James D. Bliss

Use of a probabilistic neural network to reduce costs of selecting construction rock

Rocks used as construction aggregate in temperate climates deteriorate to differing degrees because of repeated freezing and thawing. The magnitude of the deterioration depends on the rocks properties. Aggregate, including crushed carbonate rock, is required to have minimum geotechnical qualities before it can be used in asphalt and concrete. In order to reduce chances of premature and expensive repairs, extensive freeze-thaw tests are conducted on potential construction rocks. These tests typically involve 300 freeze-thaw cycles and can take four to five months to complete. Less time consuming tests that (1) predict durability as well as the extended freeze-thaw test or that (2) reduce the number of rocks subject to the extended test, could save considerable amounts of money. Here we use a probabilistic neural network to try and predict durability as determined by the freeze-thaw test using four rock properties measured on 843 limestone samples from the Kansas Department of Transportation. Modified freeze-thaw tests and less time consuming specific gravity (dry), specific gravity (saturated), and modified absorption tests were conducted on each sample. Durability factors of 95 or more as determined from the extensive freeze-thaw tests are viewed as acceptable—rocks with values below 95 are rejected. If only the modified freeze-thaw test is used to predict which rocks are acceptable, about 45% are misclassified. When 421 randomly selected samples and all four standardized and scaled variables were used to train aprobabilistic neural network, the rate of misclassification of 422 independent validation samples dropped to 28%. The network was trained so that each class (group) and each variable had its own coefficient (sigma). In an attempt to reduce errors further, an additional class was added to the training data to predict durability values greater than 84 and less than 98, resulting in only 11% of the samples misclassified. About 43% of the test data was classed by the neural net into the middle group—these rocks should be subject to full freeze-thaw tests. Thus, use of the probabilistic neural network would meanthat the extended test would only need be applied to 43% of the samples, and 11% of the rocks classed as acceptable would fail early.

Grade-tonnage and other models for diamond kimberlite pipes

Grade-tonnage and other quantitative models help give reasonable answers to questions about diamond kimberlite pipes. Diamond kimberlite pipes are those diamondiferous kimberlite pipes that either have been worked or are expected to be worked for diamonds. These models are not applicable to kimberlite dikes and sills or to lamproite pipes. Diamond kimberlite pipes contain a median 26 million metric tons (mt); the median diamond grade is 0.25 carat/metric ton (ct/mt). Deposit-specific models suggest that the median of the average diamond size is 0.07 ct and the median percentage of diamonds that are industrial quality is 67 percent. The percentage of diamonds that are industrial quality can be predicted from deposit grade using a regression model (log[industrial diamonds (percent)]=1.9+0.2 log[grade (ct/mt)]). The largest diamond in a diamond kimberlite pipe can be predicted from deposit tonnage using a regression model (log[largest diamond (ct)]=−1.5+0.54 log[size (mt]). The median outcrop area of diamond pipes is 12 hectares (ha). Because the pipes have similar forms, the tonnage of the deposits can be predicted by the outcrop area (log[size (mt)]=6.5+1.0 log[outcrop area (ha)]). Once a kimberlite pipe is identified, the probability is approximately .005 that it can be worked for diamonds. If a newly discovered pipe is a member of a cluster that contains a known diamond kimberlite pipe, the probability that the new discovery can be mined for diamonds is 56 times that for a newly discovered kimberlite pipe in a cluster without a diamond kimberlite pipe. About 30 percent of pipes with worked residual caps at the surface will be worked at depth. Based on the number of discovered deposits and the area of stable craton rocks thought to be well explored in South Africa, about 10−5 diamond kimberlite pipes are present per square kilometer. If this density is applicable to the South American Precambrian Shield, more than 70 undiscovered kimberlite pipes are predicted to be present.

Modeling surficial sand and gravel deposits

Mineral-deposit models are an integral part of quantitative mineral-resource assessment. As the focus of mineral-deposit modeling has moved from metals to industrial minerals, procedure has been modified and may be sufficient to model surficial sand and gravel deposits. Sand and gravel models are needed to assess resource-supply analyses for planning future development and renewal of infrastructure. Successful modeling of sand and gravel deposits must address (1) deposit volumes and geometries, (2) sizes of fragments within the deposits, (3) physical characteristics of the material, and (4) chemical composition and chemical reactivity of the material. Several models of sand and gravel volumes and geometries have been prepared and suggest the following: Sand and gravel deposits in alluvial fans have a median volume of 35 million m3. Deposits in all other geologic settings have a median volume of 5.4 million m3, a median area of 120 ha, and a median thickness of 4 m. The area of a sand and gravel deposit can be predicted from volume using a regression model (log [area (ha)] =1.47+0.79 log [volume (million m3)]). In similar fashion, the volume of a sand and gravel deposit can be predicted from area using the regression (log [volume (million m3)]=−1.45+1.07 log [area (ha)]). Classifying deposits by fragment size can be done using models of the percentage of sand, gravel, and silt within deposits. A classification scheme based on fragment size is sufficiently general to be applied anywhere.

Program to Prepare Standard Figures for Grade-Tonnage Models on a Macintosh

Grade-tonnage models are frequency distributions of deposit tonnage and grades of mineral deposits of a specific type. The program described here allows users to prepare standard figures of grade and tonnage distributions and display the deposit name associated with any of the data points. Titles and scales appropriate for most deposit types are plotted automatically for tonnage, Cu, Ni, Sn, Nb, W, Au, Hg, Mo, Zn, Pb, Ag, Co, Pt, Pd, Sb, Fe, Cr, Mn, and Ba.

An evaluation of sand and gravel resources in and near the Prescott National Forest in the Verde Valley, Arizona; with a section on evaluation of sand and gravel resources using selected engineering variables

NON-TECHNICAL SUMMARY This study was based on available published literature. Although no field investigation was conducted in the Prescott National Forest to the west of the Verde River, a field investigation was conducted in the summer of 1994 by this author on the Coconino National Forest, to the east of the Verde River, where units of surficial materials of the same age and similar character are found (Cox, 1995). The intent of this evaluation of sand and gravel resources in the Prescott National Forest and adjacent areas in the Verde Valley, is to provide the land managers of the U.S. Forest Service with a map that delineates sandand gravel-bearing geologic units. The map distinguishes (1) sandand gravel-bearing units that are limited to channels from those that are not, (2) sandand gravel-bearing units that are thin (generally less than 40 feet thick which is one contour interval on the topographic maps) from those that are locally thick (generally 40 feet or more), (3) sandand gravel-bearing units that are poorly sorted from those that are well-sorted4, (4) sandand gravel-bearing units that have little or no soil development from those that have greater degrees of soil development and lithification, (5) and sandand gravel-bearing units that support riparian vegetation from those that do not. These distinctive characteristics are related to the geologic age or depositional setting of the rock materials and can be distinguished where areas are mapped in detail. 4 Deposits of sand and gravel are usually more desirable for commercial development if not too well sorted (J. Bliss).