A method for calculating load resistance partial factors, a storage medium, and a device

Abstract

The present invention discloses a method for calculating load and resistance partial factors, a storage medium, and a device, belonging to the field of ballastless tracks. By establishing a structural limit state function, simplifying it, and introducing an equivalent resistance attenuation coefficient g*, an empirical calculation formula for g* can be obtained through the derivation and simplification of the equivalent resistance attenuation coefficient. On this basis, by introducing the third-moment reliability theory, μ R0 , σ G0 , α 3G0 , β 2T0 , μ RT , σ G , α 3G , β 2T and other parameters can be obtained, and the calculation formula for load and resistance partial factors considering the degradation of structural resistance performance in the whole life cycle can be accurately constructed, and the acquisition of load and resistance analysis coefficients can be quickly realized. The method in the present invention is simple in method and convenient in operation, can fully consider the attenuation of the structural resistance performance of the design object, avoid the iterative calculation process in the existing design process, simplify the calculation process of reliability design, shorten the design cycle, improve the design efficiency, and has good practical value and practical significance.

Description

Technical Field

[0001] The present invention belongs to the field of ballastless tracks, and relates to a method for calculating partial factors of load and resistance, a storage medium, and a device, and particularly relates to a method for calculating partial factors of load and resistance that takes into account the degradation of structural resistance performance and does not require iterative calculation, as well as a readable storage medium and a computer device configured in combination therewith. Background Art

[0002] Under the action of service loads, environmental factors, and internal material factors, the performance of engineering structures will gradually decline, resulting in reduced reliability and shortened service life of the structures. However, the current structural design theory does not fully consider issues such as structural performance degradation and durability, and cannot accurately reflect the safety of structures over their entire life cycle.

[0003] Generally, the amount of energy and materials consumed in structural engineering is huge. The continuously expanding construction scale not only damages the ecology, pollutes the environment, and increases the burden on nature, putting limited resources at risk of depletion; at the same time, the costs of inspection, maintenance, and reinforcement caused by insufficient durability of structural engineering also add a huge burden to the further development of society. Therefore, with the continuous development of engineering structures and the implementation of the sustainable development strategy, the design of structures over their entire life cycle is the direction and trend of the future development of structural design theory.

[0004] Currently, according to the provisions in the "Code for Railway Track Design (Limit State Method)" (Q / CR 9130-2018), in actual engineering design, the partial factor expression is usually adopted to achieve the limit state design based on reliability. Moreover, the partial factors of actions and resistances in the code are based on the current design theory, taking a fixed value for the partial factors uniformly, and not fully considering issues such as structural performance degradation and durability. As a result, the existing limit state design of engineering structures cannot correspond to the service performance of structural engineering over its entire life cycle, and there are certain design limitations. Summary of the Invention

[0005] In view of one or more of the above defects or improvement requirements of the prior art, the present invention provides a method for calculating partial factors of load and resistance, a storage medium, and a device, which can quickly obtain the partial factors of load and resistance over the entire life cycle in engineering structure design, fully consider the degradation of structural resistance performance, and reduce the iterative calculation process in the design process, ensuring the reliability of structural design while improving the efficiency of structural design.

[0006] To achieve the above object, in one aspect of the present invention, there is provided a method for calculating partial factors of load and resistance that takes into account the degradation of structural resistance performance and does not require iterative calculation, which includes the following steps:

[0007] S1: Establish the structural limit state function G(t) and the time-varying failure probability expression P f (T);

[0008] S2: Introducing the equivalent resistance attenuation coefficient g* into the performance function, we can obtain the simplified performance function G(X) and the equivalent time-varying failure probability expression P f ′(T);

[0009] S3: According to P f (T) and P f ′(T) is used to derive the calculation formula of the equivalent resistance attenuation coefficient g*; and the calculation formula is:

[0010]

[0011] Where θ = μ W / μ D , is the mean value of the control load effect μ W and the mean value of the dead load effect μ D g(T) is the ratio of the residual resistance value of the structural design service life to the initial resistance value R0; V W is the coefficient of variation of the control load effect; m0, m1, m2 and m3 are the regression coefficients under different probability distribution types;

[0012] S4: Calculate the initial resistance mean μ R0 ;

[0013] S5: Calculate the initial value of the standard deviation of the performance function G(X) G0 , initial value of skewness α 3G0 , initial value of target second-order moment reliability index β 2T0 and the mean life-cycle target resistance μ RT ;in,

