3.1 Particle Size Analysis and Gradation Curves (ASTM D422 / D6913)

3.1 Particle Size Analysis and Gradation Curves (ASTM D422 / D6913)

In geotechnical earthwork and structural fill construction, the distribution of particle sizes governs fundamental engineering behaviors: permeability, internal shear friction, susceptibility to liquefaction, frost heave potential, and compactability. As an ICC Soils Special Inspector, verifying that fill materials comply with the project geotechnical report and contract specifications begins with understanding how laboratory technicians determine grain size distributions and interpret gradation curves.

Historically, soil particle size analysis was governed by ASTM D422 (Standard Test Method for Particle-Size Analysis of Soils). Although ASTM officially withdrew D422 in 2016, replacing it with ASTM D6913 for sieve analysis and ASTM D7928 for hydrometer analysis of fine-grained soils, ASTM D422 remains widely referenced in legacy contract specifications, municipal grading manuals, and ICC certification exam questions. The Soils Special Inspector must be thoroughly proficient in both the modern standards and their historical foundations.

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Standard Sieve Designations and Critical Engineering Boundaries

A standard mechanical sieve analysis separates coarse particles using a series of woven-wire square-mesh sieves meeting ASTM E11 specifications. Each sieve is designated either by its clear opening dimension (for sizes 3/8 in. and larger) or by a wire mesh "number" indicating the approximate number of wire openings per linear inch (for sizes No. 4 and smaller).

[!IMPORTANT] On the ICC Soils Special Inspector examination, memorize the three primary structural division sieves:

1. 3-inch (75 mm): Cobble/Gravel line.
2. No. 4 (4.75 mm): Gravel/Sand line.
3. No. 200 (0.075 mm): Sand/Fines (Silt & Clay) line.

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Laboratory Sieve Analysis Procedures (ASTM D6913 / D1140)

Conducting an accurate sieve analysis requires strict adherence to sample preparation, washing, and mechanical shaking protocols:

1. Representative Sampling and Moisture Reduction

Bulk field samples must be reduced to a representative laboratory testing size using a mechanical sample splitter or by quartering in accordance with ASTM C702. Reducing an unmixed or segregated sample introduces severe bias. The minimum dry sample mass depends directly on the nominal maximum particle size (e.g., at least 500 g for 3/8-in. maximum aggregate, 5 kg for 3/4-in. aggregate, and up to 10–15 kg for 1-1/2-in. aggregate).

2. Washing over the No. 200 Sieve (ASTM D1140)

When soils contain silt and clay fines, dry sieving alone is invalid. Fine cohesive particles adhere tenaciously to larger sand and gravel grains, and desiccated clay agglomerations ("clay balls") fail to break down under dry shaking. If shaken dry, these fines remain trapped on upper sieves, falsely inflating the measured gravel/sand percentages and understating the fines content.

• The dry mass of the initial representative specimen ($M_{dry,total}$) is recorded after oven drying at $110 \pm 5^\circ\text{C}$ per ASTM D2216.
• The soil is soaked in water (frequently with a deflocculating agent) and gently washed through a No. 200 wash sieve until the wash water runs clear.
• The retained material is oven-dried again, and the dry mass ($M_{dry,washed}$) is measured.
• The mass loss ($M_{dry,total} - M_{dry,washed}$) represents the washed fines passing the No. 200 sieve.

3. Mechanical Agitation and Sieve Shaking

The washed, dried coarse material is placed into a stack of progressively smaller sieves arranged from top to bottom, resting on a collection pan at the base. The stack is shaken in an approved mechanical shaker for a standardized duration (typically 10 to 15 minutes). Under ASTM D6913, sieving adequacy is verified by hand-shaking individual sieves: no more than 0.5% (or 1% under certain older protocols) of the retained mass on any given sieve may pass during 1 minute of vigorous hand shaking.

4. Overloading Prevention

Sieves must not be overloaded. If a layer of aggregate more than one or two particles deep covers a sieve mesh, smaller particles cannot access the openings. When large quantities are processed, intermediate sieves or split batches must be employed.

