Oct 2026· Journal of Geotechnical and Geoenvironmental Engineering· 1 citation· 33 references
Abstract
This paper describes the formulation of a numerical model for simulating environmentally driven one-dimensional (1D) ground movements of expansive clay. The formulation is based on a finite-element model that simulates the redistribution of matric suction through a diffusion-type equation, explicitly accounting for volume changes due to wetting and drying of the clay. We synthesize and modify highly nonlinear constitutive relationships for (1) hysteretic soil water retention; (2) reversible soil shrinkage and expansion of clay; and (3) hydraulic conductivity, explicitly incorporating desiccation cracks through a multidomain framework and assuming a critical surface crack depth. These models are well-calibrated to published laboratory tests on a reference expansive clay, Denver bentonite. We demonstrate capabilities of the proposed formulation to simulate the response of a homogeneous expansive clay to periods of drying and wetting, considering the initial matric suction, saturated hydraulic conductivity of the intact clay, and critical crack depth as three primary sources of uncertainty. We compare ensemble model simulations with measured ground movements from an instrumented expansive clay test site in Texas over a 3-year period using detailed records of potential evapotranspiration and precipitation. By assigning weights to the ensemble simulations based on their performance, we constrain the ranges of the three key uncertain parameters. The results showed very reasonable first-order agreement with the measured data and highlight the potential of the proposed formulation. We anticipate that more reliable predictions can be achieved through direct measurements of actual in situ evaporation rates and local soil properties.
The behaviour of expansive clay soils is highly influenced by climatic variations that govern the hydric exchanges between the atmosphere and the ground surface. These fluctuations cause changes in soil suction, leading to significant volumetric variations in expansive soils and resulting in differential settlements of lightweight structures, which can induce structural damage. Despite the critical role of these hydroclimatic processes, few models are able to describe the evolution of soil suction under realistic boundary conditions. In this study, a two-dimensional diffusion model is proposed to simulate the temporal and spatial evolution of suction beneath a structure, considered as impermeable, under the influence of climatic fluctuations and over selected time steps. The model is based on the numerical solution of the diffusion equation in unsaturated porous medium, formulated in terms of suction. The boundary conditions incorporate a surface water balance accounting for infiltration and evaporation, using meteorological data from the Météo-France SIM2 model. Hydraulic soil parameters, such as unsaturated permeability and water retention curve expressing suction as a function of water content, are defined from empirical relationships reported in the literature. The model is applied to a clay soil whose parameters are derived from the Chaingy experimental site (France) using daily climatic data for the year 2025. The simulations highlight a strong seasonal variability of suction concentrated within the upper soil layers, while the presence of an impermeable surface zone representing the structure significantly attenuates suction fluctuations beneath the foundation and induces marked horizontal gradients during dry periods.
Mathilde Lefebvre, M. Morvan, A. Chateauneuf et al.· E3S Web of Conferences· 0 citations
Having reliable tools for characterizing rainfall-induced soil erosion is fundamental to the effective management of agroforestry systems in order to increase resilience against climate change. Physics-based models provide a robust, comprehensive and widely applicable framework to quantify runoff generation and soil erosion during intense rainfall events in agroforestry catchments. In this work, we propose a novel hydro-erosive model to simulate hydrodynamical flow and bed mobilization, movement and deposition. This hydro-erosive model solves the two-dimensional shallow water equations (SWE-2D) with hydrological source terms for runoff generation, coupled with the 2D depth-averaged solid transport and the soil surface evolution equations. The partial differential system is solved using a finite volume method. Alternative Integral/Differential Bed Slope and explicit upwind/implicit pointwise friction term discretization options can be used to improve performance in terms of numerical stability and conservation. The behavior of different discretization options in this hydro-erosive model is evaluated through an analytical hillslope verification, a benchmark V-catchment rainfall–runoff test and a laboratory dam-break experiment over an erodible bed. The results show that the Differential Bed Slope formulation combined with the upwind friction discretization provides the most accurate and conservative predictions. Also, an Upwind Bed Updating method for integrating soil surface elevation change is compared with the cell-centered integration of the bed change term by suppressing non-physical oscillations without compromising computational efficiency. Overall, the proposed open-source hydro-erosive model provides a reliable and computationally efficient framework for high-resolution simulations of rainfall-induced soil erosion and represents a valuable tool for environmental and agroforestry applications, but appropriate calibration and mesh resolution are required to ensure reliable predictions.
