Concrete Softening Research Articles

Influence of ambient temperature and humidity on the evolution of the tension softening behavior in concrete

The tension softening relationship is a crucial input parameter for modeling the crack propagation in concrete. To examine the influence of curing conditions on this parameter, fracture tests were performed on specimens kept at different temperatures and humidity levels across various ages. A best-fit maturity method for identifying optimal maturity model parameters was proposed and validated using test data. The results indicated that the area beneath the first branch of the softening curve increases, whereas the area under the tail decreases with ongoing hydration and higher humidity. The tensile strength ft and centroid coordinate σcg (vertical coordinate of softening curve area center) increase with rising temperatures up to 14 days, after which the trend reverses, with higher later-age ft and σcg observed in specimens exposed to elevated temperatures. Under high temperatures, the critical crack width wc (ultimate width at zero cohesive stress) and centroid coordinate wcg decrease. At the early stage, humidity has minimal effect on concrete softening properties. However, as the hydration progresses, the impact of decreasing humidity becomes more significant. At 60 days, ft, σcg, and wc are reduced by 23.3 %, 22.8 %, and 19.6 %, respectively, as humidity drops from 98 % to 30 %. The developed best-fit maturity method can predict various concrete properties with a maximum relative error within 7 %. The optimal activation energy Ea and moisture diffusion coefficient γ vary across temperature and humidity ranges, making it unfeasible to use a single set (Ea, γ) to predict properties under varying curing conditions.

Implementation of a smeared crack model in the finite element method and its application to two-dimensional nonlinear analysis of concrete beams

This paper describes the implementation of a two-dimensional rotating smeared crack model within the framework of a nonlinear finite element analysis code, and its application to the mechanical behavior of the plain concrete. In this work, the formulation of three concrete softening law subjected to fracture Mode-I is adapted, considering infinitesimal strains, static loads and two-dimensional conditions. The rotating smeared crack model and the three softening laws are all implemented in Fortran language, into the open source software for nonlinear finite element analysis HYPLAS. The pre- and post-process for a graphical representation of the mesh and the results are done with GMSH or GiD. Finally, three experimental tests of concrete beams of other authors are simulated. The concentration of the displacement contour lines obtained in the simulation represents the crack patterns in the solid. The relationship between the applied load and the representative displacement in each analysis step describes the mechanical response of the beam. Other computed parameters were the crack opening and the principal stresses in the solid. The numerical results were satisfactory in comparison with the experimental tests.

THREE-DIMENSIONAL DISPLACEMENT COMPATIBLE STRUT AND TIE METHOD FOR THREE-PILE CAPS SUBJECTED TO CONCENTRIC AXIAL LOADS

Pile caps are large structural elements that act as an interface between the superstructure and the pile foundation. The displacement Compatible Strut and Tie Method (C–STM) is an effective nonlinear modelling technique that is mainly used to simulate the behavior of structural reinforced concrete elements having considerable disturbed (D-) regions. Unlike STM, which considers only force equilibrium, C–STM considers displacement compatibility and constitutive material relationships as well. Recently, a three-dimensional (3D) C–STM was formulated and validated for the analysis of four-pile cap specimens of various shapes. In this study, the 3D C–STM is used to predict the complete load-deformation response of three-pile caps under concentric axial loads. The constitutive material relations for concrete and steel used in this study accounts for both concrete softening and tension stiffening. The overall load-deformation behavior simulated using the 3D C–STM agrees well with the experimental data. Moreover, the 3D C–STM also envisages the progression of nonlinear events leading up to the failure of three-pile cap specimen quite well.

THREE-DIMENSIONAL DISPLACEMENT COMPATIBLE STRUT AND TIE METHOD FOR THREE-PILE CAPS SUBJECTED TO CONCENTRIC AXIAL LOADS

Pile caps are large structural elements that act as an interface between the superstructure and the pile foundation. The displacement Compatible Strut and Tie Method (C–STM) is an effective nonlinear modelling technique that is mainly used to simulate the behavior of structural reinforced concrete elements having considerable disturbed (D-) regions. Unlike STM, which considers only force equilibrium, C–STM considers displacement compatibility and constitutive material relationships as well. Recently, a three-dimensional (3D) C–STM was formulated and validated for the analysis of four-pile cap specimens of various shapes. In this study, the 3D C–STM is used to predict the complete load-deformation response of three-pile caps under concentric axial loads. The constitutive material relations for concrete and steel used in this study accounts for both concrete softening and tension stiffening. The overall load-deformation behavior simulated using the 3D C–STM agrees well with the experimental data. Moreover, the 3D C–STM also envisages the progression of nonlinear events leading up to the failure of three-pile cap specimen quite well.

