Cross-scale reconstruction of rock discontinuity rough surfaces: A waveform-based extrapolation framework

Natural rock discontinuity surfaces have consistently posed significant challenges in solid geoscience and deep rock engineering. Specifically, the scale gap and the insufficient characterization of the rough morphology of these surfaces impede the comprehension of the discontinuity-controlled fluid-mechanical processes, yet direct observations across multiple scales are still constrained. The rough discontinuity surfaces exhibit pronounced topographic undulations and wave-like undulating patterns that can be conceptualized as waveform-dominated morphologies with inherent spectral characteristics. Here, we develop an integrated framework leveraging discrete cosine transform (DCT), inverse DCT (IDCT), and random phase (RP) theories to characterize and reconstruct three-dimensional rough discontinuity surface morphologies. This framework quantifies roughness through spectral parameters, amplitude and frequency, represented as surface waveform components. By incorporating RP into multi-topography twin reconstruction processes, it rapidly generates multiple surface topographies while preserving geometric similarity to parent samples. A scale-expanding reconstruction module further overcomes the periodic transformation artifacts inherent in surface wave propagation, avoiding artificial symmetry or periodicity during upscaling. Coupled with anisotropy regulation, this approach enables cross-scale simulation and inference of rock discontinuity surfaces based on localized data acquisition from limited outcrop exposure ranges, while faithfully responding to the characteristics of natural rough topographies. We validated the framework through cross-scale reconstruction of discontinuity surfaces in granite outcrops exposed at the Beishan high-level radioactive waste geological disposal site in China. Results demonstrate reduced simulation uncertainties and enhanced predictive reliability. By providing a geometrically realistic cross-scale bridge for discontinuity surfaces, this framework offers a promising pathway for investigating discontinuity-controlled fluid-mechanical processes in rock geoscience.