Some mXmas fun

With the holidays approaching we thought we would send everyone some mXmas presents! And obviously what everyone wants for mXmas are mXrap videos ?. These videos are not geotech related but come from various games, generative art, or physics simulations that we have made for fun. Scroll down for more details. The mXrap team wishes everyone well for the holidays and a happy new year. Please be aware that the mXrap offices will be closed between December 23 and January 9. We will still be able to provide limited support during this period but there may be some longer than normal delays. Now, onto the videos…   Rock Paper Scissors Game   This is a Rock – Paper – Scissors simulation where players randomly walk through the space and do battle when they come within a certain distance of one another. The losing player becomes a new member of the winners’ team. There are several ups and downs with the numbers in each team over time. There are some interesting dynamics since as one team gets low in number, it affects the encounter probability to the other teams. But anyway, place your bet and play the video to see if you’ve won!   As a fun bonus, here is another version with a more geotech flavour. Welcome to Ground Support – Rock Fall – Bogger. In this version, Ground Support stops Rock Fall, Rock Fall buries Bogger, and of course the pesky Bogger destroys Ground Support. Place your bets and don’t let your geotech feelings bias you ?.     3D Cellular Automata     Cellular Automata are processes that can generative highly complex patterns from simple cell-based rules. In a 3D grid, cells are born and survive based on the status of their neighbouring cells. Different cell rules can have very different results, generating rapid expansion, slow decay, or steady-state behaviours. Cellular Automata can be used to simulate various real-world biological processes. This next video has some Sierpinski triangle vibes. It uses cell rules based only on neighbours that share a face (up to 6). The rules for the first video were based on all neighbours in the surrounding 3×3 box (up to 26).     Chladni Patterns     Chladni Patterns are formed by sand or metal filings on a plate vibrating at various frequencies. A 2D standing wave pattern is formed and the particles settle in areas where the vibration is cancelled out. This video simulates several Chladni patterns increasing in vibration frequency. Particles randomly move a distance relative to the amplitude of the vibration at that location. If a particle falls off the plate it is replaced at a random location.   Diffusion-Limited Aggregation     Diffusion-limited aggregation can be used to model various fractal growth processes. There are several real-world examples such as crystal growth, lightning paths, coalescing dust and snowflakes, plant branching, and even mineral deposits. New particles are added to the space and randomly walk until they come within a certain distance and stick to the existing structure. Different patterns can be made based on the starting structure and where new particles are added in the space. In the video above, a circular ring is added as the starting structure and new particles are added at a random place in the circle (although not too close to the existing points). The same process can be extended to 3D space. The video below starts with points at the bottom of the cube and new particles are added from the top. The pattern formed is a lot like the growth of a forest. As some structures grow higher they start to block other structures below (like blocking sunlight) and grow even faster.     Slime Mould Simulation     Slime mould (Physarum polycephalum) is widely studied as it has no brain and yet can grow and make decisions to find food and even solve mazes. The growth behaviour can be simulated with an agent and trail system. Agents (particles) deposit chemicals as they move across the trail. An agent may continue straight or rotate left or right depending on the concentrations of chemicals it senses ahead. The chemical concentration on the trail diffuses and decays over time. Different transport networks develop over time as the agent’s paths interact. Ant colonies can be modelled in a similar way. Ants don’t have the memory to know where home or food sources are, but they follow different pheromones left by other ants. Ant colony simulation will be a nice future project ?.   Epicycles     Epicycles are radially connected circles that rotate at different frequencies. The radius and frequency of each circle comes from a Fourier transform of the input line. Any continuous line can be represented with epicycles, even an mXmas message…  

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Energy – moment relationship

