Back analysis method for support design reliability in deep roadway surrounding rock plate crack instability mode

Abstract

The invention discloses a support design reliability back analysis method under a deep roadway surrounding rock plate crack instability mode, and belongs to the technical field of mine underground roadway engineering support stability and reliability design. The method comprises the following steps: constructing a limit state equation containing support design decision parameters in a surrounding rock plate crack instability mode based on a sudden change theory; aiming at a preset reliability measurement standard in the support design, solving and calculating support design decision parameters by using a reliability back analysis method, and comparing the result with a result obtained by a traditional reliability positive analysis method to verify the feasibility and rationality of the reliability back analysis method; and on the basis, starting from different preset reliability measurement standards, supporting design under various working conditions in the surrounding rock plate crack instability mode is further carried out through a reliability back analysis method. According to the method, a calculation result which meets a preset reliability measurement standard requirement and has relatively high precision can be obtained, the number of iterative loop operations is small, and solution analysis is convenient and efficient.

Description

Technical Field

[0001] The present invention belongs to the technical field of support stability reliability design for underground roadway engineering in mines, and particularly relates to a reliability inverse analysis method for support design under the slab splitting instability mode of deep roadway surrounding rock. Background Technique

[0002] The current support design methods proposed for the slab splitting instability of deep roadway surrounding rock mainly focus on improving the physical and mechanical properties, stress conditions of the surrounding rock, and strengthening the surrounding rock to increase the bearing capacity or overall stiffness. Related methods generally belong to the category of classical deterministic support design methods. In essence, the stability of the support structure under the slab splitting instability mode is reflected by reserving a certain safety margin (such as a safety factor). However, long-term engineering practice has shown that the stability of deep roadways is usually restricted by the inherent uncertainties of various engineering factors, and the natural uncertainties of these influencing factors are important risk sources for engineering instability and cannot be completely eliminated. However, the existing deterministic support design methods based on safety margins do not explicitly consider the stable and reliable degree that the support structure should possess under the influence of uncertain factors. Therefore, it is necessary to introduce a reliability analysis method that can fully consider the uncertainties of influencing factors for the support design under the slab splitting instability mode of deep roadway surrounding rock.

[0003] In the current domestic and foreign engineering codes related to the reliability analysis of underground structure design, generally, different reliability measurement criteria are preset according to different failure modes of underground structures, and accordingly, the decision-making parameters of relevant designs are required to be calculated in reverse to ensure the stability and safety of the project. For this purpose, the traditional reliability forward analysis method can usually be used to solve the problem through a repeated debugging process. However, this process has two problems: one is that it is highly random and blind, which is likely to lead to non-convergence of the calculation results; the other is that the calculation is cumbersome and the efficiency is very low.

[0004] In view of this engineering situation, it is urgent to establish a reasonable and practical reliability inverse analysis method for the support design corresponding to the slab splitting instability mode of deep roadway surrounding rock, taking into full account the influence of uncertain influencing factors, so as to be more rigorous theoretically, more reliable in calculation results, and more efficient in calculation efficiency when solving the reverse calculation problem of the decision-making parameters of the support design for such projects. Summary of the Invention

[0005] The purpose of the present invention is to provide a reliability inverse analysis method for support design under the slab splitting instability mode of deep roadway surrounding rock, which reversely solves and calculates the decision-making parameters of the support design under the slab splitting instability mode of the surrounding rock for a preset reliability measurement standard, and can obtain calculation results that meet the requirements of different reliability measurement standards and have high accuracy, with fewer iterative loop operation times and convenient and efficient solution analysis, so as to solve at least one technical problem involved in the background technique.

[0006] To solve the above technical problems, the present invention is implemented as follows:

[0007] A method for inverse analysis of the reliability of support design under the slab splitting instability mode of deep roadway surrounding rock, comprising the following steps:

[0008] Step S1, for the instability failure process of rock slabs under the slab splitting mode of deep roadway surrounding rock, applying catastrophe theory and combining with the slab-beam mechanical model to construct a limit state equation containing support design decision parameters;

[0009] Step S2, for the preset reliability measurement criteria in support design, using the reliability inverse analysis method to carry out the solution calculation of support design decision parameters;

[0010] Step S3, comparing the calculation results of support design decision parameters with the results obtained by the traditional reliability forward analysis method to verify the feasibility and rationality of the reliability inverse analysis method;

[0011] Step S4, for the support design under the slab splitting instability mode of deep roadway surrounding rock, around the preset reliability measurement criteria, using the reliability inverse analysis method to carry out the solution calculation of support design decision parameters to complete the support design.

