Block model design strongly influences how accurately tonnage and grade are estimated and how confidently resources can be classified. This article explains how different block sizes (20×20×10 m vs 5×5×5 m) interact with a 2 m composite interval under efficient kriging, and shows how to connect block size choice to resource classification and confidence.

Block Size, Sampling Support, and Kriging

Three key factors control block‑model accuracy:

  • Sampling density and variogram range
  • Block size relative to data spacing
  • Estimation method and uncertainty diagnostics (kriging variance, kriging efficiency, slope of regression)

Block size must be chosen so that it is commensurate with the variogram range and drill spacing, typically about ½–⅓ of the drill spacing for optimal balance between accuracy and mine planning practicality (Rezaei and Fallahi, 2023; Rezaei et al., 2022; Hassani, 2019; Hekmat, Osanloo and Moarefvand, 2011). Larger blocks are easier to estimate (lower relative variance) but over‑smooth local variability and can degrade selectivity (Rezaei and Fallahi, 2023; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011). Smaller blocks capture geological detail and grade variability, but can be noisy and require more samples to keep uncertainty acceptable (Rezaei and Fallahi, 2023; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

A controlled simulation study explicitly tested multiple block sizes and estimation methods and concluded that variogram range, not just sampling density, is the main guide to block size, and proposed a geometric formula to select an “optimum” size that minimizes the discrepancy between “real” and estimated block grades (Hekmat, Osanloo and Moarefvand, 2011). This emphasizes that any choice between 20×20×10 m and 5×5×5 m must be checked against the variogram ranges and drill grid.

Evidence from Block Size Studies

Studies on real deposits and simulations show consistent patterns:

  • In a phosphate deposit, increasing block size from 3×3 m to 7×7 m produced a systematic decline in ore grade and increased losses and dilution, because coarse blocks mixed ore and waste. A 5×5 m excavation unit was identified as optimal for balancing modeling accuracy with operational feasibility and acceptable losses/dilution (Mussin et al., 2025).
  • In the Angouran Zn–Pb deposit, a 10×10×10 m block size was chosen for a 25 m drill spacing (≈½–⅓ of spacing), and this configuration gave acceptable correlation with production data and significantly reduced grade and tonnage errors compared with a previous model (Rezaei and Fallahi, 2023).
  • For an iron skarn, optimal block size was determined by a multi‑criteria optimization (VIKOR) and then used with ordinary kriging to estimate ~82–83 Mt at ~42% Fe, followed by classification based on relative estimation error variance and JORC categories (Rezaei et al., 2022; Hassani, 2019).
  • A simulation study comparing ordinary kriging, inverse distance, and nearest neighbor showed that block size strongly affects the discrepancy between “true” and estimated block grades, and that choosing block size from the variogram range yields acceptable economic outcomes and higher information value (Hekmat, Osanloo and Moarefvand, 2011).

Overall, when block dimensions approach or exceed the variogram range or exceed ~⅓ of the drill spacing, grade smoothing and misclassification (ore vs waste) increase, reducing accuracy of tonnage and grade (Mussin et al., 2025; Rezaei and Fallahi, 2023; Rezaei et al., 2022; Hassani, 2019; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

20×20×10 m vs 5×5×5 m with 2 m Composites

A 2 m composite length defines the data support, but the change of support to block size is handled through kriging and the variogram model (Nwaila et al., 2023). Two stylized situations illustrate the trade‑offs.

Assume a horizontal drill spacing of 25 m, vertical sampling close to 2 m, and a main variogram range of ~30–40 m in the horizontal directions (values typical of many case studies (Rezaei and Fallahi, 2023; Rezaei et al., 2022; Hekmat, Osanloo and Moarefvand, 2011)):

