PERMEABILITY TEST

INDUNIL J.M.G.

PG/E/GT/2016/01

CE642

27.02.2016

THEORY

Derivation of equations for constant head method and falling head method.

(a) Constant Head Method.

Constant head (h1-h2) = hLength of soil sample = lVolume of water flowed in time t = VArea of soil sample = AFlow of water = qVelocity of fluid flow = vCoefficient of permeability = kHydraulic gradient = i

From Darcy’s law,v α iv = kiv = k (h/l) --------- 1

But,V/t = q

And,q = Avq = A k (h/l)q = (Ak/l) h --------- 2

Eq 2 gives y = m x combination of parameters. So m is the gradient of q vs h graph,m = Ak/lk = lm/ A --------- 3

(b) Falling Head Method.Diameter of stand pipe = aVariable head = HArea of soil sample = ALength of soil sample = lWater flow through sample = qVelocity of water through stand pipe, v = - dh/dtVelocity of water through stand pipe, v = q/ aSo,

-dh/dt = q/ a ----------- 4But head at h,

q = Avq = A k h/l ----------- 5

From Eq 4 and Eq 5,-dh/ dt = A k h/ (l . a)

-(1/h) dh = A.k / (l . a) dtBy integrating,

−∫H0

H1 1hdh=∫

0

T Akladt

ln( H0/H1) = (Ak/ la) T

ln H1 = - (Ak/ la) T + ln H0 ---------- 6

Eq 6 is in a order of y = mx + c,

So m is the gradient of ln (H1) vs T graph,

m = - (Ak/ la)

k = - mal/ A ---------- 7

SPECIMEN CALCULATION

A) Constant Head Method.Considering 4th set of reading from Table 1,Volume of collected water, V = 216.0 mlTime taken to collect 216 ml of volume, t = 11.21 sFlow rate, q = V/ t

= 216.0 / 11.21= 19.27 ml/s

h1 = 84.4 cmh2 = 54.8 cmCorresponding head difference = h1 – h2

= 84.4 – 54.8= 29.6 cm

B) Falling Head Method.Considering 4th set of reading from Table 2,Time taken to reach head reading 70cm = 50.15sHeight of the datum of scale above the water level = 108.4 cmPressure head = 108.4 + 70

= 178.4 cm Ln(H) = ln(178.4)

= 5.18

TABULATION

Table 03: Constant head method q vs h

q/ (ml/s) h/ (cm)

22.76 32.5

21.65 30.9

20.45 28.9

19.27 29.6

17.79 25.9

Table 04: Falling head method ln(H1) vs T

ln(H1) T/ (s)

5.34 0.00

5.29 16.16

5.24 33.04

5.18 50.15

5.13 68.24

5.07 86.73

5.00 106.04

4.93 125.93

CALCULATION

(a) Constant Head Method.From Graph 01,Gradient of the graph, m =

= xx.xx cm/ (ml/s)From Eq 3,

k = l/ (Am)k = 140.9 x 10 -3 .

(49.43 x 10-4 x xx x 10-2 x 10-6)= xx.xx x 10 -x m/s

Total volume of the sample, V = 217.4x10-3 x 49.43x10-4

= 1.075x10-3 m3

VS = MS/ GS.ρw

= 1.6695/ (2.7x1000)= 0. 618 x 10-3m3

Void ratio, e = (V-Vs)/ Vs = (1.075-0.618)/ 0.618= 0.74

(b) Falling Head Method. From Graph 02,Gradient of the graph =

=

From Eq 7,k = -maL/A

= -xx x 216.31x10-6 x 121.15x10-3 Π x (102.45x10-3)2/ 4= xx m/s

RESULTS

Table 05: Coefficient of permeability and void ratios

Parameter UnitConstant Head

MethodFalling Head

MethodCoefficient of permeability

m/s

Void ratio -