engleski

Application of SPH method to create numerical models of Debris flow propagation

Debris flows generate important yearly human and property losses. Its analysis is important to assess the risk and to delimitate vulnerable areas where mitigation measures are required. Debris flows are a type of mass wasting processes. Mass movement processes can be categorized following some parameters such as the release mechanism, the sort of material, the sediment composition, the proportion of the solid phase, the velocity, the time of the event, the slope of the movement plane, the material behavior and the physical processes during the mass movement. Predicting both the runout distance and the velocity through mathematical modeling of the propagation can avoid important losses. Moreover data from modeling can be used as input in risk studies, where hazardous areas are defined and appropriate protective measures are designed. In the last decades, modeling of propagation stage has been largely carried out in the framework of the continuum mechanics, and a number of new and sophisticated numerical models are developed. Most of the available approaches handle the heterogeneous and multiphase moving mass as a single phase continuum. The Smoothed particle hydrodynamics model (SPH model) described here after consists on considering two phases, a granular skeleton with voids filled with either water or debris/mud. If the shear resistance of the fluid phase can be neglected, the stress tensor in the mixture can be decomposed into a "pore pressure" and an effective stress, and the mechanical behavior of the mixture can be described by a system of differential equations governing the dynamics of each of the phases. Once the required initial and boundary conditions are provided, the spatial and temporal integration of the system of differential equations can be carried out with numerical methods. In the SPH method, the state of a system is represented by a set of particles, which possess individual material properties and move according to the governing conservation equations. SPH method, as a meshfree, Lagrangian, particle method, has its particular characteristics. The key idea of the meshfree methods is to provide accurate and stable numerical solutions for integral equations or PDEs with all kinds of possible boundary conditions with a set of arbitrarily distributed nodes (or particles) without using any mesh that provides the connectivity of these nodes or particles. SPH method has some special advantages over the traditional grid-based numerical methods, the most significant one among which is the adaptive nature of the SPH method. This adaptability of SPH is achieved at the very early stage of the field variable approximation that is performed at each time step based on a current local set of arbitrarily distributed particles. The SPH depth integrated model is a 2D model able to predict runout distance, flow velocity, deposition pattern and final volume of debris flows. It is based on a mathematical model, on rheological models and on a numerical model. The basis of the mathematical model is a coupled depth integrated model coming from a velocity-pressure version of Biot-Zienkiewicz equations. The rheological models correspond to constitutive equations. The SPH depth integrated model is a calibration-based model, which means that the appropriate rheological parameters must be constrained by back analysis of previous real debris flows. In this paper are described the main characteristics of debris flow processes and point out the more relevant parameters and magnitudes describing debris flow. The paper also gives the main equations on which is based the SPH depth integrated model applied for Grohovo landslide. In this paper two erosion laws are presented, the Hungr erosion law and the Egashira erosion law. On the end of the paper was given a brief description of the SPH code, and some conclusions of this case study and the possible future research lines.

Debris flow; numerical modelling; SPH method; Rjecina River; Grohovo landslide

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