## 1. Introduction

[2] *Revil et al*. [2011] recently developed a new set of constitutive equations to model cross-coupled transport phenomena in porous media. This model was however restricted to fully water saturated materials and for quasi-static flow problems (inertial effects were neglected). The motivation of the present paper is to extend the macroscopic generalized (cross-coupled) Darcy and Ohm laws to unsaturated porous materials and to account for dynamic effects (harmonic pressure or harmonic electrical fields and inertial terms). The final equations couple Biot's theory for unsaturated porous media to the Maxwell equations. The coupling is electrokinetic in nature.

[3] There are broad applications of such a model for the assessment of water resources and remediation. For instance, the record of the electrical field of electrokinetic nature can be used to image nonintrusively ground water flow and to get access easily to the parameters characterizing the capillary pressure curve and the relative permeability [*Jougnot et al*., 2012; *Mboh et al*., 2012]. With a cross-coupled flow theory, it is also possible to model electroosmosis, which can be used to move solutes and nonaqueous phase liquids (NAPLs)/dense NAPLs (DNAPLs) in the vadose zone and aquifers for remediation purposes [*Acar and Alshawabkeh,* 1993; *Bruell et al*., 1992; *Han et al*., 2004]. This method can also be used to dewater clayey soils in civil engineering [*Bjerrum*, 1967]. Finally, electroosmosis can be used also to move moisture up to the roots of plants [*Huweg et al*., 2010], the required electrical field can be produced through the use of photovoltaics [*Kamel*, 1994].

[4] The theory developed herein can be used to predict the electroseismic (electric-to-seismic conversion) effect in a broad range of frequencies (from 0.1 Hz to 100 kHz). The electroseismic coupling is related to the generation of seismic waves (hydromechanical disturbances) in response to a nonstationary electrical field [*Reppert and Morgan*, 2002; *Thompson*, 2005; *Thompson et al*., 2005]. While this effect has been mainly used so far for oil-related problems, it may be used to map NAPLs and DNAPLs as well [*Hinz*, 2011]. Alternatively, the seismoelectric (seismic-to-electric, SE) effect corresponds to the generation of electromagnetic disturbances from seismic waves [e.g., *Ivanov*, 1939; *Frenkel*, 1944; *Dupuis and Butler*, 2006; *Dupuis et al*., 2009; *Jardani et al*., 2010]. Hydromechanical disturbances (e.g., Haines jumps in unsaturated flow conditions, see *Haas and Revil* [2009]) can also be responsible for the generation of electromagnetic disturbances. These disturbances can in turn be remotely monitored by electromagnetic methods. To our knowledge, this is the first theory able to predict the electroseismic and SE effects in unsaturated conditions with applications to vadose zone hydrogeology. *Dupuis et al*. [2007] has demonstrated the feasibility to measure SE conversions for vadose zone applications.