A method for calculating and verifying the crack resistance of gradient composite walls.

Abstract

This invention relates to the field of wall construction technology in building engineering, specifically to a method for calculating and verifying the crack resistance of composite walls. The method is primarily based on a gradient composite wall, which includes a base slab, reaction piers spaced apart on the base slab, and an intermediate wall poured between adjacent reaction piers, forming an integral wall structure. The calculation method includes calculating the concrete drying shrinkage index ε of the intermediate wall in the gradient composite wall. d ε, the cold shrinkage index parameter t Ultimate tensile parameter ε pa When the concrete's limiting expansion index parameter ε e Satisfying 0 < ε e -ε d -ε t <ε pa When the concrete does not crack, ε is obtained. e range ε d +ε t <ε e <ε pa +ε d +ε t Based on this, expansive concrete was prepared, and the mix proportion and construction process parameters of the expansive concrete were verified and optimized to meet the technical quality and economic requirements, so that the wall would not crack.

Description

Technical Field

[0001] This invention relates to the field of wall construction technology in building engineering, and in particular to a method for calculating and verifying the crack resistance of gradient composite walls. Background Technology

[0002] In recent years, the development and utilization of underground space has increased, resulting in many ultra-long, ultra-large, and ultra-deep basement structures. According to national and industry standards, these ultra-long, ultra-large, and ultra-deep basement structures are defined as those with a maximum side length greater than 10 meters, a planar area greater than 200 square meters, and a depth less than 5 meters. The concrete in these structures is prone to deformation and cracking during pouring. Therefore, crack control is a crucial technical aspect of underground construction projects. However, the material properties of concrete make cracking unavoidable. When cracks exist in the exterior walls of underground structures, groundwater leakage occurs, affecting structural durability and safety. Crack problems remain one of the most challenging issues in the construction industry.

[0003] Many factors contribute to cracks in concrete structures, including changes in surface humidity, volumetric deformation, creep, and temperature. These factors account for approximately 90% of structural cracks. In the past, permanent expansion joints were commonly used to control structural cracks. However, permanent expansion joints are not only expensive and may affect the building's aesthetics after installation, but they can also cause noise and vibration during use due to joint movement. Furthermore, long-term use and aging of permanent expansion joints can lead to leaks and damage, requiring timely inspection and replacement. Currently, permanent expansion joints are rarely used in basement concrete structure designs, leading to a rapid increase in ultra-long and ultra-large concrete structures.

[0004] Wall crack control technology involves multiple professional fields, including structure, materials, construction, design, and environment. Currently, there are no mature and effective crack control technologies or measures available domestically or internationally. For key projects involving ultra-large and ultra-long concrete structures, the main method for crack control is full-size concrete pouring and curing. However, this method requires a large amount of pouring formwork and has very high requirements for construction technology. It not only needs to complete concrete pouring within a short time but also requires the design of effective temperature change control schemes. It is extremely demanding in terms of construction site, schedule, and manpower, making it unsuitable for most projects. Furthermore, this method can only minimize crack formation to a certain extent, and the effect is not particularly ideal. Several other patent documents have also disclosed some wall crack control technologies. For example, patent application CN215564429U, entitled "A Device for Improving Shrinkage Cracks in Concrete Walls of Extra-Long Basements," employs a crack-prevention structure on a sealed template. This structure's special cross-section controls stress dispersion. However, this method affects the integrity of the concrete structure, resulting in poor wall load-bearing capacity. Another patent application CN115749049A, entitled "A Construction Method for Preventing Cracks in Extra-Long Shear Walls through Bidirectional Graded Induced Joints," discloses a method of controlling the formation of graded induced joints in the concrete structure by setting pre-embedded templates for induced joints. This creates pre-cracked areas, rationally guiding crack development, reducing stress concentration, and preventing disordered crack formation. However, this method is cumbersome to operate and severely impacts construction progress.

[0005] Therefore, preventing or reducing concrete shrinkage, avoiding cracks in walls due to large deformation, and ensuring the safety and normal use of ultra-long basement concrete structures are major technical issues in the construction of building walls. Moreover, reducing construction costs, simplifying construction procedures, shortening the construction period, and achieving better construction economy are also key considerations in controlling wall cracks. To address these issues, a gradient composite wall has been invented. However, how to design and calculate the crack resistance of this gradient composite wall, and how to verify whether the deformation of this gradient composite wall can prevent cracks, have become unavoidable and important technical research contents in the process of adopting this gradient composite wall. Summary of the Invention

[0006] One of the objectives of this invention is, at least, to address the issues of how to calculate the crack resistance of a designed gradient composite wall structure and how to verify that the deformation of the gradient composite wall meets the requirement of no further cracking, thus ensuring its suitability for subsequent operation and use. This invention provides a method for calculating and verifying the crack resistance of a gradient composite wall. The method calculates the concrete drying shrinkage index, concrete cold shrinkage index, and concrete ultimate tensile strength index of the gradient composite wall, and then calculates whether the concrete limited expansion index meets the requirements, thereby determining whether the gradient wall meets the crack resistance conditions and will not subsequently develop cracks.

[0007] To achieve the above objectives, the technical solution adopted by the present invention includes the following aspects.

[0008] A method for calculating the crack resistance of a gradient composite wall, characterized in that the gradient composite wall includes a base slab, reaction piers spaced apart on the base slab, and an intermediate wall cast on the base slab. The intermediate wall fills the space between two adjacent reaction piers, so that the base slab, reaction piers, and intermediate wall form an integral wall structure. The reaction piers are ordinary concrete structures, and the intermediate wall is formed by casting expansive concrete. The method for calculating the expansive concrete mix proportion and performance of the intermediate wall to meet the crack resistance requirements of the gradient composite wall includes the following steps:

[0009] Step A: Calculate the concrete drying shrinkage parameter ε of the intermediate walls in the gradient composite wall system. d ;

[0010] Step B: Calculate the concrete shrinkage index parameter ε of the intermediate wall. t ;

[0011] Step C: Calculate the ultimate tensile strength parameter ε of the concrete in the intermediate wall. pa ;

[0012] Step D: Calculate the concrete expansion limit parameter ε of the intermediate wall. e When the concrete's limiting expansion index parameter ε e Satisfying 0 < ε e -ε d -ε t <ε pa When the concrete does not crack, the concrete expansion limit parameter ε can be calculated. e The range of values ​​for ε d +ε t <ε e <ε pa +ε d +ε t Furthermore, the mix proportion and performance of expansive concrete for intermediate walls that meet the crack resistance requirements of gradient composite walls were determined.

[0013] Preferably, in step A, the concrete drying shrinkage index parameter ε of the intermediate wall is calculated. d The parameters are calculated based on the concrete properties of the intermediate wall, including the ultimate shrinkage value of concrete under standard conditions and the correction factor for concrete under non-standard conditions. In the formula, M1 represents the limit shrinkage value under standard conditions, M2, ..., Mn are correction coefficients for various non-standard conditions, including cement type M1, cement type M2, aggregate type M3, water-cement ratio M4, cement paste volume M5, initial curing time M6, ambient humidity M7, reinforcement ratio M8, and vibration operation method M9. b is an empirical coefficient, and t is the concrete age (days).

