Permeability in soil – its meaning, formula & Darcy’s law

Permeability in soil refers to the ability of soil to transmit water or other fluids through its pore spaces. It is a crucial property in hydrogeology and civil engineering, as it influences groundwater flow, drainage, and the effectiveness of septic systems.

Permeability is typically measured in terms of hydraulic conductivity, which quantifies the rate at which water can flow through a unit cross-sectional area of soil under a unit hydraulic gradient. Various factors, such as soil texture, compaction, and pore size distribution, affect a soil’s permeability. Sandy soils tend to have higher permeability, while clayey soils have lower permeability.

Permeability in soil - its meaning, formula & Darcy's law
Permeability in soil – its meaning, formula & Darcy’s law


Permeability is a physical property of a porous material that permits the flow or passage of water under saturated or nearly saturated conditions through interconnected voids in soil in which flow may be in the form of laminar flow or turbulent flow, practically flow problems of water in soil mechanics through its interconnecting voids ,in most of case flow is laminar, the quality or state of being permeable characteristics is permeability that is associated with porosity features, soil types, soil texture and its impact property.

The study of permeability is important for the engineering problems of soil that is discussed about the which soil particles will more permeable or less permeable, also discussed the it’s affecting factor, Darcy’s law , method of determining the permeability of soil.

As more water filled the pore space, the air is pushed out, when all pore spaces in the soil are filled with water, the soil becomes saturated which is not able to survived in roots of many types of plants and saturated soil on level ground results in standing water which can cause flooding and may lead to an increased volume of water entering a body of water. It’s is dependent on factors that is predict the relative strength of soil index by such factors like as soil textures, particle size distribution, roughness, shape and degree of interconnect voids.

Permeability meaning

Permeability is a physical properties of porous materials which is commonly measured in terms of the infiltration rate flow through the soil in a given period of time and that is also known as hydraulic conductivity usually expressed as a permeability rate in centimetres per day, centimetres per hour or millimetres per hour as a determine the irrigation rates, to estimate the ground water structure and mostly used to predict how water will flow through soil media in porous medium at different sites

Coefficient of permeability expressed as k in metes per second or in centimetres per second which is play important properties for civil engineering soil permeability classes determined.

Permeability in soil

Permeability in soil as the play an important role in porous media of soil samples to transmit water under saturated or nearly saturated conditions which is play a role according to the some influence factors such as soil texture, particle size distribution, roughness, shape and interconnection of particles, so we can considered the significant impact of soil structure and pore structure role to soils capabilities to transmit water.

Permeability in soil is defined as the property of soil which permits flow of water through interconnected void of soil that is important for engineering property of essential in soil engineering problem such as discribes the settlement of a soil compressible layer, settlement of building,yields of dam,well, controls the hydraulic stability of soil mass, prevent piping used in hydraulic structures.

The permeability in soil also describes how water are consist property to move through the soil, water moves very easily through highly permeable soils such as soils with Sandy taxures have consist large porous space that is very quickly move through the soil due to fact Sandy taxures are high permeability, means high infiltration rates and good drainage, otherwise clays taxures soil have small pore space due to water permits the slowly through the soil means is infiltration rate is slow and poor drainage.

Free water or gravitational water having property to flows through soil under the action of gravity and flow of water depends upon the permeability of the soil and the head ,the most important factor related with permeability in soil is hydraulic gradient.

Important point of influence in permeability in soil

1. Soils is porous materials.

2. Interconnected voids in a soil play a important role to water can flow between it’s.

3. Coarse grained soil having high permeability,such as gravel, Sandy texture etc it’s infiltration rate is also high and drainage property is good

4. Fine grained soil having low permeability,such as clay ,silty texture etc it’s infiltration rate is low and poor drainage property.

5. The more permeable the soil, the greater the seepage and waker the strength.

Factors affecting the permeability

Factors affecting the permeability are as following

1. Shape of particles

2. Size of particles

3. Properties of pore fluid

4. Structural arrangement of particles and stratification

5. Effect of degree of saturation and other foreign matter

6. Effect of adsorbed water

7. Void ratio

Shape of particles-: shape of particles affect the permeability accordance with inversely, permeability is more in rounded particles and less in angular particles due to fact that permeability is inversely proportional to surface area K proportional to 1/ ssa. Where k is permeability and ssa is specific surface area.