Energy and moment are two independent measures of the strength of a seismic event. Their physical meaning and how they are calculated was described in a previous blog post. Analysis of the relationship between the energy and moment of events can provide insight into seismic sources. For example, blasts or ore pass noise, falsely processed as real events, tend to have distinct zones on an energy-moment chart. In general, events with higher-than-average energy are associated with high relative stress. Energy index is a parameter used to estimate effective stress. To calculate energy index, the mean energy-moment relationship must be defined. Energy index is the log difference in energy from the mean energy-moment relationship. When comparing energy index in different software or from separate sites, it is important to note that if the energy-moment relationship is not the same, the energy index will not be consistent. The most common method of fitting a linear relationship between two variables is known as least squares regression (LSR). This method essentially minimizes the vertical (Y-axis) difference between the data points and the line of best fit. For the energy-moment case, this would be minimizing the energy difference. LSR is designed for cases where the independent variable (X-axis) is known perfectly (zero error) and the error is only associated with the dependent variable (Y-axis). This is not suitable for the energy-moment case as there is uncertainty in both the energy and moment parameters. The uncertainty in moment and the uncertainty in energy are also generally not the same scale. There are several linear regression methods that account for uncertainty in both parameters. Orthogonal regression minimizes the perpendicular difference between the data and best fit line, assuming a constant ratio between the X and Y variances. There is also a method known as weighted least squares which does not assume a correlation between the uncertainty of the two variables. A less complicated approach is to use the quantile-quantile (QQ) plot of the data. This plots the smallest energy against the smallest moment, the second smallest energy against the second smallest moment, etc. This approach has the effect of normalizing the different scale variances of each parameter. The ordinary LSR method can then be applied to the QQ data to obtain an accurate line of best fit. This is equivalent to the orthogonal regression method. The figure below shows the difference between the QQ fit and the least squares fit of the energy-moment data at the Tasmania mine. The QQ fit is a better match to the highest point density zones. The poor LSR fit is because the variance in energy is higher than the variance in moment. The distribution of the energy and moment departure indices is plotted below. Both distributions are slightly asymmetrical, likely due to the various seismic mechanisms superimposed. The wider variance in the energy index introduces a bias that has the effect of making a shallower least squares fit as it tries to minimise the vertical departure in the centre of the chart. If you are doing your own energy index calculations, or using different software, you should be aware of the method used to define the energy-moment relationship and the linear constants used. The least squares approach or chi-square regression should be avoided. The QQ based method is the approach used in mXrap and you can find the fitted linear equation in the footer of the energy-moment chart. You might see different parameters for “global” energy index and “local” energy index. This distinction comes from the different energy-moment relationships used. The global EI relationship is based on all events that pass the quality filter. The local EI relationship is based on events that pass the current base filter (volumetric, parameter ranges etc.).

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mXsync updates

For users who have upgraded to mXrap version 5.16+, you may have noticed the new mXsync button at the bottom left of all of the windows. This button allows users to open mXsync from within mXrap to apply patches and complete backups of the root folder. When this button is blinking, it signifies that you have been requested to either complete a backup or apply a patch. Users will be automatically reminded to complete a backup every four weeks. We recommend that a single device is used to manage the root folder in mXsync to prevent confusion. This device should be logged in to mXsync and would be responsible for completing all backups and applying patches. If you are planning on using a device for this purpose, please open the built in mXsync and make sure that you are logged in. To upgrade to the latest version of mXrap, please contact our support email address.

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Caving Suite updates

The Caving Suite is a set of applications that provide tools for the analysis and interpretation of cave monitoring data sources. Currently, four apps are included in the Caving Suite: Caving Sandbox, Fragmentation, Open Hole Dipping, and Caving Hydraulic Radius (see app overview and Geotechnical Engineering with mXrap seminar for more details) Over the past year, there has be numerous updates to the apps in the Caving Suite to assist with data visualisation, and analysis. Caving Sandbox: This app brings together all of your cave monitoring sources and puts them in one place, allowing complex multi-factor analysis. Changes include: General: Improved controls for manipulating and filtering data. This includes the addition of filter volumes, distance to survey filters, selection box filters, and data source-specific filters and controls. Users can now export event density isosurfaces, production columns, and production surfaces as DXFs to be used in external packages. Users can now easily export videos of the 3D View using time slicing or cumulative date filters. Production: Production columns can be displayed as either Height of cave, height of draw or bulked height. New Charts – production versus depth, individual drawpoint production timelines, daily activity. Production Column display modes Instrumentation: Alerts have been added for beacon displacement. Users can define the conditions for the alert, including the monitoring period and threshold displacement, from within the caving sandbox. A device inspection window has been added where users can easily inspect individual markers and beacons. Improved visualisation of beacons and network smart markers. This includes a 3D series for beacon flow, size by marker styles, and new charts. Added support for the auto-export of beacon positions, RSSI, and tilt readings from GeoHive directly into mXrap. If you are interested in setting this up at your site please contact us at our support email address. Standard smart markers can now be imported into the caving sandbox. Cave tracker beacon inspection window mXrap app integrations: We have started integrating data from other mXrap apps into the caving sandbox. We are working on tools to make this process easier and allow users to customise the sandbox to suit their needs. So far we have the following data sources integrated into the sandbox including 3D series, charts, and tables: Instrumentation – extensometers Instrumentation – prisms RMDA – rock mass quality Intervals Other apps that we plan on integrating with the caving sandbox includes more data sources from RMDA (e.g. structures), Damage Mapping and other instrumentation. Fragmentation: This app allows you to import your fragmentation data into an mXrap database, then visualise and analyse the data. Analysis can be conducted in conjunction with other relevant data sources (including production data). Changes include: New data import interface. Users can import either fixed/variable percentage or fixed/variable size data. Updated analysis tools: Cumulative fragmentation chart Particle size distribution chart User defined bin sizes Heat map Pie charts Mapping fragmentation to production columns Fragmentation analysis window For more information, please contact our info email.

