Journal of Engineering Mechanics

This paper presents a new graphic methodology for the structural analysis of domes and other surfaces of revolution, based on the combined use of funicular and projective geometry. The methodology is presented through its application to a hemispherical brick dome with a small thickness. The dome is considered a network of lines of latitude and longitude, and the equilibrium of this network is analyzed in both horizontal and vertical projections. To contrast the results obtained, the methodology has been applied to different structural situations whose analytical solution is known: complete hemisphere, hemisphere with oculus on the top, and hemisphere with lantern. The new methodology has also been applied to the analysis of structural situations different from the previous ones, by combining the following considerations: presence of the backfilling on the extrados of the dome, small inclinations of the reaction in the support, and small variations in the vertical position of the nodes in the simplified model considered. The tests included in the article have been selected to show all the possibilities of this methodology. Multiple solutions for the internal forces are obtained, whose equilibrium is guaranteed by this graphic methodology.

Fractional-order derivative (FD) models are widely used to describe the dynamic behavior of rubber-like materials. However, experiments have shown that FD models cannot reproduce the amplitude dependence and the slow stabilization phenomenon under harmonic excitation. To overcome these limitations, we introduce a modified FD Zener (MFDZ) model that incorporates a new parameter, average strain. The MFDZ model is shown to have good agreement with experimental data. Two illustrative examples are conducted to demonstrate the use of the MDFZ model for structural control. The results show that the MFDZ model can better describe rubber-like materials’ behavior and versatility when used in the dynamic analysis of structural systems.

A combined fabric evolution (CFE) model is used to predict real-world fabric evolution of a strongly anisometric granular material under triaxial loading, connecting advances in theoretical developments and experimental measurement technology for fabric evolution. X-ray tomography is used to quantify particle orientation and contact normal fabric evolution in five triaxial compression experiments on lentil specimens of different initial bedding plane angles. The CFE model coupling contact normal fabric evolution with particle orientation fabric is calibrated based on two of the experiments and used to predict the fabric evolution in the others. Good overall agreement between theoretical prediction and experimental measurement is achieved for the evolution of both types of fabric tensors. The comparison between prediction and measurement highlights an optimistic future for the development of constitutive relations incorporating fabric features based on actual experimental micromechanical observations. Nonetheless, the special case of 90° deposition is relatively poorly predicted due to the strongly heterogeneous local dilation caused by the extreme particle shape and alignment. This suggests that there is still more to be considered in the continuum description of the fabric evolution of granular materials, especially with respect to local information.

Contact fabric is commonly adopted as a micromechanical state variable in many recent constitutive models of granular materials. This is accompanied by an evolution law for the fabric usually in terms of stress, total strain, plastic strain, or combinations thereof. However, there has yet to be a consensus on what variables best describe the evolution of contact fabric. The current study provides a correlation analysis for the evolution of the second-order fabric tensor in terms of stress and strain increments. An extended stress probing technique in two-dimensional (2D) discrete-element method simulations was used in order to thoroughly traverse the space of possible loading increments at multiple states prior to the stress peak in constant mean stress and simple shear simulations. Among the 15 hypotheses considered for fabric evolution, the correlation between the contact fabric and total strain appears to be the strongest. The plastic strain, despite its adoption in previous studies, shows a weak correlation with fabric. The results also uncover anomalies that are thought to be associated with the artificial sample preparation procedure.

The accuracy of locating acoustic emission (AE) source location is closely related to the reasonability of the adopted wave velocity model. However, it is literally hard to obtain an accurate wave velocity model for a heterogeneous rock material due to its inner invisible inclusions and local defects, making the AE source localization very challenging. To obtain a more appropriate wave velocity model for the heterogeneous rock material having unknown inclusions, in this study the projective reconstruction method (PRM) was utilized to determine the wave velocity model. Because the PRM is irrelevant to the continuous assumption, the proposed wave velocity model can well reflect the discontinuous characteristics of the real wave velocity field in rock materials. Then, the proposed wave velocity model was incorporated into an arrival time-based governing equation to locate the AE source. To demonstrate the effectiveness of the proposed method in improving the AE source location accuracy and monitoring the rock failure process, lead-break tests and three-point bending tests were conducted on the composite rock and rock-like specimens, respectively. Results show that the improved wave velocity model obtained by the PRM can significantly improve the accuracy of AE source location in the heterogeneous rock material with unknown inclusions.

