Determination and Application of the Sharp Degradation Point of Concrete under Environmental Actions

INTRODUCTION

Many experimental results have indicated that the deterioration process of concrete can be divided into two stages--the nondestructive stage(stage 1) and the destructive stage(stage 2), as shown in Fig. 1(Wu, 2002;Rostam, 1993).When concrete is subjected to environmental actions, the inner energy it gains is almost balanced by the released energy when cracking in stage 1, while in stage 2 the inner energy is greater than that released.There are few remarkable degradation phenomena in concrete as cracks expand slowly and stably in stage 1, while in stage 2, concrete deteriorates rapidly and performance markedly degenerates; finally, cracks expand sharply and cut through damaged areas until the concrete fails completely.

Figure  1.  General degradation process of concrete under freeze-thaw actions

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The corresponding damage evolution process is shown in Fig. 2.In stage 1, as damage slowly accumulates in the concrete.more discontinuous and fine cracks appear.The damage is isotropic, as well as the isotropy of concrete; hence, study in this stage can be conducted using the damag continuous medium.In stage 2, e mechanics of a damage develops sharply until the terminal stage。when.D=1 and concrete collapses.The critical point between the two stages is defined as the sharp degradation point, which is a mark of accelerated damage in the degradation process.Undoubtedly, the sharp degradation point is more attractive.

Figure  2.  The developing process of concrete damage under freeze-thaw actions

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This problem has been studied by several authors(Hisham and Iqbal, 2003; Guan et al., 2001; Akhras, 1998; Alliche and Francois, 1992, 1986).However.traditional research to determine the characteristic degradation point under environmental tictions has been conducted chiefly by observational and empirical ways.In this paper, a Successful theoretical method is presented, which can easily determine the sharp degradation point in the damage evolution process of concrete.

FAILURE CHARACTERISTIC POINT OF CONCRETE UNDER LOADS

The stress-strain curve of concrete under uniaxial compression is described by the Saenz formula (Chen and Salip, 2001)

where $E_{0}$ is the initial Young's modulus; $E_{\mathrm{f}}$ is the secant modulus in accordance with the peak stress $f_{\mathrm{c}}^{\prime}$; $\varepsilon_{\mathrm{f}}$ is the peak strain.

For undamaged material, the stress-strain relationship is

According to the equivalent hypothesis of a strain, damaged material under an effective stress has an equivalent strain with the undamaged material of the same kind(Li, 2002)

Based on equations(1) and(3), the damage variable can be defined as follows

In the above expression, the damage variable D is applicable to the whole uniaxial compression process, not merely in the ascending branch.

Assuming the stress at the degradation point in the failure process of concrete under uniaxial cornpression could be described fls follows

Suppose that $E_{0} / E_{\mathrm{f}}=A, \varepsilon_{\phi} / \varepsilon_{\mathrm{f}}=B, \varepsilon_{\phi}$ is the strain at the characteristic point.

Based on equations (1), (4) and (5), $D_{\phi}$ can be obtained as follows

CHARACTERISTIC DEGRADATION POINT OF CONCRETE DURABILITY

Many experiments and research have indicated that when concrete is under a uniaxial stress, cracks begin to expand while the stress reaches its critical point (about $0.7 f'_{\mathrm{c}}-0.9 f'_{\mathrm{c}}$), which means $\alpha=0.7- 0.9$. Generally, the secant modulus is half of the Young's modulus when the stress reaches its peak, that is $A=2$. The damage at the degradation point of concrete subjected to loads can be calculated by equation (6) (shown in Table 1).

Table  1.  Damage at degradation point

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The failure process of concrete subjected to environmental actions is gradual. Under environmental actions, the degradation of concrete durability follows the sequential process of initiation, expansion and connectivity of flaws, such as microcracks and interspace, which is similar to the failure process of concrete under loads. It is feasible to solve the durability problem of concrete in a mechanical way. Based on the principle that damage at the characteristic failure point subjected to loads is equal to the damage in accordance with the characteristic degradation point of concrete durability under environmental actions, the sharp degradation point of concrete durability can be determined in the light of the one-dimensional stress-strain relationship mentioned above. According to Chen and Salip (2001), we make $\alpha=0.75$ here. Then, the damage at the sharp degradation point can be obtained: $D_{c}=D_{\phi}=0.17$.

APPLICATION: ANALYSIS OF THE DAMAGE EVOLUTION PROCESS OF CONCRETE UNDER FREEZE-THAW CYCLES

With the alternate rise and fall in temperature, concrete with sufficient water inside will generally undergo damage due to freeze-thaw actions.Concrete structures, such as hydro-structures, harbor structures, roads and bridges, are often damaged by freeze-thaw denudation.Failure induced by freezethaw actions is the most representative index of concrete durability degradation.Taking the degradation process of concrete durability in freeze-thaw cycles as an example, we apply the damage expression of the sharp degradation point to establish corresponding damage evolution equations.

Many experimental results(Wei et al., 2003; Zhao, 2003)indicate that concrete in freeze-thaw cycles goes through two stages: (1)the initial stage, when the damage within the concrete has not been lo- calized; (2)the expanding stage, in which the damage has been localized.The cut-off point between the two stages is the sharp degradation point.Freezethaw damage in the two stages could be described by the following equations

where $\alpha$ and $\beta$ are constants related to concrete material and temperature etc.; $N_{\mathrm{c}}$ is the times of freezethaw cycle and $D_{c}$ is the damage value at the sharpdegradation point.

Taking the damage evolution process of concrete under freeze-thaw actions as an example here, the accuracy of the ascertained sharp degradation point is verified with both theoretical and experimental methods. Four kinds of concrete specimens were made in dimension of $100 \mathrm{~mm} \times 100 \mathrm{~mm} \times 400 \mathrm{~mm}$, and a slow freezing method was adopted. Values of supersonic speed for each specimen were measured respectively after each freeze-thaw cycle. By constructing a variable $D=1-\frac{v_{N}^{2}}{v^{2}}$ with supersonic speed, the damage ratio of concrete after certain freeze-thaw cycles can be obtained (Zhao, 2003).

Tables 2 and 3 show the damage values of different types of concrete after consecutive freeze-thaw cycles. Three common concrete types are testedC30, C40, C60, and high performance concreteH40 (Zhao, 2001). The freeze-thaw cycle times in accordance with damage $D_{\mathrm{c}}=0.17$ are calculated with the interpolation method and shown in the last column. Based on the freeze-thaw cycle times in accordance with the sharp degradation point and the damage $D_{c}$, damage values in accordance with different freeze-thaw times are calculated with equations (7) and (8) and shown in Tables 2 and 3. Experimental and calculated values are both shown in Fig. 3. Good agreement between the two kinds of results confirms the accuracy of the calculated critical point damage.

Table  2.  Damage ratio in the freeze-thaw experimeat of C30  %

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Table  3.  Damage ratio in the freeze-thaw experiment of C40.H40 and C6  %

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Figure  3.  Comparison between experimental and forecasted values.(a)C30;(b)C40;(c)H40; (d)C60.

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CONCLUSIONS

The following conclusions can be drawn from this paper.(a)Based on the principle that damage at the characteristic failure point subjected to loads is equal to the damage at the characteristic point of concrete durability under environmental actions, the damage at the sharp degradation point can be ascertained.(b)By applying this method to the case of concrete suffering freeze-thaw actions, good accordance between experimental results and forecasted resuits indicated the rationality of the critieal point damage induced in this paper.(c)The confirmation of the critical point will help to solve the damage evolution law of concrete durability, and furthermore。it has great significance in the performance design and life evaluation field of concrete.