Journal of Engineering Mechanics

A new vision of structural health monitoring (SHM) is presented, in which the ultimate goal of SHM is not limited to damage identification, but to describe the structure by a probabilistic model, whose parameters and uncertainty are periodically updated using measured data in a recursive Bayesian filtering (RBF) approach. Such a model of a structure is essential in evaluating its current condition and predicting its future performance in a probabilistic context. RBF is conventionally implemented by the extended Kalman filter, which suffers from its intrinsic drawbacks. Recent progress on high-fidelity propagation of a probability distribution through nonlinear functions has revived RBF as a promising tool for SHM. The central difference filter, as an example of the new versions of RBF, is implemented in this study, with the adaptation of a convergence and consistency improvement technique. Two numerical examples are presented to demonstrate the superior capacity of RBF for a SHM purpose. The proposed method is also validated by large-scale shake table tests on a reinforced concrete two-span three-bent bridge specimen.

In recent years, Bayesian model updating techniques based on measured data have been applied to system identification of structures and to structural health monitoring. A fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying structural system and to its exclusive foundation on the probability axioms. The plausibility of each structural model within a set of possible models, given the measured data, is quantified by the joint posterior probability density function of the model parameters. This Bayesian approach requires the evaluation of multidimensional integrals, and this usually cannot be done analytically. Recently, some Markov chain Monte Carlo simulation methods have been developed to solve the Bayesian model updating problem. However, in general, the efficiency of these proposed approaches is adversely affected by the dimension of the model parameter space. In this paper, the Hybrid Monte Carlo method is investigated (also known as Hamiltonian Markov chain method), and we show how it can be used to solve higher-dimensional Bayesian model updating problems. Practical issues for the feasibility of the Hybrid Monte Carlo method to such problems are addressed, and improvements are proposed to make it more effective and efficient for solving such model updating problems. New formulae for Markov chain convergence assessment are derived. The effectiveness of the proposed approach for Bayesian model updating of structural dynamic models with many uncertain parameters is illustrated with a simulated data example involving a ten-story building that has 31 model parameters to be updated.

A new method for implicit solution of unsteady nonlinear advection equations is presented. This time-centered split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically nonlinear coupled equations for any number of variables. The TCS algorithm is compared to other nonlinear solution methods (local linearization, Picard iteration, and Newton iteration) and applied to the Crank-Nicolson discretization of the one-dimensional Burgers’ equation. The temporal accuracy and practical stability of the method is confirmed using an unsteady flow test case with an analytical solution. The method is shown to require computational effort similar to local linearization, but does not require discrete computation of a functional Jacobian for solution.

The ability to use multiple tuned mass dampers (TMDs) in improving inelastic structural performance to dissipate the earthquake input energy is investigated. Inelastic structural behavior is modeled using the force analogy method, which is the backbone of analytically characterizing the plastic energy dissipation in the structure. Both tuning period and placement of the multiple TMDs are studied to give the best structural performance in terms of plastic energy dissipation. Numerical simulations are performed to study the energy responses of structures with and without TMD installed, and the effectiveness of TMDs in the reduction of energy responses is also studied by using tuned mass spectra. Results show that the installation of TMDs gives the structure additional capability of dissipating a large amount of damping energy and at the same time reducing the amount of plastic energy demand and therefore reducing damage in the structure. More important, TMDs have the ability to draw the plastic energy dissipation at the lower stories and release it to the upper stories. This is particularly beneficial for structures that would otherwise suffer more damage at the lower stories than the upper stories. However, the reduction in plastic energy dissipation is quite sensitive to the earthquake vibration characteristics, and TMDs should not be used for structures with weak upper stories.

Two well-known return mapping algorithms, the closest point projection method (CPPM) and the cutting plane algorithm (CPA), have been analyzed in detail in relation to two classical failure problems in geomechanics, namely, bearing capacity and slope stability. The stability and efficiency of the algorithms have been investigated in relation to two types of stiffness operators, namely, the consistent elastoplastic modulus and the continuum elastoplastic modulus, and two types of stresses prediction strategies, namely, path independent (based on stresses at previous step) and path dependent (based on stresses at the previous iteration). The numerical experiments show that CPPM working with a consistent elastoplastic modulus and a path independent strategy gives the best performance. It was also observed, however, that the CPA with a continuum elastoplastic modulus and path dependent strategy was quite stable and efficient. This latter observation has implications for advanced constitutive modeling since CPA with a continuum elastoplastic modulus avoids the need for evaluation of the second derivatives of the plastic potential function, making it easier to deal with complicated yield surfaces.

Micromechanics of rapid granular flows is studied in a two-dimensional planar granular Couette flow apparatus. The device is capable of generating particulate flows at different shearing rates and solid fractions. Monosize plastic disks are sheared across an annular test section for several shear rates. The motion of particles is recorded through a high speed digital camera and analyzed by image processing techniques. The average and fluctuation velocity profiles are obtained and granular temperature relations with shear rate are investigated. Average streaming velocity across the shear cell decays slightly faster than exponential, and is rather Gaussian when not too close to the wall. Fluctuation velocities and granular temperature across the shear cell are related to effective shear rate. Interparticle collisions are estimated from the particle trajectories and probability distribution of collision angles obtained from particle collision data. In dense flows, three peaks of collision angles are observed, which signal the onset of triangular structure formulation and cause crystallization. It is found that the distribution of collision angles is anisotropic.

