Lecture 3.3 — Sieve Analysis, Particle Size Distribution (PSD), and Soil Grading

Overview

• Focus: qualitative aspects of engineering with a emphasis on laboratory tests to identify soil types, specifically sieve analysis and particle size distribution (PSD).
• Document reference: Lecture 3.3 in course notes.
• Learning outcomes: start to classify soil, apply PSD methods, and understand their engineering applications.
• Recommended texts (references):
  • Craig's Mechanics of Materials/Soils, sections 1.3 and 1.4 (links on Canvas with university login).
  • Holtz, Kovacs, and perhaps C. (Geotechnical Engineering) – introduction and sections on PSD.
• Context: PSD is used to characterize field soil compositions (gravel, sand, silt, clay) for geotechnical analysis, concrete aggregates, transportation, and other applications.
• Key idea: characterize a soil as mass percentages of three fractions: gravel, sand, and fines (fines = clay + silt).

Particle Size Distribution (PSD)

• PSD combines coarse and fine analyses to describe the complete particle size distribution.
• Two main tests mentioned:
  • Sieve analysis (for coarse-grained fractions)
  • Hydrometer test (for fine-grained fractions, i.e., clay and silt)
• Practical note: Hydrometer test takes hours; sieve analysis is the practical lab exercise next week.
• PSD meaning: the distribution of particle sizes across the soil; often plotted as percent passing vs. particle size (sieve opening).
• PSD abbreviation: PSD stands for Particle Size Distribution.
• Data used in PSD: you record masses retained on each sieve and the total mass, then compute percent passing.

Sieve Analysis Procedure (lab steps you’ll perform)

• Build a stack of sieves ordered from coarse to fine, ending with a pan at the bottom (e.g., top coarse sieve to 0.06 mm pan).
• Weigh all components before testing: record the mass of each sieve (tare) and the soil mass placed on the top of the stack.
• Load the soil sample on the top sieve and shake the stack to separate particle sizes.
  • Typical shaking duration: at least 10 minutes in a lab setting; in the described session, they’ll do 5 minutes.
  • A machine is often used; in the course, you’ll do it by hand.
• After shaking, collect masses:
  • For each sieve i, measure the mass of soil retained on that sieve: $m_i$.
  • Subtract the tare weight of the sieve from the combined weight to obtain the soil mass on that sieve.
• Total mass calculation:
  • The total mass of soil M is the sum of masses retained on all sieves plus any mass in the pan (fines).
  • You can verify: $M = \sum<em>i m</em>i + m_{pan}$ (depending on how you define the pan mass in your worksheet).
• For each sieve, compute percent retained:
  • $PR<em>i = \frac{m</em>i}{M} \times 100\%$
• Compute cumulative (percent passing) for plotting PSD:
  • The standard approach is to compute percent passing for each sieve as:
  • $P<em>{pass,i} = 100\% - \sum</em>{k=1}^{i} PR_k$
  • This gives the fraction of material finer than or equal to the opening of sieve i.
• Plotting PSD:
  • X-axis: sieve opening size (mm) or corresponding particle size.
  • Y-axis: percent passing, i.e., $P_{pass,i}$.
  • The largest coarse sieve yields a dot near the top-left; the curve then descends toward finer sizes.
• Practical notes on interpretation:
  • Do not extrapolate beyond your measured data when drawing the curve; join the points and interpolate between measured points only.
  • There may be multiple possible curve shapes in regions with little or no data; avoid adding speculative trends.
• Specific example described:
  • A hypothetical soil where the top sieve shows ~90–95% passing.
  • The 0.06 mm sieve marks the boundary for fines (material that goes to the hydrometer test).
• Common lab observations:
  • The stack example might show gravel on the coarser sieves, silica-like boundaries, and finer fractions on finer sieves.
  • In practice, the distribution is rarely a simple five-size example; the actual curve will be more continuous.

Recording and Calculations (what to record in your lab notebook)

• For each sieve:
  • Record the sieve weight (tare) and the total mass on the sieve after testing to obtain the mass of soil retained: $m<em>i = (W</em>{sieve+i} - W<em>{pan}) - W</em>{tare}$ (adjust naming as per your worksheet).
  • Record the mass of the sieve before the test (sieve tare) to subtract when computing the soil mass.
• Compute totals:
  • Total soil mass: $M = \sum<em>i m</em>i$ (or include fines pan as appropriate).
• Compute percent retained and percent passing:
  • $PR<em>i = \frac{m</em>i}{M} \times 100\%$
  • $P<em>{pass,i} = 100\% - \sum</em>{k=1}^{i} PR_k$
• Use the results to identify the particle size distribution categories (gravel, sand, fines) and to prepare for classification.
• Example of a derived composition from the PSD (as given in the lecture):
  • Gravel: $33\%$
  • Sand: $64\%$
  • Fines: $3\%$
• Qualitative interpretation: this example would be described as a gravelly sand with a substantial sand fraction and a small fines fraction.

