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Preparation Knowledge of Material Properties

  • Sheng-hong ChenEmail author
Chapter
Part of the Springer Tracts in Civil Engineering book series (SPRTRCIENG)

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.

References

  1. 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.zbMATHCrossRefGoogle Scholar
  2. 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
  3. Alexandrovskii SV. Plane and reinforced concrete structures calculation under thermal and hygral effects. Moskow: Stroiizolat; 1966 (in Russian).Google Scholar
  4. 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.CrossRefGoogle Scholar
  5. Amadei B. Rock anisotropy and the theory of stress measurements. Berlin: Springer; 1983.zbMATHCrossRefGoogle Scholar
  6. 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
  7. American Concrete Institute. (ACI 318-08) Building code for structural concrete. Detroit: ACI; 2008.Google Scholar
  8. Amitrano D, Helmstetter A. Brittle creep, damage, and time to failure in rocks. J Geophys Res Solid Earth. 2006;111(B11):1–17.CrossRefGoogle Scholar
  9. Anderson OL, Grew PC. Stress corrosion theory of crack propagation with applications to geophysics. Rev Geophys. 1977;15(1):77–104.CrossRefGoogle Scholar
  10. Armstrong P, Frederick C. A mathematical representation of the multiaxial Bauschinger effect. GEGB report RD/B/N731; 1966.Google Scholar
  11. Arutiunian NH, Kolmanovskii VB. Creep theory of inhomogeneous bodies. Moskow: Nauka; 1983 (in Russian).Google Scholar
  12. Atkinson BK. Subcritical crack growth in geological materials. J Geophys Res Solid Earth. 1984;89(B6):4077–114.CrossRefGoogle Scholar
  13. Auricchio F, Taylor RL. Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity. Int J Plast. 1995;11(1):65–98.zbMATHCrossRefGoogle Scholar
  14. Auvray C, Homand F, Sorgi C. The aging of gypsum in underground mines. Eng Geol. 2004;74(3):183–96.CrossRefGoogle Scholar
  15. 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
  16. Barla G. Squeezing rocks in tunnels. ISRM News J. 1995;2(3/4):44–9.Google Scholar
  17. Barla G, Bonini M, Debernardi D. Time dependent deformations in squeezing tunnels. Int J Geoeng Case Histories. 2010;2(1):819–24.Google Scholar
  18. Barton NR. A model study of rock-joint deformation. Int J Rock Mech Min Sci. 1972;9(5):579–82.CrossRefGoogle Scholar
  19. 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.CrossRefGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. 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.CrossRefGoogle Scholar
  22. Bažant ZP. Endochronic inelasticity and incremental plasticity. Int J Solids Struct. 1978;14(9):691–714.zbMATHCrossRefGoogle Scholar
  23. 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
  24. Bažant ZP, editor. Mathematical modeling of creep and shrinkage of concrete. RILEM Committee TC 69 report. Chichester and New York: Wiley; 1988.Google Scholar
  25. Bažant ZP, Bhat PD. Endochronic theory of inelasticity and failure of concrete. J Eng Mech Div ASCE. 1976;102(EM4):701–22.Google Scholar
  26. Bažant ZP, Krizek RJ. Endochronic constitutive law for liquefaction of sand. J Eng Mech Div ASCE. 1976;102(EM2):225–38.Google Scholar
  27. Bažant ZP, Prasannan S. Solidification theory for concrete creep. J Eng Mech. 1989;115(8):1691–725.CrossRefGoogle Scholar
  28. Bažant ZP, Belytschko T, Chang TP. Continuum theory for strain-softening. J Eng Mech ASCE. 1984;110(12):1666–92.CrossRefGoogle Scholar
  29. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Chichester: Wiley; 2000.zbMATHGoogle Scholar
  30. Betten J. Creep mechanics, 3rd ed. Berlin: Springer; 2008.Google Scholar
  31. Bieniawski ZT. Fracture dynamics of rock. Int J Fract Mech. 1968a;4(4):415–30.CrossRefGoogle Scholar
  32. Bieniawski ZT. The effect of specimen size on compressive strength of coal. Int J Rock Mech Min Sci. 1968b;5(4):325–35.CrossRefGoogle Scholar
  33. Bieniawski ZT. Determining rock mass deformability: experience from case histories. Int J Rock Mech Min Sci Geomech Abstr. 1978;15(5):237–47.CrossRefGoogle Scholar
  34. Bingham EC. Fluidity and plasticity. New York: McGraw-Hill; 1922.Google Scholar
  35. Birch AF, Clark H. The thermal conductivity of rocks and its dependence upon temperature and composition. Am J Sci. 1940;238(8):529–58.CrossRefGoogle Scholar
  36. Bizjak KF, Zupančič A. Rheological investigation for the landslide Slano Blato near Ajdovscina (Slovenia). Geologija. 2007;50(1):121–9.CrossRefGoogle Scholar
  37. Boland JN, Hobbs BE. Microfracturing processes in experimentally deformed peridotite. Int J Rock Mech Min Sci. 1973;10(6):623–6.CrossRefGoogle Scholar
  38. 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.CrossRefGoogle Scholar
  39. 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.CrossRefGoogle Scholar
  40. 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.CrossRefGoogle Scholar
  41. 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
  42. Brace WF, Walsh JB, Frangos WT. Permeability of granite under high pressure. J Geophys Res. 1968;73(6):2225–36.CrossRefGoogle Scholar
  43. 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.CrossRefGoogle Scholar
  44. Brebbia CA, editor. Finite element systems (A handbook). Berlin: Springer; 1985.Google Scholar
