ARTICLE IN PRESS JID: MPS [m3Gsc;October 12, 2017;20:47] Journal of the Mechanics and Physics of Solids 000 (2017) 1–13 Contents lists available at ScienceDirect Journal of the Mechanics and Physics of Solids journal homepage: www.elsevier.com/locate/jmps Hydrodynamic derivation of the work input to fully and partially saturated soils Itai Einav a,∗ , Mario Liu b a School of Civil Engineering, The University of Sydney, 2006 Sydney, Australia b Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany a r t i c l e i n f o Article history: Received 19 June 2017 Revised 8 September 2017 Accepted 6 October 2017 Available online xxx a b s t r a c t In ‘Rational Mechanics’ the work input per unit element volume can be identified from the local energy balance, itself being derived through localization from the global energy bal- ance of an arbitrary volume. On the other hand, in the search of meaning for an effective stress of partially and fully saturated soil media, in ‘Soil Mechanics’ some define the work input by adopting material assumptions and simplified homogenization. The final result depends on effective stress and various pressures that are not seen in the rational me- chanics work input expression. To resolve the discrepancy in the structure of the work in- put, this paper establishes a third approach based on the ‘Hydrodynamic procedure’, which operates solely at the level of unit volumes and thus does not require localization. The derived equations fully agree with Rational Mechanics, and yield the same work input ex- pressions. The bonus for employing the more comprehensive Hydrodynamic procedure is that it also reveals the meaning of the effective stress in relation to the various pressures. © 2017 Published by Elsevier Ltd. 1. Introduction The expression of the local energy conservation of a continuum element is known to contain different system dependent terms. In ‘Rational Mechanics,’ these terms are often recovered through the localization of the global forms of energy and power balances of arbitrary continuum volumes (Coleman and Gurtin, 1967; Coleman and Noll, 1963; Gurtin et al., 2010; Truesdell, 1965). The work input 1 can then be identified from the different terms in the local energy conservation. The explicit form of the work input is therefore also known to depend on the structure of the system. For example, in a single component continuum, the work input for first gradient media is simply the product of the Cauchy stress and the symmetric strain rate tensors (Germain, 1973; Gurtin et al., 2010). In multi-component continua, the work input additionally depends on the gradient of the product of the chemical potentials and mass supplies of the various material species (Gurtin et al., 2010). In both cases, the work input is found to depend on the total Cauchy stress. On the other hand, in ‘Soil Mechanics’ it is customary to define the constitutive relationships of the media in terms of the effective stress, rather than the total stress, both for fully (Terzaghi, 1943) and partially saturated (Bishop, 1959) soils. The use of this principle has been widely embraced empirically (e.g., see Alonso et al., 2010; Lade and De Boer, 1997). However, since the sole use of ‘Rational Mechanics’ cannot disclose the meaning of an effective stress, some have adopted a ∗ Corresponding author. E-mail addresses: itai.einav@sydney.edu.au (I. Einav), mliu@uni-tuebingen.de (M. Liu). 1 ‘Work input’ is used in the following as a shorthand for ‘the rate of work input into a continuum unit volume element’. https://doi.org/10.1016/j.jmps.2017.10.004 0022-5096/© 2017 Published by Elsevier Ltd. Please cite this article as: I. Einav, M. Liu, Hydrodynamic derivation of the work input to fully and partially saturated soils, Journal of the Mechanics and Physics of Solids (2017), https://doi.org/10.1016/j.jmps.2017.10.004