Journal of Engineering Mechanics

A rate-independent constitutive model for plain concrete on the basis of the bounding surface plasticity theory is formulated. Plastic strain rate is described by three independent plastic mechanisms without using a plastic potential surface. The actual plastic surface degenerates to the current stress point. The bounding surface shrinks in the postcritical state. Separate criteria of loading/unloading are used for the deviatoric and hydrostatic portions of stress rate. Plastic modulus functions are formulated separately for virgin loading/unloading/reloading cases on the basis of experimental data. Three different descriptions of shrinkage of the bounding surface are proposed. The important features of concrete behavior, namely, stiffness degradation, contraction/dilatation phenomenon, and different behavior of concrete in compression and in tension are satisfactorily rendered by this model. The presented model can describe concrete behavior in the plane stress state in the full range of loading including cyclic loadings.

A constitutive model for plain concrete proposed in Part I of this paper is comprehensively verified by a comparison of the model prediction obtained numerically with available experimental data for the plane stress state. At first, calibration of some model parameters is briefly discussed. Next, the model validation is made at the material point level for monotonic proportional load paths in the stress space covering all possible stress combinations, i.e., the compression-compression, compression-tension, and tension-tension regions. In the following, the postcritical behavior in uniaxial compression and tension is thoroughly studied. Next, the model prediction for cycling loadings is compared with experimental data, mostly for uniaxial compression and tension. Finally, two examples of structural computations of reinforced concrete (RC) deep beams for model implementation into an FEM code are presented. A good agreement with experimental data is found at the material point level. Also, the FEM computations render satisfactorily the actual behavior of RC deep beams.

To attenuate disturbance in residential buildings located along metropolitan railway lines, special types of track bedding have been designed, based on fixation of the rail on floating slabs, resting on elastomeric materials. Laboratory tests on small elastomeric pads show that the energy dissipation, under cyclic loading of constant amplitude, can be suitably represented by a combination of a viscous and an hysteretic damping. A significant strain-rate sensitivity is evident. As a first approximation, the stiffness has been represented as an increasing function of frequency, characterized by an asymptotic value. The frequency range of 0–100 Hz has been investigated. Eight types of elastomeric materials have been tested. Comparison shows that the stiffness increases with the increase of the material density. The analytical model has been checked in two different experiences. (1) A prototype of a floating slab track, 14.8 m long, has been assembled in the laboratory and tested under fixed amplitude and harmonic loads. While the experiments on small pads were restricted to uniform loading conditions, the track prototype was excited by a concentrated load, thus inducing different deformations along the specimen, decreasing with the increase of the distance from the point of loading. (2) An experimental track, 100 m long, made up of the same set of elements of the prototype, has been inserted in a railway line. A series of vibration records has been collected during train passages. Comparisons between measured and computed vibrations were used to provide a specific notion of the relevance in a practical problem of the analytical assumptions. Errors in the evaluation of the peak displacement and of the root-mean-square value are limited to a few percent.

In a previous paper, the writers presented a one-dimensional analytical model for the static analysis of multicell, thin-walled beams with nonhomogeneous cross sections. The proposed model accounts for shear deformations due to nonuniform bending and torsion supplementing the primary effects considered by the classical models. Here, the constitutive relations for the beam model are given and the dynamic analysis of the shear core is considered by a proper generalization of the continuous formulation. An algebraic procedure is given to evaluate the equivalent mechanical properties of the cross section. Moreover, a one-dimensional hierarchical finite element formulation is proposed for displacements and rotations. The proposed model is shown to cover the analysis of multicell, thin-walled beams, having regular cutouts, as is typical of shear cores of tall buildings. The applications include solutions to both the continuous and the discrete models.

A theory for one-dimensional self-weight subsidence of saturated soft porous media is presented. The problem is formulated in terms of volume solid fraction using the Eulerian coordinates. Two different types of constitutive relationships between the effective stress and the volume fraction of solids are considered. The governing equations and initial and boundary conditions are nondimensionalized. Self-weight subsidence behavior of unconsolidated soils is analyzed both analytically and numerically. Two sets of exact solutions corresponding to two different compressibility relationships are obtained under steady state conditions. Experimental data available in the literature are used to validate one set of exact solutions. Numerical analysis of transient settlement that allows the movement of the top boundary is presented. The validity of the numerical technique is verified by comparing with exact solutions. The model can be used to predict transient and ultimate settlement and the void ratio distribution of soft soils subsiding under their own weight.

