[Paper Review] A constitutive model for brittle granular materials considering the competition between breakage and dilation

Mehmet B. Cil, Ryan Hurley+1 more|arXiv (Cornell University)|Feb 20, 2019

Geotechnical Engineering and Soil Mechanics28 references4 citations

TL;DR

This paper presents a constitutive model for brittle granular materials that captures the competition between particle breakage and dilation during shearing. By integrating breakage mechanics with strain softening and critical state behavior, the model successfully reproduces experimental stress-dilatancy-breakage relationships in sands under varying confinement, including peak strength reduction and volumetric transition from dilatancy to compaction.

ABSTRACT

A constitutive model is presented for brittle granular materials based on a recent reformulation of the breakage mechanics theory. Compared with previous breakage mechanics-based models, the proposed model is improved to capture strain softening towards the critical state following the peak stress observed in dense specimens under shearing, and simultaneous evolution of breakage and dilation. Considering the competition between dilation and particle breakage allows the model to capture breakage-induced reduction in dilatancy and peak strength as confining pressure increases. The influence of the model parameters on the overall material response is described through a detailed calibration procedure based on a benchmark experimental dataset. Comparison of the results of drained triaxial compression experiments on two sands with the predictions of the model indicates that the enriched model successfully captures strain softening in dilatant specimens, the shearing-driven evolution of stress-strain behavior towards the critical state at different confinement levels, the transition from dilatant to compactive volumetric response, and the evolution of particle grading due to distributed breakage events. The proposed framework is capable of qualitatively reproducing the experimentally observed stress-dilatancy-breakage relationship in brittle granular materials in the low pressure regime.

Motivation & Objective

• To develop a constitutive model that captures the interplay between particle breakage and dilation in brittle granular materials.
• To address limitations in prior breakage mechanics models by incorporating strain softening and critical state behavior.
• To reproduce experimentally observed transitions from dilatant to compactive volumetric response under increasing confinement.
• To calibrate the model using a benchmark triaxial dataset for accurate prediction of stress-strain and grading evolution.
• To qualitatively reproduce the stress-dilatancy-breakage relationship in low-pressure regimes.

Proposed method

• The model is based on a reformulated breakage mechanics theory to describe particle size evolution under shear.
• It incorporates a strain-softening law that captures post-peak stress reduction in dense specimens.
• Dilation is modeled as a function of shear strain and breakage evolution, reflecting the competition between volume expansion and particle fragmentation.
• The model couples breakage and dilatancy through a degradation function that reduces dilatancy with increasing breakage.
• A calibration procedure is applied to a benchmark drained triaxial dataset for two sands to determine key parameters.
• The framework is validated against experimental data on stress-strain response, volumetric strain, and particle size distribution changes.

Experimental results

Research questions

• RQ1 How does the competition between particle breakage and dilation influence the peak strength and post-peak softening in brittle granular materials?
• RQ2 To what extent can a constitutive model capture the transition from dilatant to compactive behavior under increasing confining pressure?
• RQ3 How does breakage evolution affect the stress-dilatancy relationship in granular materials during shearing?
• RQ4 Can the model reproduce the strain-softening response towards the critical state observed in dense sand specimens?
• RQ5 How do model parameters influence the evolution of particle grading and volumetric response?

Key findings

• The model successfully captures strain softening in dilatant specimens under drained triaxial compression, matching experimental post-peak behavior.
• The transition from dilatant to compactive volumetric response is accurately reproduced across different confinement levels.
• Peak strength decreases with increasing confining pressure due to breakage-induced reduction in dilatancy, consistent with experimental observations.
• The model predicts the evolution of particle size distribution due to distributed breakage events, reflecting real material degradation.
• The stress-dilatancy-breakage relationship is qualitatively reproduced in the low-pressure regime, validating the framework's physical consistency.
• The calibration procedure effectively tunes model parameters to match experimental datasets, demonstrating predictive capability for complex granular behavior.