Constitutive Model For Concrete Research Articles

Numerical Analysis of Time-Dependent Strength and Stiffness in Palm Oil Fuel Ash-Stabilized Soil: Early and Long-Term Effects

Over the years, investigating the behavior of soft soil, stabilized using different techniques, has been recognized as a critical priority for geotechnical engineers. Numerous soil constitutive models have been utilized to simulate stabilized soil behavior, improve strength and ductility, and analyze load-deformation responses. However, further investigation is required to study stabilized soil's time-dependent strength and stiffness, especially at an early curing age. Early strength and stiffness development is crucial in engineering construction for improving building quality and efficiency and minimizing crack risk. Furthermore, estimating UCS from an early age aid in safety evaluation and ground-improvement analysis. Researchers are increasingly recognizing palm oil fuel ash (POFA) as an eco-friendly alternative to traditional soil stabilizers due to its abundant availability. This study proposes an advanced concrete constitutive model to simulate the time-dependent strength and stiffness of POFA-stabilized and cement-stabilized soil due to pozzolanic interactions. The model accurately measures strength and stiffness improvement from an early curing age to 28 days using finite element analysis (FEA) before then comparing the experimental results. Based on the experimental results, the UCS values of palm oil fuel ash-stabilized soil grew to 3.18 MPa and 3.89 MPa after seven and 28 days with an optimum content of 30% (POFA): 10% Magnesium Oxide (MgO). It exhibited a significant increase in early strength with 64.02% compared with cement-stabilized soil. For stiffness results, a slight increment of 9.26% was observed. Employing FEM, the sensitivity of the parameters to stress-strain behavior was investigated. Finally, the validity of the concrete constitutive model to predict the time-dependent strength and stiffness of stabilized soil was proved. Doi: 10.28991/CEJ-SP2024-010-05 Full Text: PDF

Ultimate strength of light-rail hybrid cable-stayed bridge including concrete tension softening effect

This paper presents the ultimate strength analysis of a light-rail hybrid cable-stayed bridge and discusses the influences of the concrete tension softening effect (CTSE) which is defined as the tensile strength of concrete being much less than the compressive strength of concrete. Both geometrical and material nonlinearities are considered. The bridge finite element model is established using the ANSYS package, and material nonlinearity is considered through the fiber beam element BEAM189. Also, an algorithm is written using the Fortran language for the uniaxial concrete constitutive model to consider the CTSE, namely the concrete smeared crack model. Results show that the CTSE significantly influences the ultimate strength of the investigated bridge when the side-span concrete girder dominates the failure of the bridge as estimated by calculations. Thus, it is essential to consider the CTSE for the evaluation of the ultimate strength of a light-rail hybrid cable-stayed bridge. Highlights: 1. The line finite element model of a light-rail hybrid cable-stayed bridge including concrete tension softening effect (CTSE) is established. 2. An algorithm is presented for considering the CTSE. 3. The CTSE can significantly influences the ultimate strength of the hybrid bridge.

Development of a Concrete Constitutive Model Considering Free Water Effect for Predicting Dynamic Responses of Concrete Structures

Development of a Concrete Constitutive Model Considering Free Water Effect for Predicting Dynamic Responses of Concrete Structures

Effective Prediction of Concrete Constitutive Models for Reinforced Concrete Shear Walls under Cyclic Loading.

One of the most challenging elements of modeling the behaviour of reinforced concrete (RC) walls is combining realistic material models that can capture the observable behaviour of the physical system. Experiments with realistic loading rates and pressures reveal that steel and concrete display complicated nonlinear behaviour that is challenging to represent in a single constitutive model. To investigate the response of a reinforced concrete structure subjected to dynamic loads, this paper's study is based on many different material models to assess the advantages and disadvantages of the models on 2D and 3D RC walls using the LS-DYNA program. The models consisted of the KCC model and the CDP model, which represented plasticity and distinct tensile/compressive damage models, and the Winfrith model, which represented plasticity and the smeared crack model. Subsequently, the models' performances were assessed by comparing them to experimental data from reinforced concrete structures, in order to validate the accuracy of the overall behaviour prediction. The Winfrith model demonstrated satisfactory results in predicting the behaviour of 2D and 3D walls, including maximum strength, stiffness deterioration, and energy dissipation. The method accurately predicted the maximum strength of the Winfrith concrete model for the 2D wall with an error of 9.24% and for the 3D wall with errors of 3.28% in the X direction and 5.02% in the Y direction. The Winfrith model demonstrated higher precision in predicting dissipation energy for the 3D wall in both the X and Y directions, with errors of 6.84% and 6.62%, correspondingly. Additional parametric analyses were carried out to investigate structural behaviour, taking into account variables such as concrete strength, strain rate, mesh size, and the influence of the element type.

