TillCliff-HM

Seasonal hydro-mechanical preconditioning of a North-European clayey glacial-till slope under prescribed coastal toe recession

Nurwahid Dimas Saputro · 2026

A computational geomechanics mini-study developed to investigate how seasonal antecedent hydraulic state modifies the distributed mechanical response of a clayey glacial-till slope subjected to prescribed coastal toe recession.

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Abstract

Seasonal wetting and drying modify pore pressure, saturation, and effective stress before coastal erosion acts on a slope. This project examines whether those antecedent hydro-mechanical conditions influence the subsequent deformation generated by an identical prescribed toe-recession sequence.

A two-dimensional unsaturated slope model was developed in OpenGeoSys 6.5.8, combining Richards flow, deformation, deformation-dependent porosity, gravity, and a Mohr–Coulomb constitutive description implemented through MFront. The hydraulic archetype is informed by published Danish clayey glacial-till data, while the mechanical properties are explicitly treated as screening assumptions rather than site-calibrated measurements.

Dry, reference, and wet antecedent branches were transferred to a common production mesh and tested under identical geometric toe recession. A controlled pressure/stress factorial decomposition was then used to separate the influence of hydraulic state from the inherited effective-stress field.

Within the present model, antecedent hydraulic state strongly controls the magnitude and spatial mode of the distributed slope response. At $E=0.25$ m, with inherited effective stress fixed at the reference state, the dry hydraulic state produces approximately 1.246 times the reference RMS response, whereas the wet hydraulic state produces approximately 0.156 times the reference response. Replacing inherited stress alone changes the response by only about one percent. The wet-state displacement field also departs progressively from the reference deformation mode, with cosine similarity decreasing to 0.7689 at $E=0.25$ m.

Mesh-refinement and localization diagnostics demonstrate that notch-front plasticity and solver nonconvergence are not mesh-objective. They are therefore excluded from physical failure interpretation.

Main finding: in this screening formulation, antecedent hydraulic state controls not only the amplitude but also the spatial structure of erosion-induced distributed deformation; the attribution experiment indicates that this effect is predominantly hydraulic rather than inherited-stress driven.

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1. Research question

How does antecedent seasonal hydraulic state alter the distributed deformation response of a clayey glacial-till slope to prescribed coastal toe recession?

The project originally examined whether an erosion threshold $E_{\mathrm{crit}}$ could be identified. That interpretation was abandoned after mesh studies demonstrated that local notch-front plasticity and nonconvergence depend strongly on the discrete element-deactivation topology.

The revised research question therefore focuses on distributed, mesh-conditional deformation response, rather than a failure threshold.

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2. Physical and numerical framework

2.1 Geological context

The hydraulic screening archetype is based on published observations of unsaturated fractured clayey till at Avedøre, Denmark, reported by Mortensen et al. (2004).

The paper provides a Danish context for:

• clayey glacial-till stratigraphy;
• shallow seasonal groundwater fluctuations;
• unsaturated fractured conditions;
• low-permeability till matrix behaviour.

The present model is not a site-calibrated reconstruction of Avedøre.

2.2 Hydraulic model

Unsaturated water flow is represented using the Richards equation with a van Genuchten-type retention formulation.

The model adopts a low intrinsic permeability consistent with the order of magnitude reported for Danish clayey till and explicitly resolves seasonal changes in pore pressure and degree of saturation.

Three antecedent branches are retained:

State	Interpretation
Dry	greater suction / lower saturation
Reference	intermediate hydraulic condition
Wet	lower suction / higher saturation

After transfer to the production mesh, all three states preserve the required ordering:

$$p_{\mathrm{dry}} < p_{\mathrm{ref}} < p_{\mathrm{wet}}$$

and

$$S_{r,\mathrm{dry}} < S_{r,\mathrm{ref}} < S_{r,\mathrm{wet}}.$$

2.3 Mechanical model

The mechanical formulation contains:

• gravity;
• elastic stiffness prior to yielding;
• Biot coupling;
• deformation-dependent porosity;
• Mohr–Coulomb plasticity;
• MFront constitutive integration.

The adopted mechanical parameters are screening assumptions and must not be interpreted as measured properties of a specific Danish till site.

2.4 Coastal toe recession

Coastal erosion is represented as a process-informed prescribed basal toe-recession sequence using element deactivation.