Size of the particles-: size of particles affect the permeability as the square of the grain size ,soil consist the different many sizes which is depend as according to K is proportional to square of the grain size.

Properties of pore fluid-: permeability is affected by the properties of pore fluid in terms of permeability is directly proportional to the unit weight of water and inversely proportional to its viscosity due to the unit weight of water does not change much with the change in temperature it’s expressed as K1/ K2 =N2.Yw1/N1.Yw2
Where K1 and K2 relatively permeability and N1,N2 viscosity and Yw1, Yw2 is unit weight of water

Temperatur- Temperature increases according to permeability increases due to temperature is directly proportional to permeability.

Structural arrangement of particles and stratification-: the structural arrangement of particles and stratification is changed according to presence of void in it’s interconnected space, this arrangement of particles may vary with same with presence of voids, voids is directly proportional to permeability,so soil particles arrangement vary accordance to directly in permeability.

Degree of saturation and other foreign matter-: The permeability is greatly reduced within air is entrapped in the voids thus reducing the degree of saturation, dissolved air in the pore water greatly affect the changing of permeability, and other foreign matter also to tendency the decreasing of permeability.

Effect of adsorbed water-: the adsorbed water consist the surrounding fine particles which is not able to free move and reduce the effective pore spaces and accordance to available pore space highly effect the changing of permeability.

Darcy’s permeability

Darcy’s law of permeability demonstrated experimental for laminar flow conditions in a saturated soil, according to this law the rate of flow or the discharge per unit time is proportional to the hydraulic gradient.

1. Darcy’s law is linear dependency

2. Linear dependency of Darcys law between the velocity of flow v and hydraulic gradient is valid only for laminar flow of soil mass.

3. Velocity of flow is less than a lower critical velocity.

4. Darcy’s law is valid for critical Reynolds number may vary from 0.1 to 0.75 .

q= k i A

V= q/A

So, V= k i
Where,k= coefficient of permeability

I= hydraulic gradient, V= discharge velocity

A= cross sectional area of soil mass

q= discharge per unit time

According to Darcy’s law of permeability for flow through the porous material, the flow consisting per unit time is directly proportional to the head causing flow and the area of cross section of the soil sample and inversely proportional to the length of the soil sample.

q= kiA

q/A= ki= v

It means velocity is proportional to the hydraulic gradient .

Hydraulic gradient

Hydraulic gradient is defined as the loss of head per unit of flow through the soil is called hydraulic gradient, it is also react at driving force that causes groundwater to move in the direction of maximum decreasing total head , regarding this also discussed about the ” what is hydraulic gradient” it means in other word say that hydraulic gradient is the slope of the water table that is consist the change in water level per unit of distance along the direction of maximum head decreases.

Hydraulic gradient formula in soil

Hydraulic gradient is the significant factor in Darcy’s permeability law for porous soil media having property of laminar flow, hydraulic gradient formula in soil mechanics is difference between the head difference divided by Length means loss of head per unit of flow calculate the hydraulic gradient and also it’s formula is consist in Darcy’s permeability law,it is generally presented in consistent units.

Hydraulic gradient (i )= Head difference/ Length

i = H2-H1/L

Seepage velocity and discharge velocity

Soil mechanics in porous media discussed about the Darcy’s law of permeability which is related to discharge velocity and seepage velocity ( real velocity of water) lead to significant role in predicting the soils ability to transmit the water, discharge velocity is Darcy’s law of discharge velocity and seepage velocity is considered the original velocity of water, however both velocity is related to porosity which is decided the dependency and velocity determination of water transmission the soils porous medium.

What is seepage velocity?

Regarding this,” what is seepage velocity?”, the seepage velocity is defined as the rate of discharge of water per unit of cross sectional area A of soil that is take place through voids of porous media,that velocity of flow through called seepage velocity and also known as interstitial velocity which consists the higher velocity than discharge velocity.

q = A.V= Av. Vs

Vs = V. A / Av

V/ Vs = Vv / V = n

Seepage velocity Vs= V/ n = k i /n

Where, V = discharge velocity

n= porosity

k= permeability coefficient

i = hydraulic gradient

Seepage velocity is the real velocity of water through the soil and consist the greatly significant in soil samples due to fact that that is based upon the void space of soil samples and also it is known as the interstitial velocity.

