■■2）■■■■2■■■）・23）t■4）2）-4h4■p8hìíî2pt■■2）2（）4h3h■■2（ ）■■■D- ■h{■■D（-（+（-Q■（p34■2pt■（p■tp■3ph4ü）ýþ=242=- Q■ -24Q■=+3- Q■=Q■+Q■+Q■=++--3+■+-432yRvr■■CL─ 2 ─（■■-4h■■■-4（■■■D-p8■h■■3h■■■D■■üýþ=ppD=2（p■■■■■properties of the concrete for predicting the concrete flow rate.For the analysis in this study, the concrete flow in the pipe was modeled by assuming not the liquid friction state at the pipe wall but a thin water film acting as lubricant at the interface between the concrete and the pipe wall.13) The slip of concrete on the wall surface in this model is based on the assumption that a Newtonian flow is caused by the pumping pressure at the water film area, where the flow velocity of the contact area between the concrete and the water film can be assumed to be equivalent to the slip velocity of the concrete. Therefore, the flow in the pipe is hypothetically a two-layer flow consisting of the thin water film and the concrete flowing inside.Based on the assumption described above, the water film thickness was experimentally estimated by using a pressure bleeding tester specified in JSCE-F502 of the Standards of Japan Society of Civil Engineers, flow rate measurement was taken by using a pipe viscometer, with the pressure gradient varied at three levels, and the Bingham fluid flow rate was determined by subtracting the concrete movement amount (amount of slip) corresponding to the flow velocity at the water film area and the water film flow rate from the measured flow rate. By solving a set of three simultaneous Buckingham equations thus constructed, plastic viscosity and yield stress were obtained for mechanical properties of the concrete which were essential to piping plans for pumping.14) ~24) The results by the proposed method were examined in comparison with those by a test using a rotating viscometer to investigate the reliability of the experiment values by the pipe viscometer.An assumption was made that part of free water in the concrete in the pipe under the pumping pressure would ooze into the gap between the concrete and the pipe wall, forming a thin water film. With reference to Fig. 1, the water film flow velocity distribution Vr can be expressed by the Hagen-Poiseuille equation as shown in Equation (1).QW : water film flow rateQS : flow rate due to slipQB : Bingham fluid flow rateFig. 1 Flow velocity distribution of the pipe flowrf : plug flow radiuswhere Vr: flow velocity at an arbitrary radius r from the center of the pipe (cm/s); R: radius of the pipe (cm); r: arbitrary radius from the center of the pipe (cm); Δ p/l: pressure gradient (Pa/cm); and, η: viscosity coefficient of water (Pa・s).With r=R-y substituted into Equation (1), the flow velocity of the contact area between the concrete and the pipe wall can be expressed by Equation (2).}2）where y: water film thickness (cm).With the water film formed between the concrete and the pipe wall assumed to act as a lubricating layer, slip velocity of the concrete VR can be considered to be equivalent to the water film flow rate in Equation (2).Therefore, flow rate due to slip of concrete Qs is:The water film flow rate QW at each pressure gradient can be given by Equation (4) which is an integration of Equation (2) from R-y to R:ì■■í4îSince concrete in the fluid state behaves like a Bingham fluid, its flow rate QB can be given by the Buckingham equation as in Equation (5):where QB: Bingham fluid flow rate (cm3/s); τf: yield stress (Pa); and, ηpl: plastic viscosity (Pa･s).Consequently, the flow rate of the concrete flowing in the pipe (measured flow rate QA) can be expressed by Equation (6) when Δp/l=i:Based on the assumption that part of free water in the concrete under a pumping pressure in a pipe would ooze into ■2/h ■■-3h■■■■■(1)(2)(3)(4)(5) (6)2. Concrete flow in pipes3. Estimation of the water film thickness
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