Journal of Engineering Mechanics

A computationally efficient continuum-based model is developed for obtaining the nonlinear response of pile foundations subjected to a static horizontal force and/or moment at the pile head. In the analysis, the soil is modeled using nonlinear elastic constitutive relationships expressed as power-law or hyperbolic equations; these relationships relate the induced shear strain in soil to the secant shear modulus. The soil displacements in the horizontal plane are expressed as products of separable functions maintaining compatibility with the horizontal pile movement, and the principle of virtual work is applied to obtain the governing differential equations describing pile and soil displacements under equilibrium. These differential equations are solved using the one-dimensional finite-difference method following an iterative algorithm. The soil resistance parameters associated with the pile-displacement differential equation capture the effect of soil nonlinearity because these parameters are related to the secant shear modulus at different points in the soil. The accuracy and computational efficiency of the present analysis are established by comparing the pile and soil responses with those obtained from equivalent three-dimensional finite-element analysis which used the same soil constitutive relationships. The present analysis framework is further validated against the results of two full-scale field pile-load tests. Furthermore, monopile responses obtained from the present analysis are compared with those of three-dimensional finite-element analyses in which the soil is modeled as an elastoplastic material. It is shown that, for the purpose of design against lateral loads, elastoplastic approaches are not necessary because the present nonlinear elastic analysis can produce sufficiently accurate pile and monopile responses.

Large-amplitude water waves can be generated in small lakes, such as moraine-dammed lakes, by resonant earthquake excitation, which may cause the overtopping failure of natural dams and result in destructive floods in downstream areas. This paper experimentally investigated the behavior of seismically induced resonant water waves (SRWWs) with a large-scale shaking table and presented the nonlinear properties of the seismically induced water waves (i.e., second-order resonance and the participation of the second-order mode in the triggered wave motion). Moreover, the effects of several factors (i.e., peak ground acceleration of the seismic wave, resonant order, and water level) on SRWWs were studied. An equation for calculating the maximum wave height of SRWWs was proposed with these experimental data and then verified for a case study of a real earthquake. The proposed equation provides a guideline for estimating whether a moraine dam will be overtopped by SRWWs, and the results of the study broaden the knowledge of the risk assessment of moraine-dammed lakes in earthquake-prone areas. It is expected that the data presented in this study will contribute to the experimental database that can be used to verify numerical models.

A viscoelastic constitutive model for an asphalt–concrete (AC) material that accounts for temperature and material degradation effects is proposed. The model is implemented within a finite-element framework and consists of a new nonlocal damage regularization approach that is based on a nondimensional equivalent stress measure. The viscoelastic model is introduced as a generalized Maxwell model with the shear modulus described in terms of Prony series. Damage behavior is described in rate form with an anisotropic damage accumulation law for tension, compression, and shear loadings. Prediction of the AC response is obtained by solving the nonlinear system, which includes an equilibrium equation that is coupled to a nonlocal damage equation. The latter introduces a length scale in the problem that renders the damage results mesh-independent. The system is solved implicitly until convergence using a robust staggered scheme. A rigorous material calibration is carried out for both viscoelastic and damage material parameters using optimization techniques. The proposed material model is validated by comparison to published experimental tests conducted on a range of temperatures from $-20°\mathrm{C}$ to 0°C. In particular, an Arrhenius-type relation is introduced to describe the dependence of material damage on temperature. Good agreement between predicted and experimental results shows that the proposed model is suitable for describing the thermoviscoelastic damage behavior of common AC.

Flexible barriers have been proven to be effective measures for mitigating natural hazards, such as rockfalls, gravel flows, and debris flows. This paper presents a new numerical ring model based on the discrete element method (DEM) to simulate a flexible ring net. The Edinburgh Bonded Particle Model is applied to create internal forces within a ring element. The mechanical behavior of a ring element was analyzed from measurements collected during quasi-static tensile tests. The systematic calibration approach of this ring model is described in detail. Two reduction factors related to the bond Young’s modulus and the bond radius are proposed to effectively adjust the bending and axial stiffnesses of the ring element. With calibrated DEM parameters from the tensile tests, the ring model is validated by reproducing these tensile tests under different boundary conditions. Finally, a three-dimensional DEM model is established for modeling the rockfall impact on a flexible ring net. A comparison between the existing test data and simulation results reveals that the new ring model can accurately reproduce the response of a flexible ring net under both static and dynamic conditions.

