1.3 Soil and Rock Classification Systems

Unified Soil Classification System (USCS - ASTM D2487)

The Unified Soil Classification System (USCS) is the standard soil classification system used in general geotechnical engineering practice. USCS categorizes soils into major groups based on grain-size distribution and Atterberg limits.

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USCS Classification Methodology

Step 1: Coarse-Grained vs. Fine-Grained Partition

• Coarse-Grained Soils: Less than $50\%$ of total dry soil mass passes the No. 200 sieve ($0.075\text{ mm}$). Designated by primary letters G (Gravel) or S (Sand).
• Fine-Grained Soils: $50\%$ or more of total dry soil mass passes the No. 200 sieve. Designated by primary letters C (Clay), M (Silt), or O (Organic).

Step 2: Coarse-Grained Soil Classification

Evaluate the coarse fraction (retained on No. 200 sieve):

• Gravel (G): $50\%$ or more of the coarse fraction is retained on the No. 4 sieve ($4.75\text{ mm}$).
• Sand (S): More than $50\%$ of the coarse fraction passes the No. 4 sieve ($4.75\text{ mm}$).

Next, evaluate the percentage of fine-grained particles passing the No. 200 sieve ($F_{200}$):

1. Clean Coarse Soils ($F_{200} < 5\%$): Use gradation criteria:

   • Coefficient of Uniformity ($C_u$): $C_u = \frac{D_{60}}{D_{10}}$
   • Coefficient of Curvature ($C_c$): $C_c = \frac{(D_{30})^2}{D_{10} \cdot D_{60}}$
   • Well-Graded Gravel (GW): $C_u \ge 4$ AND $1 \le C_c \le 3$.
   • Poorly-Graded Gravel (GP): Fails GW criteria.
   • Well-Graded Sand (SW): $C_u \ge 6$ AND $1 \le C_c \le 3$.
   • Poorly-Graded Sand (SP): Fails SW criteria.

2. Coarse Soils with High Fines ($F_{200} > 12\%$): Use Atterberg limits of fines:

   • GM / SM (Silty Gravel / Silty Sand): Fines plot below the A-line on the Plasticity Chart or $PI < 4$.
   • GC / SC (Clayey Gravel / Clayey Sand): Fines plot above the A-line on the Plasticity Chart with $PI > 7$.

3. Dual Symbol Coarse Soils ($5\% \le F_{200} \le 12\%$): Require dual symbols combining gradation and fines type (e.g., GW-GM, SP-SC).

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Step 3: Fine-Grained Soil Classification

Fine-grained soils are classified using Liquid Limit ($LL$) and Plasticity Index ($PI = LL - PL$) plotted on the Casagrande Plasticity Chart:

• A-Line Equation: $PI = 0.73 (LL - 20)$
• U-Line Equation: $PI = 0.90 (LL - 8)$ (Upper empirical bound for natural soils)

Classification Rules:

• High Plasticity ($LL \ge 50$):
  • Above A-line: CH (Fat Clay / High Plasticity Clay)
  • Below A-line: MH (Elastic Silt) or OH (Organic Clay/Silt)
• Low Plasticity ($LL < 50$):
  • Above A-line and $PI > 7$: CL (Lean Clay / Low Plasticity Clay)
  • Below A-line or $PI < 4$: ML (Silt) or OL (Organic Silt/Clay)
  • Dual Symbol CL-ML (Hatched Zone): Plots above A-line with $4 \le PI \le 7$ and $LL$ such that it falls in the transition zone.

$$\text{Plasticity Index } PI = LL - PL$$

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AASHTO Soil Classification System (M 145)

The AASHTO classification system is used primarily for highway subgrade, embankment, and pavement design. Soils are classified into groups A-1 through A-7 based on particle size distribution and Atterberg limits.

Key Division Thresholds

• Granular Materials: $\le 35\%$ passing No. 200 sieve (Groups A-1, A-2, A-3).
• Silt-Clay Materials: $> 35\%$ passing No. 200 sieve (Groups A-4, A-5, A-6, A-7).

Group Index ($GI$) Formula

To rate subgrade quality, the Group Index ($GI$) is calculated:

$$GI = (F_{200} - 35) \left[ 0.2 + 0.005(LL - 40) \right] + 0.01 (F_{200} - 15)(PI - 30)$$

Where $F_{200}$ is percentage passing No. 200 sieve (expressed as a whole number).

• $GI$ is rounded to the nearest whole integer (minimum $GI = 0$).
• A $GI = 0$ indicates an excellent subgrade, whereas $GI \ge 20$ indicates a very poor subgrade.

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Rock Mass Classification Systems

Unlike soil classification, rock mass characterization must incorporate macro-structural defects (discontinuities, joints, bedding planes, faulting).