Discharge velocity

Discharge velocity is defined as the volume of water flowing in unit time across the the cross sectional perpendicular to the Direction of flow which is lesser significant than the seepage velocity and also known as the Darcy’s discharge velocity.

Discharge velocity is a Darcy’s discharge velocity which is based upon the gross cross sectional area of the porous soil and it’s velocity is lesser than the seepage velocity.

Relation between seepage velocity and discharge velocity

Relation between seepage velocity and discharge velocity is consistent relation in which the discharge velocity is related to Darcy’s permeability of law in soil porous media and seepage velocity is significantly used in soil ability as flow of original velocity of water that is significantly consist the higher velocity than discharge velocity and depend upon the presence of void in soil , otherside discharge velocity is depend to the perpendicular direction of flow.

Seepage velocity = e+1 /e . Discharge velocity

Vs= e+1/e . V

Where e= void ratio

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Determination of permeability

Permeability of soil can be determined by mostly routine laboratory test, water pressure test and field pumping test that is consideration in situ test in standpipe piezometers which is involves different method procedure and depending upon the soil type ,it’s texture and especially in carried out this test relatively permeable soils.

The determination of coefficient of permeability is the important characteristics of permeability in fact that having this characteristic is the relative strength of index of soil which is decided the soil type, soil textures and predict the use of soil according to porous media having consolidation and impact conditions.

Determination of permeability of the soil is significant implement of the test to estimate ground water flow, to calculate seepage through dams and settlement of structure and also significant in environmental conditions, in the current methods of determining the permeability carried out in situ and requires various test mostly in routine laboratory test which is considered the constant permeability test and laboratory permeability test, water pressure test and good knowledge of the site ground conditions provides a more reliable result , some sites may be consider the variation in permeability, Determination of permeability is considered the laboratory method, indirect method and field method.

1. Laboratory method
( a) Constant head permeability test

( b) Falling head permeability test

( c) Capillarity

2. Indirect method

( a) Allen hosen equation

( b) Consolidation equation

( c) Terzaghis equation

3. Field method

( a) Unconfined flow Pumping test

( b) Confined flow pumping test

Determination of permeability in laboratory

Determination of permeability in laboratory test is mostly used and significant impact to settlement of structure, control the earthen dams, maintain the well established , the routine laboratory test is used in current time which is consist the two types of test constant head permeability test and falling variable test.

Laboratory test measures the coarse grained soil media and fine grained soil media that is depend upon the soil texture, types of soil , permeable ability of soil such as gravel and sand is highly permeable and it’s interconnected void space is more which is determined by constant head permeability test otherside fine grained soil such as silts,clays is less permeable and it’s interconnected void space is less which is determined by falling variable head permeability test.

What is constant head permeability test

Regarding this, “what is constant head permeability test?”, this test is a part of routine laboratory test which is mostly used for coarse grained soil for obtained the substantial discharge during test in small time that is mostly used in current time which is significantly allowed to flow through medium under constant head to find its permeability.

In case of constant head permeability test that is viable and economical alternatives to measure the permeability of soil media and coefficient of permeability protects in yeilds of water bearing, settlement of structure and stability of earthen dams, this type of test is a controlled field in which a well is maintained controll at a constant level.

Discharge q = V/ t

Darcy’s law q= k i A

Both comprising

q = kiA = V / t ( V= Q/A)

k= V/ tiA

= V/ t(H1-H2/L).A

k = V.L/ t(H1-H2).A

Falling variable head permeability test

Falling variable head method is a laboratory used method which is known as types of routine laboratory test that is mostly used in fine grained soil consisting the stand pipe of known area is inserted into the soil medium and water is allowed to flow through in order to noted the permeability of soil medium heights in a fixed time interval.

Falling variable head test is more suitable for small grained soils with intermediate and having low permeability soil particles such as silts ,clays within applying an undisturbed sample which is consist the high dispersion, minimum no of repitition is allowed for this test, this test is allowed permeability in range of 1×10 ka power -5 to 1x 10 ka power -9.

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