Method for calculating stress of waterproof layer of concrete structure, long-life design and manufacturing method

Abstract

The application provides a stress calculation method for a waterproof layer of a concrete structure, wherein the concrete is provided with reinforcing steel bars, and the surface of the concrete is covered with a waterproof layer; the method comprises the following steps: calculating the cracking height H of the waterproof layer when the concrete cracks cr : H cr =(α-βE e / σ cr )ln(T cr )e λWcr E e / σ cr , σ cr is the tensile strength of the waterproof layer, T cr is the thickness of the waterproof layer along the tensile direction when the concrete cracks, and W cr is the crack width of the concrete surface; calculating the remaining uncracked thickness of the waterproof layer; the method also provides a calculation method for setting a fiber reinforced material, an optimization design method for the waterproof layer and a manufacturing method; the method clearly defines the key influencing factors of the cracking height of the waterproof layer, and can guide the optimization direction of various performance indexes of the waterproof material; the waterproof layer designed according to the application still has a certain thickness surplus after being torn due to the cracking of the concrete, so as to avoid the erosion of water to the reinforced concrete structure, and significantly prolong the service life of the reinforced concrete structure; the application is applicable to bridges, buildings, roads, tunnels and hydraulic structures.

Description

Technical Field

[0001] This invention pertains to the following fields: concrete components in the field of general building construction; architectural design, design optimization, and the use of finite element methods in the field of computer-aided design; protective devices for foundations or foundation structures; layered products composed of asphalt or tar substances in the field of layered products; asphalt-based adhesives in the field of adhesives; and asphalt-based coating compositions in the field of coating compositions. Specifically, this invention relates to the field of waterproofing calculation, design, and manufacturing in general building constructions such as buildings, bridges, roads, tunnels, and hydraulic structures. In particular, it relates to stress calculation methods and long-life design and manufacturing methods for waterproofing layers (including modified bitumen waterproofing coatings, polyurethane waterproofing coatings, and waterproofing membranes) of concrete structures (especially wet joints of prefabricated concrete structures and simply supported continuous beam bridges without negative moment tendons). Background Technology

[0002] Extending the lifespan of concrete structures to over a century and ensuring their long-term safe, reliable, and efficient performance has become a hot research topic. Water is the most important factor affecting the durability of concrete structures, and reducing water erosion of reinforced concrete is of great significance for maintaining the long-term performance of various engineering structures, especially wet joints in prefabricated concrete structures (where the tensile strength of the interface between new and old concrete is low and prone to water seepage), and simply supported continuous beam bridges without negative moment bracing (where excessive tensile stress in the negative moment zone leads to cracking and leakage). Taking bridge structures as an example, the original "JTJ 021-89 General Specifications for Design of Highway Bridges and Culverts" did not have a clear provision regarding the installation of waterproof layers on bridge decks. Through nearly 30 to 40 years of engineering experience, especially the summarization of a large amount of experience in the maintenance and reinforcement of old bridges in the last 10 to 20 years, it has been gradually recognized that the main causes of defects in concrete bridges are concrete carbonation, chloride ionization, alkali content and alkali-aggregate reaction caused by reactive aggregates, as well as frost heave damage and steel corrosion. These are all factors closely related to water. Therefore, the installation of waterproof layers has become an important means to reduce defects in concrete bridges and extend their service life. Hence, the "JTG D60-2004 General Specifications for Design of Highway Bridges and Culverts" explicitly stipulated for the first time that "a waterproof layer should be installed" in bridge deck pavement.

[0003] Even with waterproofing layers, and especially considering that bridge designs typically require waterproofing materials (waterproof membranes, polyurethane waterproof coatings) to have an elongation at break of over 450%, and modified bitumen waterproof coatings require over 800%—this demonstrates that the elongation at break of waterproofing materials is far greater than the ultimate tensile strain of steel reinforcement (1%) and concrete (0.01%). Figure 1In reality, even with dense reinforcement, concrete structures are prone to water leakage at cracks after the concrete cracks, severely reducing the service life of the structure and requiring frequent maintenance. This is especially true for prefabricated concrete beam bridges with simply supported structures and continuous decks, where water damage at the deck continuity has become a common problem.

[0004] It is evident that existing waterproofing layers have failed to maintain their intended performance. The fundamental reason lies in the fact that current technology has not clearly defined the stress calculation method for waterproofing layers when cracks appear in reinforced concrete structures. It fails to consider the microscopic nature of concrete cracking and its impact mechanism on the waterproofing layer during stress calculations, and therefore does not conduct crack-resistant design and manufacturing to maintain long-term performance and extend service life. Furthermore, the current national standard, GB / T 16777-2008 "Test Methods for Building Waterproof Coatings," only conducts uniaxial tensile and shear tests on individual waterproofing layer specimens to measure tensile strength, shear strength, elongation at break, bond strength, low-temperature bending, and impermeability. It does not consider the interaction mechanism between concrete and the waterproofing layer, especially the sudden release of strain energy during concrete cracking, which can lead to tearing of the waterproofing layer. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a method for calculating the stress on a waterproof layer of a concrete structure and a method for designing and manufacturing it for long service life. This method proposes the mechanism by which concrete cracking leads to cracking of the waterproof layer and provides a formula for calculating the vertical cracking height of the waterproof layer of a concrete structure. This facilitates the calculation, design, and manufacturing of waterproofing for bridges and various reinforced concrete structures, enabling them to maintain their long-term performance and thus significantly extending their service life.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0007] A method for calculating the stress of a waterproof layer in a concrete structure, wherein the concrete 1 contains reinforcing bars 12 and the concrete surface is covered with a waterproof layer 2; the direction along the tensile direction of the concrete is defined as longitudinal, and the direction perpendicular to the surface of the waterproof layer is defined as vertical;

[0008] The calculation method includes the following steps:

[0009] Calculate the vertical crack height H of the waterproofing layer when crack 13 appears in the concrete using the following formula. cr (Unit: mm)

[0010] H cr =(α-βE) e / σ cr )ln(T cr )e λWcr Ee / σ cr ,

[0011] In the formula, α, β, and λ are all constants and all greater than 0, e is the natural constant, and E e σ is the elastic modulus of the waterproof layer, expressed in MPa. cr The tensile strength of the waterproof layer is expressed in MPa (T). cr W represents the longitudinal tensile thickness of the waterproof layer at the location where the crack occurs, expressed in nm. cr The longitudinal width of the crack on the concrete surface is expressed in mm.

[0012] The remaining uncracked thickness H of the waterproof layer is obtained by the following formula. re (Unit: mm)

[0013] H re =HH cr ,

[0014] In the formula, H is the thickness of the waterproof layer (in mm).

[0015] The technical principle and effect of the above invention are as follows: (1) The essence of concrete cracking is that the distance between the concrete material molecules on both sides of the crack changes abruptly from the nanometer level to the millimeter level visible to the naked eye. The interface between the concrete and the waterproof layer is uneven on a microscopic level. The longitudinal interaction between the concrete and the waterproof layer includes the chemical adsorption force between the molecules of the two, the static friction resistance and the mutual squeezing and biting force. Therefore, the amount of interface slip between the concrete surface and the waterproof layer when the concrete cracks can be basically ignored. Therefore, when the concrete cracks open to both sides, it will also drive the waterproof layer to open to both sides of the crack. That is, the instant the concrete cracks, there will be a tearing effect on the waterproof layer, so that the longitudinal distance between the molecules of the bottom material of the waterproof layer also changes from the nanometer level. The abrupt change to the millimeter level, meaning the distance increases by nearly 100,000 times and manifests as a crack visible to the naked eye—of course, this increase in longitudinal distance decreases rapidly as the vertical distance between the waterproofing layer molecules and the concrete surface increases. However, for the waterproofing layer material near the concrete surface, its 800% elongation at break performance is completely insufficient to withstand a nearly 100,000-fold increase in longitudinal distance. Therefore, when the concrete cracks, the waterproofing layer material near its surface will inevitably crack as well, and will stop cracking after reaching a certain vertical height. Thus, the key to calculating the stress on the waterproofing layer lies in accurately calculating the crack height of the waterproofing layer. Therefore, it is necessary to calculate the crack height of the waterproofing layer in reinforced concrete structures according to this invention to accurately obtain its remaining uncracked thickness value H. re Therefore, based on H re The value is used to determine whether the remaining uncracked thickness still meets the waterproof performance requirements. (2) Combined with the attached Figures 11-12 It can be seen that H crThe calculation results are basically unaffected by the thickness H of the waterproof layer, the longitudinal segment length L (when L≥4H) taken in the stress calculation of the waterproof layer, and the Poisson's ratio v of the waterproof layer. Therefore, these parameters do not need to be reflected in the calculation formula. (3) Further combined with the appendix Figures 13-19 It can be seen that the calculation results of this formula are close to the results of the refined nonlinear finite element method, and H cr All follow W cr The increase of the value is exponential, and its calculation accuracy is high enough. (4) This formula clarifies and quantifies the influence of various performance indicators of waterproof materials on the crack height, which can effectively avoid the problem of excessive calculation time when using a refined nonlinear finite element model, and points out the direction for reducing the amount of waterproof materials and reducing the project cost by improving the performance indicators of waterproof materials. For example, the required design thickness of the waterproof layer can be reduced by changing the elastic modulus and tensile strength of the waterproof material.

