A method for determining the waterproof failure probability of a concrete flat roof project

Abstract

This invention proposes a method for determining the probability of waterproofing failure in concrete flat roof projects, enabling quantitative calculation of this probability. The method calculates the deformation of each layer of roof materials based on temperature, humidity, and material characteristics. It allows for free combination of concrete flat roof structures with various waterproofing levels. The deformation of the material layers is correlated with the deformation of the waterproofing layer using a "cooperative deformation interface coefficient" and "effective size of the waterproofing layer's cooperative deformation." This is further validated through a 10... 4 ~10 6 The calculations were performed to obtain the waterproofing synergistic deformation value. The results of each calculation were evaluated. The waterproofing effectiveness of the material was used as the threshold for the waterproofing effectiveness of the synergistic deformation of the concrete flat roof, so that the calculated value of the waterproofing failure probability was close to the actual value of the project. The overall probability of waterproofing failure was judged.

Description

Technical Field

[0001] This invention relates to the field of waterproofing failure probability calculation technology, and specifically to a method for determining the probability of waterproofing failure in concrete flat roof projects. Background Technology

[0002] my country's waterproofing industry, as a whole, emphasizes practice and focuses on summarizing engineering experience. Current standards primarily determine waterproofing levels directly based on application scenarios, without considering the influence of related factors. Many regulations lack quantitative analytical basis, resulting in insufficient scientific rigor. The essence of engineering waterproofing levels is the probability of waterproofing failure, a key quantitative indicator linking the target performance to actual results. The waterproofing levels set in current Chinese standards are a summary of long-term practice and exploration by engineers, representing a reliability requirement based on a somewhat vague, experience-driven classification. While this has undergone long-term practical testing and established a solid foundation for waterproofing theory, its accuracy needs further verification, and the specific selection of waterproofing materials, composition, and construction methods warrant discussion.

[0003] In the field of waterproofing failure probability calculation, the effectiveness of waterproofing layer overlap is generally determined through actual observation, and then it is assumed that multiple waterproofing layers can effectively reduce the failure probability. However, the calculation algorithm remains based on classical probability and deviates significantly from the real-world scenarios of waterproofing failure. Summary of the Invention

[0004] In view of this, the present invention proposes a method for determining the probability of waterproofing failure in concrete flat roof projects, which can realize the quantitative calculation of the probability of waterproofing failure in concrete flat roof projects.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for determining the probability of waterproofing failure in a concrete flat roof project includes the following steps:

[0007] Step 1: Obtain the annual maximum relative humidity difference in the climate zone where the concrete flat roof project is located, as well as the temperature and annual maximum temperature difference of each layer of materials in the climate zone.

[0008] Step 2: Calculate the deformation of each layer based on the type and size of the surface layer, insulation layer, base layer, and parapet wall in the concrete flat roof project;

[0009] Step 3: For the waterproof layer used in the concrete flat roof project, taking the waterproof layer as a reference, construct the calculation formula for the cooperative deformation of the waterproof layer based on the cooperative deformation interface coefficient.

[0010] Step 4: Using the deformation of each layer as input value, referencing the collaborative deformation interface coefficient, and based on the probability distribution characteristics PDF, set the number of simulations, and randomly simulate the calculation formula for the collaborative deformation of the waterproof layer to obtain the distribution of each collaborative deformation.

[0011] Step 5: Sort the calculated collaborative deformation distribution by size, and compare the calculated collaborative deformation value with the corresponding waterproofing effectiveness threshold. When the collaborative deformation value is greater than the waterproofing effectiveness threshold, it indicates failure.

[0012] Step 6, calculate the probability of waterproof layer failure:

[0013]

[0014] Among them, M Δu-CBA denoted as the number of simulated failures; M represents the number of simulation calculations.

[0015] In step 2, the surface layer deformation includes horizontal surface layer deformation, surface layer deformation due to temperature, and surface layer deformation due to humidity; the insulation layer deformation is horizontal insulation layer deformation; the base layer deformation is temperature-induced base layer deformation; and the parapet wall deformation includes temperature-induced parapet wall deformation and humidity-induced parapet wall deformation.

