A B S T R A C T A simple damage model with the concept of mode-II microcracks on crack wall contributing to the irreversible strains for concrete is developed. By applying the micromechanics method, a microcell-based damage model is introduced to understand the damage behaviour. Further, by introducing the physical interpretation of the damage variable using thermodynamic method, a novel damage variable (irreversible-damage variable) is proposed to describe the irrecoverable strains generated by both mode-II microcracks and irreversible-frictional sliding. With this methodology, a simple continuum damage mechanics model is developed in which both elastic and irreversible damages are considered. As demonstrated by the comparison with experimental results, the proposed model is characterized by accuracy of solutions, sufficiency of physical sense and convenience of implementation. CDM = continuum damage mechanics FPZ = fracture process zone RVE = representative volume element STD = standard deviation SIF = stress intensity factor D = damage variable tensor D e , ω = elastic-damage variable tensor D i = irreversible-damage variable tensor I = four order identity tensor, p i ± = fitting parameters related to damage properties D ± = scalar damage for tensile/compressive uniaxial case D i ± = scalar irreversible-damage for uniaxial tensile/compressive case E = nominal Young's modulus E 0 = initial Young's modulus E = effective Young's modulus E d = degradation of Young's modulus K I = stress intensity factor K IC = critical stress intensity factor 2a = length of crack b = crack opening due to mode-II microcracks b′ = crack opening due to irreversible-frictional sliding da = increment of crack length on crack tip i = number of microcell r = stress ratio α = parameter considering the bia-compressive effects ε 0,δ , ε de,δ , ε di,δ = small additive strain Correspondence: Z. Shan.

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Here the piezoelectric Lead-Zirconate-Titanate (PZT) sensors were developed and embedded into concrete to actively provide the local excitation and simultaneously sense the structural dynamic response by using the electromechanical impedance (EMI) technique. The influences of mass variations of concrete structure and vibration condition on EMI technique were investigated. The root-mean-square deviation (RMSD) index was used to evaluate the impedance spectra variation of the PZT sensor. The results show that the EMI technique is sensitive to the mass variation of the structure, and the EMI sensitivity shows the decreasing trend with increasing the distance between the PZT sensor and additive mass loadings on the concrete structure. The vibration condition is important for the accuracy of EMI technique, which should be considered in the practical engineering application.

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