Construction and application of nonlinear fracture model of multi-element solid waste composite concrete

Abstract

The invention discloses construction and application of a multi-element solid waste composite concrete nonlinear fracture model, and aims to solve the technical problems that in the prior art, different test methods are needed for determining the fracture toughness and tensile strength of solid waste concrete, and a macroscopic model cannot reflect the influence of microscopic components. The tensile strength ft and the fracture toughness KIC of the material can be synchronously and accurately measured by adopting a single-type small-size test piece by establishing a virtual crack propagation amount calculation method (af = ndi + aVpdp + bVrdr) based on a relative size concept and combining a boundary effect model. The model can quantitatively characterize the microcosmic coupling effect of the aggregate, the rubber particles and the PET particles, the test process is remarkably simplified, the test cost is reduced, and a reliable basis is provided for material design and engineering evaluation of solid waste concrete such as RPETC, PAC and LPAC.

Description

Technical Field

[0001] This invention relates to the field of building material performance testing technology, and in particular to the construction and application of a nonlinear fracture model for multi-component solid waste composite concrete. Background Technology

[0002] With the acceleration of global industrialization, the disposal of waste tire rubber and polyethylene terephthalate (PET) plastic has become a serious environmental challenge. Waste tires degrade extremely slowly in the natural environment, and improper disposal (such as incineration and landfill) releases heavy metals and harmful gases, causing soil, water, and air pollution. PET, as a widely used raw material for single-use plastic products, also puts enormous pressure on the ecological environment due to its large-scale waste. To achieve synergy between resource utilization and environmental protection, incorporating waste rubber granules and PET granules as alternative aggregates into concrete to prepare solid waste concrete such as rubber-PET composite concrete (RPETC), PET aggregate concrete (PAC), and PET lightweight aggregate concrete (LPAC) has become an important research direction in the field of green building materials.

[0003] To ensure the safe application of this type of solid waste concrete in engineering projects, its macroscopic mechanical properties, especially tensile strength, are crucial. f t ) and fracture toughness ( K IC Accurate acquisition of these two key parameters is crucial. In existing technologies, this is mainly achieved through different types of indoor tests (such as three-point bending, splitting tensile tests, etc., see...). Figure 1 ) respectively measured f t and K IC This not only increases the complexity and economic cost of the experiment, but also introduces additional uncertainties due to the differences in specimen form and calculation method.

[0004] In terms of theoretical models, existing fracture and strength calculation models (such as the two-parameter fracture model and the double-K fracture model) are mostly based on continuum mechanics theory. They do not fully consider the quantitative influence of the particle size, dosage, and interactions of micro-components such as aggregates, rubber particles, and PET particles. Therefore, these macroscopic models cannot reveal the influence mechanism of each component on the macroscopic fracture and strength properties of composite materials from the perspective of material microstructure, thus limiting the accuracy and optimization of material design.

[0005] Furthermore, although existing studies have proposed using the size effect theory of quasi-brittle materials and small-sample test results to simultaneously determine K IC and f tThe existing methods have been successfully applied to single materials such as concrete and mortar. However, for composite systems containing multiple heterogeneous materials such as aggregates, rubber, and PET, the failure mechanisms are more complex, and the coupling effects between components are significant, making it difficult to directly apply the existing models. Currently, there is a lack of methods that can comprehensively consider microscopic factors such as aggregate gradation, particle size and dosage of rubber and PET particles, and can simultaneously and accurately predict the failure of solid waste concrete such as RPETC, PAC, and LPAC. f t and K IC The microscopic fracture analysis model. Summary of the Invention

[0006] This invention addresses the technical problems of requiring multiple types of specimens to determine the fracture parameters of solid waste concrete, the inability of macroscopic models to reflect microscopic mechanisms, and the existence of size effects. It adopts a microscopic calculation model of virtual crack propagation based on the concept of relative size, and combines boundary effect theory to simultaneously determine the size-free tensile strength and fracture toughness. This achieves the technical effect of high-precision prediction of material intrinsic parameters with only a single type of small specimen, significantly reducing test costs and constructing an accurate full fracture failure curve.

[0007] According to one aspect of this disclosure, a method for constructing a nonlinear fracture model of multi-component solid waste composite concrete is provided, comprising the following steps: (1) Obtain the peak load of multi-component solid waste composite concrete specimens containing aggregate, rubber particles and PET particles in the three-point bending fracture test. P max and the corresponding crack opening displacement data; (2) Based on the relative size theory, and taking into account the coupling effect of aggregate gradation, rubber particle size and dosage, and PET particle size and dosage, a virtual crack propagation amount is established. The microscopic computational model: ; In the formula, d i Characteristic particle size of aggregate, n It is a size factor and satisfies the relative size ( W - a 0) / ( nd i ) ≈ 10, V p and V r These represent the volumetric content of PET granules and rubber granules, respectively. d p and d r These are the characteristic particle sizes of PET granules and rubber granules, respectively. a and b The interfacial adhesion characteristic coefficient; (3) Based on the boundary effect theory, the virtual crack propagation amount Δ a fic By introducing the calculation of equivalent crack length, a nonlinear fracture control equation considering the coupling effect of the front and rear boundaries of the specimen is constructed: In the formula, For nominal stress, a e = a 0+ This is the equivalent crack length. a 0 represents the initial crack length. The length of the characteristic crack in the material. f t For the tensile strength of the material, K IC This refers to fracture toughness.

[0008] (4) Using linear fitting methods, the size-free parameters are simultaneously determined based on experimental data. f t and fracture toughness K IC .

[0009] In some embodiments of this disclosure, the nominal stress σ n Determined by the following formula: ;in, S For effective span, B The thickness of the sample. α The seam height ratio.

[0010] In some embodiments of this disclosure, the equivalent crack length a e Determined by the following formula: In the formula, a 0 represents the initial crack length of the specimen. α The seam height of the specimen. Y ( α ) represents the geometric parameters of the specimen.