[0016] In step 2, the horizontal deformation of the surface layer is:

[0017] Δu C, = cs ×750×10 -6

[0018] Where, Δu C,S The horizontal deformation of the surface layer, i.e., the shrinkage value of the surface layer in the initial stage, is expressed in meters (m) and liters (L). cs This is the length of the surface layer, in meters (m).

[0019] The horizontal deformation of the insulation layer is:

[0020] Δu I,H =L×δ I

[0021] Where L is the length of the insulation material, taken as 1.2m, δ I The moisture absorption deformation rate of the thermal insulation material;

[0022] Based on the maximum annual temperature difference of each layer of materials in the climate zone, the deformation of the surface layer, base layer, and parapet wall due to temperature is calculated using the following formulas:

[0023]

[0024] Where Δu is the amount of deformation affected by temperature, i.e., the relative displacement between materials or components, in meters; α1 is the crack width correction factor for the first layer of material, taken as 1.0; α1 is the linear thermal expansion coefficient of the first layer of material, 1 / K; ΔT1 is the temperature change of the first layer of material, calculated using the annual maximum temperature difference, in K; β1 is the comprehensive calculation coefficient of the first layer of material, in m. -1 L1 is the calculated length of the first layer of material, in meters. α2 is the crack width correction factor for the second layer material, calculated under extreme conditions, and taken as 0 or 1.0; α2 is the linear thermal expansion coefficient of the second layer material, in units of 1 / K; ΔT2 is the temperature change of the second layer material, calculated using the annual maximum temperature difference, in units of K; β2 is the comprehensive calculation coefficient for the second layer material, in units of m2. -1 L2 is the calculated length of the second layer of material, in meters.

[0025] Based on the annual average maximum relative humidity difference in the climate zone, the deformation of the surface layer, insulation layer, and parapet wall due to humidity is calculated using the following formulas:

[0026]

[0027] Where, Δu RH The deformation affected by humidity, i.e., the shrinkage deformation of the material during drying, is expressed in meters (m); L is the calculated length of the material, also expressed in meters; δ is the material's moisture content expansion coefficient, taken as 10 × 10⁻⁶ for blocks. -6 The value for mortar and concrete is 1×10. -6 ; This represents the annual average maximum relative humidity difference.

[0028] In step 3, the coordinated deformation of the surface layer and the insulation layer is:

[0029] Δu plane, = TI-T ·Δu T + TI-I ·Δu I,

[0030] Where, γ TI-T The deformation of the surface layer relative to the insulation layer, and the interface coefficient for the coordinated deformation of the surface layer and the waterproof layer; Δu T γ represents the surface deformation, measured in meters (m). TI-I The deformation of the surface layer relative to the insulation layer, and the interface coefficient for the coordinated deformation of the insulation layer and the waterproof layer; Δu I, This represents the horizontal deformation of the insulation layer, measured in meters (m).

[0031] The combined deformation of the base layer and the insulation layer is:

[0032] Δu plane, = ID-D ·Δu D + ID-I ·Δu I,

[0033] Where, γ ID-D Δu represents the deformation of the base layer relative to the insulation layer, and the interface coefficient for the coordinated deformation between the base layer and the waterproof layer. D γ represents the deformation of the base layer, in meters (m). ID-I The deformation of the base layer relative to the insulation layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; Δu I, This represents the horizontal deformation of the insulation layer, measured in meters (m).

[0034] The combined deformation of the parapet wall and the surface layer is:

[0035]

[0036] Where, γ PT-T The deformation of the parapet wall relative to the surface layer; the interface coefficient for the coordinated deformation of the surface layer and the waterproof layer; Δu T γ represents the surface deformation, measured in meters (m). PT-I The deformation of the parapet wall relative to the surface layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; Δu I, This represents the horizontal deformation of the insulation layer, measured in meters (m).

