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. 796 HYDRAULIC ENGINEERING '94 their survival rates (Shirazi and Selm 1981; Helfrich et. a1. 1986). In order to accomplish this, it is necessary to sample the different sediment composition~ in an eff laient and unbiased manner. Wolcott and Churcr (1991) addressed this issue and proposed that a sampl~ representative of the entire region could be obtained b'. taking sUbsamples of equal volumes and combining the; into one sample. Based on the results of an empirica: test they provide some guidelines and accuracy levels of such a sample. This paper suggests that in the future. similar approach may be possible using grid by number samples. Such a method would have a statistical basis and require less material to be sampled for the Same accuracy levels. This paper will briefly discuss some 01 the statistical properties and sample sizes of grid b) number samples. Aoouraov of Grid samDles Fripp and oiplas (1993), among others, assumed that the results of grid by number sampling are adequatel~' described by the binomial distribution. They ther. proceeded to calculate the accuracy level at which a gi ven particle size is sampled, based on the number of stones taken. Confidence intervals can then be given in percent of the entire grain size distribution. A computer program developed to simulate grid by number sampling is employed here to check the validity of this assumption. Diplas and Sutherland (1988) found that the following two properties applied to surface material: "(1)On a sediment surface, each grain on average, projects an area proportional to the square of its sieve diameter; and (2) a size fraction occupying p% of the volume of solids will occupy p% of the sample surface area occupied by grains." Using these properties, a computer can randomly select samples from a def ined volumetric distribution to examine if the accuracy levels of the sample do indeed correspond to a binomial distribution as Fripp and Diplas (1993) suggest. In this case, the selected distribution contained particle sizes from 10 mm to 160 mm in increments of 10 mm while sieve sizes ranged from 5 mm to 165 mm in increments of 10, This was chosen out of convenience, but seems appropriate since it is common practice in sieve analysis to lump the particles between two sieve sizes into a single size corresponding to the geometric mean of two adjacent sieve sizes. The accuracy of samples containing 45, 100 and 200 .~.. -<< ......M " '""'" '" ...".. "' ... L . . BENEFITS OF NUMBER SAMPLING 797 sam ling intensity and calculatin9 their median ~alues .1ndPdetermlnlng how many fell outSIde th.e 95% con~ldence t rval calculated from the method prOVIded by Frlpp and ~~p~as (1993). For samples of 45 stones, 3.33% fell t 'de this range while for 100 stones, 1 to 2% fell 0\.1 S1 " f th 1 t ide the conf ldence Interval. None 0 e samp es ~~t~ 200 stones fell outside this region. These ~esu~ts bout what we would expect and support the bInomIal ~~:t~ibution assumption. Figures 1 and 2 show sample ./ tributions obtained with 45 stones and 200 stones ~s tted beside the volumetric distribution and i~s 95% p ofidence limits. The first figure shows that whIle at c~n stones the median values stay within the co~fidence <l tervals the distributions waiver and fall outSIde this ~~qion ne~r the t~ils. F~gure 2, h~we~er, shOWS t~at at ;00 stones the dIstributIons are WIthIn the conf1dence Intervals and do ~ot waver back and forth nearly as much as in the first fIgure. Samples taken at 100 stones, not hown here are not as smooth as the 200 samples, but a~e ~etter nea~ the ends than obtained with ~5 sto~es. Th~S phenomenon can be explained bY referencIng f 19u~e 2, In rripp and oiplas (1993) which shows that for the bInomIal distribution to be valid in obtaining the sam~ accuracy levels near the tails, more stones are requlr.ed,' For example, the binomial method is valid in deSCrIbIng the accuracy level of 090 or 010 only when there are 200 or ~ore stones in the sample while 40 or more stones ~re required to compute the accuracy level for the med1an grain size (Fripp and Oiplas 1993). Siz. of Grid samDles Fripp and Diplas' (1993) figure 5 shows ~hat a grid sample with 400 stones is equivalent to ~e VrIes' (~971) low accuracy requirements for volumetrIc sample SIzes. If we assume that the sieve diameter is close to the nominal diameter of a particle and that 084 can be used to calculate the average grain volume for the entire distribution, as De Vries (1971) indicates, we c~n compare the mass of a 400 stone sample,to ~he volumetrIc sample mass. De vries' low accuracy crIterIon recom~ends sample masses of about 136 kg and 458 kg for sedIment deposits with 0 4 of 40 mm and 60 mm, respectively. ^ sample of 400 stones for the same sediments res~lts in volumes of about 36 kg and 120 kg, or about one thIrd the size of those recommended by De Vries. "