Mine Planning and Design
Fundamentals and Best Practices

The pit optimization runs at eight percent because eight percent is in the template. Nobody in the planning department chose eight percent. Nobody in the planning department can explain why it is eight percent rather than six or ten. The number was set by someone in corporate finance years ago, possibly inherited from a different company through an acquisition, and it has propagated through every project the company has evaluated since.

Meanwhile the acquisition model that justified buying the deposit used five percent, because at eight the deal did not clear the hurdle rate and at five it did. The company paid a price consistent with a five-percent pit. The planning team is designing a different pit, an eight-percent pit, which is smaller and higher-grading and has a different waste stripping profile. The shareholders priced one mine and the engineers are building another. This disconnect exists at every company that separates corporate evaluation from mine planning, which is every company of any size.

Changing the discount rate from eight to five percent on a large porphyry copper changes the optimal pit by something like 200 million tonnes of waste. That number is not a range or an approximation. On the project where this was first pointed out to me in a planning review, the difference was 214 million tonnes, and the senior planner said he had never been asked which discount rate he was using.

Lane's cut-off grade optimization introduces another rate. Lane's framework maximizes NPV by varying the cut-off grade over time, balancing the three bottleneck stages (mining rate, milling rate, refining/marketing rate) against the time value of money. The Lane rate is embedded in a separate calculation, usually run after the pit design is complete, often by a different person. If the Lane rate differs from the pit optimization rate, and it usually does, the cut-off strategy is optimized for a different economic reality than the pit shape. The mill is being told to process material at a cut-off derived from one discount rate inside a pit designed at a different discount rate. The incoherence is real, it affects the grade-tonnage curve the plant sees every year, and it is invisible unless someone checks both numbers side by side.

Then the production target. The board told the market ninety thousand tonnes of copper in concentrate. That number becomes a constraint in the planning software. The plan must deliver ninety thousand tonnes. If the orebody supports seventy-five thousand at the designed throughput and head grade, the planner has a problem that is not technical. The feasibility study, when published, will document the optimization methodology correctly. The inputs will have been adjusted until the output matched the target. Whether the inputs preceded the output or the output preceded the inputs is something that does not appear in the documentation.

The variogram determines every block grade in the model and receives about a tenth of the review time that the commodity price assumption receives. The commodity price is a guess. The variogram is a characterization of what is already in the ground. The guess gets debated for weeks. The characterization gets checked by one person, sometimes not even that.

The kriging system Cw = c. C is the covariance matrix between sample locations, computed from the variogram model. c is the covariance vector between samples and the target block. w is the weight vector. Change the variogram, change C, change every block grade in the model. The pit boundary sits on the marginal blocks, and the marginal blocks are the ones farthest from drill holes, and those blocks are the ones most sensitive to the variogram range. A range of 120 meters versus 180 meters along strike changes whether a block at 100 meters from the nearest sample gets a grade estimate pulled toward that sample or toward the global mean. The pit boundary moves. Millions of tonnes of waste move with it.

Fitting the variogram is subjective. The experimental variogram at short lags is noisy when the drill spacing is much wider than the mineralization wavelength, which is the normal situation. The down-dip direction usually has far fewer sample pairs than the along-strike direction because drill holes tend to be vertical or steep. A geostatistician fitting the down-dip variogram is working with sparse, noisy data and using geological reasoning to fill the gaps. The word "reasoning" here means judgment. Two people will judge differently. The difference propagates silently into every block grade. I have seen a feasibility review where two consultants independently modeled the same deposit and produced ultimate pits that differed by 35 million tonnes of ore, traceable to different variogram ranges in the down-dip direction. Neither was wrong. Both were defensible. The mine plan can only use one.

