CN105865916A - Method for determining peak load of mortar or concrete members with cracks - Google Patents

Abstract

The invention belongs to the field of civil engineering and water conservancy engineering, and in particular relates to a method for determining the peak load of cracked mortar or concrete components. The method can be personalized through the determined concrete material parameters—tensile strength f _t and fracture toughness K _IC Determination of the peak load P _max for different mortar or concrete elements or structural types with cracks. The method of the invention is simple in form and has sufficient precision.

Description

Method for Determining Peak Loads of Cracked Mortar or Concrete Members

technical field

The invention belongs to the field of civil engineering and water conservancy engineering, in particular to a method for determining the peak load of cracked mortar or concrete components.

Background technique

The main components of concrete components or structures are aggregate, sand and cement slurry, etc. Therefore, concrete is not a homogeneous material in essence, but a typical heterogeneous quasi-brittle material. The randomness of concrete aggregate distribution, concrete pouring conditions and curing conditions will have a great influence on the test results of concrete components or structures. Therefore, for components or structures made of concrete, the discreteness of test results is an inherent property.

For concrete members, the ratio of aggregate particle size to specimen size is generally 5 to 20 times. Since the ratio of the aggregate particle size of concrete to the component or structure is relatively small, the aggregate distribution has a great influence on its performance results. For example, pouring 8 concrete specimens under the same conditions, the test results may obtain 8 different peak loads. The current research can only qualitatively explain the difference or dispersion of the results of the eight specimens, but quantitative determination of the dispersion of the concrete test results is a technical problem that needs to be solved urgently.

Contents of the invention

In view of the above problems, the present invention proposes a method for individually determining the peak load of cracked mortar or concrete components. The method uses the determined concrete material parameters (tensile strength f _t , fracture toughness K _IC ) to individually determine the peak load of cracked mortar or concrete components. The peak load P _max of different mortar or concrete elements or structural types of cracks, the method of the invention is simple in form and has sufficient accuracy.

In order to solve the above technical problems, the present invention is realized through the following technical solutions:

Devise a method for determining the peak load of a cracked mortar or concrete member comprising the following steps:

1. Determine the equivalent crack length a _e of different cracked components according to the type of test piece used; a _e is calculated by formula (1):

(1)

According to the stress intensity factor manual, determine the geometric influence parameter Y(α) of different components.

If a three-point bending beam specimen is used, then

(2a)

When L/W=2.5,

(2b)

When L/W=4,

(2c)

When L/W=8,

(2d)

If compact tension or wedge split tension specimens are used, then

(3a)

(3b).

2. Substituting the known and determined material parameters of the specimen mortar or concrete—tensile strength f _t and fracture toughness K _IC —into the elastoplastic theory formula (4), the value of σ _n (P _max ) can be calculated.

(4)

3. For three-point bending beam specimens, based on the obtained σ _n (P _max ), the elastic-plastic theoretical formula (5) can be used to obtain different values of β to obtain the personalized peak load P _max of the specimen:

(5);

For compact tension or wedge split tension specimens, based on the obtained σ _n (P _max ), the elastic-plastic theory formula (6) can be used to obtain different values of β, so as to solve the personalized peak load of the specimen P _max :

(6);

In the above formulas, W ₁ =W -a ₀ ; W ₂ =W ₁ - (β·d _max ); W ₃ =W ₁ + (β·d _max ); W is the height of the specimen, and L is the length of the specimen , B is the thickness of the specimen; P _max is the peak load; a ₀ is the initial crack length, β·d _max is the crack propagation at the tip of the initial crack corresponding to the peak load P _max ; d _max is the maximum particle size of mortar or concrete aggregate . α is the fracture height ratio, that is, the ratio of the initial crack length a ₀ to the specimen height W; A(α) is a parameter affecting the specimen shape, and different values are taken for three-point bending beams and wedge split tension specimens; _σn is Consider the nominal stress affected by cracks; β is an adjustment coefficient considering the discreteness of the test piece results, β is not a fixed value, in order to accurately and individually solve the peak load of each test piece, β can be discretely taken between 0.1 and 2.0, such as 0.1 , 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8…2.0; Y(α) is the geometric influence parameter.

The present invention has the following positive and beneficial technical effects:

(1) The present invention can individually determine the peak load of different specimen structures through concrete material parameters—tensile strength and fracture toughness.

