Method for simultaneously predicting tensile strength and fracture toughness of concrete based on cube splitting specimens

Abstract

The present invention discloses a method for simultaneously predicting the tensile strength and fracture toughness of concrete based on cube splitting specimens, aiming to solve the technical problem in the prior art that it is impossible to simultaneously test and detect the tensile strength and fracture toughness of concrete based on the same cube splitting specimen. The main steps are as follows: casting cube splitting specimens of different sizes with a fixed water-cement ratio, maximum aggregate size d max and aggregate type, and the joint height ratio α by static loading test method until the specimen is damaged to obtain the peak load P max ; calculating the virtual crack length and nominal stress of the specimen σ n ; equivalent crack length a e ; substituting the σ n and a e calculated for specimens of different heights into #imgabs0# for regression analysis to obtain the tensile strength and fracture toughness of concrete. The prediction result of the method of the present invention has high accuracy, reasonable prediction method, low test cost, is simple and practical, and is convenient for popularization and application.

Description

Technical Field

[0001] The present invention relates to the technical field of concrete performance detection, and particularly relates to a method for simultaneously predicting the tensile strength and fracture toughness of concrete based on cube splitting specimens. Background Art

[0002] Concrete remains the most widely used building engineering material worldwide. However, due to the anisotropic structural characteristics inside concrete, crack damage inevitably exists during the construction process, which poses a great threat to the safe operation of concrete structures such as buildings, bridges, and dams, and thus has received great attention from engineering designers and constructors. Among them, the tensile strength f t and the fracture toughness K ⅠC are two important indicators for evaluating the properties of concrete, and they are closely related to the aggregate composition of concrete.

[0003] Concrete is a typical quasi-brittle material. In laboratory tests, the tensile strength f t and the fracture toughness K ⅠC of concrete are often predicted through three-point bending specimens of beam specimens with prefabricated cracks.

[0004] Compared with beam specimens, cube splitting specimens have many advantages, such as: ① compact and lightweight; ② easy to pour, reducing the risk of failure; ③ can be poured using ordinary concrete molds; ④ can largely ignore the influence of gravity; ⑤ simple loading and testing in laboratory tests; ⑥ specimens can be easily obtained by core sampling on site. Therefore, cube splitting specimens have been widely used in laboratory tests.

[0005] To obtain the tensile strength f t and the fracture toughness K ⅠC of concrete simultaneously using cube specimens, current laboratory test methods need to use intact cube splitting specimens and cube splitting specimens with a central prefabricated crack to obtain the tensile strength and fracture toughness of concrete respectively, resulting in a great waste of social resources. If it is possible to obtain the tensile strength f t and the fracture toughness K ⅠC simultaneously using only one type of cube splitting specimen, then it will not be necessary to fabricate intact cube splitting specimens, which can greatly save labor, material, and time costs, and has significant economic and social benefits.

[0006] The information disclosed in the above background art section is only intended to deepen the understanding of the overall background art of the present invention, and should not be regarded as an admission or any form of implication that this information constitutes the prior art known to those skilled in the art. Summary of the Invention

[0007] The object of the present invention is to provide a method for simultaneously predicting the tensile strength and fracture toughness of concrete based on a cube splitting specimen, so as to solve the technical problem in the prior art that it is impossible to simultaneously test and detect the tensile strength and fracture toughness of concrete based on the same cube splitting specimen.

[0008] To solve the above technical problem, the present invention adopts the following technical solutions:

[0009] Design a method for simultaneously predicting the tensile strength and fracture toughness of concrete based on a cube splitting specimen, including the following steps:

[0010] (1) According to the established water-cement ratio, maximum aggregate size d max and aggregate type, cast a certain number of cube splitting specimens with different sizes h×b and a crack height ratio of α, and a crack with a prefabricated length of 2a0 is in the center thereof, where h is the height of the specimen and b is the width of the specimen;

[0011] (2) After the cast cube splitting specimens are cured to the required age, set a loading platform with a width of 2t at the load positions at both ends of the cube splitting specimen, statically load until the specimen is damaged, and record the peak load P of each specimen max ;