[0014] μ RT =(Σμ Si +β 2T0 σ G0 ) / g*

[0015] Where σ G0 is the standard deviation of the performance function G(X), β 2T0 is μ R0 Calculate the target second-order moment reliability index;

[0016] S6: Calculate the standard deviation σ of the performance function G(X) G , skewness α 3G and target second-order moment reliability index β 2T , calculate the resistance R and load effect S i The separation coefficient α R and α Si ;

[0017] S7: Determine the load φ* and resistance partial factor γ considering the degradation of structural resistance performance i *;

[0018]

[0019]

[0020] Wherein, α R , α Si are the separation coefficients of the resistance R and the load effect S i respectively; V R , V Si are the coefficient of variation of the resistance R and the load effect S i respectively; μ R , μ Si are the mean values of the resistance R and the load effect S i respectively; R n is the standard value of the resistance, S ni is the standard value of the load effect, and both are determined by on-site measurement and data statistics.

[0021] As a further improvement of the present invention, in S'1, the expressions of G(t) and P f (T) are respectively:

[0022] G(t) = g(t)·R0 - D - L S (t) - W(t) (1)

[0023]

[0024] Wherein, G(t) is the performance function of the ballastless track structure at time t, D is the constant load effect whose magnitude does not change with time, L S (t) is the sustained live load effect at time t, W(t) is the control load effect at time t, g(t) is the structural resistance attenuation function, and R0 is the initial structural resistance; λ W and F W (w) are respectively the average occurrence rate and the cumulative probability distribution function of the control load W(t), μ DL is the average value of the sum of the constant load effect and the sustained live load effect; r represents the resistance random variable, and f R0 (r) is the probability density function of the initial resistance R0.

[0025] As a further improvement of the present invention, in S2, the expressions of G(X) and P f '(T) are respectively:

[0026]

[0027]

[0028] In the formula, G(X) represents the random variable of the performance function, and L Sapt represents the random variable of the sustained live load effect at any time, and represents the random variable of the maximum effect of the control load within the design service life T.

[0029] As a further improvement of the present invention, in S3, the process of obtaining the calculation formula of g* is as follows:

[0030] Simultaneously derive and calculate formulas (2) and (4). During the derivation process, consider the influence of the resistance attenuation function and the statistical characteristics of the control load effect on the value of g*, and omit the influence of the design target reliability index, the resistance variation coefficient, and the average occurrence rate of the control load effect on the value of g*.

[0031] As a further improvement of the present invention, in S4, the initial resistance mean value μ R0 is preferably estimated by the following formula:

[0032]

[0033] In the formula, μ R0 is the initial resistance mean value, β T is the design target reliability index, μ Si and σ Si are the mean value and the standard deviation of the load effect S i respectively.

[0034] As a further improvement of the present invention, in S5, σ G0 , α 3G0 and β 2T0 are respectively calculated according to the following calculation formulas,

[0035]

[0036]

[0037]

[0038] In the formula, σ G0 , α 3G0 are respectively the initial value of the standard deviation and the initial value of the skewness of the performance function G(X); β 2T0 is the initial value of the target second-order moment reliability index; σ R0 is the initial value of the standard deviation of the resistance R; σ Si is the standard deviation of the load effect S i ; α 3R , α 3i are respectively the skewness of the resistance R and the load effect S i respectively.

[0039] As a further improvement of the present invention, in S6, σ G , α 3G and β 2T are calculated by the following formulas:

[0040]

[0041]

[0042]

[0043] In the formula, σ G , α 3G are respectively the standard deviation and skewness of the performance function G(X); β 2T is the target second-moment reliability index; σ R , σ Si are respectively the standard deviations of the resistance R and the load effect S i ; α 3R , α 3i are respectively the skewnesses of the resistance R and the load effect S i .

[0044] As a further improvement of the present invention, in S6, the separation coefficient between the resistance R and the load effect S i is calculated by the following formula:

[0045] α R = σ R / σ G

[0046] α Si = σ Si / σ G

[0047] In the formula, σ R , σ Si are respectively the standard deviations of the resistance R and the load effect S i , σ G is the standard deviation of the performance function G(X).

[0048] Another aspect of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps in the load and resistance factor calculation method that considers the degradation of structural resistance performance and does not require iterative calculation are implemented.

