Principal modes of shear failure Under Footing

Principal modes of shear failure under Footing

(1) General Shear Failure: These failures occurs generally under the narrow footings of the shallow depths resting on a dense and almost incompressible soils. 

(2) Local Shear Failure: For weaker, more compressible soil and wider or deeper footings, the failure may be taken as local shear failure or punching shear failure. local shear failure is characterized by well defined slip lines below the footing but extending up to short distances in the soil mass.

(3) Punching Shear Failure: It occurs in highly compressible soils. This is characterized by lack of well defined slip lines. Vertical movement of the footing is primarily due to the compression of the soil below the footing with the soil on  the sides not being involved.

Three phase diagram of soil

Hi,

Three Phase Diagram:

A soil mass consist of the solid particles and the voids in between them. These voids are filled with air or/and water.  So there is a three phase system, but when the voids are only filled with air, or only filled with water then soil becomes a two phase system.  Three phase system can be represented with a diagram as shown below. When the voids are only filled with water, it is said to be saturated.

  

Total volume of the soil mass, V = (Va+Vw) +Vs

Where, V = Total Volume

 Va= Volume of air mass

 Vw = Volume of water mass

Vs = Volume of solids

But, Va+Vw = Vv

So,

      V = Vv+ Vs

Where Vv= Total volume of voids.

Void Ratio(e):

Void ratio is the ratio of the volume of the voids to the volume of the solid in the soil.

It is denoted by 'e'. 

e= Vv/Vs = n/(1-n)

Porosity (n): 

Porosity is defined as the ratio of the volume of the total voids to the total volume of the soil mass. 

It is denoted by 'n'

So n = Vv/V = e/(1+e)

Degree of Saturation(Sr):

Degree of saturation is defined as the ratio of the volume of the water to the total volume of the voids present in the soil mass. 

Sr = Vw/Vv,  For fully saturated soil mass Vw=Vv, So Sr=1

                      For fully dry soil mass, Vw= 0, So Sr=0

Water content(w):

It is the ratio of the weight of the water to the weight of the solids in the given soil mass. Weight of solids can be found by weighing the soil mass after drying it completely.

   w = Ww/Ws

Air Content(na): 

It is the ratio of the volume of air(Va) to the total volume of the voids(V).

   na= Va/V*100

Thanks!

Reference: 

Terzaghi's Bearing capacity theory

Assumptions:
(i) Footing is shallow, i.e. Df<=B to 2B
(ii) Footing is continuous
(iii) Footing has a rough base
(iv) Soil above the base of the footing can be replaced by equivalent surcharge Y.Df and offer no shear resistance.
Terzaghi produced a general bearing capacity equation for footing,
     qf = c.Nc + Y.D.Nq + 0.5.Y.B.Ny
where,  qf = Ultimate bearing capacity of soil in kg or tonnes/m^2
             c= cohesion in kg or tonnes/m^2
            Y= Density of soil, kg or tonnes/m^3
    B and D = Width and depth of footing respectively in meters.
 Nc, Nq and Ny = Terzaghi's bearing capacity factors .

Ultimate and net ultimate bearing capacities of saturated clay(cohesive soils) is
  qf = 5.7.Cu + Y.D   ;    Qnf = 5.7.Cu
where Cu = Shear strength in un-drained  conditions.
Effect of water table:
(i) Water table lies below the failure zone:
   qf = Y.D.Nq + 0.5.Y'.B.Ny

(ii) Water table at the base of the footing
   qf = Y.D.Nq + 0.5[Y'+Ny]
                        Y' is submerged density
(iii) Water table at the ground surface
  qf = Y'.D.Nq + Yw.D + 0.5.Y'.B.Ny

Rankine's Theory of Active Earth Pressure

Assumptions:
(1) Soil mass is a  homogeneous, dry, cohesion-less and semi infinite.
(2) Ground surface is a plane which may be horizontal or inclined.
(3) Back of the wall is smooth and vertical
(4) Wall yields about the base.

