Journal of Engineering Mechanics

Recent case histories have demonstrated that soil liquefaction can occur repeatedly at a site during a sequence of earthquake events. Field observations and laboratory tests imply that reliquefaction resistance can be markedly different, depending on the strain histories and induced fabric change. However, direct observation of fabric evolution during the entire process remains limited. In this study, we perform simulation using a three-dimensional (3D) discrete-element method (DEM) to quantify fabric evolution in granular soils during liquefaction, reconsolidation, and reliquefaction processes, with the goal of investigating the effects of fabrics on reliquefaction resistance. Clumped particles are used to construct realistic particle shapes of Toyoura sand in the DEM, and soil fabric is characterized by a coordination number $Z$ and a degree of anisotropy $a_c$. By reconsolidating samples at different states after the first liquefaction, we describe the relationships between the maximum preshear strains versus volumetric compression and the resulting soil fabrics ($Z$, $a_c$) after reconsolidation. Finally, we set up correlations between the reliquefaction resistance and soil fabrics ($Z$, $a_c$). This study shows that the effects of strain histories on reliquefaction resistance are intrinsically attributed to changes in soil fabrics before and after reconsolidation. The DEM simulation also generates data that are consistent with laboratory tests and provides micromechanical insights into the reliquefaction phenomenon.

Stochastic optimal control of structures involves the optimal design of the control law and the optimal selection of the weighting parameters adopted in the control law. The classical stochastic optimal control (CSOC) method for linear quadratic Gaussian (LQG) control problems needs to employ the assumption of Gaussian white noise excitation, and the numerical solution to the Riccati equation in deriving the control law leads to the difficulty in obtaining closed-form sensitivities with respect to the weighting parameters, which further makes it difficult to use the gradient-based optimization algorithms for the optimal selection of those parameters. In this study, an explicit stochastic optimal control (ESOC) method is developed based on the explicit time-domain method (ETDM). With the explicit formulation of structural responses, the constraint of the optimal control problem imposed by the equation of motion of the structure can be satisfied automatically, which avoids the introduction of the Riccati equation with the Gaussian white noise assumption, and therefore the optimal control can be implemented under general random excitations. On this basis, the closed-form sensitivities of the response statistics with respect to the weighting parameters are obtained for the controlled structure, which are further incorporated into the gradient-based method of moving asymptotes (MMA) for the stochastic optimal selection of the weighting parameters. Numerical examples are worked out to demonstrate the efficacy of the proposed method for the stochastic optimal control of structures.

The present study utilizes the Girsanov transformation-based framework for solving a nonlinear stochastic dynamical system in an efficient way in comparison with other available approximate methods. In this approach, rejection sampling is formulated to evaluate the Radon–Nikodym derivative arising from the change of measure due to Girsanov transformation. Rejection sampling is applied on the Euler–Maruyama approximated sample paths, which draw exact paths independent of the diffusion dynamics of the underlying dynamical system. The efficacy of the proposed framework was ensured using more accurate numerical as well as exact nonlinear methods. Finally, nonlinear applied test problems were considered to confirm the theoretical results. The test problems demonstrated that the proposed exact formulation of the Euler–Maruyama provides an almost exact approximation to both the displacement and velocity states of a second-order nonlinear dynamical system.

The deformations of Kirchhoff–Love plate elements are usually characterized by three components describing the strains in the middle plane and three components describing the bending of the plate element. It is shown that alternatively one may consider pure bending deformations about two neutral axes that generally are not in the same plane and skew to each other. This interpretation provides an intuitive understanding of the plate deformations and is particularly useful when analyzing the behavior of reinforced concrete plate elements subjected to combined bending moments and membrane forces. After a recapitulation of the conventional interpretation of Kirchhoff–Love plate deformations and their implications on the strain distribution in plate elements, this paper presents the alternative interpretation and illustrates its application for a special case with orthogonal neutral axes.

We conducted a series of axial-torsional strain-controlled experiments on thin-walled tubular specimens of aluminum alloy Al6061 in our lab, examining carefully the probed yield points in axial-torsional space. On the basis of the experimental findings, a rate-independent flow elastoplastic material model featuring an evolving cubic distortional yield hypersurface, which is articulated with two Mises hyperspheres, characteristic of internal symmetry of two elements of the projective proper orthochronous cubic distortional yield hypersurface in the plastic phase, is proposed. Associated with each Mises hypersphere in stress space is a normality plastic flow rule and a mixed-exp-AF’s rule, referring to a combined isotropic-kinematic rule of hardening-softening, which combines the isotropic exponential rule of degree 2 and the kinematic rule of Armstrong-Frederick. The model needs a total of 10 material constants. An identification procedure is presented for estimating the 10 material constants of the model from the experimental data. The cubic distortional yield hypersurface estimated by the probed experimental data of yield points and the evolving yield hypersurface simulated by the proposed model along with the identified material constants was validated satisfactorily.

A novel method of simple static loadings is developed for existing space trusses to assess the key structural stiffness, which provides the main resistance to the structural deformation caused by the load that dominates the deformation check in the structural design. For a space truss under a given dominant load, the structural displacement can be characterized by the generalized displacements along a few eigenvectors, which form a so-called key set, of the stiffness matrix of its numerical (finite-element) model. When the stiffness of the space truss deteriorates, the structural displacement can still be described by the pseudo-generalized displacements along those eigenvectors included in the key set and a small number of their adjacent eigenvectors. Moreover, the pseudo-generalized displacement can be approximately expressed as a linear combination of the generalized displacements along its neighboring eigenvectors included in the key set. Any combination coefficient can be estimated by the measured nodal displacements of the existing (deteriorated) structure under a constructed simple static load. The strategies for selecting the loaded degrees of freedom and optimizing the magnitude of loads are proposed. The selection of the measured degrees of freedom of displacement responses caused by the simple load is also discussed. For two illustrative space trusses with randomly assigned member stiffness deviations, the deterioration of their key structural stiffness is evaluated by comparing the displacement, which is indirectly obtained by simple static loadings, of the existing structure and that of the numerical model. The accuracy and validity of the proposed method are verified.

In the context of probabilistic analysis involving uncertain factors, efficient reliability methods play an important role for promoting a wider application in engineering practice. Although the ordinary Monte Carlo simulation (MCS) can simulate the probabilistic performance of a complex engineering system well and has been widely-employed in reliability analysis because of its simplicity and accuracy, the unavoidable computational burden to ensure sufficient accuracy often limits its use as a reference tool only for academic purposes. This paper proposes a modified weighted uniform simulation (WUS) method for reliability analysis involving nonnormal random variables, in which the Nataf transformation is adopted to effectively transform the correlated nonnormal variables into independent standard normal variables. This method takes into account the correlations between random variables, while the sample size is greatly reduced under the same accuracy requirements. Four examples of reliability analysis are presented to demonstrate the feasibility of the WUS method. It is shown that the proposed method can yield sufficiently accurate reliability analysis results with a reasonably small sample size compared to ordinary MCS. In particular, the most probable failure point (MPP), which is the basis for reliability-based design works, can also be directly obtained during the simulation process.