A method for calculating the early cracking risk of concrete structures under strong constraints

Abstract

This invention discloses a method for calculating the early cracking risk of concrete structures under strong constraints, comprising the following steps: establishing a concrete structure model under strong constraints using finite element software; simulating the horizontal and vertical interfaces between new and old concrete using a common-node method; calculating and determining the elastic modulus of the old concrete structure at the interface based on the characteristics of the interfaces between new and old concrete in the concrete structure model under strong constraints, to characterize the degree of strong constraints on the concrete structure; determining the thermodynamic parameters, thermodynamic boundary conditions, and initial conditions of the new and old concrete materials in the concrete structure model under strong constraints, and calculating the temperature and stress fields of the new and old concrete structures based on a hydration-temperature-humidity-constraint coupling model; selecting the maximum stress and tensile strength ratio corresponding to the structure at a certain period to analyze and determine the early cracking risk of the concrete structure under strong constraints.

Description

Technical Field

[0001] This invention belongs to the field of concrete materials technology, specifically relating to a method for calculating the early cracking risk of concrete structures under strong constraints. Background Technology

[0002] Concrete, as the most widely used building material, has long been a significant research topic in the construction field due to its early shrinkage cracking. The primary cause of early concrete cracking is the tensile stress generated by temperature shrinkage due to hydration and autogenous volume shrinkage under the constraint of the existing concrete, exceeding the tensile strength. Early shrinkage cracking significantly affects the construction quality and long-term service performance of concrete. Therefore, in order to implement targeted crack control measures to reduce or even prevent concrete shrinkage cracking, many scholars have dedicated themselves to researching how to accurately calculate the cracking risk of concrete structures. Currently, research on concrete cracking risk prediction has yielded substantial results and has been well applied in fields such as hydraulic engineering. However, most current cracking risk calculation research focuses on the calculation of concrete temperature stress under the constraint of the foundation and substructure, while paying less attention to the cracking risk calculation of concrete under the constraint of the existing concrete on the vertical side. Many engineering projects involve strongly constrained structures simultaneously constrained by the foundation and vertical construction joints, such as tunnel composite walls, bridge wet joints, and thick slabs cast in sections. Currently, there is no clear method to guide the calculation of cracking risk for such structures.

[0003] The recommended values ​​for foundation resistance and constraint in the large-volume construction code (GB50496) are limited to horizontal construction joints. Wang Tiemeng, in "Engineering Crack Control," provides recommendations for the constraint magnitude of vertical construction joints between pre-cast slabs and new slabs, but does not address other types of vertical construction joint constraints. In commonly used finite element analysis, it is generally assumed that the bond between new and old concrete at roughened horizontal construction joints is tight and without slippage, and the elastic modulus of the old concrete below the horizontal construction joint is taken as that of mature concrete. Under these simulation conditions, the constraint on the newly cast concrete is significant. For horizontal construction joints, the gravity of the new concrete results in a relatively large horizontal resistance coefficient when micro-slippage occurs at the interface, making this simulation method applicable. However, for vertical construction joints with similar roughening, the absence of gravity significantly reduces the resistance coefficient, leading to an excessively high risk of cracking when this simulation method is used again. Furthermore, in engineering projects, measures such as spraying waterproof materials at vertical construction joints are sometimes employed, which further reduces the restraining effect of the old concrete. This leads to greater errors in the simulation method and causes unnecessary waste when developing crack-resistant construction plans. Therefore, how to improve the reliability of crack risk calculations for this type of structure remains an unresolved issue in engineering. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the early cracking risk of concrete structures under strong constraints.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] This invention provides a method for calculating the early cracking risk of concrete structures under strong constraints, characterized by the following steps:

[0007] A concrete structure model under strong constraints was established using finite element software, and the common node method was used to simulate the horizontal and vertical interfaces between new and old concrete.

[0008] Based on the characteristics of the interface between old and new concrete in the concrete structure model under strong constraints, the elastic modulus of the old concrete structure at the interface is calculated and determined to characterize the degree of strong constraints on the concrete structure.

[0009] The thermodynamic parameters, thermodynamic boundary conditions, and initial conditions of the new and old concrete materials in the concrete structure model under strong constraints are determined. Based on the hydration-temperature-humidity-constraint coupling model, the temperature field and stress field of the new and old concrete structures are calculated. The maximum stress and tensile strength ratio of the structure at a certain period are selected to analyze and determine the early cracking risk of the concrete structure under strong constraints.

[0010] Furthermore, the strong constraint conditions of the concrete structure include the constraint of the bottom surface of the new concrete structure on the foundation and substructure of the old concrete structure, and the constraint of the vertical surface of the new concrete structure on the vertical surface of the old concrete structure.

