CN109030171B - Method for determining concrete fracture toughness by two-point straight line method - Google Patents

Method for determining concrete fracture toughness by two-point straight line method Download PDF

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CN109030171B
CN109030171B CN201810727792.0A CN201810727792A CN109030171B CN 109030171 B CN109030171 B CN 109030171B CN 201810727792 A CN201810727792 A CN 201810727792A CN 109030171 B CN109030171 B CN 109030171B
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CN109030171A (en
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管俊峰
姚贤华
陈记豪
李长永
李长明
陈珊珊
黄坡
郭慧敏
腾权
何双华
曲福来
李晓克
赵顺波
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North China University of Water Resources and Electric Power
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Abstract

本发明公开了一种由两点直线法确定混凝土起裂韧度的方法，其主要步骤包括：制作一组尺寸完全相同的试件、静力加载得到起裂荷载、由两点确定直线和求直线斜率，该斜率即为无尺寸效应的混凝土的起裂韧度。本发明避免了大量试验数据的拟合分析工作，考虑因素全面，预测结果具有足够精度，易判断结果合理性。

Figure 201810727792

The invention discloses a method for determining the crack initiation toughness of concrete by a two-point straight line method. The slope of the straight line, which is the crack initiation toughness of concrete without size effect. The invention avoids the fitting and analysis work of a large amount of test data, considers the factors comprehensively, has sufficient precision in the prediction result, and is easy to judge the rationality of the result.

