# GATE Questions & Answers of Soil Mechanics Civil Engineering

#### Soil Mechanics 97 Question(s)

In a shrinkage limit test, the volume and mass of a dry soil pat are found to be 50 cm3 and 88 g, respectively. The specific gravity of the soil solids is 2.71 and the density of water is 1 g/cc. The shrinkage limit (in %, up to two decimal places) is ______

At a construction site, a contractor plans to make an excavation as shown in the figure.

The water level in the adjacent river is at an elevation of +20.0 m. Unit weight of water is 10 kN/m3. The factor of safety (up to two decimal places) against sand boiling  for the proposed excavation is ______

A conventional drained triaxial compression test was conducted on a normally consolidated clay sample under an effective confining pressure of 200 kPa. The deviator stress at failure was found to be 400 kPa. An identical specimen of the same clay sample is isotropically consolidated to a confining pressure of 200 kPa and subjected to standard undrained triaxial compression test. If the deviator stress at failure is 150 kPa, the pore pressure developed (in kPa, up to one decimal place) is ______

The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be ______

The clay mineral, whose structural units are held together by potassium bond is

Three soil specimens (Soil 1, Soil 2 and Soil 3), each 150 mm long and 100 mm diameter, are placed in series in a constant head flow set-up as shown in the figure. Suitable screens are provided at the boundaries of the specimens to keep them intact. The values of coefficient of permeability of Soil 1, Soil 2 and Soil 3 are 0.01, 0.003 and 0.03 cm/s, respectively.

The value of $h$ in the set-up is

The compression curve (void ratio, e vs. effective stress, ${\sigma }_{v}^{\text{'}}$) for a certain clayey soil is a straight line in a semi-logarithmic plot and it passes through the points (e = 1.2; ${\sigma }_{v}^{\text{'}}$ = 50 kPa) and (e = 0.6; ${\sigma }_{v}^{\text{'}}$ = 800 kPa). The compression index (up to two decimal places) of the soil is ______

The total horizontal and vertical stresses at a point X in a saturated sandy medium are 170 kPa and 300 kPa, respectively. The static pore-water pressure is 30 kPa. At failure, the excess pore-water pressure is measured to be 94.50 kPa, and the shear stresses on the vertical and horizontal planes passing through the point X are zero. Effective cohesion is 0 kPa and effective angle of internal friction is $36^\circ$. The shear strength (in kPa, up to two decimal places) at point X is ______

Group I lists the type of gain or loss of strength in soils. Group II lists the property or process responsible for the loss or gain of strength in soils.

 Group I Group II P. Regain of strength with time 1. Boiling Q. Loss of strength due to cyclic loading 2. Liquefacation R. Loss of strength due to upward seepage 3. Thixotropy S. Loss  of strength due to remolding 4. Sensitivity

The correct match between Group I and Group II is

A soil sample is subjected to a hydrostatic pressure.$\style{font-family:&#39;Times New Roman&#39;}{\mathrm\sigma}$. The Mohr circle for any point in the soil sample would be

A 3 m thick clay layer is subjected to an intital uniform pore pressure of 145 kPa as shown in the figure.

For the given ground conditions, the time (in days , rounded to the nearest integer) required for 90% consolidation would be ___________

The laboratory tests on a soil sample yields the following results: natural moisture content = 18%, liquid limit =60%, plastic limit = 25%, percentage of clay sized fraction =25%. The liquidity index and activity (as per the expression proposed by Skempton) of the soil, respectively, are

A consolidated undrained ($\overline{\mathrm{CU}}$) triaxial compression test is conducted on a normally consolidated clay at a confining pressure of 100 kPa. The deviator stress at  failure is 80 kPa and the pore-water pressure measured a failure is 50 kPa. The effective angle of internal friction (in degrees, up to one decimal place) of the soil is ____________

Let G be the specific gravity of soil solids,$w$ the water content in the soil sample, $\style{font-family:'Times New Roman'}{\gamma_w}$ the unit weight of water, and $\style{font-family:'Times New Roman'}{\gamma_d}$ the dry unit weight of soil. The equation for the zero air voids line in a compaction test plot is

Consider the following statement related to the pore pressure parameters, A and B:

P. A always lies between 0 and 1.0

Q. A can be less than 0 or greater than 1.0

R. B always lies between 0 and 1.0

S. B can be less than 0 or grater than 1.0

For these statements, which one of the following options is correct?

