
Damage Estimation of Concrete by AE Rate Process Analysis in Core Test
Tetsuya Suzuki, Nippon Suiko Consultants CO., LTD., 31548 Goryo, Kumamoto, Japan
Masayasu Ohtsu, Graduate School of Science & Technology, Kumamoto Univ., 2391
Kurokami, Kumamoto, Japan
ABSTRACT
The durability of concrete structures decreases easily due to such external effects, as
neutralization and freezingthawing process. The degree of damage in concrete is, in most cases, evaluated by an unconfined compression test and a rebound hammer test.For effective maintenance and management of concrete structures, it is necessary to evaluate not only the strength of concrete but also the degree of damage. Quantitative damage evaluation of concrete is proposed by applyingacoustic emission (AE) method and damage mechanics.
In the present study, damaged concrete samples are examined, based on fracturing behavior under unconfined compression. AE behavior of the concrete under compression is dependent on the degree of damage, and could be approximated,applying the rate process analysis. Using Loland's model, a relationship between stress and strain is modeled, and a relation between AE rate and the damage parameter is correlated. By calculating the relative damage from the database based on this relation,the initial damage of the concrete in an actual structure is successfully estimated.
1. Introduction
With increasing necessity of maintenance and management techniques for concrete structures, it has become important to evaluate not only the strength but also other physical properties of concrete. For detailed inspection of concrete structures, unconfined compression tests have been frequently conducted, taking out core samples.Through a comparison between test results and the reference strength specified in the design standards, the degree of damage is conventionally estimated. However, the strength is not good enough for practical evaluation of damage degree in concrete structures. In this respect, Acoustic Emission (AE) method is known to be promising for
determining the degree of damage [1].
In the present study, AE measurements are conducted during uniaxial compression tests. Concretecore samples were taken from a thrust block of an agricultural pipeline constructed in 1967 and repaired in 1979. AE activity under unconfined compression is approximated by the rate process analysis, and the damage parameter derived from the stressstrain behavior is evaluated by using Loland's model. Then, a database is applied to make the proposed method applicable to a limited number of samples taken from an existing structure.
2. Analytical procedure
 Rate process analysis
AE behavior of a concrete sample under unconfined compression is associated with the generation of microcracks. These microcracks gradually are accumulated until final fracture that severely reduces loadbearing capacity. The number of AE events,which correspond to the generation of these cracks, increases accelerated by the accumulation of microcracks. It appears that this process is dependent on the number of cracks at a certain stress level and the progress rate of the fracture stage, and thus could be subjected to a stochastic process. Therefore, the rate process theory is introduced to quantify AE behavior under unconfined compression[1]. The following equation of the rate process is formulated to represent AE occurrence dN due to the
increment of stress from V to V+dV,
 (1)

where N is the total number of AE events and f(V) is the probability function of AE at
stress level V(%). For f(V) in Eq.1, the following hyperbolic function is assumed,
 (2)

where a and b are empirical constants. Here, The value 'a' is named the rate.
In Eq.1, the value of 'a' reflects AE activity at a designated stress level, such that at
low stress level the probability varies, depending on whether the rate 'a' is positive or
negative. Two possible relations of probability function f(V) is shown in Fig.1. In the
case that the rate 'a' is positive, the probability of AE activity is high at a low stress
level, indicating that the structure is damaged. In the case of the negative rate, the probability is low at a low stress level, revealing that the structure is in stable condition.
Therefore, it is possible to quantitatively evaluate the damage in a concrete structure using AE measurement under unconfined compression by the rate process analysis.
Fig 1: Two possible relations of probability function f(v).

Based on Eqs.1 and 2, the relationship between total number of AE events N and stress level V is represented as the following equation,
 (3)

Where C is the integration constant.
 Loland's model
A damage parameter W in damage mechanics can be defined as a relative change in modulus of elasticity, as follows,
 (4)

where E is the modulus of elasticity of concrete and E* is the modulus of elasticity of
concrete which is assumed to be intact and undamaged.
Loland assumed that the relationship between damage parameter W
and strain e under unconfined compression is expressed [2]
 (5)

where W_{0} is the initial damage at the onset of the unconfined compression test, and A_{0} and l are empirical constants of the concrete.
The following equation is derived from Eqs. 4 and 5,
 (6)

here,
 (7)

 Young's modulus of the intact concrete E* using a database
As given in Eq.5, the initial damage W_{0} in damage mechanics represents an index of damage. In Loland's model (Eq.4), it is fundamental to know Young's modulus of the intact concrete (E*). However, it is not easy to obtain E* from an existing structure. Therefore, it is attempted to estimate E* from AE measurement. Two relations between
total number of AE events and stress level and between stress and strain are taken into account. Based on a correlation between these two relationships, a procedure is developed to evaluate the intact modulus from AE analysis. A correlation between the decrease of the Young's modulus under unconfined compression, log_{e}(E_{0} E_{c}), and the rate 'a ' derived from AE rate process analysis is shown in Fig.2. Results of all samples damaged due to the freezethaw process are given. Good correlation between log_{e}(E_{0} E_{c}) and the rate 'a ' value is confirmed [3]. From Eq.4, the decrease of Young's modulus under unconfined compression (E_{0} E_{c}) is expressed, as follows ;
Fig 2: Relations between log_{e}(E_{0}E_{c}) and the ratio 'a'.

