Journal of Engineering Mechanics

The paper addresses the question of whether the number of particles in a noncemented granular assembly will affect the mechanical characteristics of the assembly: its strength and stiffness. The question is answered by applying the discrete element method to assemblies of different sizes. To isolate the effect of assembly size, apart from the scatter that usually accompanies such simulations, multiple assemblies were tested. The two-dimensional assemblies had nearly identical initial porosities and fabrics, and they were all loaded in biaxial compression. Two different boundaries were tested: periodic and wall boundaries. We find that the peak compressive strength decreases with assembly size for both types of boundaries and over a range of assembly sizes that contain 256 particles to over 66,000 particles. Stiffness is only slightly reduced and only with wall boundaries. Deformation is less uniform in the larger assemblies, with deformation concentrated in a smaller fraction of the assembly area. An analysis of deformation patterning shows that at least a few thousand particles are required for realistic microband patterning.

This paper deals with Hill’s bifurcation criterion, which is very well suited to describe various failure modes in granular media. The first part of this paper is dedicated to the analytical and numerical investigation of this criterion by considering phenomenological constitutive relations: the incrementally piece-wise linear and nonlinear relations proposed by Darve. The 3D bifurcation domain and 3D cones of unstable directions are given for these two relations. A similar analysis is performed with a micromechanical model in the second part of the article. Finally, a qualitative comparison of the results obtained with these two different approaches leads us to some key conclusions about this material instability criterion, which is studied for the first time for general 3D conditions, by considering these nonconventional constitutive relations.

Rutting has an adverse effect on safety and riding comfort of pavement. Reliable prevention and prediction of rutting has been one of the major focuses in road research. This paper summarizes the methods available for rut depth prediction and performs a case study in two separate ways based on the data acquired from a full-scale indoor circular road test. One was to formulate the possible rut depth by integrating a four-element-five-parameter viscoelastic model and the layered strain approach. The other was based on an empirical method. It is verified that both methods are applicable in predicting rut depth within the near future after open to traffic. The empirical method, however, is also capable of predicting rut depth within the whole design life. And theoretical method proves inadequate because of the limitation of the model itself and also of the method for obtaining parameters.

In this paper a new method is proposed to analyze the mechanical response of a linear viscoelastic pavement. The material parameters of the asphalt concrete are characterized by the relaxation modulus and creep compliance, which are further represented by the Prony series. By virtue of the Laplace transform and the correspondence principle, the solution in the Laplace domain is first derived. The interconversion between the relaxation modulus and creep compliance is then applied to treat the complicated inverse Laplace transform. The displacement, strain, and stress fields are represented concisely in terms of the convolution integral in the time domain, which is subsequently solved analytically. Therefore, responses of the viscoelastic pavement are finally expressed analytically in the time domain and numerically in space domain, called a semianalytical approach. Since both the relaxation modulus and creep compliance are used simultaneously, instead of only one parameter in the conventional methods, the present method is also called a dual-parameter method. The present formulation is verified at both the short- and long-term time limits analytically and at the other finite time numerically, as compared to the conventional numerical methods. We clearly show that the present dual-parameter and semianalytical method can predict accurately the time-dependent responses of the viscoelastic pavement, especially at the long-term time. The present formulation could also be employed to validate the widely used collocation method.

Structural interaction between two beam-like structures is a situation that occurs in piping systems, among other applications relevant to the nuclear, petroleum, biomedical, and automotive industries, for instance. This paper analytically investigates the repetitive impact dynamics of two orthogonal pinned–pinned beams subjected to base excitation at specified frequency and acceleration. The orthogonal beam configuration restricts the contact to a single point, and the contact interface is modeled by a spring. Although many approaches have been developed for multibody dynamics, the constraint and modal mapping method is efficiently applied herein to obtain the forced response through modal analysis. The vibration is described in a piecewise fashion as switching between the linear in-contact and not-in-contact states, and compatibility conditions are applied at their junctions. The development of the conjoined mode shapes and their orthogonality is derived in detail. The contact impulse is used to describe the structures’ complex interacting behavior through repetitive impact frequency-response functions. In order to determine major response factors, parameter studies are performed on contact stiffness, relative beam stiffness, contact location, modal damping, and stand-off gap.

An alternative to the modeling of the transient behavior of pipeline systems in the time-domain is to model these systems in the frequency-domain using Laplace transform techniques. Despite the ability of current methods to deal with many different hydraulic element types, a limitation with almost all frequency-domain methods for pipeline networks is that they are only able to deal with systems of a certain class of configuration, namely, networks not containing second-order loops. This paper addresses this limitation by utilizing graph theoretic concepts to derive a Laplace-domain network admittance matrix relating the nodal variables of pressure and demand for a network comprised of pipes, junctions, and reservoirs. The adopted framework allows complete flexibility with regard to the topological structure of a network and, as such, it provides an extremely useful general basis for modeling the frequency-domain behavior of pipe networks. Numerical examples are given for a 7- and 51-pipe network, demonstrating the utility of the method.

