DEFINITION AND USE OF THE PHI GRADE SCALE 



by 

 H.D. HoDson 



I . INTRODUCTION 



The Unified Soils, Wentworth, and phi grade scales are commonly used 

 by coastal engineers to describe sediment texture. Of these, the phi 

 scale is least understood. This report discusses why the phi scale was 

 proposed initially, and how and when it should be used. Formulas and 

 methods are presented for using the phi notation, calculating the mean 

 grain size, and sorting of sediment samples, and for converting between 

 phi- and millimeter-based size scales. 



II. GPJVDE SCALES 



Background. 



Descriptive terms such as silt, sand, and gravel are used to describe 

 natural sediments; e.g., silty sand indicates a dominantly sandy sediment 

 containing some silt. These terms also imply actual particle-size ranges 

 as defined by the particular classification scheme being used. The term, 

 particle size, refers here to grain diameter, as determined by using 

 standard sieving (Lambe, 1967) and settling techniques (Schlee, 1966) . 



Particle sizes vary on a continuous scale which is arbitrarily 

 divided by a classification scheme into a convenient number of units for 

 describing and analyzing sediments. These divisions or scale units are 

 commonly called grades, which together constitute a grade scale. Each 

 grade scale is arbitrary in the sense that it is created to reflect 

 desired sediment properties or to facilitate the purpose for which it is 

 used. 



Most grade scales have unequal-size intervals which are advantageous 

 for two main reasons. First, the sizes of natural sediments cover such 

 a large range that an unwieldly number of equal -size grades are needed 

 to classify them (e.g., a boulder 1 meter in diameter is 1 million times 

 larger than a 1 micrometer-sized clay particle) . Second, and more impor- 

 tant, the unequal-size classes can be used to describe those differences 

 that are important to the geologist or engineer. For example, a milli- 

 meter difference in boulder sizes is insignificant but the same difference 

 between sand grain sizes is usually an important inequality. 



Grade scales must be flexible enough to be used for analytic as well 

 as descriptive purposes. Therefore, the most useful scales are usually 

 those with grades that can be easily handled for computation purposes 

 and with class limits that exhibit a systematic subdivision of particle 

 sizes. Geometric grade scales are particularly advantageous where each 

 subdivision (grade) bears a fixed ratio to preceding and succeeding grades. 

 For example, particle sizes ranging from 1,000 to 0.01 millimeters could 