[0014] Preferably, in step B, the concrete shrinkage index parameter ε of the intermediate wall is obtained. t The coefficient of thermal expansion of the intermediate wall is calculated based on the concrete characteristics, including the linear expansion coefficient of the concrete, the highest central temperature during concrete pouring, the average ambient temperature, and the constraint coefficient of the intermediate wall concrete. t =a(T 温峰 -T 环境 )·R, where α is the coefficient of linear expansion of concrete, T 温峰 T represents the highest temperature (°C) at the center of the concrete. 环境 R is the average ambient temperature (°C), and R is the constraint coefficient of the intermediate wall concrete.

[0015] Preferably, the highest temperature T at the center of the concrete is... 温峰 It is obtained through calculation. During the calculation, T 温峰 =T 入模 +T 水化温升 In the formula, T 入模 T represents the average temperature of the concrete upon placement in the formwork (°C). 水化温升 The highest temperature at the center of the concrete (°C);

[0016] Wherein, the T 水化温升 =αT max α is the heat dissipation coefficient of concrete, T max The adiabatic temperature rise of the concrete (°C) is the temperature rise of the concrete. In the formula, W represents the amount of concrete cementitious materials used (kg / m³). 3 Q is the total heat of hydration of cementitious materials, c is the specific heat of concrete, ρ is the unit weight of concrete, and m is a coefficient related to cement type, pouring temperature, etc.

[0017] Wherein, the total heat of hydration of cementitious materials Q = k1·k2·Q0, k1 and k2 are the coefficients of fly ash and mineral powder under different admixture amounts, and Q0 is the total heat of hydration of cement.

[0018] Preferably, in step C, the ultimate tensile strength parameter ε of the concrete in the intermediate wall is obtained. pa The ultimate tensile strength parameters of the concrete are calculated based on the crack resistance strength of the concrete and the reinforcement details of the cross-section. In the formula, Rf is the design strength of concrete against cracking (MPa), ρ is the cross-sectional reinforcement ratio, ρ=μ×100, μ is the reinforcement ratio, and d is the reinforcement diameter (cm).

[0019] Correspondingly, this technical solution also provides a verification method for gradient composite walls. Using the expansive concrete mix proportion and performance obtained through the aforementioned crack resistance calculation method for gradient composite walls, when verifying whether the intermediate wall formed by pouring expansive concrete meets the crack resistance conditions of gradient composite walls, the following content is included:

[0020] Step 1: Verify and optimize the expansive concrete mix proportion obtained from the crack resistance calculation method of the above-mentioned gradient composite wall;

[0021] Step II: Adjust and optimize the reaction pier structure in the gradient composite wall to verify the role of the reaction pier in the gradient composite wall;

[0022] Step 3: Analyze and verify the crack resistance characteristics of the gradient composite wall based on the crack occurrence during operation.

[0023] Preferably, step I, in verifying the expansive concrete mix proportion obtained by the crack resistance calculation method of the gradient composite wall, includes the following steps:

[0024] Step I-1: Recalculate the concrete drying shrinkage index parameter ε of the intermediate wall based on the obtained expansive concrete mix proportion. d Concrete shrinkage index parameter ε t and the ultimate tensile property parameter ε of concrete pa ;

[0025] Step I-2: Calculate the concrete expansion limit parameter ε of the intermediate wall. e Verify the concrete's restricted expansion index parameter ε e Does it satisfy 0 < ε? e -ε d -ε t <ε pa If the conditions are met, proceed to step I-3; otherwise, proceed to step I-4.

[0026] Step I-3: Based on the ε obtained from the verification e The range of values ​​was further optimized to improve the mix proportion of expansive concrete and reduce the cost per unit weight of expansive concrete.

[0027] Step I-4: Based on the limiting expansion index parameter ε verified in Step I-2 e The mix proportions of the expansive concrete were readjusted, and the process was repeated in steps I-1 and I-2.

[0028] Preferably, step II, in verifying the role of the reaction piers in the gradient composite wall and adjusting and optimizing the reaction pier structure in the gradient composite wall, includes the following:

[0029] II-1: Using steel formwork + supporting structure as reaction piers to verify the function of reaction piers;

[0030] II-2: Adjust the height of the reaction piers and optimize the structural design of the gradient composite wall;

[0031] II-3: Adjust the length of the reaction pier to further optimize the structural design of the gradient composite wall.

[0032] Preferably, step III, in verifying the crack resistance characteristics of the gradient composite wall, includes verifying the calculation of the concrete tensile parameter ε by designing the reinforcement ratio and diameter of the intermediate walls. pa The accuracy of the timing.

[0033] Preferably, step III, when verifying the crack resistance characteristics of the gradient composite wall, further includes: making test blocks and conducting experiments, measuring the shrinkage parameters of the test blocks and plotting curves, and verifying that the shrinkage value of the test blocks is within the range of parameter values ​​obtained by the crack resistance calculation method.

[0034] In summary, by adopting the above technical solution, the present invention has at least the following beneficial effects:

[0035] 1. The crack resistance calculation method and verification method of the gradient composite wall in this application are based on the gradient composite wall structure. In the construction of the gradient composite wall structure, the reaction pier is a concrete pier formed by intermittent pouring. The reaction pier is first poured intermittently on the base slab. Since the reaction pier is an ordinary concrete structure, when it reaches a compressive strength of less than 2MPa, the shrinkage is small and the resulting internal stress in the concrete is negligible. Moreover, the reaction pier is small in size compared to the length of the entire wall and has small temperature deformation. The compressive strength of the concrete pier before and after initial setting can reach more than 1.5MPa, which fully meets the requirements. The tensile stress generated in the later stage is less than its own tensile stress, so the reaction pier will not have the risk of cracking, thus ensuring that the reaction pier, as part of the wall, will not crack.

[0036] 2. The crack resistance calculation and verification method for the gradient composite wall in this application is based on the gradient composite wall structure. The middle wall of the gradient composite wall uses expansive concrete. During the pouring process, when the expansive concrete is first poured and initially set, it releases a large amount of heat of hydration. At this time, the concrete expands, forming outward compressive stress. At this time, the surface temperature of the expansive concrete is low and the initial setting is fast, while the expansion amount in the central part is large and the heat of hydration is high, which will form a large outward compressive stress, causing the surface concrete to crack and form induced cracks. These induced cracks become the source of cracks in the later wall. Most of the later cracks continue to crack along the direction of the induced cracks. By setting reaction piers as a supporting structure, when the poured middle wall expands outward, it is squeezed after encountering the reaction piers and cannot compress the surface layer. The concrete exerts continuous outward pressure, effectively preventing induced cracks in expansive concrete and ensuring the safety of the wall structure. After pouring, the expansive concrete gradually cools and sets, causing inward tensile stress due to temperature deformation. Simultaneously, the concrete's subsequent shrinkage also creates inward tensile stress, which can lead to cracks due to deformation and stress. By setting concrete reaction piers, induced cracks can be prevented. Furthermore, because the pre-cast reaction piers are already formed and set, they possess significant compressive strength. When the expansive concrete extending outward encounters the reaction piers, it is compressed, establishing a substantial pre-compression stress. This pre-compression stress can offset some of the tensile stress generated by the subsequent shrinkage and temperature deformation of the intermediate wall concrete, effectively preventing structural cracks.

