Shield tunnel joint sealing gasket type selection method based on multi-criterion decision

Abstract

The invention discloses a shield tunnel joint sealing gasket type selection method based on multi-criterion decision, which comprises the following steps of: selecting design water pressure, maximum joint opening amount, maximum assembly force and allowable maximum groove filling rate as design threshold values; the average contact stress under the maximum seam opening amount, the maximum seam opening amount compatible under the design water pressure, the closing compression force, the maximum groove filling rate and the sealing gasket sectional area are selected as performance evaluation indexes, different sealing gasket evaluation index values are obtained through tests, the marginal effect of the indexes is considered, the marginal values of the sealing gasket evaluation indexes are obtained, and the performance of the sealing gasket is evaluated. And determining objective weights of the evaluation indexes by adopting a CRITIC method, and obtaining the sealing gasket with the best comprehensive performance in the different sealing gaskets by adopting a TOPSIS method according to the marginal values and the objective weights. Scientific quantitative evaluation of the waterproof performance, the assembling performance and the economical efficiency of the sealing gasket is achieved through the multiple evaluation indexes, the model selection result is more scientific, reasonable and economical, and blindness of an existing design method is avoided.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of waterproof sealing pads for shield tunnels, and particularly relates to a method for selecting a sealing pad for a shield tunnel joint based on multi-criteria decision-making, which is suitable for cross-section selection of the sealing pad, optimization of material parameters, and engineering adaptability design. BACKGROUND

[0002] Shield construction is a modern tunnel construction method, which has the advantages of construction safety, high quality and high efficiency, and is widely used not only in highway, railway and other traffic tunnel construction, but also in power, hydraulic, oil and gas, and pipe gallery construction. In the construction of shield tunnels, sealing pads play a crucial role in waterproofing, especially in tunnels with complex hydrological environments. The waterproofing performance, deformation adaptability and assembly performance of the sealing pads directly affect the construction quality and operational safety of the tunnel.

[0003] As the core waterproofing material for shield tunnels, elastic rubber sealing pads not only need to meet the waterproofing requirements against external water pressure, but also need to be compatible with the assembly errors of shield segments. In 1983, the Sheffields Tunnel in the United Kingdom first adopted a porous comb-shaped rubber sealing pad cross-section design, which has been used to this day. The design of the open structure reduces the overall stiffness of the sealing component, making the compression force grow more smoothly, effectively solving the problem of segment cracking caused by excessive closing compression force. In addition, under the same material usage, the open structure sealing pad is higher in height and larger in external size, effectively extending the compression stroke of the sealing pad, so that the sealing pad can maintain a high contact stress even under a large joint deformation, improving the deformation adaptability of the sealing. Since the completion of the Sheffields Tunnel, various rubber product manufacturers at home and abroad have developed a variety of sealing pad cross-section structures.

[0004] Due to the test cost of sealing pad waterproof performance testing, the current sealing pad cross-section design still relies heavily on experience analogy. Specifically, the engineering requirements are usually used as the design guide, and the sealing pad structure form of similar projects at home and abroad is used for direct "copying" analogy to determine the cross-section form of the sealing pad. However, the hydrological environment and design diameter of different shield tunnel projects differ greatly, and the requirements for the waterproof performance and deformation adaptability of the sealing pad are also different. The sealing pad cross-section form is complex, and the key indicators such as waterproof performance, assembly performance and economy are mutually restrictive. Blindly using the experience analogy design method is likely to lose sight of the wood for the trees, and it is difficult to find the best performance balance point and cross-section design scheme according to the actual engineering needs.

[0005] Although some design selection theories of sealing gaskets are proposed in some studies, there are still some limitations. For example, Lei Zhenyu (Lei Zhenyu. Optimization design method of rubber sealing gasket for shield tunnel segment [J]. Journal of Underground Space and Engineering, 2010, 6(04): 770-774.) proposes a sealing gasket optimization design method taking the surface contact stress of the sealing gasket and the closing compression force when fully compressed as the double control index. The key is to require the closing compression force to be as small as possible under the premise of meeting the water tightness to improve the assembly performance; Chinese invention patent application CN119760904A discloses an integrated design method and system for shield segment groove and waterproof elastic sealing gasket, which proposes to take one of the average contact stress of the contact surface, the penetration load, the fluid pressure or the groove area as the target function to optimize the design of the sealing gasket under the condition that the assembly force (closing compression force) does not exceed the limit value; Chinese invention patent application CN119760905A discloses a design method, system and terminal for shield tunnel joint waterproof elastic sealing gasket, which proposes to optimize the profile of the sealing gasket to achieve higher waterproof capacity under the condition that the assembly force (closing compression force) does not exceed the limit value.

[0006] In summary, the existing sealing gasket optimization design theory has the following limitations: 1) single evaluation index, optimization design is usually the optimization of single performance, it is difficult to balance the multiple performance requirements of the sealing gasket: most of the existing theories adopt the method of optimizing a single performance index under the constraint condition, such as reducing the closing compression force under the premise of meeting the waterproof performance constraint, or optimizing the waterproof performance under the condition that the closing compression force does not exceed the limit value, which is easy to cause the situation of losing one to save the other, resulting in poor comprehensive performance of the sealing gasket. 2) The importance of the evaluation index is not quantified: the existing theory does not quantitatively calculate the weight values of the waterproof performance, assembly performance and economic index of the sealing gasket, and cannot scientifically evaluate the comprehensive service performance of the sealing gasket, which has certain blindness in design.

