Low-frequency Amplification Research Articles

Progress in Seismic Isolation Technology Research in Soft Soil Sites: A Review

Soft soil sites can amplify the peak acceleration by a factor of 1.5 to 3.5 and exhibit the filtering effect on seismic waves. This effect results in the attenuation of high frequencies, amplification of low frequencies, and extension of the predominant period of ground motion. Consequently, soft soil sites have a more pronounced impact on isolation buildings constructed on them. The seismic isolation structure design typically involves assuming rigid foundation for calculations. However, the soil properties can significantly impact the dynamic response of the structure, affecting factors such as input ground motion, changes in vibration characteristics, radiation energy dissipation, and material damping energy dissipation. Therefore, neglecting these influences and relying solely on the rigid foundation assumption for calculations can lead to significant errors in the final seismic response analysis of the structure. Currently, there are numerous LNG storage tanks, museums, and other isolation buildings constructed on soft soil sites. Therefore, research on seismic isolation measures for soft soil sites holds significant practical importance. In light of this, this paper, firstly, provides a systematic summary of seismic isolation strategies and engineering applications for soft soil sites. Secondly, it further discusses advancements in research on the dynamic interactions of soil–isolated structures, covering analytical methods, numerical investigations, and experimental studies on soft soil sites. Lastly, the paper concludes with insights on current research progress and prospects for further studies.

Nonlinear Seismic Response of Tunnel Structures under Traveling Wave Excitation

Tunnels traditionally regarded as resilient to seismic events have recently garnered significant attention from engineers owing to a rise in incidents of seismic damage. In this paper, the reflection characteristics of the elastic plane wave incident on the free surface are analyzed, and the matrix analysis method SWIM (Seismic Wave Input Method) for the calculation of equivalent nodal loads with artificial truncated boundary conditions for seismic wave oblique incidence is established by using coordinate transformation technology, according to the displacement velocity and stress characteristics of a plane wave. The results show that the oblique incidence method is more effective in reflecting the traveling wave effect, and the “rotational effect” induced by oblique incidence must be considered for P wave and SV wave incidence, including the associated stress and deformation. This effect exhibits markedly distinct rotational phenomenon. In particular, the P wave incidence should be focused on the vault and the inverted arch due to the expansion wave. With the increase of the oblique incidence angle, the structural stress and deformation are rotated to a certain extent, and the values are significantly increased. Simultaneously, the shear action of the SV wave may result in “ovaling” of the tunnel structure, thereby facilitating damage to the arch shoulder and the sidewall components. As the oblique incidence angle, the potentially damaging effects of the “rotational effect” to the vault and the inverted arch, but the numerical value does not change significantly. In addition, in comparison to a circular cross-section, the low-frequency amplification of seismic waves in the surrounding rock and the difference of frequency response function in different parts of the lining are more pronounced. In particular, the dominant frequency characteristics are significant at P wave incidence and the seismic wave signal attenuation tends to be obvious with increasing incidence angle. In contrast, SV waves exhibit more uniform characteristics.

Seismic response characteristics of offshore sites in the Sagami Bay, Japan—Part I: Comparison of spectral inversion and ratio under weak motions

Understanding offshore site amplification (AF) characteristics is crucial for marine engineering. Thus far, the spectral ratio (SR) has been widely used to analyze offshore AF characteristics, despite its reliability not yet being fully investigated. In this study, we used 826 ground-motion data recorded at 6 offshore and 19 onshore stations in the Sagami Bay region to reveal the source, path, and AF characteristics using the generalized inversion technique (GIT). The average stress drops for the shallow crustal, subduction interface, and subduction slab earthquakes were 3.55, 6.59, and 7.07 MPa, respectively. The offshore sites were categorized into flat and steep stations based on the local slope gradient (LSG), and systematic AF characteristics were observed. We found that the topography had a negligible influence on the flat free-field station KNG205. AFs obtained using the GIT and SR were analyzed and compared, revealing two main differences: (1) SR-obtained AF values were significantly larger than GIT-obtained AF values above 0.5 Hz and 5 Hz at the flat and steep sites, respectively; (2) resonant frequencies estimated using the SR drifted to lower and higher frequencies for flat and steep sites, respectively. The ineffectiveness of the SR for flat and steep stations was attributed to the effects of topography and seawater pressure on low- and high-frequency vertical ground-motions, respectively. These results suggest that the SR is only reliable for estimating AF curves at marine free-field sites and low-frequency AFs at steep sites. The LSG may play an important role in offshore ground-motion studies.

