Category Archives: Soil Mechanics

Soil Mechanics

Seepage of soil and Flownet.

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Voids in a soil mass give rise to permeability and when a soil is permeable, water can seep through. This phenomenon of water flowing through the soil is called seepage.

 

  • Seepage pressure

Water exerts a pressure on the soil through which it percolates. This pressure is known as seepage pressure. It is produced due to the resistance or frictional drag of water flowing through the soil and it acts in the direction of flow.

If ‘h’ is the hydraulic head or head lost which causes the water to flow through a soil mass of thickness ‘L’, then seepage pressure (ps) developed is given by –

ps = 𝛾wh   [𝛾w = Sp.weight of water]

ps = 𝛾w.(h/L).L

ps = 𝛾w.i.L   [i = hydraulic gradient]

ps = iL 𝛾w

.. Total seepage force (Fs) = ps.A   [X-sec area of soil over which seepage pressure acts]

= iL𝛾wA

The above force is uniformly distributed throughout the volume of the soil mass.

.. Seepage force pr unit volume =  = i𝛾w

Depending upon the direction of flow, the seepage may increase or decrease the vertical effective pressure of soil.

If flow occurs in the downward direction, the effective pressure is increased and if it occurs upwards, the effective pressure is decreased.

.. effective pressure (σ’) in a soil mass subjected to seepage pressure is given by –    σ’ = 𝛾sub.L±ps   [𝛾sub = Submerged unit wt. of soil mass]

 

[+ve sign for seepage in downward direction & -ve for seepage in upward direction]

 

  • Importance of seepage Analysis

The seepage pressure is responsible for the phenomenon known as quick sand and is of vital importance in the stability analysis of earth pressure subjected to the action of seepage.

 

  • Assumption in seepage flow analysis
  1. The soil is fully saturated.
  2. The soil particles and water are incompressible.
  • The flow is laminar and Darcy’s law is valid.
  1. The soil layer is pervious.
  2. The quantity of water entering into the soil element is same as the quantity of leaving water.

 

  • Quick sand condition

When water flows in an upward direction through the soil, effective pressure = = 𝛾sub.L- ps

If ‘ps’ equals the pressure due to submerged weight of soil, the effective pressure reduces to zero. In such a case cohesion less soil loses all its shear strength and bearing capacity and the soil particles tend to be lifted up along with the flowing water. This phenomenon is termed as quick sand condition or quick condition or boiling condition or quick sand.

It may be noted that quick sand is not a type of sand but a flow condition occurring within cohesion less soil when its effective pressure is reduced to zero due to upward seepage pressure.

Thus during quick condition –

Ps = 𝛾sub.L

Or, i.L.𝛾w = 𝛾sub.L

Or, i = ic = 𝛾sub/𝛾w = (G-1)/(1+e)

 

The hydraulic gradient at which quick sand occurs is called the critical hydraulic gradient.

 

  • Flow net

The network framed by the two sets of curves like flow lines and equipotential line is called flow net.

The path which a particle of water follows in its course of seepage through a saturated soil mass is called flow line.

Every strip between two neighboring flow lines is called flow channel.

 

Along each flow line, there will be different head of water. A line connecting all points of equal head is called equi-potential line.

Every section of a flow channel between two successive equipotential lines is called field.

 

  • Properties of flow net
  1. Flow lines and equipotential lines meet at right angles.
  2. Flow lines never cross each other.
  • Equipotential lines never cross each other.
  1. The fields are almost square.
  2. Same quantity of water flows through each channel.
  3. Same potential drop occurs between the successive equip-potential lines.
  • Smaller is the field, greater will be the hydraulic gradient.
  • Flow lines and equi-potential lines are smooth curves.

 

  • Application of flow net

Flow net can be utilized for the following purposes –

  1. Determination of seepage.
  2. Determination of hydraulic pressure.
  • Determination of seepage pressure.
  1. Determination of exit gradient.

 

 

Soil Mechanics

Permeability of Soil and Darcys Law.

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Permeability of soil

  • Permeability

It is defined as the property of a porous material which permits the passage or seepage of water (or other fluid) through its interconnecting voids.

 

A material having continuous void is called permeable.

 

Gravels are highly permeable, while stiff clay is least permeable but for practical purposes clay is considered as impermeable.