[0007] Therefore, how to select the sealing gasket through a scientific method so that the sealing gasket has good comprehensive performance has become a technical problem to be solved in the field of sealing gaskets for shield tunnels. SUMMARY

[0008] The purpose of the present application is to solve the problem that the selection of the sealing gasket for the joint of the shield tunnel is seriously dependent on experience and analogy, and the design lacks scientific basis. A sealing gasket selection method for the joint of the shield tunnel based on multi-criteria decision is proposed, which realizes the scientific quantitative evaluation and optimization design of the waterproofness, assembly performance and economy of the sealing gasket, solves the blindness problem of experience design, and makes the sealing gasket have good comprehensive performance.

[0009] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0010] A method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making, comprising the following steps:

[0011] Step one, selecting a design water pressure T1, a maximum joint opening amount T2, a maximum assembly force T3, and an allowable maximum groove filling rate T4 as design thresholds of the sealing gasket;

[0012] Step two, selecting an average contact stress u1 under the maximum joint opening amount T2, a maximum joint opening amount u2 that is compatible under the design water pressure T1, a closing compression force u3, a maximum groove filling rate u4, and a sealing gasket cross-sectional area u5 as evaluation indexes of the sealing gasket performance;

[0013] Step three, selecting multiple sealing gaskets with different cross-sectional forms, different hardnesses, and different groove depths, and obtaining compression force-displacement curves of the different sealing gaskets through compression mechanics tests or finite element simulation tests;

[0014] Step four, determining values of the evaluation indexes of the corresponding sealing gaskets according to the compression force-displacement curves of the different sealing gaskets obtained in step three, performing normalization processing on the values of the evaluation indexes by using a maximum-minimum normalization method, and performing marginal decreasing processing on the normalized values of the evaluation indexes according to marginal effects of the evaluation indexes to obtain marginal values of the evaluation indexes of the different sealing gaskets;

[0015] Step five, determining objective weights of the evaluation indexes by using a CRITIC method;

[0016] Step six, obtaining a sealing gasket with the best comprehensive performance from the different sealing gaskets by using a TOPSIS method according to the marginal values of the evaluation indexes obtained in step four and the objective weights obtained in step five.

[0017] It should be noted that in step one, the maximum groove filling rate is calculated according to formula (2.1).

[0018] (2.1)

[0019] In the formula, η is the maximum groove filling rate, A is the cross-sectional area of the sealing gasket, and A g is the cross-sectional area of the groove of the sealing gasket.

[0020] It should be noted that in step one, the design thresholds are determined by the following method:

[0021] (1) For deep-buried tunnels and shallow-buried tunnels, the design water pressure T1 is 2 times and 3 times the maximum water pressure of the tunnel depth, respectively;

[0022] (2) According to engineering experience, for shield tunnels with a diameter of no more than 10 m, the maximum joint opening amount T2 is usually 6 mm, and for shield tunnels with a diameter of more than 10 m, the maximum joint opening amount T2 is usually 8 mm;

[0023] (3) the maximum assembly force T3 is not more than the thrust force of the shield segment erector;

[0024] (4) the allowable maximum trench filling rate T4 is not more than 100%.

[0025] It should be noted that in step two, the evaluation index and the design threshold satisfy the following conditions:

[0026] The average contact stress u1 under the maximum joint opening amount T2 is greater than or equal to the design water pressure T1, the maximum joint opening amount u2 compatible under the design water pressure T1 is greater than or equal to the maximum joint opening amount T2, the closing compression force u3 is less than or equal to the maximum assembly force T3, and the maximum trench filling rate u4 is less than or equal to the allowable maximum trench filling rate T4.

[0027] It should be noted that in step three, the hardness of the gasket is in the range of 60-70 Shore, and the maximum trench filling rate is 86.96%-100%.

[0028] It should be noted that in step three, for the same cross-sectional form, at least three different hardness, three different trench depth gaskets are selected for compression mechanics test or finite element simulation test.

[0029] It should be noted that in step four, the maximum and minimum normalization method is used to normalize the evaluation index value according to formula (4.1):

[0030] (4.1)

[0031] In the formula: is the jth evaluation index value in the ith gasket scheme; or is the maximum or minimum value of the jth evaluation index value in all gasket schemes; is the normalized value of the jth evaluation index in the ith gasket scheme.

[0032] It should be noted that in step four, according to the marginal effect of each evaluation index, the normalized evaluation index value is processed by marginal diminishing according to formula (4.2), and the marginal value of each evaluation index of different gaskets is obtained:

[0033] (4.2)

[0034] In the formula: p ij is the marginal value of the jth evaluation index in the ith gasket scheme; is the normalized value of the design threshold (maximum and minimum normalization method); α is the marginal diminishing processing discrimination coefficient, when j=1, 2, 3, 4, α takes 2, and when j=5, α takes 1.

