A method of solidifying toxic or hazardous liquid waste, including the steps of pumping an aqueous waste, e.g., from a drilling fluid holding area; through a shearing device; adding the layered phyllosilicate to said aqueous waste in an amount sufficient to solidify the aqueous waste sufficiently such that the solidified aqueous waste has no free liquid; shearing the pumped aqueous waste, containing said layered phyllosilicate, sufficiently to partially exfoliate the layered phyllosilicate into phyllosilicate platelets and tactoids while in contact with the aqueous waste; pumping the sheared aqueous waste and layered phyllosilicate to a solidification area; and allowing the sheared aqueous waste and partially exfoliated layered phyllosilicate sufficient time to solidify such that there are no free liquids remaining in the solidified waste.