Vibration Modelling

Vibration modelling aims to predict the ground movement caused by blasting. It is measured in either mm/s or in/s, and aims to calculate the peak particle velocity (PPV) of a blast at a specific location. This is the largest vibration within a timing window which is usually set at 8 ms.

To open the Vibration Modelling panel, load a tie-up into a view, and go to the Analysis ribbon > Modelling group > Vibration Modelling.

Model parameters

Vibration is dependent on explosive mass and explosive timing. BlastLogic enables you to enter the following inputs:

  • Propagation rate: The speed at which vibrations propagate through rock.
  • Timing window: The time frame within which the maximum instantaneous charge (MIC) is calculated.
  • Extent: The distance to evaluate from the blast. Larger extents will require longer calculation times.

Calculation of peak particle velocity

Follow these steps to calculate the peak particle velocity (PPV) at a particular point of observation in BlastLogic:

  1. Collect and order each detonation event within the timing window.

  2. Calculate the total explosive mass and minimum distance to the point of interest at each detonation event.

  3. Calculate the particle velocity for each total explosive mass and minimum distance to the point of interest using the following equation (referenced in the Australian Standards (AS) 2187.2, 2006):

    ,
    where is the site variable, is the minimum distance to the point of interest, is the charge mass, and is the site exponent.

    Note:  You can set the site variable and site exponent constants in Location (Home ribbon > Setup group > Site).

  4. Calculate the particle velocity for every timing window interval to determine the subsequent particle velocity for that time period. The maximum calculated particle velocity over the entire blast is reported as the predicted PPV for that point of observation.

Background model information

In the basic case scenario (one hole with a single primer), the maximum instantaneous charge (MIC) is calculated from the explosive mass loaded in the hole, and the vibration for each point on the grid is calculated using the square-root-scaled distance formula. When there are multiple holes (or multiple explosive decks in a hole), the first primer to detonate in each explosive deck is used to calculate the initiation time, and the mass entire explosive deck is used as the MIC. Secondary primers in explosive decks are ignored.

For each point in the grid, the propagation rate and initiation time per explosive deck are then used to determine which decks are interacting with each other by taking into consideration the time for the vibration wave to reach the point (that is, distance / propagation rate) and a provided timing window.

The charge mass is therefore calculated to be the sum of the charge mass in all of the decks whose vibration waves reach the same grid point within the timing window. The MIC is calculated as the maximum of these charge mass sums. This is then used in the square-root-scaled distance formula to calculate the vibration at the given point.

Important!  As the initiation time of a primer is required to determine the interaction of the vibration waves originating from different explosive decks, any hole that is not part of a tie-up will be ignored by the blast modelling tools. Additionally, holes that have no charge plan will have no effect on the model as they have no charge mass. If a hole has no primers but has been included in the evaluated tie-up, the entire hole is counted as a single explosive deck and the initiation time used is the initiation time of the hole.

Panel overview

Model inputs and outputs

Vibrations can be calculated either by Using vibration observations, Using custom site parameters, or Using location defaults.

The Using vibration observations option allows you to filter vibration observations according to the following criteria:

  • Filter by monitoring station: You can select multiple stations from the drop-down menu and only observations from those stations will be displayed.
  • Filter by detonation location: This will display all observations with detonation coordinates within the specified filter radius of the provided location.
  • Filter by tag: When you enter text in the Tag field, the list will be filtered to only include observations that have a tag containing the entered text.
  • Filter by date: This will display only the observations which were recorded between the first and the last date you provide.

The Using custom site parameters option allows you to live-edit the vibrations by modifying the Site variable and Site exponent that become editable when this option is used. The values can be saved as the default values for a selected location.

The Using location defaults option automatically changes the Vibration at locations table in Model results to display the Site variable and Site exponent using the values from their appropriate location. Vibrations will not be calculated at a location which does not have a default variable and exponent. The vibration surface view is removed in this mode.

Conservative checkbox

When calculating PPV, you can choose to apply a conservative or non-conservative approach. The conservative approach takes into account the closest distance from the point of detonation to the point of observation, which helps to model the worst case scenario. On the other hand, the non-conservative approach calculates the weighted average using the mass of explosives, which is a more technically sound method for modelling the resulting particle velocity.

Consequently, the conservative approach can be regarded as
,
whereas the non-conservative approach, where multiple detonations are taken into consideration, can be calculated for all contributing detonations according to the formula
,
where is the distance to each detonation, and is the associated charge mass.

Based on these calculations, the resultant modelled particle velocity is calculated according to the formula
,
where is the site variable, is the effective distance, is the total charge mass, and is the site exponent.

This is calculated for every timing window to determine the subsequent particle velocity for that time period. The maximum calculated particle velocity over the entire blast is reported as the predicted PPV for that receiving position.

2D heat map

When a 2D heat map is generated, all distances are calculated only on the XY plane. Next, the results are interpolated to generate the heat map. This can result in variations between the value that is displayed on a heat map for a specific 2D point of observation when compared to the calculated PPV value for that specific point.

2D heat map when the conservative approach is selected
2D heat map when the non- conservative approach is selected