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We clarify the structure obtained in H\'elein and Vey's proposition for avariational principle for the Einstein-Cartan gravitation formulated on a framebundle starting from a structure-less differentiable 10-manifold. The obtainedstructure is locally equivalent to a frame bundle which we term "generalisedframe bundle". In the same time, we enrich the model with a Dirac spinorcoupled to the Einstein-Cartan spacetime. The obtained variational equationsgeneralise the usual Einstein-Cartan-Dirac field equations in that they areshown to imply the usualy field equations when the generalised frame bundle isa standard frame bundle.

Physics and Geometry from a Lagrangian: Dirac Spinors on a Generalised Frame Bundle