Exercise set
Mine Georesource Model, Cutoff Grade, and Reconciliation Exercises
Solved mine georesource exercises for cutoff grade, block value, guarded routing, dilution, ore loss, reconciliation, blending and chance gates.
These exercises focus on georesource and grade-control decisions inside mine planning: cutoff grade, block routing, guarded grades, dilution, ore loss, contained metal, reconciliation, density tonnage, deleterious elements, scenario risk and chance-constrained release. Production scheduling, haulage and plant-feed executability are handled in a separate specialist exercise set.
Use the numbers as planning screens. Real routing decisions require a current block model, survey control, sampling basis, ore-type domains, recovery data, deleterious-element constraints, reconciliation records, geotechnical exclusions, environmental conditions and release authority.
How to use these exercises
Use the set as a model-release and grade-control rehearsal. Exercises 1 to 3 test the economic routing screen from cutoff grade to guarded block value. Exercises 4 to 7 check the physical evidence behind the routed material: dilution, ore loss, reconciliation and sampling density. Exercises 8 to 17 add uncertainty, blending, deleterious elements, price/recovery sensitivity, density and reserve conversion. Exercise 18 then applies an all-of release gate.
Keep the model version, domain, tonnage basis and assay basis beside every calculation. A cutoff result has little value if it is separated from its recovery assumption, payable fraction, density basis, ore-type domain or reconciliation period.
Release Evidence Notes
Georesource evidence should state model version, domain, data spacing, grade-control basis, density basis, recovery assumption, cutoff basis, dilution and ore-loss assumptions, reconciliation period and release approver. A positive average value is weak if uncertainty is large compared with cutoff or plant-quality margin.
The release record should also explain how the result changes mine action. State whether material is routed to mill, stockpile, waste, rehandle, resample or hold. If a block or blend is released by exception, record the uncertainty basis, scenario downside, deleterious-element margin, plant constraint and trigger for model update after production reconciliation.
Engineering Boundary Notes
The exercises below simplify economics and statistics. They do not replace resource estimation standards, geostatistics, reserve reporting, plant test work or approved mine-planning governance.
Real georesource decisions depend on drill spacing, variography, domain interpretation, density assignment, moisture, selective mining unit size, survey pickup, blast movement, metallurgical recovery, deleterious elements, geotechnical exclusion, permitting constraints and plant operating state. Treat each calculation as a transparent screen that identifies which evidence layer controls the routing decision.
Common Release Mistakes
Common mistakes include using one cutoff across unlike domains, treating model grade as exact, ignoring dilution and ore loss, blending away deleterious elements on average, reconciling tonnes but not metal, and releasing a pushback without a model-update trigger.
Other common failures are mixing wet and dry tonnes, updating price assumptions without updating recovery or payable terms, accepting average grade while chance constraints fail, using density defaults near domain boundaries, and closing monthly reconciliation by stockpile adjustment without finding the actual model or mining error.
Scenario Map
| Scenario | Exercises | Primary check | Engineering decision |
|---|---|---|---|
| Economic routing | 1, 2, 3, 11, 12 | Cutoff, block value and sensitivity | Mill, stockpile, waste or hold. |
| Grade control and reconciliation | 4, 5, 6, 7, 13, 14, 17 | Dilution, ore loss, metal variance, density and reserve factor | Update model, reroute or resample. |
| Blend and uncertainty gates | 8, 9, 10, 15, 16, 18 | Probability, quality limits and release criteria | Release, blend differently or hold schedule. |
Exercise 1: Break-Even Cutoff Grade
Net variable cost is 32 USD/t ore. Metal price is 8500 USD/t, recovery is 88 percent and payable fraction is 96 percent. Estimate break-even grade.
Solution
Engineering Comment
The cutoff is a simplified routing screen. Real policy may include fixed cost, mining cost, ore type, recovery curve, royalties and plant bottlenecks.
Plausibility Check
The result is below 1 percent because the metal price denominator is large.
Exercise 2: Block Routing Margin
A block contains 25,000 t at 0.65 percent metal. Use the price, recovery, payable fraction and cost from Exercise 1. Find simplified margin.
Solution
Engineering Comment
The block is above cutoff, but routing still depends on confidence, hardness, moisture, deleterious elements and plant capacity.
Plausibility Check
The grade exceeds 0.446 percent, so a positive margin is expected.
Exercise 3: Guarded Grade-Control Routing
Estimated grade is 0.58 percent with one-standard-deviation uncertainty of 0.08 percent. Use a one-sigma conservative grade and cutoff of 0.446 percent.
Solution
Since 0.50\%>0.446\%, the guarded routing still passes.
Engineering Comment
Guarded routing protects against sending marginal material to the mill when uncertainty is material.
Plausibility Check
The guarded grade remains only slightly above cutoff, so the decision has little margin.
Exercise 4: Dilution Feed Grade
A dig block has 18,000 t ore at 0.72 percent grade and 3,000 t waste at 0.10 percent grade diluted into the feed. Find blended grade.
Solution
Engineering Comment
Dilution can turn an apparently robust block into marginal feed if the original margin is thin.
Plausibility Check
The blend lies between 0.10 percent and 0.72 percent and closer to the ore grade.
Exercise 5: Ore-Loss Metal Shortfall
Planned ore is 20,000 t at 0.70 percent grade. Ore loss is 6 percent. Estimate contained-metal shortfall.
Solution
Engineering Comment
Ore loss removes value before the plant sees the material. It should be reconciled separately from dilution.
Plausibility Check
Six percent of 20,000 t is 1200 t, and 0.7 percent of that is 8.4 t.
