Size effect on nominal flexural strength of concrete beams influenced by damage gradient

• The sizes effect of concrete beams is studied by first-order gradient damage theory.
• A numerical implementation of the first-order gradient damage theory is proposed.
• A gradient damage sizes effect law is proposed to describe the sizes effect.
• When the beam depth → ∞, the nominal flexural strength yields to a constant value.

Based on the first-order gradient damage theory where a damage gradient D,m and internal characteristic length parameter lm were introduced into the constitutive equations, an approach is proposed to consider the influence of damage gradients on the size effect of concrete beams. In the numerical implementation of the first-order gradient damage theory, damage values at Gauss points are calculated in each iterative step of non-linear finite element analysis, then the damage gradients of Gauss points are calculated by using the finite difference method. Geometrically similar unnotched pure bending concrete beams with a fixed ratio 4 of length to depth are simulated. The results show that the nominal flexural strength Mnom increases linearly with the internal characteristic length parameter lm and decreases monotonically with the beam depth d. When lm equals to zero, the nominal flexural strength Mnom becomes a constant. Otherwise, the size effect markedly increases with the internal characteristic length parameter lm. A gradient damage size effect law (GDSEL) is proposed to predict the size effect of unnotched concrete beams. When the beam depth d → ∞, the GDSEL produces a horizontal asymptote in the plot of Mnom versus d.

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