44C

Sub: Geotechnical Engineering

Topic : Permeablity

MODULE- 44C Permeability & Seepage = 1.

The coefficients permeability of a soil in horizontal and vertical directions are 3.46 and 1.5 m/day respectively. The base length of a concrete dam resting in this soil is 100 m. When the flow net is developed for this soil with 1:25 scale factor in the vertical direction, the reduced base length of the dam will be (A) 2.63 m

(B) 4.00 m

(C) 6.08 m

(D) 5.43 m

3.

Ans:

(

= 4.86

mm/s

= 4.86

cm/s

)

An unit volume of a mass of saturated soil is subjected to horizontal seepage. The saturated unit weight is 22 kN/m3 and the hydraulic gradient is 0.3. The resultant body force on the soil mass is (a) 1.98 kN (b) 6.6 kN (c) 11.49 kN (d) 22.97 kN Ans:

= x.√ .i =3

√

As per scale =

2.

R=√ 100 √

= 2.63

4.

In a falling head permeability test the initial head of 1.0m dropped to 0.35 m in 3 hours, the diameter of the stand pipe being 5 mm. The soil specimen was 200 mm long and of 100 mm diameter. The coefficient of permeability of the soil is: (A) 4.86 ×

cm/s

(B) 4.86 ×

cm/s

(C) 4.86 ×

cm/s

(D) 4.86 ×

cm/s

= 22.2kN

The figure below shows two flow lines for seepage across an interface between two soil media of different co-efficient of permeability. If entrance angle a1=30 , the exit angle a2 will be

(a) 7.50 (c) 66.59 Ans: = =

Ans: .

JH ACADEMY

5.

22

(b) (d)

14.03 75.96

66.

In a constant head permeameter with cross 2 section area of 10 cm , when the flow was taking place under a hydraulic gradient of 0.5, the amount of water collected in 60

1

Sub: Geotechnical Engineering seconds is 600 cc. The permeability of the soil is (a) 0.002 cm/s (b) 0.02 cm/s (c) 0.2 cm/s (d) 2.0 cm/s Ans: a = k .A = k.0.5 6.

10

Topic : Permeablity 8.

k = 2cm/s

Water is flowing through the permeability apparatus as shown in the figure. The coefficient of permeability of the soil is k m/s and the porosity of the soil sample is 0.50.

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) 3.05 (B) 3.80 (C) 4.00 (D) 6.25 Ans : K= k

A) The total head, elevation head and pressure head in metres of water at the point R shown in the figure are (a) 0.8, 0.4, 0.4 (b) 1.2, 0.4, 0.8 (c) 0.4, 0, 0.4 (d) 1.6, 0.4, 1.2 Ans: Hydraulic gradient i= Head on ug to R = 0.8 = 0.8 Elevation head at R=0 Total head = 1.4 – (1.0) = 0.8 Elevation head = 0.4 Presume head = 0.8 – 0.4 = 0.4

(

)

(

)

=

9.

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.

B) What are discharge velocity and seepage velocity through the soil sample? (A) k, 2k (B) 2/3k, 4/3k (C) 2k, k (D) 4/3k, 2/3k Ans: Discharge velocity = ki = k. = k Seepage velocity = = 7.

= 2k

An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having coefficient of permeability of . 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 (A) 58.9 s (B) 75 s (C) 100s (D) 150s Ans: ⁄ t=

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a) The seepage loss (in m3 per day per unit length of the wall) of water is (A) 0.33 (B) 0.38 (C) 0.43 (D) 0.54 Ans : Q = Kh

=0.09

⁄

b) The factor of safety against the occurrence of piping failure is (A) 3.55 (B) 2.93 (C) 2.60 (D) 0.39 Ans :

2

Sub: Geotechnical Engineering

F=

(

)

(

Topic : Permeablity Ans :

)

E = 0.5

⁄ (

seepage

)

c)

⁄

=

d) (

)=(

)

Ans :

14. A flow net is drawn to obtain a) Seepage, coefficient of permeability and uplift pressure. b) Coefficient of permeability, uplift pressure and seepage quantity c) Exit gradient, uplift pressure and seepage quantity. d) Exit gradient, seepage and coefficient of permeability. Ans : ( c)

11. The soil profile below a lake with water level at elevation = 0 m and lake bottom at elevation = -10 m 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 the piezometric head is uniform in the sand layer. The quantity of water (in ) flowing into the lake from the sand layer through the silt layer per unit area of the lake bed is:

=

=

⁄ 13. If during a permeability test on a soil sample with a falling head permeameter, equal time intervals are noted for drop of head from ‘ ’ to ‘ ’ and again from ‘ ’ to ‘ ’. Then which one of the following relations would hold good? a) = b) =

10. The ratio Nf/Nd is known as shape factor, where Nf is the number of flow lines and Nd is the number of equipotential drops. Flow net is always drawn with a constant b/a ratio, where b and a are distances between two consecutive flow lines and equipotential lines, respectively. Assuming that b/a ratio remains the same, the shape factor of a flow net will change if the (A) upstream and downstream heads are interchanged (B) soil in the flow space is changed (C) dimensions of the flow space are changed (D) head difference causing the flow is changed Ans: ( C )

(A) 1.5 x (C) 1.0 x Ans : Q=KiA

velocity

15. A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy’s ‘k’ for upper and lower layers is 1x10-2cm/sec.and the middle layer is 1x 10-1 cm/sec.The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction is a) 10.0 to 1 b) 2.8 to 1 c) 2.0 to 1 d)1 to 10 Ans :

(B) 2.0 x (D) 0.5 x

= 0.04

⁄

=0.5

= 12. A soil has a discharge velocity of 6 m/s and a void ratio of 0.5. its seepage velocity is a) 18 m/s b) 12 m/s c)

6

JH ACADEMY

m/s

d) 3

m/s

16. Due to rise in temperature, the viscosity and unit weight of percolating fluid are reduced to 70% and 90% respectively. Other things being constant, the change in coefficient of permeability will be

3

Sub: Geotechnical Engineering a)

Topic : Permeablity

20.0% b)28.6%

c) 63.0%

18. A flow net constructed to determine the seepage through an earth dam which is homogenous but anisotropic, gave four flow channels and sixteen equipotenital drops. The coefficient of permeability in the horizontal and vertical directions is 4.0 m/s and 1 m/s respectively. If the storage head was 20m, then the seepage per unit length of dam (in /s) would be a) 5 b) 10

d) 77.8%

Ans : k

c) 20

d) 40

Ans : =1.2857

q= √ =0.2857

ie

28.6%

17. Match List –I (Flow type) with List –II (flow characteristics) correct

and

select

the

answer using the codes given

below the lists: List-I A. Transient flow B. Turbulent flow C. Steady-state flow D. Laminar flow List-II A. Seepage flow is a function of time B. Hydraulic gradient varies with square of velocity C. Flow at low velocity D. Governing equation in 2-D is =0 Codes: A B C a) 1 2 4 b) 3 2 1 c) 1 2 3 d) 2 1 4 Ans : ( A )

JH ACADEMY

D 3 4 4 3

h

=√ ⁄ =10 19. Assertion(A): Constant-head permeability test is not used for fine – grained soils. Reason (R): The lesser the permeability of the soil, lesser is the discharge. Codes: a) Both A and R is true and R is the correct explanation of A. b) Both A and R is true but R is not a correct explanation of A. c) A is true but R is false. d) A is false but R is true. Ans : ( A ) 20. Assertion (A): Permeability continues to decrease with the increase in dry density of a compacted soil. Reason (R): Soil particles in water surroundings may be mutually attracted or repulsed. Codes: e) Both A and R is true and R is the correct explanation of A. f) Both A and R is true but R is not a correct explanation of A. g) A is true but R is false. h) A is false but R is true. Ans : (B)

21. The configuration of flow nets depends upon

4

Sub: Geotechnical Engineering a) The permeability of the soil b) The difference in the head between upstream and downstream sides c) The boundary condition of flow d) The amount of seepage that takes place Ans : ( C ) 22. A flow net for an earth dam on impervious foundation consists of a 4 flow channels and 15 equipotential drops. The full reservoir level is 15m above the downstream permeability is 9 m/s and vertical permeability is 1 m/s, the quantity of seepage through the dam will be a) 36ML/S/m b) 25 ML/s/m c) 20 ML/s/m

d) 12 ML/s/m

Ans : q=√

⁄

= 12 ⁄

=12

c) 11.52 d) 34.56

12m ⁄

23. In a two-layer soil system, the top soil and bottom soil are of same thickness but the coefficient of permeability of the top soil is twice that of the bottom soil of coefficient of permeability ‘k’. when horizontal flow occurs, the equivalent coefficient of permeability of the system will be a) 2k b)1.5k c) 1.25k d) 1.2k

