The core of the work is a reliability analysis method for the permanent displacement of soil slopes subjected to sequential ground motions. Permanent displacement, the irreversible sliding deformation that accumulates when seismic forces momentarily exceed the resisting strength of the slope material, is a standard yardstick for judging whether a slope remains serviceable after an earthquake. The authors argue that judging this quantity from mainshock shaking alone systematically misrepresents the hazard, because aftershocks add cumulative damage to soil that has already been degraded by the first event. Their solution couples a carefully constructed stochastic description of sequence-type ground motions with the probability density evolution method, a computational framework for nonlinear stochastic dynamics originally developed by Li and co-workers and previously extended to complex slope reliability problems.

Building the seismic input was the first technical hurdle. The team assembled 96 recorded mainshock–aftershock pairs drawn from 15 seismic events in the NGA-West2 strong-motion database maintained by the Pacific Earthquake Engineering Research Center. Selection criteria were strict: the aftershock had to be the largest-magnitude event within twelve months of the mainshock, both events needed magnitudes of at least 5.0 and peak ground accelerations of at least 0.05 g, both records had to come from the same component of the same station, the site shear-wave velocity in the upper 30 meters had to fall between 100 and 700 meters per second, and rupture distances could not exceed 80 kilometers. Each sequence was configured as a mainshock followed by a twenty-second quiet interval and then the aftershock, preserving the fully non-stationary character of real sequences.

Rather than treating these recordings as isolated deterministic inputs, the researchers modeled them as zero-mean, fully non-stationary stochastic processes using an evolutionary power spectral density framework. Frequency-domain energy distribution curves were fitted for each ground motion using an optimal square approximation criterion and least-squares regression, yielding a parameter vector that defines each evolving spectrum. This random-function dimension-reduction approach generates representative ground-motion time histories together with their associated probabilities, forming a complete probabilistic set that can feed directly into the probability density evolution method. That is a crucial advantage over Monte Carlo simulation, which demands enormous sample counts and often leaves the probability structure of the sample set incomplete.

A second, equally consequential decision concerned how to measure the intensity of a ground-motion sequence. Conventional practice leans on peak ground acceleration, but a single peak value says little about the sustained, damage-accumulating character of repeated shaking. The team therefore screened 21 candidate intensity measures spanning three families: peak-based parameters such as peak ground velocity and displacement, spectral measures such as response spectral acceleration and acceleration spectral intensity, and cumulative measures including Arias intensity, significant duration, and several root-mean-square and cumulative-absolute quantities. Correlation analysis against the simulated slope responses produced a clear winner: cumulative absolute velocity, or CAV, showed the strongest correlation with permanent displacement, with a correlation coefficient of 0.872, and captured the cumulative aftershock contribution better than any peak-based alternative.

With the seismic input and intensity measure defined, the mechanical side of the analysis proceeded on a two-layer soil slope model 150 meters long and 30 meters high, built in the finite-difference platform FLAC3D with a mesh refined to roughly half a meter in the potential sliding zone. The soil, a clay from southwestern China, was represented by a Mohr–Coulomb constitutive model with a tensile cutoff, and local damping with a 5 percent critical damping fraction, corresponding to a damping coefficient of 0.157, reproduced energy dissipation during wave transmission. Because FLAC3D avoids assembling a global stiffness matrix, it is computationally efficient for the many nonlinear dynamic simulations that a probabilistic treatment requires. Ninety-six scaled sequences were run at three CAV levels of 12, 28, and 40 meters per second, generating the response ensemble needed for density evolution.

The results reveal how strongly and how variably sequences load a slope. Average permanent displacements rose from 0.067 meters at a CAV of 12 meters per second to 0.328 meters at 28 and 0.633 meters at 40 meters per second, values comparable to those produced by mainshock-only shaking at peak ground accelerations of 0.4, 0.5, and 0.6 g in earlier work. Even with CAV as the intensity measure, the displacement results remained scattered, a reminder that frequency content and duration also matter and that no single parameter fully predicts slope response. That residual variability is precisely why the authors insist on a probabilistic treatment: the probability density evolution method propagates the uncertainty through the dynamics rather than averaging it away.

The probability distributions that emerged are strikingly non-standard. The probability density curves of permanent displacement showed bimodal or multimodal shapes that cannot be described by normal or lognormal distributions, underscoring how sequence effects reshape the statistics of slope response. Reliability estimates depended heavily on the chosen failure threshold. At a CAV of 12 meters per second, displacements ranged from 0 to 0.25 meters and reliability was 48.5 percent against a low-level threshold of 0.05 meters. At 28 meters per second the range widened to 0 to 1.00 meters and reliability fell to 45.5 percent at the medium threshold of 0.25 meters, while at 40 meters per second the range stretched to 0 to 2.00 meters and reliability dropped to 31.7 percent at the high threshold of 0.50 meters.

