Journal of Engineering Mechanics

This paper proposes a precise model to investigate the time-dependent response of excess pore-water pressure in stratified saturated soil induced by coupling effects from temperature and mechanical load based on the Laplace–Hankel transform and the precise integration method (PIM). First, the partial differential equations for the thermal consolidation problem are transformed into the ordinary equations by the integral transform techniques. By combining the adjacent layer elements and considering the boundary conditions, the extended precise integration solutions to the thermal consolidation problem in the transformed domain are deduced. By applying the corresponding integral inverse transforms, state variables in the physical domain are obtained. The existing analytical solutions and model test results validate the presented model. Additionally, numerical examples explore the influence of temperature load, Young’s modulus, and permeability coefficient on the thermal consolidation behavior. Numerical results reveal that (1) thermal load has a significant influence on the peak values of excess pore-water pressure and gives rise to the Mandel-Cryer effect; (2) due to the slower velocity of heat conduction than of pore-water penetration, the dissipation time of excess pore-water pressure caused by thermal-mechanical loads lags behind that of the mechanical load; and (3) the layering behavior of soils has significant effects on the distribution of excess pore-water pressure and the consolidation process.

With the extensive studies on energy harvesting via electromagnetic devices in civil or mechanical structures, a novel dual-function device, termed electromagnetic damping and energy harvesting (EMDEH) device, has been proposed in recent years, whose design represents a dual-objective optimization problem by considering both vibration control and energy harvesting performance. However, an argument on whether or not vibration control and energy harvesting is contradictory has arisen, based mainly on the intuition that the former tries to suppress vibration magnitude while the latter benefits from large vibration amplitude. This paper clarifies this question through a theoretical analysis of coupled structure–EMDEH systems under stochastic excitations. The closed-form solutions of the damping power, as well as the output power of the EMDEH device when attached to single-degree-of-freedom (SDOF) and multidegree-of-freedom (MDOF) structures, are given based on random vibration theory. A numerical analysis of a 20-story steel structure installed with EMDEH devices is conducted to validate the theoretical predictions. The consistency between vibration control and energy harvesting in randomly excited structures with EMDEH devices in the presence of inherent structural damping is demonstrated for the first time.

In this research, the piezoelectric energy harvesting (PEH) from nonlinear vibrations of a functionally graded beam is presented. The material properties of the harvester (both the substructure and piezoelectric layers) vary as graded in thickness direction to a power law function. The coupled system of equations is obtained under consideration of von Karman nonlinearity and the Euler Bernoulli beam theory. Finally, a coupled electro-mechanical finite-element model is presented for predicting the beam deflection, the generated voltage, and the produced electrical power of piezoelectric energy harvester. The effects of base excitation amplitude, material distribution and load resistance value on the harvested power near two first resonance frequencies are investigated. Our results show that the aforementioned parameters have considerable effects on the produced power and voltage of the harvester.

Cement-stabilized pavement layers are subject to sulfate attack (SA) in sulfate-abundant regions due to internal expansion–induced damage throughout its expected service life. SA is a coupled physical-chemical-mechanical damage process for cementitious materials involving complicated chemical reactions between sulfate and components of cement composite. SA contains intricate interactions among porous media, moisture transport, and heat transfer. Engineering mechanics has been used to explain the failure process of the internal expansion caused by this coupled physical-chemical ingress phenomenon. Existing studies have considered only heat transfer or moisture content–dependent modeling. The literature lacks a comprehensive model that considers coupled interaction of temperature and humidity upon sulfate ingression. Thus, a chemomechanical (CM) model has been developed for capturing the true failure process of cement-stabilized pavement subgrades under SA. In this paper, a set of governing equations are developed, and a unique expression for a moisture-dependent and heat-dependent sulfate diffusion coefficient is proposed. Consequently, the equations are solved using the finite-element method. The results conform well with experimental results. The model has been validated to be accurate enough compared with previously implemented models. It is capable of evaluating and predicting SA-induced expansive failure in unsaturated cement-stabilized pavements. Two different models were combined to estimate the mechanical behavior of cement-stabilized subgrades subject to SA. Finally, the Drucker-Prager (DP) failure criterion was used for determining the damage zone.

