"Symbols and definitions used in geotechnical engineering" is quoted from "Lexicon in 8 languages" (the fifth edition) published in 1981 by International Society for Soil Mechanics and Geotechnical Engineering.
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3. Physical properties of soil
a) Density and Unit Weights
Symbol | Dimension | Unit | Measured quantity | Description |
\(\rho_s\) | ML^{-3} | kg/m³ | Density of solid particles | Ratio between mass and volume of solid particles |
\(\gamma_s\) | ML^{-2}T^{-2} | kN/m³ | Unit weight of solid particles | Ratio between weight and volume of solid particles |
\(\rho_w\) | ML^{-3} | kg/m³ | Density of water | |
\(\gamma_s\) | ML^{-2}T^{-2} | kN/m³ | Unit weight of water | |
\(\rho\) | ML^{-3} | kg/m³ | Density of soil | Ratio between total mass and total volume of soil |
\(\gamma\) | ML^{-2}T^{-2} | kN/m³ | Unit weight of soil | Ratio between total weight and total volume of soil |
\(\rho_d\) | ML^{-3} | kg/m³ | Density of dry soil | Ratio between mass of solid particles and total volume of soil |
\(\gamma_d\) | ML^{-2}T^{-2} | kN/m³ | Unit weight of dry soil | Ratio between weight of solid particles and total volume of soil |
\(\rho_{sat}\) | ML^{-3} | kg/m³ | Density of saturated soil | Ratio between total mass and total volume of completely saturated soil |
\(\gamma_{sat}\) | ML^{-2}T^{-2} | kN/m³ | Unit weight of saturated soil | Ratio between total weight and total volume of completely saturated soil |
\(\rho^{_{´}}\) | ML^{-3} | kg/m³ | Density of submerged soil | Difference between density of soil and density of water |
\(\gamma^{_{´}}\) | ML^{-2}T^{-2} | kN/m³ | Unit weight of submerged soil | Difference between unit weight of soil and unit weight of water |
e | - | 1 | Void ratio | Ratio between volume of voids and volume of solid particles |
n | - | 1, % | Porosity | Ratio between volume of voids and total volume of soil |
w | - | 1, % | Water content | Ratio between weight of pore water and weight of solid particles (expressed in percentage) |
\(S_r\) | - | 1, % | Degree of saturation | Ratio between volume of pore water and volume of voids |
b) Consistency
Symbol | Dimension | Unit | Measured quantity | Description |
\(w_L\) | - | % | Liquid limit | Water content of a remoulded soil at transition between liquid and plastic states (determined by a standard laboratory test) |
\(w_P\) | - | % | Plastic limit | Water content of a remoulded soil at transition between plastic and semi-solid states (determined by a standard laboratory test) |
\(w_S\) | - | % | Shrinkage limit | Maximum water content at which a reduction of water content will not cause a decrease in volume of the soil mass |
\(I_P\) | - | % | Plasticity index | Difference between liquid and plastic limit |
\(I_L\) | - | 1 | Liquidity index | \(\large I_L=\frac {\left(w-w_p\right)} {I_P}\) |
\(I_C\) | - | 1 | Consistency index | \(\large I_C=\frac {\left(w_L-w\right)} {I_P}\) |
\(e_{max}\) | - | 1 | Void ratio in loosest state | Maximum void ratio obtainable by a standard laboratory procedure |
\(e_{min}\) | - | 1 | Void ratio in densest state | Minimum void ratio obtainable by a standard laboratory procedure |
\(I_D\) | - | 1, % | Density index | \(\large I_D=\frac {\left(e_{max}-e\right)} {\left(e_{max}-e_{min}\right)}\) |
c) Grain size
Symbol | Dimension | Unit | Measured quantity | Description |
D, d | L | mm | Grain diameter | Grain size as determined by sieve analysis or wet mechanical analysis |
\(D_n,d_n\) | L | mm | n percent-diameter | Diameter corresponding to n percent by weight of finer particles |
\(C_U\) | - | 1 | Uniformity coefficient | \(\large C_U=\frac {D_{60}} {D_{10}}\) |
d) Hydraulic properties
Symbol | Dimension | Unit | Measured quantity | Description |
h | L | m |
Hydraulic head or potential |
Sum of pressure height \(\large\left(u:\gamma_w\right)\) and geometrical height (\(\large z\;\)) above a given reference level |
q | L^{3}T^{-1} | m³/s | Rate of discharge, flow | Volume of water seeping through a given area per unit of time |
v | LT^{-1} | m/s | Discharge velocity | Rate of discharge per total unit area perpendicular to direction of flow |
i | - | 1 | Hydraulic gradient | Loss of hydraulic head per unit length in direction of flow |
k | LT^{-1} | m/s | Coefficient of permeability (hydraulic conductivity) |
Ratio between discharge velocity and corresponding hydraulic gradient \(\large\left(v:i\right)\) |
j | M L^{-2}T^{-2} | kN/m³ | Seepage force | The force due to flow with which the seeping water acts upon the soil particles in a unit volume of soil \(\large\left(j=i\cdot\gamma_w\right)\) |