Journal of Engineering Mechanics

Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. This paper presents a robust multifidelity surrogate modeling strategy in which the multifidelity surrogate is assembled using an active-learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework for efficient reliability analysis. The multifidelity surrogate is assembled by first applying a Gaussian process correction to each low-fidelity model and assigning a model probability based on the model’s local predictive accuracy and cost. Three strategies are proposed to fuse these individual surrogates into an overall surrogate model based on model averaging and deterministic or stochastic model selection. The strategies also dictate which model evaluations are necessary. No assumptions are made about the relationships between low-fidelity models, while the high-fidelity model is assumed to be the most accurate and most computationally expensive model. Through two analytical and two numerical case studies, including a case study evaluating the failure probability of tristructural isotropic-coated (TRISO) nuclear fuels, the algorithm is shown to be highly accurate while drastically reducing the number of high-fidelity model calls (and hence computational cost).

Various papers have presented different methods for computations of mechanics and kinematics of discrete structural systems. However, little has been done in comparing and benchmarking the seismic response from two different discrete-system-models with experiments. This paper presents a detailed seismic performance comparison between two models—level set discrete element method (LS-DEM) and Logiciel de Mécanique Gérant le Contact (LMGC90), calibrated with shake table experiments conducted on four concrete-block configurations. Theories of both models are thoroughly explained and compared. The simulation results are benchmarked against experimental data. Finally, the principal results and significance of this benchmarking effort is discussed.

Recently, nanoparticle injection technology has been developed for the remediating and repairing cracks in wellbore systems that can be used for underground ${\mathrm{CO}}_2$ storage. The repair technology can seal the cracks and prevent the ${\mathrm{CO}}_2$ from leaking. In this work, a numerical model was developed to simulate the coupling effects among various ions in pore solution of well cement used in underground wellbore systems as well as the injection of nanoparticles during the leak repairing process in boreholes. Two main governing equations, the Nernst–Planck and Poisson’s equations, were used to derive the transport and migration of ions driven by external current in the pore solution. The governing equations were solved using the finite element method based on the multiphysics object-oriented simulation environment (MOOSE) framework. The concentration profiles of the ions in well cement were obtained at different times and depths. The nanoparticle injection process was simulated with the appearance of five different ions in the solution of well cement. The effect of the external current for penetration of nanoparticles into the cement was captured.

Machine learning (ML)–based data-driven approaches have become increasingly prevalent for predicting structural performance. Because a properly trained ML model can learn hidden patterns in databases of experimental samples, ML model performance sometimes exceeds that of mechanics-based predictive models, especially when the latter either conflates multiple phenomena into a single term or does not represent them at all. Nevertheless, there is almost always an inherent gap between the domain of the collected data—used in developing the predictive models—and the desired prediction domain. For instance, structural testing is often carried out on scaled components with approximated boundary conditions. Although mechanics-based models can usually bridge the said gaps, discrepancies are a perpetual challenge to the extrapolation capabilities of data-driven models. To address this issue, a new data-driven approach, a prior-knowledge embedded data-driven approach (PkeDA), is proposed herein, which integrates valuable prior knowledge embedded in empirical formulas into a data-driven model. A particular realization of this approach, based on artificial neural networks, PkeDA-ANN, is developed. To verify its feasibility and compare it with a model trained through a classic data-driven approach (CDA), a case study for predicting the bending capacities of reinforced concrete beams is carried out. The results indicate that when the model is trained via CDA, it exhibits good interpolation capabilities, as expected, but its extrapolation capabilities are observed to be severely limited. Under identical conditions, the proposed PkeDA was observed to have not only excellent interpolation and extrapolation capabilities but also to dramatically surpass the classic empirical formulas that have been developed for predicting the capacity of concrete beams under bending. As such, PkeDA appears to be a viable approach for developing highly accurate data-driven models when prior knowledge is available.