[0037] The deformation of the parapet wall and the base layer together is:

[0038]

[0039] Where, γ PD-D Δu represents the deformation of the substrate relative to the waterproofing layer, and is the interface coefficient for the coordinated deformation of the substrate and the waterproofing layer. D γ represents the deformation of the base layer, in meters (m). PD-I The deformation of the insulation layer relative to the waterproof layer, and the interface coefficient for the coordinated deformation of the insulation and waterproof layers; Δu I, γ represents the horizontal deformation of the insulation layer, measured in meters (m). PD-P The deformation of the parapet wall relative to the base layer; the interface coefficient for the coordinated deformation of the parapet wall base layer and the waterproof layer; Δu P This represents the deformation of the parapet wall, expressed in meters (m).

[0040] In step 3, the cooperative deformation interface coefficient is as follows:

[0041]

[0042] In step 4, the number of simulations is no less than 10^4.

[0043] In step 4, the boundary conditions for random simulation are the maximum monthly temperature difference or the maximum annual temperature difference for each layer of material, as well as the corresponding humidity difference determined according to the climate zone division.

[0044] In step 5, when multiple waterproof layers are used together, the waterproof layer is considered to have failed only when all multiple waterproof layers have failed.

[0045] Beneficial effects

[0046] 1. The method of this invention calculates the deformation of each layer of roof material based on temperature, humidity, and material characteristics; it allows for free combination of various waterproofing levels for concrete flat roof structures. The deformation of the material layers is correlated with the deformation of the waterproofing layer using a "cooperative deformation interface coefficient" and "effective size of the waterproofing layer's cooperative deformation." This is achieved through 10... 4 ~10 6 The calculations were performed to obtain the waterproofing synergistic deformation value. The results of each calculation were evaluated. The crack bridging performance was used as the threshold for the waterproofing effectiveness of the synergistic deformation of the concrete flat roof, so that the calculated value of the waterproofing failure probability was close to the actual value of the project. The overall probability of waterproofing failure was judged.

[0047] 2. The calculation of deformation of each layer of roofing materials in this invention is derived from existing research; the crack bridging performance of waterproof membranes, coatings, and polymer mortars is determined by experiments, and the data is analyzed using regression methods, which serve as indicators for evaluating waterproofing effectiveness; the combination of various waterproofing grades with concrete flat roof structures is a multi-type orthogonal combination, based on which the quantitative algorithm of this invention is constructed, combined with qualitative analysis, to form a relatively complete theoretical system and correctly guide engineering practice.

[0048] 3. The waterproof failure probability determined by this invention is a key indicator for evaluating the waterproof level of an engineering project. It is quantifiable, and by using the calculation results to analyze the waterproofing of the project, the applicability of the waterproofing material and the rationality of the structure can be accurately judged, and a scientific waterproof level can be established.

[0049] 4. The method of the present invention can be programmed using a computer to form waterproof quantitative calculation software, which covers the external and internal factors of waterproofing projects, and further supplements and improves the existing waterproofing system.

[0050] 5. This invention can calculate the combined calculations for 9 typical climate zones, concrete flat roofs with waterproofing grades 1 to 3, XPS and rock wool insulation layers, concrete and block parapet wall structures, 3 major categories of waterproofing materials, 2 types of protective layers, and roofs of different sizes. It can fill the gap in the industry and provide the waterproofing industry with a quantitative analysis tool for evaluating the applicability of waterproofing materials, the rationality of waterproofing structures, and the classification of waterproofing grades. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the method of the present invention. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0053] This invention provides a method for determining the probability of waterproofing failure in concrete flat roof projects, such as... Figure 1 As shown, it includes the following steps:

[0054] Step 1: Obtain the annual maximum relative humidity difference in the climate zone where the concrete flat roof project is located, as well as the temperature and annual maximum temperature difference of each layer of materials in the climate zone.

[0055] Step 2: Based on the type and dimensions of the surface layer, insulation layer, base layer, and parapet wall in the concrete flat roof project, calculate the deformation of each layer. Specifically, the surface layer deformation includes horizontal deformation, temperature-induced deformation, and humidity-induced deformation; the insulation layer deformation is the horizontal deformation; the base layer deformation is the temperature-induced deformation; and the parapet wall deformation includes both temperature-induced and humidity-induced deformation.

