TITLE: Liquid and Plastic limits / Atterberg’s Limits

AIM: To Determine the Liquid and Plastic Limits of a soil sample.

THEORY

When fine grain soils ( less than 0.075mm) such as clay and silt are mixed with varying amounts of water it is observed that its physical properties is affected i.e. it may change from a solid to a liquid or slurry. This phenomenon lead to the concept of boundaries or consistency limits suggested by a Swedish agriculturist in 1911 Albert Atterberg, of the four states a soil may exist depending on the moisture content. These are the liquid, plastic, semi-solid or the solid states. At high water content, the soil- water possesses the properties of a liquid, at lesser water contents, the volume of the mixture is decreased and the material exhibits the properties of a plastic. More so at even lesser water contents, the mixture behaves as a semi – solid and finally a solid. It is important to note that the change from one state to another is gradual and may vary for each soil type

In geotechnical engineering the Atterberg limits refers to the liquid, plastic and shrinkage limits however in this experiment only the liquid and plastic limits of a silty clay soil sample (soil passing the no.200 sieve) was determined. The liquid limit of the soil sample was determined by means of the Casagrande liquid limit device. By using this method the liquid limit of the soil sample is defined as the moisture content, expressed as a percentage of the dry weight of the sample, at which the part of the soil cut by the grooving tool of standard dimensions will flow together for a distance of 12mm under an impact of 25 blows in the device. In addition, the plastic limit is defined as the minimum water content at which a soil will just begin to crumble when rolled into a thread of approximately 3mm in diameter. The values obtained from the liquid and plastic limits were then used to compute the flow and plasticity indices. Atterberg limits are generally used in engineering to determine the soil strength, permeability and compressibility. It can also be used in soil classification.

Plasticity is a term used in soil mechanics to describe the rapid deformation of a material without any rupture, elastic rebound and without any volume change. More so it’s not dependent on the grain size of fine grain soils but rather on the colloidal size of the minerals found in these soils. For cohesive soils containing clay minerals of colloidal size, the degree of plasticity is defined as a function of the water content. When cohesive soils such as clay or silt clay is mixed with water it forms a plastic paste which can be molded into any form when pressure is applied. By adding water the cohesive property of the soil will decrease and if a sufficient amount of water is added the soil will no longer be able to retain its shape under its own weight. This will therefore result in a fluid that deforms freely without failure and thus exhibiting no shear strength (the ability of a soil to resist deformation by the continuous shear displacement of soil particles). Enough water can then be added until the soil grains are dispersed in a suspension.

In the latter when the water is evaporated from the suspension, the soil will pass through a number of stages known as the states of consistency. Consistency is a term used to denote the firmness of a soil i.e. whether if it’s soft, firm, sift or hard. The range in which the suspension goes from liquid to solid was divided into four stages the liquid state, the plastic state, the semi- solid state and the solid state by a Swedish agriculturist named Atterberg. In addition, he set consistency limits also known as Atterberg limits for these states in terms of the water content of the soil. The diagram below shows a graph of the total volume of the soil mass against the water content in percentage. It also shows the four states as well as the three most useful Atterberg limits used for engineering purposes and these are the liquid, plastic and shrinkage limits.

Figure 1

The liquid limit is defined as the minimum water content corresponding to the limit between the liquid and plastic states of the soil. It is at this water content that the shear strength is first apparent. In this experiment the liquid limit of a soil sample of uniform consistency was

determined using Casagrande liquid limit device. With reference to this device the liquid limit and a flow curve showing the water content versus number of blows, the liquid limit was defined as the water content at which a part of soil cut by a grove (3mm in width) will close for a distance of 12mm under the impact of 25 blows in the device. The diagram below shows a typical flow curve.

Figure 2

The equation of the flow curve is given by:

m = - Fi Log N + C……………………… (1)

Where, m = moisture content

Fi = the flow index (a constant)

N = corresponding number of blows

C = constant

Equation (1) is in the form of a straight line where the slope of the line gives the flow index. The slope of the flow curve Fi, illustrates the rate at which the soil loses its shearing resistance when the water content is increased.

