GATE Questions & Answers of Foundation Engineering Civil Engineering

The percent reduction in the bearing capacity of a strip footing resting on sand under flooding condition (water level at the base of the footing) when compared to the situation where the water level is at a depth much greater than the width of footing, is approximately

The width of a square footing and the diameter of a circular footing are equal. If both the footings are placed on the surface of sandy soil, the ratio of the ultimate bearing capacity of circular footing to that of square footing will be

A 0.5 m × 0.5 m square concrete pile is to be driven in a homogeneous clayey soil having undrained shear strength, cu = 50 kPa and unit weight, γ = 18.0 kN/m3. The design capacity of the pile is 500 kN. The adhesion factor $\style{font-family:'Times New Roman'}\alpha$ is given as 0.75. The length of the pile required for the above design load with a factor of safety of 2.0 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/m3 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 ______

The contact pressure and settlement distribution for a footing are shown in the figure.

 

The figure corresponds to a

 

A 3 m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of 30° and unit weight of 20 kN/m3. If the wall is prevented from yielding (no movement), the total horizontal thrust (in kN per unit length) on the wall is

A group of nine piles in a 3 × 3 square pattern is embedded in a soil strata comprising dense sand underlying recently filled clay layer, as shown in the figure. The perimeter of an individual pile is 126 cm. The size of pile group is 240 cm × 240 cm. The recently filled clay has undrained shear strength of 15 kPa and unit weight of 16 kN/m3 .

The negative frictional load (in kN, up to two decimal places) acting on the pile group is ______

A strip footing is resting on the ground surface of a pure clay bed having an undrained cohesion Cu. The ultimate bearing capacity of the footing is equal to

A  uniformaly distribute line load of 500 kN/m is acting on the ground surface. Based on Boussinesq's theory the ratio of vertical stress at a depth 2 m to that at 4 m, right below the line of loading is

It is proposed to drive H-piles up to a depth of 7 m at a construction site. The average surface area of the H-pile is 3m2 per meter length. The soil at the site is homogeneous sand, having an effective friction angle of $\style{font-family:'Times New Roman'}{32^\circ}$. The ground water table (GWT) is at a depth of 2 m below the ground surface. The unit weights of the soil above and below the GWT are 16kN/m3 and 19kN/m3, respectively. Assume the earth pressur coefficent, = 1.0, and the angle of wall friction, $\style{font-family:'Times New Roman'}{\delta=23^\circ}$. The total axial frictional resistance (in kN, up to one decimal place) mobilized on the pile against the driving is _______________

The infinite sand slope shown in the figure is on the verge of sliding failure. The ground water table coincides with the ground surface. Unit weight of water $\style{font-family:'Times New Roman'}{\gamma_w=9.81\;\mathrm{kN}/\mathrm m^3}$.

 

The value of the effective angle of internal friction (in degrees, up to one decimal place) of the sand 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?

The plate load test was conducted on a clayey strata by using a plate of 0.3 m × 0.3 m dimensions, and the ultimate load per unit area for the plate was found to be 180 kPa. The ultimate bearing capacity (in kPa) of a 2 m wide square footing would be

Two identical concrete piles having the plan dimensions $\style{font-family:'Times New Roman'}{50\;\mathrm{cm}\times50\;\mathrm{cm}}$ are driven into a homogeneous sandy layer as shown in the figures. Consider the bearing capacity factor Nq for 30º as 24.

If QP1 and QP2 represent the ultimate point bearing resistances of the piles under dry and submerged conditions, respectively, which one of the following statements is correct?

For the construction of a highway, a cut is to be made as shown in the figure.

The soil exhibits c’=20k Pa, $ \style{font-family:'Times New Roman'}{\phi'=18^\circ}$, and the undrained  shear strength = 80 kPa. The unit weight of water is 9.81 kN/m3. The unit weights of the soil above and below the ground water table are 18 and 20 kN/m3, 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 

Consider a square-shaped area ABCD on the ground with its centre at M as shown in the figure. Four concentrated vertical loads of P= 5000 kN are applied on this area, one at each corner.