(2) The crack expansion corresponding to the peak load is considered by the parameter β·d _max . From a statistical point of view β=1.0, the average value of the peak load of the overall member can be predicted; and when β is 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8...2.0, the peak value of each specimen can be accurately and personalized load.

Description of drawings

Figure 1 is a schematic diagram of the external load P-displacement δ curve (the same component corresponds to different peak load P _max );

Figure 2 is a schematic diagram of the crack propagation across the aggregate at the peak load in the average sense (β=1.0 when considering the average value of the test results);

Figure 3 is a schematic diagram of crack propagation across the aggregate under individualized peak loads (individually determined peak loads β=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8...2.0).

detailed description

The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Some of the steps or methods involved in the following examples are conventional methods in the art unless otherwise specified, and the materials involved are all commercially available materials unless otherwise specified.

Embodiment 1 The method for determining the peak load of a cracked mortar or concrete member includes the following steps:

Four concrete three-point bending beam members with the same size and the same joint height ratio are poured, and the size of the specimen is L×B×W=320×40×80mm, where W is the height of the specimen, B is the thickness of the specimen, and L is the thickness of the specimen. The effective length of the test piece satisfies L/W=4. The initial crack length is the same a ₀ =24mm, that is, a ₀ /W=0.3 are consistent. The maximum particle size of the aggregate is d _max =10 mm. W/d _max = 8. The material properties of the concrete are known—tensile strength f _t =4.7MPa, fracture toughness K _IC =1.3 MPa·m ^1/2 .

According to the type of specimen used, determine the equivalent crack length a _e of different cracked components. a _e can be calculated by formula (1). According to the stress intensity factor manual, the geometric influence parameter Y(α) of different components or structural types can be determined, and the three-point bending beam can be calculated by formula (2).

Substitute the known and determined material parameters of the specimen concrete—tensile strength f _t and fracture toughness K _IC into elastic formula (4) to derive the value of σ _n (P _max ).

According to formula (5), different values of β are used to inversely solve the personalized peak load P _max of different specimens. Referring to Figure 1, due to the inherent characteristics of concrete-like quasi-brittle materials, the peak load of each component is different even if components of the same size and type are poured.

Referring to Figure 2, from a statistical point of view, β = 1.0 predicts the average value of the peak load of the overall member.

See Figure 3, considering the discreteness of the test results, for the prediction of the peak load test value of each specimen, β=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8...2.0, the β value is not a fixed value , the value range is related to the discreteness of material properties.

Referring to Table 1, for the four specimens of the same size and the same slit-height ratio in this embodiment, the measured peak loads are different. By adopting the method of the present invention, the β of the four test pieces take different values of 0.9, 1.1, 0.8, and 0.7 respectively, and the predicted values are in good agreement with the test values of the four peak loads respectively. β=1.0 can predict the mean of the overall 4 components.

Table 1 Individually determined peak loads of four members with cracks

.

Embodiment 2 The method for determining the peak load of a cracked mortar or a concrete component comprises the following steps:

Four concrete three-point bending beam members with the same size and the same joint height ratio are poured, and the size of the specimen is L×B×W=320×40×80mm, where W is the height of the specimen, B is the thickness of the specimen, and L is the thickness of the specimen. The effective length of the test piece satisfies L/W=4. The initial crack length is the same a ₀ =32mm, that is a ₀ /W=0.4 are consistent. The maximum particle size of the aggregate is d _max =10 mm. W/d _max = 8. The material properties of the concrete are known—tensile strength f _t =4.7MPa, fracture toughness K _IC =1.3 MPa·m ^1/2 .

According to the type of specimen used, determine the equivalent crack length a _e of different cracked components. a _e can be calculated by formula (1). According to the stress intensity factor manual, the geometric influence parameter Y(α) of different components or structural types can be determined, and the three-point bending beam can be calculated by formula (2).

Substitute the known and determined material parameters of the specimen concrete—tensile strength f _t and fracture toughness K _IC into elastic formula (4) to derive the value of σ _n (P _max ).

According to formula (5), different values of β are used to inversely solve the personalized peak load P _max of different specimens. Referring to Figure 1, due to the inherent characteristics of concrete-like quasi-brittle materials, the peak load of each component is different even if components of the same size and type are poured.