  45. 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.zbMATHGoogle Scholar
  46. Brooks JJ. 30-year creep and shrinkage of concrete. Mag Concrete Res. 2005;57(9):545–56.CrossRefGoogle Scholar
  47. Brown ET, editor. Rock characterization, testing and monitoring: ISRM suggested methods. Oxford: Pergamon Press; 1981.Google Scholar
  48. 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.CrossRefGoogle Scholar
  49. Budiansky B, O’Connel RJ. Elastic moduli of a cracked solid. Int J Solids Struct. 1976;12(2):81–97.zbMATHCrossRefGoogle Scholar
  50. 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.CrossRefGoogle Scholar
  51. 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.CrossRefGoogle Scholar
  52. Carslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed. Oxford: Oxford University Press; 1985.Google Scholar
  53. Casagrande A. First Rankine Lecture—control of seepage through foundations and abutment of dam. Géotechnique. 1961;11(3):161–82.CrossRefGoogle Scholar
  54. Cedergren HR. Seepage, drainage and flownets, 3rd ed. New York: Wiley; 1989.Google Scholar
  55. 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.zbMATHCrossRefGoogle Scholar
  56. Chaboche JL. On some modifications of kinematic hardening to improve the description of ratchetting effects. Int J Plast. 1991;7(7):661–78.CrossRefGoogle Scholar
  57. Chen SH. Hydraulic structures. Berlin: Springer; 2015.CrossRefGoogle Scholar
  58. Chen WF, Baladi GY. Soil plasticity: theory and implementation. Amsterdam: Elsevier; 1985.zbMATHGoogle Scholar
  59. 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.CrossRefGoogle Scholar
  60. Chen WF, Drucker DC. Bearing capacity of concrete blocks or rock. J Eng Mech ASCE. 1969;95(EM4):955–78.Google Scholar
  61. 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.CrossRefGoogle Scholar
  62. Chen WF, Saleeb AF. Constitutive equations for engineering materials. 1: Elasticity and modeling, Revised ed. Amsterdam: Elsevier; 1994.Google Scholar
  63. 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
  64. Chen WF, Zhang H. Structural plasticity: theory, problems and CAE software. New York: Springer; 1991.zbMATHCrossRefGoogle Scholar
  65. 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
  66. 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.CrossRefGoogle Scholar
  67. 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
  68. 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.zbMATHCrossRefGoogle Scholar
  69. 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
  70. Chiles JP. Fractal and geostatistical methods for modelling a fracture network. Math Geol. 1988;20(6):631–54.CrossRefGoogle Scholar
  71. Chow CL, Lu TJ. On evolution laws of anisotropic damage. Eng Fract Mech. 1989;34(3):679–701.CrossRefGoogle Scholar
  72. Commission on Standardization of Laboratory and Field Tests. Suggested methods for determining shear strength (Document No. 1). Lisbon: ISRM; 1974.Google Scholar
  73. 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.CrossRefGoogle Scholar
  74. Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mech Mater. 1985;4(2):137–47.CrossRefGoogle Scholar
  75. Cristescu ND, Gioda G, editors. Visco-plastic behaviour of geomaterials. Wien: Springer; 1994.Google Scholar
  76. Cristescu ND, Suliciu I. Mechanics of plastix solids—viscoplasticity. Hague: Martinus Nijhoff Publishers; 1982.zbMATHGoogle Scholar
  77. Cruden DE. Describing the size of discontinuities. Int J Rock Mech Min Sci Geomech Abstr. 1977;14(3):133–7.CrossRefGoogle Scholar
  78. 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.CrossRefGoogle Scholar
  79. Das S, Scholz CH. Theory of time-dependent rupture in the Earth. J Geophys Res. 1981;86(B7):6039–51.CrossRefGoogle Scholar
  80. Davis HE. Autogenous volume change of concrete. Proc ASTM. 1940;40:1103–10.Google Scholar
  81. Davis RO, Selvadurai APS. Plasticity and geotechnics. Cambridge: Cambridge University Press; 2002.CrossRefGoogle Scholar
  82. de Borst R. Integration of plasticity equations for singular yield functions. Comput Struct. 1987;26(5):823–9.zbMATHCrossRefGoogle Scholar
  83. 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
  84. de Souza Neto EA, Perić D, Owen DRJ. Computational methods for plasticity: theory and applications. New York: Wiley; 2009.Google Scholar
  85. Dershowitz WS. Rock joint systems. Ph.D. thesis. Boston: Massachusetts Institute of Technology; 1984.Google Scholar
  86. Desai CS, Gioda G, editors. Numerical methods and constitutive modeling in geomechanics. Wien: Springer; 1990.zbMATHGoogle Scholar
  87. Desai CS, Toth J. Disturbed state constitutive modeling based on stress–strain and nondestructive behavior. Int J Solids Struct. 1996;33(11):1619–50.CrossRefGoogle Scholar
  88. Desai CS, Drumm EC, Zaman MM. Thin layer element for interfaces and joints. J Geotech Eng ASCE. 1985;111(6):793–815.CrossRefGoogle Scholar
  89. 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.CrossRefGoogle Scholar
  90. Doltsinis IS, editor. Advances in computational nonlinear mechanics (CISM). Wien: Springer; 1989.zbMATHGoogle Scholar
  91. 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.CrossRefGoogle Scholar
  92. Drucker DC, Prager W. Soil mechanics and plastic analysis for limit design. Q Appl Math. 1952;10(2):157–65.MathSciNetzbMATHCrossRefGoogle Scholar
