Journal of Engineering Mechanics

In the analysis of a train–bridge coupled system, fuzzy uncertainty is a factor that must be considered in the prediction of coupled vibration response, but it has not been considered so far. In this work, the concept of information entropy is used to unify the fuzzy uncertainty and random variables into the train–bridge coupled system, and the fuzzy random train–bridge coupled system is established. The fuzzy dynamic response of trains and bridges with fuzzy parameters of the bridge structures and the mass of the carriage were studied, and the mean and variance of the response quantities were calculated using the new point estimation method (NPEM). The combined effect of the fuzziness is considered and the fuzzy value of the system dynamics is obtained. The feasibility of applying this method to train–bridge problems was verified. The calculation results indicated that the maximum amplitude of the fuzzy vertical displacement of the bridge exceeded the conventional vertical displacement by 25.57%, and the maximum amplitude of the fuzzy vertical acceleration of the train exceeded the conventional vertical acceleration by 23.42%. Obviously, in this case, the traditional deterministic calculation method cannot comprehensively and accurately analyze the dynamic response of the train–bridge system. The method in this paper can provide theoretical guidance for evaluating the safety of bridge structures and running safety research in the future.

Understanding the instantaneous and creep mechanical responses of rocks subjected to the combined influence of static and dynamic loading is of great importance for designing underground works. This study developed an impact-disturbance creep loading apparatus and conducted a series of multistage impact-disturbance creep experiments on sandstones, varying static creep loads, and dynamic disturbances. The investigation analyzed specimen deformation, acoustic emission (AE) signals, and nuclear magnetic resonance (NMR) porosity changes to determine creep characteristics from microscopic damage to macroscopic failure. The experiment revealed the profound influence of dynamic disturbances on sandstone’s instantaneous and creep behavior. Initially, these disturbances induce specimen densification under low creep stress but exacerbate damage propagation beyond a certain creep stress threshold. Moreover, increased dynamic disturbance energy correlates with higher creep failure strains but lower long-term specimen strengths. AE monitoring highlighted the role of dynamic disturbances in promoting tensile failure and the dominance of tensile cracks throughout the creep process. Notably, impact disturbances cause a significant increase in specimen porosity postcreep failure, especially in large pores. To capture sandstone creep behavior comprehensively under dynamic disturbance, a viscoplastic disturbance-damage creep model is proposed by integrating a disturbance-damage instantaneous element and dynamic-damage viscous element. The model can effectively describe sandstone creep behavior under dynamic disturbance conditions, offering valuable insights for underground work design.

Disaster resilience is an emerging concept for managing the risk of civil structural systems considering not only structural safety against extreme loads but also aftermath recovery efforts. The system reliability–based resilience analysis framework facilitates the quantitative evaluation of the disaster resilience performance of structural systems by assessing reliability and redundancy for numerous disruption scenarios. However, its practical application is limited due to the substantial number of structural analyses required to estimate the reliability and redundancy indices. To address the computational challenges, this paper proposes a new importance sampling algorithm, termed Importance Sampling for Noteworthy Scenarios (ISNS). The ISNS algorithm leverages a Gaussian process–based principal point search method to identify initial disruption scenarios that dominantly impact the structure’s resilience. Subsequently, a mixture-based distribution is constructed to represent the near-optimal importance sampling density characterizing the failure domains of the noteworthy disruption scenarios. The two-step procedure enables the simultaneous estimation of both reliability and redundancy indices of the identified noteworthy scenarios. Furthermore, an active learning scheme is incorporated to efficiently train surrogates. Numerical examples of engineering applications are investigated to demonstrate the improved efficiency offered by the proposed method. However, the proposed method faces limitations in multihazard contexts and high-dimensional, highly nonlinear scenarios. These limitations necessitate further validation of the Gaussian process and mixture models to ensure robustness.