[0056] In this embodiment, the surface layer is concrete, and the horizontal deformation of the surface layer is:

[0057] Δu C,S =L cs ×750×10 -6

[0058] Where, Δu C,S The horizontal deformation of the surface layer, i.e., the shrinkage value of the surface layer in the initial stage, is expressed in meters (m) and liters (L). cs The length of the surface layer is expressed in meters (m).

[0059] The horizontal deformation of the insulation layer is:

[0060] Δu I,H =L×δ I

[0061] Where L is the length of the insulation material, taken as 1.2m, δ I XPS is taken as 10 for the moisture absorption deformation rate of the insulation material. -3 Mineral wool is valued at 10. -6 .

[0062] Based on the maximum annual temperature difference of each layer of materials in the climate zone, the deformation of the surface layer, base layer, and parapet wall due to temperature is calculated using the following formulas:

[0063]

[0064] Where Δu is the amount of deformation affected by temperature, i.e., the relative displacement between materials or components, in meters; α1 is the crack width correction factor for the first layer of material, taken as 1.0; α1 is the linear thermal expansion coefficient of the first layer of material, 1 / K; ΔT1 is the temperature change of the first layer of material, calculated using the annual maximum temperature difference, in K; β1 is the comprehensive calculation coefficient of the first layer of material, in m. -1 L1 is the calculated length of the first layer of material, in meters. α2 is the crack width correction factor for the second layer material, calculated under extreme conditions, and taken as 0 or 1.0; α2 is the linear thermal expansion coefficient of the second layer material, in units of 1 / K; ΔT2 is the temperature change of the second layer material, calculated using the annual maximum temperature difference, in units of K; β2 is the comprehensive calculation coefficient for the second layer material, in units of m2. -1 L2 is the calculated length of the second layer of material, in meters.

[0065] Based on the annual average maximum relative humidity difference in the climate zone, the deformation of the surface layer, insulation layer, and parapet wall due to humidity is calculated using the following formulas:

[0066]

[0067] Where, Δu RH The deformation affected by humidity, i.e., the shrinkage deformation of the material during drying, is expressed in meters (m); L is the calculated length of the material, also expressed in meters; δ is the material's moisture content expansion coefficient, taken as 10 × 10⁻⁶ for blocks. -6 (%) -1 For mortar and concrete, the value is 1×10. -6 (%) -1 ); The annual average maximum relative humidity difference (%).

[0068] Step 3: For the waterproofing layer used in concrete flat roof projects, taking the waterproofing layer as a reference, and based on the cooperative deformation interface coefficient (the cooperative deformation interface coefficient table is shown in Table 1), construct the calculation formula for the cooperative deformation of the waterproofing layer, as follows:

[0069] The combined deformation of the surface layer and the insulation layer is:

[0070] Δu plane,TI =γ TI-T ·Δu T +γ TI-I ·Δu I,H

[0071] Where, γ TI-T The deformation of the surface layer relative to the insulation layer, and the interface coefficient for the coordinated deformation of the surface layer and the waterproof layer; Δu T γ represents the surface deformation, measured in meters (m).TI-I The deformation of the surface layer relative to the insulation layer, and the interface coefficient for the coordinated deformation of the insulation layer and the waterproof layer; Δu I,H This represents the horizontal deformation of the insulation layer, expressed in meters (m).

[0072] The combined deformation of the base layer and the insulation layer is:

[0073] Δu plane,ID =γ ID-D ·Δu D +γ ID-I ·Δu I,H

[0074] Where, γ ID-D Δu represents the deformation of the base layer relative to the insulation layer, and the interface coefficient for the coordinated deformation between the base layer and the waterproof layer. D γ represents the deformation of the base layer, in meters (m). ID-I The deformation of the base layer relative to the insulation layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; Δu I,H This represents the horizontal deformation of the insulation layer, expressed in meters (m).

[0075] The combined deformation of the parapet wall and the surface layer is:

[0076]

[0077] Where, γ PT-T The deformation of the parapet wall relative to the surface layer; the interface coefficient for the coordinated deformation of the surface layer and the waterproof layer; Δu T γ represents the surface deformation, measured in meters (m). PT-I The deformation of the parapet wall relative to the surface layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; Δu I, This represents the horizontal deformation of the insulation layer, expressed in meters (m).