  93. Dunne FPE, Petrinic N. Introduction to computational plasticity. Oxford: Oxford University Press; 2005.zbMATHGoogle Scholar
  94. Dunnicliff J. Geotechnicul instrumentation for monitoring field performance. Chichester: Wiley; 1988.Google Scholar
  95. 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.CrossRefGoogle Scholar
  96. 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
  97. Eisenberg MA, Phillips A. A theory of plasticity with non-coincident yield and loading surfaces. Acta Mech. 1971;11(3):247–60.zbMATHCrossRefGoogle Scholar
  98. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  99. European Committee for Standardization. (Eurocode 2) Design of concrete structures. Brussels: ECS; 2004.Google Scholar
  100. Evesque P. Fluctuations, correlations and representative elementary volume (REV) in granular materials. Poudres Grains. 2000;11:6–17.Google Scholar
  101. Farmer IW. Engineering properties of rocks. London: E & FN Spon Ltd; 1968.Google Scholar
  102. 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.CrossRefGoogle Scholar
  103. 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
  104. Frémond M. Non-smooth thermomechanics. Berlin: Springer; 2002.zbMATHCrossRefGoogle Scholar
  105. 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
  106. 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.CrossRefGoogle Scholar
  107. 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
  108. 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.CrossRefGoogle Scholar
  109. 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.CrossRefGoogle Scholar
  110. Ghaboussi J, Gioda G. On the time-dependent effects in advancing tunnels. Int J Numer Anal Meth Geomech. 1977;1(3):249–69.CrossRefGoogle Scholar
  111. Gitman IM, Askes H, Sluys LJ. Representative volume: existence and size determination. Eng Fract Mech. 2007;74(16):2518–34.CrossRefGoogle Scholar
  112. Golzé AR, editor. Handbook of dam engineering. New York: Van Nostrand Reinhold Company; 1977.Google Scholar
  113. 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
  114. Goodman RE. Introduction to rock mechanics, 2nd ed. New York: Wiley; 1989.Google Scholar
  115. 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
  116. 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
  117. 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.CrossRefGoogle Scholar
  118. Griffiths DV, Gioda G. Advanced numerical applications and plasticity in geomechanics. Wien: Springer; 2000.Google Scholar
  119. Gruden DN. Single-increment creep experiments on rock under uniaxial compression. Int J Rock Mech Min Sci. 1971;8(2):127–42.CrossRefGoogle Scholar
  120. 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.CrossRefGoogle Scholar
  121. 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.zbMATHCrossRefGoogle Scholar
  122. Haimson B. Micromechanisms of borehole instability leading to breakouts in rocks. Int J Rock Mech Min Sci. 2007;44(2):157–73.CrossRefGoogle Scholar
  123. 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
  124. Hall EO. Yield point phenomena in metals and alloys. New York: Plenum Press; 1970.CrossRefGoogle Scholar
  125. Halphen B, Nguyen QS. Sur les matériaux standards généralisés. Journal de Mécanique. 1975;14(1):39–63 (in French).MathSciNetzbMATHGoogle Scholar
  126. Han W, Reddy BD. Plasticity: mathematical theory and numerical analysis. New York: Springer; 1999.zbMATHGoogle Scholar
  127. Harris D. Plasticity models for soils, granular and jointed rock materials. J Mech Phys Solids. 1992;40(2):273–90.MathSciNetzbMATHCrossRefGoogle Scholar
  128. Harza LF. The significance of pore pressure in hydraulic structures. Trans ASCE. 1949;114(1):193–214.Google Scholar
  129. Hashin Z. Analysis of composite materials—a survey. J Appl Mech. 1983;50(3):481–505.zbMATHCrossRefGoogle Scholar
  130. He J, Chen SH. A revised solution of equivalent permeability tensor for discontinuous fractures. J Hydrodyn Ser B. 2012;24(5):711–7.CrossRefGoogle Scholar
  131. 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
  132. 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.zbMATHCrossRefGoogle Scholar
  133. Hill R. Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids. 1963;11(5):357–72.zbMATHCrossRefGoogle Scholar
  134. Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J Mech Phys Solids. 1967;15(2):79–95.CrossRefGoogle Scholar
  135. Hill R. The mathematical theory of plasticity. Oxford: Oxford University Press; 1998.zbMATHGoogle Scholar
  136. Hoek E, Bray JW. Rock slope engineering, 3rd ed. London: Institution of Mining and Metallurgy; 1981.Google Scholar
  137. Hoek E, Diederichs MS. Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci. 2006;43(2):203–15.CrossRefGoogle Scholar
  138. Hoff NJ, editor. Creep in structures: IUTAM colloquium held at Stanford University (1962). Berlin: Springer; 2012.Google Scholar
  139. 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.CrossRefGoogle Scholar
  140. 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.CrossRefGoogle Scholar
  141. 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
  142. 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.CrossRefGoogle Scholar
  143. Hudson JA, Harrison JP. Engineering rock mechanics—an introduction to the principles. Oxford: Elsevier Science Ltd; 1997.Google Scholar
