The volume fraction of the solid and liquid phase of debris flows,which evolves simultaneously across terrains,largely determines the dynamic property of debris flows. The entrainment process significantly influences the amplitude of the volume fraction. In this paper,we present a depth-averaged two-phase debris-flow model describing the simultaneous evolution of the phase velocity and depth,the solid and fluid volume fractions and the bed morphological evolution. The model employs the Mohr–Coulomb plasticity for the solid stress,and the fluid stress is modeled as a Newtonian viscous stress. The interfacial momentum transfer includes viscous drag and buoyancy. A new extended entrainment rate formula that satisfies the boundary momentum jump condition(Iverson and Ouyang,2015) is presented. In this formula,the basal traction stress is a function of the solid volume fraction and can take advantage of both the Coulomb and velocity-dependent friction models. A finite volume method using Roe's Riemann approximation is suggested to solve the equations. Three computational cases are conducted and compared with experiments or previous results. The results show that the current computational model and framework are robust and suitable for capturing the characteristics of debris flows. 相似文献
Identifying and analyzing the urban–rural differences of social vulnerability to natural hazards is imperative to ensure that urbanization develops in a way that lessens the impacts of disasters and generate building resilient livelihoods in China. Using data from the 2000 and 2010 population censuses, this study conducted an assessment of the social vulnerability index (SVI) by applying the projection pursuit cluster model. The temporal and spatial changes of social vulnerability in urban and rural areas were then examined during China’s rapid urbanization period. An index of urban–rural differences in social vulnerability (SVID) was derived, and the global and local Moran’s I of the SVID were calculated to assess the spatial variation and association between the urban and rural SVI. In order to fully determine the impacts of urbanization in relation to social vulnerability, a spatial autoregressive model and Bivariate Moran’s I between urbanization and SVI were both calculated. The urban and rural SVI both displayed a steadily decreasing trend from 2000 to 2010, although the urban SVI was always larger than the rural SVI in the same year. In 17.5% of the prefectures, the rural SVI was larger than the urban SVI in 2000, but was smaller than the urban SVI in 2010. About 12.6% of the urban areas in the prefectures became less vulnerable than rural areas over the study period, while in more than 51.73% of the prefectures the urban–rural SVI gap decreased over the same period. The SVID values in all prefectures had a significantly positive spatial autocorrelation and spatial clusters were apparent. Over time, social vulnerability to natural hazards at the prefecture-level displayed a gathering–scattering pattern across China. Though a regional variation of social vulnerability developed during China’s rapid urbanization, the overall trend was for a steady reduction in social vulnerability in both urban and rural areas.