Plastic-damage Constitutive Model Research Articles

Numerical Modeling of Four-Pile Caps Using the Concrete Damaged Plasticity Model

Four-pile caps made from concrete are essential elements for the force transfer from the superstructure to piles or pipes. Due to the difficulties in carrying out full-scale tests and all the instrumentation involved, the use of numerical models as a way to study the mechanical behavior of these elements presents itself as a good alternative. Such numerical studies usually provide useful information for the update and improvement of normative standards and codes. The concrete damaged plasticity (CDP) constitutive model, which combines damage and plasticity with smeared-crack propagation, stands out in the simulation of reinforced concrete. This model is composed of five parameters: dilatation angle (ψ), eccentricity (ϵ), ratio between biaxial and uniaxial compressive strength (σbo/σco), failure surface in the deviator plane normal to the hydrostatic axis (Kc), and viscosity (μ). For unidimensional elements, the values of the CDP parameters are well defined, but for volumetric elements, such as concrete pile caps, there is a gap in the literature regarding the definition of these values. This fact ends up limiting the use of the CDP on these structural elements due to the uncertainties involved. Therefore, the aim of this research was to calibrate two numerical models of concrete four-pile caps with different failure modes for the evaluation of the sensitivity of the CDP parameters, except for ϵ, which remained constant. As a result, the parameters σbo/σco and Kc did not significantly influence the calibration of the force × displacement curves of the simulated structures. Values of ψ and μ equal to 36° and 1 × 10−4, respectively, are recommended for “static” analysis, while for “quasi-static” analysis, ψ values ranging between 45° and 50° are suggested according to the failure mode. The results also showed to be sensitive to the constitutive relation of concrete tensile behavior in both modes of analysis. For geometric parameterization, the “static” analysis is recommended due to the lower coefficient of variation (3.29%) compared to the “quasi-static” analysis (19.18%). This conclusion is supported by the evaluation of the ultimate load of the numerical models from the geometrically parametric study compared to the results estimated by an analytical model.

Numerical Modeling of Four-Pile Caps Using the Concrete Damaged Plasticity Model

Four-pile caps made from concrete are essential elements for the force transfer from the superstructure to piles or pipes. Due to the difficulties in carrying out full-scale tests and all the instrumentation involved, the use of numerical models as a way to study the mechanical behavior of these elements presents itself as a good alternative. Such numerical studies usually provide useful information for the update and improvement of normative standards and codes. The concrete damaged plasticity (CDP) constitutive model, which combines damage and plasticity with smeared-crack propagation, stands out in the simulation of reinforced concrete. This model is composed of five parameters: dilatation angle (ψ), eccentricity (ϵ), ratio between biaxial and uniaxial compressive strength (σbo/σco), failure surface in the deviator plane normal to the hydrostatic axis (Kc), and viscosity (μ). For unidimensional elements, the values of the CDP parameters are well defined, but for volumetric elements, such as concrete pile caps, there is a gap in the literature regarding the definition of these values. This fact ends up limiting the use of the CDP on these structural elements due to the uncertainties involved. Therefore, the aim of this research was to calibrate two numerical models of concrete four-pile caps with different failure modes for the evaluation of the sensitivity of the CDP parameters, except for ϵ, which remained constant. As a result, the parameters σbo/σco and Kc did not significantly influence the calibration of the force × displacement curves of the simulated structures. Values of ψ and μ equal to 36° and 1 × 10−4, respectively, are recommended for “static” analysis, while for “quasi-static” analysis, ψ values ranging between 45° and 50° are suggested according to the failure mode. The results also showed to be sensitive to the constitutive relation of concrete tensile behavior in both modes of analysis. For geometric parameterization, the “static” analysis is recommended due to the lower coefficient of variation (3.29%) compared to the “quasi-static” analysis (19.18%). This conclusion is supported by the evaluation of the ultimate load of the numerical models from the geometrically parametric study compared to the results estimated by an analytical model.

