4. Mining and Closure¶

MINEDW was designed specifically for groundwater flow problems related to mining, including open-pit and underground operations. The software provides specialized boundary conditions and features for mining simulations. For open-pit mining, MINEDW simulates mine development over time by adjusting the finite element grid and adding drain boundary conditions to simulate seepage from open-pit walls. Open-pit mining features include:

Open-Pit Development: Open-pit designs (topography contours) through time can be applied in groundwater flow model simulations.
Open-Pit Mining Seepage: MINEDW calculates the amount and location of seepage into the open pit over time.
Dewatering and Depressurization: MINEDW simulates numerous dewatering and depressurization techniques used in open-pit mining.
Pit Lake after Mining: After mining and dewatering ends, the groundwater system begins recovery. MINEDW simulates the infilling of open pits.
Open-Pit Backfilling: At mining cessation, mines commonly backfill portions of the open pit before pit-lake infilling. MINEDW simulates backfill plans through time.
Zone of Relaxation (ZOR): Mining and blasting operations commonly form a ZOR—an area of altered hydrogeologic properties surrounding the open pit. The ZOR is important when modeling stress release behind the open-pit highwall. MINEDW includes a built-in feature to simulate a ZOR around an open pit.

MINEDW also simulates underground mining using a GUI feature that allows users to create underground mine plans with drain boundary conditions. The inflows to these drain boundary conditions represent seepage into underground mine workings. The pore pressure distribution around mine workings can also be estimated. Additional underground mining features include:

Underground-Mine Development: Underground mining through time simulates using drain nodes. MINEDW features help track seepage in different mine areas over time.
Water Level Recovery after Mining (with or without backfilling): Water level recovery after mining cessation can be estimated for workings with and without backfill.
Block-Cave Zone: Block caving, a common underground mining technique for ore extraction, can be simulated in MINEDW, including the block cave zone and its impact on pore-pressure distributions and inflows.

The following sections detail each mining feature and boundary condition available in MINEDW, including mathematical formulations and common applications.

4.1. Open-Pit Mining¶

MINEDW simulates open-pit mining through a unique feature designed specifically for mining applications. The software collapses the finite-element mesh based on ground-surface elevations (open-pit designs) of the open pit. For open-pit mining, users can define:

Open-pit designs at any date interval
Open-pit schedules with progressive excavation
Multiple pits with intersecting geometries
Depth specifications for pit bottoms

Any number of open-pit designs can be imported to MINEDW at any date interval. Users may also specify the pit bottom depth on certain dates. The open-pit shape between time steps with specified pit plans or depths interpolates automatically.

MINEDW uses interpolated mining plans and schedules to simulate progressive open-pit excavation during model simulations. The excavation simulates by collapsing specified elements and their corresponding nodes in the finite-element grid at each time step. Elements and nodes collapse by decreasing their elevation to match the pit elevation specified in open-pit mine plans, while their x and y locations remain unchanged. Elevation increases of open-pit nodes are prohibited, and for intersecting pits, the lowest elevation applies.

Open-Pit Mining Seepage

MINEDW calculates the amount and location of seepage into the open pit over time. The seepage face uses drain boundary conditions implemented on the ground surface of the open pit. The equation below shows how seepage from open-pit drain nodes is calculated.

(4.1)¶\[\begin{split}q_{s} = \sum_{i=1}^{n} \begin{cases} C_{Si}\,\bigl(H_{Si} - H_i\bigr), & \text{for } H_i > H_{Si},\\ 0, & \text{for } H_i \le H_{Si}. \end{cases}\end{split}\]

Where:

\(q_s\) = functional representation of the seepage-face discharge [L³T⁻¹],
\(C_{Si}\) = coefficient representing the node i on the seepage face [L²T⁻¹],
\(H_i\) = computed hydraulic head at the node i [L],
\(H_{Si}\) = elevation of node i [L], and
n = number of nodes [Lᵒ].

Seepage from the groundwater system has a negative sign convention because it leaves the modeled domain. Seepage discharge appears in the “Mine” portion of the water balance. The seepage-face specified head (\(H_{Si}\)) equals the elevation of node i on the open-pit surface unless impacted by pit lake formation, as discussed in Pit Lake Development.

The coefficient \(C_{Si}\) is non-zero only at nodes on the surface of the open pit. Choose a value large enough so \(H_i\) approaches \(H_{Si}\) within a reasonable timeframe. However, the value must not be so large that the difference between \(H_i\) and \(H_{Si}\) is lost in computational precision.

