Journal of Engineering Mechanics

A comprehensive constitutive model for sand is formulated within the general framework of bounding surface hypoplasticity. The distinctive feature of this model is the dependence of the loading and plastic strain rate directions on the stress rate direction. This property renders the model hypoplastic. The model can simulate different features of sand behavior under loading conditions, which range from simple monbtonic to complex cyclic at different amplitudes and directions. In particular, the successful simulation of the response under “rotational shear” is one of the distinctive properties of the model, and it is mainly due to its hypoplastic character. The importance of such predictive capability in practice is related to the phenomenon of liquefaction, which may occur under such cyclic loading conditions of a complex nature, entailing cyclic changes of both principal stress values and principal stress directions. The paper presents a step‐by‐step calibration procedure of the different constants and a comparison of a series of test results and model simulations.

General equations are presented for the determination of principal direction paths of each of the Lagrangian strain ellipsoid, Eulerian strain ellipsoid, strain rate, and Cauchy stress for uniform finite deformation of thin‐walled tubes in combined tension and torsion. Specific paths are evaluated from experimental results for nonproportional loading of tubes of annealed copper (Bell and Khan 1980) and mild steel (Bell 1983a). It is found that the principal directions of Cauchy stress are not correlated with either of the strain ellipsoids, but that Cauchy stress and Eulerian strain rate are very nearly coaxial throughout the moderate finite‐deformation range of the experiments.

A damage model for monotonic and cyclic behavior of concrete is developed. The model recognizes the tortuous nature of cracks in compression, which affects the flexibility of the material in a direction coinciding with the average plane of the cracks. An elastic potential is introduced in terms of the principal stresses and a compliance tensor dependent on the accumulated damage. Damage evolution is obtained using a loading surface and bounding surface, defined in terms of the thermodynamic force conjugates of the damage variables. The damage growth during a series of unaxial compression and cyclic tests is inferred from the amplitude attenuation of ultrasonic waveforms transmitted laterally through the specimen while the tests are in progress. The behavior of concrete under compression, tension, biaxial loading and cycling, and damage growth under both monotonic and cyclic loading are found to be predicted well by the proposed theory.

The paper discusses some of the existing models for the analysis of the fatigue life of long elements and points out possible sources of error when data from lab tests or short elements is extrapolated to predict behavior in large structural components. A discussion of the assumptions leading to conservative and nonconservative results is included. Two dependent models, namely a Marshall‐Olkin and a nonstationary Poisson model, are presented and their asymptotic behavior is analyzed. The nonstationary Poisson model is demonstrated to be the most general solution of an empirical model formulated by Bogdanoff and Kozin. An illustrative example of aplication is also given, and several alternative approaches are discussed. Finally, some practical conclusions are given.

Various methods exist for estimating the experimental buckling load of a rectangular plate in edge compression from the recorded load‐lateral deflection data. Since these methods are based on nonlinear and/or graphical analysis, applications in most instances either rely heavily upon the individual judgment of the experimentalist or require elaborate numerical solution techniques. This paper presents a new method for determining a plate's critical load by a least‐squares curve fit to a linearized form of the governing load‐deflection equations. The linearity is achieved by a change of parameters and results in a technique that is shown to be both impartial and computationally straightforward, while giving excellent agreement with the nonlinear approaches. It is essential, however, that a reasonably representative sampling of data points, encompassing both the prebuckling and postbuckling ranges, be included in the computations. It is concluded that the new method can provide an attractive alternative to the more involved nonlinear techniques.

Mixed‐mode crack initiation and propagation starting from the aggregate‐matrix interface in concrete under uniaxial compression was investigated using fracture mechanics approach, finite element modeling, and holographic in‐terferometry techniques. Experiments were conducted with specimens containing stone‐matrix interface oriented at four different angles. During loading, interface debonding, initiation of matrix cracking (kink cracks), and propagation of matrix cracks were observed using laser holographic interferometry. The crack initiation and propagation were simulated by using both the analytical approach and finite element method with quarter‐tip singular elements. With an increasing kink length, the finite element solution differed from the infinite plate analytical solution. To obtain an essentially constant value of the apparent critical stress‐intensity factor for different orientation angles of the interfacial crack and for different kink extensions, a cohesive crack model was used. The magnitude of the normal and the shear tractions for the theoretical model was obtained by matching the FEM‐cal‐culated crack‐opening and sliding displacements with the experimentally measured values.

