How to Determine the Shrinkage Limit of Soil ?

Shrinkage limit can be determined in the laboratory using a disturbed or undisturbed soil sample.

Principle for Determining the Shrinkage Limit of Soil:

Figure 5.11 shows the schematic diagram in which a fully saturated soil in stage I having volume V₁ undergoes shrinkage and on complete drying reaches stage III, where the entire water is evaporated. Between stages I and III lies stage II, where the soil is at shrinkage limit water content. In stage II, the soil is fully saturated, but a further decrease in the water content does not cause any decrease in the volume of the soil and air occupies the space of the evaporated water.

The volume of the soil at shrinkage limit is equal to the total volume of oven-dried soil. It is to be noted that the volume of soil solids is constant throughout the shrinkage process, and the decrease in volume occurs only due to decrease in volume of voids. So we get –

Weight of water in stage I = – W₁ – W_d

Loss of water from stage I to II = (V₁ – V₂)γ_w

Weight of water in stage II = (W₁ – W_d) – (V₁ – V₂)γ_w

Shrinkage limit = Water content of soil in stage II

Where W₁ is the initial total weight of soil in stage-I, W_d is the dry weight of soil, V₁ is the initial volume of the soil in stage-I, V_d is the volume of soil in dry state (stage III), ω₁ is the initial water content of soil in stage-I, and γ_w is the density of water.

Apparatus for Determining the Shrinkage Limit of Soil:

The apparatus for the determination of shrinkage limit with all component parts.

It consists of the following:

1. Cylindrical stainless steel shrinkage dish with 45-mm internal diameter and 15-mm internal height.

2. Cylindrical glass cup with 50-mm internal diameter and 25-mm internal height.

3. Porcelain evaporating dish.

4. Square acrylic plastic plate of size 75 mm x 75 mm with three metal prongs.

5. Square plain plastic plate of size 75 mm x 75 mm.

6. Thermostatically controlled oven.

Test Procedure for Determining the Shrinkage Limit of Soil:

The test consists of the following steps:

1. Determination of Volume of Wet Soil:

i. The weight of the clean empty shrinkage dish is determined and recorded as W_sd.

ii. The shrinkage dish is filled overflowing with mercury, and the excess mercury is removed by pressing the plain plastic plate flush with the top of the dish.

iii. The volume of the shrinkage dish is computed by dividing the weight of mercury in the shrinkage dish with the specific gravity of mercury (13.6). This volume of shrinkage dish is recorded as the initial volume of wet soil V_1.

2. Determination of Weight of Wet Soil:

i. About 100 g of air-dried soil passing 425 µm IS sieve is taken and sufficient water is added to make a uniform thin paste. The amount of water to be added is equal to or slightly greater than the liquid limit of the soil for friable soils, and it may exceed the liquid limit by about 10% for plastic soils.

ii. The shrinkage dish is emptied of mercury, cleaned, and coated with a thin layer of silicon grease or Vaseline to prevent adhesion of the soil to the inside surface of the dish.

iii. The shrinkage dish is filled with the wet soil in increments, taking care to prevent air getting entrapped in the soil. The excess soil is removed by pressing the plain plastic plate flush with the top of the shrinkage dish.

iv. The shrinkage dish is cleaned on the outside to remove the adhering soil. The weight of the shrinkage dish with wet soil is taken and recorded as W₂.

v. Weight of wet soil filling the shrinkage dish, W₁ = W₂ – W_sd.

3. Allowing Wet Soil to Undergo Gradual Shrinkage:

i. The wet soil in the shrinkage dish is allowed to dry in air for sufficient time until the color of the soil changes from dark to light.

ii. Then, the shrinkage dish is placed in an oven to dry at 105°C – 110°C for 24 h. After completely drying, the dish with the dry soil is cooled in a desiccator.

4. Determination of Weight of Dry Soil:

i. The weight of dry soil pat plus shrinkage dish is taken and reported as W₃.

ii. Weight of dry soil pat W_d = W₃ – W_sd.

5. Determination of Volume of Dry Soil:

i. The glass cup is kept in an evaporating dish and is filled with overflowing mercury.

ii. The excess mercury is removed by pressing with plastic plate with metal prongs flush with the top of the glass cup and the mercury in the evaporating dish is removed. The glass cup with mercury is again placed in the evaporating dish.

iii. The dry soil pat is placed on the surface of mercury in the glass cup and slowly and carefully pressed down with plastic plate with metal prongs.

iv. When the plastic plate with metal prongs is pressed flush with the top of the glass cup, the excess mercury spills into the evaporating dish.

v. The glass cup is removed from the evaporating dish, and the displaced mercury in the evaporating dish is carefully weighed. The volume of dry soil pat, V_d, is computed by dividing the weight of displaced mercury with the specific gravity of mercury.

Initial water content of wet soil can be derived as –

ASTM D-4943 describes a method of using molten wax for the determination of shrinkage limit in place of mercury, since handling mercury is hazardous. In this method, the oven-dried soil pat is dipped in molten wax. The wax-coated soil pat is then cooled. Its volume is determined by submerging in water.

Shrinkage Limit in Terms of Specific Gravity:

From Fig. 5.11, shrinkage limit can be derived as –

Dry density of soil in stage II of Fig. 5.11 is given as –

Determination of Specific Gravity from Shrinkage Limit:

From Eq. (5.12),

Shrinkage Factors or Parameters:

Following shrinkage parameters are useful and used in association with the study of shrinkage of soils:

1. Shrinkage Index (I_s):

It is defined as the numerical difference between the plastic limit and the shrinkage limit. It can be mathematically expressed as –

SI = PL – SL …(5.16)

or l_S = ω_P – ω_S …(5.17)

2. Volumetric Shrinkage (VS):

It is defined as the ratio of decrease in volume of a soil to the dry volume expressed as a percentage when the water content is reduced from initial water content to shrinkage limit water content. It can be mathematically expressed as –

VS = (V₁ – V_d/V) × 100 …(5.18)

3. Shrinkage Ratio (SR):

It is defined as the ratio of given volume change expressed as a percentage of dry volume to the corresponding change in the water content. It can be mathematically expressed as –

SR = {[(V₁ – V₂)/V_d] x 100}/(ω₁ – ω₂) …(5.19)

When the final water content is equal to shrinkage limit, that is, ω₂ = ω_s, then, V₂= V_d. So we get –

Thus, the shrinkage ratio of a soil is equal to the mass specific gravity of the soil in the dry state. Shrinkage ratio is also equal to the ratio of volumetric shrinkage to the corresponding decrease in the water content up to shrinkage limit.

SR = VS/ω₁ – ω_s …(5.23)

4. Linear Shrinkage (LS):

It is defined as the ratio of decrease in length to the original length when the water con­tent is reduced from initial water content to shrinkage limit. It is usually expressed as a percentage. So –

LS = (L₁ – L_d /L₁)× 100

Linear shrinkage is related to the volumetric shrinkage by the following relation –