Dewatering and Depressurization

MINEDW simulates common dewatering and depressurization techniques including:

Perimeter dewatering wells
In-pit dewatering wells
Sub-horizontal drains
Drainage galleries

Users can track the effect of these techniques on dewatering rates, seepage into the open pit, and pore-pressure distribution. MINEDW thus evaluates the effectiveness of proposed dewatering and depressurization schemes.

Pit Lake Development

After open-pit mining ends, MINEDW simulates pit lake formation. During excavation, drain nodes simulate seepage to the open pit. When simulating a pit lake, these nodes convert to “lake nodes” with specified heads based on the predicted pit-lake surface elevation.

The pit lake simulation includes:

Groundwater interaction with the pit lake
User-specified pumping to or from the pit lake
Evaporation from the pit-lake surface
Iterative solution for pit-lake elevation based on water balance

The head at lake nodes matches the predicted elevation of the pit-lake surface. If the pit-lake elevation is sufficiently high, water may discharge into the groundwater system (not possible with drain nodes). The equation below shows the formulation for calculating discharge into or out of the pit lake.

(4.2)¶\[\begin{split}q_{s} = \sum_{i=1}^{n} \begin{cases} C_{Si}\,\bigl(H_{L} - H_i\bigr), & \text{for } H_{Si} < H_{L},\\ C_{Si}\,\bigl(H_{Si} - H_i\bigr), & \text{for } H_{Si} \ge H_{L} \text{ and } H_{Si} < H_i,\\ 0, & \text{for } H_{Si} \ge H_{L} \text{ and } H_{Si} \ge H_i . \end{cases}\end{split}\]

Where:

\(q_S\) = functional representation of discharge to or from the pit lake [L³T⁻¹],
\(C_{Si}\) = coefficient representing the node i on the open-pit surface [L²T⁻¹],
\(H_i\) = computed hydraulic head at the node i [L],
\(H_{Si}\) = elevation of node i [L],
\(H_L\) = water-surface elevation of pit lake [L], and
\(n\) = number of nodes [Lᵒ].

The coefficient \(C_{Si}\) is the same coefficient used for each node in simulating seepage to the pit while the pit was being excavated. \(C_{Si}\) is non-zero for nodes on the surface of the pit and zero elsewhere.

In the first case of the equation (\(H_{Si} < H_L\)), the open-pit node i is under the surface of the pit lake. In this case, discharge enters the groundwater system if the head calculated at the open-pit node is less than the elevation of the pit-lake surface. Discharge exits the groundwater system if the head calculated at the open-pit node is greater than the elevation of the pit lake surface.

The second case in the equation (\(H_{Si} ≥ H_L \text{ and } H_{Si} < H_i\)) describes a scenario where the open-pit node is above the pit-lake surface, and the head calculated at that node is greater than the elevation of the node. In this case, water discharges from the groundwater system to the pit lake.

The third case in the equation (\(H_{Si} ≥ H_L \text{ and } H_{Si} ≥ H_{i}\)) corresponds to open-pit nodes which are above the pit lake and have a head value less than their corresponding ground-surface elevation. In this case, there is no discharge into or out of the groundwater system. The equation describes discharge to and from the pit lake due to groundwater interactions (\(q_S\)). The total discharge to or from the pit lake (\(q_T\)) also includes user-specified pumping to or from the pit lake (\(q_P\)), and evaporation from the pit-lake surface (\(q_E\)). The mass balance relationship that defines \(q_T\) is shown below.

(4.3)¶\[q_{T} = q_{S} + q_{P} - q_{E}\]

Where:

\(𝑞_𝑇\) = total discharge into or out of open pit [L³T⁻¹]
\(𝑞_𝑃\) = additional pumping to or from pit lake [L³T⁻¹], and
\(𝑞_𝐸\) = discharge related to evaporation [L³T⁻¹].

The \(q_P\) is specified by the user and is not dependent on pit-lake surface area or elevation, though the user may specify a pit-lake elevation at which pumping initiates. The \(q_E\) is calculated as shown in the equation below. The evaporation rate from the pit lake may be specified by the user. The \(q_E\) depends on the surface area of the pit lake, which changes over time based on the pit-lake elevation (\(H_L\)).

(4.4)¶\[q_{E} = r_{E}\,A_{t}\]

Where:

\(𝑟_𝐸\) = evaporation rate from pit lake [L¹T⁻¹], and
\(A_t\) = surface area of pit lake at time step t, which is a function of HL [L²].

