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Preparation Knowledge of Material Properties

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Computational Geomechanics and Hydraulic Structures

Part of the book series: Springer Tracts in Civil Engineering ((SPRTRCIENG))

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Abstract

Termed as “rock-like materials” related to the subject of geomechanics in this book, rocks and concrete are mostly consumed in hydraulic structures whose properties are dependent on their micro-or/and meso-structures but usually described by phenomenological (conceptual) models on the macro-scale level. For the benefit of beginning students, different types of basic material properties related to hydraulics (permeability), thermodynamics (thermal stress), and mechanics (deformation and strength) are discussed in this chapter, with special reference to why and how the aggregate, cement paste, interfacial transition zone (ITZ), discontinuity, testing method, etc., affect these properties. The constitutive laws (relations, equations) related to the fields of permeability/temperature/mechanics ranging from linear to nonlinear until partial coupling of TM and HM, are concisely summarized. It is notable that the basic properties and constitutive laws elaborated in this chapter on one hand, presents preparation knowledge of rock-like materials and on the other hand, provides basic parametric inputs for the engineering cases as well as important constituents for the formulation of governing equations in the hereinafter chapters.

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References

  • Adhikary D, Dyskin A. A continuum model of layered rock masses with non-associative joint plasticity. Int J Numer Anal Meth Geomech. 1998;22(4):245–61.

    Article  MATH  Google Scholar 

  • Akanuma H. The significance of the composition of excavated iron fragments taken from Stratum III at the site of Kaman-Kalehöyük, Turkey. Anatolian Archaeol Stud. 2005;14:147–58.

    Google Scholar 

  • Alexandrovskii SV. Plane and reinforced concrete structures calculation under thermal and hygral effects. Moskow: Stroiizolat; 1966 (in Russian).

    Google Scholar 

  • Al-Raoush R, Papadopoulos A. Representative elementary volume analysis of porous media using X-ray computed tomography. Powder Technol. 2010;200(1–2):69–77.

    Article  Google Scholar 

  • Amadei B. Rock anisotropy and the theory of stress measurements. Berlin: Springer; 1983.

    Book  MATH  Google Scholar 

  • Amadei B, Goodman RE. A 3-D Constitutive relation for fractured rock masses. In: Selvadurai APS, editor. Proceedings of international symposium, mechanical behaviour structured media. Ottawa, Canada. Amsterdam: Elsevier Scientific Publ Co; 1981. p. 249–68.

    Google Scholar 

  • American Concrete Institute. (ACI 318-08) Building code for structural concrete. Detroit: ACI; 2008.

    Google Scholar 

  • Amitrano D, Helmstetter A. Brittle creep, damage, and time to failure in rocks. J Geophys Res Solid Earth. 2006;111(B11):1–17.

    Article  Google Scholar 

  • Anderson OL, Grew PC. Stress corrosion theory of crack propagation with applications to geophysics. Rev Geophys. 1977;15(1):77–104.

    Article  Google Scholar 

  • Armstrong P, Frederick C. A mathematical representation of the multiaxial Bauschinger effect. GEGB report RD/B/N731; 1966.

    Google Scholar 

  • Arutiunian NH, Kolmanovskii VB. Creep theory of inhomogeneous bodies. Moskow: Nauka; 1983 (in Russian).

    Google Scholar 

  • Atkinson BK. Subcritical crack growth in geological materials. J Geophys Res Solid Earth. 1984;89(B6):4077–114.

    Article  Google Scholar 

  • Auricchio F, Taylor RL. Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity. Int J Plast. 1995;11(1):65–98.

    Article  MATH  Google Scholar 

  • Auvray C, Homand F, Sorgi C. The aging of gypsum in underground mines. Eng Geol. 2004;74(3):183–96.

    Article  Google Scholar 

  • Baecher GB, Lanney NA, Einstein HH. Statistical description of rock properties and sampling. In: Wang FD, Clark GB, editors. Proceedings of 18th US symposium rock mechanics. Colorado: Colorado School of Mines Press; 1977. p. 5c1–8.

    Google Scholar 

  • Barla G. Squeezing rocks in tunnels. ISRM News J. 1995;2(3/4):44–9.

    Google Scholar 

  • Barla G, Bonini M, Debernardi D. Time dependent deformations in squeezing tunnels. Int J Geoeng Case Histories. 2010;2(1):819–24.

    Google Scholar 

  • Barton NR. A model study of rock-joint deformation. Int J Rock Mech Min Sci. 1972;9(5):579–82.

    Article  Google Scholar 

  • Barton NR. Some new Q-value correlations to assist in site characterisation and tunnel design. Int J Rock Mech Min Sci. 2002;39(2):185–216.

    Article  Google Scholar 

  • Barton NR, Bandis S, Bakhtar K. Strength, deformation and conductivity coupling of rock joints. Int J Rock Mech Min Sci Geomech Abstr. 1985;22(3):121–40.

    Article  Google Scholar 

  • Batra RC, Kim CH. Effect of viscoplastic flow rules on the initiation and growth of shear bands at high strain rates. J Mech Phys Solids. 1990;38(6):859–74.

    Article  Google Scholar 

  • Bažant ZP. Endochronic inelasticity and incremental plasticity. Int J Solids Struct. 1978;14(9):691–714.

    Article  MATH  Google Scholar 

  • Bažant ZP. Mathematical models for creep and shrinkage of concrete. In: Bažant ZP, Wittman FH, editors. Creep and shrinkage in concrete structure. New York: Wiley; 1982.

    Google Scholar 

  • Bažant ZP, editor. Mathematical modeling of creep and shrinkage of concrete. RILEM Committee TC 69 report. Chichester and New York: Wiley; 1988.

    Google Scholar 

  • Bažant ZP, Bhat PD. Endochronic theory of inelasticity and failure of concrete. J Eng Mech Div ASCE. 1976;102(EM4):701–22.

    Google Scholar 

  • Bažant ZP, Krizek RJ. Endochronic constitutive law for liquefaction of sand. J Eng Mech Div ASCE. 1976;102(EM2):225–38.

    Google Scholar 

  • Bažant ZP, Prasannan S. Solidification theory for concrete creep. J Eng Mech. 1989;115(8):1691–725.

    Article  Google Scholar 

  • Bažant ZP, Belytschko T, Chang TP. Continuum theory for strain-softening. J Eng Mech ASCE. 1984;110(12):1666–92.

    Article  Google Scholar 

  • Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Chichester: Wiley; 2000.

    MATH  Google Scholar 

  • Betten J. Creep mechanics, 3rd ed. Berlin: Springer; 2008.

    Google Scholar 

  • Bieniawski ZT. Fracture dynamics of rock. Int J Fract Mech. 1968a;4(4):415–30.

    Article  Google Scholar 

  • Bieniawski ZT. The effect of specimen size on compressive strength of coal. Int J Rock Mech Min Sci. 1968b;5(4):325–35.

    Article  Google Scholar 

  • Bieniawski ZT. Determining rock mass deformability: experience from case histories. Int J Rock Mech Min Sci Geomech Abstr. 1978;15(5):237–47.

    Article  Google Scholar 

  • Bingham EC. Fluidity and plasticity. New York: McGraw-Hill; 1922.

    Google Scholar 

  • Birch AF, Clark H. The thermal conductivity of rocks and its dependence upon temperature and composition. Am J Sci. 1940;238(8):529–58.

    Article  Google Scholar 

  • Bizjak KF, Zupančič A. Rheological investigation for the landslide Slano Blato near Ajdovscina (Slovenia). Geologija. 2007;50(1):121–9.

    Article  Google Scholar 

  • Boland JN, Hobbs BE. Microfracturing processes in experimentally deformed peridotite. Int J Rock Mech Min Sci. 1973;10(6):623–6.

    Article  Google Scholar 

  • Borgesson L, Chijimatsu M, Fujita T, Nguyen TS, Rutqvist J, Jing L. Thermo-hydro-mechanical characterization of a bentonite-based buffer material by laboratory tests and numerical back analysis. Int J Rock Mech Min Sci. 2001;38(1):95–104.

    Article  Google Scholar 

  • Boukharov GN, Chanda MW, Boukharov NG. The three processes of brittle crystalline rock creep. Int J Rock Mech Min Sci Geomech Abstr. 1995;32(4):325–35.

    Article  Google Scholar 

  • Bourne SJ. Contrast of elastic properties between rock layers as a mechanism for the initiation and orientation of tensile failure under uniform remote compression. J Geophys Res. 2003;108(B8):2395.

    Article  Google Scholar 

  • Boussinesq J. Mémoire sur l’influence des frottements dans les mouvements réguliers des fluides. Journal de Mathématiques Pures et Appliquées. 1868;13(2e série):377–424 (in French).

    Google Scholar 

  • Brace WF, Walsh JB, Frangos WT. Permeability of granite under high pressure. J Geophys Res. 1968;73(6):2225–36.

    Article  Google Scholar 

  • Brantut N, Heap MJ, Meredith PG, Baud P. Time-dependent cracking and brittle creep in crustal rocks: a review. J Struct Geol. 2013;52(7):17–43.

    Article  Google Scholar 

  • Brebbia CA, editor. Finite element systems (A handbook). Berlin: Springer; 1985.

    Google Scholar 

  • Bridgman PW. Studies in large plastic flow and fracture: with special emphasis on the effects of hydrostatic pressure. New York: McGrawHill Book Company Inc; 1952.

