Concrete Material Model Research Articles

Finite element modelling of RC slabs retrofitted with CFRP strips under blast loading

This paper presents nonlinear finite element (FE) simulations to predict the structural behavior of simply supported reinforced concrete (RC) slabs retrofitted with carbon fiber reinforced polymer (CFRP) as externally bonded reinforcement (EBR) and subjected to the blast loads in order to evaluate the effectiveness of using the CFRP strips as EBR for blast protection. The objective of this paper is to develop detailed numerical models in order to predict the blast response of non-retrofitted and retrofitted RC slabs during the inbound and rebound phases. A plastic material model including the strain rate effects of the material and able to predict the cracks is used to model the concrete. An elasto-plastic material model and an elastic material model are used to model the steel reinforcement and the CFRP strips, respectively. The bond interface between concrete and CFRP strip is simulated using a special contact algorithm including the strain rate effect at the interface between concrete and CFRP strip with failure criteria. The numerical results are validated by experimental tests. The maximum deflections, crack distribution and strain evolution in the steel reinforcement and in the CFRP strips found by the numerical analysis are in good agreement with the experiments. The concrete material model gives a good prediction of the blast response of the RC slab with and without EBR. Increasing the amount of the CFRP strip reduces the maximum deflection at the mid span of the slabs and the strain distribution in the steel reinforcement and in the CFRP strip. Parametric studies with respect to CFRP width and CFRP thickness are performed in order to evaluate the effects on the blast response of the RC slabs.

Damage characteristics of high-performance fiber-reinforced cement composites panels subjected to projectile impact

The authors examined both experimental and numerical studies on the structural response of high-performance fiber-reinforced cement composite (HPFRCC) panels with a matrix strength of 180 MPa and a high fiber content from 1.0 to 3.0% subjected to projectile impact. The failure mechanism, such as penetration and scabbing, of HPFRCC panels was experimentally investigated according to volume fractions, the thickness of specimens, and impact velocities. The effect of fiber volume fraction and thickness on the compressive and tensile performance of HPFRCCs was also assessed through a comparison with empirical equations. In addition, a finite element model was established by using LS-DYNA to predict the impact behavior of the panels with calibration of a concrete material model based on previous experimental data. The numerical simulations of HPFRCC panels subjected to impact were verified through comparisons with the experimental results. Based on the verified FE model, a parametric study was also conducted and discussed to better understand the mechanical characteristics of HPFRCC panels under impact loading.

Simulation of projectile impact on steel plate-lined, reinforced concrete panels using the smooth particle hydrodynamics formulation

Data from the Tsubota et al. (1993) experiments provided the basis for a numerical study that investigated the impact response of steel-plate lined, reinforced concrete panels using the SPH formulation in LS-DYNA. The simulated tests involved 50 mm (1.97 in), 70 mm (2.76 in), and 90 mm (3.54 in) thick reinforced concrete (RC) panels with steel liners and one 50-mm thick benchmark RC panel. Three of the five panels had a steel liner attached to the back face and one had a steel liner on both faces. The panels were normally impacted by a 39.6 mm (1.56 in) diameter projectile at a velocity of 170 m/s (6693 in/s). Reasonable predictions of observed damage, including perforation, liner fracture or bulging, and concrete scabbing were achieved using the MAT072R3 concrete material model. The effectiveness of adding steel liners to a concrete panel to prevent perforation and scabbing resulting from projectile impact was investigated using the numerical model and MAT072R3. Installing a steel liner on the back face of a panel, with a reinforcement ratio equal to that of the internal reinforcement, is an effective method to mitigate scabbing but has little effect on perforation resistance.

Numerical and experimental study of externally reinforced RC slabs using FRPs subjected to close-in blast loads.