[0011] Furthermore, the constraints that the vertical plane of the new concrete structure is subject to by the vertical plane of the old concrete structure include:

[0012] A vertical surface of the new concrete structure is constrained by the old concrete or bedrock, and the constrained area of ​​the vertical surface accounts for more than 30% of the total surface area of ​​the new concrete structure.

[0013] Alternatively, two or more vertical surfaces of the new concrete structure are constrained by the old concrete or bedrock, and the total area of ​​the constrained surfaces accounts for more than 20% of the area of ​​the new concrete structure.

[0014] It should be noted that in engineering, many structures are simultaneously constrained by both horizontal and vertical construction forces, such as continuously cast walls and floor slabs. In addition to being constrained by the lower slab and side walls, one end of the cast structure is also constrained by the preceding section of the structure. However, the area at the end of walls and floor slabs is very small, and the constraint at this interface is negligible compared to the bottom constraint. Therefore, they cannot be called strongly constrained concrete structures.

[0015] For structures such as composite walls and tunnel linings, when the vertical construction joints are roughened and flexible waterproof membranes are not installed, the constraint of the diaphragm wall on the wall body and the constraint of the initial support and bedrock on the lining cannot be ignored. The area of ​​the vertical interface between the old and new concrete is very large, even far exceeding the horizontal interface. In this case, the composite wall and tunnel lining can be called strongly constrained concrete. Similar structures include bridge wet joints and post-cast strips. Furthermore, for foundation slab concrete with large area and thickness, if a segmented casting method is used, a particular foundation slab may be constrained by multiple surrounding foundation slabs during casting. Even with relatively weak constraint from the underlying soil, the constraint of the surrounding foundation slabs at the vertical construction joints cannot be ignored.

[0016] Meanwhile, in finite element analysis, three methods are generally used to simulate the interface between new and old concrete: interface elements, contact elements, and common nodes. The former two reflect the constraint magnitude through the horizontal stiffness of the interface elements and the Coulomb friction coefficient of the contact elements, making the modeling process more complex. This invention adopts the common node method, assuming that there is no relative slippage between the new and old concrete, and adjusts the constraint degree by changing the value of the elastic modulus of the old concrete. This method is simpler and easier to implement.

[0017] Furthermore, the elastic modulus of the old concrete structure foundation and substructure below the horizontal interface shall be determined according to the actual test value of the foundation elastic modulus or the test value of the foundation 28d elastic modulus.

[0018] The elastic modulus of the old concrete structure on one side of the vertical interface is calculated according to the following formula:

[0019] ;

[0020] In the formula: This represents the elastic modulus of the old concrete on the vertical interface side during pretreatment. This represents the elastic modulus test value of the old concrete after 28 days. The adjustment coefficient is calculated using the following formula:

[0021] ;

[0022] In the formula: To account for the reference coefficient of chemical bonding strength between new and old concrete, a value of 0.1 to 0.2 is used. The roughness of the vertical construction joint interface is expressed in mm. is the reinforcement ratio at the vertical interface, which is the ratio of the sum of the cross-sectional areas of the steel bars at the vertical interface to the interface area; k is the ratio of the area of ​​the vertical construction joint to the total area of ​​the new concrete.

[0023] The interface constraint between new and old concrete mainly originates from the linear constraint of the reinforcing bars and the surface constraint generated by the interlocking and frictional action of the contact surfaces. This surface constraint is influenced by the degree of interlocking and axial pressure. Compared to the vertical interface, the gravity of the new concrete above the horizontal interface not only makes the interface bond and interlocking tighter but also increases the friction coefficient as axial pressure. Therefore, the degree of constraint at the vertical interface between new and old concrete can be considered different from that at the horizontal interface, and the treatment of constraints at the vertical interface in finite element analysis should not be the same as that at the horizontal interface.

[0024] Based on extensive engineering calculation experience, due to the large constraints at the horizontal interface, the calculated cracking risk using measured elastic modulus data for the foundation and subgrade in the finite element method with common nodes is largely consistent with reality, given the high degree of constraint at the horizontal interface. Furthermore, drawing on a wealth of engineering calculation and monitoring experience, this invention proposes that the elastic modulus of the old concrete on the vertical interface side should be calculated using the aforementioned formula in the finite element calculation, resulting in constraint simulation conditions that better reflect actual conditions.

[0025] Furthermore, the risk of early cracking in concrete structures under strong constraints is analyzed and determined according to the following formula:

[0026] ;

[0027] In the formula, and These represent the maximum tensile stress and tensile strength of the concrete structure at time t, respectively.

