Journal of Engineering Mechanics

Finite locally resonant metafoundations represent an innovative solution for structural seismic response mitigation based on their filtering capabilities at selected frequency ranges. They inherit the filtering properties of periodic foundations and bands in which response amplitudes are reduced, the so-called attenuation zones. Nonetheless, other bands of vibration-induced resonances amplify the components of superstructure response and are generally named nonattenuation zones. Both frequency bandwidths and amplification depend on the dynamic properties of metafoundations and superstructures as well as their coupling. Thus, in order to shed light on the mechanisms of seismic mitigation of coupled systems endowed with optimal metafoundations, this paper explores both elastic uncoupled and coupled unit-cell chains in the frequency domain based on the analysis of various transfer functions. Moreover, to address uncertainty at the excitation level, time history analyses are performed with a set of natural accelerograms that characterize operating basis earthquakes; thus, response contributions from both attenuation zones and nonattenuation zones can be distinguished by relating response variances to peak responses. Eventually, the attenuation effects of optimal metafoundations, frequency shift of superstructures due to unit cells of metafoundations, and coupling of both attenuation zones and nonattenuation zones are analyzed in depth.

This paper is concerned with the optimal design of triangular arches of a given volume of material for maximum buckling capacity. The buckling criteria of triangular arches are derived analytically by using stability functions. Optimal designs of triangular arches with various vertical load positions, base support conditions, and apical joint conditions are obtained based on an optimization procedure involving two decision variables (arch height $h$ and cross-sectional area ratio $A_A/A_B$). Based on the optimization results, design recommendations for triangular arches against buckling are (1) the optimal height for triangular arches be taken as $L/4$ where $L$ is the span length of the arch, and (2) both members of the triangular arch are to take on the same cross-sectional area (i.e., $A_A/A_B=1$) when the arch has a rigid joint at the apical point, whereas the cross-sectional area ratio $A_A/A_B$ should be determined based on the optimality condition that both members should buckle at the same time when the arch has a hinge joint. By changing the base support condition from pinned-pinned to fixed-fixed, the maximum buckling load of the optimal triangular arches is increased by about 2.05 times.

This paper proposes a theoretical method to analyze the column-supported embankment. The emphasis is on quantifying the nonuniform deformation of the soft soil beneath the embankment by two deformed shape functions, and the functions include the coupling effects of radial and vertical deformation of soils. On this basis, a modified cell model, considering the influence of the relative displacement on the friction, can be further developed to characterize the load transfer behavior of soil arching within the embankment. In addition, the impact of pile-soil interaction on the evolution of soil arching can be considered in this study. A semianalytical solution for the column-supported embankment is obtained by a simple code for convenience in preliminary design. The proposed method is synchronously verified by numerical results and laboratory observations. In the proposed method, the stress ratio and the load sharing ratio, as two significant factors affecting the soil arching, are discussed at length.

It is important to be able to construct a site-specific multivariate probability density function (PDF) of soil parameters based on limited and incomplete site-specific investigation data alone. This allows the unique features of each site (in the well-known geotechnical context that local correlations between soil parameters are different from site to site) to be captured to the extent permitted by inevitable statistical uncertainties. A method that handles Multivariate, Uncertain and unique, Sparse, and InComplete (MUSIC) data was proposed recently, but the site-specific data were assumed independent at different depths, and the typical spatial correlation among depths was not addressed. In other words, this MUSIC method cannot deal with densely sampled data with a sampling interval less than the scale of fluctuation or spatially correlated data. This study generalizes the existing method to handle spatially correlated data. The proposed new method (called the MUSIC-X method, where “X” denotes the spatial/time dimension) is more complete in the sense that it makes predictions based on all available information, by conditioning on different test results at roughly the same depth and at roughly the same location using parameter cross correlation as well as by conditioning on the data measured at nearby depths in roughly the same location where the vertical correlation is appreciable and potentially other locations where the horizontal spatial correlation is appreciable. This MUSIC-X method is also capable of simulating conditional random fields for all soil parameters within the depth range where observations are made. The MUSIC-X method is examined by numerical examples and a real case study in Taipei. It is shown that the 95% confidence interval for the depth profile of the target design parameter is generally smaller when both cross correlation and spatial correlation are incorporated into the estimation.

This paper presents a triaxial constitutive model for fiber-reinforced cementitious materials (FRCM), with an emphasis on ultra-high-performance concrete (UHPC). The model accounts for the multiaxial stress-strain behavior of the cementitious matrix and the fiber stress-versus-slip response. The distributed cracking due to the presence of fibers, the fiber confinement effect on the compressive response of the composite material, and the effect of fiber orientation on the material response are also accounted for in the proposed formulation. The new material model is calibrated and validated using material test data on UHPC. The capability of the model to allow the simulation of structural components is verified through the analysis of structural components made of UHPC.