The use of woven Fiber Reinforced Polymer (FRP) as strengthening material on full-scale Reinforced Concrete (RC) slabs was studied in this paper. Carbon (CFRP) and E-glass (GFRP) fibers were tested for comparison. The specimens of the trials were subjected to blast loads at scaled distances of 0.83 m/kg1/3, 0.42 m/kg1/3 and 0.21 m/kg1/3, varying both charge and distance to the slab. Furthermore, Finite Element (FE) numerical models have been developed to study, in-depth, the response of the structural elements. A non-reinforced slab facing the highest scaled distance has been used as calibration test. It was monitored with pressure gauges and accelerometers, obtaining errors of around 2% and 5%, respectively, compared with the models’ predictions. Seven other trials were carried out and used as validation tests. The explosive charge model was developed using the *LOAD_BLAST_ENHANCED (LBE) tool available in the LS-DYNA software. Two concrete material models have been tested, CSCM and RHT, achieving better results with the first one. To model the FRP reinforcement, *MAT_058 (LAMINATED_COMPOSITE_FABRIC) was used. Applying CFRP resulted in a generally reduced damage area on both surfaces especially at intermediate scaled distances. Concerning the specimens reinforced with GFRP, further investigation needs to be conducted as the field test outcomes were not entirely conclusive due to the bonding of the fiber on concrete. The experimental results were closely reproduced with the developed numerical models, with errors in terms or surface damage below 15%.

On the possibility of using damaged plasticity models in the assessment of structural response of gravity beams

Advent of concrete damaged plasticity material models has drastically improved the accuracy in predicting the structural response of concrete structural elements using finite element Analysis. However, exploration of the accuracy of this method in analysing complex concrete forms is scanty. Gravity Beams, a term coined in this investigation, are those beams in which gravity is used to design the topology of beam form conjointly with the novel manufacturing strategy ‘Fabric Formwork’. In this investigation these beam forms were numerically analysed using prevalent material and damage models. Numerical structural response was evaluated using these models and compared to experimental response. It was deduced from the comparative evaluation that numerical models closely predict the structural response of gravity beams. Moreover, dissimilarity analysis revealed that the diversion of the results was due the shape error between Modelled gravity beams, which were used for numerical analysis, and actual 3D scanned beams. It was deduced after analysis of experimental and numerical failure patterns that local imperfections also play a major role in the deviation in the numerical model. Furthermore, cross-sectional proportion ratio (CPR) was also introduced to give a numerical identity to gravity beams. This ratio was used to frame a parametric comparison of gravity beams and the corresponding structural response, to explore the parametric dependency.

Structural Life Analysis of Roller-compacted Concrete Asphalt Pavement

Based on the long-life test road of Yunluo expressway in Guangdong province, firstly, based on the theory of small disturbance elastic thin plate and the design code of the highway cement concrete pavement, the life analysis of the roller-compacted concrete pavement structure of the Yunluo long-life test road is carried out. The results show that the pavement structure can achieve a 53.2 years long-life. Secondly, in order to verify the reliability of the theoretical analysis results, the strain sensors and the temperature sensors were embedded in different layers of the test road. After years of continuous data collection and based on the constitutive model of the roller-compacted concrete material, the theoretical analysis of the results concluded that the pavement structure can achieve at least 45 years life. The results of theoretical and practical analysis show that the new type asphalt pavement structure on the roller-compacted concrete base can be used as a typical long-life asphalt pavement structure under high temperature, rainy and heavy load conditions in Guangdong province.

Anisotropic damage model for concrete and other quasi-brittle materials

A thermodynamically consistent formulation to model anisotropic damage for quasi-brittle materials is proposed. The model is based on proper expressions for the specific Gibbs free energy and the complementary form of the dissipation potential. Damaging of the material is described by a symmetric positive definite second order damage tensor. Especially, the failure surface is formulated in such a way that it will mimic the behaviour of the well known Ottosen’s four parameter failure surface. While testing the model against the experimental results found in literature, the results were in good agreement in uniaxial tensile and compressive loadings as well as in biaxial compression. Besides the correct failure stress states, the model predicts the correct failure modes of concrete: axial splitting along the direction of uniaxial compression and tensile damaging normal to the direction of tension.

