Modeling

Calculation Stages

The XBlast4D software complex performs rock mass fragmentation modeling as a sequential computational process that includes several interconnected stages. Based on the loaded geological, geomechanical, and technological data, a digital model of the blast block is formed, after which the mass destruction calculation and subsequent rock displacement is performed.

The calculation process includes three main stages:

1. preparation and construction of the initial model of the pit area;
2. simulation of rock mass destruction and displacement;
3. forecast of the distribution of ore quality in the formed muck pile.

Initial Model Preparation

Before starting the calculation, the system forms an integrated model of the pit area that combines geological information, the geometry of the blast block, and drill-and-blast parameters.

At this stage, the following operations are performed:

• construction of the geometric model of the blast block based on borehole coordinates;
• determination of the area boundaries, including:
  • pit surface,
  • free surfaces,
  • previously blasted zones;
• formation of the three-dimensional block model of the mass before blasting.

The block model contains rock properties and the distribution of ore components obtained from production exploration and borehole sampling data.

As part of model preparation, the following is performed:

• selection of rock types composing the blast block;
• binding of geological parameters to block model elements;
• interpolation of component contents between boreholes.

As a result, the initial digital model of the mass is formed, which is used in the further destruction calculation.

1. Fragmentation Physics Simulation

The first stage simulates the impact of blast energy on the rock mass.

The calculation is based on determining the distribution of energy impact from simultaneously detonating borehole charges. For each point in the mass, a potential velocity field is calculated, characterizing the intensity of the blast impact.

Within this stage, the following calculations are performed:

Blast Energy Propagation

The spatial distribution of energy transmitted to the rock mass from explosive charges is determined. The following are considered:

• borehole location;
• charge parameters;
• properties of the rock mass.

Fragmentation Zone

Based on the energy distribution, the mass fragmentation zone is calculated. Within this zone, loss of rock strength and transition of the mass to a loosened state occurs.

The destruction boundaries are determined taking into account:

• strength characteristics of rocks;
• mass density;
• borehole grid geometry.

Loosening Coefficients

Depending on the heterogeneity of energy impact, local loosening coefficients are calculated, characterizing the volume change of fragmented rock.

Ballistic Simulation

After fragmentation, the rock mass is considered as a set of particles moving under the influence of the received energy. For each particle, the following are calculated:

• initial velocity of motion;
• direction of displacement;
• flight trajectory.

Material movement is modeled along ballistic trajectories, after which a displaced rock mass array is formed.

2. Muck Pile Model Construction

The second stage calculates the geometry of the muck pile formed by the fragmented rock mass.

The displaced material is deposited taking into account:

• the natural slope angle of the rock;
• mutual interaction of mass fragments;
• geometry of the original bench.

As a result, a spatial model of the muck pile is formed, including:

Muck Pile Configuration

The shape of the muck pile surface and its spatial position relative to the original mass are determined.

3D Model of Displaced Mass

A volumetric block model of the formed muck pile is constructed. Each block of the model contains information about:

• block position after blasting;
• degree of loosening;
• displacement relative to the original position.

Displacement Forecast

For each block, the following are calculated:

• displacement vector;
• magnitude of horizontal and vertical displacement;
• zone of material accumulation.

3. Quality Parameter Forecast

The final stage performs the transfer of geological characteristics to the formed muck pile.

The initial quality block model of ore is transformed in accordance with the calculated rock mass displacement.

Within this stage, the following calculations are performed:

Ore Model Transfer

Contents of ore components specified in the original mass model are displaced together with the corresponding blocks.

Mixing Calculation

During rock displacement, mixing of different material types occurs. The model estimates the degree of mixing between:

• ore blocks;
• wall rock;
• areas with different ore component content.

Loss Zones and Dilution Areas

Based on the obtained model, areas are identified:

• ore loss zones — areas where ore material ends up outside the planned mining;
• dilution areas — sections of ore mixing with wall rock.

Calculation Model

Model Characteristics

The fragmentation model used in the system is based on a quasi-static approach, in which the detailed dynamics of the detonation wave is not directly modeled. Instead, the integral energy impact of charges on the mass is taken into account.

This approach allows:

• significant reduction in computation time;
• ensuring calculation stability for large models;
• obtaining reliable results for engineering drill-and-blast planning tasks.

Start Calculation

Before launching the simulation, the user sets calculation parameters through the system interface.

Verification of Source Data Loading

After loading the source data, the system automatically adds it to the current project.

When loading is correct, a Ready status appears next to each data type in the list, indicating successful processing and readiness of the data for use in further calculations.

If the Ready status is not displayed for any item, it is recommended to verify the correctness of the uploaded file and import parameters.

Viewing Loaded Data

To visually verify the loaded data, it is necessary to click the Open Visualizer button.

After clicking, the system will automatically switch to the Visualizer window, where all data added to the project will be displayed. In this mode, the user can:

• verify the correctness of data loading;

• assess the spatial location of objects;

• ensure there are no errors before starting the simulation.

Running Modeling

To run the calculation, it is necessary to go to the active project window and open the Modeling tab.

This tab contains calculation management tools. To start modeling, click the Start button.

After starting, the system will perform the calculation based on the loaded source data and selected parameters.

Calculation History

The Modeling tab also displays the history of calculations performed within the current project.

The history stores information about previously started simulations, which allows:

• tracking the sequence of completed calculations;

• returning to previous results;

• analyzing changes in modeling parameters.

Computational Environment

Calculations are performed on the system's server infrastructure.

Simulation is launched in isolated Docker containers, which provides:

• calculation stability;
• scalability of computational resources;
• ability to execute multiple calculation tasks simultaneously.

Calculation execution time depends on:

• block model size;
• number of boreholes;
• complexity of geological structure;
• selected simulation precision.