13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 μ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ + ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ D% B A A A B A E A A B C C C (5) where 1 2 3 μ μ = + − D A (6) 1 2 1 2 3 μ μ − = − − D B (7) 1 2 − = D C (8) The Mazars and Pijaudier-cabot[13] had described the damage behavior of quasi-brittle materials like concrete and rock by equal strain, this paper follows their suggestion and the definition of equal total strain is ( ) 3 2 ε ε = ∑ i i (9) where iε are the principal strains. For bituminous material the damage is only related to the tensile strain, so it is supposed that the damage is induced only by tensile strains in this paper. Then specify strain i i ε ε = if 0 iε > and 0 iε = otherwise. The damage parameter D starts at a damage threshold level ε ε = f and is updated during damage growth which occurs according to an evolution law such that ( )ε =D D , which can be determined from the uniaxial tests. a linear elastic behavior has been sustained up to a peak tensile strength point σ ε = t f E which is illustrated in Fig. 2(a), then the stress-strain curve followed by descending branch up to a strain εu at which the load-carrying capacity is exhausted(and thus 1=D ), so the proposed damage evolution law reads: ( ) 0 0< ( ) < ( ) ε ε ε ε ε ε ε ε ε ε ε ε ≤ ⎧ ⎪ − = ⎨ < ⎪ − ⎩ f u f f u u f D (10) where εf , εu represent strain for threshold of damage and strain for critical of damage respectively. Fig. 2(b) illustrates the damage evolution curve.
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