Part I
CONCRETE
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Chapter 1
FRESH CONCRETE:
RHEOLOGY
Concrete is a manufactured material that is brought in a liquid form into the formwork. Once in the formwork, it will harden turning in the course of this process from a liquid into a solid. It is thus not surprising that the quality of a concrete structure depends on the quality of the placement of the
concrete is rheology. Fresh concrete is a fluid suspension, in which cement is mixed with water, sand and larger aggregates. When these different constituents are mixed, a fluid suspension is formed that obeys the laws of fluid mechanics, namely some fluid state equations that link stresses in the fluid to pressure and (shear) strain rates, the momentum balance equation (Newton again!), and
losses in pipe or open channel flow.
1.1 Fluid State Equations: Newtonian and Non-Newtonian Fluid
As a reminder, a classical Newtonian fluid cannot sustain shear stresses unless it flows. This flow dissipates energy along fluid layers; which is expressed by the fluid state equation: OT =-p1+ (1.1) pe
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where p is the fluid pressure, T is the dissipation potential, and d is the strain
tensor in solid mechanics)
= (grad + grad*)
(1.2)
The dissipation potential carries all the information required to describe the particular behavior how a fluid flows. For instance, if the shear stress relates linearly to the shear rate -which corresponds to a Newtonian fluid-, T is a
da = d, : da, while noting that Oda/Od, = (2da)-i da, then:
L'pnz+fd-==Ppnz=1y
(1.3) Herein is the dynamic viscosity (of dimension [] = []T = L-1MT-1) Not all fluids however shear in a linear fashion in response to the applica- tion of stress; and a simple generalization is to consider a dissipation potential in function of dar . The stress-strain rate relation for such a power-fluid' thus reads: =bdn==-p+2bdn-1 n i(d ) (1.4) with (da) = bd(n-1) the capparent' (or "secant) dynamic viscosity. A further refinement to be considered for some non-Newtonian fluids incl. concrete, is the fact that the fluid suspension can sustain a shear stress without moving up to a threshold shear stress value. In addition to the viscous flow term, the dissipation function needs to consider the existence of a shear pre-stress or yield stress To:
(1.5)
This shear pre-stress governs whether nor not flow occurs. Letting T =
tensor = + pl, flow only occurs if + > To. Hence, the state equation: r=2(da)d+To =d if: T>TO = -pl+ s with: da da d,=0 if:T<To (