The continuation coordinate is numerical.

It does not represent:

• resolved wave loading;
• sediment transport;
• hydrodynamic scour;
• a physical erosion rate.

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3. Analysis design

The computational sequence is:

$$\text{seasonal HM forcing} \rightarrow \text{antecedent state} \rightarrow \text{MC equilibrium} \rightarrow \text{toe recession} \rightarrow \text{distributed deformation}.$$

The main slope-body metric is

$$R_{\mathrm{RMS}} = \sqrt{ \frac{1}{N} \sum_{i=1}^{N} \left\| \Delta \mathbf{u}_i \right\|^2 },$$

evaluated in a fixed monitoring region excluding the immediate notch-front localization zone.

A 95th-percentile displacement magnitude is retained as a complementary distributed-response metric.

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4. Results

4.1 Antecedent state changes erosion-induced deformation

The production seasonal branches show a clear separation in distributed slope-body response under identical realized toe geometry.

Figure 1. (a) Distributed deformation for the dry, reference, and wet seasonal branches as a function of actual removed toe area. (b) Controlled hydraulic/effective-stress decomposition.

At nominal toe recession $E=0.25$ m, under a common reference inherited stress state:

Numerical experiment	$R_{\mathrm{RMS}}/R_{\mathrm{ref}}$
Dry pressure + reference stress	1.2456
Reference pressure + reference stress	1.0000
Wet pressure + reference stress	0.1558
Reference pressure + dry stress	1.0027
Reference pressure + wet stress	0.9876

The hydraulic-state perturbation is therefore much larger than the inherited-stress perturbation over the tested range.

This is a numerical attribution result, not a universal physical statement that wetting stabilizes clayey slopes.

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4.2 Hydraulic state also changes deformation mode

To determine whether hydraulic state merely scales one common displacement pattern, the full slope-body displacement vectors were compared using cosine similarity,

$$C = \frac{ \Delta \mathbf{u}_{H} \cdot \Delta \mathbf{u}_{\mathrm{ref}} }{ \left\| \Delta \mathbf{u}_{H} \right\| \left\| \Delta \mathbf{u}_{\mathrm{ref}} \right\| }.$$

Figure 2. (a) Cosine similarity of pressure-controlled dry and wet displacement fields relative to the reference state. (b) Normalized residual after optimal scalar amplitude fitting.

The dry and reference responses remain nearly collinear:

$$C_{\mathrm{dry/ref}} \ge 0.99969.$$

The wet/reference similarity decreases with recession:

$E$ [m]	Wet/reference cosine
0.05	0.9249
0.15	0.9256
0.25	0.7689

The wet response is therefore not simply a reduced-amplitude copy of the reference displacement field.

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4.3 Mode difference is well above numerical drift

Because the wet response is small in absolute magnitude, a final numerical signal-floor test was performed using late-stage intact-hold displacement drift.

Figure 3. Ratio between erosion-induced slope-body response and intact-hold numerical displacement drift.

The minimum wet-state signal-to-drift ratio is

$$\mathrm{SNR}_{\mathrm{wet,min}} \approx 3.07\times10^{3}.$$

The observed wet/reference mode difference is therefore numerically resolved relative to the measured intact-hold drift floor.

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5. Numerical credibility and negative result

An important outcome of this project is also what was not claimed.

A local moving-front erosion formulation was tested on coarse, medium, and fine toe meshes. The intact medium and fine meshes agreed closely before erosion, but local EquivalentPlasticStrain and solver nonconvergence shifted strongly when the discrete element-removal topology changed.

Localization audits showed that plastic hotspots remained attached to the active/eroded notch interface.

Therefore:

solver nonconvergence is not interpreted as physical slope failure.

Likewise:

• no physical $E_{\mathrm{crit}}$ is reported;
• no factor of safety is inferred;
• no landslide initiation threshold is inferred from local plastic strain;
• notch-front mesh sensitivity is reported rather than hidden.

The monitored distributed slope body remains elastic over the primary common comparison range.

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6. Interpretation

The defensible model-specific conclusion is:

Antecedent hydraulic state strongly modifies the distributed deformation generated by prescribed coastal toe recession. In the tested formulation, the hydraulic component dominates the inherited effective-stress component, and sufficiently wet antecedent conditions modify both deformation amplitude and displacement-field structure.

