Sensitivity analysis for parameter identification in quasi-static poroelasticity
This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and test...
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| Vydané v: | International journal for numerical and analytical methods in geomechanics Ročník 29; číslo 2; s. 163 - 185 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Chichester, UK
John Wiley & Sons, Ltd
01.02.2005
Wiley |
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| ISSN: | 0363-9061, 1096-9853 |
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| Abstract | This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd. |
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| AbstractList | This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi-static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd. |
| Author | Lecampion, Brice Constantinescu, Andrei |
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| Cites_doi | 10.1080/01495738708927014 10.1080/174159794088027573 10.1002/nag.136 10.2514/3.10949 10.1016/S0021-9290(98)00161-4 10.1002/nme.1620200206 10.1063/1.1712886 10.1063/1.1721956 10.1016/0307-904X(87)90144-2 10.1016/0956-0521(91)90053-8 |
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| Keywords | Sensitivity analysis Rock mechanics Theoretical study Soil mechanics Inverse problem Formulation Poroelasticity direct differentiation method Example inverse problems Parameter Numerical simulation adjoint state method Differentiation parameter identification poroelasticity sensitivity analysis |
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| References | Wang HF. Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press: Princeton, NJ, 2000. Arora JS, Cardoso JB. Variational principle for shape sensitivity analysis. AIAA Journal 1992; 30:538-547. Cheng AHD, Ligget JA. Boundary integral equation method for linear poroelasticity with applications to soil consolidation. International Journal for Numerical Methods in Engineering 1984; 20:255-278. Dems K, Mróz Z. Variational approach to sensitivity analysis in thermoelasticity. Journal of Thermal Stresses 1987; 10:283-306. Coussy O. Poromechanics. Wiley: New York, 2004. Nocedal J, Wright SJ. Numerical Optimization. Springer: Berlin, 2002. Biot MA. General theory of three-dimensional consolidation. Journal of Applied Physics 1941; 12:155-164. Lions JL. Contrôle optimal des équations aux dérivées partielles. Dunod: Paris, 1968 (in French). Cowin SC. Bone poroelasticity. Journal of Biomechanics 1999; 32:217-238. Vidal CA, Lee HS, Haber RB. The consistent tangent operator for design sensitivity analysis of history-dependent response. Computing Systems in Engineering 1991; 2(5/6):509-523. Mahnken R, Steinmann P. A finite element algorithm for parameter identification of material models for fluid saturated porous media. International Journal for Numerical and Analytical Methods in Geomechanics 2001; 25:415-434. Tortorelli DA, Michaleris P. Design sensitivity analysis: overview and review. Inverse Problems in Engineering 1994; 1:71-103. Zienkiewicz OC. The Finite Element Method. Mc-Graw Hill: New York, 1977. Gill PE, Murray W, Wright MH. Practical Optimization. Academic Press: New York, 1982. Lecampion B, Constantinescu A, Malinsky L. Identification of poroelastic constants of tight rocks from laboratory tests. International Journal of Geomechanics 2004, submitted. Biot MA. Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics 1955; 26:182-185. Cheng AHD, Predeleanu M. Transient boundary element formulation in poroelasticity. Applied Mathematical Modelling 1987; 11:285-290. Detournay E, Berchenko I. Thermoporoelastic experiments at url. International Journal of Rock Mechanics and Mining Sciences 2004; 12:155-164. Predeleanu M. Reciprocal theorem in the consolidation theory of porous media. Anal. Univ. Bucuresti, Seria Stiitele Naturii, Matematica, Mecanica 1968; 17:75-79. 1987; 11 1955; 26 1991; 2 1984; 20 1987; 10 1968; 17 2000 1941; 12 2004; 12 1987 1999; 32 2004 1982 1992 2003 2002 1994; 1 1993; 2 2001; 25 1968 1977 1992; 30 Nocedal (10.1002/nag.409-BIB24) 2002 Bonnet (10.1002/nag.409-BIB9) 1992 Cowin (10.1002/nag.409-BIB3) 1999; 32 Lecampion (10.1002/nag.409-BIB25) 2002 Cheng (10.1002/nag.409-BIB12) 1984; 20 Tortorelli (10.1002/nag.409-BIB7) 1994; 1 Detournay (10.1002/nag.409-BIB1) 1993; 2 Detournay (10.1002/nag.409-BIB5) 2004; 12 Biot (10.1002/nag.409-BIB15) 1941; 12 Wang (10.1002/nag.409-BIB2) 2000 Predeleanu (10.1002/nag.409-BIB21) 1968; 17 Constantinescu (10.1002/nag.409-BIB6) 2004 Biot (10.1002/nag.409-BIB16) 1955; 26 Dems (10.1002/nag.409-BIB10) 1987; 10 Vidal (10.1002/nag.409-BIB20) 1991; 2 Lecampion (10.1002/nag.409-BIB4) 2004 Mahnken (10.1002/nag.409-BIB8) 2001; 25 Curran (10.1002/nag.409-BIB14) 1987 Gill (10.1002/nag.409-BIB23) 1982 Cheng (10.1002/nag.409-BIB13) 1987; 11 Lions (10.1002/nag.409-BIB22) 1968 Zienkiewicz (10.1002/nag.409-BIB18) 1977 Coussy (10.1002/nag.409-BIB11) 2004 CEA (10.1002/nag.409-BIB17) 2003 Arora (10.1002/nag.409-BIB19) 1992; 30 |