[0037] 3. Using the crack resistance calculation method for gradient composite walls proposed in this application, the concrete drying shrinkage index parameter ε is calculated respectively. d Concrete shrinkage index parameter ε t and the ultimate tensile property parameter ε of concrete pa Thus, the limiting expansion index parameter ε of expansive concrete is obtained. e The range of values ​​is determined, and a restricted expansion rate test is conducted. Based on the test structure, a suitable and economical amount of expansion agent is selected to obtain the mix proportion of expansive concrete.

[0038] 4. Using the verification method for gradient composite walls proposed in this application, the drying shrinkage index parameter ε of the expansive concrete under the obtained expansive concrete mix proportion is verified in reverse. d ε, the cold shrinkage index parameter t and ultimate tensile parameter ε pa To determine whether the requirements are met, concrete component test blocks are made to measure shrinkage, ensuring that the mix proportion of expansive concrete will not produce cracks when used in gradient composite wall structures.

[0039] 5. The core of using gradient composite walls as the anti-crack design form for basement wall structures lies in setting up reaction piers and utilizing the characteristics of expansive concrete in the intermediate walls. Through the calculation and verification methods of the gradient composite walls in this application, on the one hand, it is ensured that the expansive concrete forms sufficient external compressive stress, and the reaction piers prevent the formation of induced cracks. Moreover, the reaction piers can form a large pre-compression stress, ensuring that part of the tensile stress formed after the expansive concrete cools and sets can be offset by the pre-compression stress, thereby avoiding cracks. Through the calculation and verification methods of this application, it is ensured that the gradient composite walls have good crack resistance during the pouring process and in later operation and use, and this provides effective verification for the promotion of this technology.

[0040] 6. The crack resistance calculation and verification methods of the gradient composite wall in this application ensure that the wall structure does not generate cracks. Based on the verified and optimized expansive concrete mix ratio and construction process, the economic benefits of using the gradient composite crack-resistant wall are accurately calculated. While improving the quality of engineering technology, it can also reduce construction costs. According to the calculation, the gradient composite wall has a significant advantage in construction costs, saving 4,000 yuan per 100m of gradient composite wall structure, which has good economic benefits. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the gradient composite wall structure in this invention;

[0042] Figure 2 This is a structural schematic diagram of a gradient composite wall according to another embodiment of the present invention;

[0043] Figure 3 This is a structural schematic diagram of a gradient composite wall according to another embodiment of the present invention;

[0044] Figure 4 This is a graph showing the relationship between the deformation of the first concrete component test block and the pouring time in Example 4.

[0045] Figure 5 This is a graph showing the relationship between the deformation of the second concrete component test block and the pouring time in Example 4.

[0046] Figure 6 This is a graph showing the relationship between the deformation of the third concrete component test block and the pouring time in Example 4.

[0047] Figure 7 This is a flowchart of the crack resistance calculation method and verification method for the gradient composite wall of the present invention.

[0048] The markings in the diagram are: 1-base plate, 2-reaction pier, 21-vertical support, 22-diagonal brace, 23-horizontal support, 3-waterstop strip, 4-intermediate wall, 5-top plate. Detailed Implementation

[0049] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, so that the objectives, technical solutions, and advantages of the present invention will be clearer. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0050] Example 1

[0051] Figure 1 The present invention illustrates the structural form of a gradient composite wall according to an exemplary embodiment of the present invention. The gradient composite wall of this embodiment includes a base plate (1), reaction piers (2) spaced apart on the base plate (1), and an intermediate wall (4) cast on the base plate (1). The intermediate wall (4) fills the space between two adjacent reaction piers (2), so that the base plate (1), reaction piers (2), and intermediate wall (4) form an integral crack-resistant wall structure. The top of the integral crack-resistant wall structure is a top plate (5). A waterstop strip (3) is provided at the connection between the reaction piers (2) and the intermediate wall (4). The reaction piers (2) are reinforced concrete structures formed by casting ordinary concrete, and the intermediate wall (2) is reinforced concrete structures formed by casting expansive concrete. The reaction piers (2) have the same thickness as the integral crack-resistant wall structure. The length of the reaction piers (2) is between 10% and 35% of the length of the integral crack-resistant wall structure, and the height of the reaction piers (2) is 40% or more of the length of the integral crack-resistant wall structure.

[0052] Figure 2 This invention illustrates a gradient composite wall structure in another exemplary embodiment, where the wall length is less than 30m. Figure 1 In this form, there are two reaction piers (2), and the intermediate wall (4) is cast between the two reaction piers (2); when the wall length is more than 50m, the following is adopted: Figure 2 In this case, the number of reaction piers (2) is three or more, and the number of reaction piers (2) is designed according to the actual length. The intermediate wall (4) is poured between two adjacent reaction piers (2). When the wall length is between 30 and 50, the number of reaction piers (2) can be selected according to the engineering quality requirements. Figure 1 or Figure 2 The only difference between the two is the number of reaction piers (2), while the other structural forms are the same.

[0053] Example 2

[0054] This embodiment discloses a crack resistance calculation method for a gradient composite wall according to an exemplary embodiment of the present invention. When calculating the expansive concrete mix proportion and performance of the intermediate wall to meet the crack resistance conditions of the gradient composite wall, the method includes the following steps:

[0055] Step A: Calculate the concrete drying shrinkage parameter ε of the intermediate walls in the gradient composite wall system. d ;

[0056] Step B: Calculate the concrete shrinkage index parameter ε of the intermediate wall. t ;

[0057] Step C: Calculate the ultimate tensile strength parameter ε of the concrete in the intermediate wall. pa ;

[0058] Step D: Calculate the concrete expansion limit parameter ε of the intermediate wall. e When the concrete's limiting expansion index parameter ε e Satisfying 0 < ε e -ε d -ε t <ε pa When the concrete does not crack, the concrete expansion limit parameter ε can be calculated. e The range of values ​​is determined, and then the expansive concrete mix proportion and performance of the intermediate wall that meet the crack resistance conditions of the gradient composite wall are prepared.

[0059] The following details each calculation step when designing a gradient composite wall for a basement exterior wall with a total length of approximately 20-30m, a thickness of 0.3m, and a height of 3.7m:

[0060] Step A: Calculate the concrete drying shrinkage parameter ε of the intermediate walls in the gradient composite wall system. d The parameter value is calculated based on the concrete characteristics of the intermediate wall, including the ultimate shrinkage value of concrete under standard conditions and the correction factor for concrete under non-standard conditions. The concrete drying shrinkage parameter... In the formula, M1 represents the limit shrinkage value under standard conditions, M2, ..., Mn are correction coefficients for various non-standard conditions, including cement type M1, cement fineness M2, aggregate type M3, water-cement ratio M4, cement paste volume M5, initial curing time M6, ambient humidity M7, reinforcement ratio M8, and vibration operation method M9, b is an empirical coefficient, and t is the concrete age (days).