Cross-Sectional Analysis of the Resistance of RC Members Subjected to Bending with/without Axial Force.

This paper deals with the cross-sectional analysis of the resistance of RC members subjected to a bending moment with or without axial forces. To determine section resistance, the nonlinear material law for concrete in compression is assumed according to Eurocode 2, taking into account the effect of concrete softening. It adequately describes the concrete behavior of RC members up to failure. The idealized stress–strain relation for the reinforcing steel is assumed. For the ring cross-section subjected to bending with axial force and for areas weakened by an opening, normalized resistances have been derived by integrating corresponding equilibrium equations. They are presented in the form of interaction curves and compared with the results of testing conducted on RC eccentrically loaded columns. Furthermore, the ultimate normalized bending moment has been derived for the RC rectangle subjected to bending without axial force. It was applied to the cross-sectional analysis of steel and concrete composite beams consisting of the RC rectangular core located inside a reversed TT-welded profile. Comparative analysis indicated good agreements between the proposed section models and experimental data. The objective of the paper is the dimensioning optimization of the considered cross-sections with the fulfillment of structural safety requirements.

Quantitative Assessment of the Influence of Tensile Softening of Concrete in Beams under Bending by Numerical Simulations with XFEM and Cohesive Cracks.

Results of the numerical simulations of the size effect phenomenon for concrete in comparison with experimental data are presented. In-plane geometrically similar notched and unnotched beams under three-point bending are analyzed. EXtended Finite Element Method (XFEM) with a cohesive softening law is used. Comprehensive parametric study with the respect to the tensile strength and the initial fracture energy is performed. Sensitivity of the results with respect to the material parameters and the specimen geometry is investigated. Three different softening laws are examined. First, a bilinear softening definition is utilized. Then, an exponential curve is taken. Finally, a rational Bezier curve is tested. An ambiguity in choosing material parameters and softening curve definitions is discussed. Numerical results are compared with experimental outcomes recently reported in the literature. Two error measures are defined and used to quantitatively assess calculated maximum forces (nominal strengths) in comparison with experimental values as a primary criterion. In addition, the force—displacement curves are also analyzed. It is shown that all softening curves produce results consistent with the experimental data. Moreover, with different softening laws assumed, different initial fracture energies should be taken to obtain proper results.

Simplified plasticity damage model for large rupture strain (LRS) FRP-confined concrete

Large rupture strain (LRS) fiber-reinforced polymers (FRP) composites with an elongation greater than 5% offer an attractive solution for seismic strengthening of reinforced concrete (RC) columns. For a quick and reliable design of LRS FRP-strengthened RC columns, this paper presents a simplified plasticity damage model for LRS FRP-confined concrete under cyclic axial compression. This model consists of two parts: (a) a recent monotonic LRS FRP-confined concrete model developed by the authors’ group as an envelope curve and (b) a simplified linear plasticity damage cyclic rule for predicting unloading and reloading paths. To solve the cyclic model deviation induced by concrete softening under a large axial strain, a pseudo-plastic strain was proposed, based on which the damage degradation of FRP-confined concrete can be quantified. The model comparisons show that although the proposed model sacrificed some precision when directly applied for the cyclic axial compressive behavior of FRP-confined concrete, it can give similarly accurate predictions as a complex model does for the behavior of conventional or LRS FRP-jacketed RC columns under a combined axial load and cyclic lateral load. Thus, this simplified plasticity damage model serves as a promising basic model for simulation of the seismic performance of FRP-strengthened structures.

