(g) ease of use in probability analysis; 



(h) ease of use in computing statistical parameters; 



(i) amenability of more advanced analytical methods; 



(j] fairly close approximation to most other scales, 

 allowing easy adoption; and 



(k) phi-size screens are available commercially. 



No other grade scale is even close to satisfying this list and few have 

 more than three or four of these advantages. 



4. Conversions. 



Krumbein (1957) and U.S. Army, Corps of Engineers, Coastal Engineer- 

 ing Research Center (1977) provide a table for converting millimeters to 

 phi units. Conversions between phi units and millimeters can also be 

 performed easily on pocket calculators using the following equations: 



c|) = -1.4427 logg (d(mm)/lmm) (6) 



d(mm) = (1mm) (l "'^*^) rj. 



IV. EXAMPLE CALCULATIONS 



Table 2 gives the weight percentages for the two sample gsds shown 

 in Figures 1 and 2. These textural data are typical for beach sands taker 

 from the swash zone (sample 1) and the upper foreshore (sample 2) and 

 then shaken through a nest of wire-mesh sieves that are size-graded at 

 0.5-phi intervals. Figure 4 shows these same data replotted on log 

 probability paper. Table 3 contains the phi values at the 16th and 84th 

 percentiles ((})16 and 4)84) , the phi mean (Mcfi) and phi sorting (S(J)) 

 values as calculated using equations (3) and (4) . The millimeter equiva- 

 lents for the phi means are also included. 



Inspection of Figure 4 reveals that the samples are essentially iog- 

 normal as evidenced by their fairly straight- line plots through the 

 central region of the graph and confirmed by the symmetrical bell shapes 

 shown in Figure 2(b). Also, the slopes of the gsds can be used to 

 quickly evaluate sorting differences. Equal sloping plots have the same 

 sorting; however, steeper plots, such as for sample 1, indicate better 

 sorted sediment (smaller S^) than for flatter ones like sample 2 (e.g., 

 0.48 versus 0.81 phi units. Table 3). Finally, it is reemphasized that 

 phi means can be directly assigned equivalent millimeter values (as in 

 Table 3) using appropriate tables or equation (7) , but that phi sorting 

 represents the number of Wentworth grades on each side of the phi mean 

 and thus cannot be directly assigned a millimeter value. 



16 



