Fractal fracture-fluid controls on freeze–thaw hydro-thermo-mechanical evolution of cold-region slopes

Freeze–thaw degradation of cold-region slopes is strongly mediated by geometrically complex fracture networks, yet prevailing models subsume discontinuities into bulk, empirically tuned permeability. The fractal hydro-thermo-mechanical framework is formulated in which fracture architecture is parameterized by three scale-aware descriptors—tortuosity fractal dimension DT, population fractal dimension Ds, and roughness parameter ε—that generate closed-form permeation–diffusion closures within coupled heat–moisture–deformation equations. Depth-resolved DT, Ds, and ε are obtained directly from micro-computed tomography and scanning electron microscope imaging of an alpine road-cut slope (∼95 km northwest of Maduo County, Qinghai Province), enabling forward prediction without empirical back-fitting. The model reproduces independent freezing/thawing column experiments with root mean square moisture profile errors below ∼2% points, confirming parameter sufficiency. Field-scale application demonstrates physically partitioned controls: increasing DT (1.35 → 1.55) deepens seasonal temperature minima (≈3–4 K) and amplifies thermal amplitude (≈15%–18%) while modestly lowering unfrozen water troughs; increasing Ds (1.52 → 1.72) elevates winter mean temperature (≈2–2.5 K), raises minimum water content (≈12%–15%), and attenuates amplitude (≈8%–10%) through enhanced lateral–vertical supply; elevating ε (0.06 → 0.08) increases residual unfrozen water (≈6%–8%) and mid-winter temperature (≈1–1.3 K) while refining ice lens stratigraphy (single-lens thickness reductions ≈10%–15%). These responses establish a concise micro-to-macro-linkage in which DT governs transport efficiency and phase timing, Ds governs network-scale buffering, and ε governs retention and lens morphology. This study offers both an immediate analytical tool for infrastructure stewardship and a scalable method for multi‑physics investigations of cold‑region fluids behavior and slopes stability.