PARTICLE SIZE ANALYSIS  

AND ATTERBERG LIMITS OF A SOIL 

AND ITS CLASSIFICATION

Introduction  

The results of particle-size analysis and the Atterberg limits test combined contribute to classification of soil using the Unified Soil Classification System and the AASHTO Classification System.

Mechanical analysis is the determination of the size range of particles present in a soil, expressed as a percentage of the total dry weight.  Two methods are generally used to find the particle size distribution of soil: (1) sieve analysis­ – for particles sizes larger than 0.075 mm in diameter, and  (2) hydrometer analysis – for particle sizes smaller than 0.075 mm in diameter.  The Hydrometer analysis was not performed during the experiment.

Some type of particle-size analysis is universally used in the engineering classification of soils.  It is used in concrete and asphalt mix design for pavements.

Particle-size is one of the suitability criteria of soils for road, airfield, levee, dam, and other embankment construction.  Information obtained from particle-size analysis can be used to predict soil-water movement, although permeability tests are more generally used.  For colder climates, the susceptibility to frost action in soil can be predicted fro the particle-size analysis.

Very fine soil particles are easily carried in suspension by percolating soil water, and under-drainage systems will rapidly fill with sediments unless a filter made of appropriately graded granular materials properly surrounds them.  The proper gradation of this filter material can be predicted from the particle-size analysis.

A particle-size distribution curve can be used to determine the following four parameters for a given soil particle.

1.       Effective size (D₁₀):

This parameter is the diameter in the particle-size distribution curve corresponding to 10% finer.  The effective size of granular soils is a good measure to estimate the hydraulic conductivity and drainage through soil.

2.       Uniformity Coefficient: This parameter is defined as

                                                                                                   (1)

where D₆₀ = diameter corresponding to 60% finer

3.       Coefficient of gradation (C_z): This parameter is defined as

                                                                                          (2)

4.       Sorting coefficient (S₀): This parameter is another measure of uniformity and is generally encountered in geologic works and expressed as

                                                                                                (3)

The sorting coefficient is not frequently used as a parameter by geotechnical engineers.

The liquid and plastic limits are two of the five “limits” proposed by A. Atterberg, a Swedish agricultural scientist.  The other three limits are: cohesion limit, sticky limit, and shrinkage limit.

The Atterberg Limits Test, together with the particle-size analysis, is used as an integral part of several engineering classification systems to characterize the fine-grained fractions of soils and to specify the fine-grained fraction of construction materials.

The liquid and plastic limits are used internationally for soil identification and classification and for strength correlations.  The potential for volume change can often be detected from the liquid- and plastic-limit tests.  The liquid limit is sometimes used to estimate settlement in consolidation problems and both limits may be useful in predicting maximum density in compaction studies.  They are utilized, either individually or together, with other soil properties to correlate with engineering behavior such as compressibility, permeability, compatibility, shrink-swell, and shear strength.  The liquid limit of a soil containing substantial amounts of organic matter decreases dramatically when the soil is oven-dried before testing. Comparison of the liquid limit of a sample before and after oven-drying can therefore be used as a qualitative measure of organic matter content of a soil.

In order to place definite, reproducible values on these limits, it was proposed that the liquid limit be arbitrarily defined as that water content at which a pat of soil placed in a brass cup, cut with a standard groove, and then dropped from a height of 10 mm will undergo a groove closure of 12.7 mm when the cup of soil is dropped 25 times at the rate of 120 drops/minute.  Several variables affect the liquid-limit test but the technician doing the test can control most of these variables.

The plastic limit has been arbitrarily defined as that water content at which a soil thread just crumbles when it is rolled down to a diameter of 3 mm.  This test is somewhat more operator-dependent than the liquid-limit test, since what constitutes crumbling and a visual detection of a 3-mm diameter are subject to some interpretation (thus 3 mm is adequate instead of the 3.2mm given by ASTM).

The liquid and plastic limits of a soil can be used with the natural moisture content of the soil to express its relative consistency or liquidity index and can be used with the percentage finer that 2-mm size to determine its activity number.

These methods are sometimes used to evaluate the weathering characteristics of lay-shale materials.  When subjected to repeated wetting and drying cycles, the liquid limits of these materials tend to increase. The amount of increase is considered to be a measure of shale’s susceptibility to weathering.

