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Anisotropy is ubiquitous in the Earth's crust, which causes the elastic characteristics of seismic waves to change with direction. The study of seismic wave anisotropy is of great significance to seismic exploration, prediction and geodynamics. As one of the sources of seismic anisotropy, in situ stress belongs to secondary anisotropy as common as the intrinsic and fracture-induced anisotropy, but it is often ignored among the sources of seismic anisotropy. Therefore, we focus on the study of seismic anisotropy under the influence of in situ stress using the nonlinear acoustoelasticity theory. Based on a horizontal transversely isotropic (HTI) model and the linear slip theory, the characteristics of azimuthal seismic reflection response in anisotropic media under horizontal in situ stress are discussed in this paper. Firstly, by using the quasi-linear relationship between stress and Tsvankin’s anisotropic parameters and the transformation relationship between anisotropic and fracture parameters in HTI medium, the elastic stiffness matrix of an HTI medium with the effect of horizontal in situ stress is established. Secondly, the reflection coefficient of PP-wave seismic data for a planar weak-contrast interface separating two weak-anisotropy and small-stress HTI half-spaces is derived using both the seismic scattering theory and the stiffness matrix under horizontal in situ stress, building the quantitative relationship between azimuthal seismic reflection characteristics and the model parameters, such as the background elastic parameters, the fracture parameters and the horizontal-stress-induced anisotropic parameters. Finally, the variation rules of azimuthal seismic reflection response characteristics of four elastic interfaces under different in situ stress conditions are analyzed. The results demonstrate that the seismic inversion for fracture parameters and horizontal-stress-induced anisotropic parameters is more favorable under the condition of large incident angle. In addition, the effect of horizontal in situ stress on the reflection coefficient depends on the second- and third-order elastic properties of the rock itself. Also, the established seismic PP-wave reflection coefficient equation has provided an alternative approach to calculate the magnitude of horizontal in situ stress.Article HighlightsA novel linearized PP-wave reflection coefficient is presented for HTI media with the effect of horizontal in situ stressThe response law of azimuthal seismic reflection characteristics induced by horizontal in situ stress is demonstratedA simple inversion method is provided to calculate the magnitude of horizontal in situ stress

To make efficient use of land resources and minimize the seismic destruction of structures in the ground fissures zone, the shaking table tests and 3-dimensional numerical calculation of the soil were completed, based on the ground fissures site in Xi’an (Class II, with the shear wave velocity Vs ranging from 250 m/s to 500 m/s). Influence laws of ground motion characteristics and geological structure characteristics on seismic response spectra were revealed. Based on the statistics and analysis of seismic waves of the ground fissures site, standardized design response spectra and mathematical formula of the ground fissures site were determined. The findings indicated that: the ground fissure exerted an amplifying influence on seismic waves and changed their spectral characteristics. Moreover, the amplification effect increased with the increasing of the dip angle of ground fissure. These amplified seismic excitations heightened the response of the superstructure, with more pronounced effects observed on the hanging wall compared to the footwall, showing “hanging-wall/footwall effect”. Besides, the structural response was related to the spectral characteristics of seismic waves. Bedrock waves with rich high-frequency components were more likely to resonate with SDOF systems with short period, while Jiangyou waves and El Centro waves with more low-frequency components had more intense resonance responses. With the increasing of fault distance, the characteristic period T g increased, but platform value of response spectra β max decreased. The value of β max was between 2.52 and 3.62. The distributed patterns were respectively ∨-shaped and ∧-shaped. The research results of the design spectra can be used in the seismic design of the superstructure in the ground fissures site.

This study presents a comprehensive probabilistic evaluation of seismic response prediction methods for horizontally curved reinforced concrete (RC) bridges under bidirectional earthquake excitations with varying incident angles. A total of 14 bridge models—comprising both straight and curved configurations with different abutment conditions—were subjected to over 4,000 nonlinear time history analyses using 22 far-field ground motion records rotated across 13 angles from 0° to 180°. Seismic responses, including column drifts and abutment displacements, were assessed in global, local, and vectorial directions. A definition for “real” responses, representing resultant displacements independent of orientation, was proposed to capture maximum structural demands. The influence of horizontal curvature, abutment boundary conditions, and ground motion directionality on seismic performance was systematically examined. Results show that neglecting incident angle variability leads to underestimation of displacement demands by up to 25%. The study further evaluates the reliability of conventional combination rules—100/30, 100/40, and SRSS—in predicting maximum seismic responses. A new probabilistic framework was adopted to evaluate the likelihood of exceedance associated with the predicted structural responses under each combination rule. Findings indicate that while the 100/30 rule may be suitable for straight bridges, it underperforms for highly curved configurations. The SRSS rule consistently offers more accurate estimates, particularly when real responses are used as the benchmark. The study highlights critical limitations in existing design practices and provides targeted recommendations for selecting appropriate combination rules based on bridge geometry and abutment type, contributing to more reliable seismic design and assessment of irregular RC bridges.

