The focus of this article is on generating spectrum‐compatible acceleration, velocity, and displacement time histories for seismic analysis and design of engineering structures. If a generated acceleration time history is integrated to obtain the corresponding velocity and displacement time histories, it has been found that there are usually drifts in the resulting processes. Such drifts are due to overdeterminacy in the constants of integration. Baseline correction, although widely used, is not a suitable remedial measure to remove drift because it distorts the frequency content and renders the corrected processes no longer mutually consistent. The objective of this article is to develop an efficient and accurate method for generating drift‐free, consistent, and spectrum‐compatible time histories, which are essential properties for these time histories to be used as seismic input in time history analysis. To ensure drift‐free and consistent behavior, the eigenfunction method is applied to expand the time histories in eigenfunctions of a sixth‐order ordinary differential eigenvalue problem. The influence matrix method considering the influence of one frequency component on all others is capable of achieving perfect spectrum compatibility which has never been accomplished.

Representative volume element (RVE) is an important parameter in numerical tests of mechanical properties of heterogeneous geomaterials. For this study, a digital image processing (DIP) technology was proposed for estimating the RVE of heterogeneous geomaterials. A color image of soil and rock mixture (SRM) with size of 400 × 400 mm 2 taken from a large landslide was used to illustrate the determination procedure of the SRM. Six sample sizes ranging from 40 × 40 mm 2 to 240 × 240 mm 2 were investigated, and twelve random samples were taken from the binarized image for each sample size. A connected-component labeling algorithm was introduced to identify the microstructure. After establishing the numerical finite difference models of the samples, a set of numerical triaxial tests under different confining pressures were carried out. Results show that the size of SRM sample affects the estimation of the mechanical properties, including compressive strength, cohesion, and internal friction angle. The larger the size of the samples, the less variability of the estimated mechanical properties. The coefficient of variation (CV) was applied to measure the variability of mechanical properties, and the RVE of the SRM was determined easily with a predefined acceptance threshold of the CV. The results show that a DIP-based modeling method is an effective method got the RVE determination of heterogeneous geomaterials.

This study presents a new approach for obtaining a set of tri-directional time histories compatible with target design spectra by modifying real recorded earthquake ground motions. The influence matrix method (IMM) based on eigenfunction expansion is improved for typical design response spectra with different shapes and employed in order to achieve accurate matching with the target design spectra. By applying the Gram–Schmidt orthogonalization in each iteration of the IMM procedure, the correlation coefficient between any two components can be guaranteed to be strictly zero. Hence, the generated three components in the orthogonal directions are statistically independent. The generated time histories satisfy the requirements of current codes and standards. Two examples are presented to illustrate the procedure and the superiority of the proposed method, with the maximum relative error between the generated time histories and target design spectra being less than 0.2% in [0.6, 100] Hz, and the code requirements being satisfied strictly.

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