Figure 201810727792

Description

Method for determining concrete fracture toughness by two-point straight line method
Technical Field
The invention relates to the technical field of civil engineering material detection, in particular to a method for determining concrete fracture toughness by a two-point linear method.
Background
Stress intensity factor corresponding to the initiation load of the test piece with crack, called initiation toughness Kini. Fracture toughness of concrete under laboratory conditionsAnd (3) obvious size effect exists, and if the fracture toughness independent of the size of the test piece is to be obtained, the fracture toughness of the concrete without the size effect is determined by adopting a boundary effect theory. However, this method must be based on a large amount of experimental data and can be implemented by fitting regression analysis. And the test piece adopted must satisfy the following conditions: the seam height ratio is different with the same size; or the same seam height ratio and different sizes; or a combination of the two forms. In addition, the fracture toughness of the concrete is determined at present based on a continuous medium mechanics theory, and the important influence of concrete aggregate particles cannot be contained in the theory.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for determining the fracture toughness of concrete by a two-point straight line method; the method overcomes the size effect existing in the existing concrete fracture toughness measurement, and does not consider the influence of aggregate particles.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for determining the fracture toughness of concrete by a two-point straight line method is designed, and comprises the following steps:
(1) pouring a group of concrete test pieces with H multiplied by B multiplied by W and alpha seam height ratio, wherein H is the height of the test piece, B is the thickness of the test piece, W is the effective span of the test piece, and the initial crack length of the test piece is a0The seam height ratio α ═ a0/H；
(2) Loading the test piece in the step (1) to be damaged by adopting a wedged split type or a three-point bending type according to a static loading test method, and recording the crack initiation load P of each test piece in the loading processini,iCalculating the average value of the test piece crack initiation load and recording the average value as Pini；
(3) Calculating the average value K of the fracture toughness of the group of test pieces based on a method for determining a straight line from two pointsini: wherein the first point is the origin (0,0), and the ordinate Y of the second point is equal to the average value P of the crack initiation loads of the group of concrete samplesini；
For a wedge split type specimen, the abscissa X of the second point is
Figure GDA0002610869140000021
For a three-point bending specimen, the abscissa X of the second point is
Figure GDA0002610869140000022
In the formulas (1) and (2), B is the thickness of the test piece, alpha is the seam height ratio, H is the height of the test piece, dmaxIs the maximum particle diameter of the aggregate of concrete, ae1、ae2Is a geometric parameter;
the slope of a straight line formed by the first point (0,0) and the second point (X, Y) is the average value K of the fracture initiation toughness of the test pieceini；
(4) Calculating the fracture toughness K of each test piece of the group based on a method for determining a straight line from two pointsini,i: wherein the first point is the origin 0 point (0,0), and the ordinate Y of the second pointiEqual to the crack initiation load P of a single concrete sampleini,i；
For a wedge split type specimen, the abscissa X of the second pointiThe abscissa X of the second point is obtained from the formula (2) for the three-point bending type test piece according to the formula (1);
a first point (0,0) and a second point (X)i，Yi) The slope of the straight line is the fracture toughness K of a single test pieceini,i。
Further, in steps (3) to (4), the geometric parameter a of formula (1)e1The following formula is used to calculate,
Figure GDA0002610869140000031
in the formula (3), α is the slit height ratio of each test piece, a0As the length of the initial crack,
Figure GDA0002610869140000032
formula (2)) Geometric parameter a ofe2The following formula is used to calculate,
Figure GDA0002610869140000033
in the formula (4), α is the slit height ratio of each test piece, a0As the length of the initial crack,
Figure GDA0002610869140000034
furthermore, the height H of the test piece is 150 mm-1200 mm, and the range is wide.
Further, the seam height ratio alpha is 0.4-0.5.
Furthermore, 3-5 concrete samples are provided, and the test workload is small.
Compared with the prior art, the invention has the positive and beneficial technical effects that:
1. the invention only adopts a group of samples with the same size and the same seam height ratio, thereby avoiding the fitting analysis of a large amount of test data.
2. The invention considers the influence of concrete aggregate particles on crack initiation and is more practical.
3. The method is simple and practical, and the slope of the straight line passing through the origin is the fracture toughness.
4. The invention only needs two coordinate points, and one of the two coordinate points is fixed as an origin (0,0), so that the data volume is small; and the other point can be used for obtaining the average value of the material parameters by taking the average value of the initiation load of a group of test pieces, or obtaining each individual value of the material parameters by taking the single value of the initiation load of a single test piece in the group, so that the discreteness of the initiation toughness determination result of the rock heterogeneous material can be displayed.
