When a concrete structure is subjected to an impact, the material is subjected to high triaxial compressive stresses. Furthermore, the water saturation ratio in massive concrete structures may reach nearly 100% at the core, whereas the material dries quickly on the skin. The impact response of a massive concrete wall may thus depend on the state of water saturation in the material. This paper presents some triaxial tests performed at a maximum confining pressure of 600 MPa on concrete representative of a nuclear power plant containment building. Experimental results show the concrete constitutive behavior and its dependence on the water saturation ratio. It is observed that as the degree of saturation increases, a decrease in the volumetric strains as well as in the shear strength is observed. The coupled PRM constitutive model does not accurately reproduce the response of concrete specimens observed during the test. The differences between experimental and numerical results can be explained by both the influence of the saturation state of concrete and the effect of deviatoric stresses, which are not accurately taken into account. The PRM model was modified in order to improve the numerical prediction of concrete behavior under high stresses at various saturation states.
The upcoming need for concrete structures designed against impulsive and extreme loads due to natural hazards, industrial accidents, or terrorist attacks remains an important issue. Predicting the response of such a structure, subjected to this type of loading and characterized by a high mean stress generated in the impact zone, requires constitutive modeling capable of reproducing material behavior within this loading range (high triaxial stresses and high strain rates). Improving the knowledge on the constitutive behavior of concrete under impact is a strategic issue for many sensitive infrastructures (e.g., nuclear power plants). Protective concrete structures, like nuclear reactor containment vessels, are typically massive and remain saturated at their core several years after casting, while their surfaces dry quickly in contact with air [
In the vicinity of the zone submitted to a hard impact (for instance the fall of an aircraft turbine on a containment vessel) a triaxial stress state occurs characterized by a compression with lateral confinement. The behavior of wet concrete may differ substantially from that of dry concrete [
The high-capacity triaxial press GIGA allows testing of concrete samples under various loading paths and concrete compositions [
In this paper, triaxial tests up to 100 MPa of confining pressure performed on concrete with different degrees of saturation will be presented and analyzed. Some results of tests carried out at very high confining pressure (600 MPa) will be discussed so as to bring out the effect of the saturation ratio. These tests will be simulated thanks to the coupled damage plasticity model PRM [
The GIGA press allows loading cylindrical concrete specimens 7 cm in diameter and 14 cm high to a confining pressure up to 0.85 GPa and a maximal axial stress of 2.3 GPa. The large sample size (compared to the high stress level) allows testing real concrete samples with an aggregate size able to reach 8 mm (Figure
General view of the GIGA press (a), loading capacity (b), and sample sizes (c).
The high performance concrete mix studied herein was designed for the concrete slabs tested during the benchmark project “Improving the Robustness of Assessment Methodologies for Structures Impacted by Missiles (IRIS)” conducted by the OECD’s Nuclear Energy Agency (NEA) [
Concrete mix specifications and main properties.
Concrete mix (for 1 m3) | |
Gravel (0.5/8) (kg) | 925.9 |
Sand (kg) | 646.1 |
Water (kg) | 215 |
Cement (CEM II B 42.5) (kg) | 489 |
Fly ash (kg) | 88 |
Superplasticizer (kg) | 6.33 |
Density (kg/m3) | 2370 |
Main concrete properties | |
Compressive strength (MPa) | 67 |
Porosity accessible to water (%) | 12 |
Cement paste volume (m3 for 1 m3 of concrete) | 0.375 |
Water/cement ratio | 0.44 |
The concrete used in this study is representative of that selected for a nuclear power plant. Its unconfined strength is roughly 67 MPa for simple compressive stresses and approximately 4.5 MPa for tensile stresses. The samples were prepared for being tested with a triaxial confining pressure varying from 0 MPa to 600 MPa. Porosity and degree of saturation measurements were carried out prior to testing (Table
The maximum aggregates size used in the concrete mix is 8 mm. For triaxial tests, specimens 70 mm in diameter and 140 mm in height allow obtaining a Representative Elementary Volume (REV) with a minimum dimension of 3 to 5 times the largest aggregate. This specification serves to avoid significant variability in results due to the presence of large aggregates. To prevent edge effects due to sample faces, the samples were cored and rectified with water.
