Darcy to non-Darcy seepage transition in heterogeneous coarse-grained soil: Seepage characteristics and critical threshold prediction

Seepage in coarse-grained soil exhibits distinct non-Darcy characteristics, and the transition from linear to nonlinear seepage significantly affects the hydraulic characteristics and geotechnical applications. Due to the complexity of pore structure in heterogeneous coarse-grained soil, identifying the critical threshold for the transition from Darcy to non-Darcy seepage is challenging. This paper introduces equivalent particle size ( d ep ) and relative roughness ( λ t ) as indirect indicators reflecting the pore characteristics, quantifying the complex pore structure of heterogeneous coarse-grained soil. The formulae for the derivation of Reynolds number and resistance coefficient for heterogeneous coarse-grained soil are presented. By conducting permeability tests on coarse-grained soils with different pore structures, the effect of particle composition heterogeneity on seepage characteristics was analyzed. The flow regime of heterogeneous coarse-grained soil is divided into laminar, transitional, and turbulent stages based on the relationship between Reynolds number and resistance coefficient. The energy loss patterns in each stage are closely related to pore structure. By setting the permeability ratio k∗ = 0.95 as the critical threshold for the transition from Darcy to non-Darcy seepage, a method for calculating the critical Reynolds number ( Re cr ) for heterogeneous coarse-grained soil is proposed. Furthermore, we applied this method to other published laboratory data, analyzing the differences in the critical threshold for seepage transition between homogeneous and heterogeneous coarse-grained soil. This study aims to propose a more accurate and general criterion for the transition from Darcy to non-Darcy seepage in heterogeneous coarse-grained soil.