# Evolution Law of Contact Force Chain Network Structure of Geotechnical Granular Materials Under Unloading Stress Paths

## TL;DR

This study explores how granular materials behave under unloading stress by analyzing their contact force networks using simulations and persistent homology.

## Contribution

The paper introduces a novel application of persistent homology to quantify force chain evolution in granular materials under unloading stress paths.

## Key findings

- Dense granular specimens show strain softening and a peak in contact force network strength during unloading.
- Unloading in the minor principal stress direction increases network strength by about 20% more than in the major direction.
- Loose specimens exhibit minimal microstructural changes and lack a significant force chain network.

## Abstract

Granular materials exhibit complex mechanical behaviors during unloading, yet the underlying micro- and meso-scale mechanisms remain unclear. This study employs a discrete element method to simulate a series of triaxial tests on sand and pebble specimens with varying initial densities under different unloading stress paths. While dense specimens demonstrate strain softening and dilatancy, loose samples exhibit shear contraction. To quantify the underlying fabric evolution, persistent homology (PH) theory is adopted to analyze the particle contact force networks. The results reveal that the average strength of this network correlates strongly with the macroscopic stress–strain response. For dense samples, network strength rapidly increases to a peak coinciding with the deviatoric stress maximum, then gradually decreases with further shear. Crucially, this evolution is path-dependent: the average contact force network strength increases approximately 20% more during unloading in the minor principal stress direction compared to unloading in the major principal stress direction. This quantitative analysis of force chain degradation provides a mechanistic explanation for the observed strain softening, highlighting the dominant role of the unloading stress path. In contrast, loose specimens, which initially lack an obvious force chain network, show negligible microstructural evolution during unloading.