Second-gradient theories in mechanics have a history dating back many decades. One of the pioneering second-gradient theories in mechanics was pre- sented by Mindlin [1]. These theories are still a subject of great interest to- day due to their capability of describing higher-order effects in materials that could not be captured by classical first-order theories [2,3,4]. In recent years, second-gradient theories have been used in the diverse fields of continuum mod- eling, e.g., in the context of computational homogenization [5] and coupled problems such as flexo-electricity and poro-elasticity [6]. In the case of poro- elasticity, first-order theories are unable to predict important material features in scenarios where high displacement and fluid-flux gradients are involved. In these situations, second-gradient theories can help us to get a more accurate picture of the behavior [6]. To harness the full potential of second-order poro- mechanical theories in engineering applications, computational methods serve an important function since they enable us to study associated phenomena on arbitrary domains under different boundary conditions. In the present work, we aim to develop a space-time discrete variational formulation of a multi-field poro-elastic problem that extends the first-order poro-elastic model of Miehe et al. [7] by taking into account second-order effects. To achieve that, we exploit a Hu-Washizu-type minimization formulation of poro-elasticity that accounts for the displacement and fluid-mass content together with their gradients as pri- mary fields. The resulting mixed formulation will allow us to use C0-continuous Lagrangian shape functions in a corresponding conforming finite-element formu- lation. The predictive capabilities of the model are demonstrated by analyzing second-gradient effects in a representative sequence of numerical examples ap- plied to poro-elastic problems in which boundary- and interface effects play are crucial. References [1] R. D. Mindlin, Second gradient of strain and surface-tension in linear elas- ticity. International Journal of Solids and Structures, 1:417–438, 1965. [2] P. Steinmann, On boundary potential energies in deformational and configu- rational mechanics. Journal of the Mechanics and Physics of Solids, 56:772–800, 2008. [3] A. Javili, F. dell’Isola and P. Steinmann, Geometrically nonlinear higher- gradient elasticity with energetic boundaries. Journal of the Mechanics and Physics of Solids, 61:2381–24