Using experiments that simulate deep tectonic interfaces, known as viscous shear zones, we found that these zones spontaneously develop periodic sheets of small pores. The presence of porous layers in deep rocks undergoing tectonic deformation is significant because it requires a change to the current model of how the Earth deforms. Emergent porous layers in viscous rocks will focus mineralising fluids and could lead to the seismic failure of rocks that are never supposed to have this occur.