[0028] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0029] This invention provides a method for assessing the cracking risk of strongly constrained concrete. For concrete structures simultaneously constrained by the foundation and the vertical interface between old and new concrete, based on the constraint properties of the vertical interface, a method for determining the modulus value of the old concrete at the vertical interface in finite element simulation is proposed. Furthermore, a multi-field coupling model based on hydration, temperature, humidity, and constraint is used to calculate the structural cracking risk. Compared to conventional calculation methods, the method provided by this invention better reflects the actual constraint conditions of concrete under strong constraints, improving the accuracy of cracking risk assessment, optimizing crack resistance schemes, and helping to reduce construction crack resistance costs while meeting crack resistance requirements. Attached Figure Description

[0030] Figure 1 A finite element model diagram of the sidewall of a tunnel working shaft provided in an embodiment of the present invention;

[0031] Figure 2 This invention provides a calculation result for the maximum cracking risk of the working well sidewall.

[0032] Figure 3 The strain history of the sidewall provided for embodiments of the present invention;

[0033] Figure 4 The strain history of the sidewall is obtained using conventional methods;

[0034] Figure 5 A flowchart illustrating a method for calculating the risk of early cracking in concrete under strong constraints, provided in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0036] Example 1

[0037] Taking the composite sidewall of a tunnel working shaft as an example, such as Figure 5 As shown in the figure, this invention provides a method for calculating the risk of early cracking in concrete under strong constraints, including the following steps:

[0038] (1) The working well sidewall in this example is poured on the bottom slab. One side of the wall is diaphragm concrete. Before the sidewall is poured, the surface of the diaphragm is roughened and sprayed with 3mm thick waterproof material. It is a strong confinement concrete.

[0039] (2) The side walls are 1.5m thick and 6.5m high, with a single-cast length of 28m. The diaphragm walls and base slab are both 1.5m thick. Finite element models of the side walls, diaphragm walls, and base slab are established and meshed, as detailed below. Figure 1 As shown in the figure, mark 1 is the side wall, mark 2 is the diaphragm wall, and mark 3 is the base plate.

[0040] (3) The roughness of the diaphragm wall was obtained by actual measurement. The reinforcement ratio at the interface between new and old concrete is 30mm. The value is 0.2%, and k = 0.38. The value is 0.1, and γ = 0.52 is obtained by calculation according to the following formula.

[0041] ;

[0042] In the formula: To account for the reference coefficient of chemical bonding strength between new and old concrete, a value of 0.1 to 0.2 is used. The roughness of the vertical construction joint interface is expressed in mm. is the reinforcement ratio at the vertical interface, which is the ratio of the sum of the cross-sectional areas of the steel bars at the vertical interface to the interface area; k is the ratio of the area of ​​the vertical construction joint to the total area of ​​the new concrete.

[0043] The elastic modulus of the diaphragm wall over 28 days is 35 GPa. According to the following formula, the elastic modulus of the diaphragm wall concrete should be taken as 18 GPa in the calculation.

[0044] ;

[0045] In the formula, The elastic modulus value is determined for the old concrete next to the vertical construction joint. This is for adjusting the coefficient. The value is the elastic modulus test value of old concrete after 28 days.

[0046] (4) Determine the thermodynamic boundary conditions based on the actual working conditions of the sidewall, and based on the test results, input the adiabatic temperature rise, elastic modulus, tensile strength and autogenous volume deformation history curve of the sidewall concrete, use the hydration-temperature-humidity-constraint coupling model to calculate the structural temperature, strain and stress, and then calculate the maximum cracking risk of the sidewall concrete by the following formula.

[0047] The specific calculation method for the concrete hydration-temperature-humidity-constraint multi-field coupling model can be found in Section 4.2.2 of "Control of Early Deformation and Shrinkage Cracks in Modern Concrete" by Liu Jiaping and Tian Qian, published by Science Press in February 2020.

[0048] In this example, the relevant calculation parameters for the sidewall are shown in Table 1, and the cracking risk calculation results are as follows: Figure 2 As shown.

[0049] ;

[0050] In the formula, and These represent the maximum tensile stress and tensile strength of the concrete structure at time t, respectively.

[0051] Table 1. Thermodynamic parameters of sidewall concrete.

