Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Soil Mechanics

Civil Engineering (CE) : Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

The document Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Soil Mechanics.
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)

Constant Head Flow
Constant head permeameter is recommended for coarse-grained soils only since for such soils, flow rate is measurable with adequate precision. As water flows through a sample of cross-section area A, steady total head drop h is measured across length L.  

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Permeability is obtained from: 
Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Falling Head Flow
Falling head permeameter is recommended for fine-grained soils. 

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

 

Total head h in standpipe of area a is allowed to fall. Hydraulic gradient varies with time. Heads h1 and h2 are measured at times t1 and t2. At any time t, flow through the soil sample of cross-sectional area A is

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev    ------------------------(1)                  

Flow in unit time through the standpipe of cross-sectional area a is

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev ------------------------(2)   

Equating (1) and (2) ,

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev   
Integrating between the limits, 

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Field Tests for Permeability

 

Field or in-situ measurement of permeability avoids the difficulties involved in obtaining and setting up undisturbed samples in a permeameter. It also provides information about bulk permeability, rather than merely the permeability of a small sample.

A field permeability test consists of pumping out water from a main well and observing the resulting drawdown surface of the original horizontal water table from at least two observation wells. When a steady state of flow is reached, the flow quantity and the levels in the observation wells are noted.

Two important field tests for determining permeability are: Unconfined flow pumping test, and confined flow pumping tes

Unconfined Flow Pumping Test

 

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

In this test, the pumping causes a drawdown in an unconfined (i.e. open surface) soil stratum, and generates a radial flow of water towards the pumping well. The steady-state heads h1 and h2 in observation wells at radii r1 and r2 are monitored till the flow rate becomes steady.

The rate of radial flow through any cylindrical surface around the pumping well is equal to the amount of water pumped out. Consider such a surface having radius r, thickness dr and height h. The hydraulic gradient is

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Area of flow, Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

From Darcy's Law,

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev 
Arranging and integrating,

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev
Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Confined Flow Pumping Test
Artesian conditions can exist in a aquifer of thickness D confined both above and below by impermeable strata. In this, the drawdown water table is above the upper surface of the aquifer. 

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

For a cylindrical surface at radius r,

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev
Integrating,Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev
Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev
Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev 

Permeability of Stratified Deposits

When a soil deposit consists of a number of horizontal layers having different permeabilities, the average value of permeability can be obtained separately for both vertical flow and horizontal flow, as kVand kH respectively.

Consider a stratified soil having horizontal layers of thickness H1H2H3, etc. with coefficients of permeability k1k2k3, etc.

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

 

For vertical flow
The flow rate q through each layer per unit area is the same.

 

q = q=q2

Let be the equivalent hydraulic gradient over the total thickness and let the hydraulic gradients in the layers be i1, i2, i3etc. respectively.

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev ............... where kV = Average vertical permeability

 

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

The total head drop h across the layers is

 

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

 

Horizontal flow
When the flow is horizontal, the hydraulic gradient is the same in each layer, but the quantity of flow is different in each layer.

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

The total flow is

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Considering unit width normal to the cross-section plane,

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

 

 

Worked Examples

Example 1:  Determine the following:
(a) Equivalent coefficient of vertical permeability of the three layers
(b) The rate of flow per m2 of plan area
(c) The total head loss in the three layers

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Solution: 

(a)  Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev = 1.33 x 10-3 cm/s

(b) Considering an area A = 1 m2 =1 x 10cm2

q = k.i.A =  Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev = 7 x 10-4 x 0.25/2 x (1x104) = 0.875 cm3/s per m2 of plan area

(c) For continuity of flow, velocity is the same.

  Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev  where Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev = total head loss in three layers

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Example 2: For a field pumping test, a well was sunk through a horizontal stratum of sand 14.5 thick and underlain by a clay stratum.Two observation wells were sunk at horizontal distances of 16 m and 34 m respectively from the pumping well.The initial position of the water table was 2.2 m below ground level.

At a steady-state pumping rate of 1850 litres/min, the drawdowns in the observation wells were found to be 2.45 m and 1.20 m respectively. Calculate the coefficient of permeability of the sand.

Solution:

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

 r1 = 16 m
 r2 = 34 m
 h1 = 14.5 - 2.2 - 2.45 = 9.85 m
 h2= 14.5 - 2.2 - 1.2 = 11.1 m

   k =  Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev   = 2.82 x 10-4 m/s  = 1.41 x 10-2 cm/s 

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

,

Objective type Questions

,

shortcuts and tricks

,

pdf

,

Previous Year Questions with Solutions

,

MCQs

,

Sample Paper

,

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

,

ppt

,

Viva Questions

,

study material

,

Exam

,

Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev

,

past year papers

,

mock tests for examination

,

Semester Notes

,

Free

,

Important questions

,

practice quizzes

,

Summary

,

Extra Questions

,

video lectures

;