Journal of Engineering Mechanics

Vertical wall breakwater with culvert (VWBC) is an environmentally friendly way proposed for the encircled harbor basin, which can break waves and allow the current to pass through. This paper adopts a theoretical analysis combining physical experiments and computational fluid dynamics (CFD) numerical simulations to study the hydrodynamic performance of the VWBC and to propose an optimal culvert for engineering applications. Based on a linear wave theory, theoretical analysis demonstrates the interaction between waves and the VWBC through the matched eigenfunction expansion method. The effects of the structural parameters (culvert and rubble mound foundation) on the hydrodynamic performances, such as the wave transmission coefficient (berthing stability), wave force (structure stability), and oscillatory flow (water exchange) inside the culvert are taken into consideration. Newly designed physical experiments and CFD numerical simulations are performed to verify the correctness of the theoretical analysis and to reveal the nonlinear characteristics of the wave transmission and oscillatory flow. It is found that the berthing stability and water exchange are mainly affected by the length and height of the culvert as well as the rubble mound foundation, and a total transport flow toward the harbor basin will be produced with an increase in wave height. Furthermore, the optimal culvert is obtained through the theoretical analysis. With the optimal culvert, VWBC can improve the berthing and structure stability, further promote the water exchange, and enhance the environment in the harbor basin.

The numerical manifold method (NMM) provides a general framework for simulating both continuities and discontinuities. By cutting covers, NMM can adopt a regular-shaped triangle (or quadrilateral) for interpolation. This brings advantages of the best-shaped mesh; however, it also leads to some issues in displacement boundaries. This study shows possible issues and related treatments on boundaries inaccuracies in NMM: (1) constrained partial edges, (2) cumulative errors, and (3) boundary changes in contact iteration. In NMM, constraining a part of the edge will constrain the whole edge, and therefore bring additional stiffness. This error can be avoided by a new load-spring control method or adjusting the NMM mesh. In dynamic NMM analyses, penalty springs reapply at every time step, and they only constrain incremental displacement. As a result, cumulative errors should be avoided. If time step interval changes in contact iteration, moving boundaries need to be renewed. This paper also provides general formulas for displacement boundaries, the necessary and sufficient condition for line constraints, a load-spring control for full load–deflection responses, and a robust scheme for moving boundaries.

Operational modal identification is indispensable in bridge health monitoring because it estimates modal parameters only from the multiple-channel responses of bridges under ambient excitation. Multiple-channel responses are often slightly asynchronous due to sensor errors, which is generally ignored in response monitoring but introduces significant uncertainty to modal identification. Considering that calibrating the asynchronous responses during the sensing or data acquisition process is not economical, an identification method based on the natural excitation technique (NExT) is proposed for asynchronous responses. In the NExT method, the power spectra of monitoring responses are first calculated and then transformed into correlation functions by inverse Fourier transform. The phase characteristics of power spectra and the linearly dependent characteristics of modal components in correlation functions are compared for synchronous and asynchronous responses, respectively, with consideration of the noise level and asynchronous time. Then the enhanced NExT is proposed, in which the multiple-channel responses are synchronized by minimizing the phase slope and maximizing the linear dependency of modal components. Finally, the responses of a numerical example and a highway bridge are taken to verify the method. The results show that the multiple-channel asynchronous responses of bridges under ambient excitation can be effectively aligned to obtain high-precision mode shapes.

This paper contains a numerical study based on tests carried out at the Universitat Politècnica de València (Spain) on a U-shaped unreinforced and Textile Reinforced Mortar (TRM)-reinforced masonry structure subjected to horizontal loads. The masonry was composed of clay bricks with 10 mm thick mortar joints arranged in an English bond pattern. The prototype was tested by applying pseudodynamic displacement-driven cycles and varying cyclic amplitudes and frequencies in two different stages: (1) on the as-built structure and (2) after the application of the TRM material. A series of nonlinear numerical simulations were performed adopting the ABAQUS/Explicit version 6.14 finite-element (FE) software. The FE calibration was carried out using the results obtained during ambient vibration tests. Simulations were then used to evaluate the effectiveness of the proposed TRM strengthening technique in improving the behaviour of low-rise old masonry building subjected to horizontal loads.