[0061] Specifically: Take 3.24 × 10 -4 ;

[0062] The values ​​for cement type M1 are as follows: slag cement 1.25, rapid-hardening cement 1.12, low-heat cement 1.10, ordinary cement 1.00, pozzolanic cement 1.00, and sulfate-resistant cement 0.78.

[0063] The values ​​for cement fineness M2 are as follows: 0.9 for cement fineness 1500, 0.93 for cement fineness 2000, 1.00 for cement fineness 3000, 1.13 for cement fineness 4000, 1.35 for cement fineness 5000, 1.68 for cement fineness 6000, 2.05 for cement fineness 7000, and 2.42 for cement fineness 8000.

[0064] The values ​​for aggregate type M3 are as follows: M3 aggregate, sandstone 1.90, gravelly sand 1.00, basalt 1.00, granite 1.00, limestone 1.00, and quartzite 0.80.

[0065] The values ​​for water-cement ratio M4 are as follows: 0.65 for water-cement ratio 0.2, 0.85 for water-cement ratio 0.3, 1.00 for water-cement ratio 0.4, 1.21 for water-cement ratio 0.5, 1.42 for water-cement ratio 0.6, 1.62 for water-cement ratio 0.7, and 1.80 for water-cement ratio 0.8.

[0066] The values ​​for cement grout volume M5 are as follows: cement grout volume 15 is 0.90, cement grout volume 20 is 1.00, cement grout volume 25 is 1.20, cement grout volume 30 is 1.45, cement grout volume 35 is 1.75, cement grout volume 40 is 2.10, cement grout volume 45 is 2.55, and cement grout volume 50 is 3.03.

[0067] The values ​​for the initial maintenance time M6 are as follows: 1.11 for 1 day, 1.11 for 2 days, 1.09 for 3 days, 1.07 for 4 days, 1.04 for 5 days, 1.04 for 7 days, 0.96 for 10-13 days, and 0.93 for ≥14 days.

[0068] The values ​​for ambient humidity M7 are as follows: 1.25 for ambient humidity below 25%, 1.21 for ambient humidity between 25 and 30%, 1.18 for ambient humidity between 30 and 40%, 1.10 for ambient humidity between 40 and 50%, 1.00 for ambient humidity between 50 and 60%, 0.88 for ambient humidity between 60 and 70%, 0.77 for ambient humidity between 70 and 80%, 0.70 for ambient humidity between 80 and 90%, and 0.54 for ambient humidity above 90%.

[0069] The values ​​for reinforcement ratio M8 are as follows: 1.00 for 0.00, 0.86 for 0.05, 0.76 for 0.10, 0.68 for 0.15, 0.61 for 0.20, and 0.55 for 0.25.

[0070] The values ​​for vibration operation method M9 are as follows: mechanical vibration is 1.00, manual vibration is 1.10, steam curing is 0.85, and autoclave treatment is 0.54.

[0071] b is an empirical coefficient, generally taken as 0.01, and 0.03 when maintenance is poor;

[0072] For example, based on factors such as engineering design requirements, raw material conditions, and mix proportion reports, the values ​​in Table 1 are used to obtain the concrete drying shrinkage value.

[0073] Table 1 Concrete drying shrinkage parameter ε d Calculation value table

[0074]

[0075]

[0076] Step B: Calculate the concrete shrinkage index parameter ε of the intermediate wall. t The coefficient of thermal expansion of the intermediate wall is calculated based on the concrete characteristics, including the linear expansion coefficient of the concrete, the highest central temperature during concrete pouring, the average ambient temperature, and the constraint coefficient of the intermediate wall concrete. t =a(T 温峰 -T 环境 )·R, where α is the coefficient of linear expansion of concrete, taken as 1×10 -5 / ℃, T 温峰 T represents the highest temperature (°C) at the center of the concrete. 环境 R is the average ambient temperature (°C), and R is the constraint coefficient of the intermediate wall concrete.

[0077] The highest temperature at the center of the concrete is T 温峰 It is obtained through calculation. During the calculation, T 温峰 =T 入模 +T 水化温升 In the formula, T 入模 T represents the average temperature of the concrete upon placement in the formwork (°C). 水化温升 The highest temperature at the center of the concrete (°C);

[0078] Wherein, the T 水化温升 =αT max α is the heat dissipation coefficient of concrete, T max The adiabatic temperature rise of the concrete (°C) is the temperature rise of the concrete. In the formula, W represents the amount of concrete cementitious materials used (kg / m³). 3 Q is the total heat of hydration of the cementitious material, Q = k1·k2·Q0, where k1 and k2 are taken from Table 3, Q0 for P·O42.5 cement is 320 kJ / kg, c is the specific heat of concrete, taken as 0.96 kJ / (kg·℃), and ρ is the unit weight of concrete, taken as 2400 kg / m³. 3, where m is a coefficient related to cement type, pouring temperature, etc., and is taken as 1.4d. -1 d Initial maintenance days;

[0079] Wherein, the total heat of hydration of cementitious materials Q = k1·k2·Q0, k1 and k2 are the coefficients of fly ash and mineral powder under different admixture amounts, and Q0 is the total heat of hydration of cement.

[0080] Specifically: Calculate based on the initial concrete mix proportions in Table 2, first using conventional concrete to determine if it meets the requirements;

[0081] Table 2 Initial values ​​for concrete mix proportions

[0082]

[0083] Concrete cementitious material dosage W = 360 kg / m 3 The total heat of hydration of the cementitious material, Q = 0.878 × 1 × 320 = 280.96 kJ / kg, and the adiabatic temperature rise of the concrete, T... max =43.9℃;

[0084] The thickness of the basement exterior wall (0.3m) is much smaller than its length (between 20 and 30m). Ignoring heat dissipation along the length, we only consider heat dissipation along the thickness of the base slab. The heat dissipation coefficient α is taken as 0.6. T 水化温升 =0.6 × 43.9 = 26.34℃;

[0085] If the average concrete pouring temperature is taken as 30℃, then the highest temperature at the center of the concrete is T. 温峰 =30 + 26.34 = 56.34℃;

[0086] Query the historical seasonal average temperature of the construction site, and the average ambient temperature (T) during the construction period. 平均 =30℃. When the concrete temperature drops from its highest point to ambient temperature, it will undergo thermal shrinkage. Due to the restraint effect during shrinkage, taking the restraint coefficient R as 0.6, the concrete shrinkage value εt = 1.0 × 10 -5 ×(56.34-30)×0.6=1.58×10.0 -4 .

