FHG IKJ − −
3.6 DENSITY INDEX
Density Index (or relative density according to older terminology) of a soil, ID, indicates the relative compactness of the soil mass. This is used in relation to coarse-grained soils or sands.
In a dense condition, the void ratio is low whereas in a loose condition, the void ratio is high. Thus, the in-place void ratio may be determined and compared, with the void ratio in the loosest state or condition and that in the densest state or condition (Fig. 3.5).
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Vs Vv
Vs Vv
Vs
Vv Voids
Voids
Voids
Solids Solids Solids
Loosest state void ratio : emax
Intermediate state void ratio : e0
Densest condition void ratio : emin Fig. 3.5 Relative states of packing of a coarse-grained soil
The density index may be considered zero if the soil is in its loosest state and unity if it is in the densest state. Consistent with this idea, the density index may be defined as follows:
ID = ( )
( )
max max min
e e
e e
−
−
0 ...(Eq. 3.8)
where,
emax = maximum void ratio or void ratio in the loosest state.
emin = minimum void ratio or void ratio in the densest state.
e0 = void ratio of the soil mass in the natural state or the condition under question.
emax and emin are referred to as the limiting void ratios of the soil.
Sometimes ID is expressed as a percentage also. Equation 3.8 may be recast in terms of the dry unit weights as follows:
ID = 1 1 1 1
γmin − γ0 γmin γmax
F HG I
KJ F
−HG I
KJ
...(Eq. 3.9)= γ γ
γ γ
γ γ
max min
max min 0
F
0HG I
KJ F
−−HG I
KJ
...(Eq. 3.10)These forms are more convenient since the dry unit weights may be determined directly.
However, if it is desired to determine the void ratio in any state, the following relation-ships may be used:
e = G w
d
. γ
γ – 1 ...(Eq. 3.11)
e = V G W
w s
. . γ
– 1 ...(Eq. 3.12)
A knowledge of the specific gravity of soil solids in necessary for this purpose. The deter-mination of the volume of the soil sample may be a source of error in the case of clay soils;
however, this is not so in the case of granular soils, such as sands, for which alone the concept of density index is applicable.
The maximum unit weight (or minimum void ratio) may be determined in the labora-tory by compacting the soil in thin layers in a container of known volume and subsequently
INDEX PROPERTIES AND CLASSIFICATION TESTS 39 obtaining the weight of the soil. The compaction is achieved by applying vibration and a compressive force simultaneously, the latter being sufficient to compact the soil without breaking individual grains. The extent to which these should be applied depends on experience and judgement. More efficient packing may be achieved by applying the vibratory force (with the aid of a vibratory table as specified in IS-2720 (Part XIV)–1983)* in the presence of water;
however this needs a proper drainage arrangement at the base of the cylinder used for the purpose, and also the application of vacuum to remove both air and water. It should be noted, however, that it is not possible to obtain a zero volume of void spaces, because of the irregular size and shape of the soil particles. Practically speaking, there will always be some voids in a soil mass, irrespective of the efforts (natural or external) at densification.
In the dry method, the mould with the dry soil in it is placed on a vibratory table and vibrated for 8 minutes at a frequency of 60 vibrations per second, after having placed a stand-ard surcharge weight on top.
In the wet method, the mould should be filled with wet soil and a sufficient quantity of water added to allow a small quantity of water to accumulate on the surface. During and just after filling, it should be vibrated for a total of 6 minutes. Amplitude of vibration may be reduced during this period to avoid excessive boiling. The mould should be again vibrated for 8 minutes after adding the surcharge weight. Dial gauge readings are recorded on the sur-charge base plate to facilitate the determination of the final volume.
The wet method should be preferred if it is found to give higher maximum densities than the dry method; otherwise, the latter may be employed as quicker results are secured by this approach.
Other details are contained in the relevant Indian Standard, and its revised versions.
The minimum unit-weight (or maximum void ratio) can be determined in the laboratory by carefully letting the soil flow slowly into the test cylinder through a funnel. Once this task has been carefully performed, the top surface is struck level with the top of the cylinder by a straight edge and the weight of the soil of known volume may be found in this state, which is considered to be the loosest. Oven-dried soil is to be used. Even the slightest disturbance may cause slight densification, thus affecting the result.
If proper means are available for the determination of the final volume of vibrated sand, the known weight of sand in the loosest state may itself be used for the determination of the void ratio in the densest state. In that case the sequence of operations will change.
Thus, it may be understood, that there is some degree of arbitrariness involved in the determination of the void ratio or unit weight in the densest as well as in the loosest state.
The concept of Density Index is developed somewhat as follows:
Assuming that the sand is in the loosest state:
emax = V V
v s
max min
,
for which the corresponding value of density index is taken as zero.
*“I.S.–2720 (Part XIV)–1983 Methods of Test for Soils–Part XIV Determination of Density Index (Relative Density) for Soils” gives two approaches–the dry method and the wet method for the determi-nation of the maximum density.
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Assuming that the sand is in the densest state:
emin = V V
v s
min max
,
for which the corresponding value of density index is taken as unity.
It can be understood that the density index is a function of the void ratio:
ID = f(e) ...(Eq. 3.13)
This relation between e and ID may be expressed graphically as follows.
1
ID
O Densityindex,ID
emin e0 emax q
This fact that the relationship is linear may be guessed easily
Void ratio, e
Fig. 3.6 Void ratio-density index relationship It may be seen that:
tan θ = 1 (emax−emin)
∴ cot θ = (emax – emin) ...(Eq. 3.14)
For any intermediate value e0,
(emax – e0) = ID . cot θ ...(Eq. 3.15)
∴ ID = ( )
cot emax −e0
θ Substituting for cot θ from Eq. 3.14
ID = ( ) ( maxmax min)
e e
e e
−
−
0 ...(Eq. 3.8)
Obviously, if e0 = emax, ID = 0, and if e0 = emin, ID = 1.
For vary dense gravelly sand ID sometimes comes out to be greater than unity. This would only indicate that the natural packing does not permit itself to be repeated or simulated in the laboratory.
Representative values of density index and typical range of unit weights are given in Table 3.2.
INDEX PROPERTIES AND CLASSIFICATION TESTS 41 Table 3.2 Representative values of Density Index and typical unit
weights (Mc Carthy, 1977)
Descriptive condition Density index, % Typical range of unit weight, kN/m3
Loose Less than 35 Less than 14
Medium dense 35 to 65 14 to 17
Dense 65 to 85 17 to 20
Very dense Greater than 85 Above 20
Depending upon the texture, two sands with the same void ratio may display different abilities for densification; hence the density index gives a better idea of the unit weight than the void ratio itself.
The density index concept finds application in compaction of granular material, in various soil vibration problems associated with earth works, pile driving, foundations of machinery, vibrations transmitted to sandy soils by automobiles and trains, etc. Density index value gives us an idea, in such cases, whether or not such undesirable consequences can be expected from engineering operations which might affect structures or foundations due to vibration settlement.