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Mathematical Framework: Calculating Cumulative Percent Passing

The fundamental data extracted from a sieve analysis is the Cumulative Percent Passing for each sieve size:

1. Individual Mass Retained ($M_i$): The mass of soil caught on sieve $i$.
2. Cumulative Mass Retained ($\Sigma M_i$): The sum of all soil masses retained on sieve $i$ and all larger sieves stacked above it: $\Sigma M_i = M_1 + M_2 + \dots + M_i$
3. Cumulative Percent Retained ($CPR_i$): $CPR_i = \left( \frac{\Sigma M_i}{M_{dry,total}} \right) \times 100\%$
4. Cumulative Percent Passing ($CPP_i$): $CPP_i = 100\% - CPR_i = 100\% - \left( \frac{\Sigma M_i}{M_{dry,total}} \right) \times 100\%$

[!NOTE] The sum of the dry mass retained on all sieves plus the material in the pan must equal the initial washed dry mass within $1%$. If the discrepancy exceeds $1%$, the test is rejected and must be rerun.

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The Semi-Logarithmic Grain Size Distribution Curve

Grain size distributions are plotted on semi-logarithmic graph paper:

• Horizontal (X) Axis: Particle diameter ($D$) in millimeters plotted on a logarithmic scale (spanning typically from 100 mm down to 0.001 mm). The logarithmic scale compresses large gravel diameters and expands fine sand/silt/clay fractions, allowing five orders of magnitude to be viewed clearly on a single page.
• Vertical (Y) Axis: Cumulative Percent Passing ($0%$ to $100%$) plotted on a linear arithmetic scale.

100% |                                      ...---*** (Well-Graded S-Curve)
     |                             ..---****
 80% |                       .---**
     |                 ..---*
 60% | D60 ---------->*                        | Uniform Sand (Steep)
     |              /                         |
 40% |             /     ________ Gap-Graded   |
     |            /     /                     |
 30% | D30 ------>* ----                      |
 20% |           /                            |
 10% | D10 ----->*                             |
  0% +-----------+------+-------+------+------+------+------->
    0.001       0.01   0.075   0.425   2.0    4.75   75.0 (Grain Diameter, mm, Log Scale)
    [--- Clay/Silt ---] [------- Sand -------] [ Gravel ]

Determining Characteristic Diameters ($D_{10}$, $D_{30}$, $D_{60}$)

By interpolating directly from the plotted curve where horizontal percentage lines intersect the distribution profile, three characteristic grain diameters are determined:

• $D_{10}$ (Effective Size): The particle diameter corresponding to 10% passing by mass. Introduced by Allen Hazen, $D_{10}$ controls the pore throat sizes of a granular matrix and strongly governs hydraulic conductivity ($k \approx C \cdot D_{10}^2$).
• $D_{30}$: The particle diameter corresponding to 30% passing by mass.
• $D_{60}$: The particle diameter corresponding to 60% passing by mass.

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Gradation Coefficients: Uniformity ($C_u$) and Curvature ($C_c$)

To quantify whether a soil has an even spread of particles across all sizes or is dominated by a single size fraction, geotechnical engineers use two dimensionless numerical indices defined in ASTM D2487:

1. Coefficient of Uniformity ($C_u$)

$C_u = \frac{D_{60}}{D_{10}}$

• $C_u$ reflects the general slope and breadth of the grain size curve.
• A value of $C_u = 1.0$ indicates a perfectly uniform soil where all particles are identical in size.
• Larger $C_u$ values indicate a wide spectrum of particle sizes spanning from fine to coarse.

2. Coefficient of Curvature / Gradation ($C_c$)

$C_c = \frac{(D_{30})^2}{D_{10} \times D_{60}}$

• $C_c$ measures the smoothness and curvature of the gradation profile between $D_{60}$ and $D_{10}$.
• A well-graded soil exhibits a balanced, gently sweeping S-curve where $C_c$ falls strictly between 1.0 and 3.0.
• If $C_c < 1.0$, the soil is deficient in intermediate particle sizes (gap-graded).
• If $C_c > 3.0$, an excess of intermediate sizes produces an irregular plateau or hump.