[0016] Preferably, the constants α, β, and λ are determined as follows:

[0017] S1. Take a waterproof layer segment with a longitudinal length of L, and perform finite element model meshing using hexahedral elements. Set a discrete crack interface element in the middle of the longitudinal direction of the waterproof layer segment. The nodes on both sides of the discrete crack interface element are coupled to the hexahedral element nodes that are closest to each other on both sides.

[0018] S2. Let γ = 1, 0 < μ ≤ 0.2;

[0019] S3. Apply forced displacements γμW in opposite directions and relatively far apart to the bottom surfaces of the hexahedral units on both sides of the discrete crack interface unit. cr / 2, and γμW cr / 2 is assigned the value of vector W. cr,γ The γth element;

[0020] S4. Perform nonlinear finite element calculations and iterate until convergence to obtain the crack height of the discrete crack interface element and assign it to the vector H. cr,γ The γth element;

[0021] S5. Let γ = γ + 1, if γμW cr / 2≤2W cr If yes, proceed to step S3; otherwise, proceed to step S6.

[0022] S6. Transfer vector W cr,γ H cr,γ Substitute the above H into the corresponding values. cr W in the calculation formula cr H cr After fitting using the least squares method, the values ​​of constants α, β, and λ were determined.

[0023] The technical principle and effect of the above invention are as follows: the cracking of concrete is equivalent to applying W to the bottom surface of the waterproof layer on both sides of the crack. cr / 2 forced displacement (in conjunction with appendix) Figure 3 (A schematic diagram illustrating the mechanism by which concrete cracking leads to waterproofing layer cracking) This illustrates the essential mechanism by which concrete cracking causes waterproofing layer cracking. It should be noted that the crack height of the waterproofing layer caused by this forced displacement requires iterative calculation according to steps S1 to S4 to obtain an accurate solution. (Combined with the attached...) Figures 13-19 It can be seen that this formula can fit the refined nonlinear finite element results very well, thereby determining the values ​​of constants α, β, and λ.

[0024] Preferably, the T cr Take the average distance between material molecules or molecular clusters in concrete.

[0025] The technical principle and effect of the above invention are as follows: When calculating from a safety-oriented perspective, T can be... cr Taking a smaller value to calculate the stress on the waterproof layer, we can consider the limit principle, which assumes that the interaction force between the molecules or clusters of concrete material and the molecules or clusters of the nearest waterproof layer is infinite, and there will be no interface separation or slippage between them. In this case, the essence of cracking in both concrete and waterproof layer is that the longitudinal distance between their molecules or clusters abruptly changes from the nanometer level to the millimeter level, that is, the distance increases by nearly 100,000 times and manifests as a crack visible to the naked eye. Therefore, we can be on the safe side and use the thickness T of the waterproof layer under longitudinal tension as the value. cr The mean distance between material molecules or molecular clusters in concrete is taken as the average value. This mean can be obtained by measuring and averaging using equipment such as atomic force microscopes or scanning electron microscopes through simple random sampling.

[0026] Preferably, when the concrete is silicate concrete, T cr =20nm.

[0027] The technical principles and effects of the above invention are as follows: (1) Through calculation and research, it was found that T cr The smaller the value, the higher the crack height H of the waterproof layer. cr The larger (in conjunction with the appendix) Figure 10 It can be known that T cr For H cr It has a significant impact, that is, the thickness of the waterproof layer under longitudinal tension at the instant of initial cracking of concrete has a significant impact on the final crack height of the waterproof layer; (2) when T cr After shrinking to 100nm, H cr The value of T tends to be constant, that is, at this time T cr The value of H crThe impact is already relatively small. Considering that the 20nm scale is close to the scale of cement stone voids or hydrated calcium silicate gel in silicate concrete, when the measurement of the distance between material molecules or molecular clusters in concrete is complex, it can be simplified to measuring by T. cr =20nm to calculate the stress on the waterproof layer.

[0028] Preferably, the crack width W on the concrete surface cr Calculate W using the following formula: cr =W0(0.74h0+c s +d s / 2) / (0.74h0), where h0 is the distance from the center of the reinforcing bar to the compressive surface of the concrete, and c s d represents the thickness of the concrete cover for the reinforcing steel. s Where is the diameter of the reinforcing bar; W0 is the width of the concrete crack at the location of the reinforcing bar, and W0 = σ smax / E s ·[(c s +d s ) / (0.3+1.4ρ te )], where E s σ is the elastic modulus of the reinforcing steel. smax The maximum steel reinforcement stress that occurs during the service life of a concrete structure, and σ smax =M max / (0.87nπd s 2 / 4·h0), where n is the number of longitudinal reinforcing bars, and the direction perpendicular to both the longitudinal and vertical directions is defined as the transverse direction, M max ρ is the most unfavorable bending moment value of the transverse section at the concrete crack, calculated based on the basic load combination values ​​under the ultimate limit state of bearing capacity. te The effective reinforcement ratio of longitudinal tensile reinforcement and ρ te =nπd s 2 / 4 / [2(c s +d s / 2)b], where b is the transverse dimension of the concrete cross section.

[0029] The technical principles and effects of the above invention are as follows: (1) W0 is the calculated width of the concrete crack at the location of the reinforcing bar, combined with the attached... Figure 2 W crAs shown in the calculation diagram, the internal force arm of the reinforcing bars in reinforced concrete flexural members is generally taken as 0.87h0, that is, the distance from the reinforcing bars to the line of action of the resultant force in the compression zone of the concrete is 0.87h0. The crack height of the concrete can be calculated as 0.87h0 - (1 - 0.87h0) = 0.74h0. Considering that the elastic modulus of concrete is relatively large (much greater than that of waterproofing materials), the notch after the concrete cracks can be considered approximately triangular. Therefore, based on the geometric relationship of similar triangles, W can be derived. cr =W0(0.74h0+c s +d s / 2) / (0.74h0); (2) Because the cracking of the waterproof layer is different from the cracking of the reinforced concrete structure, under the most unfavorable load combination, although the cracks of the reinforced concrete structure will expand to a larger width value, after the load is unloaded, the cracks will be pulled back to a smaller width value by the steel bars. The size of the crack width mainly affects the durability of the steel bars. Therefore, when checking the width of concrete cracks, the "frequent combination value of load used to check the durability of the structure" is generally taken, rather than the "basic combination value of load used to check the bearing capacity of the structure". The cracking of the waterproof layer is mainly a problem of crack height. The higher the crack expands in the waterproof layer, the worse the seepage prevention performance of the waterproof layer. When the crack width of the reinforced concrete structure recovers to a smaller width value, the crack height of the waterproof layer will not recover. Therefore, for the crack height and stress calculation of the waterproof layer, the W value corresponding to the most unfavorable load basic combination value borne by the reinforced concrete structure below it should be used. cr Perform the calculation.

[0030] Preferably, the thickness H of the waterproof layer is calculated based on its solid thickness after curing and maintenance.

[0031] The technical principle and effect of the above invention are as follows: The design and construction of the waterproof layer in the prior art are controlled according to the liquid thickness after it is applied. However, the actual waterproof layer has already solidified when the concrete structure is under stress and cracks. As most waterproof coatings evaporate their water or other organic solvent components, the thickness after curing can be reduced by more than 30% compared to the liquid thickness. Therefore, when calculating the stress according to the liquid design thickness value of the prior art, the result will have a significant error. Therefore, it should be calculated according to the solid thickness after curing and maintenance.

