Concrete Damaged Plasticity Constitutive Model Research Articles

Lining Structure of Water Conveyance Tunnel under Earthquake Action Research on Damage Law

Based on the concrete damage plasticity constitutive model (CDP model) of ABAQUS software, the dynamic response of high pressure internal water conveyance tunnel during earthquake is simulated, and the dynamic response and dynamic damage law of high internal water pressure water conveyance tunnel structure under surrounding rock grade, buried depth and seismic wave intensity are analyzed. The research shows that the surrounding rock grade is closely related to the dynamic response and damage characteristics of the lining structure of the water conveyance tunnel. The dynamic damage of the tunnel under grade Ⅲ surrounding rock is only 0.08, which is far less than 0.83 under grade Ⅳ surrounding rock. It can be considered that it will not cause great damage to grade Ⅲ surrounding rock under earthquake. The surrounding rock grade is better, which can provide more stable support and reduce the stress and vibration of the structure. If the tunnel is in the seismic zone, the buried depth can be used as one of the design control indexes in the tunnel design. The lining damage is mainly distributed at the top and upper arch waist of the tunnel. With the increase of the buried depth of the tunnel, the dynamic damage amount increases from 0.021 to 0.081, then to 0.085. the damage of the lining structure also increases. This may be because the deep buried tunnel is more constrained by the underground rock and soil layer, thereby reducing the transmission of seismic load. The change of seismic wave intensity can directly affect the damage characteristics of tunnel lining structure. The dynamic damage mainly occurs at the vault and arch waist, and the damage area expands from the vault and arch waist to the side wall and corner. The increase of seismic wave intensity will lead to dramatic changes in the stress of the structure, which will lead to more complex and serious damage.

Strength reduction method for a factor of safety determination of damaged concrete structures

The paper presents the procedure for determining the factor of safety (FoS) using the strength reduction method (SRM) for the case of a concrete damage plasticity constitutive model. The SRM was originally used in a slope stability analysis and in its original form, this method was applied by reducing the shear strength of the material. Since damage in concrete occurs due to exceeding the normal stresses in the principal directions, and not due to exceeding the shear strength, this method was modified and adapted to the concrete damage plasticity constitutive model. Instead of reducing the failure surface, the parameters which describe the mechanical behavior in the case of uniaxial compression and uniaxial tension were reduced. In this way, the reduction of stress and the corresponding strain was carried out in the entire range of total strain, without changing the shape of the failure surface in the deviator plane. For the proposed methodology, a numerical algorithm was developed and implemented into the software PAK. The algorithm was verified through test examples and the obtained results were compared with analytically calculated FoS. The excellent agreement is observed between the FoS obtained by applying the proposed algorithm and the analytically calculated FoS.

Reliability Assessment of Reinforced Concrete Beams under Elevated Temperatures: A Probabilistic Approach Using Finite Element and Physical Models

A novel computational model is proposed in this paper considering reliability analysis in the modelling of reinforced concrete beams at elevated temperatures, by assuming that concrete and steel materials have random mechanical properties in which those properties are treated as random variables following a normal distribution. Accordingly, the reliability index is successfully used as a constraint to restrain the modelling process. A concrete damage plasticity constitutive model is utilized in this paper for the numerical models, and it was validated according to those data which were gained from laboratory tests. Detailed comparisons between the models according to different temperatures in the case of deterministic designs are proposed to show the effect of increasing the temperature on the models. Other comparisons are proposed in the case of probabilistic designs to distinguish the difference between deterministic and reliability-based designs. The procedure of introducing the reliability analysis of the nonlinear problems is proposed by a nonlinear code considering different reliability index values for each temperature case. The results of the proposed work have efficiently shown how considering uncertainties and their related parameters plays a critical role in the modelling of reinforced concrete beams at elevated temperatures, especially in the case of high temperatures.