[0087] Table 3. Coefficients of fly ash and mineral powder at different dosages

[0088] Dosage 0 10％ 20％ 30％ 40％ <![CDATA[Fly ash (k1)]]> 1 0.94 0.89 0.85 0.81 <![CDATA[Mineral powder (k2)]]> 1 0.97 0.95 0.91 0.86

[0089] Step C: Calculate the ultimate tensile strength parameter ε of the concrete in the intermediate wall. pa The ultimate tensile strength parameters of the concrete are calculated based on the crack resistance strength of the concrete and the reinforcement details of the cross-section. In the formula, Rf is the design strength of concrete against cracking (MPa), ρ is the reinforcement ratio of the section, ρ=μ×100, μ is the reinforcement ratio, for example, if the reinforcement ratio μ=0.2% or 0.5%, then ρ=0.2 or 0.5, and d is the reinforcement diameter (cm);

[0090] Specifically: ultimate tensile strength R of concrete f =1.43MPa, cross-sectional reinforcement ratio ρ = 1.5%, steel bar diameter d = 1.2cm, ultimate tensile strength of concrete ε pa = 0.5 × 1.43 × (1 + 1.5 / 1.2) × 10 -4 =1.61×10 -4 .

[0091] Step D: Based on the condition that the gradient combination wall does not crack, 0 < ε e- ε d- ε t <ε pa Substituting the numerical values ​​into the calculation yields the limiting expansion index parameter ε of the intermediate wall. e , is 2.29 × 10 -4 <ε e <3.90×10 -4 .

[0092] Example 3

[0093] This embodiment provides a verification method for gradient composite walls. Based on the expansive concrete mix proportion and performance obtained from the crack resistance calculation method for gradient composite walls in Embodiment 2, before applying it to engineering construction, and during the process of using the obtained expansive concrete mix proportion to prepare expansive concrete and pour it into the gradient composite wall, it is necessary to verify whether the expansive concrete poured to form the intermediate wall meets the crack resistance conditions of the gradient composite wall. The verification mainly includes:

[0094] Step 1: Verify and optimize the expansive concrete mix proportion obtained from the crack resistance calculation method of the above-mentioned gradient composite wall, and calculate the limiting expansion index parameter ε based on Example 2. e The interval value is: 2.29 × 10 -4 <ε e <3.90×10 -4 The expansive concrete was prepared according to the range of values, and the mix proportions of the expansive concrete are shown in Table 4.

[0095] Table 4. Mix Proportion Range for Expansive Concrete

[0096]

[0097] The verification of the expansive concrete mix proportions in Table 4 includes the following steps:

[0098] Step I-1: Based on the expansive concrete mix proportions in Table 4, recalculate the concrete drying shrinkage index εd, concrete cold shrinkage index εt, and concrete ultimate tensile index εpa for the intermediate wall. This mainly focuses on the parameters that change due to the change in the expansive concrete mix proportions. These changed parameters are then used to recalculate the concrete drying shrinkage index εd, concrete cold shrinkage index εt, and concrete ultimate tensile index εpa for the intermediate wall.

[0099] Step I-2: Calculate the concrete restricted expansion index parameter εe of the intermediate wall. According to the expansive concrete mix proportion in Table 4, use an expansive agent to replace cement, fly ash, and mineral powder to conduct a restricted expansion rate test to verify whether the concrete restricted expansion index parameter εe satisfies 0 < εe - εd - εt < εpa. If it satisfies, proceed to Step I-3; otherwise, proceed to Step I-4.

[0100] Step I-3: Based on the range of εe values ​​obtained from the verification, the mix proportion of expansive concrete was further optimized to reduce the cost per unit weight of expansive concrete. The final mix proportion and restricted expansion rate data of expansive concrete are shown in Table 5.

[0101] Table 5. Mix proportions and restricted expansion rate of expansive concrete.

[0102]

[0103] Step I-4: Based on the restricted expansion index parameter εe verified in Step I-2, the mix proportion of expansive concrete is readjusted. During the readjustment, the expansive agent is used to replace cement, fly ash, and mineral powder to conduct a restricted expansion rate test. Based on the test results, the dosage of the expansive agent is increased, and then the process is repeated in Step I-1 and Step I-2.

[0104] When verifying and optimizing the expansive concrete mix proportion obtained by the crack resistance calculation method of gradient composite wall, the construction process parameters can also be adjusted. The construction process parameters related to the concrete drying shrinkage index parameter εd, concrete cold shrinkage index parameter εt, and concrete ultimate tensile index parameter εp of the intermediate wall can be adjusted. When adjusting the construction process parameters to calculate the expansive concrete limiting expansion index parameter εe, the principle of construction convenience and construction economy should be taken as much as possible.

[0105] By verifying and optimizing the crack resistance calculation method of the gradient composite wall, the expansive concrete mix proportion is obtained. On the one hand, it ensures that the expansive concrete mix proportion meets the crack resistance requirements of the gradient composite wall and avoids cracks in the basement wall structure. On the other hand, the construction process parameters are adjusted and optimized, which improves the convenience and economy of the actual construction process. The construction process is carried out in accordance with the calculated construction process parameters to ensure the crack resistance performance of the walls in the basement structure.

[0106] The verification method for the gradient composite wall in this embodiment involves adjusting and optimizing the reaction pier structure in the gradient composite wall. Verifying the role of the reaction pier in the gradient composite wall is also very important, and mainly includes the following aspects:

[0107] II-1: Using steel formwork + supporting structure as reaction piers, the function of the reaction piers is verified, such as... Figure 3 As shown, in the actual construction process, a test section was selected and poured in this way. The reaction pier (2) was made of template 21. A support rod (22) was set behind the template 21. One end of the support rod (22) was connected to the template 21, and the other end was fixed to the base plate 1 or the ground. The template 21 was a steel template. In addition, hydraulic jacks and support rods (22) were set up to support the template (21) to ensure that the reaction pier (2) had sufficient compressive strength (reaching more than 1.5MPa). Then the intermediate wall (4) was poured. It was later found that 5-6 cracks appeared in the intermediate wall with a length of about 20m.

[0108] The reaction pier (2) must be made of concrete to ensure that the gradient composite wall structure has good crack resistance. When concrete piers are used, during the pouring process of the expansion concrete of the middle wall, when it is first poured and initially set, it releases a large amount of heat of hydration. At this time, the concrete of the wall expands and forms compressive stress on the outside. At this time, the surface temperature of the expansion concrete is low and the initial setting is fast, while the expansion amount in the center is large and the heat of hydration is high, which will form a large compressive stress on the outside, causing the surface concrete to crack and form induced cracks. These induced cracks become the cracks that cause the wall to crack later. The primary source of cracks is the expansion of the concrete. Most subsequent cracks propagate along the direction of the induced cracks. By using reaction piers as a supporting structure, when the intermediate wall expands outwards, it encounters the reaction piers and is compressed, preventing continuous outward pressure on the surface concrete. This effectively avoids induced cracks in the expansive concrete and ensures the structural safety of the wall. After the expansive concrete is poured, it gradually cools and sets. The wall concrete will then experience inward tensile stress due to temperature deformation. Simultaneously, the subsequent shrinkage of the wall concrete itself will also create inward tensile stress, which will further contribute to the inward cracking of the wall concrete. Deformation and stress can cause cracks. By setting concrete reaction piers, the formation of induced cracks can be prevented. Furthermore, because the pre-cast reaction piers are already formed and fully set, they possess significant compressive strength. When the expanding concrete of the intermediate wall encounters the reaction piers, it is compressed, establishing a large pre-stress. This pre-stress can offset some of the tensile stress generated by the shrinkage and temperature deformation of the intermediate wall concrete in the later stages, thus effectively preventing structural cracks. Regarding the reaction pier structure itself, the reaction piers are ordinary concrete structures, and when their compressive strength is below 2 MPa, their… The shrinkage is small, and the resulting internal stress in the concrete is negligible. Moreover, the reaction pier is small in size compared to the length of the entire wall, and the temperature deformation is small. The compressive strength of the concrete pier before and after initial setting can reach more than 1.5MPa, which fully meets the requirements. The tensile stress generated in the later stage is less than its own tensile stress, so there is no risk of cracking in the reaction pier, thus ensuring that the reaction pier, as part of the wall, will not crack. In addition, the test section also verified that only ordinary concrete structure can ensure that the gradient composite wall has good crack resistance, while reducing the material cost of the reaction pier.

