The avalanche characteristics of the destruction of porous dielectric materials are closely related to their failure mechanism. To investigate the avalanche characteristics of concrete during tensile and compressive failure based on acoustic emission statistics, concrete uniaxial compression and Brazilian splitting tests were carried out, the acoustic emission signals in the loading process were monitored, and the statistical characteristics of the acoustic emission signals such as amplitude, absolute energy, duration and waiting time were compared and analyzed. The results show that the maximum acoustic emission energy is distributed near the peak stress, but the number of signals in the splitting process is much lower than that in uniaxial compression. The b-value increases first and then decreases, and the b-value decreases earlier and the change range is larger under splitting failure, indicating that the large cracks appeare earlier and are more easily destroyed. The probability density distributions of absolute energy, amplitude and duration of acoustic emission in response to tensile and compressive failure conform to a power law. However, the corresponding avalanche exponent values are different, which is related to the failure mechanism during the process of failure. The absolute energy distribution of the splitting failure is found to be in close proximity to the pure power law distribution, while the compressive failure is consistent with the damped power law distribution, and the corresponding absolute energy exponent value is found to be larger. indicating that the proportion of large energy signals in the specimen increases with the increase of load. The probability density distribution of waiting time under tensile and compressive failure is found to be similar, thereby demonstrating the stability and the applicability of the statistical law.