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Strength Evolution of Geomaterials in the Octahedral Plane under Nonisothermal and Unsaturated Conditions

Victor Vilarrasa, Francesco Parisio, Lyesse Laloui

2017
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International Journal of Geomechanics
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25 Current geomechanical applications imply non-isothermal processes of unsaturated 26 geomaterials, in most cases following stress paths different than the classical triaxial 27 compression often used in laboratory testing. Though the effects of temperature, suction and 28 stress path direction (Lode's angle) on the strength of geomaterials have been investigated 29 independently, the integrated analysis combining the three effects has not been performed yet. 30 In this paper, we formulate a
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... r, we formulate a thermo-plastic constitutive model for unsaturated conditions that 31 accounts for the Lode's angle on the strength of geomaterials. The yield surface evolves 32 shrinking for increasing temperature, expanding for increasing suction and has its maximum 33 strength for triaxial compression and the minimum for triaxial extension. We highlight the 34 importance of accounting for temperature, suction and Lode's angle on the evolution of the 35 strength through examples that can be related to geo-energy applications. Numerical results 36 show that not considering these effects may give rise to misleading predictions of the strength 37 of geomaterials. 38 39 Keywords: Lode's angle, plane strain, thermo-plasticity, constitutive modeling, thermo-40 hydro-mechanical couplings 41 42 43 44 45 46 47 48 The strength of geomaterials is known to be dependent on the stress path direction in the 49 octahedral plane, i.e., on the Lode's angle (Potts and Gens, 1984) . The Lode's angle can be 50 accounted for in existing constitutive models using, for example, the van Eekelen formulation 51 (van Eekelen, 1980). However, deriving the parameters that describe the strength of 52 geomeaterials as a function of Lode's angle is difficult because the strength of soils is usually 53 derived from conventional triaxial tests at the laboratory scale. Despite their appellative, most 54 of the times conventional triaxial tests are to be intended as biaxial, since only two 55 components are controlled simultaneously (vertical stress and the horizontal stress, equal in 56 all directions and applied through confinement). To account for plane strain conditions, 'true 57 triaxial' tests, in which the three principal stresses, 1 , 2 and 3 , are controlled 58 simultaneously, are required (e.g. Makhnenko and Labuz, 2015). Since the actual strength is 59 lower for all stress paths different than a compressive triaxial stress path ( 23 ) (Lee, 60 1970; Peric et al., 1992; Alshibli et al., 2003; Wanatowski and Chu, 2007; Makhnenko and 61 Labuz, 2014), strength is usually overestimated in many geo-engineering problems that 62 involve stress paths different than triaxial compression (Potts and Gens, 1984), such as 63 landslides, shallow foundations and tunnel excavations. 64 In recent years, new geomechanical applications, including high-level nuclear waste disposal, 65 energy piles and geologic carbon storage, which imply temperature and suction variations, 66 have arisen because of the growing interest in geo-energies. This adds further complexity to 67 the strength evolution of geomaterials because, apart from the effect of Lode's angle, the 68 strength also evolves with temperature and suction changes. On the one hand, the yield limit 69 is enhanced as suction increases (Gens et al., 2006; Sheng, 2011) and on the other hand, the 70 yield surface shrinks for increasing temperatures (Hueckel and Baldi, 1990; Hueckel and 71 4 Borsetto, 1990; Laloui and Cekerevac, 2003). Though some efforts have been devoted to 72 determining the strength of soils for stress paths different than triaxial compression (e.g. 73 Nanda and Patra, 2015), the integrated analysis of the combined effect of temperature, suction 74 and stress path direction on the strength of geomaterials has not been performed (e.g. Xie and 75 Shao, 2012; Zhang et al., 2012). 76 This lack of integrated analysis of the strength of non-isothermal unsatured geomaterials 77 represents a big limitation to accurately predict the behavior of geomaterials in the current 78 applications that are of interest. The objective of this paper is to provide a qualitative 79 understanding of the effects of temperature, suction and stress path direction on the strength 80 of geomaterials. To do so, a non-isothermal constitutive model for unsaturated geomaterials 81 that accounts for the stress path direction is first presented. Next, we determine the evolution 82 of the strength as a function of temperature, suction and stress path direction considering 83 several examples that can be related to geo-energy applications. Finally, we discuss the 84 implications of this study and draw some conclusions. 85 86 MODEL FORMULATION 87 We describe a sophisticated constitutive model that captures the main characteristics of the 88 non-isothermal behavior of unsaturated geometarials. This constitutive model is based on the 89 work of Hujeux (1979) and its extensions to unsaturated non-isothermal conditions (Laloui 90 and François, 2009; François and Laloui, 2008; Di Donna and Laloui, 2015). It, not only 91 integrates non-linear thermoelasto-plasticity with a water retention curve model that includes 92 hysteresis between the drying and wetting paths, but also incorporates the Lode's angle to 93 account for a stress path dependent strength in the octahedral plane. 94 5 This constitutive model for unsaturated geomaterials under non-isothermal conditions is 95 formulated in terms of the generalized effective stress approach (Nuth and Laloui, 2008a; 96 Kim et al., 2013) 97 103 Changes in the effective stress will induce deformation of the geomaterial. Deformation can 104 be either elastic or plastic, where the classical decomposition of the incremental total strain 105 holds valid 106 d d d ep ε ε ε , 107 108 increment tensor and d p ε is the thermo-plastic strain increment tensor. Elastic strain will 109 occur when the stress state falls inside the yield surface. Additionally, plastic strain will occur 110 when the stress state lays on the yield surface. We adopt the sign convention of 111 geomechanics, i.e., stress and strain are positive in compression and negative in extension. 112 The rate of elastic strain is given by 113 p J J Lp J J Lp J Lp

doi:10.1061/(asce)gm.1943-5622.0000851
fatcat:elsw6s7uprhy5ccf4wjs3hdsuq