The vertical stress increment (in kPa, up to one decimal place) due to these loads according to the Boussinesq’s equation, at a point 5 m right below M, is____________

A vertical cut is to be made in a soil mass having cohesion $c$, angle of internal friction φ , and unit weight γ . Considering Ka and Kp as the coefficients of active and passive earth pressures, respectively, the maximum depth of unsupported excavation is

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 strip footing is resting on the surface of a purely clayey soil deposit. If the width of the footing is doubled, the ultimate bearing capacity of the soil

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/m2) at point A as per Rankine's theory is _________
 

 

A 4 m wide strip footing is founded at a depth of 1.5 m below the ground surface in a $c-\phi $' 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' = 35 kN/m2, $ \phi $' = 28.63°, γsat = 19 kN/m3, γbulk = 17 kN/m3 and γw = 9.81 kN/m3. The values of bearing capacity factors for different $ \phi $' are given below.

$\phi'$ $N_c$ $N_q$ $N_\gamma$
$15^\circ$ 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

 

Using Terzaghi's bearing capacity equation and a factor of safety $ F_s=2.5 $, the net safe bearing capacity (expressed in kN/m2 ) for local shear failure of the soil is __________

Which of the following statements is TRUE for degree of disturbance of collected soil sample?

A square footing (2 m x 2 m) is subjected to an inclined point load, P as shown in the figure below. The Water table is located well below the base of the footing. Considering one-way eccentricity, the net safe load carrying capacity of the footing for a factor of safety of 3.0 is _________ kN.

The following factors may be used:

Bearing capacity factors: Nq=33.3, Nγ=37.16; Shape factors : Fqs=Fγs=1.314; Depth factors: Fqd=Fγd=1.113: Inclination factors: Fqi = 0.444, Fγi = 0.02

 

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

Net ultimate bearing capacity of a footing embedded in a clay stratum

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

A pile of diameter 0.4 m is fully embedded in a clay stratum having 5 layers, each 5 m thick as shown in the figure below. Assume a constant unit weight of soil as 18 kN/m3 for all the layers. Using λ-method (λ = 0.15 for 25 m embedment length) and neglecting the end bearing component, the ultimate pile capacity (in kN) 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, $\phi$ =30o 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/m3. The total active earth pressure per unit length of the wall (in kN/m) is

The action of negative skin friction on the pile is to

A long slope is formed in a soil with shear strength parameters: c' = 0 and $\phi'$ = 34°. 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 γsat = 18 kN/m3 and γw = 10 kN/m3. 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

Group I contains representative load-settlement curves for different modes of bearing capacity failures of sandy soil. Group II enlists the various failure characteristics. Match the load-settlement curves with the corresponding failure characteristics.

Group I Group II
P. Curve J 1. No apparent heaving of soil around the footing
Q. Curve K 2. Rankine’s passive zone develops imperfectly
R. Curve L 3. Well defined slip surface extends to ground surface
   

An infinitely long slope is made up of a c-φ soil having the properties: cohesion (c) = 20 kPa, and dry unit weight (γd) = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is _________________

Group I enlists in-situ field tests carried out for soil exploration, while Group II provides a list of parameters for sub-soil strength characterization. Match the type of tests with the characterization parameters.