[0032] Preferably, the elastic modulus E of the waterproof layer e =σ 1％ / ε 1％ , σ 1％ ε 1％ The stress and strain at 1% elongation during a uniaxial tensile test of the waterproof layer are respectively the tensile strength σ of the waterproof layer. cr The total loading time for each uniaxial tensile test was calculated based on the average pre-fracture stress obtained from multiple uniaxial tensile tests, and did not exceed 1 minute.

[0033] The technical principle and effect of the above invention are as follows: When concrete cracks, the cracking of the waterproof layer is a transient process. During this process, the nonlinear creep of the waterproof material is very small. The waterproof material in the pressure zone basically exhibits linear elastic stress characteristics. Its elastic modulus can be calculated by dividing the stress under small deformation by the strain. However, the loading time of the uniaxial tensile test should not be too long to reduce the error caused by the creep effect.

[0034] Preferably, when the waterproof layer is made of polymer-modified bitumen waterproof coating or polyurethane waterproof coating for roads and bridges, the constant α = 7.7 × 10⁻⁶. -4 β = 7.4 × 10 -4 λ = 20.

[0035] The technical principle and effects of the above invention are as follows: For the two most common bridge deck waterproofing materials, the refined nonlinear finite element simulation results, corrected based on experimental measurement data, show that according to α = 7.7 × 10 -4 β = 7.4 × 10 -4 When λ = 20, the calculation results of this formula are close to those of the refined nonlinear finite element method, and its calculation accuracy is high enough.

[0036] Preferably, the waterproof layer includes fiber-reinforced material and K r BH cr σ cr / A r ≤f rd At that time, the final vertical crack height of the waterproof layer is taken as c. r In the formula, K r For the safety factor and K r >1, define the direction perpendicular to the longitudinal and vertical directions as the transverse direction, B as the transverse width of the waterproof layer, A r f is the total cross-sectional area of ​​the fiber-reinforced material along the longitudinal direction within the transverse width B of the waterproof layer. rd c is the design tensile strength value of the fiber-reinforced material. r The distance from the fiber-reinforced material to the concrete surface.

[0037] The technical principles and effects of the above invention are as follows: (1) When the total cross-sectional area of ​​the fiber-reinforced material is large, the fiber-reinforced material will bear the cracking height H of the waterproof layer when no fiber-reinforced material is used. cr The tensile force within the specified range will not cause the waterproof layer to break. Therefore, when the waterproof layer cracks to the height of the fiber reinforcement material, the crack will no longer extend upwards. The final actual crack height of the waterproof layer should be corrected to c. r(2) The addition of fiber reinforcement material effectively changes the cracking pattern and trend of the waterproof layer, transforming the "tear-prone trend along the vertical direction" of the waterproof layer into a "tear-prone trend along the longitudinal direction of the fiber reinforcement material." This ensures that the waterproof layer still has a large uncracked thickness, thereby significantly improving the crack resistance and waterproofing performance of the waterproof layer. Figure 21 The refined nonlinear finite element calculation results also reflect this characteristic; (3) from the appendix Figure 13 ~Attached Figure 19 It can be seen that H cr With W cr The exponential increase in the thickness of the waterproofing layer indicates that when the concrete cracks are wide, increasing the thickness of the waterproofing layer to enhance waterproofing performance is relatively inefficient. In this case, fiber-reinforced materials should be prioritized to improve waterproofing performance.

[0038] This invention also proposes a long-life design method for waterproof layers in concrete structures. The long-life design method is based on the aforementioned waterproof layer for concrete structures and includes the following steps:

[0039] S11. Based on the above-mentioned method for calculating the stress of the waterproof layer in concrete structures, the cracking height H of the waterproof layer is calculated. cr Remaining uncracked thickness H re ;

[0040] S12. If H re If H > 0, then let H min ≥H cr +K f H re K f For the safety factor and K f >1, and the thickness H of the waterproof layer after curing is required in the design of the waterproof layer. d Not less than H min End the waterproofing layer design; if H re If ≤0, then go to S13;

[0041] S13. Let H min ≥H-(1+K f )H re K f For the safety factor and K f >1, and the thickness H of the waterproof layer after curing is required in the design of the waterproof layer. d Not less than H min The waterproofing layer design is now complete.

[0042] The technical principle and effect of the above invention are as follows: the existing technology does not consider the tearing effect of concrete cracking on the waterproof layer, which makes it easy for water to leak at the crack after the concrete cracks, which seriously reduces the service life of the structure and the waterproof layer and leads to frequent maintenance. Therefore, ensuring that the waterproof layer still has a certain thickness margin after being torn by concrete is the key to achieving its long service life design. The long service life design method of the present invention can significantly extend the service life of reinforced concrete structures, thereby greatly reducing the maintenance and operation costs of various structures.

[0043] This invention also proposes a long-life design and manufacturing method for waterproof layers in concrete structures. The long-life design and manufacturing method is based on the aforementioned stress calculation method for waterproof layers in concrete structures, and includes the following steps:

[0044] S21. Perform step S1 as described above, and then at a distance c from the bottom surface of the aforementioned hexahedral unit... r At the location, a linear elastic truss element sharing a node with the hexahedral element is established to simulate the effect of fiber-reinforced material;

[0045] S22. Perform steps S2 to S6 above to determine the values ​​of constants α, β, and λ;

[0046] S23. According to the above H cr The calculation formula yields the vertical crack height H of the waterproof layer. cr Let the designed thickness H of the waterproof layer after curing be... d ≥K f H cr K f For the safety factor and K f >1. Complete the design of the waterproof layer;

[0047] S24. Apply c evenly to the top surface of the concrete. r A thick waterproof layer is then applied, followed by the uniform application of fiber-reinforced material with the same cross-sectional dimensions, elastic modulus, and tensile / compressive constitutive parameters as the linear elastic truss unit.

[0048] S25. Continue applying H. d -c r A thick waterproof layer is then formed, thus completing the manufacturing of the waterproof layer.

[0049] The technical principle and effect of the above invention are as follows: the fiber-reinforced material significantly inhibits the development of crack height in the waterproof layer, so it is necessary to take its influence into account for finite element calculation and obtain the corresponding values ​​of α, β, and λ; the layered coating manufacturing method is not only conducive to the full curing of the waterproof layer, but also allows for better control of the vertical position of the fiber-reinforced material, thereby giving full play to its crack resistance and saving the amount of waterproof layer material used.

[0050] The beneficial effects of this invention are summarized as follows:

[0051] I. Based on the essential mechanism of concrete cracking leading to waterproofing layer cracking, this invention provides a method for calculating the stress of waterproofing layers in concrete structures and a method for designing long service life. This ensures that the waterproofing layer still has a certain thickness margin even after being torn due to concrete cracking. The mechanism proposed in this invention is a key issue that has been overlooked by existing technologies and is also the key to significantly extending the service life of reinforced concrete structures. Using the method of this invention can significantly reduce the maintenance and operation costs of concrete components in various general building structures (especially wet joints of prefabricated concrete structures and simply supported continuous beam bridges without negative moment tendons).

[0052] II. This invention discovered that when a crack appears, the longitudinal tensile thickness T of the waterproof layer at that location... cr The final crack height H of the waterproof layer when approaching the nanoscale cr The calculation results tend to be constant, which demonstrates that H cr It is largely unaffected by the thickness H of the waterproof layer, the longitudinal segment length L (when L≥4H) used in the stress calculation of the waterproof layer, and the Poisson's ratio v of the waterproof layer.

[0053] III. This invention discovers H cr With W cr The exponential increase in the crack size indicates that when the concrete cracks are wide, increasing the thickness of the waterproof layer to enhance waterproofing performance is relatively inefficient. In this case, the use of fiber reinforcement should be prioritized. Furthermore, it was found that the use of fiber reinforcement changed the cracking pattern and trend of the waterproof layer, transforming the "tear-prone trend along the vertical direction" into a "peel-off trend along the longitudinal direction of the fiber reinforcement." This ensures that once the crack height of the waterproof layer reaches the fiber reinforcement, it is no longer significantly affected by the widening of the concrete cracks, and the cracks no longer extend vertically, thus significantly improving the crack resistance and waterproofing performance of the waterproof layer.

[0054] Fourth, this invention provides a simplified calculation formula for the crack height of the waterproof layer with and without fiber reinforcement materials, which can effectively avoid the problem of excessive calculation time when using a refined nonlinear finite element model.

