Soil Mechanics & Foundation Engg.: Compaction & consolidation Of Soil

By Deepanshu Rastogi|Updated : March 17th, 2021











































Compaction of Soil

Compaction of Soil

Compaction is the application of mechanical energy to soil so as to rearrange its particles and reduce the void ratio. 
It is applied to improve the properties of existing soil or in the process of placing fill such as in the construction of embankments, road bases, runways, earth dams, and reinforced earth walls. Compaction is also used to prepare a level surface during construction of buildings. There is usually no change in the water content and in the size of the individual soil particles.

The objectives of compaction are:

  • To increase soil shear strength and therefore its bearing capacity.
  • To reduce subsequent settlement under working loads.
  • To reduce soil permeability making it more difficult for water to flow through.

Laboratory Compaction

The variation in compaction with water content and compactive effort is first determined in the laboratory. There are several tests with standard procedures such as:

  • Indian Standard Light Compaction Test (similar to Standard Proctor Test/Light Compaction Test)
  • Indian Standard Heavy Compaction Test (similar to Modified Proctor Test/Heavy Compaction Test)


  • Indian Standard Light Compaction Test 

Soil is compacted into a 1000 cmmould in 3 equal layers, each layer receiving 25 blows of a 2.6 kg rammer dropped from a height of 310 mm above the soil. The compaction is repeated at various moisture contents.

  • Indian Standard Heavy Compaction Test

It was found that the Light Compaction Test (Standard Test) could not reproduce the densities measured in the field under heavier loading conditions, and this led to the development of the Heavy Compaction Test (Modified Test). The equipment and procedure are essentially the same as that used for the Standard Test except that the soil is compacted in 5 layers, each layer also receiving 25 blows. The same mould is also used. To provide the increased compactive effort, a heavier rammer of 4.9 kg and a greater drop height of 450 mm are used. 

Compactive energy applied per unit



  • The ratio of total energy given in heavy compaction test to that given in light compaction test


Dry Density - Water Content Relationship

  • To assess the degree of compaction, it is necessary to use the dry unit weight, which is an indicator of compactness of solid soil particles in a given volume.
  • Laboratory testing is meant to establish the maximum dry density that can be attained for a given soil with a standard amount of compactive effort. 

    In the test, the dry density cannot be determined directly, and as such the bulk density and the moisture content are obtained first to calculate the dry density as 

byjusexamprep ,

where γd = bulk density, and w = water content.

  • A series of samples of the soil are compacted at different water contents, and a curve is drawn with axes of dry density and water content. The resulting plot usually has a distinct peak as shown. Such inverted “V” curves are obtained for cohesive soils (or soils with fines), and are known as compaction curves.


  • Dry density can be related to water content and degree of saturation (S) as 

    Thus, it can be visualized that an increase of dry density means a decrease of voids ratio and a more compact soil. 

    Similarly, dry density can be related to percentage air voids (na) as


    Relation between moisture content and dry unit weight for a saturated soil is the zero air-voids line. It is not feasible to expel air completely by compaction, no matter how much compactive effort is used and in whatever manner.

Effect of Increasing Water Content

  • As water is added to a soil at low moisture contents, it becomes easier for the particles to move past one another during the application of compacting force. The particles come closer, the voids are reduced and this causes the dry density to increase. As the water content increases, the soil particles develop larger water films around them.
  • This increase in dry density continues till a stage is reached where the water starts occupying the space that could have been occupied by the soil grains. Thus the water at this stage hinders the closer packing of grains and reduces the dry unit weight. The maximum dry density (MDD) occurs at an optimum water content (OMC), and their values can be obtained from the plot.

Effect of Increasing Compactive Effort 

  • The effect of increasing compactive effort is shown. Different curves are obtained for different compactive efforts. A greater compactive effort reduces the optimum moisture content and increases the maximum dry density.


  • An increase in compactive effort produces a very large increase in dry density for soil when it is compacted at water contents drier than the optimum moisture content.It should be noted that for moisture contents greater than the optimum, the use of heavier compaction effort will have only a small effect on increasing dry unit weights.