Investigating individual, loudness-dependent equalization preferences in different driving sound conditions

In automotive audio playback systems, dynamically increasing driving sounds are typically taken into account by applying a generic, i.e., non-individualized, increase in overall level and low-frequency amplification to compensate increased masking. This study investigated the degree of individuality regarding the preferences of noise-dependent level and equalizer settings. A user study with 18 normal-hearing participants was conducted in which individually preferred level-dependent and frequency-dependent amplification parameters were determined using a music-based procedure in quiet and in nine different driving noise conditions. The comparison of self-adjusted parameters suggested that, on average, participants adjusted higher overall levels and more low-frequency amplification in noise than in quiet. However, preferred self-adjusted levels differedmarkedly between participants for the same listening conditions but were quite similar in a re-test session for each participant, indicating that individual preferences were stable and could be reproducibly measured with the employed personalization scheme. Furthermore, the impact of driving noise on individually preferred settings revealed strong interindividual differences, indicating that listeners can differ widely with respect to their individual optimum of how equalizer and level settings should be dynamically adapted to changes in driving conditions.

Seismic response of the anchored frame beam reinforced slopes in seasonally frozen regions: Shaking table test and numerical analysis

Frame beam-anchor geotechnical structures are increasingly utilized to reinforce slopes in earthquake prone areas. Their dynamic responses have been thoroughly explored. However, the influence of seasonal variation in seasonally frozen regions has been largely ignored. This paper investigates the seismic response of slopes reinforced with anchored frame beams, considering the combined effects of seasonal change and earthquakes. This is achieved through a series of shaking table tests and numerical simulations. The findings reveal that the seismic responses, including acceleration response and displacement response, are more pronounced in the warm season than in the cold season. Conversely, the total axial force of the anchors and the bending moment of the frame columns are greater in the cold season. During the warm season, the frame-anchor slope support system exhibits “high-frequency filtering and low-frequency amplification”, while the spectral characteristics in the cold season are reversed. Thus, in the seismic design of such systems in seasonally frozen regions, it is crucial to consider slope deformation in the warm season to prevent damage from excessive acceleration or displacement. Additionally, the internal forces of the anchor frame structure must be checked in the cold season to avoid mechanical failures due to the combined impact of earthquakes and freezing effects. These insights offer valuable recommendations for improving the seismic design of frame beam-anchor structures in seasonally frozen regions and pave the way for further research on the seismic responses of various retaining slope structures in these areas.

Geophysical surveys in the Kashmir valley (J&K Himalayas) part II: Anomalous seismic site-effects and exploration of alternative site classification schemes

Extensive geophysical surveys (MHVSR and MASW) conducted for the microzonation of the Kashmir Valley, Himalayas, revealed unexpected dynamic characteristics at certain sites pointing out the weak relationship between fundamental frequency (f0) and time-averaged shear wave velocity over 30 m depth (VS,30). Unusual low-frequency amplification at stiff soil sites and high-frequency amplification at weathered rock sites was obtained. On the contrary, high-frequency amplification was attained at a soft soil site over shallow bedrock. Instances of topographic amplification on slopes, hills, and valleys were encountered. Consequently, the commonly used VS,30-based single-proxy site classification failed to explain these atypical site effects, thus underscoring the caution to be exercised for site classification in geologically complex regions. These findings motivated the documentation of the anomalies and the search for the most suitable site characterisation scheme for the geological deposits of the Kashmir Valley. The coupled MHVSR-VS,30 proxy approach accomplished the best results for the study region.