Discontinuum Micromodelling of Unstrengthened and FRCM-Strengthened Masonry Cross-Vaults Subjected to Seismic Excitation

ABSTRACT Many historical buildings employ masonry cross-vaults as flooring systems. The structural response of such cross-vaults to seismic excitation still needs to be fully understood and requires investigation through experimental studies or accurate numerical simulations. This article presents a finite element discontinuum micromodelling technique to simulate a full-scale mortared masonry cross-vault (unstrengthened and subsequently strengthened with textile-reinforced mortar) recently tested on a shake table as part of a blind prediction competition. The numerical technique uses shell elements to model the brick and mortar geometry explicitly within the STKO+OpenSees finite element framework. Both brick and mortar materials are modeled using an advanced damage-plasticity constitutive model, addressing potential convergence issues associated with strain-softening materials through a novel implicit-explicit integration algorithm. The numerical models predicted the failure mechanisms and crack patterns in close agreement with the experimental results. The strengthened model displayed severe cracks spreading across a larger part of the cross-vault, whereas the unstrengthened model exhibited in-plane shear failure along the groin lines. The strengthened vault showed an almost twofold increase in peak ground acceleration capacity, demonstrating the effectiveness of textile-reinforced mortar. The proposed numerical technique will be helpful in the design of effective retrofit measures for heritage structures.

Elasto-Plastic Analysis of Two-Way Reinforced Concrete Slabs Strengthened with Carbon Fiber Reinforced Polymer Laminates

This study explores a technique for enhancing the punching strength of reinforced concrete (RC) flat slabs, namely carbon fiber reinforced polymer (CFRP). Four large-scale RC flat slabs were fabricated, to assess the efficacy of this strengthening method. One slab served as a reference and the three other specimens were strengthened with CFRP, as a method of external strengthening. These slabs, featuring identical overall dimensions and flexural steel reinforcement, underwent testing until failure, under the influence of concentrated patch loads. A concrete plastic damage constitutive model (CDP) was developed and employed to examine the strength of two-way RC slabs. Additionally, to enhance the strength of existing RC slabs, carbon fiber reinforced polymer (CFRP) strips are affixed to the tension surface of the sections. The research begins with the calibration of a numerical model, based on data from laboratory tests. The objective of this study is to constrain the plastic behavior of two-way RC slabs reinforced with CFRP, with a focus on establishing an optimal elasto-plastic analysis, aimed at controlling concrete damage plasticity using CFRP, and employing a plastic limit load multiplier. Subsequently, a series of numerical simulations, incorporating different variables, are conducted to investigate shear behavior. The numerical results indicate that an increase in the strengthening ratio has a significant impact on shear strength. Finite element simulations are carried out using Abaqus CAE®/2018.

Damage evolution and failure mechanism of masonry walls under in-plane cyclic loading

Masonry structures often exhibit poor seismic performance during earthquakes owing to their low material strength, structural integrity, and ductility. To address the mechanism of in-plane damage and collapse of masonry walls subjected to earthquake ground motion, three full-size brick walls, one with structural columns and two without structural columns, were designed and constructed in this experimental study to quantitatively investigate the effect of structural columns on the seismic performance of masonry walls. Quasi-static tests of masonry walls subjected to cyclic lateral loading were conducted using electrohydraulic servo actuators. The in-plane damage evolution and failure mode of the masonry walls under lateral loading were investigated. A numerical model with a novel plastic damage constitutive model of masonry was established. The accuracy of this model and the calculation results were verified by comparing them with the crack development and mechanical property curves obtained from the experiments. Based on the numerical model, a parametric analysis was conducted to investigate the influence of critical factors, such as mortar strength, vertical load, and height-to-width ratio, on the seismic performance of masonry structures. The test results showed that structural columns can effectively improve the performance of masonry structures. Properly installed structural columns can improve the peak load-bearing capacity, ductility, and energy dissipation of masonry structures. The masonry damage constitutive model used in this study could simulate the damage to masonry wall specimens well and reflect the hysteretic curves of the specimens within an acceptable range of accuracy. Thus, it provides a valuable reference for physical experiments. An appropriate mortar strength and vertical compressive stress can effectively enhance the load-bearing capacity of masonry structures within a certain range. For structural column walls. Walls with mortar strengths (average compressive strength) of 12.5 MPa, 10 MPa, 7.5 MPa, and 5 MPa showed an increase in peak bearing capacity of 26.2 %, 23.9 %, 18.5 %, and 9.4 %, respectively, compared to walls with mortar strengths (average compressive strength) of 2.5 Mpa. The aspect ratio had a significant impact on the shear load-bearing capacity of the masonry walls. An increase in the aspect ratio led to a transition from shear failure to flexural failure and a subsequent decrease in shear load-bearing capacity. For masonry walls with structural columns, increasing the diameter of the longitudinal steel in the structural columns can enhance the load-bearing capacity of the masonry wall, resulting in a significant improvement in its overall performance.