[0012] (3) Based on the specimen size and maximum aggregate size d determined in the step (1) max , determine the virtual crack length Δα of each cube splitting specimen by the following formula f :

[0013] Δα f =βd max ①,

[0014] In formula ①, β is a discrete coefficient, and its value is taken according to the following interval method: when η < d / d max ≤η + 2, β = 0.1(η + 2), where η = 0, 2, 4, 6, 8, 10, 12;

[0015] (4) Calculate the nominal stress σ of each cube splitting specimen based on the following formula n :

[0016]

[0017] In formula ②, ω(α) is a correction coefficient considering the crack height ratio α; b is the width of the specimen; d = 1 / 2h, Δα f is the virtual crack length of the cube splitting specimen; σ cσ is the maximum tensile stress at the alternating tension and compression point at the end of the specimen; P is the load at the end of the specimen (taking the peak load); S1 is the length of the tensile zone on the loading vertical mid-section, (it is considered in this invention to be 80% of the length of the vertical mid-section, S1 = 0.8(d - a0) - Δα f ); S3 is the length of the compression zone on the loading vertical mid-section (it is considered in this invention to be 20% of the length of the vertical mid-section, S3 = 0.2(d - a0)); δ = t / d;

[0018] (5) Based on the different initial crack lengths a0 of each cubic split specimen and the corresponding geometric structure parameter Y(α), the equivalent crack length a of each specimen is calculated by the following formula e :

[0019]

[0020] In the formula, Y(α) is the geometric shape coefficient of the cubic split specimen; Among them, σ N is the nominal stress without considering the prefabricated center crack, σ n is the nominal stress considering the prefabricated center crack, or A(α) = -0.553α + 0.901.

[0021] (6) Substitute the nominal stress σ n and the equivalent crack length a e obtained in steps (4) and (5) into formula ① for regression analysis, and the tensile strength f t and fracture toughness K IC of the concrete can be obtained:

[0022]

[0023] In the said step (4), the ω(α) is calculated by the following formula:

[0024] ω(α) = 1.025exp(-2.351α) ⑤,

[0025] In the formula, α is the crack height ratio.

[0026] In the said step (4), the σ c is calculated by the following formula:

[0027]

[0028] In formula ⑥, P is the load at the end of the specimen (taking the peak load).

[0029] In the said step (5), the σ N is calculated by the following formula:

[0030]

[0031] In the step (5), the Y(α) is calculated by the following formula:

[0032] Y(α) = A0(δ) + A1(δ)α + A2(δ)α 2 + A3(δ)α 3 + A4(δ)α 4 + A5(δ)α 5 ⑧,

[0033] In formula ⑧, α is the ratio of the length a0 of the central prefabricated crack to the height d of the specimen; A i (i = 0, 1, 2, 3, 4, 5) takes the values as shown in the following table:

[0034]

[0035] Compared with the prior art, the main beneficial technical effects of the present invention are as follows:

[0036] 1. Based on a specimen type and a test method, the present invention can simultaneously predict the tensile strength and fracture toughness of concrete, overcoming the problem that different specimen types and test methods are required to determine the tensile strength and fracture toughness of concrete at present.

[0037] 2. The specimen used in the method of the present invention is compact and lightweight, and the influence of gravity can be ignored to the greatest extent. Its production conditions have no special restrictions, and the pouring and testing of the specimen can be satisfied in an ordinary laboratory. The indoor test loading and testing are simple, easy to operate and implement, and the test cost is low.

[0038] 3. The specimen used in the present invention can also be easily obtained by coring on site, so that the indoor test results are more consistent with the engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic diagram of cube splitting in an embodiment of the present invention; among them, (a) is a loading schematic diagram; (b) is a schematic diagram of horizontal stress distribution.

[0040] Figure 2 It is a schematic diagram of a specimen with a central prefabricated crack and a stress distribution in an embodiment of the present invention.

[0041] Figure 3 It is a fitting diagram of A(α) and α in an embodiment of the present invention.

