JP2013221779A - Method of predicting drying shrinkage strain of concrete and method of predicting drying shrinkage stress of concrete - Google Patents
Method of predicting drying shrinkage strain of concrete and method of predicting drying shrinkage stress of concrete Download PDFInfo
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本発明は、コンクリート内部の相対湿度と乾燥収縮ひずみの関係を用いて、コンクリートの乾燥収縮ひずみと乾燥収縮応力を予測する方法に関する。 The present invention relates to a method for predicting the drying shrinkage strain and drying shrinkage stress of concrete using the relationship between the relative humidity inside the concrete and the drying shrinkage strain.
コンクリートは引張強度が低いため、コンクリートの収縮によりひび割れ（収縮ひび割れ）が発生する場合がある。この収縮ひび割れは、コンクリート構造物の美観を損なうほか、コンクリートの水密性・気密性の低下や鉄筋の腐食などの、構造物の耐久性低下の原因にもなっている。したがって、コンクリートの耐久性を確保するためには、収縮ひび割れを制御することが必要となる。
この収縮ひび割れの主因としてコンクリートの乾燥収縮ひずみが挙げられる。該ひずみは、図１に示すように、コンクリートの外部拘束により生じるひずみと内部拘束により生じるひずみとがある。したがって、コンクリートの収縮ひび割れを制御するには、主因となる乾燥収縮ひずみを事前に把握する必要がある。
Since concrete has low tensile strength, cracks (shrinkage cracks) may occur due to shrinkage of the concrete. This shrinkage crack not only detracts from the aesthetics of the concrete structure, but also causes a decrease in the durability of the structure, such as a decrease in watertightness and airtightness of the concrete and corrosion of reinforcing bars. Therefore, in order to ensure the durability of concrete, it is necessary to control shrinkage cracks.
The main cause of this shrinkage cracking is the drying shrinkage strain of concrete. As shown in FIG. 1, the strain includes a strain caused by external constraint of concrete and a strain caused by internal constraint. Therefore, in order to control the shrinkage crack of concrete, it is necessary to grasp in advance the drying shrinkage strain which is the main cause.
従来、コンクリートの乾燥収縮ひずみの予測式は、日本建築学会が提案する式（以下「日本建築学会式」という。）と、土木学会が提案する式（以下「土木学会式」という。）などが知られていた。
日本建築学会式は、コンクリート周囲の相対湿度、コンクリートの体積、外気に接する表面積、および体積表面積比などのパラメータを含む式に、セメント等の種類の影響を表す修正係数を含む式を乗じてなる下記の予測式である（非特許文献１の４頁、５頁、１８２頁）。
Conventionally, dry shrinkage strain prediction formulas for concrete include formulas proposed by the Architectural Institute of Japan (hereinafter referred to as “Japanese Architectural Institute formula”), formulas proposed by the Japan Society of Civil Engineers (hereinafter referred to as “Civil Engineering Society formula”), and the like. It was known.
The Architectural Institute of Japan formula is obtained by multiplying an equation containing parameters such as the relative humidity around the concrete, the volume of the concrete, the surface area in contact with the outside air, and the volume surface area ratio, and a formula containing a correction coefficient that represents the effect of the type of cement, etc. It is the following prediction formula (
また、土木学会式は、日本建築学会式と同様のパラメータを含む下記の予測式である（非特許文献２の４６頁）。 In addition, the Japan Society of Civil Engineers formula is the following prediction formula including parameters similar to those of the Architectural Institute of Japan (page 46 of Non-Patent Document 2).
しかし、図２に示すように、コンクリート内部の相対湿度は、コンクリートの中心部に近い程高く一定ではない。したがって、予測式中の相対湿度のパラメータにコンクリート周囲の相対湿度（一定値）を用いる従来の予測方法では、コンクリート内部の相対湿度の分布が反映されず、例えば図５中の土木学会式を用いた比較例に示すように、コンクリートの全断面に単一の乾燥収縮ひずみの予測値が与えられるに過ぎなかった。さらに、乾燥収縮応力を予測する場合、外部拘束のみが評価対象となり、内部拘束は考慮されないため、図６の比較例に示すように、精度の高い予測はできなかった。 However, as shown in FIG. 2, the relative humidity inside the concrete is higher and closer to the center of the concrete. Therefore, in the conventional prediction method using the relative humidity around the concrete (constant value) as the relative humidity parameter in the prediction formula, the distribution of the relative humidity inside the concrete is not reflected. For example, the formula of the Japan Society of Civil Engineers is used. As shown in the comparative example, only a single dry shrinkage prediction value was given to the entire cross section of the concrete. Further, when predicting the drying shrinkage stress, only the external constraint is evaluated, and the internal constraint is not taken into consideration, and therefore, as shown in the comparative example of FIG.