The plastic limit is the water content corresponding to a limit between the plastic and the semi- solid states of a uniformly consistent soil sample. During this stage the water content of the soil is gradually increased this in turn causes the soil’s volume together with its plasticity property to decrease while its shear strength increases. Because of this phenomenon there would come a point where the strain will cause a rupture. Formally the water content at which this occurs may be defined as the minimum water content at which a soil will just begin to crumble when rolled into a thread about 3mm in diameter is referred to as the plastic limit.

The plasticity index, PI, which is range within which a soil exhibits plastic properties, is defined numerically as the difference between the liquid and plastic limits of the soil.

Plasticity Index, PI = Liquid Limit – Plastic Limit

In general once the plasticity index, PI, and the flow index, Fi, is known the toughness index, IT, can be determined. It is defined as the ratio of the plasticity index to the flow index.

Toughness index, IT = PI/Fi

From the liquid limit test the flow curve does not extend over the plastic range, however if we assume that this straight line graph does extend between the liquid and plastic limits and that the number of blows is directly proportional to the shear resistance of the soil, we can write:

For the liquid limit: kSL = NL …………………………… (3)

And

For the plastic limit: kSP = NP……………………………. (4)

Where, k = Constant

SL = Shearing resistance at the liquid limit

SP = Shearing resistance at the plastic limit

NL = Number of blows at the liquid limit

NP = Number of blows at the plastic limit

The equation of the flow curve at the liquid and plastic is then given by:

For the liquid limit: mL = - Fi Log NL + C ………………. (5)

For the plastic limit: mp = - Fi Log NP + C……………….. (6)

Subtracting equations gives:

mL - mp = - Fi ( Log kSL - Log kSP) = PI ……...(7)

This implies, PI = - Fi log (SL / SP)

So, log (SP / SL) = PI / Fi ……………………… (8)

But log (SP / SL) = Toughness, IT, at the plastic limit.

Therefore, Toughness Index, IT = PI / Fi

APPARATUS & EQUIPMENT:

Casagrande liquid limit device / Liquid Limit Machine

Casagrande Grooving tool / Liquid Limit Grooving tool

Ground glass plate

Electronic balance

Porcelain evaporating dish

Spatula

Plastic squeeze bottle to add controlled amounts of water

Moisture cans

Drying Oven

PROCEDURE:

LIQUID LIMIT TEST

1) The mass of five empty moisture cans was determined using the electronic balance.

2) 250 g of air dried soil was then measured and placed into a porcelain evaporating dish to which distilled water was added and content mixed to a smooth paste of uniform consistency.

3) Using a spatula a portion of the paste was placed and smooth along the front edge of the brass cup of the Casagrande Liquid Limit device to a depth of about 12mm at the center of the sample.

4) By the use of the grooving tool, a trapezoid shaped groove was cut along the center line of the soil pat in the brass cup i.e. this divided the soil into two halves.

5) The cam was then rotated by turning the handle at a rate of about two revolutions per second. This caused the brass cup in the liquid limit device to rise and drop onto the hard rubber base through a vertical height of 1cm per revolution. The number of blows was then counted and recorded until the two parts of the soil sample came into contact at the bottom of the groove at a distance of about one half inch of its length.

6) The paste in the brass cup was then removed and placed into a labeled moisture can. If the number of blows was greater than 25 more water was added to the soil and the content was mixed thoroughly and experiment repeated. Likewise, if the number of blows counted were less than 25 the soil sample was allowed to dry by adding dry soil of the same soil type and the test repeated.

7) Steps 3 – 7 were repeated using four other samples of the same soil type but with varying water content.

8) The five moisture cans was then placed in an oven, in which the weights of the dry sample plus the moisture cans were later determined.

9) The water content corresponding to each number of blows was computed and a graph of water content against number of blows was plotted on semi logarithmic paper. This type of plot is known as a flow curve which is a straight line.

10) The flow curve obtained was used to determine the liquid limit i.e. water content corresponding to 25 blows on the graph. By determining the slope of the graph the flow index was obtained.

PLASTIC LIMIT TEST

1) From about 20g of soil of uniform consistency obtained from the liquid limit test (soil which required about 50 blows to close the groove) a small amount was rolled onto a dry glass plate by hand to form a thread of about 3mm in diameter.