[0042] Figure 4 It is a relationship diagram of the coefficient of variation β and d / d max in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0043] The following will illustrate the specific implementation manners of the present invention in conjunction with the accompanying drawings and embodiments. However, the following embodiments are only used to illustrate the present invention in detail and do not limit the scope of the present invention in any way.

[0044] In the following embodiments, the instrument and equipment involved are all conventional instrument and equipment unless otherwise specified; the raw materials involved are all commercially available conventional raw materials unless otherwise specified; the test or measurement methods involved are all conventional methods unless otherwise specified.

[0045] Embodiment 1: Source and Deduction of the Algorithm Model Involved in the Present Invention

[0046] The tensile strength is an important index of concrete, and the tensile strength of concrete can be directly obtained through a tensile test. However, due to the great difficulties in the installation, measurement, and loading of a direct tensile test; therefore, the splitting tensile test of cube specimens is often used to indirectly measure the tensile strength of concrete, as Figure 1 shown. In the splitting tensile test, loads are symmetrically applied at both ends of the cube specimen, as Figure 1 (a) shown. The entire splitting tensile specimen is mainly under tensile stress on the vertical section, and there is compressive stress in a small area at both ends, as Figure 1 (b) shown.

[0047] In an indoor test, to avoid local damage to the concrete at the loading position of the splitting tensile specimen, a loading platform with a width of 2t is usually set at both ends of the load, as Figure 1 (a) shown. P is the total load at both ends of the specimen, h is the height of the specimen (h = 2d), b is the width of the specimen, 2t is the loading width of the load, and let δ = t / d.

[0048] As mentioned above, the cube specimen has many advantages. Therefore, the center pre-cracked cube splitting specimen is applied to the study of fracture mechanics to obtain the fracture toughness of concrete, as Figure 2 (a) shown, with a pre-crack of length 2a0 at the center.

[0049] The inventor found in indoor experiments and related research that at the peak load P, there is a virtual crack at the tip of the pre-crack, and the length of the virtual crack is represented by Δα f , as Figure 2 (b), (c), (d) shown. The embedding, rotation, and sliding between concrete aggregates lead to the randomness of the stress distribution at the crack tip, and further lead to the randomness of Δα f . The magnitude of Δα f is closely related to the maximum coarse aggregate size d max of the concrete. To calculate Δα f , a discrete coefficient β can be introduced and calculated using Equation ①:

[0050] Δαf = βd max ①。

[0051] Considering the coefficient of variation β and the maximum aggregate size d max , the traditional BEM model is expressed as Equation ②. Through its fitting curve, the tensile strength f of concrete t and fracture toughness K IC can be obtained simultaneously:

[0052]

[0053] In Equation ②, P max is the peak value of the load P; σ n is the stress value considering the range of Δα at the tip of the specimen with a central prefabricated crack, which is a rectangular distribution, as shown in f (b)(c)(d); α Figure 2 is the equivalent crack and can be calculated by Equation ③: e

[0054]

[0055] In Equation ③, Y(α) is the geometric shape factor and can be calculated using Equation ④:

[0056] Y(α) = A0(δ) + A1(δ)α + A2(δ)α 2 + A3(δ)α 3 + A4(δ)α 4 + A5(δ)α 5 ④;

[0057] In Equation ④, the values of A i (i = 0, 1, 2, 3, 4, 5) are shown in Table 1; α is the crack height ratio, that is, the ratio of the length a0 of the central prefabricated crack to the height d of the specimen (= a0 / d);

[0058] A(α) in Equation ③ is calculated using Equation ⑤:

[0059]

[0060] In Equation ⑤, σ N is the central nominal tensile stress without considering the prefabricated crack and is calculated using Equation ⑥.