Flexural behavior of carbon-textile-reinforced concrete I-section beams

In the present work, the flexural behavior of carbon textile reinforced concrete (TRC) I-beams is investigated. Four-point bending tests were performed in I-beams, considering SBR-laminated textile and the following conditions: (a) plain cementitious matrix; (b) plain matrix and sand-coated textile; and (c) strain hardening cement-based composite (SHCC) matrix. The main goal of the research was to correlate the improvements on interface and matrix properties with the crack pattern, failure mode and ductility. For a comprehensive discussion, full mechanical characterization was performed and a design model is proposed for a better evaluation of the experimental results. Cracking behavior was greatly improved for conditions (b) and (c) with respect to (a), due to enhanced bonding between reinforcement and matrix in the former and due to fiber bridging mechanism in the latter. Beams with plain matrix exhibited brittle failure, whereas the beam having SHCC matrix showed premature local failure near load application point, resulting in an apparent ductility due to concrete softening mechanism. The reduced cracking load and the premature flange detachment along web-flange junction for condition (a) are also discussed. The proposed model is also validated through comparison with experimental results available in the literature.

Verification and Validation of Corbels Strengthened by Unbonded Tendons and Bars

Reinforced corbels are frequently used in industrial halls. A number of existing corbels are prestressed by unbonded tendons or bars in order to increase their load-bearing capacity, decrease the deflections and restrain cracks spreading. The goal of the project was experimental validation of the reinforced concrete corbel strengthened using unbonded tendons via CSFM (Compatible Stress Field Method). The method is based on materially nonlinear calculation considering the tension stiffening effect of rebars and compression softening of concrete. These effects and other assumptions implemented in CSFM capture real behavior of reinforced concrete members. Besides, CSFM is verified using an independent analysis, which is based on similar assumptions as those in Compatible Stress Field Method.

Characterizing concrete corrosion below sewer tidal levels at chemically dosed locations

Unexplainable concrete softening below the water line has been observed by Sydney Water in their gravity sewer network, some of which is subjected to corrosion control methods using chemical ferrous chloride (FeCl2) dosing of the wastewater. We applied a combination of physical and chemical tools to determine the properties of the top 20 mm of concrete cores recovered from sewer pipes. These techniques consist of neutron tomographic imaging, scanning electron microscopy, hardness mapping, and pH profiling. Concrete cores were collected from roof (crown), tidal (wall) and below flow regions of gravity sewer pipes of Sydney Water's wastewater system from locations that received no treatment as well as locations dosed with FeCl2. All samples showed a degree of softening of the surface exposed to the sewerage with an associated depletion in calcium concentration and reduced pH in the same regions.

Residual capacity assessment of reinforced concrete D-Regions affected by corrosion

The repair and rehabilitation of Reinforced Concrete (RC) structures affected by the corrosion of their reinforcement is a complex task. The estimation of the residual structural capacity of corroded RC structures is becoming a crucial factor in the decision-making process of repair or demolition. Many researchers have studied the effects of reinforcement corrosion on the load capacity of RC beams (Bernoulli or B-Regions) but little attention has been paid to disturbed or D-Regions. This piece of work presents a procedure for the assessment of the residual structural capacity of D-Regions in RC members. The bond deterioration between steel and concrete, the reduction of the cross-sectional area of reinforcement, the deterioration of the concrete area of the cross-section and the softening of concrete has been taken into consideration. The accuracy of the method has been tested with experimental results which exist in relevant literature.

Modified trilinear stress-strain diagram of concrete designed for calculation of beams with fiberglass rebar

An improved technique for determining the strength of reinforced beams with polymer composite reinforcement based on a nonlinear deformation model using a three-line diagram of concrete deformation under uniaxial compression with an elastic, elastic-plastic zone and a concrete softening zone is considered and proposed. The features of the strength analysis of beams with fiberglass reinforcement are revealed. The calculation method presented in this article allows us to minimize the use of empirical coefficients to determine the height of the compressed zone of concrete and at the same time does not lead to labor-intensive calculated dependencies. The method is based on the use of the Euler – Bernoulli beam theory and the use of physical stress-strain relations for concrete. This calculation method allows you to set accurately the height of the compressed zone of concrete, and accordingly the strength of the beam elements in the normal section. Good results of comparison with experimental data were obtained.