Cases of cohesion less soil:
(a) Dry or moist back fill with no surcharge
(b) Submerged back fill
(c) Back fill with uniform surcharge
(d) Back fill with a sloping surface

To be continued ....

Pile Load Test

Pile Load test is the method employed to find out the bearing capacity of the piles. This test is conducted on the piles to be driven at the site. Piles are driven into the soil by using the method as usual used for driving the pile. These piles are loaded with the external static loads of a value near to its failure.  The maximum load on the pile at the failure should not be less than 2.5 times the design load and on a working pile it should not be less than 1.5 times the working load.
The safe load of the pile is taken as the smallest of the following:
(i) Two third of the final load which gives a net value of settlement of 6 mm.
(ii) One half of the load at which the total settlement equal to one tenth of the pile diameter is reached.
The load on the pile is applied in increments, initially small and then larger.

Deep Foundations -Piles and well foundations

Deep Foundations:  (a) Pile Foundation    (b) Deep Foundation

(a) Pile Foundation: When the soil strata near to the surface of the earth is weak and can not take the load of the super-structure, the load is to be transferred to the hard strata at the greater depths through piles or well foundations. Pile supports the structure by gaining the strength in two ways : i)friction of the surface of shaft with the soil and ii)end bearing support to pile.
Bearing capacity of  a pile is the minimum load at which a pile continues to sink without any further increase in the load, it is called as the ultimate bearing capacity of the pile. Safe load which can be carried by a pile is determined on the basis of
(a) ultimate bearing capacity divided by some suitable factor of safety.
(b) Permissible settlement.
(c) Overall stability of the pile.
Now to classify the piles you can take the following bases:
(a) Classification based on the function of the piles:
(i) End Bearing Piles: In such piles the load is transferred to the hard strata through the end of the pile. The soil in between is soft and loose.
(ii) Friction Piles: In such piles the load is transferred to the soil through friction along the surface of the pile.
(iii) Compaction Piles: When the loose granular soil is compacted to increase the bearing capacity, compaction piles are used.
(iv) Tension Piles: Piles are used to anchor down the structures which are under the action of an uplift force has to bear the tension and so are called tension piles.
(v) Anchor Piles: Anchor piles are provided to provide anchor support against any horizontal pull.
(vi) Batter Piles: These piles are used to resist any horizontal or inclined pull due to moving ships etc.
(vii) Fender Piles and dolphins: These piles are constructed to protect the water front structures from the moving ships or floating objects.
(b) Based on method of installation: 
 (i) Pre-cast driven piles
(ii) Driven cast-in-situ piles
(iii) Bored cast-in-situ piles
(c) Based on Material Used:
     (i) Concrete Piles
              - Precast driven piles
              - cast- in-situ piles
              - pre-tested concrete piles
    (ii)  Timber Piles
   (iii) Composite Piles
               - Concrete and Timber Piles
              - Concrete and steel piles
Well Foundations:
The depth of the well foundation is based on the following criterion :
(i) The well should be taken below scour depth called grip length
(ii) The well should be sunk to sufficient depth so as to satisfy requirement of bearing capacity.

Types of Earth pressures - Active and Passive

Earth Pressures:  Soil when in contact with any structure exerts a lateral pressure to it. While designing the various retaining structures like, retaining walls, sheet piles or any earth retaining structures it is necessary to find out  the amount of the earth pressure exerted by the soil to it. If the soil is present above the top of the structure lying in the horizontal plane over it, then it is called as the surcharge.
Types of Earth pressure based on deformation of retaining wall, lateral pressure:
(a) Active Earth Pressure: When there is excessive pressure of the retained soil on the retaining wall, it tends to move away from the retained soil or back fill. It results in the separation of a wedge of the soil just behind the wall from the whole soil mass and it results in the lessening of the soil mass on the retaining wall. This failure wedge of soil wedge tends to move along with the wall. This wedge is retained at its position by a shear force along the failure plane, which is acting away from the wall. So there is a minimum pressure which is exerted by the soil mass on the wall which is called as the active earth pressure.

