『Abstract
　Ore reserve estimation and resource prediction are important aspects of deposit exploration and mining. The cutoff has great influence on the reserve and resource calculation. Despite this, the study on the mathematical relationships of the tonnage, average grade and cutoff is still scant. According to the fractal distribution of element concentrations, which are obtained from analysis of channel samples of constant length along exploration or mining works, the tonnage-cutoff and average grade-cutoff models are constructed, which are applicable in both exploration and operating mine environments. Via these models, the relationships between ore tonnage, metal tonnage and cutoff are obtained in terms of the fractal model of element concentrations. Moreover, the thickness of the mineralized zone in each exploration or mining work follows a fractal model, and assuming that the thickness is a continuous variable, a model for calculating the mass of the mineralized zone in a single deposit is established. Given the mineralized zone mass, the tonnage-cutoff and average grade-cutoff models can be utilized to calculate ore reserve and average grade, especially when the cutoff changes. A fault-controlled disseminated-and-veinlet gold deposit in Jiaodong gold province, China, is selected as a case study. The estimates of the ore reserves obtained from these models are found to be consistent with the results obtained by the traditional geometric block method.

Keywords: Tonnage; Grade; Fractal; Reserve; Cutoff; Jiaodong』

1. Introduction
　1.1. Traditional methods for ore tonnage and average grade estimation
　1.2. Models of grade, tonnage and cutoff
　1.3. Fractal distributions of geological objects
　1.4. Research objective
2. Raw data and geological models
　2.1. Raw data and geometric block method (GBM)
　2.2. Model for calculation of mineralized zone mass
　2.3. Geological model for tonnage-cutoff model
3. Number-size model
4. Calculation of the mineralized zone mass
5. Tonnage-cutoff model
6. Average grade-cutoff model
7. Applications of the tonnage-cutoff model and average grade-cutoff model
8. Case study
　8.1. Geological setting
　8.2. Deposit exploration and raw data
　8.3. Mineralized zone mass estimation
　8.4. Relationships between tonnage, average grade and cutoff
9. Discussions and conclusions
Acknowledgements
References