[0011] Preferably, the interfacial adhesion characteristic coefficient a The value ranges from 0.02 to 0.04, and the coefficient... b The value ranges from 0.05 to 0.07; the characteristic particle size of the aggregate. d i Selected from aggregate screening curves, including the maximum aggregate size. d max 9.5mm particle size, 4.75mm particle size and minimum aggregate particle size d min Any particle size in, where dmax It is 12.5~12.7mm. d min It is 2.36mm.

[0012] Preferably, the method further includes the step of optimizing the experimental design: when determining material parameters using the two-point method, controlling the ratio of the equivalent crack lengths of the two sets of specimens. a eratio = a emax / a emin ≥3; a emax The equivalent crack length is for a larger specimen. a emin For the smaller specimen, the equivalent crack length; when a eratio When the number of specimens is less than 3, increase the number of specimen groups. n and a eratio It satisfies an power function relationship.

[0013] According to a second aspect of this disclosure, a method for constructing the full fracture failure curve of multi-component solid waste composite concrete is provided, comprising the following steps: The size-free tensile strength determined using the constructed model f t and fracture toughness K IC According to the formula Plot the complete fracture failure curve, which includes: Strength when ≤0.1 f t Controlled intensity range, ≥10 K IC The controlled fracture toughness region that satisfies the linear elastic fracture mechanics requirements, and 0.1 < <10 o'clock f t , K IC A quasi-brittle fracture region jointly controlled; Verify the applicability of the full fracture failure curve and ensure that the experimental data are within ±30% of the theoretical curve.

[0014] According to a third aspect of this disclosure, a method for assessing the fracture safety of multi-component solid waste composite concrete components is provided, comprising the following steps: S1: Calculate the equivalent crack length based on the component's geometric dimensions and load conditions. a e ; S2: Based on the nonlinear fracture model, determine the component's condition. Intensity control zone ≤0.1 Fracture toughness control zone ≥10 or 0.1 < <10 Quasi-brittle fracture zone; S3: For components in the quasi-brittle fracture zone, a nonlinear fracture model is used for accurate safety assessment to avoid assessment errors caused by traditional single strength criteria or fracture criteria.

[0015] In another aspect, this disclosure provides a method for optimizing the mix proportion of multi-component solid waste composite concrete, comprising: ①Establish a relationship between rubber particle content, PET particle content and fracture toughness K IC ,tensile strength f t Quantitative relationship; ②Set the target fracture toughness and tensile strength range according to the engineering requirements; ③ The optimal combination of rubber and PET particle content and particle size is determined by inversion calculation using the constructed fracture model; ④ Verify the fracture performance of the optimized mix proportion to ensure it meets the requirements of engineering applications.

[0016] Another aspect of this disclosure provides a design optimization method for multi-component solid waste composite concrete components, comprising: 1) Determine the minimum dimensional requirements of the component to ensure that the linear elastic fracture mechanics conditions are met: initial crack length a 0. Ligament height W - a 0. Component width B All are not less than 2.5 ( K IC / f t ) 2 ; 2) Based on the constructed fracture model, calculate the crack propagation path and remaining bearing capacity of the component under different loads; 3) Assess the fracture safety of the component under ultimate conditions and ensure the equivalent crack length. a e Material characteristic crack length a* ∞ The ratio meets the design requirements; 4) Optimize the cross-sectional dimensions and reinforcement arrangement of components to improve the overall fracture performance of multi-component solid waste composite concrete components.

[0017] According to another aspect of this disclosure, a method for quality control of multi-component solid waste composite concrete is provided, comprising: (1) Prepare standard three-point bending specimens and conduct fracture tests to obtain peak loads.P max ; (2) Calculate the theoretical peak load of the specimen based on the constructed nonlinear fracture model. P theory ; (3) Compare the measured peak loads P max Compared with theoretical peak load P theory The relative error; (4) When the relative error exceeds ±30%, the batch of multi-element solid waste composite concrete is deemed to be of substandard quality and the mix proportion or production process needs to be adjusted. (5) When the relative error is within ±30%, the batch of multi-element solid waste composite concrete is deemed to be of qualified quality and can be used in engineering applications.

[0018] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: 1. Achieved efficient simultaneous determination of fracture and strength parameters: The microscopic fracture model established in this invention overcomes the drawback of existing technologies that require separate determination of fracture toughness and tensile strength through different tests. Only one fracture test using a small-sized specimen of one type is needed to simultaneously obtain fracture toughness and tensile strength parameters without size effects. K IC and f t This significantly simplifies the testing process and reduces testing costs and time.

[0019] 2. The mechanism by which microstructure affects macroscopic properties is revealed: By quantitatively correlating the virtual crack propagation with the particle size and dosage of aggregates, rubber particles, and PET particles, the model of this invention reflects the influence of each component and its interactions on the macroscopic fracture and strength properties of the composite material at the microscopic level. This provides a deeper physical insight into understanding and predicting the mechanical behavior of solid waste concrete, surpassing the limitations of traditional macroscopic models.

[0020] 3. Improved accuracy and universality of parameter prediction: Verified by test data from various solid waste concrete experiments such as RPETC, PAC, and LPAC, the parameters calculated using the model of this invention are accurate. K IC and f t Consistent with the experimental results, the average relative error remained within a reasonable range, demonstrating the model's good accuracy and reliability. Furthermore, the model is applicable to complex systems containing multiple wastes, exhibiting strong universality.

[0021] 4. A complete fracture performance characterization system was constructed: Based on the material parameters determined by the model, a failure curve reflecting the entire fracture process of solid waste concrete can be constructed, providing key input for nonlinear analysis and safety assessment of engineering structures. Furthermore, by combining the optimization suggestions for testing methods from the mesoscopic numerical model (such as the aeratio critical value), a complete technical chain from experimentation to analysis to application was formed.