Compaction elastoplastic damage constitutive model of rock under hydro-mechanical coupling: A heuristic modeling method based on internal state variables theory

Based on the internal state variables (ISV) theory, this paper employs a heuristic modeling approach to investigate the compaction elastoplastic damage constitutive model of rocks under hydro-mechanical coupling. The heuristic modeling method demonstrated herein can seamlessly integrate with existing constitutive theories, facilitating a broader spectrum of research on hydro-mechanical coupling constitutive models. Furthermore, a numerical solution was conducted in the principal axes via stress spectrum decomposition, which can well reflect the distinct characteristics of compaction deformation and the influence of water pressure on rock stress distribution. Utilizing the classic Drucker-Prager (D-P) criterion, the modeling method and numerical algorithm were implemented to derive a hydro-mechanical coupling compaction elastic–plastic damage constitutive model. This contribution expands the application domain of the classic D-P criterion within the context of hydro-mechanical coupling environments. The rationality of the model was confirmed through compression test data under various water pressures and confining pressures. Water pressure increases nonlinear compaction deformation by changing the opening degree of microcracks under low confining pressure, which has not been paid enough attention in existing research. This study thoroughly considers the influence of water pressure on compaction deformation. The developed process of “heuristic modeling method-numerical method-model application” is helpful for enriching the constitutive theory of rock under hydro-mechanical coupling.

An Anisotropic Damage-Plasticity Constitutive Model of Continuous Fiber-Reinforced Polymers.

Accurate structural analyses of continuous fiber-reinforced polymers (FRPs) are imperative for diverse engineering applications, demanding efficient material constitutive models. Nonetheless, the constitutive modeling of FRPs is complicated by the nonlinear behavior resulting from internal damages and the inherent plasticity. Consequently, this study presents an innovative anisotropic constitutive model for FRPs, designed to adeptly capture both the damage evolution and plasticity. All requisite parameters can be easily obtained through fundamental mechanical tests, rendering the model practical and user-friendly. The model utilizes the three-dimensional Puck criteria to determine damages, initiating the evolution process through a combination of continuum damage mechanics and linear stiffness attenuation methods. This evolution is coupled with a one-parameter plastic model. Subsequently, the numerical implementation method, integrated into ANSYS, is detailed. This emphasizes the Cauchy stress and consistent tangent stiffness solution strategy. Finally, the effectiveness of the developed model is demonstrated through comprehensive verification, encompassing existing biaxial tension and open-hole-tension tests conducted on carbon and glass FRP laminates. The simulation results exhibit a remarkable correspondence with the experimental data, validating the reliability and accuracy of the proposed model.

Elastic–Plastic Dynamic Damage Constitutive Model of Cement-Stabilized Steel Slag

Elastic–Plastic Dynamic Damage Constitutive Model of Cement-Stabilized Steel Slag

A non-orthogonal fractional plastic damage constitutive model for porous rock-like materials considering porosity evolution

A non-orthogonal fractional plastic damage constitutive model for porous rock-like materials considering porosity evolution

Effects of Jack Thrust on the Damage of Segment Lining Structure during Shield Machine Tunnelling

