Studying the mechanisms that control the rheology of rocks and geomaterials is crucial as much for predicting geological processes as for functionalizing geomaterials. That requires the understanding of how structural arrangements at the micro and nano scale control the physical and mechanical properties at the macroscopic scale. This is an area of rock physics still in its infancy. In this paper, we focus the attention on the formation of cementitious phases made of micro- and nano-scale fibrous structures, and the controls of the arrangement of these phases on mechanical properties. We use hydrothermal synthesis, and the properties of hydrothermal water, to promote the growth of fibrous mineral phases having nano-size diameter and length of a few microns, creating disordered and entangled mats of fibrous bundles as those found in natural samples. We draw inferences from structural microscopy to inform a statistical model that establishes an interdependence between structural parameters of fibrous structures and bulk mechanical response. Structural parameters include number and length of fibers, spatial orientation, and fraction of fibrous threads bearing the load. Mechanical properties include strength and mode of failure. Results show that as the fibrous microstructure evolves from ordered and aligned to disordered and entangled, the mechanical response of the fibrous composite transitions from a brittle to ductile behavior. Furthermore, the disordered and entangled microstructure exhibits lower strength at failure though strength increases as the number of fibers within the microstructure increases. Finally, the longer the entangled fiber, the larger the strain that the matrix can accommodate. The value of this study lies in further understanding fault healing through hydrothermal fluids and how the physical properties of fibrous microstructures resulting from it control brittle-ductile transitions, and possibly, slow slip events along subduction zones.