そこで、本発明は、コンクリート内部の湿度分布を考慮してコンクリートの乾燥収縮ひずみを予測する方法と、コンクリートの内部拘束も考慮してコンクリートの乾燥収縮応力を予測する方法を提供することを目的とする。 Therefore, the present invention aims to provide a method for predicting the drying shrinkage strain of the concrete in consideration of the humidity distribution in the concrete and a method of predicting the drying shrinkage stress of the concrete in consideration of the internal constraint of the concrete. To do.
本発明者は、前記目的にかなう予測方法を検討した結果、相対湿度と乾燥収縮ひずみの比との関係を示す特定の式を用いれば、セメントや骨材等が異なるコンクリートでも、その乾燥収縮ひずみや乾燥収縮応力を精度よく予測できることを見出し、本発明を完成させた。 As a result of studying the prediction method for the purpose, the present inventor has determined that the dry shrinkage strain can be obtained even in concrete having different cement, aggregate, etc. And the present invention has been completed.
すなわち、本発明は、以下の［１］および［２］を提供する。
［１］以下の（Ａ）〜（Ｃ）の過程を含む、コンクリートの乾燥収縮ひずみの予測方法。
（Ａ）湿度解析によりコンクリート表面から中心部に至る各位置の相対湿度を求める、湿度解析過程
（Ｂ）下記の（１）式を用いて、前記各位置の相対湿度から、該各位置の乾燥収縮ひずみの比（ε／ε６０）を算出する、乾燥収縮ひずみ比算出過程
ε／ε６０＝（１００−ＲＨ）／｛０．６５（１００−ＲＨ）＋１４｝ ・・・（１）
（式中、ＲＨは相対湿度（％）を表し、ε／ε６０は相対湿度６０％における乾燥収縮ひずみの終局値に対する任意の相対湿度ＲＨにおける乾燥収縮ひずみの終局値の比を表わす。）
（Ｃ）前記各位置の乾燥収縮ひずみの比（ε／ε６０）、および相対湿度６０％における乾燥収縮ひずみの終局値から、前記各位置の乾燥収縮ひずみの予測値を算出する、予測値算出過程
［２］さらに前記各位置の乾燥収縮ひずみの予測値から、応力解析により該各位置の乾燥収縮応力の予測値を算出する、コンクリートの乾燥収縮応力の予測方法。
That is, the present invention provides the following [1] and [2].
[1] A method for predicting drying shrinkage strain of concrete, including the following processes (A) to (C).
(A) Humidity analysis process for obtaining relative humidity at each position from the concrete surface to the center by humidity analysis. (B) Using the following formula (1), the relative humidity at each position is used to dry each position. Drying shrinkage strain ratio calculating process for calculating the shrinkage strain ratio (ε / ε 60 ) ε / ε 60 = (100−RH) / {0.65 (100−RH) +14} (1)
(In the formula, RH represents relative humidity (%), and ε / ε 60 represents the ratio of the final value of dry shrinkage strain at any relative humidity RH to the final value of dry shrinkage strain at 60% relative humidity.)
(C) Predicted value calculation for calculating a predicted value of the drying shrinkage strain at each position from the ratio of the drying shrinkage strain at each position (ε / ε 60 ) and the final value of the drying shrinkage strain at 60% relative humidity. Process [2] A method for predicting drying shrinkage stress of concrete, further comprising calculating a predicted value of drying shrinkage stress at each position from a predicted value of drying shrinkage strain at each position by stress analysis.
