What is the purpose of a soil mechanics laboratory?

A soil mechanics laboratory tests soil samples to determine physical and mechanical properties such as strength, compressibility, and permeability. These data are essential for designing foundations, retaining walls, and earthworks, ensuring structures are safe and stable under expected loads.

Which ASTM standards are commonly used in soil testing?

Common ASTM standards include ASTM D1586 for SPT, ASTM D422 for grain size, ASTM D4318 for Atterberg limits, ASTM D698 for Proctor compaction, and ASTM D2850 for unconsolidated-undrained triaxial tests. These ensure consistency and reliability across laboratories.

How does seismic zone affect foundation design?

Seismic zones, defined by ASCE 7, indicate ground motion intensity during earthquakes. Higher zones require stronger foundations, deeper embedment, and sometimes soil improvement to mitigate liquefaction risk. Our laboratory provides dynamic soil properties for seismic analysis.

Particle Size Distribution Curve and Gradation Coefficients Calculator

Based on the percentage passing each sieve, this calculator plots the semi-logarithmic particle size distribution curve, interpolates D10, D30 and D60 (diameters corresponding to 10%, 30% and 60% passing) and provides the coefficients of uniformity Cu and curvature Cc. These are central parameters for classifying coarse-grained soils according to USCS (ASTM D2487), evaluating filters and drains, and verifying the suitability of aggregates for bases and subbases according to AASHTO M 43.

What is the particle size distribution curve and when is it used?

The particle size distribution curve represents the particle size distribution of a soil. D10 (effective size), D30 and D60 are reference points that allow comparing soils and judging gradation. Cu < 4-6 indicates a uniform gradation (little variety of sizes); high Cu plus 1 ≤ Cc ≤ 3 indicates well-graded. It is applied in coarse-grained soil classification, filter design using Terzaghi's criteria, selection of aggregates for concrete, verification of design band in highways, and quality control in crushing plants.

Applied Formulas

Uniformity coefficient: Cu = D60 / D10

Coefficient of curvature (or gradation): Cc = (D30)² / (D10 × D60)

Well-graded (gravel): Cu ≥ 4 and 1 ≤ Cc ≤ 3 → GW

Well-graded (sand): Cu ≥ 6 and 1 ≤ Cc ≤ 3 → SW

Logarithmic interpolation of Dx: log(Dx) = log(Da) + ((x − %Pa) / (%Pb − %Pa)) × (log(Db) − log(Da))

where Da, Db are the sizes of adjacent sieves with passing percentages %Pa and %Pb that contain the value x.

Calculation example

Input data — crushed aggregate, Til Til quarry
Sieve	Opening (mm)	Cumulative passing (%)
1"	25.4	100
¾"	19.0	88
⅜"	9.5	58
No. 4	4.75	38
No. 10	2.00	26
No. 40	0.42	14
No. 100	0.15	8
No. 200	0.075	4

D60 falls between ⅜" (58%) and ¾" (88%). Interpolating: log(D60) = log(9.5) + ((60 − 58) / (88 − 58)) × (log(19) − log(9.5)) = 0.978 + 0.067 × 0.301 = 0.998 → D60 ≈ 9.96 mm. D30 falls between No. 10 (26%) and No. 4 (38%): log(D30) = log(2.0) + ((30 − 26) / (38 − 26)) × (log(4.75) − log(2.0)) = 0.301 + 0.333 × 0.375 = 0.426 → D30 ≈ 2.67 mm. D10 falls between No. 200 (4%) and No. 100 (8%): log(D10) = log(0.075) + ((10 − 4) / (8 − 4)) × (log(0.15) − log(0.075)) = −1.125 + 1.5 × 0.301 = −0.673 → D10 ≈ 0.21 mm. With these values Cu = 9.96 / 0.21 = 47.4 and Cc = (2.67)² / (0.21 × 9.96) = 7.13 / 2.09 = 3.41.

Result: D10 = 0.21 mm · D30 = 2.67 mm · D60 = 9.96 mm · Cu = 47 · Cc = 3.4 — gravel with sand, poorly graded (Cc outside 1-3).

Interpretation of results

Cu = 47 shows a very wide range of sizes, but Cc = 3.4 falls outside the range 1-3 required by USCS to be considered well-graded. The material has a deficit in the medium range (sizes between No. 4 and ⅜"). Although it provides density, it can cause segregation during transport and non-uniform compaction. It is recommended to adjust the dosage in the plant or mix with complementary material.

Reference standards

ASTM D422 — Standard Test Method for Particle-Size Analysis of Soils (historical)
ASTM D6913 — Particle-Size Distribution of Soils Using Sieve Analysis (current)
ASTM D7928 — Particle-Size Distribution (Fine Fraction) Using Hydrometer
ASTM C136 — Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates
ASTM C33 — Standard Specification for Concrete Aggregates
AASHTO M 43 — Section 8.202.7 (aggregates for bases and subbases)

Frequently asked questions

What is the difference between Cu and Cc?

Cu measures the total range of particle sizes (how uniform or heterogeneous the soil is). Cc evaluates the shape of the curve between D10 and D60: if Cc is between 1 and 3, the curve is smooth and continuous; if it is outside, there is a step or gap in the gradation.

Can I obtain D10 if my soil has more than 10% non-sedimented fines?

Not directly. ASTM D422 and D7928 require hydrometer analysis for the fraction below 0.075 mm when it represents a significant part of the soil. Without a hydrometer, D10 is estimated by extrapolation and loses precision — it is not recommended for formal classification.

Is this curve useful for designing a drainage filter?

Yes, it is the main input. Terzaghi/USACE criteria require that the D15 of the filter be 4-5 times greater than the D85 of the base soil, and less than 4-5 times the D15 of the base. The complete particle size distribution curve is essential to apply them.

What minimum sieves should my test include?

For USCS classification, at least 3" – ¾" – No. 4 – No. 10 – No. 40 – No. 100 – No. 200 are required. For concrete or pavement aggregates, intermediate sieves are also included according to the specific band (e.g., ½" and ⅜" for stabilized base).