The uncertainties related to the inherent properties of pavement subgrade subjected to the dynamic effect of vehicular and earthquake loading were studied extensively using probabilistic analysis. The dynamic effect of the loading on pavement was modeled using lower bound shakedown analysis. Pavement subgrade was considered to be purely cohesive and was assumed to fail through the Mohr–Coulomb yield criterion. The soil spatial variability was simulated using random fields, which were represented in the form of finite-element random variables using the Karhunen–Loéve expansion method. The effect of parameter uncertainty was investigated using stochastic results such as the mean, coefficient of variation, and failure probability of the structure using the Monte Carlo simulation technique. The effect of dynamic loading of vehicles was studied by varying the period of vehicular movement. The dynamic shakedown was analyzed using two different methods. Seismic waves were generated using modified pseudodynamic approach. The combined effect of moving vehicles and earthquake was studied to determine the worst-case scenario. It was found that the generation of seismic waves affects the direction and frequency of the moving vehicle, which reduces the effect of shakedown on pavements due to vehicular load. The worst-case scenario was found to be the pavements with period ratio of 0.06 for a deterministic analysis, whereas it was 0.48 for a probabilistic analysis.

Currently, the buffeting analysis for transmission lines (TLs) only involves the excitation of horizontal turbulence, while numerous investigations have proven that significant vertical turbulence exists in many wind fields. Additionally, overhead conductors generally exhibit nonlinear behavior, rendering the conventional multidimensional wind-excited model based on linear theories no longer applicable. To address these challenges and avoid relying on the extremely time-consuming nonlinear finite-element method, this paper proposes a closed-form solution (CFS) for predicting time-frequency buffeting responses of TLs excited by two-dimensional turbulent wind. First, the static response is determined through nonlinear static analysis. Then a two-dimensional influence line method, employed to evaluate the turbulent wind effect, is developed by decoupling the buffeting responses in two directions. Power spectral density functions for various responses are further derived, considering the cross-correlation between horizontal and vertical turbulence. Moreover, the impact of wind attack angle on various responses is revealed through parametric analyses. Finally, an amplification factor is introduced to modify the vertical wind effect on equivalent static wind load (ESWL), and the corresponding fitting formula is provided to facilitate the design. Numerical verification illustrates the high accuracy and efficiency of the CFS. Although the wind attack angle is time-varying, it is controlled by the mean wind. As it increases, the RMS of transverse and longitudinal reactions decrease, while the RMS of the vertical reaction increases. Neglecting vertical turbulence underestimates the horizontal ESWL, with the amplification factor exceeding 1.35 when a wind attack angle of 50° is considered.

This paper develops a modeling method with an incremental stress–strain–environment constitutive model to predict the change in the plastic mechanical behavior of concrete caused by environmental action. The model regards the environmental factor as a constitutive variable, similar to stress and strain. The yield condition of the model is a function of stress, the plastic internal variable, and the environmental variable. The loading–unloading criterion is established in the space constructed by the strain and the environmental variable to determine the contribution of mechanical loads and environmental factors to plastic deformation. By considering the strain rate as an environmental factor and applying the proposed method, a stress–strain–strain rate constitutive model of concrete is developed to describe the plastic flow caused by the combined action of stress and strain rate. In addition, constant- and variable-strain rate loading tests are performed to evaluate the performance of the established model. In particular, the model’s capabilities are further highlighted by comparing the simulation results of the dynamic stress–strain model and the proposed model under loading conditions with rapidly decreasing strain rates.

Moving forces are one of the major loads acting on bridge decks, and moving force identification (MFI) is essential for bridge safety. However, there are two shortcomings in existing MFI methods. First, time discrete sampling for the force leads to ill-posedness in MFI. Second, identifying moving forces by means of a fixed frequency and a single type of force dictionary cannot fully and sparsely represent these forces. To address these issues, basis functions containing a trigonometric function and variable-frequency rectangular function are used to sparsely express the force, and the Duhamel integral is used to avoid ill-posed reduction of time discrete sampling for the force. A generalized discrete estimating method (GDEM) is proposed to identify moving forces. The $l_1\text{-}\mathrm{norm}$ regularization method in a sparse solution is introduced to transform the force identification problem into an $l_1\text{-}\mathrm{norm}$ regularization solution problem. The fast-iterative shrinkage threshold algorithm (FISTA) is used to solve the $l_1\text{-}\mathrm{norm}$ regularization problem, and the coefficient of the basis functions is obtained by combining the Bayesian criteria to identify the force. To validate the GDEM, the single and double time-varying forces on a simply supported beam are identified by numerical simulation. The results illustrate that the GDEM can accurately identify moving forces with strong robustness and performs better than the dictionary method. The response combinations of MFI are also discussed.