On a Benchmark Problem for Modeling and Simulation of Concrete Dams Cracking Response

Concrete dams are massive unreinforced quasi-brittle structures prone to cracking from multiple causes. The structural safety assessment of cracked concrete dams is typically performed using computational analysis through numerical methods, with adequate representation of the material model. Advances in the last decades including computational processing power, novel material, and numerical models have enabled remarkable progress in the analysis of concrete dams. Nevertheless, classical benchmarks remain reliable references for the performance analysis of these structures. This paper presents the main aspects of modeling and simulation of a concrete gravity dam cracking response based on a broad literature survey. Emphasis is given to an in-depth review of the benchmark problem analyzed by Carpinteri et al. (1992). We then use the Abaqus concrete damage plasticity constitutive model to solve the benchmark problem and provide recommendations to obtain accurate results with an optimal computational cost. The best practices of modeling, simulation, verification, and validation are presented.

Nonlinear Finite-Element Analysis for Structural Investigation and Preservation of Reinforced Hybrid Thin Tile–Concrete Domes of the Historic School of Ballet Classrooms in Havana, Cuba

The striking tiled domes of the Ballet School of the Instituto Superior de Arte (ISA) in Havana are internationally acclaimed Cuban architectural icons. However, due to their deceptive tiled appearance and their only recently rediscovered hybrid tile–concrete constructive system, the domes have eluded the structural study and characterization which increasingly is demanded not only because of their unique morphology and monumental status, but also because of their visible damage. This work defined a suitable numerical analysis method for diagnosing these hybrid structures by applying both linear elastic and nonlinear, using the concrete damaged plasticity constitutive model, numerical analyses. A site investigation campaign provided materials and geometric data that informed the model creation and damage documentation that validated the analyses results. A new synthesis of architectural and technical sources covering the development and spread of the hybrid structural system allowed the ISA domes to be placed, for the first time, in their proper structural context and, consequently, for their conception and design to be understood more fully. The analyses, construction records, and site tests indicated a rebar placement error as the primary structural damage cause, and the contextual analysis informed a discussion of its possible sources, both technical and managerial. Because the investigation indicated significant risk of irreversible damage or failure without timely intervention, preliminary intervention explorations were conducted and, based on the holistic understanding of the structures, the technically, architecturally, and culturally optimal solution was identified. The study concluded that the homogeneous solids model, coupled with the concrete damaged plasticity mechanical model, yields realistic and insightful results illuminating the structural behavior, efficiency, condition or status, and collapse mode of the domes, providing necessary insight for the preservation planning for the Ballet School domes, which also will inform the study and understanding of other structures of similar composition and significance.

Analysis of Vertically Oriented Coupled Shear Wall Interconnected with Coupling Beams

The nonlinear static response of a vertically oriented coupled wall subjected to horizontal loading is presented in this research article. The 3 storey vertically oriented coupled wall interconnected with coupling beams is modelled as solid elements in a finite element (FE) software named Abaqus CAE and the steel reinforcement is modelled as a wire element. For simulation of concrete models, a concrete damaged plasticity constitutive model is taken into consideration in this research. Moreover, with the help of concrete damage plasticity parameters, validation of two rectangular planar walls was executed with an error of less than 10 percent. Finally, these parameters are used for modeling and analyzing the static behavior of coupled walls connected with coupling beams. Furthermore, the maximum unidirectional horizontal loading helped in obtaining the compression and tensile damage as well as scalar stiffness degradation. Significantly, the research also found the plastic hinge location in the coupled wall as well as in the coupling beam, which are of utmost importance in nonlinear analysis. Doi: 10.28991/HIJ-2022-03-02-010 Full Text: PDF

Limit design of reinforced concrete haunched beams by the control of the residual plastic deformation

