9.2 Soil Classification Systems (USCS & AASHTO) and Atterberg Limits

9.2 Soil Classification Systems (USCS & AASHTO) and Atterberg Limits

Engineering soil classification systems bridge the gap between complex geotechnical laboratory data and practical civil engineering design. By grouping soils with similar grain size distributions and plasticity characteristics into standardized categories, engineers can quickly estimate permeability, compressibility, shear strength, compaction behavior, and subgrade suitability. On the Philippine CELE, questions testing the Unified Soil Classification System (USCS / ASTM D2487) and the American Association of State Highway and Transportation Officials (AASHTO M145) classification system appear regularly in the HGE session.

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Particle Size Distribution Analysis

Soil particle size distribution is determined experimentally using two complementary laboratory procedures based on particle diameter:

1. Mechanical Sieve Analysis (ASTM D6913, which replaced the withdrawn ASTM D422): For particles larger than $0.075\text{ mm}$ (retained on the U.S. Standard No. 200 sieve). An oven-dried soil sample is shaken through a stack of wire-cloth sieves with progressively smaller square openings:
   • $3\text{ in}$ ($75\text{ mm}$): Maximum particle size dividing boulders/cobbles from gravel.
   • $\text{No. 4}$ ($4.75\text{ mm}$): Delineates Gravel from Sand.
   • $\text{No. 10}$ ($2.00\text{ mm}$): Separates coarse sand from medium sand.
   • $\text{No. 40}$ ($0.425\text{ mm}$): Separates medium sand from fine sand; also standard fraction for Atterberg limits.
   • $\text{No. 200}$ ($0.075\text{ mm}$): Delineates Coarse-Grained from Fine-Grained soils (silts and clays).
2. Hydrometer Analysis (ASTM D7928): For particles finer than $0.075\text{ mm}$ (passing No. 200). Based on Stokes' Law, which governs the terminal settling velocity ($v$) of spherical particles suspended in a viscous liquid: $v = \frac{\rho_s - \rho_w}{18 \mu} D^2$ where $\mu$ is the dynamic viscosity of water, $\rho_s$ is particle density, and $D$ is the equivalent spherical grain diameter.

The Grain Size Distribution Curve & Gradation Parameters

Results are plotted on a semi-logarithmic chart showing Grain Diameter ($D$, mm, logarithmic scale) on the horizontal axis versus Percent Finer ($N$, %, arithmetic scale) on the vertical axis. Three critical diameter parameters are extracted:

• $D_{10}$ (Effective Size): Particle diameter corresponding to 10% passing by weight. Governs hydraulic conductivity and drainage.
• $D_{30}$: Particle diameter corresponding to 30% passing.
• $D_{60}$: Particle diameter corresponding to 60% passing.

From these characteristic diameters, two dimensionless shape parameters dictate gradation quality:

$\text{Uniformity Coefficient: } C_u = \frac{D_{60}}{D_{10}}$

$\text{Coefficient of Curvature (Gradation): } C_c = \frac{D_{30}^2}{D_{60} \cdot D_{10}}$

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Atterberg Limits & Soil Consistency

Fine-grained soils (clays and silts) are profoundly influenced by the presence of water due to mineral surface charge interactions (electrical double layer). In 1911, Swedish soil scientist Albert Atterberg established four fundamental consistency states, defined by three boundary moisture contents known as Atterberg Limits:

   Dry Solid       Semi-Solid          Plastic State           Liquid State
|--------------|-------------------|-----------------------|----------------------> Moisture (w)
0             SL                  PL                      LL
              Shrinkage           Plastic                 Liquid
              Limit               Limit                   Limit

1. Liquid Limit ($LL$): The boundary water content at which soil transitions from a plastic paste to a viscous liquid exhibiting minimal shear strength. In the standard Casagrande cup device (ASTM D4318), $LL$ is the moisture content at which a trapezoidal groove cut into a soil pat closes along a length of $12.7\text{ mm}$ ($0.5\text{ in}$) after 25 drops of the brass cup falling $10\text{ mm}$. Alternatively measured via the Fall Cone Penetrometer (BS 1377) where an $80\text{ g}$, $30^\circ$ stainless cone penetrates exactly $20\text{ mm}$ in $5\text{ seconds}$.
2. Plastic Limit ($PL$): The lowest water content at which soil remains plastic. Measured experimentally as the moisture content at which a hand-rolled soil thread begins to crumble when rolled down to a diameter of exactly $3.2\text{ mm}$ ($1/8\text{ in}$).
3. Shrinkage Limit ($SL$): The moisture content below which further loss of water causes no further volumetric shrinkage of the soil mass: $SL = w - \left[\frac{(V - V_d)\rho_w}{M_d}\right] \times 100\%$ where $V$ is initial wet volume, $V_d$ is oven-dry pat volume (determined via mercury displacement), and $M_d$ is dry mass.