[0012] As a preferred improvement, the limit state equation containing support design decision parameters is expressed as:

[0013]

[0014] In the formula, X represents a random vector containing n random variables X i (i = 1, 2,..., n), X = (X1, X2,..., X n ), T , T represents the transpose matrix; D i represents the flexural rigidity of the i-th layer of rock slab; a represents the height of the rock slab; σ x , σ y respectively represent the vertical and horizontal stresses on the rock slab after the stress redistribution of the surrounding rock caused by the excavation of the deep roadway, b i represents the thickness of the i-th layer of rock slab; b i and σ y are set as support design decision parameters;

[0015] Wherein:

[0016]

[0017] In the formula, E and u respectively represent the elastic modulus and Poisson's ratio of the rock slab;

[0018] b i = b1 + (i - 1)Δ;

[0019] In the formula, i represents the sequence of the number of rock slab layers from the outside of the side wall to the inside of the surrounding rock; b1 represents the thickness of the outermost rock slab; Δ represents the slab thickness increment.

[0020] As a preferred improvement, step S2 specifically includes the following steps:

[0021] Based on the basic principle of the reliability back-analysis method, the following expression can be obtained:

[0022]

[0023] In the formula, U represents the random vector in the standardized normal space corresponding to X through standardized normal transformation, U=(U1, U2, …, U n ) T ; g(·) and G(·) respectively represent the performance functions contained in the normal space before and after standardization; represents the distribution function of X i , Φ(·) represents the standardized normal distribution function; ω represents the support design decision parameter to be solved and calculated;

[0024] The solution process of the support design decision parameter ω carries out iterative loop operations around the following formula:

[0025]

[0026] In the formula, represents the partial derivative vector of the performance function G(·) at the standardized normal random vector U=(U1, U2, …, U n ) T ; β R is the preset reliability measure standard; ω0 is the initial assignment of the iterative loop operation of the support design decision parameter ω; where:

[0027]

[0028] As a preferred improvement, the iterative loop operation process of the support design decision parameter ω specifically includes the following steps:

[0029] First, let U0 be the initial assignment of the standardized normal random vector U, and calculate and

[0030] Secondly, substitute the initial assignments (ω0, U0) of the iterative loop operation of the support design decision parameter ω and the standardized normal random vector U into the loop operation formula, and obtain the values of ω and U after the first iteration. Repeat this process until the results obtained from the jth iterative loop operation are within the convergence calculation accuracies c1 and c2, that is: if the following formula is satisfied, the iterative loop operation is terminated;

[0031]

[0032] Where ω j and U j are the final calculation results corresponding to the reliability back-analysis method.

[0033] As a preferred improvement, step S3 specifically includes the following process:

[0034] Set different numbers of iterative loop operations and initial assignments of the support design decision parameters, compare the calculation results of the support design decision parameters with the results obtained by the traditional reliability forward-analysis method, and verify the feasibility and rationality of the reliability back-analysis method.

[0035] As a preferred improvement, the solution calculation of the support design decision parameters includes the analysis and calculation of the rock slab thickness b i and the horizontal stress σ y received by the rock slab.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] (1) The present invention inversely solves and calculates the support design decision parameters under the rock slab cracking and instability mode for a preset reliability measurement standard, can obtain calculation results that meet the requirements of the reliability measurement standard and have high precision, and has few iterative loop operations, and the solution analysis is convenient and efficient;

[0038] (2) The present invention verifies that the calculation results of the reliability back-analysis method are not affected by the initial assignment in the iterative loop operation process of the support design decision parameters, and different initial assignments only have a small impact on the iterative loop operation speed during the calculation process;

[0039] (3) The present invention realizes the solution calculation of decision parameters such as support depth and support stress that meet different reliability measurement standards for the support design under the rock slab cracking and instability mode, so as to reduce the potential damage risk caused by uncertain factors as much as possible through an active quantitative disposal method of adjusting the support design decision parameters, and provide reasonable engineering guidance for the reliability of the support design under the rock slab cracking and instability mode of deep roadway surrounding rock. Description of the Drawings