  144. Hudson JA, Priest SD. Discontinuity frequency in rock masses. Int J Rock Mech Min Sci Geomech Abstr. 1983;20(2):73–89.CrossRefGoogle Scholar
  145. 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.CrossRefGoogle Scholar
  146. Huet C. Coupled size and boundary-condition effects in viscoelastic heterogeneous and composite bodies. Mech Mater. 1999;31(12):787–829.CrossRefGoogle Scholar
  147. Humpheson C, Naylor DJ. The importance of the form of the failure criterion. C/R/243/75. Swansea: University of Wales; 1975.Google Scholar
  148. ICOLD. The specification and quality control of concrete for dams (Bulletin 136). Paris: ICOLD; 2009.Google Scholar
  149. Inoue T, Kitagawa H, Shima S, editors. Computational plasticity. London: Elsevier; 1990.Google Scholar
  150. Irgens F. Continuum mechanics. Berlin: Springer; 2008.Google Scholar
  151. Iwai K. Fundamental studies of the fluid flow through a single fracture. Ph.D. thesis. Berkeley: University of California; 1976.Google Scholar
  152. Jaeger JC, Cook NGW, Zimmerman R. Fundamentals of rock mechanics, 4th ed. MA: Wiley-Blackwell; 2007.Google Scholar
  153. Jia LJ, Kuwamura H. Ductile fracture simulation of structural steels under monotonic tension. J Struct Eng ASCE. 2014;140(5):472–82.CrossRefGoogle Scholar
  154. Jirásek M, Bažant ZP. Inelastic analysis of structures. London: Wiley; 2001.Google Scholar
  155. John KW. Strength and deformability of regularly jointed rocks (Chapter 5). Berkeley: Port City Press; 1969.Google Scholar
  156. Ju JW. On energy-based coupled elastoplastic damage theories: constitutive modelling and computational aspects. Int J Solids Struct. 1989;25(7):803–33.zbMATHCrossRefGoogle Scholar
  157. 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
  158. Kacewicz M. Model-free estimation of fracture apertures with neural networks. Math Geol. 1994;26(8):985–94.CrossRefGoogle Scholar
  159. Kachanov LM. Time of the rupture process under creep conditions. Izvestiya Akademii Nauk SSSR Otdelenie Tekniches. 1958;8:26–31.Google Scholar
  160. Kachanov LM. A microcrack model of rock inelasticity. Part I: frictional sliding on microcracks. Mech Mater. 1982a;1(1):19–27.CrossRefGoogle Scholar
  161. Kachanov LM. A microcrack model of rock inelasticity. Part II: propagation of microcracks. Mech Mater. 1982b;1(1):29–41.CrossRefGoogle Scholar
  162. Kachanov LM. A microcrack model of rock inelasticity. Part III: time-dependent growth of microcracks. Mech Mater. 1982c;1(2):123–9.CrossRefGoogle Scholar
  163. 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.zbMATHCrossRefGoogle Scholar
  164. 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.zbMATHCrossRefGoogle Scholar
  165. Keener KB. Uplift pressures in concrete dams. Trans ASCE. 1950;116(1):1218–37.Google Scholar
  166. Keskin RSO, Hover KC, Grigoriu M. Size effects in modeling diffusivity of hardened mortar. Comput Struct. 2011;89(9):713–23.CrossRefGoogle Scholar
  167. Khan AS, Huang S. Continuum theory of plasticity. New York: Wiley; 1995.zbMATHGoogle Scholar
  168. 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.CrossRefGoogle Scholar
  169. 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.MathSciNetzbMATHCrossRefGoogle Scholar
  170. 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.CrossRefGoogle Scholar
  171. Kolymbas D, editor. Constitutive modelling of granular materials. Berlin: Springer; 2000.Google Scholar
  172. Krajcinovic D. Continuum damage mechanics revisited: basic concepts and definitions. J Appl Mech. 1983;52(4):829–34.CrossRefGoogle Scholar
  173. Krajcinovic D. Damage mechanics. Amsterdam: North Holland; 1996.zbMATHGoogle Scholar
  174. Kranz RL. Crack growth and development during creep of barre granite. Int J Rock Mech Min Sci. 1979;16(1):22–35.Google Scholar
  175. 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.CrossRefGoogle Scholar
  176. 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.CrossRefGoogle Scholar
  177. 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.CrossRefGoogle Scholar
  178. 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.CrossRefGoogle Scholar
  179. Lade PV, Duncan JM. Elastoplastic stress–strain theory for cohesionless soil. J Geotech Eng Div ASCE. 1975;101(GT10):1037–53.Google Scholar
  180. 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.zbMATHCrossRefGoogle Scholar
  181. Landau LD, Lipshitz EM. Theory of elasticity, 3rd ed. Oxford: Pergamon Press; 1970.Google Scholar
  182. 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.CrossRefGoogle Scholar
  183. 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.CrossRefGoogle Scholar
  184. 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.CrossRefGoogle Scholar
  185. Lemaitre J. A course on damage mechanics, 2nd ed. Berlin: Springer; 1990.Google Scholar
  186. Lemaitre J, Chaboche JL. Mechanics of solid materials. Cambridge: Cambridge University Press; 1990.zbMATHCrossRefGoogle Scholar
  187. Leroy Y, Ortiz M. Finite element analysis of strain localization in frictional materials. Int J Numer Anal Meth Geomech. 1989;13(1):53–74.CrossRefGoogle Scholar
  188. Lewis RW, Schrefler BA. The finite element method in the static and dynamic deformation and consolidation of porous media. Chichester: Wiley; 1998.zbMATHGoogle Scholar