Constructing a tunnel with a large longitudinal slope and a small-radius sharp curve is challenging. During the construction process, it necessitates a series of intricate operations, including adjusting the horizontal and vertical posture of the shield machine, controlling the tunnelling thrust, and consistently ensuring the appropriate over-excavation amount inside and outside of the turn. Improper operations can easily induce undue stress on the segments. This study establishes a finite element numerical model of lining segments subjected to jacking force under various construction conditions. The concrete damage plasticity (CDP) constitutive model was used to characterize the mechanical behavior of concrete under load. The mechanical characteristics and damage behavior of segments under construction conditions, such as significant thrust escape, vertical attitude adjustment of the shield machine, excavation in soft and hard interbedded strata, line turning, sudden failure of the propulsion system, and eccentricity of brace boots, were analyzed. The results revealed that, when advancing according to the maximum thrust design value (50 MPa), cracks in the tensile plastic damage zone near the brace boot plate and the edges of the segment can develop. This can lead to localized corner failure of the concrete at the lining’s edge. Therefore, it is recommended that the jack’s thrust value should not surpass 30 MPa. Maintaining the usual uneven jack thrust state of shield tunnelling along the design axis is unlikely to result in segment concrete cracking. Damage to the segment caused by the eccentricity of the brace boot plate is the most severe; hence, avoiding the eccentricity of the brace boot plate during construction is crucial. The findings of this research can guide the control of jack thrust during shield tunnelling construction and offer insights into the design of segment parameters.

Numerical Modelling of Impact Loads on RC Beams Utilizing Spent Garnet as a Replacement for Fine Aggregate

Spent Garnet (SG) is one of the waste materials that attracts the interest of researchers to use it as a replacement for fine aggregate in concrete materials. As experimental investigation was carried out to assess the performance of a reinforced concrete (RC) beam incorporating SG as a substitute for fine aggregate. The study involved subjecting the beam to low-velocity impact loads within a controlled testing configuration. The primary objective of this study was to determine the optimal proportion of spent garnet (SG) to replace fine aggregates in reinforced concrete (RC) beams subjected to impact loads with a 100 kg impact weight dropped from a height of 1.5m, equivalent to a velocity of 5.4 m/s. To evaluate the effectiveness of SG as a replacement for fine aggregates, RC beams with varying percentages of SG (0%, 10%, 20%, 30%, and 40%) were numerically modelled using the Finite Element Method (FEM) incorporating the Concrete Damage Plasticity (CDP) constitutive model to simulate their behaviour under low-velocity impact loads. The study aimed to comprehensively examine the failure mode of the RC beams. The findings through FEM showed that the inclusion of SG in the concrete mix enhanced the material's behaviour and decreased the failure and damage of the beams as the percentage of SG in the mix increased, indicating its effectiveness as a replacement for fine aggregates, which is consistent with the experimental results.

Thin corrugated-edge shells inspired by Nervi’s dome: Numerical insight about their mechanical behaviour

During the last decades, the constant evolution of the construction systems has led to the possibility of carrying out increasingly complex architectural project. Among the wide range of construction systems, thin concrete shells with corrugated-edge stand out for their relevance.In this paper, the mechanical behaviour of thin concrete corrugated-edge shell inspired by Nervi’s Flaminio dome has been analysed in detail, considering different load configurations (self-weight, uniform normal pressure and antisymmetric vertical load) and constraints (pure membrane vs. displacements restrained boundary conditions).Non-linear static analysis has been performed to assess the vertical load-bearing capacity of the corrugated-edge shell considering a Concrete Damaged Plasticity (CDP) constitutive model and linear and non-linear buckling analyses have been carried out to evaluate the effects of the corrugation on buckling behaviour.The results obtained from linear and non-linear analyses have been compared with those obtained for a concrete thin smooth-edge shell having the same geometric global characteristics. The comparison highlighted improvements provided by corrugated-edge in terms of structural behaviour.

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.