[0078] The deformation of the parapet wall and the base layer together is:

[0079]

[0080] Where, γ PD-D Δu represents the deformation of the substrate relative to the waterproofing layer, and is the interface coefficient for the coordinated deformation of the substrate and the waterproofing layer. D γ represents the deformation of the base layer, in meters (m). PD-I The deformation of the insulation layer relative to the waterproof layer, and the interface coefficient for the coordinated deformation of the insulation and waterproof layers; Δu I, γ represents the horizontal deformation of the insulation layer, in meters (m). PD-P The deformation of the parapet wall relative to the base layer; the interface coefficient for the coordinated deformation of the parapet wall base layer and the waterproof layer; Δu P This represents the deformation of the parapet wall, expressed in meters (m).

[0081] Table 1. Cooperative Deformation Interface Coefficients

[0082]

[0083] Step 4: Take the deformation of each layer as the input value, refer to the co-deformation interface coefficient, and set the number of simulations (no less than 10^4 times) according to the probability distribution characteristics PDF to perform random simulation and obtain the distribution of each co-deformation amount; the boundary conditions of the random simulation are the monthly maximum temperature difference or the annual maximum temperature difference of each material layer and the corresponding humidity difference determined according to the climate zone.

[0084] Step 5: Sort the calculated cooperative deformation distribution by magnitude, and compare the calculated cooperative deformation value with the corresponding waterproofing effectiveness threshold. When the cooperative deformation value is greater than the waterproofing effectiveness threshold, it indicates failure. Specifically, when multiple waterproofing layers are used together, a waterproofing layer is considered to have failed only if all multiple waterproofing layers fail. The waterproofing effectiveness threshold is the crack bridging performance (CBA); the CBA of typical waterproofing materials is shown in Table 2.

[0085] Table 2 Crack Bridging Performance of Typical Waterproofing Materials

[0086]

[0087] Table 3. Coefficient of Dimension for Cooperative Deformation of Waterproof Layer

[0088]

[0089] Step 6, calculate the probability of waterproof layer failure:

[0090]

[0091] Among them, M Δu-CBA denoted as the number of simulated failures; M represents the number of simulation calculations.

[0092] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining a waterproofing failure probability of a concrete flat roof work, characterized by, Includes the following steps: Step 1: Obtain the annual maximum relative humidity difference in the climate zone where the concrete flat roof project is located, as well as the temperature and annual maximum temperature difference of each layer of materials in the climate zone. Step 2: Calculate the deformation of each layer based on the type and size of the surface layer, insulation layer, base layer, and parapet wall in the concrete flat roof project; Step 3: For the waterproof layer used in the concrete flat roof project, taking the waterproof layer as a reference, construct the calculation formula for the cooperative deformation amount of the waterproof layer based on the cooperative deformation interface coefficient. Step 4: Using the deformation of each layer as input value, referencing the collaborative deformation interface coefficient, and based on the probability distribution characteristics PDF, set the number of simulations, and randomly simulate the calculation formula for the collaborative deformation of the waterproof layer to obtain the distribution of each collaborative deformation. Step 5: Sort the calculated collaborative deformation distribution by size, and compare the calculated collaborative deformation value with the corresponding waterproofing effectiveness threshold. When the collaborative deformation value is greater than the waterproofing effectiveness threshold, it indicates failure. Step 6, calculate the probability of waterproof layer failure: in, To simulate the number of failures; To simulate the number of calculations; In step 2, the surface layer deformation includes the horizontal deformation of the surface layer, the deformation of the surface layer affected by temperature, and the deformation of the surface layer affected by humidity; the insulation layer deformation is the horizontal deformation of the insulation layer; the base layer deformation is the deformation of the base layer affected by temperature; and the parapet wall deformation includes the deformation of the parapet wall affected by temperature and the deformation of the parapet wall affected by humidity. In step 2, the horizontal deformation of the surface layer is: wherein, is the horizontal deformation of the surface layer, i.e. the shrinkage value of the surface layer in the initial stage, in , is the length of the surface layer, in ; The horizontal deformation of the insulation layer is: Wherein, L is the length of the thermal insulation material, 1.2m, is the moisture absorption deformation rate of the thermal insulation material; Based on the maximum annual temperature difference of each layer of materials in the climate zone, the deformation of the surface layer, base layer, and parapet wall due to temperature is calculated using the following formulas: in, This refers to the deformation affected by temperature, i.e., the relative displacement between materials or components, measured in units of... ; The crack width correction factor for the first layer of material is set to 1.

