JP4593403B2 - Method for predicting cracks in concrete - Google Patents

Description

  The present invention relates to a crack prediction method for concrete that predicts cracks that occur in concrete due to changes over time.

  In shrinkage crack control design of concrete buildings, prediction of drying shrinkage is an important issue. In order to grasp the drying shrinkage strain of this concrete, there is a method of experimental measurement. In this experimental measurement method, a concrete specimen is cured under a predetermined condition, and the subsequent drying shrinkage and, consequently, cracking of the concrete are predicted from the drying shrinkage generated at that time.

  When predicting cracks with this experimental measurement method, it was necessary to set the experimental period to a certain period, for example, about six months, in order to improve the accuracy. However, if a period of six months is required as an experimental period, it will be a factor for prolonging the construction period of a concrete structure, and therefore it is desired to predict cracks in a short period. Therefore, a method for predicting contraction strain over a long period of time by applying a predetermined arithmetic expression to data obtained in a short-term experiment has been proposed.

  For example, Toshie Ishii and one other, “Prediction of Drying Shrinkage of Concrete Based on Short-term Experimental Data”, Annual Meeting of Architectural Institute of Japan (Tokai), September 2003, p. 115-116 (Non-patent Document 1) discloses a method for predicting the drying shrinkage of concrete based on short-term experimental data. In this prediction method, a method for predicting long-term strain from short-term data on drying shrinkage of concrete is disclosed. It is proposed to use the following formula (10) or (11) when making this prediction.

ε _sh (t, t ₀ ) = ε _sh (t _i , t ₀ ) / β _s (t _i −t ₀ ) · β _s (t−t ₀ )
···(Ten)
ε _sh (t, t ₀ ) = [1-exp {−0.108 (t−t ₀ ) ^0.56 }].
ε _sh (t _i , t ₀ ) / [1-exp {−0.108 (t _i −t ₀ ) ^0.56 }]
(11)
In the above equations (3) and (4),
ε _sh : predicted strain value
t: Age of concrete
β _s : Coefficient representing the rate of progress of drying shrinkage In the method for predicting the amount of drying shrinkage of concrete using the above equations (10) and (11), see the example when ti = 7 days and 28 days. As a result, it is possible to reduce the error between the calculated value obtained as the predicted strain value ε _sh and the experimental value obtained through experiments.
Toshie Ishii, 1 other "Prediction of drying shrinkage of concrete based on short-term experimental data", Abstracts of Annual Conference of Architectural Institute of Japan (Tokai), September 2003, p. 115-116

  However, in the method for predicting the drying shrinkage amount of concrete disclosed in Non-Patent Document 1, although the error between the calculated value and the experimental value is small, the error is still seen. It is desirable to reduce the error.

  Accordingly, an object of the present invention is to provide a concrete crack prediction method capable of accurately predicting the drying shrinkage of concrete based on short-term data and predicting cracks occurring in the concrete.

The method for predicting cracks in concrete according to the present invention that solves the above-described problems is to manufacture a specimen made of concrete, place the specimen in a predetermined environment, and set a plurality of specimens to a predetermined age t _i ( i = 0,1,2, ... the drying shrinkage strain occurs when it reaches the) was measured as drying shrinkage strain short data epsilon (t _i), corresponding to a plurality of drying shrinkage strain short data epsilon measured (t _i) age of t _i reaches drying shrinkage individual final prediction value at Ipushironsh _∞ seeking (t _i), based on a plurality of drying shrinkage strain individual final prediction value εsh _∞ (t _i), drying shrinkage strain in the concrete specimen to obtains a final prediction value Ipushironsh _∞, based on the dry shrinkage strain final prediction value Ipushironsh _∞ obtained, drying shrinkage strain LTP value _ε shJ _{(t, t 0)} der what and obtains the .

In the cracking method for predicting relates concrete present invention, based on the plurality of strain individual final prediction value εsh _∞ (t _i), determine the drying shrinkage strain final prediction value Ipushironsh _∞ in the concrete specimen, drying shrinkage strain final prediction value Based on εsh _∞ , a dry shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) is obtained. For this reason, the amount of drying shrinkage can be predicted with higher accuracy than when the final predicted value of drying shrinkage strain is simply obtained from short-term drying shrinkage strain data. Therefore, the crack which arises in concrete can be estimated accurately.

Minimum Here, calculated drying shrinkage strain individual final prediction value Ipushironsh _∞ a _{(t i)} by the following equation (1), the hyperbola a relationship between the age of _{t i} and the drying shrinkage strain individual final prediction value Ipushironsh _{∞ (t i)} It is possible to obtain a drying shrinkage strain final predicted value εsh _∞ by square approximation and to obtain a drying shrinkage strain long-term predicted value _εshJ (t, t ₀ ) by the following equation (2).