Seismic Response of Nenana Sedimentary Basin, Central Alaska

ABSTRACTNenana basin in central Alaska is a long (90 km), narrow (12 km), and deep (7 km) sedimentary basin aligned with an active fault zone producing Mw≥6 earthquakes. From 2015 to 2019, 13 broadband seismic stations were deployed in the region as part of the Fault Locations and Alaska Tectonics from Seismicity project. These stations recorded a wide range of earthquakes, including Mw 3–4 directly below the basin as well as several regional earthquakes Mw>6. These 43 local and regional earthquakes, in addition to five teleseismic events and continuously recorded ambient noise, provide a data set that we use to quantify the response of Nenana basin to the seismic wavefield. We calculate spectral ratios between each station and a bedrock reference station for 48 earthquakes. We find amplification of 11–14 dB (amplification ratio 3.5–5.0) for low frequencies (0.1–0.5 Hz), and 8–15 dB (amplification ratio 2.5–5.6) for high frequencies (0.5–4.0 Hz) on the vertical component. At low frequencies, amplification of the earthquake wavefield agrees well with amplification of seismic noise, with both data sets exhibiting stronger amplification on the horizontal components, in comparison with the vertical component. Furthermore, stations overlying the deeper part of the basin exhibit stronger amplification, whereas stations at the margin of the basin exhibit minimal low-frequency amplification. At higher frequencies, amplification occurs at both deeper basin stations and also marginal basin stations. Our study establishes a catalog of diverse events for future theoretical and numerical studies that can use Nenana basin to better understand the complex influence of sedimentary basins on the seismic wavefield.

Low-frequency amplification of propeller tonal noise due to the scattering by a compact rigid cylinder

The present work addresses the scattering of the tonal noise of a low-speed propeller by a rigid cylinder, as a generic configuration representative of installed marine propellers. Both propeller and cylinder axes are parallel to each other. The diameters of the propeller and of the cylinder are much smaller than the acoustic wavelengths, as well as the propeller-cylinder distance. This corresponds to a compact regime of diffraction. Only the hydrodynamic tonal noise of the propeller at the first multiples of the blade-passing frequency is considered, assuming rigid blades, in a two-dimensional formulation. The direct and scattered sound fields are expressed in terms of spinning modes, with respect to the propeller and cylinder axes, respectively. Use is made of the exact Green’s function of the cylinder for the Helmholtz equation. The modes of orders ±1 are found the only efficient ones in the direct field, whereas higher-order modes rapidly decay. Yet, in the presence of the cylinder, higher-order modes are scattered into the contra-rotating mode of order 1 in the reference frame of the cylinder, with a strong amplification. A simple experiment, performed in air but with Helmholtz numbers typical of marine applications, confirms these results as key features of the asymptotic Green’s function of the cylinder. The same modal behavior is reproduced as closed-form simple expressions from a low-frequency approximation of the Green’s function. The results show that the installation effect is crucial for the tonal noise of marine propellers at very low frequencies.

Amplification and Attenuation Due to Geologic Conditions in the Sichuan Basin, Central China

