Conversely, if the borrow and native materials have nearly equal phi sort- 

 ing values, small errors in determining the difference in phi means can 

 cause enormous errors in computation of the critical ratio. As an example, 

 where the ratio of borrow phi sorting to native phi sorting is lo25, the 

 normalized difference in phi means is 0.5 unit so that the true difference 

 is 1»0 unit. The true critical ratio is about 3.0 which means twice as 

 much borrow material is required than that estimated with the erroneous 

 value. On the other hand, where the sorting ratio is 3, the same "erro- 

 neous" and "true" values apply to the normalized difference in phi means. 

 Here the two critical ratios are approximately 3.05 and 3.20, a difference 

 of only 5 percent. This example indicates that selecting a poorly sorted 

 borrow material may be safer when the borrow material must be finer than 

 the native material. 



Application of the above techniques is demonstrated below with two 

 example problems. 



************** EXAMPLE PROBLEM *************** 



GIVEN : Composite native beach material phi parameters 



084 = 2.47 (0.180 mm) , 



(Ajg ^ 1.41 (p (0.376 mm) . 

 composite borrow material parameters 



084 = 3.41 (0.094 mm) , 

 0jg = 1.67 (0.314 mm) . 

 FIND : 



(a) R^ Q-^i^ 



(b) Applicable case for computing overfill ratio 



(c) Interpreted overfill ratio (cy fill/cy project requirements) 

 SOLUTION : 



(a) Using Equation 5-3 



084 +"^16 

 Ma = , 



and 



2.47 + 1.41 

 M0„ = 2 " ^ (0.261mm) , 



3.41 + 1.67 

 M^. = = 2.54 (0.172 mm) . 



5-16 