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings, where:

[0041] Figure 1The beam mechanics model corresponding to the slab cracking analysis of the surrounding rock in deep roadway provided by the present invention;

[0042] Figure 2 The different reliability measure criteria β provided by the present invention R The relationship diagram between the height a of the rock slab corresponding to the surrounding rock slab cracking mode and the thickness t of the outermost rock slab to be calculated;

[0043] Figure 3 The different reliability measure criteria β provided by the present invention R The relationship diagram between the height a of the rock slab corresponding to the surrounding rock slab cracking mode and the combined rock slab thickness (support depth) to be calculated;

[0044] Figure 4 The different horizontal stresses (bonding stresses) σ received by the rock slab provided by the present invention y Under the reliability measure criterion β R The relationship diagram with the combined rock slab thickness (support depth) to be calculated;

[0045] Figure 5 The different reliability measure criteria β provided by the present invention R Under the combined rock slab thickness (support depth) and the horizontal stress (bonding stress) σ received by the rock slab to be calculated y Relationship diagram. Specific implementation manner

[0046] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0047] The terms "first", "second", etc. in the description and claims of the present invention are used to distinguish similar objects, rather than to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are usually of the same type, and the number of objects is not limited. For example, the first object can be one or multiple. In addition, "and / or" in the description and claims means at least one of the connected objects, and the character " / " generally represents an "or" relationship between the associated objects before and after.

[0048] This embodiment provides a reliability back-analysis method for support design under the slab cracking instability mode of the surrounding rock in deep roadway, including the following steps:

[0049] Step S1: For the instability failure process of rock slabs in the deep roadway surrounding rock slab splitting mode, the catastrophe theory is used and combined with the plate-beam mechanical model to construct the limit state equation containing the support design decision parameters.

[0050] For the deep roadway surrounding rock slab splitting instability mode, due to the tangential stress, its typical manifestation is that the sidewall surrounding rock splits into multiple approximately parallel rock slabs with unequal thicknesses and interacting with each other. The strain-type rockburst occurring after the rock slab instability can be regarded as a sudden change in the complex nonlinear systematic state. Therefore, taking the surrounding rock slab splitting at the sidewall of the deep roadway as an example, assuming that the rock slab thickness is distributed in an arithmetic progression, the thickness of each layer of rock slab is expressed as:

[0051] b i = b1 + (i - 1)Δ;

[0052] In the formula, i represents the rock slab layer number sequence from the outside of the sidewall to the inside of the surrounding rock; b i represents the thickness of the i-th layer of rock slab; b1 represents the thickness of the outermost layer of rock slab; Δ represents the plate thickness increment.

[0053] The limit state equation containing the support design decision parameters is expressed as:

[0054]

[0055] In the formula, X represents a random vector containing n random variables X i (i = 1, 2,..., n), X = (X1, X2,..., X n ) T , T represents the transpose matrix; D i represents the flexural rigidity of the i-th layer of rock slab; a represents the height of the rock slab; σ x , σ y respectively represent the vertical and horizontal stresses on the rock slab after the stress redistribution of the surrounding rock caused by the excavation of the deep roadway, b i represents the thickness of the i-th layer of rock slab; b i and σ y are set as the support design decision parameters;

[0056] Among them:

[0057]

[0058] In the formula, E and y respectively represent the elastic modulus and Poisson's ratio of the rock slab;

[0059] σ y can be regarded as the bonding stress between rock slabs and can provide a design reference for the required support stress; the rock slab thickness b i can provide a design basis for the effective support depth of support measures such as anchor bolts in the support design scheme. Therefore, b i and σ yThat is, it is set as the decision-making parameter for the support design.

[0060] Step S2: For the preset reliability measurement criteria in the support design, use the reliability back-analysis method to carry out the solution calculation of the decision-making parameter for the support design.