Change of support. Kriging estimates the average grade of a block, not a point. The block grade variance is lower than the point grade variance because averaging over a volume suppresses internal variability. How much suppression depends on the block size relative to the variogram range. If the block is large relative to the range, the smoothing is heavy. If the block size does not match the SMU (the smallest volume the mine can selectively route to ore or waste), the model misrepresents selectivity. Blocks bigger than the SMU overstate selectivity because the grade is already averaged beyond operational resolution. Blocks smaller than the SMU imply a precision the excavator cannot deliver. The block size is chosen at the start of the project, rarely revisited, and its interaction with the variogram range is the single largest determinant of the information content in the ore/waste classification. Getting this wrong by a factor of two in any dimension biases every tonne classified as ore for the life of the mine.

Conditional simulation does what kriging cannot: preserve the grade variance. A hundred simulated orebodies, each honoring the drill data, each reproducing the histogram and variogram. Run the pit optimizer against all hundred. The output is a hundred pits, a hundred NPVs. The spread matters. The JORC code and NI 43-101 and the lending criteria of every major resource-sector bank are built around point estimates. A reserve is a number. Until the reporting frameworks change, simulation stays in the background as a risk tool rather than becoming the basis for the reserve statement. This is moving, slowly, at the larger companies.

Resource geologists want the resource to be large and well-classified. Mine planners want the resource to be conservative and reliable. A geologist who pushes material from Inferred to Indicated with minimal additional drilling gives the planner more tonnes to schedule and worse information to schedule with. The tension does not have a technical resolution. It has a governance resolution, which is a Competent Person or QP whose accountability runs to the accuracy of the statement rather than to the size of it.

Domain boundaries. If the histogram within a domain is bimodal, there are two populations in one domain. If the variogram changes character across a proposed boundary, the boundary is geological. These tests are fast. Skipping them embeds a systematic grade bias in every block near the contact.

Nested shells are generated by scaling the revenue factor from about 0.3 to 1.0. The incremental value curve starts steep and flattens. Where it flattens is where marginal returns collapse. On a specific copper-gold project I can think of, the shells between revenue factor 0.75 and 1.0 added 410 million tonnes to the pit and 31 million dollars to the NPV. The shells between 0.3 and 0.5 added 190 million tonnes and 780 million dollars. Committing to mining the outer shells means building haul roads to them, sizing trucks for them, permitting the waste dumps for them, and operating at a marginal strip ratio that makes money only if the copper price stays above $3.80. If copper drops to $3.20 for eighteen months, the outer pushback is uneconomic and the sunk cost in roads and dump preparation is stranded.

The backwards optimization problem. A project needs a certain reserve size for the financing package. The optimization output is smaller than needed. Somebody nudges the price assumption up 8 percent. Or shaves 4 percent off the processing cost. Or asks geotechnical if the slope can steepen by two degrees. The optimization reruns. The pit grows to the desired size. The feasibility study documents Whittle optimization, nested shells, pushback design, scheduling. All correct methodology. All correctly applied. The inputs were chosen to produce the output. A reader of the study cannot detect this because a study where the inputs preceded the output looks identical on paper. The people who were in the room know. Others do not.

Slopes. I am not a geotechnical engineer and I will not pretend to write like one, which is itself a relevant point: most mine planning texts attempt to cover geotechnical design in the same depth as pit optimization and scheduling, which is suspect because very few people work at the same depth in both. What matters from the planning side is this: the slope angle has enormous economic leverage, something like 20 to 40 million tonnes of waste per degree on a large pit, the geotechnical data at the feasibility stage is limited, and the resulting angle has a confidence interval that is wider than the reserve estimate's confidence interval. The plan uses the angle as a fixed number.

Slopes degrade over time and most designs do not account for time-dependent strength reduction on joint surfaces. The monitoring data before large failures almost always showed acceleration. Trigger-action response plans that invoke automatic restrictions at predefined displacement rate thresholds, removing the need for an individual to argue with the general manager, are a structural improvement over relying on a person to escalate.