Abstract The Sichuan basin is an intracontinental basin in central China containing extensive Paleozoic, Mesozoic, and Cenozoic sedimentary sequences of varying thicknesses. We used seismic recordings from 189 regional earthquakes with magnitude Ms 4.0–7.0 occurring from 2010 to 2020 recorded by 22 stations from the China Digital Seismological Observation Network to estimate the kappa values (κ0) in the Sichuan basin using Lg waves and coda waves. The Lg and coda κ0 values agree well with each other and show positive correlation with the thickness of sediments in the basin. The average κ0 for the Sichuan basin is estimated as 0.0475 s, similar to results reported in previous studies. The average estimate of κ0 is 0.06 s for stations in the western part of the basin that are underlain by sediments approximately 8 km thick. The quality factor Q of Lg waves in the crustal waveguide is estimated as Q(f)=335f0.72. We estimated site response in the Sichuan basin from Lg spectral inversion, coda spectral ratios, and Lg horizontal to vertical spectral ratios, respectively, and investigated correlation between the site response values and sediment thickness. Consistent patterns are observed in the three sets of site response, which are clearly dependent on the thickness of sediments. Maximum averaged amplification factors of the sediments occur around 2–4 Hz reaching ∼4.5 for sites overlying 8 km sediments. Stronger attenuation effects are observed at stations lying on thicker sediment columns at frequencies higher than 9.66 Hz. This spatial dependence of low-frequency amplification and high-frequency attenuation should be incorporated in ground-motion prediction models for the Sichuan basin. The results of this study can be applied to sites in the Sichuan basin where the thickness of the sedimentary section exceeds 2 km.

Ground vibration analysis under combined seismic and high-speed train loads

The rise of high-speed railway induces an increased probability of serious derailment accidents of operating high-speed trains during earthquakes. A two-and-half-dimensional finite element model (2.5D FEM) was developed to investigate the ground vibration under combined seismic and high-speed train loads. Numerical examples were demonstrated and the proposed method was turned out to provide an effective means for estimating ground vibration caused by high-speed train load during earthquakes. The dynamic ground displacement caused by combined seismic and high-speed train loads increases with the increase of the train speed, and decreases with the increase of the stiffness of ground soil. Compared with the seismic load alone, the coupling effect of the seismic and high-speed train loads results in the low-frequency amplification of ground vibration. The moving train load dominants the medium–high frequency contents of the ground vibration induced by combined loads. It is observed that the coupling effects are significant as the train speed is higher than a critical speed. The critical train speed increases with the increase of the ground stiffness and the intensity of the input earthquake motion.

A shaking table-based experimental study of seismic response of shield-enlarge-dig type's underground subway station in liquefiable ground

In instances where earthquakes with large magnitude occur, liquefaction-induced lateral deformation of ground has caused thorough destruction to the underground structure of urban rail transit. A sequence of shaking table experiments was conducted on shield-enlarge-dig type's subway station structure in liquefiable ground exposed to the near field earthquake and the far field earthquake. Outcomes of these experiments are discussed in items of foundation deformation, pore water pressure, acceleration response, dynamic soil pressure, and macroscopic failure of model structure. The measured data infers that, when subjected to a high intensity earthquake, the model structure generates an upward movement relative to the foundation. The difference between the soil pressure above and below the structure is the internal cause of the liquefaction-induced uplift of the structure. The shear deformation to the soil layer of the foundation happened, and the displacement peak values of the left and right pendula were asymmetric. The acceleration response and its amplification coefficient in the model foundation gradually increases towards the surface from the bottom as a result of a low intensity earthquake, but for medium and high intensity earthquakes, the acceleration response decreases first and then increases. A notable phenomenon of high frequency filtering and low frequency amplification ensued during the seismic wave propagation from the bottom to the surface of soil. For the same depth of measuring points in foundation soil, the time when the pore-pressure ratio reaches the peak lags behind the time when the acceleration reaches the peak, and the hysteresis is more intense with a rise in magnitude of ground movement. The response spectrum of a low intensity earthquake is characterized by low period accumulation and amplification, while the response spectrum of medium and high intensity is characterized by moves from short period to long period and multi-peaks. The pore pressure accumulation of the model foundation experienced a change process of “rapid growth and slow dissipation,” and the time period of its sharp increase was consistent with that of the sharp increase of the acceleration arias strength. The existence of the underground structure notably inhibits an increase in pore water pressure. The earthquake damage mechanism of the underground subway station of shield-enlarge-dig type in liquefiable ground occurred in three phases: shear failure occurred on the column and damaged the opening position and spandrel of the tunnel; connection parts of the side wall and roof exhibited tensile damage; and the underground structure collapsed.