ε _sh∞ (t _i ) = ε _sh (t _i , t ₀ ) / β _s (t _i −t ₀ ) (1)
ε _shJ (t, t ₀ ) = α ₁ × [1 / b · β _s (T) − {1 / b · β _s (T ′) − ε _shf (t _i , t ₀ )}] ( 2)
In each of the above formulas,
T: t−t ₀
T ′: t _i −t ₀
β _s : coefficient representing the rate of progress of drying shrinkage
α ₁ : Coefficient related to the dimensions of the specimen
b: 1 / ε _sh∞
Thus, the drying shrinkage amount of concrete can be accurately predicted by using the above equations (1) and (2).

  According to the method for predicting cracks in concrete according to the present invention, it is possible to accurately predict the amount of drying shrinkage of concrete by short-term data and to predict cracks occurring in concrete.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. In the concrete crack prediction method according to the present embodiment, a concrete specimen is manufactured, and the specimen is cured under predetermined conditions. Then, the amount of drying shrinkage strain is calculated as short-term data at regular intervals, the amount of drying shrinkage of the concrete after a long period of time is predicted from these short-term data, and the crack of the concrete is predicted based on this amount of drying shrinkage. Is.

  FIG. 1 shows a specimen used for crack prediction, where (a) is a plan view and (b) is a side view. As shown in FIG. 1, the specimen 1 includes a specimen body 2 and a strain gauge 3. The specimen body 2 is made of concrete, and the bottom surface is circular as shown in FIG. As shown in FIG. 1B, it has a columnar columnar shape.

In addition, as shown in FIG. 1B, the strain gauge 3 includes a plate-like sensor 11. The sensor 11 is covered with a waterproof material 12 made of a film, and water contact with the sensor 11 is prevented. A cable 13 is connected to the sensor 11. The sensor 11 measures the time-dependent change ε _sh of the drying shrinkage strain generated in the specimen body 2 and transmits the measurement result to a measuring device (not shown) via the cable 13.

  The specimen 1 is cured under a stable temperature environment until solidification to some extent proceeds, and then cured under water. Then, the amount of dry shrinkage generated in the specimen body 2 is measured under a predetermined environment. As the strain gauge 3 here, for example, PFL-120, PFL-60, PMLF-120, PMLF-60, Kyowa Denki KM-120, KMC-70, etc. manufactured by Tokyo Sokki Kenkyujo Co., Ltd. are preferably used.

The manufacturing procedure of the specimen 1 will be described. First, a specimen mold having an inner shape substantially the same diameter as the outer shape of the specimen 1 is prepared, and the sensor 11 is installed in the specimen mold. Next, concrete is placed in the specimen formwork. Subsequently, the mold is sealed until the mold is removed after a predetermined period of time, and the mold is cured in a temperature condition as stable as possible. Then, the specimen form is removed, and the specimen 1 is cured in water at a predetermined temperature until a predetermined age is reached. And the specimen 1 is pulled up from water and installed in a predetermined temperature environment. When the specimen 1 is installed in a predetermined temperature environment, the cable of the strain gauge 3 is connected to a measuring instrument, and the dry shrinkage strain generated in the specimen body 2 is measured every predetermined time. The amount of drying shrinkage after a long period of time (hereinafter referred to as “long-term predicted value of drying shrinkage strain”) is predicted from the short-term data of the generated drying shrinkage strain. The procedure will be described below.

Short-term data epsilon _shf, drying shrinkage strain long-term prediction value when an age becomes _{t ε shJ (t, t 0} ) when predicting may use the following equation (2).

ε _shJ (t, t ₀ ) = α ₁ × [1 / b · β _s (T) − {1 / b · β _s (T ′) − ε _shf (t _i , t ₀ )}] ( 2)
In the above equation (2),
T: t−t ₀
T ′: t _i −t ₀
β _s : coefficient indicating the rate of progress of drying shrinkage
α ₁ : Coefficient related to the dimensions of the specimen
b: 1 / ε _sh∞
Here, the following equation (3) can be used to calculate the coefficient β _s representing the rate of progress of drying shrinkage.

β _s (T) = {(T) / (0.035 × 50 ² + (T))} ^0.5 (3)
In the above formula (2), the dry shrinkage strain final predicted value εsh _∞ is used. Here, a method for obtaining the dry shrinkage strain final predicted value εsh _∞ will be described. In obtaining the drying shrinkage strain final prediction value Ipushironsh _∞ obtains multiple age of t _i Drying shrinkage in strain individual final prediction value Ipushironsh _∞ a (t _i) by the following equation (1).

