Journal of Engineering Mechanics

A diffusion-based and creep-based chemo-mechanical model for calculating the evolution of damage caused in concrete and concrete structures by the alkali-silica reaction (ASR) is developed. First the model of Bažant and Steffens for the diffusion controlled kinetics of ASR is reviewed and used to calculate the rate of production of the ASR gel within the aggregate. The next step is the formulation of a nonlinear diffusion model for the penetration of gel into the micropores and nanopores in a mineral aggregate grain, into the interface transition zone (ITZ) and into the nearby microcracks created in the cement paste of mortar. The gel that penetrates the pores and cracks in cement paste is considered to calcify promptly and stop expanding. A novel point, crucial for unconditional numerical stability of time step algorithm, is that the diffusion analysis is converted to calculating the pressure relaxation at constant gel mass during each time step, with sudden jumps between the steps. The gel expansion in the aggregate and the ITZ causes fracturing damage in the surrounding concrete, which is analyzed by microplane model M7, into which the aging creep of a broad retardation spectrum is incorporated. The gel and the damaged concrete are macroscopically treated as a two-phase (solid-fluid) medium of nonstandard type because of load-bearing but mobile water in nanopores. The condition of equilibrium between the phases is what mathematically introduces the fracture-producing load into the concrete. Depending on the stress tensor in the solid phase, the cracking damage is oriented and the expansion is directional. The creep is found to have a major mitigating effect on multidecade evolution of ASR damage, and is important even for interpreting laboratory experiments. Validation and calibration by experimental data from the literature is relegated to Part II.

The theory for the material and structural damage due to the alkali-silica reaction (ASR) in concrete is calibrated and validated by finite element fitting of the main test results from the literature. The fracture mechanics aspects, and particularly the localization limiter, are handled by the crack band model. It is shown that the theory can capture the following features quite well: (1) the effects of various loading conditions and stress states on the ASR-induced expansion and its direction; (2) degradation of the mechanical properties of concrete, particularly its tensile and compressive strength, and elastic modulus; (3) the effect of temperature on ASR-induced expansion; and (4) the effect of drying on the ASR, with or without simultaneous temperature effect. The finite element simulations use microplane model M7. The aging creep, embedded in M7, is found to mitigate the predicted ASR damage significantly. The crack band model is used to handle quasi-brittle fracture mechanics and serve as the localization limiter. The moisture diffusivity, both the global one for external drying and the local one for mortar near the aggregate, decreases by one to two orders of magnitude as the pore humidity drops. The fits of each experimenter’s data use the same material parameters. Close fits are achieved and the model appears ready for predicting the ASR effects in large structures.

This paper aims to present a mixed, or combined, numerical approach to modeling advanced degradation and predicting failure in reinforced concrete (RC) structures. The discrete-element method (DEM) is used to model the cohesive behavior and fracturing of concrete, whereas the standard finite-element method (FEM) is applied to represent steel reinforcement through an elastic-plastic beam model. Because of specificity in the geometric support, which does not allow for hierarchical mesh refinement, convergence of the spherical DEM has never been proved, making it difficult to master DE simulations. In this paper the authors present results of a computational study conducted by means of deforming a DEM sample and varying several parameters, which allowed determining the minimum discretization required for a DEM sample to correctly reproduce the macroscopic behavior of concrete, and thus evaluating consistency of the spherical DEM used herein. An original steel-concrete bond model, developed to simulate the interaction between the steel and concrete models, is also presented. This model was devised to decouple normal and tangential responses, which allows fitting them separately in accordance with experimental data. The numerical simulations of tests performed on unreinforced and reinforced concrete samples and the modeling of the hard-type impact on a RC beam indicate the relevance of the proposed approach for simulating advanced damage in civil engineering structures under both static and dynamic loads.

For better performance evaluation, it is of significance to investigate the factors affecting moisture distribution in concrete pavement slabs. This study provides methodology on both experimental measurement and numerical simulation of moisture distribution in concrete slabs with three water-to-cement (w/c) ratios of 0.3, 0.4, and 0.5. The effects of w/c ratio, slab thickness, and the environmental conditions on moisture distribution are evaluated in terms of the equivalent temperature difference, slab corner uplift, and the maximum tensile stress generated in concrete pavement slabs. A model is proposed for predicting the relative humidity profile along the slab depth. An equivalent temperature difference $\mathrm{\Delta }{T}_{eq}$ is used to quantify the moisture gradient effect. Greater $\mathrm{\Delta }{T}_{eq}$ is obtained in thin concrete slabs with high w/c ratio and when exposed to lower environmental relative humidity conditions. This renders concrete slab to excessive warping and tensile stress at the slab top surface when combined with traffic loadings. A thick slab with low w/c ratio possibly might reduce the warping deformation and the maximum tensile stress.