本発明の予測方法は、コンクリート内部の湿度分布を考慮して、コンクリート断面に沿って乾燥収縮ひずみや乾燥収縮応力を精度よく予測できる。したがって、コンクリートの収縮ひび割れの判定や評価において、ひび割れが発生する可能性を高い精度で予測することができる。 The prediction method of the present invention can accurately predict the drying shrinkage strain and the drying shrinkage stress along the concrete section in consideration of the humidity distribution inside the concrete. Therefore, in judgment and evaluation of shrinkage cracks in concrete, it is possible to predict the possibility of cracks with high accuracy.
本発明は、前記のとおり、（Ａ）湿度解析過程、（Ｂ）乾燥収縮ひずみ比算出過程、および(Ｃ)予測値算出過程を含むコンクリートの乾燥収縮ひずみの予測方法と、該乾燥収縮ひずみの予測値に基づくコンクリートの乾燥収縮応力の予測方法である。
以下に、本発明について、１．乾燥収縮ひずみの予測方法と、２．乾燥収縮応力の予測方法に分け詳細に説明する。
As described above, the present invention provides a method for predicting dry shrinkage strain of concrete including (A) humidity analysis process, (B) dry shrinkage strain ratio calculation process, and (C) predicted value calculation process, and This is a method for predicting the drying shrinkage stress of concrete based on the predicted value.
The present invention is described below. 1. a method for predicting drying shrinkage strain; This will be described in detail by dividing the drying shrinkage stress prediction method.
１．乾燥収縮ひずみの予測方法
（Ａ）湿度解析過程
該過程は、湿気解析ソフトを用いて、コンクリートの壁表面から中心部に至る相対湿度とその経時変化を解析する過程である。該ソフトとして、例えば、３次元湿気移動解析機能を備えた「ＡＳＴＥＡ ＭＡＣＳ」（計算力学研究センター社製）や「ＪＣＭＡＣ３」（日本コンクリート工学会が販売）を用いることができる。前記「ＡＳＴＥＡ ＭＡＣＳ」を用いて求めたコンクリート内部の相対湿度分布の一例を図２に示す。
1. Drying Shrinkage Strain Prediction Method (A) Humidity Analysis Process This process is a process of analyzing relative humidity from the wall surface of the concrete to the center and its change over time using moisture analysis software. As the software, for example, “ASTEA MACS” (manufactured by Computational Mechanics Research Center) or “JCMAC3” (sold by Japan Concrete Institute) having a three-dimensional moisture movement analysis function can be used. An example of the relative humidity distribution inside the concrete determined using the “ASTEA MACS” is shown in FIG.
（Ｂ）乾燥収縮ひずみ比算出過程
該過程は、前記（１）式を用いて、前記湿度解析により得られたコンクリート内部の各位置の相対湿度から、該各位置の乾燥収縮ひずみの比（ε／ε６０）を算出する過程である。
なお、（１）式は、例えば以下の方法により求めることができる。
（i）複数の種類のセメントと骨材を用いて、中心部にひずみ計を設置した１００×１００×４００ｍｍのコンクリート供試体を作製する。
（ii）前記供試体を、相対湿度６０％のほか、複数の任意の相対湿度において、供試体の乾燥収縮ひずみがほぼ一定（終局値）になるまで乾燥させて、乾燥収縮ひずみの経時変化を測定する。相対湿度が４０％、６０％、８０％、および９０％における乾燥収縮ひずみの経時変化の一例を図３に示す。
（iii）相対湿度６０％におけるコンクリートの乾燥収縮ひずみの終局値（ε６０）に対する、任意の相対湿度の乾燥収縮ひずみの終局値（ε）の比（ε／ε６０）と、該任意の相対湿度との関係から、該比と該相対湿度の関係を示す式を回帰分析（フィッティング）により求める。このようにして求めた（１）式は、セメントや骨材の種類、および配合等が異なるコンクリートに対しても広範囲に適用でき汎用性が高い。
(B) Drying Shrinkage Strain Ratio Calculation Process This process is based on the equation (1), and the ratio of the drying shrinkage strain at each position (ε) from the relative humidity at each position inside the concrete obtained by the humidity analysis. / Ε 60 ).
In addition, (1) Formula can be calculated | required with the following method, for example.
(I) Using a plurality of types of cement and aggregate, a 100 × 100 × 400 mm concrete specimen with a strain gauge installed at the center is prepared.