A new identification method based on QR decomposition for nonlinear time-varying systems is proposed in this paper, which is applied in a time-varying multiple-degree-of-freedom (MDOF) dynamic system to locate and estimate nonlinearities without a priori knowledge of them. This new procedure provides a continuous-time model with which a MDOF system can be partitioned into a number of different subsystems. After an orthogonalizing algorithm and an error reduction ratio (ERR) process, all information about the masses and linear and nonlinear connections in the subsystems can be detected and estimated with a high degree of accuracy. In this procedure, the time expressions of the time-varying parameters are also given. Because of its simplicity and efficiency, this new method will have wide application in practical engineering. The reliability of the identification method is demonstrated by a numerical example.

A high-order doubly asymptotic open boundary (DAOB) for the modeling of a semi-infinite reservoir with constant cross section is developed, in which the compressibility of water and the absorption characteristic of a reservoir bottom are considered. The dynamic stiffness matrix is approximated by a doubly asymptotic continued fraction solution with an additional factor matrix to improve its numerical robustness. The continued fraction solution converges throughout the entire frequency range quickly as the increasing orders of approximation and is verified by a rigid dam example. Introducing the auxiliary variables, a temporally local high-order DAOB is formulated. Coupling the high-order DAOB with the finite-element method (FEM) straightforwardly, an efficient procedure for the transient analysis of dam–reservoir interaction is developed and implemented in an open-source finite-element software OpenSees. Gravity dam and arch dam examples subject to dynamic loading conditions including the dam–reservoir interaction are analyzed. It is demonstrated that this proposed procedure is of high accuracy and computational efficiency.

The extended Kalman filter with unknown inputs (EKF-UI) method has been extensively studied for application in system and input identification of multiple-degrees-of-freedom systems. The inverse problem is, however, unidentifiable for the case of a single-degree-of-freedom system with unknown system parameters and excitation. This study presents a strategy to address this problem based on output using only the EKF-UI method. A numerical example is given to validate the proposed method for system parameters and input identification. The strategy is then applied to identify the aerodynamic load and system parameters of a tower model in a wind tunnel test. Both system stiffness and damping were found to vary with the incident wind speed, and the vortex shedding-induced excitation in the cross-wind direction was clearly noted in the power spectrum of the identified wind load.

Studying the time-dependent behavior of gas shale formations is important for understanding the mechanical performance of source rocks in response to drilling, hydraulic fracturing, and pressure depletion due to production, among others. Compared with nonsource-rock shales, the role of the organic matter (OM) on creep rates of gas shale formations remains to be uncovered, which is the focus of this paper. By means of a hybrid experimental–modeling approach involving creep nanoindentation and microindentation and first-order modeling within the framework of the correspondence principle of viscoelasticity, it was found that organic matter drives creep rates of shale rocks, whereas the confining texture of the inorganic phases decelerate the creep rate. By means of micromechanical textural models used to analyze nanoindentation results, it is shown that creep in source rocks entail changes in packing density related to total organic carbon (TOC)-dependent energy-dissipation mechanisms in the microstructure: dilation in organic-poor and overmature source rocks, and compaction in organic-rich mature ones. Finally, a comparison of microindentation results with first-order creep homogenization modeling that considers the organic matter as the dominant creeping phase reveals that the relevant creep rate of organic-rich shale is situated within two asymptotes defined by texture: an upper bound defined by the self-consistent scheme representing mature disordered systems, and a lower bound defined by a continuous creeping matrix of immature OM with rigid clay inclusions. These morphologies relate to the connectivity of OM and, thus, to maturity.