[0022] 5. Promotes the resource utilization and green development of solid waste: This model provides a theoretical basis and design tools for optimizing the blending scheme of rubber and PET in concrete, which helps to promote the large-scale and rational application of solid waste concrete in actual engineering projects, in line with the sustainable development strategy of environmental protection and resource recycling.

[0023] In summary, this invention, through the innovative establishment of a microscopic fracture analysis model, effectively solves the problems of cumbersome testing, macroscopic modeling, and difficulty in reflecting microscopic mechanisms in existing technologies, providing strong technical support for the accurate evaluation and engineering application of the mechanical properties of solid waste concrete. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of common fracture test loading in existing technologies.

[0025] Figure 2 Interfacial features of rubber / PET-cement as revealed by existing technology Figure 3 This represents the virtual crack propagation length of the RPRTC specimen in the embodiments of this disclosure.

[0026] Figure 4 The differences in the interfacial bonding characteristics between rubber particles and PET particles and the cement matrix in the embodiments of this disclosure are as follows.

[0027] Figure 5 This illustrates the relationship between structural characteristics and material parameters in the embodiments of this disclosure.

[0028] Figure 6 The stress distribution in this embodiment of the disclosure takes into account the propagation of a virtual crack.

[0029] Figure 7 The test specimen and three-point bending load test are shown in the embodiments of this disclosure.

[0030] Figure 8 The RPETC determined based on the PET effect in the embodiments of this disclosure. f t and K IC .

[0031] Figure 9 In this embodiment of the disclosure, the PAC is determined based on the effect of PET.f t , K IC .

[0032] Figure 10 In this embodiment of the disclosure, the PAC is determined based on the effect of PET. f t , K IC .

[0033] Figure 11 This is one of the full fracture failure curves in the embodiments of this disclosure.

[0034] Figure 12 This is the second of the full fracture failure curves in the embodiments of this disclosure.

[0035] Figure 13 This is a simplified two-point method design diagram of material parameters in the embodiments of this disclosure.

[0036] Figure 14 The numerical model is established for the embodiments of this disclosure.

[0037] Figure 15 This is a linear softening model in the embodiments of this disclosure.

[0038] Figure 16 This represents the convergence trend of the average peak load of PAC0-1 in the embodiments of this disclosure.

[0039] Figure 17 The results are simulated peak load values ​​in the embodiments of this disclosure.

[0040] Figure 18 Multiple sets of embodiments of this disclosure K IC and f t The calculation process.

[0041] Figure 19 As described in this embodiment of the disclosure f t and K IC One of the convergence curves of the mean with the number of groups.

[0042] Figure 20 As described in this embodiment of the disclosure f t and K IC The second convergence curve of the mean with the number of groups.

[0043] Figure 21 As described in this embodiment of the disclosure f t and KIC The smallest number of n varies a eratio The changing pattern.

[0044] Figure 22 Two-point method analysis of the fracture parameters of PAC in the embodiments of this disclosure. Detailed Implementation

[0045] Example 1: Construction of a microscopic fracture model reflecting the coupling effect of aggregate, rubber, and PEF 1. Interfacial characteristics of concrete containing PET and rubber particles The interfacial transition zone (ITZ) of concrete is considered the weakest area in the concrete structure. Due to the different properties of various materials, this region has high porosity and relatively weak connectivity, directly affecting the strength and durability of the concrete. Scholars from various countries have also conducted relevant research on the ITZ of concrete with added rubber and PET.

[0046] Zhang et al. tested the fracture properties of concrete with different rubber contents using quasi-static splitting tests. They found that when the rubber volume content did not exceed 20%, the crack path curvature increased due to the weak debonding zone between the rubber and the cement matrix, resulting in a more tortuous and complex crack path. They also observed the characteristics of the rubber-cement micro-interface using scanning electron microscopy (SEM): due to sidewall effects and micro-bleeding effects, the interfacial transition zone (ITZs) between the rubber particles and the cement matrix was 30-80 μm wide, exhibiting a porous, broken, and loose structure with obvious microcracks, such as... Figure 2 As shown in (a), Dehdezi et al. observed the microscopic morphology of the interface transition zone between rubber and cement matrix using scanning electron microscopy (SEM). They found obvious microcracks and pores in the interface transition zone, indicating poor micro-interface bonding between rubber and cement matrix. Wang et al. used SEM to observe the microstructure of recycled rubber concrete cured under constant temperature and humidity for 28 days: the addition of rubber inhibited the degree of cement hydration, reduced the formation of hydration products in the ITZ, and increasing the rubber content and particle size also increased the width of microcracks in the ITZ.

[0047] Meanwhile, Hannawi et al. replaced sand with 3%, 10%, 20%, and 50% PET waste aggregate. The results showed that replacing sand with a small amount of PET had no significant effect on water absorption and porosity. SEM analysis revealed that the bonding performance between the plastic aggregate and the matrix was weaker than that between sand and the matrix, with gaps of 5-60 μm present. Figure 2 As shown in (b), Chen et al. analyzed the differences in the width of the interfacial transition zone (ITZ) between different aggregates and cement matrix using energy dispersive spectroscopy (EDS) line scanning. The comparative analysis showed that the ITZ around PET particles was wider than that around quartz sand, approximately 6-9 μm.

[0048] In summary, the interfacial bonding characteristics between rubber and PET particles and the cement matrix differ. Compared to the PET particle-cement matrix interface, the ITZ (interfacial zone) between rubber particles and the cement matrix is ​​wider, indicating a weaker bond. Mousavimehr et al. compared the flexural strength, toughness, and fracture energy of concrete with 15% tire rubber and 15% PET particles replacing natural sand, respectively. The results showed that at room temperature, concrete with 15% tire rubber exhibited higher flexural strength, toughness, and fracture energy compared to concrete with 15% PET particles. Because of the wider ITZ and weaker bond between rubber particles and the cement matrix, micro-defects are more easily formed internally, leading to energy dissipation through multi-crack propagation and thus improving its deformability and toughness.