Group I Group II
P. Pressuremeter Test (PMT)                                     1. Menard’s modulus (Em)
Q. Static Cone Penetration Test (SCPT) 2. Number of blows (N)
R. Standard Penetration Test (SPT) 3. Skin resistance (fc)
S. Vane Shear Test (VST) 4. Undrained cohesion (cu)
   

A single vertical friction pile of diameter 500 mm and length 20 m is subjected to a vertical compressive load. The pile is embedded in a homogeneous sandy stratum where: angle of internal friction (φ) = 30°, dry unit weight (γd) = 20 kN/m3 and angle of wall friction (δ) = 2φ/3. Considering the coefficient of lateral earth pressure (K) = 2.7 and the bearing capacity factor (Nq) = 25, the ultimate bearing capacity of the pile (in kN) is _______________

A circular raft foundation of 20 m diameter and 1.6 m thick is provided for a tank that applies a bearing pressure of 110 kPa on sandy soil with Young's modulus, Es' = 30 MPa and Poisson's ratio, vs = 0.3. The raft is made of concrete (Ec = 30 GPa and vc = 0.15). Considering the raft as rigid, the elastic settlement (in mm) is

Four columns of a building are to be located within a plot size of 10 m x 10 m. The expected load on each column is 4000 kN. Allowable bearing capacity of the soil deposit is 100 kN/m2. The type of foundation best suited is

The soil profile above the rock surface for a 25o infinite slope is shown in the figure, where su is the undrained shear strength and γ t is total unit weight. The slip will occur at a depth of

Two different soil types (Soil 1 and Soil 2) are used as backfill behind a retaining wall as shown in the figure, where γ t is total unit weight, and c' and $\mathrm\phi$ ' are effective cohesion and effective angle of shearing resistance. The resultant active earth forceper unit length (in kN/m) acting on the wall is:

A multistory building with a basement is to be constructed. The top 4 m consists of loose silt, below which dense sand layer is present up to a great depth. Ground water table is at the surface. The foundation consists of the basement slab of 6 m width which will rest on the top of dense sand as shown in the figure. For dense sand, saturated unit weight = 20 kN/m3, and bearing capacity factors Nq = 40 and N γ = 45. For loose silt, saturated unit weight = 18kN/m3, Nq = 15 and N γ = 20.Effective cohesion c' is zero for both soils.Unit weight of water is 10 kN/m3. Neglect shape factor and depth factor.
Average elastic modulus E and Poisson’s ratio μ of dense sand is 60 x 103 kN/m2 and 0.3 respectively.

Using factor of safety = 3, the net safe bearing capacity (in kN/m2) of the foundation is:

A multistory building with a basement is to be constructed. The top 4 m consists of loose silt, below which dense sand layer is present up to a great depth. Ground water table is at the surface. The foundation consists of the basement slab of 6 m width which will rest on the top of dense sand as shown in the figure. For dense sand, saturated unit weight = 20 kN/m3, and bearing capacity factors Nq = 40 and N γ = 45. For loose silt, saturated unit weight = 18kN/m3, Nq = 15 and N γ = 20.Effective cohesion c' is zero for both soils.Unit weight of water is 10 kN/m3. Neglect shape factor and depth factor.
Average elastic modulus E and Poisson’s ratio μ of dense sand is 60 x 103 kN/m2 and 0.3 respectively.

The foundation slab is subjected to vertical downward stresses equal to net safe bearing capacity derived in the above question. Using influence factor If = 2.0, and neglecting embedment depth and rigidity corrections, the immediate settlement of the dense sand layer will be:

A smooth rigid retaining wall moves as shown in the sketch causing the backfill material to fail. The backfill material is homogeneous and isotropic, and obeys the Mohr-Coulomb failure criterion. The major principal stress is

 

An embankment is to be constructed with a granular soil (bulk unit weight = 20 kN/m3) 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

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

A singly under-reamed, 8-m long ,RCC pile(shown in the adjoining figure) weighing 20 kN with 350 mm shaft diameter and 750 mm under-ream diameter is installed within stiff, saturated silty clay(undrained shear strength is 50 kpa, adhesion factor is 0.3, and the applicable bearing capacity factor is 9) to counteract the impact of soil swelling on a structure constructed above. Neglecting suction and the contribution of the under-ream to the adhesive shaft capacity, what would be the estimated ultimate tensile capacity(rounded off to the nearest interger value of kN) of the pile?

