Concrete structure waterproof layer stress calculation method and long-life design and manufacturing method

Abstract

According to the concrete structure waterproof layer stress calculation method, reinforcing steel bars are arranged in concrete, and the surface of the concrete is covered with a waterproof layer; the method comprises the steps that the cracking height Hcr of the waterproof layer during concrete cracking is calculated, Hcr = (alpha-beta Ee / sigma cr) ln (Tcr) e lambda WcrEe / sigma cr, sigma cr is the tensile strength of the waterproof layer, Tcr is the thickness of the waterproof layer in the tensile direction when a concrete crack occurs, and Wcr is the width of the concrete surface crack; and calculating the residual non-cracking thickness of the waterproof layer. The invention further provides a calculation method for setting the fiber reinforced material, a waterproof layer optimization design method and a manufacturing method. According to the method, key influence factors of the cracking height of the waterproof layer are clarified, and the optimization direction of various performance indexes of the waterproof material can be guided. The waterproof layer designed according to the invention still has a certain thickness after being torn due to cracking of concrete, so that erosion of water to a reinforced concrete structure is avoided, and the service life of the reinforced concrete structure is remarkably prolonged. The method is applicable to bridges, buildings, roads, tunnels and hydraulic structures.

Description

Technical Field

[0001] The present invention belongs to the following fields: concrete components in the field of general building structures, architectural design, design optimization and the use of finite element methods in the field of computer-aided design, protective devices for foundations or infrastructure, layered products composed of asphalt or tar substances in the field of layered products, adhesives based on asphalt materials in the field of adhesives, and coating compositions based on asphalt materials in the field of coating compositions; specifically, the present invention relates to the fields of waterproof calculation, design and manufacturing of general building structures such as buildings, bridges, roads, tunnels, and hydraulic structures, and in particular to a force calculation method and long-life design and manufacturing method for waterproof layers (including modified asphalt waterproof coatings, polyurethane waterproof coatings and waterproof membranes) of concrete structures (especially wet joints of prefabricated concrete structures and continuous beam bridges with simply supported bridge decks but no negative bending moment beams). Background Art

[0002] How to extend the life of concrete structures to more than 100 years and ensure their long-term working performance is safe, reliable and efficient has become a research hotspot today. Water is the most important factor affecting the durability of concrete structures. Reducing water erosion on reinforced concrete is of great significance to maintaining the long-term performance of various engineering structures, especially wet joints in prefabricated concrete structures (the low tensile strength at the interface between new and old concrete makes water seepage prone to occur) and continuous beam bridges with simply supported bridge decks but no negative bending moment tendons (excessive tensile stress in the negative bending moment zone leads to cracking and leakage). Taking bridge structures as an example, the original "JTJ 021-89 General Specifications for Highway Bridge and Culvert Design" did not have clear regulations on the installation of bridge deck waterproofing layers. Through nearly 30 to 40 years of engineering experience, especially the summary of a large number of experiences in the maintenance and reinforcement of old bridges in the past 10 to 20 years, it has been gradually recognized that the main causes of concrete bridge diseases are alkali-aggregate reaction caused by concrete carbonization, chloride ionization, alkali content and active aggregate, as well as frost heave damage of concrete and steel corrosion, and these are all factors closely related to water. Therefore, the installation of a waterproof layer has become an important means to reduce concrete bridge diseases and extend their service life. Therefore, in the "JTG D60-2004 General Specifications for Highway Bridge and Culvert Design", it was clearly stipulated for the first time that "a waterproof layer should be installed" in the bridge deck pavement.

[0003] However, even if a waterproof layer is set up, the performance requirements for the elongation at break of the waterproof layer material (waterproof membrane, polyurethane waterproof coating) in bridge design are usually as high as 450% or more, and the requirements for modified asphalt waterproof coating are as high as 800% or more. It can be seen that the elongation at break of the waterproof layer material is much greater than the ultimate tensile strain of steel bars (1%) and the ultimate tensile strain of concrete (0.01%). However, if Figure 1Even with densely reinforced concrete structures, cracking can still lead to water leakage, severely reducing the service life of the structure and requiring frequent repairs. Water damage at the continuous deck has become a common problem, especially for prefabricated concrete beam bridges with simply supported structures and continuous decks.

[0004] It can be seen that existing waterproof layers have not maintained the good performance expected by their design. The fundamental reason is that existing technologies still lack a clear method for calculating the stress on the waterproof layer when cracking occurs in reinforced concrete structures. This method does not consider the microscopic nature of concrete cracking and its impact on the waterproof layer, and does not use this basis to calculate the stress on the waterproof layer and conduct crack-resistant design and manufacturing to achieve long-term performance and extend its service life. Furthermore, the current national standard "GBT 16777-2008 Test Methods for Building Waterproof Coatings" for testing existing waterproof materials uses uniaxial tension and shear tests on separate waterproof layer specimens to measure tensile strength, shear strength, elongation at break, bond strength, low-temperature flexural strength, and impermeability. This method does not consider the interaction mechanism between concrete and the waterproof layer, particularly the sudden release of strain energy during the transient process of concrete cracking, which causes the waterproof layer to tear. Summary of the Invention

[0005] To solve the above problems, the present invention provides a stress calculation method for the waterproof layer of a concrete structure and a long-life design and manufacturing method. The method proposes the mechanism by which cracking of concrete leads to cracking of the waterproof layer, and provides a calculation formula for the vertical crack height of the waterproof layer of a concrete structure. This method can facilitate the waterproof calculation, design, and manufacturing of bridges and various reinforced concrete structures and achieve their long-term performance maintenance, thereby significantly extending their service life.

[0006] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0007] A method for calculating the stress of a waterproof layer of a concrete structure, wherein a steel bar 12 is provided in the concrete 1 and a waterproof layer 2 is covered on the surface of the concrete; the direction of tension along 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 comprises the following steps:

[0009] The vertical crack height H of the waterproof layer when the concrete crack 13 is calculated as follows: cr (Unit: mm):

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

[0011] Where α, β, and λ are all constants and are all greater than 0, e is a natural constant, and E e is the elastic modulus of the waterproof layer and the unit is MPa, σ cr is the tensile strength of the waterproof layer and the unit is MPa, T cr W is the thickness of the waterproof layer in the longitudinal direction when the crack appears and the unit is nm. cr is the longitudinal width of the crack on the concrete surface and the unit is 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] Where H is the thickness of the waterproof layer (in mm).