Systematic quantification of modeling uncertainties in tank–foundation coupled systems

Traditionally, uncertainty quantification in the context of liquid storage tanks has primarily focused on ground motion record-to-record variability, along with partial consideration of material randomness. This paper presents a comprehensive framework for addressing “modeling uncertainty” in the seismic analysis of rectangular tanks, including the influence of foundation interactions. The framework encompasses uncertainties inherent in both general finite element and mathematical modeling techniques, as well as uncertainty in modeling parameters (e.g., hydrodynamic mass and concrete constitutive model). This is achieved through the implementation of an efficient design of experiments. By employing an innovative intensifying artificial acceleration, over 26,000 transient simulations are conducted, spanning the full spectrum of structural behavior from linear to nonlinear regimes. Through a series of uncertainty quantification and sensitivity analyses, this study assesses bias and dispersion arising from diverse model assumptions. Furthermore, fragility analysis and machine learning post-processing techniques are employed to extract latent insights from the generated data. The outcomes underscore that numerical and mathematical modeling uncertainties can bear comparable significance to ground motion record-to-record variability. The adoption of distinct modeling strategies introduces biases in fragility curves, particularly within higher damage states. Consequently, it is advised to account for modeling randomness directly (via simulation) or approximately (leveraging the insights from this study) in any uncertainty quantification related to storage tanks.

Confinement mechanism of cross-shaped steel reinforced concrete columns

A novel confined concrete constitutive model for steel-reinforced concrete (SRC) columns with cross-shaped steel (CSS) sections is proposed. The model is based on the similar characteristics of descending branches in the stress–strain curves of confined and unconfined concrete (UCC), considering confinement degradation caused by buckling of the steel section or longitudinal reinforcement. The confined region of SRC columns with CSS sections was divided into four parts: highly steel-confined concrete (HSCC), partially steel-confined concrete (PSCC), stirrup-confined concrete (StCC) and UCC. Relevant effective confinement coefficient expressions were also derived. Simulations of existing tests showed that (a) the load–strain curves obtained using the modified stress–strain constitutive model agreed well with the experimental results, with the error in the descending branch less than 5%; (b) the HSCC region for SRC columns with CSS sections in the finite-element model was in good agreement with that in the proposed region division; (c) the simulation of confined concrete region boundaries for SRC columns with CSS sections were determined using plumb lines for improving the calculation efficiency.

A confined concrete model considering strain gradient effect of CFST column under eccentric load

This paper analyzes the axial and eccentric compression mechanisms of concrete-filled steel tube (CFST) columns and proposes a confined concrete constitutive model that considers gradient effects. The model is based on the gradient effect of stress and strain under eccentric compression to deduce the gradient effect of confinement force, and obtain the calculation formula of confinement force under different eccentricities, so as to obtain the corresponding constitutive model of confined concrete. The model is used to modify the fiber model and Chinese Codes, which are affected by loading eccentricity. Six sets of CFST material constitutive test data are collected to validate the constitutive model. Eight sets of moment-curvature curves of section tests and twelve sets of eccentric compression bearing capacity tests were collected for validation. The data collected from these two sets of experiments were compared with the modified calculation values of the fiber models and the design codes, respectively, to confirm the reliability of the modification effect. The results indicate that the utilization of the model proposed in this paper successfully reflects the influence of eccentric loading on the confined concrete constitutive relationship, improves the prediction accuracy of existing formulas, and facilitates the analysis efficiency of CFST.

