A theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method accuracy is presented. An example calculated by LS-DYNA software is discussed. Chronological development of Smooth Particle Hydrodynamics is presented. Theoretical basics of SPH method stability and consistency in SPH formulation, artificial viscosity and boundary treatment are discussed. Time integration techniques with stability conditions, SPH+FEM coupling, constitutive equation and equation of state (EOS) are presented as well.

Abstract. Numerical analyses of stability are presented for a hypothetical dikes constructed of dredged materials and bottom ash, in varying proportions. The paper is related to the international research project DredgDikes, which focused on the use of anthropogenic materials in dikes construction and flood protection. The aim of this project was to investigate the possibility of using anthropogenic materials from rivers and sea dredging and coal combustion products in dikes construction. The influence of different proportions of ash and dredged materials on the stability of dike is discussed. Mechanical and hydraulic parameters of various dredged material-ash mixtures are based on the results of laboratory and field tests performed in DredgDikes project. Numerical calculations are carried out using geotechnical software Plaxis. Cementation phenomenon and its effect on the performance of ash and dredged material mixtures is discussed.