Output-only modal identification plays an important role in the structural health monitoring of large-scale structures. In recent years, blind source separation (BSS) has achieved great success in structural modal identification. Sparse component analysis (SCA), which is one of the most popular methods of BSS, has the capability to handle nonstationary excitation and underdetermined problems. In the process of SCA, clustering number, which is equal to the number of active modes, plays an important role in the estimation of modal matrix, in which the hierarchical clustering algorithm is used. However, the clustering number is always unknown in the clustering step, which makes application inconvenient. To fill this gap, an improved SCA method, equipped with a process of estimating the clustering number, is proposed in this paper. After transforming the signals into time-frequency (TF) domain, the single-source-points (SSPs) detection process is applied to pick out the TF points at which only one mode makes a contribution to the responses. The clustering technique is preceded by a preprocessing step to determine the clustering number. The key idea is that the clustering number is equal to the number of columns in the modal matrix, which is reflected in the number of lines in the scatter plot of two observations. A normalization method is proposed to distinguish the clusters clearly. The number of clusters is acquired through statistical analysis of the normalized vectors. After obtaining the modal matrix, the smoothed zero-norm algorithm is used to recover the modal responses in order to extract natural frequencies and damping ratios. An experimental cantilever beam and a three degree-of-freedom (DOF) numerical system with closely spaced modes were used to verify the effectiveness of the proposed method. The results showed that the improved SCA could detect the number of active modes for the beam and the numerical system. Full-scale data measured from the Green Building located at the Massachusetts Institute of Technology (MIT) campus and the Tianjin Yonghe Bridge were analyzed to verify the effectiveness of the proposed method in practical applications.

The scale of fluctuation (SOF) of a spatially variable soil property has been known to be the most important parameter that characterizes the effect of spatial averaging, whereas the type of the autocorrelation model (e.g., single exponential versus squared exponential model) is thought to be of limited impact. This paper shows that when extending this statement (SOF is the most important parameter) to the probability of failure, one must be cautious regarding whether the limit-state function is completely governed by spatial averaging. Spatial averaging is a function of the input random field in its classical form—it is not related to the limit-state function. For a limit state that happens to be completely governed by spatial averaging, e.g., a friction pile under axial compression, the statement is indeed true, but for a limit state that is not completely governed by spatial averaging, the statement may not be true and the type of autocorrelation model can have significant impact. This paper shows that the second type of limit-state functions are not uncommon. In particular, this paper shows that the sample path smoothness can be another important feature that signifcantly affects the probability of failure for this type of limit-state function. An autocorrelation model that can control the sample path smoothness using a smoothness parameter $\nu$ is adopted in this paper. Five practical examples are presented to illustrate the effect of $\nu$. It is observed that $\nu$, which is another characteristic of the autocorrelation model that is distinctive from the scale of fluctuation, can have significant impact on the probability of failure for these examples.

In a real-time hybrid simulation (RTHS), the actuator delay in experimental results might deviate from actual structural responses and even destabilize the real-time test. Although the assumption of a constant actuator delay helps simplify the stability analysis of RTHS, experimental results often show that the actuator delay varies throughout the test. However, research on the effect of time-varying delay on RTHS system stability is very limited. In this study, the Lyapunov-Krasovskii functional is introduced for the stability analysis of RTHS system. Two stability criteria are proposed for a linear system with a single constant delay and a time-varying delay. It is demonstrated that (1) the stable region of a time-varying delay system shrinks with the increase of the first derivative of time-varying delay; and (2) the stable region of the time-varying delay system is smaller than that of constant-time-delay system. Computational simulations were conducted for RTHS systems with a single degree of freedom to evaluate the proposed criteria. When the experimental specimen is an ideal elastic spring, the stability region of RTHS system with time-varying delay is shown to depend on the stiffness partition, structural natural period, and damping ratio. Significant differences in stability regions indicate that the time-varying characteristics of actuator delay should be considered for stability analysis of RTHS systems.

This study presents a deep convolutional neural network (CNN)-based approach to estimate the dynamic response of a linear single-degree-of-freedom (SDOF) system, a nonlinear SDOF system, and a full-scale 3-story multidegree of freedom (MDOF) steel frame. In the MDOF system, roof acceleration is estimated through the input ground motion. Various cases of noise-contaminated signals are considered in this study, and the conventional multilayer perceptron (MLP) algorithm serves as a reference for the proposed CNN approach. According to the results from numerical simulations and experimental data, the proposed CNN approach is able to predict the structural responses accurately, and it is more robust against noisy data compared with the MLP algorithm. Moreover, the physical interpretation of CNN model is discussed in the context of structural dynamics. It is demonstrated that in some special cases, the convolution kernel has the capability of approximating the numerical integration operator, and the convolution layers attempt to extract the dominant frequency signature observed in the ideal target signal while eliminating irrelevant information during the training process.