[0109] By verifying the structure and materials of the reaction piers, it was found that using reinforced concrete piers as reaction piers when designing gradient composite wall structures not only ensures that the walls have good crack resistance, but also simplifies the construction process. After the reaction piers are poured first, when constructing the intermediate walls, it is no longer necessary to set up formwork or other supporting pouring structures at the reaction pier locations.

[0110] II-2: Adjusting the height and length of the reaction piers to further optimize the structural design of the gradient composite wall. This verification in this embodiment mainly targets cases where the total length of the gradient composite wall is within 50m. Through multiple different test sections, with the thickness of the reaction piers being the same as the thickness of the gradient composite wall, different reaction pier heights and lengths were used to verify the influence of the height and length of the reaction piers on the crack resistance performance of the gradient composite wall. The verification results show that when the length of the reaction pier is between 10% and 35% of the overall crack-resistant wall structure length, the longer the length and the closer the reaction pier length is to the 10% endpoint, the gradient composite wall exhibits a few minor cracks. When the height of the reaction pier is 40% or more of the overall crack-resistant wall structure length, and near the 40% endpoint, a few minor cracks appear in some test sections of the gradient composite wall. When the length of the reaction pier is optimized to be between 15% and 30% of the overall crack-resistant wall structure length, and the height of the reaction pier is 60% or more of the overall crack-resistant wall structure length, the gradient composite wall no longer exhibits cracks. Design principles for the length of reaction piers: When the overall crack-resistant wall structure is between 10m and 20m, the length of the reaction pier should be selected from the range of 35% closer to the endpoint; when the overall crack-resistant wall structure is between 20m and 30m, the length of the reaction pier should be selected from the range of approximately 20% closer to the endpoint; when the overall crack-resistant wall structure is greater than 30m, the length of the reaction pier should be selected from the range of approximately 10% closer to the endpoint. The ideal length of the reaction pier is between 3m and 8m, and can be selected based on both the overall crack-resistant wall structure length and the ideal length of the reaction pier. When the total length of the gradient composite wall is greater than 50m, the ideal length of the reaction pier is between 3m and 8m, with multiple reaction piers spaced 20m to 40m apart.

[0111] Step III: Based on the crack occurrence of the gradient composite wall during operation, analyze and verify the crack resistance characteristics of the gradient composite wall, including the following:

[0112] Ⅲ-1: By preparing test blocks with the mix proportion of expansive concrete, the expansion curve of the test blocks under the curing conditions of the set construction process is obtained, thereby obtaining the total difference in shrinkage between the base plate and the overall wall structure on the time scale.

[0113] Ⅲ-2: Obtain the deformation values ​​of the intermediate wall before and after initial setting, calculate the tensile strength of the overall wall structure when cooled to the same temperature as the atmosphere, and obtain the strain value that can be withstood at this tensile strength. Also, calculate the deformation value that the intermediate wall can resist at the standard tensile strength of the standard curing age. Add these three data together.

[0114] Ⅲ-3: Compare the sum of the three data in Ⅲ-2 with the total difference in shrinkage in Ⅲ-1 to verify whether the gradient combination wall meets the crack resistance requirement.

[0115] This embodiment uses a basement exterior wall with a total length of 20-30m, a thickness of 0.3m, and a height of 3.7m as an example. Reaction blocks are arranged on both sides of the wall, with a longitudinal section of 300mm × 2500mm and a cross-section of 300mm × 3000mm. Monitoring points are placed at different locations on the gradient composite wall, and test blocks are fabricated for verification.

[0116] According to III-1, the total shrinkage difference between the base plate and the overall wall structure on the time scale is approximately 240 με. According to III-2, the deformation value of the intermediate wall before and after initial setting is 70–90 με. The tensile strength of the overall wall structure when cooled to the same temperature as the atmosphere is calculated to withstand a strain value of 90 με. The deformation value that the intermediate wall can resist under the standard tensile strength at the standard curing age is approximately 100 με. Adding these three data, we get 240 με < 90 με + 100 με + 99 με. Obviously, there is still nearly 50 με of crack control reserve on the 28th day. Therefore, no cracks are generated. The internal force calculation of the reaction pier is controlled by the pre-compression of 120 με in the intermediate section. The reaction pier means that it provides a pre-compression reaction force of 0.5 × 1875 kN.

[0117] In step III-2, since the strength of concrete increases very slowly or even stops after 28 days of curing, the standard curing age for the intermediate wall is 28 days. Because the intermediate wall uses expansive concrete, its tensile strength after 28 days can be calculated based on its mix proportions or directly measured to obtain its resistance to deformation. Since the construction method for the gradient composite wall is to first pour reaction piers, when the subsequently poured intermediate wall cools to the same temperature as the atmosphere, it no longer undergoes plastic deformation. At this point, the wall concrete has a certain tensile strength, and the resistance to deformation under this tensile strength can be obtained. At this time, due to the presence of reaction piers, the intermediate wall concrete is under compression and there is no risk of cracking. The intermediate wall is in a plastic deformation period before and after initial setting; during this time, the stress generated by the resistance to plastic deformation is negligible.

[0118] For intermediate wall concrete with a compressive strength below 2MPa, the internal stress caused by shrinkage is negligible. The tensile strength of the concrete is approximately 1 / 20 of the compressive strength, and its future strength will be above 20MPa. If it does not crack at this point, the impact on the calculation results will be minimal.

[0119] More than 40 days after the pouring, no cracks were found in the wall under the construction process of reaction pier + micro-expansion outer wall (intermediate wall). However, 12 cracks with a length of 2m and a width of 0.15mm to 0.2mm were found in the inner wall, which did not take such crack control measures. The inner wall was 10m shorter than the outer wall (50m).

[0120] Based on this, the economic efficiency can be calculated as follows:

[0121] Using traditional construction methods, leaks are plugged after cracks appear. With epoxy resin plugging, there are approximately 30 cracks per 100m, each 2.5m long, and the plugging cost is approximately 8400 yuan / 100m (84 yuan / m).