[0015] The technical principles and effects of the above invention are as follows: (1) The essence of concrete cracking is that the distance between the molecules of the concrete material on both sides of the crack suddenly changes from the nanometer level to the millimeter level visible to the naked eye, and the interface between the concrete and the waterproof layer is uneven at the microscopic level. The longitudinal interaction between the concrete and the waterproof layer includes the chemical adsorption force, static friction and mutual extrusion and bite force between the molecules of the two. Therefore, when the concrete cracks, the interfacial slip between the concrete surface and the waterproof layer can be basically ignored. Therefore, when the concrete crack opens to both sides, it will also drive the waterproof layer to open to both sides of the crack, that is, the tearing effect on the waterproof layer will occur at the moment of concrete cracking, so that the longitudinal distance between the molecules of the bottom surface material of the waterproof layer will also change from the nanometer level to the millimeter level. The vertical distance increases by nearly 100,000 times and appears as a crack visible to the naked eye. Of course, the increment of the longitudinal distance will decrease rapidly as the vertical distance between the waterproof layer molecules and the concrete surface increases. However, for the waterproof layer material near the concrete surface, its fracture elongation performance of only 800% is completely insufficient to withstand the nearly 100,000-fold increment of the longitudinal distance. Therefore, when the concrete cracks, the waterproof layer material near the surface will inevitably crack as well, and will stop cracking after the vertical cracking reaches a certain height. Therefore, the key to calculating the stress of the waterproof layer is to accurately calculate the crack height of the waterproof layer. Therefore, it is necessary to calculate the crack height of the waterproof layer of the reinforced concrete structure according to the present invention to accurately obtain its remaining uncracked thickness value H. re , so according to H re The remaining uncracked thickness can be used to determine whether it 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 not affected by the thickness H of the waterproof layer, the longitudinal segment length L (when L≥4H) taken when calculating the force 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) Figures 13-19 It can be seen that the calculation results of this formula are close to the refined nonlinear finite element results, and H cr All with W cr The increase in the crack height is exponential, and the 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 refined nonlinear finite element models. It also points out the direction for reducing the amount of waterproof materials used and lowering 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 of longitudinal length L and perform finite element model meshing using hexahedral units. Set a discrete crack interface unit in the longitudinal middle of the waterproof layer segment. The nodes on both sides of the discrete crack interface unit are coupled with the nodes of the hexahedral units closest to both sides.

[0018] S2. Let γ = 1, 0 < μ ≤ 0.2;

[0019] S3. Apply forced displacements γμW in opposite directions and relatively far away from each other 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 to vector W cr,γ the γth element of ;

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

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

[0022] S6. Vector W cr,γ 、H cr,γ Substitute the above H cr W in the calculation formula cr 、H cr , and after fitting using the least squares method, the values ​​of constants α, β, and λ are determined.

[0023] The technical principle and effect of the above invention are: the cracking of concrete is equivalent to applying various W to the bottom surface of the waterproof layer on both sides of the crack. cr / 2 forced displacement (combined with the attached Figure 3 Schematic diagram of the mechanism of concrete cracking causing waterproof layer cracking), which is the essential mechanism of concrete cracking leading to waterproof layer cracking; it should be noted that the crack height of the waterproof layer caused by the forced displacement needs to be iteratively calculated according to steps S1 to S4 in order to be accurately solved; combined with the attached Figures 13-19 It can be seen that this formula can be used to fit the refined nonlinear finite element results 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: when calculating from a safe perspective, T cr Take a smaller value to calculate the stress on the waterproof layer. At this time, we can consider it according to the limit principle, that is, assuming that the interaction force between the molecules or clusters of concrete material and the most adjacent molecules or clusters of waterproof layer is infinite, and there will be no interface separation or slip between the two. At this time, the essence of the cracking of concrete and waterproof layer is that the longitudinal distance between its molecules or clusters suddenly changes from nanometer level to millimeter level, that is, the distance increases by nearly 100,000 times and appears as cracks visible to the naked eye. Therefore, it is safe to use the thickness of the waterproof layer in the longitudinal tension T cr It is taken as the mean distance between material molecules or molecular clusters in concrete. The mean can be obtained by measuring and averaging simple random sampling using equipment such as atomic force microscope and scanning electron microscope.

[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 is found that T cr The smaller the value, the higher the crack height H of the waterproof layer. cr The larger (combined with the Figure 10 It can be seen that T cr For H cr The thickness of the waterproof layer in the longitudinal direction at the moment of initial cracking of the concrete has a significant effect on the final cracking height of the waterproof layer; (2) When T cr When the size is as small as 100nm, H cr The value of tends to be constant, that is, T cr The value of H crThe influence of T is small. Considering that the scale of 20 nm is close to the scale of cement stone voids or hydrated calcium silicate gel in silicate concrete, when the distance measurement between material molecules or molecular clusters in concrete is more complicated, it can also be simplified to T cr = 20nm to calculate the stress on the waterproof layer.

[0028] Preferably, the crack width W on the concrete surface is cr Calculate as follows: W cr =W0(0.74h0+c s +d s / 2) / (0.74h0), where h0 is the distance from the center of the steel bar to the compressive surface of the concrete, c s is the thickness of the steel bar cover, d s is the diameter of the steel bar; W0 is the width of the concrete crack at the steel bar position, and W0 = σ smax / E s ·[(c s +d s ) / (0.3+1.4ρ te )], where E s is the elastic modulus of the steel bar, σ smax is the maximum reinforcement stress that occurs during the use of the concrete structure and σ smax =M max / (0.87nπd s 2 / 4·h0), n is the number of longitudinal stress reinforcement, and the direction perpendicular to the longitudinal and vertical directions is defined as the transverse direction, M max is the most unfavorable bending moment value of the transverse section at the concrete crack calculated according to the basic load combination value under the ultimate bearing capacity state, ρ te is the effective reinforcement ratio of the longitudinal tensile reinforcement and ρ te =nπd s 2 / 4 / [2(c s +d s / 2)b], b is the transverse dimension of the concrete transverse 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 steel bar position, combined with the attached Figure 2 Middle W crFrom the calculation diagram, we can see that the internal force arm of the steel bar of the reinforced concrete bending member is generally taken as 0.87h0, that is, the distance from the steel bar to the line of action of the resultant force in the concrete compression zone is 0.87h0. It can be deduced that the crack height of the concrete crack is 0.87h0-(1-0.87h0)=0.74h0. Considering that the elastic modulus of concrete material is large (much larger than that of waterproof material), it can be considered that the gap after the concrete crack is approximately triangular. Therefore, according to the geometric relationship of similar triangles, W can be deduced. 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 develop 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 the concrete crack, the "frequent load combination value used to check the durability of the structure" is generally used, rather than the "basic load combination value used to check the bearing capacity of the structure" - and the cracking of the waterproof layer is mainly a problem of crack height. The higher the crack develops in the waterproof layer, the worse the anti-seepage performance of the waterproof layer. Moreover, when the crack width of the reinforced concrete structure returns to a smaller width value, the crack height of the waterproof layer will not recover. Therefore, for the calculation of the crack height and force of the waterproof layer, the W corresponding to the most unfavorable load basic combination value borne by the reinforced concrete structure below should be used. cr Perform calculations.