Classification and Abbreviations (how soils are described)

• Core categories: gravel (G), sand (S), fines (clay + silt).
• Silts are abbreviated as M in the lecture’s convention (Norwegian or other international considerations may use M for silt).
• Fines: clay and silt together.
• Well-graded vs poorly graded:
  • Well graded: broad distribution across particle sizes with no dominant size; the PSD curve is smooth and spread out.
  • Poorly graded: two subtypes
  • Uniform (almost vertical line): nearly a single particle size dominates (very narrow size range).
  • Gap-graded: two dominant ranges with a gap in between (a staircase-like PSD).
• Practical implication: well-graded soils tend to have different hydraulic and compaction properties than poorly graded soils (e.g., drainage, void spaces). Poorly graded soils may drain more easily because they often have larger voids, but gaps can cause issues like layering or clogging in drainage scenarios when fines are present.
• Quick qualitative heuristics from the lecture:
  • Uniform soil (poorly graded, vertical-like curve): little size variation, strong dominance of a single particle size.
  • Gap-graded soil (two dominating sizes with a gap): strong coarse and fine components but lacking intermediate sizes, creating a step-like PSD.
  • Well graded soil (no dominant size, smooth spread): broad distribution across sizes.

Quantitative metrics (readable from PSD plots)

• Effective size definitions (D-values):
  • $D<em>{10}$: the particle size corresponding to 10% passing (effective size) -> reading from the $P{pass}$ curve where P_{pass} = 10 ext{ %}.
  • $D_{30}$: corresponding to 30% passing.
  • $D_{50}$: corresponding to 50% passing (the median size).
  • $D_{60}$: corresponding to 60% passing.
  • In the example: $D<em>{10} \approx 0.2\,\text{mm}, \ D</em>{50} \approx 1\,\text{mm}, \ D_{60} \approx 2\,\text{mm}.$
• Coefficients of grading (classical soil mechanics definitions):
  • Coefficient of uniformity: $Cu = \frac{D<em>{60}}{D</em>{10}}$
  • Coefficient of curvature: $Cc = \frac{(D<em>{30})^{2}}{D</em>{10}\cdot D_{60}}$
• Interpretation using Cu and Cc:
  • Cu > ~4 and 1 < Cc < ~3 typically indicate well-graded soils (varies with standard and fine content).
  • Cu close to 1 or a small Cu with unusual Cc indicates poorly graded soils or gap-graded characteristics.

Practical implications and insights from the lecture

• The PSD and soil grading influence:
  • Hydraulic conductivity and drainage (especially with fines in layered soils).
  • Compaction and strength properties (well-graded soils often behave differently than poorly graded soils under compaction).
  • Stability of soils under load and in drainage applications (fines can be washed into or clogged within coarser layers).
• The lab exercise emphasizes:
  • Accurate mass measurements and subtraction of sieve weights to obtain soil mass per sieve.
  • Proper calculation of percent retained and percent passing.
  • Plotting the PSD and interpreting the curve without over- extrapolating beyond measured data.
• Important caveat from the lecture:
  • Extrapolating the PSD curve beyond the observed data is discouraged; always join measured points and avoid unfounded predictions.
• Why two analyses:
  • Sieve analysis captures the coarse-grain (gravel and sand) fractions.
  • Hydrometer captures the fine fraction (clay and silt).
  • Together, they form a complete PSD for the material.

Example worked through (from the lecture)

• Given a PSD sample with a measured distribution:
  • % finer than gravel boundary = 60% (example). From the curve, you compute the gravel fraction as 100% - 60% = 40%? (The lecturer then discusses deriving gravel, sand, and fines values; in the example, the final stated composition was):
  • Gravel: $33\%$
  • Sand: $64\%$
  • Fines: $3\%$
• Reading D-values from the curve:
  • D10 ≈ $0.2\,\text{mm}$, D50 ≈ $1\,\text{mm}$, D60 ≈ $2\,\text{mm}$.
• Derived properties (from the PSD in the example):
  • Coefficient of uniformity: $Cu = \frac{D<em>{60}}{D</em>{10}} = \frac{2}{0.2} = 10$ (illustrative)
  • Coefficient of curvature: $Cc = \frac{(D<em>{30})^{2}}{D</em>{10}D_{60}}$ (requires D30 value not given in the transcript; would be computed from the curve if provided).

Tomorrow’s topics (what to expect)

• We’ll discuss using the PSD curve to compute the coefficient of uniformity and the coefficient of curvature more thoroughly.
• We’ll explore additional interpretations and case studies.
• We’ll discuss how PSD results feed into subsequent geotechnical analyses and design decisions.

References and further reading

• Craig, Mechanics of Geotechnical Engineering, Sections 1.3 and 1.4 (via Canvas access).
• Holtz, Kovacs, and (third author) – Geotechnical Engineering: Introduction and PSD-related chapters.
• Course materials and lecture notes for Lecture 3.3 (Sieve Analysis and PSD).