Rock Mass Rating (RMR System - Bieniawski 1989)

The RMR system evaluates five basic parameters (total rating 0 to 100):

1. Uniaxial compressive strength of intact rock ($q_u$).
2. Rock Quality Designation ($RQD$).
3. Spacing of discontinuities.
4. Condition of discontinuities (roughness, aperture, infilling, weathering).
5. Groundwater conditions.

The sum of these ratings is adjusted for joint orientation relative to the excavation direction:

$$RMR_{final} = RMR_{basic} - \text{Adjustment for Joint Orientation}$$

Geological Strength Index (GSI - Hoek & Brown)

GSI is a visual qualitative classification system (ranging from 10 to 100) based on rock mass structure (blocky, disintegrated, laminated) and surface quality of discontinuities (very good, fair, slickensided), used directly in non-linear Hoek-Brown strength failure criteria.

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Detailed Worked Numerical Examples

Worked Example 1: USCS Soil Classification

A sieve analysis and Atterberg limit test on a soil sample yield:

• Percent passing No. 4 sieve ($4.75\text{ mm}$): $90\%$
• Percent passing No. 200 sieve ($0.075\text{ mm}$): $8\%$
• $D_{60} = 1.20\text{ mm}$, $D_{30} = 0.45\text{ mm}$, $D_{10} = 0.08\text{ mm}$
• Liquid Limit $LL = 38\%$, Plastic Limit $PL = 18\%$

Classify the soil under USCS.

Solution:

1. Coarse vs Fine: $F_{200} = 8\% < 50\% \implies$ Coarse-Grained Soil.
2. Gravel vs Sand: Coarse fraction retained on No. 200 is $100 - 8 = 92\%$. Fraction passing No. 4 is $90\%$. Coarse fraction passing No. 4 is $90 / 92 = 97.8\% > 50\% \implies$ Sand (S).
3. Fines Content ($F_{200} = 8\%$): Falls between $5\%$ and $12\% \implies$ Dual Symbol required (e.g., SW-SC, SP-SM, etc.).
4. Check Gradation: $$C_u = \frac{D_{60}}{D_{10}} = \frac{1.20}{0.08} = 15.0 \ge 6$$ $$C_c = \frac{(D_{30})^2}{D_{10} \cdot D_{60}} = \frac{(0.45)^2}{0.08 \times 1.20} = \frac{0.2025}{0.096} = 2.11 \quad (1 \le C_c \le 3)$$ Gradation meets well-graded criteria $\implies$ SW.
5. Check Fines Type: $$PI = LL - PL = 38 - 18 = 20\%$$ A-line $PI_{A-line} = 0.73(LL - 20) = 0.73(38 - 20) = 0.73 \times 18 = 13.14\%$. Since actual $PI = 20\% > 13.14\%$ (above A-line) and $PI > 7 \implies$ Clayey fines (SC).
6. Final USCS Classification: SW-SC (Well-graded sand with clay).

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Worked Example 2: AASHTO Classification and Group Index

A soil sample tested for highway subgrade evaluation has:

• Percent passing No. 10 sieve: $85\%$
• Percent passing No. 40 sieve: $62\%$
• Percent passing No. 200 sieve: $55\%$
• Liquid Limit $LL = 48\%$, Plasticity Index $PI = 24\%$

Determine the AASHTO classification and Group Index ($GI$).

Solution:

1. Granular vs Silt-Clay: $F_{200} = 55\% > 35\% \implies$ Silt-Clay Material (Groups A-4, A-5, A-6, or A-7).
2. Check A-7 Subgroups: For $LL = 48\% < 50\%$, compare $PI$ with $(LL - 30) = 48 - 30 = 18\%$. Since $PI = 24\% > 18\%$ and $LL \ge 40$, $PI \ge 11$, soil belongs to Group A-6 or A-7-6. For $LL = 48\%$, Group A-6 has max $LL = 40$. Thus it is A-7-6 ($PI > LL - 30$).
3. Calculate Group Index ($GI$): $$GI = (F_{200} - 35) \left[ 0.2 + 0.005(LL - 40) \right] + 0.01 (F_{200} - 15)(PI - 30)$$
   • Part 1: $(55 - 35) \left[ 0.2 + 0.005(48 - 40) \right] = 20 \times [0.2 + 0.04] = 20 \times 0.24 = 4.80$
   • Part 2: $0.01 \times (55 - 15) \times (24 - 30) = 0.01 \times 40 \times (-6) = -2.40$
   • Total $GI = 4.80 - 2.40 = 2.40 \approx 2$

AASHTO Symbol: A-7-6 (2).