PM4Sand-Based Nonlinear Constitutive Modeling of Sand Behavior under Seismic Loading
Abstract
This paper presents an analytical review of nonlinear constitutive modeling of granular soils under seismic loading with emphasis on the PM4Sand model. The revised manuscript addresses a central problem in the original draft: the earlier version was written with the rhetoric of an original numerical study, while it did not report a reproducible simulation program, calibrated datasets, or quantitative results. In the present version, the study is explicitly reframed as a structured literature-based review and engineering workflow. The paper first clarifies the mechanics of nonlinear sand response, including stiffness degradation, hysteretic damping, excess pore-pressure generation, cyclic mobility, and post-liquefaction deformation. It then synthesizes how PM4Sand has been implemented, calibrated, validated, and used in recent earthquake-geotechnical applications. A practical workflow is proposed for model selection, calibration evidence, response metrics, and engineering interpretation. The review further consolidates reported response trends with respect to seismic intensity, density state, and confinement, and critically discusses the benefits and limitations of PM4Sand in site response, liquefaction assessment, and soil-structure interaction problems. The main novelty of the paper lies in integrating constitutive theory, calibration logic, and engineering interpretation into a single analytical framework that can support future simulation-based studies and practice-oriented applications. This study is positioned as an analytical and workflow-oriented contribution, aiming to synthesize existing evidence and provide a structured framework for future simulation-based research.
Keywords:
PM4S, Nonlinear soil behavior, Seismic loading, Liquefaction, Constitutive modeling, Analytical review, Earthquake geotechnicsReferences
- [1] Pretell, R., Ziotopoulou, K., & Abrahamson, N. A. (2022). Conducting 1D site response analyses to capture 2D VS spatial variability effects. Earthquake spectra, 38(3), 2235–2259. https://doi.org/10.1177/87552930211069400
- [2] Janusz, P., Bergamo, P., Bonilla, L. F., Panzera, F., Roten, D., Loviknes, K., & Fäh, D. (2024). Multistep procedure for estimating non-linear soil response in low seismicity areas—a case study of Lucerne, Switzerland. Geophysical journal international, 239(2), 1133–1154. https://doi.org/10.1093/gji/ggae324
- [3] Güler, E. (2024). Non-linear site response and liquefaction analysis of soil site in Kahramanmaras during the Mw 7.7 and Mw 7.6 Turkey earthquakes. Engineering science and technology, an international journal, 57, 101751. https://doi.org/10.1016/j.jestch.2024.101751
- [4] Shamsher, S., Won, M. S., Park, Y. C., Park, Y. H., & Sayed, M. A. (2025). Effect of nonlinear constitutive models on seismic site response of soft reclaimed soil deposits. Journal of marine science and engineering, 13(7), 1333. https://doi.org/10.3390/jmse13071333
- [5] Ziotopoulou, A. K. (2014). A sand plasticity model for earthquake engineering applications. University of California, Davis. https://www.semanticscholar.org/paper/A-Sand-Plasticity-Model-for-Earthquake-Engineering-Ziotopoulou/acff10c7651aac521eac56e4ce919a247b5dcfc4
- [6] Chen, L., & Arduino, P. (2021). Implementation, verification, and validation of the PM4Sand model in OpenSees. Pacific earthquake engineering research (PEER) center. University of california, berkeley, berkeley, usa, report, 2, 2021. https://peer.berkeley.edu/sites/default/files/2021_chen_final.pdf
- [7] Contreras, C. A., Yniesta, S., Jahanbakhshzadeh, A., & Aubertin, M. (2023). Calibration of the PM4Sand model for hard-rock mine tailings based on laboratory and field testing results. Canadian geotechnical journal, 60(7), 966–977. https://doi.org/10.1139/cgj-2021-0257
- [8] Dinesh, N., Banerjee, S., & Rajagopal, K. (2022). Performance evaluation of PM4Sand model for simulation of the liquefaction remedial measures for embankment. Soil dynamics and earthquake engineering, 152, 107042. https://doi.org/10.1016/j.soildyn.2021.107042
- [9] Xu, B., & Athanasopoulos-Zekkos, A. (2025). Calibration and assessment of sand-based constitutive models for gravel cyclic response via numerical single element analyses. Soil dynamics and earthquake engineering, 196, 109461. https://doi.org/10.1016/j.soildyn.2025.109461
- [10] Shen, Y., Zhong, Z., Li, L., & Du, X. (2022). Nonlinear solid-fluid coupled seismic response analysis of layered liquefiable deposit. Applied sciences, 12(11), 5628. https://doi.org/10.3390/app12115628
- [11] Hutabarat, D., & Bray, J. D. (2021). Effective stress analysis of liquefiable sites to estimate the severity of sediment ejecta. Journal of geotechnical and geoenvironmental engineering, 147(5), 4021024. 10.1061/(ASCE)GT.1943-5606.0002503.