5. The invention can adopt a wedge split or three-point bending type, and is not limited by the size and the type of a test piece; the size of the selected test piece is in a selection range (the height H of the test piece can be any value between 150mm and 1200 mm), and the method is wider than that of other test pieces.
6. In the test process, only the crack initiation loads of 3-5 test pieces need to be measured, other test quantities do not need to be measured, the workload is small, and the test process is simple.
Drawings
FIG. 1 is a schematic diagram of the determination of the average value of the fracture toughness of concrete by a two-point straight line method according to the present invention;
FIG. 2 is a diagram illustrating the determination of discrete values of the fracture toughness of concrete by a two-point straight line method according to the present invention.
Detailed Description
The following examples are intended to illustrate the present invention in detail and should not be construed as limiting the scope of the present invention in any way.
Some of the steps or methods involved in the following examples are conventional in the art, unless otherwise specified, and all of the materials involved are commercially available, unless otherwise specified.
Example 1: the method for determining the fracture toughness of the concrete by a two-point straight line method comprises the following steps:
pouring a group of concrete test pieces with H multiplied by B multiplied by W and alpha seam height ratio, wherein H is the height of the test piece, B is the thickness of the test piece, W is the effective span of the test piece, and the initial crack length of the test piece is a0The seam height ratio α ═ a0H; loading the test piece to be damaged by adopting a wedged split type or a three-point bending type according to a static loading test method, and recording the crack initiation load P of each test piece in the loading processini,iCalculating the average value of the test piece crack initiation load and recording the average value as Pini(ii) a Determining a straight line based on two points, wherein the first point is an original point (0,0), and the ordinate Y of the second point is equal to the average value P of the crack initiation loads of the group of concrete samplesini；
For a wedge split type specimen, the abscissa X of the second point is
Figure GDA0002610869140000051
For a three-point bending specimen, the abscissa X of the second point is
Figure GDA0002610869140000052
Wherein B is the thickness of the specimen, alpha is the seam height ratio, H is the height of the specimen, dmaxIs the maximum particle diameter of the aggregate of concrete, ae1、ae2Is a geometric parameter;
Figure GDA0002610869140000053
Figure GDA0002610869140000054
Figure GDA0002610869140000055
the slope of the straight line formed by the first point (0,0) and the second point (X, Y) is the average value K of the fracture initiation toughness of the test pieceiniSee, fig. 1; if the ordinate Y of the second pointiEqual to the crack initiation load P of a single concrete sampleini,i(ii) a For a wedge split type specimen, the abscissa X of the second pointiThe X-axis coordinate of the second point is still obtained by the formula (2) for the three-point bending type test piece; at this time, a first point (0,0) and a second point (X)i，Yi) The slope of the straight line is the fracture toughness K of a single test pieceini,i. See fig. 2.
Example 2: method for determining concrete fracture toughness by two-point straight line method
In the embodiment, the wedged split type concrete sample is adopted, and the maximum particle size d of the aggregatemax10 mm. The test pieces are divided into five groups according to the size:
the first group H × B × W is 1200 × 200 × 1440mm, and the seam height ratio α is a0The total of 3 specimens was 0.5/W. By adopting the method, the crack initiation load is based on 3 test piecesThe fracture initiation toughness determined by the 3 test pieces and the average value of the fracture initiation load of the first group of test pieces can be respectively obtained, and the results are shown in table 1.
The second group H × B × W is 1000 × 200 × 1200mm, and the seam height ratio α is a0And W is 0.5, and the total number of the test pieces is 4. By adopting the method, the fracture initiation toughness determined by 4 test pieces and the average value of the fracture initiation load of the second group of test pieces can be respectively obtained based on the fracture initiation loads of the 4 test pieces, and the result is shown in table 1.
The third group H × B × W is 800 × 200 × 960mm, and the slit height ratio α is a0And W is 0.5, and the total number of the test pieces is 4. Based on the crack initiation loads of the 4 test pieces, the crack initiation toughness determined by the 4 test pieces and the average value of the crack initiation loads of the third group of test pieces can be respectively obtained, and the result is shown in table 1.
A fourth group H × B × W is 600 × 200 × 720mm, and a seam height ratio α is a0And W is 0.5, and the total number of the test pieces is 4. By adopting the method, the cracking toughness determined by the 4 test pieces and the average value of the cracking toughness obtained by the average value of the cracking loads of the fourth group of test pieces can be respectively obtained based on the cracking loads of the 4 test pieces, and the result is shown in table 1.
A fifth group H × B × W is 150 × 200 × 150mm, and the seam height ratio α is a0The total of 3 specimens was 0.5/W. By adopting the method, the cracking toughness determined by 3 test pieces and the average value of the cracking toughness obtained by the average value of the cracking load of the fifth group of test pieces can be respectively obtained based on the cracking load of the 3 test pieces, and the result is shown in table 1.