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

[0031] The technical principle and effect of the above invention are as follows: the design and construction of the waterproof layer in the existing technology are controlled according to the liquid thickness after the application. However, the actual waterproof layer has already become solid when the concrete structure is subjected to stress and cracks. As the moisture or other organic solvent components of most waterproof coatings evaporate, the thickness after solidification can be reduced by more than 30% compared with the liquid thickness. Therefore, when the stress is calculated according to the liquid design thickness value of the existing technology, there will be significant errors in the results. Therefore, it should be calculated according to the solid thickness after solidification and maintenance.

[0032] Preferably, the elastic modulus E of the waterproof layer e =σ 1％ / ε 1％ , σ 1％ , ε 1％ are respectively the stress and strain at 1% elongation when the waterproof layer is subjected to a uniaxial tensile test, and the tensile strength σ of the waterproof layer cr The total loading time of each uniaxial tensile test shall not exceed 1 minute, calculated based on the average stress before fracture measured by multiple uniaxial tensile tests.

[0033] The technical principles and effects of the above invention are as follows: when concrete cracks, the cracking of the waterproof layer is a transient process, during which the nonlinear creep of the waterproof material is very small. The waterproof material in the compression zone basically exhibits linear elastic stress characteristics, and its elastic modulus can be calculated by dividing the stress by the strain under small deformation. 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 asphalt waterproof coating or polyurethane waterproof coating for roads and bridges, the constant α is 7.7×10 -4 β=7.4×10 -4 ,λ=20.

[0035] The technical principle and effect of the above invention are as follows: for the two most common bridge deck waterproof materials, the refined nonlinear finite element simulation results after correction based on the experimental measured 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 the refined nonlinear finite element results, 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 When the final vertical crack height of the waterproof layer is c r , where K r is the safety factor and K r >1, the direction perpendicular to the longitudinal and vertical directions is defined as the transverse direction, B is 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 is the design tensile strength value of the fiber reinforced material, c r is the distance from the fiber reinforcement 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 crack height H of the waterproof layer when no fiber-reinforced material is provided. cr The tensile force within the range will not be broken, so when the waterproof layer cracks to the height of the fiber reinforced material, the crack will no longer expand upwards. The actual crack height of the waterproof layer should be corrected to c r(2) After the fiber reinforcement material is set, the cracking mode and trend of the waterproof layer are changed, and the "vertical tearing trend" of the waterproof layer is changed to the "longitudinal peeling trend along the fiber reinforcement material", ensuring that the waterproof layer still has a large uncracked thickness, thereby significantly improving the crack resistance and waterproof performance of the waterproof layer. Figure 21 The refined nonlinear finite element calculation results also reflect this feature; (3) Figure 13 ~Attachment Figure 19 It can be seen that H cr With W cr It increases exponentially with the increase of the concrete crack, indicating that when the concrete crack is wider, the cost-effectiveness of thickening the waterproof layer to enhance the waterproof performance is relatively low. At this time, priority should be given to setting fiber-reinforced materials to improve the waterproof performance.

[0038] The present invention also proposes a long-life design method for a concrete structure waterproof layer. The long-life design method is implemented based on the above-mentioned concrete structure waterproof layer, and the long-life design method includes the following steps:

[0039] S11. According to the above-mentioned concrete structure waterproof layer stress calculation method, calculate the crack height H of the waterproof layer cr , Remaining uncracked thickness H re ;

[0040] S12. If H re >0, then let H min ≥H cr +K f H re , K f is the safety factor and K f >1, and when designing the waterproof layer, the thickness value H after the waterproof layer is cured is required d Not less than H min , end the waterproof layer design; if H re ≤0, go to S13;

[0041] S13. Let H min ≥H-(1+K f )H re , K f is the safety factor and K f >1, and when designing the waterproof layer, the thickness value H after the waterproof layer is cured is required d Not less than H min , ending the waterproof layer design.

[0042] The technical principles and effects of the above invention are as follows: the existing technology does not take into account the tearing effect of concrete on the waterproof layer at the moment of cracking, which leads to water leakage at the cracks after the concrete cracks, seriously reducing the service life of the structure and waterproof layer at that location and requiring frequent maintenance. Therefore, ensuring that the waterproof layer still has a certain thickness surplus after being torn by concrete is the key to achieving its long-life design. The long-life design method of the present invention can significantly extend the life of reinforced concrete structures, thereby greatly reducing the maintenance and operation costs of various structures.

[0043] The present invention also proposes a long-life design and manufacturing method for a concrete structure waterproof layer. The long-life design and manufacturing method is implemented based on the above-mentioned force calculation method for a concrete structure waterproof layer. The long-life design and manufacturing method includes the following steps:

[0044] S21. Execute the above step S1, and then at a distance c from the bottom surface of the above hexahedral unit r A linear elastic truss element sharing a common node with the hexahedral element is established at a position to simulate the influence of the fiber-reinforced material;

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

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

[0047] S24. Apply c evenly on the top surface of the concrete r A waterproof layer of thickness is formed, and then a fiber reinforcement material having the same cross-sectional size, elastic modulus and tension and compression constitutive parameters as those of the linear elastic truss unit is evenly spread;

[0048] S25. Continue to paint H d -c r The waterproof layer of thickness is completed.

[0049] The technical principles and effects of the above invention are: 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 conducive to the full curing of the waterproof layer, and can better control the vertical position of the fiber-reinforced material, thereby giving full play to its anti-cracking effect to save the amount of waterproof layer material.

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

[0051] 1. Based on the essential mechanism of cracking of the waterproof layer caused by cracking of concrete, the present invention provides a force calculation method and a long-life design method for the waterproof layer of the concrete structure, ensuring that the waterproof layer still has a certain thickness surplus after being torn due to the cracking of the concrete. The mechanism proposed by the present invention is the key issue ignored by the existing technology and is also the key to significantly extending the life of reinforced concrete structures. The use of the method of the present invention can greatly reduce the maintenance and operation costs of concrete components of various general building structures (especially wet joints of prefabricated concrete structures and continuous beam bridges with simple support and then bridge deck without negative bending moment tendons).

[0052] Second, the present invention found that when cracks appear, the longitudinal tensile thickness T of the waterproof layer at that location cr The final crack height H of the waterproof layer close to the nanoscale cr The calculated results tend to be constant, proving that H cr It is basically not affected by the thickness H of the waterproof layer, the longitudinal segment length L (when L≥4H) taken when calculating the force of the waterproof layer, and the Poisson's ratio v of the waterproof layer.

[0053] 3. The present invention discovered that H cr With W cr It increases exponentially with the increase of the thickness of the waterproof layer, indicating that when the concrete cracks are wider, the cost-effectiveness of thickening the waterproof layer to enhance the waterproof performance is relatively low. At this time, the setting of fiber-reinforced materials should be given priority. It was also found that when the fiber-reinforced materials were set, the cracking mode and trend of the waterproof layer were changed, and the "vertical tearing trend" of the waterproof layer was changed to the "longitudinal peeling trend along the fiber-reinforced material", thereby ensuring that after the crack height of the waterproof layer develops to the fiber-reinforced material, it is basically no longer affected by the widening of the concrete cracks, and the cracks no longer expand vertically, thereby significantly improving the crack resistance and waterproof performance of the waterproof layer.