Exercise 6: Reconciliation Variance
Planned contained metal was 145 t. Reconciled contained metal is 132 t. The replanning trigger is 6 percent variance. Decide.
Solution
The trigger is exceeded, so replanning is required.
Engineering Comment
The review should check model grade, ore boundaries, dilution, survey pickup, stockpile records and plant assays.
Plausibility Check
The shortfall is 13 t out of 145 t, close to one tenth.
Exercise 7: Sampling Density Gate
A grade-control pattern covers 60,000 t with 24 samples. The release rule requires at least one sample per 2000 t. Check the gate.
Solution
The gate fails because 2500 t/sample is weaker than 2000 t/sample.
Engineering Comment
Weak sampling density is especially dangerous near cutoff or domain boundaries.
Plausibility Check
Fewer samples over the same tonnage make tonnes per sample larger, so the result fails.
Exercise 8: Probability of Below-Cutoff Grade
A domain grade is normally screened with mean 0.55 percent and standard deviation 0.07 percent. Cutoff is 0.446 percent. Estimate the z-score.
Solution
Engineering Comment
A z-score near -1.5 suggests below-cutoff outcomes are possible but not dominant.
Plausibility Check
The mean is above cutoff by about one and a half standard deviations.
Exercise 9: Two-Stockpile Blend Grade
Blend 12,000 t at 0.80 percent with 8,000 t at 0.45 percent. Find feed grade.
Solution
Engineering Comment
Blend calculations should use dry tonnes and consistent assay basis.
Plausibility Check
Because the larger stockpile is higher grade, the blend is above the simple midpoint of 0.625 percent.
Exercise 10: Deleterious Element Blend Limit
Plant arsenic limit is 0.18 percent. Blend 10,000 t at 0.12 percent As with 5,000 t at 0.28 percent As. Check the limit.
Solution
The blend passes the 0.18 percent limit.
Engineering Comment
Passing average arsenic does not eliminate local risk if feed variability is high.
Plausibility Check
The result lies between the two source grades and closer to the larger low-As mass.
Exercise 11: Cutoff Sensitivity to Price
If price falls from 8500 to 7600 USD/t with other assumptions unchanged, find the new cutoff.
Solution
Engineering Comment
Lower price raises cutoff and can reroute marginal material to stockpile or waste.
Plausibility Check
The denominator is smaller than before, so cutoff must increase.
Exercise 12: Recovery Sensitivity
With price 8500 USD/t and payable fraction 96 percent, recovery drops to 80 percent. Find cutoff.
Solution
Engineering Comment
Recovery is often domain-specific, so one cutoff can misroute difficult ore.
Plausibility Check
Lower recovery raises cutoff compared with Exercise 1.
Exercise 13: Density Tonnage Estimate
A block volume is 7200 m3 and dry bulk density is 2.65 t/m3. Estimate tonnage.
Solution
Engineering Comment
Density uncertainty can create material tonnage reconciliation errors even when geometry is correct.
Plausibility Check
The density is a little under 3, so tonnage should be a little under 21,600 t.
Exercise 14: Assay Mean Check
Four grade-control assays are 0.52, 0.61, 0.48 and 0.57 percent. Find the mean grade.
Solution
Engineering Comment
The mean is useful only if the samples represent the mining unit and domain.
Plausibility Check
The mean lies between 0.48 and 0.61 percent.
Exercise 15: Downside Scenario Probability
Out of 100 georesource scenarios, 18 have negative value. Find downside probability.
Solution
Engineering Comment
Downside probability should influence contingency, stockpile strategy and release authority.
Plausibility Check
Eighteen out of one hundred directly equals 18 percent.
Exercise 16: Chance-Constrained Blend Release
A blend must have at least 0.60 percent grade with 90 percent confidence. Scenario results pass in 87 of 100 cases. Decide.
Solution
The chance gate fails.
Engineering Comment
Mean grade may pass while confidence fails. The blend needs adjustment or a lower-risk feed source.
Plausibility Check
The pass count is below the required 90 cases out of 100.
Exercise 17: Reserve Conversion Factor
Measured and indicated resource is 12.5 Mt. After modifying factors, mineable reserve is 9.8 Mt. Find conversion factor.
Solution
Engineering Comment
Conversion losses should be explained by pit limits, recovery, dilution, geotechnical exclusions, economics or permitting.
Plausibility Check
Reserve is less than resource, so the factor is below 100 percent.
Exercise 18: Georesource Release Gate
A release gate requires guarded grade above cutoff, sampling density pass and reconciliation variance within 6 percent. Results are pass, fail and -4 percent. Decide.
Solution
The release fails because sampling density is not adequate.
Engineering Comment
One failed evidence layer can block release even when the economic and reconciliation screens pass.
Plausibility Check
The decision follows directly from the failed sampling criterion.
Validation Package Checklist
- model version, domain and grade-control basis are stated;
- cutoff, recovery, payable fraction and cost basis are explicit;
- dilution, ore loss and density assumptions are separated;
- contained metal and reconciliation variance are checked, not only tonnes;
- blend grades and deleterious elements are tested against plant limits;
- uncertainty or scenario evidence is tied to a release, hold or resampling action.
- sampling density, selective mining unit and domain boundary controls are documented;
- stockpile, mill feed and survey records use the same wet/dry tonnage basis;
- recovery and payable assumptions match the ore type being routed;
- model-update triggers are defined before reconciliation variance accumulates.
The final acceptance question is whether the routing decision would still be defensible after survey, grade control, plant assay and reconciliation data arrive. If the decision only works under the current average model grade, it should be treated as a hold, resample or conditional release rather than final ore routing.