The stiffness tensor relating the stress and strain in the generalized Hooke's law can take various forms depending upon the symmetry of the mechanical properties of the granular material. This material symmetry is expected to be closely related to the packing structure of the granular material. In this paper, the microstructural continuum method is employed to study the relationship between the symmetry of mechanical properties and the packing structure for random granular packings. The distribution density functions characterizing the packing structure are represented by spherical harmonics expansion. Closed‐form solutions for the stiffness tensor are derived for anisotropic granular packings of equal spheres with linear interparticle contact interactions. The relation between the “fabric” parameters describing the density functions and the material symmetry are discussed. Bounds imposed by the condition of positive definiteness of strain energy on fabric parameters are also studied. Parametric study is performed to show the effect of packing structure and contact stiffness on the mechanical behavior of a packing.

The dynamic behavior of a surface‐mounted pipeline under seismic excitation is investigated. The ground motion is modeled as a superposition of decaying random traveling waves, and the pipeline is modeled as an infinitely long Euler‐Bemoulli beam attached to evenly spaced ground supports. Thus, the pipeline is a spatially periodic structure composed of identically constructed units, and it receives seismic excitations through the periodic supports. Damping in the soil as well as the pipeline material is taken into consideration. Closed‐form solutions are found for the pipeline response, permitting clear physical insights into the related physical phenomena. In particular, large response is found when significant excitation energy is contained within the wave‐passage frequency bands, typical of spatially periodic structures. The most severe response occurs under a coincidence condition when the propagation of seismic excitation matches the propagation of structural waves in the pipeline. This condition is specified in terms of structural and soil properties, and the incident angle between the pipeline and the propagation direction of the surface waves. These theoretical results are fundamentally important and are useful for structural design of surface‐mounted pipelines.

An approximate deterministic method of analysis is presented for assessing the effects of ground‐motion incoherence and of the associated soil‐structure interaction on the seismic response of structure‐foundation‐soil systems. The free‐field ground motion in this approach is specified by an acceleration history and a spatial incoherence function. Numerical solutions are presented that illustrate the procedure and elucidate the nature and relative importance of the kinematic and inertial interaction effects. The results are shown to be consistent with those obtained in a recent companion study by formal application of the stochastic approach.

Longitudinal cracks were observed in asbestos‐cement pipes that were in service for some time before bursting. Preliminary tests using a slitting technique showed residual stresses in the hoop directions. Absolute peak stresses are critical for determining the bursting strength of the asbestos‐cement (asb/cem) pipes. The experimental techniques of photoelastic coating and the blind‐hole drilling method were implemented in measuring local residual stresses and determining their principal values and directions. Relatively high residual stresses were recorded, which is an indication of the cause of the cracks. Conditions of manufacturing, storing, and environment during service are investigated. Moisture content, storing conditions, and chemical reaction of the asbestos‐cement mixture seem to be the major causes of the cracks. Coating the pipes would be an effective precaution.

A method of analysis for built‐up columns is presented. The method is an extension of the classical Engesser method for columns and the Timoshenko shear‐beam theory for beams. The two column chords are treated as beams connected by a shear panel simulating the web. The governing differential equation changes from a fourth‐ to a sixth‐order equation with a corresponding increase in the number of boundary conditions. It then becomes possible to include the effect of stay plates on the buckling load in a rational manner. It is found that the stay plates have a very significant effect on the buckling load. It is also found that the buckling load depends not only on the bending and shear stiffness of the column but also on the relative value of the chords' bending stiffness to the overall column bending stiffness. The solution for a simply supported column is given. The classical Engesser solution is always conservative.

Dynamic analysis of primary‐secondary systems with consideration of inelastic response has recently become an important issue in the design of civil engineering structures. The purpose of this paper is to develop a fundamental understanding of the response of such systems to wide‐band input. Previous research on linear response has shown that two‐degree‐of‐freedom (2‐DOF) primary‐secondary systems contain most of the essential properties of more general systems, yet are sufficiently simple to allow derivation of analytical expressions that mathematically quantify and characterize these properties. In this paper, these results are combined with nonlinear random vibrations theory to examine how nonlinear response differs from linear response. By assuming moderately small nonlinearities, perturbation methods are used to develop analytical expressions for wide‐band nonlinear response. The results show that small nonlinearities results in significant reduction of the response. In the final section of the paper, the results are extended to degrading systems subjected to nonstationary excitation.

Paper presents a point‐sink fundamental solution obtained by the Hankel‐Laplace transform technique. Based on this solution, an approximate solution scheme is developed for land‐subsidence simulation. The mathematical model was then applied to predict the subsidence in Bangkok area due to ground‐water recovery by using the superposition and Duhamel principles. This simplified model is also a useful tool for predicting land subsidence due to other fluid recovery such as oil and gas.