Journal of Engineering Mechanics

We derive and discuss the Green’s function of the linearized de Saint-Venant equations (LSVEs) for shallow water waves in channels and rivers. The analysis offers a unified description of previous results on LSVEs regarding, in particular, the existence of three simple linear waves whose interplay determines all the evolution of the solution, the role of the Froude number $\left(\mathsf{F}\right)$ in all its range of variability (both in subcritical and supercritical conditions), and the physical reason of the instability for $\mathsf{F}>2$ and its convective nature.

The postbuckling analysis of symmetric and antisymmetric cross-ply laminated cylindrical shell panels subjected to thermomechanical loading is examined in this paper. The formulation is based on an extension of Reissner’s shallow shell simplifications and accounts for parabolic distribution of transverse shear strains. Adopting a multiterm Galerkin’s method, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations. The nonlinear equilibrium paths through limit points are traced using the Newton–Raphson method in conjunction with Riks approach. Numerical results are presented for symmetric $\left[0∕90∕0\right]$ and antisymmetric $\left[0∕90\right]$ cross-ply laminated cylindrical shell panels, that illustrate the influence of mechanical edge loads, lateral distributed load, initial imperfection, and temperature field on the limit loads and snap-through behavior.

The determination of the fundamental stress versus crack opening $\left(\sigma \text{-}w\right)$ response of concrete under uniaxial tension is performed in this study through inverse analysis using data from notched beam tests. The procedure used for optimizing the parameters of the $\sigma \text{-}w$ relation using the load versus crack mouth opening displacement response of the notched beam is described. Satisfactory comparisons have been obtained between the $\sigma \text{-}w$ curves obtained through the inverse analysis and those directly measured in uniaxial tension tests. The use of weighting functions in the inverse analysis may be necessary when large crack widths are to be considered.

Upsetting tests were conducted on cylindrical specimens made of a typical fresh short fiber-reinforced cementitious composite (SFRCC) paste for extrusion at various boundary conditions to derive the paste’s constitutive behavior. Due to friction present at the specimen and the equipment platens interfaces, stress was not uniformly distributed in the specimen and had to be corrected. In this study, two analytical methods were utilized to derive the true flow stress of the fresh SFRCC paste through correcting the nominal yield stress obtained from the upsetting test. One of them was the stress extrapolation method, which required a large number of experimental data and predetermined boundary friction. It was found that the results corrected by this method from experiments at the lubricated boundary were more reliable than those at the dry boundary and this method could also give an approximate estimation of the boundary friction coefficient. As comparison, the flow stress correction method required only a small amount of experimental data and no predetermined boundary friction. It was found that this method provided better results at the dry boundary than at the lubricated boundary. The fresh SFRCC paste exhibited both strain and strain rate hardening characteristics whereas strain rate hardening effect was more significant and dominated.

This paper presents the development of a methodology for microstructure analysis and modeling of hot mix asphalt (HMA). This methodology relies on using effective local material properties and strain gradient theory in the finite element analysis of HMA microstructure. The effective local properties are calculated using an analytical micromechanical model that captures the influence of percent of particles on the microscopic response of HMA. Strain gradient elasticity is used in order to account for the effect of particle size in the finite element analysis. The autocorrelation function and the moving window technique are used to determine the microstructure characteristic length scales that are used in strain gradient elasticity. A number of asphalt mixes with different aggregate types and size distributions are analyzed in this paper.

The objective of this study was to characterize hot-mix asphalt (HMA) viscoelastic properties at intermediate and high temperatures and to incorporate laboratory-determined parameters into a three-dimensional finite element (FE) model to accurately simulate pavement responses to vehicular loading at different temperatures and speeds. Results of the developed FE model were compared against field-measured pavement responses from the Virginia Smart Road. Results of this analysis indicated that the elastic theory grossly underpredicts pavement responses to vehicular loading at intermediate and high temperatures. In addition, the elastic FE model could not simulate permanent deformation or delayed recovery, a known characteristic of HMA materials. In contrast, results of the FE viscoelastic model were in better agreement with field measurements. In this case, the average error in the prediction was less than 15%. The FE model successfully simulated retardation of the response in the transverse direction and rapid relaxation of HMA in the longitudinal direction. Moreover, the developed model allowed predicting primary rutting damage at the surface and its partial recovery after load application.

The Karhunen–Loève, spectral, and sampling representations, referred to as the KL, SP, and SA representations, are defined and some features/limitations of KL-, SP-, and SA-based approximations commonly used in applications are stated. Three test applications are used to evaluate these approximate representations. The test applications include (1) models for non-Gaussian processes; (2) Monte Carlo algorithms for generating samples of Gaussian and non-Gaussian processes; and (3) approximate solutions for random vibration problems with deterministic and uncertain system parameters. Conditions are established for the convergence of the solutions of some random vibration problems corresponding to KL, SP, and SA approximate representations of the input to these problems. It is also shown that the KL and SP representations coincide for weakly stationary processes.