 

  • Darcy’s law

The percolation of water through soil was first studied by “Darcy” in (1856), who demonstrated experimentally that for flow missing condition in a saturated soil, the rate of flow i.e. discharge is proportional to hydraulic gradient.

i.e. q = KiA

or, v = q/A = Ki  ——-(i)

[Where, q = Rate of flow

A = Cross Sec. Area of soil mass, perpendicular to the direction of flow

i = Hydraulic gradient

v = Avg. discharge velocity

K = Darcy coefficient of permeability]

From equation (i)

If i = 1 then v = K

Thus coefficient of permeability may be defined as the average velocity of flow that will occur through the total cross sec. Area of soil under unit hydraulic gradient.

Unit of K is cm/sec or m/sec.

 

  • Note

“v” is called superficial velocity (apparent). Actual velocity of water flowing in the voids is called seepage velocity (vs).

vs = v/n

  • Validity of Darcy’s law

Flow of water may be laminar or turbulent depending upon the mode of travel of water particles. If all water particle follow definite path which never intersect one another, the flow is termed as laminar.

If the particle paths are haphazard and irregular, it is turbulent flow.

Darcy’s law is valid only for laminar flow. Again the soil must be saturated.

 

  • Factors affecting Permeability

From Poiseuille Equation,    Q = cde2xxiA

Comparing the equation with Darcy’s law –    K = cde2x

Thus the following factors affecting permeability –

 

(i) Grain size

(ii) Properties of pore fluid

(iii) Void ratio of soil

(iv) Structural arrangement of soil particles and stratification

(v) Entrapped air and foreign matter

(vi) Adsorbed water

 

  • Grain size

Permeability varies approximately as the square of the grain size.

As per Allen Hazen formula, for clean sand with particle size between 0.1 mm and 3 mm,

K = CD102

[CD10 = Effective grain size in cm

K = Coefficient of permeability in cm/sec

C = Constant ≈ 100

 

  • Properties of pore fluid

The permeability is directly proportional to the unit weight of percolating water and inversely proportional to its viscosity

i.e. K ∞ 𝛾w/𝜂

[𝛾w = Unit weight of water

𝜂 = Viscosity of water]

 

  • Void ratio of soil

The variation of permeability with void ratio (e) has been empirically established from laboratory investigations and the equations are –

K ∞ e3/(1+e)

Sometimes it may be – K ∞ e2

[Where, e = void ratio of soil]

 

  • Structural arrangement of soil particles and stratification

For the same soil at the same void ratio, the permeability may vary with different methods of placement or compaction resulting in different arrangement and shape of voids.

It is much pronounced in fine grained soils because their natural structure when once disturbed can never be reconstructed.

Stratified soil masses have marked variation in their permeability in the direction parallel and perpendicular to stratification, the permeability parallel to stratification being always greater.

 

  • Entrapped air and foreign matter

Permeability is greatly reduced if air entrapped in the voids thus reducing its degree of saturation as we know the theory of permeability where relations have been experimentally established on soils with 100% degree of saturation.

It will also be affected if organic impurities are present in the pores of a soil.

[Thickness = 10 to 15 Ao where 1 Ao = 10-10 m

 

  • Adsorbed water

The adsorbed water surrounding the fine soil particles is not free to move and hence it causes an obstruction to the flow of free water by reducing the effective pore space, thus affecting permeability.

[ As per Casagrande 0.1 may be taken as void ratio occupied by adsorbed water and accordingly

K ∞ (e – 0.1)2 ]

 

  • Determination of permeability in the laboratory by constant head method

 

  • Object

To determine the coefficient permeability of coarse grained soil.

 

  • Apparatus

Constant head permeameter with all accessories, Stop watch, Graduated measuring jar etc.

  • Materials

Coarse grained soil, water.

  • Theory

As per Darcy’s law –

q = KiA

Or,

Or, K =     —–(i)

[ Where, Φ = Volume of water collected in the measuring jar in time ‘t’.

h = Constant head of water.

L = Length of soil sample.

A = Cross sectional area of soil sample perpendicular to the flow of water.

q = Discharge.

i = Hydraulic gradient.

K = Coefficient of permeability of soil ]

  • Procedure

(i) The soil sample is placed in the vertical cylinder between two porous plates, as shown in fig. and the bottom tank is filled with water missing

(ii) The outlet tube of the constant head tank is connected to the inlet of the permeameter after removing the air.

(iii) The hydraulic head will be adjusted such that ‘h’ will be constant during the test.

(iv) The test will be started now and stop watch will be ‘on’. Test will be continued for some convenient time during which water collected in the measuring jar. The time is recorded.

