MODELING OF CONCRETE SLABS UNDER FIRE*

The ability to assess the integrity of concrete structures after a severe thermal shock is extremely important not only for fire safety but also for the economy. A mathematical model, capable of rationally determining of fire response and correctly simulating the heat and mass transfer in concrete structures has been developed. Based on the concept of continuum mechanics, the conservation of mass, momenta, and energy equations have been used to yield a set of three coupled nonlinear partial differential equations with time dependent nonlinear mixed boundary conditions. Approximately a finite difference model has been developed for simulating the concrete structure under fire. The discrete set of implicit finite difference equations, after being quasi-linearized, is used and solved by a computer. Efficiently controlling time-step, the running computing time is minimized without detrimental effects on accuracy. The numerical results predict the phenomenon of “moisture clog” and show that: the permeability of concrete is an essential parameter. This parameter controls the buildup of pressure during the fire exposure. The explosive spalling of concrete under fire is predicted.     

A numerical model for elastic modulus of concrete considering interfacial transition zone

The effect of interfacial transition zone on mechanical properties of concrete has been found to be significant, thus the interfacial transition zone should be considered in the analysis for better estimation of elastic modulus of concrete. However, it is difficult to estimate elastic modulus of concrete practically using simple models proposed so far. In this study, a numerical concrete model that adopts three-phase model and finite element with material discontinuity was proposed to analyze concrete with complex interface in three dimensions. The validity of the proposed model was verified by comparing the calculated elastic moduli of concrete with those obtained from experiments. The effect of interfacial transition zone on elastic modulus of concrete with either low or high w/c was also investigated. The analysis results suggest that careful selection of characteristics for interfacial transition zone should be made for the accurate estimation of elastic modulus of concrete.     

Capillary suction and diffusion model for chloride ingress into concrete

A numerical approach, named TransChlor, is proposed to simulate transport phenomena of various substances in concrete. This approach is a theoretical model based on finite elements and finite differences methods. The model consists of coupled nonlinear partial differential equations based on Fick's diffusion law and on kinematics equations. Simulation results from a parametrical study highlight the influence of microclimatic conditions, exposure to deicing salts and concrete cover permeability and thickness on chloride ingress in concrete. The results show that the chloride ion concentration increases quickly in concrete cover when a structure is exposed to deicing salts at a mountainous location; whereas permeability of concrete cover is an insignificant parameter when the concrete is in direct or splash water contact.     

A homogenization approach to macroscopic strength criterion of steel fiber reinforced concrete

The present study aims to investigate the strength properties of the fiber reinforced concrete (FRC) by means of a micromechanics approach combining the static approach of limit analysis and the homogenization theory. The macroscopic strength criterion for FRC can be theoretically obtained from the knowledge of the strength properties of the individual constituents, namely, concrete matrix and fibers. Adopting a Drucker–Prager failure condition for the concrete matrix and assuming a simplified geometrical model for fiber orientations and length, an approximate static-based model is formulated for the overall strength properties. Explicit analytical expressions have been derived emphasizing the reinforcing contribution of fiber addition.Additionally, numerical solutions are computed by means of finite element tool implementing an elastoplastic step-by-step algorithm. The main objective of the numerical approach is twofold: qualify the relevance of the analytical results and investigate the influence of real fiber morphology on the composite strength properties.     

严寒地区冻融混凝土内钢筋应力滑移模型及OpenSEES有限元模拟

在严寒地区冻融混凝土与钢筋局部粘结滑移模型的基础上,基于冻融混凝土内钢筋沿锚固长度的受力机理分析及迭代过程分析,建立了冻融混凝土内钢筋应力滑移计算方法,提出了冻融混凝土内钢筋的应力滑移关系骨架曲线。基于有限元计算软件OpenSEES,将推导的冻融混凝土内钢筋应力滑移关系曲线嵌套于零长度截面单元,并将该单元应用于梁柱纤维模型,对3根既有的冻融钢筋混凝土框架柱进行模拟,与试验结果进行对比分析。结果表明,冻融钢筋混凝土柱有限元模型的模拟结果与试验结果的符合程度良好,从构件层次验证了推导的冻融混凝土内钢筋应力滑移关系曲线具有较好的精度和可靠性。研究成果可为严寒地区冻融混凝土内钢筋应力滑移推导及有限元模拟提供理论参考。     