[0035] It should be noted that in step five, the objective weight of each evaluation index is determined according to the CRITIC method and formula (5.1);

[0036] (5.1)

[0037] In the formula: w j is the objective weight value of the jth evaluation index; I j is the information amount of the jth evaluation index;

[0038] In the formula, I j is determined according to formula (5.2)-(5.4):

[0039] (5.2)

[0040] (5.3)

[0041] (5.4)

[0042] In the formula: p jr is the Pearson correlation coefficient of the jth evaluation index and the rth evaluation index, j and r are two different representations of the evaluation index, r = 1, 2, 3, 4, 5; k is the total number of sealing gasket schemes; or is the marginal value of the jth or rth evaluation index in the ith alternative scheme; or is the average value of the marginal value of the jth or rth evaluation index in all alternative sealing gasket schemes; s j is the standard deviation of the jth evaluation index.

[0043] It should be noted that in step six, according to the marginal value of each evaluation index and the objective weight, the comprehensive performance value of different sealing gaskets is calculated according to formula (6.1) by using the TOPSIS method, and the sealing gasket with the largest comprehensive performance value is selected as the best sealing gasket:

[0044] (6.1)

[0045] In the formula: C i + is the comprehensive performance value of the sealing gasket; D i + is the distance from the weighted decision matrix of the ith sealing gasket to the positive ideal solution; D i - is the distance from the weighted decision matrix of the ith sealing gasket to the negative ideal solution;

[0046] In the formula, D i+ and D i - Determined according to formula (6.2), (6.3) respectively:

[0047] (6.2)

[0048] (6.3)

[0049] In the formula: z ij The weighted decision value of the i-th sealing gasket j-th evaluation index; z j + Or z j - The maximum or minimum value of the weighted decision value of the j-th evaluation index;

[0050] Wherein, z ij Determined according to formula (6.4):

[0051] (6.4).

[0052] Compared with the prior art, the present application has the following beneficial technical effects:

[0053] (1) The present application establishes a sealing gasket selection method based on multi-criteria decision-making, uses multiple evaluation indexes, realizes scientific and quantitative evaluation of the waterproof performance, assembly performance and economy of the sealing gasket of the shield tunnel joint, and solves the problem of blindness in current experience-based analogy design.

[0054] (2) The process of the present application is clear and feasible. The weights of the evaluation indexes are determined based on objective data using the CRITIC method, which to some extent avoids the human bias and errors caused by subjective judgment or expert experience, making the results more objective. The TOPSIS method is used to determine the best scheme of the sealing gasket, providing the optimal performance balance point.

[0055] (3) The present application uses the principle of marginal diminishing to preprocess the data of the evaluation indexes, improves the data input of the traditional evaluation model, reduces the interference of extreme data points on the evaluation results, solves the problem of excessive pursuit of a certain performance in traditional design, ensures the optimal balance of cost and benefit, realizes the optimal resource input-output ratio, makes the selection method more accurate to find the design scheme that meets the actual engineering requirements, avoids the cost waste caused by excessive design or selection of unsuitable materials, and improves the scientificity and rationality of the selection method.

[0056] (4) The application has wide applicability, can realize comprehensive evaluation of sealing pad schemes according to different design requirements, and improves the reliability and safety of the sealing scheme for shield tunnel projects under different hydrogeological conditions and construction technical conditions. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 For the scheme technical roadmap.

[0058] Figure 2 For 60 kinds of sealing pad cross-sectional forms.

[0059] Figure 3 For the compression curve and index value determination of a typical sealing scheme (M46 sealing pad, 65H A hardness, 14mm groove depth).

[0060] Figure 4 For the normalization and marginal decrease processing of the evaluation index value; wherein, Figure 4 (a) is the normalization and marginal decrease processing result of the evaluation index u1 value; Figure 4 (b) is the normalization and marginal decrease processing result of the evaluation index u2 value; Figure 4 (c) is the normalization and marginal decrease processing result of the evaluation index u3 value; Figure 4 (d) is the normalization and marginal decrease processing result of the evaluation index u4 value; Figure 4 (e) is the normalization and marginal decrease processing result of the evaluation index u5 value.

[0061] Figure 5 For the correlation coefficient matrix of the index. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application.

[0063] Please refer to Figure 1 The application provides a shield tunnel joint sealing pad selection method based on multi-criteria decision, which comprehensively considers various performance requirements (i.e., multiple targets) of the sealing pad for waterproof performance, assembly performance and economy, comprehensively evaluates and sorts the alternative sealing pad schemes, and finds the optimal or satisfactory sealing pad scheme that meets the engineering requirements.

[0064] The selection method specifically includes the following steps:

[0065] Step 1, determining design threshold values:

[0066] Selecting design water pressure T1, maximum joint opening amount T2, maximum assembly force T3 and allowable maximum groove filling rate T4 as the design threshold values of the sealing pad.

[0067] The maximum groove filling rate η can be calculated by formula (1.1).

[0068] (1.1)

[0069] In the formula: η is the maximum groove filling rate; A is the cross-sectional area of the gasket; A g is the cross-sectional area of the gasket groove.

[0070] According to the hydrogeological conditions and construction technical conditions of the shield tunnel, the specific value of the design threshold can be determined by the following method:

[0071] (1) Design water pressure T1: determined by the external water pressure borne by the tunnel and the long-term service safety factor coefficient. According to the design specification "Technical Code for Waterproofing of Underground Engineering" GB50108-2008, for deep buried tunnels and shallow buried tunnels, 2 times and 3 times of the maximum water pressure of the tunnel buried depth can be taken respectively.