/day /day

Ans : q=4 ⁄ ⁄ ⁄

=11.52

25. The following data were obtained when a sample of medium sand was tested in a constant head parameter : Cross-section area of sample: 100 Hydraulic gradient : 10 Discharge collected : 10cc/s The coefficient of permeability of the sand is a) 0.1 m/s b) 0.01m/s c) 1

⁄

=12

Topic : Permeablity

m/s

d) 1

m/s

Ans : 10 = k K=0.01

⁄

⁄

26. A Stratified soil deposit has 3 layers of thickness: =4, =1, =2 units and the corresponding permeabilites of = 2, = 1, = 4 units, respectively. The average permeability perpendicular to the bending planes will be a) 4 b) 2 c)

8

d) 16

Ans :

Ans : = 1.5 k

24. A flow net of a coffer dam foundation has 6 flow channels and 18 equipotenital drops. The head of water lost during seepage is 6m. if the coefficient of permeability of foundation is 4 m/min, then the seepage loss per metre length of dam will be a) 2.16 /day b) 6.48 /day

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27. Match List-I(Soil description ) with List – II( Coefficient of permeability mm/s) and select the correct answer using the codes given below the lists: List-I List-II A. Gravel 1. 1 B. Clay silt admixtures 2. to C. Loess 3. D. Homogeneous clays 4. to Codes:

5

Sub: Geotechnical Engineering A a) b) c) d)

B

C

D

4 1 1 4 4 1 1 4 Ans :

3 3 2 2

2 2 3 3

28. Consider the following statements: 1. Coarse sand is more than a million times permeable than a high plasticity clay. 2. The permeability depends on the nature of soil and not on properties of liquid flowing through soil. 3. If a sample of sand and a sample of clay have the same void ratio .both samples will exhibit the same permeability. 4. Permeability of soil decreases as the effective stress acting on the soil increases. Which of these statements are correct? a) 1 and 2 b) 1 and 3 c) 1 and 4

Topic : Permeablity Ans : , ⁄ ⁄

=

31. A soil mass under seepage has a downward flow of water. Which of the following statements are correct with regard to stresses at any point in the soil mass? 1. Effective stress is decreased by an amount equal to the seepage force 2. Effective stress is increased by an amount equal to the seepage force 3. Total stress will change 4. Total stress will be unaltered Select the correct answer using the codes given below: a)

1 and 3

c) 1 and 4

b) 2 and 3 d) 2 and 4

Ans : ( D )

d) 2 and 3

Ans : (C) 29. In a falling head permeability test on a soil, the time taken for at the head to fall from to is t. the test is repeated with same initial head , the final head is noted in time ⁄ . Which one of the following equations gives the relation between , and ? a) c)

=

⁄

=

b) d)

√

30. A soil deposit has three layers having same thickness each but the permeabilities of the layers are in ratio of 1:2:4 from top to bottom. What is the ratio of average permeability in the horizontal direction to that in the vertical direction? a) 7:2 b) 14:6

JH ACADEMY

c) 1.5

d) 1.5

=√

Ans : ( D )

c) 28:24

32. For a sheet pile wall constructed in a soil having effective size = 0.1mm, the difference of the upstream and downstream water levels is 3m. if the flow net drawn for the problem yields 2 as the ratio of number of flow channels, then what is the discharge in unit of /s/m length of sheet pile wall? a) 3.0 b) 3.0

33.

Consider the following statements: 1. Permeability of a soil decreases as the effective stress acting on the soil increases. 2. The presence of organic matter in the soil increases its permeability. 3. Entrapped air decreases the permeability of a soil.

Which of these statements is/are correct? a)

1 only

c) 2 and 3

b) 1 and 2 d) 1 and 3

d) 49:36

6

Sub: Geotechnical Engineering

Topic : Permeablity

Ans : ( D )

c) 2 and 3 only

d) 2 only

Ans : (A) 34. A homogeneous earth dam is 43m high with 3m as free board and a 30m long horizontal filter at the downstream end. The flow net drawn in the dam section consists of 5 flow channels and 15 potential drops. If the dam is 500m long and the permeability of the material of the dam is uniformly 3 m/s, the total discharge permeating through the body of the dam will be a) 0.0004 /s b) 0.0036 /s c)

0.0039

/s

d) 0.20

/s

Ans : ⁄

q=3

35.