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

[0055] 5. The calculation formula of the present 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 asphalt waterproof coatings, polyurethane waterproof coatings and waterproof membranes), thereby quickly realizing the force calculation and design optimization of waterproof layers of various concrete structures, achieving the reduction of waterproof material usage and cost savings. It is applicable to concrete structures in multiple industries such as bridges, roads, tunnels, buildings, and hydraulic engineering. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0057] Figure 2 This invention W cr Schematic diagram of the calculation;

[0058] Figure 3 Schematic diagram of the mechanism of cracking of the waterproof layer caused by cracking of concrete according to the present invention;

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

[0060] Figure 5 The initial finite element model of the embodiment of the present invention is W cr Schematic diagram of deformation when =0.1mm;

[0061] Figure 6 The initial finite element model of the embodiment of the present invention is W cr Schematic diagram of deformation when =0.18mm;

[0062] Figure 7 The initial finite element model of the embodiment of the present invention is W cr = 0.18 mm (showing only the units near the crack);

[0063] Figure 8 The initial finite element model of the embodiment of the present invention is W cr =0.18mm when T cr Schematic diagram of the element longitudinal stress in the region;

[0064] Figure 9 The initial finite element model of the embodiment of the present invention is W cr Schematic diagram of deformation when =0.2mm;

[0065] Figure 10 The initial finite element model of the embodiment of the present invention is shown in FIG. cr Schematic diagram of the comparison of cracking results under ;

[0066] Figure 11 2 is a schematic diagram comparing the cracking results of the initial finite element model of an embodiment of the present invention under different longitudinal lengths L;

[0067] Figure 12 3. This is a schematic diagram comparing the cracking results of the initial finite element model of an embodiment of the present invention at different vertical thicknesses H;

[0068] Figure 13 The initial finite element model of the embodiment of the present invention is in σ cr =0.5MPa,εcr =800%, E e = 1.0 MPa when the calculation results of the finite element method are compared with the calculation results of the formula of the present invention;

[0069] Figure 14 The initial finite element model of the embodiment of the present invention is in σ cr =0.5MPa,ε cr =800%, E e = 0.8MPa when the calculation results of the finite element method are compared with the calculation results of the formula of the present invention;

[0070] Figure 15 The initial finite element model of the embodiment of the present invention is in σ cr =0.5MPa,ε cr =800%, E e =1.2MPa when the calculation results of the finite element method are compared with the calculation results of the formula of the present invention;

[0071] Figure 16 The initial finite element model of the embodiment of the present invention is in σ cr =1.0MPa,ε cr =800%, E e =2.2MPa when the calculation results of the finite element method are compared with the calculation results of the formula of the present invention;

[0072] Figure 17 The initial finite element model of the embodiment of the present invention is in σ cr =1.0MPa,ε cr =800%, E e =1.8MPa when the calculation results of the finite element method are compared with the calculation results of the formula of the present invention;

[0073] Figure 18 The initial finite element model of the embodiment of the present invention is in σ cr =2.45MPa,ε cr =450%, E e =4.0MPa when the calculation results of the finite element method are compared with the calculation results of the formula of the present invention;

[0074] Figure 19 The initial finite element model of the embodiment of the present invention is in the condition of σcr=2.45MPa, ε cr =450%, E e =6.0MPa when the calculation results of the finite element method are compared with the calculation results of the formula of the present invention;

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

[0076] Figure 21 The initial finite element model of the embodiment of the present invention is added with fiber reinforcement material in W cr Schematic diagram of deformation when =0.2mm;

[0077] Figure 22 The initial finite element model of the embodiment of the present invention is added with fiber reinforcement material in W cr Schematic diagram of fiber stress when =0.2mm;

[0078] Figure 23 This is a photo of the cracking test loading of the fiber-free waterproof layer;

[0079] Figure 24 It is a photo of cracks and water leakage in the fiber-free waterproof layer;

[0080] Figure 25 These are photos of the cracking test of the fiber-containing waterproof layer and the structural cracking situation.

[0081] Description of reference numerals:

[0082] 1. Concrete; 12. Steel bars; 13. Cracks; 14. T in the middle of the waterproofing layer segment cr Planar unit of the region; 15, fiber reinforcement material; 2, waterproof layer; 21, middle part of waterproof layer segment T cr The waterproof layer grid on the left side of the area; 22. T in the middle of the waterproof layer segment cr Waterproof layer grid 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 , the vertical crack height of the waterproof layer. DETAILED DESCRIPTION

[0083] The present invention is further described in detail below in conjunction with test examples and specific implementation methods, but this should not be understood as the scope of the above-mentioned subject matter of the present invention being limited to the following embodiments. All technologies implemented based on the contents of the present invention belong to the scope of the present invention.

[0084] Example A

[0085] The present invention provides a method for calculating the stress of a waterproof layer of a concrete structure, wherein a steel bar 12 is provided in the concrete 1, and a waterproof layer 2 is covered on the surface of the concrete 1; the tensile direction along the concrete 1 is the longitudinal direction, and the direction perpendicular to the surface of the waterproof layer 2 is the vertical direction; the calculation method comprises the following steps:

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

[0087] H cr =(α-βE e / σ cr )ln(T cr )e λWcr E e / σ cr , where α, β, and λ are all constants and are all greater than 0, e is a natural constant, and E e is the elastic modulus of the waterproof layer 2 and the unit is MPa, σ cr is the tensile strength of the waterproof layer 2 and the unit is MPa, T cr W is the thickness of the waterproof layer 2 in the longitudinal direction when the crack 13 appears and the unit is nm. cr is the longitudinal width of the crack 13 on the surface of the concrete 1 and the unit is mm; the remaining uncracked thickness H of the waterproof layer 2 is obtained by the following formula re :H re =HH cr , H is the thickness of the waterproof layer 2 and the unit is mm.

[0088] In this embodiment, the force calculation method for the waterproof layer of the concrete structure is based on the fact that water erosion is the most important factor affecting the durability of reinforced concrete structures. Reducing water erosion on reinforced concrete structures can significantly extend the service life of reinforced concrete structures. The force calculation method for the waterproof layer of the concrete structure is based on the mechanism of the cracking of concrete 1 leading to the cracking of waterproof layer 2. Studies have found that the essence of the cracking of concrete 1 is that the distance between the molecules of the concrete 1 material on both sides of the crack 13 suddenly changes from the nanometer level to the millimeter level visible to the naked eye, and the interface 3 between the concrete 1 and the waterproof layer 2 is microscopically uneven. The longitudinal interaction between concrete 1 and the waterproof layer 2 includes the chemical adsorption force between the molecules of the two, static friction resistance and mutual extrusion and bite force. Therefore, when the concrete 1 cracks, the slippage of the interface 3 between the surface of the concrete 1 and the waterproof layer 2 can be basically ignored. Therefore, when the concrete crack 13 opens to both sides, it will also drive the waterproof layer 2 to open to both sides of the crack 13, that is, the moment the concrete 1 cracks, A tearing effect occurs on the waterproof layer 2, causing the longitudinal distance between the molecules of the bottom surface 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 cracks 13 visible to the naked eye. Of course, the increment of this longitudinal distance will decrease rapidly as the vertical distance between the waterproof layer 2 molecules and the surface of the concrete 1 increases. However, for the waterproof layer 2 material near the surface of the concrete 1, its fracture elongation performance of only 800% is completely insufficient to withstand the nearly 100,000-fold increment of the longitudinal distance. Therefore, when the concrete 1 cracks, the waterproof layer 2 material near its surface will inevitably crack as well, and stop cracking after the vertical cracking reaches a certain height. Therefore, the key to the force calculation of the waterproof layer lies in accurately calculating the crack height of the waterproof layer 2.