An analytical model is presented in this paper to predict the three-dimensional dynamic response of a circular tunnel in an elastic multilayered half-space. By applying the transfer matrix method and wave transformation, the circular tunnel was coupled with the soil via the continuity condition of the tunnel–soil interface. The coupled tunnel-soil model could simulate the asymmetric dynamic responses induced by the load at an arbitrary angle. The track system was subsequently coupled to the tunnel-soil model by means of three-line support. After being validated via comparison with existing models in two special cases, the present model was applied to calculate the soil vibrations from a large-diameter double-line tunnel in a three-layered half-space. The results showed that the insertion gains for vertical and horizontal displacements between the single- and double-line loading cases are $-15\mathrm{to}20\mathrm{dB}$ and $-15\mathrm{to}11\mathrm{dB}$, respectively, depending on the position of the observation point and frequency. The vibration levels generated by the double-line load were smaller than those generated by the single-line load at specific load frequencies.

The mechanical behavior of cellular solids has been extensively studied in the literature. Nevertheless, possible structural effects of inhomogeneities in the form of elastoplastic struts have not yet been investigated. We present a numerical analysis of the tensile behavior of triangular, diamond, and hexagonal hybrid lattices composed of both elastic and elastoplastic struts. In particular, some struts are assumed to behave as strain-hardening elastoplastic beams while others are assumed to behave as a linear elastic material. It is found that both the stiffness and the strength of the lattices decrease with increasing percentage of elastoplastic struts. Furthermore, the presence of elastoplastic struts markedly alters fracture toughness. The effect of relative density on the tensile behavior of hybrid lattices is also investigated. It is concluded that in addition to the microstructure of cellular solids, the constitutive behavior of individual struts significantly affects their macroscopic mechanical response. Thus, the spatial distribution of struts with different material properties can be considered a novel approach in the design of cellular solids with desired properties.

This paper introduces a methodology for Bayesian model updating of a linear dynamic system using the modal data that consists of the posterior statistics of the modal properties, identified from dynamic test data using a Bayesian modal identification method. To avoid direct mode matching or solving the eigenvalue problem, Eigen system equation is used to establish the relationship between modal data and the structural model parameters. The dynamic condensation technique is proposed to reduce the full system model to a smaller model with the degrees of freedom (DOFs) in the reduced model corresponding to the observed DOFs. This eliminates the need for selecting the observed DOFs of the full system mode shape. The proposed methodology is computationally efficient because neither iteration nor numerical optimization is required to obtain the reduced model. The performance and effectiveness of the proposed methodology was demonstrated by means of two simulated examples. The transitional Markov chain Monte Carlo (TMCMC) method is used to obtain samples distributed according to the posterior distribution.

In evaluating of the response of linear systems to arbitrary intermittent loadings, traditional methods have been exclusively conducted in the time domain where the time resolution must be carefully chosen. In this paper, an accurate and efficient Laplace-time domain method is developed to perform the dynamic analysis of multi-degree-of-freedom (MDOF) systems to arbitrary intermittent loadings. The proposed method is a Laplace-time domain approach in the sense that (1) for each individual nonzero segment of an intermittent loading, the computation for the corresponding response is carried out in the Laplace domain (complex plane) by using algebraic pole-residue operations, and (2) for the total response calculation that accounts for all segments of intermittent loadings, the principle of linear superposition is applied in the time domain. Three numerical examples ranging from single-degree-of-freedom (SDOF) to 600-degree-of-freedom (DOF) systems are provided in this paper. Through numerical examples, this study demonstrates the superiority of the proposed method over traditional time-domain methods in terms of both accuracy and computational efficiency.

