The main purpose of this paper was to theoretically elucidate the compressive strength of concrete using the empirical formula with exponential form for the ultrasonic testing method through a generalization of the one-dimensional wave equation. The approximate solutions derived from a generalization of the one-dimensional wave propagation theory using the separation of variables method can be represented as the exponential form. If the viscosity of the concrete materials in stress wave method is neglected, the elastic waves can then be reduced to the ultrasonic waves. Through the membership function concept in the fuzzy set theory, the approximate solution with exponential form can be represented as the empirical formulae for the ultrasonic testing method in predicting the compressive strength of concrete. This present study indicates that both the ultrasonic pulse velocity (UPV) and ultrasonic pulse amplitude (UPA) methods are just a special case of the combined method. The predicted results of the combined method are actually better than the results obtained from either the UPV or UPA method.
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