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# Shrinkage Limit Method To Determine Specific Gravity

Shrinkage limit is defined as the smallest water content at which the soil is saturated. It is also defined as the maximum water content at which a reduction of water content will not cause a decrease in the volume of the soil mass. In other words, at this water content, the shrinkage ceases.

In the below block diagram, stage 1 represents a soil sample which is fully saturated with a water content greater than shrinkage limit. Stage 2 represents soil sample which has water content equal to shrinkage limit. Stage 3 represents the soil sample when it is oven dried, i.e., the water content is removed completely. The total volume V3 in stage 3 is same as the total volume V2in stage 2. Let Msbe the mass of solids.

Mass of water in stage 1= M1-MS
Loss of mas of water from stage 1 to stage 2= (V1-V2)pW

Mass of water in stage 2= (M1-Ms) – (V1-V2)pW

According to the definition provided above, shrinkage limit= water content in stage 2

wS= {(M1-Ms)-(V1-V2) pW}/ Ms

ws= w1– {(V1-V2)/Ms} pw

where w1 is the water content in stage 1

For determination of the shrinkage limit in the laboratory, about 50gm of soil passing a 425µ sieve is taken and mixed with distilled water to make a creamy paste. The water content (w1) of the soil is kept greater than the liquid limit.

A circular shrinkage dish, made of porcelain or stainless steel having a diameter 30 to 40mm and a height of 15 mm is taken. The shrinkage dish has a flat bottom and has its internal corners well rounded. The capacity of the shrinkage dish is first determined by filling with mercury.  The shrinkage dish is placed in a large porcelain evaporating dish and filled with mercury. Excess mercury is removed by pressing a plain glass plate firmly over the top of the shrinkage dish. The mass of mercury is obtained by transferring the mercury into a mercury weighing dish.  The capacity of the shrinkage dish in ml is equal to the mass of mercury in gram divided by the specific gravity of mercury (usually taken as 13.6).

The inside surface of the empty shrinkage dish is coated with a thin layer of Vaseline or silicon grease. The mass of empty shrinkage dish is obtained accurately. The soil sample is placed in the shrinkage dish, about one-third its capacity. The dish is tapped on a firm surface to ensure that no air is entrapped. More soil is added and the tapping continued till the dish is completely filled with soil. The excess soil is removed by striking off the top surface with a straight edge. The mass of the shrinkage dish with soil is taken to obtain the mass (M1) of the soil. The volume of the soil V1 is equal to the capacity of the dish.The soil in the shrinkage dish is allowed to dry in air until the color of the soil pat turns light. It is then dried in oven. The mass of the shrinkage dish with dry soil is taken to obtain the mass of dry soil, Ms.

For determination of the volume of the dry pat, a glass cup, about 50 mm diameter and 25 mm height, is taken and placed in large dish. The cup is filled with mercury. The excess mercury is removed by pressing a glass plate with three prongs firmly over the top of the cup. Any mercury adhering to the side of the cup is wiped off, and the cup full of mercury is transferred to another large dish.The dry pat of the soil is removed from the shrinkage dish, and placed on the surface of the mercury in the cup and submerged into it by pressing it with the glass plate having prongs. The mercury displaced by the soil pat is transferred to a mercury weighing dish and weighed. The volume of the mercury is determined from its mass and specific gravity. The volume of the dry pat Vd  is equal to the volume of the mercury displaced.  The total volume V2 will be equal to Vd.

The shrinkage limit of the soil is determined using the following equation, from the measured values of V1,V2,M1 and  Ms.

Shrinkage limit, ws=((M1-Ms)-(V1-V2)pw)/Ms

where pw is the density of water.