A new anisotropic poroelasticity model to describe damage accumulation during cyclic triaxial loading of rock

Vladimir Lyakhovsky* (Corresponding Author), Ivan Panteleev, Eyal Shalev, John Browning, Thomas Mitchell, David Healy, Philip G. Meredith

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
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Crustal rocks undergo repeated cycles of stress over time. In complex tectonic
environments where stresses may evolve both spatially and temporally, such as
volcanoes or active fault zones, these rocks may experience not only cyclic loading and unloading, but also rotation and/or reorientation of stresses. In such situations, any resulting crack distributions form sequentially and may therefore be highly anisotropic. Thus, the tectonic history of the crust as recorded in deformed rocks may include evidence for complex stress paths, encompassing different magnitudes and orientations. Despite this, the ways in which variations in principal stresses influence the evolution of anisotropic crack distributions remain poorly constrained. In this work, we build on the previous non-linear anisotropic damage rheology model by presenting a newly developed poroelastic rheological model which accounts for both coupled anisotropic damage and porosity evolution. The new model shares the main features of previously developed anisotropic damage and scalar poroelastic damage models, including the ability to simulate the entire yield curve through a single formulation. In the new model, the yield condition is defined in terms of invariants of the strain tensor, and so the new formulation operates with directional yield conditions (different values for each principal direction) depending on the damage tensor and triaxial loading conditions. This allows us to discern evolving yield conditions for each principal stress direction and fit the measured amounts of accumulated damage from previous loading cycles. Coupling between anisotropic damage and anisotropic compaction along with the damage-dependent yield condition produces a reasonable fit to the experimentally obtained stress-strain curves. Furthermore, the simulated time-dependent cumulative damage is well correlated with experimentally observed acoustic emissions during cyclic loading in different directions. As such, we are able to recreate many of the features of the experimentally observed directional 3D Kaiser ‘damage memory’ effect.
Original languageEnglish
Pages (from-to)179-201
Number of pages22
JournalGeophysical Journal International
Issue number1
Early online date11 Feb 2022
Publication statusPublished - Jul 2022

Bibliographical note

The paper benefited from useful comments by two referees, Manolis Veveakis
and Klaus Regenauer-Lieb, and the editor, Alexis Maineult. The contributions by
Lyakhovsky and Shalev was supported by grant from the Israel Science Foundation, ISF 363/20. The contributions by Browning, Meredith, Healy and Mitchell were supported by UKRI NERC awards NE/N003063/1, NE/N002938/1, NE/T007826/1, NE/T00780X/1. The contributions by Browning was also supported by FONDECYT
grant number 11190143. The contribution by Panteleev was supported by Russian Science Foundation (project N 19-77-30008).

Data Availability Statement

Experimental data may be obtained from J.B. (e-mail: jbrowning@ing.puc.cl).


  • Mechanics
  • theory and modelling
  • Elasticity and anelasticity
  • creep and deformation
  • fracture and flow


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