The concrete unconfined compressive strength increase with the loading rate observed by some authors [
This section presents triaxial compression test results for a confining pressure varying from 0 MPa to 600 MPa.
The triaxial tests performed consist of applying a hydrostatic pressure around the specimen thanks to a noncompressible fluid at a rate of 1.7 MPa/s (for quasi-static testing) up to a pressure value
After this first hydrostatic phase, a constant displacement rate of 14
Figure
Axial stress versus axial and circumferential strains for various confining pressures (LVDT for axial strains and strain gauges for circumferential strains).
Figure
Nevertheless, as proposed by Vu et al. [
Mean stress versus volumetric strain for various confining pressures.
Even though the good level of test repeatability can be visualized during the hydrostatic part (Figures
Axial stress versus axial and circumferential strains for triaxial tests under 26 MPa of confining pressure (LVDT for axial strains and strain gauges for orthoradial strains).
Mean stress versus volumetric strains for triaxial tests under 26 MPa of confining pressure (LVDT for axial strains and strain gauges for orthoradial strains).
A triaxial test at a 50 MPa confining pressure has been performed on a saturated concrete specimen in order to study the influence of the saturation ratio (SR). The procedure for testing saturated samples is described in [
Comparison of axial behavior at 50 MPa confining pressure for two saturation ratios (curve with circles: SR = 60%,
The previous section demonstrated that the influence of saturation ratio remains limited at moderate confining pressures. Nevertheless, in case of impact, the concrete may be subjected to very high triaxial stresses [
Hydrostatic behavior of VTT concrete: effect of the saturation ratio (SR) (curve with circles: SR = 60%; curve with squares: SR = 100%).
The concrete responses displayed in Figure
In the event of an impact load, the concrete is not only subjected to a hydrostatic loading but also subjected to shear stresses. Figure
Axial behavior, comparison of the shear behavior of concrete for several saturation ratios (curve with circles: SR = 10%; curve with squares: SR = 60%; curve with triangles: SR = 100%).
Two tests with different rates were performed on concrete cured under the same conditions (i.e., an SR equal to about 60%). For the test with the faster loading rate (1.7 MPa/s), the mean stress is higher than the one with the lowest loading rate (0.5 MPa/s) (Figure
Hydrostatic behavior of VTT concrete at two loading rates (V1.7 = 1.7 MPa/s, V0.5 = 0.5 MPa/s).
The shear limit state of concrete subjected to triaxial loading depends on both the confinement level and the free water content. For moderate confining pressures, the water content has little influence on the limit state. The shear limit state is defined as the maximum deviatoric stress obtained under triaxial loading. This maximum stress however is not observed at high confining pressures, especially for dry samples. As briefly explained above, another criterion should be used: Vu et al. [
The measured limit states are plotted on Figures
Shear limit state of concrete and failure patterns of samples: maximum deviatoric stress (
Close-up of Figure
Figure
For a moderate confining pressure (i.e., less than 50 MPa), the influence of free water on concrete behavior seems to be limited, whereas the influence of the degree of saturation is significant at a confining pressure on the order of 500 MPa. Consequently, the concrete shear stress limit is highly dependent not only on confining pressure but also on the concrete free water content as well. This important result may exert a major effect on the response of a concrete structure subjected to an impact and should be taken into account when modeling concrete behavior.
The failure patterns of concrete samples are also presented in Figures
The presence of free water seems to also have an impact on the failure pattern. Whereas for specimens with 60% saturation ratio the failure pattern could be assimilated to a compaction band (more or less clearly depending on the reached dilatancy rate), the failure pattern of saturated concrete is, on the other hand, clearly composed of a macroscopic crack network. This modification is probably due to the presence of water in the cement matrix, which as a result could not be compacted.