[0049] Another aspect of the present invention further provides a computer device, which includes a memory, a processor, and a computer program,

[0050] The computer program is stored in a memory and is configured to be executable by a processor. When the processor executes the computer program, the steps in the load and resistance factor calculation method that takes into account the degradation of structural resistance performance and does not require iterative calculation are implemented.

[0051] As long as the above-improved technical features do not conflict with each other, they can be combined with each other.

[0052] Generally speaking, compared with the prior art, the beneficial effects of the above technical solutions conceived by the present invention include:

[0053] (1) In the load and resistance factor calculation method of the present invention, by establishing a structural limit state function, simplifying it and introducing an equivalent resistance attenuation coefficient g*, through the derivation and simplification of the equivalent resistance attenuation coefficient, an empirical calculation formula for g* can be obtained. On this basis, by introducing the third-order moment reliability theory, the acquisition of parameters such as μ R0 , σ G0 , α 3G0 , β 2T0 , μ RT , σ G , α 3G , β 2T can be quickly realized, and the calculation formulas for the life-cycle load and resistance factors can be accurately constructed. While considering the degradation of the structural resistance performance of the design object, the iterative calculation process in the acquisition of relevant parameters is effectively avoided, the reliability design process of the structural object is simplified, and the efficiency and accuracy of the reliability design of the ballastless track structure are improved.

[0054] (2) In the load and resistance factor calculation method of the present invention, by establishing a structural limit state function and its time-varying failure probability expression, and combining the structural limit state equivalent simplification function and its time-varying failure probability expression, the operation and acquisition of the equivalent resistance attenuation coefficient can be quickly realized, and an empirical calculation formula for the equivalent resistance attenuation coefficient can be quickly obtained, reducing the operation difficulty of the equivalent resistance attenuation coefficient and improving the efficiency of the reliability design of the structural object.

[0055] (3) In the load and resistance factor calculation method of the present invention, by introducing the third-order moment reliability theory and setting the calculation formulas for the corresponding parameters, the calculation of relevant parameters in the reliability design process can be directly carried out, avoiding the iterative operation process in the calculation process, effectively reducing the amount of calculation in the design process, and shortening the cycle and time of the reliability design.

[0056] (4) The load and resistance factor calculation method of the present invention is simple and easy to operate, capable of quickly calculating the load and resistance factors of the design object, achieving the life-cycle reliability design of the design object, and fully considering the attenuation of the structural resistance performance of the design object during the design process, making the reliability design more in line with the actual working conditions of the design object; at the same time, by introducing the third-order moment reliability theory into the calculation method to determine the life-cycle load and resistance factors, it can effectively avoid the iterative calculation process in the existing design process, simplify the calculation process of the load and resistance factors, shorten the reliability design cycle of the design object, improve the efficiency of the reliability design of the design object, and has good practical value and practical significance. Brief Description of the Drawings

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0058] Figure 1 It is a schematic diagram of the operation process of the load and resistance factor calculation method in the embodiment of the present invention;

[0059] Figures 2 to 4 It is a comparison diagram of the calculation results of formula (5) and the calculation results of the theoretical method when controlling the load effect to be lognormal distribution; where, Figure 2 represents the influence of g(T) on g*; Figure 3 represents μ W / μ D the influence on g*; Figure 4 represents V W the influence on g*;

[0060] Figures 5 to 7 It is a comparison diagram of the calculation results of formula (5) and the calculation results of the theoretical method when controlling the load effect to be extreme value type I distribution; where, Figure 5 represents the influence of g(T) on g*; Figure 6 represents μ W / μ D the influence on g*; Figure 7 represents V W the influence on g*;

[0061] Figures 8 to 10 It is a comparison diagram of the calculation results of formula (5) and the calculation results of the theoretical method when controlling the load effect to be extreme value type II distribution; where, Figure 8 represents the influence of g(T) on g*; Figure 9 represents μW / μ D Effect on g*; Figure 10 Represents V W Effect on g*;

[0062] Figure 11 It is a schematic diagram showing the law of the reliability index varying with time within the designed service life in a specific embodiment. Specific implementation manner

[0063] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0064] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0065] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, "a plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0066] In the present invention, unless otherwise clearly defined and limited, the terms "installed", "connected", "connected", "fixed", etc. should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or integrated; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements or the interaction relationship between two elements, unless otherwise clearly limited. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0067] In the present invention, unless otherwise clearly specified and defined, the first feature being "on" or "under" the second feature may mean that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, the first feature being "above", "over" and "on top of" the second feature may mean that the first feature is directly above or obliquely above the second feature, or merely indicates that the horizontal height of the first feature is higher than that of the second feature. The first feature being "under", "beneath" and "underneath" the second feature may mean that the first feature is directly below or obliquely below the second feature, or merely indicates that the horizontal height of the first feature is less than that of the second feature.