[0055] V. The calculation formula of this invention clarifies the key influencing factors of the crack height of the waterproof layer, including the elastic modulus and tensile strength of the waterproof material. It can clearly guide the optimization direction of various performance indicators of waterproof materials (including modified bitumen waterproof coatings, polyurethane waterproof coatings and waterproof membranes), thereby quickly realizing the stress calculation and design optimization of waterproof layers of various concrete structures, reducing the amount of waterproof material used and saving costs. It is applicable to concrete structures in multiple industries such as bridges, roads, tunnels, buildings, and hydraulic engineering. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of a concrete beam with a waterproof layer and reinforcing steel bars, and its cracks, which are common in the background art of this invention.

[0057] Figure 2 This invention is W cr A schematic diagram of the calculation;

[0058] Figure 3 This is a schematic diagram illustrating the mechanism by which concrete cracking leads to cracking of the waterproof layer, as described in this invention.

[0059] Figure 4 This is an overall schematic diagram of the initial finite element model in an embodiment of the present invention;

[0060] Figure 5 The initial finite element model of this invention embodiment is in W cr A schematic diagram of the deformation when the diameter is 0.1 mm;

[0061] Figure 6 The initial finite element model of this invention embodiment is in W cr A schematic diagram of the deformation when the diameter is 0.18 mm.

[0062] Figure 7 The initial finite element model of this invention embodiment is in W cr A schematic diagram of deformation at a thickness of 0.18 mm (only elements near the crack are shown);

[0063] Figure 8 The initial finite element model of this invention embodiment is in W cr When T = 0.18mm cr A schematic diagram of the longitudinal stress of the unit in the region;

[0064] Figure 9 The initial finite element model of this invention embodiment is in W cr A schematic diagram of the deformation when the diameter is 0.2 mm;

[0065] Figure 10 The initial finite element model of this invention is subjected to different longitudinal tensile thicknesses T. cr A comparative diagram of the cracking results below;

[0066] Figure 11 This is a schematic diagram comparing the cracking results of the initial finite element model of this invention under different longitudinal lengths L;

[0067] Figure 12 This is a schematic diagram comparing the cracking results of the initial finite element model of this invention under different vertical thicknesses H.

[0068] Figure 13 The initial finite element model of this embodiment of the invention is in σ cr =0.5MPa, εcr =800%, E e A schematic diagram comparing the calculation results of the finite element method with the calculation results of the formula of this invention when the pressure is 1.0 MPa.

[0069] Figure 14 The initial finite element model of this embodiment of the invention is in σ cr =0.5MPa, ε cr =800%, E e A schematic diagram comparing the calculation results of the finite element method with the calculation results of the formula of this invention when the pressure is 0.8 MPa.

[0070] Figure 15 The initial finite element model of this embodiment of the invention is in σ cr =0.5MPa, ε cr =800%, E e A schematic diagram comparing the calculation results of the finite element method with the calculation results of the formula of this invention when the pressure is 1.2 MPa.

[0071] Figure 16 The initial finite element model of this embodiment of the invention is in σ cr =1.0MPa, ε cr =800%, E e A schematic diagram comparing the calculation results of the finite element method with the calculation results of the formula of this invention when the pressure is 2.2 MPa.

[0072] Figure 17 The initial finite element model of this embodiment of the invention is in σ cr =1.0MPa, ε cr =800%, E e A schematic diagram comparing the calculation results of the finite element method with the calculation results of the formula of this invention when the pressure is 1.8 MPa.

[0073] Figure 18 The initial finite element model of this embodiment of the invention is in σ cr =2.45MPa, ε cr =450%, E e A schematic diagram comparing the calculation results of the finite element method with the calculation results of the formula of this invention when the pressure is 4.0 MPa.

[0074] Figure 19 The initial finite element model of this embodiment of the invention is based on σcr = 2.45 MPa and ε cr =450%, E e A schematic diagram comparing the calculation results of the finite element method with the calculation results of the formula of this invention when the pressure is 6.0 MPa.

[0075] Figure 20This is an overall schematic diagram of the initial finite element model of this invention after adding fiber reinforcement material;

[0076] Figure 21 After adding fiber reinforcement material to the initial finite element model of this embodiment of the invention, the W... cr A schematic diagram of the deformation when the diameter is 0.2 mm;

[0077] Figure 22 After adding fiber reinforcement material to the initial finite element model of this embodiment of the invention, the W... cr A schematic diagram of fiber stress at a thickness of 0.2 mm;

[0078] Figure 23 These are photos of a cracking test on a fiber-free waterproof layer under load.

[0079] Figure 24 These are photos of cracks and leaks in the fiber-free waterproof layer.

[0080] Figure 25 These are photos of cracking tests and structural cracking of a fibrous waterproof layer.

[0081] Explanation of reference numerals in the attached figures:

[0082] 1. Concrete; 12. Reinforcing steel; 13. Cracks; 14. T-shaped section in the middle of the waterproof layer segment. cr Planar unit of the area; 15. Fiber-reinforced material; 2. Waterproof layer; 21. T-shaped section of waterproof layer segment. cr Waterproofing mesh on the left side of the area; 22. T in the middle of the waterproofing segment. cr Waterproof mesh on the right side of the area; 3. Interface; G Z Vertical rigid support; W cr Longitudinal width of cracks on the concrete surface; H cr Vertical crack height of the waterproof layer. Detailed Implementation

[0083] The present invention will be further described in detail below with reference to experimental examples and specific embodiments. However, it should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments. All technologies implemented based on the content of the present invention are within the scope of the present invention.

[0084] Example A

[0085] This invention proposes a method for calculating the stress of a waterproof layer in a concrete structure. The concrete 1 contains reinforcing bars 12, and the surface of the concrete 1 is covered with a waterproof layer 2. The tensile direction of the concrete 1 is defined as longitudinal, and the direction perpendicular to the surface of the waterproof layer 2 is defined as vertical. The calculation method includes the following steps:

[0086] Calculate the vertical crack height H of waterproof layer 2 when crack 13 appears in concrete 1 using the following formula (referred to as the "simplified formula").cr (Unit: mm)

[0087] H cr =(α-βE) e / σ cr )ln(T cr )e λWcr E e / σ cr In the formula, α, β, and λ are all constants and all greater than 0, e is the natural constant, and E e σ is the elastic modulus of waterproof layer 2, expressed in MPa. cr The tensile strength of waterproof layer 2 is expressed in MPa and T. cr W represents the longitudinal tensile thickness of the waterproof layer 2 at the location where crack 13 occurs, expressed in nm. cr The longitudinal width of crack 13 on the surface of concrete 1 is given in mm; the remaining uncracked thickness H of waterproof layer 2 is calculated using the following formula. re H re =HH cr H represents the thickness of waterproof layer 2 in mm.

[0088] In this embodiment, the method for calculating the stress of the waterproof layer in a concrete structure is based on the fact that water erosion is the most important factor affecting the durability of reinforced concrete structures, and reducing water erosion of reinforced concrete structures can significantly extend their service life. This method is based on the mechanism by which cracking of concrete 1 leads to cracking of the waterproof layer 2. Research has found that the essence of cracking in concrete 1 is the abrupt change in the distance between the material molecules of concrete 1 on both sides of crack 13 from the nanometer level to the visible millimeter level. The interface 3 between concrete 1 and waterproof layer 2 is microscopically uneven. The longitudinal interaction between concrete 1 and waterproof layer 2 includes the chemical adsorption force between their molecules, static friction, and mutual compressive and interlocking forces. Therefore, when concrete 1 cracks, the slippage of the interface 3 between the surface of concrete 1 and waterproof layer 2 is negligible. Thus, when the concrete crack 13 opens to both sides, it also causes the waterproof layer 2 to open to both sides of crack 13. That is, the instant the concrete 1 cracks, the… The tearing effect on the waterproof layer 2 causes the longitudinal distance between the molecules of the bottom material of the waterproof layer 2 to suddenly change from the nanometer level to the millimeter level, that is, the distance increases by nearly 100,000 times and appears as a crack 13 visible to the naked eye. Of course, the increase in this longitudinal distance will decrease rapidly as the vertical distance between the molecules of the waterproof layer 2 and the surface of the concrete 1 increases. However, for the waterproof layer 2 material near the surface of the concrete 1, its tensile elongation at break of only 800% is completely insufficient to withstand the increase in longitudinal distance of nearly 100,000 times. Therefore, when the concrete 1 cracks, the waterproof layer 2 material near its surface will inevitably crack as well, and will stop cracking after cracking vertically to a certain height. Therefore, the key to the stress calculation of the waterproof layer is to accurately calculate the crack height of the waterproof layer 2.