[0072] (2) Maximum joint opening amount T2: the most unfavorable deformation condition that the shield tunnel joint can reach, determined by the joint connection form of the shield tunnel segment and the construction assembly quality. Generally, the larger the diameter and the segment size of the shield tunnel, the more difficult to control the joint deformation. According to engineering experience, for medium and small diameter shield tunnels with diameter ≤10m, the maximum joint opening amount T2 is usually taken as 6mm, and for large diameter shield tunnels with diameter >10m, the maximum joint opening amount T2 is usually taken as 8mm.

[0073] (3) Maximum assembly force T3: the compression reaction force per meter of gasket when the joint is compressed to the opening amount of 0mm, which shall not exceed the jacking force of the segment assembling machine of the shield machine.

[0074] (4) Allowable maximum groove filling rate T4: due to the invariance of rubber material in compression process, according to the design specification, in order to prevent the gasket from crushing the concrete segment, the groove filling rate T4 of the gasket when compressed to the joint opening amount of 0mm shall not exceed 100%.

[0075] The distinction between deep buried tunnels and shallow buried tunnels can be based on "Railway Tunnel Design Specification" TB10003-2016. Step two, determine the performance evaluation index of the gasket:

[0076] Select the average contact stress u1 under the maximum joint opening amount T2, the maximum joint opening amount u2 that can be compatible under the design water pressure T1, the closed compression force u3, the maximum groove filling rate u4, and the gasket cross-sectional area u5 as the evaluation index of the gasket performance.

[0077] Considering the performance requirements of the gasket in the design specification and the cost required by the engineering construction, and referring to the experience of experts in the shield tunnel construction industry, the following 5 evaluation indexes uj to evaluate the waterproof performance, assembly performance and economy of the sealing gasket:

[0078] (1) Average contact stress u1 under the maximum joint opening amount T2: the larger u1 is, the greater the external water pressure that the sealing gasket can withstand under the designed joint deformation amount, and the waterproof performance of the sealing scheme is positively correlated;

[0079] (2) Maximum joint opening amount u2 that can be compatible under the design water pressure T1: the larger u2 is, the greater the additional joint opening deformation that the sealing gasket can be compatible with without leakage, reflecting the safety reserve of the sealing gasket to the joint deformation, and the waterproof performance of the sealing scheme is positively correlated;

[0080] (3) Closing compression force u3: representing the compression force of the sealing gasket when compressed to the joint opening amount of 0 mm, a smaller closing compression force is conducive to flexible adjustment of the geometry of the segment in the assembly construction process, reduces the assembly error, and improves the quality of segment assembly. The larger u3 is, the higher the requirement for the thrust force of the shield jacks, and the assembly performance of the sealing scheme is negatively correlated;

[0081] (4) Maximum groove filling rate u4: the larger u4 is, the higher the risk of segment cracking when the sealing gasket is fully compressed, and the assembly performance of the sealing scheme is negatively correlated.

[0082] (5) Sealing gasket cross-sectional order u5: the larger u5 is, the higher the material cost required by the scheme, and the economy of the sealing scheme is negatively correlated.

[0083] In fact, the sealing gasket design needs to meet the following conditions: the average contact stress u1 under the maximum joint opening amount T2 is greater than or equal to the design water pressure T1, the maximum joint opening amount u2 that can be compatible under the design water pressure T1 is greater than or equal to the maximum joint opening amount T2, the closing compression force u3 is less than or equal to the maximum assembly force T3, and the maximum groove filling rate u4 is less than or equal to the allowable maximum groove filling rate T4.

[0084] The selection of the above evaluation indexes and design thresholds comprehensively considers the key performance requirements of the sealing gasket material in the design, construction and service process of the shield tunnel. In the prior art, most of the existing sealing gasket design selection theories only consider the influence of the average contact stress u1 and the closing compression force u3, and the following shortcomings exist:

[0085] (1) The economy of the sealing gasket scheme is not considered. The material cost of the sealing gasket is one of the important considerations in engineering construction, so the sealing gasket cross-sectional order u5 is supplemented as an index for evaluating the economy of the scheme.

[0086] (2) Only using the average contact stress u1 as the waterproof performance index of the sealing gasket is not comprehensive enough. The sealing gasket of the shield tunnel is not only a sealing component of the segment joint, but also a connecting component, which needs to meet the requirements of resisting water pressure and being compatible with joint deformation, so the present application supplements the maximum joint opening amount u2 which can be compatible as another evaluation index for evaluating the waterproof performance of the sealing gasket.

[0087] (3) Only using the closed compression force u3 as the assembly performance index of the sealing gasket is not comprehensive enough. The closed compression force index is mainly used to evaluate the assembly difficulty of the segment, which affects the assembly accuracy of the segment. In actual engineering, considering the size error of the concrete segment and the sealing gasket product, part of the segments will crack due to the maximum groove filling rate exceeding the limit value, which also seriously affects the assembly quality. Therefore, the present application supplements the maximum groove filling rate u4 as another index for evaluating the assembly performance of the sealing gasket.

