Can the Slump-Flow Spread Give the Yield Stress of Fresh Concrete? A Parameter-Free Test of the Thin-Layer Solution on 103 Laboratory Mixes

The slump-flow test spreads fresh concrete from an Abrams cone and records the final diameter. The thin-layer (pancake) solution of Roussel and Coussot converts that diameter into a yield stress, tau0 = 225 rho g Omega squared / (128 pi squared R to the fifth), where Omega is the cone volume and R the final radius. I derive the solution and a second consequence that is rarely used: the final height at the centre must equal h0 = 15 Omega / (8 pi R squared), with no free parameter. The UCI Concrete Slump Test data (103 mixes by Yeh) record both the spread and the slump, so the centre height 30 minus slump can be compared with the prediction. For the 59 mixes with a spread of at least 50 cm, the yield stresses implied by the spread have a median of 41.7 Pa, the model is in its thin-layer range (median h0/R of 0.11), and the measured centre height correlates 0.52 with the prediction but exceeds it by 2.92 cm on average (sd 2.45 cm); only 40.7% of mixes fall within 2 cm. The correlation falls as the spread widens, to 0.34 above 60 cm. Of 5,063 pairs of mixes with different slumps, 660 have a higher slump and a smaller spread, which no single-parameter yield-stress model allows. I also prove that tau0 varies as the fifth power of the inverse spread, so a 1 cm reading error at a 50 cm spread changes the estimate by 9.4%. The spread-based yield stress should be reported with this uncertainty.