    MATH  Google Scholar 

  • Brooks JJ. 30-year creep and shrinkage of concrete. Mag Concrete Res. 2005;57(9):545–56.

    Article  Google Scholar 

  • Brown ET, editor. Rock characterization, testing and monitoring: ISRM suggested methods. Oxford: Pergamon Press; 1981.

    Google Scholar 

  • Brown ET. Fifty years of the ISRM and associated progress in rock mechanics. In: Qian Q, Zhou XY, editors. Proceedings of 12th ISRM congress. Beijing: ISRM; 2011. p. 29–45.

    Chapter  Google Scholar 

  • Budiansky B, O’Connel RJ. Elastic moduli of a cracked solid. Int J Solids Struct. 1976;12(2):81–97.

    Article  MATH  Google Scholar 

  • Burgisser A, Chevalier L, Gardner JE, Castro JM. The percolation threshold and permeability evolution of ascending magmas. Earth Planet Sci Lett. 2017;470:37–47.

    Article  Google Scholar 

  • Cai M, Kaiser PK, Uno H. Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci. 2004;41(1):3–19.

    Article  Google Scholar 

  • Carslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed. Oxford: Oxford University Press; 1985.

    Google Scholar 

  • Casagrande A. First Rankine Lecture—control of seepage through foundations and abutment of dam. Géotechnique. 1961;11(3):161–82.

    Article  Google Scholar 

  • Cedergren HR. Seepage, drainage and flownets, 3rd ed. New York: Wiley; 1989.

    Google Scholar 

  • Cervera M, Codina R, Galindo M. On the computational efficiency and implementation of block-iterative algorithms for non-linear coupled problems. Eng Comput. 1996;13(6):4–30.

    Article  MATH  Google Scholar 

  • Chaboche JL. On some modifications of kinematic hardening to improve the description of ratchetting effects. Int J Plast. 1991;7(7):661–78.

    Article  Google Scholar 

  • Chen SH. Hydraulic structures. Berlin: Springer; 2015.

    Book  Google Scholar 

  • Chen WF, Baladi GY. Soil plasticity: theory and implementation. Amsterdam: Elsevier; 1985.

    MATH  Google Scholar 

  • Chen G, Chugh Y. Estimation of in situ visco-elastic parameter of weak floor strata by plate-loading tests. J Geotech Geol Eng. 1996;14(2):151–67.

    Article  Google Scholar 

  • Chen WF, Drucker DC. Bearing capacity of concrete blocks or rock. J Eng Mech ASCE. 1969;95(EM4):955–78.

    Google Scholar 

  • Chen SH, Pande GN. Rheological model and finite element analysis of jointed rock masses reinforced by passive, fully-grouted bolts. Int J Rock Mech Min Sci Geomech Abstr. 1994;31(3):273–7.

    Article  Google Scholar 

  • Chen WF, Saleeb AF. Constitutive equations for engineering materials. 1: Elasticity and modeling, Revised ed. Amsterdam: Elsevier; 1994.

    Google Scholar 

  • Chen Z, Schreyer HL. Formulation and computational aspects of plasticity and damage models with application to quasi-brittle materials. Contractor report, SAND95–0329. California: Sandia National Laboratories; 1995.

    Google Scholar 

  • Chen WF, Zhang H. Structural plasticity: theory, problems and CAE software. New York: Springer; 1991.

    Book  MATH  Google Scholar 

  • Chen SH, Wang HR, Xiong WL. Study of the seepage characteristics of joint. J Wuhan Univ Hydraul Electr Eng (WUHEE). 1989;22(1):51–60 (in Chinese).

    Google Scholar 

  • Chen G, Chenevert ME, Sharma MM, Yu M. A study of wellbore stability in shales including poroelastic, chemical, and thermal effects. J Petrol Sci Eng. 2003;38(3–4):167–76.

    Article  Google Scholar 

  • Chen SH, Qin WX, Xu Q. Composite element method and application of trace simulation for strain localization bands. Chin J Rock Mech Eng. 2007;26(6):1116–22 (in Chinese).

    Google Scholar 

  • Chen SH, Feng XM, Shahrour I. Numerical estimation of REV and permeability tensor for fractured rock masses by composite element method. Int J Numer Anal Meth Geomech. 2008;32(12):1459–77.

    Article  MATH  Google Scholar 

  • Chen SH, Zhang GX, Zhu YM. Thermal stresses and temperature control of concrete. In: Zhou JP, Dang LC, editors. Handbook of hydraulic structure design, vol. 5. Concrete dams (Chapter 6). Beijing: China Water Power Press; 2011 (in Chinese).

    Google Scholar 

  • Chiles JP. Fractal and geostatistical methods for modelling a fracture network. Math Geol. 1988;20(6):631–54.

    Article  Google Scholar 

  • Chow CL, Lu TJ. On evolution laws of anisotropic damage. Eng Fract Mech. 1989;34(3):679–701.

    Article  Google Scholar 

  • Commission on Standardization of Laboratory and Field Tests. Suggested methods for determining shear strength (Document No. 1). Lisbon: ISRM; 1974.

    Google Scholar 

  • Counto UJ. The effect of the elastic modulus of the aggregate on the elastic modulus, creep and creep recovery of concrete. Mag Concr Res. 1964;16(48):129–38.

    Article  Google Scholar 

  • Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mech Mater. 1985;4(2):137–47.

    Article  Google Scholar 

  • Cristescu ND, Gioda G, editors. Visco-plastic behaviour of geomaterials. Wien: Springer; 1994.

    Google Scholar 

  • Cristescu ND, Suliciu I. Mechanics of plastix solids—viscoplasticity. Hague: Martinus Nijhoff Publishers; 1982.

    MATH  Google Scholar 

  • Cruden DE. Describing the size of discontinuities. Int J Rock Mech Min Sci Geomech Abstr. 1977;14(3):133–7.

    Article  Google Scholar 

  • Danilova GN, Bogdanov SN. Determination of thermophysical properties of concretes and gravels used in the construction of concrete dams. Hydrotechnical Constr. 1967;1(4):326–9.

    Article  Google Scholar 

  • Das S, Scholz CH. Theory of time-dependent rupture in the Earth. J Geophys Res. 1981;86(B7):6039–51.

    Article  Google Scholar 

  • Davis HE. Autogenous volume change of concrete. Proc ASTM. 1940;40:1103–10.

    Google Scholar 

  • Davis RO, Selvadurai APS. Plasticity and geotechnics. Cambridge: Cambridge University Press; 2002.

    Book  Google Scholar 

  • de Borst R. Integration of plasticity equations for singular yield functions. Comput Struct. 1987;26(5):823–9.

    Article  MATH  Google Scholar 

  • de Borst R, Pankaj P, Bićanić N. A note on singularity indicators for Mohr-Coulomb type yield criteria. Comput Struct. 1991;39(1–2):219–20.

    Google Scholar 

  • de Souza Neto EA, Perić D, Owen DRJ. Computational methods for plasticity: theory and applications. New York: Wiley; 2009.

    Google Scholar 

  • Dershowitz WS. Rock joint systems. Ph.D. thesis. Boston: Massachusetts Institute of Technology; 1984.

    Google Scholar 

  • Desai CS, Gioda G, editors. Numerical methods and constitutive modeling in geomechanics. Wien: Springer; 1990.

    MATH  Google Scholar 

  • Desai CS, Toth J. Disturbed state constitutive modeling based on stress–strain and nondestructive behavior. Int J Solids Struct. 1996;33(11):1619–50.

    Article  Google Scholar 

  • Desai CS, Drumm EC, Zaman MM. Thin layer element for interfaces and joints. J Geotech Eng ASCE. 1985;111(6):793–815.

    Article  Google Scholar 

  • Detournay E, Cheng AHD. Poroelastic response of a borehole in a nonhydrostatic stress field. Int J Rock Mech Min Sci. 1988;25(3):171–82.

    Article  Google Scholar 

  • Doltsinis IS, editor. Advances in computational nonlinear mechanics (CISM). Wien: Springer; 1989.

    MATH  Google Scholar 

  • Dragon A, Mróz Z. A model for plastic creep of rock-like materials accounting for the kinetics of fracture. Int J Rock Mech Min Sci. 1979;16(4):235–59.

    Article  Google Scholar 

  • Drucker DC, Prager W. Soil mechanics and plastic analysis for limit design. Q Appl Math. 1952;10(2):157–65.

    Article  MathSciNet  MATH  Google Scholar 

  • Dunne FPE, Petrinic N. Introduction to computational plasticity. Oxford: Oxford University Press; 2005.

    MATH  Google Scholar 

  • Dunnicliff J. Geotechnicul instrumentation for monitoring field performance. Chichester: Wiley; 1988.

    Google Scholar 

  • Dusseault MB, Fordham CJ. Time-dependent behavior of rocks. In: Hudson JA, editor. Comprehensive rock engineering: principles, practice, and projects, vol. 3. Oxford: Pergamon Press; 1993. p. 119–49.

    Chapter  Google Scholar 

  • Einstein HH, Nelson RA, Bruhn RW, Hirschfield RC. Model studies of jointed rock behaviour. In: Proceedings of 11th US symposium on rock mechanics (Chapter 6). Berkeley: Port City Press; 1969.

