Fractal models for ore reserve estimation

Wang, Qingfei; Deng, Jun; Liu, Huan; Yang, Liqiang; Wan, Li; Zhang, Ruizhong

doi:10.1016/j.oregeorev.2009.11.002

Cited by 80 publications

(22 citation statements)

References 43 publications

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“…The number-size model [42,43] is the most often used among the various fractal models, which also include the box counting model [44,45]; the radial density model [46]; the grade-tonnage model [44,47]; the self-affine model [43]; and the multifractal model [48,49]. Wang et al [35] developed an ore estimation method based on the fractal number-size model. Since the traditional geometric and geo-statistic methods based on linear mathematics are not able to handle the skewed distribution of karst caverns, fractal models that belong to nonlinear mathematics are deemed as effective tools for describing the skewed distribution of geological objects [35,42,43].…”

Section: Methodsmentioning

confidence: 99%

“…Mandelbrot (1983) [34] developed the fractal theory, which can be utilized to describe the distribution of geotechnical objects that are neither random nor homogeneous. Wang et al [35] established an estimation method for an ore reserve based on the number-size model. Since fractal theory can handle irregularly distributed karst caverns with various shapes, this may be helpful in predicting the total volume of karst caverns along a shield tunneling alignment [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

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Fractal Prediction of Grouting Volume for Treating Karst Caverns along a Shield Tunneling Alignment

et al. 2017

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Karst geology is common in China, and buried karst formations are widely distributed in Guangdong province. In the process of shield tunneling, the abundant water resources present in karst caverns could lead to the potential for high water ingress, and a subsequent in situ stress change-induced stratum collapse. The development and distribution of karst caverns should therefore be identified and investigated prior to shield tunnel construction. Grouting is an efficient measure to stabilize karst caverns. The total volume of karst caverns along the shield tunneling alignment, and its relationship with the required volume of grouts, should be evaluated in the preliminary design phase. Conventionally, the total volume of karst caverns is empirically estimated based on limited geological drilling hole data; however, accurate results are rarely obtained. This study investigates the hydrogeology and engineering geology of Guangzhou, the capital of Guangdong province, and determines the fractal characteristics of the karst caverns along the tunnel section of Guangzhou metro line no. 9. The karst grouting coefficients (V R ) were found to vary from 0.11 in the case of inadequate drilling holes to 1.1 in the case where adequate drilling holes are provided. A grouting design guideline was furthermore developed in this study for future projects in karst areas.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractal Prediction of Grouting Volume for Treating Karst Caverns along a Shield Tunneling Alignment

et al. 2017

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“…Since the fault displacement in a fault system follows the number-size model, Scholz and Cowie (1990) constructed a model to calculate the total displacement of the fault system. Wang et al (2010a) applied the number-size model to describe the distributions of mineralization variables, such as orebody thickness and grade-thickness in a single deposit, and then derived a fractal model for ore reserve estimation. Wang et al (2010b) further deduced a tonnagecutoff model for a single deposit, based on the number-size model of element concentrations of the samples with constant length along exploration or mining works, and proposed that the ore tonnage and cutoff, corresponding to the variables, number and size, in the number-size model respectively, follow a fractal relationship.…”

Section: Itmentioning

confidence: 99%

Number-average size model for geological systems and its application in economic geology

Wang

Wan

Zhang

et al. 2011

Nonlin. Processes Geophys.

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Abstract.Various natural objects follow a number-size relationship in the fractal domain. In such relationship, the accumulative number of the objects beyond a given size shows a power-law relationship with the size. Yet in most cases, we also need to know the relationship between the accumulative number of the objects and their average size. A generalized number-size model and a number-average size model are constructed in this paper. In the number-average size model, the accumulative number shows a power-law relationship with the average size when the given size is much less than the maximum size of the objects. When the fractal dimension D s of the number-size model is smaller than 1, the fractal dimension D m of the number-average size model is almost equal to 1; and when D s > 1, the D m is approximately equal to D s . In mineral deposits, according to the numberaverage size model, the ore tonnage may show a fractal relationship with the grade, as the cutoff changes for a single ore deposit. This is demonstrated by a study of the relationship between tonnage and grade in the Reshuitang epithermal hotspring gold deposit, China.

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“…Examples of fractal models include the number-size (N-S) model proposed by Mandelbrot [14], the concentration-area (C-A) model of Cheng et al [16], the concentration-perimeter (C-P) model of Cheng et al [17], the concentration-distance (C-D) model proposed by Li et al [18], and the concentrationvolume (C-V) model of Afzal et al [19]. Fractal/multifractal modeling assists in identifying relationships between geological, geochemical, and mineralogical settings and linking them to spatial information obtained from mineral deposits [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Various geochemical and mineralization processes can be defined due to differences in fractal dimensions, based on analysis of relevant geochemical data.…”

Section: Introductionmentioning

confidence: 99%

Identification of mineralized zones in the Zardu area, Kushk SEDEX deposit (Central Iran), based on geological and multifractal modeling

et al. 2016

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Abstract:The aim of this paper is to delineate the different lead-zinc mineralized zones in the Zardu area of the Kushk zinc-lead stratabound SEDEX deposit, Central Iran, through concentration-volume (C-V) modeling of geological and lithogeochemical drillcore data. The geological model demonstrated that the massive sulfide and pyrite+dolomite ore types as main rock types hosting mineralization. The C-V fractal modeling used lead, zinc and iron geochemical data to outline four types of mineralized zones, which were then compared to the mineralized rock types identified in the geological model. 'Enriched' mineralized zones contain lead and zinc values higher than 6.93% and 19.95%, respectively, with iron values lower than 12.02%. Areas where lead and zinc values were higher than 1.58% and 5.88%, respectively, and iron grades lower than 22% are labelled "high-grade" mineralized zones, and these zones are linked to massive sulfide and pyrite+dolomite lithologies of the geological model. Weakly mineralized zones, labelled 'low-grade' in the C-V model have 0-0.63% lead, 0-3.16% zinc and > 30.19% iron, and are correlated to those lithological units labeled as gangue in the geological model, including shales and dolomites, pyritized dolomites. Finally, a log-ratio matrix was employed to validate the results obtained and check correlations between the geological and fractal modeling. Using this method, a high overall accuracy (OA) was confirmed for the correlation between the enriched and highgrade mineralized zones and two lithological units -the massive sulfide and pyrite+dolomite ore types.

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Fractal models for ore reserve estimation

Cited by 80 publications

References 43 publications

Fractal Prediction of Grouting Volume for Treating Karst Caverns along a Shield Tunneling Alignment

Fractal Prediction of Grouting Volume for Treating Karst Caverns along a Shield Tunneling Alignment

Number-average size model for geological systems and its application in economic geology

Identification of mineralized zones in the Zardu area, Kushk SEDEX deposit (Central Iran), based on geological and multifractal modeling

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