[0089] Therefore, it is necessary to calculate the crack height of the waterproof layer 2 of the reinforced concrete structure according to the present invention to accurately obtain the remaining uncracked thickness value H re , so according to H re The value is used to judge 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 the concrete 1, a certain thickness is retained so that the waterproof layer 2 can still play a waterproof role after the reinforced concrete structure is cracked, thereby significantly extending the life of the reinforced concrete structure and greatly reducing the maintenance and operation costs of various structures.

[0090] Moreover, combined with the Figures 11-12 It can be seen that H cr The calculation results are basically not affected by the thickness H of the waterproof layer 2, the longitudinal segment length L (when L≥4H) taken when calculating the force of the waterproof layer, and the Poisson's ratio v of the waterproof layer 2. Therefore, these parameters have no significant effect on H. cr The calculation results do not have any impact, so they do not need to be reflected in the calculation formula. Figures 13-19 It can be seen that the calculation results of this formula are close to the refined nonlinear finite element results, and H cr All with W cr The formula shows an exponential increase with increasing crack height, and its calculation accuracy is sufficiently high. This formula clearly defines and quantifies the impact of various waterproofing material performance indicators on crack height, effectively avoiding the excessive calculation time required when using refined nonlinear finite element models. It also points the way to reducing waterproofing material usage and lowering project costs by improving its performance indicators. For example, the required design thickness of waterproof layer 2 can be reduced by changing the elastic modulus and tensile strength of the waterproofing material.

[0091] In summary, this calculation formula clarifies the key factors affecting the crack height of the waterproof layer 2, including the elastic modulus and tensile strength of the waterproof material, and clearly guides the optimization direction of various performance indicators of the waterproof material. It can thus quickly realize the force calculation and design optimization of the waterproof layer 2 of various concrete structures, achieve the reduction of waterproof material usage and cost savings, and is applicable to concrete 1 structures 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 of longitudinal length L and use hexahedral units to mesh the finite element model. Set a discrete crack interface unit in the longitudinal middle of the waterproof layer segment 2. The nodes on both sides of the discrete crack interface unit are coupled with the closest hexahedral unit nodes on both sides.

[0094] S2. Let γ = 1, 0 < μ ≤ 0.2;

[0095] S3. Apply forced displacements γμW in opposite directions and relatively far away from each other 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 to vector W cr,γ the γth element of ;

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

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

[0098] S6. Vector W cr,γ 、H cr,γ Substitute H cr W in the calculation formula cr 、H cr , and after fitting using the least squares method, the values ​​of constants α, β, and λ are determined.

[0099] In this embodiment, 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 (combined with the attached Figure 3 Schematic diagram of the mechanism of concrete cracking causing waterproof layer cracking), which is the essential mechanism of concrete cracking leading to waterproof layer cracking; it should be noted that the crack height of the waterproof layer caused by the forced displacement needs to be iteratively calculated according to steps S1 to S4 in order to be accurately solved; combined with the attached Figures 13-19 It can be seen that this formula can be used to fit the refined nonlinear finite element results well, thereby determining the values ​​of constants α, β, and λ.

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

[0101] In addition, in order to ensure safety during the calculation process, T crTake a smaller value to calculate the stress on the waterproof layer. At this time, we can consider it according to the limit principle, that is, assume that the interaction force between the molecules or clusters of concrete 1 and the molecules or clusters of the most adjacent waterproof layer 2 is infinite, and there will be no interface 3 separation or slip between the two. At this time, the essence of the cracking of concrete 1 and waterproof layer 2 is that the longitudinal distance between their molecules or clusters suddenly changes from the nanometer level to the millimeter level, that is, the distance increases by nearly 100,000 times and appears as cracks visible to the naked eye 13. Therefore, it is safe to set the thickness of the waterproof layer 2 in the longitudinal tension direction T cr The distance between the material molecules or molecular clusters in the concrete 1 is taken as the average value, which can be obtained by measuring and averaging simple random sampling using equipment such as an atomic force microscope and a scanning electron microscope.

[0102] Furthermore, when the concrete 1 is silicate concrete 1, T cr =20nm. Figure 10 As shown in the calculation, it is found that T cr The smaller the value, the higher the crack height H of the waterproof layer 2. cr The larger the T cr For H cr The thickness of the waterproof layer 2 in the longitudinal direction at the moment of initial cracking of the concrete 1 has a significant effect on the final cracking height of the waterproof layer 2. cr When the size is as small as 100nm, H cr The value of tends to be constant, that is, T cr The value of H cr The influence of is already small. Considering that the scale of 20 nm is close to the scale of cement stone voids or hydrated calcium silicate gel in silicate concrete 1, when the distance measurement between material molecules or molecular clusters in concrete 1 is more complicated, it can also be simplified to T cr = 20nm to calculate the stress on the waterproof layer.

[0103] like Figure 2 As shown, the width W of the crack 13 on the surface of the concrete 1 is cr Calculate as follows: W cr =W0(0.74h0+c s +d s / 2) / (0.74h0), where h0 is the distance from the center of the steel bar 12 to the compressive surface of the concrete 1, c s is the protective layer thickness of steel bar 12, d s is the diameter of the steel bar 12; W0 is the width of the crack 13 in the concrete 1 at the steel bar 12, and W0 = σ smax / E s ·[(c s +d s ) / (0.3+1.4ρ te )], where E sis the elastic modulus of steel bar 12, σ smax is the maximum reinforcement stress that occurs during the use of concrete 1 and σ smax =M max / (0.87nπd s 2 / 4·h0), n is the number of longitudinally stressed steel bars, and the direction perpendicular to the longitudinal and vertical directions is defined as the transverse direction, M max is the most unfavorable bending moment value of the transverse section at the concrete crack 13 calculated according to the basic load combination value under the ultimate bearing capacity state, ρ te is the effective reinforcement ratio of the longitudinal tensile reinforcement 12 and ρ te =nπd s 2 / 4 / [2(c s +d s / 2)b], 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 position of the steel bar 12. Figure 2 -W cr From the calculation diagram, we can see that the internal force arm of the steel bar 12 of the steel bar 12 concrete 1 bending member 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 the concrete 1 is 0.87h0. It can be deduced that the crack height of the concrete crack 13 is 0.87h0-(1-0.87h0)=0.74h0. Considering that the elastic modulus of the concrete 1 material is large, its elastic modulus is much greater than that of the waterproof material, it can be considered that the gap after the crack of the concrete 1 is approximately triangular. Therefore, according to the geometric relationship of similar triangles, W can be deduced. cr =W0(0.74h0+c s +d s / 2) / (0.74h0);