    Google Scholar 

  • Eisenberg MA, Phillips A. A theory of plasticity with non-coincident yield and loading surfaces. Acta Mech. 1971;11(3):247–60.

    Article  MATH  Google Scholar 

  • Erlicher S, Point N. Endochronic theory, non-linear kinematic hardening rule and generalized plasticity: a new interpretation based on generalized normality assumption. Int J Solids Struct. 2006;43(14–15):4175–200.

    Article  MathSciNet  MATH  Google Scholar 

  • European Committee for Standardization. (Eurocode 2) Design of concrete structures. Brussels: ECS; 2004.

    Google Scholar 

  • Evesque P. Fluctuations, correlations and representative elementary volume (REV) in granular materials. Poudres Grains. 2000;11:6–17.

    Google Scholar 

  • Farmer IW. Engineering properties of rocks. London: E & FN Spon Ltd; 1968.

    Google Scholar 

  • Fernandez G, Moon J. Excavation-induced hydraulic conductivity reduction around a tunnel—Part 1: guideline for estimate of ground water inflow rate. Tunn Undergr Space Technol. 2010;25(5):560–6.

    Article  Google Scholar 

  • François D, Pineau A, Zaoui A. Mechanical behaviour of materials. Volume II: viscoplasticity, damage, fracture and contact mechanics. Dordrecht: Kluwer Academic Publishers; 1993.

    Google Scholar 

  • Frémond M. Non-smooth thermomechanics. Berlin: Springer; 2002.

    Book  MATH  Google Scholar 

  • Gale JE. The effects of fracture type (induced vs. natural) on the stress–fracture closure permeability relationships. In: Goodman RE, Heuze FE, editors. Proceedings of 23rd US symposium on rock mechanics. Rotterdam: AA Balkema; 1982. p. 290–8.

    Google Scholar 

  • Gangi AF. Variation of whole and fractured porous rock permeability with confining pressure. Int J Rock Mech Min Sci Geomech Abstr. 1978;15(5):249–57.

    Article  Google Scholar 

  • Ge XR, Jiang Y, Lu YD. Testing study of fatigue deformation law of rock under cyclic loading. Chin J Rock Mech Eng. 2003;22(10):1581–5 (in Chinese).

    Google Scholar 

  • Gerrard CM. Equivalent elastic moduli of a rock mass consisting of orthorhombic layers. Int J Rock Mech Min Sci Geomech Abstr. 1982a;19(1):9–14.

    Article  Google Scholar 

  • Gerrard CM. Elastic models of rock masses having one, two and three sets of joints. Int J Rock Mech Min Sci Geomech Abstr. 1982b;19(1):15–23.

    Article  Google Scholar 

  • Ghaboussi J, Gioda G. On the time-dependent effects in advancing tunnels. Int J Numer Anal Meth Geomech. 1977;1(3):249–69.

    Article  Google Scholar 

  • Gitman IM, Askes H, Sluys LJ. Representative volume: existence and size determination. Eng Fract Mech. 2007;74(16):2518–34.

    Article  Google Scholar 

  • Golzé AR, editor. Handbook of dam engineering. New York: Van Nostrand Reinhold Company; 1977.

    Google Scholar 

  • Gonze P. Techniques de calcul utilisées en congé lation des terrains. In: La thermomé canique des roches. vol. 16. BRGM; 1988 (in French).

    Google Scholar 

  • Goodman RE. Introduction to rock mechanics, 2nd ed. New York: Wiley; 1989.

    Google Scholar 

  • Goodman RE, Dubois J. Duplication of dilatancy in analysis of jointed rocks. J Soil Mech Found Div ASCE. 1972;98(SM4):399–422.

    Google Scholar 

  • Goodman RE, Taylor R, Brekke TL. A model for the mechanics of jointed rock. J Soil Mech Found Div ASCE. 1968;94(SM3):637–59.

    Google Scholar 

  • Gran JD, Rundle JB, Turcotte DL. A possible mechanism for aftershocks: time dependent stress relaxation in a slider-block model. Geophys J Int. 2012;191(2):459–66.

    Article  Google Scholar 

  • Griffiths DV, Gioda G. Advanced numerical applications and plasticity in geomechanics. Wien: Springer; 2000.

    Google Scholar 

  • Gruden DN. Single-increment creep experiments on rock under uniaxial compression. Int J Rock Mech Min Sci. 1971;8(2):127–42.

    Article  Google Scholar 

  • Gurson AL. Continuum theory of ductile rupture by void nucleation and growth. I. Yield criteria and flow rules for porous ductile media. J Eng Mater Technol. 1977;99(1):2–15.

    Article  Google Scholar 

  • Guz IA, Soutis C. A 3-D stability theory applied to layered rocks undergoing finite deformations in biaxial compression. Eur J Mech A Solids. 2001;20(1):139–53.

    Article  MATH  Google Scholar 

  • Haimson B. Micromechanisms of borehole instability leading to breakouts in rocks. Int J Rock Mech Min Sci. 2007;44(2):157–73.

    Article  Google Scholar 

  • Hakami E, Larsson E. Aperture measurement and flow experiments on a single natural fracture. Int J Rock Mech Min Sci Geomech Abstr. 1990;33(5):395–404.

    Google Scholar 

  • Hall EO. Yield point phenomena in metals and alloys. New York: Plenum Press; 1970.

    Book  Google Scholar 

  • Halphen B, Nguyen QS. Sur les matériaux standards généralisés. Journal de Mécanique. 1975;14(1):39–63 (in French).

    MathSciNet  MATH  Google Scholar 

  • Han W, Reddy BD. Plasticity: mathematical theory and numerical analysis. New York: Springer; 1999.

    MATH  Google Scholar 

  • Harris D. Plasticity models for soils, granular and jointed rock materials. J Mech Phys Solids. 1992;40(2):273–90.

    Article  MathSciNet  MATH  Google Scholar 

  • Harza LF. The significance of pore pressure in hydraulic structures. Trans ASCE. 1949;114(1):193–214.

    Google Scholar 

  • Hashin Z. Analysis of composite materials—a survey. J Appl Mech. 1983;50(3):481–505.

    Article  MATH  Google Scholar 

  • He J, Chen SH. A revised solution of equivalent permeability tensor for discontinuous fractures. J Hydrodyn Ser B. 2012;24(5):711–7.

    Article  Google Scholar 

  • Hecker SS. Experimental studies of yield phenomena in biaxially loaded metals. In: Stricklin JA, Saczalski KH, editors. Constitutive equations in viscoplasticity: computational and engineering aspects. AMD, vol. 20. New York: ASME; 1976. p. 1–33.

    Google Scholar 

  • Hellmich Ch, Ulm FJ, Mang HA. Consistent linearisation in finite element analysis of coupled chemo-thermal problems with exo- or endothermal reactions. Comput Mech. 1999;24(4):238–44.

    Article  MATH  Google Scholar 

  • Hill R. Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids. 1963;11(5):357–72.

    Article  MATH  Google Scholar 

  • Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J Mech Phys Solids. 1967;15(2):79–95.

    Article  Google Scholar 

  • Hill R. The mathematical theory of plasticity. Oxford: Oxford University Press; 1998.

    MATH  Google Scholar 

  • Hoek E, Bray JW. Rock slope engineering, 3rd ed. London: Institution of Mining and Metallurgy; 1981.

    Google Scholar 

  • Hoek E, Diederichs MS. Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci. 2006;43(2):203–15.

    Article  Google Scholar 

  • Hoff NJ, editor. Creep in structures: IUTAM colloquium held at Stanford University (1962). Berlin: Springer; 2012.

    Google Scholar 

  • Hsieh PA, Neuman SP. Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media. 1: Theory. Water Resour Res. 1985;21(11):1655–65.

    Article  Google Scholar 

  • Hsieh PA, Neuman SP, Stiles GK, Simpson ES. Field determination of the three dimensional hydraulic conductivity tensor of anisotropic media. 2: Methodology and application to fractured rocks. Water Resour Res. 1985;21(11):1667–76.

    Article  Google Scholar 

  • Hu J, Chen SH. Air element method for modeling the drainage hole in seepage analysis. Rock Soil Mech. 2003;24(2):281–7 (in Chinese).

    Google Scholar 

  • Hu FX, Shi G, Shi YJ. Constitutive model for full-range elasto-plastic behavior of structural steels with yield plateau: calibration and validation. Eng Struct. 2016;118(7):210–27.

    Article  Google Scholar 

  • Hudson JA, Harrison JP. Engineering rock mechanics—an introduction to the principles. Oxford: Elsevier Science Ltd; 1997.

    Google Scholar 

  • Hudson JA, Priest SD. Discontinuity frequency in rock masses. Int J Rock Mech Min Sci Geomech Abstr. 1983;20(2):73–89.

    Article  Google Scholar 

  • Hudson JA, Stephansson O, Andersson J, Jing L. Coupled T-H-M issues relating to radioactive waste repository design and performance. Int J Rock Mech Min Sci. 2001;38(1):143–61.

    Article  Google Scholar 

  • Huet C. Coupled size and boundary-condition effects in viscoelastic heterogeneous and composite bodies. Mech Mater. 1999;31(12):787–829.

    Article  Google Scholar 

  • Humpheson C, Naylor DJ. The importance of the form of the failure criterion. C/R/243/75. Swansea: University of Wales; 1975.

    Google Scholar 

  • ICOLD. The specification and quality control of concrete for dams (Bulletin 136). Paris: ICOLD; 2009.