[0089] Therefore, it is necessary to calculate the cracking height of the waterproof layer 2 in the reinforced concrete structure according to the present invention in order to accurately obtain its remaining uncracked thickness value H. re Therefore, based on H re The value is used to determine whether the remaining uncracked thickness still meets the waterproof performance requirements, thereby ensuring that when the waterproof layer 2 is torn due to the cracking of concrete 1, it still retains a certain thickness margin so that the waterproof layer 2 can still play a waterproof role after the reinforced concrete structure cracks, thereby significantly extending the service life of the reinforced concrete structure and greatly reducing the maintenance and operation costs of various structures.

[0090] Furthermore, in conjunction with the appendix Figures 11-12 It can be seen that H cr The calculation results are basically unaffected by the thickness H of the waterproof layer 2, the longitudinal segment length L (when L≥4H) used in the stress calculation of the waterproof layer, and the Poisson's ratio v of the waterproof layer 2. Therefore, these parameters have little impact on H. cr The calculation results do not have an impact, therefore they do not need to be reflected in the calculation formula. Further, according to the appendix... Figures 13-19 It can be seen that the calculation results of this formula are close to the results of the refined nonlinear finite element method, and H cr All follow W cr The increase in value is exponential, and its calculation accuracy is sufficiently high. This formula clearly and quantifies the influence of various performance indicators of waterproof materials on crack height, which can effectively avoid the problem of excessive calculation time when using refined nonlinear finite element models. It also points the way to reducing the amount of waterproof materials used and lowering project costs by improving the performance indicators of waterproof materials. For example, the required design thickness of the waterproof layer can be reduced by changing the elastic modulus and tensile strength of the waterproof material.

[0091] In summary, this calculation formula clarifies the key influencing factors of the crack height of the waterproof layer 2, including the elastic modulus and tensile strength of the waterproof material. It provides clear guidance for optimizing various performance indicators of the waterproof material, thereby enabling rapid stress calculation and design optimization of the waterproof layer 2 in various concrete structures. This reduces the amount of waterproof material used and saves costs, and is applicable to concrete structures 1 in various industries such as bridges, roads, tunnels, buildings, and hydraulic engineering.

[0092] In a preferred embodiment, the constants α, β, and λ are determined as follows:

[0093] S1. Take a waterproof layer segment with a longitudinal length of L, and perform finite element model meshing using hexahedral elements. Set a discrete crack interface element in the middle of the longitudinal direction of the waterproof layer segment 2. The nodes on both sides of the discrete crack interface element are coupled to the nearest hexahedral element nodes on both sides respectively.

[0094] S2. Let γ = 1, 0 < μ ≤ 0.2;

[0095] S3. Apply forced displacements γμW in opposite directions and relatively far apart to the bottom surfaces of the hexahedral elements on both sides of the discrete crack interface element. cr / 2, and γμW cr / 2 is assigned the value of vector W. cr,γ The γth element;

[0096] S4. Perform nonlinear finite element calculations and iterate until convergence, obtain the crack height of the discrete crack interface element, and assign it to the vector H. cr,γ The γth element;

[0097] S5. Let γ = γ + 1, if γμW cr / 2≤2W cr If yes, proceed to step S3; otherwise, proceed to step S6.

[0098] S6. Transfer vector W cr,γ H cr,γ Substitute H accordingly cr W in the calculation formula cr H cr After fitting using the least squares method, the values ​​of constants α, β, and λ were determined.

[0099] In this embodiment, the cracking of the concrete is equivalent to applying W to the bottom surface of the waterproof layer on both sides of the crack. cr / 2 forced displacement (in conjunction with appendix) Figure 3 (A schematic diagram illustrating the mechanism by which concrete cracking leads to waterproofing layer cracking) This illustrates the essential mechanism by which concrete cracking causes waterproofing layer cracking. It should be noted that the crack height of the waterproofing layer caused by this forced displacement requires iterative calculation according to steps S1 to S4 to obtain an accurate solution. (Combined with the attached...) Figures 13-19 It can be seen that this formula can fit the refined nonlinear finite element results very well, thereby determining the values ​​of constants α, β, and λ.

[0100] In a preferred embodiment, T cr This represents the average distance between material molecules or molecular clusters in concrete 1. In this embodiment, the present invention discovered that when crack 13 appears, the longitudinal tensile thickness T of the waterproof layer 2 at that location is... cr The final crack height H of waterproof layer 2 when approaching the nanoscale cr The calculation results tend to be constant, which demonstrates that H cr It is basically unaffected by the thickness H of the waterproof layer 2, the longitudinal segment length L (when L≥4H) taken in the stress calculation of the waterproof layer, and the Poisson's ratio v of the waterproof layer 2.

[0101] Furthermore, to ensure safety during the calculation process, T is... crTaking a smaller value to calculate the stress on the waterproof layer, we can consider the limit principle, that is, assuming that the force between the molecules or clusters of concrete 1 and the molecules or clusters of the adjacent waterproof layer 2 is infinite, and there will be no interface separation or slippage between them. In this case, the cracking of concrete 1 and waterproof layer 2 is essentially due to the abrupt change in the longitudinal distance between their molecules or clusters from the nanometer level to the millimeter level, that is, the distance increases by nearly 100,000 times and manifests as a crack 13 visible to the naked eye. Therefore, we can conservatively assume that the thickness T of the waterproof layer 2 under longitudinal tension is... cr The mean distance between material molecules or molecular clusters in concrete 1 is taken as the average value. This mean value can be obtained by measuring and averaging using equipment such as atomic force microscopes or scanning electron microscopes through simple random sampling.

[0102] Furthermore, when concrete 1 is silicate concrete 1, T cr =20nm. For example... Figure 10 As shown, calculations revealed that T cr The smaller the value, the higher the crack height H of the waterproof layer. cr The larger T is cr For H cr There is a significant impact, namely, the thickness of the waterproof layer 2 under longitudinal tension at the instant of initial cracking of concrete 1 has a significant impact on the final crack height of waterproof layer 2; when T cr After shrinking to 100nm, H cr The value of T tends to be constant, that is, at this time T cr The value of H cr The impact is already relatively small. Considering that the 20nm scale is close to the scale of cement stone voids or hydrated calcium silicate gel in silicate concrete 1, when the measurement of the distance between material molecules or molecular clusters in concrete 1 is complicated, it can be simplified to measuring by T. cr =20nm to calculate the stress on the waterproof layer.

[0103] like Figure 2 As shown, the width W of crack 13 on the surface of concrete 1 cr Calculate W using the following formula: cr =W0(0.74h0+c s +d s / 2) / (0.74h0), where h0 is the distance from the center of steel bar 12 to the compressive surface of concrete 1, c s d represents the protective layer thickness of rebar 12. s W is the diameter of reinforcing bar 12; W0 is the width of crack 13 in concrete 1 at reinforcing bar 12, and W0 = σ smax / E s ·[(c s +d s ) / (0.3+1.4ρ te )], where E sLet σ be the elastic modulus of steel bar 12. smax The maximum stress of the reinforcing steel bar 12 that occurs during the use of concrete 1 is σ. smax =M max / (0.87nπd s 2 / 4·h0), n is the number of longitudinal reinforcing bars (12), and the direction perpendicular to both the longitudinal and vertical directions is defined as the transverse direction, M max ρ is the most unfavorable bending moment value at the transverse section of the concrete crack 13, calculated based on the basic load combination value under the ultimate limit state of bearing capacity. te The effective reinforcement ratio of longitudinal tensile reinforcement 12 and ρ te =nπd s 2 / 4 / [2(c s +d s / 2)b], where b is the transverse dimension of the transverse section of concrete 1.