ε _sh∞ (t _i ) = ε _sh (t _i , t ₀ ) / β _s (t _i −t ₀ ) (1)
Here, t ₀ : Age 0 (day)
ε _sh (t _i , t ₀ ): dry shrinkage amount from t ₀ to t _i For example, as material age t _i , first material age t ₁ = 7 (day), second material age t ₂ = 14 (day) The third material age t ₃ = 21 (day) is set. Ε _sh (t ₁ , t ₀ ), ε _sh (t ₂ , t ₀ ), ε _sh (t ₃ , t ₀ ) measured by these respective ages t ₁ , t ₂ , t ₃ and the strain gauge 3 Is substituted into the above equation (1). In this way, the drying shrinkage strain individual final predicted values ε _{sh ∞} (t ₁ ), ε _{sh ∞} (t ₂ ), and ε _{sh ∞} (t ₃ ) at the respective ages t ₁ , t ₂ , and t ₃ are _obtained . FIG. 2 shows the relationship between the ages t ₁ , t ₂ and t ₃ and the final predicted shrinkage strain values ε _{sh ∞} (t ₁ ), ε _{sh ∞} (t ₂ ), and ε _{sh ∞} (t ₃ ). Show.

Here, as can be seen from FIG. 2, ages t ₁ , t ₂ , t ₃ and dry shrinkage strain individual final predicted values ε _{sh ∞} (t ₁ ), ε _{sh ∞} (t ₂ ), ε _sh∞ (t ₃ ) When the relationship is plotted, as shown in FIG. 3, it converges to the dry shrinkage strain final predicted value εsh _∞ . Therefore, the relation between the age of age t _i and the individual final predicted shrinkage strain value ε sh _∞ (t _i ) is approximated by the least squares by a hyperbola. Then, the hyperbola shown in FIG. 3 is defined by the following equation (4), and the drying shrinkage strain final predicted value εsh _∞ (= 1 / b) is obtained.

y = t _i / (a + bt _i ) (4)
Thus, by obtaining the dry shrinkage strain final predicted value εsh _∞ , the dry shrinkage strain long-term predicted value _εshJ can be obtained using the above equation (2).

Thus, in the cracking prediction method of the concrete according to the present embodiment, based on the plurality of strain individual final prediction value εsh _∞ (t _i), determine the drying shrinkage strain final prediction value Ipushironsh _∞ in the concrete specimen, then, A dry shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) is obtained based on the dry shrinkage strain final predicted value ε sh _∞ . For this reason, the amount of drying shrinkage can be predicted with higher accuracy than when the final predicted value of drying shrinkage strain is simply obtained from short-term drying shrinkage strain data.

Thus, when the dry shrinkage strain long-term predicted value (t, t ₀ ) at the age of t is obtained, the state of cracks occurring in the concrete is predicted based on the prediction result of the dry shrinkage. As described above, since the drying shrinkage strain long-term predicted value (t, t ₀ ) can be predicted with high accuracy, cracks occurring in the concrete can be predicted with high accuracy.

In the embodiment described above, the age as the short-term data is measured three times to obtain the dry shrinkage strain long-term predicted value ε _shJ . However, the number of times of measurement is not limited and is two times or four times or more. You can also.

  Examples of the present invention will be described below.

In this example, the specimen 1 was manufactured in the same procedure as in the above embodiment. The dimensions of the specimen 1 were a bottom diameter of 100 mm and a height of 200 mm. The specimen 1 was cured for 2 days until the specimen 1 was removed from the mold. Furthermore, after demolding, water curing is performed in water having a water temperature of 20 ° C. until the age of the material reaches 7 days. Environment)). And the strain in the specimen main body 2 was measured by the strain gauge 3 at intervals of 3 hours, and the measurement result was transmitted to the measuring instrument. As the wood age indicated by t _i, it shows a wood age under curing environment after cured in water.

In the measuring instrument, the strain amount of the specimen body 2 transmitted from the strain gauge 3 is recorded. Further, the drying shrinkage strain individual final predicted value εsh _∞ (t _i ) based on the above equation (1) and the drying based on the above equation (2) as appropriate from the strain amount transmitted from the strain gauge 3 and the age measured separately. The contraction strain long-term predicted value ε _shJ (t, t ₀ ) and the like are calculated. Further, in the above equation (2), since the specimen 1 has the above dimensions, the coefficient α ₁ related to the dimensions of the specimen is set to 0.925.

In the present embodiment, the strain of the specimen body 2 transmitted from the strain gauge 3, the long-term dry shrinkage strain predicted value ε _shJ (t, t ₀ ) obtained using the above equation (2), and JIS are prescribed. Comparison of data by a drying shrinkage strain measurement method (hereinafter referred to as “JIS method”) was performed. The dry shrinkage strain measuring method defined in JIS is defined as a standard method in JIS A 1121.