A sheet pile has an embedment depth of 12 m in a homogeneous soil stratum. The coefficient of permeabilty of soil is 10-6 m/s. Diffrence in the water levels between the sides of the sheet pile is 4 m. The flow net is constructed with five number of flow lines and eleven number of equipotential lines. The quantity of seepage (in cm3/s per m, up to one decimal place) under the sheet pile is___________

Following are the statements related to the stress paths in a triaxial testing of soils:

P. If $\style{font-family:'Times New Roman'}{\sigma_1=\sigma_3}$, the stress point lies at the origin of the p-q plot

Q. If $\style{font-family:'Times New Roman'}{\sigma_1=\sigma_3}$ the stress point lies on the p-axis of the p-q plot

R. $\style{font-family:'Times New Roman'}{\sigma_1>\sigma_3}$ both the stress points p and q are positive.

For the above statements, the correct combinations is

In the consolidated undrained triaxial test on a saturated soil sample, the pore water pressure is zero

A fine grained soil is found to be plastic in the water content range of 26.48%. As per Indian Standerd Classification System, the soil is classified as

The porosity (n) and the degree of saturation (S) of a soil sample are 0.7 and 40%, respectively. In a 100 m3 volume of the soil, the volume (expressed in m3) of air is _________

An undisturbed soil sample was taken from the middle of a clay layer (i.e., 1.5 m below GL), as shown in figure. The water table was at the top of clay layer. Laboratory test results are as follows:

 Natural water content of clay : 25% Preconsolidation pressure of clay : 60 kPa Compression index of clay : 0.50 Recompression index of clay : 0.05 Specific gravity of clay : 2.70 Bulk unit weight of sand : 17 kN/m3

A compacted fill of 2.5 m height with unit weight of 20 kN/m3 is placed at the ground level.

Assuming unit weight of water as10 kN/m3, the ultimate consolidation settlement (expressed in mm) of the clay layer is ____________

A seepage flow condition is shown in the figure. The saturated unit weight of the soil ${\gamma }_{sat=18}$ kN/m3. Using unit weight of water,${\gamma }_{w=9.81}$ kN/m3, the effective vertical stress (expressed in kN/m2) on plane X-X is ________

A drained triaxial compression test on a saturated clay yielded the effective shear strength parameters as c' = 15 kPa and $\style{font-family:'Times New Roman'}{\phi'=22^\circ}$ . Consolidated Undrained triaxial test on an identical sample of this clay at a cell pressure of 200 kPa developed a pore water pressure of 150 kPa at failure. The deviator stress (expressed in kPa) at failure is _________

Seepage is occurring through a porous media shown in the figure. The hydraulic conductivity values (k1, k2, k3) are in m/day.

The seepage discharge (m3/day per m) through the porous media at section PQ is

The relationship between the specific gravity of sand (G) and the hydraulic gradient (i) to initiate quick condition in the sand layer having porosity of 30% is

The results of a consolidation test on an undisturbed soil, sampled at a depth of 10 m below the ground level are as follows:

 Saturated unit weight : 16 kN/m3 Pre-consolidation pressure : 90 kPa

The water table was encountered at the ground level. Assuming the unit weight of water as 10 kN/m3, the over-consolidation ratio of the soil is

Profile of a weir on permeable foundation is shown in figure I and an elementary profile of 'upstream pile only case' according to Khosla's theory is shown in figure II. The uplift pressure heads at key points Q, R and S are 3.14 m, 2.75 m and 0 m, respectively (refer figure II).

What is the uplift pressure head at point P downstream of the weir (junction of floor and pile as shown in the figure I)?

The seepage occurring through an earthen dam is represented by a flownet comprising of 10 equipotential drops and 20 flow channels. The coefficient of permeability of the soil is 3 mm/min and the head loss is 5 m. The rate of seepage (expressed in cm3/s per m length of the dam) through the earthen dam is _________

OMC-SP and MDD-SP denote the optimum moisture content and maximum dry density obtained from standard Proctor compaction test, respectively. OMC-MP and MDD-MP denote the optimum moisture content and maximum dry density obtained from the modified Proctor compaction test, respectively. Which one of the following is correct?