[0061] According to the basic principle of the reliability back-analysis method, the following expression can be obtained:

[0062]

[0063] In the formula, U represents the random vector in the standardized normal space corresponding to X through standardized normal transformation, U = (U1, U2,..., U n ) T ; g(·) and G(·) respectively represent the performance functions contained in the normal space before and after standardization; represents the distribution function of X i , Φ(·) represents the standardized normal distribution function; ω represents the decision-making parameter for the support design that needs to be solved and calculated;

[0064] The solution process of the decision-making parameter ω for the support design is carried out by iterative loop operation around the following formula:

[0065]

[0066] In the formula, represents the partial derivative vector of the performance function G(·) at the standardized normal random vector U = (U1, U2,..., U n ) T ; β R is the preset reliability measurement criterion; ω0 is the initial assignment for the iterative loop operation of the decision-making parameter ω for the support design; where:

[0067]

[0068] Correspondingly, the iterative loop operation process is as follows:

[0069] First, let U0 be the initial assignment of the standardized normal random vector U, and calculate and

[0070] Second, substitute the initial assignments (ω0, U0) of the decision-making parameter ω for the support design and the standardized normal random vector U into the loop operation formula, and obtain the values of ω and U after the first iteration. Repeat this process until the results obtained from the jth iterative loop operation are within the convergence calculation accuracies c1 and c2, that is: if the following formula is satisfied, then terminate the iterative loop operation;

[0071]

[0072] where ω j and U j are the final calculation results of the corresponding reliability back-analysis method.

[0073] Step S3: Compare the calculation results of the support design decision parameters with the results obtained by the traditional reliability forward-analysis method to verify the feasibility and rationality of the reliability back-analysis method.

[0074] Step S3 specifically includes the following process:

[0075] Set different numbers of iterative loop operations and initial assignments of the support design decision parameters, compare the calculation results of the support design decision parameters with the results obtained by the traditional reliability forward-analysis method, and verify the feasibility and rationality of the reliability back-analysis method.

[0076] Step S4: For the support design under the slab splitting instability mode of the deep roadway surrounding rock, around the preset reliability measurement criteria, use the reliability back-analysis method to carry out the solution calculation of the support design decision parameters and complete the support design.

[0077] The solution calculation of the support design decision parameters includes the analysis and calculation of the rock slab thickness b i and the horizontal stress σ y acting on the rock slab.

[0078] Example 1

[0079] In this example, the random variables are taken as the elastic modulus E of the rock slab, the Poisson's ratio u of the rock slab, and the vertical stress σ x acting on the rock slab, and all three follow a normal distribution. Among them, the mean of E is 30.7 GPa, and the standard deviation is 3.684 GPa; the mean of u is 0.26, and the standard deviation is 0.0208; the mean of σ x is 50 MPa, and the standard deviation is 6 MPa. In addition, for the deterministic parameters, the horizontal stress (bonding stress) σ y acting on the rock slab is taken as 10 MPa, and the height a of the rock slab is 1 m; taking the example of the slab splitting situation where 4 layers of rock slabs are generated in the rock slab layer sequence from the outside of the roadway sidewall to the inside of the surrounding rock, let the slab thickness increment Δ be 0.005 m.

[0080] Regarding the thickness b1 of the outermost rock slab as the known decision parameter, and taking the following values respectively: 0.020, 0.025, 0.030, 0.035, 0.040, 0.045, and 0.050 m. Then, for each b1, calculate the thicknesses b2, b3, and b4 of the other layers of rock slabs corresponding to each b1, and based on the traditional reliability forward-analysis method, solve the reliability index β Hand the corresponding spatial design points before standardization, and the calculation results are shown in the column of "Positive reliability analysis method" in Table 1.

[0081] Then, take the reliability index β obtained by the positive reliability analysis method H as the reliability metric standard β R , and at this time, regard the thickness b1 of the outermost rock slab as the decision parameter t to be calculated. Based on the reliability inverse analysis method provided by the present invention, the value of t (and the corresponding spatial design points before and after standardization) is solved through iterative loop operations. Note that in this process, the initial assignment of t is taken as 0.01 m, and the calculation results and the number of iterative loop operations are shown in the column of "Reliability inverse analysis method" in Table 1.

