Journal of Engineering Mechanics

Simulation of sample realizations of stochastic processes is the bedrock of the Monte Carlo method, and the accurate modeling of stochastic processes is crucial to determine realistic structural responses. For seismic ground motion, its nonstationary property and spatially variability are well known. Furthermore, its non-Gaussian feature has been observed in some works. It is then necessary to simulate spatially varying ground motions accounting for its nonstationary and non-Gaussian characteristics. For this purpose, a computational procedure is developed for the simulation of non-Gaussian nonstationary spatially varying ground motions based on the spectral representation method (SRM). Translation process theory for the nonstationary non-Gaussian vector process is first proposed. By applying the proposed translation process theory, an iterative scheme is developed to estimate the underlying Gaussian evolutionary power spectral density (EPSD) matrix. The resulting underlying Gaussian EPSD matrix is used to simulate the underlying Gaussian ground motion by the SRM, which is finally mapped to the desired non-Gaussian nonstationary spatially varying ground motions. The capabilities of the proposed procedure are demonstrated by a numerical example. The statistical properties of the simulated non-Gaussian ground motions are compared with those of the simulated Gaussian ground motions.

This paper presents the results of an extensive experimental campaign of bond tests aimed to assess and compare the influence of several environmental conditioning factors (humidity and temperature) on the bond behavior of two different types of composites systems glued to concrete elements: a fiber-reinforced polymer (FRP) system made of a carbon sheet applied with epoxy resin and a polybenzoxozole (PBO) grid applied with a cement-based mortar, i.e., a fiber-reinforced cementitious matrix (FRCM) system. Several environmental conditions have been considered (partial immersion in water at 23, 30, and 40°C for short and long periods with and without further drying processes, exposure in air at 30 and 40°C) before testing the specimens according to two well-known setups for bond tests: a single push-pull shear test and a beam test. The experimental results were mainly analyzed in terms of failure modes and loads, showing a clearly negative effect of the conditioning factors for the specimens with the carbon fibre reinforced polymer (CFRP) sheet as the conditioning time increases because of the plasticization phenomena of the epoxy adhesive. Conversely, for the specimens with the PBO grid, the failure loads were slightly lower or even greater than the ones relieved for the reference specimens as the exposure periods increase, whereas in the case of short exposure, the bond strength reduced and the scattering of the experimental resulted increased.

This paper presents an extension of an energy-based method for analysis of statically indeterminate trusses under mechanical-thermal-assembly loadings. Using the Lagrange multiplier method, internal forces of statically indeterminate trusses under the effect of mechanical-thermal-assembly loadings are investigated by generalized variational principles. Introducing the Lagrange multipliers and connecting with static equilibrium equations, a new functional from unconditional generalized variational principles is presented. By solving the extremal problem of the new functional, a matrix form of general solutions for internal forces of statically indeterminate trusses is obtained. Compared with the literature results, the accuracy and universality of the present method is confirmed. The results show that it cannot only overcome the defect of compatibility equations by traditional geometry method, but that it also has the advantages of simple process and good generality.

Plane Couette flow between two parallel smooth walls is one of the classic wall-bounded shear flows. Analytical description of this flow is still limited to the linear law for laminar flow, the classic law of the wall, and the velocity defect law for fully turbulent flow, although extensive direct numerical simulations (DNS) and laboratory experiments are available. This paper integrates the existing knowledge of mean velocity distribution from theory, experiments, and DNS into a single velocity distribution law by introducing a rational eddy viscosity model. Specifically, the eddy viscosity distribution is approximated by an even rational function which is cubic near the wall, linear in the log-law overlap, and symmetrical about the channel centerline. The rational eddy viscosity model leads to a general velocity distribution law in terms of four inverse hyperbolic tangent functions. This law reduces to the linear law for laminar flow, agrees with the classic van Driest law in the inner region, and is antisymmetrical about the channel centerline. Particularly, it well reproduces DNS and laboratory data for transitional and turbulent flows. Furthermore, this general velocity distribution law results in a general friction law. Finally, the rational eddy viscosity model has clear implications for other wall-bounded flows in future studies.

Destructive tsunami waves may cause failure of the pile-supported nearshore structures, hence, accurate prediction of tsunami wave interaction with piles is a primary engineering concern in the field of coastal management and hazard mitigation. This study numerically investigated tsunami-like solitary waves propagating over a surface-piercing double row of vertical slotted piles. A three-dimensional numerical wave tank based on an open-source computational fluid dynamics (CFD) tool was developed in this study. The Navier-Stokes equations for two-phase incompressible flow were solved using the large eddy simulation (LES) method for turbulence closure and the volume of fluid (VOF) method for tracking the free surface. Laboratory measurements of the wave, flow, and dynamic pressure were performed to validate the numerical model. The model was then applied to examine the three-dimensional distribution of free-surface elevation and the vertical distribution of dynamic pressure in the vicinity of the piles. Via numerical results, the variations of wave runup and impact force on the piles were also analyzed in view of the wave nonlinearity and the ratio of pile spacing to its diameter. Finally, the drag coefficients were discussed through the Morison equation to account for the interfering effects among the piles.