  • 20×20×10 m blocks
    • Horizontal dimensions ≈ drill spacing, vertical dimension much larger than composite.
    • Advantages:
      • Lower kriging variance per block; fewer blocks per volume, easier estimation (Rezaei and Fallahi, 2023; Rezaei et al., 2022).
      • Good for high‑level, strategic tonnage/grade forecasts.
    • Disadvantages:
      • Strong change of support: 10 m vertical thickness aggregates 5 composites; smoothing reduces local grade contrasts.
      • Greater risk of ore–waste mixing, dilution, and loss, particularly in thin or layered deposits (Mussin et al., 2025; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).
      • Less selectivity for short‑term scheduling.
  • 5×5×5 m blocks
    • Dimensions much smaller than drill spacing; vertical dimension closer to composite length.
    • Advantages:
      • Better representation of geological heterogeneity and grade variability, lower dilution in thin orebodies (Mussin et al., 2025; Nwaila et al., 2023).
      • More selective mining and better alignment with excavation unit sizes where such equipment is available; 5×5 m was optimal in the phosphate case study (Mussin et al., 2025).
    • Disadvantages:
      • Higher kriging variance per block (each block is informed by fewer samples) if no sub‑blocking or careful search strategy is used (Rezaei and Fallahi, 2023; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).
      • Requires more computational effort, careful control of minimum/maximum samples, and sometimes post‑processing (e.g., microblocks aggregated to macroblocks) (Nwaila et al., 2023; Nwaila and Carranza, 2025).

Which is more accurate in tonnage and grade?

Accuracy can be defined two ways:

  1. Global accuracy: how close total tonnage and mean grade are to reality.
  2. Local/selective accuracy: how well individual blocks or mining panels represent true grade (minimizing misclassification, dilution, and ore loss).

Evidence indicates:

  • Larger blocks (like 20×20×10) tend to reduce random local error but introduce systematic smoothing, which can bias recovered ore tonnage and grade selectivity (Mussin et al., 2025; Rezaei and Fallahi, 2023; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).
  • Smaller blocks (like 5×5×5) improve selective mining accuracy, reduce dilution and ore loss, and better match complex geology when coupled with adequate estimation constraints (Mussin et al., 2025; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

Where adequate drill density and robust variograms exist, and if the block size still respects the ½–⅓ drill spacing rule, smaller blocks generally give better reconciliation of selective tonnage and grade, especially in thin or heterogeneous deposits (Mussin et al., 2025; Rezaei and Fallahi, 2023; Rezaei et al., 2022; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011). However, if drilling is sparse and variogram ranges are long, very small blocks will carry high uncertainty and may not improve practical accuracy without further constraints (Rezaei and Fallahi, 2023; Nwaila and Carranza, 2025; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

Efficient Kriging and Quantifying Block Uncertainty

Modern resource classification practice applies kriging and associated uncertainty diagnostics to guide both block size and classification:

  • Kriging variance: formal estimate of the estimation variance per block.
  • Block error or relative estimation error variance: ratio of estimation variance to the true block variance, often used directly in classification (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Rezaei et al., 2022; Hassani, 2019).
  • Kriging efficiency (KE): usually defined as 1 – (estimation variance / sample variance); higher KE indicates more reliable estimates (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nwaila and Carranza, 2025; Nwaila et al., 2023).
  • Slope of regression (SoR): ratio of the “true” grade variance reproduced by the estimate; SoR close to 1 indicates an unbiased, efficient estimate (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nwaila and Carranza, 2025).

Case studies have used combinations of kriging variance, KE, SoR, and the number and distance of samples to classify blocks into Measured, Indicated, and Inferred according to JORC (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Rezaei et al., 2022; Hassani, 2019). For example, in a uranium deposit, block models estimated by kriging were classified by:

  • Low kriging variance, high KE, SoR near 1, many close composites → Measured
  • Intermediate values → Indicated
  • Higher variance, low KE, few or distant samples → Inferred (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021).

A recent semi‑automatic methodology applied kriging estimation variance, number of composites, and average distance as input variables in a machine‑learning clustering approach to assign blocks to Measured, Indicated, and Inferred categories in porphyry Cu and high‑sulfidation Au systems (Hernández, 2024). Blocks closest to dense drilling with low kriging variance and many samples were classified as higher confidence; extrapolated zones with sparse data were Inferred (Hernández, 2024).

In laterite nickel modeling, Relative Kriging Standard Deviation (RKSD) has been used as a quantitative measure to classify blocks: small RKSD values indicate high confidence and were used to assign Measured resources in an ordinary kriging model (Nawir et al., 2023). Another nickel laterite study classified resources using the average distance between block and samples, with shorter distances corresponding to higher confidence categories (Bargawa, 2022).