[0068] Example:

[0069] Please refer to Figure 1 , the load and resistance factor calculation method in the preferred embodiment of the present invention is used to meet the requirements of the whole-life design of engineering structures, and preferably includes the following steps:

[0070] S1: Establish the structural limit state function and the time-varying failure probability expression;

[0071] In the preferred embodiment, the whole-life reliability function of the structure is preferably expressed as:

[0072] G(t) = g(t)·R0 - D - L S (t) - W(t) (1)

[0073] In formula (1), D is the constant load effect that does not change with time, L S (t) is the continuous live load effect at time t, W(t) is the control load effect at time t, g(t) is the structural resistance attenuation function, and R0 is the initial resistance of the structure.

[0074] Meanwhile, the time-varying failure probability of the structure within the target service life T is preferably expressed as:

[0075]

[0076] In formula (2), λ W and F W (w) are respectively the average occurrence rate and the cumulative probability distribution function of the control load W(t), μ DL is the average value of the sum of the constant load effect and the continuous live load effect; r represents the resistance random variable, and f R0 (r) is the probability density function of the initial resistance R0.

[0077] S2: Introduce the equivalent resistance attenuation coefficient g* into the function to simplify the function and establish an equivalent time-varying failure probability expression;

[0078] By introducing the equivalent resistance attenuation coefficient g*, the calculation of the failure probability can be simplified and the function can be equivalent to:

[0079]

[0080] In formula (3), G(X) represents the random variable of the performance function, g* is the equivalent resistance attenuation coefficient, and L Sapt represents the random variable of the sustained live load effect at any time, represents the random variable of the maximum effect of the control load within the design service life T.

[0081] Correspondingly, the corresponding time-varying failure probability is equivalently expressed as:

[0082]

[0083] S3: Determine the calculation formula of the equivalent resistance attenuation coefficient g*;

[0084] In actual operation, for the determination of g*, the following several methods are preferably adopted:

[0085] (1) Theoretical calculation method of g*

[0086] By making formula (2) equivalent to formula (4) through simultaneous equations, making the failure probability calculated by formula (2) equal to the failure probability obtained by formula (4), the value of the equivalent resistance attenuation coefficient g* can be determined in this way.

[0087] However, the above theoretical calculation method for determining the value of g* involves the calculation of the structural failure probability and the solution of the integral equation, and the process is relatively complex and not applicable in engineering practice, and further simplification is required.

[0088] (2) Empirical calculation method of g*

[0089] In the process of calculating g* by simultaneously solving formula (2) and formula (4), it is found that the factors affecting the calculation result of the equivalent resistance attenuation coefficient g* are: design target reliability index, resistance attenuation function, resistance variation coefficient, and average occurrence rate and statistical characteristics of the control load effect, etc. After a large number of trial calculations and analyses, it is found that the design target reliability index, resistance variation coefficient, and average occurrence rate of the control load effect have little influence on the value of g*, while the resistance attenuation function and the statistical characteristics of the control load effect have a greater influence on the value of g*.

[0090] Therefore, for the sake of simplifying the calculation, the preferred embodiment further proposes an empirical calculation formula considering the main influencing factors of g*. In the derivation process, it mainly considers the influence of the resistance attenuation function and the statistical characteristics of the control load effect on the value of g*, and omits the influence of the design target reliability index, resistance variation coefficient, and average occurrence rate of the control load effect on the value of g*, and obtains the following calculation formula:

[0091]

[0092] In formula (5), θ = μ W / μ D , which is the ratio of the mean value μ W of the control load effect to the mean value μ D of the dead load effect; g(T) is the ratio of the remaining resistance value of the structure's design service life to the initial resistance value R0; V W is the coefficient of variation of the control load effect; m0, m1, m2, and m3 are regression coefficients under different probability distribution types and can be obtained by looking up tables. Given the known conditions of these three variables, g(T), θ, and V W , the regression coefficients can be obtained by looking up Table (1), and then the value of the equivalent resistance attenuation coefficient g* can be calculated.

