CALCULATING GRADE AND TONNAGE OF ORE

    in Geology

    Average Grade

    The average grade of a block of ore is calculated from the average grades of the sampled openings which bound it. In a typical vein de-posit the openings consist of drifts on the levels that form the top and bottom of the block plus raises that connect the levels and form the ends of the block. The usual method of calculating the value of the block is illustrated in the following example:

    If there is much discrepancy in the values of different sides of the block, a more accurate result may be obtained by dividing the block into triangles as in Figure 12. Either method is necessarily an approximation which may give incorrect results with special and peculiar modes of ore distribution. For example, a rich patch at the corner of a block will unduly raise the assays for two of the sides. In general, wherever any part of a block is distinctly divergent in grade from the whole, it is best to calculate its value separately and then combine the result with the value of the rest of the block in proportion to volume.

    Volume

    The weight of a block of ore is estimated by first calculating the vol¬ume and then applying a factor to convert volume into tonnage.

    Tonnage

    Conversion of volume into tonnage is very simple where metric measurements are in use. All that is necessary is to multiply the volume in cubic meters by the specific gravity to get metric tons. If the volume is expressed in cubic feet, divide it by the tonnage-volume factor (the number of cubic feet in a ton of ore). This factor may be obtained in one of several ways:

    1.    Weigh the ore from an excavation of known dimensions. If this in-formation is not available from past mining operations, tests may be made by measuring one, or preferably several, faces before and after blasting and weighing the cars of ore that come from each face. Alternatively, a small-scale test may be made by excavating a hole a few feet in dimensions, weigh¬ing the material from it, and determining its volume by filling it with a measured quantity of shot, grain, or other material, Plaster of Paris may be used to make a cast of the hole. When the cast has been coated with paraffin, its volume may be measured by water displacement. The small-scale test is satisfactory if the ore is uniform but it must be repeated in many places if the ore is variable in density.

    2.    Weigh several cars of broken ore even though its original volume in place is not known. Correction is then made for voids, which amount to about 35% of the volume, but this percentage varies with uniformity of particle-size, and thus constitutes a source of error if a precise factor is required.

    3.      Measure the specific gravity of samples. Specific gravity of powdered ore is easiest to measure but gives too high a result if the ore is porous or vuggy. Specific gravity of a specimen (coated with paraffin or shellac if necessary) gives better results but does not take large vugs or cavities into account.

    4.      Estimate the specific gravity from the mineralogical composition.     (See Tables 1 and 2.)  This is subject to the same errors as Method 3, plus any inaccuracy in estimating the percentage of each mineral.    The mineralogical composition of simple ores can be calculated from the assay or the chemical analysis.

    Since ore-estimates are always on a "dry" (moisture-free) basis, any test on "natural" ore should be corrected for moisture-content. Actually, small errors in the tonnage-volume factor are less serious than errors in grade, since they do not affect the profit per ton. What they do affect is the life of the mine, which in any case cannot be estimated precisely except in plenemensurate deposits (see p. 477).

    The tonnage and average grade of each block having been calculated, the tonnages of the individual blocks are added together and their aver¬age is determined by weighting the grade of each block by the tonnage:


    Volume is average thickness times area. The average thickness will have been determined while computing the average assay. Area is either calculated by mensuration or is measured on the longitudinal sec¬tion by means of a planimeter. If widths have been measured horizontally, the area is measured directly on a longitudinal section, but if true widths are used the area as shown on the longitudinal section needs to be divided by the sine of the dip in order to correct for the foreshortening in the projection. Although the procedure just outlined is for ore on a steep vein, analogous methods would be used, of course, for a fiat-lying orebody depicted on a composite plan.

    For the volumes of thick or pipe-like orebodies, it may be convenient to use the prismoidal formula:
     

     TonsGradeTons x Grade
    Block 1
    Block 2
    Block 3
    1760
    2384
    5760
    6.1%
    8.4%
    7.4%
    10736
    20026
    42624
    Total
    Average
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