Multiscale and Multiphysics Behavior of Heterogenous Quasi-Brittle - - PowerPoint PPT Presentation

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Multiscale and Multiphysics Behavior of Heterogenous Quasi-Brittle - - PowerPoint PPT Presentation

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Multiscale and Multiphysics Behavior of Heterogenous Quasi-Brittle Materials: From Concrete to Rock. Gianluca Cusatis Special Lecture Tokyo Institute of Technology July 25, 2018 1 / 49 July-2018 :: Gianluca Cusatis Acknowledgments

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Multiscale and Multiphysics Behavior of Heterogenous Quasi-Brittle Materials: From Concrete to Rock.

Gianluca Cusatis

Special Lecture Tokyo Institute of Technology July 25, 2018

1 / 49 July-2018 :: Gianluca Cusatis

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Acknowledgments

Collaborators Weixin Li, Northwestern University, Evanston (IL), USA. Lin Wan & Roman Wendner, BOKU, Wien, Austria. Financial Support Institute for Sustainability and Energy at Northwestern (ISEN) SEGIM Center

2 / 49 July-2018 :: Gianluca Cusatis

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Presentation Outline

1

Civil Engineering at Northwestern University

2

Motivation For Shale Research

3

Fluid Transport in Fractured Shale

4

Martian Concrete

5

Conclusions

3 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Northwestern University

4 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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US News and World Report Ranking (2013)

1 Princeton University 2 Harvard University 3 Yale University 4 Columbia University 5 Stanford University 6 University of Chicago 7 Duke University 8 Massachusetts Institute of Technology 9 University of Pennsylvania 10 California Institute of Technology 11 Dartmouth College 12 Johns Hopkins University 13 Northwestern University 14 Brown University 15 Washington University 5 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Northwestern Multiple Campuses and Schools

Judd A. and Marjorie Weinberg College of Arts and Sciences (1851) School of Communication (1878) School of Continuing Studies (1933) School of Education and Social Policy (1926) Robert R. McCormick School of Engineering and Applied Science (1909) Graduate School (1910) Medill School of Journalism, Media, Integrated Marketing Communications (1921) School of Law (1859) J.L. Kellogg School of Management (1908) Feinberg School of Medicine (1859) Henry and Leigh Bienen School of Music (1895) Northwestern University in Qatar (2008)

6 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Robert R. McCormick School of Engineering and Applied Science (McC)

Faculty: 180 Undergraduates: 1,700 undergraduate students Graduate Students: 581 (MS) and 762 (PhD) Biomedical Engineering Chemical and Biological Engineering Civil and Environmental Engineering Electrical Engineering and Computer Science Engineering Sciences and Applied Mathematics Industrial Engineering and Management Sciences Materials Science and Engineering Mechanical Engineering

7 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Research in Civil and Environmental Engineering

8 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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SEGIM Center

Launched in Summer 2014 13 Affiliated Faculty Currently PIs are funded with grants from NSF, DOE, NRC, ONR, and ERDC SEGIM seminar series featuring weekly presentations from external and internal speakers Internal Reports on newly completed research projects are periodically published on the center website and self-archived on http://arxiv.org/

9 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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SEGIM Center Mission

Our Mission is to establish partnerships with industry, federal agencies, and national laboratories to develop the scientific knowledge and technological know-how for the sustainable engineering of geological and infrastructure materials. Our vision is to lead the technical community to future engineering practices that advance the development of natural energy resources and the growth of the built environment in a way that is economically viable, environmentally safe, and benefits the society on the whole.

10 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Sustainability and Resilience

Sustainability and Resilience are the two key characteristics of modern

  • infrastructures. Scientists, engineers, educators and policy makers

have the responsibility to ensure that our infrastructures are SURE – both SUstainable and REsilient. Inftrastructure aging Infrastructure growth Preservation of hystorical heritage

11 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Some of my current research thrusts

Experimental and Computational Characterization of Ultra-High Performance, Fiber Reinforced Concrete (NSF, ERDC) Dynamic Behavior of Concrete (ERDC) Alkali Silica Reaction (ASR) Deterioration of Concrete Structures: Experiments and Multiscale Computations (DHS, NRC) Multiscale and Multiphysiscs Modeling of Concrete (NSF, NRC) Multiscale Modeling of Sandstone and Shale (ISEN) Experimental and Computational Characterization of Waterless Martian Concrete (unfunded)

12 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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My research group today

1 Post-Doc (Weixin Li) 5 PhD Students (Chenyang, Madura, Faysal, Matthew, Elham) 3 MS Students (Xin, Boqin,Tianjiao) 4 Visiting Students (Michele, Lin, Zhongfeng, Jiaojiao) Some of my research group alumni: Roozbeh Rezakhani Post-Doc at EPFL; Mohammed Alnaggar, Assistant professor at RPI; Jovanca Smith, Assistant Professor at the University of West Indies; Marco Salviato, Assistant Professor at the University of Washington; Congrui Jin, Assistant Professor at SUNY-Binghamton.

