Effect of transverse obstacle porosity on viscoplastic debris flows

Viscoplastic debris flows exert significant forces on protective installations in steep and flood-prone regions, yet the response of horizontal obstacles under such flows remains poorly understood. Three-dimensional viscoplastic flow simulations are conducted to investigate a single row of uniform horizontal obstacles, varying porosities (ϕ=0.3–1), and channel inclination (θ = 0°–30°). Maximum total forces on the obstacles and the downstream end wall, along with flow runout and unyielded regions, are quantified. Results reveal a strong nonlinear dependence of forces on both porosity and slope. For shallow slopes, obstacle forces increase with porosity, peaking near ϕ≈0.8, while very low porosities reduce end wall loads due to lateral flow redistribution and persistent unyielded zones. Increasing slope from 0° to 10° dramatically amplifies forces; e.g., the maximum obstacle force at ϕ=0.3 rises from 10.3 to 63.8 kN. At higher slopes, forces may decrease for certain porosities due to flow bypassing. End-wall forces generally increase with slope and porosity, exceeding 30 kN at θ = 30° and ϕ=1.0, with intermediate porosities (0.7 ≲ ϕ ≲ 0.9) producing locally elevated loads. End-wall forces are well captured by an exponential fit with porosity and slope. These findings emphasize the key role of porosity and slope in yielded/unyielded zones, force amplification, and runout, offering practical guidance for the design and placement of horizontal obstacles to mitigate hydrodynamic hazards.