Journal of Engineering Mechanics

The dynamic response of heterogeneous deep-sea sediments under moving nonuniform mining collector loading was determined analytically. The heterogeneity of deep-sea sediments is associated with the elastic modulus increasing nonlinearly with depth. The ground pressure of the mining collector with longitudinal eccentricity was assumed to have a trapezoidal distribution. The complex Fourier series method was used to expand the soil displacement and the loading function of the ground pressure with eccentricity. Thus, the governing partial differential equations (PDEs) of motion for the soil were reduced to ordinary differential equations (ODEs) with respect to the horizontal direction $x$ and the time $t$. The analytical solution of the ODEs was solved by the method of Frobenius. After verifying the analytical solution by means of comparisons with the Abaqus simulated results for the special cases of homogeneity under uniform load, this analytical solution was utilized to assess the effect of heterogeneity, eccentricity, and pedrail length on the response of deep-sea sediments.

The first articulation of the second type of dilatational wave propagating through fluid-saturated geomaterials has been traced to Heinrich’s formulation built on Fillunger’s framework of the mixture theory and Terzaghi’s principle of effective stress. Although this Fillunger–Heinrich theory (FHT) precedes the celebrated Biot’s wave theory and Frenkel’s theory, research has yet to systematically investigate the FHT’s predictive ability. To value the scientific heritage, the original formulation of FHT was first revisited with minor corrections and then reformulated in a dimensionless form. Using the method of separation of variables, an analytical solution was developed for the dimensionless FHT in the context of consolidation under instantaneously applied surcharge and with one-way drainage at the top boundary of the consolidating stratum. The predictive power of FHT was validated against available wave measurements; the proposed solution was verified against the finite-difference method with nonclassical Newmark’s integration schemes. The parametric analysis conducted herein further suggests that FHT can qualitatively interpret observed complex phenomena, including the consolidation delay effect, the top-down progressive pattern, and the initial settlement overestimation. FHT significantly fills the knowledge gap between Terzaghi’s classic theory and Biot’s theory, thus enabling engineers to analyze the one-dimensional dynamic behavior of saturated geo-/poro-materials with incompressible constituents.

Structural health monitoring (SHM) systems use nondestructive testing principles for damage identification. As part of SHM, the propagation of ultrasonic guided waves (UGW) is tracked and analyzed for the changes in the associated wave pattern. These changes help identify the location of a structural damage, if any. We advance the existing research by accounting for uncertainty in the material and geometric properties of a structure. The physics model employed in this study comprises a monolithically coupled system of elastic and acoustic wave equations, known as the wave propagation in fluid–structure and their interface (WpFSI) problem. Because the numerical simulation of the WpFSI problem becomes computationally extremely expensive for many realizations of the uncertainty, we developed an efficient algorithm in this work that employs machine learning techniques like Gaussian process regression and convolutional neural networks to predict UGW propagation in a fluid–structure and their interface under uncertainty. First, a small set of training images for different realizations of the uncertain parameters of the inclusion inside the structure is generated using the computationally costly physics model. Next, Gaussian processes trained with these images are used for predicting the propagated wave with convolutional neural networks for further enhancement to produce high-quality images of the wave patterns for new realizations of the uncertainty. The results indicate that the proposed approach provides an accurate prediction for the WpFSI problem in the presence of uncertainty.

Adding redundant cables to tensegrity structures is an inevitable requirement for the engineering application of this type of structure. Here we investigated the form-finding and stability of several typical classes of tensegrities with additional cables. An energy minimization–based form-finding method was presented and validated by the analytical solutions developed for prismatic and antiprismatic tensegrities. Some new multistable configurations of typical tensegrities were identified by the proposed algorithm, which demonstrates the robustness of the present form-finding method. It can be revealed from the present analysis that the stability and mechanical properties of the tensegrities with additional cables depended both on the number and the method of adding cables. The stiffness of the antiprismatic tensegrity increased with the increase of the number of additional cables and the reduction of the natural length of the additional cable. But for a more general case, the resistance to deformation of the tensegrity could not always be increased by increasing the number of additional cables. Additional cables could improve the possibility of obtaining more equilibrium states of the tensegrity, but the stability of those equilibrium states was not guaranteed. The transition between two stable self-equilibrated states of a tensegrity could be achieved by just reducing the length of additional cables.