Biaxial reinforced concrete constitutive models for implicit and explicit solvers with reduced mesh sensitivity

A new set of constitutive models named TsingHua University Concrete 2D (THUC2) is developed for use in ABAQUS. THUC2 has reduced mesh sensitivity and is based on the decoupling assumption and the fixed-angle crack assumption in order to consider the pinching effect, confinement, strength degradation, and shear softening of concrete. In the developed biaxial reinforced concrete models, the uniaxial model is first established, and the biaxial model is subsequently assembled from the uniaxial model. First, the proposed uniaxial constitutive model of concrete is reported. The mesh sensitivity of the model is reduced by adjusting the descending branch of the concrete model based on mesh size. Second, a total of five biaxial constitutive models of concrete are reported to cover a wide range of simulation requirements in engineering design. Third, the numerical implementation of the proposed concrete model in both ABAQUS implicit and explicit solvers is discussed. Subsequently, the modified two-way fixed angle crack model is validated by monotonic and hysteretic panel tests. The FE model exhibits little mesh sensitivity when the element number increased from 4 to 400. The developed model accurately predicts the pinching effect and the softening effect of the panels. Finally, previous tests on two nuclear containment vessels under lateral loads are simulated, and the modified two-way fixed angle crack model demonstrates adequate accuracy in terms of predicting the initial stiffness, ultimate capacity, and pinching effect. The proposed subroutine package for simulating RC members includes the dominant mechanical behaviors of concrete and can be adopted for high-efficiency simulation of RC shear wall structures.

Analysis and Experimental Study on Shear Bearing Mechanism of Underpinning Beams Based on Truss-Arch Model

To establish a simplified analysis model of the shear bearing capacity of underpinning beams and study the shear bearing mechanism of underpinning beams, two underpinning beams adopting the roughening + planting bar + building glue connection method were tested and analyzed. The experimental and numerical analysis results show that the initial slip bearing capacity and initial slip amount of the underpinning beam are small, indicating that the connection method of roughening + planting bar + building glue is effective and feasible.The failure mode and mechanical performance of the underpinning beams are similar to the bending shear failure of a cast-in-place deep beam, and the crack development rule and failure mode of the specimen are in good agreement with the mechanical characteristics of the truss-arch model. Moreover, the theoretical and numerical results show that by increasing the reinforcement ratio of the stirrups, the ultimate bearing capacity of the underpinning beam can be improved, and the slippage between the new-to-old concrete of the beam can be effectively reduced. Finally, based on the truss-arch model theory and considering the concrete arch effect and softening effect, the shear bearing capacity calculation formula of the underpinning beam is established. The results show that the truss-arch model is applicable to the bearing capacity analysis of underpinning beams and provides a new perspective for the bearing capacity calculation of similar underpinning beams.

Maximum torsional reinforcement ratio of reinforced concrete beams

The amount of maximum torsional reinforcement is specified to prevent the failure of concrete compressive struts before the reinforcement yielding in reinforced concrete members subjected to torsion. The maximum torsional reinforcement presented in the design codes, however, differs by up to more than three times. This study therefore aimed to theoretically derive the maximum torsional reinforcement ratio. The proposed ratio was derived based on the equilibrium and compatibility conditions. The parametric study results of the torsional behavior analysis were also used to reflect key variables, such as tensile resistance of concrete, the cross-sectional area surrounded by shear flow, the concrete softening factor, and the average stress factor, in a simple form. In addition, the maximum reinforcement was presented not only in transverse direction but also in longitudinal direction to predict the failure modes of torsional members according to the yielding of reinforcements. The validation was performed by comparison with the experimental results of 98 beams under pure torsion collected from the literature, and the maximum torsional reinforcement ratio proposed in this study was found to reflect the failure modes of reinforced concrete beams subjected to pure torsion better than those suggested by other researchers and the design codes.

Modelling four-pile cap behaviour using three-dimensional compatibility strut-and-tie method

Pile caps are critical structural members that transfer loads from columns and bridge piers to the pile foundation. They are large concrete blocks with significant disturbed (D-) regions, low shear span-to-depth ratio, low longitudinal reinforcement ratio, and typically no vertical ties which makes them vulnerable to shear failure. The current major concrete codes of practice suggest both the sectional approach, and the Strut-and-Tie Method (STM) for the design of pile caps. Neither of the approaches accurately capture the ultimate capacity, force-deformation behaviour, complex strain variation, or the final mode of failure of pile caps. Compatibility Strut-and-Tie Method (C-STM) is an efficient, minimalist, non-linear modelling approach that satisfies equilibrium, compatibility, and constitutive material relationships and effectively simulates the behaviour of shear-critical reinforced concrete members. A displacement based three-dimensional (3D) C-STM is proposed to simulate the behaviour of four-pile caps. Appropriate geometry and material constitutive relationships, including tension stiffening and softening effects, are incorporated into the model. The effects of concrete softening due to transverse tensile strains are also incorporated in the model. To establish the generality of the model, the load and deformation corresponding to cracking, yield, and failure of 33 four-pile cap specimens with varying shapes, sizes and material properties are considered. The model satisfactorily simulates the overall force-deformation behaviour, internal strain behaviour, and sequentially predicts the non-linear events that lead to the failure of the pile caps. The results from the 3D C-STM are in good agreement with the experimental results and observations of four-pile cap specimens.

