Journal of Engineering Mechanics

In shear failure, reinforced concrete (RC) beams always develop, in a stable manner, a finite length crack before the maximum load is reached. Thus, the crack tip location cannot sample a large volume of material with random strength because a small region in which the crack tip can lie is fixed by fracture mechanics. Consequently, the size effect on the mean strength cannot be statistical. It must be predominantly energetic or deterministic and, thus, must follow the Type-2 size effect law. What has not yet been clarified is the size effect on the coefficient of variation (CoV) of beam strength, which is important for anchoring the probability distribution of shear strength and choosing the safety factor. In this study, we run thousands of explicit finite element simulations using Abaqus-Explicit version 6.14 with microplane model M7, each with a random input of material strength and Young’s modulus for each finite element in the structure. The CoV of beam strength is found to decrease with the structure size when geometrically similar beams are compared, although the CoV tends to a constant for large sizes. This size effect on the CoV is similar to that in ductile failure governed by a Gaussian distribution of strength and contrasts with that in brittle failures following the Weibull distribution, for which the CoV is size independent. To characterize the size dependence of the strength CoV, an analytical formula is developed based on the statistics of the sample quantiles of a series of random variables.

In this paper, a new analytical formula is proposed to determine the mean outcrossing rate of nonstationary non-Gaussian performance functions. The performance function is firstly transformed into a standard Gaussian process using its first four moments and autocorrelation coefficient function, and the mean outcrossing rate of the time-variant performance function is then derived from the transformed standard Gaussian process and the cumulative distribution function of the correlated bivariate standard normal random variable. Based on the proposed mean outcrossing rate, an efficient methodology is then developed to evaluate the time-dependent structural failure probability of nonstationary non-Gaussian performance functions under the assumption that the outcrossing event (i.e., structural failure) is modeled as a Poisson process. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. It can be concluded that the proposed method provides an efficient and useful tool for time-dependent structural reliability assessment in engineering applications.

Magnetorheological (MR) dampers provide a viable alternative for vibration control of structures subjected to external excitations. Realistic modeling of MR dampers is critical for control development and structural design. Many existing phenomenological models of MR dampers are optimized from experimental observations for deterministic parameter values. However, vibration control design based on deterministic values might not provide reliable response prediction due to inherent parameter uncertainties from optimization. Parametric uncertainty analysis of damper models using laboratory experiments enables quantification of potential effect on vibration control design and evaluation. Several existing MR damper models were evaluated for their parametric uncertainties based on characterization tests of a $200\text{-}\mathrm{kN}$ large-scale MR damper. Markov-chain Monte Carlo (MCMC) simulation was integrated with the generalized likelihood uncertainty estimation (GLUE) method to derive the posterior distribution of model parameters. Prediction of MR damper behavior was used to illustrate the influence of model parametric uncertainties. The MR damper models were compared in terms of energy dissipation in the real-time tests with predefined displacements.

Aggregates in contact constitute the skeleton of the asphalt mixture and affect load transmission in the mixture, which determines its deformation resistance. The objective of this study is to characterize the aggregate skeleton for the evaluation of the stability of the asphalt mixture. The methodology has four main steps: (1) aggregates in specimens are three-dimensionally (3D) reconstructed before surface triangulation; (2) the geometry and orientation of contact areas between aggregates are detected to obtain the contact network of aggregates; (3) effective contacts are identified to determine force chains represented by a weighted directed graph; and (4) all force chains constitute the aggregate skeleton, which is then evaluated for load transfer efficiency by the characterization of the skeleton. Simulations of compression tests on three virtual specimens with different skeletons were conducted to obtain the stress and strain distribution within the mixture. The results indicate that a skeleton with a higher evaluation index has a more uniform stress and strain distribution, which indicates that the mixture bears the load better to resist deformation. The proposed method also facilitates the study of the correlation between the mixture stability and the gradation and morphology of aggregates.

Free-strain solutions for consolidation of ground with partially penetrating prefabricated vertical drains (PVDs) cannot be solved analytically using the integral transform method due to the irregularity of the solving domain and the complexity of boundary conditions. In view of this, the solving domain is simplified based on the smear zone equivalent method, which can be immediately solved using integral transform, boundary transform, and local discretization methods with different vertical boundary conditions. The effectiveness of the simplified model and the proposed semi-analytical solution is then evaluated against calculations using the finite-element method. Once the proposed approach is calibrated successfully, a parametric investigation is carried out to assess how the consolidation behavior of the PVD-improved ground is influenced by the permeability coefficient, radius, and penetrating depth of PVD. Results show that a larger permeability coefficient/radius of PVD can decrease the well resistance, resulting in a higher radial average degree of consolidation in the ground at all depths. However, the increase of penetrating depth of PVD not only provides more drainage channels, but also increases the well resistance of PVD, which decreases the radial average degree of consolidation in the improved layer locally.