In this paper, a finite-element implementation of linear second-strain gradient elasticity is introduced based on a Hellinger-Reissner variational principle in order to use standard finite-element methods. Displacement boundary conditions are applied to one or more vertices of different polyhedrons. As a result, a smooth deformation around deformed vertices of the polyhedrons can be observed, in contrast to the appearance of singularities in the first-order theory, i.e., a Cauchy continuum, where strain singularities appear in such cases.

This article deals with the behavior under service loads of thin-walled, precast, prestressed beams that are frequently used to build floors and roofs of shopping centers, industrial buildings, and warehouses. Because of the dissymmetric shape, their dead load gives rise to torsion, to which the beam reacts according to Vlasov’s theory. This work applies Vlasov’s theory to a heterogeneous beam made with a homogenous linear viscoelastic material (i.e., concrete) and a linear elastic one (i.e., the reinforcement). The beam is subjected to long-term bending and torsional moments, and the solving system takes into account the noncompatible strains imposed between the two materials (i.e., prestressing).

The resetting semiactive stiffness damper (RSASD) has been shown to be effective at controlling vibrations in civil structures in the presence of near-field earthquakes. Although it has the advantages of being mechanically simple and relatively inexpensive, the RSASD requires a multicomponent feedback control system consisting of sensors, a microcontroller, a servo valve, and a battery to operate, rendering it less reliable during a seismic event. In the present work, the resetting passive stiffness damper (RPSD) is presented as an improvement to the RSASD, whereby the RSASD feedback control system is replaced by a novel mechanism to achieve resetting of the damper force. The results of laboratory studies on a small-scale RPSD demonstrate that the resetting mechanism performs as proposed. Results of numerical simulations performed for a five-story base-isolated building subject to four benchmark earthquakes indicate that the RPSD is capable of a similar control performance as the RSASD. Furthermore, it is shown that the RPSD dissipates comparable energy to the RSASD using fewer resets for earthquakes characterized by high peak accelerations and high velocity pulses with long periods, i.e., near-field earthquakes.

Multiribbed composite wall structures with an open frame at the bottom (MRCWSFB) have been developed in recent years and increasingly used in China. This paper develops an analytical model to analyze vertical stress distribution of a wall beam in the MRCWSFB. The multiribbed composite wall can be equivalent to the elastic foundation and the trimmer beam can be treated as inverted elastic foundation beam. Therefore, the vertical stress distribution of the wall beam can be obtained using the Pasternak double-parameter elastic foundation beam theory. The accuracy of this model is verified against the results from finite-element analysis. A parametric study is then carried out using the analytical model to study the effects of the section of the frame column, section height of the concealed beam, wall depth, division of the ribbed frame, and the Young’s modulus of filling blocks on the internal forces of the bottom trimmer beams, where the influencing factors are identified.

A computationally efficient technique to simulate the dynamic response of a beam colliding with rigid obstacles is described in this paper. The proposed method merges three key concepts. First, a low-order discretization scheme that maximizes the number of nodes of the discrete model (where impacts are detected) at the expense of the degree of continuity of the constructed displacement field is used. Second, the constrained problem is transformed into an unconstrained one by formulating the impact by using a Signorini complementarity law involving the impulse generated by the collision and the preimpact and postimpact velocity linked through a coefficient of restitution. Third, Moreau’s midpoint time-stepping scheme developed in the context of colliding rigid bodies is used to advance the solution. The algorithm is first validated on the nonimpact problem of a cantilever Rayleigh beam subjected to an impulsive discrete load. Then the problem of a cantilever beam vibrating between two (symmetrically located) stops is analyzed. Both cases of discrete and continuous obstacles are considered, and the numerical predictions are compared with published results or those obtained with a commercial code.

According to classical critical state theory (CST) of granular mechanics, two conditions on the stress ratio and void ratio are satisfied when reaching and maintaining a critical state (CS). Therefore, CST dictates the necessity of these two conditions although their sufficiency has not been demonstrated, but only assumed. The present work challenges this assumption based on the results of a virtual two-dimensional (2D) discrete element method (DEM) experiment. The virtual sample is first brought to CS and then rotation of the principal axes (PA) of stress is imposed while keeping stress principal values fixed. The rotation induces a void ratio reduction and thus, abandonment of CS, despite the fact the two CST conditions are satisfied at the initiation of the rotation process, since the stress principal values remain fixed and the void ratio is at its critical state value for the given fixed pressure. The recently proposed anisotropic critical state theory (ACST) remedies this incompleteness of CST by enhancing its two conditions by a third, related to the critical state value of a fabric anisotropy variable, defined as the trace of the product of the fabric anisotropy tensor and the loading direction tensor. This third condition is violated by the stress PA rotation and can explain the aforementioned void ratio reduction. ACST can also explain various other response characteristics that cannot be addressed by classical CST with no fabric anisotropy consideration. In conclusion, the three conditions of ACST are shown to be both necessary and sufficient for reaching and maintaining CS.