This study employed tri-component continuous monitoring data from 10 measurement points on both sides of a base isolation layer in the basement of a large-span high-rise building in Beijing, as well as from a free-field station and roof frame, during a Mw 5.5 magnitude earthquake in Pingyuan, Shandong, in 2023. The H/V spectral ratio method was used to evaluate the structural dynamic response characteristics of the building and analyze the regulatory effect of the base-isolation layer on seismic waves. The results indicate that during the earthquake, the peak frequency of the free-field and the measurement points below the base-isolation layer was stable at 0.17 Hz, whereas the main frequency of the measurement points above the base-isolation layer increased to 0.75–1.18 Hz, which is 4–6 times greater than that of the points below. The amplitude was suppressed by more than 70%, confirming that the base isolation layer effectively isolated the low-frequency energy from the ground and increased the response frequency of the building. When the building was excited by an earthquake, a three-tier frequency gradient was formed throughout the building: “base-isolation layer (0.17 Hz)-main body (1.18 Hz)-roof frame (3.83 Hz)”, which can effectively avoid resonance of the entire building. In addition, the composite base-isolation device changed the dynamic characteristics of the structure. The resonance period was extended from 0.74 s (theoretical value without base isolation) to 5.9 s (calculated value), and the resonance frequency was reduced from 1.35 to 0.17 Hz. This finding indicates that the base-isolation layer can enhance seismic performance by increasing flexibility and damping.

The geological structure and stratum lithology have important roles in the seismic stability of complex slopes; however, their roles complicate engineering construction. Four three-dimensional, layered granite slope models with infinite boundaries were modeled via the finite element method. The seismic response characteristics of slopes are systematically analyzed in the time–frequency domain. A frequency-domain analysis method of complex slopes, including modal and spectrum conjoint analysis, is proposed. Modal analysis can directly display the main vibration modes of slopes. The combination of modal and spectral analysis can clarify the inherent characteristics of slopes and reveal the interaction mechanism between the inherent frequency of slopes and their dynamic characteristics. The results illustrate that structural planes have significant effects on the propagation characteristics of waves within rock masses, and complex refraction/reflection phenomena occur near these discontinuities, thus leading to different dynamic response characteristics in the slope. Layered slopes have an apparent magnification effect of slope surface and altitude. The directions of seismic excitation and structural plane types affect the dynamic response of slopes. Horizontal waves mainly affect the middle and upper parts of high-steep slopes, while vertical waves have an obvious influence on the slope crest. Additionally, Fourier spectral analysis shows that structural planes have filtering effects on high-frequency waves. Combined with modal analysis, this finding further explains that the high-frequency section of waves mainly triggers local deformation of slopes, while the low-frequency component controls their overall deformation. The instability regions and evolution process of slopes were predicted based on time–frequency conjoint analysis.

The Italian seismic code provides a simplified approach to account for the effect of local seismostratigraphical configuration on the expected ground motion. This approach, common with other seismic codes, provides specific ‘soil factors’ as a function of a set of reference subsoil conditions (soil classes): these factors are considered in 1D subsoil configurations to modify the uniform probability hazard spectrum deduced from probabilistic seismic hazard at reference soil conditions. It is inferred that, to provide a coherent management of uncertainty affecting the response spectrum to be used for the design, the contribution of uncertainty affecting soil factors must be carefully considered to avoid biases in the hazard evaluation. In the present study, variability of soil factors representative of each soil class has been explored by numerical simulation relative to many seismostratigraphical configurations inferred from seismic microzonation studies available in Italy relative to 1689 municipalities. This analysis shows that variability of soil factors is of the same order of magnitude of variability affecting reference response spectra, which implies that the former cannot be neglected as presently happens in the common practice. It is also shown that neglecting this contribution can lead to underestimate the impact of subsoil configuration on the regularized response spectrum provided by the norm, in particular, in the short period range.