Experimental Study and Numerical Modelling on Flexural and Shear Strengthening of RC Beam with Prestressed FRP Bars

Abstract: The most prevalent and widely used building material in the world is reinforced concrete. The primary building material for the majority of constructions, including buildings, bridges, etc., is reinforced concrete. Because of various factors, some of these buildings or portions of them are failing to perform as designed. The best solution to increase the load carrying capacity and extend the useful life of these inadequate structures is to strengthen them because replacing them would need significant investments and not be an appealing alternative. Even though the effectiveness of other techniques is widely accepted,a new effective and promising technique of strengthening civil engineering structures externally is gaining popularity, where fibre-reinforced polymer (FRP) is used. One of the most popular strengthening methods recently is the use of carbon fibre reinforced polymer (CFRP) to strengthen reinforced concrete beams. It provides a desirable way to improve the shear and flexural strengths of RC beams. The manner in which these composites are bonded to the beam has a significant impact on the behaviour of reinforced concrete beams in shear and flexure. The purpose of this study was to present a three-dimensional nonlinear finite element analysis (FEA) of a reinforced concrete beam (RC beam) reinforced by prestressed carbon fibre plate (CFRP plate). While there are many commercial programmes available for three-dimensional nonlinear FEA, each one has a unique ability to represent complex behaviour of composite materials, such as RC beams strengthened with prestressed CFRP plate and the contact interaction. Because of its reputation for accuracy in simulating the behaviour of a range of materials, including concrete, and its potent contact algorithms, the ABAQUS finite element programme was chosen for this work. Steel reinforcements were modelled as elastic- perfectly plastic materials, while concrete was studied using the concrete damage plasticity (CDP) constitutive model. The CFRP plate was modelled as an entirely elastic substance that breaks under the highest tensile strain. Concrete and steel reinforcement were considered to have a perfect connection, and the behaviour of concrete and CFRP plate was represented using a contact model. The FEA's findings were verified against experiment findings that were published in the literature. In terms of load-deflection behaviour, crack patterns, and mode of failure, the results were compared. The proposed FEA model was able to accurately simulate the behaviour of RC beams strengthened with prestressed CFRP plate based on the validation. To find out the impact of the thickness, width, and length of the CFRP plate, as well as the prestressing levels and steel grades, a parametric research was done. In particular, the strength of the RC beam for the ultimate load was shown to be increased by increasing prestressing of the CFRP plate. However, as prestressing increased, the fracture of the CFRP plate altered the mechanism of failure, preventing the ultimate load from increasing further. The use of higher grade steel improved the ability to support additional weight. Although the general load carrying capability of the CFRP plate was increased by lengthening the plate, it was discovered that strengthening RC beams by 25% of their shear span was sufficient and cost- effective. The load-deflection curve, failure modes, and crack patterns from the experiments are fairly reflected in the FE model.

Comprehensive inter-fibre failure analysis and failure criteria comparison for composite materials using micromechanical modelling under biaxial loading

Inter-fibre failure analysis of carbon fibre-reinforced polymer (CFRP) composites, under biaxial loading conditions, has been a longstanding challenge and is addressed in this study. Biaxial failure analysis of IM7/8552 CFRP unidirectional (UD) composites is conducted under various stress states. Two widely accepted failure criteria, the interactive Tsai-Wu and non-interactive Hashin failure criteria, are comprehensively assessed with finite element-based micromechanical analysis. High-fidelity three-dimensional representative volume elements (RVEs) are subjected to biaxial loadings with imposed periodic boundary conditions. Carbon fibres are assumed to be transversely isotropic and linearly elastic. The Drucker-Prager plastic damage constitutive model and cohesive zone model are utilised to simulate the mechanical response of the matrix and fibre-matrix interface, respectively. Coulomb friction is assumed between the fibres and matrix after interface failure. Two sets of biaxial loading scenarios (i.e. transverse stress dominated and shear stress dominated) with the associated failure modes are selected for the failure analysis and assessment of these failure criteria. A data-driven failure envelope for the composites under biaxial loadings is developed using a univariate cubic spline function. Failure mode transition points are determined under biaxial loadings. It is found that the micromechanics-based numerical model is effective in assessing these two existing criteria.

