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

148

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

 

levels. This aspect is considered in the early age model, as it can be relevant for predicting 

cracking risk during the cement hydration process. 

The mechanical characteristics of concrete are simulated through the concept of degree of 

hydration or maturity [12]. In this study, these are described as a function of the equivalent 

age. Details of the formulation and validation of the early age model can be found in [9]. 

 

2.3  Mature mechanical model 

The fibre beam model [10] was used in the mechanical simulation of the loading test at 

mature age. The model is based on the Timoshenko beam theory with the cross section 

discretized into fibres of concrete and smeared stirrups and longitudinal steel filaments, as in 

the model for early age analysis. A sectional formulation accounts for nonlinear axial force-

bending-shear interaction. Cracking of concrete is based on the smeared rotating crack 

approach. 

 

 

3.  Simulation of the Concrack2 RG8 test 

 

3.1  Description of the experimental test 

The experimental test under study here is the full scale beam subjected to restrained shrinkage 

(RG8 test) of ConCrack Benchmark [1, 2] (Figure 1). The central part is 5.9 m long, 0.50 m 

wide and 0.80 m high, longitudinal reinforcement of 2% and concrete cover equal to 50 mm. 

The two massive heads are 0.90 m long, 2.2 m wide and 0.90 m high. Two cylindrical struts 

with a diameter equal to 32.2 cm and thickness of 4 cm are anchored to concrete heads in both 

ends of the beam.  

The beam was thermally insulated during the first 2 days after casting. Then, the insulation 

and the formwork were removed and the beam was kept at ambient conditions for 2 months. 

The heads were prestressed just before formwork removal. Subsequently, the beam was 

transferred to the testing bench and loaded until near bending capacity. Figure 3 shows a 

scheme of the RG8 beam on the testing bench. The two concentrated loads were applied in 16 

loading steps of 50kN/jack (until a maximum of 800kN/jack). A pre-loading of 200 kN was 

applied and removed before the start of the test.  

The beam was largely instrumented, both externally and internally with the following types of 

sensors: temperature; vibrating wire for deformations; displacement sensors for the loading 

phase; optical fibre sensors; electrical strain gauges placed on reinforcement bars. During the 

test, the observation of the development of cracks and forces was the prime focus.  

Figure 3: Loading scheme of the RG8 test [1] 

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149

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

 

3.2  Parameters of the model for early age analysis 

The thermal characterization of concrete was done with the data provided by the benchmark: 

mix proportion, chemical composition of the cement, volumetric mass, ambient temperatures 

and the temperatures development in an adiabatic test (which for operational reasons began 

three hours after the beam was cast). As the adiabatic test should start right after mixing of 

concrete (5-10 min) in order to capture the entire hydration temperature, the hydration degree 

was modelled according to Freiesleben-Hansen and Pedersen [13], with the parameters 

suggested by Schindler and Folliard [14] depending on the water/cement ratio (w/c), cement 

fineness (specific surface area) and cement chemical composition [3]. 

In the 2D model for early age thermal-analysis, the cross section was discretized into 640 

elements, 20 equal length divisions in the horizontal direction and 32 equal length divisions in 

the vertical direction. Time domain was discretized into 15 minutes steps. 

The development of the mechanical properties was adjusted with the models of the 

Norwegian University of Science and Technology (NTNU) [15]. 

As the experimental information available about creep was limited to one loading age (2 days) 

the  Linear Logarithmic Creep Model was used considering the parameters proposed by 

Larson and Jonasson [16, 17] for a concrete with a similar modulus of elasticity. For more 

details about the creep models used, see [3]. Due to the lack of experimental tests for the 

characterization of the instantaneous mechanical behaviour of concrete, a linear constitutive 

equation for concrete with effective tensile strength equal to 90% of the tensile strength was 

considered. This hypothesis may have a relevant effect in the stress state predicted for early 

ages [18]. 

 

Figure 4: FE model for early age analysis 

The model for the mechanical analysis is presented in Figure 4: the beam was divided into 10 

elements of different lengths, the mesh of the cross section being the same as in the thermal 

analysis. The heads were modelled with eight elements and the struts with one element. 

The input solicitations in the model were the temperatures generated by the heat of hydration 

and atmospheric environment and the degree of hydration in each filament. No friction was 

considered between the formwork and the beam. The heads were considered to have the same 

maturity as the central part of the cross section at each instant of time. 

 

3.3  Parameters of the model for loading test at mature age 

The longitudinal mesh is represented in Figure 5 consisting of 35 finite elements and the cross 

section discretization equal to the one used in early age thermo-mechanical analysis. 

Pertaining to the boundary conditions, the elastic supports represent the stiffness of the 

Macalloy bars that tie the beam to the bending bench (k=503077 kN/m) and there is a 

z=0

z=0

z=0

z=0

y= z=0

x= y= z=0

x

y

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