Meso-scale modelling of compressive fracture in concrete with irregularly shaped aggregates

Abstract

This paper presents a meso-scale modelling framework to investigate the fracture process in concrete subjected to uniaxial and biaxial compression accounting for its mesostructural characteristics. 3D mesostructure of concrete consisting of coarse aggregates, mortar and interfacial transition zone between them was developed using an in-house code based on the Voronoi tessellation and splining method, which enables to generate the realistic-look aggregates with controllable structural features such as content, location, size and shape. Based on the generated 3D mesostructure, the concrete damage plasticity approach was employed to simulate the compressive fracture behaviour of concrete in terms of crack morphology and stress-strain response against the shape parameters of aggregate. Results indicate that the shape of aggregate has a negligible effect on compressive strength of concrete, which is highly associated with the random location and size distribution of aggregate. The aggregate irregularity has a significant influence on crack initiation and growth of concrete.

Introduction

Concrete is the most widely used construction material in the world. To date, tremendous efforts have been made to enhance the characterisation of concrete fracture using different experimental and analytical approaches [1]. However, it was found that the mechanical response is difficult to be faithfully captured during damage process in experiments, while the analytical methods may become very complex due to nonlinearity and randomness in a heterogeneous material like concrete [[2], [3], [4], [5], [6], [7], [8]]. The numerical approaches seem to be more effective to predict the fracture behaviour of concrete, among which the mesostructure-based models have been attracting more attention as the mesoscopic properties of concrete play an important role in fracture process in concrete [[9], [10], [11], [12], [13], [14]]. These models make it possible to explicitly investigate the effects of structural features of concrete on fracture behaviour at the mesoscopic level, where concrete can be treated as a multiphase composite material consisting of coarse aggregates, mortar matrix and interfacial transition zone (ITZ) between them [[15], [16], [17]].

In order to accurately analyse damage mechanism, a mesostructure model is expected to provide reliable quantitative and qualitative data on fracture process, which can be characterised by both stress-strain response [18] and crack pattern properties [[19], [20], [21], [22]]. The crack morphology does not only have a significant influence on mechanical strengths but also on transport properties such as permeability, diffusivity and absorptivity, which are strongly related to the long-term durability of concrete [1]. For instance, the crack development can facilitate the penetration of aggressive species (e.g. chlorides) into concrete, leading to deterioration of concrete and shortened service life of concrete structures. In recent years, numerous meso-scale models of concrete with the simplified geometries (e.g. 2D framework or using spherical-shaped aggregates) have been proposed, which might be able to predict the stress-strain response of concrete with an adequate precision but cannot properly simulate crack propagation in complex 3D mesostructures of concrete. The stress-strain data alone would be insufficient for the structural design of concrete and it is very important to provide the credible information on crack morphology. Therefore, all critical morphologic features should be considered to generate a model with a proper level of accuracy.

The model fidelity can be evaluated by comparing the properties of virtual and real mesostructures based on three experimental criteria related to coarse aggregates, which represent three levels of accuracy in hierarchical order: (1) Volume fraction: it is also known as parking density that represents the volume of coarse aggregates occupying the whole unit cell. The volume fraction of aggregate is typically between 30 and 50% based on the mix design suggested for normal strength concrete [18]. In terms of aggregate size, this is the lowest level of accuracy required to be considered in a model. Most of the previous models were able to adjust the volume fraction of aggregates [9,18,23]. (2) Size distribution: it is a list of values or a mathematical function that indicates the relative amount of aggregate present according to size [18]. A model adjusted based on this criterion meets the acceptable standard of validity regarding aggregate size. The previous studies showed that it was feasible to fulfil it in a model [9,18,23,24]. (3) Shape: the highest accuracy would be reached if both the size distribution and shape of aggregates could be configured in reference to the real data. Although, the complications start here in terms of measurement and simulation techniques due to the irregular nature of aggregates. Several shape parameters may be required to quantitatively describe the morphology, while even the accuracy of measurement methods would be disputable. The shape parameters obtained from the empirical data are the only way to validate a model. Regarding simulation, it is not easy to model irregular aggregates in random media with the desired shape properties and size distribution. In the following, the key issues will be more discussed on the simulation of aggregates with the realistic morphology.

In general, two main approaches are used to simulate a mesostructure based on computational geometric algorithms including image-dependent and image-independent methods [25]. An image-dependent approach can produce a realistic model by scanning an actual sample. However, it is a time-consuming and computationally expensive method and is highly dependent on image resolution [[26], [27], [28], [29], [30], [31], [32]]. These specifications limit the shape variations and number of models, which can be possibly produced. Consequently, it causes some difficulties in a typical statistical analysis, which is an essential part of the study of such random system. In contrast, the image-independent method is known as a computational cost-effective methodology with more producibility and less restriction of real samples [33]. Nevertheless, the actual aggregate shape was disregarded by using the simplified geometry in many previous models [2,15,[34], [35], [36], [37], [38], [39]].

To address the limitations mentioned, this study aims to develop a novel modelling framework with a high level of accuracy and low computational cost to investigate the effect of 3D mesostructure of concrete on crack morphology. The framework is based on the previous work [25] on the development of the image-independent simulation tools to generate the 3D particulate mesostructure model using the combination of Voronoi tessellation method and splining technique. It could create a realistic-looking geometry model with controllable structural parameters including shape, size and distribution of particles. This integrated model has two remarkable capabilities: (1) The model programmability allows designing a methodology that integrates the undiscovered aspects of fracture analysis affected by the irregular-shape of aggregates. (2) The controllability of the model enables to systematically adjust the overall and local shape of the aggregates in regard to the shape parameters including sphericity, elongation and roundness, which can be used to describe irregularity [25]. Thus, the mechanical response can be quantitatively characterised against the shape parameters. The triangulated surface representation of the aggregate model eases the measurement of these parameters and the simulation process of ITZ around each aggregate. The geometric model generated with the configuration designed can be applied to the continuum-based nonlinear finite element (FE) analysis to simulate the concrete fracture. Among different material models, concrete damage plasticity (CDP) that has been successfully developed, used and tested in many case studies [[40], [41], [42], [43], [44], [45], [46]] is adopted to predict the post-peak softening and crack pattern through mortar and ITZ in this study. Its combination with the mesostructure model proposed can precisely simulate two main failure modes including tensile cracking and compressive crushing.

In this paper, the fracture process in concrete under uniaxial and biaxial compression is investigated accounting for its mesostructural characteristics. Firstly, the 3D mesostructure of concrete composed of coarse aggregates, ITZ and mortar are generated by the in-house package developed in MATLAB considering the content, random location, size distribution and shape of aggregate. The size distribution of aggregate is adjusted based on the sieve analysis obtained from the experiments, while the shape properties are set up using a systematic strategy to gradually change the irregularity level. The spherical and polyhedron shaped aggregates involved in this study highlight the effect of geometric simplifications. The method to generate spherical aggregates follows the conventional algorithm, as presented in the literature [2,15,34,35]. The simulated aggregates are compared with two of the most common aggregates used for concrete production, i.e. natural gravels and crushed rocks [47]. Because of their structural characteristics, they cover a wide range of shape variations required for a comprehensive analysis targeted here. Natural gravels represent rounded aggregates with a quasi-spherical geometry and crushed rocks stand for rough aggregates with angular, elongated or flaky structure. Afterwards, based on the generated 3D mesostructure of concrete and CDP material model, the FE simulations are carried out using ABAQUS/Explicit to explore the fracture process in concrete under compression in terms of stress-strain response and crack morphology. Finally, the effects of shape parameters of aggregate on concrete fracture behaviour are estimated and discussed in detail.