Hysteresis energy-based failure indicators for concrete and brittle rocks under the condition of fatigue loading

Hysteresis energy-based failure indicators for concrete under cyclic loading conditions are proposed: hysteresis occurrence ratio (HOR) and hysteresis energy ratio (HER) considering the hysteresis characteristics and dissipated energy. A two-step approach to predict the failure of concrete is introduced. The first step: HOR has two critical values. These two critical values for the specific concrete used in our laboratory testing are 75% and 95%. In detail, when HOR is under 75%, the concrete has no risk to fail, when HOR is between 75% and 95%, the concrete has the possibility to fail, when HOR is larger than 95%, the concrete will fail very likely within the next few cycles. The second step contains two criteria: if HOR is larger than 75% and HER is larger than 0.3 at the same time, the concrete will fail. Different multi-level cyclic loading strategies have been designed to verify the effectiveness of these failure indicators and the failure prediction approach. First laboratory test results verified that HOR and HER are reliable failure indicators.