A non-probabilistic robust reliability analysis method for slab crack support in deep hard rock chambers

Abstract

The present invention discloses a non-probabilistic robust reliability analysis method for slab crack support of a deep-buried hard rock chamber, and belongs to the technical field of non-probabilistic reliability design of underground engineering structures. The method includes using the mutation theory to construct a mechanical mutation model of layered combined rock plate failure under the slab crack mode; using the information-deficient non-probabilistic theory to establish a nested convex set model that quantitatively characterizes uncertainty parameters; constructing a performance function for support stability under the slab crack mode of a deep-buried hard rock chamber, and constructing a robust function based on the relationship between the output response value of the performance function and the critical satisfaction value; defining a robust reliability index based on the constructed robust function; and selecting support design decision variables based on the obtained robust reliability index. The present invention uses a non-probabilistic reliability method to analyze and process the practical problem of support stability reliability design under the slab crack mode of a deep-buried hard rock chamber, and can be applied to the engineering problem of severe lack of statistical data of uncertainty parameters in the reliability design of underground engineering structures.

Description

Technical Field

[0001] The present invention belongs to the technical field of non-probabilistic reliability design of underground engineering structures, and specifically relates to a non-probabilistic robust reliability analysis method for plate crack support of a deep-buried hard rock chamber based on information missing non-probability. Background Art

[0002] For the excavation of hard rock chambers in deep buried environments, the slab cracking damage of the surrounding rock caused by high ground stress has a wide impact range and a long duration. If the corresponding support measures are not taken in time, it will not only affect the construction progress, but also easily cause severe rock dynamic damage (such as strain-type rock burst, etc.), seriously threatening the safety of life and property. In view of the actual engineering characteristics that there are many uncertain factors and a large degree of uncertainty that lead to slab cracking damage in deep buried hard rock chambers, the analysis of the support reliability under the slab cracking mode of such underground projects must consider the influence of uncertain factors. However, at this stage, most of the research on support under the slab cracking mode of deep buried hard rock chambers focuses on deterministic analysis, and has not yet clearly considered the influence of uncertain factors that lead to slab cracking damage, and this influence becomes more and more significant with the increasing depth of the chamber.

[0003] At present, the method for dealing with uncertainty factors in deep buried underground projects mainly adopts analysis methods based on probability reliability. As we all know, the traditional probability reliability method takes a large amount of statistical data of uncertainty factors as a prerequisite for its smooth implementation, that is, if enough statistical data of uncertainty factors can be fully mastered, the method is undoubtedly applicable. However, for complex underground projects such as deep buried hard rock chambers, it is extremely difficult to obtain a large amount of statistical data of uncertainty factors due to the influence of the geological environment and the great limitations of exploration technology. That is, the actual characteristics of the project are that the statistical data of uncertainty parameters are severely scarce. This makes it difficult to meet the above prerequisites for the smooth implementation of the traditional probability reliability method, which leads to insurmountable difficulties in solving the uncertainty problems of deep buried hard rock chamber projects.

[0004] In view of the above engineering application problems, it is urgent to establish a reliability analysis method for slab crack support of deep-buried hard rock chambers from a non-probabilistic perspective that is more in line with engineering practice. Summary of the invention

[0005] The purpose of an embodiment of the present invention is to provide a non-probabilistic robust reliability analysis method for slab crack support in a deeply buried hard rock chamber, which adopts a non-probabilistic approach of reliability design to analyze and solve practical problems, and analyzes the support stability reliability under the slab crack mode of a deeply buried hard rock chamber from aspects such as the accuracy of reliability calculation, the concept of uncertainty processing, the characteristic description of uncertainty parameters, and the interpretation of reliability expression methods, so that it can be applied to the engineering problem of severe lack of statistical data of uncertainty parameters in the reliability design of underground engineering structures, thereby solving at least one technical problem involved in the background technology.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] The embodiment of the present invention provides a non-probabilistic robust reliability analysis method for plate crack support of a deep-buried hard rock chamber, comprising the following steps:

[0008] Step S1, focusing on the sudden buckling failure of the layered composite rock slab during the slab cracking process of the deep-buried hard rock chamber, a mechanical catastrophe model of the failure of the layered composite rock slab under the slab cracking mode is constructed by using the catastrophe theory;

[0009] Step S2, in view of the actual engineering characteristics that the statistical data of uncertainty parameters that cause plate cracking failure in deep hard rock chambers are severely scarce, a nested convex set model for quantitatively characterizing uncertainty parameters is established by using information-deficient non-probability theory;

[0010] Step S3, constructing a performance function of support stability under a slab cracking mode of a deep-buried hard rock chamber based on a mechanical mutation model;

[0011] Step S4, constructing a robust function according to the relationship between the output response value of the performance function and the critical satisfaction value;

[0012] Step S5, based on the constructed robust function, the maximum fluctuation range of the allowable uncertainty parameter change when meeting the stability performance requirements of the chamber support in the plate cracking mode is defined as a robust reliability index;

[0013] Step S6, based on the robust reliability index, select the support design decision variables to provide a basis for judging the stability and reliability of the deep-buried hard rock chamber support.

[0014] Preferably, in step S1, the total potential energy V of the layered composite rock slab in the slab cracking mode is equal to the sum of the load potential energy W and the strain energy U, which is expressed by the following formula:

[0015]

[0016] Where U i is the strain energy of the i-th rock plate, W Pi is the vertical load potential energy of the i-th rock slab, W Niis the horizontal load potential energy of the i-th rock slab;

[0017] in:

[0018]

[0019] Where D i is the bending stiffness of the i-th rock plate, a is the height of the rock plate, ω 0 is the deflection at the center of the rock plate in the height direction, and is the maximum deformation of the rock plate before failure; σ P is the vertical stress, b i is the thickness of the i-th rock plate, T is the maximum horizontal support anchoring force that the anchor rod can provide;

[0020] in:

[0021]

[0022] b i =b 1 +(i-1)d (6)

[0023] In the formula, E is the elastic modulus of the rock plate, u is the Poisson's ratio of the rock plate, assuming that the thickness of the rock plate follows an arithmetic progression, b 1 is the thickness of the first rock slab, and d is the slab thickness increment.

[0024] Preferably, in step S2, the uncertainty parameters include the height a of the rock slab and the elastic modulus E of the rock slab.

[0025] Preferably, in step S2, the nested convex set model is expressed by the following formula:

[0026]

[0027] In the formula, α is an uncertain parameter, which represents the gap between the unknown true value and the known nominal value of the uncertainty parameter, and reflects the fluctuation range of the uncertainty parameter; and They correspond to the known nominal values ​​of the rock plate thickness a and the rock plate elastic modulus E in the uncertainty parameters respectively.

[0028] Preferably, in step S3, the mechanical catastrophe model is represented by the following formula:

[0029] Δ=8m 3 +27n 2 (8)

[0030] In the formula, m and n are control variables;

[0031] in:

[0032]

[0033] Preferably, in step S3, a performance function of support stability in a deep-buried hard rock chamber plate cracking mode is constructed, specifically including:

[0034] The mutation characteristic value Δ of the layered composite rock slab is used as the criterion for judging whether the structure is stable, the rock slab thickness a and the rock slab elastic modulus E are used as uncertainty parameters to form the uncertainty vector u=[a,E], and the maximum horizontal support anchoring force T that the anchor can provide is used as the design decision variable. The performance function R(q,u) for ensuring support stability under the slab cracking mode of the deep buried hard rock chamber can be obtained, which is expressed by the following formula:

[0035]

[0036] R(q,u)=Δ| [T,(a,E)] ≥Δ c (12)

[0037] In the formula, Δ c It is the critical satisfactory value of the mutation characteristic value, which is expressed as the minimum acceptable value of the performance function R(q,u) when the combined rock slab structure does not undergo instability mutation.