[0093] Table 1 Values of regression coefficients in the new calculation formula of the equivalent resistance attenuation coefficient g*

[0094]

[0095] Furthermore, to verify the effectiveness of the empirical formula for g*, a structural member that bears dead load, sustained live load, and control load (wind load or seismic action) and whose performance decays over time is assumed. According to the foregoing records, its performance function is constructed with reference to formula (3), and the probability models and statistical characteristics of each random variable are shown in Table 2, and the structural resistance attenuation function model is shown in Table 3. Assume that the design service life is 100 years and the design target reliability index is β T = 1.0 - 5.0, and the values in parentheses are taken when other parameters in the table are not specified.

[0096] Table 2 Probability models of random variables (random processes)

[0097]

[0098] Table 3 Structural resistance attenuation function model

[0099]

[0100] Correspondingly, Figures 2 to 10 presents a comparison diagram of the calculation results of g* when the control load effect is of different distribution models.

[0101] Among them, Figures 2 to 4 presents a comparison diagram of the calculation results of formula (5) and the theoretical method (solving by combining formula (2) and formula (4)) when the control load effect is a lognormal distribution (W is a lognormal distribution, β T = 2.0).

[0102] Figures 5 to 7 presents a comparison diagram when the control load effect is a Type I extreme value distribution (W is a Type I extreme value distribution, βT Comparison diagram of the calculation results of formula (5) and the theoretical method when the control load effect follows an extreme value type II distribution (W follows an extreme value type II distribution, β

[0103] Figures 8 to 10 = 3.0). T Comparison diagram of the calculation results of formula (5) and the theoretical method when the control load effect follows an extreme value type II distribution (W follows an extreme value type II distribution, β

[0104] = 4.0). According to the above comparison diagrams, it can be seen that when the control load effect follows a lognormal, extreme value type I, and extreme value type II distributions, the estimation error of formula (5) for g* is within 2%, and the impact on the calculation results of the reliability index is very small. Therefore, formula (5) can be considered effective. Compared with the theoretical method, the calculation formula (5) of the equivalent resistance attenuation coefficient is simple and effective, and is more practical in actual engineering design.

[0105] S4: Calculate the initial resistance mean value μ R0 ;

[0106] The initial resistance mean value μ R0 Is preferably estimated by the following formula:

[0107]

[0108] In formula (6), μ R0 Is the initial resistance mean value, β T Is the design target reliability index, μ Si And σ Si Are the mean value and standard deviation of the load effect S i Respectively.

[0109] S5: Calculate the initial values of the standard deviation σ G0 , skewness α 3G0 , target second-order moment reliability index initial value β 2T0 And the mean value of the full-life design resistance μ RT ;

[0110] In the preferred embodiment, the full-life load and resistance partial coefficients are determined based on the third-order moment reliability theory. Among them, the reliability index formula of the third-order moment reliability analysis method is:

[0111]

[0112] In formula (7), β 3M Is the third-order moment reliability index corresponding to the performance function; β 2M And α 3G Are the second-order moment reliability index and skewness corresponding to the performance function respectively.

[0113] When the third-order moment reliability design is adopted, the third-order moment reliability index of the performance function shall not be less than the design target reliability index, that is,

[0114] β 3M ≥β T (8)

[0115] At the same time, in a preferred embodiment, β 2M and α 3G Calculate using formula (9) and formula (10) respectively:

[0116]

[0117]

[0118] In formula (9) and formula (10), μ G , σ G are the mean and standard deviation of the performance function G(X); μ R 、μ Si are resistance R and load effect S respectively i The mean of R , σ Si are resistance R and load effect S respectively i The standard deviation of 3R , α 3Si are resistance R and load effect S respectively i skewness.

[0119] From formula (7) and formula (8), we can deduce:

[0120] β 2M ≥β 2T (11)

[0121] Among them, β 2T It is defined as the target second-order moment reliability index and is calculated using the following formula

[0122]

[0123] By using formula (9), formula (10), and formula (12), the initial value σ of the standard deviation of the performance function G(X) can be calculated respectively: G0 , initial value of skewness α 3G0 , initial value of target second-order moment reliability index β 2T0 and the mean life-cycle target resistance μ RT :

[0124]

[0125]

[0126]

[0127]

[0128] S6: Calculate σ respectively G , α 3G and β 2T .

