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Abstract A relationship between the damage variable and the loading time has been obtained from the rheologic-ultrasonic tests of salt rock. On the basis of the classical three elements model，a fractional derivative three elements model for salt rock considering the damage evolution was established employing the theory of fractional calculus and damage. The model is structural concise and has less fitting parameters. The parameters of the model can be determined by the fitting analysis of least-squares using the data from the uniaxial rheological tests. The fractional derivative three elements model can fit the three stages of rheologic of the experimental data of the salt rock with high accuracy and is better than the classical one in characterizing the tertiary rheological stage. Furthermore，it is shown that the classical three elements model is a special case of the new model.
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Received: 28 June 2013
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2014, Vol. 33 
