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Related Experiment Video

Updated: Apr 4, 2026

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
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Global stability for an inverse problem in soil-structure interaction.

G Alessandrini1, A Morassi2, E Rosset1

  • 1Università degli Studi di Trieste , Trieste, Italy.

Proceedings. Mathematical, Physical, and Engineering Sciences
|September 8, 2015
PubMed
Summary

This study determines the Winkler subgrade reaction coefficient for a clamped elastic plate foundation using deflection data. A global Hölder stability estimate is proven for the inverse problem, ensuring reliable coefficient determination.

Keywords:
Hölder stabilityWinkler soil–foundation interactionelastic plateinverse problems

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Area of Science:

  • Solid Mechanics
  • Applied Mathematics
  • Geotechnical Engineering

Background:

  • Foundation design relies on accurately modeling soil-structure interaction.
  • The Winkler subgrade reaction model is a common simplification for soil behavior under foundations.
  • Inverse problems are crucial for inferring material properties from observed data.

Purpose of the Study:

  • To determine the Winkler subgrade reaction coefficient of a thin elastic plate foundation.
  • To analyze the inverse problem of identifying this coefficient from deflection measurements.
  • To establish stability estimates for the inverse problem solution.

Main Methods:

  • Modeling the foundation as a thin elastic plate clamped at the boundary.
  • Applying a concentrated force to the plate.
  • Measuring the transversal deflection at interior points.
  • Utilizing mathematical analysis to derive stability estimates.

Main Results:

  • A global Hölder stability estimate was proven for the inverse problem.
  • The estimate quantifies the stability of determining the Winkler coefficient.
  • Mild regularity assumptions were placed on the unknown coefficient.

Conclusions:

  • The study provides a rigorous mathematical foundation for determining the Winkler subgrade reaction coefficient.
  • The results contribute to more accurate and reliable foundation design.
  • The established stability estimate is essential for practical applications of inverse problem solving in geomechanics.