  189. 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.CrossRefGoogle Scholar
  190. Lin FB, Bažant ZP. Convexity of smooth yield surface of frictional material. J Eng Mech. 1986;112(11):1259–62.CrossRefGoogle Scholar
  191. 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.CrossRefGoogle Scholar
  192. Lockner DA. A generalized law for brittle deformation of Westerly granite. J Geophys Res. 1998;103(B3):5107–23.CrossRefGoogle Scholar
  193. Лoмизe M (Lomize M). Фильтpaция в тpeщинoвaтыx пopoдax (Flow in fractured rocks). Гocэнepгoизaт (Gosenergoizdat). Moscow; 1951 (in Russian).Google Scholar
  194. Look BG. Handbook of geotechnical investigation and design tables. London: Taylor & Francis Group; 2007.CrossRefGoogle Scholar
  195. 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
  196. Louis C. Rock hydraulics. In: Müller L, editor. Rock mechanics. Wien: Springer; 1974a. p. 299–387.Google Scholar
  197. Louis C. Introduction a l’Hydraulique des Roches. Orleans: Bureau de Recherches Geologiques et Minieres; 1974b (in French).Google Scholar
  198. 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
  199. 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
  200. Lubliner J. A simple theory of plasticity. Int J Solids Struct. 1974;10(3):313–9.MathSciNetzbMATHCrossRefGoogle Scholar
  201. Lubliner J. An axiomatic model of rate-independent plasticity. Int J Solids Struct. 1980;16(8):709–13.MathSciNetzbMATHCrossRefGoogle Scholar
  202. Lubliner J. A maximum-dissipation principle in generalized plasticity. Acta Mech. 1984;52(3):225–37.MathSciNetzbMATHCrossRefGoogle Scholar
  203. Lubliner J. Plasticity theory. NY: Macmillan Publishing Company; 1990.zbMATHGoogle Scholar
  204. Lubliner J, Auricchio F. Generalized plasticity and shape-memory alloys. Int J Solids Struct. 1996;33(7):991–1003.zbMATHCrossRefGoogle Scholar
  205. 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.zbMATHCrossRefGoogle Scholar
  206. Machida N, Uehara K. Nonlinear thermal stress analysis of a massive concrete structure. Comput Struct. 1987;26(1–2):287–96.Google Scholar
  207. 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
  208. 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.CrossRefGoogle Scholar
  209. Malan DF. Simulating the time-dependent behaviour of excavations in hard rock. Rock Mech Rock Eng. 2002;35(4):225–54.Google Scholar
  210. Malvern LE. Introduction to the mechanics of a continuous medium. Englewood Cliffs: Prentice-Hall Inc; 1969.zbMATHGoogle Scholar
  211. Manzari MT, Nour MA. Significance of soil dilatancy in slope stability analysis. J Geotech Geoenviron Eng ASCE. 2000;123(1):75–80.CrossRefGoogle Scholar
  212. Maranini E, Brignoli M. Creep behaviour of a weak rock: experimental characterization. Int J Rock Mech Min Sci. 1999;36(1):127–38.CrossRefGoogle Scholar
  213. 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.zbMATHCrossRefGoogle Scholar
  214. 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
  215. Mehta PK, Monteiro PJM. Concrete: microstructure, properties, and materials, 3rd ed. New York: McGraw-Hill; 2006.Google Scholar
  216. Michino MJ, Findley WN. An historical perspective of yield surface investigation for metals. Int J Non-linear Mech. 1976;11(1):59–82.zbMATHCrossRefGoogle Scholar
  217. 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.CrossRefGoogle Scholar
  218. 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
  219. 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
  220. Morland LW. Continuum model of regularly jointed mediums. J Geophys Res. 1974;79(2):357–62.CrossRefGoogle Scholar
  221. 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
  222. Mukherjee S. Boundary elements in creep and fracture. London: Applied Science Publishers; 1982.zbMATHGoogle Scholar
  223. Müller L. Address to the opening session. In: Proceedings of 1st ISRM congress. Lisbon: LNEC; 1967. p. 80–3.Google Scholar
  224. Müller L, editor. Rock mechanics. Wien: Springer; 1974.Google Scholar
  225. Murakami S. Notion of continuum damage mechanics and its application to anisotropic creep damage theory. J Eng Mater Technol. 1983;105(2):99–105.CrossRefGoogle Scholar
  226. Murakami S. Mechanical modeling of material damage. J Appl Mech. 1988;55(2):280–6.CrossRefGoogle Scholar
  227. 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
  228. Nayak GC, Zienkiewicz OC. Convenient form of stress invariants for plasticity. J Struct Div ASCE. 1972;98(ST4):949–53.Google Scholar
  229. Nemat-Nasser S, Obata M. A microcrack model of dilatancy in brittle materials. J Eng Mech ASCE. 1988;55(1):24–35.CrossRefGoogle Scholar
  230. Neville AM. Creep of concrete as a function of its cement paste content. Mag Concr Res. 1964;16(46):21–30.CrossRefGoogle Scholar
  231. Neville AM, Diger WH, Brooks JJ. Creep of plain and structural concrete. London: Construction Press; 1983.Google Scholar
  232. 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.CrossRefGoogle Scholar
  233. 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.zbMATHCrossRefGoogle Scholar
  234. 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.CrossRefGoogle Scholar
  235. 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.CrossRefGoogle Scholar
  236. Nuezil CE, Tracy JV. Flow through fractures. Water Resour Res. 1981;17(2):191–9.CrossRefGoogle Scholar