In this paper, a novel computational (optimization) model is presented to control the plastic behaviour of reinforced concrete haunched beams using complementary strain energy of residual forces formed inside the steel reinforcing bars. For this purpose, a numerical model validation process was held and then two non-linear optimization problems were outlined. In these optimization problems, different objective functions were considered applying the optimal elasto-plastic analysis and design of haunched reinforced concrete beams aiming to find the maximal loading or the minimum volume of the steel used to reinforce the beams as the plastic deformations are controlled by using constraints on the complementary strain energy of the residual internal forces of the steel bars. Moreover, the effect of these constraints on different haunch angle beams is studied. The applied method is described in terms of nonlinear mathematical programming and providing solutions when the plastic reserves of the body are not fully exhausted. It is worth mentioning that in this study a concrete damage plasticity constitutive model is applied in the numerical problems and calibrated in accordance with the data gained from laboratory tests. The optimal solutions of the nonlinear mathematical problems were calculated by MATLAB programming codes written by the authors taking into consideration different objective functions and equality and inequality constraints for each case. Finally, by performing a parametric study, the different optimization problems showed how beams behaved differently under different complementary strain energy limit values shifting from elastic into elasto-plastic state and then reaches the fully plastic state where results showed different comparisons taking into consideration the effect of the different complementary strain energy limit values on the maximum applied load, geometry of the beam and steel volume used to reinforce the beams. Thus, complementary strain energy limit value is used to control the plastic deformation inside steel bars during loading progress where avoiding the formation of the plastic deformation in the steel bars would reflect on the general behaviour of the haunched reinforced concrete beams.

High strength fiber reinforced one-part alkali activated slag composites from industrial side streams

This paper details the effect of fiber reinforcement on mechanical characteristics of by-products based one-part alkali activated material (AAM). Two different binder matrices were considered in this study, such as, plain slag, and ternary blended slag, to understand their efficiency in fiber reinforced system. These matrices were reinforced with 1% v/v of three different fibers (steel, glass and basalt) to improve the flexural performance of high strength mortar blends. Steel fiber reinforced one-part AAM outperforms mineral fibers in compressive strength contribution. The fracture energy of steel fiber reinforced compositions was roughly 4 times higher than that of mineral fiber reinforced materials. In addition, the flexural performance of ternary blended matrix was higher than that of slag-based composition regardless fiber types and properties. Finally, preliminary finite element modelling was considered to assess the applicability of the concrete damage plasticity constitutive model in predicting the nonlinear behavior of the developed composites. The numerical predictions proved the accuracy of the model with good agreement between experimental and numerical results.

Seismic damage assessment of a historic masonry building under simulated scenario earthquakes: A case study for Arge-Tabriz

Damage prediction of existing buildings against natural events is a challenge for engineers. Although several approaches have been proposed in the bibliography for damage assessment of steel and concrete structures, more studies are required to survey the damage state of masonry buildings.In this research, seismic damage of a historical masonry building, named Arge-Tabriz, has been assessed using region-specified simulated ground motion records. The main goal of the research is to predict the damage levels of Arge-Tabriz monument under probable earthquakes. Potential scenario earthquakes with different magnitudes are simulated to evaluate the seismic damage of the Arge-Tabriz building. For ground motion simulation of the scenario earthquakes, the stochastic finite-fault methodology, which employs a finite-fault approach comprised of point-source models, is used. The building is modeled using macro-modeling approach; and for the masonry material, concrete damaged plasticity constitutive model is utilized. After performing nonlinear dynamic analyses of the model in ABAQUS commercial software, the damage state of the building is assesses through failure area and failure volume methods, Park-Ang damage index, performance limits proposed by FEMA 356, and finally tensile damage variable DAMAGET as ABAQUS output variable. The accuracy of the employed numerical method is verified through comparison of the developed damage patterns with the existing damage patterns of the building. The results disclose that failure area and failure volume indices have the highest accuracy, while the drift limits of FEMA 356 have the lowest precision to predict the damage level of the building. The application of region-specific simulated scenario earthquakes reveals that the building has adequate strength to resist against weak seismic events and it experiences moderate damage, keeping up its whole stability under moderate potential events; while it is susceptible to collapse against severe earthquakes, and therefore, a rehabilitation scheme seems to be essential for preserving this valuable heritage.