 

The test should be repeated at least twice more under the same head and for the same time interval.

From this, we will get average value of ‘Φ’

Knowing Φ, L, h, A and t, the coefficient of permeability of soil sample can be obtained from equation(i)

 

  • Conclusion

To avoid large error, it is necessary that quantity of water collected should be large. Hence this method is suitable for pervious soil or coarse grained soil.

 

  • Determination of permeability in the laboratory by falling head test

 

  • Object

To determine the coefficient of permeability of fine grained soil.

 

  • Apparatus

Falling head permeameter with all accessories, stop watch etc.

 

  • Materials

Fine grained soil, water

 

  • Theory

In falling head test, a stand pipe is fitted on the top of the permeameter and the change in hydraulic head with time is recorded.

Let ‘h’ be the head of water at any intermediate time ‘t’, from where head drops by ‘dh’ in time ‘dt’

Now, discharge in time dt,

q =

[ -ve sign is used as head decreases when time increases]

Again as per Darcy’s law –

q = KiA

  • Procedure

(i) The soil sample is placed in vertical cylinder between two porous plates. The inside area of the cylinder is measured which gives cross sectional area of soil sample (A) and length of the soil sample (L) is measured between the porous plates.

(ii) The permeameter mould assembly is placed in the bottom tank and the bottom tank is filled with water.

(iii) The permeameter is connected to the stand pipe having cross sectional area ‘a’, water is permitted to flow for some reasonable time.

(iv) With the help of stop watch, the time interval (T) required for the water level in the stand pipe to fall from some convenient initial head (h1) to final head (h2) is noted.

(v) Knowing the values of A, L, a, T, h1 and h2, coefficient of permeability (k) will be obtained from the above equation.

 

  • Conclusion

In this test, quantity of water collected is small and hence this method is suitable exclusively for fine grained soil.

 

 

 

 

 

 

 

 

 

 

 

 

Soil Mechanics

Consistency or Atterberg Limits of Soil

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  • Introduction

Consistency is a term used to describe the degree of firmness of soil in a qualitative manner by using descriptions such as soft, medium, stiff or hard. It indicates the relative ease with which a soil can be deformed.

 

  • This term is associated only with fine grained soils, especially clays.

 

  • Atterberg Limits

The physical properties of clays are considerably influenced by the amount of water present in them.

 

Depending upon the water content, the following four stages or states of consistency are used to describe the consistency of clayey soil –

  1. Liquid State.
  2. Plastic State.
  • Semisolid State.
  1. Solid State.

 

The boundary water contents at which the soil undergoes a change from one state to another are called consistency limits.

In 1911, Mr. Atterberg (A Swedish soil scientist) first demonstrated the significance of these limits, hence these limits are termed as Atterberg limits. These limits are liquid limit, plastic limit and shrinkage limit.

They are of great significance in understanding the behaviour of clays.

  • Liquid Limit (wL)

The boundary water content between liquid state and plastic states of consistency of soil is called liquid limit (As shown in above figure.)

It can also be defined as minimum water content at which soil flows by gravity with a little or no shearing resistance.

 

  • As per laboratory concern, w.r.t. standard liquid limit device, it is defined as the minimum water content at which a part of soil cut by a groove of standard dimension will flow together for a distance of 12mm (0.5’’) under an impact of 25 blows in the device.

 

  • Plastic Limit (wp)

The boundary water content between plastic state and semisolid state of consistency of soil is called plastic limit. (As shown in the fig.)

It can also be defined as minimum water content at which a soil will just begin to crumble when rolled into a thread of about 3mm in diameter.

 

  • In the plastic state, the soil can be moulded to different shapes without rupturing it.

 

  • Shrinkage Limit (ws)

The boundary water content between semisolid state and solid state of consistency of soil is called shrinkage limit (As shown in fig.)

It can be defined as the maximum water content at which a reduction in water content will not cause a decrease in the volume of soil mass. It is also the lowest water content at which a soil can still be completely  saturated.

 

  • In the semisolid state, the soil does not have plasticity and it will be brittle.

 

  • Shrinkage Ratio (SR)

It is defined as the ratio of a given volume expressed as a percentage of dry volume, to the corresponding change in water content above shrinkage limit.

i.e. SR =

Where, V1 = vol. of soil mass at water content w1 %

V2 = vol. of soil mass at water content w2 %

Vd = vol. of dry soil mass.