(1. Beijing University of Technology, Beijing100044; 2. Engineering Earthquake Research Center of China Academy of Water Resources and Hydropower Research, Beijing 100044)

This paper introduces the research methods of concrete meso-mechanics, summarizes the research results of concrete experimental research and meso-level numerical simulation so far, and analyzes and discusses in detail the advantages and disadvantages of three numerical models of meso-mechanics: lattice model, random aggregate model and random mechanical property model. At present, the research of concrete micromechanics mainly focuses on the research of mesoscopic numerical model, and the established mesoscopic numerical model needs to be improved, and there is still a lack of systematic experimental results of mechanical characteristics parameters of various materials. There is still much work to be done to replace some experimental tasks with numerical simulation of micromechanics.

Keywords: concrete; Mesomechanics; Numerical simulation; experimental investigation

China Library Classification Number: TV3 13 Document Identification Number: A.

1 Introduction

Concrete is a composite material composed of water, cement and coarse and fine aggregates. General concrete internal structure is divided into three levels according to different characteristic dimensions and research methods (as shown in figure 1): (1) micro level. The structural unit scale of the material is at the atomic and molecular level, that is, from less than 10-7 cm to 10-4 cm, and the microstructure of cement hydrate is emphatically analyzed. It is composed of crystal structure and molecular structure, which can be observed and analyzed by electron microscope, and is the research object of material science. (2) The meso level. From the molecular scale to the macro scale, the scale of its structural units ranges from 10-4cm to several centimeters, or even more, focusing on the fine and coarse aggregates, cement hydrates, pores, interfaces and other meso-structures, forming multiphase composites, which can be numerically analyzed according to various calculation models. At this level, concrete is considered to be a three-phase material composed of coarse aggregate, hardened cement mortar and the transition zone (bonding zone) between them. The pores in mortar are small, numerous and randomly distributed, and the mechanical properties of cement mortar can be regarded as meso-uniform damage. Mortar specimens with the same mixture ratio and the same conditions usually have relatively stable mechanical properties, which can be directly determined by experiments. The initial bond cracks between coarse aggregate and cement mortar are caused by bleeding, drying shrinkage and temperature change, and the development of these meso-internal cracks will directly affect the macro-mechanical properties of concrete; (3) Macro level. When the characteristic size is more than a few centimeters, concrete, as a heterogeneous material, has a characteristic volume, which is generally considered to be equivalent to 3 ~ 4 times the maximum aggregate volume. When it is smaller than the characteristic volume, the heterogeneity of the material will be very obvious; When it is larger than the characteristic volume, the material is considered to be uniform. The results of finite element calculation reflect the average effect in a certain volume, and the relationship between the average stress and the average strain of this characteristic volume becomes a macro stress-strain relationship.

Figure 1 concrete hierarchy diagram

For a long time, people have attached great importance to the mechanism, constitutive relation, mechanical model and calculation method of the whole process of macro-mechanical properties deterioration of concrete materials and components, and studied them with various theories and methods. In order to study the structure of materials, the development of cracks and the relationship between uniaxial, biaxial and triaxial stress and strength, people have done a lot of experiments. Strength theory has also developed from the simplest maximum tensile stress theory and maximum tensile strain theory to single shear stress series, octahedral shear stress series and double shear stress series. So far, there are three unified strength theories: (1) elastic constitutive model, including linear elastic constitutive model and nonlinear elastic constitutive model; (2) Constitutive model based on classical plasticity theory; (3) Constitutive model based on irreversible thermodynamics, including intrinsic time model and damage mechanics model.

The research on the microstructure of concrete shows that there are micro-cracks in concrete even before loading. Generally, this kind of microcrack is first formed on the contact surface (bonding zone) between larger aggregate particles and mortar, which is called initial bonding crack. This is caused by the drying shrinkage of cement mortar during concrete hardening. The interface between mortar and coarse aggregate is the weak link in concrete, which leads to low tensile strength of concrete. The number of bonding cracks depends on many factors, including aggregate particle size and its gradation, cement dosage, water-cement ratio, curing strength, curing conditions, environmental humidity, concrete calorific value and so on. Due to the different stiffness of aggregate and mortar, this kind of crack will further develop during loading, thus making the macro stress-strain curve of concrete nonlinear. Non-uniformity is the most essential feature of concrete materials, and microcracks are the dominant factor to determine its properties.