Different from the conventional transfer coefficient method widely used for calculating landslide thrust, the vector sum method can incorporate the complete stress state from any numerical simulation into a limit equilibrium analysis, with the vector characteristics of force featured. In this paper, the vector sum method is improved to calculate the landslide thrust under design factor of safety before the reinforcement of landslide. The main sliding direction is theoretically determined by the principle of minimum potential energy. The distribution of landslide thrust along the slip surface can be directly calculated from the trailing edge to the leading edge of landslide, which can benefit the reinforcement design of the slope. Finally, three examples are used to verify the proposed method, and the calculated results demonstrate the accuracy and the broader applicability of the proposed method.

The behavior of remolded kaolin clay is examined using cyclic triaxial and resonant column tests. The damping of kaolin is shown to be largely hysteretic, and its cyclic degradation behavior is affected predominantly by strain level and number of cycles. From the observed behavior, a hyperbolic model incorporating Masing’s rules and degradation effects is proposed. The performance of the model is assessed by comparing the model predictions with experimental results for three problems: (1) cyclic triaxial tests, (2) uniform clay bed subjected to base shaking, and (3) pile-raft foundation in soft clay subjected to base shaking. In general, good agreements are found between model predictions and experimental data for small to medium strain levels (i.e., below 1%). At large strains, the predictions are less accurate due to significant effect of soil damping.

A novel Wiener path integral (WPI) technique is developed for determining the response of stochastically excited nonlinear oscillators. This is done by employing functional series expansions in conjunction with quadratic approximations. The technique can be construed as an extension and enhancement in terms of accuracy of the standard (semiclassical) WPI solution approach where only the most probable path connecting initial and final states is considered for determining the joint response probability density function (PDF). In contrast, the technique developed herein accounts also for fluctuations around the most probable path, thus yielding an increased accuracy degree. An additional significant advantage of the proposed enhancement as compared to the most probable path approach relates to the fact that low-probability events (e.g., failure probabilities) can be estimated directly in a computationally efficient manner by determining only a few points of the joint response PDF. Specifically, the normalization step in the standard approach, which requires the evaluation of the joint response PDF over its entire effective domain, is circumvented. The performance of the technique is assessed in several numerical examples pertaining to various oscillators exhibiting diverse nonlinear behaviors, where analytical results are set vis-à-vis pertinent Monte Carlo simulation data.

This paper concerned an analytical method to obtain exact solutions for displacements of submerged hemi-ellipsoidal shells. Based on the linear membrane theory, the membrane forces and strain components were defined in terms of the radius of a parallel circle. General solutions for normal and tangential displacements were established, which could be written in the simplest form when considered at the apex and equatorial points. To investigate the accuracy of the results, a finite-element modeling technique was used to verify the analytical solutions. The fundamentals of differential geometry and the principle of virtual work were used to develop the stiffness matrix for nonlinear finite-element procedures. This led to the numerical results for validation of the analytical solutions. The effect of shape ratios, thickness, and seawater depth on the forces and displacements of submerged hemi-ellipsoidal shells were also presented in this study.

In determining structural responses under random excitation using the Monte Carlo method, simulation of non-Gaussian processes is always a challenge. Various methods have been developed to simulate non-Gaussian processes but literature suggests that the complete expression of the Gaussian correlation function matrix (CFM) and the corresponding applicable range of the target non-Gaussian CFM have not been attempted in the transformation based on the Hermite polynomial model (HPM) to date. The intention of this paper is to derive a complete transformation model of CFM from non-Gaussian to Gaussian processes with the applicable range of the target non-Gaussian CFM based on the unified Hermite polynomial model (UHPM). An efficient procedure for simulating stationary non-Gaussian processes is also presented for easy application. It is found in the paper that the complete transformation model of Gaussian CFM is necessary because HPMs are not always monotonic and that the proposed method can simulate stationary non-Gaussian processes efficiently and accurately. The proposed method can equip researchers and engineers with a more efficient and accurate tool to handle non-Gaussian processes frequently encountered in engineering practices.

This study develops a three-dimensional multishear bounding surface model for simulating the constitutive response of interfaces between the granular soil and structure. Based on the plasticity slip theory, the model is established by splitting the overall response of interfaces into a macronormal response and a series of orientated microshear responses in microshear structures. This discrete approach provides a simple and effective means to predict the macroshear response of interfaces by superposition of individual responses from all microshear structures. The microshear structure consists of a microshear response and a micronormal response due to dilatancy, which are described by a microstress–strain relation and a microstress–dilatancy relation, respectively. By introducing a state parameter related to the critical state of granular soils, the model is suitable for predicting the constitutive response of interfaces for various soil densities and normal stresses. The effectiveness of the model is confirmed by simulating the granular soil–structure interface tests with different boundary and load conditions.