[0129] The standard deviation σ of the performance function G(X) G :

[0130]

[0131] Combined with the calculation data in S5, the skewness α 3G and the second - order moment reliability index β 2T of the performance function G(X) can be obtained according to Formula (10) and Formula (12).

[0132] S7: Determine the load φ* and the resistance partial factor γ i * considering the degradation of structural resistance performance;

[0133] Substitute Equation (9) into Equation (11), then

[0134]

[0135] By transposing terms and arranging and transforming the above formula, we can get:

[0136]

[0137] Among them,

[0138] α R =σ R / σ G , α Si =σ Si / σ G (20)

[0139] In the formula, α R and α Si are the separation coefficients of the resistance R and the load effect S i respectively.

[0140] So, Equation (19) can be simplified to:

[0141] g*·μ R (1 - α R V R β 2T )≥Σμ Si (1 + α Si V Si β 2T ) (21)

[0142] Wherein, V R , V Si are respectively the coefficient of variation of the resistance R and the load effect S i .

[0143] Since the general partial factor design expression is in the form of:

[0144] φ*·R n ≥∑γ i *·S ni (22)

[0145] Wherein, φ* is the full-life load, R n is the standard value of the resistance, γ i * is the full-life resistance partial factor of the load effect S i , S ni is the standard value of the load effect S i , and it and R n are determined through field measurement and data statistics.

[0146] By comparing Equation (21) and Equation (22), the full-life load and resistance partial factors based on the third-order moment method can be obtained as follows:

[0147]

[0148]

[0149] Equations (23) and (24) are the explicit calculation formulas for the full-life load and resistance partial factors based on the third-order moment reliability theory, which consider the attenuation of the structural resistance performance of the design object during the full-life cycle, and no iteration is required in the whole calculation process.

[0150] As follows, through a specific embodiment, the calculation process of the above load resistance partial factor will be introduced by way of example.

[0151] In this specific embodiment, a certain building structural member bears three kinds of uniformly distributed loads: dead load, live load and snow load. Among them, the snow load is the control load and has time-varying randomness. It is assumed that the resistance degradation process of the member is a deterministic attenuation function: g(t) = 1 - a*t^0.5, where the value of a is determined by the ratio of the remaining resistance value to the initial resistance value of the design service life.

[0152] Specifically, when carrying out the ultimate limit state design of this member based on the full-life reliability according to the method in the foregoing embodiment, the main process is as follows:

[0153] (1) The performance function is expressed as:

[0154] G(X) = g*·R - D - L - S

[0155] In the formula, \(g^*\) is the equivalent resistance attenuation coefficient, \(R\) is the resistance, \(D\) is the dead load effect, \(L\) is the live load effect, and \(S\) is the snow load effect. Assume that the design service life of the structural member is 100 years, and the probability parameters of the resistance and related load effects refer to Table 4.

[0156] Table 4 Probability models of random variables (random processes) in the example

[0157]

[0158] Note: The snow load effect \(S(100)\) in the table represents the statistical characteristics of the maximum snow load effect in 100 years.

[0159] (2) Calculate the equivalent resistance attenuation coefficient \(g^*\);

[0160] According to the known conditions, \(g(T)=g(100)=0.7\), the coefficient of variation of the control load: \(V_s = 0.21\), \(\mu\) S / \(\mu\) D \(= 2.946\). The control load (snow load) follows the Gumbel distribution, and the resistance attenuation function is a square root type function.

[0161] The equivalent resistance attenuation coefficient obtained by the theoretical method is: \(g^* = 0.7474\).

[0162] When calculating using the calculation formula (5), it can be seen from Table 1 that the coefficients \(m_0 = 3.341\), \(m_1 = 2.308\), \(m_2 = 0.00713\), \(m_3 = -0.00759\). Substitute the known data into the new formula, and we have

[0163]

[0164] It is not difficult to see that the relative error between the equivalent resistance attenuation coefficient calculated by the simplified empirical calculation formula (5) and the result calculated by the theoretical method is 0.87%. However, the simplified empirical calculation formula (5) is simple to operate and is more applicable to engineering practice than the theoretical method.