A. Braga, S. Martínez-Aranda, P. García-Navarro· Water· 0 citations
The distribution of soil moisture, resulting from the movement of infiltrated water, plays a fundamental role in the hydrological dynamics of hillslopes and in the triggering of landslides. Although water flow in soils occurs in multiple directions due to combined vertical and lateral fluxes, one‐dimensional (1D) flow models are widely adopted as a simplifying assumption in slope‐scale studies, frequently without explicit verification of their validity by researchers. This study evaluates the applicability of the one‐dimensional flow hypothesis under different hydrological conditions and over time. Soil moisture dynamics were simulated using the Hydrus‐1D model, driven by observed precipitation data and calibrated and validated against in situ soil moisture measurements collected at different depths. The results suggest that, at temporal scales associated with rainfall events capable of triggering landslides, one‐dimensional modelling can adequately to represent soil moisture dynamics in slope environments when coupled with measured soil moisture data for the calibration of hydraulic parameters. In contrast, simulations using soil hydraulic parameters estimated from pedotransfer functions showed limited ability to represent the hydraulic behavior of the soils.
Danúbia Teixeira, G. P. Michel, N. Fernandes et al.· Soil Science Society of Amer...· 0 citations
(English) The top layer of soil on a slope is highly dynamic, influenced by atmospheric forces and the presence of vegetation. The vegetation condition plays a crucial role in determining the amount of water transpiration and evaporation from the slope surface, thus affecting slope performance by altering temperature, water content, and pore water pressure within the soil mass. Many numerical models often neglect the vegetation impact on soil performance. To capture these effects, this study employs a finite element model in CODE_BRIGHT that integrates vegetation and climate-driven interactions, aiming to bridge the gap between reality and simulation. A specialized boundary condition is developed to simulate soil–vegetation–atmosphere (SVA) processes with hydraulic hysteresis, linking canopy resistance to solar radiation, vapor pressure deficit, and soil saturation. Model validation using three years of field data from the Agropolis slope in Barcelona shows strong agreement, confirming its ability to reproduce vegetation effects on slope hydrothermal behavior. Results reveal pronounced daily temperature variations in the root zone, higher temperatures on south-facing slopes, and stronger drying under vegetation during hot, dry periods.
Parametric analysis identifies leaf area index (LAI), root density, and vegetation fraction as key factors influencing soil moisture. Root density and LAI most strongly affect water retention, dense roots lower summer saturation by up to 40%, while high LAI reduces surface drying by 30%. Vegetation fraction enhances winter storage but intensifies summer drying.
To better represent unsaturated soils, a hysteretic soil–water retention model is implemented in CODE_BRIGHT, coupling suction and void ratio changes to improve accuracy in scenarios such as rainfall-induced landslides.
Finally, an enhanced Barcelona Basic Model (BBM-VEG) is formulated within a thermo-hydro-mechanical (THM) framework. The model introduces a strain-dependent reinforcement factor (Rpveg), correlated with root mass fraction and activation strain, allowing soil stiffness and strength to evolve dynamically. Validated with triaxial and tensile tests, it accurately captures the mechanical response of rooted soils. Slope simulations under hydraulic (infiltration rates of 0.001–0.003 and 0.0005 kg/s) and thermal (15–60 °C) cycles show that vegetation limits infiltration, enhances evapotranspiration, expands the unsaturated zone, and reduces deformation by up to 70% compared to bare slopes.