[0038] Preferably, in step S4, the robust function is expressed by the following formula:

[0039]

[0040] In the formula, It is a robust and reliable indicator.

[0041] Preferably, step S7 is also included, in which a mechanical mutation model of layered combined rock slab failure under a slab cracking mode in a deep-buried hard rock chamber is used to verify the support stability reliability analysis method based on non-probability of information missing.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. The present invention characterizes the relevant nested features of the information missing non-probability convex set quantization model, applies it to practical projects such as deep-buried hard rock chambers, in order to characterize the dynamic changes of uncertainty parameters, and proposes robust reliability indicators and uncertainty processing rules based on information missing non-probability. Starting from the non-probability perspective, an algorithm is provided for the support stability design of deep-buried hard rock chambers, and a corresponding non-probability reliability analysis method is established.

[0044] 2. The present invention breaks the fixed mode of describing uncertainty parameters in the existing interval non-probabilistic method. On the premise of ensuring that the project does not fail, it explores the dynamic changes of the amplitude range of uncertainty parameters under disturbance in actual engineering.

[0045] 3. For the robust reliability index, the present invention can transform passive coping into active handling during the analysis process, so that when faced with the influence of uncertainty parameters, it has the ability to actively resist the dynamic changes of uncertainty parameters and autonomously improve the degree of anti-interference. The corresponding robust reliability index value can reflect the influence of the dynamic changes of uncertainty parameters on the support stability under the slab cracking mode of deep-buried hard rock chambers, and also characterize the sensitivity of the support stability to the fluctuation of uncertainty parameters.

[0046] 4. In actual engineering design, the present invention can reduce the potential instability risk caused by the fluctuation of uncertain parameters as much as possible through such active disposal methods as quantitatively controlling the design decision variables such as the support anchoring force. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0048] Figure 1 A monotonicity discriminant diagram of a relationship curve between a performance function and an uncertainty parameter when the support anchoring force T=15 MPa provided by the present invention;

[0049] Figure 2 A monotonicity discriminant diagram of a relationship curve between a performance function and an uncertainty parameter when the support anchoring force T=18MPa provided by the present invention;

[0050] Figure 3 The robust reliability calculation result diagram of the layered composite rock slab at different support anchoring forces provided by the present invention;

[0051] Figure 4 A comparison chart of the robust reliability calculation results of the layered composite rock slab when the support anchoring force provided by the present invention is T=15MPa and T=18MPa;

[0052] Figure 5 A sensitivity analysis diagram of the rock plate thickness a and the rock plate elastic modulus E in the uncertainty parameters provided by the present invention to the robust performance of the layered composite rock plate structure;

[0053] Figure 6 The vertical stress σ of the rock plate provided by the present invention is P Robust reliability calculation results corresponding to different support anchoring forces when =35MPa;

[0054] Figure 7 The vertical stress σ of the rock plate provided by the present invention is PRobust reliability calculation results corresponding to different support anchoring forces when =40MPa;

[0055] Figure 8 The vertical stress σ of the rock plate provided by the present invention is P Robust reliability calculation results corresponding to different support anchoring forces when =45MPa;

[0056] Fig. 9 The vertical stress σ of the rock plate provided by the present invention is P Robust reliability calculation results corresponding to different support anchoring forces when =50MPa;

[0057] Fig.10 Schematic diagram of the mechanical mutation model of layered combined rock slab destruction under the slab cracking mode provided by the present invention. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] The terms "first", "second", etc. in the specification and claims of the present invention are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, 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 generally of the same type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0060] The embodiment of the present invention provides a non-probabilistic robust reliability analysis method for plate crack support of a deep-buried hard rock chamber, comprising the following steps:

[0061] Step S1, focusing on the sudden buckling failure of the layered composite rock slab during the slab cracking process of the deep-buried hard rock chamber, a mechanical catastrophe model of the failure of the layered composite rock slab under the slab cracking mode is constructed using the catastrophe theory;