Modification of the Constitutive Model of Concrete Material Considering the Effect of Structural Size

As the size of the structure increases, the size effect on the mechanical properties of the structure cannot be ignored. During the service period, the reinforced concrete structure will be affected by the size effect. At present, there is no item concerning material size effect in the current regulations in my country. This paper summarizes the existing size effect theory and finds a function that expresses the size effect of concrete. The peak strength size effect coefficients of domestic and foreign researchers are analyzed, and the logarithmic function form is used to calculate the peak strength size effect coefficients obtained by various researchers. The average value was fitted. We found the size effect coefficient of the ultimate strain of concrete based on the test results, and took the size effect coefficient of the ultimate strain of the concrete with a cube side length of 150 mm as one for analysis. Finally we revised the constitutive relationship of concrete.

Simplified Nonlinear Simulation of Rectangular Concrete-Filled Steel Tubular Columns

In detailed three-dimensional (3D) finite-element modeling, two-dimensional and/or 3D elements are widely used because of their high accuracy and ease of use despite the high computational cost. In contrast, simplified modeling based on fiber beam element (FBE) formulation is preferred for developing macro models to simulate structural frames due to its simplicity and computational efficiency. As for the FBE simulation of concrete-filled steel tubular (CFST) columns, its accuracy largely depends on the input steel and concrete material models, which should implicitly consider the material nonlinearity and interaction between the steel and concrete components. The authors have previously developed a FBE model for circular CFST columns, and this paper is a continuation of the previous work. In this paper, uniaxial effective stress–strain relationships are developed for the steel and concrete materials in rectangular CFST columns based on rigorous analysis of data generated from 3D finite-element modeling of stub columns. Thus, the material models have implicitly considered the effects of yielding and local buckling of the steel tube and passive confinement to the concrete. Meanwhile, the size effect is also considered in the concrete model. The accuracy of the proposed material models is verified against a database of rectangular CFST stub columns covering a wide range of material and geometric parameters. The developed material models are further used to simulate rectangular CFST slender columns and beam-columns, and a reasonably good agreement is achieved between the experimental and predicted load–deformation curves.

Constitutive modelling of UHPCC material under impact and blast loadings

Ultra-high performance cement based composite (UHPCC) is a prospective material for protective structures subjected to intensive loadings such as impact and blast due to its prominent dynamic mechanical properties. With the aid of an accurate material model, numerical simulation plays an increasingly important role in prediction of dynamic responses of UHPCC structures. It is known that existing concrete material models are developed for traditional concrete and cannot be applied to UHPCC material directly. In the present study, a new constitutive model of UHPCC material under impact and blast loadings is developed, which involves proposing a new tensile damage model for UHPCC which is then incorporated into the Kong-Fang material model recently developed (Int J Impact Eng 2018, 120: 60-78), and calibrating parameters of this modified material model based on existing test data. The modified material model for UHPCC is implemented into the finite element code LS-DYNA through user defined material model. Single element tests including unconfined uniaxial compression and tension and triaxial compression are firstly conducted to demonstrate the improved performances of the modified material model for UHPCC material. Then three selected experiments on UHPCC structures subjected to impact and blast loadings are numerically simulated and compared with corresponding experimental data. Numerical predictions by the modified material model are well consistent with experimental data in terms of impact force, deflection and failure.

Study on Modeling Method of Reinforced Concrete Pier Based on OpenSees

In this paper, the method of model established on reinforced concrete pier based on OpenSees was studied, and the parameter sensitivity analysis to OpenSees was carried out according to the test data. On the basis of introducing the related material model and element type, how to determine material model and element division as well as section meshing were studied, and the method of model established both reasonable and effective was given. The model of concrete material which can improve the convergence of calculation and the model of reinforced materials which can simulate elastic and reinforced plastic stage accurately were given in this paper. The results show that the distributed plastic beam-column element based on displacement can get higher calculation precision. At the same time, the bridge pier structure should be meshed sufficient number of elements and girds to meet the requirement of calculated accuracy.