0. is the coefficient of thermal linear expansion of the first layer material, in units of 1 / K; The temperature change of the first layer material is calculated using the maximum annual temperature difference, in units of... ; This is the comprehensive calculation coefficient for the first layer of material, in units of... ; The calculated length of the first layer of material, in units of ; This is the crack width correction factor for the second layer material, taking either 0 or 1.0 under extreme conditions. The coefficient of thermal linear expansion of the second layer material is given in units of 1000 kJ / m². ; The temperature variation of the second layer material is calculated using the maximum annual temperature difference, in units of... ; This is the comprehensive calculation coefficient for the second layer material, in units of... ; The calculated length of the second layer of material, in units of ; Based on the annual average maximum relative humidity difference in the climate zone, the deformation of the surface layer, insulation layer, and parapet wall due to humidity is calculated using the following formulas: in, This refers to the amount of deformation affected by humidity, i.e., the shrinkage deformation of the material during drying, expressed in units of... ; The calculated length of the material, in units of ; The coefficient of thermal expansion of the material at moisture content is taken as the building block's coefficient of thermal expansion. Mortar and concrete values ​​are taken as follows: ; This represents the annual average maximum relative humidity difference. In step 3, the amount of cooperative deformation of the surface layer and the thermal insulation layer is: in, The deformation of the surface layer relative to the insulation layer, and the interface coefficient of the coordinated deformation between the surface layer and the waterproof layer; This represents the surface deformation, in units of... ; The deformation of the surface layer relative to the insulation layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; This represents the horizontal deformation of the insulation layer, measured in units of... ; The amount of cooperative deformation of the base layer and the thermal insulation layer is: in, The deformation of the base layer relative to the insulation layer, and the interface coefficient of the coordinated deformation between the base layer and the waterproof layer; This represents the deformation of the base layer, in units of... ; The deformation of the base layer relative to the insulation layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; This represents the horizontal deformation of the insulation layer, measured in units of... ; The combined deformation of the parapet wall and the surface layer is: in, The deformation of the parapet wall relative to the surface layer, and the interface coefficient for the coordinated deformation of the surface layer and the waterproof layer; This represents the surface deformation, in units of... ; The deformation of the parapet wall relative to the surface layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; This represents the horizontal deformation of the insulation layer, expressed in units of... ; The amount of deformation of the parapet wall in cooperation with the base layer is: in, The deformation of the substrate relative to the waterproof layer, and the interface coefficient for the coordinated deformation of the substrate and the waterproof layer; This represents the deformation of the base layer, in units of... ; The deformation of the insulation layer relative to the waterproof layer, and the interface coefficient of the coordinated deformation between the insulation layer and the waterproof layer; This represents the horizontal deformation of the insulation layer, measured in units of... ; The deformation of the parapet wall relative to the base layer, and the interface coefficient of the coordinated deformation between the parapet wall base layer and the waterproof layer; The deformation of the parapet wall is expressed in units of 1. ; In step 3, the cooperative deformation interface coefficients are as follows: 。 2. The method of claim 1, wherein, In step 4, the number of simulations is no less than 10^4.

3. The method of claim 1, wherein, In step 4, the boundary conditions for random simulation are the maximum monthly temperature difference or the maximum annual temperature difference for each layer of material, as well as the corresponding humidity difference determined according to the climate zone division.

4. The method of claim 1, wherein, In step 5, when multiple waterproof layers are used together, the waterproof layer is considered to have failed only when all multiple waterproof layers fail.

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