Consider the following statements: 1. Void ratio of the soil. 2. Duration of flow. 3. Equivalent diameter of the soil grains. 4. Shape of the circle. Which of these statements is/are correct? a)

1,2,3 and 4

c) 1, 3, and 4 only

b) 2 and 3 only d) 3 and 4 only

Ans : (C) 36. A soil has a discharge velocity of 5 m/s and a void ratio of 0.50. its seepage velocity will be a) 15 m/s b) 10 m/s c) 20

m/s

d) 30

m/s

Ans : ⁄(

)

= 15

⁄

37. Consider the following statements: 1. The hydraulic head at a point in the soil includes piezometric head as well as datum head 2. Piping in soil occurs when effective pressure becomes equal to zero. 3. Piping in soil occurs when soil is highly porous. Which of these statements is/are correct? a)

1,2 and 3

JH ACADEMY

b) 1 and 2 only

38. Assertion (A): The possibility of piping failure in earth dams is more if black cotton soil is the foundation material. Reason (R): The highly expansive black cotton soils are the most common soils whatever basalt rock is present. Codes: a) Both A and R are true and R is the correct explanation of A b) Both A and R are true but R is not a correct explanation of A c) A is true but R is false d) A is false but R is true

39. Assertion (A): Flow net is dependent on permeability of soil through which flow is taking place. Reason(R): The flow net is useful in finding the discharge. Codes: a) Both A and R are true and R is the correct explanation of A b) Both A and R are true but R is not a correct explanation of A c) A is true but R is false d) A is false but R is true Ans : ( D ) 40. A flow net for seepage under a sheet pile wall has =4, = 8 and the permeabilities of soil in the horizontal and vertical directions are : = 8 m/sec and = 2 m/ sec. if the head loss through the soil is 2m, the quantity of seepage per meter length of the wall will be a) 2 /sec b) 4 /sec c) 8 /sec d) 16 /sec Ans : Q=√ =4

⁄

41. Two observation wells penetrating into a confined aquifer are located 1500m apart

7

Sub: Geotechnical Engineering

Topic : Permeablity

in the direction of flow. H eads of 50m and 25m are indicated at these two observation wells. If the coefficient of permeability for the aquifer is 30m/day and its porosity is 0.25, the time of travel of an inert tracer from one well to another is a) 75 days b) 750d c) 1200d d)3000d Ans : I= ⁄

V = ki=30 Time =

=

= 750days

42. Coefficient of permeability of an underground stratum is 0.001m/s. discharge obtained from a well of area 20 dug into this stratum (with drawdown of 2m) will be a) 2400 lpm b) 2000 lpm c)

1200 lpm

d) 1000 lpm

43. If number of flow channels are 10, number of drops are 6, the total hydraulic head difference is 4m, the length of dam is 50m and the coefficient of permeability is 2 , the total loss of water per day in is a) 576 b) 5760 c) 57600 d) 576000 Ans : ⁄ Q=2 =0.6667

⁄

44. A flow line makes angles and with the normal to the interface of the soils having permeabilities 3 and 1 before and after deflection. According to the law of deflection of flow lines at the interface of the dissimilar soils, the is a) b) c) d)

45. The coefficient of permeability of a soil is 5 cm/sec for a certain pore fluid. If the viscosity of the pore fluid is reduced to half, the co-efficient of permeability will be a) 5 cm/sec

JH ACADEMY

b) 10 c) 2.5 d) 1.25 Ans :

cm/sec cm/sec cm/sec

k if (B) 46. According to Darcy’s law for flow through porous media, the velocity is proportional to a) Effective stress b) Hydraulic gradient c) Cohesion d) Stability number Ans : (B)

47. The soil profile below a lake with water level at elevation =0 m and lake bottom at elevation =-10 m is shown in fig. where k is permeability co-efficient. A piezometer installed in sand layer shows a reading of +10 m elevation. Assume that the piezometric head is uniform in the sand layer. The quantity of water (in ) flowing into the lake from the sand layer through the silt layer per unit area of lake bed is a) 1.5 b) 2.0 c) 1.0 d) 0.5

48. A homogeneous anisotropic earth dam which is 20m high constructed on an impermeable foundation. m/s and m/s. the water level on reservoir side is at 18m from the base of the dam. Downstream side is dry. It is seen that there are 4 flow channels and 18 equi potential drop in a square flow net drawn in the transformed dam section. Estimate the quantity of seepage per unit length. Ans : Q=√ ⁄

8

Sub: Geotechnical Engineering

Topic : Permeablity

49. The equation transformed

can be to

by

substituting a) b) c)

√

d)

√ (D)

50. For an anisotropic soil, permeabilities in and directions are and respectively in a two dimensional flow. The effective permeability for the soil is given by (A)

(B)

(C) (

)

(D) (

)

(D)

JH ACADEMY

9