[0122] The crack control measures adopted for the gradient combination wall structure, which have been calculated and verified, are calculated based on a 100m long wall. The amount of expansive concrete used (wall height 2.5m, thickness 300mm) is about 71 cubic meters, with an additional cost of 35-40 yuan per cubic meter (expansion agent cost), an additional 6 square decimeters of end formwork (60 yuan / square meter, multiplied by a difficulty coefficient of 1.3), and an additional 20m of waterstop steel plate (25 yuan / m), totaling about 4000 yuan / 100m. Under the condition of ensuring construction quality, 4000 yuan is saved per 100m, which is quite economical. The amount of reaction pier (ordinary concrete) concrete used for a 100m long wall also needs to be deducted, making the cost even lower.

[0123] As part of the implementation of further improving the verification method of gradient composite walls, the correctness of calculating the concrete tensile index parameter εpa was verified by designing the reinforcement ratio and diameter of the intermediate walls. Since the cross-sectional reinforcement ratio of the transverse steel bars in most walls is less than 5%, only the longitudinal reinforcement of the columns can reach a reinforcement ratio of 5%. According to the calculation formula of the concrete ultimate tensile index parameter εpa, it can be seen that increasing the cross-sectional reinforcement ratio of the intermediate walls is completely infeasible or uneconomical. For example, when the tensile stress of concrete is 3MPa, the concrete will crack. At this time, the stress of the steel bars is only 30MPa, which is less than 1 / 10 of the yield strength of the steel bars. For through cracks, its effect is negligible.

[0124] To verify whether the intermediate wall formed by expansive concrete meets the crack resistance conditions of a gradient composite wall, test blocks are made and tested. The parameters of the test blocks are measured and curves are plotted for verification, including the following:

[0125] Step S1: Tests are conducted using square concrete component test blocks with various cross-sectional dimensions, including test blocks with larger and smaller cross-sectional dimensions;

[0126] Step S2: Measure the autogenous shrinkage of the concrete component specimen when the compressive strength reaches 2-3 MPa;

[0127] Step S3: Investigate the effect of temperature rise and fall on the concrete component test blocks before and after initial setting, and draw the deformation curve of deformation amount versus time, and verify whether the shrinkage of the concrete component test blocks is within the range of parameter values ​​obtained by the crack resistance calculation method.

[0128] Step S4: Obtain the effect of temperature change on the deformation of the concrete component test block based on step S3.

[0129] The above content will be explained in detail below:

[0130] In step S1, three types of square concrete component test blocks with different cross-sectional dimensions are used for testing, including a first concrete component test block, a second concrete component test block, and a third concrete component test block. The dimensions of the first concrete component test block are: 0.1m (width) × 0.1m (height) × 2m (length); the dimensions of the second concrete component test block are: 0.5m (width) × 0.5m (height) × 2m (length); and the dimensions of the third concrete component test block are: 1m (width) × 1m (height) × 2m (length).

[0131] In steps S2 and S3, the deformation data of the three types of concrete component test blocks in step S1 are measured in relation to the pouring time. Table 6 is a table showing the relationship between the deformation of the first concrete component test block and the pouring time, Table 7 is a table showing the relationship between the deformation of the first concrete component test block and the pouring time, and Table 8 is a table showing the relationship between the deformation of the first concrete component test block and the pouring time.

[0132] Table 6 Correspondence between Deformation and Pouring Time of the First Concrete Component Test Block

[0133] Pouring time (d) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Shrinkage (με) 100 125 150 160 175 180 185 196 205 210 220 225 225 230

[0134] Table 7 Correspondence between Deformation and Pouring Time of Second Concrete Component Test Blocks

[0135] Pouring time (d) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Shrinkage (με) 250 250 150 160 175 180 185 196 205 210 220 225 225 230

[0136] Table 8 Correspondence between Deformation and Pouring Time of Third Concrete Component Test Blocks

[0137] Pouring time (d) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Shrinkage (με) 650 600 400 360 275 230 185 196 205 210 220 225 225 230

[0138] To facilitate observation and analysis, the data from Tables 6, 7, and 8 are plotted as curves, as shown below. Figure 4 , Figure 5 and Figure 6 As shown.

[0139] Combined with Table 6-8 and Figure 4-6 As can be seen, the compressive strength of the concrete component test blocks reaches 2-3 MPa in about 3 days. At this time, the shrinkage of the first and second concrete component test blocks is 150 με, and the shrinkage of the third concrete component test block is 400 με. Since the time and deformation measured at the small section can be regarded as the autogenous shrinkage curve of concrete unaffected by temperature, the value measured at the large section is subtracted from the value measured at the small section to obtain the value affected by temperature. The temperature deformation value of the third concrete component test block is 250 με. The shrinkage of the three concrete component test blocks is the same from the 7th day, indicating that the third concrete component test block was affected by temperature changes before the 7th day and was unaffected from the 7th day onwards.

[0140] The autogenous shrinkage of concrete member specimens when the compressive strength reaches 2-3 MPa is deducted when calculating tensile stress in the future. The final monitored shrinkage of the three concrete member specimens was 230 με. After deducting 150 με, the shrinkage was 80 με. Thereafter, the shrinkage value of expansive concrete changed little, remaining at around 100 με. This value is less than the calculated ultimate tensile index parameter ε of expansive concrete. pa With an ε value of 161 μ, the expansive concrete can remain crack-free.

[0141] The third concrete component test block and the third concrete component test block are affected by temperature. At the beginning, the shrinkage is large. When the expansive concrete is applied to the gradient composite wall, the reaction pier is set. The reaction pier can absorb the compressive stress brought by this part of the deformation, thereby establishing pre-compression stress. When the concrete begins to cool and shrink later, this part of the pre-compression stress can partially offset the later shrinkage deformation.

[0142] from Figure 4-6 As can be seen, the temperature rise has a significant impact on the concrete component test blocks before and after initial setting. The first concrete component test block is not affected by temperature. After the temperature drops after pouring, all three component test blocks show a large shrinkage in a short period of time. The shrinkage of the three concrete component test blocks is the same from the 7th day onwards, indicating that the third concrete component test block was affected by temperature changes before that, but was unaffected from the 7th day onwards.