It can be seen that the compaction curve is not a unique soil characteristic. It depends on the compaction effort. For this reason, it is important to specify the compaction procedure (light or heavy) when giving values of MDD and OMC.

Factors Affecting Compaction

The factors that influence the achieved degree of compaction in the laboratory are:

  • Plasticity of the soil
  • Water content
  • Compactive effort

Compaction of Cohesionless Soils

For cohesionless soils (or soils without any fines), the standard compaction tests are difficult to perform. For compaction, application of vibrations is the most effective method. Watering is another method. To achieve maximum dry density, they can be compacted either in a dry state or in a saturated state.

  • For these soil types, it is usual to specify a magnitude of relative density (ID) that must be achieved. If is the current void ratio or gd is the current dry density, the relative density is usually defined in percentage as




where emax and emin are the maximum and minimum void ratios that can be determined from standard tests in the laboratory, and gdmin and gdmax are the respective minimum and maximum dry densities

On the basis of relative density, sands and gravels can be grouped into different categories: 

Relative density (%)         Classification

       < 15               Very loose

      15-35              Loose

      35-65              Medium

      65-85              Dense

       > 85               Very dense

It is not possible to determine the dry density from the value of the relative density. The reason is that the values of the maximum and minimum dry densities (or void ratios) depend on the gradation and angularity of the soil grains. 

Engineering Behaviour of Compacted Soils

The water content of a compacted soil is expressed with reference to the OMC. Thus, soils are said to be compacted dry of optimum or wet of optimum (i.e. on the dry side or wet side of OMC). The structure of a compacted soil is not similar on both sides even when the dry density is the same, and this difference has a strong influence on the engineering characteristics.

  1. Soil Structure
    For a given compactive effort, soils have a flocculated structure on the dry side (i.e. soil particles are oriented randomly), whereas they have a dispersed structure on the wet side (i.e. particles are more oriented in a parallel arrangement perpendicular to the direction of applied stress). This is due to the well-developed adsorbed water layer (water film) surrounding each particle on the wet side. 

  2. Swelling
    Due to a higher water deficiency and partially developed water films in the dry side, when given access to water, the soil will soak in much more water and then swell more.
  3. Shrinkage 
    During drying, soils compacted in the wet side tend to show more shrinkage than those compacted in the dry side. In the wet side, the more orderly orientation of particles allows them to pack more efficiently.
  4. Construction Pore Water Pressure
    The compaction of man-made deposits proceeds layer by layer, and pore water pressures are induced in the previous layers. Soils compacted wet of optimum will have higher pore water pressures compared to soils compacted dry of optimum, which have initially negative pore water pressure. 
  5. Permeability 
    The randomly oriented soil in the dry side exhibits the same permeability in all directions, whereas the dispersed soil in the wet side is more permeable along particle orientation than across particle orientation.
  6. Compressibility

At low applied stresses, the dry compacted soil is less compressible on account of its truss-like arrangement of particles whereas the wet compacted soil is more compressible. 

The stress-strain curve of the dry compacted soil rises to a peak and drops down when the flocculated structure collapses. At high applied stresses, the initially flocculated and the initially dispersed soil samples will have similar structures, and they exhibit similar compressibility and strength. 

Some extra details about compaction - 






  1. Coarse grained well graded – Higher γd
  2. In clays with higher plasticity - γd decrease
  3. V shape due to bulking of pure sand


Compression and Consolidation of Soils

When a soil layer is subjected to vertical stress, volume change can take place through rearrangement of soil grains, and some amount of grain fracture may also take place. The volume of soil grains remains constant, so change in total volume is due to change in volume of water. In saturated soils, this can happen only if water is pushed out of the voids. The movement of water takes time and is controlled by the permeability of the soil and the locations of free draining boundary surfaces.

It is necessary to determine both the magnitude of volume change (or the settlement) and the time required for the volume change to occur. The magnitude of settlement is dependent on the magnitude of applied stress, thickness of the soil layer, and the compressibility of the soil.