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Unified Soil Classification System (USCS) Well-Graded Criteria

Under ASTM D2487, coarse-grained soils with less than 5% fines passing the No. 200 sieve are classified as either well-graded or poorly graded based on strict numerical criteria:

Gravels (GW vs. GP)

A coarse-grained soil is a Gravel if more than 50% of its coarse fraction (material retained on No. 200) is retained on the No. 4 sieve:

• Well-Graded Gravel (GW): Must satisfy BOTH: $C_u \ge 4.0 \quad \text{AND} \quad 1.0 \le C_c \le 3.0$
• Poorly Graded Gravel (GP): Fails either the $C_u$ requirement, the $C_c$ requirement, or both.

Sands (SW vs. SP)

A coarse-grained soil is a Sand if 50% or more of its coarse fraction passes the No. 4 sieve:

• Well-Graded Sand (SW): Must satisfy BOTH: $C_u \ge 6.0 \quad \text{AND} \quad 1.0 \le C_c \le 3.0$
• Poorly Graded Sand (SP): Fails either the $C_u$ requirement, the $C_c$ requirement, or both.

[!WARNING] A common exam trap: A soil may have a very high $C_u$ (e.g., $C_u = 18$), indicating a wide size range, but if its $C_c = 0.7$, it fails the well-graded test because of a gap in intermediate particle sizes. It must be classified as GP or SP.

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Gradation Curve Typologies and Field Engineering Behavior

1. Well-Graded Soils (GW / SW):
   • Exhibit smooth, continuous S-shaped curves extending across a broad size spectrum.
   • Smaller particles fit snugly into voids between larger aggregate stones, achieving high compacted dry unit weights, excellent grain-to-grain interlocking, high internal friction angles ($\phi$), and minimal post-construction settlement. Ideal for structural building pads and road subbases.
2. Uniformly Graded Soils (Poorly Graded - GP / SP):
   • Exhibit steep, nearly vertical curves across a narrow range of sieve openings (e.g., dune sand, beach sand, pea gravel).
   • Particles are nearly all one size. Voids between grains cannot be filled by smaller grains, leading to lower compacted densities, poor stability under wheel traffic, and high susceptibility to liquefaction under cyclic seismic loading.
3. Gap-Graded Soils (Skip-Graded):
   • Exhibit a distinct flat, horizontal shelf or step on the semi-log curve, showing that intermediate particle sizes are completely missing.
   • Engineering Hazard: Under steady seepage forces, fine particles can wash through the large interconnected voids of the un-keyed coarse matrix without resistance—a catastrophic internal erosion process known as suffusion or piping.

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Hydrometer Analysis for Fine-Grained Soils (ASTM D7928 / ASTM D422)

When a significant percentage of soil passes the No. 200 sieve ($<0.075\text{ mm}$), mechanical sieves can no longer physically separate particles. The distribution of silt ($0.075\text{ mm}$ to $0.002\text{ mm}$) and clay ($<0.002\text{ mm}$ / 2 µm) is evaluated using sedimentation hydrometer analysis.

1. Physical Principle: Stokes' Law

Hydrometer testing relies on Stokes' Law, which governs the terminal settling velocity ($v$) of spherical particles suspended in a viscous liquid: $v = \frac{\gamma_s - \gamma_w}{18\eta} D^2$ Where:

• $v$ = terminal settling velocity ($L / t$),
• $\gamma_s$ = unit weight of soil solids ($G_s \cdot \gamma_w$),
• $\gamma_w$ = unit weight of water,
• $\eta$ = dynamic viscosity of water (temperature dependent),
• $D$ = equivalent spherical particle diameter.

Larger, denser particles settle rapidly to the bottom of a 1000 mL suspension cylinder, whereas microscopic colloidal clay particles remain suspended for hours or days.

