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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Back to Practice Questions
CivilSoil Mechanics
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The shape of particle size curve can be represented by

A

CuC_uCu​

B

CcC_cCc​

C

IpI_pIp​

D

IfI_fIf​

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilSoil Mechanics
Option B

CcC_cCc​

Quick Summary:

The shape of the particle size distribution curve is defined by the Coefficient of Curvature (CcC_cCc​). While the Coefficient of Uniformity (CuC_uCu​) indicates the range of particle sizes present, CcC_cCc​ provides information about the smoothness and shape of the gradation curve.

⚙️TETechnical SolutionConcept & Principle
💡 Explanation

The shape of the particle size distribution curve is defined by the Coefficient of Curvature (CcC_cCc​). While the Coefficient of Uniformity (CuC_uCu​) indicates the range of particle sizes present, CcC_cCc​ provides information about the smoothness and shape of the gradation curve.

🔢 Key Formulas

Cc=(D30)2D60×D10C_c = \frac{(D_{30})^2}{D_{60} \times D_{10}}Cc​=D60​×D10​(D30​)2​ — Coefficient of Curvature

Cu=D60D10C_u = \frac{D_{60}}{D_{10}}Cu​=D10​D60​​ — Coefficient of Uniformity

⚙️ Working Principle

The particle size distribution curve represents the percentage of soil particles passing through various sieve sizes. CcC_cCc​ is defined as the ratio of the square of the diameter at 30% passing to the product of the diameters at 60% and 10% passing. A value of CcC_cCc​ between 1 and 3 for gravelly soils and 1 and 3 for sands generally indicates a well-graded soil, meaning the soil particles are distributed over a wide range of sizes with a smooth, continuous curve.

📌 Key Points
  • ▸

    A well-graded soil must satisfy both the CuC_uCu​ and CcC_cCc​ criteria.

  • ▸

    For gravel, a soil is well-graded if Cu>4C_u > 4Cu​>4 and 1≤Cc≤31 \le C_c \le 31≤Cc​≤3.

  • ▸

    For sand, a soil is well-graded if Cu>6C_u > 6Cu​>6 and 1≤Cc≤31 \le C_c \le 31≤Cc​≤3.

  • ▸

    CcC_cCc​ is dimensionless.

✅ Advantages
  • ▸

    Helps in identifying gap-graded soils.

  • ▸

    Essential parameter for engineering classification of soils.

❌ Disadvantages / Limitations
  • ▸

    Does not account for soil plasticity or chemical properties.

  • ▸

    Requires full sieve analysis data to calculate.

🛠️ Applications / Uses
  • ▸

    Filter design in earth dams.

  • ▸

    Stability analysis of geotechnical structures.

  • ▸

    Classification of soils in the Unified Soil Classification System (USCS).

📄 Additional Information
  • ▸

    If CcC_cCc​ falls outside the 1-3 range, the soil is generally considered poorly graded or gap-graded.

  • ▸

    Option A (CuC_uCu​) represents the uniformity of particle sizes (range), not the shape of the curve.

  • ▸

    Option C (IpI_pIp​) is the Plasticity Index, related to soil consistency (Atterberg limits).

📊 Diagram / Illustration
Coefficient of Curvature (C꜀)(D₃₀)²D₆₀ × D₁₀
✅

B is correct — The Coefficient of Curvature (CcC_cCc​) represents the shape of the particle size distribution curve.

Core Concepts Used
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Particle Size Distribution Soil Gradation Geotechnical Classification
💡 EXAM TIP

Remember: CuC_uCu​ measures the spread of sizes (steepness), while CcC_cCc​ measures the curvature (shape).

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