[0052] Age / day Adiabatic temperature rise / °C Elastic modulus / GPa Tensile strength / MPa Self-generated volumetric deformation / με 1 30.6 22.0 1.62 488 3 43.8 31.5 2.32 540 7 46.8 33.7 2.48 538 14 47.3 34.0 2.51 505

[0053] The calculated temperature and strain results of the concrete sidewall in this example are compared with the actual monitoring data, such as... Figure 3 As shown, Figure 4 The figure shows the calculation results for the elastic modulus of the diaphragm wall concrete, using the 28-day elastic modulus test value. As can be seen from the figure, the strain results calculated by this invention are in excellent agreement with the monitored data, with a peak strain error of less than 10%, and the strain change history is also more consistent with reality. When using conventional methods to directly use the 28-day elastic modulus test value for the diaphragm wall, the calculated strain values ​​along the length of the side wall center and inner surface are significantly smaller than the monitored data, with a peak strain error exceeding 50%. Therefore, it can be considered that the cracking risk calculation method of this invention is more consistent with actual constraints, and the calculation results are more accurate.

[0054] The results of the side wall concrete cracking risk calculation are as follows: Figure 3 and Figure 4 As shown, when calculated using conventional methods, the maximum cracking risk of the wall exceeds 0.9, indicating a high risk of cracking. To reduce the cracking risk to below the safe threshold of 0.7, further calculations suggest controlling the concrete pouring temperature to 20°C or increasing the density of cooling water pipes to reduce the peak wall temperature by 4°C. However, using the calculation method of this invention, the maximum cracking risk is calculated to be 0.66, which is less than the safe threshold of 0.7. It can be assumed that under the current conditions, cracking of the side wall is unlikely. Based on observations two months after the side wall was poured, no cracks appeared, and strain monitoring showed no jumps, confirming the accuracy of the calculation results. This embodiment demonstrates that the calculation method provided by this invention for assessing cracking risk and designing anti-cracking schemes for composite walls makes the cracking risk assessment more reliable and can, to some extent, weaken anti-cracking measures, reducing the cost of anti-cracking measures in engineering projects.

Claims

1. A method for calculating the early cracking risk of concrete structures under strong constraints, characterized in that, The methods and steps include the following: A concrete structure model under strong constraints was established using finite element software, and the common node method was used to simulate the horizontal and vertical interfaces between new and old concrete. Based on the characteristics of the interface between old and new concrete in the concrete structure model under strong constraints, the elastic modulus of the old concrete structure at the interface is calculated and determined to characterize the degree of strong constraints on the concrete structure. The thermodynamic parameters, thermodynamic boundary conditions, and initial conditions of the new and old concrete materials in the concrete structure model under strong constraints are determined. Based on the hydration-temperature-humidity-constraint coupling model, the temperature field and stress field of the new and old concrete structures are calculated. The maximum stress and tensile strength ratio of the structure at a certain period are selected to analyze and determine the early cracking risk of the concrete structure under strong constraints. Strong constraints on concrete structures include the constraint of the bottom surface of the new concrete structure on the foundation and substructure of the old concrete structure, and the constraint of the vertical surface of the new concrete structure on the vertical surface of the old concrete structure. The constraints that the vertical plane of the new concrete structure is subject to by the vertical plane of the old concrete structure include: A vertical surface of the new concrete structure is constrained by the old concrete or bedrock, and the constrained area of ​​the vertical surface accounts for more than 30% of the total surface area of ​​the new concrete structure. Alternatively, two or more vertical surfaces of the new concrete structure are constrained by old concrete or bedrock, and the total area of ​​the constrained surfaces accounts for more than 20% of the area of ​​the new concrete structure. The elastic modulus of the old concrete structure foundation and substructure below the horizontal interface shall be determined according to the actual test value of the elastic modulus of the foundation or the test value of the elastic modulus of the foundation at 28 days. The elastic modulus of the old concrete structure on one side of the vertical interface is calculated according to the following formula: ； In the formula: This represents the elastic modulus of the old concrete on the vertical interface side during pretreatment. This represents the elastic modulus test value of the old concrete after 28 days. The adjustment coefficient is calculated using the following formula: ； In the formula: To account for the reference coefficient of chemical bonding strength between new and old concrete, a value of 0.1 to 0.2 is used. The roughness of the vertical construction joint interface is expressed in mm. is the reinforcement ratio at the vertical interface, which is the ratio of the sum of the cross-sectional areas of the steel bars at the vertical interface to the interface area; k is the ratio of the area of ​​the vertical construction joint to the total area of ​​the new concrete.

2. The method for calculating the early cracking risk of concrete structures under strong constraints as described in claim 1, characterized in that, The risk of early cracking in concrete structures under strong confinement conditions is determined using the following formula: ； In the formula, and These represent the maximum tensile stress and tensile strength of the concrete structure at time t, respectively.

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