[0062] Step S2, in view of the actual engineering characteristics that the statistical data of uncertainty parameters that cause plate cracking failure in deep hard rock chambers are severely scarce, a nested convex set model for quantitatively characterizing uncertainty parameters is established by using information-deficient non-probability theory;

[0063] Step S3, based on the mechanical mutation model of layered combined rock plate failure, construct a performance function of support stability under the plate cracking mode of the deep-buried hard rock chamber;

[0064] Step S4, constructing a robust function according to the relationship between the output response value of the performance function and the critical satisfaction value;

[0065] Step S5, based on the constructed robust function, the maximum fluctuation range of the allowable uncertainty parameter change when meeting the stability performance requirements of the chamber support in the plate cracking mode is defined as a robust reliability index;

[0066] Step S6, based on the obtained robust reliability index, select reasonable support design decision variables to provide a basis for judging the stability and reliability of deep-buried hard rock chamber support.

[0067] In step S1, the total potential energy V of the layered composite rock slab in the slab cracking mode is equal to the sum of the load potential energy W and the strain energy U:

[0068]

[0069] Where U i is the strain energy of the i-th rock plate, W Pi is the vertical load potential energy of the i-th rock slab, W Ni is the horizontal load potential energy of the i-th rock slab.

[0070] in:

[0071]

[0072] Where D i is the bending stiffness of the i-th rock plate, a is the height of the rock plate, ω 0 is the deflection at the center of the rock plate in the height direction (i.e. x = a / 2), which is the maximum deformation of the rock plate before failure; σ P is the vertical stress, b i is the thickness of the i-th rock plate, T is the maximum horizontal support anchoring force that the anchor rod can provide;

[0073] in:

[0074]

[0075] b i =b 1 +(i-1)d (6)

[0076] In the formula, E is the elastic modulus of the rock plate, u is the Poisson's ratio of the rock plate, assuming that the thickness of the rock plate follows an arithmetic progression, b 1 is the thickness of the first rock slab, and d is the slab thickness increment.

[0077] In step S2, the uncertainty parameters include the height a of the rock slab and the elastic modulus E of the rock slab.

[0078] The nested convex set model based on information-deficient non-probabilistic theory is expressed as follows:

[0079]

[0080] In the formula, α is an uncertain parameter, which represents the gap between the unknown true value and the known nominal value of the uncertainty parameter, and reflects the fluctuation range of the uncertainty parameter; and are the known nominal values ​​of the uncertainty parameters rock plate thickness a and rock plate elastic modulus E respectively.

[0081] In step S3, the mechanical mutation model of layered composite rock plate failure is expressed as follows:

[0082] Δ=8m 3 +27n 2 (8)

[0083] In the formula, m and n are control variables, m is mainly related to the vertical force σ P n is mainly related to the maximum horizontal support anchoring force T that the anchor can provide;

[0084] in:

[0085]

[0086] The performance function of support stability under the slab cracking mode of deep-buried hard rock chamber is constructed, including:

[0087] The mutation characteristic value Δ of the layered composite rock slab is used as the judgment standard of whether the structure is stable (i.e., the output response value), the rock slab thickness a and the rock slab elastic modulus E are used as uncertainty parameters to form the uncertainty vector u=[a,E], and the maximum horizontal support anchoring force T that the anchor can provide is used as the design decision variable. The performance function R(q,u) for ensuring the support stability under the slab cracking mode of the deep buried hard rock chamber can be obtained, which is expressed by the following formula:

[0088]

[0089] R(q,u)=Δ| [T,(a,E)] ≥Δ c (12)

[0090] In the formula, Δ c It is the critical satisfactory value of the mutation characteristic value, which is expressed as the minimum acceptable value of the performance function R(q,u) when the combined rock slab structure does not undergo instability mutation.

[0091] In step S4, the robust function is expressed as follows:

[0092]

[0093] In the formula, It is a robust and reliable indicator.