A three-dimensional finite-element model of a human head for predicting the objective occlusion effect induced by earplugs

In a noisy environment, wearing a correctly fitted earplug is the sine qua non condition to prevent noise-induced hearing loss. However, this condition is often unfulfilled due to the discomforts induced by the wearing of the earplug, among which the acoustical discomfort is influenced by the occlusion effect. Objectively, this phenomenon is quantified by a low frequency amplification of the sound pressure in the earcanal, induced by bone-conduction when the earcanal is occluded. Numerical models can go beyond the practical and ethical limits of experiments on living humans. Thus they can be an efficient and helpful tool to evaluate the occlusion effect. They also make it possible to better understand its underlying physical mechanisms associated with different factors concerning the anatomy, earplug and stimulation and ultimately how to reduce it. Thereby, a three-dimensional finite-element model of a human head is developed to compute the occlusion effect induced by earplug under a bone-conducted stimulation. Good agreement is obtained between the simulation results and the experimental data available in the literature giving confidence in the model to predict the occlusion effect. The model is exploited to investigate the individual effects of various factors (e.g., earplug and tissue properties) on the occlusion effect.

Shaking table test on seismic response characteristics of prefabricated subway station structure

This paper is based on the research and development of the first fully prefabricated subway station in Changchun as the engineering background. Through the first large-scale shaking table test of a fully prefabricated subway station structure in China, the macroscopic phenomena of the model system in an actual earthquake occurrence were qualitatively reproduced. Based on the macroscopic phenomena of video surveillance, the seismic responses of the model structure were graded and evaluated. The analysis showed that under the same earthquake action, the seismic responses of the lower layer of the station were stronger than those of the upper layer, the Beijing wave was the strongest, the Taft wave was the second strongest, and the Mingshan wave was the weakest. The acceleration and lateral displacement of the model foundation and the acceleration, structural strain, joint deformation and soil pressure of the model structure were tested and analysed. The results showed that the closer the main frequency of seismic wave was to the main frequency of the model system, the more intense the seismic response was. With an increase in seismic intensity, obvious phenomena of low-frequency amplification and high-frequency filtering occurred. Shear deformation occurred laterally in the model foundation, and the peak displacement appeared obviously asymmetrical in the process of left and right lateral displacement. The existence of the underground structure obviously changed the propagation law of the seismic wave in the model foundation, and the closer the structure was, the more significant the difference was. The strength of the mortise-groove joint was better than that of the prefabricated component, which showed excellent integrity and mechanical properties. The model station structure had excellent cooperative work and deformation resistance properties. When rare earthquake loading occurs, the vault would gradually degenerate into a three-hinged arch mechanism and maintain a relatively stable state.

Empirical estimate of resonance frequency at the Dead Sea basin

We carried out assessments of the fundamental frequencies of the southern Dead Sea basin using records of teleseisms and local earthquakes, obtained by the DESERT2000 (13 events) and DESIRE (40 events) projects that aimed in studying the Dead Sea fault in general and in particular the Dead Sea basin. The observed ground motions are from teleseisms with magnitude larger than 6.5 at distances of 1340–14,800 km, and of local earthquakes in the magnitude range 3.8–4.9 at distances of 90–660 km. We determine the fundamental resonance frequencies of the Dead Sea basin using (1) ratio between the spectra of seismograms recorded on site and those recorded at a reference site and (2) horizontal-to-vertical S-wave spectral ratio. Our results allow dividing the study area into three segments of different lengths: first 22 km (stations JB12–IB13), second 5 km (stations IB15–IB17), and third 45 km (stations IB19–ID27) with fundamental frequencies 0.1, 0.2, and 0.1 Hz, respectively. Amplification factors vary from 2 to 5. Thirteen reference stations are located on rock, at distances of 1–10 km away from the basin, which recorded vibrations in the range of 0.1–0.5 Hz, generated in the Dead Sea basin. We did not find locally induced surface waves, causing significant lengthening of the shaking duration and strong low-frequency amplification. It can be explained by the linear dimensions of the Dead Sea basin, its shape, and the relatively high velocity of shear waves that varies with depth from 800 to 3200 m/s. We use stochastic optimization algorithm to calculate the velocity model, yielding 1-D transfer function matching the observed H/V curves and resonance peaks.