  237. Oda M. Fabric tensor for discontinuous geological materials. Soils Found. 1982;22(4):96–108.CrossRefGoogle Scholar
  238. 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.CrossRefGoogle Scholar
  239. Oda M. Similarity rule of crack geometry in statistically homogeneous rock masses. Mech Mater. 1984;3(2):119–29.CrossRefGoogle Scholar
  240. 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.CrossRefGoogle Scholar
  241. 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.CrossRefGoogle Scholar
  242. 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.CrossRefGoogle Scholar
  243. Oda M, Suzuki K, Maeshibu T. Elastic compliance for rock-like materials with random cracks. Soils Found. 1984;24(3):27–40.CrossRefGoogle Scholar
  244. 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.CrossRefGoogle Scholar
  245. 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.CrossRefGoogle Scholar
  246. Oden JT. Finite elements of nonlinear continua. New York: McGraw-Hill; 1972.zbMATHGoogle Scholar
  247. Odqvist FKG. Mathematical theory of creep and creep rupture, 2nd ed. Oxford: Clarendon; 1974.Google Scholar
  248. Öhman J, Niemi A. Upscaling of fracture hydraulics by means of an oriented correlated stochastic continuum model. Water Resour Res. 2003;39(10):1277.CrossRefGoogle Scholar
  249. 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.CrossRefGoogle Scholar
  250. 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.CrossRefGoogle Scholar
  251. 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.zbMATHCrossRefGoogle Scholar
  252. Ortiz M, Popov EP. Accuracy and stability of integration algorithms for elastoplastic constitutive relations. Int J Numer Meth Eng. 1985;21(9):1561–76.MathSciNetzbMATHCrossRefGoogle Scholar
  253. Ortiz M, Leroy Y, Needleman A. A finite element method for localized failure analysis. Comput Meth Appl Mech Eng. 1987;61(2):189–214.zbMATHCrossRefGoogle Scholar
  254. Owen DRJ, Hinton E. Finite elements in plasticity: theory and practice. Swansea: Pineridge Press Ltd; 1980.zbMATHGoogle Scholar
  255. Owen DRJ, Hinton E, Onate E. Computational plasticity: models, software and applications. Swansea: Pineridge Press Ltd; 1989.zbMATHGoogle Scholar
  256. 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.CrossRefGoogle Scholar
  257. 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
  258. Paul B. A modification of the Coulomb-Mohr theory of fracture. J Appl Mech. 1961;28(2):259–68.MathSciNetCrossRefGoogle Scholar
  259. Perzyna P. The constitutive equations for rate sensitive plastic materials. Q Appl Math. 1963;20(4):321–32.MathSciNetzbMATHCrossRefGoogle Scholar
  260. Pijaudier-Cabot G, Bažant ZP. Nonlocal damage theory. J Eng Mech Div ASCE. 1987;113(10):1512–33.zbMATHCrossRefGoogle Scholar
  261. Pisarenko GS, Lebedev AA. Deformation and strength of material under complex stressed state. Kiev: Naukova Dumka; 1976 (in Russian).Google Scholar
  262. 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.CrossRefGoogle Scholar
  263. Pramono E, Willam K. Implicit integration of composite yield surface with corners. Eng Comput. 1989;6(3):186–97.CrossRefGoogle Scholar
  264. Prandtl L, editor. Proceedings of 1st international congress for applied mechanics. Delft: IUTAM; 1924.Google Scholar
  265. 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.CrossRefGoogle Scholar
  266. 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
  267. Rappaz M, Bellet M, Deville M. Numerical modeling in materials science and engineering. Berlin: Springer; 2003.zbMATHCrossRefGoogle Scholar
  268. 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.CrossRefGoogle Scholar
  269. Reuss A. Berucksichtigung der elastichen, Formanderung in der Plastizitatstheorie. ZaMM. 1930;10:266 (in German).zbMATHCrossRefGoogle Scholar
  270. Rhodes JA. Prediction of creep, shrinkage and temperature effects in concrete structures. ACI report 209R-92. Detroit: ACI Committee 209; 1992.Google Scholar
  271. 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.zbMATHCrossRefGoogle Scholar
  272. 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
  273. Rice JR. Thermodynamics of quasi-static growth of Griffith cracks. J Mech Phys Solids. 1978;26(2):61–78.zbMATHCrossRefGoogle Scholar
  274. 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.CrossRefGoogle Scholar
  275. Rockafellar RT. Convex analysis. Princeton: Princeton University Press; 1969.zbMATHGoogle Scholar
  276. Poмм EC (Romm ES). Фильтpaциoнныe cвoиcтвa тpeщинoвтыx гopныx пopoд (Flow characteristics of fractured rocks). Mocквa (Moscow): Издaтeльcтвo Heдpa (Nedra); 1966 (in Russian).Google Scholar
  277. Romana MR. A geomechanical classification for slopes: slope mass rating. In: Hudson JA, editor. Comprehensive rock engineering. Oxford: Pergamon Press; 1993. p. 575–600.CrossRefGoogle Scholar
  278. 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
  279. Rudnicki JW, Rice JR. Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids. 1975;23(6):371–94.CrossRefGoogle Scholar
  280. Runesson K, Sture S, Willam K. Integration in computational plasticity. Comput Struct. 1988;30(1–2):119–30.zbMATHCrossRefGoogle Scholar
  281. 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.CrossRefGoogle Scholar
  282. 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.CrossRefGoogle Scholar