  First, the measurement result of the drying shrinkage strain measured by the JIS method was compared with the measurement result of the drying shrinkage strain according to this experimental example. In the result according to the present experimental example, curing is performed for 6 months in a curing environment without obtaining a predicted value, and then the strain amount measured by the strain gauge 3 is used. Similarly, curing was performed for 6 months in the JIS method.

FIG. 4 shows the relationship between the measurement result by the JIS method and the measurement result according to this experimental example. In FIG. 4, a value obtained by multiplying the alpha ₁ on the obtained measurement results in this experimental example on the horizontal axis, and the vertical axis the measurement results obtained by the JIS method. As can be seen from FIG. 4, the value obtained from the measurement result according to this experimental example and the measurement result obtained by the JIS method had a very high correlation. From this, it was found that the drying shrinkage strain measurement with the same accuracy as the JIS method can be performed by the measurement method according to this experimental example.

Next, the curing period is 4 weeks, the first age t ₁ = 7 (days), the second age t ₂ = 14 (days), and the third age t ₃ = 21 (days) (2 ) The drying shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) was determined from the formula, and compared with the measurement result of the drying shrinkage strain measured by the JIS method. The result is shown in FIG. In FIG. 5, the dry shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) obtained from equation (2) is on the horizontal axis, and the measurement result obtained by the JIS method is on the vertical axis.

As can be seen from FIG. 5, like the measurement results according to this experimental example, the dry shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) and the measurement results obtained by the JIS method have a very high correlation. there were. Specifically, a result equivalent to the JIS method was obtained with an accuracy within ± 10%. From this, it was found that the measurement method using the dry shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) according to this experimental example can measure the dry shrinkage strain with the same accuracy as the JIS method.

Then, the example by the prediction method disclosed by the said nonpatent literature 1 is shown as a comparative example. FIG. 6 is a diagram showing the relationship with the actual strain measurement value (actual measurement value) after 6 months while _{obtaining the} dry shrinkage strain long-term prediction value ε _shJ (t, t ₀ ) using the above equation (10). is there. As can be seen from FIG. 6, in the method disclosed in Non-Patent Document 1, an error of the prediction system is about ± 20%. From the above, it was found that the measurement method according to this experimental example can measure the drying shrinkage strain with high accuracy.

It is a figure which shows the specimen used for a crack prediction, (a) is a top view, (b) is a side view. It is a figure which shows the relationship between material age and the drying shrinkage | contraction individual separate prediction value. It is a figure which shows the relationship between material age and the drying shrinkage distortion final prediction value. It is a figure which shows the relationship between the measurement result by JIS method, and the measurement result which concerns on this experiment example. Drying Shrinkage term prediction value _ε shJ _{(t, t 0)} and a diagram showing the relationship between the measurement result of the measured drying shrinkage strain by JIS method. It is a figure which shows the relationship between the drying shrinkage long-term prediction value calculated | required using said Formula (10), and an actual strain measurement value.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Specimen 2 ... Specimen main body 3 ... Strain gauge 11 ... Sensor 12 ... Waterproof material 13 ... Cable

Claims (2)

Producing concrete specimens,
The specimen is placed in a predetermined environment,
The specimen is measured more set predetermined age of _{t i (i = 0,1,2, ...} ) the drying shrinkage strain occurs when it reaches the as drying shrinkage strain short data epsilon (t _i),
Obtains a plurality of drying shrinkage strain short data measured ε drying shrinkage strain individual final prediction value Ipushironsh _∞ in the ages t _i upon reaching corresponding to (t _i) (t _i),
Based on a plurality of dry shrinkage strain individual final predicted values εsh _∞ (t _i ), a dry shrinkage strain final predicted value εsh _∞ in the concrete specimen is obtained,
A concrete crack prediction method, characterized in that a dry shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) is obtained based on the obtained dry shrinkage strain final predicted value εsh _∞ . The drying shrinkage strain individual final predicted value εsh _∞ (t _i ) is obtained by the following equation (1),
The dry shrinkage strain final predicted value εsh _∞ is obtained by approximating the relationship between the age of age t _i and the individual final shrinkage strain predicted value εsh _∞ (t _i ) by a least squares with a hyperbola,
The method for predicting cracks in concrete according to claim 1, wherein the dry shrinkage strain long-term predicted value ε _shJ (t, t ₀ ) is obtained by the following equation (2).
ε _sh∞ (t _i ) = ε _sh (t _i , t ₀ ) / β _s (t _i −t ₀ ) (1)
ε _shJ (t, t ₀ ) = α ₁ × [1 / b · β _s (T) − {1 / b · β _s (T ′) − ε _shf (t _i , t ₀ )}] ( 2)
In each of the above formulas,
T: t−t ₀
T ′: t _i −t ₀
β _s : coefficient indicating the rate of progress of drying shrinkage
α ₁ : Coefficient related to the dimensions of the specimen
b: 1 / ε _sh∞

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