(Ii) The specimen is dried at a plurality of arbitrary relative humidity in addition to a relative humidity of 60% until the drying shrinkage strain of the specimen becomes substantially constant (final value). taking measurement. An example of the time-dependent change of the drying shrinkage strain when the relative humidity is 40%, 60%, 80%, and 90% is shown in FIG.
(Iii) The ratio (ε / ε 60 ) of the final value (ε) of the drying shrinkage strain at any relative humidity to the final value (ε 60 ) of the drying shrinkage strain of the concrete at a relative humidity of 60% and the arbitrary relative From the relationship with the humidity, an expression showing the relationship between the ratio and the relative humidity is obtained by regression analysis (fitting). The formula (1) thus determined can be applied to a wide range of concretes with different types of cement and aggregates, blending, etc., and is highly versatile.
(Ｃ)予測値算出過程
該過程は、前記乾燥収縮ひずみの比（ε／ε６０）、および相対湿度６０％における乾燥収縮ひずみの終局値（ε６０）から、前記各位置における乾燥収縮ひずみの予測値（ε）を算出する。コンクリートの壁表面からの各位置における、乾燥収縮ひずみの予測値の経時変化の一例を図５に示す。
(C) Predicted value calculation process This process is based on the ratio of the drying shrinkage strain (ε / ε 60 ) and the final value of the drying shrinkage strain at 60% relative humidity (ε 60 ). A predicted value (ε) is calculated. An example of the change with time of the predicted value of the drying shrinkage strain at each position from the concrete wall surface is shown in FIG.
ここで、前記比（ε／ε６０）をとる理由は、以下のとおりである。
（ａ）相対湿度６０％におけるコンクリートの乾燥収縮ひずみの測定は、前記のＪＩＳ Ａ １１２９の附属書Ａ（参考）に規定されていること。（ｂ）「鉄筋コンクリート造建築物の収縮ひび割れ制御設計・施工指針（案）・同解説」（日本建築学会発行）や「建築工事標準仕様書・同解説」ＪＡＳＳ５（日本建築学会発行）、および「コンクリート標準示方書」（土木学会発行）に、前記ＪＩＳの規定に従って乾燥収縮ひずみを測定するとされている。したがって、相対湿度６０％における乾燥収縮ひずみの測定が普及した結果、多種類のコンクリートについて相対湿度６０％における乾燥収縮ひずみの膨大なデータが蓄積されていること。（ｃ）前記比（ε／ε６０）を用いれば、相対湿度６０％における乾燥収縮ひずみの既存のデータから、乾燥収縮ひずみの予測値が容易に算出できるため、既存のデータを有効に活用できること。
Here, the reason for taking the ratio (ε / ε 60 ) is as follows.
(A) The measurement of the drying shrinkage strain of concrete at a relative humidity of 60% shall be specified in Annex A (reference) of the above JIS A 1129. (B) “Shrinkage crack control design / construction guideline (draft) / commentary explanation” (published by the Architectural Institute of Japan), “Standard Building Construction Specification / Commentary” JASS5 (published by Architectural Institute of Japan), and “ According to the “Standard Specification for Concrete” (published by the Japan Society of Civil Engineers), the drying shrinkage strain is measured in accordance with the JIS regulations. Therefore, as a result of widespread measurement of drying shrinkage strain at a relative humidity of 60%, a huge amount of data on drying shrinkage strain at a relative humidity of 60% has been accumulated for various types of concrete. (C) If the ratio (ε / ε 60 ) is used, the predicted value of the drying shrinkage strain can be easily calculated from the existing data of the drying shrinkage strain at a relative humidity of 60%, so that the existing data can be used effectively. .
よって、本発明の予測方法を用いれば、相対湿度６０％における乾燥収縮ひずみを新たに測定することなく、既存のデータを活用して乾燥収縮ひずみを精度よく予測することができる。もっとも、予測精度をさらに高めるために、予測対象のコンクリートと同じ配合の供試体を用いて相対湿度６０％における乾燥収縮ひずみを実測し、既存のデータの代わりに該実測値を用いてもよい。 Therefore, if the prediction method of the present invention is used, the drying shrinkage strain can be accurately predicted using existing data without newly measuring the drying shrinkage strain at a relative humidity of 60%. However, in order to further improve the prediction accuracy, a dry shrinkage strain at a relative humidity of 60% may be measured using a specimen having the same composition as the concrete to be predicted, and the actually measured value may be used instead of the existing data.