 (8)

Here W_{c} is the damage at the final stage. Based on a linear correlation equation in Fig.2,
 (9)

Here, it is assumed that E_{0}=E* when a=0. This allows us to estimate Young's modulus
of intact concrete E* from AE rate process analysis as,
 (10)

3. Experiments
 Specimens
Cylindrical samples of 5cm in diameter and 10cm in height were taken from a thrust block of an agricultural pipeline in Kasanohara district, Kagoshima prefecture, Japan.This pipeline was constructed in 1967 and repaired in 1979. The degree of neutralization samples was measured by spraying 1% phenolphthalein solution in 1967 samples. As a result, it is found that neutralization penetrates extremely in depth. The concrete pipeline had been buried at the depth of 3 meters in Ando soil originated from Sakurajima Island. Table 1 shows the soil properties.
Soil
 Texture
 Particle Density (g/cm^{3})
 pH (H_{2}O_{2})
 Sulfate
 WaterContent(%)

Ando soil  LiC  2.424  6.7  Detected  84

Table 1: Soil properties.

 AE measurement
A uniaxial compression test of the samples was conducted as shown in Fig.3. Silicon grease was pasted on the top and the bottom of the specimen, and a Teflon sheet was inserted to reduce AE events generated by friction. MISTRASAE system (manufactured by PAC) was employed as a measuring device. AE hits were counted by using an AE sensor UT1000 (resonance frequency: approx. 1MHz). The frequency range was from 60kHz to 1MHz. To count the number of AE hits, the threshold level
was set to 60dB with a 40dB gain in a preamplifier and 20dB gain in a main amplifier.For event counting, the dead time was set as 2msec. It should be noted that AE measurement was conducted with two channels as the same as the measurement of axial and lateral strains. Averaged values of the two channels were used for the analysis.
Fig 3: AE measurement system.

4. Results and discussion
In the present study, the initial tangential Young's modulus E_{0}, was quantitatively determined as a tangential gradient of the stressstrain curve by approximating as,
 (11)

Here, a_{1} and a_{2} are empirical constants. By the approximation of the stressstrain relation in Eq.11, the initial modulus E_{0} is derived as tangential modulus : ds / de at e = 0,
a_{1} = E_{0}
Thus, the moduli of elasticity, E_{0} and E_{c} were determined. Here, E_{c} is the secant Young's modulus at final fracture. Table 2 shows mechanical properties of all the samples. Initial Young's modulus E_{0} varies from 8.7 to 34.0 GPa, while the unconfined compression strength varies from 8.0 to 20.4 MPa.
The rate process analysis was conducted at stress level in the range from 30% to 80%. This is because AE events occurring at initial loading below 30% strength due to contact with the loading plate and at an accelerated stage above 80% has little to do with the damage.
Fig 4: Relative moduli E0/E^{*} in an actual structure.

It is demonstrated that Young's modulus of intact concrete E* can be estimated by Eq.10 [4, 5]. Thus, to estimate relative damage of the concrete, ratios E_{0}/E* are obtained,
and are summarized in Fig.4. To determine E* from the relation in Fig.2, it is necessary
to analyze a large number of specimens. However, the number of concrete cores available is limited in existing structures. Therefore a database, which could allow even a single concrete core to be evaluated, is constructed as shown in Fig.2. By using this database, Young's modulus of the normal concrete E* and the relative damage of the samples are calculated . The samples enrolled in a database in Fig.2 are all tested in the previous research. Fig.4 shows results, by employing the database. E_{0}/E* of the sound specimens is to be obtained as equal to 1.0 or over. In Fig.4, relative moduli E_{0}/E*, vary from 0.48 to 1.25. Relative damages in 9 samples are estimated as below 1.0. Though the degree of damage in the concrete samples is not clearly identified by the unconfined compression test in the figure, it is quantitatively estimated, using the relative damage evaluated by the AE measurement.
No.
 Construction
 Neutralization (%)
 f'_{c}(MPa)
 E_{0}(GPa)
 E_{c}(GPa)
 E_{D}(GPa)

1  1979  13.4  20.4  26.2  18.2  29.8

2  1979  4.7  19.0  34.0  13.1  36.7

3  1979  6.8  9.9  22.9  11.9  34.0

4  1979  62.9  8.0  10.4  4.4  21.7

5  1967  100.0  18.0  19.9  10.0  24.7

6  1967  100.0  13.8  18.4  7.8  26.7

7  1967  16.3  15.7  18.6  8.2  25.6

8  1967  100.0  9.7  18.4  12.2  16.6

9  1967  100.0  8.7  8.7  4.2  15.0

10  1967  100.0  9.6  16.1  6.8  22.1

Table 2: Mechanical properties.

f'_{c}: Compressive strength, E_{D}: Dynamic Young's modulus
Thus, the effectiveness of the relative damage based on Young's modulus of intact concrete E* using the database is demonstrated. The database is applicable to evaluate the relative damage even in the case that there are not enough the number of specimens available from existing structures.
5. Conclusion
Unconfined compression tests are conducted using the AE measurement in the core samples taken from a pipeline structure, in order to evaluate the degree of damage quantitatively. The close relation is confirmed between the AE generating behavior and the internal damage of concrete, which is analyzed based on the rate process theory and damage mechanics. Thus, the degrees of damage in concrete samples are quantitatively evaluated, even when the initial physical properties of concrete structure at the time of construction are unknown. Conclusions are summarized below.
 AE behavior in concrete is dependent on the damage, and could be approximated by applying the rate process analysis.
 Loland's model could approximate the relation between stress and strain, and the
applicability of the damage parameter in the model is confirmed.
 Based on the correlation between the decrease of Young's modulus and the rate ' a',
Young's modulus of intact concrete is successfully evaluated. As the ratio to the initial
tangential Young's modulus, the relative damage of the concrete can be determined.
 Using the database, it is demonstrated that Young's modulus of intact concrete is
calculated from a small number of core samples taken from existing structures.
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