  283. Rutter EH. Kinetics of rock deformation by pressure solution. Philos Trans R Soc Lond. 1976;A283(1312):203–19.CrossRefGoogle Scholar
  284. 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.CrossRefGoogle Scholar
  285. Salamon MDG. Elastic moduli of a stratified rock mass. Int J Rock Mech Min Sci. 1968;5(6):519–27.CrossRefGoogle Scholar
  286. Samier P, Onaisi A, Fontaine G. Comparisons of uncoupled and various coupling techniques for practical field examples. SPE J. 2006;11(1):89–102.CrossRefGoogle Scholar
  287. 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.zbMATHCrossRefGoogle Scholar
  288. Scheunemann P. The influence of failure criteria on strength prediction of ceramic components. J Eur Ceram Soc. 2004;24(8):2181–6.CrossRefGoogle Scholar
  289. Scholtz CH. Mechanism of creep in brittle rock. J Geophys Res. 1968;73(10):3293–302.Google Scholar
  290. Schrefler BA. Computer modelling in environmental geomechanics. Comput Struct. 2001;79(22–25):2209–23.CrossRefGoogle Scholar
  291. 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
  292. 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.CrossRefGoogle Scholar
  293. 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.CrossRefGoogle Scholar
  294. Selvadurai APS, Nguyen TS. Mechanics and fluid transport in a degradable discontinuity. Eng Geol. 1999;53(3–4):243–9.CrossRefGoogle Scholar
  295. 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
  296. 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.CrossRefGoogle Scholar
  297. 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
  298. 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.CrossRefGoogle Scholar
  299. 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.CrossRefGoogle Scholar
  300. Simo JC, Hughes TJR. Elastoplasticity and viscoplasticity—computational aspects. New York: Springer; 1988.Google Scholar
  301. Simo JC, Hughes TJR. Computational inelasticity. NewYork: Springer; 1998.zbMATHGoogle Scholar
  302. 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.CrossRefGoogle Scholar
  303. 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.CrossRefGoogle Scholar
  304. Singhal BBS, Gupta RP. Applied hydrogeology of fractured rocks, 2nd ed. Dordrecht: Springer; 2010.CrossRefGoogle Scholar
  305. Skarzynski L, Tejchman J. Determination of representative volume element in concrete under tensile deformation. Comput Concr. 2012;9(1):35–50.CrossRefGoogle Scholar
  306. Sloan SW, Booker JR. Removal of singularities in Tresca and Mohr-Coulomb yield function. Comm Appl Num Meth. 1986;2(2):173–9.zbMATHCrossRefGoogle Scholar
  307. Snow D. Anisotropic permeability of fractured media. Water Resour Res. 1969;5(6):1273–89.CrossRefGoogle Scholar
  308. 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.CrossRefGoogle Scholar
  309. Stagg KG, Zienkiewicz OC, editors. Rock mechanics in engineering practice. NewYork: Wiley; 1986.Google Scholar
  310. 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
  311. Sterpi D. An analysis of geotechnical problems involving strain softening effects. Int J Numer Anal Meth Geomech. 1999;23(13):1427–54.zbMATHCrossRefGoogle Scholar
  312. 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
  313. 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
  314. 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.zbMATHCrossRefGoogle Scholar
  315. Sutcliffe DJ, Yu HS, Page AW. Lower bound limit analysis of unreinforced masonry shear walls. Comput Struct. 2001;79(14):1295–312.CrossRefGoogle Scholar
  316. 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.CrossRefGoogle Scholar
  317. 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.zbMATHCrossRefGoogle Scholar
  318. 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.zbMATHCrossRefGoogle Scholar
  319. Taliercio A, Landriani GS. A failure condition for layered rock. Int J Rock Mech Min Sci Geomech Abstr. 1988;25(5):299–305.CrossRefGoogle Scholar
  320. Tappennier P, Brace WF. Development of stress–induced microcracks in Westerly granite. Int J Rock Mech Min Sci. 1976;13(4):103–12.CrossRefGoogle Scholar
  321. Tazawa E, Miyazawa S. Experimental study on mechanism of autogenous of concrete. Cem Concr Res. 1995;25(8):1633–8.CrossRefGoogle Scholar
  322. Thomas HR, Cleall PJ. Inclusion of expansive clay behaviour in coupled thermo hydraulic mechanical models. Eng Geol. 1999;54(1–2):93–108.CrossRefGoogle Scholar
  323. 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.zbMATHCrossRefGoogle Scholar
  324. 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.zbMATHCrossRefGoogle Scholar
  325. Tien YM, Kuo MC. A failure criterion for transversely isotropic rocks. Int J Rock Mech Min Sci. 2001;38(3):399–412.CrossRefGoogle Scholar
  326. 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.CrossRefGoogle Scholar
  327. Timoshenko SP. History of strength of materials. New York: McGraw-Hill Book Company Inc; 1953.Google Scholar
  328. Triantafyllidis T, Gerolymatou E. Estimation of the strength of stratified rock mass. Rock Mech Rock Eng. 2014;47(2):535–47.CrossRefGoogle Scholar
  329. 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
  330. Tsang CF, editor. Coupled processes associated with nuclear waste repositories. New York: Academic Press; 1987.Google Scholar