    Google Scholar 

  • Inoue T, Kitagawa H, Shima S, editors. Computational plasticity. London: Elsevier; 1990.

    Google Scholar 

  • Irgens F. Continuum mechanics. Berlin: Springer; 2008.

    Google Scholar 

  • Iwai K. Fundamental studies of the fluid flow through a single fracture. Ph.D. thesis. Berkeley: University of California; 1976.

    Google Scholar 

  • Jaeger JC, Cook NGW, Zimmerman R. Fundamentals of rock mechanics, 4th ed. MA: Wiley-Blackwell; 2007.

    Google Scholar 

  • Jia LJ, Kuwamura H. Ductile fracture simulation of structural steels under monotonic tension. J Struct Eng ASCE. 2014;140(5):472–82.

    Article  Google Scholar 

  • Jirásek M, Bažant ZP. Inelastic analysis of structures. London: Wiley; 2001.

    Google Scholar 

  • John KW. Strength and deformability of regularly jointed rocks (Chapter 5). Berkeley: Port City Press; 1969.

    Google Scholar 

  • Ju JW. On energy-based coupled elastoplastic damage theories: constitutive modelling and computational aspects. Int J Solids Struct. 1989;25(7):803–33.

    Article  MATH  Google Scholar 

  • Ju JW, Lee X. Micromechanical damage models for brittle solid. Part I: tensile loadings and II: compressive loading. J Eng Mech ASCE. 1991;117(7):1495–536.

    Google Scholar 

  • Kacewicz M. Model-free estimation of fracture apertures with neural networks. Math Geol. 1994;26(8):985–94.

    Article  Google Scholar 

  • Kachanov LM. Time of the rupture process under creep conditions. Izvestiya Akademii Nauk SSSR Otdelenie Tekniches. 1958;8:26–31.

    Google Scholar 

  • Kachanov LM. A microcrack model of rock inelasticity. Part I: frictional sliding on microcracks. Mech Mater. 1982a;1(1):19–27.

    Article  Google Scholar 

  • Kachanov LM. A microcrack model of rock inelasticity. Part II: propagation of microcracks. Mech Mater. 1982b;1(1):29–41.

    Article  Google Scholar 

  • Kachanov LM. A microcrack model of rock inelasticity. Part III: time-dependent growth of microcracks. Mech Mater. 1982c;1(2):123–9.

    Article  Google Scholar 

  • Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct. 2003;40(13–14):3647–79.

    Article  MATH  Google Scholar 

  • Kawamoto T, Ichikawa Y, Kyoya T. Deformation and fracturing behaviour of discontinuous rock mass and damage mechanics theory. Int J Numer Anal Meth Geomech. 1988;12(1):1–30.

    Article  MATH  Google Scholar 

  • Keener KB. Uplift pressures in concrete dams. Trans ASCE. 1950;116(1):1218–37.

    Google Scholar 

  • Keskin RSO, Hover KC, Grigoriu M. Size effects in modeling diffusivity of hardened mortar. Comput Struct. 2011;89(9):713–23.

    Article  Google Scholar 

  • Khan AS, Huang S. Continuum theory of plasticity. New York: Wiley; 1995.

    MATH  Google Scholar 

  • Kim YR, Lutif J, Allen D. Determining representative volume elements of asphalt concrete mixtures without damage. Transp Res Rec J Transp Res Board. 2009;2127(2):52–9.

    Article  Google Scholar 

  • Koiter WT. Stress–strain relations, uniqueness and variational theorems for elastic-plastic materials with singular yield surface. Q Appl Math. 1953;11(3):350–4.

    Article  MathSciNet  MATH  Google Scholar 

  • Kolditz O. Modelling flow and heat transfer in fracture rocks: conceptual model of a 3-d deterministic fracture network. Geothermics. 1995;24(3):451–70.

    Article  Google Scholar 

  • Kolymbas D, editor. Constitutive modelling of granular materials. Berlin: Springer; 2000.

    Google Scholar 

  • Krajcinovic D. Continuum damage mechanics revisited: basic concepts and definitions. J Appl Mech. 1983;52(4):829–34.

    Article  Google Scholar 

  • Krajcinovic D. Damage mechanics. Amsterdam: North Holland; 1996.

    MATH  Google Scholar 

  • Kranz RL. Crack growth and development during creep of barre granite. Int J Rock Mech Min Sci. 1979;16(1):22–35.

    Google Scholar 

  • Kranz RL, Frankel AD, Engelder T, Scholz CH. The permeability of whole and jointed barre granite. Int J Rock Mech Min Sci. 1979;16(4):225–34.

    Article  Google Scholar 

  • Kulatilake PHSW, Panda BB. Effect of block size and joint geometry on jointed rock hydraulics and REV. J Eng Mech ASCE. 2000;126(8):850–8.

    Article  Google Scholar 

  • Kulatilake PHSW, Wu TH. The density of discontinuity traces in sampling windows. Int J Rock Mech Min Sci Geomech Abstr. 1984;21(6):345–7.

    Article  Google Scholar 

  • Kulatilake PHSW, Wathugala DN, Stephansson O. Joint network modeling, including a validation to an area in Stripa Mine, Sweden. Int J Rock Mech Min Sci Geomech Abstr. 1993;30(5):503–26.

    Article  Google Scholar 

  • Lade PV, Duncan JM. Elastoplastic stress–strain theory for cohesionless soil. J Geotech Eng Div ASCE. 1975;101(GT10):1037–53.

    Google Scholar 

  • Lai YS, Wang CY, Tien YM. Modified Mohr-Coulomb-type micromechanical failure criteria for layered rocks. Int J Numer Anal Meth Geomech. 1999;23(5):451–60.

    Article  MATH  Google Scholar 

  • Landau LD, Lipshitz EM. Theory of elasticity, 3rd ed. Oxford: Pergamon Press; 1970.

    Google Scholar 

  • Larsson R, Runesson K. Implicit integration and consistent linearization for yield criteria of the Mohr-Coulomb type. Mech Cohesive-Friction Mater. 1996;1(4):367–83.

    Article  Google Scholar 

  • Lechner M, Hellmich CH, Mang NA. Short-term creep of shotcrete—thermochemoplastic material modeling and nonlinear analysis of a laboratory test and of a NATM excavation by the finite element method. In: Vermeer PA, Diebels S, Ehlers W, Herrmann HJ, Luding S, Ramm E, editors. Continuous and discontinuous modelling of cohesive-frictional materials. Lecture notes in physics, vol. 568. Berlin: Springer; 2001. p. 47–62.

    Chapter  Google Scholar 

  • Lee H, Peng K, Wang J. An anisotropic damage criterion for deformation instability and its application to forming limit analysis of metal plates. Eng Fract Mech. 1985;21(5):1031–54.

    Article  Google Scholar 

  • Lemaitre J. A course on damage mechanics, 2nd ed. Berlin: Springer; 1990.

    Google Scholar 

  • Lemaitre J, Chaboche JL. Mechanics of solid materials. Cambridge: Cambridge University Press; 1990.

    Book  MATH  Google Scholar 

  • Leroy Y, Ortiz M. Finite element analysis of strain localization in frictional materials. Int J Numer Anal Meth Geomech. 1989;13(1):53–74.

    Article  Google Scholar 

  • Lewis RW, Schrefler BA. The finite element method in the static and dynamic deformation and consolidation of porous media. Chichester: Wiley; 1998.

    MATH  Google Scholar 

  • Li XX, Chen SH, Xu Q, Xu Y. Modeling the three-dimensional unsaturated water transport in concrete at the mesoscale. Comput Struct. 2017;190:61–74.

    Article  Google Scholar 

  • Lin FB, Bažant ZP. Convexity of smooth yield surface of frictional material. J Eng Mech. 1986;112(11):1259–62.

    Article  Google Scholar 

  • Liu L, Xu WY, Wang HL, Wang RB, Wang W. Experimental studies on hydro-mechanical properties of metamorphic rock under hydraulic pressures. Eur J Environ Civil Eng. 2016;20(1):45–59.

    Article  Google Scholar 

  • Lockner DA. A generalized law for brittle deformation of Westerly granite. J Geophys Res. 1998;103(B3):5107–23.

    Article  Google Scholar 

  • Лoмизe M (Lomize M). Фильтpaция в тpeщинoвaтыx пopoдax (Flow in fractured rocks). Гocэнepгoизaт (Gosenergoizdat). Moscow; 1951 (in Russian).

    Google Scholar 

  • Look BG. Handbook of geotechnical investigation and design tables. London: Taylor & Francis Group; 2007.

    Book  Google Scholar 

  • Louis C. A study of groundwater flow in jointed rock and its influence on the stability of rock masses. Rock mechanics research report 10. London: Imperial College; 1969.

    Google Scholar 

  • Louis C. Rock hydraulics. In: Müller L, editor. Rock mechanics. Wien: Springer; 1974a. p. 299–387.

    Google Scholar 

  • Louis C. Introduction a l’Hydraulique des Roches. Orleans: Bureau de Recherches Geologiques et Minieres; 1974b (in French).

    Google Scholar 

  • Louis C, Maini YN. Determination of in-situ hydraulic parameters in jointed rock. In: Proceedings of 2nd ISRM congress. Belgrade: ISRM; 1970. p. 235–45.

