The document Laboratory Measurement of Permeability Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Soil Mechanics.

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**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**.

Permeability **k **is obtained from:

**Falling Head Flow**

Falling head permeameter is recommended for fine-grained soils.

Total head **h** in standpipe of area **a** is allowed to fall. Hydraulic gradient varies with time. Heads **h _{1}** and

------------------------(1)

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

------------------------(2)

Equating **(1) **and **(2) **,

Integrating between the limits,

**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**

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 **h _{1}** and

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

Area of flow,

From Darcy's Law,

Arranging and integrating,

**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.

For a **cylindrical surface** at radius **r**,

Integrating,

**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 **k _{V}**and

Consider a stratified soil having horizontal layers of thickness **H _{1}**,

**For vertical flow**

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

q = q_{1 }=q_{2}

Let **i **be the equivalent hydraulic gradient over the total thickness **H **and let the hydraulic gradients in the layers be **i _{1}, i_{2}, i_{3}, **etc. respectively.

............... where** k _{V}** = Average vertical permeability

The total head drop ** h** across the layers is

**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.

The total flow is

Considering unit width normal to the cross-section plane,

**Worked Examples**

**Example 1: ** Determine the following:

(a) Equivalent coefficient of vertical permeability of the three layers

(b) The rate of flow per m^{2} of plan area

(c) The total head loss in the three layers

**Solution:**

(a) = 1.33 x 10^{-3 }cm/s

(b) Considering an area A = 1 m^{2} =1 x 10^{4 }cm^{2}

q = k.i.A = = 7 x 10^{-4} x 0.25/2 x (1x10^{4}) = 0.875 cm^{3}/s per m^{2} of plan area

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

where = total head loss in three layers

**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:**

r_{1} = 16 m

r_{2} = 34 m

h_{1} = 14.5 - 2.2 - 2.45 = 9.85 m

h_{2}= 14.5 - 2.2 - 1.2 = 11.1 m

k = = 2.82 x 10^{-4 }m/s = 1.41 x 10^{-2} cm/s

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