Haul roads. The optimal gradient depends on the specific truck model's torque curve and the road's rolling resistance coefficient, which changes with moisture and maintenance frequency. A CAT 793F loaded on a 10 percent grade in first gear at 8 km/h is slower per cycle than the same truck on an 8 percent grade holding second at 12 km/h, even though the 8 percent ramp is longer. TALPAC or Haul Infinity model this. Using them to co-design the haul network with the extraction sequence is straightforward and I am routinely surprised by how many operations do not do it.

I have less direct experience here than with open pit and I think that is relevant to state rather than to paper over. The field is different enough that the overlap between a good open pit planner and a good underground planner is thinner than outsiders assume.

Mining method selection. Nicholas classification narrows the field. The final choice involves things the matrix ignores: what the local workforce knows how to do, whether backfill material is available in the right quantity and rheology, and the stress regime at depth. A narrow-vein gold deposit designed for longhole open stoping at $1,800/oz has a minimum stoping width around 3 meters (set by the drill rig dimensions and the need for the LHD to operate in the stope). Vein material narrower than that gets diluted or left. At $2,500/oz, mechanized cut-and-fill on narrow sections starts to pay. Revisiting the mining method after a sustained price move is operationally disruptive and politically difficult and it is also sometimes the right thing to do.

No underground mine reaches design production rate on schedule. Development hits unexpected ground conditions. Ground support requirements escalate. Ventilation raises take longer. The backfill plant discovers that the tailings at full-scale production have different rheology than the bench-scale tests predicted. Two to three years to steady state is standard. Financial models showing full production from year one overstate the early cash flows that NPV weighting amplifies most. The NPV difference between a realistic ramp-up and an instant-steady-state model is 10 to 20 percent of total project NPV on the projects where I have seen both versions side by side.

Backfill. Cemented paste fill uses 3 to 7 percent binder by dry tailings mass. Cement hydration rate roughly doubles per 10°C rise. In a Canadian operation in January, ventilation air at minus-20°C flowing through a recently filled stope can extend the cure time from the design 14 days to 35 or more. The sequencing plan says blast the adjacent secondary stope in week 3. The fill has not cured. Either the blast waits or it fires against uncured fill and the consequences unfold. This specific failure mode recurs.

Stope sequencing and stress management through numerical modeling (Map3D for elastic boundary-element mine-scale work, FLAC3D for near-field plasticity) is standard at well-run operations. The retreat direction governs where stress concentrates and whether it concentrates on intact ore, backfilled stopes, or abutment rock.

The MIP formulation assigns blocks to periods subject to precedence, capacity, and quality constraints. The solver converges. The result may require moving the primary shovel to a new working area every period because that is what maximizes NPV by 0.2 percent. Each relocation takes a shift. The haul road ruts. The new face setup costs half a shift. The schedule does not know this.

Experienced schedulers add constraints that are not in textbook formulations: minimum time in a work area, maximum active face count, seasonal exclusion of sectors with drainage problems. These constraints come from having been on sites where the schedule said one thing and the pit did another.

Blending. Flotation recovery versus head grade is concave. A plant receiving steady 0.9 percent copper recovers more metal annually than the same plant receiving alternating 0.5 and 1.3 percent that average to 0.9, because the recovery loss at 0.5 is proportionally larger than the recovery gain at 1.3. Blend constraints in the scheduling optimization must be hard per-period constraints. Soft annual averages miss the problem entirely.

The gap between the long-range plan and what actually gets mined every week is where value is destroyed. Block 4,200 was scheduled for Q3. A wet blast, a broken truck, and the foreman mines block 3,800 because it is accessible. Each substitution is locally reasonable. After two years of them the pit geometry has drifted from design. The long-range plan is re-optimized from the current surface and presented as "the plan." The original plan is overwritten. If nobody preserved the original baseline, the cumulative drift is invisible. Plotting cumulative ore tonnes against the original plan, on a chart that is never overwritten, makes the divergence visible.