[0088] Step three, establishing the compression mechanics data set of the sealing gasket:

[0089] Select multiple sealing gaskets with different cross-sectional forms, different hardness and different groove depths, and obtain the compression force-displacement curves of different sealing gaskets through compression mechanics test or finite element simulation test.

[0090] Among them, the hardness and groove depth of the alternative sealing gasket need to meet the requirements of the national standard "Shield Tunnel Engineering Design Standard" GB / T 51438-2021, the hardness range of the sealing gasket is 60-70 Shore, and the cross-sectional area A of the sealing gasket groove is 1-1.15 times the cross-sectional area of the sealing gasket, i.e. the maximum groove filling rate η=86.96%-100%. g Among them, the hardness and groove depth of the alternative sealing gasket need to meet the requirements of the national standard "Shield Tunnel Engineering Design Standard" GB / T 51438-2021, the hardness range of the sealing gasket is 60-70 Shore, and the cross-sectional area A of the sealing gasket groove is 1-1.15 times the cross-sectional area of the sealing gasket, i.e. the maximum groove filling rate η=86.96%-100%.

[0091] First, collect several alternative sealing gasket cross-sectional forms. The profile and size of the sealing gasket cross-section can be selected from the product manual of the sealing material supplier, or the hole structure of the sealing gasket can be designed and adjusted by referring to other shield projects or similar projects as an alternative cross-section; Next, for each sealing gasket cross-sectional form, set several different hardness and groove depths under the premise of meeting the hardness and maximum groove filling rate requirements to enrich the evaluation data set; For the same cross-sectional form, at least three different hardness and three different groove depth sealing gaskets are selected to carry out compression mechanics test or finite element simulation test.

[0092] Step four, normalization and marginal decrease of the evaluation index value:

[0093] According to the compression force-displacement curves of different sealing gaskets obtained in step three, the evaluation index values u ij of the corresponding sealing gaskets are determined, and the minimum maximum normalization method is used to normalize the evaluation index values u ijThe normalized evaluation index value x is obtained by normalization ij ; according to the marginal effect of each evaluation index, the normalized evaluation index value x ij is subjected to marginal diminishing processing to obtain the marginal value p of each evaluation index of the different sealing gaskets ij ;

[0094] According to the sealing gasket compression mechanical property data set obtained in step three, the performance evaluation index value of each sealing gasket scheme can be determined, and the jth performance evaluation index value of the ith sealing gasket scheme is summarized to obtain the original matrix U=(u ij ) k×5 , and k is the total number of sealing gasket schemes used to construct the evaluation model.

[0095] In order to eliminate the dimensional differences between the indexes, the maximum and minimum normalization method is used to normalize the original matrix, and the data in the original matrix is scaled to the interval [0, 1] to obtain the normalized evaluation index value and the normalized matrix X=(x ij ) k×5 , wherein x ij is the normalized value of the original data u ij , x ij =0 represents the most unfavorable case, and x ij =1 represents the most favorable case.

[0096] For positively correlated indexes u1, u2, i.e. j=1, 2, the larger the evaluation index value, the better the performance of the sealing gasket scheme, and the positive normalization formula (4.1a) is used to normalize the evaluation index value:

[0097] (4.1a)

[0098] In the formula: is the jth performance evaluation index value of the ith alternative scheme; or is the maximum or minimum of the jth evaluation index value of all alternative schemes; is the normalized value of the jth performance evaluation index of the ith alternative scheme.

[0099] For negatively correlated indexes u3, u4, u5, i.e. j=3, 4, 5, the smaller the evaluation index value, the better the performance of the sealing gasket scheme, and the negative normalization formula (4.1b) is used to normalize the evaluation index value:

[0100] (4.1b).

[0101] In order to avoid unnecessary investment caused by blindly pursuing high performance, and to achieve the optimal balance between cost and benefit, the normalized index value is processed by marginal diminishing using formula (4.2) to obtain the marginal value p of each performance evaluation index of different sealing gaskets ij The marginal diminishing matrix P=(p ij ) k×5 Since the four performance evaluation indexes u1, u2, u3, and u4 have corresponding design threshold constraints, when the performance evaluation index u j far exceeds the design threshold T j , the actual improvement benefit of the project is not significant, that is, the marginal effect occurs. In order to avoid the over-pursuit of a single performance by the evaluation model (multi-criteria decision model), when j=1, 2, 3, 4, α takes 2 to consider the marginal diminishing effect of the sealing scheme performance; and the performance index u5 (cross-sectional area) as a cost index does not have strict design threshold constraints, and is not processed by marginal diminishing, so when j=5, α takes 1 to make the index still maintain a linear rule.

[0102] (4.2)

[0103] In the formula, p ij is the marginal value of the jth performance evaluation index of the ith sealing gasket scheme; is the normalized value of the design threshold T .

[0104] In fact, when j=5, α takes 1, so formula (4.2) is simplified to .

[0105] The characteristics of using formula (4.2) to process the normalized index value x ij by marginal diminishing are: the distribution interval of the normalized index value x ij is not changed, and the marginal value p ij after marginal diminishing is still in the distribution range of [0, 1], ensuring that the data of different indexes are in the same data magnitude; when the performance evaluation index u j reaches the design threshold T j , the performance improvement Δp ij caused by the unit increment of u j is the largest; when the performance index u j gradually deviates from the design threshold T j , the performance improvement Δp ij caused by the unit increment of u j gradually decreases, reflecting the marginal diminishing effect of performance improvement on the overall benefit of the scheme.

