Soil Mechanics: Weight-Volume Relationships and Soil Properties

Comprehensive vocabulary flashcards covering fundamental equations, volumetric/gravimetric relations, gradation indices, and classification ratings in geotechnical engineering and soil mechanics.

Volume Equations

Fundamental volume relationships in soil phase diagrams stating that void volume is $V_v = V_a + V_w$ and total volume is $V_T = V_v + V_s$, where $V_a$ is air volume, $V_w$ is water volume, and $V_s$ is solid volume.

Weight Equations

The basic weight relationship in soil mechanics stating that total weight is $W_T = W_s + W_w$, where $W_s$ is the weight of solid soil particles and $W_w$ is the weight of water.

Void Ratio ($e$)

The ratio of the volume of voids to the volume of soil solids, defined by the formula $e = \frac{V_v}{V_s}$.

Porosity ($n$)

The ratio of the volume of voids to the total soil volume, defined by the formula $n = \frac{V_v}{V_T}$.

Degree of Saturation ($S$)

The ratio of the volume of water to the volume of voids, defined by the formula $S = \frac{V_w}{V_v}$.

Water/Moisture Content ($\omega$)

The ratio of the weight (or mass) of water to the weight (or mass) of soil solids, defined as $\omega = \frac{W_w}{W_s} = \frac{M_w}{M_s}$.

Dry Unit Weight ($\gamma_d$)

The ratio of the weight of dry soil solids to the total soil volume, defined by the formula $\gamma_d = \frac{W_d}{V_T}$.

Moist Unit Weight ($\gamma_m$)

The ratio of the moist soil weight to the total volume, defined by the formula $\gamma_m = \frac{W_m}{V_T}$.

Saturated Unit Weight ($\gamma_{sat}$)

The unit weight of soil when all voids are completely filled with water, defined by the formula $\gamma_{sat} = \frac{W_{sat}}{V_T}$.

Submerged/Buoyant Unit Weight ($\gamma'$)

The effective unit weight of soil submerged below water, defined by the formula $\gamma' = \gamma_{sat} - \gamma_w$.

Unit Weight of Solids ($\gamma_s$)

The ratio of the weight of soil solid particles to their solid volume, defined by the formula $\gamma_s = \frac{W_s}{V_s}$.

Bulk Specific Gravity ($G$)

The ratio of the unit weight of a soil mass to the unit weight of water, defined by the formula $G = \frac{\gamma}{\gamma_w}$.

Specific Gravity of Solids ($G_s$)

The ratio of the unit weight of solid soil particles to the unit weight of water, defined by the formula $G_s = \frac{\gamma_s}{\gamma_w}$.

Air Content ($a_c$)

The ratio of the volume of air to the total soil volume, defined by $a_c = \frac{V_a}{V_T} = n(1 - S)$.

Air Void Ratio ($n_a$)

The ratio of the volume of air to the volume of voids, defined by the formula $n_a = \frac{V_a}{V_v} = 1 - S$.

Critical Hydraulic Gradient ($i_{cr}$)

The hydraulic gradient at which effective stress becomes zero, calculated as $i_{cr} = \frac{\gamma'}{\gamma_w} = \frac{G_s - 1}{1 + e}$.

Relative Density or Density Index ($D_r$)

A parameter indicating the degree of packing of granular soils, defined as $D_r = \frac{e_{\max} - e}{e_{\max} - e_{\min}} \times 100\%$, or in terms of dry unit weight as $D_r = \frac{1/\gamma_{d\min} - 1/\gamma_d}{1/\gamma_{d\min} - 1/\gamma_{d\max}} \times 100\% = \frac{\gamma_d - \gamma_{d\min}}{\gamma_{d\max} - \gamma_{d\min}} \left(\frac{\gamma_{d\max}}{\gamma_d}\right) \times 100\%$.

Relative Density ($D_r$) Classifications

Soil condition descriptions based on $D_r$ ranges: $0 - 15$ is Very Loose, $15 - 35$ is Loose, $35 - 65$ is Medium Dense, $65 - 85$ is Dense, and $85 - 100$ is Very Dense.

Relative/Percent Compaction ($R$)

The ratio of the in-situ dry unit weight to the maximum laboratory dry unit weight, expressed as $R = \frac{\gamma_d}{\gamma_{d\max}} \times 100\%$.

Effective Grain Size ($D_{10}$)

The diameter on a soil grain-size distribution curve corresponding to $10\%$ of the soil particles being finer by weight.

Average Grain Size ($D_{50}$)

The median particle diameter on a grain-size distribution curve corresponding to $50\%$ of the soil particles being finer by weight.

Coefficient of Uniformity ($C_u$)

A parameter indicating the particle size range in a soil, defined by the ratio $C_u = \frac{D_{60}}{D_{10}}$.

Coefficient of Gyration/Curvature ($C_c$)

A parameter describing the shape and gradation curve of a soil, defined by the formula $C_c = \frac{D_{30}^2}{D_{60} D_{10}}$.

Sorting Coefficient ($S_o$)

A measure of the uniformity of grain sizes in a soil sample, defined by the formula $S_o = \sqrt{\frac{D_{75}}{D_{25}}}$.

Suitability Number ($S_n$)

An empirical index used to assess backfill material suitability, defined as $S_n = 1.7 \sqrt{\frac{3}{D_{50}^2} + \frac{1}{D_{20}^2} + \frac{1}{D_{10}^2}}$.

Suitability Number ($S_n$) Ratings

Backfill ratings defined by $S_n$ value intervals: $0 - 10$ is Excellent, $10 - 20$ is Good, $20 - 30$ is Fair, and $30 - 50$ is Poor.