Nonlinear finite element analysis of partially encased composite columns under non-uniform moments

This paper presents a numerical investigation to evaluate the behavior of partially encased composite (PEC) columns with compact sections of three different heights submitted to non-uniform moment distribution. A 3D finite element model developed using the software ABAQUS was calibrated based on results from previous experimental research. The influence of concrete constitutive model parameters, column slenderness, load eccentricities, and moment distribution along height was investigated. The parametric study showed that constant moment distribution (case 1) is the most critical compared to linear moment variation (cases 2 and 3). This pattern is a direct consequence of the larger displacements at the mid-height section that causes higher second-order moments in the case 1 column. Long columns activated more confinement when a single curvature bending moment was applied at a minor axis. An increase in slenderness decreased the load capacity for non-uniform bending moments through the major axis.

Predictive maturity of non-linear concrete constitutive models for impact simulation

This paper explores the concept of predictive maturity for non-linear concrete constitutive models employed in the computational prediction of the structural response of reinforced concrete structures to impact from free-flying missiles. Such concrete constitutive models are widely varied in complexity. Three constitutive models were utilized within the same finite element structural model to simulate the response of the IRIS III experiment. Each of the models were individually calibrated with available material testing data and also re-calibrated assuming limited availability of test data. When full calibration is possible, more sophisticated constitutive models appear to provide more predictive maturity; however, when this data is not available (e.g. for an existing structure where representative test specimens may not be available), the expected maturity is reduced. Indeed, this hypothesis is supported by the simulations that indicate good agreement with measured experimental response quantities from the IRIS III tests with complex constitutive models and full calibration, and accordingly poor predictions when less complex models are used or when the more sophisticated models are poorly calibrated. Thus, predictions of structural response where complete material testing data is not obtainable should be understood as less predictive.

Investigation of constitutive models of HPFRCC subjected to static and dynamic loadings

High-performance fiber-reinforced cement composite (HPFRCC), an advanced construction material, has superior material properties than normal concrete. As concrete constitutive models, such as the Karagozian & Case (K&C) and continuous surface cap (CSC) models, are utilized in various numerical analyses of HPFRCC structures under static and dynamic loadings, here, calibration methods for these two constitutive models are suggested to describe the material behaviors of HPFRCC more precisely based on uniaxial and triaxial test data. Multi-element analysis of laboratory material tests is performed on the calibrated models with four different element sizes not only to examine their reliability but also to investigate their mesh-size dependency. Moreover, the differences in the performance of these models are analyzed in terms of their theoretical background, and numerical simulations are performed on the HPFRCC structures subjected to a low-velocity impact as well as near-field blast tests. By comparing the numerical and experimental results, the CSC model is found to exhibit strength for simulating crack distribution at low strain rates, whereas the K&C model shows reasonable predictions of the failure behavior of HPFRCC structures at high strain rates.

Seismic Behaviors of Novel Steel-Reinforced Concrete Composite Frames Prestressed with Bonding Tendons

To investigate the seismic behaviors of novel steel-reinforced concrete composite frames prestressed with bonding tendons (PSRCFs), 15 groups of PSRCF specimens were designed with the following main parameters: the cubic compressive strength of high-strength concrete (fcu), the axial compression ratio of frame columns (n), the slenderness ratio of frame columns (β), the steel ratio of angle steel (α), the span–height ratio of frame beams (L/hb), and the prestressing degree (λ). Based on the modified concrete constitutive model proposed by Mander and the prestressing effect applied by the cooling method, the finite element models of PSRCFs were established by using ABAQUS software, the static analysis on the frame structures under the combined actions of axial forces and horizontal loads was carried out, and the monotonic load–displacement curves were explored. By comparing with the skeleton curves obtained by the experimental hysteretic curves, the rationality of the modeling method was verified. The PSRCFs had good mechanisms of strong columns and weak beams. Based on this, the influences of different parameters on the seismic behaviors such as hysteretic curves, skeleton curves, stiffness degradations, energy dissipation capacities, and ductility of the specimens were investigated. The results show that the hysteretic curves of the PSRCFs are full and have no pinch phenomenon. The ultimate load and the stiffness degradation of specimens can be improved significantly by increasing α, and on the contrary, the ultimate load and stiffness degradation decreased by increasing β. The ductility of the specimens decreased gradually with the increasing β and n. The energy dissipation capacity of the specimens decreased with the increasing β. The trilinear model of the skeleton curves and the restoring force model of PSRCFS were established by statistical regression, which agree well with the numerically simulated results. These can provide theoretical support for the elastoplastic analysis on this kind of PSRCF structure.

