key mechanical parameters of root.

This study employs response surface methodology (RSM) integrated with a hybrid Box-Behnken and D-optimal experimental design to unravel the multi-parameter coupling effects of root reinforcement on the hydro-mechanical behavior of expansive soils. The experimental framework systematically investigated root diameter (1–5 mm), length (30–50 mm), quantity (3–5 roots), and distribution patterns (horizontal, inclined, composite), with quantitative assessments of disintegration amount (DA), swelling force (SF), and swelling rate (SR). Key findings reveal that root diameter (X1) and quantity (X4) dominate disintegration control, exhibiting significant main effects (Fx1 = 173.8, Fx2 = 112.9, p < 0.0001), while the synergistic interaction between diameter and length (X1X2, , p = 0.0012) further enhances stabilization through mechanical interlocking. Composite root distribution (D3) outperformed horizontal (D1) and inclined (D2) patterns, reducing DA by3.2 g (p < 0.0001) via its 3D interwoven structure, which constrains particle displacement and pore connectivity Quadratic polynomial models effectively predicted SF (R2 = 0.901) and rate (R2 = 0.822), with composite distribution suppressing SF by 41% under optimized parameters (X1 = 5 mm, X4 = 5 roots) through multi-axial confinement. A strong positive correlation (r = 0.92 for SF, r= = 0.90 for SR, p < 0.01) links DA to swelling behavior, where disintegration amplifies swelling via clay mineral activation and cementation breakdown, quantified as Y2 = 0.074Y12 + 0.305Y1 + 3.977. The results establish composite-root systems with high root density (X4 = 5 roots) and large diameter (X1 = 5 mm) as optimal for minimizing disintegration (predicted DA = 5.6g) and swelling (SR = 3.8%), providing a quantitative framework for eco-engineering slope stabilization in expansive soils through morphology-driven root-soil synergy.