Units and Symbols - Unsaturated Soil Mechanics in Engineering Practice - page 858

APPENDIX

Units and Symbols

The universal and consistent system of units The Interna-
tional System of Units (SI) is used throughout the topic. This
version of the metric system is described in the American
Society for Testing and Materials (ASTM) (1966) Metric
Practice Guide and in ASTM Standard for Metric Prac-
tice. The SI system, which was formally recognized by the
General Conference on Weights and Measures, Rome, in
1960, has now been adopted in many countries (e.g., Great
Britain, Australia, New Zealand, Canada, and most Euro-
pean countries).
The SI system is based on seven basic units to cover the
entire spectrum of science and engineering. The units are
comprehensive and coherent. These basic units are length
(meter), mass (kilogram), time (second), electric current
(ampere), thermodynamic temperature (Kelvin), luminous
intensity (candela), and amount of a substance (mole). All
units are independent of the nature of the physical process
being considered. Only the first

gravity. Acceleration due to gravity can generally be taken
as 9.807 m/s 2 .
Table A.1 contains a list of derived units of interest to
geotechnical engineering. Pressure or stress has derived
units of pascals or newtons per square meter. This unit
is relatively small and is often used in conjunction with
a prefix. Table A.2 lists prefixes which can be used to
indicate multiples and submultiples of basic or derived
units. The prefixes are used to render numbers lying within
the range of 10 -9 -10 9.
In soil science, the picofarad has been used to desig-
nate negative pore-water pressures (Glossary of Soil Science
Terms, 1975). The picofarad was defined as the logarithm
of the negative pore-water pressure expressed as the height
of a column of water in centimeters. This unit is now con-
sidered obsolete (Johnson, 1981) and is not used in this
topic. Rather, negative pore-water pressure is expressed in
standard SI units (e.g., kilopascals).
There is often need to convert variables to other units
although the topic is written using the SI designation of
units. Table A.3 contains some conversion factors useful in
making conversions between the SI (metric) system and the
British Engineering system of units.
The symbols used throughout this topic are, for the most
part, consistent with those used in soil and rock mechanics.
The extensive list of symbols published by the Interna-
tional Society for Soil Mechanics and Foundation Engineer-
ing (ISSMFE, 1977) has been used as a guide. However,
it has been necessary to extend some of the symbols for
unsaturated soil mechanics. For example, the soil has two
fluid phases, and it becomes necessary to carry a subscript
to differentiate the air and water phases (e.g., u a and u w ).
All symbols are defined upon their first usage in the topic.
Some of the definitions are repeated from one chapter to
another. Some of the main symbols used in the topic are
summarized in Table A.4.

three units, as well as

temperature, are used in this topic.
Other physical quantities can be derived from the basic
units. For example, the unit of force is a newton. The unit
of force is derived from Newton's second law, F Ma ,

where mass M is in kilograms and acceleration a is in
meters per square second. The correct unit to express the
weight of an object is the newton, and weight is a func-
tion of gravitational acceleration. It is recommended that a
mass designation be used in engineering practice whenever
possible.
Confusion is generated when the word “weight” is used
to refer to obtaining the “mass” of an object. A laboratory
balance, for example, is used to compare two masses with
the objective of obtaining an unknown mass. This process
is commonly referred to as “weighing the object.”
The unit weight of a soil is another derived unit used
in engineering practice. It is preferable, however, to
use the density of a soil multiplied by acceleration due

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