Concrete Armor
Units for
Breakwaters
calculations show importance of limiting residual stresses arising during hardening
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R ubble mound breakwaters are constructed worldwide
to protect harbors and habitats against hydraulic
forces induced by high waves. These revetments usually
mixture’s adiabatic temperature development during the
initial 7 days of curing (Fig. 1(a)). Ten cubes were used
for compression and tension tests at ages of 1, 2, 3, 7, and
comprise rock or concrete armor over a core of rock, 28 days. Tensile strength as a function of time is provided
gravel, or sand. Many are protected against wave action in Fig. 1(b). With the exception of Mixture 3, which had
by an armor layer of large concrete elements. Mostly high fly ash content, the mixtures reached tensile
unreinforced, these elements exist in different sizes and strengths of about 4 MPa (580 psi) at 28 days.
shapes, varying from simple massive cubes to complicated
shapes like Accropodes® or Xblocs® (see Reference 1). nUMeriCAl Model
Resistance against wave action has been the main design During concrete hardening, chemical-physical reaction
criterion for armor units, but several cases of failure have processes generate exothermic heat, leading to increases
highlighted the importance of structural integrity. Our in concrete temperature. A temperature increment ∆T
research team set out to answer the question: Can can lead to deformations that, when restrained, cause an
internal mechanisms occurring during hardening of the incremental stress ∆σ, given by
concrete contribute to cracking or breakage of concrete
armor units? ∆σ = (∆T ⋅ αc + ∆εa) ⋅ Ε ⋅ y ⋅ R (1)
ConCrete properties where αc = the coefficient of thermal expansion in units of
Mixture proportions strain per degree temperature change; ∆εa = the incremental
To study the influence of the concrete composition strain resulting from autogenous shrinkage (a negative
on the concrete properties, six different mixtures were value); E = the elastic modulus; y = the relaxation
studied (Table 1). For each mixture, the cementitious coefficient; and R = the degree of restraint (y and R range
material content was 420 kg/m3 (760 lb/yd3) and the from 0 to 1). Of course, consistent units must be applied.
water-cementitious material ratio (w/cm) was 0.45. The properties, αc, E, and y change during hardening, so
Water reducers were not used to reduce the number of the stress σ consists of the summation of the ∆σ values
mixture ingredients. found for each time increment.
To calculate these stresses for the concrete armor
experimental testing blocks, numerical tools must also account for nonlinear
For each mixture, properties were determined using material behaviors. We used a hardening model called
150 mm (6 in.) cubes. One cube was used to measure the Finite element Concrete Curing Control System, or
34 october 2009 / Concrete international
Table 1:
O verview Of The cOncreTe mixTures used in This sTudy
Concrete Mixture Cement
type no. type Binder Aggregate Comments
1 cem iii/b blended cement sand-gravel 30% portland cement; 70% slag cement
Normal
2 cem i Na sand-gravel reference mixture
3 cem i Fly ash (