    Google Scholar 

  • Lourenço PB, Rots J. A multi-surface interface model for the analysis of masonry structures. J Eng Mech Div ASCE. 1997;123(EM7):660–8.

    Google Scholar 

  • Lubliner J. A simple theory of plasticity. Int J Solids Struct. 1974;10(3):313–9.

    Article  MathSciNet  MATH  Google Scholar 

  • Lubliner J. An axiomatic model of rate-independent plasticity. Int J Solids Struct. 1980;16(8):709–13.

    Article  MathSciNet  MATH  Google Scholar 

  • Lubliner J. A maximum-dissipation principle in generalized plasticity. Acta Mech. 1984;52(3):225–37.

    Article  MathSciNet  MATH  Google Scholar 

  • Lubliner J. Plasticity theory. NY: Macmillan Publishing Company; 1990.

    MATH  Google Scholar 

  • Lubliner J, Auricchio F. Generalized plasticity and shape-memory alloys. Int J Solids Struct. 1996;33(7):991–1003.

    Article  MATH  Google Scholar 

  • Lubliner J, Taylor RL, Auricchio F. A new model of generalized plasticity and its numerical implementation. Int J Solids Struct. 1993;30(22):3171–84.

    Article  MATH  Google Scholar 

  • Machida N, Uehara K. Nonlinear thermal stress analysis of a massive concrete structure. Comput Struct. 1987;26(1–2):287–96.

    Google Scholar 

  • Mahtab M, Goodman RE. Three dimensional analysis of joint rock slope. In: Proceedings of 2nd ISRM congress, vol. 3. Beograd: Privredni Pregled; 1970. p. 353–60.

    Google Scholar 

  • Majorana CE, Zavarise G, Borsetto M, Giusepetti M. Nonlinear analyses of thermal stresses in mass concrete castings. Cem Concr Res. 1990;20(4):559–78.

    Article  Google Scholar 

  • Malan DF. Simulating the time-dependent behaviour of excavations in hard rock. Rock Mech Rock Eng. 2002;35(4):225–54.

    Google Scholar 

  • Malvern LE. Introduction to the mechanics of a continuous medium. Englewood Cliffs: Prentice-Hall Inc; 1969.

    MATH  Google Scholar 

  • Manzari MT, Nour MA. Significance of soil dilatancy in slope stability analysis. J Geotech Geoenviron Eng ASCE. 2000;123(1):75–80.

    Article  Google Scholar 

  • Maranini E, Brignoli M. Creep behaviour of a weak rock: experimental characterization. Int J Rock Mech Min Sci. 1999;36(1):127–38.

    Article  Google Scholar 

  • Masters I, Pao WKS, Lewis RW. Coupling temperature to a double-porosity model of deformable porous media. Int J Numer Anal Meth Geomech. 2000;49(3):421–38.

    Article  MATH  Google Scholar 

  • Matsumoto Y, Chung K, Yamada S. Experimental study on the hysteresis behavior of structural steel under multi-axial cyclic loading. J Struct Constr Eng. 2005;588:1881–8 (in Japanese).

    Google Scholar 

  • Mehta PK, Monteiro PJM. Concrete: microstructure, properties, and materials, 3rd ed. New York: McGraw-Hill; 2006.

    Google Scholar 

  • Michino MJ, Findley WN. An historical perspective of yield surface investigation for metals. Int J Non-linear Mech. 1976;11(1):59–82.

    Article  MATH  Google Scholar 

  • Mielke P, Bär K, Sass I. Determining the relationship of thermal conductivity and compressional wave velocity of common rock types as a basis for reservoir characterization. J Appl Geophys. 2017;140:135–44.

    Article  Google Scholar 

  • Min KB, Rutqvist J, Tsang CF, Jing LR. Stress–dependent permeability of fractured rock masses: a numerical study. Int J Rock Mech Min Sci. 2004;41(7):1191–210.

    Google Scholar 

  • Miyoshi T. Foundations of the numerical analysis of plasticity. Lectures notes in numerical and applied analysis, vol. 7. Tokyo: Kynokunia Company Ltd; 1985.

    Google Scholar 

  • Morland LW. Continuum model of regularly jointed mediums. J Geophys Res. 1974;79(2):357–62.

    Article  Google Scholar 

  • Mott NF. A theory of work-hardening of metals. Part II: flow without slip-lines, recovery and creep. Phil Mag Ser 7. 1953;44(354):742–65.

    Google Scholar 

  • Mukherjee S. Boundary elements in creep and fracture. London: Applied Science Publishers; 1982.

    MATH  Google Scholar 

  • Müller L. Address to the opening session. In: Proceedings of 1st ISRM congress. Lisbon: LNEC; 1967. p. 80–3.

    Google Scholar 

  • Müller L, editor. Rock mechanics. Wien: Springer; 1974.

    Google Scholar 

  • Murakami S. Notion of continuum damage mechanics and its application to anisotropic creep damage theory. J Eng Mater Technol. 1983;105(2):99–105.

    Article  Google Scholar 

  • Murakami S. Mechanical modeling of material damage. J Appl Mech. 1988;55(2):280–6.

    Article  Google Scholar 

  • Mutschler TO, Fröhlich BO. Analytical calculation of the strength behaviour of interbedded rock mass. In: Herget G, Vongpaisal S, editors. Proceedings of 6th ISRM congress. Rotterdam: AA Balkema; 1987. p. 1167–71.

    Google Scholar 

  • Nayak GC, Zienkiewicz OC. Convenient form of stress invariants for plasticity. J Struct Div ASCE. 1972;98(ST4):949–53.

    Google Scholar 

  • Nemat-Nasser S, Obata M. A microcrack model of dilatancy in brittle materials. J Eng Mech ASCE. 1988;55(1):24–35.

    Article  Google Scholar 

  • Neville AM. Creep of concrete as a function of its cement paste content. Mag Concr Res. 1964;16(46):21–30.

    Article  Google Scholar 

  • Neville AM, Diger WH, Brooks JJ. Creep of plain and structural concrete. London: Construction Press; 1983.

    Google Scholar 

  • Nicholl MJ, Rajaram H, Glass RJ, Detwiler R. Saturated flow in a single fracture: evaluation of Reynolds equation in measured aperture fields. Water Resour Res. 1999;35(11):3361–73.

    Article  Google Scholar 

  • Nithiarasu P, Sujatha KS, Ravindran K, Sundararajan T, Seetharamu KN. Non-Darcy natural convection in a hydrodynamically and thermally anisotropic porous medium. Comput Methods Appl Mech Eng. 2000;188(1–3):413–30.

    Article  MATH  Google Scholar 

  • Noorishad J, Tsang CF. Coupled thermo-hydroelasticity phenomena in variably saturated fractured porous rocks—formulation and numerical solution. In: Stephansson O, Jing L, Tsang CF, editors. Coupled thermo-hydro-mechanical processes of fractured media. Rotterdam: Elsevier; 1996. p. 93–134.

    Chapter  Google Scholar 

  • Noorishad J, Tsang CF, Witherspoon PA. Theoretical and field studies of coupled hydromechanical behaviour of fractured rocks. 1: Development and verification of a numerical simulator. Int J Rock Mech Min Sci Geomech Abstr. 1992;29(4):401–9.

    Article  Google Scholar 

  • Nuezil CE, Tracy JV. Flow through fractures. Water Resour Res. 1981;17(2):191–9.

    Article  Google Scholar 

  • Oda M. Fabric tensor for discontinuous geological materials. Soils Found. 1982;22(4):96–108.

    Article  Google Scholar 

  • Oda M. A method for evaluating the effect of crack geometry on the mechanical behavior of cracked rock masses. Mech Mater. 1983;2(2):163–71.

    Article  Google Scholar 

  • Oda M. Similarity rule of crack geometry in statistically homogeneous rock masses. Mech Mater. 1984;3(2):119–29.

    Article  Google Scholar 

  • Oda M. An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses. Water Resour Res. 1986a;22(13):1845–56.

    Article  Google Scholar 

  • Oda M. A stereological study on crack geometry of discontinuous rock masses. In: Ishizaka S, Kato Y, Takaki R, Toriwaki J, editors. Proceedings of 1st international symposium for science on form. Tokyo: KTK Scientific Publisher; 1986b. p. 183–9.

    Chapter  Google Scholar 

  • Oda M. A method for evaluating the representative elementary volume based on joint survey of rock masses. Can Geotech J. 1988;25(3):440–7.

    Article  Google Scholar 

  • Oda M, Suzuki K, Maeshibu T. Elastic compliance for rock-like materials with random cracks. Soils Found. 1984;24(3):27–40.

    Article  Google Scholar 

  • Oda M, Yamabe T, Ishizuka Y, Kumasaka H, Tada H, Kimura K. Elastic stress and strain in jointed rock masses by means of crack tensor analysis. Rock Mech Rock Eng. 1993;26(2):89–112.

    Article  Google Scholar 

  • Oda M, Katsube T, Takemura T. Microcrack evolution and brittle failure of Inada granite in triaxial compression tests at 140 MPa. J Geophy Res Solid Earth (1978–2012). 2002;107(B10):ECV 9-1–17.

    Article  Google Scholar 

  • Oden JT. Finite elements of nonlinear continua. New York: McGraw-Hill; 1972.

    MATH  Google Scholar 

  • Odqvist FKG. Mathematical theory of creep and creep rupture, 2nd ed. Oxford: Clarendon; 1974.