A temporal multiscale model was developed to characterize the damage that evolves in concrete structures throughout a complete scenario of dynamic fatigue loading. The damage was decomposed into quasistatic and dynamic components, and its evolution was controlled by introducing negative and positive feedback mechanisms. Fatigue damage evolution equations of the power law type were used together with a deduced temporal multiscale scheme to allow a computationally efficient finite-element method (FEM) simulation of the damage that evolves during the whole loading process. The validity and computational efficiency of the FEM model were assessed by comparing its predictions with published experimental data.

Flexibility plays an important role in bridge load-carrying capacity assessment. The flexibility of bridges has been extracted from the measured data of numerical impact testing and in laboratory experiments. Recently, substructuring impact testing has been increasingly investigated and developed because it avoids deploying sensors throughout bridges while obtaining the same results as full-structure testing. However, most substructuring testing methods require overlapping transition areas between the divided substructures, thereby affecting the operability and efficiency of the test. This study proposes a novel substructuring flexibility integration method that uses limited instruments to sequentially test different substructures subdivided from the whole girder bridge structure without requiring the overlapping reference points of adjacent substructures. Using the basis that the structural mode shapes satisfy the orthogonality and mode node theorem, the parameters of each substructure can be efficiently integrated and the entire flexibility matrix can be identified from the sparse flexibility matrices of the substructures. Case studies using experimental data from a cantilever beam and a continuous girder bridge are considered to verify the availability and effectiveness of the proposed method.

Model updating, the process of inferring a model from data, is prone to the adverse effects of modeling error, which is caused by simplification and idealization assumptions in the mathematical models. In this study, an adaptive recursive Bayesian inference framework is developed to jointly estimate model parameters and the statistical characteristics of the prediction error that includes the effects of modeling error and measurement noise. The prediction error is usually modeled as a Gaussian white noise process in a Bayesian model updating framework. In this study, the prediction error is assumed to be a nonstationary Gaussian process with an unknown and time-variant mean vector and covariance matrix to be estimated. This allows one to better account for the effects of time-variant model uncertainties in the model updating process. The proposed approach is verified numerically using a 3-story 1-bay nonlinear steel moment frame excited by an earthquake. Comparison of the results with those obtained from a classical nonadaptive recursive Bayesian model updating method shows the efficacy of the proposed approach in the estimation of the prediction error statistics and model parameters.

Rock salt is a sedimentary rock found in nature as bedded or domal deposits due to evaporating inland seas or any enclosed bodies of saline water. Rock salt hosts caverns within the underground deposits that can potentially serve as a long-term and safe repository for carbon dioxide, radioactive nuclear waste, and the waste of oil drilling operations. The accuracy of simulating the constitutive response of rock salt hinges on the fidelity of both the engineering model and the geometrical representation of the cracked material. The main constituent of rock salt is the halite mineral, which has a building block of sodium chloride (NaCl), forming a cubic crystal system with a constitutive response that is dependent on strain rate and deforming temperature. The constitutive behavior of rock salt has so far been simulated using phenomenological creep models that lack the representation of its microscale crystal structure. Accordingly, this paper seeks to develop a three-dimensional (3D) dislocation density–based crystal plasticity model that can enhance the current numerical representation of crack mechanisms and growth in rock salt. The model was introduced and then validated using literature experiments on single-crystal specimens of artificial rock salt tested in triaxial extension against different crystal orientations, a wide range of strain rates, and various temperatures. When implementing the model to predict the response of natural single-crystal rock salt specimens tested in unconfined one-dimensional (1D) compression, the model parameters needed fine recalibration via a genetic optimization procedure due to the existence of cleavage planes in the natural rock salt material. The viscoplastic nature of the calibrated model was also evaluated to accurately replicate the ratcheting plastic deformations in natural rock salt specimens when tested in cyclic unconfined 1D compression. Overall, the proposed dislocation density–based crystal plasticity model form is able, through reasonable parameter adjustment, to simulate both the monotonic and cyclic response of high-purity artificial and natural single-crystal rock salt.

A computationally efficient semianalytical framework for obtaining the consolidation settlement of flexible foundations such as beams and strip footings resting on nonlinear, saturated, poroelastic, and multilayered continua (soil) is developed. Two-dimensional (2D) plane strain is assumed, and Biot’s consolidation theory is used in the analysis. The differential equations governing the displacements and excess pore pressure dissipation of the beam-soil system are developed using the variational principles of mechanics in which the soil is modeled as a simplified continuum and the foundation is modeled as an Euler-Bernoulli beam. The developed differential equations are coupled and are solved following a unique iterative algorithm using one-dimensional (1D) finite-element analysis. The numerical solution is less expensive than conventional 2D numerical methods. A distinct feature of the developed framework is that the effect of soil stress-strain nonlinearity is considered in the calculation of the consolidation settlement, which is usually not considered in Terzaghi’s and Biot’s consolidation theories. It is observed that soil nonlinearity and foundation flexibility can significantly impact the foundation settlement and consolidation rate. The developed framework provides a fast, easy-to-use, and accurate method for estimating the consolidation settlement of flexible shallow foundations.