Because a structure’s modal parameters (natural frequencies and mode shapes) are affected by structural damage, finite- element model updating techniques are often applied to locate and quantify structural damage. However, the dynamic behavior of a structure can only be observed in a narrow knowledge space, which usually causes nonuniqueness and ill-posedness in the damage detection problem formulation. Thus, advanced optimization techniques are a necessary tool for solving such a complex inverse problem. Furthermore, a preselection process of the most significant damage parameters is helpful to improve the efficiency of the damage detection procedure. A new approach, which combines a parameter subset selection process with the application of damage functions is proposed herein to accomplish this task. Starting with a simple 1D beam, this paper first demonstrates several essential concepts related to the proposed model updating approach. A more advanced example considering a 2D model is then considered. To determine the capabilities of this approach for more complex structures, a trust region-based optimization method is adopted to solve the corresponding nonlinear minimization problem. The objective is to provide an improved robust solution to this challenging problem.

This paper presents a coupled approach using an artificial neural network (ANN) and the finite difference method (FDM) that has been developed to predict the distribution of axial load along fully grouted standard cable bolts in the field using laboratory pullout test data. A back-propagation training algorithm was used in ANN to determine axial loads in the cables tested in the laboratory. The ANN component of the computational model was trained using two different types of data sets. At first, the ANN was trained to predict the axial loads in a series of short cables grouted with Portland cement at a specific water-to-cement ratio and subjected to different radial confining stiffness values. Next, the ANN model was trained for an expanded case to include the influence of lateral confining stress on the distribution of axial load in the cable reinforcement. Finally, the ANN model was implemented into a widely used, FDM-based geotechnical software (FLAC). The accuracy of the ANN–FDM model is demonstrated in this paper against measured data from laboratory and field tests. The analysis approach introduced in this study is a valuable computational tool that can be used to determine the axial load distribution in long standard cable bolts, which are commonly installed to stabilize rock masses in various geotechnical, transportation, and mining applications.

Viscoelastic dampers are being used in structures to mitigate dynamic effects. The models of varying complexities from simple maxwell element to differential models with fractional and complex order derivatives have been used to represent their frequency-dependent force deformation characteristics. More complex models are able to capture the frequency dependence of the material properties better, but are difficult to use in analyses. However, the classical models consisting of assemblies of Kelvin and/or Maxwell elements with an adequate number of parameters can be formed to capture the frequency dependence as accurately as the more sophisticated fractional derivative models can do. The main advantage in adopting these classical models is a simpler and smaller system of equations, which can be conveniently analyzed for nonlinear and linear systems. In this study, the two classical mechanical models consisting of Kelvin chains and Maxwell ladder are used. It is shown that these mechanical models are as effective as the fractional derivative model in capturing the effect of the frequency dependence of the material properties in response calculations and are more convenient to use in dynamic response analyses.

Models of varying complexities are being used to represent the frequency-dependent dynamic force deformation characteristics of viscoelastic dampers. More sophisticated models with real or complex fractional derivatives can definitely capture the frequency-dependent properties better. However, since these advanced models add complexity in the analysis of structures, the use of two classical models—a Kelvin chain and a Maxwell ladder—consisting of usual dashpots and springs is suggested. In this technical note, we provide explicit steps and necessary formulas to calculate the parameters of these two proposed models to provide desired frequency-dependent characteristics represented by the storage and loss moduli.

A numerical procedure is presented for calculation of the mixed-mode elastodynamic stress intensity factors for a stationary three-dimensional curved crack with nonplanar surfaces. The computational scheme is developed by modifying the concept of the elastodynamic $J_k$ integrals, which are shown to be surface independent in a modified sense. As the near-front region needs to be included in the calculation, special treatment is thus addressed to modeling the elastodynamic singular behavior. Neither extra auxiliary solutions nor singular finite elements are required for the computation

The stability of a pair of line vortices is considered. The two line vortices are different in strength of circulation and can be counter- or corotating. This work is a generalization reported by Crow in 1970 and Jimenez in 1975. We find that the most unstable wave number and the maximum growth rate of instability are influenced by the circulation difference between the vortices for a pair of counterrotating vortices. For a pair of corotating vortices, we find that their stability properties are not significantly influenced by their circulation difference. Although the physically most-amplified wave number is not apparent based on linear stability analysis, a pair of corotating vortices is unstable irrespective of the circulation difference.