This work presents a collocation method for study of the static behavior of composite beams with consideration of linear and nonlinear partial interactions. The collocation concept is first introduced; the internal global trial functions for the displacement field are then assumed in terms of Fourier series expansion representations. In order to obtain the unknown coefficients, several collocation points, distributed uniformly along the span of a composite beam, are adopted to set up the systems of equations by satisfying governing equations and boundary conditions. Both single- and multispan composite beams are investigated and validated against other analytical and numerical methods, where good agreement is always obtained. The efficiency of the collocation technique is then tested with different numbers of collocation points or harmonic terms to generate converged results. The collocation technique is also applied to the nonlinear analysis of partial-interaction composite beams. The theoretical distinctions between the present technique and other methods are finally explained.

A micromechanics-based model is developed to study the fatigue response of cementitious composites. Microcrack growth, which is the predominant mechanism responsible for fatigue damage, is explicitly modeled at the mesoscale. The damaged state at the macroscopic scale is determined by using energetic criterion. The dissipated energy associated with each stage of microcrack propagation is computed numerically based on the elastic solutions of the stress and displacement quantities at the mesoscale. The model is used to predict the fatigue life of plain concrete beams under fatigue load cycles. The influence of the various properties of the constituent phases on the fatigue life of the composite is investigated through a parametric study.

The main purpose of this paper is to find a suitable method for determining the in-plane shear characteristics of a type of “cellular metal” plain-woven stainless steel wire mesh. That no ready-made standard test exists for investigating the in-plane shear properties of the wire mesh must be noted. Two types of in-plane shear test methods that are normally used for shear tests of textile structures, that is, the bias-extension test and the picture-frame test, were conducted and employed in this work. To determine whether they can provide a pure and uniform shear region during a test, the Digital Image Correlation (DIC) approach is used as an auxiliary measurement of strain distribution for both methods. Based on the comparison and analysis of results from those two tests, a picture-frame test with a corners cut-off sample was found to be a more suitable method than a bias-extension test for determining the shear properties of the wire mesh. However, the bias-extension test can provide a simple and reliable method for determining the lock-angle of a wire mesh.

The spectral matrix decomposition is a significant task for a wind velocity field simulation. However, the decomposition requires significant computational time and memory for large-scale structures with a large number of simulation points. To reduce the computational demand, the explicitly expressed Cholesky decomposition of a spectral matrix has been used widely to simulate the wind velocity field evenly distributed along a horizontal axis. In this study, a new closed-form solution of the Cholesky decomposition is proposed for the wind velocity field simulation in which the simulation points can be arbitrarily distributed along the horizontal axis, the autospectra at various points can be different, and the wave passage effect can be considered. Additionally, this closed-form solution is extended to the wind velocity fields along vertical and inclined axes with little approximation. Further, the proposed approach is applied to the nonstationary wind velocity field simulation and random vibration analysis. Finally, numerical examples demonstrate that the proposed approach has good performance.

The application of the spectral representation method to the conditional simulation of ground motions can break down because of nonconvergence in inverting the conditioning covariance matrix, and the time-averaged power spectral density (PSD) functions of simulated records can deviate significantly from the target PSD functions. These two issues are discussed and explained. A procedure is proposed to overcome the two observed drawbacks. Its application can result in a close approximation of the means of the PSD functions of the conditionally simulated nonstationary ground motions to those estimated from observed ground motions. The close approximation becomes equality if the stationary processes are considered.