[0061]

[0062] Table 1 Values of A i List of values

[0063]

[0064] ​Based on the test results of splitting tensile of cubic specimens with a center prefabricated crack, in order to obtain the tensile strength \(f_t\) and fracture toughness \(K_{IC}\) of concrete by fitting with Equation ②, it is necessary to propose the calculation values of \(A(α)\), nominal stress \(\sigma(P,β_d)\) and coefficient of variation \(β\) applicable to the splitting tensile of cubic specimens with a center prefabricated crack. t and fracture toughness \(K_{IC}\) IC , it is necessary to propose the calculation values of \(A(α)\), nominal stress \(\sigma(P,β_d)\) and coefficient of variation \(β\) applicable to the splitting tensile of cubic specimens with a center prefabricated crack. n (P max ,βd max )

[0065] 1. Calculation of \(A(α)\)

[0066] Numerical simulation can be used to deeply study the fracture problem of prefabricated crack splitting tensile specimens. The expression of \(A(α)\) of prefabricated crack splitting tensile specimens is only related to the crack height ratio \(α\). In the research of this invention, based on the ABAQUS numerical software, cubic splitting tensile specimens with different crack height ratios \(α\) were established, and a load of 1000 N was applied to both ends of the specimens, with the loading relative width \(\delta = 0\).

[0067] Without considering the prefabricated crack, \(\sigma\) is calculated by Equation ⑥. Considering the prefabricated center crack, \(\sigma\) is obtained by extracting the horizontal stress at the tip of the prefabricated crack of the numerical specimen, and then \(A(α)\) is calculated by Equation ⑤. Finally, \(A(α)\) is fitted with the crack height ratio \(α\), and the final fitting results are distributed as N and shown in Equation ⑦: n and shown in Equation ⑦: Figure 3 A(α) = -0.553α + 0.901 ⑦.

[0068] A(α) = -0.553α + 0.901 ⑦.

[0069] 2. Derivation of nominal stress \(\sigma\) n

[0070] The stress distribution of prefabricated crack splitting specimens was simplified as shown in Figure 2 . According to the stress distribution characteristics of cubic splitting specimens, it can be seen that the center vertical section is mainly in tension stress, and there is local compression stress near the loading point. In order to conveniently obtain the expression of nominal stress \(\sigma\) of the three splitting specimens, the following assumptions were made in the research of this invention: n

[0071] (1) The load \(P\) at the end of the specimen is evenly distributed within the loading range, as shown in Figure 2 .

[0072] (2) The stress distribution is as shown in Figure 2 (b), and the nominal stress \(\sigma\) within the range of \(\Deltaα\) at the crack tip f nIt is distributed in a rectangle, then linearly changes to point C, and then linearly changes from point C to point F at the end of the specimen. Since the local compressive stress at the end is relatively large, the length of the actual S2 region is smaller than the length of the compressive region S3. At the same time, for the convenience of formula derivation and to avoid high-order polynomials, the length of the S2 region is ignored, that is, the stress suddenly changes from point C to point E (the tension-compression boundary point), as Figure 2 (c) shows.

[0073] (3) According to symmetry, one-quarter of the split specimen is taken for research, as Figure 2 (d) shows.

[0074] (4) The stress at the lower interface of the one-quarter specimen is mainly vertical stress, and the horizontal stress is relatively small; therefore, the present invention ignores the horizontal stress and only considers the vertical stress at the lower interface of the one-quarter specimen. Further assume that the vertical stress is distributed in a triangle, that is, it is 0 at the end and the maximum value σ z at the crack, as Figure 2 (d) shows.

[0075] (5) As Figure 2 (d) shows, the total length of the tensile section in the vertical section is Δα f + S1, and the total length of the compressive section is S3; let η = (Δα f + S1) / S3. The present invention assumes that η = 4, that is, 80% of the vertical section is in tension and 20% is in compression; subsequent calculation results show that the value of η has little effect on the fracture toughness K IC , but has a greater effect on the tensile strength f t , that is, the larger the value of η, the smaller the predicted tensile strength f t .

[0076] (6) σ c is the maximum tensile stress at the tension-compression alternating point E at the end of the specimen, as Figure 2 (d) shows; the tension-compression alternating point E is relatively far from the crack tip, and σ c can be calculated by Equation ⑧:

[0077]

[0078] The maximum compressive stress at the compressive stress F point at the end of the specimen is σ s , as Figure 2 (d) shows. According to Figure 2 (d)'s horizontal force balance, Equation ⑨ can be obtained:

[0079]

[0080] In Equation ⑨, S1 = 0.8(d - a0) - Δα f , S3 = 0.2(d - a0).