Comparisons against a conventional PGA-based analysis highlight the practical payoff of the new approach. At the 50 percent cumulative probability level, CAV-based displacements were approximately 0.07, 0.32, and 0.55 meters for the three intensity levels, against roughly 0.20, 0.50, and 0.70 meters for the corresponding PGA cases, and the PGA-based curves showed heavier large-displacement tails. Overall, switching from PGA to CAV reduced the dispersion of predicted displacements by about 40 percent on average, producing tighter, more informative reliability estimates. The authors caution that their results apply to clayey soil slopes of the kind found in southwestern China and to shallow crustal earthquake sequences, and that soil-parameter and geometric variability were not yet included, an extension they expect will further improve engineering applicability.

For disaster prevention, the message is clear: the aftershock is not a footnote but a first-order player in landslide hazard. By embedding sequence effects into a rigorous probabilistic framework and identifying cumulative absolute velocity as the intensity measure that best tracks cumulative damage, the study gives engineers a defensible way to quantify how likely a slope is to exceed critical displacement limits when the ground refuses to stay still. As seismic safety requirements tighten worldwide, methods that treat mainshock–aftershock sequences as the coupled, cumulative phenomena they truly are may well become the standard against which slope stability is judged.

Subject of Research: Probabilistic reliability analysis of soil slope permanent displacement under mainshock–aftershock earthquake sequences

Article Title: Reliability analysis method for soil slopes permanent displacement under mainshock–aftershock sequences

Article References: Wang, T., Zhang, C., Zhang, J., Chen, S., & Dai, Z. (2026). Reliability analysis method for soil slopes permanent displacement under mainshock–aftershock sequences. Natural Hazards and Earth System Sciences, 26(9), 4611-4619. https://doi.org/10.5194/nhess-26-4611-2026

Image Credits: AI Generated

DOI: 10.5194/nhess-26-4611-2026

Keywords: aftershocks, mainshock–aftershock sequences, slope stability, permanent displacement, cumulative absolute velocity, probability density evolution method, reliability analysis, landslides, ground motion intensity measures, FLAC3D, seismic hazard, soil slopes

Arias intensity and cumulative absolute velocity, often abbreviated as Ia and CAV, are not the household names of earthquake science that peak ground acceleration has become, but among engineers they are prized quantities. Arias intensity, introduced by the Chilean engineer Arturo Arias in 1970, measures the cumulative energy per unit weight absorbed by a simple oscillator subjected to a ground motion record, effectively capturing the total energy content of shaking over its entire duration. Cumulative absolute velocity, developed in the United States in the late 1980s as a criterion for judging whether a nuclear facility had experienced an earthquake exceeding its operating basis, sums the absolute acceleration over time and has proven a robust indicator of structural damage potential. Both measures are central to assessing landslide triggering, liquefaction, and the performance of buildings and infrastructure during prolonged shaking.

Despite their importance, most prediction equations for these intensity measures were built from onshore data. Offshore ground motions, recorded on the seafloor rather than on land, follow different propagation and site amplification rules, and treating them as interchangeable with onshore shaking can lead to serious misestimates of hazard for submarine cables, ports, coastal cities, and offshore infrastructure. The new study, led by Jingyang Tan and Xialei Zhu of China Three Gorges University together with Jinjun Hu and Yinan Zhao of the Institute of Engineering Mechanics, China Earthquake Administration, set out to close that gap for the Japan Trench region using data from the Seafloor Observation Network for Earthquakes and Tsunamis along the Japan Trench, known as S-net.

S-net, operated by the National Research Institute for Earth Science and Disaster Resilience, is the world’s largest cabled ocean-bottom monitoring network, spanning the trench that produced the devastating magnitude 9.0 Tohoku earthquake of 2011. The researchers assembled an exceptionally large dataset for offshore ground motion modeling: 28,950 three-component records from 150 ocean-bottom stations. These records captured 553 earthquakes across three tectonic families, including 130 subduction interface events, where the Pacific plate grinds beneath the Okhotsk plate; 243 slab earthquakes, occurring within the descending plate at depth; and 180 shallow crustal and upper mantle earthquakes. This breadth allowed the team to develop models covering the full range of earthquake mechanisms that threaten the region.

