Dynamic Behavior of Concrete Structures
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In the model, the concrete is assumed in a macroscopic view as homogeneous continuum with pre-existing microcracks. The evaluation of damage is formulated based on the continuum fracture mechanics of microcrack nucleation, growth and coalescence. Based on the damage function, the stress response at a particular time, and hence the stress—strain relationship, can be established for a given strainrate.
The required material constants representing initial crack properties can be derived from material dynamic property tests. The nominal fragment sizes of concrete and fracture strain energy are also derived. Such rate dependence is observed for nearly all the brittle materials Clifton, Concrete exhibits also an enigmatic phenomenon of increased resistance when it is loaded at a very high rate. For the evaluation of fracture and formation of fragments, the elastic strain energy will be critical.
In some early continuum models for brittle materials Grady and Kipp, ; Taylor et al. In more recent studies Zhang et al. It was demonstrated that the use of the critical value makes it Y.
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This consideration is also adopted in the present study of concrete materials. An appropriate theory to explain this phenomenon is yet to be established. Intermediate values of D correspond to the partially damaged material. As mentioned before, considering the fact that certain time duration is needed for fracture to take place when a brittle material like concrete is subjected to a stress higher than its static strength Zhang et al.
Modelling of dynamic behaviour of concrete materials under blast loading - PDF Free Download
According to Yang et al. Obviously the crack density increment vanishes if the tensile strain e 6 ecr. With the assumption of constant strain loading rate, from Eqs. Once b and m are available, the dynamic stress—strain relationship can be determined according to Eqs. The higher dynamic strength at higher strain rates is consistent with the observed test results.
According to Reinhardt et al. During the crack propagation, the energy barriers delay the total failure of material. This observation agrees with the experimental results reported by Shah and John and Yon et al. Herein a cohesive crack model is used to model the material softening process. The stress on the microcrack surface is related to the nominal strain. On the macrocrack, no interaction is assumed between the two surfaces, i.
The pointed symbol denotes the increment. The dynamic softening curve can therefore be expressed as 2! Based on the dynamic strength of the concrete material established earlier, the fragmentation can be evaluated by applying the method proposed for rock materials Grady and Kipp, ; Zhang et al. It is known that fragments are associated with crack initiation, propagation and coalescence. Thus, it is necessary to know the crack size in order to predict the fragment size. At fracture coalescence, the fracture faces form the fragment sizes.
Subsequently, the debris throw velocity can be determined. Modeling results The above described theoretical procedure is applied to model the dynamic behaviour of concrete materials in conjunction with pertinent experimental data. The experimental results used to derive the material parameters include concrete and mortar under tensile and compressive loading. The mortar is regarded as representing the matrix phase of concrete. Based on the test data, the parameters a and b in Eq.
The damage is considered equal zero at this stage under dynamic loading. The measured dynamic strength and static strength data are employed to evaluate the material constants b and m according to Eq. The results are then applied in the theoretical model to predict the dynamic strength and establish the dynamic stress—strain relationships for the materials under varying strain loading rate, as well as the fragment size and the fracture strain energy.
Concrete under tension In the dynamic tests of concrete material under tension and compression reported in Tedesco et al. The predicted dynamic strength to static strength ratios are compared with the test results in Fig. It can be observed that the predicted values agree very well with the collective experimental data. Normalized dynamic concrete tensile strength vs. Concrete under compression The concrete material for dynamic compression tests used for the evaluation of b and m had the same static material properties as mentioned in the previous section.
The nominal quasistatic compressive strength from the various specimens was about 40 MPa. Subsequently, the predicted dynamic compressive strength can be obtained based on Eq. The predicted stress—strain relationship of concrete under compression is compared with experimental results obtained by Donze et al. A favourable agreement is observed. Normalized concrete compressive strength vs. However, it is interesting to note that if the rate enhancement is to be viewed in terms of the absolute strength increase, then the increases of strength under tension and comparison are actually comparable.
Mortar under compression The mortar specimens tested by Grote et al.
Normalized mortar compressive strength vs. The measured dynamic failure stress, shown in Fig. The modelling results of the dynamic strength using these b and m values are depicted in solid line in Fig. Whereas to accelerate the corrosion process, impress current technique is used in which a current is externally applied to induce corrosion in reinforcement and then crack widths and vibration natural frequencies were measured.
Dynamic behavior of concrete structures /
A numerical model is proposed with the help of FEM based Auto desk Algor simulation software to predict attack penetration depth. Keyword : reinforced concrete, corrosion, residual life, non-destructive testing. This work is licensed under a Creative Commons Attribution 4.
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Home Archives Vol 10 No 1 Articles. Corrosion impact analysis on residual life of structure using cathodic technique and algor simulation software. Vol 10 No 1 Submitted: Apr 20, Published: Apr 27, Range Graph Chart Graph. Keyword : reinforced concrete, corrosion, residual life, non-destructive testing How to Cite Nayak, C.
Engineering Structures and Technologies , 10 1 , Published in Issue. Abstract Views. Ahmad, S. Reinforcement corrosion in concrete structures, its monitoring and service life prediction — a review. Floor vibrations due to human activity. Autodesk Algor Simulation Professional. Alonso, C. Factors controlling cracking of concrete affected by reinforcement corrosion. Materials and Structures, 31, Influence of reinforcement distribution in the corrosive process of reinforced concrete beams.
Magazine of Concrete Research, 61 3 , Influence of reinforcement corrosion in the compressive zone on the behaviour of RC beams. As listed in Table 5. The first three are well known from experimental results but, as far as the author is aware, the results in the literature are at low strain rates in the case of the strain rate dependency for compression, while the results on residual strength are for static and not dynamic loading.
Furthermore, the depth of penetration is mesh- dependent. These are well known from literature, but in the last case only for uniaxial loading. Other factors that influence the depth of penetration and the crater size are the geometry of the target and the properties of the projectile. For example, the crater size will increase with increasing projectile diameter. In this comparison, a 6.
A more detailed parameter study has been performed with the Lagrangian method, according to the parameters of mesh dependency, residual strength and the criteria for erosion. In addition, a phenomenological study of the strain rate dependency for tension has been carried out.