Recent interpretations of wetting-induced compaction revealed that water sensitivity can cause a loss of controllability in samples subjected to fluid injection. This paper elaborates these findings by focusing on fabric anisotropy, i.e., a feature of unsaturated clays not encompassed by previous studies. For this purpose, a hydromechanical elastoplastic model with rotational hardening is developed to capture fabric effects. The model performance has been validated under both saturated and unsaturated conditions with reference to laboratory tests on Lower Cromer Till (LCT). To inspect the role of the material properties, parametric analyses have been conducted, thus identifying the parameters which govern the transition from stable to unstable conditions upon wetting. The results show that fabric anisotropy affects only the deformations prior to wetting-collapse, without changing the value of suction at the onset of volumetric instability. By contrast, it is found that the model parameter governing the intensity of suction-hardening is able to alter the value of critical suction at the loss of control regardless of the intensity of fabric evolution. These results corroborate previous findings obtained through isotropic constitutive laws and emphasize the crucial role of hydromechanical constitutive couplings on the inelasticity of unsaturated porous media.

Modeling errors that prevent the eight-node Mindlin plate finite element to behave correctly, namely shear locking and spurious zero-energy modes, can be explained using strain gradient notation. This notation is physically interpretable, and it allows for the sources of shear locking and spurious zero-energy modes to be clearly identified a priori. This means that spurious terms in shear strain polynomials are precisely identified as parasitic shear terms. Once this is done, such spurious terms are simply removed to correct the element model, resulting in a shear locking-free element. In order to avoid introducing spurious zero-energy modes, the analyst must recognize and retain the compatibility modes in the shear strain polynomials. As the study shows, compatibility modes can easily be confused with parasitic shear terms. Numerical displacement and stress solutions from models containing parasitic shear terms revisit important locking effects. Further, solutions obtained using corrected models are qualitatively correct and have higher rates of convergence.

Image processing methods combined with scanning techniques—for example, microscopy or microtomography—are now frequently being used for constructing realistic microstructure models that can be used as representative volume elements (RVEs) to better characterize heterogeneous material behavior. As a complement to those efforts, the present study introduces a computational homogenization method that bridges the RVE and material-scale properties in situ. To define the boundary conditions properly, an assignment problem is solved using Euclidean bipartite matching through which the boundary nodes of the RVE are matched with the control nodes of the rectangular prism bounding the RVE. The objective is to minimize the distances between the control and boundary nodes, which, when achieved, enables the bridging of scale-based features of both virtually generated and image-reconstructed domains. Following the minimization process, periodic boundary conditions can be enforced at the control nodes, and the resulting boundary value problem can be solved to determine the local constitutive material behavior. To verify the proposed method, virtually generated domains of closed-cell porous, spherical particle-reinforced, and fiber-reinforced composite materials are analyzed, and the results are compared with analytical Hashin-Shtrikman and Halpin-Tsai methods. The percent errors are within the ranges from 0.04% to 3.3%, from 2.7% to 14.9%, and from 0.5% to 13.2% for porous, particle-reinforced, and fiber-reinforced composite materials, respectively, indicating that the method has promising potential in the fields of image-based material characterization and computational homogenization.

To evaluate short crack growth and fatigue damage accumulation in steel structures, efforts have been made based on a two-dimensional (2D) grain-based model for fatigue life assessment under variable amplitude loads. However, crack arrested in a 2D field could be problematic since the arrested 2D crack might propagate toward the out-of-plane direction. In addition, the pure plane stress/plain assumption in 2D simulation could not be applied to many complex stress states. In this paper, a three-dimensional (3D) fatigue damage estimation model is proposed based on a twofold nonlinear grain-based fatigue life assessment method. The persistent slip band based short fatigue crack growth model is implemented in this model combined with Miner’s rule for grain fatigue accumulation evaluations. Rain-flow counting method and the linear damage rule in grains are employed for fatigue damage growth within each grain. Meanwhile, in the grain and subgrain regime, the crack is assumed to nucleate and grow along with persistent slip bands. Also, an adjacent persistent slip band detection algorithm is developed to locate the potential crack propagation path. Therefore, fatigue damage is calculated grain by grain until the crack length reaches the characteristic length (such as over 0.1 mm), where linear elastic fracture mechanics (LEFM) thoery becomes more reliable. Sensitivity analysis is conducted for the number of grains and the element size in statistical volume element model under constant amplitude loads. Finally, a case study is performed to demonstrate the proposed method for variable amplitude loads, and the results are compared with the 2D model results in the literature.