[0165] (3) Calculate the full-life load resistance partial factor based on the third-order moment method;

[0166] First, calculate the initial resistance mean according to formula (6):

[0167]

[0168] And calculate \(\sigma\) G0 , \(\alpha\) 3G0 and \(\beta\) 2T0 respectively according to formulas (13) - (15):

[0169]

[0170]

[0171]

[0172] Accordingly, substitute the above calculation results into formula (16) and obtain the mean value μ of the full-life target resistance RT :

[0173]

[0174] Subsequently, calculate σ G , α 3G and β 2T :

[0175] σ G = 3.412μ D , α 3G = 0.570, β 2T = 3.396

[0176] Obtain α R and α Si :

[0177] α R = σ R / σ G = 0.982

[0178] α D = σ D / σ G = 0.029

[0179] α L = σ L / σ G = 0.030

[0180]

[0181] Finally, determine the full-life load and resistance partial factors based on the third-moment method:

[0182] φ* = μ R · g* · (1 - α R V R β 2T ) / R n = 0.354

[0183] γ D * = μ D (1 + α D V D β 2T ) / D n = 1.010

[0184] γL * = μ L (1 + α L V L β 2T ) / L n = 0.371

[0185]

[0186] In summary, the full - life LRFD expression based on the third - moment method and the mean value of the full - life target resistance are as follows:

[0187] 0.35R n ≥1.01D n + 0.37L n + 1.11S n

[0188]

[0189] Based on this full - life LRFD expression, the time - varying reliability of the component is back - calculated using the first - order reliability method (FORM), and the variation law of the reliability over time within the design service life is as Figure 11 shown. From Figure 11 it can be seen that using the full - life LRFD expression based on the third - moment method can achieve the structural design goal based on full - life reliability and meet the full - life design requirements of engineering structures.

[0190] Furthermore, in order to facilitate the application of the load and resistance factor calculation method that considers the attenuation of structural resistance performance and does not require iterative calculation in the preferred embodiment, a computer - readable storage medium and a computer device are also provided correspondingly in the preferred embodiment.

[0191] Among them, for the computer - readable storage medium in the preferred embodiment, a computer program is stored thereon, and when the computer program is executed by a processor, the steps in the aforementioned load and resistance factor calculation method that considers the attenuation of structural resistance performance and does not require iterative calculation are implemented. Correspondingly, the computer device includes a memory, a processor, and a computer program; wherein, the computer program is stored in the memory and is configured to be executable by the processor, and when the processor executes the computer program, the steps in the aforementioned load and resistance factor calculation method that considers the attenuation of structural resistance performance and does not require iterative calculation are implemented.

[0192] The load and resistance factor calculation method in the present invention is simple and easy to operate, capable of quickly calculating the load and resistance factors of the design object, achieving the full-life reliability design of the design object, and fully considering the attenuation of the structural resistance performance of the design object during the design process, making the reliability design more in line with the actual working conditions of the design object. At the same time, by introducing the third-order moment reliability theory into the calculation method to determine the full-life load and resistance factors, it can effectively avoid the iterative calculation process in the existing design process, simplify the calculation process of the load and resistance factors, shorten the reliability design cycle of the design object, improve the efficiency of the reliability design of the design object, and has good practical value and practical significance.