[0105] However, the cracking of the waterproof layer 2 is different from the cracking of the reinforced concrete structure. Under the most unfavorable load combination, although the crack 13 of the reinforced concrete structure will expand to a larger width value, the crack 13 will be pulled back to a smaller width value by the steel bar 12 after the load is unloaded due to the elasticity of the steel bar 12. The width of the crack 13 mainly affects the durability of the steel bar 12. Therefore, when verifying the width of the concrete crack 13, the "frequent load combination value used to verify the durability of the structure" is generally used instead of the "basic load combination value used to verify the bearing capacity of the structure". The cracking of the waterproof layer 2 is mainly a problem of the height of the crack 13. The higher the crack 13 expands in the waterproof layer 2, the worse the anti-seepage performance of the waterproof layer 2. Moreover, when the width of the crack 13 of the reinforced concrete structure recovers to a smaller width value, the height of the crack 13 of the waterproof layer 2 will not recover. Therefore, the height and force calculation of the crack 13 of the waterproof layer 2 should be based on the W corresponding to the most unfavorable load basic combination value borne by the reinforced concrete structure below. cr Perform calculations.

[0106] Furthermore, the thickness H of the waterproof layer 2 is the solid thickness of the waterproof layer 2 after curing and maintenance. e =σ 1％ / ε 1％ ,σ 1％ is the stress at 1% elongation during uniaxial tensile test of waterproof layer 2, ε 1％ The tensile strength σ of the waterproof layer 2 is the strain at 1% elongation during the uniaxial tensile test. cr The total loading time of each uniaxial tensile test shall not exceed 1 minute, calculated based on the average stress before fracture measured by multiple uniaxial tensile tests.

[0107] In this embodiment, the conventional waterproof layer 2 is designed and constructed based on its liquid thickness after application. However, the actual waterproof layer 2 is already in a solid state when the concrete 1 structure is subjected to stress and cracking. Most waterproof coatings can reduce their thickness by more than 30% after curing, as their water or other organic solvent components evaporate. Therefore, using the conventional liquid design thickness for stress calculations will result in significant error. Therefore, calculations should be based on the solid thickness after curing and curing. In the elastic modulus measurement test of the waterproof layer 2, since cracking of the concrete 1 is a transient process, the nonlinear creep of the waterproof material is minimal during this process. The waterproof material in the pressure zone exhibits essentially linear elastic stress characteristics. Therefore, its elastic modulus can be calculated as the stress divided by the strain under small deformation. However, the loading time of the uniaxial tensile test should be kept short to minimize errors caused by creep effects.

[0108] In a preferred embodiment, when the waterproof layer 2 is made of polymer modified asphalt waterproof coating or polyurethane waterproof coating for roads and bridges, the constant α is 7.7×10-4 β=7.4×10 -4 ,λ=20. For the two most common bridge deck waterproof materials, the refined nonlinear finite element simulation results based on the test data were found to be corrected according to α=7.7×10 -4 β=7.4×10 -4 When λ=20, the calculation results of this formula are close to the refined nonlinear finite element results, and its calculation accuracy is high enough.

[0109] like Figure 13-19 As shown, the waterproof layer 2 includes a fiber reinforcement material 15; K r BH cr σ cr / A r ≤f rd When the final vertical crack height of waterproof layer 2 is c r , where K r is the safety factor and K r >1, the direction perpendicular to the longitudinal and vertical directions is defined as the transverse direction, B is the transverse width of the 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 is the design tensile strength value of the fiber reinforced material 15, c r is the distance from the fiber reinforced material 15 to the surface of the concrete 1 beam.

[0110] In this embodiment, when the total cross-sectional area of ​​the fiber reinforcement material 15 is large, the fiber reinforcement material 15 will bear the crack height H of the waterproof layer 2 when the fiber reinforcement material 15 is not provided. cr The tensile force within the range will not be broken, so when the waterproof layer 2 cracks to the height of the fiber reinforcement material 15, the crack 13 will no longer expand upwards, and the actual crack height of the waterproof layer 2 should be corrected to c r The provision of the fiber reinforcement material 15 is equivalent to changing the cracking mode and tendency of the waterproof layer 2, changing the "vertical tearing tendency" of the waterproof layer 2 to the "longitudinal peeling tendency along the fiber reinforcement material 15", ensuring that the waterproof layer 2 still has a large uncracked thickness, thereby significantly improving the crack resistance and waterproof performance of the waterproof layer 2, and Figure 21 The refined nonlinear finite element calculation results also reflect this feature; in summary, it can be found that H cr With W crThe increase in the thickness of the waterproof layer 2 increases exponentially, indicating that when the concrete crack 13 is wide, thickening the waterproof layer 2 to enhance its waterproofing performance is relatively cost-effective. In this case, the installation of fiber-reinforced material 15 should be prioritized. Furthermore, it was found that the installation of fiber-reinforced material 15 altered the cracking pattern and trend of the waterproof layer 2, transforming the waterproof layer 2's "trend of vertical tearing" into a "trend of longitudinal peeling along the fiber-reinforced material 15." This ensures that after the crack height of the waterproof layer 2 reaches the fiber-reinforced material 15, it is essentially no longer affected by the widening of the concrete crack 13, and the crack 13 no longer expands vertically, thereby significantly improving the crack resistance and waterproofing performance of the waterproof layer 2. Furthermore, the present invention provides a simple calculation formula for the crack height of the waterproof layer 2 with and without fiber-reinforced material 15, which effectively avoids the problem of excessive computational time when using a refined nonlinear finite element model.

[0111] Example B

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

[0113] S11. According to the concrete structure waterproof layer stress calculation method, calculate the crack height H of waterproof layer 2 cr , Remaining uncracked thickness H re ;

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

[0115] S13. Let H min ≥H-(1+K f )H re , K f is the safety factor and K f >1, and when designing the waterproof layer 2, the thickness value H after the waterproof layer 2 is cured is required d Not less than H min , ending the waterproof layer 2 design.