Derived Consistency Indices

• Plasticity Index ($PI$): The magnitude of the plastic range: $PI = LL - PL$
  • $PI = 0$: Non-plastic (clean sand, silt)
  • $PI < 7$: Slightly plastic
  • $7 \le PI \le 17$: Medium plasticity
  • $PI > 17$: Highly plastic (expansive clays)
• Liquidity Index ($LI$): Quantifies natural in-situ moisture ($w$) relative to consistency states: $LI = \frac{w - PL}{PI}$
  • $LI < 0$ ($w < PL$): Semi-solid or solid state; brittle, overconsolidated clay.
  • $0 \le LI \le 1$ ($PL \le w \le LL$): Plastic state; soil deforms plastically under shear.
  • $LI > 1$ ($w > LL$): Viscous liquid state; sensitive or "quick" clay susceptible to catastrophic shear failure upon remolding.
• Consistency Index ($CI$): Relative consistency: $CI = \frac{LL - w}{PI} = 1 - LI$
• Skempton's Activity ($A$): Ratio of plasticity index to clay fraction ($< 0.002\text{ mm}$): $A = \frac{PI}{\text{\% finer than } 0.002\text{ mm}}$
  • Inactive ($A < 0.75$), Normal ($0.75 \le A \le 1.25$), Active ($A > 1.25$, e.g., Montmorillonite).

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The Unified Soil Classification System (USCS / ASTM D2487)

The USCS employs a two-letter group symbol where the first letter designates the primary grain size and the second describes gradation or plasticity:

• Primary Symbols: G = Gravel, S = Sand, M = Silt (Inorganic), C = Clay (Inorganic), O = Organic Silt/Clay, Pt = Peat.
• Secondary Symbols: W = Well-graded, P = Poorly-graded, M = Silty, C = Clayey, L = Low Plasticity ($LL < 50$), H = High Plasticity ($LL \ge 50$).

Loading diagram...

The Casagrande Plasticity Chart

The plasticity chart plots Liquid Limit ($LL$) versus Plasticity Index ($PI$):

• A-Line: Separates inorganic clays from inorganic silts: $PI = 0.73(LL - 20)$
  • Points plotting above the A-line represent inorganic clays (C).
  • Points plotting below the A-line represent inorganic silts (M) or organic soils (O).
• U-Line (Upper Limit): Upper empirical boundary of valid natural soil data: $PI = 0.90(LL - 8)$
• Dual Zone ($CL-ML$): The narrow horizontal strip where $LL < 50$, $4 \le PI \le 7$, and the point plots above the A-line. Designated as silty clay (CL-ML).

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The AASHTO Soil Classification System (M145)

Developed specifically for highway subgrade and embankment construction, the AASHTO system classifies soils into groups A-1 through A-7, with an assigned Group Index (GI).

1. Primary Classification Division

• Granular Materials ($\le 35\%$ passing No. 200 sieve): Subdivided into groups A-1, A-2, and A-3.
  • A-1: Stone fragments, gravel, and sand (A-1-a and A-1-b).
  • A-3: Fine beach sand or desert windblown sand (non-plastic).
  • A-2: Silty or clayey gravel and sand (A-2-4, A-2-5, A-2-6, A-2-7; granular skeleton containing up to 35% fines).
• Silt-Clay Materials ($> 35\%$ passing No. 200 sieve): Subdivided into groups A-4, A-5, A-6, and A-7.
  • A-4: Typical silty soils ($LL \le 40, PI \le 10$).
  • A-5: Elastic silty soils ($LL \ge 41, PI \le 10$; high compressibility).
  • A-6: Typical plastic clay soils ($LL \le 40, PI \ge 11$; high volume change).
  • A-7: Highly plastic clay soils ($LL \ge 41, PI \ge 11$):
    • A-7-5: $PI \le LL - 30$ (moderate plasticity index, elastic behavior).
    • A-7-6: $PI > LL - 30$ (high plasticity index, severe swelling/shrinkage).

2. AASHTO Group Index (GI) Formulation

The Group Index evaluates subgrade quality beneath highway pavements. Lower GI values indicate superior pavement subgrade performance:

$\text{GI} = (F_{200} - 35)[0.2 + 0.005(LL - 40)] + 0.01(F_{200} - 15)(PI - 10)$

where $F_{200}$ is the percentage passing the No. 200 sieve expressed as a whole number.

