Influence of post-cyclic loading on hemic peat

Construction on peat soils has proven to be a challenging task to civil engineers since this soil type has a significant issue that arises from common problems construction of roads, housing and embankment construction with regard to peat are stability, settlements and major problems were encountered especially on deep peat. For many years, in road design as an example, static loading method was applied in road designed by considering soil shear strength through static load and do not take into account the vehicular dynamic loading and shear strength thereafter. This fact is related to the shear strength of peat soil after dynamically loaded. The aim of this research is to establish the post-cyclic behaviour of peat soil after cyclically loaded and to assess the effect of parameters changes on static and post-cyclic behaviour of peat soil. 200 specimens are tested, and prepared under consolidated undrained triaxial with effective stresses at 25kPa, 50 kPa, and 100 kPa with different location from Parit Nipah, Johor, Parit Sulong, Batu Pahat, Johor and Beaufort, Sabah. These specimens tested using GDS Enterprise Level Dynamic Triaxial Testing System (ELDYN) apparatus. Whereas, dynamic load tests are carried out in different frequencies to simulate the loading type such as vibration of machineries, wind, traffic load and earthquake in field from 1.0 Hz, 2.0 Hz and 3.0 Hz with 100 numbers of loading cycles. Post-cyclic monotonic shear strength results and then compared to the static monotonic results. Significantly, showed some vital changes that leads to the changes of stress-strain behaviour. Apparently, the result shows that post-cyclic shear strength decreases with the increase of frequencies. Prior to critical yield strain level, the peat specimen experience a significant deformation. The deformation of peats triggers changes in soil structures that causes reduction in stress-strain behaviour. Thus, it can be concluded that the stress-strain behaviour of peat soil decreased after 100 numbers of cyclic loading in post-cyclic test as compared to the static tests, and it decreased substantially when frequencies were applied. The post-cyclic specimen had a lower undrained parameters than did the static. Reduction of cohesion value in postcylic compared to static almost 70% and reduction of friction angle is about 46.34%

Generation of upstream advancing solitons by moving disturbances

This study investigates the recently identified phenomenon whereby a forcing disturbance moving steadily with a transcritical velocity in shallow water can generate, periodically, a succession of solitary waves, advancing upstream of the disturbance in procession, while a train of weakly nonlinear and weakly dispersive waves develops downstream of a region of depressed water surface trailing just behind the disturbance. This phenomenon was numerically discovered by Wu & Wu (1982) based on the generalized Boussinesq model for describing two-dimensional long waves generated by moving surface pressure or topography. In a joint theoretical and experimental study, Lee (1985) found a broad agreement between the experiment and two theoretical models, the generalized Boussinesq and the forced Korteweg de Vries (fKdV) equations, both containing forcing functions. The fKdV model is applied in the present study to explore the basic mechanism underlying the phenomenon. To facilitate the analysis of the stability of solutions of the initial-boundary-value problem of the fKdV equation, a family of forced steady solitary waves is found. Any such solution, if once established, will remain permanent in form in accordance with the uniqueness theorem shown here. One of the simplest of the stationary solutions, which is a one-parameter family and can be scaled into a universal similarity form, is chosen for stability calculations. As a test of the computer code, the initially established stationary solution is found to be numerically permanent in form with fractional uncertainties of less than 2% after the wave has traversed, under forcing, the distance of 600 water depths. The other numerical results show that when the wave is initially so disturbed as to have to rise from the rest state, which is taken as the initial value, the same phenomenon of the generation of upstream-advancing solitons is found to appear, with a definite time period of generation. The result for this similarity family shows that the period of generation, T[sub]S, and the scaled amplitude [alpha] of the solitons so generated are related by the formula T[sub]S = const [alpha]^-3/2. This relation is further found to be in good agreement with the first-principle prediction derived here based on mass, momentum and energy considerations of the fKdV equation