[0106] Step five, determine the objective weight of each evaluation index by using the CRITIC method.

[0107] The CRITIC method (Criteria Importance Through Intercriteria Correlation) is used to determine the weight value of the index. This method is an objective weighting method based on data statistical analysis. The core idea is to calculate the weight through the comparison intensity and conflict between indexes. The stronger the conflict and independence of the index, the higher the objective weight value.

[0108] Standard deviation σ j Reflects the performance dispersion degree of different sealing gasket schemes in the evaluation index j. The standard deviation σ j Can be calculated by formula (5.1):

[0109] (5.1)

[0110] Wherein, is the average value of the jth performance index.

[0111] Pearson correlation coefficient ρ of index j and index r jr Can be calculated by formula (5.2):

[0112] (5.2)

[0113] In the formula: ρ jr is the Pearson correlation coefficient of evaluation index j and evaluation index r; k is the total number of sealing gasket schemes used to construct the evaluation model; Or is the marginal value of the jth or rth evaluation index in the ith alternative scheme; Or is the average value of the marginal decrease of the jth or rth evaluation index in all alternative schemes.

[0114] Then the conflict C of evaluation index j j Can be calculated by formula (5.3):

[0115] (5.3)

[0116] Multiply the standard deviation and the conflict to get the information amount I of index j j , as formula (5.4):

[0117] (5.4)

[0118] Wherein, the standard deviation σ j reflects the dispersion of index j itself, and the larger σ j , the larger the information amount contained in index j; the conflict Cj Reflects the conflict between the index j and other indicators, if the correlation coefficient between index j and other indicators is larger, the information contained in other indicators of index j is more, the conflict of index j C j The smaller. Conversely, the lower the correlation coefficient between index j and other indicators r, the higher the conflict of index j, the stronger the independence of the index, and the higher weight value should be given. The information amount I j Normalized, the objective weight value w j of the jth index is calculated as formula (5.5).

[0119] (5.5)

[0120] In the formula: w j is the objective weight value of the jth evaluation index; I j is the information amount of the jth evaluation index.

[0121] Step six, calculate the relative proximity of different sealing gasket schemes and sort, get the best sealing gasket scheme:

[0122] According to the marginal value of each evaluation index obtained in step four and the objective weight obtained in step five, the TOPSIS method (Technique for Order Preference by Similarity to Ideal Solution) is used to determine the preferred order of different sealing gasket schemes. This method compares the geometric proximity of the ideal solution of the alternative scheme and the ideal solution, and realizes the comprehensive performance evaluation and sorting of the scheme. The detailed steps include:

[0123] Each element p ij in the marginal decreasing vector matrix P is multiplied by the weight value w j , and the weighted decision matrix Z=(z ij ) k×5 is obtained, where z ij is calculated according to formula (6.1):

[0124] (6.1)

[0125] The positive ideal solution Z + of each evaluation index can be determined by formula (6.2), and the negative ideal solution Z - can be determined by formula (6.3):

[0126] (6.2)

[0127] (6.3)

[0128] In the formula: zj + or z j - The first and the second are the positive ideal value or negative ideal value of the jth evaluation index.

[0129] The distance D of the ith sealing gasket scheme to the positive ideal solution i + The distance D of the ith sealing gasket scheme to the negative ideal solution can be calculated by formula (6.4) i - The distance D of the ith sealing gasket scheme to the negative ideal solution can be calculated by formula (6.4)

[0130] (6.4);

[0131] (6.5).

[0132] The relative closeness C of the ith sealing gasket scheme i + The relative closeness C of the ith sealing gasket scheme

[0133] (6.6).

[0134] The relative closeness C of the ith sealing gasket scheme i + The value range of C is [0,1], and the greater the value of C, the better the comprehensive performance of the scheme. i + The schemes that do not meet the design threshold are screened out, and the remaining schemes are sorted in descending order according to C. i + The ranking order of the scheme is represented by R, and the ranking of each alternative sealing gasket scheme is determined. k i + The sealing gasket seat with the maximum relative closeness C is the optimal sealing gasket design scheme. Specific embodiments

[0135] Please refer to Figures 1-5 ; this embodiment is a shield tunnel joint sealing gasket selection method based on multi-criteria decision-making, and the specific implementation process is as follows:

[0136] 1) Design threshold setting:

[0137] Taking a certain shield tunnel project as an example, the diameter of the tunnel is 6.3m, the water head height is 20m, the buried depth is 5.7m, and the surrounding rock grade is V. According to the Railway Tunnel Design Specification TB10003-2016, it is determined that it is a shallow tunnel. According to the hydrogeological conditions and construction technical conditions of the project, the design threshold is determined as follows:

[0138] (1) Design water pressure T1=0.6MPa; ​

[0139] (2) the maximum joint opening T2 = 6 mm;

[0140] (3) the maximum assembly force per meter of segment T3 = 80 kN / m;

[0141] (4) the maximum allowable groove filling rate T4 = 100%.