As can be seen from Table 1, the fracture initiation toughness determined by five groups of different test pieces respectively is more consistent by adopting the method, and the effectiveness and the rationality of the method provided by the invention are proved.
Table 1 cracking toughness of concrete determined in example 1
Figure GDA0002610869140000071
Fracture initiation and fracture of the concrete given by the double-K fracture modelRange of variation of toughness Kini＝0.65-0.77MPa·m1 /2. Therefore, the fracture initiation toughness determined by the method provided by the invention is well consistent with the calculation of the double-K fracture model, the calculation precision of the method is slightly better than that of the double-K fracture model, the calculation result is not changed along with the size of the test piece, and the size effect is avoided.
Example 3: method for determining concrete fracture toughness by two-point straight line method
In the experiment of this example, a three-point bending loading type is adopted, and the maximum particle size d of the concrete aggregatemax10 mm. The test pieces are divided into four groups according to the size:
the first group H × B × W is 500 × 200 × 2000mm, and the seam height ratio α is a0The total of 3 specimens was 0.5/W. By adopting the method, the cracking toughness determined by 3 test pieces and the average value of the cracking toughness obtained by the average value of the cracking load of the first group of test pieces can be respectively obtained based on the cracking load of the 3 test pieces, and the result is shown in table 2.
The second group H × B × W is 400 × 200 × 1600mm, and the seam height ratio α is a0And W is 0.5, and the total number of the test pieces is 4. By adopting the method, the cracking toughness determined by the 4 test pieces and the average value of the cracking toughness obtained by the average value of the cracking load of the second group of test pieces can be respectively obtained based on the cracking loads of the 4 test pieces, and the result is shown in table 2.
The third group H × B × W is 300 × 200 × 1200mm, and the seam height ratio α is a0The total of 5 specimens was 0.5/W. Based on the crack initiation loads of the 5 test pieces, the crack initiation toughness determined by the 5 test pieces and the average value of the crack initiation loads of the third group of test pieces can be respectively obtained, and the result is shown in table 2.
A fourth group H × B × W is 150 × 200 × 600mm, and a seam height ratio α is a0And W is 0.5, and the total number of the test pieces is 4. By adopting the method, the cracking toughness determined by the 4 test pieces and the average value of the cracking toughness obtained by the average value of the cracking loads of the fourth group of test pieces can be respectively obtained based on the cracking loads of the 4 test pieces, and the result is shown in table 2.
As can be seen from Table 2, the fracture initiation toughness determined by four different test pieces is consistent with that determined by the method, and the effectiveness and the reasonability of the method are proved.
Table 2 fracture initiation toughness of concrete determined in example 2
Figure GDA0002610869140000091
The fracture initiation fracture toughness variation range K of the concrete is given by a double-K fracture modelini＝0.40-0.67MPa·m1 /2. Therefore, the fracture initiation toughness determined by the method provided by the invention is well consistent with the calculation of the double-K fracture model, and the calculation result of the method provided by the invention does not change along with the size of the test piece and has no size effect.
Example 4: method for determining concrete fracture toughness by two-point straight line method
The test of this embodiment adopts a wedge split-pull loading type, and the maximum particle diameter d of the concrete aggregatemax25 mm. The test piece is divided into three groups according to the size of the test piece:
the first group H × B × W is 300 × 200 × 360mm, and the seam height ratio α is a0The total of 4 specimens was 0.4/W. By adopting the method, the fracture initiation toughness determined by 4 test pieces and the average value of the fracture initiation load of the first group of test pieces can be respectively obtained based on the fracture initiation loads of the 4 test pieces, and the result is shown in table 3.
The second group H × B × W is 800 × 240 × 960mm, and the seam height ratio α is a0The total of 4 specimens was 0.4/W. By adopting the method, the fracture initiation toughness determined by 4 test pieces and the average value of the fracture initiation load of the second group of test pieces can be respectively obtained based on the fracture initiation loads of the 4 test pieces, and the result is shown in Table 3.
The third group H × B × W is 1000 × 250 × 1200mm, and the seam height ratio α is a0The total of 5 specimens was 0.4/W. Based on the crack initiation loads of the 5 test pieces, the crack initiation toughness determined by the 5 test pieces and the average value of the crack initiation loads of the third group of test pieces can be respectively obtained, and the result is shown in table 3.
As can be seen from Table 3, the fracture initiation toughness determined by three different test pieces is more consistent with the method of the present invention, and the effectiveness and the rationality of the method of the present invention are proved.
Table 3 cracking toughness of concrete determined in example 3
Figure GDA0002610869140000101
While the present invention has been described in detail with reference to the drawings and the embodiments, those skilled in the art will understand that various specific parameters in the above embodiments can be changed without departing from the spirit of the present invention, and a plurality of specific embodiments are formed, which are common variation ranges of the present invention, and will not be described in detail herein.

