Modes of Shear Failure

Q. A 4 m wide strip footing is founded at a depth of 1.5 m below the ground surface in a $c-\varphi$ soil as shown in the figure. The water table is at a depth of 5.5 m below ground surface. the soil properties are c' = 25 kN/$m^2$, ${\varphi }^{\prime }$ = ${28.63}^o$, ${\gamma }_{sat}$ = 19 kN/$m^3$, ${\gamma }_{bulk}$ = 17 kN/$m^3$ and ${\gamma }_w$ = 9.81 kN/$m^3$. the values of bearing capacity factors for different ${\varphi }^{\prime }$ are given below.

$\begin{array}{cccc}{\varphi }^{{}^{\prime }}& N_c& N_q& N_{\gamma }\\ {15}^{\circ }& 12.9& 4.4& 2.5\\ {20}^{\circ }& 17.7& 7.4& 5.0\\ {25}^{\circ }& 25.1& 12.7& 9.7\\ {30}^{\circ }& 37.2& 22.5& 19.7\end{array}$

Using Terzaghi's bearing capacity equation and a factor of safety $F_s=2.5,$ the net safe bearing capacity (expressed in kN/$m^2$) for local shear failure of the soil is

1. 298.48

Q. Consider the following statements associated with local shear failure of soils:
1. Failure is sudden with well-defined ultimate load.
2. This failure occurs in highly compressible soils.
3. Failure is preceded by large settlement.
Which of these statements are correct?

1. 1, 2 and 3
2. 1 and 2
3. 2 and 3
4. 1 and 3

Q. An embankment is to be constructed with a granular soil $(bulkunitweight=20kN/m^3)$
on a saturated clayey silt deposit (undrained shear strength = 25 kPa). Assuming undrained general shear failure and bearing capacity factor of 5.7, the maximum height (in m) of the embankment at the point of failure is

1. 
   7.1
2. 
   5.0
3. 
   4.5
4. 
   2.5

Q. A 2 m $\times$ 4 m rectangular footing has to carry a uniformly distributed load of 120 kPa. as per the 2 : 1 dispersion method of stress distribution, the increment in vertical stress (kPa) at a depth of 2 m below the footing is

1. 40

Q. Likelihood of general shear failure for an isolated footing in sand decreases with

1. 
   Decreasing footing depth
2. 
   Decreasing inter-granular packing of the sand
3. 
   Increasing footing width
4. 
   Decreasing soil grain compressibility

Q. Consider the following statements as suggestive of the bearing capacity of soil:
1. The maximum net loading intensity at which neither the soil fails in shear nor is there excessive settlement detrimental to the structure.
2. The maximum net pressure which the soil can carry without shear failure.
3. The net ultimate bearing capacity of the soil divided by a factor of safety.
Which of the above statements is/are correct?

1. 1, 2 and 3
2. 1 only
3. 2 only
4. 3 only

Q. In case of footing on the surface or shallow depth in very dense sand which one of the following types of failure is likely to occur?

1. Punching shear failure
   
2. Local shear failure
3. General shear failure
4. Any of the above three

Q. Assertion (A): Larger footings settle more than the smaller footings under the same load intensity.
Reason (R): Size of the pressure bulb depends upon the size of the footing.

1. both A and R are true and R is the correct explanation of A
   
2. both A and R are true but R is not a correct explanation of A
3. A is true but R is false
4. A is false but R is true

Q. A rigid footing subjected to vertical central load fails under general shear failue. The rupture surface developed is

1. circular one sided rotational failure
2. plane surface of failure originating at the edge of footing and extending downwards with orientation of Rankine passive state equilibrium
3. symmetrical failure surface consisting of segment of spiral and Rankine's passive state failure surface
4. symmetrical failure surface consisting of segments of log spiral and plane failure surface as per Rankine active state of equilibrium
   

Q. Group I contains representative load- settlement curves for different modes of bearing capacity failure of sandy soil. Group II enlists the various failure characteristics. match the load settlement curves with the corresponding failure characteristic.
$\begin{array}{cccc}& \text{Group I}& & \text{Group II}\\ \text{P}& \text{Curve J}& \text{(i)}& \text{No apparent heaving of soil around the footing}\\ \text{Q}& \text{Curve K}& \text{(ii)}& \text{Ranking passive zone develops imperfectly}\\ \text{R}& \text{Curve L}& \text{(iii)}& \text{Well defined slip surface extends to ground surface}\end{array}$

J K L

1. P - 1, Q - 3, R - 2
2. P - 3, Q - 2, R - 1
3. P - 3, Q - 1, R - 2
4. P - 1, Q - 2, R - 3