Water flows from P to Q through two soil samples, Soil 1 and Soil 2, having cross sectional area of 80 cm2 as shown in the figure. Over a period of 15 minutes, 200 ml of water was observed to pass through any cross section. The flow conditions can be assumed to be steady state. If the coefficient of permeability of Soil 1 is 0.02 mm/s, the coefficient of permeability of Soil 2 (expressed in mm/s) would be ________

A fine-grained soil has 60% (by weight) silt content. The soil behaves as semi-solid when water content is between 15% and 28%. The soil behaves fluid-like when the water content is more than 40%. The ‘Activity’ of the soil is

Which of the following statements is TRUE for the relation between discharge velocity and seepage velocity ?

In an unconsolidated undrained triaxial test, it is observed that an increase in cell pressure from 150 kPa to 250 kPa leads to a pore pressure increase of 80 kPa. It is further observed that, an increase of 50 kPa in deviatoric stress results in an increase of 25 kPa in the pore pressure. The value of Skemptons’s pore pressure parameter B is:

Which of the following statements is NOT correct ?

A water tank is to be constructed on the soil deposit shown in the figure below. A circular footing of diameter 3 m and depth of embedment 1 m has been designed to support the tank. The total vertical load to be taken by the footing is 1500 kN. Assume the unit weight of water as 10 kN/m3 and the load dispersion pattern as 2V:1H. The expected settlement of the tank due to primary consolidation of the clay layer is ______mm.

A 20 m thick clay layer is sandwiched between a silty sand layer and a gravelly sand layer. The layer experiences 30 mm settlement in 2 years.

Given:

Where Tv is the time factor and U is the degree of consolidation in %.
If the coefficient of consolidation of the layer is 0.003 cm2/s, the deposit will experience a total of 50 mm settlement in the next ________ years.

A non-homogeneous soil deposit consists of a silt layer sandwiched between a fine-sand layer at top and a clay layer below. Permeability of the silt layer is 10 times the permeability of the clay layer and one-tenth of the permeability of the sand layer. Thickness of the silt layer is 2 times the thickness of the sand layer and two-third of the thickness of the clay layer. The ratio of equivalent horizontal and equivalent vertical permeability of the deposit is ________.

If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is

A 588 cm3 volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of solids, G is 2.67. Assuming density of water as 1 gm/cm3, the void ratio is ______.

A 4 m thick layer of normally consolidated clay has an average void ratio of 1.30. Its compression index is 0.6 and coefficient of consolidation is 1 m2/yr. If the increase in vertical pressure due to foundation load on the clay layer is equal to the existing effective overburden pressure, the change in the thickness of the clay layer is_______mm.

Stress path equation for tri-axial test upon application of deviatoric stress is, . The respective values of cohesion, c (in kPa) and angle of internal friction, $\phi$ are :

For a saturated cohesive soil, a triaxial test yields the angle of internal friction (φ) as zero. The conducted test is

A given cohesionless soil has emax = 0.85 and emin = 0.50. In the field, the soil is compacted to a mass density of 1800 kg/m3 at a water content of 8%. Take the mass density of water as 1000 kg/m3 and Gs as 2.7. The relative density (in %) of the soil is

The following data are given for the laboratory sample.

If thickness of the clay specimen is 25 mm, the value of coefficient of volume compressibility is ___________ ×10-4 m2/kN

The flow net constructed for the dam is shown in the figure below. Taking the coefficient of permeability as 3.8×10−6 m/s, the quantity of flow (in cm3/s) under the dam per meter of dam is ______________

As per Indian Standard Soil Classification System (IS: 1498 - 1970), an expression for A-line is

The clay mineral primarily governing the swelling behavior of Black Cotton soil is

The contact pressure for a rigid footing resting on clay at the centre and the edges are respectively

A certain soil has the following properties: Gs = 2.71, n = 40% and w = 20%. The degree of saturation of the soil (rounded off to the nearest percent) is __________

Water is flowing at a steady rate through a homogeneous and saturated horizontal soil strip of 10 m length. The strip is being subjected to a constant water head (H) of 5 m at the beginning and 1 m at the end. If the governing equation of flow in the soil strip is $\frac{{d}^{2}H}{d{x}^{2}}=0$ (where x is the distance along the soil strip), the value of H (in m) at the middle of the strip is ___________

Following statementsare made on compacted soils, wherein DS stands forthe soils compacted on dry side of optimum moisture content and WS stands for thesoils compacted on wet side of optimum moisture content. Identify the incorrect statement.