(Català) La capa superior del sòl en un talús és altament dinàmica, influïda per les forces atmosfèriques i la presència de vegetació. L’estat de la vegetació té un paper crucial en la determinació de la quantitat de transpiració i evaporació d’aigua des de la superfície del talús, afectant així el seu comportament mitjançant l’alteració de la temperatura, el contingut d’aigua i la pressió intersticial dins de la massa de sòl. Molts models numèrics sovint descuiden l’impacte de la vegetació en el comportament del sòl. Per capturar aquests efectes, aquest estudi utilitza un model d’elements finits a CODE_BRIGHT que integra les interaccions impulsades per la vegetació i el clima, amb l’objectiu de reduir la bretxa entre la realitat i la simulació. Es desenvolupa una condició de contorn especialitzada per simular els processos sòl–vegetació–atmosfera (SVA) amb histèresi hidràulica, vinculant la resistència del dosser amb la radiació solar, el dèficit de pressió de vapor i la saturació del sòl. La validació del model amb tres anys de dades de camp del talús d’Agropolis a Barcelona mostra una forta concordança, confirmant la seva capacitat per reproduir els efectes de la vegetació en el comportament hidrotermal del talús. Els resultats revelen variacions diàries pronunciades de temperatura a la zona radicular, temperatures més elevades als talussos orientats al sud i un assecat més intens sota vegetació durant períodes càlids i secs.
L’anàlisi paramètrica identifica l’índex d’àrea foliar (LAI), la densitat radicular i la fracció de vegetació com a factors clau que influeixen en la humitat del sòl. La densitat radicular i el LAI afecten amb més intensitat la retenció d’aigua: arrels denses poden reduir la saturació estival fins a un 40%, mentre que un LAI elevat disminueix l’assecat superficial en un 30%. La fracció de vegetació millora l’emmagatzematge hivernal, però intensifica l’assecat estival.
Per representar millor els sòls no saturats, s’implementa a CODE_BRIGHT un model histèric de retenció sòl–aigua que acobla la succió i els canvis en el volum de buits per millorar la precisió en escenaris com ara esllavissades induïdes per la pluja.
Finalment, es formula un Model Bàsic de Barcelona millorat (BBM-VEG) dins d’un marc termo-hidro-mecànic (THM). El model introdueix un factor de reforç dependent de la deformació (Rpveg), correlacionat amb la fracció de massa radicular i la deformació d’activació, permetent que la rigidesa i la resistència del sòl evolucionin dinàmicament. Validat mitjançant assaigs triaxials i de tracció, el model captura amb precisió la resposta mecànica dels sòls amb arrels. Les simulacions de talussos sota cicles hidràulics (taxes d’infiltració de 0,001–0,003 i 0,0005 kg/s) i tèrmics (15–60 °C) mostren que la vegetació limita la infiltració, potencia l’evapotranspiració, amplia la zona no saturada i redueix la deformació fins a un 70% en comparació amb talussos nus.
(Español) La capa superior del suelo en una ladera es altamente dinámica y está influenciada por las fuerzas atmosféricas y la presencia de vegetación. El estado de la vegetación desempeña un papel crucial en la determinación de la cantidad de agua transpirada y evaporada desde la superficie de la ladera, afectando así su comportamiento al modificar la temperatura, el contenido de agua y la presión de poros dentro de la masa del suelo. Muchos modelos numéricos suelen pasar por alto el impacto de la vegetación en el desempeño del suelo. Para capturar estos efectos, este estudio emplea un modelo de elementos finitos en CODE_BRIGHT que integra las interacciones impulsadas por la vegetación y el clima, con el objetivo de reducir la brecha entre la realidad y la simulación. Se desarrolla una condición de contorno especializada para simular los procesos suelo–vegetación–atmósfera (SVA) con histéresis hidráulica, vinculando la resistencia del dosel a la radiación solar, el déficit de presión de vapor y la saturación del suelo.
La validación del modelo con tres años de datos de campo del talud de Agropolis en Barcelona muestra una fuerte concordancia, confirmando su capacidad para reproducir los efectos de la vegetación en el comportamiento hidrotermal de la ladera. Los resultados revelan variaciones diarias pronunciadas de temperatura en la zona radicular, temperaturas más altas en laderas orientadas al sur y una mayor desecación bajo vegetación durante periodos cálidos y secos.