Referring to Figure 2, from a statistical point of view, β = 1.0 predicts the average value of the peak load of the overall member.

Referring to Figure 3, considering the discreteness of the test results, for the prediction of the peak load test value of each specimen, β=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8...2.0, the value of β is not a fixed value , the value range is related to the discreteness of material properties.

Referring to Table 2, for the four specimens of the same size and the same slit-height ratio in this embodiment, the measured peak loads are different. By adopting the method of the present invention, the β of the four test pieces take different values of 1.6, 0.9, 1.1, and 1.3 respectively, and the predicted values are in good agreement with the test values of the four peak loads respectively. β=1.0 can predict the mean of the overall 4 components.

Table 2 Individually determined peak loads of four members with cracks

.

Embodiment 3 The method for determining the peak load of a cracked mortar or concrete member comprises the following steps:

Four concrete three-point bending beam members with the same size and the same joint height ratio were poured, and the specimen size L×B×W =400×100×100 mm, where W is the height of the specimen, B is the thickness of the specimen, and L is The effective length of the test piece, the test piece satisfies L/W=4. The initial crack length is the same a ₀ =40mm, that is a ₀ /W=0.4 are consistent. The maximum particle size of the aggregate is d _max =20 mm. W/d _max = 5. The material properties of the concrete are known—tensile strength f _t =4.7MPa, fracture toughness K _IC =2.2 MPa·m ^1/2 .

According to the type of specimen used, determine the equivalent crack length a _e of different cracked components. a _e can be calculated by formula (1). According to the stress intensity factor manual, the geometric influence parameter Y(α) of different components or structural types can be determined, and the three-point bending beam can be calculated by formula (2).

Substitute the known and determined material parameters of the specimen concrete—tensile strength f _t and fracture toughness K _IC into elastic formula (4) to derive the value of σ _n (P _max ).

According to formula (5), different values of β are used to inversely solve the personalized peak load P _max of different specimens. Referring to Figure 1, due to the inherent characteristics of concrete-like quasi-brittle materials, the peak load of each component is different even if components of the same size and type are poured.

Referring to Figure 2, from a statistical point of view, β = 1.0 predicts the average value of the peak load of the overall member.

See Figure 3, considering the discreteness of the test results, for the prediction of the peak load test value of each specimen, β=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8...2.0, the β value is not a fixed value , the value range is related to the discreteness of material properties.

Referring to Table 3, for the four specimens of the same size and the same slit-height ratio in this embodiment, the measured peak loads are different. By adopting the method of the present invention, the β of the four test pieces take different values of 0.9, 1.2, 0.95, and 1.0 respectively, and the predicted values are in good agreement with the test values of the four peak loads respectively. β=1.0 can predict the mean of the overall 4 components.

Table 3 Individually determined peak loads of four members with cracks

.

Embodiment 4 The method for determining the peak load of a cracked mortar or concrete member may include the following steps:

Five concrete three-point bending beam members with the same size and the same joint height ratio were poured, and the specimen size L×B×W =400×100×100 mm, where W is the height of the specimen, B is the thickness of the specimen, and L is The effective length of the test piece, the test piece satisfies L/W=4. The initial crack length is the same a ₀ =50mm, that is a ₀ /W=0.5 are consistent. The maximum particle size of the aggregate is d _max =20 mm. W/d _max = 5. The material properties of the concrete are known—tensile strength f _t =4.7MPa, fracture toughness K _IC =2.2 MPa·m ^1/2 .

According to the type of specimen used, determine the equivalent crack length a _e of different cracked components. a _e can be calculated by formula (1). According to the stress intensity factor manual, the geometric influence parameter Y(α) of different components or structural types can be determined, and the three-point bending beam can be calculated by formula (2).

Substitute the known and determined material parameters of the specimen concrete—tensile strength f _t and fracture toughness K _IC into elastic formula (4) to derive the value of σ _n (P _max ).

According to formula (5), different values of β are used to inversely solve the personalized peak load P _max of different specimens. Referring to Figure 1, due to the inherent characteristics of concrete-like quasi-brittle materials, the peak load of each component is different even if components of the same size and type are poured.

Referring to Figure 2, from a statistical point of view, β = 1.0 predicts the average value of the peak load of the overall member.

