Journal of Engineering Mechanics

This paper is concerned with the in-plane elastic stability of arches with a symmetric cross section and subjected to a central concentrated load. The classical methods of predicting elastic buckling loads consider bifurcation from a prebuckling equilibrium path to an orthogonal buckling path. The prebuckling equilibrium path of an arch involves both axial and transverse deformations and so the arch is subjected to both axial compression and bending in the prebuckling stage. In addition, the prebuckling behavior of an arch may become nonlinear. The bending and nonlinearity are not considered in prebuckling analysis of classical methods. A virtual work formulation is used to establish both the nonlinear equilibrium conditions and the buckling equilibrium equations for shallow arches. Analytical solutions for antisymmetric bifurcation buckling and symmetric snap-through buckling loads of shallow arches subjected to this loading regime are obtained. Approximations for the symmetric buckling load of shallow arches and nonshallow fixed arches and for the antisymmetric buckling load of nonshallow pin-ended arches, and criteria that delineate shallow and nonshallow arches are proposed. Comparisons with finite element results demonstrate that the solutions and approximations are accurate. It is found that the existence of antisymmetric bifurcation buckling loads is not a sufficient condition for antisymmetric bifurcation buckling to take place.

Permeability of a liquefiable soil profile may affect the rate of pore-pressure buildup and subsequent dissipation during and after earthquake excitation. Consequently, effective soil confinement and available resistance to shear deformations may be significantly dependent on permeability in many practical situations. If present, spatial variation in permeability may even have a more profound impact on available overall shear resistance. Indeed, case histories and experimental evidence (shake table and centrifuge tests) suggest that spatial permeability variation in stratified liquefiable deposits can highly influence the nature and extent of associated lateral deformation. In such situations, the onset of liquefaction-induced densification may result in water or water-rich thin interlayers trapped below overlying low-permeability strata. The presence of these low-shear-strength interlayers may trigger excessive (or even unbounded) localized shear deformations (flow failure mechanism). In this paper, numerical modeling is employed in order to investigate the influence of permeability and the spatial variation thereof on liquefaction-induced shear deformations. The involved response characteristics are numerically simulated using a fully coupled two-phase (solid–fluid) Finite Element program.

Significant interest has been shown in identifying the nonlinear mechanisms that induce a ringing type response in offshore structural systems. This high frequency transient type response has been observed in offshore systems, particularly in tension leg platforms (TLPs). Given the implications of this behavior on the fatigue life of TLP tendons, it is essential that ringing be considered in the overall response evaluation. This study presents two non-Gaussian probabilistic models of nonlinear viscous hydrodynamic wave forces that induce ringing. The response of a single-degree-of-freedom system exposed to these non-Gaussian wave force models is then evaluated using analytical and numerical studies based on the Ito⁁ differentiation rule and the Monte Carlo simulation procedure, respectively. The results demonstrate that the proposed models induce ringing type response in a simplified structure. This study provides a probabilistic framework for modeling ringing type phenomenon which will serve as a building block for more refined hydrodynamic load models.

The crack-tip toughness of materials with two-dimensional random orientation of ribbon cracks is evaluated theoretically. The effective elastic moduli reduce when the cracks exist within the isotropic material so as to enhance the material toughness. The results show that the crack density and the Poisson ratio of the matrix dominate the behavior of the overall effective toughness. As crack density $\eta =1\text{,}$ the toughness increment is 0.44–0.48 of the original toughness approximately, but three out of five moduli, ${\mu }_{12}\text{,}$ ${\mu }_{23}\text{,}$ and ${\kappa }_{23}\text{,}$ reduce at least 0.57 of their moduli. The explicit forms of the crack-tip toughness and five transversely isotropic moduli of the material containing ribbon cracks are also shown.