A modified K&C model for concrete subjected to coupled effect of high temperature and high strain rate

The K&C model is a commonly used constitutive model for concrete that simulates its dynamic response to blasts and impacts. However, this model is calibrated using data obtained at room temperature and is therefore not suitable for high-temperature conditions. To address this limitation, we propose a new constitutive model, named the KC-HT model, which is based on extensive modifications to the commercially available K&C model. The new model incorporates a failure surface that takes into account the temperature effect, which was established through triaxial compressive tests performed at high temperatures. The plastic hardening and softening behaviors of heated concrete are also considered by a new damage determination algorithm. The KC-HT model was integrated into the ABAQUS software using the VUMAT interface for simulation purposes, and its accuracy was confirmed through both single-element simulation and numerical SHPB tests. Finally, the KC-HT model was further validated by predicting the dynamic behavior of fire-damaged RC beams. The results reveal that the KC-HT model can replicate the dynamic behavior and crack morphology of concrete with different fire durations, while the K&C model is unable to take into account the temperature effect or the combined effect of high temperature and high strain rate.

Experimental and Numerical Analysis of the Ribbed Reinforced Concrete Fracture Behavior Based on the Mesoscale FE Model

This study presented a meso-model for the fracture analysis of the reinforced concrete (RC) structure. A modeling method of RC meso-structure was proposed, and the rebars were allowed to separate from the concrete. The model was built using the cohesive zone model (CZM). The zero-thickness cohesive elements were adopted to characterize the mechanical behavior of potential fracture surfaces and rebar–concrete interfaces. The constitutive model for concrete was developed by considering the damage relation and friction effect, and the corresponding constitutive for the rebar–concrete interface (especially ribbed rebar) was developed by considering the influence of normal separation on the tangential bond–slip relation. To validate the proposed meso-model, a series of ribbed RC beams with an initial notch was designed and tested by four-point bending loading to obtain different fracture patterns. Through comparison, the developed RC meso-model was validated to simulate the RC structure's fracture behavior appropriately. The influence of the rebar–concrete interface constitutive model on the simulation results was investigated. The investigation results indicate that neglecting normal separation would result in an overestimation of the structure's stiffness and bearing capacity (the peak load was overestimated by more than 10%). Finally, an analysis was conducted on the energy consumption during the failure process of the RC beams. It was found that the proportion of energy consumption during tensile failure of the beam decreased from approximately 86% to 89% in the early stage to approximately 43% to 52% in the later stage, indicating a transition in the beam's failure mode from tensile failure to shear failure.

An elastoplastic damage constitutive model for capturing dynamic enhancement effect of rock and concrete through equivalent stress history

The strength enhancement effect of rock and concrete under dynamic loading is one of the significant response characteristics differing from quasi-static loading. Typically, current dynamic constitutive models describe this phenomenon by adopting strain/stress rate dependent functions. In this study, a novel elastoplastic damage constitutive model that captures the dynamic strength increase through the equivalent stress history is developed by coupling the incubation characteristic time (ICT) criterion and the unified strength theory (UST). Specifically, the ICT criterion substitutes the stress history for the strain/stress rate to predict dynamic yield strength of rock and concrete. And the equivalent stress expressed by the UST provide an appropriate selection of the stress history in the ICT criterion under complex stress states. Furthermore, based on the non-associated plastic flow rule and the plastic-damage evolution law, combined with the equation of state, the proposed constitutive model is established and implemented numerically. The dynamic stress-strain curves of granite were reconstructed by a series of numerical tests on a single element, which verified the accuracy of the proposed constitutive model and the reliability of the numerical algorithm by comparing the experimental data. The proposed model was applied to the numerical simulation of dynamic compression-shear tests on inclined sandstone specimens loading by the split Hopkinson pressure bar (SHPB) and fragmentation experiments of single borehole granite specimens under blast loading, respectively. And the experimental dynamic crack patterns on the specimen surface captured by high-speed cameras match the simulated damage distribution well. In addition, several common concrete constitutive models and the proposed model were employed to simulate the dynamic response of reinforced concrete beams under near-field blast loading. The damage patterns and the mid-span residual displacement calculated numerically by the proposed model are more consistent with the experiments than other concrete models. As a conclusion, the proposed model, coupled the ICT criterion and the UST, provides a new perspective and paradigm for characterizing the responses of rock and concrete subjected to intense dynamic loads.

