This paper reports the results of a search for strong production of supersymmetric particles in 20.1 fb(-1) of proton-proton collisions at a centre-of-mass energy of 8 TeV using the ATLAS detector at the LHC. The search is performed separately in events with either zero or at least one high-p (T) lepton (electron or muon), large missing transverse momentum, high jet multiplicity and at least three jets identified as originated from the fragmentation of a b-quark. No excess is observed with respect to the Standard Model predictions. The results are interpreted in the context of several supersymmetric models involving gluinos and scalar top and bottom quarks, as well as a mSUGRA/CMSSM model. Gluino masses up to 1340 GeV are excluded, depending on the model, significantly extending the previous ATLAS limits.