  In the hydraulic fracturing of natural rocks, understanding and predicting
crack penetrations into the neighboring layers is crucial and relevant in terms
of cost-efficiency in engineering and environmental protection. This study
constitutes a phase field framework to examine hydraulic fracture propagation
in naturally-layered porous media. Biot's poroelasticity theory is used to
couple the displacement and flow field, while a phase field method helps
characterize fracture growth behavior. Additional fracture criteria are not
required and fracture propagation is governed by the equation of phase field
evolution. Thus, penetration criteria are not required when hydraulic fractures
reach the material interfaces. The phase field method is implemented within a
staggered scheme that sequentially solves the displacement, phase field, and
fluid pressure. We consider the soft-to-stiff and the stiff-to-soft
configurations, where the layer interface exhibits different inclination angles
$\theta$. Penetration, singly-deflected, and doubly-deflected fracture
scenarios can be predicted by our simulations. In the soft-to-stiff
configuration, $\theta=0^\circ$ exhibits penetration or symmetrical
doubly-deflected scenarios, and $\theta=15^\circ$ exhibits singly-deflected or
asymmetric doubly-deflected scenarios. Only the singly-deflected scenario is
obtained for $\theta=30^\circ$. In the stiff-to-soft configuration, only the
penetration scenario is obtained with widening fractures when hydraulic
fractures penetrate into the soft layer.