The block model predicted 1.2 g/t. The mill received 1.05 g/t. The reconciliation spreadsheet says: model factor 0.88, mining dilution 5 percent.

That explains nothing. Was the resource model biased in a specific domain because the variogram overstated grade continuity in the down-dip direction? Was the grade control blast hole sampling contaminated by material from the bench above because the blast hole collars were not cleaned? Was the dig line 0.5 meters below the designed floor because the excavator GPS was not calibrated? Was there a truck dispatch error that sent a load from a waste face to the ROM pad? The word "dilution" accommodates all of these and diagnoses none. Tracking the resource-to-grade-control reconciliation factor by geological domain over time isolates modeling bias from operational error. If domain A consistently reconciles at 0.95 and domain B at 0.78, domain B has a geological modeling problem.

The rolling re-forecast. Q1 misses by 8 percent. The forward plan is revised down. Q2 misses the revised plan by 6 percent. Revised again. By year-end cumulative production is 15 percent below the original budget and every quarter reported a variance under 5 percent of its re-forecast. An independent technical services group that preserves the original plan and publishes cumulative deviation without editing is the organizational mechanism that makes this visible.

I will be brief on these because they are done to death in the environmental literature and usually underdone in the mine planning literature, and the gap between the two bodies of writing is itself the problem. The mine planner and the environmental engineer work from different schedules. When they work from the same schedule, waste sequencing and dump construction can be coordinated with extraction. When they do not, acid-generating waste gets placed without appropriate encapsulation because the dump was not configured to receive it in the period it arrived.

Water derails more mine plans than geology does. Pore pressure on pit slopes. Underground inflow. Regulatory discharge limits. Dewatering wells in low-permeability rock need years to draw down. The geological model and the hydrogeological model are built by different consultants in different software at different resolutions and sometimes in different coordinate systems. Integrating them falls between two contracts and often does not get done.

Closure. Discounting a $500 million closure cost at 8 percent over 25 years gives a present value around $73 million. The cash cost when it arrives is still $500 million, plus escalation. Progressive rehabilitation during mining reduces the outstanding liability, generates reclamation performance data, and reduces bonding requirements.

Five percent dilution. Ninety-five percent mining recovery. Eighty-eight percent met recovery.

These three numbers have appeared in feasibility studies for sublevel caving operations in Sweden, cut-and-fill operations in Peru, open pit operations in Mongolia, and longhole stoping operations in Ontario. The geological estimation beneath them was performed with variography, cross-validation, and classification criteria. The modifying factors are round numbers pulled from a template.

The software ships with defaults. Block size, bench height, slope templates, scheduling periods, dilution skins. A planner who used 10-meter benches at the last project brings 10-meter benches to the next project. The rock mass may support 15-meter benches. Nobody checks because the template was already populated.

On a specific gold project in West Africa in 2018, a consulting firm delivered a feasibility study with 12-meter benches. The rock mass was a competent, thinly bedded metasediment with widely spaced joints. The geotechnical report noted that 15-meter benches were feasible. Nobody changed the template. The 12-meter bench height persisted through detailed design, adding approximately 20 percent more drill-and-blast cycles per vertical meter of pit advance than 15-meter benches would have required, at a cumulative cost over the life of mine in the range of $40 million. The template was from the firm's previous project, which was in a very different rock mass.

Scheduling algorithms converge on solutions. Whether those solutions can be executed depends on conditions the algorithm does not model. Wet season trafficability. Equipment availability during shutdowns. Workforce skills. Explosives supply lead time in remote locations. This gap between the algorithm's output and mine capacity is filled by the judgment of planners who have spent years on sites. That judgment is leaving the industry through retirements and it is not codified anywhere.

Maintaining alignment between the life-of-mine plan, the annual budget, the quarterly schedule, and the weekly dig plan is organizational work. The mines that hold alignment measure short-range compliance as a KPI, investigate deviations procedurally, and preserve the original baseline plan as a reference that does not get overwritten when the plan is updated.