Lightweight Concrete for High Strength - Expanded Shale & Clay

Drying Shrinkage Model. Similar to creep, ACI-209 shrinkage model has constants that
determine the shrinkage asymptotic value, shrinkage rate and rate change. Equation B.3 shows
such a model.
( ε
sh
)
t
( t − t )
= )
u
(B.3)
f + ( t −
α
0
⋅ ( ε
α sh
t0)
where
t: age of concrete (days)
t 0 : age at the beginning of drying (days)
(ε sh ) t : shrinkage strain after “t-t 0 ” days under drying (in/in)
α: constant depending on member shape and size
f: constant depending on member shape and size
(ε sh ) u : ultimate shrinkage strain (in/in)
ACI-209 recommends a value for f of 35 and 55, for seven days moist curing and 1 to 3 days
steam curing, respectively, while a value of 1.0 is suggested for α. Ultimate shrinkage value
depends on the factors described in Equation B.4. As shown in Equation B.4, ACI-209 proposes
an average value of 780 µε for shrinkage which is multiplied by seven factors depending on
particular conditions.
( ε
sh
)
u
= 780 ⋅γ
λ
⋅γ
vs
⋅γ
s
⋅γ
ψ
⋅γ
c
⋅γ
α
(B.4)
where
(ε sh ) u : ultimate shrinkage strain
⎧1.40
−1.0
⋅ h for 0.40 ≤ h ≤ 0.80
γ
λ
= ⎨
; ambient relative humidity factor
⎩3.00
− 3.0 ⋅ h for h > 0.80
h: relative humidity in decimals
γ
VS
= 1.2 ⋅ exp{ − 0. 12 ⋅ V }; volume-to-surface ratio factor
S
V: specimen volume (in 3 )
S: specimen surface area (in 2 )
γ = 0.89 + 0. 041⋅
s ; slump factor
s
B-6