[0193] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A calculation method for load and resistance factor that considers the performance degradation of structural resistance and does not require iterative calculation, characterized in that, It includes the following steps: S1: Establish the structural limit state function G(t) and the expression of time-varying failure probability P f (T); where the expressions of G(t) and P f (T) are respectively: G(t) = g(t)·R0 - D - L S (t) - W(t) (1) In the formula, G(t) is the function of the ballastless track structure at time t; D is the permanent load effect that does not change with time; L S (t) is the continuous live load effect at time t; W(t) is the control load effect at time t; g(t) is the structural resistance attenuation function; R0 is the initial structural resistance; λ W and F W (w) are the average occurrence rate and cumulative probability distribution function of the control load W(t) respectively; μ DL is the average value of the sum of the permanent load effect and the continuous live load effect; r represents the resistance random variable; f R0 (r) is the probability density function of the initial resistance R0; S2: Introduce the equivalent resistance attenuation coefficient g* into the performance function to obtain the simplified performance function G(X) and the equivalent time-varying failure probability expression P f ′(T); where the expressions of G(X) and P f ′(T) are respectively: Wherein, G(X) represents the random variable of the performance function, and L Sapt represents the random variable of the sustained live load effect at any time, represents the random variable of the maximum effect of the control load within the design service life T; S3: According to P f (T) and P f '(T) to derive the calculation formula of the equivalent resistance attenuation coefficient g*; and the calculation formula is: Where, θ = μ W / μ D , which is the ratio of the mean value of the control load effect μ W to the mean value of the dead load effect μ D ; g(T) is the ratio of the remaining resistance value of the structure's design service life to the initial resistance value R0; V W is the coefficient of variation of the control load effect; m0, m1, m2, and m3 are regression coefficients under different probability distribution types; S4: Calculate the mean value μ of the initial resistance R0 ; S5: Calculate the initial standard deviation σ of the performance function G(X) G0 , the initial skewness α 3G0 , the initial target second moment reliability index β 2T0 and the mean value μ of the design resistance RT ; where where, μ Si is the mean value of the load effect S i , σ G0 is the standard deviation of the performance function G(X), and β 2T0 is the initial value of the target second moment reliability index calculated from μ R0 ; S6: Calculate the standard deviation σ G , skewness α 3G and the target second-order moment reliability index β 2T , and obtain the separation coefficients α i and α R between the resistance R and the load effect S Si ; S7: Determine the load φ* and resistance partial factor γ considering the degradation of structural resistance performance i *; where where α R and α Si are the separation coefficients of the resistance R and the load effect S i respectively; V R and V Si are the coefficient of variation of the resistance R and the load effect S i respectively; μ R and μ Si are the mean values of the resistance R and the load effect S i respectively; R n is the standard value of the resistance, and S ni is the standard value of the load effect, and both are determined by on-site measurement and data statistics.

2. The load and resistance factor calculation method according to claim 1, which takes into account the degradation of structural resistance performance and does not require iterative calculation, is characterized in that In S3, the process of obtaining the calculation formula of g* is as follows: Simultaneously derive and calculate formulas (2) and (4). During the derivation process, consider the influence of the resistance attenuation function and the statistical characteristics of the control load effect on the value of g*, and omit the influence of the design target reliability index, the resistance variation coefficient, and the average occurrence rate of the control load effect on the value of g*.

3. The load and resistance factor calculation method according to claim 1, which takes into account the degradation of structural resistance performance and does not require iterative calculation, is characterized in that In S4, the initial mean resistance μ R0 is estimated by the following formula: where μ R0 is the mean value of the initial resistance, β T is the design target reliability index, μ Si and σ Si are the mean value and the standard deviation of the load effect S i , respectively.

4. The load and resistance factor calculation method according to any one of claims 1 to 3, which takes into account the degradation of structural resistance performance and does not require iterative calculation, is characterized in that In S5, σ G0 , α 3G0 and β 2T0 are calculated respectively according to the following calculation formulas: where, σ G0 , α 3G0 are respectively the initial standard deviation value and the initial skewness value of the performance function G(X); β 2T0 is the initial value of the target second-order moment reliability index; σ R0 is the initial standard deviation value of the resistance R; σ Si is the standard deviation of the load effect S i ; α 3R , α 3i are respectively the skewness of the resistance R and the load effect S i .

5. The load and resistance factor calculation method according to claim 4, which considers the degradation of structural resistance performance and does not require iterative calculation, is characterized in that In S6, σ G , α 3G and β 2T are calculated by the following formula: where σ G , α 3G are the standard deviation and skewness of the performance function G(X) respectively; β 2T is the target second moment reliability index; σ R , σ Si are the standard deviations of the resistance R and the load effect S i respectively; α 3R , α 3i are the skewnesses of the resistance R and the load effect S i respectively.

6. The load and resistance factor calculation method according to claim 5, which considers the degradation of structural resistance performance and does not require iterative calculation, is characterized in that In S6, the separation coefficient of the resistance R and the load effect S i is calculated by the following formula: α R = σ R / σ G α Si = σ Si / σ G where σ R , σ Si are the standard deviations of the resistance R and the load effect S i respectively, and σ G is the standard deviation of the performance function G(X).

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps in the load and resistance factor calculation method described in any one of claims 1 to 6, which considers the degradation of structural resistance performance and does not require iterative calculation.

8. A computer device, comprising a memory, a processor, and a computer program, characterized in that the computer program is stored in the memory and is configured to be executable by the processor, and when the processor executes the computer program, it implements the steps in the load and resistance factor calculation method described in any one of claims 1 to 6, which considers the degradation of structural resistance performance and does not require iterative calculation.

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