Experimental and numerical studies of tubular concrete structures subjected to blast loading

The E39 coastal highway route along the west coast in Norway is envisioned a future without ferries. A submerged floating tube bridge built in concrete has been suggested as a means of crossing wide and deep fjords, and an internal blast load against this structure could have disastrous consequences. To investigate the response of tubular concrete structures subjected to blast loading, standard off-the-shelf concrete pipes were tested using live explosives. The tests were monitored by high-speed cameras and pressure sensors. Three different positions for the explosive charges were used and the charge size was varied for each position. It was found that a contact charge detonated from the outside requires approximately twice the explosive amount to breach the pipe than a contact charge detonated from the inside, suggesting a significant confinement effect. Charges placed in the centre of the cross-section produced longitudinal cracking and fragmentation. Measurements show that the pressure inside the pipe is notably higher than immediately outside. As one would expect, reinforcement increased the blast capacity of the pipes significantly. Material test specimens (cubes and cylinders) were cut from the pipes and tested quasi-statically to determine the mechanical properties. The material tests were used to calibrate a concrete material model for finite element simulations, where the blast load was described by a particle-based method. The structural response from the simulations showed good agreement with the experimental data. This applied to the contact charges as well although no special measures were taken to account for the contact detonation.

Numerical study and experimental tests on full-scale RC slabs under close-in explosions

This paper investigates the response of three reinforced concrete slabs subjected to a dynamic (explosive) load at close range, through full-scale testing and its subsequent simulation with numerical models. The first slab was subjected to 1.74 kg of TNT equivalent at one-meter distance and instrumented with pressure and acceleration sensors. In the second slab, the load was increased to 13.05 kg of TNT equivalent while maintaining the distance; finally, the load from the second case was maintained but the distance was decreased to half a meter. The results of the three slabs were compared with respect to the concrete damage surfaces. A well-known Finite Element (FE) model with LOAD BLAST ENHANCED (LBE) tool has been used to numerically describe the slab and the explosive charge, respectively. Three different concrete material models have been used for the description of the first slab with the FE-LBE model. Numerical models adopting coupled Finite Element (FE) and Smoothed Particle Hydrodynamics (SPH) (for the charge definition) have also been developed for the same slab, including the three concrete material models and two alternatives to describe the explosive mass. After comparing the damage evolution with different material models for the concrete in the first test, the remaining tests have been simulated with the concrete model that presented the best results. In the FE-SPH models the load has been simulated with three geometries (cylinder, cube and bag) to account for the uncertainty in geometry of the explosive charge. The cylindrical charge is the best replicating the detonation pressure, the cubic charge is the best reproducing the surface damage and the bag shaped gets the best results regarding the acceleration. FE-SPH models are able to reproduce the shape of the surface damage slightly better than the classic FE-LBE, an important finding when the explosive charges are not spherical. On the contrary, the ratio of surface damage is closer to that obtained in the tests for the FE-LBE models compared to the FE-SPH models.

Finite element modelling of plain and reinforced concrete specimens with the Kotsovos and Pavlovic material model, smeared crack approach and fine meshes

Modelling of concrete through 3 D constitutive material models is a challenging subject due to the numerous nonlinearities that occur during the monotonic and cyclic analysis of reinforced concrete structures. Additionally, the ultimate limit state modelling of plain concrete can lead to numerical instabilities given the lack of steel rebars that usually provide with the required tensile strength inducing numerical stability that is required during the nonlinear solution procedure. One of the commonly used 3 D concrete material models is that of the Kotsovos and Pavlovic, which until recently it was believed that when integrated with the smeared crack approach, it can only be used in combination with relatively larger in size finite elements. The objective of this study is to investigate into this misconception by developing different numerical models that foresee the use of fine meshes to simulate plain concrete and reinforced concrete specimens. For the needs of this research work, additional experiments were performed on cylindrical high strength concrete specimens that were used for additional validation purposes, whereas results on a reinforced concrete beam found in the international literature were used as well. A discussion on the numerical findings will be presented herein by comparing the different experimental data with the numerically predicted mechanical response of the under study concrete material model.