[0104] In this embodiment, W0 is the calculated width of the concrete crack 13 at the location of the reinforcing bar 12, combined with the attached... Figure 2 -W cr As shown in the calculation diagram, the internal force arm of the steel bar 12 in the flexural member of concrete 1 with steel bar 12 is generally taken as 0.87h0, that is, the distance from the steel bar 12 to the line of action of the resultant force in the compression zone of concrete 1 is 0.87h0. It can be deduced that the crack height of concrete crack 13 is 0.87h0-(1-0.87h0)=0.74h0. Considering that the elastic modulus of concrete 1 is relatively large, much larger than that of waterproof material, the notch after cracking of concrete 1 can be considered to be approximately triangular. Therefore, W can be derived based on the geometric relationship of similar triangles. cr =W0(0.74h0+c s +d s / 2) / (0.74h0);

[0105] Because the cracking of waterproof layer 2 differs from that of reinforced concrete structures, in reinforced concrete structures, although crack 13 may expand to a large width under the most unfavorable load combination, the elasticity of the reinforcing steel 12 pulls the crack 13 back to a smaller width after the load is unloaded. The width of crack 13 mainly affects the durability of the reinforcing steel 12. Therefore, when verifying the width of concrete crack 13, the "frequent load combination value used to verify structural durability" is generally used, rather than the "basic load combination value used to verify structural bearing capacity." However, the cracking of waterproof layer 2 is mainly a matter of crack height 13. The higher the crack 13 expands in waterproof layer 2, the worse its seepage prevention performance. Furthermore, when the width of crack 13 in the reinforced concrete structure returns to a smaller width, the height of crack 13 in waterproof layer 2 does not return to its original value. Therefore, for the calculation of crack height and stress in waterproof layer 2, the W value corresponding to the most unfavorable basic load combination value borne by the underlying reinforced concrete structure should be used. cr Perform the calculation.

[0106] Furthermore, the thickness H of waterproof layer 2 is the solid thickness of waterproof layer 2 after curing and maintenance. The elastic modulus E of waterproof layer 2... e =σ 1％ / ε 1％ , σ 1％ ε is the stress at 1% elongation during a uniaxial tensile test of waterproof layer 2. 1％ To determine the strain at 1% elongation during a uniaxial tensile test of waterproof layer 2, the tensile strength σ of waterproof layer 2 is... cr The total loading time for each uniaxial tensile test was calculated based on the average pre-fracture stress obtained from multiple uniaxial tensile tests, and did not exceed 1 minute.

[0107] In this embodiment, the existing waterproof layer 2 is designed and constructed based on its liquid thickness after application. However, the actual waterproof layer 2 solidifies when the concrete 1 structure is under stress and cracks. Since most waterproof coatings lose more than 30% of their liquid thickness after curing due to the evaporation of water or other organic solvent components, stress calculations based on the existing liquid design thickness will result in significant errors. Therefore, the calculation should be based on its solid thickness after curing and maintenance. In the elastic modulus measurement test of the waterproof layer 2, since the cracking of the waterproof layer 2 when the concrete 1 cracks is a transient process, the nonlinear creep of the waterproof material is very small during this process. The waterproof material in the pressure zone basically exhibits linear elastic stress characteristics. Therefore, its elastic modulus can be calculated by dividing the stress under small deformation by the strain. However, the loading time of the uniaxial tensile test should not be too long to reduce the error caused by the creep effect.

[0108] In a preferred embodiment, when the waterproof layer 2 is made of polymer-modified bitumen waterproof coating or polyurethane waterproof coating for road and bridge applications, the constant α = 7.7 × 10⁻⁶.-4 β = 7.4 × 10 -4 λ = 20. For the two most common bridge deck waterproofing materials, the refined nonlinear finite element simulation results, corrected based on experimental data, show that according to α = 7.7 × 10 -4 β = 7.4 × 10 -4 When λ = 20, the calculation results of this formula are close to those of the refined nonlinear finite element method, and its calculation accuracy is high enough.

[0109] like Figure 13-19 As shown, the waterproof layer 2 includes fiber-reinforced material 15; K r BH cr σ cr / A r ≤f rd At that time, the final vertical crack height of waterproof layer 2 was c. r In the formula, K r For the safety factor and K r >1. Define the direction perpendicular to the longitudinal and vertical directions as the horizontal direction. B is the horizontal width of waterproof layer 2. A r f is the total cross-sectional area of ​​the fiber-reinforced material 15 in the longitudinal direction within the transverse width B of the waterproof layer 2. rd c is the design tensile strength value of fiber-reinforced material 15. r The distance from the fiber-reinforced material 15 to the surface of the concrete beam 1.

[0110] In this embodiment, when the total cross-sectional area of ​​the fiber-reinforced material 15 is large, the fiber-reinforced material 15 will bear the cracking height H of the waterproof layer 2 when the fiber-reinforced material 15 is not present. cr The tensile force within the range will not cause it to break. Therefore, when the waterproof layer 2 cracks to the height of the fiber reinforcement material 15, the crack 13 will no longer extend upwards. The final actual crack height of the waterproof layer 2 should be corrected to c. r The addition of fiber reinforcement material 15 effectively alters the cracking pattern and trend of waterproof layer 2, transforming its "tear-prone vertical trend" into a "peeling-prone longitudinal trend along fiber reinforcement material 15." This ensures that waterproof layer 2 retains a significant uncracked thickness, thereby substantially improving its crack resistance and waterproofing performance. Figure 21 The refined nonlinear finite element calculation results also reflect this characteristic; in summary, it can be found that H cr With W crThe exponential increase in the crack height of the concrete crack 13 indicates that when the concrete crack 13 is wide, increasing the thickness of the waterproof layer 2 to enhance waterproofing performance is relatively inefficient. In this case, the addition of fiber reinforcement material 15 should be prioritized. Furthermore, it was found that the addition of fiber reinforcement material 15 altered the cracking pattern and trend of the waterproof layer 2, transforming its "tear-prone trend along the vertical direction" into a "peel-off trend along the longitudinal direction of the fiber reinforcement material 15." This ensures that once the crack height of the waterproof layer 2 reaches the fiber reinforcement material 15, it is no longer significantly affected by the widening of the concrete crack 13, and the crack 13 no longer extends vertically, thus significantly improving the crack resistance and waterproofing performance of the waterproof layer 2. Further, this invention provides a simplified calculation formula for the crack height of the waterproof layer 2 with and without fiber reinforcement material 15, effectively avoiding the problem of excessive calculation time when using a refined nonlinear finite element model.

[0111] Example B

[0112] This invention also proposes a long-life design method for a concrete structure waterproof layer 2. The long-life design method is based on the above-mentioned concrete structure waterproof layer 2 and includes the following steps:

[0113] S11. Based on the stress calculation method for waterproof layers in concrete structures, the cracking height H of waterproof layer 2 is calculated. cr Remaining uncracked thickness H re ;

[0114] S12. If H re If H > 0, then let H min ≥H cr +K f H re K f For the safety factor and K f >1, and the thickness value H of waterproof layer 2 after curing is required in the design of waterproof layer 2. d Not less than H min End of waterproof layer 2 design; if H re If ≤0, then go to S13;

[0115] S13. Let H min ≥H-(1+K f )H re K f For the safety factor and K f >1, and the thickness value H of waterproof layer 2 after curing is required in the design of waterproof layer 2. d Not less than H min The design of the second waterproof layer is now complete.

[0116] In this embodiment, the prior art does not consider the tearing effect of the concrete 1 on the waterproof layer 2 at the moment of cracking. As a result, water leakage is still likely to occur at the crack 13 after the concrete 1 cracks, which seriously reduces the service life of the reinforced concrete structure and the waterproof layer 2 at that location. It also leads to frequent maintenance of the reinforced concrete structure and the waterproof layer 2 at that location. Therefore, ensuring that the waterproof layer 2 still has a certain thickness margin after being torn by the concrete 1 is the key to achieving its long service life design. The long service life design method of the present invention can ensure that the waterproof layer 2 still has a certain thickness margin after being torn by the concrete 1, guarantee the waterproof performance of the waterproof layer 2, avoid water erosion of the reinforced concrete structure, significantly extend the service life of the reinforced concrete structure, and thus greatly reduce the maintenance and operation costs of various structures.

