The numerical studies provide an understanding of propagation of ultrasonic waves in concrete and aid in the planning and interpretation of experimental work. A few key results from these analyses will be presented as following:

1. Coarse aggregate content and size have great influence on wave velocity and attenuation, but little on strength of concrete. This can cause unacceptable error when predicting concrete strength from velocity.

2. Concrete is a dispersive material. Experiments show that the pulse velocity in concrete increases with higher frequency. But in FEM analysis, another dispersion phenomenon can be observed due to the element discretization [4, 5]. The two dispersion should be distinguished in numerical analysis.

3. Ultrasonic attenuation is a much more sensitive indicator of crack growth than pulse velocity.

4. Ultrasonic attenuation comes from divergence, material internal damping, dissipation caused by particles and voids. Dissipation is the main factor at high frequency. The practical consequences of these results are pointed out.

1. Sandor Popovics, Joseph L. Rose, John S. Popovics, "The Behaviour of Ultrasonic Pulses in Concrete", Cement and Concrete Research, Vol. 20, No. 2, pp. 259-270, 1990.
2. Wilma Suaris, Viraj Fernado, "Ultrasonic Pulse Attenuation as a Measure of Damage Growth During Cyclic Loading of Concrete", ACI Material Journal, V. 84, No. 3, pp. 185-193, 1987.
3. Sansalone M., Carino N. J., Hsu N. N., "Finite Element studies of Transient Wave Propagation", Proceedings of the Reveiw of Progress in Quantitative Nondestructive Evaluation, V. 6, Plenum Publishing Corp., 1987.
4. Zong Fukai, "Frequency-Dispersion Characteristics and Discretization of the Finite Element Analysis in Wave Propagation Problems", Explosion and shock waves, V. 4, No. 4, 1984, China.
5. Liao Zhenpeng, Liu Jingbo, "Elastic Wave Motion in Discrete Grids", Earthquake Eng. & Eng. Vibration, V. 6, No. 2, 1986, China