2) The thread was then gathered up, kneaded and again rolled into a 3mm thread.

3) Step 2 was repeated until the thread crumbled or broke into parts.

4) The thread crumbles were then placed into labeled moisture can and weighed, dried out (by means of the oven) and reweighed.

5) Steps 1-4 was then repeated and the two labeled cans were placed in an oven in which the weights of the dry sample plus the moisture cans were later determined.

6) The water content was then determined for each and the average of the two were obtained. This value represents the plastic limit of the sample.

RESULTS:

LIQUID LIMIT

Container # E3 D1 D2

# of blows 30.00 18.00 8.00

Wt. of Tare Wet 65.20 65.20 61.60

Wt. of Tare Dry 55.50 54.80 51.60

Wt. of Water 9.70 10.40 10.00

Tare Wt. 31.50 31.20 31.40

Wt. of Dry Soil 24.00 23.60 20.20

Water content (%) 40.42 44.07 49.50

PLASTIC LIMIT

Container # G1 B

Wt. of Tare Wet 70.90 50.40

Wt. of Tare Dry 63.70 45.60

Wt. of Water 7.20 4.80

Tare Wt. 31.40 23.50

Wt. of Dry Soil 32.30 22.10

Water content (%) 22.29 21.72

SAMPLE CALCULATIONS:

Weight of water = (Weight of Sample + Tare Wet) – (Weight of Sample + Tare Dry) ……… (1)

Weight of dry soil = (Weight of Sample + Tare Dry) - (Weight of Tare)……………………... (2)

Weight of wet soil = (Weight of Sample + Tare Wet) - (Weight of Tare)…………………….. (3)

Consider container number E3 from the Liquid Limit Test with,

Number of Blows, N = 30

Wt. of Tare = 31.50g

Wt. of Sample + Tare Wet Wt. = 65.20g

Wt. of Sample + Tare Dry Wt. = 55.50g

From equation (2)

Wt. of dry soil = 55.50g – 31.50g = 24.00g

From equation (3)

Weight of wet soil = 65.20g – 31.50g = 33.70g

From equation (1)

Weight of water = 33.70g – 24.00g = 9.7g

To obtain the moisture content, w%, the following equation was used:

w (%) = (Weight of Sample+TareWet )– (Weight of Sample+Tare Dry)

(Weight of Sample+Tare Dry)−(Weight of Tare) * 100

Therefore by using the information above we get:

w (%) = 33.70−24.00

24 * 100 = 40.42%

Graph Data

LIQUID LIMIT

Container # E3 D1 D2

# of blows 30.00 18.00 8.00

Sample Graph of Moisture content vs. Number of Blows

4.00 40.000.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

Number of blows

moi

stur

e co

nten

t (%

)

liquid limit

CALCULATIONS:

Liquid Limit

25

Since the water content at 25 blows from the flow curve is equal to the Liquid Limit, LL:

From graph the Liquid Limit, LL = 41.8%

Using two points on the flow curve as seen on the graph: (10, 48) & (40, 38.5)

Flow index, Fi = (w2 % – w1 %) / (log N2 – log N1)

= (48 – 38.5) / (log 10 - log 40)

= 9.5

−0.602059991328

= −15.8 %

Plastic Limit

Since Plastic Limit, PL = Water Content (w %)

Let PL1 denote the plastic limit obtained from soil contained in can I3

Let PL2 denote the plastic limit obtained from soil contained in can D3

Then Plastic limit of soil = PL 1+PL2

2 = 22.29+21.72

2 = 22.01 %

Therefore the Plasticity Index, PI = Liquid Limit – Plastic Limit

= 41.8 % - 22.01%

= 19.79 %

And hence the Toughness index, IT = PI / Fi

= 19.79/15.80

= 1.25

DISCUSSION:

In this experiment two of Atterberg limits, the liquid and plastic limits were determined for a silty clay soil sample passing the no. 200 sieve (soil grains less than 0.075mm in diameter). These limits are also known as consistency limits and they define the upper and lower bounds of the plastic state. In engineering the determination of these two important Atterberg limits has proven to be quite useful in soil classification and identification. It is also used in determining the strength, permeability and compressibility of a soil sample.