  331. Tsang CF. Coupled thermomechanical and hydrochemical processes in rock fractures. Rev Geophys. 1991;29(4):537–48.CrossRefGoogle Scholar
  332. Tsang YW, Witherspoon PA. Hydromechanical behavior of a deformable rock fracture subject to normal stress. J Geophys Res. 1981;86(B10):9287–98.CrossRefGoogle Scholar
  333. Ulm FJ, Coussy O. Modeling of thermochemomechanical couplings of concrete at early ages. J Eng Mech ASCE. 1995;121(7):785–94.CrossRefGoogle Scholar
  334. 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
  335. Ulusay R, editor. The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014. Cham: Springer; 2015.Google Scholar
  336. 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
  337. Valanis KC. A theory of viscoplasticity without a yield surface. Archiwum Mechaniki Stossowanej. 1971;23(4):517–51.MathSciNetzbMATHGoogle Scholar
  338. 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
  339. Valanis KC, Wu HC. Endochronic representation of cyclic creep and relaxation of metals. J Appl Mech ASME. 1975;42(1):67–73.zbMATHCrossRefGoogle Scholar
  340. 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.CrossRefGoogle Scholar
  341. 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
  342. Vermeer JPA, de Borst R. Non-associated plasticity for soils, concrete and rock. HERON. 1984;29(3):3–64.Google Scholar
  343. 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
  344. Von Mises R. Mechanik der Festen Korper im plastisch deformablen Zustand. Göttin Nachr Math Phys. 1913;1:582–92 (in German).zbMATHGoogle Scholar
  345. 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.CrossRefGoogle Scholar
  346. 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.CrossRefGoogle Scholar
  347. 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.zbMATHCrossRefGoogle Scholar
  348. Wardle LJ, Gerrard CM. The ‘‘equivalent’’ anisotropic properties of layered rock and soil masses. Rock Mech Rock Eng. 1972;4(3):155–75.CrossRefGoogle Scholar
  349. 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.zbMATHCrossRefGoogle Scholar
  350. 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.CrossRefGoogle Scholar
  351. 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.CrossRefGoogle Scholar
  352. 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
  353. Wilson CR, Witherspoon PA. An investigation of laminar flow in fractured porous rocks. Berkeley: University of California; 1970.Google Scholar
  354. 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.CrossRefGoogle Scholar
  355. Wittmann FH. Creep and shrinkage mechanisms. In: Bažant ZP, Wittmann FH, editors. Creep and shrinkage of concrete structures. London: Wiley; 1982. p. 129–61.CrossRefGoogle Scholar
  356. 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
  357. 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
  358. 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.CrossRefGoogle Scholar
  359. 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.CrossRefGoogle Scholar
  360. 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).CrossRefGoogle Scholar
  361. 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).MathSciNetGoogle Scholar
  362. 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
  363. 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.CrossRefGoogle Scholar
  364. Young JF, Mindness S, Gray RJ, Bentur A. The science and technology of civil engineering materials. NJ: Prentice Hall; 1998.Google Scholar
  365. 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.CrossRefGoogle Scholar
  366. Yu MH, Li JC. Computational plasticity with emphasis on the application of the unified strength theory. Hangzhou: Zhejiang University Press; 2012.Google Scholar
  367. 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
  368. 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
  369. 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.CrossRefGoogle Scholar
  370. 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.CrossRefGoogle Scholar
  371. 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.CrossRefGoogle Scholar
  372. 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
  373. 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
  374. Zhu BF. On the formula for modulus of elasticity of concrete. J Hydraul Eng. 1996;26(3):89–90 (in Chinese).MathSciNetGoogle Scholar
  375. Zienkiewicz OC, editor. Rock mechanics in engineering practice. New York: Wiley; 1968.Google Scholar
  376. Zienkiewicz OC, Cormeau IC. Viscoplasticity solution by finite element process. Arch Mech. 1972;24(5–6):873–88.zbMATHGoogle Scholar
  377. 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
  378. 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
  379. 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
  380. 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.CrossRefGoogle Scholar
  381. 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.zbMATHCrossRefGoogle Scholar
  382. 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.zbMATHCrossRefGoogle Scholar
  383. Zimmerman RW. Coupling in poroelasticity and thermoelasticity. Int J Rock Mech Min Sci. 2000;37(1):79–87.CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Water Resources and Hydropower EngineeringWuhan UniversityWuhanP.R. China

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