[0116] In this embodiment, the prior art does not take into account the tearing effect of the concrete 1 on the waterproof layer 2 at the moment of cracking, which results in water leakage at the crack 13 even after the concrete 1 cracks, seriously reducing the service life of the reinforced concrete structure and the waterproof layer 2 at that location, and causing the reinforced concrete structure and the waterproof layer 2 at that location to require frequent maintenance. Therefore, ensuring that the waterproof layer 2 still has a certain thickness surplus after being torn by the concrete 1 is the key to achieving its long-life design. The long-life design method of the present invention can ensure that the waterproof layer 2 still has a certain thickness surplus after being torn by the concrete 1, thereby ensuring the waterproof performance of the waterproof layer 2, preventing the reinforced concrete structure from being eroded by water, and significantly extending the life of the reinforced concrete structure, thereby greatly reducing the maintenance and operation costs of various structures.

[0117] Example C

[0118] The present invention also proposes a long-life design and manufacturing method for a concrete structure waterproof layer. The long-life design and manufacturing method is implemented based on the above-mentioned force calculation method for a concrete structure waterproof layer. The long-life design and manufacturing method includes the following steps:

[0119] S21. Take a waterproof layer segment of longitudinal length L and divide it into finite element model meshes using hexahedron units. Set a discrete crack interface unit in the longitudinal middle of the waterproof layer segment. The nodes on both sides of the discrete crack interface unit are coupled with the nodes of the hexahedron units closest to both sides. Then, at a distance of c from the bottom surface of the finite element model mesh, r Establishing a linear elastic truss unit having a common node with the finite element model grid at a position to simulate the influence of the fiber reinforced material;

[0120] S22. Execute 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 vertical crack height H of the waterproof layer is obtained by calculation cr , let the thickness of the waterproof layer after curing be designed to be H d ≥K f H cr , K f is the safety factor and K f >1. Complete the design of the waterproof layer;

[0122] S24. Apply c evenly on the top surface of the concrete r A waterproof layer of thickness is formed, and then a fiber reinforcement material having the same cross-sectional size, elastic modulus and tension and compression constitutive parameters as those of the linear elastic truss unit is evenly spread;

[0123] S25. Continue to paint H d -c rThe waterproof layer of thickness is completed.

[0124] In this embodiment, 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 in finite element calculations and obtain the corresponding values ​​of α, β, and λ; and the manufacturing method of layered coating is beneficial to the full curing of the waterproof layer and can better control the vertical position of the fiber-reinforced material, thereby giving full play to its anti-cracking effect to save the amount of waterproof layer material.

[0125] Example D

[0126] In order to verify the technical effect of the present invention, a waterproof layer segment with a longitudinal length of L = 10 mm, a vertical thickness of H = 1 mm, and a transverse width of B = 1 mm was selected to establish a refined initial finite element model as shown in FIG. Figure 4 As shown in Figure 1, the main modeling parameters are as follows: (1) Boundary: Assuming that the concrete crack 13 appears in the longitudinal middle of the waterproof layer 2 segment, concrete 1 is a vertical rigid constraint on the waterproof layer 2, that is, a vertical rigid support is set on the bottom surface of the waterproof layer 2 to simulate the vertical constraint of concrete 1 on the waterproof layer 2; (2) Grid: The average value of the distance between material molecules or molecular clusters in concrete 1 is 20nm, that is, the thickness T of the waterproof layer 2 in the longitudinal direction at the moment when concrete 1 initially cracks. cr = 20nm, so the longitudinal length T of the middle part of the waterproof layer 2 segment cr The area with a vertical height of H is divided into grids using a plane unit with a longitudinal length of 20 mm and a vertical height of 0.01 mm. cr The plane stress unit grid size of the waterproof layer 2 near the plane unit 14 in the area is 0.01mm×0.01mm, and the grid size farther away is thickened to 0.05mm×0.01mm to reduce the calculation amount of the finite element analysis; (3) Material: Elongation at break ε of the waterproof layer 2 material cr =800% and tensile strength σ cr =0.5MPa (equivalent to the performance parameters of the common PB-I type polymer modified asphalt waterproof coating 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 area reaches 800%×T cr When the stiffness value of the corresponding unit suddenly changes to 0, it is equivalent to the occurrence of brittle cracking and the deletion of the unit at the corresponding position. At this time, the longitudinal tensile stress of the corresponding unit also suddenly changes to 0; (4) Load: For T cr All nodes on the bottom surface of the waterproof layer 2 segment on the left side of the area are applied with W to the left. cr / 2 forced displacement, and W is applied to the bottom surface of the waterproof layer 2 on the right side. cr / 2 forced displacement, W cr The load is divided into 100 levels from 0 to 0.2 mm, that is, W for each load step cr The increment is 0.002mm.

[0127] During the calculation process, geometric nonlinearity and material nonlinearity are enabled at the same time, and the modified Newton-Raphson method is used for iterative solution. The calculation results of the above initial finite element model are as follows: Figures 5 to 9 As shown, the analysis shows that: (1) Figure 5 This shows that the above model is loaded into W cr =0.1mm, we can know the crack height H of the waterproof layer 2 at this time. cr =0.14mm, at this time there is still a large margin of uncracked height; (2) Figures 6 and 7 This shows that the above model is loaded into W cr =0.18mm, we can know the crack height H of the waterproof layer 2 at this time. cr =0.51mm, at this time the waterproof layer 2 has serious cracks; Figure 8 This indicates that the above model is loaded into W cr =0.18mm when T cr The longitudinal stress of the unit in the region shows that the stress value of the cracked region 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 stress of the uncracked unit at other locations. This is also consistent with the stress distribution in the conventional crack 13 expansion theory; (3) Figure 9 This shows that the above model is loaded into W cr =0.2mm, we can see the deformation of T cr The waterproof layer 2 segments on both sides of the area have been completely separated, that is, the crack 13 of the waterproof layer 2 has penetrated its full height, indicating that the actual width of the crack 13 in the concrete 1 structure is W cr When the thickness reaches 0.2 mm, the waterproof layer 2 with a thickness of H = 1 mm will be completely cracked and fail, so the design of the waterproof layer 2 should be improved. Figure 23 The specimen with 12 steel bars, 1 concrete beam and 2 waterproof layer was loaded. Figure 24 As shown, when the concrete cracks 13 appear, the waterproof layer 2 leaks. It can be seen that the test results are consistent with the calculation conclusions of the present invention.

[0128] Based on the initial finite element model, the thickness T of the waterproof layer 2 in the longitudinal direction at the moment of initial cracking of the concrete 1 is calculated. cr When different values ​​are taken in the range of 10nm to 10000nm, the crack height H is calculated. cr The results are plotted on a logarithmic scale. Figure 10 , we can see that: (1) when Tcr When the scale is above 100nm, T cr The larger the value, the higher the crack height H of the waterproof layer 2. cr The smaller the T cr For H cr has a significant effect; (2) when T cr When the size is as small as 100nm, H cr tends to a stable value.

[0129] Based on the initial finite element model, the longitudinal length L of the model was calculated with different values ​​in the range of 0.4mm to 10mm, and the 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 crack height H of the waterproof layer 2 cr The larger the L is, the greater the cr (2) When L≥4H=4mm, H cr The change tends to be stable, at this time H cr The calculation result is basically unaffected by L, and in practice the longitudinal laying length of the waterproof layer 2 is thousands of times longer than its thickness. Therefore, the calculation result of the crack height of the waterproof layer 2 is basically unaffected by its longitudinal length. Therefore, its longitudinal length parameter does not need to be reflected in the calculation formula.