High-performance control systems (HPCSs), including active, hybrid, and semiactive control strategies, can perform over a wide excitation bandwidth and are therefore good candidates for multihazard mitigation. However, the number of HPCS applications in the field is very limited. This is likely due to the perceived higher costs of installation, maintenance, possible malfunction, and lack of tools to financially justify their implementation. Such financial justifications could be conducted through life-cycle cost (LCC) analysis, but would result in a computationally demanding task due to the very large number of simulations required given the large number of uncertainties. In this paper, two sets of methods for conducting LCC analyses are compared and their performance is assessed as a function of LCC estimation accuracy and computational requirements. The first set is based on deterministic scenarios and on the simulation of all possible scenarios; it is termed “what-if analysis.” Variations of the what-if method are investigated, where the simulations are conducted only for the most likely scenarios, termed “most-likely (ML)” analysis. The second set is based on stochastic scenarios and on Monte-Carlo (MC) analysis. Variations of the MC method are investigated, one based on the coefficient of variation of output data and one proposed by the authors based on the convergence of the estimated costs, termed bounded MC. A demonstration of the LCC analysis methodology is conducted where an HPCS is used for the mitigation of seismic-induced vibrations on a five-story structure. Uncertainties under consideration include sensor failure, mechanical wear, tear, and seismic events. Results are compared against the uncontrolled structure and a passive viscous strategy, and demonstrate that (1) the LCC methodology can be used to financially justify the utilization on an HPCS; and (2) the bounded MC method leads to accurate cost estimations using a lower number of simulations.

Since the early 2000s, suction stress has been conceptualized as a unitary way to quantify effective stress in soil, i.e., effective stress equal to total stress minus suction stress. Suction stress is the part of effective stress purely due to soil-water interaction. When soil is saturated, suction stress is the pore water pressure, whereas when soil is unsaturated, suction stress is a characteristic function of soil called the suction stress characteristic curve (SSCC). Two physicochemical soil-water retention mechanisms are responsible for the SSCC: capillarity and adsorption. These two mechanisms are explicitly considered to develop a closed-form equation for the SSCC and effective stress. The SSCC data from the literature for a variety of soils ranging from clean sand to silty and clayey soils are used to validate the equation, indicating that the equation can well represent the data. Additional validation is achieved using experimental data of the apparent elastic modulus and the SSCC to predict the soil shrinkage curves. The equation can be reduced to Lu et al.’s previous closed-form equation for the SSCC when capillarity dominates soil-water retention, can be reduced to the Bishop’s effective stress equation when capillarity is the sole soil-water retention mechanism, and can be reduced to the Terzaghi’s classical effective stress equation when soil is saturated.

A two-step methodology is presented for evaluating the extreme value distribution (EVD) of the response of random nonlinear structures under fully nonstationary stochastic seismic excitations. The fully nonstationary stochastic seismic excitations are modeled by the spectral representation method (SRM) based on the evolutionary power spectral density. In this regard, the randomness in both structural properties and external excitations is considered, whereby a problem involving a high-dimensional random-variate space needs to be tackled. In the proposed methodology, the probability density evolution method (PDEM) is first employed, where Latin hypercube simulation (LHS) is incorporated, to provide an estimated solution of the EVD of the response with efficiency. Then, a highly flexible distribution model named the shifted generalized lognormal distribution (SGLD) model is fitted, where the estimated solution is served as the original data. The parameters in SGLD model are then specified, and the entire range of accurate EVD of the response can be recovered accordingly. A numerical example involving a nonlinear random structure exhibiting hysteretic behavior under stochastic seismic ground motions is used to illustrate the implementation of the proposed methodology and assess its accuracy and efficiency, especially for the tail distribution. Some features of the EVD of the dynamic response are also discussed.