２．乾燥収縮応力の予測方法
該方法は、応力解析ソフトを用いて、前記各位置の乾燥収縮ひずみの予測値から、該各位置の乾燥収縮応力の予測値とその経時変化を算出するものである。該ソフトとして、例えば、３次元応力解析機能を兼備した前記の「ＡＳＴＥＡ ＭＡＣＳ」や「ＪＣＭＡＣ３」を用いることができる。なお、コンクリートの壁表面からの各位置における、乾燥収縮応力の予測値の経時変化の一例を図６に示す。
2. Method for Predicting Drying Shrinkage Stress In this method, the predicted value of drying shrinkage stress at each position and its change with time are calculated from the predicted value of drying shrinkage strain at each position using stress analysis software. As the software, for example, the above-mentioned “ASTEA MACS” or “JCMAC3” having a three-dimensional stress analysis function can be used. An example of the change with time of the predicted value of the drying shrinkage stress at each position from the concrete wall surface is shown in FIG.
以下、本発明を実施例により説明するが、本発明はこれらの実施例に限定されない。
１．各種の相対湿度におけるコンクリートの乾燥収縮ひずみの測定
セメントは普通ポルトランドセメントと高炉セメントＢ種を用い、また、粗骨材は３種類の硬質砂岩砕石と１種類の石灰岩砕石を用いて水セメント比が５０％のコンクリートを混練し、中心部にひずみ計を設置した１００×１００×４００ｍｍの供試体を作製した。
次に、該供試体は、２０℃の水中に浸漬して材齢７日まで養生を行った後、温度が２０℃で、相対湿度がそれぞれ４０％、６０％、８０％および９０％の環境下で乾燥させて、該供試体の長さ変化（乾燥収縮ひずみ）を測定した。各種の相対湿度における乾燥収縮ひずみの経時変化を図３に示す。
EXAMPLES Hereinafter, although an Example demonstrates this invention, this invention is not limited to these Examples.
1. Measurement of drying shrinkage strain of concrete at various relative humidity Cement is normal Portland cement and blast furnace cement type B, and coarse aggregate is 3 types of hard sandstone crushed stone and 1 type of limestone crushed stone. A 100 × 100 × 400 mm specimen was prepared by kneading 50% concrete and installing a strain gauge in the center.
Next, the specimen was immersed in water at 20 ° C. and cured until the age of 7 days, and then the temperature was 20 ° C. and the relative humidity was 40%, 60%, 80% and 90%, respectively. It was made to dry under and the length change (dry shrinkage | contraction strain) of this test body was measured. FIG. 3 shows changes with time in drying shrinkage strain at various relative humidities.
２．相対湿度と乾燥収縮ひずみ比の関係式
図３のデータに基づく回帰分析により前記（１）式を求めた。該式とその曲線を図４に示す。
2. Relational Expression of Relative Humidity and Drying Shrinkage Strain Ratio The above expression (1) was obtained by regression analysis based on the data of FIG. The equation and its curve are shown in FIG.
３．コンクリート内部の各位置における湿度解析
長さ３ｍ、高さ２．５ｍ、および厚さ３０ｃｍで、鉄筋比が０．３％のコンクリートの壁部材を想定し、気温を２０℃でコンクリート周囲の相対湿度を６０％に設定して、前記「ＡＳＴＥＡ ＭＡＣＳ」を用いて湿度解析を行った。コンクリートの壁表面から中心部に至る各位置における相対湿度の予測値の経時変化を図２に示す。
3. Humidity analysis at each position inside the concrete Assuming a concrete wall member with a length of 3m, a height of 2.5m and a thickness of 30cm and a rebar ratio of 0.3%, the relative humidity around the concrete at 20 ° C Was set to 60%, and humidity analysis was performed using the “ASTEA MACS”. FIG. 2 shows changes with time in the predicted value of relative humidity at each position from the concrete wall surface to the center.
４．コンクリート内部の各位置における乾燥収縮ひずみの予測
前記（１）式を用いて、コンクリート内部の各位置における乾燥収縮ひずみの予測値を算出した。該予測値とその経時変化を図５に示す。また、比較のため、土木学会式を用いた従来の方法による予測結果も併記した。
4). Prediction of drying shrinkage strain at each position inside the concrete Using the above equation (1), a predicted value of drying shrinkage strain at each position inside the concrete was calculated. The predicted value and its change with time are shown in FIG. For comparison, the prediction results by the conventional method using the Japan Society of Civil Engineers are also shown.