| References_xml | – reference: Lecampion B, Constantinescu A, Malinsky L. Identification of poroelastic constants of tight rocks from laboratory tests. International Journal of Geomechanics 2004, submitted. – reference: Coussy O. Poromechanics. Wiley: New York, 2004. – reference: Wang HF. Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press: Princeton, NJ, 2000. – reference: Nocedal J, Wright SJ. Numerical Optimization. Springer: Berlin, 2002. – reference: Cowin SC. Bone poroelasticity. Journal of Biomechanics 1999; 32:217-238. – reference: Dems K, Mróz Z. Variational approach to sensitivity analysis in thermoelasticity. Journal of Thermal Stresses 1987; 10:283-306. – reference: Mahnken R, Steinmann P. A finite element algorithm for parameter identification of material models for fluid saturated porous media. International Journal for Numerical and Analytical Methods in Geomechanics 2001; 25:415-434. – reference: Cheng AHD, Ligget JA. Boundary integral equation method for linear poroelasticity with applications to soil consolidation. International Journal for Numerical Methods in Engineering 1984; 20:255-278. – reference: Arora JS, Cardoso JB. Variational principle for shape sensitivity analysis. AIAA Journal 1992; 30:538-547. – reference: Predeleanu M. Reciprocal theorem in the consolidation theory of porous media. Anal. Univ. Bucuresti, Seria Stiitele Naturii, Matematica, Mecanica 1968; 17:75-79. – reference: Tortorelli DA, Michaleris P. Design sensitivity analysis: overview and review. Inverse Problems in Engineering 1994; 1:71-103. – reference: Cheng AHD, Predeleanu M. Transient boundary element formulation in poroelasticity. Applied Mathematical Modelling 1987; 11:285-290. – reference: Biot MA. Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics 1955; 26:182-185. – reference: Gill PE, Murray W, Wright MH. Practical Optimization. Academic Press: New York, 1982. – reference: Biot MA. General theory of three-dimensional consolidation. Journal of Applied Physics 1941; 12:155-164. – reference: Zienkiewicz OC. The Finite Element Method. Mc-Graw Hill: New York, 1977. – reference: Lions JL. Contrôle optimal des équations aux dérivées partielles. Dunod: Paris, 1968 (in French). – reference: Vidal CA, Lee HS, Haber RB. The consistent tangent operator for design sensitivity analysis of history-dependent response. Computing Systems in Engineering 1991; 2(5/6):509-523. – reference: Detournay E, Berchenko I. Thermoporoelastic experiments at url. International Journal of Rock Mechanics and Mining Sciences 2004; 12:155-164. – year: 1982 – volume: 2 start-page: 509 issue: 5/6 year: 1991 end-page: 523 article-title: The consistent tangent operator for design sensitivity analysis of history‐dependent response publication-title: Computing Systems in Engineering – start-page: 73 year: 1987 end-page: 78 – volume: 17 start-page: 75 year: 1968 end-page: 79 article-title: Reciprocal theorem in the consolidation theory of porous media publication-title: Anal. Univ. Bucuresti, Seria Stiitele Naturii, Matematica, Mecanica – volume: 12 start-page: 155 year: 2004 end-page: 164 article-title: Thermoporoelastic experiments at url publication-title: International Journal of Rock Mechanics and Mining Sciences – volume: 2 year: 1993 – year: 1968 – year: 2004 article-title: Identification of poroelastic constants of tight rocks from laboratory tests publication-title: International Journal of Geomechanics – year: 2002 – volume: 1 start-page: 71 year: 1994 end-page: 103 article-title: Design sensitivity analysis: overview and review publication-title: Inverse Problems in Engineering – volume: 20 start-page: 255 year: 1984 end-page: 278 article-title: Boundary integral equation method for linear poroelasticity with applications to soil consolidation publication-title: International Journal for Numerical Methods in Engineering – volume: 11 start-page: 285 year: 1987 end-page: 290 article-title: Transient boundary element formulation in poroelasticity publication-title: Applied Mathematical Modelling – volume: 26 start-page: 182 year: 1955 end-page: 185 article-title: Theory