A model on one-dimensional unsteady suspended sediment transport has been developed in this study by including the effect of hindered settling and from mixing length point of view. The sediment diffusion term has been related to mixing length, which has been taken as a function of concentration. The mixing length and settling velocity are reduced due to the presence of particles in the flow. By considering these effects in the governing equation, the resulting partial differential equation (PDE), which becomes highly nonlinear, has been solved numerically using the most generalized boundary conditions available in the literature. For the purpose of validation, the derived model is compared with similar existing works under certain specified conditions. Apart from that, the obtained solution has also been compared with available laboratory data for steady and uniform flow because over a large span of time, the model behaves like a steady one. Furthermore, effects of damping function and hindered settling are explained both graphically and physically.

Viscoelastic (VE) dampers are one of the most promising techniques for reducing vibration in engineering structures caused by earthquakes and wind. This work aims to develop a kind of high-dissipation VE damper for civil structures at low frequency and large amplitude in shear mode. First, nitrile rubber (NBR)/organic small-molecule composite VE materials are optimized and then made into VE damper. In order to test the mechanical performance and energy dissipation performance of the VE damper, the dynamic mechanical performance experiments at different temperatures, frequencies, and amplitudes were implemented. The experimental results show that the VE damper exhibits great stiffness and excellent energy dissipation capacity under different loading conditions. Second, a fractional derivative model based on Gauss microchain, Williams–Landel–Ferry (WLF) equation, and internal variable theory is proposed to accurately describe the effects of temperature, frequency, and amplitude on the dynamic mechanical properties of VE dampers. Finally, the accuracy of the mathematical model of VE damper is verified by comparing the calculated results with the experimental results. The study provides a theoretical basis for effective vibration reduction of civil structures with VE dampers at low frequency.

The objective of this research is to develop a technical basis of the impulse-response test for condition assessment and to improve its diagnostics for concrete plates. Impulse-response tests were performed on a fully supported concrete plate with artificial delaminations of various planar sizes at different depths. Defect detection was first performed using the empirical damage indices defined in ASTM C1740, which are based on the shape characteristics of the frequency response function (FRF) between 10 and 800 Hz. Next, the test procedure was modified for extending the frequency range of FRF, revealing that delaminations introduce vibration modes with distinctive high frequencies not present in intact portions of the plate and not detectable in the currently used frequency range of the test due to the hammer tip typically used. A validated 3D finite element model of the experimental plate is used to correlate the dynamic response of test points with experimental FRFs, indicating that the distinctive high frequencies in the extended FRF measured on delaminations correspond to the first bending mode characterized by a local reduction in flexural rigidity and in the damping of the plate. The effect of experimental setups, such as the relative distance between the sensor and the hammer, is shown to have a significant effect on the accuracy of defect delineation for large and shallow delaminations. A new damage index based on the resonant frequency from the extended FRF with a modified experimental setup is proposed for estimating the planar size and depth of delaminations. The performance of the proposed index is demonstrated through experimental data as well as parametric numerical simulations. Multiple regression is used to estimate the detectability, depth, and extent of delaminations as a function of the proposed and currently used damage indices. The resonant frequency is found to be more informative for the planar size of the delamination compared to the depth, while the average accelerance is more informative for the depth of delamination and less for its planar size. Furthermore, the results indicate that the test may have limited detectability and application for delaminations deeper than 300 mm. Finally, the prediction accuracy for the depth and size of delamination is demonstrated based on Gaussian processes and is presented in the form of confidence ellipses. The prediction model is shown to be reasonably accurate for shallow defects ($<300\mathrm{mm}$), which are the most critical for durability and structural performance. While the impulse-response test has been used since the early 1990s for condition assessment of concrete elements other than drilled shaft piles, this study is among the most comprehensive on its physical basis, the influence of experimental setups, the extension of the frequency range, the characterization of delaminations, and detection limitations of the test.

Optimal life-cycle management is a challenging task for large-scale structures. The complexity of structural states, represented by the numerous combinations of component conditions, and the vast number of inspection and maintenance options often prompt the decision-makers to adopt a simple time- or condition-based management method rather than a performance-based one. To improve this situation, this study proposes a novel method for adaptive risk-based life-cycle management of large-scale structures. The proposed method can yield bespoke inspection and maintenance plans at the individual component level based on their contribution to the overall structural performance. The obtained plan can also adapt itself to the unfolding information gained from inspection and maintenance actions. This advanced method, termed DeepLCM, is enabled by (1) efficient surrogate modeling based on deep neural networks for structural risk assessment; and (2) a deep reinforcement learning algorithm for adaptive life-cycle management. The method is applied to a steel girder bridge in Montgomery County, Pennsylvania. The inspection and maintenance plan obtained using DeepLCM is compared with those obtained using the conventional life-cycle management techniques including time-, condition-, and risk-based methods. The case study also investigates the effect of the spatial granularity of inspection and maintenance actions on the resulting life-cycle cost.