Claims (4)

1.一种由两点直线法确定混凝土起裂韧度的方法，其特征在于，包括下列步骤：1. a method for determining the crack initiation toughness of concrete by two-point straight line method, is characterized in that, comprises the following steps: (1)浇筑一组尺寸均为H×B×W且缝高比均为α的混凝土试件，其中，H为试件高度，B为试件厚度，W为试件有效跨度，试件的初始裂缝长度为a0，缝高比α＝a0/H；(1) Pour a set of concrete specimens with dimensions of H×B×W and joint height ratio of α, where H is the height of the specimen, B is the thickness of the specimen, W is the effective span of the specimen, and the length of the specimen is The initial fracture length is a 0 , and the fracture height ratio α=a 0 /H; (2)采用楔入劈拉型或三点弯曲型，按静力加载试验方法将步骤(1)所述混凝土试件加载至被破坏，记录加载过程中每个试件的起裂荷载Pini,i，计算出混凝土试件起裂荷载的平均值记为Pini；(2) Using the wedge-splitting type or the three-point bending type, load the concrete specimen described in step (1) until it is damaged according to the static loading test method, and record the crack initiation load P ini of each specimen during the loading process , i , the average value of the crack initiation load of the concrete specimen is calculated as P ini ; (3)基于两点确定直线的方法，计算该组混凝土试件的起裂韧度的平均值Kini：其中，第一个点为原点(0,0)，第二个点的纵坐标Y等于该组混凝土试件起裂荷载的平均值Pini；(3) Based on the method of determining a straight line based on two points, calculate the average value K ini of the crack initiation toughness of the group of concrete specimens: where the first point is the origin (0,0), and the ordinate Y of the second point equal to the average value P ini of the crack initiation load of this group of concrete specimens; 对于楔入劈拉型试件，第二个点的横坐标X为For wedged and split-pull specimens, the abscissa X of the second point is
Figure FDA0002868645200000011
Figure FDA0002868645200000011
 对于三点弯曲型试件，第二个点的横坐标X为For a three-point bending specimen, the abscissa X of the second point is
Figure FDA0002868645200000012
Figure FDA0002868645200000012
 式(1)、(2)中，B为试件厚度，α为缝高比，H为试件高度，dmax为混凝土的骨料最大粒径，ae1、ae2为几何参数；In formulas (1) and (2), B is the thickness of the specimen, α is the joint height ratio, H is the height of the specimen, d max is the maximum particle size of the concrete aggregate, and a e1 and a e2 are geometric parameters; 第一个点(0,0)和第二个点(X，Y)所成直线的斜率即为试件起裂韧度的平均值Kini；The slope of the straight line formed by the first point (0, 0) and the second point (X, Y) is the average value K ini of the crack initiation toughness of the specimen; (4)基于两点确定直线的方法计算该组每个试件的起裂韧度Kini,i：其中，第一个点为原点0点(0,0)，第二个点的纵坐标Yi等于单个混凝土试件的起裂荷载Pini,i；(4) Calculate the crack initiation toughness K ini,i of each specimen in this group based on the method of determining a straight line with two points: where the first point is the origin point 0 (0,0), and the ordinate of the second point Y i is equal to the crack initiation load P ini,i of a single concrete specimen; 对于楔入劈拉型试件，第二个点的横坐标Xi由式(1)求得，对于三点弯曲型试件，第二个点的横坐标X由式(2)求得；For the wedge-splitting specimen, the abscissa X i of the second point is obtained by formula (1), and for the three-point bending specimen, the abscissa X of the second point is obtained by formula (2); 第一个点(0,0)和第二个点(Xi，Yi)所成直线的斜率即为单个试件的起裂韧度Kini,i；在所述步骤(3)～(4)中，式(1)的几何参数ae1，由下式计算，The slope of the line formed by the first point (0,0) and the second point (X i , Y i ) is the crack initiation toughness K ini,i of a single specimen; in the steps (3) to ( 4), the geometric parameter a e1 of formula (1) is calculated by the following formula,
Figure FDA0002868645200000021
Figure FDA0002868645200000021
 式(3)中，α为各试件的缝高比，a0为初始裂缝长度，In formula (3), α is the fracture height ratio of each specimen, a 0 is the initial fracture length,
Figure FDA0002868645200000022
Figure FDA0002868645200000022
 式(2)的几何参数ae2，由下式计算，The geometric parameter a e2 of formula (2) is calculated by the following formula,
Figure FDA0002868645200000023
Figure FDA0002868645200000023
 式(4)中，α为各试件的缝高比，a0为初始裂缝长度，In formula (4), α is the fracture height ratio of each specimen, a 0 is the initial fracture length,
Figure FDA0002868645200000024
Figure FDA0002868645200000024
 2.根据权利要求1所述的由两点直线法确定混凝土起裂韧度的方法，其特征在于，所述试件高度H为150mm～1200mm。2 . The method for determining the crack initiation toughness of concrete by the two-point straight line method according to claim 1 , wherein the height H of the test piece is 150 mm to 1200 mm. 3 . 3.根据权利要求1所述的由两点直线法确定混凝土起裂韧度的方法，其特征在于，所述缝高比α为0.4～0.5。3 . The method for determining the crack initiation toughness of concrete by a two-point straight line method according to claim 1 , wherein the joint height ratio α is 0.4-0.5. 4 . 4.根据权利要求1所述的由两点直线法确定混凝土起裂韧度的方法，其特征在于，所述试件为3～5个。4 . The method for determining the crack initiation toughness of concrete by a two-point straight line method according to claim 1 , wherein the number of the test pieces is 3 to 5. 5 .
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