See Figure 3, considering the discreteness of the test results, for the prediction of the peak load test value of each specimen, β=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8...2.0, the β value is not a fixed value , the value range is related to the discreteness of material properties.

Referring to Table 4, for the five specimens of the same size and the same slit-to-height ratio in this embodiment, the measured peak loads are different. By adopting the method of the present invention, if the β of the five test pieces take different values of 0.55, 0.85, 1.0, 1.1, and 1.4 respectively, the predicted values will be in good agreement with the five peak load test values respectively. β = 1.0 is able to predict the mean of the overall 5 components.

Table 4 Individually determined peak loads of four members with cracks

.

The above descriptions of the disclosed embodiments enable those skilled in the art to implement or use the present invention, but it is obvious that the described embodiments are only illustrative partial implementations of the present invention, and are not intended to limit the scope of the present invention. Equivalent changes and modifications made by those skilled in the art without departing from the concepts and principles of the present invention shall fall within the protection scope of the present invention.

Claims (7)

1. A method for determining band cracked mortar or concrete member peak load, is characterized in that, comprises the following steps: (1) Determine the equivalent crack length a _e of different cracked components according to the type of specimen used; a _e is calculated by formula (1): (1) In the formula, a ₀ is the initial crack length; α is the fracture height ratio, that is, the ratio of the initial crack length a ₀ to the specimen height W; Different values are taken for the tensile specimens; Y(α) is a geometric influence parameter; (2) Substituting the known and determined material parameters of the specimen mortar or concrete—tensile strength f _t and fracture toughness K _IC —into the elastoplastic theory formula (4), the value of σ _n (P _max ) can be calculated: (4) where P _max is the peak load; σ _n is the nominal stress considering the influence of cracks; (3) Based on the obtained σ _n (P _max ), according to the elastic-plastic theory formula, by taking different values of β, the corresponding personalized peak load P _max of the specimen is solved; β is considering the discretization of the specimen results sex adjustment factor. 2. The method for determining the peak load of a cracked mortar or concrete component according to claim 1, characterized in that: in the step (1), according to the stress intensity factor manual, determine the geometric influence parameter Y of different components according to a conventional method (α). 3. The method for determining the peak load of cracked mortar or concrete members according to claim 1, characterized in that: in the step (1), if a three-point bending beam specimen is used, then (2a); When L/W=2.5, (2b); When L/W=4, (2c); When L/W=8, (2d); In the formula, L is the length of the specimen, and W is the height of the specimen. 4. The method for determining the peak load of a cracked mortar or concrete member according to claim 1, characterized in that: in the step (1), if the compact tension or wedge split tension specimen is used, then (3a) (3b). 5. determine the method for band cracked mortar or concrete member peak load according to claim 1, it is characterized in that: In the step (3), for the three-point bending beam specimen, based on the obtained σ _n (P _max ), the individuality of the specimen can be solved by taking different values of β from the elastoplastic theory formula (5) Optimized peak load P _max : (5) In the formula, W ₁ =W -a ₀ ; W ₂ =W ₁ - (β·d _max ); W ₃ =W ₁ + (β·d _max ); W is the height of the specimen, L is the length of the specimen, B is the thickness of the specimen; P _max is the peak load; a ₀ is the initial crack length, β d _max is the crack extension at the tip of the initial crack corresponding to the peak load P _max ; d _max is the maximum particle size of mortar or concrete aggregate. 6. determine the method for band cracked mortar or concrete member peak load according to claim 1, it is characterized in that: In the step (3), for compact tension or wedge split tension specimens, based on the obtained σ _n (P _max ), the elastoplastic theory formula (6) can be used to take different values of β to solve Individualized peak load P _max of the test piece: (6) In the formula, W ₁ =W -a ₀ ; W ₂ =W ₁ - (β·d _max ); W ₃ =W ₁ + (β·d _max ); W is the height of the specimen, L is the length of the specimen, B is the thickness of the specimen; P _max is the peak load; a ₀ is the initial crack length, β d _max is the crack extension at the tip of the initial crack corresponding to the peak load P _max ; d _max is the maximum particle size of mortar or concrete aggregate. 7. The method for determining the peak load of a cracked mortar or concrete member according to claim 5 or 6, characterized in that: said β takes a value of 0.1-2.0.