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.