1965) developed a technique that may be used to indicate probable be- 

 havior of the borrow material on the beach» 



The procedure requires enough core borings in the borrow zone and 

 samples from the beach and nearshore zones to adequately describe the 

 size distribution of borrow and beach material. Mechanical size analyses 

 of the borings and samples are used to compute composite size distributions 

 for the two types of material. These composite distributions are compared 

 to determine the suitability of the borrow material. Almost any borrow 

 source near the shore will include some material of suitable size. Since 

 the source will control cost to a major degree, evaluation of the propor- 

 tional volume of material of the desired characteristics in the borrow 

 areas is important in economic design. Krumbein and James (1965) provide 

 the design engineer with criteria for estimating an additional amount of 

 borrow material required to meet project dimensions when the borrow mate- 

 rial does not match the characteristics of native sand or those required 

 for a stable beach. These techniques have not been fully tested in the 

 field, and should be used only as a general indication of possible fill 

 behavior. The techniques have been evaluated in one field situation with 

 favorable results (Section 6.3 PROTECTIVE BEACHES), but further investi- 

 gations are required before the quantitative reliability of these tech- 

 niques can be assessed. 



The mathematical basis of the technique is straightforward. Given 

 a borrow material with a size distribution different from the native or 

 stable material size distribution, the method determines the proportion 

 of material which must be removed from each size class of the borrow 

 material to produce a modified borrow material size distribution with 

 the same shape as that of the native material. If size distributions of 

 native and borrow material are known, and if there is some borrow material 

 in each size class that comprises the native material, the computation 

 could be made directly by finding the phi size class with the maximum 

 ratio of native to borrow weight proportions. This ratio, called the 

 cxrit-ioal ratio (R^, (^i-j^) , represents the estimated cubic yards of fill 

 material required to produce one cubic yard of material having the desired 

 particle size distribution (i.e., similar to native or stable material). 



In practice this procedure is usually not reliable. Several factors 

 lead to errors in the estimates of weight proportions of both size distri- 

 butionso These errors can be due to sampling inadequacy, estimation of 

 composite properties from individual samples, and laboratory error in 

 mechanical analysis. Computation of the critical ratio is usually subject 

 to less error if the first two graphic moments of each size distribution 

 are computed, and these values substituted into the following equation: 



^<t> crit 





■(^V« - ^#)' 



2(^0" -^0b) 



(5-1) 



5-10 