The result should not be translated into the statement that wetting universally stabilizes natural clay slopes.

The observed ordering emerges from this particular coupled formulation, geometry, hydraulic constitutive description, boundary conditions, and screening mechanical parameter set.

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7. Scope and limitations

Item	Status
Coupled unsaturated flow–deformation	Included
Seasonal dry/reference/wet antecedent states	Included
Deformation-dependent porosity	Included
Mohr–Coulomb constitutive response	Included
Danish clayey-till hydraulic context	Literature anchored
Site-specific Danish mechanical calibration	Not included
Wave-resolved coastal erosion	Not included
Sediment transport	Not included
Mesh-objective post-localization model	Not included
Physical failure threshold	Not claimed
Hazard/risk prediction	Outside scope

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8. Reproducibility

The compact numerical tables behind the main figures are included in data/processed/.

data/processed/
├── antecedent_state_comparison.csv
├── decomposition_response.csv
├── mode_shape_audit.csv
└── signal_to_drift_audit.csv

Rebuild the figures with:

conda env create -f environment.yml
conda activate tillcliff-hm

python src/make_publication_figures.py

The complete raw VTU/PVD solver histories are intentionally excluded from the repository because of their size.

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9. Repository structure

tillcliff-hm/
├── README.md
├── LICENSE
├── CITATION.cff
├── references.bib
├── environment.yml
├── data/
│   └── processed/
├── docs/
│   ├── methods.md
│   └── results.md
├── figures/
│   ├── fig00_graphical_abstract.*
│   ├── fig01_hydraulic_state_response.*
│   ├── fig02_deformation_mode.*
│   └── fig03_signal_quality.*
├── model/
│   └── OpenGeoSys project files
└── src/
    └── model-building and analysis scripts

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10. References actually used

Danish clayey-till hydraulic context

1. Mortensen, A. P., Jensen, K. H., Nilsson, B., & Juhler, R. K. (2004). Multiple Tracing Experiments in Unsaturated Fractured Clayey Till. Vadose Zone Journal, 3(2), 634–644. https://doi.org/10.2136/vzj2004.0634

Unsaturated hydraulic formulation

2. Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12(3), 513–522. https://doi.org/10.1029/WR012i003p00513

3. van Genuchten, M. T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44(5), 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x

Mohr–Coulomb constitutive implementation

4. Abbo, A. J., & Sloan, S. W. (1995). A smooth hyperbolic approximation to the Mohr–Coulomb yield criterion. Computers & Structures, 54(3), 427–441. https://doi.org/10.1016/0045-7949(94)00339-5

5. Abbo, A. J., Lyamin, A. V., Sloan, S. W., & Hambleton, J. P. (2011). A C2 continuous approximation to the Mohr–Coulomb yield surface. International Journal of Solids and Structures, 48(21), 3001–3010. https://doi.org/10.1016/j.ijsolstr.2011.06.021

Numerical software

6. Kolditz, O., Bauer, S., Bilke, L., et al. (2012). OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. Environmental Earth Sciences, 67(2), 589–599. https://doi.org/10.1007/s12665-012-1546-x

7. Helfer, T., Michel, B., Proix, J.-M., Salvo, M., Sercombe, J., & Casella, M. (2015). Introducing the open-source MFront code generator: Application to mechanical behaviours and material knowledge management within the PLEIADES fuel element modelling platform. Computers & Mathematics with Applications, 70(5), 994–1023. https://doi.org/10.1016/j.camwa.2015.06.027

8. OpenGeoSys Community (2026). OpenGeoSys 6.5.8, software release used for the reported simulations. https://www.opengeosys.org/stable/releases/6.5.8/

BibTeX entries are provided in references.bib.

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11. Citation

If referring specifically to this computational study:

Saputro, N. D. (2026).
TillCliff-HM: Seasonal hydro-mechanical preconditioning of a
North-European clayey glacial-till slope under prescribed coastal
toe recession. Version 1.0.1.

Machine-readable metadata are available in CITATION.cff.

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12. License

Project code, documentation, and original figures are released under the BSD 3-Clause License.

See LICENSE.

Third-party software, publications, and external datasets remain subject to their respective original licenses and copyright terms.