Properties of Soils - 2 - Civil Engineering SSC JE (Technical) - Civil Engineering

Methods for the Determination of In-situ Unit Weight

Unit weight (also called unit mass or bulk density) of soil at a given depth is required to compute the overburden pressure and for many geotechnical calculations. Common in-situ methods to determine unit weight are described below.

(I) Core-Cutter Method

• Applicability: Suitable for non-cohesive soils (sands). Not suitable for very hard or very gravely soils.
• Principle and procedure: A cylindrical core-cutter of known volume (commonly 1000 cm³) is driven into the soil and removed. The cutter, filled with the in-situ soil, is trimmed and weighed. The bulk unit weight is obtained by dividing the mass of the soil in the cutter by the cutter volume.
• Dry unit weight: If the water content is determined (in the laboratory) for the same sample, the dry unit weight can be computed from the measured bulk unit weight and water content.
• Formulas:     

(II) Sand Replacement Method

• Applicability: Used to determine in-place dry density of natural or compacted fine- to medium-grained soils and is applicable to surface layers not exceeding about 15 cm thickness. It is also used where cores cannot be obtained, and it is suitable for hard and gravely soils.
• Principle and procedure: An excavation is made at the test location and the removed soil is collected and weighed. The volume of the hole is measured by refilling it with standard sand of known unit weight; the mass of the excavated soil divided by the measured volume gives the in-situ bulk unit weight. Dry unit weight is then obtained by correcting for water content.

(III) Water Displacement Method

• Applicability: Suitable for cohesive soils where an intact lump sample can be trimmed to a regular shape.
• Principle and procedure: A trimmed, regular-shaped specimen is first weighed (W₁), then coated with paraffin wax and re-weighed (W₂). The waxed specimen is placed in a container of water filled to the brim and the displaced volume of water (V_w) is measured. The volume of the uncoated specimen, V, equals the displaced volume minus the volume of wax coating.
• Formula for specimen volume: V = V_w - (W₂ - W₁)/g_p, where g_p is the unit weight of paraffin wax.
• Dry density: Dry density = (W₁/V) ÷ (1 + w), where w is the water content (expressed as a ratio).

Grain Size Distribution (Particle Size Analysis)

Grain size distribution describes the proportions of different particle sizes in a soil sample. The common laboratory methods are chosen according to the dominant grain size.

• Coarse-grained soils (gravels and sands): Sieve analysis is used. For very coarse fractions,dry sieve analysis is used. For finer sand fractions a wet sieve analysis may be employed to avoid particle aggregation.
• Fine-grained soils (silts and clays): Sedimentation analysis is used. Two standard sedimentation methods are the hydrometer method and the pipette method.

(I) Sieve Analysis

Soil retained on the 4.75 mm sieve is treated as the gravel fraction and is analysed using coarse sieve analysis. Soil passing the 4.75 mm sieve is further tested using fine sieves (for sand), or a combined sieve and sedimentation analysis when silt and clay are present.

Concepts

• Cumulative percent retained: Sum of the percentage retained on that sieve and on all coarser (larger) sieves.
• Percentage finer than a given sieve: 100% - cumulative percent retained.

(II) Sedimentation Analysis

Sedimentation methods are based on particle settling velocities in a fluid governed by Stoke's law (for small Reynolds numbers, laminar flow). The terminal settling velocity, v, for a spherical particle of diameter D is given by Stoke's relation:

where r_s is the particle density (g/cm³), r_w is the water density (g/cm³), µ is the dynamic viscosity of water, g is acceleration due to gravity and D is particle diameter.

By substituting standard values at 20°C, a practical approximation used in soil testing is:

v = 91 D², where v is in cm/s and D is in mm.

Stoke’s law is valid for nearly spherical soil particles with diameters between 0.2 mm and 0.0002 mm. For larger particles, turbulent flow occurs, and for smaller particles, Brownian motion affects settling, making the results unreliable.

Pipette Method

In the pipette method the mass of solids per unit volume of suspension is determined directly by collecting a known volume (for example, 10 cm³) of the soil suspension from a specified sampling depth and time.

If m_d is the dry mass of solids obtained after drying the pipetted sample, the mass of solids per unit volume of suspension and the percentage finer are calculated from measured quantities and correction factors as per the standard procedure.

Hydrometer Method

In the hydrometer method the specific gravity (density) of a soil suspension is measured as a function of time. From the suspension density at a known effective depth the concentration (mass of soil per unit volume) of solids remaining in suspension is inferred, and hence the percentage finer for the corresponding particle size.

Calibration of the Hydrometer

Calibration establishes the relation between the hydrometer reading R_H and the effective depth H_e at which the hydrometer measures the density. The effective depth is the vertical distance from the suspension surface to the plane where the hydrometer senses the density. It is given by

H_e = H₁ + (1/2) (h - V_h / A_j),

where A_j is the cross-sectional area of the jar, V_h is the volume of the hydrometer bulb and H₁ is the distance from the hydrometer neck reference to the chosen hydrometer reading.