Finite element analysis of rectangular RC beams strengthened with FRP laminates under pure torsion

AbstractComposite materials have attracted wide attention in strengthening of structural members. In this study, the behavior of rectangular reinforced concrete (RC) strengthened with fiber reinforced polymer (FRP) laminates under pure torsion was investigated numerically and validated by existing data from literature. Various practical strengthening configurations were considered and the efficiency of them was illustrated. Concrete damage plasticity constitutive model was used and required parameters was drawn. Good agreement in terms of torque–twist behaviors of RC beams strengthened with FRP laminates before and after cracking was found. Reasonable steel and FRP reinforcement responses as well as crack patterns were achieved and the failure modes of all the specimens were modeled correctly. A parametric study was carried out and parameter such as number of FRP plies, concrete compressive strength, and FRP strip orientations were considered. The results showed that the torsional capacity could improves by increasing the number of FRP plies and concrete compressive strength. Moreover, no significant change in the torsional capacity of RC beams when it was strengthened with a 45° or with a 90° FRP laminate was observed.

Numerical analysis of bonding between masonry and steel reinforced grout using a plastic–damage model for lime–based mortar

This paper shows a numerical investigation with single-lap shear bond tests between Peruvian brick masonry and SRG system. For this purpose, the finite element method, elements and constitutive models implemented in ABAQUS library were used. Eight-node continuum elements were employed for modelling mortar, masonry and steel fibers assuming a linear-elastic behaviour for the last two materials. Eight-node cohesive elements with zero-thickness were used to model substrate-mortar and steel-mortar interfaces. Due to experimental results showed the detachment of the steel fiber from the mortar accompanied by cracking of the outer mortar layer, the non-linearity of the mortar was also considered by using a Concrete Damage Plasticity constitutive model. The effect of the mortar non-linearity was compared with other models assuming a linear and rigid material for mortar, as recommended by literature. This shows that modelling a non-linear mortar leads to more accurate results for future design and strengthening purposes, thus, its implementation is encouraged. A comparison in time between Bond–Slip Law (BSL) at steel–mortar interface and mortar constitutive law is analysed in order to investigate the stress-transfer mechanism during single–lap shear tests.

Numerical and experimental investigation of electro-mechanical impedance based concrete quantitative damage assessment

This paper presents a numerical and experimental investigation of the concrete quantitative damage assessment using the smart aggregate (SA) sensor based on the electro-mechanical impedance method. In the numerical simulation, a concrete cube finite element model with an embedded SA sensor is established using concrete damaged plasticity constitutive model to simulate the damage process under uniaxial compression. The concrete damage degree is evaluated using the conductance signatures of the embedded SA sensor and damage volume ratio (DVR). In the experimental study, three concrete cubes are casted and subjected to compressive loading. The experimental study verifies the numerical simulation model by comparing the root mean square deviation (RMSD) indices of conductance signals. Furthermore, the DVR is proposed as an effective damage evaluation index. The relationship curve between the DVR and the RMSD is fitted. The results illustrate that the RMSD index of the SA sensor and the DVR of the concrete have a linear relationship. The level of concrete damage can be quantitatively evaluated by RMSD index according the relationship between the RMSD and DVR.

Exploration on Damage Mechanism and Equivalent Damage Model of High Arch Dams under Earthquakes

Damage identification technology of high arch dams has been well developed under strong earthquakes. However, the failure mechanism of high arch dams at different locations remains unclear. For this purpose, a series of deterministic dynamic analyses for a 3D 289-m-high arch dam based on concrete damaged plasticity constitutive model are performed. The failure mechanism at different locations of high arch dams under earthquakes is studied systematically. According to the sensitivity of different indicators to different damaged positions, an effective sensor placement scheme is proposed to assess the seismic reliability in practical engineering. Furthermore, a new effective equivalent damage model based on prior information is proposed, which can improve the efficiency of damage identification, as well as solving the problem that the real damage is concealed by homogenizing the damage in a pre-set region. The results provide suggestions and theoretical basis for sensor placement in actual monitoring of high arch dams; and the equivalent damage model provides a new solution to balance the efficiency and accuracy of damage identification.