El análisis paramétrico identifica el índice de área foliar (LAI), la densidad radicular y la fracción de vegetación como los principales factores que influyen en la humedad del suelo. La densidad de raíces y el LAI afectan más intensamente la retención de agua: las raíces densas reducen la saturación estival hasta en un 40%, mientras que un LAI elevado disminuye la desecación superficial en un 30%. La fracción de vegetación aumenta el almacenamiento invernal, pero intensifica la desecación durante el verano.
Para representar mejor los suelos no saturados, se implementa en CODE_BRIGHT un modelo histerético de retención agua–suelo, acoplando los cambios de succión y relación de vacíos para mejorar la precisión en escenarios como los deslizamientos inducidos por lluvia.
Finalmente, se formula un Modelo Básico de Barcelona mejorado (BBM-VEG) dentro de un marco termo-hidro-mecánico (THM). El modelo introduce un factor de refuerzo dependiente de la deformación (Rpveg), correlacionado con la fracción de masa radicular y la deformación de activación, lo que permite que la rigidez y la resistencia del suelo evolucionen dinámicamente. Validado con ensayos triaxiales y de tracción, el modelo reproduce con precisión la respuesta mecánica de los suelos con raíces. Las simulaciones de laderas bajo ciclos hidráulicos (tasas de infiltración de 0.001–0.003 y 0.0005 kg/s) y térmicos (15–60 °C) muestran que la vegetación limita la infiltración, mejora la evapotranspiración, amplía la zona no saturada y reduce la deformación hasta en un 70% en comparación con laderas desnudas.
Water uptake through plant transpiration is a critical hydraulic boundary condition in modelling geostructures under climatic loading. Transpiration occurs in two regimes: energy-limited, controlled by atmospheric evaporative demand; and water-limited, governed by soil hydraulic conductivity around roots. While energy-limited (potential) transpiration is generally modelled using a physically based approach, the water-limited regime is usually modelled macroscopically by way of an empirical transpiration reduction function. This paper first presents an experimental investigation into the influence of soil hydraulic behaviour and potential transpiration rate on water-limited transpiration. Two soil textures were tested – silty sand and clayey-silty sand – planted with Medicago sativa. The use of high-capacity tensiometers enabled the investigation of an unprecedented suction range in clayey soils. Results show that the water-limited branch of the reduction function is non-linear, and its decay is strongly influenced by unsaturated hydraulic conductivity. Furthermore, the suction marking the transition from energy- to water-limited regimes varied with potential transpiration rate and soil hydraulic behaviour. A novel physically based, closed-form reduction function is then formulated to advance water uptake modelling in the water-limited regime. This function is shown to compactly capture the combined effects of soil hydraulic conductivity, root system architecture expressed through root length density and potential transpiration rate on transpiration in the water-limited regime, consistent with observations from both this experimental campaign and the literature data.
Eve Roberts-Self, A. Tarantino· Geotechnique· 0 citations
Rainfall infiltration frequently triggers slope failures by elevating pore water pressure and compromising the shear strength of unsaturated soil layers. Modeling these severe geological events remains computationally challenging. Standard grid-based techniques, such as the Finite Element Method (FEM), typically fail due to severe mesh distortion under large deformations, whereas the Discrete Element Method (DEM) demands excessive computational resources. Addressing this gap, we develop an advanced theoretical framework utilizing the Material Point Method (MPM) integrated with a liquid-solid-gas three-phase mechanics model. We first verify the algorithmic accuracy using a 1D unsaturated soil column test. Subsequently, the framework is deployed to capture the dynamic displacement and mechanical responses of a 2D rainfall-induced landslide. Benchmarking against FEM data confirms that our multiphase MPM accurately models the infiltration process and subsequent structural collapse. Ultimately, this approach offers a highly robust computational strategy for analyzing large-scale landslide deformations and improving predictive assessments.
Long Zhu, Lele Wang, Xiao Liu et al.· E3S Web of Conferences· 0 citations
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