Assessment on concrete constitutive models for numerical simulations of vehicular collisions with RC bridge piers

Accident statistics showed that vehicular collision caused serious shear damage or failure of reinforced concrete (RC) bridge piers and even resulted in overall collapse of bridge structures. For the resistance evaluation of RC components under impact loads, numerical simulations have been performed by adopting different concrete constitutive models and obtained different results, e.g., Karagozian and Case Concrete (KCC) model and Continuous Surface Cap (CSC) model widely used, as well as Kong-Fang (KF) model recently proposed. This study mainly evaluates the accuracy of the above three concrete constitutive models in numerical analyses of vehicular collisions with RC bridge piers. Firstly, basic mechanical behaviors of these models are systematically compared based on single element simulations. Then, the scope of investigation is extended to component level by simulating a drop hammer test on RC beam and a lateral impact test on RC column, and the dynamic behaviors of impacted RC components are deeply compared. Finally, these models are further compared at structure level through performing the refined numerical simulation of a real truck colliding with a prototype bridge and evaluating its global structural behaviors and damage. The results show that, (i) KF model well reflects the post-peak softening behavior, stable strain-rate effect and independence of mesh size of concrete materials under uniaxial loading conditions at different loading rates; KCC and KF models both capture the brittle to ductile transition of concrete materials with increasing confinement pressure; (ii) KF model yields a better prediction in dynamic responses and damage characteristics of impacted RC beam and column, while KCC and CSC models both overestimate the damage degree; (iii) KF model better simulates the shear failure of RC pier in the real accident and provides the reasonable structural dynamic responses, but KCC and CSC models much underestimates the damage degree of impacted bridge pier and adjacent components.

A machine-learning-based model for seismic performance assessment of interior slab-column connections

Slab-column connections are the most critical components in flat plate systems under seismic actions due to their brittle failure mode. Finite element analysis (FEA) can be adopted as an extension of experimental testing to potentially lead to the development of modern design codes by providing significant information on the punching shear failure process of connections. However, the available concrete constitutive models in FEA packages fail in simulating the hysteretic response of the connections under cyclic loads. Moreover, it is shown that the available design code recommendations and empirical models are not accurate tools for assessing the seismic performance of these connections (e.g., unbalanced moment and/or drift capacity). In an effort to overcome these limitations, a dataset of previously tested experiments is compiled to predict the ultimate load and drift of the connections using the multi-variate non-linear regression model. Additionally, there is a need to develop a new constitutive material model for seismic performance assessment of the connections to capture the complete hysteretic response of the connection using numerical FEA. Consequently, a deep neural network is trained over the accumulated dataset and integrated into the OpenSees source code to determine the seismic performance of the connections. For data augmentation, a generative neural network model of autoencoders known as Generative Adversarial Networks (GANs) is constructed to generate synthetic data. The proposed material model is found to have significantly improved precision in capturing the hysteretic response of flat plates. The developed models showed higher accuracy than the design code estimations and empirical models.

Numerical Investigation of Axial Force–Bending Moment Interaction for FRP-Confined Reinforced Concrete Columns with Internal Steel Transverse Reinforcement

Externally bonded fiber-reinforced polymer (FRP) laminates are widely used in the retrofitting and rehabilitation of reinforced concrete (RC) columns because they can increase the axial and bending moment capacities of these columns through a confinement mechanism. The confinement produced by FRP laminates acts in addition to that exerted by the internal transverse steel, although the latter is often neglected in current design standards and guidelines. In this study, a recently developed FRP-and-steel-confined concrete constitutive model was employed to numerically investigate the axial force–bending moment interaction for FRP-confined RC columns modeled using finite-element (FE) analysis. The proposed model was first validated against experimental data available in the literature and then used to quantify, through an extensive parametric study, the effects of transverse steel confinement, FRP strength, FRP stiffness, FRP reinforcement ratio, column diameter, concrete compressive strength, and load eccentricity ratio on the strength of FRP-confined RC columns subject to combined axial compression and bending moment. It was found that the internal steel confinement can substantially enhance the strength of these columns, especially for low concrete compressive strengths, large cross sections, and small eccentricities. When design code provisions limiting concrete and FRP deformations were considered for eccentrically loaded columns, the contribution of the steel confinement increased for increasing FRP reinforcement ratio. Based on the parametric study results, this investigation proposed an extension to eccentric axial compression of two relative confinement coefficients, which were previously developed to describe the contribution of transverse steel confinement to the peak strength of FRP-confined RC columns subject to pure compression.