Large-amplitude cable vibrations are remarkably common on cable-stayed bridges due to various aerodynamic loading mechanisms and/or motion of the cable ends. Geometric nonlinearity can be important in the dynamic behavior, and significant local bending stresses can arise at the anchorages, where rotation is restrained. This leads to a concern about the fatigue of these cables from the cyclic stress variations. This paper presents an analytical bending fatigue model for estimating the fatigue life of low-sag cables subjected to harmonic loading. Using this framework, the fatigue life of cables at the anchorage zone and guide deviator (if present) under external loading can be predicted. The results show that the use of a guide deviator can significantly extend the cable’s fatigue life at the anchorage. For cables with a guide deviator subject to severe loading conditions, the fatigue life is limited by the behavior at the guide rather than the anchorage, which is consistent with previous observations. The fatigue life is greatly reduced if the cable jumps to a multimodal dynamic response due to the cable nonlinearity. The single-mode zone where the dynamic response of the cable is always stable in a single mode, leading to a relatively long fatigue life, has been identified. Finally, the effect of cable inclination angle and ratio of cable weight to tension on the fatigue life has been analyzed.

An asymptotic approximation methodology for solving standard random eigenvalue problems is generalized herein to account for structural systems with singular random parameter matrices. In this regard, resorting to the concept of the Moore–Penrose matrix inverse and generalizing expressions for the rate of change of the eigenvalues, novel closed-form expressions are derived for the joint moments of the system natural frequencies. Two indicative examples pertaining to multiple-degree-of-freedom structural systems are considered for demonstrating the reliability of the methodology. Comparisons with pertinent Monte Carlo simulation data are included as well.

This paper proposes a multiphase computational fluid dynamics (CFD) model to investigate the mixing process of an off-road self-loading concrete mixer drum. A multiphase Eulerian-Eulerian approach is used in a transient simulation for studying how sand and gravel move into the cement paste during the drum rotation. Inert materials were simulated as dispersed solid particles with various diameters and the cement paste as a continuum non-Newtonian-fluid. An experimental calibration of the separated materials was performed. For the solid–liquid interaction, a model found in the literature was used. The results describe motion of the mixture, accumulation areas of the aggregates, and calculated velocities of sand and gravel into the cement paste during the drum rotation. Furthermore, viscosity of the mixture as a function of the solid volume fractions has been analyzed. Validation was achieved by experimental numerical comparison of the drum torque curve at the start of mixing. This model can be used to design more efficient concrete mixers and to better understand some fluid dynamics aspects at the beginning of the concrete mixing process.

The governing equations of motion for bridges with rocking piers of unequal height and unequal span lengths are derived accounting for the effect of the end joint gaps and the abutment-backfill system. The attenuation of the rocking motion stems from the impacts at the rocking interfaces, described through the coefficient of restitution, and also from the impacts (pounding) of the superstructure on the abutment backwalls. This is the first study to the author’s knowledge that combines both energy-dissipation sources in the analytical derivation of the equations of motion. The results of response-history analysis of bridges with different levels of asymmetry in their pier height show that the performance of both the symmetric and asymmetric configurations is very similar with regard to longitudinal displacements. Although the studied bridges safely resisted ground motions with an intensity about twice that of the design earthquake, regardless of the degree of asymmetry, it was found that the higher the difference in the pier height, the larger the rotation of the superstructure due to the differential uplift of the piers, a point that must be addressed in seismic design for rocking response.