Materials and physicists study the mechanism of micro-defects from a micro perspective, but the results are not easily related to macro-mechanical quantities. The theory and method of concrete fracture mechanics take macro crack analysis as the core, and mainly study the stress field, strain field and energy release rate near the crack tip, thus establishing the criteria of macro crack initiation, stable crack propagation and unstable crack propagation. However, fracture mechanics cannot analyze the influence of the formation and development of micro-defects or micro-cracks in materials on the mechanical properties of materials before the appearance of macro-cracks.

In order to establish the relationship between the meso-structural defects of concrete and its heterogeneity and macro-mechanical properties, concrete has been regarded as a heterogeneous composite material since the late 1970s, and the structure, mechanical properties and crack propagation process of concrete are studied from the micro level. With the development of computing technology, numerical methods are directly used to simulate the crack propagation process and failure form of concrete specimens or structures at the meso level, which directly reflects the damage and failure mechanism of specimens, and has attracted wide attention. In recent ten years, many meso-mechanical models have been proposed to study the fracture process of concrete based on the meso-structure of concrete. The most typical models are lattice model and random particle model. These models all assume that concrete is a three-phase composite material composed of mortar matrix, aggregate and the bonding zone between them, and a simple constitutive relation is used to simulate the complex macro-fracture process at the meso level. In addition, the literature puts forward (as shown in Figure 4). In order to consider the randomness of mechanical properties distribution of concrete members, the material properties of each member are assigned according to the given Weibull distribution. Various components (including mortar matrix, aggregate and interface) are projected on the grid for finite element analysis, and different mechanical parameters are given to the material units of each phase, and a concrete numerical sample with random mechanical properties is obtained numerically. The stress and displacement of these meso-elements are calculated by finite element method. According to the elastic damage constitutive relation, the damage evolution of meso-unit is described. The maximum tensile stress (or tensile strain criterion) and Mohr Coulomb criterion are used as the threshold conditions for tensile damage and shear damage of meso-elements respectively. Literature [29] used this model to systematically simulate uniaxial tension and compression, biaxial tension and compression combination, tensile mode I fracture, three-point bending and tensile-shear fracture of concrete. However, the randomness of aggregate distribution at all levels in the specimen is not considered. In fact, the randomness of concrete aggregate gradation and spatial distribution has an influence on the calculation results.

Fig. 4 Stochastic mechanical characteristic model

Up to now, the numerical simulation of concrete meso-level is mostly a plane static problem, and it is only limited to the study of small-sized concrete specimens with less gradation. Most literatures focus on the numerical simulation of failure process, which is far from the purpose of replacing some tests, but it is still blank to simulate the failure process of fully graded concrete under static and dynamic actions.

5 concluding remarks

So far, although there are many achievements and advantages in numerical simulation with lattice model, this model can not reflect the actual deformation form of the element, and the failure of the element is an irreversible process, which is difficult to reflect the problems of unloading and dynamic repeated loading. The random aggregate model does not consider the random distribution of mechanical properties of each phase in the calculation domain, and the random mechanical properties model does not consider the random distribution of aggregate particles in the calculation domain. In fact, the random distribution of coarse aggregate particles and the random distribution of mechanical properties of meso-materials in the specimen domain have certain influence on the macro-mechanical properties of concrete specimens, so these meso-models need to be improved. The micromechanics of concrete is based on practical tests, and the mechanical properties, damage constitutive relation and damage evolution law of each phase of concrete must be determined through tests. Meso-mechanics method combines continuum mechanics, damage mechanics and computational mechanics, combines the uncertainty of input parameters with probability and statistics theory, and combines experiments and calculations to build a bridge between the microstructure and macro-mechanical properties of concrete. The improvement of experimental observation means and the rapid development of computer technology show a broad prospect for the study of concrete micromechanics.

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