Ignoring the shotcrete hardening property in tunnel design may lead to an overestimation of the bearing capacity of shotcrete liners and underestimation of tunnel convergence. However, accounting for this nonlinear hardening behavior of shotcrete in the tunnel analytical model is difficult because of the complexity of the mathematical derivation. This study aims to establish an analytical model to estimate the influence of the shotcrete hardening property on tunnel response. To overcome this challenge, the shotcrete hardening age was divided into several linear stages, and the corresponding equivalent Young’s modulus in each stage was calculated. A unified time-dependent solution was then proposed for predicting tunnel displacement and shotcrete liner pressure, with the tunnel face advancing effect and the installation delay of the shotcrete liner taken into consideration. The proposed analytical solution was applied to the Rong Jiawan tunnel in China, and the general trend of the analytical results agreed with that of the field data. Finally, a comprehensive parametric investigation including the sensitivity of the division of shotcrete age, geostress, and shotcrete hardening model was conducted based on the analytical model, and some useful recommendations for tunnel design are presented. The outcomes of this research can support tunnel design in similar projects.

This paper addresses the first passage problem of linear systems subjected to non-Gaussian excitations by means of simulation. A non-Gaussian simulation technique based on the unified Hermite polynomial model (UHPM) is adopted to model input excitations, and then the output responses are further obtained through time-domain analysis. The novel contribution of this paper is to construct an efficient importance sampling (IS) density function based on UHPM and the first-order reliability method (FORM) to release the computational burden. A simple and efficient sampling procedure is also provided for convenient implementation. Such an approach allows the failure probabilities in the order of ${10}^{-3}$ or lower to be estimated reliably with a reduced computational cost. The accuracy and efficiency of the proposed method are demonstrated by three examples, including a single-degree-of-freedom oscillator, a 3-story linear shear frame, and a relatively large-scale finite-element model.

This work investigated the interaction of surface waves with a dual-barrier system comprising two vertical viscoelastic thin sheets with variable spacing in finite water depth without preassumption of its dynamic behavior. The two sheets were assumed to be made of the same material and under different tensions, and both penetrated into the water depth partially with unequal drafts. The viscoelastic behavior of the sheet material, which accounts for its elastic deformation and internal energy dissipation, is represented by the Voigt model. Using the eigenfunction expansion and least square determination, analytical solutions were obtained for the dual-barrier system, including the asymptotic case of a single sheet when the second sheet draft approaches zero. Subsequently, the effects of hydroelastic regimes and viscoelasticity were examined. With the single-sheet system, the wave transmission decreases as the tensioned sheet shifts from platelike to membranelike, and its material has higher internal energy dissipation (i.e., viscosity). When the size of the bottom opening increases to a gap ratio larger than $\sim 0.6$, however, the wave transmission becomes dominated by the diffraction through the gap, and the influence of sheet material characteristics is no longer significant. With the double-sheet system, the results show that the performance of the wave barrier improves significantly by the presence of the second sheet, even with a small draft. Complex resonating patterns can be observed with increase in sheet spacing for the dual-barrier system, which reduces the wave transmission. The presence of viscosity of the double-sheet system dampens the resonance, but also reduces the wave transmission by itself through the viscous dissipation of the incident wave energy.

Experiments and a simulation of the effect of localized tensile strength in European white oak boards and predictions of the effect of the board’s length on global tensile strength are reported. Furthermore, the cross-correlation of local strength with a local modulus of elasticity (MOE) is investigated. This knowledge is a fundamental prerequisite for stochastic simulations of glued laminated timber with adequate representation of the lamination effect. The sample consisted of 47 boards, each subdivided virtually into 15 consecutive cells 100 mm in length and for which local MOE and its autocorrelation had been previously determined. The remnants of the first, that is, global, failure in the axial tension tests were loaded to rupture in secondary loadings up to four times. This procedure, resulting in a total of 102 primary and secondary strengths, was enabled by the rather blunt failure planes presented by the investigated oak boards. The censored localized strength data, including the lower bounds of the unbroken virtual cells, were analyzed using survival analysis with a modified likelihood function (LHF) applied to six different strength distribution models: (1) four censored parametric distributions (two-parameter Weibull, beta, grafted Weibull–Gaussian, and Duxbury–Leath–Beale); and (2) two censored regression models (Weibull and beta) with shape and scale parameters depending on global MOE. A detailed analysis of the lower tail of the experimental distribution evidenced the quasibrittle nature of the material, thus supporting the use of the Weibull–Gaussian distribution. The simulation of the tensile strength variation along the board’s length was conducted by an adapted vector autoregressive (VAR) model. Here, the localized MOEs were cross-correlated with the obtained cell-related strength distributions employing Gaussian normalization of both distributions, followed by mapping the normalized strength values into the LHF-derived strength distributions. The length effect of tensile strength was analyzed with virtual boards of different lengths with 50,000 simulations per board length and a strength distribution model. The obtained length effect exponent of a simple power law, usually applied in timber engineering, was roughly equal to 0.33 for the mean strength level for all models and grade combinations. At the 5%-quantile level, the calculated exponents varied and were grade-dependent and model-dependent from 0.14 to 0.34. The simulated length effects were similar to those of softwoods at the 5%-quantile level but markedly higher at the mean level, which is well explained by the finite weakest link theory by considering the more general size dependency that governs quasibrittle materials.