Tsunami & Forced Korteweg de Vries Equation

A systematic and comprehensive study of forced solitons in Tsunami waves that can be modelled mathematically by forced Korteweg-de Vries (fKdV). This equation have lost the translation-invariant type of group symmetries due to forcing. The traditional group-theoretical such as inverse scattering method, Backlund transformations and other known approaches can no longer generate analytic solutions of solitons, because there are no infinitely many conservation laws. Numerical simulations and approximate solutions seem the only ways to solve the forced nonlinear evolution equations. Numerical simulations of forced solitons will be implemented by a user-friendly software package FORSO. In this paper we show how approximate scheme can be used to generate forced solitons. Approximate solution also gives various profiles of fKdV such as the depth of depression zone; , amplitude; , speed; s and the period; of generation of forced solitons in Tsunami waves

Generation of two-dimensional water waves by moving bottom disturbances

We investigate the potential and limitations of the wave generation by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape which can be displaced according to a prescribed trajectory. We address the practical question of computing the wavemaker shape and trajectory generating a wave with prescribed characteristics. For the sake of simplicity we model the hydrodynamics by a generalized forced Benjamin-Bona-Mahony (BBM) equation. This practical problem is reformulated as a constrained nonlinear optimization problem. Additional constraints are imposed in order to fulfill various practical design requirements. Finally, we present some numerical results in order to demonstrate the feasibility and performance of the proposed methodology.Comment: 21 pages, 7 figures, 1 table, 69 references. Other author's papers can be downloaded at http://www.denys-dutykh.com

Transcritical shallow-water flow past topography: finite-amplitude theory

We consider shallow-water flow past a broad bottom ridge, localized in the flow direction, using the framework of the forced SuGardner (SG) system of equations, with a primary focus on the transcritical regime when the Froude number of the oncoming flow is close to unity. These equations are an asymptotic long-wave approximation of the full Euler system, obtained without a simultaneous expansion in the wave amplitude, and hence are expected to be superior to the usual weakly nonlinear Boussinesq-type models in reproducing the quantitative features of fully nonlinear shallow-water flows. A combination of the local transcritical hydraulic solution over the localized topography, which produces upstream and downstream hydraulic jumps, and unsteady undular bore solutions describing the resolution of these hydraulic jumps, is used to describe various flow regimes depending on the combination of the topography height and the Froude number. We take advantage of the recently developed modulation theory of SG undular bores to derive the main parameters of transcritical fully nonlinear shallow-water flow, such as the leading solitary wave amplitudes for the upstream and downstream undular bores, the speeds of the undular bores edges and the drag force. Our results confirm that most of the features of the previously developed description in the framework of the unidirectional forced Kortewegde Vries (KdV) model hold up qualitatively for finite amplitude waves, while the quantitative description can be obtained in the framework of the bidirectional forced SG system. Our analytic solutions agree with numerical simulations of the forced SG equations within the range of applicability of these equations

Weakly nonlinear ion sound waves in gravitational systems

Ion sound waves are studied in a plasma subject to gravitational field. Such systems are interesting by exhibiting a wave growth that is a result of energy flux conservation in inhomogeneous systems. The increasing wave amplitude gives rise to an enhanced interaction between waves and plasma particles that can be modeled by a modified Korteweg-de Vries equation. Analytical results are compared with numerical Particle-in-Cell simulations of the problem. Our code assumes isothermally Boltzmann distributed electrons while the ion component is treated as a collection of individual particles interacting through collective electric fields. Deviations from quasi neutrality are allowed for.Comment: 30 pages, 9 figure

Investigating overtaking collisions of solitary waves in the Schamel equation

This article presents a numerical investigation of overtaking collisions between two solitary waves in the context of the Schamel equation. Our study reveals different regimes characterized by the behavior of the wave interactions. In certain regimes, the collisions maintain two well-separated crests consistently over time, while in other regimes, the number of local maxima undergoes variations following the patterns of $2\rightarrow 1\rightarrow 2\rightarrow 1\rightarrow 2$ or $2\rightarrow 1\rightarrow 2$. These findings demonstrate that the geometric Lax-categorization observed in the Korteweg-de Vries equation (KdV) for two-soliton collisions remains applicable to the Schamel equation. However, in contrast to the KdV, we demonstrate that an algebraic Lax-categorization based on the ratio of the initial solitary wave amplitudes is not feasible for the Schamel equation. Additionally, we show that the statistical moments for two-solitary wave collisions are qualitatively similar to the KdV equation and the phase shifts after soliton interactions are close to ones in integrable KdV and modified KdV models

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.Comment: 34 pages, 24 figure