    Google Scholar 

  • Öhman J, Niemi A. Upscaling of fracture hydraulics by means of an oriented correlated stochastic continuum model. Water Resour Res. 2003;39(10):1277.

    Article  Google Scholar 

  • Ohnaka M, Mogi K. Frequency characteristics of acoustic emission in rocks under uniaxial compression and its relation to the fracturing process to failure. J Geophys Res. 1982;87(B5):3873–84.

    Article  Google Scholar 

  • Ohnishi Y, Tanaka M, Jing L. Hydro-mechanical response of a fractured granite rock mass to excavation of a test pit—the Kamaishi mine experiments in Japan. Int J Rock Mech Min Sci. 2001;38(1):79–94.

    Article  Google Scholar 

  • Ohno N, Wang JD. Kinematic hardening rules with critical states of dynamic recovery. Parts I and II. Int J Plast. 1993;9(3):375–403.

    Article  MATH  Google Scholar 

  • Ortiz M, Popov EP. Accuracy and stability of integration algorithms for elastoplastic constitutive relations. Int J Numer Meth Eng. 1985;21(9):1561–76.

    Article  MathSciNet  MATH  Google Scholar 

  • Ortiz M, Leroy Y, Needleman A. A finite element method for localized failure analysis. Comput Meth Appl Mech Eng. 1987;61(2):189–214.

    Article  MATH  Google Scholar 

  • Owen DRJ, Hinton E. Finite elements in plasticity: theory and practice. Swansea: Pineridge Press Ltd; 1980.

    MATH  Google Scholar 

  • Owen DRJ, Hinton E, Onate E. Computational plasticity: models, software and applications. Swansea: Pineridge Press Ltd; 1989.

    MATH  Google Scholar 

  • Palmstrom A, Singh R. The deformation modulus of rock masses—comparisons between in situ tests and indirect estimates. Tunn Undergr Space Technol. 2001;16(2):115–31.

    Article  Google Scholar 

  • Pande GN, Gerrard CM. The behaviour of reinforced jointed rock masses under various simple loading states. In: Proceedings of 5th ISRM congress. Melbourne: Brown Prior Anderson Pty Ltd; 1983. p. F217–23.

    Google Scholar 

  • Paul B. A modification of the Coulomb-Mohr theory of fracture. J Appl Mech. 1961;28(2):259–68.

    Article  MathSciNet  Google Scholar 

  • Perzyna P. The constitutive equations for rate sensitive plastic materials. Q Appl Math. 1963;20(4):321–32.

    Article  MathSciNet  MATH  Google Scholar 

  • Pijaudier-Cabot G, Bažant ZP. Nonlocal damage theory. J Eng Mech Div ASCE. 1987;113(10):1512–33.

    Article  MATH  Google Scholar 

  • Pisarenko GS, Lebedev AA. Deformation and strength of material under complex stressed state. Kiev: Naukova Dumka; 1976 (in Russian).

    Google Scholar 

  • Pivonka P, Lackner R, Mang HA. Shapes of loading surfaces of concrete models and their influence on the peak load and failure mode in structural analyses. Int J Eng Sci. 2003;41(13–14):1649–65.

    Article  Google Scholar 

  • Pramono E, Willam K. Implicit integration of composite yield surface with corners. Eng Comput. 1989;6(3):186–97.

    Article  Google Scholar 

  • Prandtl L, editor. Proceedings of 1st international congress for applied mechanics. Delft: IUTAM; 1924.

    Google Scholar 

  • Prat PC, Bažant ZP. Tangential stiffness of elastic materials with systems of growing or closing cracks. J Mech Phys Solids. 1997;45(4):611–36.

    Article  Google Scholar 

  • Ramamurthy T. Strength and modulus responses of anisotropic rocks. In: Hudson JA, editor. Comprehensive rock engineering: fundamentals. Oxford: Pergamon Press; 1993. p. 313–29.

    Google Scholar 

  • Rappaz M, Bellet M, Deville M. Numerical modeling in materials science and engineering. Berlin: Springer; 2003.

    Book  MATH  Google Scholar 

  • Raven KG, Gale JE. Water flow in a natural rock fracture as a function of stress and sample size. Int J Rock Mech Min Sci Geomech Abstr. 1985;22(4):251–61.

    Article  Google Scholar 

  • Reuss A. Berucksichtigung der elastichen, Formanderung in der Plastizitatstheorie. ZaMM. 1930;10:266 (in German).

    Article  MATH  Google Scholar 

  • Rhodes JA. Prediction of creep, shrinkage and temperature effects in concrete structures. ACI report 209R-92. Detroit: ACI Committee 209; 1992.

    Google Scholar 

  • Rice JR. Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity. J Mech Phys Solids. 1971;19(6):433–55.

    Article  MATH  Google Scholar 

  • Rice JR. Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In: Argon AS, editor. Constitutive equations in plasticity. Cambridge: MIT Press; 1975. p. 23–79.

    Google Scholar 

  • Rice JR. Thermodynamics of quasi-static growth of Griffith cracks. J Mech Phys Solids. 1978;26(2):61–78.

    Article  MATH  Google Scholar 

  • Robert A. Dielectric permittivity of concrete between 50 MHz and 1 GHz and GPR measurements for building materials evaluation. J Appl Geophys. 1998;40(1–3):89–94.

    Article  Google Scholar 

  • Rockafellar RT. Convex analysis. Princeton: Princeton University Press; 1969.

    MATH  Google Scholar 

  • Poмм EC (Romm ES). Фильтpaциoнныe cвoиcтвa тpeщинoвтыx гopныx пopoд (Flow characteristics of fractured rocks). Mocквa (Moscow): Издaтeльcтвo Heдpa (Nedra); 1966 (in Russian).

    Google Scholar 

  • Romana MR. A geomechanical classification for slopes: slope mass rating. In: Hudson JA, editor. Comprehensive rock engineering. Oxford: Pergamon Press; 1993. p. 575–600.

    Chapter  Google Scholar 

  • Roy DM, Scheetz BE, Sabol S, Brown PW, Shi D, Licastro PH, Idom GM, Andersen PJ, Johanson V. Maturity model and curing technology. Washington DC: National Academy of Sciences; 1994.

    Google Scholar 

  • Rudnicki JW, Rice JR. Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids. 1975;23(6):371–94.

    Article  Google Scholar 

  • Runesson K, Sture S, Willam K. Integration in computational plasticity. Comput Struct. 1988;30(1–2):119–30.

    Article  MATH  Google Scholar 

  • Rutqvist J, Borgesson L, Chijimatsu M, Kobayashi A, Jing L, Nguyen TS, Noorishad J, Tsang CF. Thermo-hydro-mechanics of partially saturated geological media: governing equations and formulation of four finite element models. Int J Rock Mech Min Sci. 2001a;38(1):105–27.

    Article  Google Scholar 

  • Rutqvist J, Borgsson L, Chijimatsu M, Nguyen TS, Jing L, Noorishad J, Tsang CF. Coupled thermo-hydro-mechanical analysis of a heater test in fractured rock and bentonite at Kamaishi mine—comparison of field results to predictions of four finite element codes. Int J Rock Mech Min Sci. 2001b;38(1):129–42.

    Article  Google Scholar 

  • Rutter EH. Kinetics of rock deformation by pressure solution. Philos Trans R Soc Lond. 1976;A283(1312):203–19.

    Article  Google Scholar 

  • Sakash A, Moondra S, Kinsey BL. Effect of yield criterion on numerical simulation results using a stress–based failure criterion. J Eng Mater Technol. 2006;128(3):436–44.

    Article  Google Scholar 

  • Salamon MDG. Elastic moduli of a stratified rock mass. Int J Rock Mech Min Sci. 1968;5(6):519–27.

    Article  Google Scholar 

  • Samier P, Onaisi A, Fontaine G. Comparisons of uncoupled and various coupling techniques for practical field examples. SPE J. 2006;11(1):89–102.

    Article  Google Scholar 

  • Santurjian O, Kolarow L. A spatial FEM model of thermal stress state of concrete blocks with creep consideration. Comput Struct. 1996;58(3):563–74.

    Article  MATH  Google Scholar 

  • Scheunemann P. The influence of failure criteria on strength prediction of ceramic components. J Eur Ceram Soc. 2004;24(8):2181–6.

    Article  Google Scholar 

  • Scholtz CH. Mechanism of creep in brittle rock. J Geophys Res. 1968;73(10):3293–302.

    Google Scholar 

  • Schrefler BA. Computer modelling in environmental geomechanics. Comput Struct. 2001;79(22–25):2209–23.

    Article  Google Scholar 

  • Schubert W, Button EA, Sellner PJ, Solak T. Analyse zeitabhaengiger Verformungen im Tunnelbau (Analysis of time-dependent displacements of tunnels). Felsbau (Rock Soil Eng). 2003;21(5):96–103.

    Google Scholar 

  • Sebsadji SK, Chouicha K. Determining periodic representative volumes of concrete mixtures based on the fractal analysis. Int J Solids Struct. 2012;49(21):2941–50.

    Article  Google Scholar 

  • Selvadurai APS, Nguyen TS. Scoping analyses of the coupled thermal-hydrological- mechanical behaviour of the rock mass around a nuclear fuel waste repository. Eng Geol. 1996;47(4):379–400.