Infrared radiation constitutive model of sandstone during loading fracture

The significant increase in energy demand will inevitably boost the exploitation of natural resources. The exploitation of resources including coal, oil, geothermal, natural gas, shale gas, and other energy has to be extracted with deep mining to fulfill the industry energy demand. With the increase of mining depth and the utilization of deep rock mass, the problem of high ground stress has become increasingly prominent. During high ground stress conditions, the mechanical behavior of hard rock will change significantly. Constructing a reasonable stress–strain damage constitutive model of hard rock is the basis for the design of a resource mining construction scheme, numerical simulation analysis, more accurate acquisition of rock mechanical characteristics, and evaluation of engineering rock stability. This is very crucial that needs to be addressed in a better way to solve the scientific problems of rock engineering. In this research, the infrared radiation observation experiments of sandstone biaxial under different lateral stresses are carried out. It is found that the infrared radiation energy has a near power function relationship with the effective stress in loading and fracture process. The quantitative characterization method of infrared radiation of the first invariant of stress and the second invariant of deviator stress is established. The cumulative high-temperature point scale factor amplitude is proposed to characterize the plastic volumetric strain of sandstone. Based on the effective stress and plastic strain, the plastic and damage models are established respectively. The three-dimensional plastic damage constitutive model of loaded sandstone based on infrared radiation is constructed. The model has clear input parameters having physical significance, and the compaction stage of sandstone is considered. The stress prediction of sandstone during biaxial loading is realized through the secondary development of a finite element software subroutine. The research results can lay a theoretical foundation for the analysis and evaluation of the mechanical characteristics of hard rock in the process of deep energy exploitation.

Trans-scale elastic–plastic damage analysis of 3D tubular braided composites with void defects

Three-dimensional (3D) tubular braided composites exhibit irreversible plastic deformation and nonlinear behavior due to the void defects and plastic effects of the matrix. Therefore, this paper establishes an elastic–plastic damage constitutive model of 3D tubular braided composites with defects, which is coupled with plastic effects and damage accumulation. Firstly, 3D tubular braided composite models with defects are established by sequential trans-scale analysis method to transfer the mechanical properties of the component materials. Then, according to the brittleness of the fiber or yarn and the plasticity of the matrix, the elastic and elastic–plastic damage model of the fiber and the matrix are established, respectively. On this basis, an interface element is established to characterize the mechanical properties of the interface with the tractor-separation constitutive model. Finally, the finite element results of the axial compression properties of 3D tubular braided composites coupled with the porosity and plasticity of the matrix, the longitudinal shear nonlinearity of the yarn and the bilinear constitutive relationship of the interface are in good agreement with the experimental results.

Elasto-plastic analysis and optimal design of composite integral abutment bridge extended with limited residual plastic deformation

Due to the growing significance of structural theories concerning the composite structure analysed and designed plastically, this paper introduces a new optimisation method for controlling the plastic behaviour of a full-scale composite integral abutment bridge by employing complementary strain energy of residual forces that existed within the reinforcing rebars. Composite bridges are structures made of components such as steel and concrete, which are frequent and cost-effective building methods. Thus, various objective functions were used in this work when applying optimum elasto-plastic analysing and designing the composite integrated bridge structure that was tested experimentally in the laboratory. In contrast, the plastic deformations were constrained by restricting the complementary strain energy of the residual internal forces aiming to find the maximum applied load and the minimum number of steel bars used to reinforce the concrete column part of the structure. The numerical model employed in this paper was validated and calibrated using experimental results, which were considered inside ABAQUS to produce the validated numerical model, using concrete damage plasticity (CDP) constitutive model and concrete data from laboratory testing to solve the nonlinear programming code provided by the authors. This paper presents a novel optimization method using complementary strain energy to control the plastic behaviour of a full-scale composite integral abutment bridge, with the original contribution being the incorporation of residual forces within reinforcing rebars to limit plastic deformations. Following that, a parametric investigation of the various optimisation problems revealed how models performed variously under different complementary strain energy values, which influenced the general behaviour of the structure as it transitioned from elastic to elasto-plastic to plastic; also results showed how the complementary strain energy value is connected with the amount of damaged accrued in both concrete and steel.

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.