[0049] 2. Consider the virtual crack propagation amount based on relative size. In determining the tensile strength and fracture toughness values ​​of PAC and RPETC, loading tests are required on the specimens. Taking the fracture loading process of a three-point bending specimen as an example, due to the heterogeneity of concrete, irregular and discontinuous crack propagation zones appear at the initial crack tips. Recent research results define these crack propagation lengths as virtual crack propagation amounts. Due to the interaction of factors such as aggregate, rubber particles, PET particles and front and rear boundaries of the specimen, specimens of different sizes exhibit different structural characteristics during fracture.

[0050] The formation of crack propagation zones in PAC and RPETC is actually the destruction of the bonds between aggregates, rubber particles, and PET particles at the microscopic level. Fracture requires breaking the bridging effect between these aggregates, rubber particles, and PET particles, causing them to lose their adhesive force. Based on statistical analysis of a large amount of preliminary experimental data, a relative size method was adopted, comprehensively considering aggregate gradation and PET particle size (…). d p ) and dosage ( V p ), rubber particle size ( d r ) and dosage ( V r )and By relating them, we can determine △ a fic The simplified calculation method is as follows: (1); In the formula, For virtual crack expansion, d i The aggregate particle size, which plays a controlling role, can be determined based on screening curves, etc., and can be taken as... d 1, d 2, d 3,d 4. d 1 represents the maximum aggregate particle size. d max , d 4 Minimum aggregate particle size d min , n The value is determined based on the ligament height of the specimen ( Wa 0), acceptable n =1, 2, 3, 4..., making the relative dimensions of the specimen... . a、b The coefficient is determined by the interfacial bonding characteristics between the rubber and PET particles and the cement matrix. V p , d p The volumetric doping of PET particles and their maximum particle size are given. V r , d r This represents the volumetric content of rubber particles and the maximum particle size. d i , d p and d r The calculation method of virtual crack propagation under mutual influence is as follows: Figure 3 As shown.

[0051] Summarize the interfacial bonding characteristics of rubber and PET particles with cementitious matrices, and attribute the differences in interfacial properties between rubber and PET particles and cementitious matrices. Figure 4 1) Compared to PET, rubber exhibits more interfacial pores between the rubber and cement matrix; 2) The hydration reaction within the ITZ region between the rubber and cement matrix is ​​weaker, resulting in increased micropores. Based on the different interfacial bonding characteristics between rubber and PET particles and the cement matrix, this example adopts... a =0.03, b =0.06.

[0052] 3. Relationship between material parameters and structural properties: The boundary effect model (BEM) proposed by Hu and Duan differs from the traditional size effect model. The boundary effect model posits that the size effect of material parameters arises from the combined action of the front and rear boundaries of the specimen and the fracture process zone of the crack, rather than being simply influenced by the specimen size. Based on quasi-brittle fracture experiments of small-sized specimens under laboratory conditions, the BEM model uses extrapolation to determine material parameters without size effects, such as… Figure 5 As shown.

[0053] For finite-size specimens under laboratory conditions, the basic expression for the boundary effect model is as follows (2): In the formula, The nominal stress represents the stress that takes into account the effects of structural cracks. a e Indicates the equivalent crack length. Indicates the length of a material-specific crack. f t This refers to the tensile strength of the material.

[0054] It is determined by the strength of the material f t and fracture toughness K IC Sure: (3); For the equivalent crack length of the three-point bending specimen a e It can be determined by the following formula: (4); In the formula, a 0 represents the initial crack length of the specimen. α It is the crack height ratio of the specimen (initial crack length). a 0 / Specimen height W ), Let be the stress intensity factor, when S / W When =2.5: (5).

[0055] Equivalent crack The influence of the front and rear boundaries of the specimen on fracture failure is considered uniformly. When the strength is ≤0.1, the concrete specimen is under the control of the strength criterion; When the value is ≥10, the concrete specimen is under the control of the fracture toughness criterion. For finite-size specimens, it is generally under the control of the fracture toughness criterion. Between , The combined effect results in a quasi-brittle fracture state. ASTM E399 specifies the specimen dimensions as follows: initial crack length. ligament height The specimen width B is not less than At this time, the requirements for linear elastic fracture can be met to obtain a solution without size effect. This is consistent with BEM. The specimen was in accordance with the fracture toughness criterion control condition.

[0056] Formulas (2) and (3) can be transformed into the form of regression analysis: (6); The determined RPETC, PAC, and LPAC A boundary effect model is introduced to determine the peak load. Pmax The nominal stress of the structure below ( Figure 6 ).

[0057] according to Figure 6 The stress distribution shown is used to establish the nominal stress under peak load based on the force-moment balance. σ n expression: (7); among which, S It is the effective span of the specimen. B It is the thickness of the sample.

[0058] Peak load obtained based on basic dimensional parameters of the specimen and test results P max And the model proposed in this invention calculated Substituting into equation (7) will determine σ n The value can be determined by substituting the specimen size parameters into equation (4). a e The value will eventually be obtained. and a e Substituting into equation (6), the tensile strength of PAC and RPETC can be determined simultaneously through linear fitting. f t and fracture toughness K IC .

