A search for three-jet hadronic resonance production in pp collisions at a centre-of-mass energy of 8 TeV has been conducted by the CMS Collaboration at the LHC with a data sample corresponding to an integrated luminosity of 19.4 inverse femtobarns. The search method is model independent, and events are selected that have high jet multiplicity and large values of jet transverse momenta. The signal models explored assume R-parity-violating supersymmetric gluino pair production and have final states with either only light-flavour jets or both light- and heavy-flavour jets. No significant deviation is found between the selected events and the expected standard model multijet and t t-bar quark background. For a gluino decaying into light-flavour jets, a lower limit of 650 GeV on the gluino mass is set at a 95% confidence level, and for a gluino decaying into one heavy- and two light-flavour jets, gluino masses between 200 and 835 GeV are, for the first time, likewise excluded.