Analytical model for critical corrosion level of reinforcements to cause the cracking of concrete cover

This paper proposes an analytical model to calculate the critical corrosion level of reinforcements embedded in the concrete. The porous zone, the plasticity and strain softening of concrete were considered. The proposed model was verified by the simulation and test results, and the test validation shows that the predicted critical corrosion level of reinforcements for both natural aggregate concrete (NAC) and recycled aggregate concrete (RAC) based on the proposed model has a relative error lower than 5.0% compared with the test result when the replacement ratio of recycled aggregates is lower than 33.3%. It concludes that the proposed model can be applied to the prediction of the critical corrosion level of reinforcements in both NAC and RAC, and further the analysis of durability of concrete structures.

Influence of tensile softening of concrete on crack development and failure in concrete and reinforced concrete beams

In the paper, the own test results were presented. The experimental investigation was focused at determining the cracking and load capacity of beams made of concrete. The beams were characterized by different longitudinal reinforcement ratio from zero — plain concrete beams, through low ratio 0.12% — slightly reinforced concrete beams, middle ratio 0.9% — typical reinforced concrete beams, up to the ratios 1.3% and 1.8% — higher reinforced concrete beams. On the basis of the performed experiments and the results of numerical calculations, the process of crack’s formation and crack’s development in plain concrete, slightly reinforced concrete and reinforced concrete beams with different reinforcement ratio was described. When discussing cracking process in the beams, the contribution of strain softening of tensile concrete in the microcracked zone on the character of beams’ failure was analysed as well. Keywords: civil engineering, concrete and reinforced concrete members, cracking and load capacity.

On a nonlinear hybrid method for multiscale analysis of a bearing-capacity test of a real-scale segmental tunnel ring.

SummaryA nonlinear hybrid method is developed for multiscale analysis of a bearing‐capacity test of a real‐scale segmental tunnel ring subjected to point loads. The structural analysis consists of two parts. Part I refers to modeling of bending‐induced tensile cracking of the segments, resulting from the external loading. The segments are subdivided into elements, according to the crack spacing. Each element is either intact or contains one central crack band, flanked by lateral undamaged domains. A multiscale model for tensile softening of concrete is used to describe the progressive deterioration of the crack bands. After iterative determination of their state of damage, the effective bending and extensional stiffnesses of the corresponding elements are quantified by means of Voigt‐Reuss‐Hill estimates. The effective stiffnesses are used for linear‐elastic simulations of the segmental tunnel ring. Part II refers to the relative rotation angles at the joints, which are estimated from monitoring data, using the Bernoulli‐Euler hypothesis. Since the validity of this hypothesis is questionable for neck‐like joints, the relative rotation angles are post‐processed such that they refer to rigid body displacements of the segments. The following conclusions are drawn: The presented approach yields good estimates of crack widths. Relative rotation angles at the joints mainly result in rigid body displacements of the segments, governing the convergences. Because realistic interface models are lacking, hybrid analysis based on displacement‐monitoring data allows for performing ultimate‐load analysis of segmental tunnel rings.

Objective modeling of multixial softening of concrete

AbstractConcrete in tension and low confined compression is characterized by strain‐softening, which leads to highly localized cracks or shear bands. Attempting to incorporate this response in standard continuum descriptions causes numerical instabilities and mesh sensitive results. This work presents a regularized plasticity‐damage model, which ensures mesh objectivity for general multixial strain softening. Combining plasticity and damage is necessary to describe the cyclic response of concrete. The damage part contains a split to consider the transition between compression and tension. Regularization of the model is achieved by an over‐nonlocal implicit gradient formulation. The model is implemented into a 3D finite element code and its capabilities are illustrated by numerical examples.