    Article  Google Scholar 

  • Selvadurai APS, Nguyen TS. Mechanics and fluid transport in a degradable discontinuity. Eng Geol. 1999;53(3–4):243–9.

    Article  Google Scholar 

  • Serafim JL. Influence of interstitial water on the behaviour of rock masses. In: Stagg KG, Zienkiewicz OC, editors. Rock mechanics in engineering practice. London: Wiley; 1968. p. 55–97.

    Google Scholar 

  • Sercombe J, Hellmich CH, Ulm FJ, Mang HA. Modeling of early-age creep of shotcrete. I: model and model parameters. J Eng Mech ASCE. 2000;126(3):284–91.

    Article  Google Scholar 

  • Settari A, Mourits FM. Coupling of geomechanics and reservoir simulation models. In: Siriwardane HJ, Zeman MM, editors. Computer methods and advances in geomechanics. Rotterdam: AA Balkema; 1994. p. 2151–8.

    Google Scholar 

  • Shen DJ, Shi X, Zhu SS, Duan XF, Zhang JY. Relationship between tensile Young’s modulus and strength of fly ash high strength concrete at early age. Constr Build Mater. 2016;123:317–26.

    Article  Google Scholar 

  • Silva RV, de Brito J, Dhir RK. Establishing a relationship between modulus of elasticity and compressive strength of recycled aggregate concrete. J Clean Prod. 2016;112:2171–86.

    Article  Google Scholar 

  • Simo JC, Hughes TJR. Elastoplasticity and viscoplasticity—computational aspects. New York: Springer; 1988.

    Google Scholar 

  • Simo JC, Hughes TJR. Computational inelasticity. NewYork: Springer; 1998.

    MATH  Google Scholar 

  • Simo JC, Ju JW, Pister KS, Taylor RL. Assessment of cap model: consistency return algorithms and rate-dependent extension. J Eng Mech. 1988;114(2):191–218.

    Article  Google Scholar 

  • Singh B. Continuum characterization of jointed rock masses: Part I—the constitutive equations. Int J Rock Mech Min Sci Geomech Abstr. 1973;10(4):311–35.

    Article  Google Scholar 

  • Singhal BBS, Gupta RP. Applied hydrogeology of fractured rocks, 2nd ed. Dordrecht: Springer; 2010.

    Book  Google Scholar 

  • Skarzynski L, Tejchman J. Determination of representative volume element in concrete under tensile deformation. Comput Concr. 2012;9(1):35–50.

    Article  Google Scholar 

  • Sloan SW, Booker JR. Removal of singularities in Tresca and Mohr-Coulomb yield function. Comm Appl Num Meth. 1986;2(2):173–9.

    Article  MATH  Google Scholar 

  • Snow D. Anisotropic permeability of fractured media. Water Resour Res. 1969;5(6):1273–89.

    Article  Google Scholar 

  • Sonmez H, Gokceoglu C, Ulusay R. Indirect determination of the modulus of deformation of rock masses based on the GSI system. Int J Rock Mech Min Sci. 2004;41(5):849–57.

    Article  Google Scholar 

  • Stagg KG, Zienkiewicz OC, editors. Rock mechanics in engineering practice. NewYork: Wiley; 1986.

    Google Scholar 

  • Stephansson O. The Nasliden Project–rock mass investigations. In: Stephansson O, Jones MJ, editors. Applications of rock mechanics to cut and fill mining. London: IMM; 1981. p. 145–61.

    Google Scholar 

  • Sterpi D. An analysis of geotechnical problems involving strain softening effects. Int J Numer Anal Meth Geomech. 1999;23(13):1427–54.

    Article  MATH  Google Scholar 

  • Stratford RG, Herbert AW, Jackson CP. A parameter study of the influence of aperture variation on fracture flow and the consequences in a fracture network. In: Barton NR, Stephansson O, editors. Rock joints. Rotterdam: AA Balkema; 1990. p. 413–22.

    Google Scholar 

  • Stroeven P, Stroeven M. Size of representative volume element of concrete assessed by quantitative image analysis and computer simulation. Image Anal Stereol. 2001;20(Suppl. 1):216–20.

    Google Scholar 

  • Stroeven M, Askes H, Sluys LJ. Numerical determination of representative volumes for granular materials. Comput Meth Appl Mech Eng. 2004;193(30–32):3221–38.

    Article  MATH  Google Scholar 

  • Sutcliffe DJ, Yu HS, Page AW. Lower bound limit analysis of unreinforced masonry shear walls. Comput Struct. 2001;79(14):1295–312.

    Article  Google Scholar 

  • Swaddiwudhipong S, Lu HR, Wee TH. Direct tension test and tensile strain capacity of concrete at early age. Cem Concr Res. 2003;33(12):2077–84.

    Article  Google Scholar 

  • Swoboda G, Yang Q. An energy-based damage model of geomaterials. I: formulation and numerical results. Int J Solids Struct. 1999a;36(4):1719–34.

    Article  MATH  Google Scholar 

  • Swoboda G, Yang Q. An energy-based damage model of geomaterials. II: deduction of damage evolution laws. Int J Solids Struct. 1999b;36(4):1735–55.

    Article  MATH  Google Scholar 

  • Taliercio A, Landriani GS. A failure condition for layered rock. Int J Rock Mech Min Sci Geomech Abstr. 1988;25(5):299–305.

    Article  Google Scholar 

  • Tappennier P, Brace WF. Development of stress–induced microcracks in Westerly granite. Int J Rock Mech Min Sci. 1976;13(4):103–12.

    Article  Google Scholar 

  • Tazawa E, Miyazawa S. Experimental study on mechanism of autogenous of concrete. Cem Concr Res. 1995;25(8):1633–8.

    Article  Google Scholar 

  • Thomas HR, Cleall PJ. Inclusion of expansive clay behaviour in coupled thermo hydraulic mechanical models. Eng Geol. 1999;54(1–2):93–108.

    Article  Google Scholar 

  • Thomas HR, Missoum H. Three-dimensional coupled heat, moisture and air transfer in a deformable unsaturated soil. Int J Numer Meth Eng. 1999;44(7):919–43.

    Article  MATH  Google Scholar 

  • Thomas HR, Yang HT, He Y. A sub-structure based parallel solution of coupled thermo-hydro-mechanical modeling of unsaturated soil. Eng Comput. 1999;16(4):428–42.

    Article  MATH  Google Scholar 

  • Tien YM, Kuo MC. A failure criterion for transversely isotropic rocks. Int J Rock Mech Min Sci. 2001;38(3):399–412.

    Article  Google Scholar 

  • Tien YM, Kuo MC, Juang CH. An experimental investigation of the failure mechanism of simulated transversely isotropic rocks. Int J Rock Mech Min Sci. 2006;43(8):1163–81.

    Article  Google Scholar 

  • Timoshenko SP. History of strength of materials. New York: McGraw-Hill Book Company Inc; 1953.

    Google Scholar 

  • Triantafyllidis T, Gerolymatou E. Estimation of the strength of stratified rock mass. Rock Mech Rock Eng. 2014;47(2):535–47.

    Article  Google Scholar 

  • Troxell GE, Raphael JM, Davis RE. Long-time creep and shrinkage tests of plain and reinforced concrete. Proc ASTM. 1958;58:1101–20.

    Google Scholar 

  • Tsang CF, editor. Coupled processes associated with nuclear waste repositories. New York: Academic Press; 1987.

    Google Scholar 

  • Tsang CF. Coupled thermomechanical and hydrochemical processes in rock fractures. Rev Geophys. 1991;29(4):537–48.

    Article  Google Scholar 

  • Tsang YW, Witherspoon PA. Hydromechanical behavior of a deformable rock fracture subject to normal stress. J Geophys Res. 1981;86(B10):9287–98.

    Article  Google Scholar 

  • Ulm FJ, Coussy O. Modeling of thermochemomechanical couplings of concrete at early ages. J Eng Mech ASCE. 1995;121(7):785–94.

    Article  Google Scholar 

  • Ulm FJ, Coussy O, Hellmich CH. Chemoplasticity: a review of evidence. In: de Borst R, Bićanić N, Mang R, Meschke G, editors. Computational modeling of concrete structures, Proceedings of EUROCK 1998. Rotterdam: AA Balkema; 1998. p. 421–40.

    Google Scholar 

  • Ulusay R, editor. The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014. Cham: Springer; 2015.

    Google Scholar 

  • Ulusay R, Hudson JA, editors. The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. Ankara: ISRM Turkish National Group; 2007.

    Google Scholar 

  • Valanis KC. A theory of viscoplasticity without a yield surface. Archiwum Mechaniki Stossowanej. 1971;23(4):517–51.

    MathSciNet  MATH  Google Scholar 

  • Valanis KC. Fundamental consequences of a new intrinsic time measure. Plasticity as a limit of the endochronic theory. Archiwum Mechaniki Stossowanej. 1980;32(2):171–91.

    Google Scholar 

  • Valanis KC, Wu HC. Endochronic representation of cyclic creep and relaxation of metals. J Appl Mech ASME. 1975;42(1):67–73.

    Article  MATH  Google Scholar 

  • Van Mier JGM, Van Vliet MRA. Influence of microstructure of concrete on size/scale effects in tensile fracture. Eng Fract Mech. 2003;70(16):2281–306.

