Paint your entire mantel white, and allow the paint to dry. Then, apply a glaze coat over the whole mantel, but go back with a moist cotton rag and wipe off the excess. You can buy premixed glaze at home improvement retailers, or you can mix from a glaze kit available at those same places, or from specialty craft shops. Generally, the ratio is one part of paint for every three parts of glaze.
Add in layers of different brown paints (raw sienna or even burnt umber), applying with a sponge brush or a cotton rag in the crevices around the trim accents. The more shades you can mix in between white and brown, the closer you will get to a look like rock.
Go back and add your mixture of colors to lines that run along the mantel. Put another layer of glaze over the entire mantel once you have finished swirling paints and textures on the fireplace.