Dear Lu Lu: the mantle does contain water, of course it is combined water in the form of the oxydrile (OH)- anion. High pressure polymorphs of olivine, wadsleyite and ringwoodite have spinel-like structures which allow protonization of part of their oxygen, transforming it in (OH). Surely the proportion of (OH) in these minerals is very low, not more than a few % in weight, but they abbundance is such in the mantle transition zone that it is believed that the total of water stored in them could double the total water present in world oceans. A microscopic inclusion of ringwoodite (spinel structured olivine) found in a diamond in Mato Grosso, Brazil some years ago, was analyzed and contained some 6% H20 in the form of (OH), the color is the tiny mineral grain is deep blue, almost suggesting water presence in it... I think the (2014) paper suggested by Bachir Achour refers precisely to this finding. Also, astenospheric mantle is considered to have some 1% water, in order to make it flow in a visco-plastic manner, thus allowing plate tectonics movements. And moreover, parts of the mantle get hydrated in subduction zones, especially the mantle lithosphere wedge below volcanic arcs and active margins, with fluids coming from dehydration of subducted oceanic crust, acording to prevailing models of petrogenesis in magmatic arcs. So there's quite a lot of water in the mantle, but it has to be released by partial fusion at a definite temperature, different for each mineral, else it stays combined in the minerals. With regards. Sebastian.
Here some ref: Beier et al., 2012 JVGR; Bonatti 1990 Science; Asimov et al. 2004 ; Geochemistry Geophysics, Geosystems; Schilling et al., 1980 PTRS London among others. Hope this can help you. Regards,