This paper presents an experimental study into the influence of localization length ($L_c$) and its evolution during the postpeak response of cylindrical low-carbon steel bars. A novel longitudinal strain method for the determination of the localization length is compared to the average strain method. Four specimen lengths [38.1 mm (1.5 in.), 76.2 mm (3 in.), 152.4 mm (6 in.), and 304.8 mm (12 in.)] with a diameter of 12.7 mm (0.5 in.) were tested according to ASTM A370 standards. A three-dimensional digital image correlation (3D DIC) measurement system was used to record the longitudinal and transverse deformations along the specimen length. The results indicate that the engineering stress-strain relation up to the peak load is almost identical for all tested specimens. However, the postpeak response shows a steeper softening response for longer specimens. Two methods were used to extract the localization length from the longitudinal engineering strain profile. The average strain method shows a length dependence for different specimen lengths, while the longitudinal strain method eliminates the length dependence. The consistency of the localization length obtained through the longitudinal strain method enables improved generalized analytical relationships. Linear and exponential curve fitting formulae are given to predict the localization length for a generic specimen.

A novel approach, referred to as sparse Kriging–NARX (KNARX), is proposed for the uncertainty quantification of nonlinear stochastic dynamical systems. It combines the nonlinear autoregressive with exogenous (NARX) input model with the high fidelity surrogate model Kriging. The sparsity in the proposed approach is introduced in the NARX model by reducing the number of polynomial bases using the least-angle regression (LARS) algorithm. Sparse KNARX captures the nonlinearity of a problem by the NARX model, whereas the uncertain parameters are propagated using the Kriging surrogate model, and LARS makes the model efficient. The accuracy and the efficiency of the sparse KNARX was measured through uncertainty quantification applied to three nonlinear stochastic dynamical systems. The time-dependent mean and standard deviation were predicted for all the numerical examples. Instantaneous stochastic response characteristics and maximum absolute response were also predicted. All the results were compared with the full scale Monte Carlo simulation (MCS) results and a mean error was calculated for all the numerical problems to measure the accuracy. All the results had excellent agreement with the MCS results at a very limited computational cost. The efficiency of the sparse KNARX also was measured by the CPU time and the required number of surrogate model evaluations. In all instances, sparse KNARX outperformed other state-of-the-art methods, which justifies the applicability of this model for nonlinear stochastic dynamical systems.

Laminated glass, made by bonding glass plies together through polymeric interlayers, is a redundant system that allows for stress redistribution after partial failure. This study analyzes how the structural safety level of laminates made by two or three plies of annealed glass varies with the ratio between the thicknesses of the layers and their placement in the package. The probability of failure of laminated glass elements, in which the layers are arranged in different order, is statistically analyzed under gust wind loads, accounting for all the potential sequences of breakage for the plies. The gain obtainable from a tailored composition is quantitatively estimated through specific safety factors to be used in semiprobabilistic (Level I) design and calibrated through comparison in paradigmatic case studies with full-probabilistic (Level III) methods. Optimal laminated packages are thus determined as a function of the target probability of failure classified according to four distinct classes of consequences for malfunction or failure.

This paper is concerned with the nonlinear performance of the grouted liner with a crown void under a concentrated load. The liner consists of three deformed shapes based on three void sizes: the small void, the contact, and the noncontact case, respectively. The theoretical studies are conducted firstly to derive the maximum load (buckling load), which is later verified successfully by the numerical results for all three examined cases. A later developed numerical simulation is implemented to track the load-displacement curves, from which the maximum load is extracted. We found a small crown void shows a negligible reduction on the load capacity (buckling load), compared with the fully grouted liner. This observation suggests the void be constrained that is not larger than the small size level in practical systems. Finally, a full evaluation is taken by analyzing the influence of length and thickness of the void on the buckling load, which indicates the increase of length or thickness of the void reduces the maximum load except for the small void case.

In reinforced concrete structures built before the 1970s, it was common for columns to be constructed with short lap splices and widely spaced transverse bars at the column base, leading to increased likelihoods of pull-out failures and structural collapse during seismic events. In the modeling and analysis of reinforced concrete columns with short lap splices, several challenges arise, particularly with softening behavior that leads to strain localization and scaling and convergence issues in analyses. This research presents a methodology to regularize force-based beam-column elements with softening lap-splice material response. In the methodology, a constant energy release criterion is imposed with the constant postpeak energy of the lap-splice region determined from relevant experimental data. With the proposed regularization, the numerical model shows objective results that are independent of the length of the element and number of integration points used. Whereas the accuracy in estimating, for example, the displacement at 20% strength drop using existing nonregularized models changes with the number of integration points, the accuracy using the proposed model remains constant across numbers of integration points used with a mean accuracy of 94% compared with experimental tests. Results from static pushover and cyclic analyses show an order of magnitude decrease in standard deviation of the response using the regularized model. Increased accuracy and increased convergence for the method across the number of integration points used is shown in static and dynamic analyses. The proposed regularization approach is able to alleviate strain localization issues and facilitates the scaling of analyses from small-scale to full-scale structures.