The viscous effect on the roll motion of a rectangular structure was investigated in a two-dimensional wave tank. The structure was used to simulate a simplified barge in the beam sea condition. The structure with a draft one-half of its height was hinged at the center of gravity and free to roll (1 degree of freedom) by waves. The dynamic characteristics of the structure were first identified, including its roll natural period. The dynamic response of the barge-like structure under wave actions was then tested with regular waves with a range of wave periods that are shorter, equal to, and longer than its roll natural period. Particle image velocimetry was used to obtain the velocity field in the vicinity of the structure. The coupled interactions between the incident waves and the structure were demonstrated by examining the vortical flow fields to elucidate the effect of viscous damping (also called the eddy making damping) to the roll motion of the structure over wave periods. For incoming waves with a wave period same as the roll natural period, the structure roll motion was, as expected, greatly reduced by the viscous-damping effect. At wave periods shorter than the roll natural period, the structure roll motion was slightly reduced by the viscous effect. However, at wave periods longer than the roll natural period, the viscous effect due to flow separation at structure corners indeed amplified the roll motion. This indicates that not only can the viscous effect damp out the roll motion, it can also amplify the roll motion.

Two methods are illustrated to effectively calculate the ground motion induced by constant speed moving loads. On the one hand, the dynamic Betti–Rayleigh reciprocity theorem allows one to take full advantage of the availability of Green’s functions for a homogeneous or a horizontally layered half-space. On the other hand, the spectral element method allows one to deal with complicated configurations, including dynamic soil-structure interaction, with an accuracy that is significantly higher than classical finite element or finite difference methods. Both the Betti–Rayleigh and spectral element methods are considered in three dimensions. After validating both methods, the decay of peak ground motion with distance is analyzed as a function of load speed and frequency. For speeds lower than the Rayleigh wave velocity in the soil, the decay turns out to be much faster than for a stationary point load. This effect is studied in detail by an analytical approach and interpreted in terms of destructive interference. Finally, the previous analytical and numerical results are checked against the records obtained at Ath, Belgium, during a field experiment to study ground motion induced by high-speed trains in soft soil conditions.

This paper presents the development of a novel numerical scheme to study solitary wave phenomena using velocity–vorticity formulation instead of the primitive variable (velocity-pressure) form for the Navier–Stokes equations. The free surface boundary conditions are accordingly modified to obtain the equations in the velocity and vorticity form without involving the pressure term. The kinematics of the fluid domain for the free surface flow is described using an arbitrary Lagrangian–Eulerian method. The proposed model is first validated with numerical and analytical solutions available from the literature for the following cases: (1) an oblique rigid-lid driven cavity flow and (2) an incident solitary wave. Then the versatility of the algorithm is demonstrated by obtaining numerical results for (3) periodic waves generated in a channel by a piston wavemaker, and (4) solitary waves generated by critical flow over a submerged solid structure. The salient characteristics of the propagation of solitary waves are well-illustrated in the present study.

The paper introduces a complete set of Boussinesq-type equations suitable for water waves and wave-induced nearshore circulation over an inhomogeneous, permeable bottom. The derivation starts with the conventional expansion of the fluid particle velocity as a polynomial of the vertical coordinate $z$ followed by the depth integration of the vertical components of the Euler equations for the fluid layer and the volume-averaged equations for the porous layer to obtain the pressure field. Inserting the kinematics and pressure field into the Euler and volume-averaged equations on the horizontal plane results in a set of Boussinesq-type momentum equations with vertical vorticity and $z$ -dependent terms. A new approach to eliminating the $z$ dependency in the Boussinesq-type equations is introduced. It allows for the existence and advection of the vertical vorticity in the flow field with the accuracy consistent with the level of approximation in the Boussinesq-type equations for the pure wave motion. Examination of the scaling of the resistance force reveals the significance of the vertical velocity to the pressure field in the porous layer and leads to the retention of higher-order terms associated with the resistance force. The equations are truncated at $O\left({\mu }^4\right)$ , where $\mu =$ measure of frequency dispersion. An analysis of the vortical property of the resultant equations indicates that the energy dissipation in the porous layer can serve as a source of vertical vorticity up to the leading order. In comparison with the existing Boussinesq-type equations for both permeable and impermeable bottoms, the complete set of equations improve the accuracy of potential vorticity as well as the damping rate. The new equations retain the conservation of potential vorticity up to $O\left({\mu }^2\right)$ . Such a property is desirable for modeling wave-induced nearshore circulation but is absent in existing Boussinesq-type equations.