The mobilization of side resistance of rock-socketed pile strongly depends on the shear behavior of the pile-rock interface. In this study, an asperity-based model was developed to investigate essential responses of interface shear, where asperities develop from sliding with interface dilation to residual shear under the condition of constant normal stiffness (CNS). The emphasis was on quantifying the magnitude of interface dilation in terms of limit analysis solutions. Followed by the proposed upper bound (UB) and lower bound (LB) solutions for asperity collapse loads, the mean value was chosen for approaching the potential exact solution. Laboratory experiments of direct shear tests under CNS conditions were also carried out by the authors, and observations were regarded as evidence that the proposed modeling provided a rational explanation of shear behavior for a pile-rock interface. Parametric studies indicated that two key factors, roughness and material properties, significantly impact the mobilization of ultimate side resistance.

The mechanical behavior of fiber-reinforced concrete at high temperature is investigated, and a constitutive model considering the damage effect is developed based on the thermodynamic theory. By comparing the experimental results of steel fiber–reinforced concrete, the hardening function and yield theory of concrete at different temperatures are proposed. Meanwhile, a damage evolution model for concrete matrix at high temperature is developed by incorporating the free energy function. The influence of fibers on the concrete strength is investigated at different temperatures, and a parameter considering the deterioration of fiber properties at high temperature is introduced based on experimental observations. Theoretical predictions of the developed model are compared with the experimental data and show reasonable accuracy.

Understanding the effect of particle size on the shear strength of granular materials is important for geotechnical design and construction. However, previous studies show contradicting results on the relationship between particle size and shear strength. Additionally, the effect of particle breakage on this relationship has not been fully revealed. In this study, a series of biaxial tests have been simulated with the discrete element method to explore the particle-size effect of sand considering the role of particle breakage. The sand specimens have parallel particle-size distributions. The sequential breakage model has been used to simulate particle breakage, which is a combination of replacement and cluster methods. The main conclusions of this study are: (1) the relationship of peak shear strength and particle size depends on the crushability of particles and relative density of specimens; (2) the particle size and crushability have a very slight effect on the residual shear strength; and (3) at the microscale, the relationship between shear strength and particle size is positively related to the friction utilization ratio.

Rock materials are often subjected to medium- and low-strain-rate dynamic cyclic loading such as earthquake action; however, few dynamic constitutive models for rock materials under dynamic cyclic loading are available. Therefore, it is important for evaluating the stability of rock engineering when analyzing the effects of seismic loading to establish a reasonable dynamic constitutive model for rock materials. This model can simulate the main characteristics of rock materials, such as the hysteresis loop, cumulative plastic deformation, strain rate effect, and damage effect. Thus, the formulation of a new dynamic constitutive model able to reproduce the cyclic behavior and dynamic mechanical properties of rock materials under dynamic cyclic loading is demonstrated and validated. First, by analyzing the variation of Young’s modulus for different rock materials under static and dynamic cyclic loading, it is assumed that there exist strain rate effect and damage effect on the Young’s modulus of rocks when subjected to dynamic cyclic loading. The expression of Young’s modulus for rock materials suitable for medium- and low-strain-rate dynamic cyclic loading is established. Second, like the variation of Young’s modulus, the expressions of cohesion and internal friction angle with strain rate and damage variable for rock materials under dynamic cyclic loading are also established. Then, a dynamic constitutive model for rock materials considering strain rate, damage effect, and the coupling of the former two effects is constructed based on the static constitutive model proposed by a previous study. Finally, the dynamic and static constitutive models are applied to simulate the behavior of a ${\mathrm{T}}_{\mathrm{2y}}6$ marble and a material similar to basalt under uniaxial constant amplitude dynamic cyclic loading and triaxial damage-controlled cyclic dynamic loading (using increasing mean and amplitude stress). The results show that the results obtained by the proposed model, in terms of reproducing the compressive strength, Young’s modulus, and residual strain in cyclic tests of the two rock materials, are much better than those predicted by the static constitutive model.