Implementing effects of site conditions in damage estimated at urban scale

Local site effects due to geotechnical conditions modify seismic motions on surface. This implies that during a given earthquake, buildings located on soft sites may experience a higher damage than similar buildings resting on nearby rock sites. The aim of this study is to provide an estimation of the influence of site conditions on the buildings damage distribution. We combine an approach adapted from the Hazus methodology for the assessment of building damage, with the Borcherdt non linear site amplification factors, that enable to characterize the high and low frequency amplification as a function of VS30 (the average shear wave velocity in the upper 30 m) and ground motion levels. Analysis of obtained results indicates that, seismic damage expressed by the normalized mean damage index depends not only on seismic shaking level and building typology but also on site conditions through the shear wave velocity proxy. A regression relationship is established between the seismic damage and both shaking levels and site conditions, aiming at presenting a simple, rapid tool for estimating this damage at urban areas. An index, the “damage increase ratio”, is proposed to quantify the increase of damage resulting from site effects, and its dependence on loading level and site conditions are quantified and discussed for the main building typologies present in Algeria. Depending on the building typology, the overall damage may vary within a range of 2–5 for moderate shaking (0.1 g) between hard rock and very soft soil, and within a range 1–1.5 for strong shaking (0.5 g). The reduction of the impact of site conditions with increasing shaking level is directly linked with the nonlinear soil behavior.

Quadrature Errors and DC Offsets Calibration of Analog Complex Cross-Correlator for Interferometric Passive Millimeter-Wave Imaging Applications.

The design and calibration of the cross-correlator are crucial issues for interferometric imaging systems. In this paper, an analog complex cross-correlator with output DC offsets and amplitudes calibration capability is proposed for interferometric passive millimeter-wave security sensing applications. By employing digital potentiometers in the low frequency amplification circuits of the correlator, the outputs characteristics of the correlator could be digitally controlled. A measurement system and a corresponding calibration scheme were developed in order to eliminate the output DC offsets and the quadrature amplitude error between the in-phase and the quadrature correlating subunits of the complex correlator. By using vector modulators to provide phase controllable correlated noise signals, the measurement system was capable of obtaining the output correlation circle of the correlator. When injected with −18 dBm correlated noise signals, the calibrated quadrature amplitude error was 0.041 dB and the calibrated DC offsets were under 26 mV, which was only 7.1% of the uncalibrated value. Furthermore, we also described a quadrature errors calibration algorithm in order to estimate the quadrature phase error and in order to improve the output phase accuracy of the correlator. After applying this calibration, we were able to reduce the output phase error of the correlator to 0.3°.

Integrated Circuit for Super-Regenerative Low-Frequency Amplification

An improved topology for the baseband super-regenerative sampling amplifier is proposed and analyzed, which employs a series-capacitors output load to realize positive feedback. As in the conventional circuit, the gain of the amplifier is continuously variable by controlling the length of the capacitor charging phase. It is shown that decreasing feedback enhances the linearity of the circuit while trading off with a lower sampling speed. Entirely removing the feedback yields the integrating amplifier circuit. This is a practical implementation in terms of linearity, power, noise, and gain in low-frequency applications, including biomedical signal amplification. The analysis is verified by measured results from an integrated circuit prototype in 180-nm CMOS technology.