Abstract

This paper aims to introduce a highly efficient computational model compared to the current cycle-by-cycle simulation strategy to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. An explicit constitutive relation for viscoelastic solids in multiple time scales was developed based on the temporal homogenization. The original initial-boundary value problem was divided into a global part in the slow time scale and a local part in the fast time scale. Two simulation studies were presented to validate the computational accuracy and efficiency of the proposed model: (1) a cylindrical asphalt concrete subject to a uniaxial cyclic compression load, and (2) a pavement structure subject to a locally cyclic loading. The laboratory test results and field measurements were compared with the modeled responses to validate the models before comparing with the reference solutions. Results indicate that the temporal homogenization-based viscoelastic model saves considerable computational cost and maintains a satisfactory accuracy. The absolute values of relative error of the modeled responses between the time homogenization and reference solutions are lower than 1% and 4% for the cylindrical asphalt concrete and pavement structure under locally cyclic loadings, respectively. Based on the proposed computational approach, only 4 min are needed to model the response of a cylindrical asphalt concrete subject to ${10}^4$ repeated load cycles under a uniaxial compression load. The computational time is reduced from 7 h of the reference solution to 38 min of the temporal homogenization solution to model ${10}^3$ load cycles of a viscoelastic pavement structure.

Practical Applications

This study introduces a highly efficient computational model to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. Multiple time scales were applied to an explicit constitutive relation of asphalt concretes to obtain the formula of global and local initial-boundary value problems. Its computational accuracy and efficiency were verified by comparing the temporal homogenization-based solutions with the testing results and reference solutions for a cylindrical sample and a pavement structure. It is the basis for the long-term pavement performance prediction after including the fatigue damage analysis in the present temporal homogenization framework. By successfully implementing a mechanistic framework for the long-term pavement performance prediction, the pavement design can more rely on the material inherent properties instead of using redundant empirical transfer functions. It is promising that the local calibrations of the current empirical performance transfer functions can be minimized as the proposed pavement long-term performance predictions depend on the material inherent properties and constitutive models.

In this paper, a state-space method for double-beam systems with variable cross sections is developed, making it possible to calculate the transverse vibration of the double-beams accurately and effectively. Due to the variability in the double-beam cross sections with the viscoelastic interlayer in between, the governing equations of vibration for the systems become highly coupled partial differential equations, making the problem difficult to solve. A basic double-beam system is introduced to modify the original governing equations to two inhomogeneous differential equations. Given the separation of variables, several mode-shape coefficients and a state variable are defined to construct the state-space equations. The coupling terms and variables are transferred into the constant coefficient matrix of the state-space equations, decoupling them. Numerical procedures are presented to solve the state-space equations to obtain homogenous and inhomogeneous solutions, including the natural frequencies and mode shapes in free vibration and the dynamic responses in forced vibration, respectively. The method has substantial advantages in decoupling high-order partial differential equations and can be further extended to solve complex structural systems. Numerical results also demonstrate that the method is accurate and efficient. Finally, an engineering application with a rail-bridge with a floating slab track is discussed in detail with the method.

Understanding the dynamic behavior of poroelastic soil adjacent to an axially vibrating pile is crucial to the seismic design and vibration reduction of various geotechnical engineering projects; however, few analytical studies exist on this issue to this point. In this study, to obtain the dynamic response of fully saturated soil around and beneath a vibrating pile, the solving scheme of the pile-fictitious soil pile (FSP) coupled model is extended to the pile-porous FSP coupled model and surrounded by multiple poroelastic medium layers with finite thickness. The semianalytical solutions of the pile-porous FSP-saturated soil-coupled vibration system are resolved and verified by existing solutions under different degradation situations. The developed model and the solutions are then employed to investigate the wave propagation mechanism in the fully saturated soil. The results show a certain degree of hysteresis in the fluid phase response during the vibration. As the permeability of the poroelastic material decreases, the hysteresis effect of the fluid phase relative to the solid phase weakens, resulting in an increase in excess pore-fluid pressure and a wider range of influence from the vibration. The conclusions derived from this study can also provide practical guidance for pile testing techniques, such as the parallel seismic (PS) method and low-strain pile integrity test (PIT) onsite.

Frequency-domain modeling is a core tool for the analysis of linear time-invariant structures. In a process that has been unclear, additional Dirac delta distributions can arise in the frequency-domain transfer functions of certain structures, beyond those seemingly given by the structural model—e.g., in the mechanical impedance of a linear spring. Previous analyses have manually appended these “hidden deltas” to the relevant transfer functions in to ensure that they remain causal, but questions remain as to their exact origin and behavior in in noncausal models. Here, we demonstrate that these hidden deltas arise from the theory of distributions and the solution of the distributional division equation. We demonstrate a rigorous and reliable method for deriving these hidden deltas in which the role of causality constraints are made clear. Furthermore, we demonstrate that the appropriate frequency-domain conditions for causality in such systems are generalized—not classical—Hilbert transform relations, and that the process of appending delta distributions is related to the analysis of causality via these generalized relations.