2. Testing Protocol

• Approximately 50 g of fine soil passing the No. 10 or No. 40 sieve is mixed with distilled water and a chemical dispersing agent—standardly sodium hexametaphosphate (commercial "Calgon", 40 g/L solution). The dispersing agent neutralizes electrostatic surface charges on clay minerals, preventing them from flocculating into artificial clusters.
• The slurry is agitated thoroughly and placed in a 1000 mL sedimentation cylinder.
• A calibrated glass hydrometer (standard ASTM 151H or 152H) is inserted at precise logarithmic time intervals (e.g., 2, 5, 15, 30, 60, 240, and 1440 minutes) to measure the specific gravity or suspension density.
• Raw hydrometer readings must be corrected for temperature variations (viscosity changes), meniscus height (reading at the top of the dark fluid meniscus vs. liquid level), and the specific gravity of the dispersing agent.

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Worked Engineering Example: Calculating Gradation Parameters and USCS Symbol

Problem Statement

A sample of imported granular base material from a crushing plant is submitted for quality assurance testing. The total initial dry mass of the sample prior to washing is $M_{dry,total} = 2,500.0\text{ g}$. Washing over the No. 200 sieve leaves an oven-dried mass of $2,425.0\text{ g}$. After 15 minutes of mechanical shaking, the cumulative masses retained are recorded. The semi-log grain size curve plotted from the data yields the following characteristic diameters:

• $D_{10} = 0.42\text{ mm}$
• $D_{30} = 1.80\text{ mm}$
• $D_{60} = 6.30\text{ mm}$
• Percent passing No. 4 sieve ($4.75\text{ mm}$): $42.0%$
• Percent passing No. 200 sieve ($0.075\text{ mm}$): $3.0%$

Step 1: Determine Coarse vs. Fine and Gravel vs. Sand Proportions

1. Fines Content: Percent passing No. 200 is $3.0%$. Because $<50%$ passes No. 200, the soil is coarse-grained.
2. Coarse Fraction: $100% - 3.0% = 97.0%$ of the total sample is coarse aggregate.
3. Gravel vs. Sand Split: The percent passing the No. 4 sieve is $42.0%$. Therefore, the percent retained on the No. 4 sieve is: $\% \text{ Gravel} = 100\% - 42.0\% = 58.0\%$ Since $58.0%$ is more than half of the total coarse fraction ($58.0% / 97.0% = 59.8% > 50%$), the primary coarse constituent is Gravel.

Step 2: Calculate the Coefficient of Uniformity ($C_u$)

$C_u = \frac{D_{60}}{D_{10}} = \frac{6.30\text{ mm}}{0.42\text{ mm}} = 15.0$

Step 3: Calculate the Coefficient of Curvature ($C_c$)

$C_c = \frac{(D_{30})^2}{D_{10} \times D_{60}} = \frac{(1.80\text{ mm})^2}{(0.42\text{ mm}) \times (6.30\text{ mm})} = \frac{3.24}{2.646} = 1.22$

Step 4: Evaluate USCS Well-Graded Criteria

For a Gravel with $<5%$ fines:

• Check $C_u$: Is $C_u \ge 4.0$? Yes ($15.0 \ge 4.0$).
• Check $C_c$: Is $1.0 \le C_c \le 3.0$? Yes ($1.0 \le 1.22 \le 3.0$).

Both conditions are fully satisfied. The material is classified under ASTM D2487 as Well-Graded Gravel (GW).

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Special Inspector Field Verification Checklist

When reviewing laboratory gradation reports or observing on-site field testing, the Soils Special Inspector must confirm:

1. Representative Sampling: Sampling locations were chosen randomly without skimming off coarse surface cobbles or segregating fines.
2. Moisture Washing Protocol: Coarse samples containing silt or clay were properly washed over a No. 200 sieve per ASTM D1140 before dry mechanical shaking.
3. Mass Balance Check: Total retained dry mass plus pan mass matches pre-wash dry mass within $1%$.
4. Specification Conformance: Plotted gradation curve falls completely within the upper and lower boundary envelopes defined in the project structural earthwork specifications.