When soil is loaded undrained, the pore pressure increases. As the excess pore pressure dissipates and water leaves the soil, settlement takes place. This process takes time, and the rate of settlement decreases over time. In coarse soils (sands and gravels), volume change occurs immediately as pore pressures are dissipated rapidly due to high permeability. In fine soils (silts and clays), slow seepage occurs due to low permeability.

Components of Total Settlement
The total settlement of a loaded soil has three components: Elastic settlement, primary consolidation, and secondary compression.

Elastic settlement is on account of change in shape at constant volume, i.e. due to vertical compression and lateral expansion. Primary consolidation (or simply consolidation) is on account of flow of water from the voids, and is a function of the permeability and compressibility of soil. Secondary compression is on account of creep-like behaviour.

Primary consolidation is the major component and it can be reasonably estimated. A general theory for consolidation, incorporating three-dimensional flow is complicated and only applicable to a very limited range of problems in geotechnical engineering. For the vast majority of practical settlement problems, it is sufficient to consider that both seepage and strain take place in one direction only, as one-dimensional consolidation in the vertical direction. 

Compressibility Characteristics

Soils are often subjected to uniform loading over large areas, such as from wide foundations, fills or embankments. Under such conditions, the soil which is remote from the edges of the loaded area undergoes vertical strain, but no horizontal strain. Thus, the settlement occurs only in one-dimension.

The compressibility of soils under one-dimensional compression can be described from the decrease in the volume of voids with the increase of effective stress. This relation of void ratio and effective stress can be depicted either as an arithmetic plot or a semi-log plot.


In the arithmetic plot as shown, as the soil compresses, for the same increase of effective stress Ds'the void ratio reduces by a smaller magnitude, from De1 to De2. This is on account of an increasingly denser packing of the soil particles as the pore water is forced out. In fine soils, a much longer time is required for the pore water to escape, as compared to coarse soils.

It can be said that the compressibility of a soil decreases as the effective stress increases. This can be represented by the slope of the void ratio – effective stress relation, which is called the coefficient of compressibility, av.


For a small range of effective stress, byjusexamprep

The -ve sign is introduced to make av a positive parameter.

If e0 is the initial void ratio of the consolidating layer, another useful parameter is the coefficient of volume compressibilitymv, which is expressed as


It represents the compression of the soil, per unit original thickness, due to a unit increase of pressure. 

NC & OC Clays


OP corresponds to initial loading of the soil. PQ corresponds to unloading of the soil. QFR corresponds to a reloading of the soil. Upon reloading beyond P, the soil continues along the path that it would have followed if loaded from O to R continuously.

The preconsolidation stress, s'pc, is defined to be the maximum effective stress experienced by the soil. This stress is identified in comparison with the effective stress in its present state. For soil at state Q or F, this would correspond to the effective stress at point P.

If the current effective stress, s', is equal (note that it cannot be greater than) to the preconsolidation stress, then the deposit is said to be normally consolidated (NC). If the current effective stress is less than the preconsolidation stress, then the soil is said to be over-consolidated (OC).

It may be seen that for the same increase in effective stress, the change in void ratio is much less for an overconsolidated soil (from e0 to ef), than it would have been for a normally consolidated soil as in path OP. In unloading, the soil swells but the increase in volume is much less than the initial decrease in volume for the same stress difference.

The distance from the normal consolidation line has an important influence on soil behaviour. This is described numerically by the overconsolidation ratio (OCR), which is defined as the ratio of the preconsolidation stress to the current effective stress.


Note that when the soil is normally consolidated, OCR = 1

Settlements will generally be much smaller for structures built on overconsolidated soils. Most soils are overconsolidated to some degree. This can be due to shrinking and swelling of the soil on drying and rewetting, changes in ground water levels, and unloading due to erosion of overlying strata.

For NC clays, the plot of void ratio versus log of effective stress can be approximated to a straight line, and the slope of this line is indicated by a parameter termed as compression index, Cc.