Shear behaviour of ambient cured geopolymer concrete beams reinforced with BFRP bars under static and impact loads

The use of fiber reinforced polymer (FRP) bars in GeoPolymer Concrete (GPC) structures has drawn increasing attention in recent years. The application of GPC with basalt fiber reinforced polymer (BFRP) reinforcements in replacing Ordinary Portland cement Concrete (OPC) and steel reinforcements leads to green and sustainable constructions. Currently, very limited studies have been conducted to investigate the performance of GPC beams reinforced with BFRP bars under static loads, but no study on their performance under impact loads has been reported yet in open literature. In this study, ambient-cured GPC beams reinforced with BFRP bars were designed, cast and tested under static and impact loads. The damage mode and quantitative results such as midspan deflection, reinforcement strain, and impact and reaction forces were recorded and analysed. Test results showed that spiral stirrups led to superior performance of the beams under both static and impact loads as compared to conventional rectangular stirrups. The commonly used concrete material model *Mat_072R3 in LS-DYNA was modified based on test data to model GPC material. With the modified GPC material model, numerical models were developed and calibrated against the impact test results. Parametric studies were carried out to investigate the influences of GPC material strength and longitudinal and stirrup reinforcement ratios on the performance of beams subjected to impact loads. It was also found that using steel bars as the compression reinforcements led to better performance because BFRP bars under shear and compression were vulnerable to splitting damage subjected to impact loads.

Modelling damage mechanisms of concrete under high confinement pressure

Dynamic failures (e.g., crater, crack and spall) can be observed in concrete structures when suffered from possible blast and impact loadings. Understanding the physical mechanisms behind these failures needs a sound material model that thoroughly considers the damage mechanisms of concrete material, especially under the high confinement situation existed near the projectile and explosion. Modelling the damage mechanisms is a challenging problem that is not fully resolved in the commonly-used concrete material models. In this study, three kinds of damage mechanisms of concrete material, i.e., the hydrostatic damage due to pore collapse, shear damage due to shear-induced microcracking and tensile damage due to tensile microcracking are identified and physically modelled respectively using corresponding damage indexes. The interaction of the three damage is also considered by introducing two stress-dependent factors. The damage model is implemented into the Kong-Fang material model recently proposed, in which improvements on the strength surfaces, strain-rate enhancement and erosion criterion are accompanied made based on a few years use of this model. Numerical triaxial compression test and hydrostatic compression to unconfined compression test are conducted using a single element to validate the proposed hydrostatic damage model and the shear damage model. And the competition mechanism between hydrostatic damage and shear damage during the triaxial compression test is discussed. Then the modified Kong-Fang model is used to numerically simulate the reinforced concrete slabs subjected to a contact explosion load and projectile impact load, in which the physical mechanisms of the experimentally observed crater, crack, tunnel and spall failures are revealed.

