A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking

Heider, Yousef; Sun, WaiChing

doi:10.1016/j.cma.2019.112647

Title: A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking

Abstract

This work introduces a unified mathematical framework to replicate both desiccation-induced and hydraulic fracturing in low-permeable unsaturated porous materials observed in experiments. The unsaturated porous medium is considered as a three-phase solid–liquid–gas effective medium of which each constituent occupies a fraction of the representative elementary volume. As such, an energy-minimization-based phase-field model (PFM) is formulated along with the Biot’s poroelasticity theory to replicate the sub-critical crack growth in the brittle regime. Unlike hydraulic fracturing where the excess pore liquid pressure plays an important role at the onset and propagation of cracks, desiccation cracks are mainly driven by deformation induced by water retention. Therefore, the wettability of the solid skeleton may affect the evolution of the capillary pressure (suction) and change the path-dependent responses of the porous media. This air–water–solid interaction may either hinder or enhance the cracking occurrence. This difference of capillary effect on crack growth during wetting and drying is replicated by introducing retention-sensitive degradation mechanisms in our phase field fracture approach. To replicate the hydraulic behaviors of the pore space inside the host matrix and that of the cracks, the path-dependent changes of the intrinsic permeability due to crack growth and porosity changes are introduced to model themore »« less

Authors:

Heider, Yousef ^[1];

^[2]

Columbia Univ., New York, NY (United States); RWTH Aachen Univ. (Germany)
Columbia Univ., New York, NY (United States)

Publication Date:: Wed Oct 30 00:00:00 EDT 2019

Research Org.:: Columbia Univ., New York, NY (United States)

Sponsoring Org.:: USDOE Office of Nuclear Energy (NE); National Science Foundation (NSF); US Army Research Office (ARO); US Air Force Office of Scientific Research (AFOSR)

OSTI Identifier:: 1801239

Alternate Identifier(s):: OSTI ID: 1580796

Grant/Contract Number:: NE0008534; W911NF-18-2-0306; FA9550-17-1-0169; CMMI-1846875

Resource Type:: Accepted Manuscript

Journal Name:: Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:: Journal Volume: 359; Journal Issue: C; Journal ID: ISSN 0045-7825

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; engineering; mathematics; mechanics; unsaturated porous media; desiccation cracking; hydraulic fracturing; phase field fracture

Citation Formats


                    Heider, Yousef, and Sun, WaiChing. A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking.  United States: N. p., 2019. 
Web.  doi:10.1016/j.cma.2019.112647.

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                    Heider, Yousef, & Sun, WaiChing. A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking.  United States.  https://doi.org/10.1016/j.cma.2019.112647

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                    Heider, Yousef, and Sun, WaiChing. Wed .  
"A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking".  United States.  https://doi.org/10.1016/j.cma.2019.112647.  https://www.osti.gov/servlets/purl/1801239.

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@article{osti_1801239,

  title        = {A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking},

  author       = {Heider, Yousef and Sun, WaiChing},

  abstractNote = {This work introduces a unified mathematical framework to replicate both desiccation-induced and hydraulic fracturing in low-permeable unsaturated porous materials observed in experiments. The unsaturated porous medium is considered as a three-phase solid–liquid–gas effective medium of which each constituent occupies a fraction of the representative elementary volume. As such, an energy-minimization-based phase-field model (PFM) is formulated along with the Biot’s poroelasticity theory to replicate the sub-critical crack growth in the brittle regime. Unlike hydraulic fracturing where the excess pore liquid pressure plays an important role at the onset and propagation of cracks, desiccation cracks are mainly driven by deformation induced by water retention. Therefore, the wettability of the solid skeleton may affect the evolution of the capillary pressure (suction) and change the path-dependent responses of the porous media. This air–water–solid interaction may either hinder or enhance the cracking occurrence. This difference of capillary effect on crack growth during wetting and drying is replicated by introducing retention-sensitive degradation mechanisms in our phase field fracture approach. To replicate the hydraulic behaviors of the pore space inside the host matrix and that of the cracks, the path-dependent changes of the intrinsic permeability due to crack growth and porosity changes are introduced to model the flow conduit in open and closed cracks. Numerical examples of drying-induced and hydraulic fracturing demonstrate the capability of the proposed model to capture different fracture patterns, which qualitatively agrees with the fracture mechanisms of related experiments documented in the literature.},

  doi          = {10.1016/j.cma.2019.112647},

  journal      = {Computer Methods in Applied Mechanics and Engineering},

  number       = C,

  volume       = 359,

  place        = {United States},

  year         = {Wed Oct 30 00:00:00 EDT 2019},

  month        = {Wed Oct 30 00:00:00 EDT 2019}

}

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Title: A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking

Abstract

Citation Formats

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A Phase-Field Method for Propagating Fluid-Filled Fractures Coupled to a Surrounding Porous Medium
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Deformation and localization analysis of partially saturated soil
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Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids
journal, September 2015

Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approaches
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Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions: PHASE FIELD MODEL FLUID-DRIVEN FRACTURE
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Mathematical framework for unsaturated flow in the finite deformation range: FRAMEWORK FOR UNSATURATED FLOW IN THE FINITE DEFORMATION RANGE
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A continuum phase field model for fracture
journal, December 2010

Diffusive fluid‐driven brittle fracture in saturated porous media
journal, December 2018

A Variational Approach to the Numerical Simulation of Hydraulic Fracturing
conference, April 2013

Determination of fracture storativity in hard rocks using high-pressure injection testing
journal, October 1998

A microstructurally based effective stress for unsaturated soils
journal, December 2010

A quasi-static phase-field approach to pressurized fractures
journal, April 2015

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journal, April 2019

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journal, January 1980

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journal, August 1998

An updated Lagrangian LBM–DEM–FEM coupling model for dual-permeability fissured porous media with embedded discontinuities
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A phase-field approach embedded in the Theory of Porous Media for the description of dynamic hydraulic fracturing, Part II: The crack-opening indicator
journal, November 2018

Optimal approximations by piecewise smooth functions and associated variational problems
journal, July 1989

Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
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Damage, gradient of damage and principle of virtual power
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Inf–sup conditions for twofold saddle point problems
journal, March 2011

Dynamics of unsaturated poroelastic solids at finite strain: DYNAMICS OF UNSATURATED POROELASTIC SOLIDS AT FINITE STRAIN
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Permeability due to the Increase of Damage in Concrete: From Diffuse to Localized Damage Distributions
journal, September 2009

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journal, November 2015

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journal, December 2016

Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two-dimensional variational approach
journal, March 2013

Partitioned analysis of coupled mechanical systems
journal, March 2001

Fracture of a model cohesive granular material
journal, January 2017

Mechanics of Hydraulic Fractures
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Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures
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Desiccation cracking of soils
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On the effective stress in unsaturated porous continua with double porosity
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A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
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Free Energy of a Nonuniform System. I. Interfacial Free Energy
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A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain
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A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
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The Variational Approach to Fracture
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A numerical manifold method model for analyzing fully coupled hydro-mechanical processes in porous rock masses with discrete fractures
journal, April 2017

A formulation for an unsaturated porous medium undergoing large inelastic strains
journal, March 2002

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journal, April 2000

A stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain: STABILIZED FEM FOR THERMO-HYDRO-MECHANICS AT FINITE STRAIN
journal, April 2015

Formation of drying crack patterns in soils: a deterministic approach
journal, August 2012

Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media
journal, June 2016

Hydraulic fracturing and its peculiarities
journal, May 2014

Automatic integration of Euler-Lagrange equations with constraints
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A two-scale approach for fluid flow in fractured porous media
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Desiccation and cracking behavior of three compacted landfill liner soils
journal, June 2000

Soil desiccation cracks as a suction–contraction process
journal, December 2017

A survey of selected coupled multifield problems in computational mechanics
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Preferential Mode of gas invasion in sediments: Grain-scale mechanistic model of coupled multiphase fluid flow and sediment mechanics
journal, January 2009

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Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model
journal, June 2016

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journal, May 2017

Modelling the deterioration of the near surface caused by drying induced cracking
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Minimization principles for the coupled problem of Darcy–Biot-type fluid transport in porous media linked to phase field modeling of fracture
journal, September 2015

A review on phase-field models of brittle fracture and a new fast hybrid formulation
journal, December 2014

Cracking and damage from crystallization in pores: Coupled chemo-hydro-mechanics and phase-field modeling
journal, June 2018

Computational thermo-hydro-mechanics for multiphase freezing and thawing porous media in the finite deformation range
journal, May 2017

Phase-field modeling of proppant-filled fractures in a poroelastic medium
journal, December 2016

Porous media fracturing dynamics: stepwise crack advancement and fluid pressure oscillations
journal, February 2018

Laboratory experiments on desiccation cracking of thin soil layers
journal, December 2006

Phase-field modeling of hydraulic fracture
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