A new methodology for incorporating stochastic models in integrity maintenance management for high-pH stress corrosion cracking (SCC) in gas pipelines has been presented. The generation of new crack features along with the growth of existing ones are included in the stochastic modeling, by means of nonhomogeneous Poisson process (NHPP) and nonhomogeneous gamma process (NHGP), respectively. The dependence (correlation) among the growths of individual cracks is considered by employing the Gaussian copula method. Data from multiple in-line inspections (ILI) are used to evaluate the parameters of the stochastic models by means of Bayesian updating. Hence, a hierarchical Bayesian framework is developed that can efficiently account for the ILI associated measurement errors and the probability of detection (PoD) of the crack features. The Bayesian updating is performed through subset simulation, a structural reliability method (SRM) conjointly with the data augmentation (DA) technique. Multiple simulated crack features from different ILI inspections are employed for the implementation and validation of the methodology. At the end, the time-dependent system reliability is evaluated along with a parametric study that examines the impact of correlations among stochastic growths of crack features on the posterior growth model and system reliability.

The different joint arrangements resulting from different segmental assemblies between adjacent rings may inevitably give rise to the interaction for staggered jointed lining, which is crucial for the structural analysis of segmental-tunnel lining. However, most existing analytical solutions only consider the straight jointed lining and are not applicable to the staggered jointed lining. By using the state-space method, a unified analytical solution is obtained for the circular segmental-tunnel lining irrespective of the layout of segmental assemblies between adjacent rings, and the interaction effect between adjacent rings is explicitly addressed. The segments were treated as curved Euler beams, while the longitudinal joints between the segments were modeled by a set of springs with three-directional resistances, and the circumferential joints between the adjacent rings were modeled by shear springs with both radial and circumferential resistances. A rigorous theoretical proof is implicitly embedded to eliminate the rigid-body displacements of the proposed method as a self-balancing condition of external loads acting on the lining. Finally, the solutions are verified through comparisons with both the experimental and analytical results in the literature. The results show that the present method exhibits high efficiency and suitability for both linings with straight joints and those with staggered joints.

Structural reliability analysis without the exclusion of random variables with unknown distributions has attracted increasing attention, and many endeavors have been devoted to this aspect. Recently, linear moments (L-moments) have been found increasing use for characterizing random variables with unknown distributions, in part since they show less sensitivity to distribution tails and are more stable than the ordinary central moments (C-moments). In this paper, the clear definition of the complete monotonic expressions of the third-order polynomial normal transformation (TPNT) under different combinations of the first four L-moments of random variables is first proposed. Additionally, the applicable boundaries and monotonic regions of TPNT based on L-moments are also determined. The advantages of the TPNT based on L-moments are that it has a wider applicable range and is much more stable under a small sample size compared with the TPNT based on C-moments, which are demonstrated through numerical example studies. Through the numerical examples, the proposed TPNT based on the first four L-moments is found to be quite effective for normal transformation.

The self-loosening process of a bolted joint due to ratcheting consists of two distinct external loading stages. The first stage of self-loosening, with relatively small loading magnitude, is due to the ratcheting deformation of the materials at the thread of bolt. The second stage of self-loosening, with relatively large loading magnitude, is characterized by the ratcheting deformation of the materials at the bolt bar. The present work concentrated on an experimental investigation of these two stages for self-loosening of a bolt joint with superelastic shape-memory alloy (SMA). The experiments consisted of two members joined by a SMA bolt and two nuts which were subjected to cyclic alternating tension loading. The stress–strain relationship curves of the stud were tested by strain gauges, one attached to the bar of the stud, and another attached to an aluminum washer, which served as a force-test apparatus. The larger preload force and magnitude of alternating loading produced a larger reduction of clamping force of the bolt. The martensite residual strain accumulation under an increasing number of loading cycles is suggested to be responsible for the reduction of the clamping force. A series of microscopic evolution observations for the change law of the residual martensite morphology, the dislocation density, and the phase transformation temperatures under different numbers of loading cycles and different locations of the bolt for the identical loading case were carried out to support this viewpoint and to further clarify the mechanism of the self-loosening behavior of bolt joints with superelastic SMA.