    Article  Google Scholar 

  • Van Vliet MRA, Van Mier JGM. Experimental investigation of size effect in concrete and sandstone under uniaxial tension. Eng Fract Mech. 2000;65(2.3):165–188.

    Google Scholar 

  • Vermeer JPA, de Borst R. Non-associated plasticity for soils, concrete and rock. HERON. 1984;29(3):3–64.

    Google Scholar 

  • Videla CC, et al. Guide for modeling and calculating shrinkage and creep in hardened concrete. ACI report 209.2R-08. Farmington Hills: ACI Committee 209; 2008.

    Google Scholar 

  • Von Mises R. Mechanik der Festen Korper im plastisch deformablen Zustand. Göttin Nachr Math Phys. 1913;1:582–92 (in German).

    MATH  Google Scholar 

  • Walsh JB. Effect of pore pressure and confining pressure on fracture permeability. Int J Rock Mech Min Sci Geomech Abstr. 1981;18(5):429–35.

    Article  Google Scholar 

  • Wang L, Lee TC. The effect of yield criteria on forming limit curve prediction and deep drawing process simulation. Int J Mach Tools Manuf. 2006;46(9):988–95.

    Article  Google Scholar 

  • Wang XC, Schrefler BA. A multi-frontal parallel algorithm for coupled thermo-hydro-mechanical analysis of deformable porous media. Int J Numer Meth Eng. 1998;43(6):1069–83.

    Article  MATH  Google Scholar 

  • Wardle LJ, Gerrard CM. The ‘‘equivalent’’ anisotropic properties of layered rock and soil masses. Rock Mech Rock Eng. 1972;4(3):155–75.

    Article  Google Scholar 

  • Watanabe O, Atluri SN. Internal time, general internal variable, and multi-yield-surface theories of plasticity and creep: a unification of concepts. Int J Plast. 1986;2(1):37–57.

    Article  MATH  Google Scholar 

  • Wei ZQ, Hudson JA. The influence of joints on rock modulus. In: Tan ZY, editor. Proceedings of the international symposium on engineering in complex formations. Beijing: Science Press; 1986. p. 54–62.

    Chapter  Google Scholar 

  • Wei ZQ, Egger P, Descoeuders F. Permeability prediction for jointed rock masses. Int J Rock Mech Min Sci Geomech Abstr. 1995;32(3):251–61.

    Article  Google Scholar 

  • Willam KJ, Warnke EP. Constitutive models for the triaxial behavior of concrete. Proceedings of International Association for Bridge and Structural Engineering. Report 19, Section III. Bergamo: ISMES; 1975. p. 1–30.

    Google Scholar 

  • Wilson CR, Witherspoon PA. An investigation of laminar flow in fractured porous rocks. Berkeley: University of California; 1970.

    Google Scholar 

  • Witherspoon PA, Wang JSY, Iwai K, Gale JE. Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res. 1980;16(6):1016–24.

    Article  Google Scholar 

  • Wittmann FH. Creep and shrinkage mechanisms. In: Bažant ZP, Wittmann FH, editors. Creep and shrinkage of concrete structures. London: Wiley; 1982. p. 129–61.

    Chapter  Google Scholar 

  • Wu AQ, Zhou HM. Rock mechanics. In: Liu ZM, Wang DX, Wang DG, editors. Handbook of hydraulic structure design, vol. 1. Fundamental theories (Chapter 5). Beijing: China Water Power Press; 2013 (in Chinese).

    Google Scholar 

  • Xiong WL. Symmetric formulation of tangential stiffnesses for non-associated visco-plasticity with an implicit time integration scheme. Appl Math Mech. 1993;14(3):251–7 (in Chinese).

    Google Scholar 

  • Xu T, Tang CA, Zhao J, Li L, Heap MJ. Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks. Geophys J Int. 2012;189(3):1781–96.

    Article  Google Scholar 

  • Xu Y, Xu Q, Chen SH, Li XX. Self-restraint thermal stress in early-age concrete samples and its evaluation. Constr Build Mater. 2017;134:104–15.

    Article  Google Scholar 

  • Yamada S, Imaeda T, Okada K. Simple hysteresis model of structural steel considering the Bauschinger effect. J Struct Constr Eng Arch Inst Jpn. 2002;67(559):225–32 (in Japanese).

    Article  Google Scholar 

  • Yi D, Chen SH. Effect of the earth surface denudation on the initial stress back analysis of rock masses. Rock Soil Mech. 2003;24(2):254–6 (in Chinese).

    MathSciNet  Google Scholar 

  • Yi D, Xu MY, Chen SH. Application of genetic algorithms to back analysis of initial stress field of rock masses. Chin J Rock Mech Eng. 2001;20(Supp.2):1618–22 (in Chinese).

    Google Scholar 

  • Yoshinaka R, Yamabe T. Jointed stiffness and the deformation behavior of discontinuous rock. Int J Rock Mech Min Sci Geomech Abstr. 1986;23(1):295–303.

    Article  Google Scholar 

  • Young JF, Mindness S, Gray RJ, Bentur A. The science and technology of civil engineering materials. NJ: Prentice Hall; 1998.

    Google Scholar 

  • Yu MH. Advances in strength theories for materials under complex stress state in the 20th century. Appl Mech Rev ASME. 2002;55(3):169–218.

    Article  Google Scholar 

  • Yu MH, Li JC. Computational plasticity with emphasis on the application of the unified strength theory. Hangzhou: Zhejiang University Press; 2012.

    Google Scholar 

  • Zhang JL, Chen SH. Study of time-stepping adaptivity in FEM analysis of time-dependent problems. J Wuhan Univ Hydraul Electr Eng (WUHEE). 1996;29(1):79–84 (in Chinese).

    Google Scholar 

  • Zhang JL, Chen SH. An implicit scheme algorithm of elastic-viscoplastic FEM with time-stepping adaptive for bolted jointed rock masses. J Hydraul Eng. 1997;19(Supplement):168–75 (in Chinese).

    Google Scholar 

  • Zhang C, Rothfuchs T. Experimental study of the hydro-mechanical behaviour of the Callovo-Oxfordian argillite. Appl Clay Sci. 2004;26(1–4):325–36.

    Article  Google Scholar 

  • Zhang X, Sanderson DJ, Harkness RM, Last NC. Evaluation of the 2D permeability tensor for fractured rock masses. Int J Rock Mech Min Sci Geomech Abstr. 1996;33(1):17–37.

    Article  Google Scholar 

  • Zhou C, Huang B, Shu X. Micromechanical model for predicting coefficient of thermal expansion of concrete. J Mater Civ Eng. 2013;25(9):1171–80.

    Article  Google Scholar 

  • Zhu BF. Computation of thermal stresses in mass concrete with consideration of creep effect. In: Proceedings of XV ICOLD congress (Lausanne). Paris: ICOLD; 1985a.

    Google Scholar 

  • Zhu BF. The elastic modulus, creep compliance and stress relaxation coefficient of concrete. J Hydraul Eng. 1985b;15(9):54–61 (in Chinese).

    Google Scholar 

  • Zhu BF. On the formula for modulus of elasticity of concrete. J Hydraul Eng. 1996;26(3):89–90 (in Chinese).

    MathSciNet  Google Scholar 

  • Zienkiewicz OC, editor. Rock mechanics in engineering practice. New York: Wiley; 1968.

    Google Scholar 

  • Zienkiewicz OC, Cormeau IC. Viscoplasticity solution by finite element process. Arch Mech. 1972;24(5–6):873–88.

    MATH  Google Scholar 

  • Zienkiewicz OC, Cormeau IC. Visco-plasticity and plasticity—an alternative for finite element solution of material nonlinearities. Computing methods in applied sciences and engineering (Part 1). Berlin: Springer; 1974. p. 259–87.

    Google Scholar 

  • Zienkiewicz OC, Mróz Z. Generalized plasticity formulation and applications to geomechanics. In: Desai CS, Gallagher RH, editors. Mechanics of engineering materials. New York: Wiley; 1984. p. 655–79.

    Google Scholar 

  • Zienkiewicz OC, Pande GN. Some useful forms of isotropic yield surfaces for soil and rock mechanics. In: Gudehus G, editor. Finite element in geomechanics. New York: Wiley; 1977a. p. 179–90.

    Google Scholar 

  • Zienkiewicz OC, Pande GN. Time-dependent multilaminate model of rocks—a numerical study of deformation and failure of rock masses. Int J Numer Anal Meth Geomech. 1977b;1(3):219–47.

    Article  Google Scholar 

  • Zienkiewicz OC, Valliappan S, King IP. Elasto-plastic solutions of engineering problems “initial stress”, finite element approach. Int J Numer Meth Eng. 1969;1(1):75–100.

    Article  MATH  Google Scholar 

  • Zienkiewicz OC, Huang M, Pastor M. Localization problems in plasticity using finite element with adaptive remeshing. Int J Numer Anal Mech Geomech. 1995;19(2):127–48.

    Article  MATH  Google Scholar 

  • Zimmerman RW. Coupling in poroelasticity and thermoelasticity. Int J Rock Mech Min Sci. 2000;37(1):79–87.

    Article  Google Scholar 

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Chen, Sh. (2019). Preparation Knowledge of Material Properties. In: Computational Geomechanics and Hydraulic Structures. Springer Tracts in Civil Engineering . Springer, Singapore. https://doi.org/10.1007/978-981-10-8135-4_2

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