Roll waves are frequently observed in the spillway chutes of hydropower stations, flood discharge channels, and diversion canals. In order to understand the physical characteristics of roll waves in detail, a full two-dimensional numerical model based on the Reynolds-averaged Navier-Stokes equation with the renormalized group $k\text{-}\epsilon$ turbulence model and a volume of fluid technique is established to simulate the evolution of the roll wave. A series of periodic roll waves generated by different combinations of slopes and discharges is successfully simulated, which compares well with the famous Brock’s roll wave experiments. Compared with the traditional study by the Saint-Venant equations, the distribution characteristics of roll waves, such as flow velocity and turbulent kinetic energy, are obtained. Simulated results show that the turbulent effect is not evenly distributed and may play an important role in roll wave generation and evolution. Further, an additional parameter examination shows the roll wave amplitude ratio and wave speed decrease with the increase of the fluid viscosity. These detailed flow structures of roll waves might be helpful in understanding the physical mechanism of roll waves and the spillway design and bed erosion study.

A novel kind of seismic isolation technique called “Periodic Barriers,” which combines trench-type wave barriers and metamaterial, is introduced in this research. Metamaterial possesses a unique frequency-selective property that enables the metamaterial to manipulate the wave propagation. By infilling the metamaterials in the trench-type wave barriers, the periodic barriers are expected to display advantages of both the wave barriers and the metamaterials. The two-dimensional (2D) finite-element (FE) simulation is conducted to study the performance of the barriers adapting the metamaterial. This FE model is validated with the experiment on the metamaterial-based foundation. The convergence test on mesh size with different element types are investigated, and the minimum mesh size and property element type are determined for simulating the behavior of metamaterial. To simulate the unbounded domain, the absorbing boundary is implemented to eliminate the reflection from the boundaries. The dynamic responses obtained from models with infinite element boundary and viscoelastic boundary are found to converge with the increasing model size. To boost the computing efficiency, two analysis methods (fix-frequency harmonic analysis, and the time-history analysis) are adopted and found to have a strong correlation with each other. Based on the proposed modeling techniques and the analysis methods, the simulation of the periodic barriers embedded in the soil is performed. With various loading distance and the number of periodic barriers, the performance of the periodic barriers is found to comply with its theoretical frequency band gaps.

This paper presents a structure- and sampling-adaptive approach for analyzing human footstep-induced structural floor vibrations to estimate footstep ground reaction forces (GRFs) and gait balance symmetry. Balance symmetry and footstep GRFs are critical indicators of overall gait health and elderly fall risks. Prior works, including direct observation by trained medical personnel, computer vision-, pressure sensor-, and wearable-based sensing, are limited due to operational restrictions. We introduce a nonintrusive balance symmetry monitoring approach, which utilizes sparse structural vibration sensing. The intuition is that footstep-induced floor vibration responses are proportional to footstep GRFs, and balance symmetry can be defined using consecutive GRF pairs. However, GRF-vibration relationships are also influenced by spatially-varying structural properties and gait sampling bias, introducing errors to real-world estimations. We address these challenges first by extracting structural regions to overcome spatially-varying vibration behavior and then by developing a kernel-based robust regression model to overcome biased training data and enable robust GRF and balance symmetry modeling. We evaluate our approach through real-world experiments, achieving a balance symmetry index estimation accuracy as high as 96.5%.

Circular plate foundation is an essential foundation in the engineering of marine anchor plates, oil storage tanks, and cell towers. These circular plates are usually treated as the rigid circular foundation (RCF) because the stiffness of these foundations is much larger than that of the surrounding soils. This paper develops a boundary element method (BEM) and analytical layer element method (ALEM) coupling model to look into the time-dependent behavior of plate–soil interaction subjected to mechanical or thermal load. The solutions for this interaction problem were obtained by applying BEM, which took the ALEM solution of layered saturated soils (LSS) due to an interior ring mechanical or thermal load as the fundamental solution. Detailed verifications against numerical solutions and experimental results were provided to confirm the robustness of the present model, followed by extensive parametric studies to analyze the influence of soil layering characteristics on plate–soil interaction. It is evident that the present model can be utilized to evaluate the time-dependent behavior of the RCF in LSS subjected to both the mechanical and thermal loads.