This study proposes a novel data-driven Bayesian machine learning method for constructing site-specific multivariate probability distribution models in geotechnical engineering. There is a trade-off for constructing a site-specific model: a model developed from generic data may not be fully applicable to a local site, but a model purely developed from limited site-specific data may be very imprecise due to significant statistical uncertainty. The proposed method is based on the hybridization between site-specific and generic data in the way that it is governed by site-specific data when site-specific data are abundant and by generic data when site-specific data are sparse. This method broadly follows how an engineer currently estimates design soil parameters from limited site-specific information. The proposed method admits incomplete multivariate data, so it can handle missing data that are commonly encountered in site investigation. It is a Bayesian method, so uncertainties are rigorously quantified. Actual case studies are used to demonstrate the usefulness of the proposed method. Analysis results show that the proposed method can effectively capture the correlation behaviors in site-specific data and, moreover, can make meaningful predictions even when site-specific data are very sparse.

This paper presents the theoretical solution to the response of a square plate undergoing plastic deformation due to a generic localized blast pulse. A localized blast load function was assumed multiplicative of its spatial distribution and temporal pulse shape. The spatial distribution was representative of constant pressure over the central zone, while exponentially decaying outside that zone. Considering an appropriate moment function and ignoring the membrane, transverse shear, and rotary inertia effects, the static plastic collapse was found, whereby the analysis was extended to the dynamic case by assuming a kinematically admissible, time-dependent velocity profile. The analytical model, which was validated against the numerical results obtained through ABAQUS hydrocode, showed close correlation in terms of the permanent transverse deflection profile. In order to consider the effect of temporal pulse shape, the results were formulated for rectangular as well as exponentially and linearly decaying pulses. For blast loads of high magnitude, the pressure load was replaced by an impulsive velocity. The calculations were simplified by utilizing the dimensionless form, and the results were corroborated with theoretical and experimental results from the literature. The model showed improvements in predicting the final deformation of square plates over previous models of simplified loading function.

The ability to detect spatially-distributed defects and material changes over time is a central theme in structural health monitoring. In recent years, numerous computational approaches using electrical, electromagnetic, thermal, acoustic, optical, displacement, and other nondestructive measurements as input data for inverse imaging regimes have aimed to localize damage as a function of space and time. Often, these regimes aim to reconstruct images based off one set of data disregarding prior information from previous structural states. In this paper, we propose a stacked approach for one increasingly popular modality in structural health monitoring, namely quasi-static elasticity imaging. The proposed approach aims to simultaneously reconstruct spatial changes in elastic properties based on data from before and after the occurrence of damage in the presence of an inhomogeneous background. We conduct numerical studies, investigating in-plane plate stretching and bending, considering geometries with various damage levels. Results demonstrate the feasibility of the proposed imaging approach, indicating that the inclusion of prior information from multiple states visually improves reconstruction quality and decreases root mean-square error (RMSE) with respect to true images.

Evaluating the statistical moments of performance functions from the perspective of balancing accuracy and efficiency remains a challenge. This paper proposes an efficient algorithm for evaluating the statistical moments of performance functions. The main procedure of the proposed method consists of three steps. First, based on the bivariate dimension-reduction method, the performance function is approximated by a summation of one-dimensional and two-dimensional functions. Next, according to the criterion of delineating the existence of cross terms, the two-dimensional functions are decomposed as functions including and excluding cross terms. Third, the one-dimensional point estimate method is used to evaluate the statistical moments of the one-dimensional functions and the two-dimensional functions without cross terms, whereas the two-dimensional sparse grid stochastic collocation method is applied to estimate the statistical moments of the two-dimensional functions with cross terms. Several numerical examples are presented to illustrate the efficiency, accuracy, and applicability of the proposed method. The results demonstrate that the proposed method achieves a good balance between accuracy and efficiency and provides a useful tool for evaluating the statistical moments of performance functions.