Scale-bridging Modeling of Microstructural Changes in Concrete and Damage Analysis of Concrete Structures for the Identification of Coda Signals

M.Sc. Giao Vu

To establish a model-based characterization of the degradation of concrete at multiple scales and to enable a classification of the level of damage using simulated and measured coda data is the objective of the CoDA research unit.

Figure 1: Strategy for simulation-based identification of damage pursued in the first phase of the project.

Generation of realistic virtual concrete specimens

Figure 2: (a) Illustration of virtual aggregates with different roughness and elongation, (b) section of aggregate with concave surfaces, (c) large-scale concrete sample generated by stacking 8 blocks of concrete specimens (30x30x20cm), (d) synthetic concrete sample generated from experimental data (TUM1), (e) comparison of generated and actual aggregate distributions, (f, g) cross-sections of virtual and real concrete mesostructure.

In order to simulate realistic fracture processes in concrete, a virtual concrete micro- and mesostructure generator was developed that simulates distributed microcracks using a multiscale micromechanical model. The algorithm is capable of generating extremely realistic concrete mesostructures given a particle size distribution. The coarse aggregates are modeled as polyhedra with multiple faces, different aspect ratios, and concave depressions (Figs. 2a and 2b). These are assembled into a mortar matrix using a hierarchical sequential random adsorption algorithm considering the particle size distribution (Fig. 2e). Fig. 2c shows a large-scale concrete model generated by stacking 8 copies of a single concrete block by exploiting the periodicity of the mesostructure. Figs. 2f and 2g show a comparison between the actual and numerical concrete cross sections. A Python implementation of PyCMG has been developed and is available as open access/source at

Simulation of damage in uniaxial compression

Results of a uniaxial compression simulation are summarized in Fig. 4. Fig. 4a shows the reduced-order concrete specimen. As can be seen in Fig. 4b, the model prediction is in agreement with the experimental data (measured by TUM1). Model predictions show that microcracking occurs predominantly in the vicinity of the aggregates as a consequence of local stress concentrations, which is in agreement with experimental observations [9]. It is to be noted that, i) no implicit macroscopic constitutive law needs to be employed, and ii) microcracking is a direct consequence of mesoscopic heterogeneity and pre-existing defects in concrete. The model-order reduction has enabled a substantial speed up that is 10⁴ times faster than an equivalent numerical simulation.

Figure 3: Schematic illustration of the multiscale model of concrete.

Generating damaged concrete specimens using multiscale modeling

The central theme of the Research Unit RUB1 is to identify the level of damage in concrete using diffuse ultrasonic coda waves. To generate virtual concrete specimens at various levels of damage, a reduced-order multiscale model was developed in the first phase of the project. At the scale of the cement paste, microcrack growth is modelled using a combination of continuum micromechanics and linear elastic fracture mechanics. The micromechanics model is incorporated into a reduced-order Lippmann-Schwinger based mesomodel for concrete. A schematic illustration of the multiscale model is described in Fig. 3.

Figure 4: a) Visualization of the reduced-order concrete specimen, b) Model prediction vs. laboratory tests (uniaxial compression test). The 12 load levels at which the microstructure snapshots are extracted for machine learning are marked by colored dots, c) Microcracks in the specimen at 63.41 MPa.

Damage identification and classification in the pre-peak regime

In this study, 12 voxel data snapshots of damaged specimens obtained from the uniaxial compression simulation are grouped into 3 phases (see Fig. 4). The 12 corresponding degraded stiffness field serve as input for the forward wave propagations simulation. Ultrasonic wave simulations are used to acquire a dataset of 972 time series signals, which are analysed using Coda Wave Interferometry. Machine Learning methods like Random Forests, Support Vector Machines and Neural Networks are used to train a classifier to identify the level of damage from the coda signals. The signals are normalized, reshaped into images and fed into a Convolutional Neural Network classifier, which achieved an 85% accuracy in predicting the 3 damage phases. However, there is still some difficulty in distinguishing between diffuse microcracking and microcrack coalescence (Phase 1-2), resulting in approximately 15% misclassification (see Fig. 5)

Figure 5: a) Deep learning CNN architecture used for damage identification: The input is a normalized time-series signal that is re-shaped into a matrix and the output is the material state. The re-shaping is realized by partitioning the time series (1D array) into a finite set of smaller arrays; thus, each row of the input matrix corresponds to a portion of the 1D signal. Phase 1: Elastic deformation and crack closure, Phase 2: Microcrack growth, Phase 3: Initial stages of microcrack coalescence, b) Performance of the classifier shown as a confusion matrix (the diagonal values are the fraction of correct classification, and the off-diagonals are miss-classifications); Right: Training and validation accuracy and loss.


M.Sc. Giao Vu
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