A Multi-Basis Spacing Algorithm for Modeling Directional Uncertainty in In-situ Block Size Distribution of Rock Masses with Non-Persistent Joints

Only when the propagation histories of fracture networks in crystalline rock masses are honored can statistical Discrete Fracture Network (DFN) models accomplish realism in the estimation of emergent In-situ Block Size Distribution (IBSD) models, while considering directional uncertainties as a result of fracture arrests within the DFN. The fracture network hierarchy of a DFN can be modeled using the quantification of topological graph representations of fracture traces as input parameters, along with power-law-distributed fracture sizes. In this study, a new algorithm called the multi-basis spacing algorithm (MBS) is developed based on both standard and Eulerian multi-basis rotational local coordinate system configurations for IBSD estimation. The MBS code is verified via idealized SRM models, rotated obliquely with respect to the standard basis coordinate system. We effectively demonstrate the capability of the MBS method in modeling uncertainty in IBSD via a topologically non-persistent power-law DFN model. Our results show that both the progressive standard multi-basis and the Eulerian multi-basis rotation reveal directional variability in IBSD curves, providing a method for capturing directional uncertainty in IBSD. Fundamentally, the MBS-based computation in IBSD innovates modeling directional variability in topologically non-persistent rock masses in rock mass characterization, enhancing the reliability of rock engineering design.