Methodology

A. The Sieve Analysis of Soil

Sieve analysis consists of shaking the soil sample through a set of sieves that have progressively smaller openings. The list of equipment include:  (1) set of sieves;  (2) mortar and pestle; and  (3) balance sensitive to 0.1 g. The flowchart at the right shows the general procedure in performing the sieve analysis.  The sieves used for soil analysis are generally 203mm (8 in) in diameter.  To conduct a sieve analysis, one must first oven-dry the soil and then break all lumps into smaller particles.  The soil is then shaken through a stack of sieves with openings of decreasing size from top to bottom (a pan is placed below the stack).  The smallest-size sieve that should be used for this type of test is the U.S. No. 200 sieve.  After the soil is shaken, the mass of soil retained on each sieve is determined.  When cohesive soils are analyzed, breaking the lumps into individual particles may be difficult.   In this case, the soil may be mixed with water to make slurry and then washed through the sieves.  Portions retained on each sieve are collected separately and oven-dried before the mass retained on each sieve is measured.

1. Determine the mass of soil retained on each sieve and in the pan.

2. Determine the total mass of the soil.

3. Determine the cumulative mass of soil retained above each sieve.

4. The mass of soil passing the ith sieve is SM – (M₁ + M₂ + …+ M_i)

5. The percent of soil passing the ith sieve (or percent finer) is

                                                        (4)

Once the percent finer for each sieve is calculated, the calculations are plotted on a semi-logarithmic graph paper with percent finer as the ordinate (arithmetic scale) and sieve opening size as the abscissa (logarithmic scale).  This plot is referred to as the particle-size distribution curve.

B. The Liquid Limit Determination 

The liquid limit device consists of a brass cup and a hard rubber base.  The brass cup can be dropped onto the base by a cam operated by a crank. To perform the liquid limit test, one must place a soil paste in the cup.  A groove is then cut at the center of the soil pat with the standard grooving tool.  By the use of the crank-operated cam, the cup is lifted and dropped from a height of 10 mm (0.394 in.).  The moisture content, in percent, required to close a distance of 12.7 mm (0.5 in.) along the bottom of the groove after 25 blows is defined as the liquid limit. The flowchart at the right shows the general procedure in performing the liquid limit test. It is difficult to adjust the moisture content in the soil to meet the required 12.7 mm (0.5 in.) closure of the groove in the soil pat at 25 blows.  Hence, at least three tests for the same soil are conducted at varying moisture contents, with the number of blows, N, required to achieve closure varying between 15 and 35. The moisture content of the soil, in percent, and the corresponding number of blows are plotted on semi-logarithmic graph paper.  The relationship between moisture content and log N is approximated as a straight line.  This line is referred to as the flow curve.  The moisture content corresponding to N=25, determined from the flow curve, gives the liquid limit of the soil.

The slope of the flow line is defined as the flow index and may be written as

                                                                                       (5)

where I_F is the ­flow index; w₁ is the moisture content corresponding to N₁ blows; and w₂ is the moisture content corresponding to N₂ blows.  Thus, the equation of the flow line can be written in a general form as

                                                                                (6) 

where C is a constant.

C. The Plastic Limit Determination 

The plastic limit is defined as the moisture content in percent, at which the soil crumbles, when rolled into thread of 3.2 mm (1/8 in.) in diameter.   The plastic limit is the lower limit of the plastic stage of soil.  The plastic limit test is simple and is performed by repeated rollings of an ellipsoidal-size soil mass by hand on a ground glass plate.   The procedure for the plastic limit is given by ASTM in test Designation D-4318.  The flowchart at the right shows, in general, the procedure of the test. The list of equipment of both the liquid- and plastic-limit tests include:  1. Casagrande with grooving tool;     2.  moisture cans;  3.  plastic limit plate (optional);  4.   porcelain dish;  5.   spatula;  6.   balance sensitive to 0.01g; and   7.   Sieve No. 40, pan and lid.

Calculations

There are two kinds of samples being utilized in performing the tests: one is cohesionless soil and the other one is cohesive soil.  The samples are already amply air-dried before being oven-dried.

A. Calculations for Particle-size Analysis

Table 1 shows the raw and calculated data for the cohesionless soil. 

          Table 1. Calculation of Percent Passing for the Cohesionless Soil

       Table 2. Calculation of Percent Passing for the Cohesive Soil

Note that there is less than 12% (as specified by the USCS, no equivalent from AASHTO ) passing Sieve No. 200 as shown in Table 1 for the cohesionless soil. The coefficient of uniformity (C_u) and the coefficient of gradation (C_z) will be calculated.  For the second soil sample, the computations for these coefficients will not be necessary since the results will bear no significance because of the mere fact that the particles passing Sieve No. 200 is greater than 12%.

Figure 1. Particle-size Distribution Curves for Both Types of Soils

From the red curve in Figure 1,

 (effective size)

The uniformity coefficient,

The coefficient of gradation,

B. Calculations for Liquid- and Plastic-Limit Tests

Table 3 shows the raw and calculated data for the cohesionless soil.  Figure 2 shows the flow curve of the determination of the liquid limit.  The linear equation shown was produced by Excel.  The corresponding liquid limit is 25.57% and the plastic limit is 0% rendering the soil as non-plastic.