Laplace equation for water flow in soils is given below.

$\frac{{\mathrm{\partial }}^{2}H}{\mathrm{\partial }{x}^{2}}+\frac{{\mathrm{\partial }}^{2}H}{\mathrm{\partial }{y}^{2}}+\frac{{\mathrm{\partial }}^{2}H}{\mathrm{\partial }{z}^{2}}=0$

Head H does not vary in y and z directions.
Boundary conditions are: at x = 0, H = 5;and $\frac{dH}{dx}=-1$

What is the value of H at x = 1.2? __________

The soil profile below a lake with water level at elevation = 0m and lake bottom at elevation = -10m is shown in the figure, where k is the permeability coefficient. A piezometer (stand pipe) installed in the sand layer shows a reading of +10 m elevation. Assume that thepiezometric headis uniform in the sand layer. The quantity of water (in m3/s) flowing into the lake from the sand layer through the silt layer per unit area of the lake bed is:

The effective stress friction angle of a saturated, cohesionless soil is 38$°$. The ratio of shear stress to normal effective stress on the failure plane is

Two series of compaction tests were performed in the laboratory on an inorganic clayey soil employing two different levels of compaction energy per unit volume of soil. With regard to the above tests, the following two statements are made.

I  The optimum moisture content is expected to be more for the tests with higher energy.
II The maximum dry density is expected to be more for the tests with higher energy.

The CORRECT option evaluating the above statements is

As per the Indian Standard soil classification system, a sample of silty clay with liquid limit of 40% and plasticity index of 28% is classified as

Two soil specimens with identical geometric dimensions were subjected to falling head permeability tests in the laboratory under identical conditions. The fall of water head was measured after an identical time interval. The ratio of initial to final water heads for the test involving the first specimen was 1.25. If the coefficient of permeability of the second specimen is 5-times that of the first, the ratio of initial to final water heads in the test involving the second specimen is

A layer of normally consolidated, saturated silty clay of 1 m thickness is subjected to one dimensional consolidation under a pressure increment of 20 kPa. The properties of the soil are: specific gravity = 2.7, natural moisture content = 45%, compression index = 0.45, and recompression index = 0.05. The initial average effective stress within the layer is 100 kPa. Assuming Terzaghi’s theory to be applicable, the primary consolidation settlement (rounded off to the nearest mm) is

Steady state seepage is taking place through a soil element at Q, 2 m below the ground surface immediately downstream of the toe of an earthen dam as shown in the sketch. The water level in a piezometer installed at P, 500 mm above Q, is at the ground surface. The water level in a piezometer installed at R, 500 mm below Q, is 100 mm above the ground surface. The bulk saturated unit weight of the soil is 18 kN/m3 and the unit weight of water is 9.81 kN/m3. The vertical effective stress (in kPa) at Q is

The flow net around a sheet pile wall is shown in the sketch. The properties of the soil are: permeability coefficient = 0.09 m/day (isotropic), specific gravity = 2.70 and void ratio = 0.85. The sheet pile wall and the bottom of the soil are impermeable.

The seepage loss (in m3 per day per unit length of the wall) of water is

The flow net around a sheet pile wall is shown in the sketch. The properties of the soil are: permeability coefficient = 0.09 m/day (isotropic), specific gravity = 2.70 and void ratio = 0.85. The sheet pile wall and the bottom of the soil are impermeable.

The factor of safety against the occurrence of piping failure is

The results for sieve analysis carried out for three types of sand P,Q and R, are gives in the adjoining figure. If the fineness modulus values of the three sands are given as FMP,FMQ and FMR, it can be stated that

For a saturated sand deposit, the void ratio and the specific gravity of solids are 0.70 and 2.67 respectively. The critical (upward) hydraulic gradient for the deposit would be

For a sample of dry, cohesionless soil with friction angle $\phi$, the failure plane will be inclined tothe major principal plane by an angle equal to

Two geometrically identical isolated footings, X (linear elastic) and Y (rigid), are loaded identically (shown alongside). The soil reactions will

A soil is composed of solid spherical grains of identical specific gravity and diameter between 0.075mm and 0.0075mm. if the terminal velocity of the largest particle falling through water without flocculation is 0.5 mm/s, that for the smallest particle would be

Identical surcharge are placed at ground surface at sites X and Y, with soil conditions shown alongside and water table at ground surface. The silty clay layers at X and Y are identical. The thin sand layer at Y is continuous and free-draining with a very larger discharge capacity. If primary consolidation at X is estimated to complete in 36 months, what would be the corresponding time for completion of primary consolidation at Y?