[0082] Table 1 Comparison of reliability calculation results

[0083]

[0084]

[0085] As can be seen from Table 1, a series of values of the thickness t of the outermost rock slab to be calculated obtained by the reliability inverse analysis method are consistent with the corresponding values of b1 calculated by the positive analysis method, and the design point values calculated by the inverse analysis method and the positive analysis method are also almost the same, indicating that the reliability inverse analysis method is accurate enough. In addition, as shown in Table 1, the amount of calculation corresponding to the inverse analysis method is less, and the corresponding results can generally be obtained through 7 - 10 iterative loop operations, indicating that its solution analysis is convenient and efficient.

[0086] As mentioned above, when using the reliability inverse analysis method, the initial assignment of the support design decision parameter to be solved and calculated needs to be given during the iterative loop operation. Therefore, it is necessary to further explore the relationship between the initial assignment and the calculation results of the reliability inverse analysis method. Taking the thickness b1 of the outermost rock slab in Table 1 = 0.035 m and the corresponding β H = 3.847887 as an example, let β R = β H= 3.847887. Initial values of the thickness t of the outermost rock slab to be calculated are respectively taken as t = 0.005, 0.01, 0.05, 0.1, 0.5, 1 m, and the reliability back-analysis method is used for solution calculation. As shown in Table 2, for different initial values of the thickness t of the outermost rock slab to be calculated, the calculation results all converge to t ≈ 0.035 m, which is consistent with the b1 value in the corresponding reliability forward-analysis method calculation. There are only certain differences in the number of iterative loop operations. For example, the number of iterative loop operations (8 times) when the initial value of t is taken as 0.005 is less than that (23 times) when the initial value of t is taken as 0.5, but the number of their iterative loop operations is relatively small, and the difference between the two is not large, indicating that the initial value only affects the iterative loop operation speed of the reliability back-analysis method to a certain extent, but does not affect its final calculation result.

[0087] Table 2 Calculation results of the reliability back-analysis method for the decision parameter t (thickness of the outermost rock slab) to be calculated

[0088]

[0089]

[0090] For the support design under the instability mode of surrounding rock slab cracking, to avoid the occurrence of strain-type rock bursts, it is necessary to prevent sudden changes in the slab-cracked surrounding rock. When the rock slab thickness is used as the decision parameter for support design, it can provide a design basis for the effective support depth of support measures such as bolts, while when the bonding stress σ y is used as the decision parameter for support design, it can provide corresponding reference for the required support stress. Therefore, for the preset reliability measure standard β R the following values are taken respectively: 3.0, 3.5, 4.0, 4.5, 5.0, and 5.5.

[0091] First, taking the thickness t of the outermost rock slab as the decision parameter for support design to be calculated, considering the varying rock slab height a under different slab-cracked situations, the corresponding t is calculated for different reliability measure standards β R . The results are as Figure 2 shown. It can be seen from Figure 2 that when the combined rock slab thickness is greater than (4t + 0.03) m, the sudden change condition is no longer satisfied, which indicates that the maximum depth of rock burst is (4t + 0.03) m. Therefore, the bolts in the support design should have an effective support depth of at least (4t + 0.03) m to meet the corresponding reliability measure standards. In the calculation and analysis of this example, when the combined rock slab thickness is regarded as the support depth corresponding to β R , it shows that the thicker the rock slab, the less likely it is to occur rock bursts, which is in line with the general understanding in engineering.

[0092] Further considering the combined rock slab thickness, for different rock slab heights a, the values of the combined rock slab thickness when meeting different reliability measure criteria β R are shown in Figure 3 . As Figure 3 shown, when the reliability measure criterion β R and the measured rock slab height a in the actual project are known, the effective support depth required to meet β R can be obtained. Taking Figure 3 shown β R = 5.5 as an example, when a = 0.4m, the required support depth needs to reach 0.10036m; when a = 0.8m, the required support depth needs to reach 0.19218m; when a = 1.2m, the required support depth increases to 0.26441m; when a = 1.6m, a support depth of 0.31908m needs to be met; for other β R , the required support depth can be obtained in a similar way. Therefore, for the reliability measure criterion β R to be met, around the different rock slab heights generated during the splitting process of the surrounding rock slab, the required support depth can be intuitively determined through the curve in Figure 3 , thus providing corresponding engineering guidance for the support design scheme.

