weight. If the depth of water in river is 5 meters, the factor of safety of pier against shear failure based on skempton’s approach is

A
2
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B
3
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C
2.5
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D
2.7
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Solution

The correct option is B 3
S=Cu=15 tonnes/m2

Qy=25,000

Foundation area = 10×40=400 m2

q=25000400=62.5 t/m2

Due to wall cohesion
Adhesion force

Qs=Cu2×P×L=152×2×(10+40)×6

Qs=4500 tons

Equivalent pressure due to cohesive =QsA=450010×40=11.25 kN/m2

Pressure due to self weight of soil = γD=2×6=12 t/m2

Pressure due to boundary = γw×5

γw=1 g/cc=1 t/m3=1×5=5 t/m2

Net pressure, qn=qrDWall CohesionBuoyancy pressure

=62.51211.255

qn=34.25 t/m2

Design :

qnqns

qn=qnuF

From skempton's approach

qnu=CNc=5[1+0.2DB][1+0.2BL]×C

=5[1+0.2610][1+0.21040]×15

qnu=105.84 kPa

qnu=qnuF

F=105.8434.25=3.09

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