Numerical investigation of FRP-confined short square RC columns

Finite element (FE) simulation of confined RC columns is a complex task, as it involves the precise representation of a concrete material model that could express the volumetric change of concrete under a triaxial state of stress. The problem of confining RC columns using fiber-reinforced polymer (FRP) is more complex. This is due to the passive nature of FRP containment. Recently, the concrete damage plasticity (CDP) model available in an FE software product (ABAQUS) has been widely used to represent RC columns subjected to axial loading. The present paper aims to calibrate the concrete dilatancy angle and viscoplastic regularization parameters in the CDP model for the applications of square RC columns confined with FRP sheets. Ten experimental FRP-confined RC column specimens are incorporated in the calibration. In addition, a parametric study is investigated, including 96 cases, to obtain the influence of various design variables on the ratio between the confined to unconfined concrete compressive strength (fcc/fc). Four design variables are considered (i.e., the corner radius, concrete compressive strength, FRP reinforcement ratio, and cross-sectional size of columns). The study also focuses on assessing the reliability of four design codes: ACI-440, ECP-208, CSA-S806 and FIB-Bulletin-14. The numerical results show that a viscoplastic regularization with a fixed value equal to 0.0005 could provide accurate behavior. Nevertheless, the dilation angle cannot be considered a fixed value and should be related to the confinement degree coefficient Cd, which depends on the cross-sectional geometrical and FRP properties. Among the four considered design codes, ACI-440 and ECP-208 provide more accurate behavior than CSA-S806 and FIB-Bulletin-14.

Kinetic Energy Penetrator (KEP) impact on confined concrete

Understanding concrete response facing warheads threats is important for both the design of strategic infrastructure protection and the prediction of warhead performances. This ongoing study aims at building a robust approach for the characterisation of concrete behaviour under ballistic impact of Kinetic Energy Penetrator (KEP). A set of tests has been developed and performed to fit the main parameters of the Holmquist Johnson Cook Concrete material model. Highly instrumented tests are conducted to improve the model prediction capability and to identify its limits. After a brief description of the test configuration, the paper focuses on the analysis of an impact test and presents preliminary simulation results.

Modelling the Tensile Softening Behaviour of Concrete in LS-Dyna Software

The problematic of the paper focuses on the numerical modelling of tensile softening behaviour of concrete. For this purpose, the explicit finite element software LS-Dyna contains several nonlinear material models. The tensile softening behaviour of a total of four selected explicit nonlinear concrete models (namely the Concrete Damage models Release 1 and Release 3, the Winfrith Concrete model and the Continuous Surface Cap model) is tested within numerical simulations of this paper. The task used within the numerical simulations is represented by so-called UUT (Unconfined Uniaxial Tension) test. For this test, specific concrete specimens are used. The numerical simulations are performed with using explicit finite elements. Results of numerical simulations are shown by l-d (load-displacement) diagrams of the UUT test for individual nonlinear concrete models. These results are compared with results obtained from the laboratory measurements for the purpose of validation of the numerical models. The comparisons enable to obtain information about differences between individual nonlinear concrete material models in terms of the tensile softening behaviour. They also show the accuracy of approximations of experimental results by numerical simulations. Based on the comparisons, it can be concluded which nonlinear material models are best for the description of behaviour of concrete in uniaxial tension. Based on the obtained results, it can further be discussed the suitability of nonlinear concrete models in terms of other tests for measuring the tensile mechanical properties of concrete.

Flexural behaviour of ambient cured geopolymer concrete beams reinforced with BFRP bars under static and impact loads

The applications of GeoPolymer Concrete (GPC) with basalt-fiber-reinforced-polymer (BFRP) reinforcements could be alternative for conventional structural designs with Portland Cement Concrete reinforced with steel bars for green and sustainable constructions. Very limited studies, however, have been carried out to investigate the performance of GPC beams reinforced with BFRP bars subjected to static loads, and no study of their performance under impact load is available in open literature yet. In this study, ambient-cured GPC beams reinforced with BFRP bars were tested under static and impact loads. Their damage modes, static and dynamic responses were recorded and analysed. The test results showed that the beams experienced flexural failure mode under static load while combined flexure-shear failure mode was observed under impact load. The impact-loading tested beams were further statically loaded to examine their residual capacities. Additionally, numerical models of the tested GPC beams were developed adopting the commonly used concrete material model *Mat_072R3 (KCC model) in LS-DYNA with modified parameters based on the GPC material testing data. The calibrated numerical model was used for parametric simulations. The results showed that with the increased impact velocity, failure mode of the beam shifted from the flexure-governed to punching-shear-governed along with the rupture of longitudinal BFRP bars.