[0093] Again, from the changing trends of the curves in Figure 3 , when the reliability measure criterion β R is fixed, for the combined rock slab thickness, that is, the support depth will increase with the increase of the rock slab height a, and the curve shows a monotonically increasing trend, indicating that in the support design to keep the reliability measure criterion unchanged, the larger the rock slab height, the larger the combined rock slab thickness required to avoid the buckling deformation of the rock slab and the accumulation of elastic strain energy, that is, the greater the support depth, which is consistent with the engineering practice. In addition, when the rock slab height a takes the same value, the higher the reliability measure criterion β R , the larger the combined rock slab thickness required, that is, the support depth. For example, when a = 1.5, the support depth corresponding to β R = 3.0 is 0.18141m, the support depth corresponding to β R = 3.5 is 0.20194m, the support depth corresponding to β R = 4.0 is 0.22364m, the support depth corresponding to β R = 4.5 is 0.24746m, the support depth corresponding to β R = 5.0 is 0.27463m, the support depth corresponding to β R = 5.5 is 0.30706m. The above situations show that for the rock slab with splitting occurring at a certain height, the higher the reliability measure criterion required by the support design, the greater the required support depth, which can reduce the failure risk, and this is obviously consistent with the engineering practice.

[0094] Then, for solving the combined rock slab thickness (support depth) by the reliability back analysis method, the variation of the support depth required with the change of the reliability measure standard β can also be considered for different bonding stresses σ y , with the reliability measure standard β R changing. Now, taking the bonding stresses σ y as 5 MPa, 10 MPa, 15 MPa, and 20 MPa respectively, when the rock slab height a = 1 m, the combined rock slab thickness (support depth) to be calculated can be obtained, as shown in Figure 4 . Figure 4 When β in R takes a fixed value, the greater the bonding stress σ y , the smaller the resulting combined rock slab thickness (support depth). Considering that the increase in σ y is equivalent to an increase in the support stress, and to keep β R unchanged, the combined rock slab thickness (support depth) must necessarily be reduced, which obviously conforms to the engineering practice.

[0095] Finally, the bonding stress σ y received by the rock slab can also be used as the support design decision parameter to be calculated, that is: considering the change with the combined rock slab thickness (support depth), calculate σ R that meets the reliability measure standard β y by the reliability back analysis method, as shown in Figure 5 . It can be seen from Figure 5 that when the reliability measure standard β R and the combined rock slab thickness (support depth) are known, the bonding stress required to meet β R can be obtained. Taking β Figure 5 in R = 5.5 as an example, when the combined rock slab thickness (support depth) is 0.11 m, the bonding stress should reach 28.71003 MPa; when the combined rock slab thickness (support depth) is 0.15 m, the bonding stress should reach 23.56611 MPa; when the combined rock slab thickness (support depth) is 0.19 m, the bonding stress is reduced to 17.04624 MPa; when the combined rock slab thickness (support depth) is 0.23 m, the bonding stress is 10.08940 MPa; for other value cases of β R , the bonding stress can be obtained in a similar manner.

[0096] In addition, for Figure 5 the changing trends of the curves in, for a certain reliability measure standard β R, the bond stress to be calculated will decrease with the increase of the combined rock slab thickness (support depth), and the curve shows a monotonic decrease. This indicates that the smaller the aspect ratio of the rock slab, the more difficult it is to deform, and the less likely it is to accumulate energy and mutate, resulting in a smaller required bond stress, which is consistent with the engineering practice. Further comparison Figure 5 Among the curves in R , it can also be observed that when the combined rock slab thickness (support depth) is constant, the higher the reliability measure standard β R is, the greater the required bond stress. For example, when the combined rock slab thickness (support depth) is 0.15 m, the bond stress corresponding to β R = 3.0 is 9.60071 MPa, the bond stress corresponding to β R = 3.5 is 11.71891 MPa, the bond stress corresponding to β R = 4.0 is 14.11000 MPa, the bond stress corresponding to β R = 4.5 is 16.82445 MPa, the bond stress corresponding to β R = 5.0 is 19.93736 MPa, and the bond stress corresponding to β

[0097] = 5.5 is 23.56611 MPa. When the combined rock slab thickness (support depth) takes other fixed values, the corresponding bond stress can also be obtained in the same way. This shows that when the combined rock slab thickness (support depth) is constant, the higher the reliability measure standard required for the support design, the greater the required bond stress, that is, the support stress, which is obviously also consistent with the engineering practice.