Strict Mathematical Rules for Group Index:

1. If the calculated $\text{GI}$ is negative, report $\text{GI} = 0$.
2. Always round $\text{GI}$ to the nearest whole integer (e.g., $3.4 \to 3$, $3.5 \to 4$).
3. For groups A-2-6 and A-2-7, only the second (partial) term of the equation is calculated: $\text{GI}_{\text{partial}} = 0.01(F_{200} - 15)(PI - 10)$
4. For groups A-1-a, A-1-b, A-3, A-2-4, and A-2-5, the Group Index is identically zero ($\text{GI} = 0$).
5. Final notation format: Group followed by GI in parentheses, e.g., A-7-6 (14).

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CELE Board-Exam Worked Situational Problem

Problem Statement

Two soil borrow sources are evaluated for a DPWH bypass road project in Cavite:

• Soil A (Coarse Borrow):
  • Sieve Analysis: Passing No. 4 sieve = 74%, Passing No. 200 sieve = 8%.
  • Grain Diameters: $D_{10} = 0.080\text{ mm}$, $D_{30} = 0.400\text{ mm}$, $D_{60} = 1.600\text{ mm}$.
  • Atterberg Limits on fraction passing No. 40: $LL = 34\%$, $PL = 26\%$.
• Soil B (Subgrade Cut):
  • Sieve Analysis: Passing No. 10 = 88%, Passing No. 40 = 64%, Passing No. 200 = 52%.
  • Atterberg Limits: $LL = 48\%$, $PL = 22\%$.

Calculate:

1. Classify Soil A under the Unified Soil Classification System (USCS).
2. Classify Soil B under the AASHTO Soil Classification System, including the Group Index (GI).

Step-by-Step Solution

Part 1: USCS Classification of Soil A

1. Coarse vs. Fine Division:
   • Percentage passing No. 200 = $8\% \le 50\%$. Therefore, Soil A is Coarse-Grained.
   • Total coarse fraction retained on No. 200 = $100\% - 8\% = 92\%$.
2. Gravel vs. Sand Division:
   • Percentage retained on No. 4 = $100\% - 74\% = 26\%$.
   • Percentage of coarse fraction passing No. 4 = $\frac{74\% - 8\%}{92\%} \times 100\% = \frac{66\%}{92\%} \times 100\% = 71.7\%$.
   • Because more than 50% of the coarse fraction passes the No. 4 sieve, the primary coarse constituent is Sand (S).
3. Fines Assessment:
   • The fines content is 8% (between 5% and 12%), requiring a Dual Symbol.
4. Gradation Evaluation: $C_u = \frac{D_{60}}{D_{10}} = \frac{1.600}{0.080} = 20.0 \ge 6$ $C_c = \frac{D_{30}^2}{D_{60} \cdot D_{10}} = \frac{(0.400)^2}{1.600 \times 0.080} = \frac{0.1600}{0.1280} = 1.25$
   • Because $C_u \ge 6$ and $1 \le C_c \le 3$, the sand is Well-Graded (SW).
5. Fines Plasticity Evaluation:
   • $PI = LL - PL = 34 - 26 = 8.0\%$.
   • Casagrande A-line at $LL = 34\%$: $PI_A = 0.73(LL - 20) = 0.73(34 - 20) = 0.73(14) = 10.22\%$
   • Because actual $PI = 8.0\% < PI_A = 10.22\%$, the fines plot below the A-line, designating them as Silt (M).
   • Final USCS Classification for Soil A: SW-SM (Well-graded sand with silt).

Part 2: AASHTO Classification of Soil B

1. Granular vs. Silt-Clay Division:
   • Percentage passing No. 200 = $52\% > 35\%$. Soil B is a Silt-Clay Material (A-4, A-5, A-6, or A-7).
2. Group Determination:
   • Liquid Limit: $LL = 48\% > 40\%$.
   • Plasticity Index: $PI = LL - PL = 48 - 22 = 26\% > 10\%$.
   • In the AASHTO classification table, soils with $LL \ge 41\%$ and $PI \ge 11\%$ belong to Group A-7.
3. Subgroup Distinction (A-7-5 vs. A-7-6):
   • Criterion value: $LL - 30 = 48 - 30 = 18\%$.
   • Compare with actual $PI$: $PI = 26\% > 18\%$.
   • Because $PI > LL - 30$, Soil B belongs to subgroup A-7-6.
4. Group Index Calculation: $\text{GI} = (F_{200} - 35)[0.2 + 0.005(LL - 40)] + 0.01(F_{200} - 15)(PI - 10)$ $\text{GI} = (52 - 35)[0.2 + 0.005(48 - 40)] + 0.01(52 - 15)(26 - 10)$ $\text{GI} = 17 \times [0.2 + 0.040] + 0.01(37)(16)$ $\text{GI} = 17 \times 0.240 + 5.920 = 4.080 + 5.920 = 10.00$
   • Rounding to the nearest whole integer yields $\text{GI} = 10$.
   • Final AASHTO Classification for Soil B: A-7-6 (10).

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CELE Board Examination Traps & Critical Pitfalls