This paper investigated an intermediate discontinuity in a frame structure and its capability to mitigate the effects of seismic ground motions. The discontinuity represents a sudden change in the stiffness of the frame. The behavior of a structure after the introduction of discontinuity was studied by means of an archetype dynamically equivalent three-degree-of-freedom model. Two auxiliary systems were introduced to evaluate the effectiveness of the discontinuity. The first auxiliary system represented the structure without discontinuity. The second represented a system in which the part of the structure below the discontinuity is rigid. These two auxiliary systems allowed us to evaluate whether discontinuity is able to reduce the displacements of frame structure. The results were summarized using three gain coefficients that portray the ratio of displacements and drifts with and without the discontinuity. When the gain coefficients are less than unity, the discontinuity improves the dynamic behavior of the frame. To check the effectiveness of the proposed archetype model, results provided by an archetype and by spatial shear-type frames were compared. Then the archetype three-degrees-of-freedom system was used to conduct an extensive parametric analysis by varying geometrical and mechanical parameters. The results were organized in gain maps that represent the contour plot of the gain coefficients. Some maps were built using the spectrum compatibility criterion so that the results depend only on the seismic design spectrum. The gain maps show several ranges of the parameters’ region in which discontinuity is effective.

Fine grains play an important role in mechanical properties of granular materials as they control how plastic strain may develop, which has a noticeable impact on mechanical stability. In this work, we use numerical simulations based on a discrete element method (DEM) to analyze the stress contribution of fine grains to the total stress. Different from usual DEM simulations, the analysis is conducted directly at the mesoscopic scale by considering an idealized grain assembly. The results show how fine grains get progressively jammed and increasingly participate in stress transmission. Fine contribution to contact stress is shown to be nonisotropic. The principal anisotropy direction coincides with the principal direction of contraction and the anisotropy ratio (i.e., the ratio between the largest and the smallest eigenvalues of the fine stress) is shown to be limited (${\sigma }_{\max }/{\sigma }_{\min }\simeq 2$). By performing strain controlled directional analyses, an analytical model is proposed to account for the stress contribution of fine grains along various loading paths. Its simple form will help to enrich advanced micromechanically-based constitutive formulations and better account for the constitutive behavior of widely graded granular materials.

Prompt identification of structural damage is essential for effective postdisaster responses. To this end, this paper proposes a deep neural network (DNN)–based framework to identify seismic damage based on structural response data recorded during an earthquake event. The DNN in the proposed framework is constructed by Variational Autoencoder, which is one of the self-supervised DNNs that can construct the continuous latent space of the input data by learning probabilistic characteristics. The DNN is trained using the flexibility matrices obtained by operational modal analysis (OMA) of simulated structural responses of the target structure under the undamaged state. To consider the load-dependency of OMA results, the undamaged state of the structure is represented by the flexibility matrix, which is closest to that obtained from the measured seismic response in the latent space. The seismic damage of each member is then estimated based on the difference between the two matrices using the flexibility disassembly method. As a numerical example, the proposed method is applied to a 5-story, 5-bay steel frame structure for which structural analyses are first performed under artificial ground motions to create train and test datasets. The proposed framework is verified with the near-real-time simulation using ground motions of El Centro and Kobe earthquakes. The example demonstrates that the proposed DNN-based method can identify seismic damage accurately in near-real-time.

The rotational failure mechanism with a log-spiral is most efficient in upper-bound limit analysis for homogenous slopes, but it cannot work well in regard to layered slopes. In this study, the log-spiral rotational mechanism is extended for layered slopes by a multicenter method that focuses on the variations of slip surfaces between adjacent soil layers. There are multiple rigid blocks, each of which rotates around a separate center, in the proposed mechanism, and the additional rupture surface is between the adjacent blocks. Several typical examples are analyzed by the proposed method and other published mechanisms based on the limit equilibrium method or limit analysis method. Benefiting from the log-spiral, the proposed mechanism has fewer rigid blocks than that in other published mechanisms based on the limit equilibrium method or upper-bound limit analysis. The factors of safety obtained by the proposed method are smaller than existing upper-bound mechanisms, and the slip surfaces lie well in the plastic zones obtained by the finite element method (FEM). These comparisons demonstrate the applicability and advantages of the proposed failure mechanism. Furthermore, the influence of nonassociated flow rule on a two-layer slope is considered, and associated effect charts are given.