In this study, the porous thermoelastic behavior in a half-space microstretch elastic media enveloped in an unbounded inviscid liquid with rotation using memory-dependent derivative, utilizing Green–Naghdi theory mode III (G-N III) and the three-phase-lag model (3PHL). The analytical technique used to obtain the ordinary differential equations was normal mode analysis, followed by elimination of six ordinary differential equations, and finally the characteristic equation to obtain the exact formula of the physical quantities. A Gauthier composite element is employed in an implementation to start comparing the observations rotating on thermo-microstretch elastic porous medium employing a memory-dependent derivative completely covered in the endless fluid of G-N III theory with those for the model of 3PHL. The rotation has been observed to make a significant impact over each physical quantity. Comparisons have also been made for three various wavenumber values.

Abstract

Concrete cracks in service conditions, and this accelerates the degradation of both cementitious matrix and steel reinforcement. The inherent capacity of cementitious materials of autonomously sealing the cracks might result in a higher durability in aggressive environments. Recently, at Politecnico di Milano, the effect of both autogenous and crystalline admixture-stimulated healing on chloride penetration has been experimentally investigated for an ultra high performance concrete (UHPC). In this research work, the whole laboratory campaign has been numerically simulated through a multiphysics-lattice discrete particle model (M-LDPM)-based numerical model, in order to validate its capability of simulating the effect of autogenous and stimulated healing on the chloride penetration. The healing process is simulated through an improved version of the hygro-thermo-chemical (HTC) model, in which the effect of cracks (opening and closure) on permeability is implemented. Aiming to capture the results obtained through the afore-mentioned experimental campaign, the healing model is coupled and harmonized with an existing M-LDPM-based chloride diffusion model for saturated and nonsaturated concrete. The numerical results prove the model capability of capturing both the reduction of chloride penetration due to the cracks sealing, and the different degree of closure reachable with and without employing crystalline admixtures as healing agents, and thus pave the way toward incorporation of the benefits of self-healing cement based materials in predictive modeling and design tools. The research activity from which this work stems was framed into the H2020 project ReSHEALience.

Practical Applications

The prediction of how chloride penetration in concrete is affected by mix composition and damage might enable a more aware management of both design and maintenance processes. This article presents an innovative numerical model to simulate the chloride ingress into cracked fiber reinforced concrete. Furthermore, the model allows to account for the inherent capability that cementitious materials have to autonomously repair the cracks, mainly due to the delayed hydration of unreacted cement particles. The approach relies on a discrete modeling of concrete matrix and steel fibers. Then, it is also able to simulate accurately the response of innovative cement-based materials, such as ultra high performance concrete (UHPC). The numerical model is validated against experimental evidence, recently collected at Politecnico di Milano. The comparison between simulations and experimental results shows that the model does have the capability of predicting the chloride ingress in presence of cracks and crack self-healing. For the latter, also the effect of crystalline admixtures—which are expected to act as healing promoters—is simulated.

Although it is often asserted that, in view of their reduced length, axially compressible beams have a higher buckling load than their inextensible counterparts, a detailed analysis demonstrates that this is not necessarily the case. The argument to arrive at this conclusion is made in terms of relatively straightforward concepts of elasticity and structural mechanics. It is shown that for certain classes of materials, the reduced prebuckling length is more than compensated for by a softening of the elastic response, leading to a reduction of the Euler critical load.

Double-beam systems have found many applications in civil and mechanical engineering. Extensive works of research have been conducted on the investigation of double-beam systems in which some have studied the vibration characteristics of general double-beam systems without considering the effect of axial load, whereas others investigated the vibration and buckling of axially loaded double-beam systems with classical boundary conditions. A few previous studies have considered a general axially loaded double-beam system, but none of them have provided a general solution to calculate the critical buckling load of the system with arbitrary boundary conditions. In the present study, free vibration and buckling of an axially loaded double-beam system, which was composed of two nonidentical beams with generalized boundary conditions, were analytically studied by using the Euler–Bernoulli beam theory. A semianalytical method was proposed to calculate the natural frequencies and mode shapes of the system, and an explicit formula was derived to determine the critical buckling load of the system. Parametric investigations were performed to study the influences of the connecting stiffness of the interlayer and axial loads on the dynamic characteristics and critical buckling load of the system. Results show that the proposed method can be used for free vibration and buckling analyses of generalized double-beam systems subjected to axial loads.