the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Apr 2026
Reliability Analysis Method for Soil Slopes Permanent Displacement under Mainshock-Aftershock Sequences
Abstract. After a primary seismic event, subsequent aftershocks frequently induce progressive damage to slopes. Evaluating the response of slopes to mainshock-aftershock sequence (MAS) from a probabilistic perspective is crucial for disaster prevention and mitigation. Current research primarily focuses on single mainshock events, with limited consideration of the aftershock effects. Our study addresses the MAS events. Firstly, the random input field of the MAS is constructed through the collaboration of theoretical models and real data. Then, considering the peak characteristics, cumulative characteristics and spectral characteristics of the MAS, the numerical simulation method is used to explore the control parameters for the soil slope response. Ultimately, leveraging the probability density evolution method (PDEM), we introduce a reliability assessment framework for soil slope behavior under MAS loading. Compared with the existing approaches, the new method fully accounts for aftershock characteristics and assesses the degree of slope permanent displacement response with greater precision. These results offer substantial practical utility for engineering applications and serve as guidance for slope stability assessment and disaster mitigation strategies.
- Preprint
(1486 KB) - Metadata XML
- BibTeX
- EndNote
Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-638', Tuncay Taymaz, 09 May 2026
-
RC2: 'Comment on egusphere-2026-638', Anonymous Referee #2, 26 May 2026
Reviewer Comments
The manuscript presents a framework for evaluating slope permanent displacement under mainshock–aftershock sequences (MAS) using PDEM and CAV as the controlling intensity measure. The topic is relevant and the proposed framework is promising. However, several important technical and clarity issues need to be addressed before the manuscript can be considered for publication.
- Clarity and Presentation
- Line 31: The statement “more severe damage” is vague and requires clarification. The authors should specify the reference condition and support the claim with appropriate quantitative evidence or citations.
- Lines 50, 53, 57–60: The writing quality requires improvement. In particular, Lines 57–60 should clearly define the research gap, motivation, and main objectives of the study. This section currently does not adequately frame the contribution.
- Line 97: The phrase “Seismic in Section 3” is unclear and should be rewritten to explicitly describe the seismic input or dataset.
- Ground Motion Selection and Scaling
- Line 151: The manuscript does not sufficiently justify the selection of the 96 MAS records. The authors should provide:
- selection criteria (magnitude, distance, mechanism, site conditions)
- statistical representativeness of the dataset
- scaling methodology and its compliance with established practices
- relevant ground motion characteristics (PGA, PGV, duration, frequency content)
As the dataset is derived from NGA-West2, it represents shallow crustal earthquakes only, which limits the generality of the conclusions. The sensitivity of the results to the selected dataset should be discussed or mentioned. Example relevant references for comparison and checking's are:
- Bray & Macedo (2019) – seismic slope displacement under crustal earthquakes
- Yeznabad et al. (2022, Soil Dynamics and Earthquake Engineering) – probabilistic slope displacement assessment
- Displacement Thresholds
Line 173: The use of Jibson (2009) requires clarification. This framework is based on Newmark-type analysis and is typically used for regional hazard mapping.In engineering practice ~15 cm displacement is widely used to indicate high hazard, ~25 cm is also commonly adopted. The thresholds of 0.5 m and 1 m represent very large displacements, generally associated with severe damage or failure
The authors should justify their chosen displacement thresholds within an engineering context.
- Evaluation of Intensity Measures
- Line 188: The conclusion that CAV is superior to PGA requires stronger quantitative support (e.g., correlation values, reduction in dispersion, improvement in reliability).
Although 21 intensity measures were initially evaluated, the final comparison is limited to CAV versus PGA. Important intensity measures such as: PGV, spectral acceleration , duration-related measures are not included in the final analysis. The values should be added or the rationale for excluding these measures should be clearly explained.
- Scatter in Displacement Results (Key Concern)
- Figure 5: The displacement results show a large spread for each CAV level, ranging from negligible values to very large displacements.
This raises a critical issue:
If displacement varies significantly at a fixed CAV level, how robust is CAV as a predictive parameter?
This behavior suggests that additional factors—such as frequency content, duration distribution, and dynamic interaction effects—play an important role in slope response.
This observation is consistent with:
- Rathje & Saygili (2008, 2010), which demonstrate the importance of both scalar and spectral ground motion characteristics
- Yeznabad et al. (Earthquake Spectra), which highlight the role of frequency compatibility in displacement prediction
The manuscript should explicitly discuss this limitation.
- Model Assumptions and Limitations
The study considers:
- a single slope geometry
- a single soil stratigraphy
Thus, key parameters such as slope angle, layering, and soil variability are not investigated. These factors are known to significantly influence slope response.
In addition: Only crustal ground motions are considered, No assessment is made for subduction or intraslab events, which exhibit different characteristics
These limitations should be clearly acknowledged and supported with appropriate references.
- Frequency Content and CAV Applicability
CAV is a cumulative intensity measure but does not explicitly capture frequency-dependent response. The manuscript does not evaluate the sensitivity of results to frequency content or site conditions.
Previous studies (Rathje & Saygili, 2008; Yeznabad et al. SDEE 2021 and 2022) demonstrate that frequency content plays a critical role in seismic slope displacement.
The authors should either: provide supporting justification for using CAV as a standalone parameter, or clearly acknowledge this limitation.
Citation: https://doi.org/10.5194/egusphere-2026-638-RC2
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 220 | 50 | 16 | 286 | 17 | 21 |
- HTML: 220
- PDF: 50
- XML: 16
- Total: 286
- BibTeX: 17
- EndNote: 21
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
I am happy to recommend accept after Minor Revision as it clearly needs a revision on Abstract, Results & Analyses and Conclusions sections how about clear Discussions ? in order to streamline the message right.