[0059] Example 2: Model Validation 1. Experimental Data: Fracture test results of RPETC, PAC, and LPAC with different PET particle content, as described in existing literature, were used for verification. Specimen information is shown in Tables 1-3. RPETC contained 15% rubber tire granules and different amounts (0%, 5%, 10%, 15%) of PET particles, while PAC and LPAC contained different amounts (0%, 5%, 10%, 15%) of PET particles. In each mixture, the fine aggregate was natural sand with a fineness modulus of 2.82 and a specific gravity of 2.75. The coarse aggregate was natural crushed stone, with the maximum particle size of crushed stone used in RPETC and PAC being 12.7 mm, and the maximum particle size of crushed stone in LPAC being 12.5 mm. All had a specific gravity of 2.51. PET has a melting point of 260℃, a tensile strength of 60 MPa, and a maximum particle size of PET particles of [missing information]. d p It has a diameter of 7mm and a specific gravity of 1.11, and is used to replace fine aggregate. In concrete containing rubber tire particles, the rubber tire particles are prepared by mechanically crushing waste rubber tires, and the content of rubber tire particles is 15% of the volume of fine aggregate. The maximum size of rubber tire particles... d rThe thickness is 4.75 mm, and the specific gravity is 1.122. Lightweight aggregate expanded clay (LECA) is used in LPAC to replace part of the fine aggregate in the literature, where the expanded clay has a specific gravity of 0.74 and a 24-hour water absorption rate of 16%.

[0060] Considering the model established in this invention, the virtual crack propagation Δ under peak loads of concrete with different aggregates a fic In the calculation formula, aggregate particles d i Desirable d 1= d max =12.7 / 12.5mm, d 2 = 9.5mm, d 3 = 4.75mm d 4= d min =2.36mm, d max The maximum particle size of the aggregate. d min denoted as the minimum particle size of the aggregate.

[0061] To analyze the effect of PET particle substitution on the fracture parameters of RPETC, PAC, and LPAC, concrete specimens containing precast cracks were prepared with heights of 38.1 mm, 76.2 mm, 152.4 mm, and 304.8 mm, and a width of 38.1 mm, with a span-to-height ratio of 2.5. Figure 7 As shown. Three-point bending loading tests were conducted on RPETC, PAC, and LPAC using a displacement-controlled servo-controlled testing machine. Further details can be found in the literature.

[0062] Table 1 Detailed Dimensions and Material Parameters of RPETC .

[0063] Table 2 Detailed Dimensional Information and Material Parameters of PAC .

[0064] Table 3 Detailed Dimensions and Material Parameters of LPAC .

[0065] 2. Simultaneously determine the RPETC with different PET content. f t and K IC Test data of geometrically similar specimens (RPETC-0, RPETC-5, RPETC-10, and RPETC-15, with heights of 38.1 mm, 76.2 mm, 152.4 mm, and 304.8 mm, respectively) were analyzed. For geometrically similar specimens with different heights, the effects of relative dimensions and different aggregate particle sizes were considered, along with the influence of rubber and PET particles on crack propagation, to determine the virtual crack propagation Δ under peak load. a fic Based on the previously proposed microscopic fracture model ， The tensile strength of RPETC with different PET content was determined by linear fitting. f t and fracture toughness K IC ,like Figure 10 As shown.

[0066] Depend on Figure 8 As shown in Table 4, for different RPETCs, controlling the relative size ( W - a 0 ) / nd i ≈10, determine the virtual crack propagation amount for different PET dosages. , obtained through fitting f t , K IC The correlation coefficient of the curve R 2 The tensile strengths of the RPETC-0, RPETC-5, RPETC-10, and RPETC-15 specimens used are clearly stated in the literature. f t The fracture toughnesses are 6.09 MPa, 5.84 MPa, 5.74 MPa, and 5.44 MPa, respectively. K IC 0.97 MPa·m 1 / 2 0.98 MPa·m 1 / 2 0.97 MPa·m 1 / 2 0.98 MPa·m 1 / 2 The tensile strength values ​​of specimens at different heights were calculated using the model method of this invention. f t The fracture toughnesses are 4.31 MPa, 4.01 MPa, 3.79 MPa, and 3.47 MPa, respectively. K IC The value is 0.84 MPa·m 1 / 2 0.86 MPa·m 1 / 2 0.87 MPa·m1 / 2 0.92MPa·m 1 / 2 Using the model proposed in this invention, the calculated tensile strength and fracture toughness values ​​agree well with the experimental values ​​in the original literature. It should be noted that the experimental tensile strength values ​​given in the literature have a size effect, while the tensile strength obtained using the model of this invention is without a size effect.

[0067] Table 4. RPETC determined by the model proposed in this invention. f t , K IC Comparison with experimental values .

[0068] 3. Analysis of PAC Results with Different PET Content To verify the rationality and applicability of the proposed model, experimental data of geometrically similar specimens from PAC-0, PAC-5, PAC-10, and PAC-15 were analyzed. For geometrically similar specimens with different heights, the effects of relative dimensions and different aggregate particle sizes were considered, along with the influence of PET particles on crack propagation, to determine the virtual crack propagation amount under peak load. Based on the previously proposed mesoscopic fracture model Δ... a fic = nd i + aV p d p The tensile strength and fracture toughness of PAC with different PET content were determined by linear fitting. Figure 9 As shown.

[0069] from Figure 9 As shown in Table 5, the RPETC exhibits the same pattern as those with different PET content, when the relative size ( W - a 0 ) / nd i ≈10, determine the virtual crack propagation amount Δ for concrete with different PET admixtures. a fic , obtained through fitting f t , K IC The correlation coefficient of the curve R 2 High. For different PACs, the literature clearly specifies the tensile strength of the PAC-0, PAC-5, PAC-10, and PAC-15 specimens used. f tThe fracture toughnesses are 6.93 MPa, 6.62 MPa, 6.10 MPa, and 5.59 MPa, respectively. K IC 0.92 MPa·m 1 / 2 0.93 MPa·m 1 / 2 0.96 MPa·m 1 / 2 0.92MPa·m 1 / 2 The tensile strength values ​​of specimens at different heights were calculated using this model method. f t The fracture toughnesses are 6.15 MPa, 5.52 MPa, 4.76 MPa, and 4.22 MPa, respectively. K IC The value is 0.75 MPa·m 1 / 2 0.77 MPa·m 1 / 2 0.80 MPa·m 1 / 2 0.78 MPa·m 1 / 2 The tensile strength and fracture toughness values ​​calculated by the model of this invention are in good agreement with the experimental values ​​in the original text.