of elasticity and consolidation for a porous anisotropic solid publication-title: Journal of Applied Physics – volume: 30 start-page: 538 year: 1992 end-page: 547 article-title: Variational principle for shape sensitivity analysis publication-title: AIAA Journal – year: 2004 – volume: 25 start-page: 415 year: 2001 end-page: 434 article-title: A finite element algorithm for parameter identification of material models for fluid saturated porous media publication-title: International Journal for Numerical and Analytical Methods in Geomechanics – year: 2003 – year: 2000 – year: 1977 – year: 1992 – volume: 10 start-page: 283 year: 1987 end-page: 306 article-title: Variational approach to sensitivity analysis in thermoelasticity publication-title: Journal of Thermal Stresses – volume: 32 start-page: 217 year: 1999 end-page: 238 article-title: Bone poroelasticity publication-title: Journal of Biomechanics – volume: 12 start-page: 155 year: 1941 end-page: 164 article-title: General theory of three‐dimensional consolidation publication-title: Journal of Applied Physics – volume: 10 start-page: 283 year: 1987 ident: 10.1002/nag.409-BIB10 publication-title: Journal of Thermal Stresses doi: 10.1080/01495738708927014 – volume: 2 volume-title: Fundamentals of Poroelasticity, Comprehensive Rocks Engineering year: 1993 ident: 10.1002/nag.409-BIB1 – volume: 12 start-page: 155 year: 2004 ident: 10.1002/nag.409-BIB5 publication-title: International Journal of Rock Mechanics and Mining Sciences – volume: 1 start-page: 71 year: 1994 ident: 10.1002/nag.409-BIB7 publication-title: Inverse Problems in Engineering doi: 10.1080/174159794088027573 – volume: 25 start-page: 415 year: 2001 ident: 10.1002/nag.409-BIB8 publication-title: International Journal for Numerical and Analytical Methods in Geomechanics doi: 10.1002/nag.136 – volume: 30 start-page: 538 year: 1992 ident: 10.1002/nag.409-BIB19 publication-title: AIAA Journal doi: 10.2514/3.10949 – year: 2003 ident: 10.1002/nag.409-BIB17 – year: 2002 ident: 10.1002/nag.409-BIB25 – volume-title: Practical Optimization year: 1982 ident: 10.1002/nag.409-BIB23 – volume-title: Poromechanics year: 2004 ident: 10.1002/nag.409-BIB11 – volume: 32 start-page: 217 year: 1999 ident: 10.1002/nag.409-BIB3 publication-title: Journal of Biomechanics doi: 10.1016/S0021-9290(98)00161-4 – year: 2004 ident: 10.1002/nag.409-BIB4 publication-title: International Journal of Geomechanics – volume-title: A Global Computational Approach in Engineering Problems: Identification and Fatigue year: 2004 ident: 10.1002/nag.409-BIB6 – volume: 20 start-page: 255 year: 1984 ident: 10.1002/nag.409-BIB12 publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.1620200206 – volume-title: Numerical Optimization year: 2002 ident: 10.1002/nag.409-BIB24 – volume: 12 start-page: 155 year: 1941 ident: 10.1002/nag.409-BIB15 publication-title: Journal of Applied Physics doi: 10.1063/1.1712886 – volume-title: Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology year: 2000 ident: 10.1002/nag.409-BIB2 – volume-title: Contrôle optimal des équations aux dérivées partielles year: 1968 ident: 10.1002/nag.409-BIB22 – volume: 17 start-page: 75 year: 1968 ident: 10.1002/nag.409-BIB21 publication-title: Anal. Univ. Bucuresti, Seria Stiitele Naturii, Matematica, Mecanica – volume-title: The Finite Element Method year: 1977 ident: 10.1002/nag.409-BIB18 – volume: 26 start-page: 182 year: 1955 ident: 10.1002/nag.409-BIB16 publication-title: Journal of Applied Physics doi: 10.1063/1.1721956 – year: 1987 ident: 10.1002/nag.409-BIB14 – volume-title: IUTAM Symposium on Inverse Problems in Engineering Mechanics year: 1992 ident: 10.1002/nag.409-BIB9 – volume: 11 start-page: 285 year: 1987 ident: 10.1002/nag.409-BIB13 publication-title: Applied Mathematical Modelling doi: 10.1016/0307-904X(87)90144-2 – volume: 2 start-page: 509 year: 1991 ident: 10.1002/nag.409-BIB20 publication-title: Computing Systems in Engineering doi: 10.1016/0956-0521(91)90053-8 |
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| SubjectTerms | adjoint state method Applied sciences Buildings. Public works Computation methods. Tables. Charts direct differentiation method Engineering Sciences Exact sciences and technology Geophysics Geotechnics inverse problems Mechanics parameter identification Physics poroelasticity sensitivity analysis Soil mechanics. Rocks mechanics Solid mechanics Structural analysis. Stresses |
| Title | Sensitivity analysis for parameter identification in quasi-static poroelasticity |
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