FRP筋和钢筋混合配筋混凝土梁受弯性能数值模拟及理论分析

近年来,FRP筋和钢筋混合配筋混凝土结构已逐渐成为土木工程界的研究热点问题之一。在试验研究基础上,应用有限元分析软件ANSYS建立了GFRP筋和钢筋混合配筋混凝土梁的数值模型,对其抗弯性能进行了有限元分析,提出了FRP筋和钢筋混合配筋混凝土梁名义配筋面积的概念,并结合中国《纤维增强复合材料建设工程应用技术规范》建立理论模型,对混合配筋混凝土梁的抗弯承载力和挠度进行了理论分析。通过与试验结果对比,证明了有限元模型的精确性以及基于《纤维增强复合材料建设工程应用技术规范》提出的理论计算模型对混合配筋混凝土梁的有效指导性。     

聚丙烯纤维混凝土中硫酸盐扩散过程数值模拟

为了研究聚丙烯纤维混凝土中硫酸盐的扩散过程,首先根据聚丙烯纤维在混凝土中的空间分布特征,将其空间分布分为贯通型、半贯通型和内嵌型3种类型,分别计算了3种类型聚丙烯纤维对孔隙率的影响规律,然后基于Fick第二定律及反应动力学方程,建立了硫酸根离子在聚丙烯纤维混凝土中的扩散模型,并采用有限差分法进行数值求解,实现了对任意位置处硫酸根离子浓度的数值求解;最后采用聚丙烯纤维混凝土硫酸盐侵蚀试验对数值模拟结果进行对比验证.结果表明,数值计算结果与实际试验结果相对误差不超过17.65%,精度较高.     

2 — D model for carbonation and moisture/heat flow in porous materials

The previously-published one-dimensional finite element model for the analysis of the carbonation mechanism is extended to two-dimensional problems. The governing equations for the propagation of aggressive agents through concrete are rewritten for two-dimensional domains. A comparison is made with the one-dimensional model and some examples are developed to test the method. Finally, the study of a reinforcing bar placed at the corner of a concrete structure is presented in detail to show that the proposed numerical model is able to demonstrate the effects of the multidimensional moisture, heat and carbon dioxide transport through concrete.     

Multiphase Thermo-Hydro-Mechanical Model for Concrete Under Drying at High Temperatures

This article presents a numerical study for the analysis of the thermo-hydro-mechanical behavior of concrete subjected to high temperatures. Concrete is considered as a multiphase porous medium. The model, describing the strong coupling between mass, heat, and momentum transfers, takes into account the dehydration of the solid skeleton caused by a temperature increase. Simulations of the governing equations are presented in a two-dimensional configuration using the finite element method. Drying kinetics and mechanical behavior of concrete are presented and discussed in terms of moisture content, temperature, gas pressure, porosity, saturation, normal and shear stresses, and volumetric shrinkage evolutions. The model is validated in comparison with numerical and experimental results taken from the literature.     

结合压缩薄膜效应对BFRP筋自密实混凝土桥面板工作性能有限元分析

采用非线性有限元方法对英国北爱尔兰Thompson桥中的BFRP筋增强自密实混凝土桥面板进行数值分析,通过对比数值模拟结果和试验结果表明所建立的有限元模型能够较准确地反映BFRP筋增强自密实混凝土桥面板在轮压负载下的工作性能。基于有限元模型的有效性,采用非线性数值模拟对该新型桥面板进行极限承载力和破坏模式进行预测及参数化分析。结果表明,BFRP筋自密实桥面板极限承载力大约为欧洲轮压负载150 k N的6倍(100 t),由于现行桥面板设计规范忽略了压缩薄膜效应的存在而导致桥面板极限承载力设计过于保守,参数化分析发现配筋率和筋材类型对桥面板极限承载力影响不大,而混凝土强度和跨高比是影响桥面板极限承载力的主要因素。     