[0081] According to Figure 2 the horizontal force balance in (d), Equation ⑩ can be obtained as follows:

[0082]

[0083] From Equation ⑩, it can be solved that:

[0084]

[0085] In Figure 2(d), taking moment balance with point E as the rotation center, the moment M generated by internal stress b-T is:

[0086]

[0087] Corresponding to the internal stress, the moment M generated by external stress p-T is:

[0088]

[0089] According to the moment balance equation M p-T = M b-T , by combining Equation ⑨ - Equation it can be solved that:

[0090]

[0091] Since Figure 2 the stress distribution shown in is assumed according to the stress distribution law of a complete splitting tensile specimen, without considering the influence of prefabricated cracks on the stress distribution of the vertical section. Therefore, a correction coefficient ω(α) considering only the crack height ratio α needs to be introduced based on Equation , then Equation becomes:

[0092]

[0093] In Equation , the proposed expression of ω(α) is:

[0094]

[0095] 3. Value of the coefficient of variation β

[0096] Based on long-term practical research, the present invention believes that the coefficient of variation β of a prefabricated cracked cubic splitting specimen needs to be taken according to the interval method, that is, it is considered that the coefficient of variation β takes different values according to the ratio d / d max of the specimen size to the maximum aggregate size, and the detailed values are as shown in Figure 4 .

[0097] Finally, substitute all the parameters of the obtained center pre-cracked cube splitting tensile specimen into Equation ②, and according to the test results of the center pre-cracked cube splitting specimen, the tensile strength f t of concrete and the fracture toughness K IC can be obtained simultaneously by fitting method.

[0098] Example 2:

[0099] The indoor test results show that the fracture parameters of concrete are related to the water-cement ratio, strength, maximum aggregate size, and aggregate type (aggregates include pebbles, crushed stones, natural sand, artificial sand, etc., which play a skeleton role in concrete. The interface between the aggregate and the cement matrix is often weak in strength, so the interface is more likely to crack during loading); Table 2 lists the basic information of the materials of the cube concrete specimens.

[0100] Use the algorithm model obtained in Example 1 of the present invention to perform fitting analysis on the test data of the center crack cube concrete splitting tensile specimens made of the materials in Table 2, and simultaneously obtain the tensile strength f t of concrete and the fracture toughness K IC simultaneously.

[0101] Compare the fitting results obtained by the algorithm of the present invention with the indoor actual test results, as shown in Tables 3 to 8.

[0102] By comparing the fracture toughness K IC , it can be seen that the average relative error is 4.95%, and the fluctuation range is 0.6% - 12.10%. By calculating the ratio of the tensile strength f t and the compressive strength f c , it can be seen that the average ratio is 0.096, and the fluctuation range is 0.083 - 0.12; a large number of experimental studies show that the ratio range of the tensile strength to the compressive strength of concrete is 0.083 - 0.125.

[0103] As can be seen from the above, the tensile strength predicted by the present invention based on the splitting specimen BEM model is within a reasonable range. By comparing the results of the tensile strength f t and the fracture toughness K IC , the rationality and reliability of the prediction method of the present invention are effectively verified, and the prediction result has high precision. Generally speaking, this method is simple and practical, easy to operate in the implementation process, and has low test cost.

[0104] Table 2 Material Information of Center Pre-cracked Cube Splitting Tensile Concrete Specimens

[0105]

[0106] Table 3 Concrete Parameters of Q4 Series

[0107]

[0108] Table 4 Concrete Parameters of Q8 Series

[0109]

[0110] Table 5 Concrete Parameters of Q16-1 Series

[0111]

[0112] Table 6 Concrete Parameters of Q17 Series

[0113]

[0114] Table 7 Concrete Parameters of Q28 Series

[0115]

[0116] Table 8 Concrete Parameters of Q32 Series

[0117]

[0118] The present invention has been described in detail above in conjunction with the accompanying drawings and embodiments. However, those skilled in the art can understand that without departing from the concept of the present invention, various specific parameters in the above embodiments can be changed, or equivalent substitutions can be made for relevant methods, steps and materials, thereby forming multiple specific embodiments, which are all within the common variation range of the present invention and will not be elaborated herein one by one.

