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SI Units in Geotechnical Engineering

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SI Units in Geotechnical Engineering R. D. Holtz ~ SI Units in Geotechnical Engineering REFERENCE: Holtz, R. D., "SI Units in Geoteehnleal Engineering," tinental European engineers. At least they tried to keep the distinc- Geotechnical Testing Journal, GTJODJ, Vol. 3, No. 2, June 1980, pp. tion between mass and force by calling the kilogram-force a "kilo- 73-79. pond" (kp). ABSTRACT: A brief description is presented of the International A modernized version of the metric system has been developing System of Units (SI) as it might be applied to geotechnical engineering. over the past 30 years. The system is known as SI, which stands for Base as well as derived SI units that are of interest to geotechnical le Syst~me International d'Unitds (The International System of engineers are described in detail, and conversion factors for units in Units). It is described in detail in ASTM E 380, the Standard for common usage are given. A few examples of conversions are also Metric Practice, available in the back of every part of the Annual presented. Book of ASTM Standards. The system may soon become the KEY WORDS: units of measurement, metric system, symbols common system in the United States and the few other countries still using Imperial or British Engineering units. In fact, Great Within the scientific and engineering community, there has Britain itself converted completely to SI in 1972, and Australia, always been some confusion as to the proper system of units for Canada, and New Zealand are presently well along the way to physical measurements and quantities. Many schemes have been conversion. Most European countries already have de facto advanced throughout the past few centuries and some, such as the conversion to SI, especially in engineering practice. Imperial or British Engineering system, the so-called metric system, and a few hybrids, have achieved moderately wide popular usage. Recently, with the growth of international cooperation and The SI Metric System trade, it has become increasingly apparent that one single, com- monly accepted system of units would be not only convenient but The SI metric system is a fully coherent and rationalized system. also of tremendous practical value. It is founded on seven basic units: for length (metre, m), mass Even though geotechnical engineering may not have the greatest (kilogram, kg), time (second, s), electric current (ampere, A), confusion of units, it undoubtedly ranks near the top of all fields in thermodynamic temperature (kelvin, K), luminous intensity the number of different systems in common usage. Laboratory (candela, cd), and amount of substance (mole). All of these basic engineers, following their counterparts in the physical sciences, units have precise definitions, names, and symbols. Units for all have attempted to use some sort of metric system, usually the cgs other physical quantities can be derived in terms of these basic (centimetre-gram-second) system for the simpler laboratory tests. units. Sometimes the derived quantities are given specific names, But they also apply the mks (metre-kilogram-second) system to such as the newton (N) for force and the watt (W) for power. The measurements of pressure and stress in consolidation and triaxial derived unit of force replaces the kilogram-force (kgf) of the mks tests and use British Engineering units for compaction tests. As system so that the name of the unit indicates that it is a unit of any teacher of soil mechanics can testify, the confusion to the force, not mass. A great advantage is that one and only one unit uninitiated is tremendous. At least practicing geotechnical exists for each physical quantity, and all other mechanical quan- engineers in North America have been somewhat consistent in the tities such as velocity, force, work, and so on can be derived from use of the British Engineering system for laboratory and field den- the basic units. In addition, the SI units for force, energy, and sities, stress measurements, and the like, although they commonly power are independent of the nature of the physical process, alternate between pounds per square foot, kips per square foot, whether mechanical, electrical, or chemical. tons per square foot, and pounds per square inch, depending on Another major advantage of SI is that it is a fully coherent system. how they or their clients feel about the subject. Fortunately, 1 ton- This means that a product or quotient of any two unit quantities is force per square foot is within 2% of 1 kgf/cm 2, a common a unit of the resulting quantity. For example, unit length squared laboratory unit for stress and pressure, and the foundation should be unit area, and unit force should be unit mass times unit engineer using