13 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Granular and Porous Structure of Quasi-Brittle Materials

Heterogeneity and fluid/gas filled porosity are key featured shared by many quasi-brittle materials.

14 / 49 Civil Engineering at Northwestern University July-2018 :: Gianluca Cusatis

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Presentation Outline

1

Civil Engineering at Northwestern University

2

Motivation For Shale Research

3

Fluid Transport in Fractured Shale

4

Martian Concrete

5

Conclusions

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Energy Sources in the US

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Natural Gas Production in the US

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Fracking

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Shale is Important for Other Applications Too

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Multiscale Character of Black Shale

Key aspects Poro-mechanical behavior at multiple length scales Material anisotropy & heterogeneity Influence of anisotropy on elastic and inelastic behavior Effect of fracture on permeability

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Scale 6 :: Geometry and Kinematic at Grain level

Geometry 3D cell Discrete compatibility

y y y y I J y y y c c I J m

IJ

t

JI

m J t

2 1 1 2 I J I J C

I (b) (c)

IJ JI

Facet Strains ǫα = 1 r uC · eα; uC = 1 r

  • UJ + ΘJ × cJ − UI − ΘI × cI

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Scale 6 :: Constitutive Equations and Equilibrium

Constitutive Laws Fracture and cohesion due to tension and tension-shear ε =

  • ε2

N + α(ε2 M + ε2 L), t =

  • t2

N + (tM + tL)2/α

tN = (t/ε)εN; tM = α(t/ε)εM; tL = α(t/ε)εL. σbt = σ0(ω) exp [−H0(ω)ε − ε0(ω)/σ0(ω)]; Compaction and pore collapse from compression −σbc(εD, εV ) ≤ tN ≤ 0; σbc = σc0 + −εV − εc0Hc(rDV ); Frictional Behavior ˙ tM = ET ( ˙ εM − ˙ εp

M) ˙

tL = ET ( ˙ εL − ˙ εp

L);

ϕ =

  • t2

M + t2 L − σbs(tN)

σbs = σs + (µ0 − µ∞)σN0[1 − exp(tN/σN0)] − µ∞tN Translational and rotational equilibrium equations of each particle M I

u ¨

UI − V Ib0 =

FI AtIJ ;

M I

θ ¨

Θ

I = FI A(cI × tIJ + mIJ)

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Scale 6 :: Material Microscale Anisotropy

Source of Anisotropy

1

Preferred orientation of clay minerals

2

Oriented distribution of organic matter Transverse Isotropy The LDPM model parameters are formulated as function of the angle θ The selected functional form of the variation with orientation is f(θ) =

  • a sin2 θ + cos2 θ

−1

15 30 45 60 75 90 20 40 60 80 θ EN

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Scale 6 :: Material Microscale Anisotropy, Cont.

Elastic behavior EN(θ) = EN0

  • βN sin2 θ + cos2 θ

−1 ET (θ) = ET 0

  • βT sin2 θ + cos2 θ

−1 α(θ) = ET (θ) EN(θ) = α0 βN sin2 θ + cos2 θ βT sin2 θ + cos2 θ Fracture and cohesion σt(θ) = σt0(βt sin2 θ + cos2 θ)−1 σs(θ) = σs0(βs sin2 θ + cos2 θ)−1 Gt = ltσ2

t

2EN = ltσ2

t0

  • βt sin2 θ + cos2 θ

−2 2EN0

  • βN sin2 θ + cos2 θ

−1 Frictional behavior µ0 = µ00(βµ sin2 θ + cos2 θ)−1

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Scale 5 :: Modeling of Bedding Planes

Sandstone with cross-bedding Layered oil well shale (Woodford) Marcellus shale from

  • utcrop

Eagle Ford shale Results from changing depositional environment Leads to layering of properties: different texture, porosity, and strength at different layers

25 / 49 Motivation For Shale Research July-2018 :: Gianluca Cusatis

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Scale 5 :: Modeling of Bedding Planes

Symbol dmax dmin nF s tm (units) (mm) (mm) (mm) (mm) Value 0.05 0.03 0.5 1 0.08

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Scale 5 :: Modeling of Bedding Planes, Cont.

Elastic behavior Eb

N = CNEN; Eb T = CT ET

αb = Eb

T

Eb

N

= CT CN α; 0 < CN, CT < 1 CT = CN for simplicity Fracture and cohesion σb

t = CNtσt; σb s = CT sσs

Gb

t = C2 Nt

CN Gt; 0 < CNt, CT s < 1 Frictional behavior µb

0 = Cµµ0

0 < Cµ < 1

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Elastic Anisotropy

Table: Elastic constants for Boryeong shale E (GPa) E′ (GPa) ν ν′ G′ (GPa) 34.00 16.55 0.14 0.15 11.20 CN EN1 (GPa) EN0 (GPa) βN ET 1 (GPa) ET 0 (GPa) βT 0.1 82.3 44.4 0.54 35.1 8.0 0.23 0.2 94.1 21.6 0.23 34.0 19.2 0.56 0.4 94.0 22.5 0.24 31.7 4.0 0.13 0.6 100.3 23.3 0.23 36.3 3.7 0.10

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Uniaxial Compression Tests

Unconfined compressive strength Minimum strength occurred at 0 deg ≤ θ ≤ 75 deg The reduced strength is caused by the effect of

  • lamination. When the failure plane coincided with

the plane of lamination, the failure occurs at a lower stress level

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Uniaxial Compression Tests, Cont.