A central innovation of the study lies in how it characterizes the ground beneath each station. Rather than relying on geological maps, the team classified sites using the horizontal-to-vertical spectral ratio technique, or HVSR, which compares the amplitude of horizontal and vertical shaking at a site to reveal its resonant frequency, a fingerprint of soil stiffness and sediment thickness. This site classification scheme, applied uniformly across the ocean-bottom network, allowed the researchers to incorporate site effects directly into their prediction equations. The models account for the key explanatory variables that govern shaking: moment magnitude, rupture distance, focal depth, site class, and, uniquely for offshore settings, the installation condition of the seafloor instruments.

That last variable turned out to matter far more than anyone might have guessed. S-net stations come in different flavors: some instruments are buried in the sediment, while others sit unburied on the seafloor inside pressure vessels. The analysis revealed that the installation method significantly influences recorded Arias intensity and cumulative absolute velocity, with unburied stations exhibiting notably higher values. The likely culprit is the natural vibration of the instrument housing and its coupling with the soft seafloor, which can introduce amplification that is not representative of the true ground motion. For engineers using offshore records, this finding is a caution: ignoring installation conditions could inflate or deflate energy estimates and skew hazard calculations.

The site classification itself proved to be the study’s most valuable uncertainty-reducing tool. When site classes were explicitly included in the models, the model uncertainty, expressed statistically as the standard deviation of the residuals, dropped substantially compared with models that omitted site effects. By contrast, two other candidate explanatory variables, water depth and sedimentary thickness, had only negligible effects on model uncertainty. This is a practically important result, because it suggests that a relatively simple HVSR-based site classification captures most of the site-related variability in offshore energy measures, sparing modelers the difficulty of obtaining detailed sediment profiles from the deep ocean floor.

Comparing their offshore models with existing onshore equations revealed a systematic and physically meaningful difference. Offshore Arias intensity and cumulative absolute velocity exhibit a substantially greater energy accumulation effect than onshore ground motions at comparable distances and magnitudes. The researchers attribute this to amplification by soft seafloor sediments, the water-saturated, low-velocity materials that blanket much of the Japan Trench margin. Soft sediments lengthen the duration of shaking and concentrate seismic energy at low frequencies, inflating cumulative measures even when instantaneous peaks remain moderate. The finding echoes earlier comparisons of peak ground acceleration and response spectra between land and ocean-bottom stations in northeast Japan, but extends the picture to energy-based measures that are more directly tied to damage in flexible structures and to soil failure phenomena such as liquefaction.

Beyond the prediction equations themselves, the team developed spatial correlation models for offshore Arias intensity and cumulative absolute velocity. These geostatistical tools quantify how similar the shaking is at two sites separated by a given distance during the same earthquake, a quantity known as spatial correlation. In seismic risk analysis, spatial correlation governs whether damage concentrates in one neighborhood or spreads across an entire region, which is critical for estimating losses to distributed systems like power grids, pipelines, and transportation networks. By characterizing the spatial dependence of offshore energy measures for the first time in this region, the models enable more realistic simulations of earthquake scenarios that span both land and sea.

The practical reach of the new models extends across the earthquake engineering pipeline. Arias intensity feeds into empirical methods for predicting earthquake-induced landslide displacements through Newmark’s sliding block analysis, while cumulative absolute velocity underpins thresholds for structural damage and liquefaction assessment, including criteria originally developed for nuclear facilities and more recent applications to lateral spreading evaluation. With reliable offshore predictions of both measures, engineers can now assess hazards to submarine infrastructure, evaluate the seismic performance of coastal facilities, and refine probabilistic seismic hazard analyses for the densely populated Pacific coast of northern Japan. The researchers note that the models are applicable to the Japan Trench region and can serve as a reference for seismic hazard assessment in offshore areas more broadly, offering a template for other subduction zones, from Cascadia to Nankai, where ocean-bottom networks are expanding and the seafloor is no longer a blind spot in earthquake science.

Subject of Research: Development of offshore ground motion prediction models for Arias intensity and cumulative absolute velocity in the Japan Trench region using HVSR-based site classification

Article Title: A new ground motion prediction model for Arias intensity and cumulative absolute velocity in the Japan Trench region based on HVSR site classification

Article References: A new ground motion prediction model for Arias intensity and cumulative absolute velocity in the Japan Trench region based on HVSR site classification. (n.d.). https://doi.org/10.1007/s10518-026-02683-7

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02683-7

Keywords: Arias intensity, cumulative absolute velocity, ground motion prediction, Japan Trench, S-net, ocean-bottom seismology, HVSR site classification, seismic hazard assessment, subduction earthquakes, site amplification, spatial correlation, offshore ground motion