The accuracy and efficiency of an approach using surrogate models are investigated, in comparison with traditional structural reliability methods, in the analysis of two steel structures subjected to natural fire. For this purpose, an algorithm is used, coupled to a finite-element computational package, which includes the first-order reliability method (FORM), the approximate method most used in this type of problem, and Monte Carlo simulation (MCS), which is usually taken as a reference. On the other hand, the literature indicates surrogate models as a promising alternative to maintain, at acceptable levels, the computational cost in similar analyses. Therefore, two approaches using surrogate models are also applied to the algorithm, more specifically adaptive and nonadaptive artificial neural networks. The analyses led to differences of up to 21.83% between the failure probabilities obtained via FORM and via MCS. Furthermore, while the nonadaptive approach fails to achieve sufficient accuracy, the adaptive approach is confirmed to be a viable alternative, with differences, on average, close to 1.00% and computational times less than 1.60% of the time required by MCS.

The link between the fracture behavior of fiber–reinforced concrete composite and the underlying mechanisms that influence the pullout behavior of fiber are studied. The influence of the fiber-matrix bond on the cohesive stress response in fracture is evaluated for normal vibration compacted concrete (NC) and self-compacting concrete (SCC) matrixes. The fracture response of steel fiber–reinforced SCC (SFSCC) improves significantly when compared with steel fiber–reinforced NC (SFNC). The cohesive stress-crack opening ($\sigma -w$) relationship derived from the measured fracture responses indicates that a significantly higher crack closing stress is generated at smaller crack opening in SFSCC than SFNC. The pullout resistance of the steel fiber embedded in the SCC matrix improves significantly compared with NC. The enhancements in the cohesive debonding and frictional components of resistance contribute to the improved pullout resistance of the steel fiber from SCC. The improvement in the fiber-SCC matrix bond results in increased efficiency of the fibers and produces an increase in stiffness and peak load in the resistance to the pullout of fiber from the SCC matrix when compared with NC. The enhancement in the pullout response of the fibers from SCC contributes to improvements in the cohesive stress mobilized at smaller crack openings in SFSCC.

This paper proposes a novel method to capture efficiently the probability distribution of the limit state function (LSF) for structural reliability analysis. This method works by decomposing the probability distribution of the LSF into a Gaussian mixture and applying the scaled unscented transformation to approximate the required statistics for each mixture component. The number of mixture components is specified according to Akaike’s information criterion. Because the required sample size grows linearly with the number of random inputs, little computational effort is required to recover the entire distribution of the LSF with precision. The effectiveness of the proposed method was validated through numerical examples, in which the results obtained from pertinent Monte Carlo simulations and other approaches are compared. The results demonstrated that the proposed method efficiently can yield accurate estimates of the probability distribution of the LSF in the entire range, and the probability of failure accordingly can be evaluated straightforwardly. Issues that need to be studied further were discussed.

This study investigated the effect of loading frequency on the fatigue damage process in concrete using digital imaging and acoustic emission techniques. It was found that the complex fatigue damage process in heterogeneous concrete is reflected in the amplitude of acoustic energy. The distribution of acoustic energy levels was utilized to classify micro- and macro-structural activities. It was found that fatigue failure at higher frequencies is governed predominantly by microcracks, while at lower frequencies both micro- and macro-cracks contribute to failure. The applied loading frequency had a marked influence on the size of the fracture process zone (FPZ). A fatigue model encapsulating frequency effects in terms of FPZ width is proposed using a unified damage and fracture mechanics approach within the framework of dimensional analysis and similitude concepts.

A recently developed discrete-element capability was used to study the effect of mesogeometry on flexural failure in concrete. Fabric anisotropy in angular specimens was found to retard flexural crack growth. The fabric also played a key role in determining the geometry of the fracture process zone. Greater dispersion in the local fabric resulted in more tortuous cracks. Specimens with angular particles exhibited more crack branching and tortuosity, and hence had higher macrofracture energy, than specimens with rounded aggregates. Aggregate shape affected the peak stress and postpeak response of notched specimens. The slowing of crack growth and nonmonotonic evolution of the fracture process zone, also observed in experiments, was investigated. Crack tip shielding was found to play a critical role in explaining this behavior.

