Retaining Wall Earth Pressure Theories – GATE CE Geotechnical EngineeringPractice Questions & PYQs

Consider the statements $\mathrm{P}$ and $\mathrm{Q}$ related to the analysis/design of retaining walls. P: When a rough retaining wall moves toward the backfill, the wall friction force/resistance mobilizes in upward direction along the wall. Q: Most of the earth pressure theories calculate the earth pressure due to surcharge by neglecting the actual distribution of stresses due to surcharge. Which of the following options is CORRECT?

A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of $30^{\circ}$ . The inclinations of failure planes with respect to the major principal plane for Rankine's active and passive earth pressure condition, respectively are

The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces acting on the failure wedge are: $P$ as the reaction force between the wall and the soil, $R$ as the reaction force on the failure plane, $C$ as the cohesive force along the failure plane and $W$ as the weight of the failure wedge. Assuming that there is no adhesion between the wall and the wedge, identify the most appropriate force polygon for the wedge.

A smooth vertical retaining wall supporting layered soils is shown in figure. According to Rankine's earth pressure theory, the lateral active earth pressure acting at the base of the wall is ____ $\mathrm{kPa}$ (round off to one decimal place)

A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, $k_{H}$ and coefficient of vertical permeability, $k_{V}$ . In order to draw the flow net for the isotropic condition, the embedment depth of the wall should be scaled by a factor of _____, without changing the horizontal scale.

A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is ________. (in integer)

Let $\sigma _v'$ and $\sigma _h'$ denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a soil element to reach the failure state under Rankine?s passive earth pressure condition?

As per Rankine's theory of earth pressure, the inclination of failure planes is $(45+\frac{\phi }{2})^{\circ}$ with respect to the direction of the minor principal stress. The above statement is correct for which one of the following options?

A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is $20^{\circ}$ . The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine's earth pressure theory. Take unit weight of water, $\gamma_{w}=9.81 \mathrm{kN} / \mathrm{m}^{3}$ . The factor of safety (round off to two decimal places) against sliding failure of the retaining wall after ignoring the passive earth pressure will be ________________

A vertical retaining wall of 5 m height has to support soil having unit weight of 18 $kN/m^3$ , effective cohesion of 12 $kN/m^2$ , and effective friction angle of $30^{\circ}$ . As per Rankine's earth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length (in kN/m, round off to two decimal places), is ______.

A retaining wall of height H with smooth vertical backface supports a backfill inclined at an angle $\beta$ with the horizontal. The backfill consists of cohesionless soil having angle of internal friction $\phi$ . If the active lateral thrust acting on the wall is $P_a$ , which one of the following statements is TRUE?

An earthen dam of height H is made of cohesive soil whose cohesion and unit weight are c and $\gamma$ , respectively. If the factor of safety against cohesionis $F_c$ , the Taylor's stability number ( $S_n$ ) is

A 3 m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of $30^{\circ}$ and unit weight of 20 $kN/m^{3}$ . If the wall is prevented from yielding (no movement), the total horizontal thrust (in kN per unit length) on the wall is

A rigid smooth retaining wall of height 7 m with vertical backface retains saturated clay as backfill. The saturated unit weight and undrained cohesion of the backfill are 17.2 kN/ $m^{3}$ and 20 kPa, respectively. The difference in the active lateral forces on the wall (in kN per meter length of wall, up to two decimal places), before and after the occurrence of tension cracks is ______

Consider a rigid retaining wall with partially submerged cohesionless backfill with a surcharge. Which one of the following diagrams closely represents the Rankine's active earth pressure distribution against this wall?

A homogeneous gravity retaining wall supporting a cohesionless backfill is shown in the figure. The lateral active earth pressure at the bottom of the wall is 40 kPa. The minimum weight of the wall (expressed in kN per m length) required to prevent it from overturning about its toe (Point P) is

A vertical cut is to be made in a soil mass having cohesion c, angle of internal friction $\phi$ , and unit weight $\gamma$ . Considering $K_{a}$ and $K_{p}$ as the coefficients of active and passive earth pressures, respectively, the maximum depth of unsupported excavation is

The soil profile at a site consists of a 5 m thick sand layer underlain by a $c-\phi$ soil as shown in figure. The water table is found 1 m below the ground level. The entire soil mass is retained by a concrete retaining wall and is in the active state. The back of the wall is smooth and vertical. The total active earth pressure (expressed in $kN/m^{2}$ ) at point A as per Rankine's theory is _________.

Surcharge loading required to placed on the horizontal backfill of a smooth retaining vertical wall so as to completely eliminate tensile crack is:

A 6 m high retaining wall having a smooth vertical back face retains a layered horizontal backfill. Top 3 m thick layer of the backfill is sand having an angle of internal friction, $\phi=30^{\circ}$ while the bottom layer is 3 m thick clay with cohesion, c = 20 kPa. Assume unit weight for both sand and clay as 18 kN/ $m^{3}$ . The totalactive earth pressure per unit length of the wall (in kN/m) is: