Unit - 5
Consolidation of Soil
Consolidation:
- When load is applied on a saturated cohesive soil, initially, entire load is taken by pore water, and later on, due to gradual escape/seepage of water, load is transferred on soil.
- This process of gradual load transfer from pore water to soil Skeleton, and gradual compression is called as consolidation
Compaction:
- This is the simplest method of increasing the performance, characteristics, especially bearing capacity of soil.
- In this method, by the application of force or vibrations, the soil particles are more closely packed thereby increasing the density and hence bearing capacity of the soil.
- Increasing the density of soil by application of mechanical energy is called compaction.
- Compaction is also defined as the process where the density is increased by reducing air voids. It may involve modification of water content or gradation of soil or both.
- The theory of compaction was first developed by R.R. Proctor while building a dam in the USA.
- The principles of compaction developed by him were published in a series of articles in Engineering News record in 1933.
Purpose of Compaction
Compaction of soil is undertaken for a number of purposes. These are listed below:
- To increase density and thereby shear strength and bearing capacity of soil, this is required in the case of slope stability improvement.
- To decrease the permeability of soil, this is required for earth dams.
- To reduce the settlement of structures after construction.
- To reduce danger of piping, this is required for seepage control of earth dam.
- To increase resistance towards erosion of soil by rain and other causes.
Primary consolidation settlement (Sc):
- Primary consolidation settlement (Sc) is the settlement resulted due to resistance to flow of water under induced hydraulic gradient.
Secondary consolidation settlement (Ss):
- Secondary consolidation settlement (Ss) is due to plastic deformation of soil at zero excess pore water pressure.
- Mathematically, S= total settlement =S₁=Si + Sc + Ss
- This is shown in curve (b) in Fig. For cohesive soil; which take long time. As against this incase of sandy soil, the entire settlement will not take more time as shown in curve (a) in Fig.
Fig 1: Showing time settlement relation in respect of cohesive and non-cohesive soil
- When compressive load is applied on saturated soil, it will tend to expel water in soil, and thereby cause decrease in volume and settlement.
- If the soil is permeable, water will be expelled quickly, whereas if soil is impermeable, expulsion of water will take time, and settlement will take place gradually.
- Initially, when load is applied, very less load is taken by soil, and the balance load is borne by water called as pore water pressure.
- At any point of time,
Total stress = Stress taken by water + Stress taken by soil
= (Pore water pressure) + (Effective stress)
At time, t=0, effective stress taken by soil = 0
∴Pore water pressure = Total stress
- As time passes, gradually, water is expelled, pore water pressure decreases and effective stress increased.
- When pore water pressure reduces to zero, complete or 100% consolidation is achieved,
And Total stress = Effective stress
- Consolidation is time dependent process and depending upon impermeability of soil, may take long time.
Assumptions in Terzaghi's 1-Dimensional Consolidation Theory
Terzaghi's theory is based on following assumptions
- Compression and flow are one-dimensional (vertical).
- Darcy's law is valid throughout the consolidation process.
- The soil is homogeneous and isotropic.
- The soil is fully saturated.
- The soil grains and water are both incompressible. The consolidation occurs due to expulsion of water from the voids.
- Strains are small; that is, the applied load increment produces virtually no change in thickness, and k and a, remain constant.
- The time lag in consolidation is due entirely to the low permeability of the soil.
- There is a unique relationship, independent of time, between void ratio and effective stress, that is
e=-a
,p, while av is assumed constant over the stress increment.
- The consolidation cell consists of a circular metal ring in which the soil specimen is kept, and it does not allow the horizontal or the lateral movement (deformation) of the soil sample.
- On the top and bottom of the soil sample, porous stones and filter paper are placed to permit two-way drainage of water from or into the sample, as desired.
- Axial vertical loads can be applied through the loading machine, on the soil sample. Due to loading, the sample volume decreases, its vertical deformation or compression (lateral deformation prevented) can be measured on a dial gauge attached to the apparatus at top.
Fig 2: Fixed ring consolidation cell
- In a fixed ring consolidation cell, only the top porous stone is permitted to move downward, as the specimen compresses.
- Direct measurement of permeability of the soil sample at any stage of loading can be made only in the fixed ring consolidation cell, and hence such an arrangement is widely adopted.
- An axial vertical load is applied on soil sample by means of loading yoke.
- The load is transmitted centrally from the loading yoke through a steel ball bearing, which rests on a circular loading plate.
- This provides a uniform pressure distribution on the soil sample.
- A dial gauge, provided near the top end of the machine, measures the compression up to 0.002 mm.
- Near the top end of the soil sample is placed a water jacket, filled with water, around the porous filter stone. This prevents excessive evaporation from the soil sample during the test, and ensures that it remains saturated.
- At the bottom end of the soil sample, the water expelled from the soil flows through the filter stone, and is forced into the stand pipe, which is a sort of a falling or rising head permeameter, and thus helps measuring soil permeability during the progress of consolidation or compression test.
- For performing the test, usually a soil sample of 60 mm diameter is taken. Samples of 50, 70 and 100 mm diameter can also be used in special cases. The diameter to thickness ratio of the sample should be minimum of 3.
- An initial setting load of 5 kN/m² is applied. The compression is noted by taking the diameter reading after 24 hours of the application of the initial setting load.
- Then load increment of say 10 kN/m2 is given and dial gauge readings are taken after 0.25, 1, 2.25, 4, 6.25, 9, 12.25, 16, 20.25, 25, 36, 49, 60 minutes and 1, 2, 4, 8 and 24 hours recorded to indicate the settlement of the sample when the compression virtually ceases.
- After recording the compression readings with time for the first incremental load, the load is increased further by giving further incremental loading, and the test is repeated. Again, load is increased and test repeated, and so on.
- The sequence of the increased loadings (extra to the initial setting load) generally adopted is 10, 20, 40, 80, 160, 320, 640, 800, 1000 kN/m².
- The specimen is unloaded after completion consolidation and is allowed to swell.
- The final dial reading corresponding to the completion of swelling is recorded, and specimen is taken out and dried to determine: (a) its water content; and; (b) mass of the soil solids.
Following two methods are used to find Cv, the coefficient of consolidation
- Logarithm of time fitting method by Casagrande.
- Square root of time fitting method by Taylor.
Logarithm of time fitting method by Casagrande
- Plot graph of compression of soil by dial gauge reading Vs logarithm of time as shown in Fig.
Fig: 3
- Select point A and B on the initial part of the curve, such that time required for point B is four times time required for point A. Let Z1 be vertical the distance between point A and B. Select point C, above point A such that vertical distance between point C and A is same as that between A and B (viz Z₁).
- Through C draw a horizontal line to denote zero primary consolidation.
- Extend the initial straight line portion CD to E.
- Draw tangent to the last portion of curve FGH and let it meet line DE in G.
- Draw horizontal line at G to mark time for 100% consolidation. (Viz G R100)
- Draw a horizontal line R50 by dividing vertical distance between R0 and R100 and let it cut the curve in T50. X co-ordinate Tso indicates time required for 50% consolidation.
Where 0.197 represents time factor Tv for 50% consolidation
d = thickness of sample
t50 = time required to attain 50% consolidation
Numericals:
Q. A clay stratum 5 m thick has the initial void ratio of 1.50. When the sample is subjected to increase in pressure of 120 kN/m² the void ratio reduces to 1.44. Determine the coefficient of volume compressibility and final settlement of stratum.
Given:
H=5m
e0=1.5
ef=1.44
Q. A clay stratum 6 meters thick has initial void radio of 1.52 and effective overburden pressure of 125 kN/m². When the sample is subjected to increase in pressure of 100 kN/m², the void ratio reduces to 1.45. Determine the coefficient of volume compressibility, compression index and final settlement of stratum.
Given:
Final settlement,
Q. In a consolidation test void ratio decreased from 0.70 to 0.65, when the load was changed from 50 kN/m² to 100 kN/m². Compute compression index and coefficient of volume change.
Given:
e0=0.7
Pp=50KN/m2
ef=0.65
p+
To find:
=
Q. A saturated clay layer of 5 m thickness takes 1.5 year for 50% primary consolidation, when drained on both sides. Its coefficient of volume change m, is 1.5 x 103 m²/kN. Determine the coefficient of compressibility (in m³/yr) and the coefficient of permeability (in m/yr.) Assume 
w= 10 kN/m³
Given:
U=0.5
H=5m
d =
=
Tv =
∴
…. Ans.
K=?
K=
=0.818m2/yr×1.5×10^-3 m2/KN
K=0.0123m/yr …. Ans
Q. The time of reach 60% consolidation is 30 seconds for a sample of 1 cm thick tested in a laboratory under condition of double drainage. How many years will the corresponding layer in nature required to reach the same degree of consolidation, if it is 10m thick and drained on one side only?
Given:
=
Lab condition:
=0.5cm=5×10^-3m
Field condition: d2=H=10m
=
References:
- Principles of Geotechnical Engineering by Braja M. Das, Cengage learning
- Soil Mechanics and Foundation Engineering by K.R. Arora, Standard Publishers
- Soil mechanics and Foundation Engineering by B.N.D. Narsingarao, Wiley India Pvt. Ltd.
- Basic and applied soil mechanics, by Gopal Ranjan, A.S.R Rao, New age International publishers