 Table 3. Calculation of Water Content for Liquid Limit Test of the Cohesionless Sample

Figure 2. Flow Curve for the Liquid Limit Determination of the Cohesionless Soil

Table 4. Calculation of Water Content for the Liquid Limit Test for the Cohesive Sample

Table 5. Calculation of Water Content for the Plastic Limit Test of the Cohesive Sample

Figure 3. Flow Curve for the Liquid Limit Determination of the Cohesive Soil

Table 4 and Table 5 show the raw and calculated data for the cohesive soil.  Figure 3 shows the flow curve of the determination of the liquid limit.  The linear equation shown was produced by Excel.  The corresponding liquid limit is 44.1% and the plastic limit is 24% giving a value of plasticity index of 20.1%.

Results and Discussions

Table 5 shows the summary of calculations made earlier.  Table six, on theother hand shows the side-by-side classification for both types of samples. 

                                Table 5. Summary of Calculated Results

To evaluate the quality of a soil as a highway subgrade material, one must also incorporate a number called the group index (GI) with the groups and subgroups of the soil.  This index is written in parentheses after the group or subgroup designation. The group index is given by the equation

                  (7)

The group index for a A-2-4 is automatically 0.  To calculte for the group index of the cohesive sample

Table 6. Sample Classification Using the USCS and AASHTO Systems

Considering the results of the laboratory tests, a number of concerns have to be addressed and are discussed separately as follows.

A. Soil Expansion

When subjected to loads, fine-grained soil undergoes deformation or volume change due to the expulsion of water from the pores of the soil. If not properly addressed, excessive deformation or expansion may induce undue stresses that can cause damage on a structure or its components.

Expansion of soil occurs due to the variation of in density and moisture condition from the wet season to the dry season.  Primary factors are the availability of moisture, and the amount and type of the clay-size particles in the soil.  In general, expansion potential increases as the dry density increases and the moisture content decreases.  Also, the expansion potential increases as the surcharge pressure decreases.

The cohesive sample used in the experiment has a plasticity index of 24.  Based on the Table 7 below, this parameter, together with clay content, is enough to distinguish the expansion potential of the soil. However, the clay content is not known since the Hydrometer Analysis was not performed.  It is therefore conservative to say that the expansion potential is Medium.  This may characterize into a 5-10% swell @ 2.8 kPa (60 psf) lod.

The other sample does not apply here.  

                        Table 7. Typical Soil Properties Versus Expansion Potential

B. Liquefaction Vulnerability

Liquefaction is the phenomenon of temporary loss (or significant reduction) of shear strength of saturated medium to fine-grained sands when subjected to cyclic or shock loading such as earthquake.

In the July 1990 earthquake, several areas in North Luzon were severely affected by this phenomenon, manifested in considerable ground subsidence or uplift, tilting structures and damaged buildings and pavements.

H. Bolton, Seed and Idriss have established empirically the following criteria for soils with liquefaction potential:

1.   SPT N-value <10;

2.   D₅₀, between 0.02mm to 2;

3.  Saturated soil material or below the water table;

4.   Non-plastic fines (cohesionless); and

5.   Intensity and duration of ground shaking.

The cohesive sample clearly does not apply here.

The cohesionless sample used in the experiment has a D₅₀=0.18mm. This type of material, though  having a generally good subgrade rating (for road projects), has a high risk and vulnerability in liquefaction.  

Conclusions

The foregoing analyses and discussions were based on the available data used in the experiment. The experiment procedures was referred to the ASTM Manual, in assumption that the AASHTO Manual is almost a copy of it.

While performing the experiment, there was always a doubt regarding the correctness of the interpretation of the procedure. Thus, in order to avoid this situation for future expriments, an experiment manual must be made costumized to better comprehension and readability.

Another very important issue is the availability of adequate and necessary equipment and faclities.  This must be provided complementary to the production of a manual.

References

A. General References

[1]        Bowles, Joseph E., Engineering Properties of Soils and Their Measurements,

            3^rd edition, 1986.

[2]        Das, Braja M., Principles of Geotechnical Engineering, 5^th edition, 2002. 

[3]        Geotechnical Engineering Manual

B. References for Particle-size Analysis—Mechanical Method

[1]        ASTM D 421 (Sample Preparation) 

[2]        ASTM D 422 (Test Procedure) 

[3]        AASHTO T 87 (Sample Preparation) 

[4]        AASHTO T 88 (Test Procedure)

C. References for Liquid- and Plastic-Limit Tests

[1]        ASTM D 4318 (Liquid Limit, Plastic Limit and Plasticity Index of Soils) 

[2]        AASHTO T 89 

[3]        AASHTO T 90