Cemented paste backfill behaves as a Bingham plastic: it will not shear at all until the applied stress exceeds a yield stress τ0, after which it shears with plastic viscosity μp. Both rise steeply with solids concentration and cement content because more fines/binder means more inter-particle friction and a stronger flocculated network:
τ0 = 2·e^[20(Cw−0.65)]·(1+0.10·binder) Pa
μp = 0.02·e^[9(Cw−0.65)]·(1+0.05·binder) Pa·s
For laminar Bingham flow in a pipe of radius R and length L, the Buckingham–Reiner equation gives the flow rate for a given wall shear stress τw:
Q = (πR³τw)/(4μp) · [1 − (4/3)(τ0/τw) + (1/3)(τ0/τw)⁴]
Each frame the sim bisects this equation for τw so it matches your target tonnage (converted to a volumetric flow via the mix density), then reports ΔP = 2Lτw/R and pump power P = QΔP. The unsheared core where local stress stays below τ0 rides as a solid plug of radius r_p = Rτ0/τw — flatten the shear sliders and watch the plug swallow more of the pipe until, at high solids with too small a pipe, the required pressure exceeds a realistic 9 MPa positive-displacement pump limit and the system reports overload.
- Plug core — fraction of the pipe cross-section moving as an unsheared solid slug.
- Pump load — required pressure as a % of a 9 MPa reference pump capacity; over 100% means this mix cannot be pumped at the requested rate through this pipe.