[0070] Table 5. PAC determined by the model proposed in this invention. f t , K IC Comparison with experimental values .

[0071] 4. Results Analysis of Lightweight Concrete with Different PET Contents To further verify the rationality and applicability of the proposed model, experimental data of geometrically similar specimens of lightweight concrete with added PET particles were analyzed. This analysis was based on the previously proposed microstructural fracture model. The tensile strength and fracture toughness of lightweight concrete (LPAC) with different PET content can be determined by linear fitting, such as... Figure 10 As shown.

[0072] from Figure 10 As can be seen from Table 6, the PAC follows the same pattern as different PET content, when the relative size ( W - a 0 ) / nd i ≈10, determine the virtual crack propagation of concrete with different PET admixtures. , obtained through fitting f t , K IC The correlation coefficient of the curve R 2High. For different LPACs, the literature clearly specifies the tensile strength of the LPAC-0, LPAC-5, LPAC-10, and LPAC-15 specimens used. f t The fracture toughnesses are 5.61 MPa, 5.46 MPa, 4.73 MPa, and 4.61 MPa, respectively. K IC 0.75 MPa·m 1 / 2 0.76 MPa·m 1 / 2 0.74 MPa·m 1 / 2 0.75 MPa·m 1 / 2 The tensile strength values ​​of specimens at different heights were calculated using this model method. f t The fracture toughnesses are 5.01 MPa, 4.59 MPa, 3.71 MPa, and 3.43 MPa, respectively. K IC The value is 0.61 MPa·m 1 / 2 0.62 MPa·m 1 / 2 0.61 MPa·m 1 / 2 0.65MPa·m 1 / 2 The tensile strength and fracture toughness values ​​calculated by the model of this invention are in good agreement with the experimental values ​​in the original text.

[0073] Table 6. LPAC determined by the model proposed in this invention. f t , K IC Comparison with experimental values .

[0074] Example 3: Constructing the complete fracture failure curves of RPETC, PAC, and LPAC Determined by linear fitting method f t and K IC The fracture failure curve can be constructed according to equation (6). There are three fracture zones in the concrete structure, such as... Figure 5 As shown, they are respectively Strength when ≤0.1 f t Controlled intensity range, a e / a*∞ ≥10 K IC The controlled fracture toughness region that satisfies the linear elastic fracture mechanics requirements, and 0.1≤ ≤10 ft , K IC A quasi-brittle fracture region under common control. Using the model proposed in this invention, the complete fracture failure curve is constructed as follows: Figure 11 , Figure 12 As shown. By Figure 11 , Figure 12 It can be seen that the experimental data of RPETC, PAC, and LPAC are almost all distributed in the quasi-brittle fracture region (0.1≤ ≤10), and all are within the range of ±30% of the upper and lower limits.

[0075] Example 4: Construction and Application of Numerical Models The structural geometric parameters in the improved model of this invention a e Absolute dimensions were taken into account. W The influence of the specimen front boundary (initial crack length) a e ) and posterior boundary (ligament height) Wa The coupling effect of 0). Compared to the absolute size, a e This is more conducive to the study of size effects. The present invention uses different specimens... a e Obtained through linear relationship K IC and f t According to mathematical principles, a straight line can be determined by any two points. This is true if only two sets of test specimens are used. a ei The experimental results were calculated to obtain K IC and f t This will significantly reduce the workload of experiments and improve research efficiency. However, due to the dispersion of concrete experimental results, the two-point method... a ei The ratio between ( a eratio = a emax / a emin The critical value for ) is still undetermined, such as Figure 13 As shown. Therefore, this example employs numerical analysis to explore the solution. a eratio The critical value.

[0076] 1. Numerical Model Establishment: Based on PFC 2DCommercial general-purpose software was used to simulate the cement matrix using spherical particle elements, while random polymorphic clumps were employed to simulate the aggregate. The mechanical response of the matrix was reflected through the contact interactions between particles, establishing a three-point bending numerical model. A lower fixed wall was used to simulate the two lower support points in the three-point bending test, and an upper fixed wall was used to simulate the loading device. The program applied a constant downward vertical velocity of 0.0002 m / s to the upper fixed wall to achieve loading. Figure 14 As shown. To accurately obtain the mechanical performance parameters of the model, the vertical forces of the two lower fixed walls and the upper loading wall were monitored in real time during the loading process. The average value of the multiple sets of vertical forces obtained was taken as the final peak load. P max .

[0077] To accurately simulate the mechanical response of concrete as a quasi-brittle material, this example employs a displacement softening contact model, defining the mechanical behavior criteria of particle contact from both normal and tangential dimensions. The relationship between normal force and displacement is as follows: Figure 15 As shown in (a), the relationship between normal force and displacement is given by equation (8). When the displacement reaches its maximum value... U en At this point, the contact force reaches its maximum value. Afterward, as the displacement increases, the contact force decreases linearly, entering the plastic softening stage. When the displacement reaches its maximum value... U tn At that time, contact fracture occurs. The relationship between tangential force and displacement is as follows: Figure 15 As shown in (b), the relationship between tangential force and displacement is as shown in equation (9). The tangential force increases with the increase of tangential displacement and breaks after reaching its peak value.

[0078] (8); (9); In the formula, K n For normal stiffness, C n Normal bond strength, K np The slope of the region behind the peak of the normal force-normal displacement at the contact between two particles. U en This is the elastic limit displacement. U tn This represents the ultimate normal displacement. K S For tangential stiffness, C S For tangential bond strength, Ues For the ultimate tangential displacement ( Figure 15 ).

