Assignment 5-Permeability

ASSIGNMENT 5

1) The following data were recorded in a constant head permeability test: Internal diameter of permeameter = 7.5 cm head lost over a sample length of 18 cm = 24.7 cm Quantity of water collected in 60 Seconds = 626 ml porosity of soil sample = 44% Calculate the coefficient of hydraulic conductivity of soil. Also, determine the discharge velocity and the seepage velocity during the test. Ans: 0.537 cm/s 2) A soil sample 20 sq. cm in cross-sectional area and 10 cm long is tested for permeability in a variable head permeameter. The stand pipe has a cross-sectional area of 1 sq.cm and the head drops from 30 cm to 10 cm in 6 minutes and 20 seconds. Find the permeability of soil. Ans: 1.44x10-3 cm/s

3) A horizontal stratified soil deposit consists of three layers each uniform in itself. The permeabilities of layers are 8 x10-4, 50 x10-4 and 15x10-4 cm/s and their thicknesses are 6, 3 and 12 m, respectively. Find the effective average permeability of the deposit in horizontal and vertical directions. Ans: 13.04x10-4 cm/s 4) (A) In an experiment setup as shown in figure, flow is taking place under a constant head through the soils 1 and 2, of different hydraulic properties

(a) Determine the hydraulic head and piezometric heads at the point A. Ans: 0.95 m (b) If the 40% of the excess hydrostatic pressure is lost in flowing through soil A, then what is the hydraulic head and piezometric head at point B? Ans: 0.49 m (c) If the permeability of soil 1 is 40 mm/s, what quantity of water is flowing through unit plan area of soil per second? Ans: 2.13x10-4 m3/s (d) What is the coefficient of permeability of soil B? Ans: 2.22x10-4 m/s (B) If the void ratios and specific gravity of soil 1 and 2 are as given below, then Soil1: e = 0.55 G = 2.65

Soil2: e = 0.65 G = 2.7 Determine: (i) The discharge velocity and seepage velocity through each soil, and Ans: 2.13x10-4 m/s and 6.0x10-4 m/sec (ii) the hydraulic head at which instability occurs. Ans: 0.4 to 0.43m 5. If the 80 % of the excess hydrostatic pressure is lost in flowing through the soil B which has a coefficient of permeability of 0.01 cm/sec, determine the discharge velocity and seepage velocity through each soil. Void ratio of soil A and B are 0.3 and 0.4, respectively.

60cm

Question No. 5

Soil A

50cm

Soil B

40cm

1.5 m

Soil 1

1.5 m

Soil 2

1.5 m

Soil A

Soil B

Question No. 6

6. The two soils, 1 and 2 are arranged in the manner shown in the above figure. Determine the quantity of flow in each case. Assume, k1 = 1 cm/sec, k2 = 0.2 cm/sec. 7. A laboratory constant-head permeability test was conducted on a silty specimen of void ratio 0.45. The cylindrical specimen had a diameter of 7.3 cm and a height of 16.8 cm. The head during the test was 75 cm. After 1 minute of testing at the room temperature of 20 oC, a total 775.6 gm of water was collected. Compute the coefficient of permeability in meter per sec. If the void ratio changes to 0.38, what would be the change in permeability? Ans. 6.92x10-4 m/s & 4.41x10-4 m/s

8. Calculate the coefficient of permeability of a soil sample, 6 cm. in height and 50 cm 2 in cross sectional area, if a quantity of water equal to 450 ml passed down in 10 minutes under an effective constant head of 40 cm. On oven drying, the test specimen weighs 495 g. Taking the specific gravity of soil solids as 2.65, calculate the seepage velocity of water during the test. Ans. 3.98 mm/s. 10. A 3 m thick soil stratum has co-efficient of permeability of 3x10 -7 m/sec. A separate test gave porosity 40% and bulk unit weight 21 kN/m 3 at a moisture content of 31%. Determine the head at which upward seepage will cause quick sand condition. What is the flow required to maintain critical condition? Ans. 3.1m & 3.1x10-7 m3/sec/m2