Stability Analysis Of Slopes Practice Questions

A cut slope is made in a silty clay soil for a new road project, as shown in the figure. The locations of ground water table (GWT) and potential failure surface are shown in the figure. After the cut is made, the excess pore water pressure is fully dissipated, and the shear stress at the point $A$ is $60 \mathrm{kN} / \mathrm{m}^{2}$ . The factor of safety at the point $A$ for longterm stability is _________ (rounded off to 2 decimal places). Note : Shear strength properties of silty clay: $c^{\prime}=15 \mathrm{kN} / \mathrm{m}^{2}, \phi^{\prime}=15^{\circ}$ , and $c_{u}=75 \mathrm{kN} / \mathrm{m}^{2}$ Unit weight of soil above the $\operatorname{GWT}(\gamma)=19 \mathrm{kN} / \mathrm{m}^{3}$ Unit weight of soil below the $\operatorname{GWT}\left(\gamma_{\text {sat }}\right)=20 \mathrm{kN} / \mathrm{m}^{3}$ Unit weight of water $\left(\gamma_{w}\right)=9.81 \mathrm{kN} / \mathrm{m}^{3}$

An infinite slope is made up of cohesionless soil with seepage parallel to and upto the sloping surface. The angle of slope is $30^{\circ}$ with respect to horizontal ground surface. The unit weight of the saturated soil and water are $20 \mathrm{kN} / \mathrm{m}^{3}$ and $10 \mathrm{kN} / \mathrm{m}^{3}$ respectively. The minimum angle of shearing resistance of soil (in degrees) for the critically stable condition of the slope is _____ (rounded off to the nearest integer).

At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance $q_c$ was 1000 kPa at a certain depth. The friction ratio ( $f_r$ ) was estimated as 1% at the same depth. The value of sleeve (side) friction (in kPa) at that depth was _______ . (in integer)

An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle $50^{\circ}$ with the horizontal. The slope material comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip circle KLM, with a radius 25 m, passes through the crest and toe of the slope and it subtends an angle $60^{\circ}$ at its center O. The weight of the active soil mass (W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance of 10 m from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface. Considering the trail slip circle KLM, the factor of the safety against the failure of slope under undrained condition (round off to two decimal places) is ___________

A 10 m high slope of dry clay soil (unit weight = 20 $kN/m^3$ ), with a slope angle of $45^{\circ}$ and the circular slip surface, is shown in the figure (not drawn to the scale). The weight of the slip wedge is denoted by W. The undrained unit cohesion ( $c_u$ ) is 60 kPa. The factor of safety of the slope against slip failure, is

A fully submerged infinite sandy slope has an inclination of $30^{\circ}$ with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 $kN/m^3$ and $38^{\circ}$ , respectively. The unit weight of water is 10 $kN/m^3$ . Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.

For the construction of a highway. A cut is to be made as shown in the figure. The soil exhibits $c'=20kPa,\; \; \phi '=18^{\circ}$ and the undrained shear strength = 80 kPa. The unit weight of water is 9.81 $kN/m^{3}$ . The unit weights of the soil above and below the ground water table are 18 and 20 $kN/m^{3}$ , respectively. If the shear stress at Point A is 50 kPa, the factors of safety against the shear failure at this point, considering the undrained and drained conditions, respectively, would be

The infinite sand slope shown in the figure is on theverge of sliding failure. The ground water tablecoincides with the ground surface. Unit weight of water $\gamma _{w}=9.81\; kN/m^{3}$ . The value of the effective angle of internal friction (indegrees, up to one decimal place) of the sand is________

In friction circle method of slope stability analysis, if r defines the radius of the slip circle, the radius of friction circle is:

A long slope is formed in a soil with shear strength parameters: ${c}'=0$ and ${\phi }'=34^{\circ}$ . A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use $\gamma_{sat}=18 kN/m^{3}$ and $\gamma_{w}=10 kN/m^{3}$ . The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would be

An infinitely long slope is made up of a $c-\phi$ soil having the properties: cohesion (c)=20 kPa, and dry unit weight $(\gamma _{d} )= 16kN/m^{3}$ . The angle of inclination and critical height of the slope are $40^{\circ}$ and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degree) is _____

The soil profile above the rock surface for a 25 $^{\circ}$ infinite slope is shown in the figure, where $s_{u}$ is the undrained shear strength and $\gamma _{t}$ is total unit weight. The slip will occur at a depth of

The factor of safety of an infinite soil slope shown in the figure having the properties c=0, $\phi =35^{\circ},\; \gamma _{dry}=16kN/m^{3}$ and $\gamma _{sat}=20kN/m^{3}$ is approximately equal to

List-I below gives the possible types of failure for a finite soil slope and List-II gives the reasons for these different types of failure. Match the items in List-I with the items in List-II

For two infinite slopes (one in dry condition and other in submerged condition) in a sand deposit having the angle of shearing resistance 30 $^{\circ}$ , factor of safety was determined as 1.5 (for both slopes). The slope angles would have been

An infinite soil slope with an inclination of $35^{\circ}$ is subjected to seepage parallel to its surface. The soil has $c'=100 kN/m^{2} \; and \; {\phi}' =35^{\circ}$ . Using the concept of mobilized cohesion and friction, at a factor of safety of 1.5 with respect of shear strength, the mobilized friction angle is

A granular soil possesses saturated density of 20 $kN/m^{3}$ . Its effective angle of internal friction is 35 degrees. If the desired factor of safety is 1.5, the safe angle of slope for this soil, when seepage occurs at and parallel to the slope surface, will be

A canal having side slopes 1:1 is proposed to be constructed in a cohesive soil to a depth of 10 m below the ground surface. The soil properties are: $\phi _u=15^{\circ}$ , $C_n$ =12kPa, e=1.0, $G_{s}$ =2.65. If there is a sudden draw down of water in the canal and if Taylor's Stability Number for the reduced value of $\phi _v$ is 0.126, the factor of safety with respect to cohesion against the failure of bank slopes will be

An infinite slope is to be constructed in a soil. The effective stress strength parameters of the soil are c'=0 and ${\phi}' =30^{\circ}$ . The saturated unit weight of the slope is 20 $kN/m^{3}$ and the unit weight of water is 10 $kN/m^{3}$ . Assuming that seepage is occurring parallel to the slope, the maximum slope angle for a factor of safety of 1.5 would be