Fractal Characteristic Analysis Of Near-fault Ground Motions

Near-fault ground motions present the forward directivity effect, fling-step effect, hanging wall effect and other kinetic characteristics, and cause severe structural damage. Thus, they draw intensive attention of the community of earthquake engineering. As is known, three main attributes of ground motions include the amplitude, frequency content and duration, which are closely related with engineering damage and are considered as important factors in structural seismic design. However, the high irregularity and complexity of earthquake ground motions pose a challenge to correctly represent and understand their engineering characteristics. This paper explores the irregularity and complexity of earthquake ground motions from the perspective of fractal geometry, and constructs the connection with the frequency content of ground motions.Firstly, with respect to single fractal analysis, the box-counting fractal dimensions and five representative period parameters of near-fault ground motions from Chi-Chi earthquake and Northridge earthquake are calculated and compared, respectively. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistically self-affine fractal property, and the influence of velocity pulses of near-fault ground motions on their box dimensions and period parameters is remarkable. The average fractal dimension of near-fault impulsive ground motions is smaller, while the mean fractal dimension of non-pulse ground motions is larger and the irregular degree of their wave forms is higher. Moreover, the box dimension D of acceleration histories shows the considerably negative correlation with the mean period Tm. Meanwhile, the box dimension Dvel of velocity histories is quite negatively correlated with the characteristic period Tc and improved characteristic period Tgi. The box dimensions of ground motions reflect their frequency property to a large extent, and can be regarded as an alternative indicator to represent their frequency content. In addtion, for the time histories of seismic dynamic responses of elastic and inelastic single degree of freedom (SDOF) systems subjected to near-fault ground motions, their fractal dimensions are computed via the approach of box dimension, and their fractal property is examined.Then, as for the multifractal analysis, the multifractal parameters of 30 acceleration time series of near-fault ground motions are calculated, and the correlations with box-counting fractal dimensions and two period parameters (Tc and Tm) are analyzed. Hurst exponenet H, singularity exponentαmin, Tc and Tm show a considerably positive correlation with each other. Meanwhile, H,αmin,Tc and Tm are quite negatively correlated with D and Dvel. The more high frequency components are there in the record of near-fault ground motion, the weaker its long-range correlation is, the larger the local change of its wave form, thus its wave form is sharper and the singularity is stronger. However, the probability measure distribution (namely, amplitude distribution of near-fault ground motion) and multifractal singulary degree of ground motion have the complicated relationship with long-range correlation and frequency content. Finally, it is pointed out that the longe-range correlation is the reason for what acceleration time histories of near-fault ground motion possess multifractal characteristic.