The application of well-established identification procedures in the time domain for finite element (FE) models with a larger number of degrees of freedom (DOF) in general causes quite severe difficulties; i.e., the solution diverges in most cases and the procedures are computationally too demanding. In this paper, a two-step identification approach is presented that is especially suitable for FE models with many DOF. The two complementary approaches are a least-square-based method and a special form of the Extended Kalman Filter. Both approaches use modal decomposition as a key for avoiding the initially mentioned problems. To enable the identification of local damping phenomena, nonclassically damped structures are assumed throughout the computational procedures, implying the solution of the complex eigenvalue problem. For this purpose, a subspace iteration is used for solving the eigenvalue problem advantageously.

Cylindrical tanks that are not anchored effectively to their foundations often rock during seismic loading. Vertical compressive forces in the tank wall that are required to resist seismic overturning moments then tend to be concentrated over a small portion of the circumference of the tank, where the tank wall remains in contact with the foundation. This together with the effect of internal pressures often leads to plastic buckling of the tank wall at the base or the so-called elephant foot bulge. This paper aims at predicting not only whether elephant foot bulging will occur, but also the extent of elephant foot bulging. This is done by means of a nonlinear dynamic time history analysis on a simplified rigid cylinder model, in which equivalent springs are used to represent elastic tank deformations, as well as nonlinear effects including geometric and plastic shortening of the tank wall caused by elephant foot bulging, and the resistance to uplift provided by the hold-down action of the floor plate. A physically based approach is provided to calculate the properties and location of the equivalent springs using finite-element analyses of the tank that can be performed with minimal computational effort. This leads to a simplified model for which key aspects of the behavior (dynamic as well as static) match that of the real tank. The approach is applied to a tank that was damaged during the 1977 San Juan earthquake. Although field measurements of the amount of elephant foot bulging are not available, photographs taken after the earthquake show an amount of bulging that is consistent with the predictions.

Thermodynamics of open continua, when applied directly at the macroscopic engineering scale, allows one to extend unambiguously the principal concepts of continuum thermomechanics of solids to polyphasic porous materials, whose fluid constituents are subject to liquid-vapor phase change. This approach provides a consistent and relevant framework for the formulation of the constitutive equations of partially saturated deformable porous materials such as concrete. After recalling the general theory, the modeling is specified for porous materials that are partially saturated by a liquid water phase changing into its vapor phase, the latter forming with the dry air an ideal mixture. The nonlinear poroelasticity, as reference modeling, is then detailed. The theory is applied to the modeling of the drying shrinkage of concrete samples with isothermal sorption curves as only experimental data. The predicted shrinkage is found to be in close agreement with the observed one for a range of humidity greater than 50%. The drying shrinkage of a wall is finally examined. The analysis includes the study of the temperature variations due to latent heat effects. These variations are shown to be negligible.

A frequency-domain solution approach for the response of a system whose inputs are nonlinear transformations of non-Gaussian (nonlinear) wave kinematic processes is introduced. Particularly, this paper compares the probabilistic response characteristics of jacket-type platforms in deep water that are subjected to both Gaussian and non-Gaussian random wave loadings. Unlike earlier analytical treatments of this class of system, a statistical description of the wave forces is first developed to reflect nonlinearities and associated non-Gaussianity in the wave field kinematics. The kinematics are derived from Laplace's equation and nonlinear boundary conditions using a second-order Stokes' perturbation expansion. The deck response resulting particularly because of the effects of the second-order contribution to the loads on an idealized platform is computed. Consideration is given to the importance of the spacing of the legs to the response of the structure. The impact of swell in addition to locally wind-generated waves also is assessed. Ignoring the nonlinearity of the waves results in underestimation of the response level for all scenarios considered.

New explicit closed-form solutions are derived for the evolutionary correlation and power spectral–density (PSD) matrices characterizing the nonstationary response of linear elastic, both classically and nonclassically damped, multi-degree-of-freedom (MDOF) systems subjected to a fully nonstationary earthquake ground motion process. The newly developed earthquake ground motion model considered represents the temporal variation of both the amplitude and the frequency content typical of real earthquake ground motions. To illustrate the analytical results obtained, a three-dimensional unsymmetrical building equipped with viscous bracings is considered with a single-component ground motion acting obliquely with respect to the building principal directions. These new analytical solutions for structural response statistics are very useful in gaining more physical insight into the nonstationary response behavior of linear dynamic systems subjected to realistic stochastic earthquake ground motion models. Furthermore, the evolution in time of the cross-modal correlation coefficients is examined and compared with the classical stationary solution for white-noise ground motion excitation. The effects of cross-modal correlations on various mean-square response quantities also are investigated using the analytical solutions obtained.

This technical note provides closed-form deflection and stress corrections to the well-known and practical problem of a ring plate clamped along its inner radius and subjected to a point load on its free outer edge. The corrected solution predicts radial stress distributions, which in some cases are significantly different from that reported in the original analysis and subsequently reprinted in contemporary references.