(b) Passive Earth Pressure: Under any natural cause when the retaining wall tends to move towards the soil back-fill, it will have a tendency to move the failure wedge in the opposite direction or towards the retained soil. The soil will get compressed in itself. Shear stresses will get developed along  the shear failure plane but now in a direction towards the retaining wall. Shear stresses will be developed up to a maximum value when it reaches the soil strength. So there will be a maximum pressure exerted by the soil mass on the retaining wall under the maximum shear stress conditions and it is known as the Passive Earth Pressure.

(c) Earth pressure at rest: When there is no movement of the retaining wall, neither towards the back-fill nor away from back-fill soil exerts a pressure on the retaining wall at rest. This pressure is higher than the active earth pressure and lower than the passive earth pressure. So this pressure exerted by the soil on the retaining wall at rest is known as the earth pressure at rest.

Boussinesq's equation- Stress in soil- Civil Engineering

Boussinesq's equation for the vertical stress distribution in the soil is given by:

Pz = Ib(Q/z^2),

Where, Pz= Pressure on soil at the depth z at a horizontal distance of r from the center line.

Ib = Boussinesq's constant = 3/2*pi[ 1+ 1/(1+ r^2/z^2) ]^(5/2)

pi = 3.14

For the various points on the line P1P2 Ib is constant. Using this equation you can find out the stress at a vertical distance of z and at a horizontal distance of r from center line.

Bearing Capacity of soil

The load or pressure developed under the foundation without introducing any damaging movement in the foundation and in the supporting soil is known as the bearing capacity of the soil, or in other words, the load which the soil under the foundation can bear without getting failed is known as the bearing capacity of the soil.
Ultimate Bearing capacity:
As the name suggests, it is the minimum load which can cause the shear failure of the supporting soil.
Net ultimate bearing capacity(qnf)
If we subtract the weight of the soil replaced by the footing, from the qf, we get net ultimate bearing capacity. It is the minimum net pressure causing shear failure,
numerically, qnf = qf- YD
here, Y= unit weight of soil
             D= Depth of foundation.

Safe Bearing Capacity(qs):
Simply, maximum pressure which the soil can carry without risk of shear failure is called safe bearing capacity.                   or    qs= qnf/F + YD.
where, F =Factor of Safety with which net ultimate bearing strength is to be divided.
Allowable Bearing Capacity:
It is the pressure which is considered safe both with respect to shear failure and settlement of the footing.

Rankine's Minimum depth of foundation:
You can use the formula given to find out the minimum depth of the footin.
According to theories given by Rankine,
 Depth, D = q/Y [( 1-  sin@' )/ (1+sin@')]^2
where, q= intensity of loading (N/mm2)
@' = effective angle of shearing
Y= density of the soil solids.

(Ref:GATE 2013, GK Publishers)

Compaction Equipment and their uses

You might have heard about the various compaction equipment like Rammers or tampers, smooth wheeled rollers, pneumatic tyred rollers, sheep foot rollers and vibratory rollers, each of these equipment are used in a specific kind of soil. You can find out the list below:
1. Rammers or tampers -
These are suitable for all kinds of soils, but more economical in the confined areas such as fills behind retaining walls, basement walls etc. and trench fills.
2. Smooth Wheeled rollers:-
They are suitable for the crushed rocks, gravels sands and so they generally are used in the road construction projects.
3. Pneumatic tyred rollers:-
They can be used in sands, gravels silts or clayey soils, and generally are used in the base, sub-base and embankment compaction for highways, air fields etc. and in earth dams.
4. Sheep foot rollers:-
Clayey soils need sheep foot rollers, so they are used in the core of the earth dams.
5. Vibratory rollers:-
They are used in sandy soils  generally used in the embankments for oil storage tanks etc.

reference: A hand-book on civil Engineering - by Made-easy  publications