Geotechnical centrifuge testing has long been one of the most powerful tools available to engineers trying to understand why slopes fail. By spinning a scaled-down model at high speed, researchers can recreate the stress conditions of a full-sized hillside or embankment inside a laboratory container, compressing decades of gravitational loading into hours of testing. But a subtle enemy has always lurked inside the box: friction. When a model slope slides, the moving soil drags against the rigid sidewalls of the container, and that friction makes narrow laboratory models appear more stable than the real, effectively infinite slopes they are meant to represent. A new study published in Scientific Reports by Fangxue Liu, Lijun Sun, and Yue Wang now offers a practical, physics-based way to quantify and correct this distortion.

The core problem is one of similitude. Centrifuge slope models are designed under the assumption of plane strain, meaning the soil is supposed to deform in a two-dimensional cross-section, exactly as it would in an infinitely long prototype slope. In reality, the model sits in a container with finite width, bounded by rigid walls on both sides. As the sliding mass moves downslope during a test, it shears against those walls, and the resulting frictional resistance does extra work that the prototype would never experience. The consequence is systematic: finite-width models register a higher critical acceleration, or apparent stability factor, than the ideal plane-strain reference they are supposed to mimic. Engineers comparing model results with field predictions or numerical analyses have therefore had to live with an unquantified bias.

Liu and colleagues approached the problem through the framework of limit analysis, specifically the upper-bound method, a classical technique in soil mechanics that estimates the load or acceleration at which a soil mass will fail by balancing the rate of work done by external forces against the rate of energy dissipated along an assumed failure mechanism. In a conventional plane-strain upper-bound calculation for a slope, the energy balance includes the work done by the soil’s self-weight moving along a curved failure surface and the internal dissipation along that surface. The innovation of the new work is to insert an additional term into this balance: the rate of work dissipated by friction between the sliding mass and the two sidewalls, evaluated from an assumed distribution of lateral normal stress acting on the walls.

Because the true three-dimensional stress state inside a centrifuge container is fiendishly difficult to measure or compute, the authors describe their approach as pseudo-three-dimensional. They do not attempt a full 3D failure mechanism. Instead, they retain the classical two-dimensional failure geometry and augment the global work rate balance with a sidewall-friction term derived from a reasonable assumption about how normal stresses are distributed laterally against the container walls. This keeps the calculation tractable while capturing the dominant physical effect of the boundaries. The result is a correction that can be applied to the kind of stability charts and calculations geotechnical engineers already use, rather than requiring a wholesale shift to computationally expensive three-dimensional simulations.

To find the most dangerous failure surface for any given set of parameters, the researchers employed a random-search optimisation technique. Rather than guessing the geometry of the critical slip surface, the algorithm explores many candidate surfaces and identifies the one that yields the lowest stability factor, which corresponds to the most likely mode of failure. This combination of an augmented energy balance with automated optimisation allows the method to produce, for any specified slope geometry, soil strength, sidewall friction angle, and model width, both the critical failure surface and the corrected stability factor that accounts for sidewall interference.

The authors did not leave the formulation untested. They first verified that their corrected solution reduces appropriately to the classical plane-strain upper-bound result, providing a mathematical sanity check on the new term. They then compared their calculated critical acceleration scale factors against published centrifuge test data. Across the configurations reported, the calculated and measured values show the same decreasing trends with increasing model height and with increasing slope inclination, which is an encouraging sign that the physics of the correction is capturing real behaviour. The authors are candid, however, that substantial differences remain for individual cases, a reminder that the method rests on an assumed lateral stress distribution and inherits the idealisations of the upper-bound framework itself.

Perhaps the most practically valuable outcome of the study is its parametric analysis of when sidewall friction matters and when it does not. The calculations reveal that sidewall friction significantly inflates the apparent stability factor at low width-to-height ratios, precisely the situation faced by researchers who must squeeze a tall slope model into a limited container width. As the width-to-height ratio increases, the discrepancy diminishes rapidly, confirming the intuition that wide models approach true plane-strain behaviour. For the representative cases examined at a slope angle of sixty degrees, the sidewall friction angle and the width-to-height ratio exert a larger influence on the relative deviation caused by the sidewalls than the soil’s own internal friction angle does, although the soil strength remains explicitly embedded in the broader reference solutions.

To make these insights usable in the design office, the team developed reference charts and tables that quantify the width-dependent deviation for selected combinations of slope angle, soil friction angle, sidewall friction angle, and width-to-height ratio, organised by relative-deviation thresholds. With such a chart, an experimentalist planning a centrifuge campaign can estimate in advance how much apparent extra stability a given model width will introduce, and can either widen the model, adjust the interpretation of the measured critical acceleration, or accept and document a known bias. The authors emphasise that these resources are preliminary and assumption-dependent, intended as guides for selecting model widths and interpreting sidewall-induced deviations rather than as exact corrections.

The significance of this work extends beyond a single laboratory technique. Centrifuge modelling underpins safety assessments for embankments, tailings dams, natural slopes, and coastal structures around the world, and the field’s credibility rests on the fidelity with which small models reproduce prototype behaviour. Boundary effects of the kind quantified here have been acknowledged qualitatively for decades, but turning that awareness into a predictive, parameterised correction is what allows experimental programmes to report results with defensible uncertainty. A method that converts an unquantified systematic error into a charted, correctable deviation is a meaningful step toward more trustworthy model-to-prototype extrapolation.

The study, published open access in Scientific Reports on 12 October 2026, was funded by the Fundamental Research Funds for the Central Universities under grant number B250201198. Its authors are based at Jiangsu Open University in Nanjing and Hohai University, also in Nanjing. For the growing community of engineers using centrifuges to stress-test the world’s slopes, the message is clear: the walls of the box are not neutral observers. They take a measurable cut of the energy in every test, and with the pseudo-three-dimensional work-balance correction now available, that cut can finally be estimated, charted, and designed around, bringing laboratory-scale simulations one step closer to the full-scale ground truth they strive to represent.

Subject of Research: A pseudo-three-dimensional work-balance correction quantifying sidewall friction effects on slope stability in centrifuge model tests

Article Title: A pseudo-three-dimensional work-balance correction for sidewall friction effects in centrifuge slope models

Article References: Liu, F., Sun, L., & Wang, Y. (2026). A pseudo-three-dimensional work-balance correction for sidewall friction effects in centrifuge slope models. Scientific Reports. https://doi.org/10.1038/s41598-026-72078-w

Image Credits: AI Generated

DOI: 10.1038/s41598-026-72078-w

Keywords: centrifuge modelling, slope stability, sidewall friction, upper-bound analysis, pseudo-three-dimensional analysis, width-to-height ratio, geotechnical engineering, limit analysis, boundary effects, critical acceleration, soil mechanics, model testing