[0143] The above description is merely a detailed illustration of specific embodiments of the present invention and is not intended to limit the invention. Various substitutions, modifications, and improvements made by those skilled in the art without departing from the principles and scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the crack resistance of a gradient composite wall, characterized in that, The gradient composite wall includes a base plate (1), reaction piers (2) spaced apart on the base plate (1), and an intermediate wall (4) cast on the base plate (1). The intermediate wall (4) fills the space between two adjacent reaction piers (2) and covers the top of the reaction piers (2), so that the base plate (1), reaction piers (2), and intermediate wall (4) form an integral wall structure. The top of the integral wall structure is a top plate (5). A waterstop strip (3) is provided at the connection between the reaction piers (2) and the intermediate wall (4). The reaction piers (2) are reinforced concrete structures formed by casting ordinary concrete, and the intermediate wall (4) is a reinforced concrete structure formed by casting expansive concrete. The reaction piers (2) have the same thickness as the integral wall structure, and the length of the reaction piers (2) is between 10% and 35% of the length of the integral wall structure. When calculating the expansive concrete mix ratio and performance of the intermediate wall (4) to meet the crack resistance conditions of the gradient composite wall, the following steps are included: Step A: Calculate the concrete drying shrinkage parameter ε of the intermediate walls in the gradient composite wall system. d ; Step B: Calculate the concrete shrinkage index parameter ε of the intermediate wall. t This includes the constraint factor R of the intermediate wall concrete; Step C: Calculate the ultimate tensile strength parameter ε of the concrete in the intermediate wall. pa ; Step D: Calculate the concrete expansion limit parameter ε of the intermediate wall. e When the concrete's limiting expansion index parameter ε e Satisfying 0 < ε e -ε d -ε t <ε pa When the concrete does not crack, the concrete expansion limit parameter ε can be calculated. e The range of values ​​for ε d +ε t <ε e <ε pa +ε d +ε t Furthermore, the mix proportion and performance of expansive concrete for intermediate walls that meet the crack resistance requirements of gradient composite walls were determined.

2. The crack resistance calculation method for gradient composite walls according to claim 1, characterized in that, In step A, the concrete drying shrinkage index parameter ε of the intermediate wall is calculated. d The parameters are calculated based on the concrete characteristics of the intermediate wall, including the ultimate shrinkage value of concrete under standard conditions and the correction factor for concrete under non-standard conditions, as well as the concrete drying shrinkage index parameters of the intermediate wall. In the formula, M1 represents the limit shrinkage value under standard conditions, M2, ..., Mn are correction coefficients for various non-standard conditions, including cement type M1, cement fineness M2, aggregate type M3, water-cement ratio M4, cement paste volume M5, initial curing time M6, ambient humidity M7, reinforcement ratio M8, and vibration operation method M9, b is an empirical coefficient, and t is the concrete age in days.

3. The crack resistance calculation method for gradient composite walls according to claim 1, characterized in that, In step B, the concrete shrinkage index parameter ε of the intermediate wall is obtained. t The calculations were based on the concrete characteristics of the intermediate wall, including the linear expansion coefficient of the concrete, the highest central temperature during concrete pouring, the average ambient temperature, and the constraint coefficient of the intermediate wall concrete. The concrete cold shrinkage index parameter ε of the intermediate wall was also included. t =a(T 温峰 -T 环境 )·R, where α is the coefficient of linear expansion of concrete, T 温峰 The highest temperature at the center of the concrete is ℃, T 环境 R is the average ambient temperature in °C, and R is the constraint coefficient of the intermediate wall concrete.

4. The crack resistance calculation method for gradient composite walls according to claim 3, characterized in that, The highest temperature at the center of the concrete is T 温峰 It is obtained through calculation. During the calculation, T 温峰 =T 入模 +T 水化温升 In the formula, T 入模 T represents the average concrete pouring temperature in °C. 水化温升 The highest temperature at the center of the concrete is ℃; Wherein, the T 水化温升 =αT max α is the heat dissipation coefficient of concrete, T max The adiabatic temperature rise of the concrete is ℃. In the formula, W represents the amount of concrete cementitious material used (kg / m³). 3 Q is the total heat of hydration of cementitious materials, c is the specific heat of concrete, ρ is the unit weight of concrete, and m is a coefficient related to cement type and pouring temperature. Wherein, the total heat of hydration of cementitious materials Q = k1·k2·Q0, k1 and k2 are the coefficients of fly ash and mineral powder under different admixture amounts, and Q0 is the total heat of hydration of cement.

5. The crack resistance calculation method for gradient composite walls according to claim 1, characterized in that, In step C, the ultimate tensile strength parameter ε of the concrete in the intermediate wall is obtained. pa The ultimate tensile strength parameters of the concrete in the intermediate wall were calculated based on the concrete's crack resistance and the reinforcement details of the cross-section. In the formula, R f Let ρ be the design strength for crack resistance of concrete (MPa), ρ be the cross-sectional reinforcement ratio (ρ = μ × 100), μ be the reinforcement ratio, and d be the reinforcement diameter (cm).

6. A verification method for gradient composite walls, characterized in that, The expansive concrete mix proportion and performance obtained by the crack resistance calculation method for gradient composite walls as described in any one of claims 1-5, when verifying whether the intermediate wall formed by expansive concrete pouring meets the crack resistance conditions of gradient composite walls, include the following: Step 1: Verify and optimize the expansive concrete mix proportion obtained from the crack resistance calculation method of the above-mentioned gradient composite wall; Step II: Adjust and optimize the reaction pier structure in the gradient composite wall, and verify the role of the reaction pier in the gradient composite wall, including the following: II-1: Using steel formwork + supporting structure as reaction piers to verify the function of reaction piers; II-2: Adjust the height of the reaction piers and optimize the structural design of the gradient composite wall; II-3: Adjust the length of the reaction piers to further optimize the structural design of the gradient composite wall; Step 3: Analyze and verify the crack resistance characteristics of the gradient composite wall based on the crack occurrence during operation.

7. The verification method for gradient composite walls according to claim 6, characterized in that, Step I, in verifying the expansive concrete mix proportion obtained by the crack resistance calculation method of the gradient composite wall, includes the following steps: Step I-1: Recalculate the concrete drying shrinkage index parameter ε of the intermediate wall based on the obtained expansive concrete mix proportion. d ε, the concrete shrinkage index parameter of the intermediate wall t And the ultimate tensile strength parameter ε of the concrete in the intermediate wall. pa ; Step I-2: Calculate the concrete expansion limit parameter ε of the intermediate wall. e Verify the concrete expansion limit parameter ε of the intermediate wall. e Does it satisfy 0 < ε? e -ε d -ε t <ε pa If the conditions are met, proceed to step I-3; otherwise, proceed to step I-4. Step I-3: Based on the ε obtained from the verification e The range of values ​​was further optimized to improve the mix proportions of expansive concrete and reduce the cost per unit weight of expansive concrete. Step I-4: Based on the concrete restricted expansion index parameter ε of the intermediate wall verified in Step I-2. e The expansive concrete mix ratio is then readjusted, and the process is repeated in steps I-1 and I-2.

8. The verification method for gradient composite walls according to claim 6, characterized in that, Step III, in verifying the crack resistance characteristics of the gradient composite wall, includes verifying the calculation of the concrete tensile index parameter ε of the intermediate wall by designing the reinforcement ratio and diameter of the intermediate wall. pa The accuracy of the timing.

9. The verification method for gradient composite walls according to claim 6, characterized in that, Step III, when verifying the crack resistance characteristics of the gradient composite wall, also includes: making test blocks and conducting tests, measuring the shrinkage parameters of the test blocks and plotting curves, and verifying that the shrinkage value of the test blocks is within the range of parameter values ​​obtained by the crack resistance calculation method.

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