Determining Resource Classification from Confidence

Across codes (JORC, SAMREC, etc.), resources are classified as:

  • Measured: high geological and grade continuity, low uncertainty.
  • Indicated: reasonable continuity and moderate uncertainty.
  • Inferred: limited confidence; inferred from sparse or indirect data (Mwasinga, 2020; Owusu and Dagdelen, 2024).

Quantitative criteria often include:

  • Kriging variance or RKSD thresholds (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nawir et al., 2023; Rezaei et al., 2022; Hassani, 2019).
  • Number of composites (NS) and minimum number of drillholes (NDH) contributing to each block (Hernández, 2024; Owusu and Dagdelen, 2024).
  • Average distance of composites (AD) to the block (Bargawa, 2022; Hernández, 2024; Owusu and Dagdelen, 2024).
  • Variogram range fractions, with search ellipsoids commonly set to some percentage of the range for each classification level (Owusu and Dagdelen, 2024).

Typical practice (illustrative, project‑specific in reality) might be:

  • Measured:
    • NS ≥ 8–12, NDH ≥ 3.
    • AD < 25–30% of variogram range.
    • Low kriging variance, high KE (e.g., >0.7–0.8) and SoR near 1 (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Mwasinga, 2020; Rezaei et al., 2022; Hassani, 2019).
  • Indicated:
    • Fewer samples or larger AD (e.g., 30–70% of range).
    • Moderate kriging variance, moderate KE.
  • Inferred:
    • Sparse samples, AD approaching or exceeding variogram range.
    • High kriging variance, low KE (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nawir et al., 2023; Bargawa, 2022; Hernández, 2024; Mwasinga, 2020; Owusu and Dagdelen, 2024).

Machine‑learning based approaches extend this by clustering blocks with similar KV, NS, AD and other indicators, then smoothing to obtain consistent, reproducible classification that reflects confidence levels while reducing subjective variability between practitioners (Hernández, 2024; Cevik et al., 2021).

Simple Worked Example: Comparing 20×20×10 vs 5×5×5

Consider a simplified scenario with ordinary kriging:

  • Drillhole spacing: 25 m (both X and Y).
  • Vertical sampling (composite) interval: 2 m.
  • Variogram horizontal range: 35 m; vertical range: 10 m.

Define three confidence bands by average composite‑to‑block distance relative to range and by kriging variance:

  • High confidence: AD ≤ 0.3×range, low KV → candidate Measured.
  • Medium confidence: 0.3×range < AD ≤ 0.7×range → candidate Indicated.
  • Low confidence: AD > 0.7×range or high KV → candidate Inferred (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nawir et al., 2023; Bargawa, 2022; Hernández, 2024; Rezaei et al., 2022; Owusu and Dagdelen, 2024).

Now compare the two block sizes in a simplified central area:

20×20×10 m Blocks

  • Each block volume is relatively large and centered close to a grid of drillholes.
  • A central block may be informed by, say, 12 composites from 4 drillholes at distances of 10–20 m (AD ≈ 15 m).
  • Horizontal AD/range ≈ 15/35 ≈ 0.43, vertical AD/range ≈ 5/10 = 0.5 (composites span the height).
  • Kriging variance is relatively low because of many samples in a compact neighborhood; kriging efficiency is high (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nwaila and Carranza, 2025; Nwaila et al., 2023).
  • This central block falls in the medium confidence band by distance but with very low variance; a practitioner could reasonably classify it as Indicated, possibly Measured if other criteria (geological continuity, multiple benches, quality control) are strong (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Mwasinga, 2020; Rezaei et al., 2022; Hassani, 2019).