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Rock Mass Data Analyser updates

The Rock Mass Data Analyser (RMDA) application allows a user to import various types of geotechnical data (rock mass quality, structural, stress and intact rock strength) into mXrap, creating a geotechnical database which may be visualised and analysed in 3D, on charts and in stereonets (see previous blog post for more details). Since the release of the RMDA, various updates have been made to assist with data analysis and setting up the rock mass database. Interface: The application is now split into two apps: the Rock Mass Data Importer and the Rock Mass Data Analyser. This has been done to streamline the data import process and allow users to focus on data analysis in the analyser application. Geology: Geology logs may now be imported into the application. These logs can be used to update other borehole databases (e.g. geotechnical logs, structural logs, etc.) with lithology data. Lithology groups may also be created, allowing for the grouping of lithologies from geology logs into broader groups that are more suited for geotechnical purposes. Structures:  A digital mapping data section has been introduced, where structural data from photogrammetry and LiDAR scans may be imported. This data may be combined with structural data from boreholes and scanline mapping, contributing to the structural database. True spacing statistics for each defined discontinuity set has been added (note that discontinuity sets may be outlined in the application). Users can now visualise and correct for orientation and sampling biases. Alpha and beta values imported from structural logs can now be converted to dip and dip direction, where the user is required only to provide details on how the beta angle was measured. A core stick illustration is also provided to assist with choosing a beta measurement option. borehole structures where dip and dip directions have been calculated from alpha and beta values Stress: A section to visualise and assess stress data has been added to the application. Borehole stress measurements and borehole breakout observations can now be imported, allowing for the creation of a stress database which can be updated as required. Tools in this section allow a user to: Visualise stress data along boreholes. Visualise the orientation of principal stresses. Analyse stress orientations with respect to depth below the surface. Calculate the Euclidean mean of the stress measurements. Produce a summary report. stress data window Other updates: Various new filters and markerstyles have been added. This includes a structure type filter for structural data and a failure type filter for intact rock strength data. VSA Filters have been added for all data sources. This allows the filtering of data based on a given user defined volume. Intact rock strength window with “failure type” filter applied to data in the Hoek-Brown chart and 3D view VSA filter applied to rock mass quality data Future plans for the RMDA application include the development of tools to define and edit geotechnical domains interactively. There are also plans to continue to integrate the RMDA into other mXrap applications. For more information or if you would like to try the RMDA application, please contact our support email address 

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Update to Paste Backfill Design app

We have made a couple of changes to the Paste Backfill Design application since the original release. See the previous blog post for the main details of the app. Since the first release, we have modified the paste volume calculations to allow for multiple pouring locations and beach angles. This will be helpful for cases where there is an initial waste rock dump in the stope. The video below demonstrates a scenario where the stope is first filled with beach angle 37°, then filled with material at 3° beaching. The multiple pouring locations can be used if the waste rock is dumped from a different place to the paste pouring. See video below. If you already have the app, get in touch with our support email address to help you upgrade your root folder. If you would like to try the app, contact our info email to set up a free trial.