To illustrate the influence of differential settlement along the lateral direction of subgrade on the dynamic performance of a high-speed vehicle system, based on the vehicle–track coupling dynamic theory and finite-element method, a vehicle–track–subgrade spatial coupling dynamic model considering the lateral mechanical characteristics of the vehicle system is established, and the dynamic performance of the vehicle system under different lateral differential settlement parameters (amplitude/wavelength) of subgrade on one side and both sides and the vehicle speeds are studied. The study reveals the following. The vehicle dynamic response under the lateral differential settlement of subgrade on both sides is generally greater than that under the lateral differential settlement of subgrade on one side, and the difference becomes more obvious with increases in the lateral differential settlement amplitude. However, there is little difference between the two lateral differential settlement modes on the car body lateral acceleration. The wheel/rail vertical force of the left rail (with large settlement amplitude) is greater than that of the right rail (with small settlement amplitude), while the wheel/rail lateral force of the right rail is greater than that of the left rail. The dynamic response of the vehicle system increases with increases in the lateral differential settlement amplitude; the dynamic response of the vehicle system increases noticeably when the amplitude of lateral differential settlement exceeds 25 mm. The lateral differential settlement wavelength is inversely proportional to the dynamic response of the vehicle system, and the wavelength range $5–15\mathrm{m}$ has the greatest impact on the dynamics of the vehicle system. The vehicle driving speed is directly proportional to the vehicle system dynamic response, and the vehicle system dynamic response increases significantly when the driving speed exceeds $250\mathrm{km}/\mathrm{h}$.

Glaze ice is more likely to occur on the rotating blade, and greatly decreases the energy utilization efficiency of wind turbines. Moreover, due to its complex and irregular shape, a high-quality grid and more grid cells are needed in aerodynamic calculation. To improve this situation, this study develops a novel multiobjective optimization method for the blunt trailing edge of airfoils under glaze ice conditions. The parametric representation of the asymmetric trailing-edge profile is given by the B-spline function. The aerodynamic coefficients of the airfoils without and with glaze ice are calculated using the computational fluid dynamics (CFD) method and back propagation (BP) neural network, respectively. The update mode of the potential well center of nonoptimal particles is modified by the social learning and the optimal particle position is identified using the Lévy flight and greedy algorithm for quantum particle swarm optimization (QPSO) algorithm. The optimizer based on the improved QPSO algorithm integrated with CFD method and BP network seeks the trailing-edge control parameters maximizing the lift coefficient and lift-drag ratio. The lift and drag coefficients, lift-drag ratios, and pressure contours of the original and optimized airfoils are investigated before and after icing. Significant improvements of the aerodynamic performance are achieved in this process, confirming that the presented method constitutes a valuable tool for the airfoil design of wind turbines operating in icing conditions.

This study proposed a three-dimensional (3D) multiscale modeling method to investigate the responses of asphalt pavement subjected to coupled temperature-stress fields. In this method, finite element models of asphalt pavement at two different scales, i.e., the macroscale (pavement level) and mesoscale (mixture level), were developed separately and connected through a two-way coupled approach, including a homogenization (upscaling) procedure and a mapping (downscaling) procedure. X-ray computed tomography (CT) scanning technology was adopted to acquire realistic mesostructure images of asphalt concrete, and a digital image processing technology was employed to reconstruct its 3D mesoscale representative volume element model from these CT images. Both thermal and mechanical properties of asphalt concrete at the two scales were considered in the multiscale simulation. Also, actual climatic data sets, including air temperature history, solar radiation history, and mean wind speeds, were incorporated into the computation. The results showed that the developed multiscale method furnishes an in-depth insight into the thermomechanical behaviors of asphalt pavement at different length scales under both tire loading and realistic environmental factors. The consideration of coupled temperature-stress fields varying with time has a significant impact on the accurate determination of the critical responses within asphalt pavement. Because the developed method is capable of simultaneously taking into account multiple factors, including mixture component properties and mesostructures, pavement structures, tire loads, and climatic information, it can be expected to serve as a mechanistic tool for facilitating and enhancing the analysis and design of asphalt pavement.

Recovering the probability distribution of the limit state function is an effective method of structural reliability analysis, in which it still is challenging to balance the precision and computational efforts. This paper proposes an adaptive mixture of normal-inverse Gaussian distributions which exhibits high flexibility to deal with this issue. First, the mixture distributions with two components were revisited briefly, and the limitations are pointed out. Then the proposed mixture distribution was established. According to the limit condition, one or two components are employed in the proposed mixture distribution to represent the unknown distribution of the limit state function (LSF), which makes the mixture distribution adaptive. To specify the unknown parameters effectively, the Laplace transform at some discrete values is utilized, in which a set of nonlinear equations can be solved easily. An effective cubature rule is utilized to assess numerically the Laplace transform and the involved moments, which can guarantee the efficiency and precision for structural reliability computation. After the LSF’s distribution is attained, the failure probability can be evaluated readily via an integral over the distribution. Five numerical examples were provided to indicate the result of the proposed method.