On performing the liquid limit test by means of the Casagrande liquid limit device, a series of moisture contents of the soil sample each corresponding to a number of blows within close proximity to 25 was obtained. A linear graph known as a flow curve was then drawn on semi logarithmic paper which illustrated the relationship between the number of blows and the moisture content. From the curve it was clearly seen that the number of blows required to close the 3mm grove for a distance of about 12mm in the brass cup was inversely proportional to the water content of the soil. Because of this linear relationship that exist between the water content and the number of blows is it more convenient to obtain the liquid limit of the soil from the flow curve rather by adjusting the water content of the soil until the exact value is found by trail to close the grove when 25 blows is applied. Therefore from the graph the liquid limit i.e. the water content corresponding to 25 blows of the silty clay soil sample was found to be 41.8%. As the liquid limit of soils depends on the amount and type of clay minerals present, the result obtained showed that the soil sample contained the clay mineral Kaolinite, since the liquid limit of soils containing this mineral falls within the approximated range (35 - 100) %. Further the flow index, Fi which was determined by finding the magnitude of the slope of the flow curve and this was found to be -15.80%. For convenience it is usually taken to be positive. The slope of the flow

curve, Fi, indicates the rate at which a soil loses shearing resistance with increasing water content. In addition, it shows how the number of blows required to close the grove in the device is dependent on the shearing resistance of the soil. The flow index can also be calculated by obtaining the difference in water content over one cycle of the logarithmic scale.

In general the liquid limit of fine grain soils can be obtained either by using the Casagrande apparatus as in this case or by using a cone penetrometer. The cone – penetration test however is most preferable when determining the liquid limit of fine grain soils as it is easier to carry out and the test procedure is less dependent upon the judgment of the operator.

The second part of the experiment involved determining the plastic limit of the soil sample defined as lowest water content at which the soil can be rolled into threads approximately 3mm in diameter without crumbling or breaking into pieces. The plastic limit of the sample used was found to be 22.01 %. The plasticity and toughness indices were then calculated using the values obtained for the liquid limit, plastic limit and the flow index of the soil sample. The plasticity index or plastic number, PI, of a given soil is the numerical difference between the liquid limit and the plastic limit. It is used to indicate the range of consistency within which a soil exhibits plastic properties. In this experiment the plastic index of the soil sample was calculated to be 19.79% which fell in the range of regular plastic clays. The plasticity index can also be used to determine the activity, A, of clay soils. Finally the toughness index, IT, defined as the shearing resistance at the plastic limit was calculated to be 1.25.In general the toughness index for most clays varies from 0 – 3 but in some cases can be as high as 5. A soil is considered to be friable at the plastic limit if the toughness index is less than 1.

PRECAUTIONS AND SOURCES OF ERRORS:

Liquid Limit

1) Ensure soil and water is mixed properly i.e. to a smooth paste of uniform consistency.

2) Distilled water should be used in order to minimize the possibility of ion exchange between the soil and any impurities in the water.

3) To minimize the drying of the surface of the soil while being tested it is better to conduct the test in a humid room.

4) Lack of perfection in the observer in determining the water content.

5) The soil sample must be the same for both the liquid and plastic limit tests.

6) Ensure that the electronic balance is adjusted properly.

Plastic Limit

1) Ensure that when approaching the 3mm diameter thread, the pressures applied by your fingers is neither relieved nor increased to attain the necessary diameter.

2) Ensure that the glass surface is clean and dry.

CONCLUSION:

On performing the liquid and plastic limits tests on a portion of soil passing the no. 200 sieve the following were obtained as stated in the table below:

LIQUID LIMIT, LL

FLOW INDEX, Fi

PLASTIC LIMIT, PL

PLASTIC INDEX, PI

TOUGHNESS INDEX, IT

41.8 % -15.8 % 22.01 % 19.79 % 1.25

REFERENCES

M. Budhu: Soil Mechanics and Foundations 3rd Edition, Wiley, 2010

T. William Lambe: Soil Mechanics, John Wiley & Sons, 1969