In this paper, the shearing behavior of soil-steel interfaces sheared at different planes is examined using a modified suction–controlled direct shear apparatus (MDSA). Direct shear tests on soil-steel interfaces sheared at three shear planes at three different suction values were conducted. Test results show that matric suction has a significant influence on interface shear behavior and shear strength and that the critical (or minimum) interface shear strength depends on the applied matric suction. Net normal stress affects both peak and postpeak shear stresses of the interfaces and those of the pure soil. The suction envelope for the interfaces is nonlinear. The interface shear strength values from experimental results are compared with the values predicted from an existing analytical model that considers the influence of soil dilation. The results indicate that the analytical model is suitable for predicting the unsaturated interface shear strength of rough soil-steel interfaces.

This paper presents a beam element for which the cross section remains neither plane nor orthogonal to the beam axis. The cross section with arbitrary geometry is modeled by two-dimensional (2D) finite elements. The element kinematics is defined by the displacement shapes of the cross sections and the axial functions of their corresponding averaged movements. The deformed displacement shapes are obtained by minimizing the potential energy of a beam slice submitted to the compatibility constraints of the kinematics framework. The recursive procedure that yields the higher-order deformed displacement shapes is initiated with the rigid-body components of the displacement field. The mechanical model is validated through examples of linear-elastic materials with isotropic and nonisotropic cross sections. Higher-order beam elements yield three-dimensional (3D) stresses and strains that correspond to elasticity solutions and 3D solid element models, for concentrated and distributed loads. The beam elements do not require shear coefficients. The first-order formulation is extended to nonlinear materials.

This article investigates the structural stability of prismatic columns with elastically restrained ends under axial compressive force. An emphasis is placed on the analysis of the effect of Engesser’s and Haringx’s hypotheses on buckling. Based on the Timoshenko beam theory and a higher-order shear-deformable beam theory, simple characteristic equations were derived for buckling of an axially loaded elastic column with two ends linked to translational and rotational springs. By introducing orientation factor $\alpha$, a buckling load falls between those corresponding to Engesser’s ($\alpha =0$) and Haringx’s ($\alpha =1$) models. For freely standing, simply supported, and clamped columns, explicit expressions for each critical load were obtained. The effects of Engesser’s and Haringx’s hypotheses as well as of the translational and rotational spring stiffnesses at the elastically restrained end on buckling loads are analyzed in detail. Obtained results indicate that Engesser’s and Haringx’s hypotheses hardly affect buckling loads for a column with strong shear rigidity, and they have a significant influence on buckling loads for a column with weak shear rigidity. The effect of translational spring stiffness on buckling loads is more pronounced than that of rotational spring stiffness.

An unbonded concrete overlay (UBCO) is an increasingly popular technique for pavement rehabilitation. Its current thickness design is based on empirical equations or highly simplified mechanistic models. This paper conducts a lifecycle simulation study for UBCO for the first time. Its sophisticated three-dimensional finite-element model is created and the fatigue reflection crack initiation and propagation under the cyclic traffic loading are simulated. The fatigue parameters are calibrated and corrected according to the size effect law. The simulation results reveal the three-dimensional cracking mechanism of the UBCO and show that increasing the overlay thickness is the most efficient way to improve the fatigue life. The present study offers a practical approach for evaluation of the UBCO’s fatigue life and thus sheds light on a next-generation fatigue life–based design procedure for the UBCO.

In this study, analytical solutions are presented for the axisymmetrical consolidation of an unsaturated soil stratum on the basis of Fredlund and Hasan’s one-dimensional consolidation theory. Two different loading conditions, i.e., instantaneous loading and ramp loading, were considered. The derivation process of the proposed analytical solution is simpler in contrast to the existing analytical solutions and it was verified to be accurate using an analytical solution in the literature. In addition to the analytical solutions under the assumption of free strain, the analytical solutions under the assumption of equal strain were further derived. In the parametric study, the variations in the excess pore-water and pore-air pressures as well as the average degree of consolidation are presented. Graphs are given to show the influence of the different hydraulic conductivity ratios between the air and water phases as well as the construction time (under a ramp loading condition) to the consolidation process. These two factors have significant impact on the consolidation of the air phase but little influence on the consolidation process of the water phase.