[0142] 2) Performance evaluation index selection:

[0143] For example, as Figure 3 M46 sealing gasket, 65H A hardness, 14 mm groove depth (maximum groove filling rate 95.99%) sealing scheme, according to the compression mechanics curve and geometric size of the sealing scheme, the evaluation index of the sealing scheme is determined as follows:

[0144] (1) the average contact stress u1 = 0.69 MPa when the maximum joint opening T2 = 6 mm;

[0145] (2) the maximum joint opening u2 = 6.83 mm that can be compatible when the design water pressure T1 = 0.6 MPa;

[0146] (3) the closure compression force u3 = 70.52 kN / m when the sealing gasket is compressed to the joint opening 0 mm;

[0147] (4) the maximum groove filling rate u4 = 95.99%;

[0148] (5) the cross-sectional area u5 = 564.42 mm².

[0149] 3) Establish the compression mechanics data set of the sealing gasket:

[0150] Collect and summarize the sizes and cross-sectional areas of various types of shield sealing gaskets produced by domestic and foreign rubber product manufacturers, a total of 60 cross-sectional shapes, numbered M01~M60 according to the cross-sectional area from small to large, such as Figure 2 .

[0151] For each type of sealing gasket cross-section (a total of 60), consider 3 hardnesses and 3 groove depths for uniaxial compression numerical simulation, and finally obtain the compression force-displacement curve of 60 x 3 x 3 = 540 sealing gasket schemes. The compression force-displacement curve is also the compression force-joint opening curve.

[0152] Determination of hardness: According to the national standard GB / T18173.4-2010 "High Polymer Waterproof Materials Part 4: Rubber Sealing Gasket for Shield Tunnel Segment", the Shore hardness of shield tunnel joint porous sealing gasket should be between 60~70H A , the hardness used for numerical simulation is 60H A65H A and 70H A .

[0153] Determination of trench depth: According to the national standard GB / T51438-2021 "Design Standard for Shield Tunnel Engineering", it is recommended that the cross-sectional area of ​​the sealing gasket trench be within the range of 1 to 1.15 times the cross-sectional area of ​​the sealing gasket (i.e., the maximum trench filling rate η = 86.96% to 100%). Based on the filling rate requirements, three relatively suitable trench depths were determined by back-calculation as numerical simulation schemes, where the trench depth is an integer multiple of 0.5 mm. For example, the three trench depths for sealing gasket M46 are 14 mm, 14.5 mm, and 15 mm, corresponding to maximum trench filling rates of 95.99%, 92.68%, and 89.59%, respectively.

[0154] 4) Data normalization and diminishing marginal returns processing:

[0155] Based on the gasket compression mechanical property dataset obtained in step three, the performance evaluation index values ​​for each of the 540 sealing schemes can be determined. By summing the j-th performance evaluation index value for the i-th gasket scheme, the original matrix U=(u ij ) 540×5 .

[0156] (1)

[0157] According to equations (4.1a) and (4.1b), the original matrix is ​​normalized to obtain the normalized matrix X=(x ij ) k×5 Then perform X=(x ij ) k×5 Treatment of diminishing marginal returns, such as Figure 4 As shown, the marginal decreasing matrix P = (p ij ) 540×5 .

[0158] (2)

[0159] 5) Determining the weights of each evaluation indicator:

[0160] According to equation (5.1), the standard deviation of each evaluation index value is calculated as follows:

[0161] (3)

[0162] The correlation coefficient ρ between the values ​​of each evaluation index is calculated according to equation (5.2). jr Matrix as Figure 5 As shown.

[0163] Based on equations (5.3) to (5.5), the weight vectors of each evaluation index are calculated as follows:

[0164] (4)

[0165] 6) Calculate the relative closeness of the schemes and sort them:

[0166] According to formula (6.1), the weighted decision matrix Z=(z ij ) 540×5 .

[0167] (5)

[0168] According to formula (6.2)-(6.6), the relative closeness C i + of each sealing gasket scheme is determined, schemes that do not meet the design threshold are screened out, and 155 alternative schemes are obtained and sorted.

[0169] Table 1 shows the comprehensive evaluation and sorting results of some sealing gasket schemes, and the results show that the optimal scheme (R k =1) has a waterproof performance u1 that is 37.70% higher than that of the worst scheme (R k =155), a compatible joint deformation u2 that is 29.46% higher, a closed compression force u3 that is 5.51% lower, a maximum groove filling rate u4 that is 10.09% lower, and a cross-sectional area that is 55.53% lower. By using the multi-criteria decision model of the technical scheme to compare and select the sealing scheme, the waterproof performance, assembly performance, and economic performance of the shield tunnel joint waterproof design scheme are simultaneously improved.

[0170]

[0171] The above description is only used to illustrate the technical scheme of the present application and not to limit it, and modifications or replacements of the technical scheme made by other technical personnel in the field should be covered in the scope of the claims of the present application as long as they do not deviate from the connotation of the technical scheme of the present application.