Numerical modeling of the damage mechanism of concrete-soil multilayered medium subjected to underground explosion using the GPU-accelerated SPH

The prediction of the damage mechanism of the concrete-soil multilayered medium subjected to underground explosion is a challenging task to address. In this paper, the smoothed particle hydrodynamics methodology is introduced to deal with the soil fragmentation and fracture propagation in concrete which are involved in the physical process of explosion in this double-layered medium. The Drucker–Prager constitutive model and the Holmquist–Johnson–Cook concrete constitutive model are employed to describe the dynamic behavior of the soil and concrete, respectively. Firstly, the numerical model was validated by two cases, namely the high velocity impact of an aluminium sphere on a concrete plate and the fracture propagation of rock medium under blast loading. Subsequently, the explosion in the three-dimensional concrete-soil multilayered medium involving millions of particles was simulated and investigated using GPU-accelerated smoothed particle hydrodynamics methodology. The numerical results obtained using smoothed particle hydrodynamics are compared against the available experimental data, which shows that the present SPH model can reproduce the failure pattern and fracture propagation of the concrete medium with cylindrical hole in the concrete plate and different burial depths of the explosive.

The two-level probabilistic description of the compressive constitutive parameters of concrete

The constitutive model of concrete is the critical basis for the nonlinear analyses of concrete structures. Due to the fact that the mechanical behavior of concrete exhibits remarkable randomness, the probabilistic modeling of the key parameters of the concrete constitutive model is of paramount significance. In the present study, a two-level probabilistic model is proposed to describe the dependent random constitutive parameters based on the compressive test results of several batches of concrete specimens of different strength grades. Both the local probabilistic dependence, i.e., the dependence of the parameters of intra-batch specimens, and the global probabilistic dependence, i.e., the dependence of the parameters of inter-batch specimens, are captured by the proposed method. To this end, the constitutive parameters of concrete are first standardized by their means and coefficients of variation (COVs). In this way, the local dependence can be represented by the same copula model for the concrete of different strength grades. The global dependence is expressed as the empirical formulae in terms of the means and COVs of the parameters. The full probabilistic model can then be obtained by synthesizing the local and global dependence models. The effectiveness of the proposed approach is demonstrated by comparing the generated samples with the test results. To illustrate the effect of the probabilistic dependence of the compressive constitutive parameters on the structural evaluation result, the nonlinear stochastic dynamic response analysis of a reinforced concrete frame is carried out. The results indicate that the probabilistic dependence of the constitutive parameters of concrete has a non-negligible effect on the structural response and reliability, and should be reasonably considered in practice.

Axial compressive performance of ultra-high strength concrete-filled dual steel tubular short columns with outer stiffened tubes and inner circular tubes

Previous literature shows that studies of ultra-high strength concrete-filled dual steel tubular (UHS-CFDST) short columns under concentric compression are rare, and there is no relevant research on ultra-high strength concrete-filled dual stiffened steel tubular (UHS-CFDSST) short columns. In addition, existing design specifications do not include ultra-high strength concrete (UHSC). Therefore, the axial compressive response and resistance of UHS-CFDSST short columns are investigated herein. First, the behaviour of CFDSST columns with normal-strength concrete (NSC) was replicated by finite element (FE) modelling using ABAQUS software. Additionally, the experimental results of square and circular ultra-high strength concrete-filled steel tubular (UHS-CFST) short columns were collected from the available literature, and finite element (FE) modelling is performed accordingly. The results showed that the applied concrete constitutive model is suitable for UHSC and the modelling strategy for UHS-CFST columns and CFDSST columns with NSC is suitable for UHS-CFDSST short columns. Accordingly, parametric studies were carried out on UHS-CFDSST to investigate the effects of geometrical and material properties of different steel and concrete components on the performance of these columns. It was found that the strength of the sandwiched concrete has the greatest effect on the resistance of the columns compared to the other parameters considered. Finally, the axial resistance of the UHS-CFDSST short columns was compared to the resistances calculated by using the European, British and Chinese codes, and it was found that the Chinese code gives the best results.