Current models of the modulus of elasticity, $E$ , of concrete recommended by the American Concrete Institute and the American Association of State Highway and Transportation Officials are derived for normally vibrated concrete (NVC). Because self-consolidated concrete (SCC) mixtures differ from NVC in the quantities and types of constituent materials, supplementary cementing materials, and chemical admixtures, the current models, may not take into consideration the complexity of SCC, and thus they may predict the $E$ of SCC inaccurately. Although some authors recommend specific models to predict $E$ of SCC, they include only a single variable of assumed importance, namely, the design compressive strength of concrete, $f_c^{\prime }$ . However, there are other parameters that may need to be accounted for while developing a prediction model for $E$ of SCC. In this paper, a Bayesian variable selection method is used to identify the significant parameters in predicting the $E$ of SCC, and more accurate models for $E$ are generated using these variables. The models have a parsimonious parametrization for ease of use in practice and properly account for the prevailing uncertainties.

We propose a micromechanics model for aging basic creep of early-age concrete. Therefore, we formulate viscoelastic boundary value problems on two representative volume elements, one related to cement paste (composed of cement, water, hydrates, and air), and one related to concrete (composed of cement paste and aggregates). Homogenization of the “nonaging” elastic and viscoelastic properties of the material’s contituents involves the transformation of the aforementioned viscoelastic boundary value problems to the Laplace-Carson (LC) domain. There, formally elastic, classical self-consistent and Mori-Tanaka solutions are employed, leading to pointwisely defined LC-transformed tensorial creep and relaxation functions. Subsequently, the latter are back-transformed, by means of the Gaver-Wynn-Rho algorithm, into the time domain. Temporal derivatives of corresponding homogenized creep and relaxation tensors, evaluated for the current maturation state of the material (in terms of current volume fractions of cement, water, air, hydrates, and aggregates; being dependent on the hydration degree, as well as on the water-cement and aggregate-cement ratios) and for the current time period since loading of the hydrating composite material, allow for micromechanical prediction of the aging basic creep properties of early-age concrete.

This paper presents a viscoelastic model of asphalt mixtures with the discrete element method, where the viscoelastic behaviors of asphalt mastics (fine aggregates, fines, and asphalt binder) are represented by a Burger’s model. Aggregates are simulated with irregular shape particles consisting of balls bonded together by elastic contact models, and the interplaces between aggregates are filled with balls bonded with viscoelastic Burger’s model to represent asphalt mastic. Digital samples were prepared with the image analysis technique. The micromechanical model was developed with four constitutive laws to represent the interactions at contacts of discrete elements (balls) within an aggregate, within mastic, between an aggregate and mastic, and between two adjacent aggregates. Each of these constitutive laws consists of three parts: a stiffness model, a slip model, and a bonding model in order to provide a relationship between the contact force and relative displacement and also in order to describe slipping and tensile strength at a particular contact. The relationship between the microscale model input and macroscale material properties was derived, and an iterative procedure was developed to fit the dynamic modulus test data of asphalt mastic with Burger’s model. The favorable agreement between the discrete element prediction and the lab results on dynamic moduli and phase angles indicates that the viscoelastic discrete element model developed in this study is very capable of simulating constitutive behavior of asphalt mixtures.

An accurate and rapid estimation of the pavement temperature field is desired to better predict pavement responses and for pavement system design. In this paper, an innovative method to derive the theoretical solution of an axisymmetric temperature field in a multilayered pavement system is presented. The multilayered pavement system was modeled as a two-dimensional heat transfer problem. The temperature at any location $(r,z)$ and any time $t$ in an $N$ -layer pavement system can be calculated by using the derived analytical solution. The Hankel integral transform with respect to the radial coordinate is utilized in the derivation of the solution. The interpolatory trigonometric polynomials based on discrete Fourier transform are used to fit the measured air temperatures and solar radiation intensities during a day, which are essential components in the boundary condition for the underlying heat transfer problem. A FORTRAN program was coded to implement this analytical solution. Measured field temperature results from a rigid pavement system demonstrate that the derived analytical solution generates reasonable temperature profiles in the concrete slab.

A constitutive model for rate-dependent and thermomechanically coupled plasticity at finite strains is presented. The plasticity model is based on a $J_2$ model and rate-dependent behavior is included by use of a Perzyna-type formulation. Adiabatic heating effects are handled in a consistent way and not, as is a common assumption, through a constant conversion of the internal work rate into rate of heating. The conversion factor is instead derived from thermodynamic considerations. The stored energy is assumed to be a function of a single internal variable which differs from the effective plastic strain. This allows a thermodynamically consistent formulation to be obtained which, as shown, can be calibrated by use of simple procedures. Choosing 100Cr6 steel in two differently heat treated conditions as prototype material, experimental tests are performed, enabling the model to be calibrated. Significant differences in deformation behavior are noted as the differently heat treated specimens are compared. In addition, the local stress-updating procedure is reduced to a single scalar equation, permitting a very efficient numerical implementation of the model. The constitutive formulation proposed was employed in an explicit finite element solver, illustrative simulations of a high-velocity metal forming process being performed to demonstrate the capabilities of the model and certain characteristic traits of the materials that were studied.