对FRP筋混凝土桥梁面板承载力性能的非线性有限元分析

为了研究FRP筋混凝土梁面板的承载能力,采用了大型商用软件ABAQUS对Sherif EI-Gamal等的钢混桥梁模型进行了数值模拟。将非线性有限元计算结果同试验结果进行对比分析,非线性有限元的计算结果与试验结果吻合良好。基于数值模准确的分析结果,对结构体系中的压缩薄膜效应进行了分析,并开展了一系列的参数学习,包括混凝土强度、支撑梁刚度以及横隔梁。分析结果表明,压缩薄膜效应对FRP筋混凝土桥面板的承载能力有显著的影响。     

对FRP筋混凝土桥梁面板承载力性能的非线性有限元分析

为了研究FRP筋混凝土梁面板的承载能力,采用了大型商用软件ABAQUS对Sherif EI-Gamal等的钢混桥梁模型进行了数值模拟。将非线性有限元计算结果同试验结果进行对比分析,非线性有限元的计算结果与试验结果吻合良好。基于数值模准确的分析结果,对结构体系中的压缩薄膜效应进行了分析,并开展了一系列的参数学习,包括混凝土强度、支撑梁刚度以及横隔梁。分析结果表明,压缩薄膜效应对FRP筋混凝土桥面板的承载能力有显著的影响。     

混凝土中氯离子二维扩散分析的边界元法

混凝土二维扩散分析的有限元法等常用数值法通常需要在空间域和时间域中同时采取细密的离散网格,计算量大.针对混凝土中氯离子二维扩散问题,提出了计算长度的概念及其计算表达式,首次建立了相应的边界元计算方法,确定了时间域离散的步长.通过该计算模型研究了混凝土结构的拐角等几何形状复杂位置的氯离子分布规律.由于边界元法可以将二维问题简化为一维离散问题,而且该计算模型在时间域内的离散网格非常稀疏,因此,相对于其他数值方法,该方法计算量很小,算例分析验证了该方法具有很高的计算精度和计算效率.同时,对角点等位置的氯离子浓度的计算结果表明,二维方法能够更准确地反映氯离子在混凝土结构中的扩散和积聚规律.     

Non-structural cracking in RC walls: Part I. Finite element formulation

In this paper, a three-dimensional finite element model for the analysis of non-structural cracks occurring in reinforced concrete (RC) walls is introduced. The numerical model could take into account both time-dependent temperature variations due to hydration heat and non-uniform moisture distribution during drying, and the coupling effect between the heat transfer and the moisture diffusion. Calculation of the temperature and internal relative humidity variations of RC walls is followed by determination of stresses due to thermal gradients, differential drying shrinkage, and average drying shrinkage. The mechanical properties of early age concrete, determined from numerous experimental studies, are taken into consideration to improve the accuracy of the numerical results, and a discrete steel element derived using the equivalent nodal force concept is also used to simulate reinforcing steels embedded in a concrete matrix. The validity of the proposed procedure is verified by comparing the measured experimental data with the analytical results for RC walls.     

Predicting carbonation in early-aged cracked concrete

Carbonation in cracked concrete is considered as one of major deteriorations accelerating steel corrosion in reinforced concrete structures. For durable concrete structures, it is necessary to control crack in concrete through crack resistance evaluation for early-aged concrete structures, but often unavoidable cracks in early-aged concrete may occur. These cracks become a main path for CO₂ penetration inside concrete so that the carbonation is accelerated in cracked concrete.In this study, an analytical technique for carbonation prediction in early-aged cracked concrete was developed for considering both CO₂ diffusion of pore water in sound concrete and in cracked concrete. Then, characteristics of diffusivity on the carbonation in early-aged concrete are studied through finite element analysis implemented with the so-called multi-component hydration heat model and micro-pore structure formation model. The carbonation behaviour in sound concrete and cracked concrete are also simulated by using the derived diffusivity with consideration of reaction with dissolved CO₂. Finally, numerical results obtained for cracked concrete made with 3 different W / C ratios (45%, 55%, and 65%) with different crack widths were compared with experimental results.     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

