Nonlinear Wave Propagation And Absorbing Boundary Conditions In Soil

The theory of nonlinear wave propagation finds its applications in many geotechnical engineering problems.The nonlinearity may arise due to the constitutive law of the soil or the geometric nature of the problem under study.When considering the material nonlinearity,stress waves varying in their velocities propagate and interact in the medium making the analysis complicated.With the technological improvements in software and hardware,the Finite Element Method(FEM)has been widely used for solving geotechnical engineering problems due to its versatility and reliability.When the spatial domain of the problem is unbounded,appropriate absorbing boundary conditions are needed to be imposed on the truncated boundary that account for unobstructed propagation of waves from the near field to the far field.As geotechnical materials under normal engineering conditions always present a nonlinear mechanical behavior,the development of absorbing boundary conditions for the dynamic problems of the media with corresponding nonlinear mechanical behavior is attempted in this study.On the other hand,geological setting of the soils such as stratification introduces geometrical nonlinearities resulting in reflections and refractions around interfaces as a soil system is subjected to blast loads.The existing design blast pressure attenuation relationships in practice among design practitioners falls short of considering the effect of soil layer interfaces.This argument is validated through a numerical study.Firstly,to study the nonlinear 1D dilatational wave propagation problem,analytical and numerical solutions for rectangular and triangular load cases are developed.Method of characteristics is traditionally used to study 1D dilatational wave propagation problem which is used here to derive novel analytical solutions for complex load cases such as a triangular load.The analytical solution for rectangular load case is derived for the scenario where the residual velocity after unloading happens is greater than twice of particle velocity at yield.The stress distribution plots in the considered examples are determined using the graphical solutions obtained using the method of characteristics.To develop numerical solutions,a finite element method based numerical scheme is proposed which is implemented in a self-developed FORTRAN code.The analytical solutions are then verified using several numerical examples which show a good match with some discrepancies around discontinuities.The second part of the thesis is to develop novel absorbing boundary conditions for1 D dilatational wave propagation problem in a linear isotropic hardening plastic material.Based on the selected constitutive law,three stress paths are identified which are elastic loading,plastic loading and unloading.An arbitrary wave shape expression is used to derive the absorbing boundary conditions for each stress path where strains expressed in the form of the arbitrary wave shape are substituted in the stress path expressions.The three derived absorbing boundary conditions are then introduced into the proposed numerical scheme of the wave propagation problem.A parametric investigation about the efficiency and applicability of these conditions is then carried out.The performance evaluation of the derived conditions in comparison with the traditional viscous boundary highlights their accuracy in absorbing the three propagating stresses for different load cases.Moreover,the applicability of the derived absorbing boundary conditions with respect to the distance from the impact end is also studied.Lastly,a parametrical investigation on the effects of the presence of soil layers in ground as well as different soil properties on the propagation of surface blast pressures in dry soils is carried out.The 1D numerical scheme proposed in the first part of the thesis is extended to 2D problem which is then implemented in a self-developed FORTRAN code.To capture two important properties of soil behavior under high impact loadings which are nonlinearity and pressure-dependency,a variable modulus type nonlinear elastic constitutive material with a coulomb type shear surface is selected for this study.The parameters of study include blast load definition,Poisson's ratio and friction angle of homogenous soils and soil stratification where a two-layer and three-layer soil systems are considered.Moreover,the results from the three-layer system is then compared with the response obtained from the blast pressure attenuation relationship of the design manual US Army Corps of Engineers TM5-855-1.The design manual relationship yields a sharp smooth reduction in pressure attenuation curves and disappearance of blast pressures at significant distances from the source whereas the numerical study reveals that due to the presence of soil layer interfaces,the attenuation curves show intermediate peaks at the interface locations as well as large stresses propagate at significant distances form the blast source.