A field vane testing instrument(show alongside) was inserted completely into a deposit of soft, saturated silty clay with the vane rod vertical such that the top of the blades were 500 mm below the ground surface. Upon application of a rapidly increasing torque about the vane rod, the soil was found to fail when the torque reached 4.6 Nm. Assuming mobilization of undrained shear strength on All failure surfaces to be uniform and the resistance mobilized on the surface of the vane rod to be negligible , what would be the peak undrained shear strength(rounded off to the nearest interger value of kPa) of the soil?

A sand layer found at sea floor under 20 m water depth is characterized with relative density=40%, maximum void ratio=1.0, minimum void ratio =0.5 and specific gravity of soil solids =2.67. Assume the specific gravity of sea water to be 1.03 and the unit weight of fresh water to be 9.81 kN/m3

what would be the effective stress(rounded off to the nearest integer value of kpa) at 30 m depth into the sand layer?

A sand layer found at sea floor under 20 m water depth is characterized with relative density=40%, maximum void ratio=1.0, minimum void ratio =0.5 and specific gravity of soil solids =2.67. Assume the specific gravity of sea water to be 1.03 and the unit weight of fresh water to be 9.81 kN/m3

what would be the change in the effective stress (rounded off to the nearest integer value of kpa) at 30 m depth into the sand layer if the sea water level permanently rises by 2 m?

In a compaction test, G, w, S and e represent the specific gravity, water content, degree of saturation and void ratio of the soil sample, respectively. If ${\gamma }_{w}$ represents the unit weight of water and ${\gamma }_{d}$ represents the dry unit weight of the soil, the equation for zero air voids line is

A fine grained soil has liquid limit of 60 and plastic limit of 20. As per the plasticity chart, according to IS classification, the soil is represented by the letter symbols

Quick sand condition occurs when

The e-log p curve shown in the figure is representative of

An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having coefficient of permeability of 10-2 m / s. The barrel stands on a saturated bed of gravel. The time required for the water level in the barrel to drop by 0.75 m is

Deposit with flocculated structure is formed when

The laboratory test results of a soil sample are given below:

Percentage finer than 4.75 mm = 60
Percentage finer than 0.075 mm = 30
Liquid Limit = 35%
Plastic Limit = 27%

The soil classification is

A saturated undisturbed sample from a clay strata has moisture content of 22.22% and specific weight of 2.7. Assuming $\gamma$w = 10 kN/m3, the void ratio and the saturated unit weight of the clay, respectively are

Using the properties of the clay layer derived from the above question, the consolidation settlement of the same clay layer under a square footing (neglecting its self weight) with additional data shown in the figure below (assume the stress distribution as 1H:2V from the edge of the footing and $\gamma$w = 10 kN/m3) is

Group symbols assigned to silty sand and clayey sand are respectively

Compaction by vibratory roller is the best method of compaction in case of

The liquid limit (LL), plastic limit (PL) and shrinkage limit (SL) of a cohesive soil satisfy the relation

A direct shear test was conducted on a cohesion-less soil (c=0) specimen under a normal stress of 200 kN/m2. The specimen failed at a shear stress of 100 kN/m2. The angle of internal friction of the soil (degrees) is

A saturated clay stratum draining both at the top and bottom undergoes 50 percent consolidation in 16 years under an applied load. If an additional drainage layer were present at the middle of the clay stratum, 50 percent consolidation would occur in

A weir on a permeable foundation with downstream sheet pile is shown in the figure below. The exit gradient as per Khosla’s method is

Water emerges from an ogee spillway with velocity = 13.72 m/s and depth = 0.3 m at its toe. The tail water depth required to form a hydraulic jump at the toe is