A spherical smart aggregate sensor based electro-mechanical impedance method for quantitative damage evaluation of concrete

In this study, the concrete damage induced by compression is evaluated quantitatively using spherical smart aggregate sensor based on electro-mechanical impedance method. The sensitivity of the spherical smart aggregate sensor embedded in concrete cubes is investigated by comparing the electrical signals recorded during the compressive process with those of the smart aggregate sensor embedded in concrete cubes. Furthermore, the finite element model of concrete cube with an embedded spherical smart aggregate sensor is developed to simulate the concrete compressive tests. The concrete damaged plasticity constitutive model is utilized to simulate the concrete damage process. The numerical model is verified with the experimentally measured compressive test results. Finally, the damage volume ratio is presented to quantify the damage level of concrete based on the numerical model. The relationship between the root mean square deviation index of the conductance signatures obtained from experiments and the damage volume ratio computed by numerical simulation is established to quantify the concrete damage level. The results show that the spherical smart aggregate sensor is more sensitive than the smart aggregate sensor in monitoring the three-dimensional concrete structures. The proposed empirical fitting curve can effectively evaluate the concrete damage level quantitatively.

Damage Detection in Reinforced Concrete Berthing Jetty Using a Plasticity Model Approach

A conventional method of damage modeling by a reduction in stiffness is insufficient to model the complex non-linear damage characteristics of concrete material accurately. In this research, the concrete damage plasticity constitutive model is used to develop the numerical model of a deck beam on a berthing jetty in the Abaqus finite element package. The model constitutes a solid section of 3D hexahedral brick elements for concrete material embedded with 2D quadrilateral surface elements as reinforcements. The model was validated against experimental results of a beam of comparable dimensions in a cited literature. The validated beam model is then used in a three-point load test configuration to demonstrate its applicability for preliminary numerical evaluation of damage detection strategy in marine concrete structural health monitoring. The natural frequency was identified to detect the presence of damage and mode shape curvature was found sensitive to the location of damage.

Response modification factor due to ductility of screen-grid ICF wall system in high seismic risk zones

Insulating Concrete Form (ICF) includes permanent formworks, most commonly expanded polystyrene foam. Insulating Concrete Forms create a formwork for concrete that stays in place as permanent building insulation. Structures usually experience plastic deformations during major earthquakes; however, because of complexity of performing non-linear analysis, codes consider effects of inelastic behavior through reduction factors (R) and allow linear analysis instead. Reduction factor has not been presented for Screen-Grid ICF (SGICF) wall system until now. In this research, reduction factors due to ductility of SGICF wall systems are determined by non-linear static analysis (Pushover) and Concrete Damaged Plasticity constitutive model (CDP) in ABAQUS 6.12. Then the results are compared to those of the experimental model. Results from this research show that such structural system, if used in high seismic risk zones, has an acceptable ductility.

Plastic Behavior of Integral Bridge, Consisting of Supporting Steel Beams and Concrete Superstructure, under Spatially Varying Seismic Shock

The paper presents the dynamic response of an integral bridge to an earthquake registered in Central Europe. The acceleration history of the shock was scaled up to peak ground accelerations predicted for this seismic zone (0.4 g). The seismic action was implemented in the form of two models of three dimensional kinematic excitation: uniform and non-uniform (spatially varying). In the uniform model the assumption was made that the motion of all supports of the bridge was identical. In the case of the spatially varying excitation the wave passage effect was taken into consideration, assuming that the seismic wave propagated along the bridge forcing subsequent supports of the bridge to repeat the same motion with a time delay dependent on the wave velocity. The structural system of the integral bridge consisted of steel girders and crossbars whereas the superstructure was made of a concrete material. To represent the inelastic behavior of the integral bridge during the earthquake, plastic models of both the steel and the concrete material were implemented. For the steel material the classical metal plasticity model with the dynamic failure model of progressive damage, provided by the ABAQUS software, was applied. For the concrete material of the superstructure the concrete damaged plasticity constitutive model was taken into consideration. It turned out that when the non-uniform excitation model was imposed, the tensile damage (cracking) and the degradation of the support zones of the concrete deck were more significant than in case of uniform excitation. The non-uniform excitation model also caused considerably higher inelastic strains of the steel girders and crossbars than the uniform model. This resulted from quasi-static effects caused by ground deformations imposed on the bridge supports during the seismic shock.