If σh,σv,σh" and σv," represent the total horizontal stress, total vertical stress, effective horizontal stress and effective vertical stress on a soil element, respectively, the coefficient of earth pressure at rest is given by

The vertical stress at point P1 due to the point load Q on the ground surface as shown in figure is σ2. According to Boussinesq’s equation, the vertical stress at point P2 shown in figure will be

The ultimate load capacity of a 10 m long concrete pile of square cross section 500 mm x 500 mm driven into a homogeneous clay layer having undrained cohesion value of 40 kPa is 700 kN. If the cross section of the pile is reduced to 250 mm x 250 mm and the length of the pile is increased to 20m, the ultimate load capacity will be

The unconfined compressive strength of a saturated clay sample is 54 KPa

The value of cohension for the clay is

The unconfined compressive strength of a saturated clay sample is 54 KPa

If a square footing of size 4 m x 4 m is resting on the surface of a deposit of the above clay, the ultimate bearing capacity of the footing (as per Terzaghi’s equation) is

A precast concrete pile is driven with a 50 kN hammer falling through a height of 1.0 m with an efficiency of 0.6. The set value observed is 4 mm per blow and the combined temporary compression of the pile, cushion and the ground is 6 mm. As per Modified Hiley Formula, the ultimate resistance of the pile is

In quadrantal bearing system, bearing of a line varies from

A plate load test is carried out on a 300 mm × 300 mm plate placed at 2 m below the ground level to determine the bearing capacity of a 2 m × 2 m footing placed at same depth of 2 m on a homogeneous sand deposit extending 10 m below ground. The ground water table is 3m below the ground level. Which of the following factors does not require a correction to the bearing capacity determined based on the load test?

Examine the test arrangement and the soil properties given below:

The maximum pressure that can be applied with a factor of safety of 3 through the concrete block, ensuring no bearing capacity failure in soil using Terzaghi’s bearing capacity equation without considering the shape factor, depth factor and inclination factor is

Examine the test arrangement and the soil properties given below:

The maximum resistance offered by the soil through skin friction while pulling out the pile from the ground is

When a retaining wall moves away from the back-fill, the pressure exerted on the wall is termed as

A footing 2 m × 1 m exerts a uniform pressure of 150 kN/m2 on the soil. Assuming a load dispersion of 2 vertical to 1 horizontal, the average vertical stress (kN/m2) at 1.0 m below the footing is

A pile of 0.50 m diameter and length 10 m is embedded in a deposit of clay. The undrained strength parameters of the clay are cohesion = 60 kN/m2 and the angle in internal friction = 0. The skin friction capacity (kN) of the pile for an adhesion factor of 0.6, is

A test plate 30 cm × 30 cm resting on a sand deposit settles by 10mm under a certain loading intensity. A footing 150 cm × 200 cm resting on the same sand deposit and loaded to the same load intensity settles by

A column is supported on a footing as shown in the figure below. The water table is at a depth of 10m below the base of the footing.

The net ultimate bearing capacity (kN/m2) of the footing based on Terzaghi’s bearing capacity equation is

A column is supported on a footing as shown in the figure below. The water table is at a depth of 10m below the base of the footing.

The safe load (kN) that the footing can carry with a factor of safety 3 is

The vertical stress at some depth below the corner of a 2m×3m rectangular footing due to a certain load intensity is 100 kN/m2. What will be the vertical stress in kN/m2 below the centre of a 4m×6m rectangular footing at the same depth and same load intensity?

The bearing capacity of a rectangular footing of plan dimensions 1.5 m × 3 m resting on the surface of a sand deposit was estimated as 600 kN/m2 when the water table is far below the base of the footing. The bearing capacities in kN/m2 when the water level rises to depths of 3 m, 1.5 m and 0.5 m below the base of the footing are

What is the ultimate capacity in kN of the pile group shown in the figure assuming the group to fail as a single block?

Subjects of Geotechnical Engineering