However, consider thin ore layers 3–4 m thick within the 10 m vertical block: mixing ore and waste elevates dilution and misclassification risk and can reduce selective recovery despite apparently good global statistics (Mussin et al., 2025; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

5×5×5 m Blocks

  • A central macro‑volume covered by a single 20×20×10 m block would now be represented by 64 smaller blocks (4×4×2).
  • A typical 5×5×5 m block might lie 5–10 m away from the nearest drillhole in horizontal directions (AD ≈ 10–20 m depending on location relative to the grid).
  • Horizontal AD/range similar (≈0.3–0.57), but vertical AD/range ≤ 0.25–0.5 since block height is closer to composite length.
  • Because each small block may be informed by fewer composites (say 6–8) and possibly from fewer drillholes, kriging variance per block is higher than for the large block (Rezaei and Fallahi, 2023; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

Yet, in zones where ore is thin or grades change rapidly, these small blocks can:

  • Isolate high‑grade lenses without mixing them with adjacent low‑grade material.
  • Reduce dilution and ore loss at practical cut‑off grades, improving the grade–tonnage curve and realized recovered grade, even if per‑block variance is higher (Mussin et al., 2025; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

From a confidence classification perspective, some 5×5×5 m blocks close to drillholes may meet or exceed the same AD and KV criteria as the 20×20×10 m blocks and therefore achieve Indicated or Measured status (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nawir et al., 2023; Bargawa, 2022; Hernández, 2024; Rezaei et al., 2022; Hassani, 2019). Peripheral 5×5×5 m blocks between holes, however, may fall into Inferred due to larger distances and higher kriging variance. This is often desirable: the classification is more granular, reflecting real spatial variation in data support.

Integrating Block Size Choice with Confidence‑Based Classification

Research on classification and uncertainty strongly emphasizes that resource category and block size decisions should be linked through quantitative criteria:

  • Use variogram ranges to bound block size: horizontal and vertical block dimensions typically ½–⅓ of drill spacing and within variogram ranges (Rezaei and Fallahi, 2023; Rezaei et al., 2022; Hassani, 2019; Hekmat, Osanloo and Moarefvand, 2011).
  • Quantify uncertainty for each candidate block size using:
    • Kriging variance, relative estimation error, KE, SoR (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nwaila and Carranza, 2025; Rezaei et al., 2022; Hassani, 2019; Nwaila et al., 2023).
    • RKSD or related standardized deviations (Nawir et al., 2023).
  • Derive classification rules:
    • Thresholds on KV, KE, SoR, NS, NDH, AD relative to variogram range for Measured/Indicated/Inferred (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nawir et al., 2023; Bargawa, 2022; Hernández, 2024; Mwasinga, 2020; Rezaei et al., 2022; Owusu and Dagdelen, 2024; Hassani, 2019).
    • Optionally, ML clustering of these variables to obtain more objective, reproducible boundaries (Hernández, 2024; Cevik et al., 2021).

A practical workflow could be:

  1. Build two block models (20×20×10 and 5×5×5) using the same 2 m composites, variogram, and kriging parameters.
  2. For both models, compute:
    • Kriging variance (KV) and KE per block.
    • Number of composites (NS), NDH, and AD (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nawir et al., 2023; Bargawa, 2022; Hernández, 2024; Rezaei et al., 2022; Owusu and Dagdelen, 2024).
  3. Calibrate classification thresholds against:
    • Variogram ranges.
    • Drill spacing and geological continuity.
    • If possible, production or densely sampled “truth” panels (Rezaei and Fallahi, 2023; Nwaila and Carranza, 2025; Rezaei et al., 2022; Hassani, 2019; Hekmat, Osanloo and Moarefvand, 2011).
  4. Compare:
    • Proportion of tonnage in each classification category.
    • Grade–tonnage curves and misclassification (ore–waste) rates near cut‑off (Mussin et al., 2025; Rezaei and Fallahi, 2023; Nwaila and Carranza, 2025; Rezaei et al., 2022; Hassani, 2019; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).

In deposits with complex geometry or thin mineralized layers, studies suggest that a smaller block (e.g., 5×5×5 m) often delivers higher effective accuracy in tonnage and grade at mining selectivity scale, provided kriging parameters are tuned and classification is based on robust confidence indicators (Mussin et al., 2025; Rezaei and Fallahi, 2023; Rezaei et al., 2022; Hassani, 2019; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011). Larger blocks (e.g., 20×20×10 m) may still be appropriate for early‑stage, low‑confidence models or very wide, homogeneous orebodies, but will generally offer less control over selective mining and finer classification detail.