Interlocking over cracked surfaces is one of the primary sources of the shear force–resisting mechanism of general reinforced concrete structures. From the interlocking, shear stress develops in a substantially complex way due to the irregular asperity of cracked surfaces and the heterogeneous mixture of aggregate and cement. Previously, the author proposed a three-dimensional (3D) interlocking model that is rooted in microphysical interaction between a rigid particle and a soft matrix. However, the small deformation assumption and mesh sensitivity remain challenges. This study focuses on a novel computational method to achieve mesh objectivity of the 3D interlocking mechanism that can cover large deformations of general complex 3D RC structures. The proposed method exploits the deformation gradient at a separate domain where physical information of the crack-normal gap and crack-tangential sliding is rigorously defined. A generalized 3D version of the well-known crack band theory is infused into the interlocking mechanism, thereby giving rise to the mesh objectivity. This method can be directly applied to the large displacement and large rotation conditions.

This study serves three purposes: (1) to review a synthesis formula for simulation of band-limited stochastic processes based on the sinc expansion; (2) to implement this synthesis formula in the tail-equivalent linearization method (TELM); and (3) to demonstrate increased computational efficiency when the sinc expansion is implemented in this context. The proposed representation enables the reduction and control of the number of random variables used in the simulation of band-limited stochastic processes. This is of great importance for gradient-based reliability methods, including TELM, for which the computational cost is proportional to the total number of random variables. A direct application of the representation is used in TELM analysis. Examples of single-degree-of-freedom and multiple-degrees-of-freedom nonlinear systems subjected to Gaussian band-limited white noise simulated by use of sinc expansion are presented. The accuracy and efficiency of the representation are compared with those of the current time-domain discretization method used in TELM. The analysis concludes by shedding light on the specific cases for which the introduced reduction technique is beneficial.

In this paper, the static and dynamic behaviors of a finite microstructured rectangular membrane were studied. The microstructured membrane model comprised an equal number of elastic springs in both directions forming a rectangular lattice membrane. The authors considered the out-of-plane displacement of each node of this two-dimensional lattice. The rectangular lattice membrane was fixed at its boundary. A nonlocal continuous membrane model was developed to approximate the behavior of the finite lattice model. A continualization procedure was applied to the discrete equations in which the difference operators were approximated by differential operators. The resulting nonlocal continuum was governed by some length scales in each direction that depended on the size of the microstructure. This nonlocal continuum exactly coincided with the one elaborated by Rosenau in the 1980s in the dynamics range. The authors showed that such a nonlocal medium also can be used for static deflection of microstructured membranes. A comparison of both discrete (the reference lattice model) and continualized nonlocal responses brought out the effectiveness of this micromechanics-based approach. The continualized nonlocal continuum also was compared with a phenomenological Eringen’s nonlocal model.

In this paper, a novel numerical algorithm for simulating thermal-cracking function during the fracture process of rocks in the framework of general particle dynamics (GPD) is proposed. The thermal-cracking algorithm was embedded in general particle dynamics code to describe fracture behaviors of particles under thermal function. In general particle dynamics code, interaction among discrete particles was formulated by using the virtual-bond method. Fractures of virtual bond among particles were determined through the Hoek-Brown damage evolution law of rocks. The fractured virtual bond could only bear the compressive behavior between two particles, whereas the completed virtual bond could bear tensile, shear, and compressive behaviors. Furthermore, the temperature-dependent elastic-brittle behavior was considered in an explicit manner of GPD, so thermally induced rock damage could be realistically simulated in a thermomechanical coupling problem. The two numerical cases were given to verify the stability and accuracy of the numerical algorithm. Then, the numerical results were compared with analytical solutions and experimental results. It was found that the numerical results were in good agreement with the experimental ones.

To simulate fully nonstationary earthquake ground motion, an improved generalized evolutionary spectrum model derived from a counterpart of stationary seismic processes is proposed in the present paper. Through integrating the proposed generalized evolutionary spectrum model and updated spectral representation method (U-SRM), a renewed simulation scheme is adopted to represent fully nonstationary seismic accelerations. The complete set of representative samples of earthquake ground motion with assigned probabilities can thus be readily generated. For the purpose of comprehensively evaluating the dynamic reliability of a concrete gravity dam structure, three relative displacement angles are suggested. Using the renewed simulation scheme combined with the probability density evolution method (PDEM), the nonlinear stochastic responses and dynamic reliability analysis for a randomly base-excited concrete gravity dam are examined. Numerical results reveal the physical mechanism of nonlinear seismic responses of concrete gravity dams. It thus indicates that the renewed scheme integrating the proposed generalized evolutionary spectrum model and U-SRM accommodates a more logical indicator for the seismic design of concrete gravity dams than the deterministic seismic design currently used in practice with recorded seismic accelerations.

When a sphere impacts a granular bed such as a sand bed, the penetration depth is often determined by empirical scaling laws or numerical simulations. This paper uses a unified force law for granular impact cratering to obtain a simple, explicit, and exact solution for the maximum penetration depth in terms of the Lambert function. The exact solution is confirmed with published laboratory data and numerical simulations; thus it can be used to determine the drag coefficients accurately.