Performance of Steel Pipeline with Concrete Coating (Modeled with Concrete Damage Plasticity) Underseismic Wave Passage

The paper presents the analysis of the dynamic response of a steel pipeline with concrete coating to a real earthquakeregistered in central Poland in 2012. The peak ground acceleration of the shock was scaled up to maximal values predicted for this seismic zone. To represent theinelastic behavior of the material of the concrete coating under dynamic loading, the concrete damaged plasticity constitutive model was assumed.The modelallows to describeplastic strains and irreversible tensile and compression damage that occurs during the cracking process.For seismic analysis two models (uniform and non-uniform) of kinematic excitation were applied. In the modelof uniform excitation it was assumed that the motion of all supports was identical. Inthe model of non-uniform excitation, typical for long structures, the wave passage along the pipelinewith different velocities (500, 400 and 300 m/s) was taken into account. It occurred that for the model of uniform excitation the concrete material of the coating remained elastic with no tensile damage. For the model of non-uniform excitation, inelastic behaviour of the coating was observed. The plastic strain areas appeared above all supports. The tensile damage (cracking) wasalso noticed in these areas: the lower wave velocity was assumed, the greater area of concrete coating was affected by plastic strains and tensile damage (cracking). It was the consequence of the quasi-static effects which resulted from ground deformations imposed on the pipeline during the seismic shock.

Cooling Tower Shell under Asynchronous Kinematic Excitation Using Concrete Damaged Plasticity Model

The paper presents the analysis of the dynamic response of a cooling tower to moderate earthquake. To represent inelastic behavior of the concrete material of the tower under dynamic loading, the concrete damaged plasticity constitutive model was assumed. The model consists of the combination of non-associated multi-hardening plasticity and scalar damaged elasticity to describe the irreversible damage that occurs during the fracturing process. Two different models of seismic excitation were used. Initially, a classical model of uniform kinematic excitation was applied. In this model it was assumed that excitation at all supports was identical. Then, a model of non-uniform kinematic excitation, typical for large multiple-support structures, was introduced. In that model the wave passage along the foundation ring was taken into account. It occurred that the assumption of asynchronous excitation led to the increase of the dynamic response of the tower with respect to the assumption of uniform ground motion. The tensile damage (cracking) in some parts of the tower appeared and the stiffness of the concrete was degraded when non-uniformity of excitation was considered. This was due to the quasi-static effects resulting from changes of subsoil geometry during the shock. The analysis indicated that the classical assumption of uniform excitation may lead to non-conservative assessment of the dynamic response of the shell described with concrete damaged plasticity model.

Three-Dimensional Damage Analysis of Concrete Surrounding the Spiral Case in the Nuozhadu Hydropower Station

Studies have shown that the internal pressure of the spiral case could cause damage of the surrounding concrete, and the damage range and level are possible to grow with the repeated action of water hammer pressure. The security of spiral case structure may be adversely affected by damage of the surrounding concrete. In this paper, the case study of a spiral case which located in Nuozhadu hydropower station in Yunnan Province is presented. In order to analyze the damage effect of surrounding concrete under the repeated maximal water hammer pressure, a three-dimensional finite element model is established by ABAQUS software. In calculation, the contact elements are used to simulate the feature of frictional contact between steel liner and surrounding concrete, and the concrete damage plasticity constitutive model is adopted to describe the tensile characteristic of concrete. At last, according to the results of simulation, the damage range and level are investigated.