- [12] Hutabarat, D., & Bray, J. D. (2021). Seismic response characteristics of liquefiable sites with and without sediment ejecta manifestation. Journal of geotechnical and geoenvironmental engineering, 147(6), 4021040. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002506
- [13] Basu, D., Montgomery, J., & Stuedlein, A. W. (2022). Observations and challenges in simulating post-liquefaction settlements from centrifuge and shake table tests. Soil dynamics and earthquake engineering, 153, 107089. https://doi.org/10.1016/j.soildyn.2021.107089
- [14] Basu, D., Montgomery, J., & Stuedlein, A. W. (2024). Postliquefaction reconsolidation settlement of a soil deposit considering spatially variable properties and ground motion variability. Journal of geotechnical and geoenvironmental engineering, 150(3), 4024001. https://doi.org/10.1061/JGGEFK.GTENG-11768
- [15] Peng, X. B., Gao, Y., Xue, Y. Y., Tao, X. S., & Xu, L. Y. (2024). Dynamic effective stress analysis of a site with liquefiable interlayer: considering vertical and horizontal ground motion. Frontiers in earth science, 12, 1489096. https://doi.org/10.3389/feart.2024.1489096
- [16] Dhakal, R., & Cubrinovski, M. (2025). Liquefaction response of reclaimed soils from effective stress analysis. Soils and foundations, 65(5), 101677. https://doi.org/10.1016/j.sandf.2025.101677
- [17] He, H., Ji, H., Shi, Y., Ke, X., & Miao, Y. (2024). Nonlinear seismic response analysis of liquefiable sites based on effective stress method. Computers and geotechnics, 175, 106684. https://doi.org/10.1016/j.compgeo.2024.106684
- [18] Zhou, H., Liu, X., Tan, J., Zhao, J., & Zheng, G. (2023). Seismic fragility evaluation of embankments on liquefiable soils and remedial countermeasures. Soil dynamics and earthquake engineering, 164, 107631. https://doi.org/10.1016/j.soildyn.2022.107631
- [19] Saade, C., Li, Z., Escoffier, S., & Thorel, L. (2023). Centrifuge and numerical modeling of the behavior of homogeneous embankment on liquefiable soil subjected to dynamic excitation. Soil dynamics and earthquake engineering, 172, 107999. https://doi.org/10.1016/j.soildyn.2023.107999
- [20] Wang, R., Liu, H., Kutter, B. L., & Zhang, J. M. (2023). Influence of centrifuge test soil-container friction on seismic sheet-pile wall response in liquefiable deposit: Insights from numerical simulations. Journal of geotechnical and geoenvironmental engineering, 149(9), 04023068. https://doi.org/10.1061/JGGEFK.GTENG-11064
- [21] Pakzad, A., & Arduino, P. (2024). Assessment of soil constitutive models for predicting seismic response of sheet pile walls: A LEAP-2022 project study. Soil dynamics and earthquake engineering, 178, 108447. https://doi.org/10.1016/j.soildyn.2023.108447
- [22] Zeng, S., Reyes, A., & Taiebat, M. (2024). Modeling cyclic liquefaction and system response of a sheet-pile supported liquefiable deposit: Insights from LEAP-2022. Soil dynamics and earthquake engineering, 179, 108548. https://doi.org/10.1016/j.soildyn.2024.108548
- [23] Manandhar, S., Lee, S. R., Manzari, M. T., & Cho, G. C. (2024). Seismic performance of sheet pile walls in liquefiable soil using centrifuge tests and an assessment of nonlinear effective stress analysis using PM4Sand. Soil dynamics and earthquake engineering, 183, 108777. https://doi.org/10.1016/j.soildyn.2024.108777
- [24] Zakerinia, M., Hayden, C. P., McGann, C. R., & Wotherspoon, L. M. (2024). Stress-density model validation: Free-field liquefaction analysis. Soil dynamics and earthquake engineering, 180, 108614. https://doi.org/10.1016/j.soildyn.2024.108614