[0079] 2. Detailed parameter calibration: The experimental results of the indoor PAC0-1 specimen were analyzed. The dimensions of the numerical test specimen were consistent with those of the indoor test specimen, including height. W =95.25mm, height H =38.1mm, precast crack a 0 = 7.62 mm. Minimum particle size of the numerical specimen. R min =0.18mm, maximum value R max =0.25, maximum aggregate size d max =12.7mm. The peak loads obtained from indoor experiments were 1535.7N, 1568.8N, 1745.4N, and 1782.2N, with an average of 1680.2N. Considering the randomness of aggregate distribution during numerical simulation, PAC0-1 generated 100 randomly distributed aggregate numerical specimens for simulation and micro-parameter calibration. The calibrated micro-parameters are shown in Table 7. The convergence curves of the 100 numerical calculations are shown in... Figure 16 As shown, the minimum peak load value in the numerical simulation was 1115.2 N, and the maximum value was 2425.4 N, covering the results of the indoor experiments. The convergence mean was 1701.2 N, which also agrees with the indoor experimental results. Figure 16 It can be seen that when the number of numerical specimens exceeds 60, the simulation results of the peak load tend to converge, and subsequent numerical specimens are analyzed using simulation results of 60 specimens.

[0080] Table 7 Calibration of microscopic parameters .

[0081] 3. a eratio Critical value exploration: Using the aforementioned calibrated mesoscopic parameters, different... a e Numerical simulation of three-point bending of concrete (Table 8): a emin All specimen dimensions were obtained using AE1 numerical values. a emax Numerical specimen dimensions were successively applied using AE1.5, AE2, AE2.5, AE3, AE3.5, and AE4. Therefore, a eratio (= a emax / a eminThe values ​​of ) were 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0, respectively; similarly, considering the discreteness of concrete aggregate distribution, 60 calculations were performed for each numerical specimen with random aggregate distribution. The simulated peak load results are as follows: Figure 17 As shown. a emin and a emax Three points were randomly selected from each of the 100 numerical simulation results, and a set of results was obtained using the fitting method. K IC and f t ( Figure 18 And by repeatedly selecting randomly, multiple groups were obtained. K IC and f t and obtained K IC and f t The convergence curve of the mean with the number of groups ( Figure 19 , Figure 20 ). And then K IC and f t Using 5% of the convergence mean as the error control point, we obtain the minimum number of indoor specimens n required for the two-point method.

[0082] According to different a eratio Down f t and K IC The convergence curve of the mean as a function of the number of groups can be used to obtain the minimum number of indoor specimens n required for the two-point method. a eratio The pattern of change ( Figure 21 ),when a eratio When the values ​​are 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0, f t The minimum number of indoor specimens n required for the two-point method corresponding to the mean are 45, 6, 6, 5, 3, and 3, respectively. K IC The minimum number of indoor specimens n required for the two-point method corresponding to the mean values ​​are 42, 32, 14, 9, 3, and 3, respectively. (Parameters) f t and K IC The minimum number of indoor specimens n required for the two-point method corresponding to the mean varies with... a eratio They all exhibit the changing pattern of a power function, when aeratio When the value is 3, the curves tend to flatten out, therefore it can be considered that... a eratio The critical value is 3.

[0083] Table 8 Numerical specimen dimensions .

[0084] 4. Two-point verification: Numerical analysis results show that... a eratio The critical value is 3, meaning that when using the two-point method, the two sets of specimens... a eratio It needs to be greater than 3. (For verification) a eratio To assess the accuracy and applicability of the critical values, this example selected different types of specimens from the PAC group. a eratio For the experimental data of 4, the two-point method was used to obtain the analysis results, such as Figure 22 As shown in Table 9, it is easy to see that the two-point method... K IC and f t The calculation results are in good agreement with the previous calculation results.

[0085] Table 9 Comparison of PAC Group's Two-Point Method with Previous Calculation Results Table 9 Comparison of P .

[0086] In summary, this invention proposes a microscopic fracture analysis model that can simultaneously determine the tensile strength and fracture toughness of RPETC, PAC, and LPAC: (1) Taking into account aggregate gradation, PET particle size and dosage, and rubber particle size and dosage, based on relative size ( Wa 0 ) / d i The concept of virtual extension quantity is proposed, and a method for calculating virtual extension quantity is given, namely: A microscopic fracture analysis model was established to reflect the effects of various waste materials on solid waste concrete from a microscopic perspective. This model can be used to obtain the tensile strength of small-sized solid waste concrete specimens. f t and fracture toughness K IC .

[0087] (2) Using the model proposed in this invention, the material parameters of solid waste concrete such as RPETC, PAC and LPAC were obtained. K IC f tBy comparing with experimental results, the fracture toughness of all groups of RPETC specimens was... K IC The average relative error was 15.43% for all groups. f t The average relative error was 21.53%. All groups of PAC specimens. K IC The average relative error was 16.62% for all groups. f t The average relative error was 18.38%. All groups of LPAC specimens. K IC The average relative error was 16.97% for all groups. f t The average relative error is 18.45%. It should be noted that the material parameters determined by the model in this paper ( K IC f t The original experimental data showed no size effect, while the experimental data in the original literature exhibited a size effect, which is the reason for the error between the two results. The material parameters determined by the model in this invention ( K IC f t The results are basically consistent with the experimental values ​​and show the same trend, which fully verifies the rationality of the model proposed in this invention.

[0088] (3) Material parameters obtained using the microscopic fracture analysis model proposed in this invention ( K IC f t A complete fracture failure curve for solid waste concrete was constructed, and the experimental data for RPETC, PAC, and LPAC were all within the upper and lower limits ±30%. Finally, considering the dispersion of aggregate distribution, a three-point bending DEM micro-fracture numerical analysis model was established, and the results were conducted using the two-point method. a eratio (= a emax / a emin Discussion of the critical value; numerical analysis results show that... a eratio The value must be greater than 3, and this was verified using experimental results from PAC.

