Identification of Expansive Soils

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• Identification of Expansive Soils:

Expansive soils can be identified by studying their mineralogy, which can be identified by the following tests:

1. X-Ray Diffraction test.
2. Microscopic examination.
3. Differential Thermal Analysis(DTA).

There are certain simpler tests to determine the expansive characteristic from engineering point of view.

1. Free swell test 
2. Differential free swell test.

   

   Swelling Index determination

In  free swell test 10 gm of soil passing through 425 mic. IS-sieve if poured in a cylinder containing 100 ml of distilled water, and left undisturbed for 24 hours. The volume of the soil is measured and the free swell Sf is given as  (Vs-Vi)/Vi *100.

Where,

Vi= Initial Volume

Vs= Volume of the swelled soil.

The Bentonite may swell from 1200 to 2000%;  Kaolinite - about 80 % ; Illite - 30 to 80%.

In differential free swell test, two samples of 10 gm dry soil passing through 425 mic. IS - sieve are poured in 50 ml graduated cylinders, one containing non-polarizing liquid(Kerosene) and another water. Both the jars are kept undisturbed for 24 hours and differential free swell (DFS) is given as,

   

Differential Free Swell (DFS) = [ Vs(w) - Vs(k)]/ Vs(k) *100 

Where,   Vs(w) = Volume of soil in water.

               Vs(k) = Volume of soil in kerosene.

A relationship between differential free swell (DFS) and degree of expansion is given in the table below:

         Differential Free Swell (DFS)[%]                 Degree of expansion

1.     <20                                                                     Low
2.     20-35                                                                 Moderate
3.    35-50                                                                  High
4.       > 50                                                                Very High

Holtz and Gibbs(1956), gave the following table to classify the expansive soils into low, moderate, high and very high expansive categories based on volume change(%), Colloidal content(%), Plasticity Index(PI) and Shrinkage Limit(SL).

 

              Property                                                     Property Ranges for

                                                         Low               moderate             High           Very High

1. Volume Change(%)               0-10                10-20                 20-30               >30
2. Colloidal Content(%)             0-15                10-25                 20-35              >25
3. Plasticity Index(PI)(%)           0-15                 10-35                20-45              >30
4. Shrinkage Limit(SL)(%)         12                    8-18                   6-12                10

R.B. Peck, W.E. Hanson & T.H. Thornburn (1974), gave the following relation between the Plasticity Index(PI) and Swelling Potential:

                     Swelling Potential                 Plasticity Index(PI)

1.              Low                                                 0-15
2.              Medium                                          10-35
3.              High                                                20-55
4.              Very High                                       >=35

Gromko, G.J. (1974) has related shrinkage limit(SL) to the linear shrinkage(LS) and degree of expansion:

            SL(%)                      LS(%)                 Degree of expansion

1.   <10                           >8                             Critical
2.   10-12                       5-8                             marginal
3.    >12                         0-5                            non-critical

Sridharan et al. gave another relationship between the swell potential and free swell index.

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Standard one dimensional Consolidation Test

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Standard one dimensional consolidation test is usually carried out on saturated specimens of about 25.4 mm thick and 63.5 mm in diameter. The soil specimen is kept inside a metal ring, with a porous stone on the top and another at the bottom.

The load P is applied on to the specimen using a lever arm, and compression of the specimen is measured with the help of a micrometer dial gauge. The load is usually doubled every 24 hours.  The specimen is kept under water throughout the test.

For each load increment, the specimen deformation and the corresponding time t are plotted on a semilogarithmic graph paper. The graph consists of three distinct parts:

1. Upper curved portion(Stage I). It is mainly due to the result of pre-compression.
2. A Straight line portion (Stage II), is referred to as the primary consolidation. At the end of primary consolidation, a major extent of the excess pore water generated by the increased loading is dissipated.
3. A lower straight line portion (Stage III), is called the secondary consolidation. During this stage, specimen undergoes small deformation with time.
   

Note that at the end of of the test for each loading, the stress on the specimen is the effective stress. Once the specific gravity of the soil solids, the initial dimensions of the specimen, and the specimen deformation at the end of each load have been determined, the corresponding void ratio can be calculated.

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Vertical piles subjected to Eccentric Loading

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Let's have two cases of eccentric loading on a pile group.

• e is about one axis.

In this case load is given as, Vp = V/n  +- (V.e.xj.A)/Ig

V = Total vertical load on pile group
n = No. of the piles
e = Eccentricity w.r.t.  C.G.(Center of Gravity) of pile group.
xj = Distance of the center of the pile group from center of pile, measured parallel to e.
Ig = Moment of Inertia of pile group about axis normal to axis of eccentricity.

• e is about both the axis

Vp = V/n  +- (V.ex.xj.A)/Ix +- (V.ey.yj.A)/Iy

Where ex and ey are the eccentricities w.r.t. center of pile group, measured along x and y axis respectively.


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Uplift capacity of the Footing

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Footings are sometimes subjected to uplift or tension forces, few examples are:

1. Legs of the elevated water tank
2. Anchorages to the anchor of the footings.
3. Footings of the transmission line towers.

Bala(1961) developed the expressions along with the following procedure for their use:

• A footing may be considered as shallow or deep if    Df/B < H/Blimiting.  Which depends upon angle of internal friction. 

             Angle of Internal friction (Degrees)              H/Blimiting

                                     20                                        2.5

                                     25                                         3.0

                                     30                                         4.0

                                     35                                         5.0

                                     40                                         7.0

                                     45                                         8.0

• For shallow footing, i.e. Df/B < H/Blimiting

1.  For Circular Footings  
   
    
2. For Rectangular Footings

• For Deep Footing Df/B > H/Blimiting

1.  For Circular Footings 
   
2. For Rectangular Footings
   

Where,

                 Sf= Shape Factor = 1+m.Df/B - For shallow

                                             = 1+ m.H/B  - For Deep

                 K = Co-efficient of earth pressure at rest.

The value of m: 

          Angle of friction       H/Blimiting              m

                      20                       2.5                0.05

                      25                       3.0                0.10

                      30                       4.0                0.15

A factor of safety of 2.0 to 2.5 may be adopted to find the allowable bearing capacity.

If soil is very poor, Pu may be taken equal to W. In this case FOS of 1.5 may be taken to determine the pull capacity Pa.

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Terzaghi's One Dimensional Consolidation Theory

Dr. Karl Terzaghi is known as the father of Soil Mechanics, he gave the theory of one dimensional consolidation. For it, he made the following assumptions:

1. Soil is completely saturated.
2. Soil & water are virtually incompressible.
3. The compression is one- dimensional.
4. Darcy's Law is valid.
5. Certain properties like, soil permeability are constant.

He followed these assumptions to give this one dimensional consolidation theory as follows:

• Water flow due to consolidation:

When the water present in the saturated soil starts to expel out of the soil sample, its velocity may decrease at the following rate.

Similarly, the rate of change of the soil sample may be taken as follows:

According to the second assumption, the water and soil are virtually incompressible, so whatever rate of change in the volume of the pore water takes place, same will happen to the soil.

It may be written as follows:

It is known as Storage Equation: 

• Applying  Darcy's Law

Velocity of the water flow is given by Darcy's law:

Note that because only flows due to consolidation are of interest, the head

h = u/Yw

• Stress Strain relationship for soil

Assume soil behaves elastically, Elastic response:

• Principle of Effective Stress:

Terzaghi combined these 3 equations to form another differential equation, as follow:

If the soil is homogeneous, then

This equation can be used to find out the pore water pressure u. As the total stress remains constant, we can neglect the last term, so we get:

The solution of the above equation gives us the value of the pore water pressure.

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Settlement Tilt and Horizontal displacement of Footing

Hi,

Eccentrically obliquely loaded footings settle down as shown in the figure. Let Se & Sm be the settlements of the points under the load and edge of the footing.
Let 't' be the tilt of the footing,

Sm = Se + (B/2-e).Sin.t

After carrying out a number of tests Agarwal(1986) & Agarwal and Saran(1991), gave the following relationship:

Se/S' = A' + A1(e/B) + A2(e/B)^2

Sm/S' = B' + B1(e/B).

Where, A' = 1- 0.56(i/phi) - 0.82(i/phi)^2  
            A1 = -3.51 + 1.47(i/phi) + 5.67 (i/phi)^2
            A2 = 4.74 - 1.38(i/phi) - 12.45(i/phi)^2
             B' = 1- 0.48.(i/phi) - 0.82(i/phi)^2
            B1 = -1.80 + 0.94(i/phi) + 1.63(i/phi)^2
 here, phi = angle of friction
           i = e/B

Generalized correlation:

Hd/B = 0.121(i/phi) - 0.682(i/phi)^2 + 1.99(i/phi)^3 + 2.01(i/phi)^4

Here, Hd = Horizontal Displacement of the footing.


Settlement of Footing on Slope:

Sud(1985) gave the following relationship

Ss/S' = 0.00385.s + (1-0.00125.s) De/B

Here, Ss= Settlement on slopes
          s= slope with the horizontal
           De = Distance of edge of footing from the top of the slope.


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Allowable Bearing Pressure(ABP) in Well Foundation

Hi, this post is the continuation of the lecture notes for the subject "Advanced Foundation Engineering".Read the last post: Settlement of the Pile GroupIn this post, I am going to lay down the criteria for finding out the Allowable Bearing Pressure in Well Foundations.

For well foundations, the allowable bearing pressure can be estimated by satisfying the 2 criterias:

1. Shear Failure criteria
2. Settlement criteria

As per Indian Standard Code the allowable bearing pressure can be found by the following equations:
    
 Q = 5.4.N^2.B + 16(100+N^2).Df
           
Here, Q = Allowable bearing pressure in kg/cm^2
          N = Corrected N value from SPT.
          B = Smaller dimension of the well cross section
          D = Depth of foundation below the scour level.

Points to be remembered:

• In case of cohesive soils, undisturbed samples need to be taken to determine the shear and consolidation characteristics of deposit.
• The settlement of the well foundation can be obtained by Terzaghi's theory of one dimensional consolidation.
• If the bed is resting into the hard rock then it can be obtained by crushing strength or UCS of the rock core samples taken from the field and accordingly the various corrections for fissures, joints, presence of water table, dip and strike & presence of fines in the joints etc. can be obtained from the field and  the corrections can be applied accordingly. The RMR values from the ABP values can be obtained using IS: 17270.   IRC: 78 says, normally ABP exceeding 2 MPa shall not be adopted.

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