A one-dimensional technical theory for pretwisted isotropic linearly elastic beams loaded in tension and torsion was developed. The analysis was based on a kinematically admissible field written in terms of three generalized displacements, which were determined from the theorem of minimum potential energy. A general analytical solution was developed. The problem of a pretwisted beam with a built-in end and loaded in tension and torsion at the other end was analyzed. The problem also was solved by carrying out detailed three-dimensional finite-element calculations. The predictions of the technical theory agreed very well with the results of the finite-element solution. The effects of Poisson’s ratio were examined, and the applicability of the model to beams of various lengths was discussed.

We present an adaptive importance sampling (IS) method to estimate the reliability of linear structures with parameter uncertainties that are subjected to Gaussian process excitation. Structural failure is defined as a union of multiple first-passage failure events. The main contribution is the introduction of an efficient IS density for the uncertain structural parameters. This density is determined by minimizing the cross-entropy (CE) between the theoretically optimal IS density of the structural parameters and a chosen parametric family of probability distributions. The CE minimization procedure requires evaluation of the system failure probability conditional on fixed values of the uncertain parameters. A closed-form analytical approximation of this conditional failure probability was derived based on an upper bound on the out-crossing rate. Finally, a joint IS density of the random excitation and the uncertain structural parameters was introduced to estimate the series system failure probability involving parameter uncertainties. The accuracy and efficiency of the proposed method was demonstrated by means of two examples: a Gaussian white noise–excited two-story linear shear frame; and a six-story, three-bay moment-resisting steel frame subjected to a filtered nonstationary Gaussian excitation.

Hybrid simulation is a tool for investigating the dynamic response of a structural prototype subjected to realistic loading. Hybrid simulation is conducted using a hybrid model that combines physical and numerical substructures interacting with each other in a feedback loop. As a result, the tested substructure interacts with a realistic assembly subjected to a credible loading scenario. In the current practice, experimental results obtained via hybrid simulation support conceptualization and calibration of computational models for structural analysis. Instead, this paper extends the scope of hybrid simulation in constructing a safe/failure state classifier for the tested substructure by adaptively designing a sequence of parametrized hybrid simulations. Such a classifier is intended to compute the state of any physical-substructure-like component within system-level numerical simulations. It follows that the main contribution of this paper lies in the way experimental results are aggregated and integrated with structural analysis. The proposed procedure is experimentally validated for a three-degrees-of-freedom hybrid model subjected to Euler buckling.

This paper presents the experimentation and finite-element analysis of a unique structure called a celestial icosahedron. The structure is being considered in a project related to lighter-than-air vehicles. The dimensions of the vehicle are adjusted to fit into an additive manufactured facility. A celestial is made up of nine rings symmetrically placed in a spherical arrangement. This is one of several structures that have been considered in the overall project. The uniqueness of this structure lies in its makeup; nine rings combined together through an additive manufactured (AM) facility. The structure was experimentally loaded in a MTS Systems Corporation machine under a concentrated compression load. A finite-element analysis was carried out, and the results compared with the experiment. The model considers the effect of anisotropic characteristics through the use of the rule of mixtures based on the presence of compression and tension moduli in specific portions of the load distribution yielding a generalized effective modulus. It was found, with the use of commercially available software, that the results of nonlinear analysis compared reasonably well with the experimental findings.

Design of external dampers for stay cables requires repetitive evaluation of damping ratios for target modes of cables under various damper parameters and installation positions, and explicit formulas with high accuracy to estimate the modal-damping ratios for a cable-damper system are helpful in designing external dampers. This study deals with the evaluation of the modal damping of cables with an external viscous damper close to the anchorage. A considerably accurate and explicit formula for calculating the modal-damping ratios of the cable-damper system is derived by evaluating the imaginary and real part of the complex frequency equation. It is demonstrated that the formula is able to predict the modal-damping ratios of the cable-damper system both for lower and higher modes. Based on the proposed formula, the effects of the modal order and installation position on the modal-damping ratio of the cable-damper system are studied. A closed-form solution for the optimal damping coefficient is proposed and the maximum attainable modal damping is also obtained.