Exercise set

Tailings Storage Water Balance and Seepage Exercises

Solved tailings storage exercises for solids, slurry, pond balance, freeboard, seepage, drain response, piezometers, beach slope and release gates.

Branch: Mining and Georesources Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

These exercises focus on active tailings storage facility operation: dry solids, deposited volume, slurry concentration, pond water balance, freeboard, seepage, drain response, piezometer trends, storm drawdown, beach slope, pond setback and operating release gates. Mine-waste routing, closure cover, reclamation and bonding are handled in a separate specialist exercise set.

Use these calculations as governance screens. Real TSF decisions require site-specific design, consequence classification, surveillance records, trigger-action response plans, independent review, water-quality evidence, emergency preparedness and responsible approval.

How to use these exercises

Use the set as an operating-state review for an active TSF. Exercises 1 to 3 establish the solids, deposited volume and slurry water basis. Exercises 4 to 7 connect pond water balance, pond rise, freeboard and emergency drawdown. Exercises 8 to 13 screen seepage, travel time, drain response, piezometer trends, guarded stability margin and beach slope. Exercises 14 to 18 add pond setback, storm runoff, reclaim pump margin, decant blockage and the operating release gate.

Before calculating, state the raise stage, pond elevation datum, deposition point, survey date, water-balance period, instrumentation health, operating trigger level and response owner. A positive freeboard number is not enough if pond setback, drain response or piezometer trends are moving in the wrong direction. The engineering comment below each exercise identifies the operating evidence that must be checked before continuing deposition or pond-rise authorization.

Release Evidence Notes

Tailings storage evidence should state facility state, raise stage, deposition point, pond location, survey datum, water-balance period, flow measurements, rainfall basis, seepage observation, piezometer health, drain condition, trigger level and release authority.

The evidence package should separate production accounting, pond accounting and surveillance evidence. Production accounting controls solids and storage consumption. Pond accounting controls water inflows, reclaim, storm runoff, decant capacity and freeboard. Surveillance evidence controls seepage, drains, pore pressure, beach slope, pond setback and trigger-action response. Mixing these evidence streams can hide a failing instrument or operating condition.

Operating release should also preserve time and forecast context. A facility may pass today’s freeboard but fail after forecast rainfall, reclaim downtime, blocked decant or continued deposition. Release evidence should therefore show current state, short-term forecast and response capacity.

Engineering Boundary Notes

The calculations below simplify storage, hydraulics and monitoring. They do not replace dam-safety review, seepage modelling, stability analysis, construction quality assurance, operating manuals or emergency action plans. Treat pass results as operational screens and failed results as trigger-action inputs, not as standalone dam-safety decisions.

The main boundary is instrumentation confidence. Flow meters, pond surveys, piezometers, drains and rainfall records must be healthy and on the same datum or time window. The second boundary is consequence: small numeric deficits can be unacceptable where consequence classification, downstream exposure or regulatory trigger levels demand conservative response.

Common Release Mistakes

Common mistakes include mixing wet slurry and dry solids, using positive freeboard as proof of seepage control, ignoring pond setback, treating clear seepage as harmless without trend review, and accepting a water balance that does not reconcile with surveyed pond level.

Another common mistake is treating one passing gate as compensation for another failing gate. Freeboard, pond setback, drain response and pore-pressure trend protect different failure modes. A good pond position does not cure a weak drain response, and a positive water balance does not prove embankment stability.

Do not wait for a formal failure before escalating. Trigger-action response plans exist so rising heads, reduced drain flow, decant blockage, narrowing freeboard or unexplained water-balance mismatch can be investigated while operational options still exist.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Production and storage basis	1, 2, 3	Dry solids, storage volume and slurry water	Confirm deposition and storage consumption.
Pond and freeboard control	4, 5, 6, 7, 14, 15, 16, 17, 18	Water balance, freeboard, drawdown, runoff, pump capacity and pond setback	Continue, restrict pond rise or trigger response.
Seepage and monitoring	8, 9, 10, 11, 12, 13	Darcy seepage, travel time, drain response, piezometer trend and beach slope	Inspect, increase monitoring or hold operation.

Exercise 1: Tailings Solids Mass

A plant processes 18,000 t/day of ore. Concentrate is 6.5 percent of feed by mass. Estimate dry tailings solids.