[0117] Example C

[0118] This invention also proposes a long-life design and manufacturing method for waterproof layers in concrete structures. The long-life design and manufacturing method is based on the aforementioned stress calculation method for waterproof layers in concrete structures, and includes the following steps:

[0119] S21. Take a waterproof layer segment with a longitudinal length of L, and mesh it using hexahedral elements for a finite element model. Set a discrete crack interface element in the middle of the longitudinal direction of the waterproof layer segment. The nodes on both sides of the discrete crack interface element are coupled to the nearest hexahedral element nodes on both sides. Then, at a distance c from the bottom surface of the finite element model mesh... r At the location, linear elastic truss elements with nodes shared with the finite element model mesh are established to simulate the influence of fiber-reinforced materials;

[0120] S22. Perform steps S2 to S6 in the method for determining constants α, β, and λ to determine the values ​​of constants α, β, and λ;

[0121] S23. According to the above H cr The calculation formula yields the vertical crack height H of the waterproof layer. cr Let the designed thickness H of the waterproof layer after curing be... d ≥K f H cr K f For the safety factor and K f >1. Complete the design of the waterproof layer;

[0122] S24. Apply c evenly to the top surface of the concrete. r A thick waterproof layer is then applied, followed by the uniform application of fiber-reinforced material with the same cross-sectional dimensions, elastic modulus, and tensile / compressive constitutive parameters as the linear elastic truss unit.

[0123] S25. Continue applying H. d -c rA thick waterproof layer is then formed, thus completing the manufacturing of the waterproof layer.

[0124] In this embodiment, the fiber-reinforced material significantly inhibits the development of crack height in the waterproof layer. Therefore, it is necessary to take its influence into account and perform finite element calculations to obtain the corresponding values ​​of α, β, and λ. The layered coating manufacturing method is not only conducive to the full curing of the waterproof layer, but also allows for better control of the vertical position of the fiber-reinforced material, thereby giving full play to its crack-resistant effect and saving the amount of waterproof layer material used.

[0125] Example D

[0126] To verify the technical effect of the present invention, a refined initial finite element model was established for two segments of the waterproof layer with a longitudinal length L = 10 mm, a vertical thickness H = 1 mm, and a transverse width B = 1 mm, as shown below. Figure 4 As shown, the main modeling parameters are as follows: (1) Boundary: It is assumed that the concrete crack 13 appears in the longitudinal middle of the waterproof layer 2 segment, and the concrete 1 has a rigid constraint on the waterproof layer 2 in the vertical direction. That is, a vertical rigid support is set on the bottom surface of the waterproof layer 2 to simulate the vertical constraint of the concrete 1 on the waterproof layer 2; (2) Mesh: The average distance between material molecules or molecular clusters in the concrete 1 is taken as 20nm, that is, the thickness T of the waterproof layer 2 under longitudinal tension at the instant the concrete 1 initially cracks. cr =20nm, therefore the longitudinal length T in the middle of the two segments of the waterproof layer is... cr The area with a vertical height of H is meshed using planar units with a longitudinal length of 20nm and a vertical height of 0.01mm. The middle section T of this waterproof layer consists of two segments. cr The mesh size of the planar stress element of the waterproof layer 2 near the planar element 14 in the region is 0.01mm×0.01mm, and the mesh size of the distant part is thickened to 0.05mm×0.01mm to reduce the computational load of the finite element analysis; (3) Material: the elongation at break of the waterproof layer 2 material ε cr =800% and tensile strength σ cr =0.5MPa (comparable to the performance parameters of common PB-I type polymer-modified asphalt waterproof coatings for roads and bridges), elastic modulus E e =1.0MPa, Poisson's ratio v=0.3, define T cr The longitudinal tensile stress in the region reaches σ cr When the relative longitudinal displacement of the nodes on both sides of the region reaches 800% × T cr When the stiffness value of the corresponding element suddenly becomes 0, it is equivalent to brittle cracking and the element at the corresponding position is deleted. At this time, the longitudinal tensile stress of the corresponding element also suddenly becomes 0; (4) Load: for T cr Apply W to the left side of all nodes on the bottom surface of the two-segment waterproof layer on the left side of the area. cr A forced displacement of / 2 correspondingly applies W to the bottom surface of the right-side waterproof layer segment 2 on the right. cr / 2 forced displacement, W cr The load is applied in 100 levels, from 0 to 0.2 mm, meaning each load step has a W value. cr The increment is 0.002 mm.

[0127] This calculation process simultaneously enables geometric nonlinearity and material nonlinearity, and employs a modified Newton-Raphson method for iterative solution. The calculation results of the initial finite element model are as follows: Figures 5-9 As shown in the figure, the analysis shows that: (1) Figure 5 This indicates that the above model is loaded into W. cr The deformation at 0.1mm indicates the crack height H of waterproof layer 2. cr =0.14mm, at which point there is still a large margin of uncracked height; (2) Figures 6-7 This indicates that the above model is loaded into W. cr The deformation at a thickness of 0.18 mm indicates that the crack height H of waterproof layer 2 is at this point. cr =0.51mm, at which point the second waterproof layer has already shown significant cracking; Figure 8 This indicates that the above model is loaded into W. cr When T = 0.18mm cr The longitudinal stress of the unit in the region shows that the stress value of the cracked area is 0 and no longer participates in the stress. Moreover, the unit stress at the top tip of the crack 13 in the waterproof layer 2 is significantly greater than the unit stress in other uncracked locations, which is consistent with the stress distribution in the conventional crack 13 propagation theory; (3) Figure 9 This indicates that the above model is loaded into W. cr The deformation at T = 0.2 mm can be seen. cr The waterproof layer 2 segments on both sides of the area have completely separated, meaning that crack 13 in waterproof layer 2 has penetrated its entire height, indicating that the actual width W of crack 13 in the concrete structure 1 is... cr When the thickness reaches 0.2mm, a waterproof layer 2 with a thickness of H=1mm will completely crack and fail. Therefore, the design of waterproof layer 2 should be improved. To verify the calculation effect of this invention, another sample was fabricated as shown below. Figure 23 Loading tests were conducted on specimens of reinforced concrete beam 12 with waterproof layer 2. During the test, if... Figure 24 As shown, when concrete crack 13 appeared, the waterproof layer 2 leaked, indicating that the test results are consistent with the calculation conclusions of this invention.

[0128] Based on the initial finite element model, the thickness T of the waterproof layer 2 under longitudinal tension at the instant of initial cracking of concrete 1 is considered. cr The crack height H was calculated by taking different values ​​within the range of 10 nm to 10000 nm. cr The results are plotted in logarithmic coordinates. Figure 10 It can be seen that: (1) when Tcr When taking values ​​at scales above 100 nm, T cr The larger the value, the greater the crack height H of the resulting waterproof layer. cr The smaller, T cr For H cr It has a significant effect; (2) when T cr After shrinking to 100nm, H cr It tends to a stable value.

[0129] Based on the initial finite element model, calculations were performed for different values ​​of the longitudinal length L within the range of 0.4 mm to 10 mm, and the resulting crack height H was obtained. cr The results are as follows Figure 11 As shown, it can be seen that: (1) When L < 4H = 4mm, the larger the value of L, the greater the crack height H of the resulting waterproof layer 2. cr The larger L is, the more it affects H cr It has a significant impact; (2) When L≥4H=4mm, H cr The changes in H tend to stabilize, at which point H cr The calculation results are basically unaffected by L. In reality, the longitudinal laying length of the waterproof layer 2 is thousands of times its thickness. Therefore, the calculation results of the crack height of the waterproof layer 2 are basically unaffected by its longitudinal length. Thus, its longitudinal length parameter does not need to be reflected in the calculation formula.

[0130] Based on the initial finite element model, calculations were performed for different values ​​of the vertical thickness H within the range of 0.3 mm to 1 mm, and the resulting crack height H was obtained. cr The results are as follows Figure 12 As shown, it can be seen that: except for the case where the waterproof layer 2 cracks earlier due to an excessively low H value, H... cr The calculation results are basically unaffected by H. That is, when the waterproof layer 2 is not too thin, its crack height is basically unrelated to its vertical thickness value. Therefore, its vertical thickness parameter does not need to be reflected in the calculation formula.

[0131] Based on the initial finite element model, calculations were performed for the Poisson's ratio of the waterproof material when v = 0.2, 0.3, and 0.4. It was found that H... cr The calculation results are basically unaffected by v.

[0132] To verify the calculation accuracy of the stress calculation method of the present invention, based on the initial finite element model, the calculation of the stress of waterproof materials was performed. cr ε cr E e When taking different values ​​(keeping T) cr =20nm, α=7.7×10 -4 β = 7.4 × 10 -4For cases where λ = 20, calculations are performed using the finite element method and the simplified formula of this invention, respectively, where σ cr =0.5MPa, ε cr =At 800%, its performance parameters are comparable to those of the common PB-I type polymer-modified bitumen waterproof coating for roads and bridges, σ cr =1.0MPa, ε cr =At 800%, its performance parameters are comparable to those of the common PB-II type polymer-modified bitumen waterproof coating for roads and bridges, σ cr =2.45MPa, ε cr When the concentration is 450%, its performance parameters are comparable to those of common polyurethane waterproof coatings used for roads and bridges. See the comparison of calculation results below. Figures 13-19 It can be seen that the calculation results of the simplified formula are close to those of the refined nonlinear finite element method, and H cr All follow W cr As the value increases, it exhibits an exponential growth, and the calculation accuracy of the simplified formula is sufficiently high.

