Proceedings of the International rilem conference Materials, Systems and Structures in Civil Engineering 2016

117

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

 

mesoscale models 

 

particles and cement paste have significantly different properties. This includes 

the time-dependent hydration of the cement paste compared to the fixed properties 

of the aggregates, only cement paste is prone viscous deformations and the 

different properties, e.g. in the simplest case the Young’s modulus, lead to a 

heterogeneous distribution of the quantity of interest, e.g. stresses.  

 

2. Mesoscale 

generation 

In the following, a special focus is given to 

mesoscale models.  

For modelling purposes, the procedure of 

simulating virtual concrete specimens with a 

direct discretization of the mesoscale 

structure can either be performed by 

scanning real specimens [2] or by sampling 

“virtual” concrete specimens. In the latter 

case, the grading curve characterizes the size 

distribution of the aggregates within the 

material. In this case, the discretization can 

be decomposed into a take and a place 

phase. In the first phase, the particles 

numbers shapes are generated, whereas in 

the second step these particles are placed 

into the specimen with the constraint that 

overlapping is not allowed. In our current model, an algorithm based on [3] is used. The 

particles are assumed to be spherical and inserted at random positions within the specimen 

with a reduced diameter. This requires checks to avoid overlapping, but due to the reduced 

diameter and the corresponding low particle volume this is computationally not expensive and 

can be performed with standard checks enhanced with special subboxes to reduced the 

number of overlapping checks. In the second step, an event-driven molecular dynamics 

simulation is performed with initial random velocities of the particles and a slow growth of 

the particle radii up to the envisages size. For detailed information, the reader is refered to [3]. 

An example of mesoscale geometries created with the enhanced algorithm is given in Figure 

1. 

3.  Multiphysics modelling of shrinkage 

Shrinkage in concrete is usually determined experimentally for stress free conditions. For 

modelling purposes, this experimentally determined shrinkage strain is often subtracted from 

the macroscopic strain assuming that shrinkage only produces stresses if the macroscopic 

deformation of the specimen is constrained. 

Looking at concrete on a mesoscale level, a heterogeneous material consisting of aggregates 

and cement paste is present, where only the latter is prone to shrinkage deformations. As a 

consequence, internal stresses at the particle boundaries occur. Especially at early ages, these  

 

Figure 1 : Mesoscale geometry of a concrete 

cube with spherical aggregates. 

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118

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

stresses are significant and lead to a microcrack evolution and a pre-damage (without any 

mechanical loads). 

In this paper, shrinkage is assumed to be a reversible process related to the moisture content 

of the material. It is difficult to test this assumption experimentally, since fully rewetting the 

specimen is not possible. Moreover, the aging effects are always present resulting in 

additional permanent strains that are sometimes interpreted as permanent shrinkage strains.  

A two-phase moisture transport model based on [4] has been implemented. In Figure 2, an 

exemplary moisture distribution within a concrete specimen (40mm x 160mm) after 28 days 

of drying is illustrated. A Fullers-curve for the aggregate size distribution with a maximum 

aggregate size of 16mm was used. The drying process starts once the relative humidity of 

95% is reduced to 40%. A large gradient of the moisture distribution is observed with the core 

of the specimen remaining almost at the initial RH of 95%. Under the assumption of the 

moisture content being the driving force of shrinkage strains, this leads to a very 

heterogeneous distribution even for this small specimen as illustrated in Figure 3. Another 

remark is related to the hydration of the concrete material that is characterizing the 

development of the material strength. The hydration stops at relative humidities below 80%. 

 

Figure 3 : Ratio between local and macrospic strain 

in horizontal direction. 

 

 

Figure 2 : Distribution of relative humidity after 28    

days of drying. 

 

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119

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

As a consequence, any experimental test that measures the concrete strength (or similar the 

Young’s modulus) as a function of the time or degree of hydration should take this 

heterogeneous distribution into account. Otherwise, size effects are present and the 

generalization of the results is very difficult since other effects such as e.g. creep strongly 

influence the results. 

There are many different approaches on how to include the relation between shrinkage and 

moisture content in the numerical model. The first approach follows a strain based model [5]. 

Based on the simulation of the moisture distribution and an experimental  shrinkage tests, an 

additional strain component is calculated. Note that when using this approach with a direct 

discretization  of the mesoscale structure, substantial tensile stresses are obtained.  

Calibrating a shrinkage model based on weighting the specimen, that is  calculating the loss of 

water in a homogeneous way,  might significantly deviate from the real situation, since – as 

already discussed – the moisture distribution is strongly heterogeneous. Due to the drying  

 

Figure 2 : Minimum principal stress after drying of 

28 days (stress based approach).  

 

 

Figure 3 :  Maximum principal stress after drying of 

28 days (stress based approach). 

 

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