Solution

m_t=18000(1-0.065)=16830\ \text{t/day}

Engineering Comment

Dry solids are the storage basis. Water, voids and density must be handled separately.

Plausibility Check

Concentrate is small compared with ore feed, so most mass reports to tailings.

Exercise 2: Annual Deposited Volume

Dry solids are 16,830 t/day for 350 operating days. Deposited dry density is 1.45 t/m3. Find annual volume.

Solution

V=\dfrac{16830(350)}{1.45}=4062414\ \text{m}^3

Engineering Comment

If actual density is lower than assumed, storage is consumed faster than planned.

Plausibility Check

About 5.9 Mt divided by density near 1.5 t/m3 gives about 4 million m3.

Exercise 3: Slurry Solids Concentration

Slurry contains 16,830 t/day dry solids and 11,220 t/day water. Find solids mass fraction.

Solution

C_s=\dfrac{16830}{16830+11220}=0.60=60\%

Engineering Comment

Solids concentration affects beaching, pumping, water inventory and reclaim demand.

Plausibility Check

The solids mass is one and a half times the water mass, giving 60 percent solids.

Exercise 4: Pond Water Balance

Inflows are 22,000 m3/day process water and 8500 m3/day rainfall/runoff. Reclaim is 24,000 m3/day and evaporation plus seepage is 1500 m3/day for 4 days. Find volume change.

Solution

\Delta V=(22000+8500-24000-1500)(4)=20000\ \text{m}^3

Engineering Comment

The pond is rising. Release should check stage-storage curve and forecast rainfall.

Plausibility Check

Daily net inflow is 5000 m3/day, so four days gives 20,000 m3.

Exercise 5: Pond Rise

If active pond area is 180,000 m2, find the rise caused by the 20,000 m3 volume increase.

Solution

\Delta h=\dfrac{20000}{180000}=0.111\ \text{m}

Engineering Comment

A small level rise can still matter when freeboard or pond setback margin is tight.

Plausibility Check

Spreading 20,000 m3 over a large area gives a rise near 0.1 m.

Exercise 6: Freeboard Check

Crest elevation is 455.0 m and pond elevation is 453.9 m. Required freeboard is 1.0 m. Check margin.

Solution

F=455.0-453.9=1.1\ \text{m},\qquad M=1.1-1.0=0.1\ \text{m}

Engineering Comment

The pass margin is small and should not be treated as robust under forecast uncertainty.

Plausibility Check

The pond is below the crest, so freeboard is positive.

Exercise 7: Emergency Drawdown Capacity

Emergency pumping is 3800 m3/h for 10 h. Required drawdown volume is 42,000 m3. Check capacity.

Solution

V_p=3800(10)=38000\ \text{m}^3

The pump plan is short by 4000 m3.

Engineering Comment

Pump capacity must be verified before the storm, not after the pond has risen.

Plausibility Check

Ten hours at less than 4200 m3/h cannot reach 42,000 m3.

Exercise 8: Darcy Seepage Flow

A low-permeability zone has $K=3.0\times10^{-7}$ m/s, gradient 0.42 and area 4200 m2. Estimate seepage per day.

Solution

Q=KiA=3.0\times10^{-7}(0.42)(4200)=5.292\times10^{-4}\ \text{m}^3/\text{s}

Q_d=5.292\times10^{-4}(86400)=45.7\ \text{m}^3/\text{day}

Engineering Comment

The estimate is only credible if the flow path and construction quality match the assumption.

Plausibility Check

Low conductivity gives a small daily flow even over a large area.

Exercise 9: Seepage Travel Time

Seepage velocity is 2.75 m/year across a 35 m control distance. Estimate travel time.

Solution

t=\dfrac{35}{2.75}=12.7\ \text{yr}

Engineering Comment

Long travel time means short-term monitoring may not prove closure performance.

Plausibility Check

At a little under 3 m/year, 35 m takes a little over 12 years.

Exercise 10: Drain Flow Deficit

Expected drain flow is 110 m3/day. Measured flow is 65 m3/day. Find response ratio.

Solution

R=\dfrac{65}{110}=0.591=59.1\%

Engineering Comment

Low drain response can indicate blockage, bypass, meter error or changed hydraulic path.

Plausibility Check

Measured flow is a bit more than half the expected value.

