Specific gravity of soil mass is the ratio of

Question

Examoogle · Accepted Answer

The correct answer is Option C: $\frac{\gamma_s}{\gamma_w}$. The specific gravity ($G$) of soil solids is defined as the ratio of the unit weight of soil solids ($\gamma_s$) to the unit weight of distilled water ($\gamma_w$) at a standard temperature, typically $4^\circ C$. It is a dimensionless quantity that reflects the density of the soil particles relative to water.

Step-by-Step Solution & Concepts:
The specific gravity ($G$) of soil solids is defined as the ratio of the unit weight of soil solids ($\gamma_s$) to the unit weight of distilled water ($\gamma_w$) at a standard temperature, typically $4^\circ C$. It is a dimensionless quantity that reflects the density of the soil particles relative to water.

Working Principle: The principle relies on Archimedes' buoyancy and density definitions. By determining the mass of a known volume of dry soil particles using a pycnometer and comparing it to the mass of an equal volume of water, the specific gravity is calculated, which serves as a fundamental index property for classifying soil and calculating void ratios.

Key Formulas: $G = \frac{\gamma_s}{\gamma_w}$ — Definition of specific gravity of soil solids; $G = \frac{M_s}{V_s \cdot \gamma_w}$ — Mass-volume relationship form

Key Points: Specific gravity is a dimensionless quantity.; For most inorganic soils, $G$ typically ranges between 2.60 and 2.80.; The value is essential for determining void ratio ($e$) using the relationship $e = \frac{G \cdot \gamma_w}{\gamma_d} - 1$.; It is usually determined in the laboratory using a pycnometer or density bottle.

Advantages: Useful in calculating the void ratio and degree of saturation.; Assists in identifying mineralogical composition of soil.

Disadvantages: Does not account for the influence of organic matter (which lowers $G$).; Experimental measurement requires precise temperature control.

Applications: Soil classification and index property determination.; Calculation of dry density and unit weight relations in geotechnical engineering.

Additional Info: The value of $G$ is generally taken as 2.65 for quartz-based sands.. Option A is incorrect as it represents the bulk unit weight ratio, Option B is inverted, and Option D is the reciprocal of specific gravity.

Answer: C is correct — Specific gravity of soil solids is defined as the ratio of the unit weight of soil solids to the unit weight of distilled water.

Exam Tip: Remember that specific gravity of solids ($G_s$) is distinct from bulk specific gravity ($G_m$); always check if the question specifies 'soil mass' or 'soil solids'.

Examoogle · Answer

Option A: $\frac{\gamma}{\gamma_w}$

Examoogle · Answer

Option B: $\frac{\gamma_w}{\gamma_s}$

Examoogle · Answer

Option D: $\frac{\gamma_w}{\gamma}$

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