If R_c is the corrected hydrometer reading, the specific gravity of the suspension is equal to 1 + R_c/100. The immersed weight of solids per unit volume of suspension can be related to the hydrometer reading and the particle specific gravity G_s. One useful expression obtained in standard practice is

W_d = (G_s / (G_s - 1)) × (R_c / 100),

where W_d is the mass of dry solids per unit volume of suspension represented by the corrected hydrometer reading.

Corrections to Hydrometer Readings

• Meniscus correction (C_m): Hydrometer readings refer to the top of the meniscus; a correction is applied so that the reading represents the true level.
• Temperature correction (C_t): Hydrometers are calibrated at a standard temperature (typically 27°C). If the test temperature differs, a temperature correction is added (if test temperature > standard) or subtracted (if test temperature < standard).
• Dispersing-agent correction (C_d): Addition of dispersing (deflocculating) agent changes the density of the suspension; this causes a correction (C_d), which is generally subtracted. C_d is usually negative.

Corrected hydrometer reading: R_H(corrected) = R_H + C_m ± C_t - C_d.

Grain Size Distribution Curves

Typical gradation curves and their interpretations:

• Curve-1 - Well graded: Smooth curve, particles well distributed over a wide size range.
• Curve-2 - Poorly graded (uniform): Most particles are of approximately the same size; the curve is steep in some region.
• Curve-3 - Gap graded: Some intermediate particle sizes are missing.
• Curve-4 - Predominantly coarse: Very coarse particles dominate the sample.
• Curve-5 - Predominantly fine: Fine particles dominate the sample.

A steep slope implies a poorly graded (uniform) soil and a gently inclined curve implies a well graded soil.

Key diameters from the curve: D₁₀ (effective size) is the particle diameter corresponding to 10% finer by weight. D₃₀ and D₆₀ correspond to 30% and 60% finer, respectively.

Shape Parameters from Grain-Size Curve

Coefficient of Uniformity, C_u:

Coefficient of Curvature, C_c:

Acceptance criteria for a well-graded soil:

• For gravels: 1 < C_c < 3 and C_u > 4.
• For sands: 1 < C_c < 3 and C_u > 6.
• C_u > 1 corresponds to non-uniform (poorly graded) soils. C_u close to 1 indicates uniform (single-sized) material.

Consistency of Clays - Atterberg Limits

Important limits:

• W_L - Liquid limit: Water content at which soil changes from plastic to liquid behaviour.
• W_P - Plastic limit: Water content at which soil changes from semi-solid to plastic behaviour.
• W_S - Shrinkage limit: Water content at which soil stops shrinking on drying.

(I) Plasticity Index, I_P: I_P = W_L - W_P. It is the range of water contents over which the soil behaves plastically. Soils with large W_L and large I_P are termed highly plastic or fat clays; soils with small values are lean clays.

Coarse-grained soils generally cannot show plasticity, so W_L and W_P coincide and I_P ≈ 0. When limits cannot be determined, the soil may be reported as non-plastic. If W_P ≥ W_L, report I_P = 0.

(II) Consistency Index, I_C:

Interpretation:

• If W_n = W_L, I_C = 0 (soil at liquid limit).
• If W_n = W_P, I_C = 1 (soil at plastic limit).
• If I_C < 0, natural water content exceeds the liquid limit and the soil behaves like a liquid (on disturbance).
• If I_C > 1, soil is in semi-solid or solid state and will be very stiff or hard.

(III) Liquidity Index, I_L:

For soils in the plastic state 0 < I_L < 1.

(IV) Flow Index, I_f:

Flow Curve Analyis in water content graph

(V) Toughness Index, I_t:

When I_t < 1 the soil is friable (easily crushed) at the plastic limit.

Shrinkage Ratio (SR)

Definitions related to shrinkage:

• V₁ = volume of soil mass at water content W₁%
• V₂ = volume of soil mass at water content W₂%
• V_d = volume of dry soil mass

At the shrinkage limit, W₂ = W_S and V₂ = V_d, and the shrinkage ratio and related expressions are obtained from the standard relations below.

Stress-Strain Behaviour for Different Consistency States

Unconfined compressive strength, q_u: Defined as the load per unit area at which an unconfined prismatic or cylindrical specimen of standard dimensions fails in simple compression. For undrained tests on clays,

q_u = 2 × shear strength (undrained condition).

Sensitivity (S_t)

Sensitivity is defined as the ratio of the unconfined compressive strength of an undisturbed specimen to the unconfined compressive strength of the same soil after remoulding at the original water content:

Classification based on sensitivity:

Thixotropy: Some clays show thixotropic behaviour - after remoulding they regain part of the strength if left undisturbed at the same moisture content. Higher sensitivity soils typically show greater thixotropic hardening.

Relative Density / Density Index (for Granular Soils)

Relative density (density index) is a measure of compactness of granular soils and is defined by:

• e_max = void ratio in the loosest state
• e_min = void ratio in the densest state
• e = void ratio in the natural state

Relative density, I_D, is calculated from the standard relation (see figure/equation):

Typical classification based on relative density:

For idealised granular material formed of uniform spherical grains, approximate limiting void ratios are:

• e_max ≈ 0.91
• e_min ≈ 0.35