Exercise 11: Piezometer Trend

Piezometric head rises from 12.4 m to 13.3 m over 30 days. Find rise rate.

Solution

r=\dfrac{13.3-12.4}{30}=0.030\ \text{m/day}

Engineering Comment

Trend should be checked against trigger-action levels and nearby instruments.

Plausibility Check

The total rise is 0.9 m over one month, so 0.03 m/day is correct.

Exercise 12: Stability Margin Screen

Calculated factor of safety is 1.42 and the operating trigger is 1.35. Instrument uncertainty is 0.06. Check guarded margin.

Solution

FS_g=1.42-0.06=1.36,\qquad M=1.36-1.35=0.01

Engineering Comment

The guarded pass is marginal and should trigger review if pore pressure continues to rise.

Plausibility Check

The nominal margin is 0.07; subtracting 0.06 leaves only 0.01.

Exercise 13: Beach Slope

The pond edge is 420 m from the spigot and elevation drops 2.1 m. Find beach slope.

Solution

S=\dfrac{2.1}{420}=0.005=0.5\%

Engineering Comment

Beach slope affects pond location, freeboard and seepage-sensitive zones.

Plausibility Check

A 2.1 m fall over 420 m is one half percent.

Exercise 14: Pond Setback Margin

Required pond setback from the embankment is 300 m. Surveyed setback is 335 m with 12 m survey uncertainty. Find guarded margin.

Solution

M_g=335-12-300=23\ \text{m}

Engineering Comment

Guarded setback is the better release number when survey or pond-edge definition is uncertain.

Plausibility Check

The unguarded margin is 35 m, and uncertainty reduces it to 23 m.

Exercise 15: Storm Runoff Volume

A 40 ha catchment contributes runoff from a 55 mm storm with runoff coefficient 0.65. Estimate runoff volume.

Solution

V=0.65(0.055)(400000)=14300\ \text{m}^3

Engineering Comment

Catchment basis and storm depth must match the facility water-balance boundary.

Plausibility Check

Full rainfall volume is 22,000 m3, and 65 percent runoff is 14,300 m3.

Exercise 16: Reclaim Pump Margin

Required reclaim is 24,000 m3/day. Installed pumps can deliver 1050 m3/h for 22 h/day. Check margin.

Solution

Q=1050(22)=23100\ \text{m}^3/\text{day}

The system is short by 900 m3/day.

Engineering Comment

Small daily deficits accumulate quickly during wet operation.

Plausibility Check

The daily capacity is slightly below the required 24,000 m3/day.

Exercise 17: Decant Blockage Pond Rise

A decant blockage removes 6000 m3/day of outflow for 3 days. Pond area is 150,000 m2. Estimate additional rise.

Solution

\Delta h=\dfrac{6000(3)}{150000}=0.12\ \text{m}

Engineering Comment

Decant blockage should trigger inspection and response even when freeboard remains positive.

Plausibility Check

Eighteen thousand cubic metres over 150,000 m2 gives 0.12 m.

Exercise 18: TSF Operating Release Gate

A release gate requires freeboard margin at least 0.20 m, guarded setback at least 20 m and drain response at least 70 percent. Results are 0.10 m, 23 m and 59.1 percent. Decide.

Solution

0.10<0.20,\qquad 23>20,\qquad 59.1\%<70\%

The operating release fails because freeboard margin and drain response fail.

Engineering Comment

One acceptable pond-position result cannot compensate for weak freeboard and hydraulic evidence.

Plausibility Check

Two of three required criteria fail, so the hold decision is unambiguous.

Validation Package Checklist

dry solids, slurry water, pond water and seepage bases are separated;
pond rise reconciles with survey, flow meters and rainfall records;
freeboard and pond setback are both checked;
seepage flow, drain response and piezometer trends are interpreted together;
emergency pumping and decant availability are verified;
instrument health, datum, survey date and trigger-action levels are recorded;
forecast storm, reclaim outage and decant blockage cases are bounded;
responsible owner and response action are named for each failed gate;
release decision states continue, restrict, investigate, pump down or hold.

A complete validation package should make the operating decision reproducible across shifts. Another engineer should be able to see the pond state, water-balance reconciliation, surveillance trend, response capacity and authority for any decision to continue, restrict or hold deposition.

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