A micromechanics-inspired fabric-dependent thermodynamic model is developed to simulate the critical-state and phase-transformation behavior of sands. A generalized fabric tensor that considers the statistical distribution of granular fabric is proposed. The fabric tensor is the sum of three families of a transversely isotropic tensor, which is assumed to be characterized by the probability density function of the normal distribution. The new tensor variable is incorporated into the reversible and irreversible thermodynamic models, and the fabric-dependent hyperelastic and plastic constitutive relations are then derived. The hyperelastic instability leads to a yield criterion that depends on fabric distribution and its evolution. Plastic strain development is linked to fabric distribution by a concept of accumulative yielding probability transitions, which in turn provides smooth transition from macroscopic elasticity to plasticity and finally to the critical state upon shearing. Using this theoretical framework, the physical mechanism underlying the phase-transformation and critical-state behavior of sands are interpreted from the evolution of fabric distribution. The performance of the model is verified by simulating various shear tests of Toyoura sand and a discrete element method (DEM)-modeled sand. The effects of $b$-value and principal stress direction on the stress-strain behavior are related to the evolution of fabric distribution. The noncoaxiality among stress, strain, and fabric is also captured by the model.

This study proposes two-dimensional (2D) pollutant migration in a semi-infinite geological formation with spatial varying transport parameters. Because the groundwater flow is bidirectional, the impact of off-diagonal dispersion also was taken into account. A decay parameter was considered in the aqueous phase as well as in the solid phase. We assumed that the groundwater reservoir was not plume-free, because some scale-varying pollutant exists there very initially, decaying with space. A change in the source at the inlet boundary in the presence of off-diagonal dispersion (ODD) alters the strength of pollutant concentration. The existing solutions can be reduced into other existent solutions for various geological formations. The Laplace transform technique (LTT) was applied to obtain the pollutant concentration profile in the 2D anisotropic heterogeneous porous medium. The Crank–Nicolson finite-difference (CNFD) technique was adopted for a numerical simulation. We demonstrated the validity of the analytical result. The numerical result and some previously available data from literature were compared and good agreement was found.

In order to analyze the edge debonding and intermediate flexural crack–induced debonding of fiber-reinforced polymer (FRP)-strengthened concrete beams, several innovative beam finite elements were developed in this paper. The proposed elements were capable of modeling the concrete, adhesive layer, and FRP sheet in one macroscopic element. The explicit formulations of the proposed element stiffness matrices were given to simulate the adhesive layer in different loading stages. Comparisons against several numerical examples available in the literature were given to validate the proposed elements. The effects of the FRP tapering ends, load, and crack location on the interfacial shear stress within adhesive layers were effectively investigated using the proposed elements. It was found that the proposed elements could conveniently predict the edge and flexural crack–induced debonding behavior of FRP-strengthened beams with accuracy and computational efficiency.

This paper proposes simplified analytical solutions for longitudinal tunnel settlements induced by axially loading single pile and pile group. The solutions are based on the extended shear displacement method and the two-parameter beam on elastic foundation model. By comparing with three-dimensional finite-element analysis results and beam on elastic foundation model calculation results on typical case histories, the performance of the proposed solutions is verified. Moreover, the effects of pile diameter, distance between pile and tunnel, and distance between two piles in a group on the induced longitudinal tunnel settlement are captured by performing parametric analysis with the proposed solutions. Due to the simplicity, effectiveness, and ability to account for soil shear and squeezing effects as well as shield effect involved in pile group, the proposed solutions have the potential to be conveniently applied in preliminary estimation of longitudinal tunnel settlement induced by axially loading single pile or pile group.

In this paper, a novel direct probability integral method (DPIM) is proposed to address stochastic response and dynamic reliability analyses of nonlinear multidegree-of-freedom (MDOF) systems subjected to additive random excitations. First, the probability density integral equation (PDIE) with a Dirac delta function is established to characterize the randomness propagation of the MDOF system based on the principle of probability conservation. DPIM decouples the PDIE and governing differential equation of the system and efficiently solves PDIE by using the partition of probability space and smoothing of the Dirac function to achieve the probability density function of stochastic response. Moreover, the equivalent relation among the PDIE, Fokker-Planck-Kolmogorov (FPK), and Chapman-Kolmogorov-Smoluwski (CKS) equations in the Markov system is also derived, demonstrating the applicability of DPIM for the Markov system. Then, the first-passage dynamic reliability of the MDOF system under additional excitations is assessed by introducing equivalent extreme value mapping of the stochastic process. Finally, two examples of nonlinear MDOF systems subjected to filtered Gaussian white noise and nonstationary seismic excitation are investigated, respectively. Comparing the calculated results for nonlinear MDOF systems with those using the path integral method and Monte Carlo simulation indicates the high accuracy and efficiency of DPIM. Specifically, the numerical example of a 9-story frame building with a nonlinear hysteretic model and soil-structure interaction (SSI) indicates that as the stiffness of soil decreases, the dynamic reliability of frame building is gradually reduced.