５．コンクリート内部の各位置における乾燥収縮応力の予測
前記「ＡＳＴＥＡ ＭＡＣＳ」を用いて、前記乾燥収縮ひずみの予測値に基づきコンクリートの外部拘束と内部拘束を考慮して、乾燥収縮応力の予測値を求めた。該予測値とその経時変化を図６に示す。また、比較のため、前記土木学会式を用いコンクリートの外部拘束のみを考慮した従来の方法による予測結果も併記した。
5. Prediction of drying shrinkage stress at each position inside concrete Using “ASTEA MACS”, the predicted value of drying shrinkage stress was calculated in consideration of the external and internal constraints of concrete based on the predicted value of drying shrinkage strain. . The predicted value and its change with time are shown in FIG. In addition, for comparison, the prediction result by the conventional method using only the above-mentioned civil engineering formula and considering only the external constraint of concrete is also shown.
図５と図６に示すように、本発明の予測方法は、コンクリート内の各位置に対応して、各位置に固有の乾燥収縮ひずみと乾燥収縮応力を表わす曲線（予測値）が得られた。これに対し、従来の予測方法では、単一の乾燥収縮ひずみと乾燥収縮応力を表わす曲線しか得られなかった。
したがって、本発明の予測方法は、コンクリート内部の湿度分布を考慮してコンクリートの乾燥収縮ひずみや乾燥収縮応力を精度よく予測できるため、コンクリートの収縮ひび割れの判定や評価において、ひび割れが発生する可能性を高い精度で予測することができる。
As shown in FIGS. 5 and 6, the prediction method of the present invention obtained a curve (predicted value) representing the drying shrinkage strain and the drying shrinkage stress specific to each position corresponding to each position in the concrete. . On the other hand, in the conventional prediction method, only a curve representing a single drying shrinkage strain and drying shrinkage stress was obtained.
Therefore, since the prediction method of the present invention can accurately predict the drying shrinkage strain and drying shrinkage stress of concrete in consideration of the humidity distribution inside the concrete, there is a possibility that cracks may occur in judgment and evaluation of shrinkage cracks in concrete. Can be predicted with high accuracy.
Claims (2)
（Ａ）湿度解析によりコンクリート表面から中心部に至る各位置の相対湿度を求める、湿度解析過程
（Ｂ）下記の（１）式を用いて、前記各位置の相対湿度から、該各位置の乾燥収縮ひずみの比（ε／ε６０）を算出する、乾燥収縮ひずみ比算出過程
ε／ε６０＝（１００−ＲＨ）／｛０．６５（１００−ＲＨ）＋１４｝ ・・・（１）
（式中、ＲＨは相対湿度（％）を表し、ε／ε６０は相対湿度６０％における乾燥収縮ひずみの終局値に対する任意の相対湿度ＲＨにおける乾燥収縮ひずみの終局値の比を表わす。）
（Ｃ）前記各位置の乾燥収縮ひずみの比（ε／ε６０）、および相対湿度６０％における乾燥収縮ひずみの終局値から、前記各位置の乾燥収縮ひずみの予測値を算出する、予測値算出過程 The prediction method of the drying shrinkage | contraction strain of concrete including the process of the following (A)-(C).
(A) Humidity analysis process for obtaining relative humidity at each position from the concrete surface to the center by humidity analysis. (B) Using the following formula (1), the relative humidity at each position is used to dry each position. Drying shrinkage strain ratio calculating process for calculating the shrinkage strain ratio (ε / ε 60 ) ε / ε 60 = (100−RH) / {0.65 (100−RH) +14} (1)
(In the formula, RH represents relative humidity (%), and ε / ε 60 represents the ratio of the final value of dry shrinkage strain at any relative humidity RH to the final value of dry shrinkage strain at 60% relative humidity.)
(C) Predicted value calculation for calculating a predicted value of the drying shrinkage strain at each position from the ratio of the drying shrinkage strain at each position (ε / ε 60 ) and the final value of the drying shrinkage strain at 60% relative humidity. process
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