Estimation of Preconsolidation Stress

It is possible to determine the preconsolidation stress that the soil had experienced. The soil sample is to be loaded in the laboratory so as to obtain the void ratio - effective stress relationship. Empirical procedures are used to estimate the preconsolidation stress, the most widely used being Casagrande's construction which is illustrated.


The steps in the construction are:

•  Draw the graph using an appropriate scale.

•  Determine the point of maximum curvature A.

•  At A, draw a tangent AB to the curve.

•  At A, draw a horizontal line AC.

•  Draw the extension ED of the straight line portion of the curve.

•  Where the line ED cuts the bisector AF of angle CAB, that point corresponds to the preconsolidation stress.

Coefficient of Compression (Cc)







For undisturbed soil of medium sensitivity.

WL = % liquid limit.



For remolded soil of low sensitivity



For undisturbed soil of medium sensitivity eo = Initial void ratio


For remoulded soil of low sensitivity.

Cc = 1.15(e0-0.35)


Cc = 0.115w where, w = Water content

Over consolidation ratio


O.C.R > 1 For over consolidated soil.

O.C.R = 1 For normally consolidated soil.

O.C.R < 1 For under consolidated soil.


Differential Equation of 1-D Consolidation


where, u = Excess pore pressure.

image041 = Rate of change of pore pressure

C= Coefficient of consolidation

image042 = Rate of change of pore pressure with depth.

Coefficient of volume compressibility image043 where, e0 = Initial void ratio

mv = Coefficient of volume compressibility

Compression modulus

image044 where, Ec =Compression modulus.

Degree of consolidation


image045 where,

%U = % degree of consolidation.

U = Excess pore pressure at any stage.

U1 = image046 = Initial excess pore pressure

at image047

at image048


 image049 where,

ef = Void ratio at 100% consolidation.

i.e. of t = ∞

e = Void ratio at time 't'

e0 = Initial void ratio i.e., at t = 0

(iii) image050 where,

Δ= Final total settlement at the end of completion of primary consolidation i.e.,

at t = ∞

Δh = Settlement occurred at any time 't'.

Time factor

image051 where, TV = Time factor

C= Coeff. of consolidation in cm2/sec.

d = Length of drainage path

t = Time in 'sec'

image052 For 2-way drainage

d = HFor one-way drainage.

where, H0 = Depth of soil sample.

Some cases

(i) image053 if u ≤ 60% T50 = 0.196

(ii) image054 if u > 60%

Method to find 'Cv'

(i) Square Root of Time Fitting Method

image055 where,

T90 = Time factor at 90% consolidation

t90 = Time at 90% consolidation

d = Length of drainage path.

(ii) Logarithm of Time Fitting Method

image056 where, T50 = Time factor at 50% consolidation

t50 = Time of 50% consolidation.

Compression Ratio

(i) Initial Compression Ratio


where, Ri = Initial reading of dial gauge.

R0 = Reading of dial gauge at 0% consolidation.

Rf = Final reading of dial gauge after secondary consolidation.

(ii) Primary Consolidation Ratio


where, R100 = Reading of dial gauge at 100% primary consolidation.

(iii) Secondary Consolidation Ratio


Total Settlement

S = Si + Sp + Ss where, Si = Initial settlement

Sp = Primary settlement

Ss = Secondary settlement

(i) Initial Settlement


For cohesionless soil.

where, image062

where, Cr = Static one resistance in kN/m2

H0 = Depth of soil sample image063 For cohesive soil.

where, It = Shape factor or influence factor

A = Area.

(ii) Primary Settlement

  • image064
  • image065
  • image066
  • image067image068 

image069 = Settlement for over consolidated stage

image070 = Settlement for normally consolidation stage


(ii) Secondary Settlement


where, image073

100 = Thickness of soil after 100% primary consolidation.

e100 = Void ratio after 100% primary consolidation.

t2 = Average time after t1 in which secondary consolidation is calculated


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