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Splitting (Brazilian) Tensile Tests

15 30 45 60 75 90 5 10 15 20 Anisotropy Angle,θ (°) Brazilian tensile strength, ft(θ) (MPa)

Indirect tensile strength Tensile strength decreases as the anisotropy angle increases At angles 0 deg ≤ θ ≤ 15 deg, the failure mode is purely tensile splitting failure At angles 30 deg ≤ θ ≤ 75 deg, the failure mode is a mixed tensile/shear failure mode

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Splitting (Brazilian) Tensile Tests, Cont.

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Presentation Outline

1

Civil Engineering at Northwestern University

2

Motivation For Shale Research

3

Fluid Transport in Fractured Shale

4

Martian Concrete

5

Conclusions

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Dual Lattice Model :: Discretization

2D Discretization 3D Discretization

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Dual Lattice Model :: Discretization

2D Discretization 3D Discretization

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Dual Lattice Model :: Formulation

Diffusion Equation ¯ Cj 3 f1 f2

  • ˙

pj + ¯ Dj 1 −1 −1 1

  • pj +

¯ Sj 3 f1 f2

  • = 0

¯ Cj = ALρ0

f

1

M + cf Ac A

  • ;

¯ Dj = A

Lρf

  • κ

µf + 3

i=1 liw3 Ni

12µf A

  • ¯

Sj = AL

  • q − ρf
  • b˙

ǫ +

˙ Ac A

  • ; f1 = L1/L; f2 = L2/L

35 / 49 Fluid Transport in Fractured Shale July-2018 :: Gianluca Cusatis

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Dual Lattice Model :: Formulation, Cont.

Effective Facet Normal Stress ¯ σN = σN + bp σN + bp = f(εN, εT , ...) where b is Biot’s coefficient Explicit Two-way Coupling Scheme

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Confined Shear Test

References: Carey, J. W. et al. 2015, Journal of Unconventional Oil and Gas Resources Frash, L. P. et al. 2016, Journal of Geophysical Research: Solid Earth

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Confined Shear Test, Cont.

Test Setup: Asymmetric shear loading is applied through two offset, semi-circular disks; tests are controlled by displacement under 3.4 MPa confinement. A constant differential pressure (water) across the core is applied; upstream and downstream flow rates are recorded. Average permeability is calculated through Darcy‘s law.

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Confined Shear Test, Cont.

Results: Permeability increases significantly after the stress reaches the peak. The effective permeability is measured for two nominal axial strains equal to 5/1000 and 7/1000. The measured permeability values stabilized at 6 and 8 mD for the two strain levels. These values are ahigher than the experimental ones (1 to 2 mD) due to the effect of sample size.

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Confined Shear Test, Cont.

Size Effect: Because of damage localization, the fracture width h is indepenent of specimen size. Q0 = (κ0πr2)/µL Qf = (2κfπrh)/µL Qtot = Q0 + Qf = (κeffπr2)/µL κeff = κ0 + κf(2h/πr)

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Confined Shear Test, Cont.

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Presentation Outline

1

Civil Engineering at Northwestern University

2

Motivation For Shale Research

3

Fluid Transport in Fractured Shale

4

Martian Concrete

5

Conclusions

42 / 49 Martian Concrete July-2018 :: Gianluca Cusatis

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Extreterrestrial Infrastructure Materials

43 / 49 Martian Concrete July-2018 :: Gianluca Cusatis

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Sulfur Concrete with Simulated Martian Soil

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Experiment – Unconfined Compression

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3D Printing on MARS for Human Settlements

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Presentation Outline

1

Civil Engineering at Northwestern University

2

Motivation For Shale Research

3

Fluid Transport in Fractured Shale

4

Martian Concrete

5

Conclusions

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Conclusions

LDPM is a robust and reliable method to simulate solids with granular internal structure. It captures effectively certain fundamental aspects of material heterogeneity especially relevant to fracture and failure. It can be extended to simulate material anisotropy in both the elastic and inelastic regime. It can be coupled easily to discrete diffusion equations for the simulation of a large variety of multiphysical phenomena. It has been used for concrete, shale and several other quasi-brittle materials. Experimental data at different length scales are needed to improve the theoretical formulation and rigorous calibration/validation of the model. All LDPM-based algorithms are currently implemented in the commercially available MARS software – www.mars.es3inc.com

48 / 49 Conclusions July-2018 :: Gianluca Cusatis

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Thank You ! g-cusatis@northwestern.edu

Free time with my students and collaborators x

49 / 49 Conclusions July-2018 :: Gianluca Cusatis