The existence of local soft interlayer can significantly amplify or attenuate the ground motion and thus might influence the lagged spatial coherency between spatially varying earthquake ground motions. A target site with a local soft interlayer was assumed first, and then two numerical examples were set. In example 1, linear soil behavior was considered and a large amount of quasi-stationary spatially varying earthquake ground motions were generated by combining the one-dimensional wave propagation theory and the classical spectral representation method. The influence regularity of varying shear wave velocity, buried depth, and thickness of the soft interlayer on the characteristics of lagged spatial coherency was investigated. In example 2, non-linear soil behavior was taken into account and fully non-stationary spatially varying earthquake ground motions were thus generated by using time-varying transfer function and spectral representation method. An overall evaluation was carried out to shed light on the differences of characteristics of spatial coherency between non-linear soil and linear soil cases. It showed that: (i) As the shear wave velocity of interlayer declines and as the buried depth and thickness increase, remarkable reduction of spatial coherency showed up; (ii) the reduction of lagged spatial coherency caused by varying buried depth may be more inclined to concentrate in the lower frequency range; (iii) the non-linear soil behavior can cause greater further reduction of lagged spatial coherency in comparison with linear soil behavior, especially in the higher frequency range; (iv) the troughs of lagged spatial coherency curve tend to be located in the variation range of vibration frequency of time-varying spectral ratio.

The research on the attenuation law of blasting vibration has become the foundation and precondition of the effective control of blasting vibration damage. Aiming at the characteristics of low frequency, low velocity, and strong amplitude of the R wave, an improved wave component separation method based on R wave suppression is proposed. Combined with the measured vibration signals of a field test, the attenuation parameters of different types of waves in the propagation process of blasting seismic waves are studied. The analysis results show that, in the process of blasting seismic wave propagation, the attenuation parameters of different types of waves are significantly different. With an increase in propagation distance, the proportion of the different types of waves will also change. The study of attenuation law with only coupled particle peak vibration velocity often showed high discreteness. The fitting correlation coefficient and prediction accuracy of peak vibration velocity without distinguishing wave modes are lower than those induced by the P wave or R wave alone, which should be attributed to the conversion of dominant wave modes in blasting vibration at different distances.

The longitudinal seismic response characteristics of a shallow-buried water-conveyance tunnel under non-uniform longitudinal subsurface geometry and obliquely incident SV-waves was studied using the numerical method, where the effect of the non-uniform longitudinal subsurface geometry due to the existence of a local one-sided rock mountain on the seismic response of the tunnel was focused on. Correspondingly, a large-scale three-dimensional (3D) finite-element model was established, where different incidence angles and incidence directions of the SV-wave were taken into consideration. Also, the non-linearity of soil and rock and the damage plastic of the concrete lining were incorporated. In addition, the wave field of the site and the acceleration response as well as damage of the tunnel were observed. The results revealed the following: (i) a local inclined subsurface geometry may focus an obliquely incident wave due to refraction or total reflection; (ii) a tunnel in a site adjacent to a rock mountain may exhibit a higher acceleration response than a tunnel in a homogeneous plain site; and (iii) damage in the tunnel in the site adjacent to a rock mountain may appear in multiple positions, and the effect of the incidence angle on the mode of compressive deformation and damage of the lining is of significance.

In this study, we investigated the characteristics of the seismic response of a subway shield tunnel beneath a rock mountain through the finite-element method based on a practical subway tunnel project in China. We discuss the influence of the spectral nonstationarity of seismic motion on tunnel responses. First, a set of quasistationary (QS) and fully nonstationary (FN) bedrock motions were artificially simulated. Second, the background information of the referenced project was briefly discussed, and correspondingly, several refined numerical models were established. Finally, the mutual relationship between a subway tunnel and the overlying rock mountains under QS bedrock motions was studied, and the results under the QS and FN bedrock motions were compared to clarify the effect of the spectral nonstationarity of ground motions. We found that i) an overlying rock mountain can suppress the acceleration response of an underground tunnel, and combined with the seismic motion, high confining pressure owing to the existence of an overlying mountain aggravates the radial shear-stress response and damage to the tunnel; ii) the spectral nonstationarity of input motions results in higher acceleration responses at the mountaintop and on the tunnel and causes greater radial shear stress and damage to the tunnel, even though the input PGAs and waveforms for QS and FN motions are the same. Therefore, artificial seismic motions exhibiting spectral nonstationarity may provide conservative results.

The effect of the influence regularity of site saturation and water level on the coherency loss between spatially varying earthquake ground motions (SVEGMs) in a vertical direction is not yet clear. Therefore, taking an onshore-offshore site as an example, the influence regularity of site saturation and water level on the coherency loss of SVEGMs in a vertical direction was studied, in which the saturation degree of the whole site (SD), the groundwater level (GWL), and the thickness of the surface water layer (WLT) were considered. Under each case mentioned above, a large number of vertical in-plane SVEGMs were synthesized and then correspondingly, the mean lagged coherency loss and phase angle of coherence function were obtained, and a series of comparisons were carried out to shed light on the varying trend of the value of lagged coherency loss and phase angle, with predefined parameters. The results showed that SD, GWL, and WLT possess significant effects on the varying trend of the coherence function of vertical SVEGMs.

This paper is an extension of the random amplitude-based improved Hilbert spectral representation method (IHSRM) that the authors developed previously for the simulation of spatially correlated earthquake ground motions (SCEGMs) possessing the nonstationary characteristics of the natural earthquake record. In fact, depending on the fundamental types (random phase method and random amplitude method) and matrix decomposition methods (Cholesky decomposition, root decomposition, and eigendecomposition), the IHSRM possesses various types. To evaluate the influence of different types of this method on the statistic errors, i.e., bias errors and stochastic errors, an error assessment for this method was conducted. First, the random phase-based IHSRM was derived, and its reliability was proven by theoretical deduction. Unified formulas were given for random phase- and random amplitude-based IHSRMs, respectively. Then, the closed-form solutions of statistic errors of simulated seismic motions were derived. The validness of the proposed closed-form solutions was proven by comparing the closed-form solutions with estimated values. At last, the stochastic errors of covariance (i.e., variance and cross-covariance) for different types of IHSRMs were compared, and the results showed that (1) the proposed IHSRM is not ergodic; (2) the random amplitude-based IHSRMs possessed higher stochastic errors of covariance than the random phase-based IHSRMs; and (3) the value of the stochastic error of covariance for the random phase-based IHSRM is dependent on the matrix decomposition method, while that for the random amplitude-based one is not.