[0133] Furthermore, such as Figure 20 Based on the initial finite element model, at a vertical distance c from the bottom surface of waterproof layer 2 r A linear elastic truss element sharing a node with the plane stress element is established at a position of 0.2 mm to simulate the effect of fiber reinforcement material 15. The design tensile strength of fiber reinforcement material 15 is f. rd =400MPa, the cracking condition of waterproof layer 2 is calculated as follows Figures 21-22 As shown, it can be seen that after the crack in the waterproof layer 2 reaches the fiber reinforcement material 15, the crack 13 no longer propagates upwards, that is, the crack height H of the waterproof layer 2 is... cr =0.2mm, its H cr With c r The values ​​are comparable, and the maximum stress of fiber-reinforced material 15 is 225 MPa, which is much smaller than its design tensile strength f. rd To verify the computational effectiveness of this invention, another sample was fabricated as shown below. Figure 25 The actual specimens shown were subjected to loading tests. During the test, when the width of the crack 13 in the reinforced concrete beam 1 reached 1.5 mm, the waterproof layer 2 still did not leak. It can be seen that the test results are consistent with the calculation conclusions of this invention.

[0134] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the stress of a waterproof layer in a concrete structure, characterized in that, The concrete contains reinforcing bars, and the surface of the concrete is covered with a waterproof layer; the direction along which the concrete is subjected to tension is longitudinal, and the direction perpendicular to the surface of the waterproof layer is vertical; The calculation method includes the following steps: Calculate the vertical crack height H of the waterproof layer when cracks appear in the concrete using the following formula. cr : H cr =(α-βE e / s cr )ln(T cr )e λWcr E e / s cr , In the formula, α, β, and λ are all constants and all greater than 0, E e σ is the elastic modulus of the waterproof layer. cr T represents the tensile strength of the waterproof layer. cr W represents the longitudinal tensile thickness of the waterproofing layer at the location where the crack occurs. cr The longitudinal width of the crack on the concrete surface; The remaining uncracked thickness H of the waterproof layer is obtained by the following formula. re : H re =HH cr H represents the thickness of the waterproof layer.

2. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, The method for determining the constants α, β, and λ is as follows: S1. Take a waterproof layer segment with a longitudinal length of L, and perform finite element model meshing using hexahedral elements. Set a discrete crack interface element in the middle of the longitudinal direction of the waterproof layer segment. The nodes on both sides of the discrete crack interface element are coupled to the hexahedral element nodes that are closest to each other on both sides. S2. Let γ = 1, 0 < μ ≤ 0.2; S3. Apply forced displacements γμW in opposite directions and relatively far apart to the bottom surfaces of the hexahedral units on both sides of the discrete crack interface unit. cr / 2, and γμW cr / 2 is assigned the value of vector W. cr,γ The γth element; S4. Perform nonlinear finite element calculations and iterate until convergence to obtain the crack height of the discrete crack interface element and assign it to the vector H. cr,γ The γth element; S5. Let γ = γ + 1, if γμW cr / 2≤2W cr If yes, proceed to step S3; otherwise, proceed to step S6. S6. Transfer vector W cr,γ H cr,γ Substituting the H in claim 1 cr W in the calculation formula cr H cr After fitting using the least squares method, the values ​​of constants α, β, and λ were determined.

3. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, The T cr It is the average distance between material molecules or molecular clusters in the concrete.

4. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, When the concrete is silicate concrete, T cr =20nm.

5. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, The crack width W on the concrete surface cr Calculate W using the following formula: cr =W0(0.74h0+c s +d s / 2) / (0.74h0), where h0 is the distance from the center of the reinforcing bar to the compressive surface of the concrete, and c s d represents the thickness of the protective layer for the reinforcing steel. s Where W is the diameter of the reinforcing bar; W0 is the crack width of the concrete at the location of the reinforcing bar, and W0 = σ smax / E s ·[(c s +d s ) / (0.3+1.4ρ te )], where E s Let σ be the elastic modulus of the steel reinforcement. smax The maximum steel reinforcement stress that occurs during the use of the concrete and σ smax =M max / (0.87nπd s 2 / 4·h0), where n is the number of longitudinally stressed steel bars, and the direction perpendicular to both the longitudinal and vertical directions is defined as the transverse direction, M max ρ is the most unfavorable bending moment value of the transverse section at the concrete crack, calculated based on the basic load combination value under the ultimate limit state of bearing capacity. te The effective reinforcement ratio of longitudinal tensile reinforcement and ρ te =nπd s 2 / 4 / [2(c s +d s / 2)b], where b is the transverse dimension of the concrete transverse section.

6. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, The thickness H of the waterproof layer is the solid thickness of the waterproof layer after it has been cured and maintained.

7. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, The elastic modulus E of the waterproof layer e =σ 1％ / ε 1％ , σ 1％ ε represents the stress at 1% elongation during a uniaxial tensile test of the waterproof layer. 1％ The tensile strength σ of the waterproof layer is the strain at 1% elongation during a uniaxial tensile test. cr The total loading time for each uniaxial tensile test was calculated based on the average pre-fracture stress obtained from multiple uniaxial tensile tests, and did not exceed 1 minute.

8. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, When the waterproof layer is made of polymer-modified bitumen waterproof coating or polyurethane waterproof coating for roads and bridges, the constant α = 7.7 × 10⁻⁶. -4 β = 7.4 × 10 -4 λ = 20.

9. The method for calculating the stress of a waterproof layer in a concrete structure according to claim 1, characterized in that, The waterproof layer includes fiber-reinforced materials; K r BH cr σ cr / A r ≤f rd At that time, the final vertical crack height of the waterproof layer was c. r In the formula, K r For the safety factor and K r >1, define the direction perpendicular to the longitudinal and vertical directions as the transverse direction, B as the transverse width of the waterproof layer, A r f is the total cross-sectional area of ​​the fiber-reinforced material in the longitudinal direction within the transverse width B of the waterproof layer. rd c is the design tensile strength value of the fiber-reinforced material. r The distance from the fiber-reinforced material to the surface of the concrete beam.

10. A long-life design method for a waterproof layer of a concrete structure, wherein the long-life design method is implemented based on the stress calculation method for a waterproof layer of a concrete structure according to any one of claims 1-9, characterized in that, The long-life design method includes the following steps: S11. Based on the stress calculation method for the waterproof layer of the concrete structure, the cracking height H of the waterproof layer is calculated. cr Remaining uncracked thickness H re ; S12. If H re If H > 0, then let H min ≥H cr +K f H re K f For the safety factor and K f >1, let the designed thickness H of the waterproof layer after curing be... d ≥H min The waterproof layer design is now complete; if H re If ≤0, then go to S13; S13. Let H min ≥H-(1+K f )H re K f For the safety factor and K f >1, let the designed thickness H of the waterproof layer after curing be... d ≥H min The waterproofing layer design is now complete.

11. A method for designing and manufacturing a long-life waterproof layer for concrete structures, wherein the long-life design and manufacturing method is implemented based on the stress calculation method for waterproof layers of concrete structures according to claim 2, characterized in that, The long-life design and manufacturing method includes the following steps: S21. Then, at a distance c from the bottom surface of the hexahedral unit... r At the location, a linear elastic truss element sharing a node with the hexahedral element is established to simulate the effect of fiber-reinforced material; S22. Determine the values ​​of the constants α, β, and λ; S23. Calculate the vertical crack height H of the waterproof layer. cr Let the designed thickness H of the waterproof layer after curing be... d ≥K f H cr K f For the safety factor and K f >1. Complete the design of the waterproof layer; S24. Apply c evenly to the top surface of the concrete. r A thick waterproof layer is then applied, followed by the uniform application of fiber-reinforced material with the same cross-sectional dimensions, elastic modulus, and tensile / compressive constitutive parameters as the linear elastic truss unit. S25. Continue applying H. d -c r A thick waterproof layer completes the manufacturing of the waterproof layer.

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