The PRM coupled model was developed by Pontiroli et al. [
The PRM coupled model allows obtaining a good prediction of concrete behavior under impact loading for thin slabs [
The plasticity model assumes that inelastic volumetric and shear strains are obtained independently. The volumetric strain (
The effect of the deviatoric stress
To improve this PRM model, the curve depicting the volumetric behavior of concrete is not assumed to be bijective; instead, it is assumed to be bounded by both the hydrostatic and oedometric curves (Figure
Hydrostatic and oedometric constitutive behaviors and resulting triaxial behavior of concrete; mean stress versus volumetric strain.
The variation in mean stress
In formulae (
Two types of approaches are available to characterize the behavior of a porous medium at its homogenized scale from microscopic-level properties. Firstly, the “mixing law” approach takes into account, at the microscopic level, the interaction between the two phases (liquid + solid) by means of simple rheological models for each phase, whether they are associated in series or associated in parallel. Secondly, the poromechanical approach [
In the original PRM coupled model, the concept of effective stress is applied to take into account the presence of water in confined concrete when using the first approach. The drawback with such an approach is that the material behavior becomes elastic after reaching the consolidation point (once all open pores are closed), which is not observed experimentally. In the improved model, the poromechanical approach allows taking the effect of free water into account.
The studied porous medium is assumed to be composed of both a solid phase (skeleton) and a fluid phase occupying the voids [
The calculation of pore pressure
From (
With this new hypothesis, whenever the material reaches the point of consolidation (i.e., void pores become closed), the volumetric behavior remains nonlinear due to the fact that the voids filled with water continue to be compressed under compaction. Another advantage of this model improvement is the unique point of consolidation instead of two points in the original PRM model (Figure
Stress calculation diagram according to the poromechanical approach, as the concrete consolidates.
The simulation results obtained with the original PRM coupled model as well as with the new model are compared to experimental results in Figures
Axial stress versus axial and circumferential strains: comparisons of experimental findings with simulation results obtained from the original (PRM-O) and new (PRM-N) models for a wet concrete specimen under moderate confining pressure.
Figures
Mean stress versus volumetric strain: comparisons of experimental findings with simulation results obtained from the original (PRM-O) and new (PRM-N) models for a wet concrete specimen under moderate confining pressure.
Mean stress versus volumetric strain: comparisons of experimental findings with simulation results obtained from the original (PRM-O) and new (PRM-N) models for saturated concrete and dry concrete under high confining pressure.
Figure
This paper has presented new experimental results performed on a high performance concrete specimen tested within the framework of the IRIS project, along with the simulation of these tests using the PRM coupled model improved to fit the experimental results better.
Triaxial compression tests were performed at both moderate and high confining pressures on concrete specimens with two saturation ratios. Significant differences in the maximum stresses attained have been highlighted. For a moderate confining pressure (i.e., less than 50 MPa), the influence of free water on concrete behavior indeed seems to be quite small, whereas the influence of the degree of saturation is significant at a high confining pressure (500 MPa). The volumetric strains are lower under hydrostatic loading for saturated concrete, though the water also tends to limit the shear stress level. Moreover, the water modifies failure patterns for the saturated samples.
This paper has also provided some limitations associated with the PRM model, and a number of improvements have been proposed. The modified PRM model takes into account the influence of deviatoric stress on volumetric behavior. The influence of the saturation ratio on concrete behavior under triaxial compression has been modified as well thanks to the poromechanical approach that yields a unique consolidation point and a more realistic concrete behavior for wet concrete beyond this point. These changes have considerably improved the concrete behavior prediction under triaxial compression. Such improvements may exert a major effect on the response of a concrete structure subjected to an impact.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research project was supported by both the French Institute of Radio-Protection and Nuclear Safety (Institut de Radioprotection et de Sureté Nucléaire, IRSN) and by CEA Gramat. The authors would like to thank Dr. Eric Buzaud and Dr. C. Pontiroli of the CEA-Gramat Center for the very helpful scientific exchanges throughout this study.