[0097] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the present invention and the claims, and all belong to the protection scope of the present invention.

Claims

1. A reliability back analysis method for support design under the instability mode of surrounding rock slab cracking in deep tunnels, characterized in that: The steps include: Step S1, for the instability and failure process of the rock slab in the surrounding rock slab cracking mode of the deep tunnel, the limit state equation containing the support design decision parameters is constructed by using the catastrophe theory and combining the plate-beam mechanical model; Step S2, according to the reliability metric standard preset in the support design, the reliability back analysis method is used to carry out the solution calculation of the support design decision parameters; Step S3, comparing the calculation results of the support design decision parameters with the results obtained by the traditional reliability forward analysis method to verify the feasibility and rationality of the reliability inverse analysis method; Step S4, for the support design under the deep tunnel surrounding rock slab cracking instability mode, based on the preset reliability metric standard, the reliability inverse analysis method is used to carry out the solution calculation of the support design decision parameters to complete the support design.

2. The reliability back analysis method for support design under the deep tunnel surrounding rock slab cracking instability mode according to claim 1 is characterized in that: The limit state equation containing the support design decision parameters is expressed as: In the formula, X represents a random vector, containing n random variables X i (i=1,2,…,n), X=(X1,X2,…,X n ) T , T represents the transposed matrix; D i represents the bending stiffness of the i-th rock slab; a represents the height of the rock slab; σ x , σ y They represent the vertical and horizontal stresses on the rock slab after the surrounding rock stress is redistributed due to deep tunnel excavation, and b i represents the thickness of the i-th rock slab; b i With σ y Set as support design decision parameter; in: In the formula, E and u represent the elastic modulus and Poisson's ratio of the rock plate respectively; b i =b1+(i-1)Δ; In the formula, i represents the sequence of rock slab layers from the outside of the side wall to the inside of the surrounding rock; b1 represents the thickness of the outermost rock slab; Δ represents the increment of slab thickness.

3. The reliability back analysis method for support design under the deep tunnel surrounding rock slab cracking instability mode according to claim 2 is characterized in that: Step S2 specifically includes the following steps: According to the basic principle of reliability back analysis method, the following expression can be obtained: Where U represents a random vector in the normalized space corresponding to X through the normalized transformation, U = (U1, U2, ..., U n ) T ; g(·) and G(·) represent the functional functions contained in the normal space before and after standardization, respectively; Represents X i distribution function, φ(·) represents the standardized normal distribution function; ω represents the support design decision parameter that needs to be solved and calculated; The solution process of the support design decision parameter ω is based on the following iterative cycle operation: In the formula, represents the performance function G(·) on the normalized normal random vector U=(U1,U2,…,U n ) T The partial derivative vector at β R is the preset reliability metric standard; ω0 is the initial value of the iterative cycle operation of the support design decision parameter v; where:

4. The reliability back analysis method for support design under the deep tunnel surrounding rock slab cracking instability mode according to claim 3 is characterized in that: The iterative cycle calculation process of the support design decision parameter ω specifically includes the following steps: First, let U0 be the initial value of the normalized random vector U, and calculate and Secondly, the initial assignment (ω0, U0) of the iterative loop operation of the support design decision parameter ω and the standardized normal random vector U is substituted into the loop operation formula, and the values ​​of ω and U are obtained after the first iteration. This process is repeated until the result obtained by the jth iterative loop operation is within the range of the convergent calculation accuracy c1 and c2, that is: if the following formula is satisfied, the iterative loop operation is terminated; In the formula, ω j and U j That is the final calculation result of the corresponding reliability back analysis method.

5. The reliability back analysis method for support design under the deep tunnel surrounding rock slab cracking instability mode according to claim 4 is characterized in that: Step S3 specifically includes the following process: By setting different numbers of iterative cycle operations and initial assignments of support design decision parameters, the calculation results of the support design decision parameters are compared with those obtained by the traditional reliability forward analysis method to verify the feasibility and rationality of the reliability inverse analysis method.

6. The reliability back analysis method for support design under the deep tunnel surrounding rock slab cracking instability mode according to claim 5 is characterized in that: The calculation of support design decision parameters includes the thickness of the rock plate b i and the horizontal stress σ of the rock plate y Analytical calculation.

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