Spectral element modelling of seismic wave propagation in visco-elastoplastic media including excess-pore pressure development

Numerical modelling of seismic wave propagation, considering soil nonlinearity, has become a major topic in seismic hazard studies when strong shaking is involved under particular soil conditions. Indeed, when strong ground motion propagates in saturated soils, pore pressure is another important parameter to take into account when successive phases of contractive and dilatant soil behaviour are expected. Here, we model 1-D seismic wave propagation in linear and nonlinear media using the spectral element numerical method. The study uses a three-component (3C) nonlinear rheology and includes pore-pressure excess. The 1-D– 3C model is used to study the 1987 Superstition Hills earthquake (ML 6.6), which was recorded at the Wildlife Refuge Liquefaction Array, USA. The data of this event present strong soil nonlinearity involving pore-pressure effects. The ground motion is numerically modelled for different assumptions on soil rheology and input motion (1C versus 3C), using the recorded borehole signals as input motion. The computed acceleration–time histories show low-frequency amplification and strong high-frequency damping due to the development of pore pressure in one of the soil layers. Furthermore, the soil is found to be more nonlinear and more dilatant under triaxial loading compared to the classical 1C analysis, and significant differences in surface displacements are observed between the 1C and 3C approaches. This study contributes to identify and understand the dominant phenomena occurring in superficial layers, depending on local soil properties and input motions, conditions relevant for site- specific studies.

A stochastic model with a low-frequency amplification feedback for the stratospheric northern annular mode

We consider three indices to measure the polar stratospheric mass and stratospheric meridional mass circulation variability: anomalies of (1) total mass in the polar stratospheric cap (60–90°N, above the isentropic surface 400 K, PSM), (2) total adiabatic mass transport across 60°N into the polar stratosphere cap (AMT), (3) and total diabetic mass transport across 400 K from the polar stratosphere into the troposphere below (DMT). It is confirmed that the negative stratospheric Northern Annular Mode (NAM) and PSM indices have a nearly indistinguishable temporal evolution and a similar red-noise-like spectrum with a de-correlation timescale of 4 weeks. This enables us to examine the low-frequency nature of the NAM in the framework of mass circulation, namely, $$\frac{d}{{dt}}{\text{PSM}}={\text{AMT}} - {\text{DMT}}$$ . The DMT index tends to be positively correlated with the PSM with a red-noise-like spectrum, representing slow radiative cooling processes giving rise to a de-correlation timescale of 3–4 weeks. The AMT is nearly perfectly correlated with the day-to-day tendency of PSM, reflecting a robust quasi 90° out-of-phase relation between the AMT and PSM at all frequency bands. Variations of vertically westward tilting of planetary waves contribute mainly to the high-frequency portion of AMT. It is the wave amplitude’s slow vacillation that plays the leading role in the quasi 90° out-of-phase relation between the AMT and PSM. Based on this, we put forward a linear stochastic model with a low-frequency amplification feedback from low-frequency amplitude vacillations of planetary waves to explain the amplified low-frequency response of PSM/NAM to a stochastic forcing from the westward tilting variability.

Seismic performance of an immersed tunnel considering random soil properties and wave passage effects

This paper presents the results of the dynamic finite element analysis of the Hong Kong–Zhuhai–Macau immersed tunnel, conducted to study the effects of the random soil properties and the wave passage effect. According to the results of the free-field analysis, it was found that the wave passage effect could decrease peak ground acceleration (PGA) and causes a time lag in wave arrivals. Conversely, the random soil properties enlarge PGA sharply. The ‘low-frequency amplification, high-frequency filter’ phenomenon also occurs. The results of the structural dynamic analysis indicate that the soil properties and the wave passage effect have a significant influence on dynamic responses of the immersed tunnel. Although random soil properties only alter bending moments slightly, it can enlarge axial forces by up to 230% and the deformations of Gina gaskets. The wave passage can increase bending moments, Gina gaskets deformations and especially axial forces. The inertial force is the main cause for the sharp increases in axial forces. The combined effects of the random soil properties and the wave passage effect are remarkable. In some cases, Gina gasket deformations will exceed their upper and lower limits of compression, raising the possibility of joint failure and leakage. Thus, it is necessary to consider the influences of the random soil properties and the wave passage effect when conducting a practical seismic design.