the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Jun 2026
Thermo-hydrological and thermo-mechanical modeling of freezing soil and frost quake occurrence
Abstract. Frost quakes are seismic events originating in frozen ground, traditionally attributed to ice expansion when air temperature decreases rapidly, the soil is saturated and has little or no snow cover. However, novel observations presented here question the necessity of some of the previous assumption and meteorological conditions, driving us to consider alternative mechanisms. This study investigates frost quake formation through numerical modeling and seismological and hydrological observations in Tähtelä, Finland, during winter 2022–2023. We analyzed soil and atmospheric conditions during frost quake occurrences, noting a strong correlation with rapid air temperature decrease below -20 °C, and with varying snow cover. We modeled the thermo-hydrological (TH) processes, such as cryosuction-driven ice lens growth, using Amanzi-ATS, while the thermo-mechanical (TM) evolution was modeled with OpenGeoSys (OGS). The ATS TH simulation results suggest an important role of cryosuction for the appearance of frost quakes. Focusing on volumetric effects, the OGS TM simulation results reveal tensional and shear stress rates in the soil, both of which are able to cause fracturing leading to frost quakes. Future work should integrate fully-coupled thermo-hydro-mechanical simulations and laboratory experiments to refine predictive models and assess infrastructure risks in cold climates.
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Status: open (until 11 Aug 2026)
- CC1: 'Comment on egusphere-2026-2611', Ivo Baselt, 08 Jul 2026 reply
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RC1: 'Comment on egusphere-2026-2611', Kehua You, 18 Jul 2026
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This study challenges the conventional understanding of frost quakes by demonstrating, through the integration of field observations, thermo-hydrological modeling, and thermo-mechanical modeling, that frost quakes can occur under conditions that have not been recognized in previous studies. The work highlights the importance of using a fully coupled thermo-hydro-mechanical model to investigate the mechanisms governing frost quakes. Overall, the manuscript is well written, and I only have a few minor comments.
- Line 178: What does (L_f) represent? Please define it when it is first introduced.
- Most seismic events were observed in wetlands and irrigated channels. A common characteristic of these environments is their relatively high water content. Does this observation suggest that water content is an important controlling factor for frost quake occurrence?
- Line 203: The simulated ice content decreases from 0.42 to 0.044 (approximately one order of magnitude) when the cell size increases from 2 cm to 5 cm. Is this result correct? If so, could the authors explain the strong sensitivity to spatial resolution?
- Line 211: The simulation domain extends from the ground surface to a depth of 25 m. Why is a boundary condition specified at a depth of 5 m rather than at the bottom of the model domain?
- Table 1: Both lambda_s and lambda_sR are mentioned. Are these two parameters different? If so, please clarify their definitions.
- Please include the equation used to calculate the bulk thermal conductivity. Because bulk thermal conductivity is a key parameter in the model and can be estimated using different mixing models.
- Line 245: The thermo-mechanical model uses the parallel model to calculate bulk thermal conductivity. Is the same approach also used in the thermo-hydrological model? If different formulations are adopted, please explain the rationale and discuss any potential impact on the simulation results.
- Figure 5a: I suggest adding a horizontal line indicating the -20 oC temperature to facilitate interpretation of the results.
- Line 313: What does "temperature rate" refer to? Would "rate of temperature change" or "temperature change rate" be a clearer description?
Citation: https://doi.org/10.5194/egusphere-2026-2611-RC1
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I would like to congratulate the authors on this very interesting and timely contribution. I particularly appreciate the attempt to combine seismological observations with thermo-hydrological and thermo-mechanical modelling to reassess the mechanisms behind frost quake occurrence.
One aspect that I found especially stimulating is the potential link between frost-quake-related crack formation and preferential-flow concepts in frozen soils. The authors already highlight the broader relevance of their work for wintertime hydrological processes, especially where rain, snowmelt, freezing, and thawing interact in the Earth´s Critical Zone. However, the manuscript mainly focuses on the formation mechanism of cracks and does not further discuss the possible thermo-hydraulic consequences of such cracks once they have formed.
This connection seems highly relevant because there is a related branch of cryosphere and frozen-soil research that investigates how macropores and preferential pathways affect infiltration, heat transport, refreezing, drainage onset, and runoff generation in seasonally frozen soils. Many experimental studies necessarily rely on idealised representations of such preferential structures (e.g. Watanabe and Kugisaki, 2017; Mohammed et al., 2018; Pittman et al., 2020; Bauer et al., 2026). These experiments provide important benchmark data for dual-porosity, dual-permeability, and dual-domain modelling approaches, in which macropores are represented as a separate flow or continuum domain (e.g. Larsbo et al., 2019; Heinze and Blöcher, 2019; Mohammed et al., 2021; Heinze, 2021; Heinze, 2025; Khanahmadi et al., 2026).
This is where I see a particularly interesting contribution of the present manuscript. The crack formation discussed here could provide a mechanistic bridge between idealised macropore concepts and naturally generated preferential structures in frozen ground. In other words, frost-quake-related cracks may not only be interpreted as a mechanical consequence of freezing, but potentially also as transient macropore-like structures that influence subsequent water flow, heat transport, refreezing, and cryosuction during rainfall or snowmelt events. The causal direction may even be twofold: macropores may lose functionality when they refreeze, while newly formed cracks may subsequently create a new macropore-like system that becomes hydraulically active.
