The SPH Method to Simulate River Levee Failures

Hirotoshi Mori, Cambridge University

Geotechnical Engineering Group

**Abstract**

This thesis describes the development of a numerical code using the Smoothed Particle Hydrodynamic (SPH) method for geotechnical engineering. The purpose of this study is to simulate the progressive failure of river levees. Results show great performance of the SPH code in simulating large deformation of earth structures. The following conclusions are made for the study.

1. Computing speed

The SPH method needs more computing power than the Finite Element Method (FEM). The interaction between different particle pairs needs to be identified at each time step anew, which adds considerable computing cost. In order to speed up the computation, the new SPH package was developed for the open source molecular dynamics code “LAMMPS” (Large-scale Atomic/Molecular Massively Parallel Simulator). By using a fast pair searching algorithm and a parallelization algorithm provided by LAMMPS, this approach is inherently scalable and more than 800 times faster than the original code for the 40,401 particles case running with 32 Central Processing Units (CPUs).

2. Soil models and boundary treatments

Two soil models, a Mohr-Coulomb model and a Modified Cam-Clay model, have been implemented in addition to the existing fluid model by the equation of state (EOS). Several boundary treatments including a virtual (ghost) particle technique and the up-wind method are proposed to enforce displacement boundary conditions or pressure boundary conditions, which are commonly used in geotechnical engineering. The SPH package with the new soil models and the boundary treatments is tested by simulating simple compression tests. It shows that the results are identical to the theoretical values or Lagrangian code FLAC2D results. The proposed boundary treatments can generate more variety of boundary conditions such as moving and/or slip boundary conditions.

3. Soil-Fluid coupling

Biot’s theory is used to build a coupling algorithm beside Darcy’s law for both saturated and unsaturated conditions. The model of multi-phase analysis consists of a seepage layer and a soil skeleton layer. The parameters for coupling (pore pressure, porosity and velocity of soil skeleton) are exchanged between the layers at each time step. The SPH package with the coupling algorithm is tested by simulating a bucket problem, a consolidation test and a column infiltration test. The results are identical to the theoretical values.

4. Simulating a large scale levee failure experiment

The SPH method was used to simulate a large scale levee failure experiment, in which the progressive failure was observed. The simulation utilized the soil model, the boundary treatments and the soil-fluid coupling algorithm developed in this study. The SPH package successfully reproduced the mode of the progressive failure qualitatively.