Tailings, Mine Waste, and Closure Engineering Exercises

These exercises practise first-pass calculations used in tailings, mine waste, and closure engineering. They connect mine-plan material balance, storage volume, water balance, seepage, freeboard, slurry density, closure cover logistics, monitoring trends, failure-mode ranking, and handover evidence.

Assume simplified nominal values unless an exercise states otherwise. Real tailings and closure decisions require site-specific investigation, geotechnical design, geochemistry, water balance modelling, independent review, consequence classification, operating governance, monitoring triggers, emergency planning, and closure obligations.

How to Use These Exercises

For each problem:

1. define the facility, mine phase, material stream, and operating condition;
2. separate dry solids, water, voids, storage, seepage, and closure materials;
3. state whether the result is a design basis, operating trigger, or closure evidence check;
4. keep mass, volume, density, flow, and time units consistent;
5. identify which monitoring or governance record would validate the result.

The most common mistake is treating tailings as a uniform end-of-pipe material. Tailings and mine waste change with ore domain, processing route, water management, deposition plan, and closure stage.

Use the exercises as facility-governance gates: adjust deposition, reserve freeboard, inspect drains, restrict pond rise, verify seepage controls, reconcile closure material, escalate trigger response, or keep handover open when monitoring, water balance, construction, or evidence records are incomplete.

Exercise 1: Tailings Solids Mass from Ore Feed

A plant processes 18{,}000\ \text{t/day} of ore. Concentrate production is 6.5\% of ore feed by mass. Ignore minor losses.

Estimate dry tailings solids mass per day.

Solution

Concentrate mass:

Tailings solids:

Engineering Comment

This dry-solids basis is only the start. Storage design also needs water content, settled density, consolidation, deposition method, contingency, and variability in ore domain and recovery.

Exercise 2: Annual Storage Volume

The dry tailings solids rate is 16{,}830\ \text{t/day}. The facility operates 350 days per year. Expected average dry density after deposition and consolidation is 1.45\ \text{t/m}^3.

Estimate annual deposited solids volume.

Solution

Annual dry mass:

Deposited volume:

Engineering Comment

The value is sensitive to density. If actual density is lower than assumed, the facility consumes storage faster. Density verification should be part of operating surveillance.

Exercise 3: Pond Water Balance for a Storm Period

During a wet operating period, a tailings pond receives process water inflow Q_{in}=22{,}000\ \text{m}^3/\text{day} and direct rainfall/runoff Q_r=8{,}500\ \text{m}^3/\text{day}. Reclaim pumping removes 24{,}000\ \text{m}^3/\text{day} and evaporation/seepage losses remove 1{,}500\ \text{m}^3/\text{day}. The period lasts 4 days.

Estimate pond volume change.

Solution

Net daily change:

Four-day change:

Engineering Comment

The pond is rising. The operating response should check freeboard, pond location, reclaim capacity, spillway status, pump availability, forecast rainfall, and trigger-action levels.

Exercise 4: Seepage Through a Low-Permeability Zone

A low-permeability control zone has hydraulic conductivity K=8.0\times10^{-8}\ \text{m/s}, hydraulic gradient i=0.35, and flow area A=1800\ \text{m}^2.

Estimate seepage flow.

Solution

Darcy flow:

Convert to cubic metres per day:

Engineering Comment

This estimate assumes the flow path and material properties are represented correctly. Defects, cracks, foundation windows, abutment contacts, and construction quality can dominate actual seepage.

Exercise 5: Freeboard Check

A tailings pond water surface is surveyed at elevation 642.35\ \text{m}. The operating crest elevation is 645.00\ \text{m}. The minimum operating freeboard requirement is 2.4\ \text{m}.

Check the freeboard margin.

Solution

Available freeboard:

Margin above requirement:

Engineering Comment

The facility is above the minimum requirement by a small margin. Operating decisions should consider survey accuracy, wave run-up, storm forecast, beach width, pond location, emergency storage, and whether the crest elevation is continuous around the facility.

Exercise 6: Slurry Solids Concentration by Mass

A tailings slurry stream contains 780\ \text{t/h} of dry solids and 520\ \text{t/h} of water.

Find the solids concentration by mass.

Solution

Total slurry mass:

Solids concentration:

Engineering Comment

Solids concentration affects deposition, pumpability, beach slope, water recovery, segregation, and rheology. A plant upset that changes solids concentration can invalidate deposition assumptions.

Exercise 7: Closure Cover Material Requirement

A closure cover trial requires 0.45\ \text{m} of growth medium over 28\ \text{ha}. Bulk density of placed material is 1.35\ \text{t/m}^3.

Estimate required material volume and mass.

Solution

Area:

Volume:

Mass:

Engineering Comment

Closure material availability should be reconciled with the mine plan. Borrow source quality, erosion resistance, trafficability, vegetation, contamination, moisture, and placement season can control whether the cover works.

Exercise 8: Piezometer Trend Trigger

A piezometer in a tailings embankment has monthly readings:

The amber trigger is 19.2\ \text{m}. Identify the trigger condition after the fourth reading and estimate average monthly rise over the three intervals.

Solution

Fourth reading:

Since:

the amber trigger has been exceeded.

Average rise:

Engineering Comment

The trigger should cause a defined response: data validation, seepage inspection, pond-position review, deposition check, drain inspection, and engineering review before continuing as normal.

Exercise 9: Drain Blockage RPN

A failure mode is “underdrain blockage raises pore pressure.” Initial scores are:

After adding flow alarms and inspection ports, occurrence is estimated as O=2 and detection as D=2.

Find initial and revised risk priority numbers.

Solution

Initial:

Revised:

Reduction:

Engineering Comment

The lower RPN is credible only if alarms are maintained, inspection ports are accessible, trigger levels are defined, and staff have authority to act before pore pressures become critical.

Exercise 10: Closure Handover Evidence

A closure handover package requires 72 records. Sixty-five are accepted, 4 monitoring baselines are pending, and 3 as-built drainage records are rejected.

Find the accepted-record percentage and unresolved-record count.

Solution

Accepted percentage:

Unresolved records:

Engineering Comment

Closure handover should remain open. Monitoring baselines and drainage as-builts are not administrative details; they define how long-term performance will be checked and maintained.

Review Checklist

Before accepting a tailings or closure screening calculation, check:

• whether dry solids, water, voids, and storage basis are separated;
• whether density and water balance assumptions are verified during operation;
• whether seepage estimates include construction quality and foundation uncertainty;
• whether freeboard checks include storm, wave, pond position, and survey uncertainty;
• whether slurry properties are tied to deposition and pumpability;
• whether closure material quantities are reconciled with source quality and mine plan;
• whether monitoring triggers have named accountable actions;
• whether trigger responses include data validation, field inspection, operating restriction, engineering review, and closeout evidence;
• whether closure records preserve the evidence future teams need to maintain the facility.
• whether handover remains blocked when as-built drainage, monitoring baselines, cover quality, or long-term maintenance ownership is unresolved.

Good tailings and closure engineering keeps material, water, stability, chemistry, monitoring, governance, and long-term evidence in one controlled system.