In this context, it would be very helpful if the manuscript could further discuss, or at least provide order-of-magnitude estimates for, the expected geometry of frost-quake-related cracks. Possible crack aperture, penetration depth, lateral extent, spacing, orientation, and connectivity would be highly relevant parameters. I fully understand that these quantities may not be directly observable from the present data set. Nevertheless, even a discussion of plausible ranges inferred from frost depth, ice-body thickness, seismic source locations, or the simulated stress and ice zones would substantially increase the value of the study for future modelling efforts.
Such information would allow two complementary modelling strategies. At the continuum scale, frost-quake-induced cracks could be represented in dual-porosity or dual-permeability frameworks, where the frozen matrix and the crack or macropore domain are treated as interacting domains with different hydraulic and thermal properties. For this, approximate geometric information would be required to estimate the corresponding macroporosity or crack-domain volume fraction. At a more explicit scale, crack aperture, length, spacing, and connectivity could be used to resolve individual cracks as discrete preferential pathways in numerical models. This would be a natural next step beyond idealised cylindrical macropores and would directly connect thermo-mechanical crack formation with thermo-hydrological function.
I therefore suggest extending the introduction and/or the discussion by explicitly addressing the possible hydrological relevance of frost-quake-related cracks. In particular, it would be valuable to clarify whether the authors view these cracks primarily as mechanical failure features, or whether they may also act as transient preferential-flow structures after their formation. This could open an interesting path for future work linking frost-quake mechanics, crack geometry, dual-domain modelling, and discrete crack-scale simulations in seasonally frozen soils.
Let me also add three minor comments which might help to improve the manuscript:
Line 125: From my point of view, it would be useful to cite the original work for the Kozeny-Carman method, Carman (1956), in addition to the more recent source.
Line 296: Shouldn´t the year in 17.11.2023 be 2022? Also, the text between 294 to 298 refer to dates between 2022 (I guess) until May 2024. However, the caption in Fig. 7 shows only the period until 2023. So, is Fig. 7 only one example?
Figure 1: According to the caption, subfigure c shows the soil station installation. However, I can only identify a borehole with some wires. Perhaps the subfigure could be improved by using a clearer image or by adding text arrows that indicate the relevant components of the installation.
References:
Bauer, Julian; Müller, Sebastian; Heinze, Thomas; Khanahmadi Bafghi, Homa; Baselt, Ivo (2026): Thermohydraulic experiments on water infiltration into frozen slopes: the role of macropores and initial water content. In: The Cryosphere 20 (6), S. 3483–3509. DOI: 10.5194/tc-20-3483-2026.
Carman, Philip Crosbie (1956): Flow of Gases Through Porous Media: Academic Press.
Heinze, Thomas; Blöcher, Johanna R. (2019): A model of local thermal non-equilibrium during infiltration. In: Advances in Water resources 132, S. 103394. DOI: 10.1016/j.advwatres.2019.103394.
Heinze, Thomas (2021): A Multi‐Phase Heat Transfer Model for Water Infiltration Into Frozen Soil. In: Water Resour. Res. 57 (10). DOI: 10.1029/2021WR030067.
Heinze, Thomas (2025): A local thermal non-equilibrium model for rain-on-snow events. In: Hydrol. Earth Syst. Sci. 29 (8), S. 2059–2080. DOI: 10.5194/hess-29-2059-2025.
Khanahmadi, Homa; Bauer, Julian; Baselt, Ivo; Heinze, Thomas (2026): The influence of macropores on the thermal state of soil during infiltration in the absence of thermal equilibrium. In: Journal of Hydrology 668, S. 134983. DOI: 10.1016/j.jhydrol.2026.134983.
Larsbo, Mats; Holten, Roger; Stenrød, Marianne; Eklo, Ole Martin; Jarvis, Nicholas (2019): A Dual‐Permeability Approach for Modeling Soil Water Flow and Heat Transport during Freezing and Thawing. In: Vadose zone j. 18 (1), S. 1–11. DOI: 10.2136/vzj2019.01.0012.
Mohammed, Aaron A.; Kurylyk, Barret L.; Cey, Edwin E.; Hayashi, Masaki (2018): Snowmelt Infiltration and Macropore Flow in Frozen Soils: Overview, Knowledge Gaps, and a Conceptual Framework. In: Vadose zone j. 17 (1), S. 1–15. DOI: 10.2136/vzj2018.04.0084.
Mohammed, Aaron A.; Cey, Edwin E.; Hayashi, Masaki; Callaghan, Michael V. (2021): Simulating preferential flow and snowmelt partitioning in seasonally frozen hillslopes. In: Hydrol. Process. 35 (8), Artikel e14277, e14277. DOI: 10.1002/hyp.14277.
Pittman, Freda; Mohammed, Aaron; Cey, Edwin (2020): Effects of antecedent moisture and macroporosity on infiltration and water flow in frozen soil. In: Hydrol. Process. 34 (3), S. 795–809. DOI: 10.1002/hyp.13629.
Watanabe, Kunio; Kugisaki, Yuki (2017): Effect of macropores on soil freezing and thawing with infiltration. In: Hydrol. Process. 31 (2), S. 270–278. DOI: 10.1002/hyp.10939.