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Nov3,4 2005 NSF/JHU Workshop on Nonlinear Modeling of GeotechnicalProblems: From Theory to Practice

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Toward Mesh-independent Finite Element Modelingof Three-dimensional Localized Failure Mechanismsin Saturated and Partially-Saturated Geomaterials

Richard A. RegueiroDepartment of Civil, Environmental, and Architectural Engineering

University of Colorado at Boulder

Overall research objective: Develop a framework for predicting 3Dlocalized failure mechanisms in saturated and partially-saturatedgeomaterials (soil and rock) via well-coordinated experiments,computational modeling, and simulation of field case studies.


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Challenges• Modeling transition to post-bifurcation constitutive response in a physically-

based, well-posed manner:– is it satisfactory to derive a bifurcation criterion from loss of ellipticity for a local

inelastic constitutive model with material parameters derived fromhomogeneously deforming cylindrical biaxial test specimens?

– can generalized continuum inelasticity models (i.e., micromorphic, micropolar,…) model this transition in a physically-based, well-posed manner?

• Extending computational failure mechanics to 3D is NOT trivial:– development of embedded strong and weak discontinuity finite elements and

meshfree approaches– are simulations independent of spatial discretization?

• Failure model parameter determination and separate model validation• Maturing the failure modeling framework such that a commercial

computational code will implement it and make it accessible to thepractitioner:

– developing in an opensource, research code (tahoe.ca.sandia.gov), to enable thistechnology transfer: 2D and 3D finite elements, meshfree (RKPM), cohesivesurface elements, multifield solvers for coupled-physics (thermo-mechanical,mixtures, …), transient dynamics, parallel computation


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Motivation: 3D localized failure in braced excavation


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Soils that exhibit localized deformation (Atkinson 1993)


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Plane strain localized failure in dense sand(Vardoulakis et al. 1978, 1981)


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Problem: mesh-dependence associated with classical, strain-softening, local plasticity model


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Problem: mesh-dependence associated with classical, strain-softening, local plasticity model


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Problem: ill-posed PDE as a result of classical, strain-softening plasticity (Sandler &Wright 1984, Read & Hegemier 1984, Needleman 1988, Loret & Prevost 1990, Sluys & de Borst 1992)


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Kinematics of localized deformation at finite strain


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One Solution: embedded discontinuity element and post-bifurcation constitutivemodel: plane strain localization in Gosford Sandstone

(Ord et al. 1991, Regueiro & Borja 2001)


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Embedded discontinuity element and post-bifurcation constitutive model:plane strain localization in slope (Regueiro & Borja 2001)


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Embedded discontinuity element and post-bifurcation constitutive model:plane strain localization in slope (Regueiro & Borja 2001)


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Various approaches to numerical implementation of post-bifurcationconstitutive models and localized deformation modes

• Embedded Discontinuity finite Element (EDE) Method: (Simo et al. 1993, Oliver et al. 2004,Regueiro et al. 2005) Model directly strong and weak discontinuities. Advantages: computationallyefficient and nearly mesh-independent; account for large deformations along discontinuities eventhough the element is not split to accommodate the localized deformation. Disadvantages: Jumpdisplacements and shear bands are not continuous across element interfaces, and stress cannot beresolved at a crack tip.

• Meshfree Method: Model directly strong (Klein et al. 2001) and weak (Li et al. 2001)discontinuities. Advantages: Allows for large deformation of nodes, avoiding potential remeshingof an EDE method upon large shearing. Disadvantages: It is relatively more expensivecomputationally than a FE method.

• Cohesive Surface finite Element (CSE) Method: (Ortiz et a. 1999, Pandolfi et al. 2000, Ruiz et al.2000, Klein et al. 2001) Use CSEs along continuum element faces to model strong discontinuities.Advantages: No bifurcation criterion needed. Disadvantages: If CSE is elasto-plastic, simulationsare mesh-dependent with regard to refinement and alignment. Using rigid-plastic CSEs alleviatesthis problem (Klein et al. 2003), yet some sensitivity to mesh alignment still remains. It cannotmodel weak discontinuities.

• eXtended Finite Element Method (X-FEM): Involves embedding linear elastic, analytical solutionat crack tip into X-FEM (Moes et al. 2002). Advantages: It models crack displacements ascontinuous across element interfaces, and can resolve stress at a crack tip. Disadvantages: It is notclear whether X-FEM can incorporate arbitrary post-bifurcation, inelastic traction-displacementmodels along the strong discontinuity. It is more computationally expensive because it requiresadditional global degrees of freedom as the crack propagates through the mesh. The extension to3D requires level sets (Gravouil et al. 2002) and potentially more computation time than using anEDE.


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Enhanced strain hexahedral and tetrahedral finite elements with embeddedstrong discontinuity (Regueiro et al. 2005)


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3D corner shear of Gosford sandstone (Regueiro et al. 2005)


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Specific steps that can be taken to promote the use of advancednonlinear numerical methods in geotechnical engineering practice

1. Education, Education, Education: soil mechanics, continuum mechanics,constitutive modeling, computational mechanics; application togeotechnical engineering problems

2. Realize we all (researchers, practitioners, policy makers, decisionmakers, etc.) have the same overall goal: to prevent catastrophicgeotechnical engineering failures such as the levee failures in NewOrleans as a result of Hurricane Katrina, and to do so in a cost-effectivemanner

3. Collaborate with geotechnical engineering practitioners as much aspossible: learn about their problems, and in turn educate the practitionerson advanced numerical modeling

4. Be realistic about progress and expectations of nonlinear numericalmodeling research and development

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