The present invention provides a wet press process and admixture components for making concrete slabs (flags) (16), curb (kerb) units, panels, boards, and other flat shapes, whereby colloidal silica and at least one alkanolamine and optional rheology control components are employed to provide an ideal combination of pressing time, green strength, surface definition, stack-ability, final concrete strength, and permeability. Stack-ability can be expressed in terms of minimum deflection or non-eccentricity of the units while standing on thickness edges at distances apart less than width or standing height. A wet press process typically involves introducing a highly fluid concrete mix into a mold (10,12), applying hydraulic pressure to consolidate the concrete (e.g., 1000-3000 PSI) and to extract excess water, removing the pressed concrete (16) while in a green state from the mold (10,12), and then standing the slab (16) units immediately upon removal from the mold (10,12) while in a green state, on an edge adjacent to but spaced apart from other edge-standing units. In further embodiments, rounded aggregates such as naturally occurring sand and/or gravel obtained from local sources can be incorporated into the concrete slabs without defeating (vertical) stack-ability in the green state.