Summary

  • Block size, sampling spacing, and variogram range jointly control kriging efficiency and the reliability of tonnage and grade estimates (Rezaei and Fallahi, 2023; Rezaei et al., 2022; Hassani, 2019; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).
  • Smaller blocks (such as 5×5×5 m) with a 2 m composite are more consistent with selective mining and can provide higher effective accuracy in recoverable tonnage and grade, especially in thin or heterogeneous deposits, if supported by data density and careful kriging setup (Mussin et al., 2025; Rezaei and Fallahi, 2023; Nwaila et al., 2023; Hekmat, Osanloo and Moarefvand, 2011).
  • Resource classification into Measured, Indicated, and Inferred should be based on quantitative confidence metrics (kriging variance, KE, SoR, RKSD, NS, NDH, AD relative to variogram range), linking block size explicitly to confidence level (Taghvaeenezhad et al., 2020; Taghvaeenejad, Shayestehfar and Moarefvand, 2021; Nawir et al., 2023; Bargawa, 2022; Hernández, 2024; Mwasinga, 2020; Rezaei et al., 2022; Owusu and Dagdelen, 2024; Hassani, 2019; Nwaila et al., 2023; Cevik et al., 2021).
  • An objective, data‑driven classification framework—possibly enhanced by machine learning—reduces subjectivity and ensures that block size choice is consistent with the desired confidence level and the underlying sampling support (Hernández, 2024; Nwaila and Carranza, 2025; Nwaila et al., 2023; Cevik et al., 2021; Hekmat, Osanloo and Moarefvand, 2011).

References

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Mussin, R., Yachsishin, M., Golik, A., & Akhmatnurov, D., 2025. Block modeling reserves estimation. Kompleksnoe Ispolzovanie Mineralnogo Syra = Complex Use of Mineral Resources. https://doi.org/10.31643/2026/6445.44

Taghvaeenejad, M., Shayestehfar, M., & Moarefvand, P., 2021. Applying Analytical and Quantitative Criteria to Estimate Block Model Uncertainty and Mineral Reserve Classification: A Case Study: Khoshumi Uranium Deposit in Yazd. **.

Nawir, A., Thamsi, A., Sanjaya, H., & Aswadi, M., 2023. Resources Estimation of Laterite Nickel Using Ordinary Kriging Method at PT Mahkota Semesta Nikelindo District Wita Pond Morowali District. International Journal of Applied Sciences and Smart Technologies. https://doi.org/10.24071/ijasst.v5i2.6939

Bargawa, W., 2022. THE PERFORMANCE OF ESTIMATION TECHNIQUES FOR NICKEL LATERITE RESOURCE MODELING. Jurnal Teknologi. https://doi.org/10.11113/jurnalteknologi.v84.17560

Rezaei, M., & Fallahi, S., 2023. BLOCK MODEL OPTIMIZATION AND RESOURCE ESTIMATION OF THE ANGOURAN MINE BY TRANSFERRING THE EXPLORATORY DATA FROM THE LOCAL COORDINATE SYSTEM TO THE UTM. Rudarsko-geološko-naftni zbornik. https://doi.org/10.17794/rgn.2023.3.1

Hernández, H., 2024. A semiautomatic multi criteria method for mineral resources classification. Applied Earth Science, 133, pp. 211 – 223. https://doi.org/10.1177/25726838241298187

Nwaila, G., & Carranza, E., 2025. Uncertainty Quantification of Microblock-Based Resource Models and Sequencing of Sampling. Natural Resources Research, 34, pp. 1927 – 1952. https://doi.org/10.1007/s11053-025-10485-y

Mwasinga, P., 2020. Approaching resource classification: General practices and the Integration of geostatistics. Computer Applications in the Mineral Industries. https://doi.org/10.1201/9781003078661-18

Rezaei, A., Hassani, H., Moarefvand, P., Golmohammadi, A., & Jabbari, N., 2022. Three-dimensional Subsurface Modeling and Classification of Mineral Reserve: A Case Study of the C-North Iron Skarn Ore Reserve, Sangan, NE Iran. Arabian Journal of Geosciences, 15. https://doi.org/10.1007/s12517-022-09625-y

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