The cumulative discharge to or from the pit lake over time (Q) is calculated throughout the model run using the average discharge rate over the current time step and the previous time step, as shown below.

(4.5)¶\[Q^{t} = Q^{t-1} + \frac{q_{T}^{t-1} + q_{T}^{t}}{2}\,\Delta t\]

Where:

Q = cumulative discharge into lake [L³],
\(q_T\) = total discharge rate to the pit lake [L³T⁻¹],
Δt = time-step length [T].

Each term of the equation depends on the pit-lake elevation. Since the pit-lake elevation at a given time step t both depends on and informs the local groundwater head distribution, it must be determined iteratively to minimize error within the local groundwater head distribution and the pit-lake formulation.

Zone of Relaxation (ZOR)

Mining and blasting operations commonly form a Zone of Relaxation (ZOR), an area of altered hydrogeologic properties surrounding the open pit. The increase in hydraulic conductivity is generally accepted to be up to three orders of magnitude, and is dependent on rock properties and mining activities (Read and Stacey, 2009 [4]). MINEDW has a built-in feature that allows users to easily simulate a ZOR around an open pit by specifying scaling factors that multiply the hydraulic conductivity of affected units.

The ZOR function in the MINEDW GUI enables users to efficiently simulate altered rock properties from mining activities. To use the ZOR function, users specify a scaling factor (\(α_j\)) by which the hydraulic conductivity of each affected unit is multiplied, as shown below.

(4.6)¶\[K_{zj} = \alpha_{j}\,K_{0j}\]

Where:

\(K_{zj}\) = hydraulic conductivity of unit j in ZOR [L¹T⁻¹],
\(α_j\) = scaling factor for unit j in ZOR [L⁰], and
\(K_{0j}\) = initial hydraulic conductivity of unit j [L¹T⁻¹].

For open-pit mining simulations, the thickness of the ZOR around the open pit can be user-specified or calculated as a function of the open pit depth. The MINEDW manual explains this in detail. The user-specified ZOR significantly affects pore-pressure distribution around the open pit. This tool is useful for slope-stability analysis performed with pore-pressure input from MINEDW.

Open-Pit Backfill

Open pit backfilling after mining cessation can be simulated. Users specify:

Hydraulic properties of backfill material,
Elevation to which backfill is added (constant or varied), and
Timing of backfill placement.

4.2. Underground Mining¶

MINEDW includes built-in tools to simulate underground mining over time using drain boundary conditions. Additionally, MINEDW simulates changes in hydraulic conductivity from underground mining activities (e.g., block-cave mining) and water-level recovery in underground excavations.

Underground-Mine Development

The user specifies drain nodes, as discussed in Section 3.1.2, through which water can discharge from the groundwater system but not into it, to achieve a user-specified head. To simulate an underground mine, the user specifies drain nodes at which the head is equal to the elevation of the mine workings. The nodes are grouped into mining tunnels or workings so users can track seepage from different mine areas over time. Each drain node has a user-specified leakance factor \(C_{di}\), related to the local hydraulic conductivity of mine walls. For example, a low \(C_{di}\) value may be chosen to simulate mine workings which have been grouted, while a high \(C_{di}\) value may be chosen for freshly blasted mine workings.

Water Level Recovery

The recovery of water level in and around underground mine workings can be simulated:

Without backfill - If backfill is not used, groundwater discharges from the modeled domain into the empty mine workings. This volume cannot be simulated using hydrology concepts because the mine workings are not porous media. Water level recovery is simulated similar to pit lakes using an iterative approach to minimize error between the local groundwater head distribution and the mine working volume to water level relationship. Surface area input is not required because evaporation is assumed to be negligible underground.
With backfill - Water level recovery follows standard groundwater flow equations. Users specify hydraulic conductivity and specific yield of backfill material, as well as the time step at which the mine workings are backfilled. Once water-level recovery begins, all drain nodes which are related to mining are turned off. Seepage into the mine workings fills porosity contained in the backfill material, and the water level in the mine workings is simulated using the same general groundwater flow equations as in the rest of the groundwater model.

Block-Cave Zone

Block-cave mining typically increases hydraulic conductivity of surrounding rock. This can be simulated using a Zone of Relaxation similar (ZOR) to open-pit mining, where users specify:

Elements impacted by block-cave mining,
Hydraulic conductivity multiplication factors,
Timing of application, and
Multiple ZOR units with different factors for inner and outer portions.