The initial stresses existing in the natural ground are anisotropic in the sense that the vertical stress is typically larger than the lateral stresses. The construction activities, such as embankments and excavation, induce anisotropy in the stress system. The stress-deformation behavior and excess pore water pressure response of soils are affected by the inherent and induced stress anisotropy. This paper presents an improved soil model based on the anisotropic critical state theory and bounding surface plasticity. The anisotropic critical state theory of Dafalias was extended into three-dimensional stress space. In addition to the isotropic hardening rule, rotational and distortional hardening rules were incorporated into the bounding surface formulation with an associated flow rule. The projection center that is used to map the actual stress point to the imaginary stress point was specified along the $K_0$ line instead of the hydrostatic line or at the origin of the stress space. A simplified form of plastic modulus was used and the proposed model requires a total of 12 material parameters, the same number as that of the single-ellipse time-independent version of the Kaliakin–Dafalias model. The model was validated against the undrained isotropic and anisotropic triaxial test results under compression and extension shearing modes for Kaolin Clay, San Francisco Bay Mud, and Boston Blue Clay. The effects of stress anisotropy and overconsolidation were well captured by the model. The time effect was not included in the formulations presented in this paper.

The effects of the ground motion spatial variation and of the canyon geometry on the dynamic response of arch dams during the event of an earthquake is studied in this paper. The seismic response of a dam subject to time harmonic longitudinal, shear, and Rayleigh waves impinging the dam site from different directions is analyzed. Several canyon and reservoir geometries are considered. A three-dimensional boundary element model which allows for the rigorous representation of the dynamic interaction between the dam, the foundation rock, and the water is used. The foundation rock is modeled as a uniform viscoelastic boundless domain where the incident traveling wave field is defined by its analytical expression, which may include any spatial variation. The obtained results show the importance of three-dimensional effects which are many times neglected.

The paper presents a macroscopic failure criterion for structural masonry. This criterion is derived within the framework of the critical plane approach. First, a general discussion is provided examining the performance of this framework in the context of classical linear as well as nonlinear criteria. Subsequently, a bilinear form of failure criterion for structural masonry is proposed incorporating a set of distribution functions for describing the spatial variation of material properties. Extensive numerical study is performed examining the behavior in biaxial compression–tension and compression–compression regimes for different orientations of the sample relative to the loading direction. The results are compared with the available experimental data.

The extraction of fluids from deformable underground formations has resulted in surface subsidence above the formation in several field cases. This paper demonstrates the necessity of using the coupled Biot’s equations for deformation-flow problems in deformable fluid-saturated porous media, particularly for problems involving fluid extraction or injection in underground formations. It is shown that it is not possible to decouple the fluid flow and deformation fields from Biot’s theory except for idealized one-dimensional cases where the total stresses are constant and the deformation mode can be assumed. The deficiencies of the uncoupled approach are also shown via an analysis of a case involving production-induced subsidence in a hydrocarbon field. An important prediction of the coupled analysis is the increase of pore pressure above the initial value during continuous withdrawal of fluids from deformable formations.

The resonant frequency response of large static pressure loaded, nonlinear rectangular plates with a cross stiffener have been investigated theoretically. The nonlinear Berger equation was solved by applying the finite-difference method. Replacing the partial differential equation governing the small amplitude vibration of static pressure loaded plates and the boundary conditions by the finite-difference equations approximately, the simultaneous, homogeneous, and algebraic equations are obtained. Under the condition that the determinant of coefficient matrix must be equal to zero, the resonant frequencies are determined. The numerical procedure is simpler than the procedures based on the von Kármán theory, and reasonable results are obtained.

The feasibility of protecting tall buildings against progressive downwards collapse following catastrophic structural failure at high level is explored and various design suggestions made.

This paper examines the glass cladding damage accumulation caused by wind loading. The primary focus is the effect of the non-Gaussian nature of wind pressure fluctuations. The damage is estimated using the Monte Carlo methodology and Brown’s integral formulation. The pressure time histories are generated by a numerical procedure based on the translation model, which is calibrated on experimental data. The stress field in the glass is calculated using the von Kármán plate model. A sensitivity analysis is performed estimating the damage statistical moments, up to the fourth order, and its probability density function. The obtained results demonstrate that the classical Gaussian assumption used to model wind pressure is unsafe. The accurate modeling of the non-Gaussian features produces a significant amplification of the damage mean value and higher variability of the damage distribution.