Claims

1. A method for selecting joint sealing gaskets for shield tunnels based on multi-criteria decision-making, characterized in that: Includes the following steps: Step 1: Select the design water pressure T1, maximum joint opening T2, maximum assembly force T3, and maximum allowable groove filling rate T4 as the design thresholds for the sealing gasket. Step 2: Select the average contact stress u1 under the maximum joint opening T2, the maximum joint opening u2 that can be compatible under the design water pressure T1, the closing compression force u3, the maximum groove filling rate u4, and the gasket cross-sectional area u5 as evaluation indicators for the gasket performance. Step 3: Select various sealing gaskets with different cross-sectional shapes, hardness, and groove depths, and obtain the compression force-displacement curves of different sealing gaskets through compression mechanics tests or finite element simulation tests. Step 4: Based on the compression force-displacement curves of different gaskets obtained in Step 3, determine the evaluation index values ​​of the corresponding gaskets, and normalize the evaluation index values ​​using the maximum-minimum normalization method; based on the marginal effect of each evaluation index, perform marginal reduction processing on the normalized evaluation index values ​​to obtain the marginal values ​​of each evaluation index for different gaskets. Step 5: Determine the objective weights of each evaluation indicator using the CRITIC method; Step Six: Based on the marginal values ​​of each evaluation index obtained in Step Four and the objective weights obtained in Step Five, the TOPSIS method is used to obtain the gasket with the best overall performance among different gaskets.

2. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step one, the maximum trench filling rate is calculated according to formula (2.1): （2.1） Where: η is the maximum groove filling rate; A is the cross-sectional area of ​​the sealing gasket; A g This is the cross-sectional area of ​​the sealing gasket groove.

3. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step one, the design threshold is determined as follows: (1) For deep-buried tunnels and shallow-buried tunnels, the design water pressure T1 is taken as 2 times and 3 times the maximum water pressure at the tunnel burial depth, respectively; (2) For shield tunnels with a diameter not exceeding 10m, the maximum joint opening T2 is 6mm; for shield tunnels with a diameter exceeding 10m, the maximum joint opening T2 is 8mm. (3) The maximum assembly force T3 shall not exceed the propulsion force of the shield tunnel segment assembly machine; (4) The maximum allowable trench filling rate T4 shall not exceed 100%.

4. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step two, the evaluation indicators and design thresholds must meet the following conditions: The average contact stress u1 under the maximum joint opening T2 is greater than or equal to the design water pressure T1. The maximum joint opening u2 that can be compatible under the design water pressure T1 is greater than or equal to the maximum joint opening T2. The closing compression force u3 is less than or equal to the maximum assembly force T3. The maximum groove filling rate u4 is less than or equal to the maximum allowable groove filling rate T4.

5. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step three, the hardness of the sealing gasket is in the range of 60~70 Shore, and the maximum groove filling rate is 86.96%~100%.

6. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step three, for the same cross-sectional shape, at least three different hardnesses and three different groove depths of sealing gaskets should be selected for compression mechanical tests or finite element simulation tests.

7. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step four, the evaluation index values ​​are normalized using the maximum-minimum normalization method according to equation (4.1): （4.1） In the formula: It is the normalized value of the j-th evaluation index in the i-th sealing gasket scheme; It is the value of the j-th evaluation index in the i-th sealing gasket scheme; or This represents the maximum or minimum value of the j-th evaluation index among all sealing gasket schemes.

8. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step four, based on the marginal effect of each evaluation index, the normalized evaluation index values ​​are subjected to marginal reduction processing according to formula (4.2) to obtain the marginal values ​​of each evaluation index for different sealing gaskets: （4.2） In the formula: p ij Let be the marginal value of the j-th evaluation index in the i-th sealing gasket scheme; Is it a design threshold? The normalized value; α is the marginal decrease discrimination coefficient. When j=1, 2, 3, 4, α takes the value of 2, and when j=5, α takes the value of 1.

9. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making as described in claim 1, characterized in that: In step five, the objective weights of each evaluation index are determined using the CRITIC method according to formula (5.1); （5.1） In the formula: w j I represents the objective weight value of the j-th evaluation indicator; j Let j be the information content of the j-th evaluation indicator; Among them, I j Determine according to formulas (5.2) to (5.4): （5.2） （5.3） （5.4） In the formula: ρ jr The Pearson correlation coefficient between evaluation index j and evaluation index r; k is the total number of sealing gasket schemes; or Let be the marginal value of the j-th or r-th evaluation index in the i-th alternative; or σ is the average of the marginal values ​​of the j-th or r-th evaluation index among all alternative options; j Let be the standard deviation of the evaluation index j.

10. The method for selecting a shield tunnel joint sealing gasket based on multi-criteria decision-making according to claim 1, characterized in that: In step six, based on the marginal values ​​and objective weights of each evaluation index, the TOPSIS method is used to calculate the comprehensive performance value of different gaskets according to formula (6.1), and the gasket with the highest comprehensive performance value is taken as the best gasket: （6.1） In the formula: C i + This represents the overall performance value of the sealing gasket; D i + D represents the distance from the weighted decision matrix of the i-th type of sealing gasket to the positive ideal solution; i - Let be the distance from the weighted decision matrix of the i-th type of sealing gasket to the negative ideal solution; Among them, D i + and D i - Determine according to equations (6.2) and (6.3) respectively: （6.2） （6.3） In the formula: z ij z is the weighted decision value of the j-th evaluation index for the i-th type of sealing gasket; j + or z j - This represents the maximum or minimum weighted decision value of the j-th evaluation indicator. Among them, z ij Determine according to formula (6.4): （6.4） In the formula: p ij w represents the marginal value of the j-th evaluation index in the i-th sealing gasket scheme. j Let be the objective weight value of the j-th evaluation indicator.

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