Claims

1. A method for constructing a nonlinear fracture model of multi-component solid waste composite concrete, characterized in that, Includes the following steps: (1) Obtain the peak load of multi-component solid waste composite concrete specimens containing aggregate, rubber particles and PET particles in the three-point bending fracture test. P max and the corresponding crack opening displacement data; (2) Based on the relative size theory, and taking into account the coupling effect of aggregate gradation, rubber particle size and dosage, and PET particle size and dosage, a virtual crack propagation amount is established. The microscopic computational model: ； In the formula, d i Characteristic particle size of aggregate, n It is a size factor and satisfies the relative size requirement. , V p and V r These represent the volumetric content of PET granules and rubber granules, respectively. d p and d r These are the characteristic particle sizes of PET granules and rubber granules, respectively. a and b The interfacial adhesion characteristic coefficient; (3) Based on the boundary effect theory, the virtual crack propagation amount Δ a fic By introducing the calculation of equivalent crack length, a nonlinear fracture control equation considering the coupling effect of the front and rear boundaries of the specimen is constructed: ； In the formula, For nominal stress, This is the equivalent crack length. a 0 represents the initial crack length. The length of the characteristic crack in the material. f t For the tensile strength of the material, K IC This refers to fracture toughness.

2. (4) Using linear fitting methods, the size-free parameters are simultaneously determined based on experimental data. f t and fracture toughness K IC .

3. The construction method according to claim 1, characterized in that, The nominal stress σ n Determined by the following formula: ； in, S The effective span of the specimen. B The thickness of the sample. α This refers to the seam height ratio of the specimen. The construction method according to claim 2, characterized in that the equivalent crack length a e Determined by the following formula: ； In the formula, a 0 represents the initial crack length of the specimen. α The seam height of the specimen. Y ( α ) represents the geometric parameters of the specimen.

4. The construction method according to claim 3, characterized in that, The interfacial adhesion characteristic coefficient a The value ranges from 0.02 to 0.04, and the coefficient... b The value ranges from 0.05 to 0.07; the characteristic particle size of the aggregate. d i Selected from aggregate screening curves, including the maximum aggregate size. d max 9.5mm particle size, 4.75mm particle size and minimum aggregate particle size d min Any particle size in, where d max It is 12.5~12.7mm. d min It is 2.36mm.

5. The construction method according to claim 1, characterized in that, It also includes the step of optimizing the experimental design: When determining material parameters using the two-point method, the ratio of the equivalent crack lengths of the two sets of specimens should be controlled. a eratio = a emax / a emin ≥3; among which, a emax The equivalent crack length is for a larger specimen. a emin The equivalent crack length for the smaller specimen; when a eratio When the number of specimens is less than 3, increase the number of specimen groups. n and a eratio It satisfies an power function relationship.

6. A method for constructing the full fracture failure curve of multi-component solid waste composite concrete, characterized in that, Includes the following steps: Size-free tensile strength determined using the model constructed according to any one of claims 1-5 f t and fracture toughness K IC According to the formula Plot the complete fracture failure curve, which includes: Strength when ≤0.1 f t Controlled intensity range, ≥10 K IC The controlled fracture toughness region satisfies the linear elastic fracture mechanics requirements, and 0.1 < <10 o'clock f t , K IC A quasi-brittle fracture region jointly controlled; Verify the applicability of the full fracture failure curve and ensure that the experimental data are within ±30% of the theoretical curve.

7. A method for assessing the fracture safety of multi-component solid waste composite concrete components, characterized in that, Includes the following steps: S1: Calculate the equivalent crack length based on the component's geometric dimensions and load conditions. a e ; S2: Based on the nonlinear fracture model, determine the component's condition. Intensity control zone ≤0.1 Fracture toughness control zone ≥10 or 0.1 < <10 Quasi-brittle fracture zone; S3: For components in the quasi-brittle fracture zone, a nonlinear fracture model is used for accurate safety assessment to avoid assessment errors caused by traditional single strength criteria or fracture criteria.

8. A method for optimizing the mix proportion of multi-component solid waste composite concrete, characterized in that, Includes the following steps: ①Establish a relationship between rubber particle content, PET particle content and fracture toughness K IC ,tensile strength f t Quantitative relationship; ②Set the target fracture toughness and tensile strength range according to the engineering requirements; ③The optimal combination of rubber particles and PET particles in terms of content and particle size is determined by inversion calculation using the nonlinear fracture model constructed according to any one of claims 1-5. ④ Verify the fracture performance of the optimized mix proportion to ensure it meets the requirements of engineering applications.

9. A design optimization method for multi-component solid waste composite concrete components, characterized in that, Includes the following steps: 1) Determine the minimum dimensional requirements of the component to ensure that the linear elastic fracture mechanics conditions are met: initial crack length a 0. Ligament height W - a 0. Component width B All are not less than 2.5 ( K IC / f t ) 2 ; 2) Based on the nonlinear fracture model constructed according to any one of claims 1-5, calculate the crack propagation path and remaining bearing capacity of the component under different load levels; 3) Assess the fracture safety of the component under ultimate conditions and ensure the equivalent crack length. a e Material characteristic crack length a* ∞ The ratio meets the design requirements; 4) Optimize the cross-sectional dimensions and reinforcement arrangement of components to improve the overall fracture performance of multi-component solid waste composite concrete components.

10. A method for quality control of multi-component solid waste composite concrete, characterized in that, Includes the following steps: (1) Prepare standard three-point bending specimens and conduct fracture tests to obtain peak loads. P max ; (2) Calculate the theoretical peak load of the specimen based on the nonlinear fracture model constructed according to any one of claims 1-5. P theory ; (3) Compare the measured peak loads P max Compared with theoretical peak load P theory The relative error; (4) When the relative error exceeds ±30%, the batch of multi-element solid waste composite concrete is deemed to be of substandard quality and the mix proportion or production process needs to be adjusted. (5) When the relative error is within ±30%, the batch of multi-element solid waste composite concrete is deemed to be of qualified quality and can be used in engineering applications.

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