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NEW APP – Paste Backfill Design

We have developed a new app to aid in the design of paste backfill in stoping operations. The app has tools to help you to: If you would like to try out the app, please contact our info email. Paste volumes The paste volume calculations use the mine geometry app to input surveyed geometry. Walls/barricades and bunds can be added to the geometry. Paste is deposited into the geometry from a specified pouring location. The path of the paste flow is simulated according to the beach angle. The beach angle informs the maximum horizontal spread of the paste. The effect of overburden pressure (pushing paste uphill) or additional flow effects are not considered. The video below shows an example of a paste filling scenario. In this case the beach angle is 3°. Bund capacities can be calculated by turning off the relevant wall and finding the volume at which the bund has overflowed. Stability Analysis Several analytical methods from various sources have been implemented in the app to estimate the stresses within the fill mass and the required UCS for vertical and horizontal exposures. The methods to compute stresses are listed below. The stresses at the base of the stope are reported in a table and charts show the variation in stress by fill depth. Method Reference Description Martson’s cohesionless model Martson 1930 2D arching, no cohesion, active earth pressure Modified Martson’s cohesionless model Aubertin et al. 2003 Martson method with passive or at-rest earth pressure Terzaghi’s cohesive material model Terzaghi 1943 2D arching, with cohesion Van Horn’s 3D model Van Horn 1964 3D analytical arching solution Hydrostatic stress – Stress from overburden weight (K=1) The methods to compute the required UCS for vertical exposures are listed below. Most methods only apply to a single vertical exposure. One approach looks at multiple vertical exposures where the arching effect is related to how much of the stope perimeter has not yet been exposed. The order of wall exposure can be adjusted by editing the exposure priority. Method Reference Description Askew narrow face method Askew et al. 1978 2D finite element based, includes Terzaghi arching Frictional sliding block Mitchell et al. 1982 Sliding Block LE, cohesion resistance on side walls equal to fill cohesion, failure plane 45° + φ/2, height >> width Frictionless sliding block Mitchell 1983 Sliding Block LE, without side wall resistance, cohesion = UCS/2 (Tresca), failure plane 45° + φ/2, height >> width Modified Mitchell Li and Aubertin 2012 Includes surcharge, includes friction on sliding plane, cohesion between fill and rock a fraction of fill cohesion, high and low aspect ratio stopes treated differently Block and wedge Li 2013 Generalised solution includes friction on each wall, limit equilibrium approach for a wedge and overlying rectangular block Multiple exposures Bloss (1992)   Winch (1999) General arching solution, arching effect reduced based on the proportion of stope perimeter exposed. The required UCS for horizontal exposure is computed for a 2D beam. The 2D beam might be considered the first “plug” run. There is optional beam loading to represent additional fill mass above the beam. The beam loading can be estimated from the vertical stress. The 2D beam analysis is based on Mitchell & Roettger (1989) that considers a number of failure modes of a sill pillar: Horizontal exposure is also assessed using voussoir beam analysis based on the original work of Evans (1941) and later Beer & Meek (1982) that considers the strength of a compressive arch within a rectangular beam. The analysis looks at crushing and sliding failure. The procedure was also described in Diederichs & Kaiser (1998). Paste Testing A database of UCS test results can be used to fit a strength prediction model. The model can be used to predict the UCS based on the binder and tailings type, binder %, and age. The curing model is based on the following equation: UCS = (A.Binder+B).log10(Age) + C.Binder + D + Epsilon A number of charts can be used to interrogate the UCS results and curing model. The chart below shows the UCS percentiles for 5% cement paste (UCS tests shown between 4.5% and 5.5%). Percentile lines are plotted for 10%. 25%. 50%, 75%, and 90%. The chart below shows the curing profile of different cement content percentages. The 50th percentile line is plotted for cement contents of 3%, 4%, 5%, 6%, 7%, and 8%. There are also charts to show the UCS distribution for a particular test age or the age distribution to reach a particular UCS. The distributions below are for 5% cement paste. The UCS distribution after 7 days curing is on the left and the age distribution for 200 kPa UCS is on the right. Reticulation The pressure profile along the paste reticulation path can be analysed to ensure the paste gravitational flow will overcome the pipe friction and reach the stope. The annotations tool can be used to draw a polyline along the paste delivery path. Any saved annotation can be used as the retic path. Once the diameter has been set for each pipe segment, the friction loss is calculated based on the work of Goldsack (1998). There is also an option to use a constant friction loss for all pipe segments. The Goldsack (1998) friction loss is based on the following equation: ΔP/L = 16τ0/3D + 32ηV/D² The first term (with yield stress) tends to dominate the second term (with viscosity). This is why many people ignore the second term and base the friction loss on yield stress and diameter alone. You have the choice to include the viscosity term or not. The yield stress can be determined from a shear vane test or a slump test. There is a tool to calculate yield stress from the maximum torque of a shear vane test, based on Dzuy & Boger (1983). There are also tools to calculate yield stress from a modified slump test (cylindrical test), based on Pashias et al. (1996) or the generalised slump test (cone), from Saak et al.

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