Claims

1. A method for simultaneously predicting the tensile strength and fracture toughness of concrete based on cube splitting specimens, characterized in that, It includes the following steps: (1) According to the established water-cement ratio, maximum aggregate size d max and aggregate type, a certain number of cube splitting specimens with different sizes h×b and a seam height ratio of α are cast and formed, and a crack with a length of 2a0 is prefabricated at the center thereof, where h is the height of the specimen and b is the width of the specimen; After the cast cube splitting specimens are cured to the required age, loading platforms with a width of 2t are set at both ends of the cube splitting specimens for loading, and static loading is applied until the specimens are damaged, and the peak load P of each specimen is recorded. max ; (3) Based on the specimen size determined in the above step (1) and the maximum aggregate size d max , the virtual crack length Δα of each cubic splitting specimen is determined by the following formula f : Δα f = βd max ①, In Equation ①, β is the coefficient of dispersion, and its value is taken according to the following interval method: when η < d / d max ≤ η + 2, β = 0.1(η + 2), where η = 0, 2, 4, 6, 8, 10, 12; (4) Calculate the nominal stress σ of each cube splitting specimen based on the following formula n :[[]]END]] In Equation ②, ω(α) is the correction coefficient considering the crack height ratio α; b is the width of the specimen; d = 1 / 2h, Δα f is the virtual crack length of the cubic splitting specimen; σ c is the maximum tensile stress at the tensile-compressive alternating point at the end of the specimen; P is the load at the end of the specimen, taking the peak value of the load; S1 is the length of the tensile zone on the loading vertical mid-section; S3 is the length of the compression zone on the loading vertical mid-section; δ = t / d; (5) Based on the different initial crack lengths a0 of each cube splitting specimen and the corresponding geometric structure parameter Y(α), the equivalent crack length a of each specimen is calculated by the following formula e :[[]]END]] In Equation ③, Y(α) is the geometric shape factor of the cubic split specimen; Among them, σ N is the nominal stress without considering the prefabricated central crack, and σ n is the nominal stress considering the prefabricated central crack, or A(α) = -0.553α + 0.901; (6) Substitute the nominal stress σ n and the equivalent crack length a e of each cubic splitting specimen obtained in steps (4) and (5) into Equation ④ for regression analysis, and then the tensile strength f t and fracture toughness K IC of the concrete can be obtained as follows:

2. The method for simultaneously predicting the tensile strength and fracture toughness of concrete based on a cube splitting specimen according to claim 1, wherein In the step (4), ω(α) is calculated by the following formula: ω(α) = 1.025exp(-2.351α) ⑤, In formula ⑤, α is the ratio of joint height.

3. The method for simultaneously predicting the tensile strength and fracture toughness of concrete based on cube splitting specimens according to claim 1, characterized in that, In the step (4), the σ c is calculated by the following formula: In formula ⑥, P is the load at the end of the specimen, taking the peak value of the load.

4. The method for simultaneously predicting the tensile strength and fracture toughness of concrete based on a cube splitting specimen according to claim 1, characterized in that, In the step (5), the σ N is calculated by the following formula:

5. The method for simultaneously predicting the tensile strength and fracture toughness of concrete based on a cube splitting specimen according to claim 1, characterized in that, In the step (5), Y(α) is calculated by the following formula: Y(α) = A0(δ) + A1(δ)α + A2(δ)α 2 + A3(δ)α 3 + A4(δ)α 4 + A5(δ)α 5 ⑧, In Equation ⑧, α is the ratio of the length a0 of the central prefabricated crack to the height d of the specimen; A i (i = 0, 1, 2, 3, 4, 5) takes the values shown in the following table:

6. The method for simultaneously predicting the tensile strength and fracture toughness of concrete based on a cube splitting specimen according to claim 1, characterized in that, In the said step (3), S1 = 0.8(d - a0) - Δα f ; S3 = 0.2(d - a0).

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