This paper presents a model of heterogenous diffusion in capillary porous materials during the process of drying. The governing heat and mass transfer equations have been established using the liquid as well as vapor flow. Two models have been presented. Model 1 does not consider the heat conduction while the model 2 has been established by considering the conduction. The developed models and the numerical solutions of the resulting differential equations can take into account the moisture and temperature dependent thermophysical properties of the product. All equations have been established in spherical coordinates but the programme written for the purpose of calculations can be used for other geometries also. Numerical calculations have been performed for gas concrete and tiles using model 1, while model 2 has been used for gas concrete only because of the lack of data for thermophysical properties of the tile. For gas concrete it was seen that conduction has only marginal effect on the drying process and the numerical predictions of the drying process were reasonably accurate.     

Multi-scales modelling for the behaviour of damaged concrete

The aim of this study is to investigate and to simulate damage mechanisms of concrete under fire conditions. A micro-mechanical model has been developed by coupling the effective moduli approach with a finite element model based on the representation of the heterogeneous materials random microstructure. Numerical simulations have been carried out in order to analyze the effective behaviour of confined concrete samples subjected to high temperatures coupled to compressive loads and to localize damage on the microstructure scale. These simulations show that the ‘transient thermal strain’, noticed during experimental tests, is due to the thermal damage of concrete.     

A discrete crack approach to normal/shear cracking of concrete

This paper presents a numerical procedure for mixed mode fracture of quasi-brittle materials. The numerical procedure is based on the cohesive crack approach and extends it to mixed mode fracture. The crack path is obtained, and the mixed mode fracture model is incorporated into the crack path. The crack model is based on the formulation of the classical plasticity. The model is incorporated into a commercial finite element code by an user subroutine and is contrasted with experimental results. The numerical results agree quite well with two experimental sets of mixed mode fracture of concrete beams; one from Arrea and Ingraffea, the other from a nonproportional loading by the authors. Two other sets of experimental fracture results were modeled based on double-edge notched testing. The numerical procedure, mainly based on standard properties of the material measured by standard methods, predicts the experimental records of the load versus displacement at several control points of the specimens for three homothetic sizes of specimen.     

A micromechanical approach to elastic and viscoelastic properties of fiber reinforced concrete

Some aspects of the constitutive behavior of fiber reinforced concrete (FRC) are investigated within a micromechanical framework. Special emphasis is put on the prediction of creep of such materials. The linear elastic behavior is first examined by implementation of a Mori-Tanaka homogenization scheme. The micromechanical predictions for the overall stiffness prove to be very close to finite element solutions obtained from the numerical analysis of a representative elementary volume of FRC modeled as a randomly heterogeneous medium.The validation of the micromechanical concepts based on comparison with a set of experiments, shows remarkable predictive capabilities of the micromechanical representation.The second part of the paper is devoted to non-ageing viscoelasticity of FRC. Adopting a Zener model for the behavior of the concrete matrix and making use of the correspondence principle, the homogenized relaxation moduli are derived analytically. The validity of the model is established by mean of comparison with available experiment measurements of creep strain of steel fiber reinforced concrete under compressive load. Finally, the model predictions are compared to those derived from analytical models formulated within a one-dimensional setting.     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

ABSTRACT

This paper presents a model of heterogenous diffusion in capillary porous materials during the process of drying. The governing heat and mass transfer equations have been established using the liquid as well as vapor flow. Two models have been presented. Model 1 does not consider the heat conduction while the model 2 has been established by considering the conduction. The developed models and the numerical solutions of the resulting differential equations can take into account the moisture and temperature dependent thermophysical properties of the product. All equations have been established in spherical coordinates but the programme written for the purpose of calculations can be used for other geometries also. Numerical calculations have been performed for gas concrete and tiles using model 1, while model 2 has been used for gas concrete only because of the lack of data for thermophysical properties of the tile. For gas concrete it was seen that conduction has only marginal effect on the drying process and the numerical predictions of the drying process were reasonably accurate.