[0130] Based on the initial finite element model, the vertical thickness H of the model was calculated with different values ​​in the range of 0.3mm to 1mm. The crack height H cr The results are as follows Figure 12 As shown in the figure, it can be seen that: except for the case where the H value is too small, which causes the waterproof layer 2 to crack earlier, H cr The calculation result is basically not affected by H, that is, when the waterproof layer 2 is not too thin, its crack height has basically nothing to do with its own vertical thickness value, so its vertical thickness parameter does not need to be reflected in the calculation formula.

[0131] Based on the initial finite element model, the calculations were performed for the cases where the Poisson's ratio of the waterproof material was 0.2, 0.3, and 0.4. It was found that H cr The calculation results are basically not affected by v.

[0132] In order to verify the calculation accuracy of the force calculation method of the present invention, based on the initial finite element model, the σ cr , ε cr 、E e When taking different values ​​(keeping T cr =20nm,α=7.7×10 -4 β=7.4×10 -4, λ=20), the calculation is performed according to the finite element method and the simple formula of the present invention, where σ cr =0.5MPa,ε cr =800%, which is equivalent to the performance parameters of the common PB-I type polymer modified asphalt waterproof coating for roads and bridges. cr =1.0MPa,ε cr =800%, which is equivalent to the performance parameters of the common PB-II type polymer modified asphalt waterproof coating for roads and bridges. cr =2.45MPa,ε cr =450% is equivalent to the performance parameters of common polyurethane waterproof coatings for roads and bridges. Figures 13 to 19 , it can be seen that the calculation results of the simple formula are close to the refined nonlinear finite element results, and H cr All with W cr The calculation accuracy of the simple formula is high enough.

[0133] Furthermore, if Figure 20 Based on the initial finite element model, at a vertical distance c from the bottom surface of the waterproof layer 2 r = 0.2 mm, a linear elastic truss element with a common node as the plane stress element is established to simulate the effect of the fiber reinforced material 15, the design tensile strength of the fiber reinforced material 15 is f rd =400MPa, the cracking of waterproof layer 2 is calculated as follows Figures 21 and 22 As shown in the figure, it can be seen that the crack 13 of the waterproof layer 2 does not develop upward after the crack reaches the position of the fiber reinforcement material 15, that is, the crack height H of the waterproof layer 2 is cr =0.2mm, its H cr with c r The value is comparable, and the maximum stress of the fiber reinforced material 15 is 225MPa, which is much smaller than its design tensile strength f rd In order to verify the calculation effect of the present invention, another Figure 25 The actual specimen shown was subjected to a loading test. During the test, when the width of the crack 13 between the steel bar 12 and the concrete 1 beam 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 conclusion of the present invention.

[0134] The above are only 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 in the scope of protection of the present invention.

Claims

1. A method for calculating the stress of a concrete structure waterproof layer, characterized in that: The concrete is provided with steel bars, and the surface of the concrete is covered with a waterproof layer; the tensile direction along the concrete is the longitudinal direction, and the direction perpendicular to the surface of the waterproof layer is the vertical direction; The calculation method comprises the following steps: The vertical crack height H of the waterproof layer when cracks appear in the concrete is calculated as follows: cr : H cr =(α-βE e / s cr )ln(T cr )e λWcr E e / s cr , Where α, β, and λ are all constants and are all greater than 0, E e is the elastic modulus of the waterproof layer, σ cr is the tensile strength of the waterproof layer, T cr W is the thickness of the waterproof layer in the longitudinal direction when the crack appears. cr is 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 is the thickness of the waterproof layer.

2. The method for calculating the stress of the concrete structure waterproof layer according to claim 1, characterized in that: The constants α, β, and λ are determined as follows: S1. Take a waterproof layer segment of longitudinal length L and perform finite element model meshing using hexahedral units. Set a discrete crack interface unit in the longitudinal middle of the waterproof layer segment. The nodes on both sides of the discrete crack interface unit are coupled with the nodes of the hexahedral units closest to both sides. S2. Let γ = 1, 0 < μ ≤ 0.2; S3. Apply forced displacements γμW in opposite directions and relatively far away from each other 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 to vector W cr,γ the γth element of ; S4. Perform nonlinear finite element calculation and iterate until convergence, obtain the crack height of the discrete crack interface unit and assign it to the vector H cr,γ the γth element of ; S5. Let γ=γ+1, if γμW cr / 2≤2W cr , then go to step S3, otherwise go to step S6; S6. Vector W cr,γ 、H cr,γ Correspondingly substitute 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 are determined.

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

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

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

6. The method for calculating the stress of the concrete structure waterproof layer according to claim 1, characterized in that: The thickness H of the waterproof layer is the solid thickness of the waterproof layer after solidification and curing.

7. The method for calculating the stress of the concrete structure waterproof layer according to claim 1, characterized in that: The elastic modulus E of the waterproof layer e =σ 1％ / ε 1％ , σ 1％ is the stress at 1% elongation when the waterproof layer is subjected to a uniaxial tensile test, ε 1％ is the strain at 1% elongation when the waterproof layer is subjected to a uniaxial tensile test, and the tensile strength σ of the waterproof layer is cr The total loading time of each uniaxial tensile test shall not exceed 1 minute, calculated based on the average stress before fracture measured by multiple uniaxial tensile tests.

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

9. The method for calculating the stress of the concrete structure waterproof layer according to claim 1, characterized in that: The waterproof layer includes fiber reinforcement material; K r BH cr σ cr / A r ≤f rd When the final vertical crack height of the waterproof layer is c r , where K r is the safety factor and K r >1, the direction perpendicular to the longitudinal and vertical directions is defined as the transverse direction, B is 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 is the design tensile strength value of the fiber reinforced material, c r is the distance from the fiber reinforced material to the surface of the concrete beam.

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

11. A method for designing and manufacturing a long-life waterproof layer of a concrete structure, the method being implemented based on the stress calculation method for a waterproof layer of a concrete structure according to claim 2, characterized in that: The long life design and manufacturing method comprises the following steps: S21. Then, at a distance c from the bottom surface of the hexahedral unit r A linear elastic truss element sharing a common node with the hexahedral element is established at a position to simulate the influence of the 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 thickness of the waterproof layer after curing be designed to be H d ≥K f H cr , K f is the safety factor and K f >1. Complete the design of the waterproof layer; S24. Apply c evenly on the top surface of the concrete r A thick waterproof layer is formed, and then a fiber reinforcement material having the same cross-sectional size, elastic modulus and tension and compression constitutive parameters as those of the linear elastic truss unit is evenly spread; S25. Continue to paint H d -c r A thick waterproof layer is formed, thus completing the manufacture of the waterproof layer.

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