The time-frequency analysis method based on Hilbert-Huang transform is proposed and used to the seismic response analysis of accumulation landslide reinforced by pile-plate retaining wall. Taking the landslide along the Chengdu-Lanzhou Railway as the prototype, the shaking table test of the accumulation landslide reinforced by pile-plate retaining wall with a physical dimension similarity ratio of 1: 10 is designed and carried out. The results show that the acceleration response of the accumulation landslide shows obvious elevation effect in the process of loading different amplitude seismic waves, and the elevation effect of the landslide is the most significant under the 0.3g seismic wave. Then the elevation effect decreases with the increase of seismic wave amplitude. The dynamic earth pressure of the pile is distributed nonlinearly along the pile body, and the size and range of its envelope are directly proportional to the seismic wave amplitude. The maximum dynamic earth pressure of the pile appears at the embedded section, so attention should be paid to the reinforcement design of this part. The displacement response of pile also increases gradually with the seismic amplitude, and the coupling displacement mode changes from translation to rotation. In addition, it is feasible to use the time-frequency analysis method based on HHT transform to study the seismic stability of accumulation landslide reinforced by pile-plate retaining wall. The Hilbert energy spectrum analysis shows that the seismic energy is mainly concentrated in time domain of 2–6 s, and the corresponding frequency domain is 10–50 Hz. With the increase of input seismic amplitude, the difference of Hilbert energy between sliding bed and sliding body measurement points in time-frequency domain increases, and the difference of seismic response between them increases significantly. The damage inside the landslide can be identified by Hilbert marginal spectrum. Under the action of pile plate retaining wall, the damage at the bottom of the landslide mainly occurs on the slope, while the damage in the middle of the landslide mainly occurs inside.

Based on criticisms raised in the past by researchers about the effectiveness of the design rules reported in the European seismic code for the design of concentrically braced frames, a new design procedure has been proposed and included in the upcoming version of Eurocode 8. The upcoming version of Eurocode 8 is in the enquiry stage. Hence, it is important to evaluate the effectiveness of the design procedure reported in the code using accurate numerical models and seismic inputs. In the present paper, a four-story building with concentrically braced frames in the chevron configuration is designed according to the upcoming version of Eurocode 8. A seismic performance assessment is carried out by the means of multiple-stripe analyses performed on refined numerical models. The seismic input is defined based on one-dimensional local site response analyses. The numerical analyses prove that the use of local site response analysis to properly account for the soil-filtering effects is of paramount importance, and that the design procedure reported in the upcoming version of Eurocode 8 for chevron concentrically braced frames leads to reasonably low probabilities of exceeding the considered limit states.

This research introduces an advanced method for predicting seismic responses and hysteresis curves of instrumented bridge piers and bearings under various loading conditions, leaning solely on a single deep learning architecture and the same hyperparameters tuning. Test specimens are subjected to ground accelerations including vertical seismic loads and axial forces. To accurately capture peak values, particularly on the negative side of the hysteresis loop (unloading region), the model employs a stacked deep architecture. A key component to overcome the challenges is the self-attention-Mamba-driven transformer layer, which enhances the model’s ability to capture long-range dependencies in seismic data. This layer works in conjunction with other deep learning techniques to ensure robust and precise predictions. Implemented with Python’s Keras functional API, the model processes inputs like ground accelerations, actuator loads, effective height, moment of inertia, and superstructure mass. The model is evaluated with a dataset of 95 real-time hybrid simulation (RTHS) tests for lead rubber bearings, 29 RTHS tests for bridge piers, and 17 cyclic tests (10 fast and 7 slow). Extensive hyperparameter tuning demonstrates the model’s proficiency to capture hysteresis and residual deformations accurately. Achieving an impressive correlation with experimentally measured values, ranging from 88.1 to 98.9%, and a reasonable dissipated energy error ratio are notable. The deep learning model reduces the need for additional tests, offering time and cost savings, and provides rapid, and accurate insights into bridge behavior. This supports timely and precise bridge design and aids decision-makers during emergencies.

In seismic structural health monitoring (SHM), a structure is normally instrumented with limited sensors at certain locations to monitor its structural behavior during an earthquake event. To reconstruct the responses at non-instrumented locations, an effective regression method has to be used given the measured data from the sensed locations. In addition, determination of where to place the sensors directly affects the ability of the system to infer the behaviour of the entire structure. In this study, a practical framework is proposed for sensor placement and seismic response reconstruction at non-instrumented locations, which adopts a novel attention-based deep neural network (DNN). The developed DNN model is trained by using structural displacements at measured locations as input and the structural displacements at unmeasured locations of interest as output. The proposed framework is demonstrated by a case study of an instrumented long-span girder bridge in California. Different sensor placement schemes are investigated using the proposed DNN model. Real-time seismic assessment of the bridge is achieved by issuing each reconstructed output in 1.5 ms. The case study validates the effectiveness and accuracy of the proposed method to be used as part of a seismic SHM system.