consolidation test data can convert directly with lit- acceleration. Obviously, many of the engineering units in common tle error. Strictly speaking, the use of force as a basic unit is incor- use (for example, acre, pound-force, or kilogram-force), are not rect; mass should be the basic unit, with force derived according to coherent units. Also, units that might be related to basic units by Newton's Second Law of Motion. Use of the kilogram as a unit of powers of ten are not consistent within the SI system. A good ex- force is one of the difficulties with the so-called metric system, a ample is the litre (L), which is a cubic decimetrc. The equivalent modified version of the mks system that was common among con- volume of the litre has been defined as exactly 10 -3 m 3 (1000 cm3). Additional advantages of SI include the use of unique and well- IAssociate professor, School of Civil Engineering, Purdue University, defined symbols and abbreviations and the convenient decimal W. Lafayette, Ind. 47907. Member of ASTM. relation between multiples and submultiples of the basic units. © 1980 by the American Society for Testing and Materials 0149-6115180/0006-0073500.40 73 Copyright by ASTM Int'l (all rights reserved); Fri Apr 1 08:46:32 EDT 2011 Downloaded/printed by Universidade de Braslia pursuant to License Agreement. No further reproductions authorized. 74 GEOTECHNICAL TESTING JOURNAL Basle and Derived SI Metric Units TABLE 2--Prefixes for $I units. Factor Prefix Symbol Base Units The three base units of interest to geotechnical engineers are 1018 exa E 1015 peta P length, mass, and time. The SI units for these quantities are the 1012 tern T metre, the kilogram, and the second. Temperature, which might 109 giga G also be of interest, is expressed in kelvins, although the system does 106 mega M allow for use of the degree Celsius (°C), which has the same inter- 103 kilo k 102 hecto h val. Electric current is expressed in amperes. Supplementary units 101 deka da include the radian (rad) and steradian (sr), the units of plane and 10 - I deci d solid angle, respectively. 10 -2 centi c As mentioned, these basic SI units have precise physical defini- 10 -3 milli m tions. For example, contrary to a popular misconception, the 10 -6 micro /~ 10 -9 nano n metre is not the distance between two bars in Paris, but rather has 10-12 pico p been defined as being exactly equal to a certain number of wave- 10-15 femto f lengths of radiation corresponding to a specific transition level in 10 - Is atto a krypton 86. The standard kilogram is equal to the mass of the in- ternational prototype kilogram, a cylinder of platinum-iridium alloy preserved in a vault at Le Bureau International des Poids et Law, F = Ma, where the mass M is in kilograms, and the accelera- Mesures at S~vres, France. Similar standard kilograms can also be tion a is in m/s 2, all basic units. For derived combinational units found at the U.S. National Bureau of Standards near Washington, such as pressure or stress (pascals or newtons per square metre), D.C. The second has been defined as the duration of a certain multiples and submultiples of the basic metric units (in this case number of periods of the radiation corresponding to a specific metres) should be avoided. For example, N/cm 2 and N/mm 2 are transition state in cesium 133. wrong; the appropriate prefix should be used with the numerator to indicate larger or smaller quantities, for example, kPa (kN/m 2) or MPa (MN/m2). Derived Units Derived units geoteehnical engineers might use are listed in SI Units of Interest to Geoteehnleal Engineers Table 1. Prefixes are used to indicate multiples and submultiples of the basic and derived units. SI prefixes are listed in Table 2. The Length prefixes should be applied to indicate orders of magnitude of the basic or derived units and to reduce redundant zeros so that The SI unit for length, the metre, should already be familiar. numerical values lie between 0.1 and 1000. They should not be ap- (By the way, metre, not meter, is the recommended ASTM spell- plied to the denominator of compound units (kilogram is an excep- ing.) Useful SI length multiples and submultiples are the kilometre tion since it is a basic unit in the SI system). Note that spaces, not (kin), millimetre (ram), micrometre (#m), and nanometre (nm). commas, should be used to separate groups of zeros. (This latter Conversion factors for common British Engineering and mks units item was a concession to the Europeans, so that they would stop are given in Table 3. using a comma where Americans would use a decimal point.) Good SI practice suggests that multiple and submultiple metric To maintain the coherence of the system, it is recommended that units be used in increments of 1000, for example, millimetre, only basic units be used to form derived units.
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