[0094] In step S5, generally speaking, the maximum acceptable value of the mutation characteristic value of the layered composite rock plate is greater than 0, but the value in the actual project will change according to different design requirements, and the uncertainty parameters a and E will also change dynamically. This process ensures that the structure is not unstable and economic benefits can be guaranteed. Therefore, a reasonable design decision variable is selected, that is, the maximum horizontal support anchoring force T that the anchor can provide, to obtain the change law of the robust reliability index, which provides a basis for judging the stability and reliability of the support.

[0095] The non-probabilistic robust reliability analysis method for deep-buried hard rock chamber slab crack support provided by the embodiment of the present invention also includes step S7, which uses the mechanical catastrophe model of layered combined rock plate failure under the slab crack mode of the deep-buried hard rock chamber to verify the support stability reliability analysis method based on information missing non-probabilistic, specifically including:

[0096] The monotonicity of the relationship curve between the stability performance function and the uncertainty parameter is judged, that is, the calculation result curve is obtained and its monotonicity is judged; according to the robust active treatment function of this method, when the vertical stress σ P When and are fixed, the maximum horizontal support anchoring force T that the anchor can provide is changed, and then the robust reliability index calculation result is obtained; on this basis, it is further emphasized that the mutation characteristic value Δ c The dynamic change of is used as the basis for judging the stability of the layered composite rock plate structure, and the permissible mutation characteristic value Δ c The stability design problem under dynamic changes is solved by comparing the calculation results with the actual engineering situation to verify the rationality of this method.

[0097] The non-probabilistic robust reliability analysis method for slab crack support of a deep-buried hard rock chamber provided by the present invention is described in detail below with reference to specific embodiment 1.

[0098] Example 1

[0099] According to the support reliability analysis method under the slab cracking mode of the deep-buried hard rock chamber provided by the present invention, the following is verified and the stability design is carried out through engineering case data and theoretical formulas. Fig.10 shown.

[0100] First, the changing trends of uncertainty parameters a and E with the performance function are calculated respectively, as follows: Figure 1 and Figure 2 As shown, it can be seen that the performance function is a monotonically increasing function of the uncertainty parameters a and E within a certain range.

[0101] According to the parameter values ​​and the above formula, the relationship between the stability performance function and the uncertainty parameter when the design decision variable T = 15, 18, 21, 24, and 27 MPa is calculated. The results are as follows: Figure 3 As shown, for Figure 3 Any curve in the range of mutation characteristic value critical satisfaction value greater than 0, with the rock slab cracking failure mutation characteristic value critical satisfaction value Δ c Continuously decreasing, robust and reliable indicators (T,Δ c ) will continue to increase, indicating that the stability of the combined rock plate structure is less sensitive to changes in uncertainty parameters, that is, less sensitive to disturbances of uncertain factors. Correspondingly, the greater the tolerance to parameter uncertainty, the greater the support reliability and the better the robustness. When the critical satisfaction value of the mutation characteristic value is less than 0, the combined rock plate structure has the risk of instability mutation, that is, the possibility of buckling failure. It is necessary to actively select appropriate design decision variables so that the critical satisfaction value is greater than 0, thereby ensuring the reliability of the support. In addition, for the curve of the design decision variable T = 18MPa, when the critical satisfaction value of the mutation characteristic value of the plate cracking failure is Δ c When the value is 3.05, the robust reliability index is 0.2, indicating that the combined rock plate structure can allow the disturbance range of uncertainty parameters to be ±20%, that is, a is When the critical satisfaction value of the rock slab mutation characteristic value in the above curve is 19.49, the robust reliability index is 0, indicating that there is no deviation between the true value of a and the nominal value, and the minimum acceptable value of the mutation characteristic value is 19.49. In this case, any slight deviation between the actual value of the uncertainty parameter a and the nominal value will affect the stability of the structure, that is, it cannot resist any disturbance of the uncertainty parameter. It can be considered that the robustness in this case is very poor and the reliability is very low. Even a slight disturbance may lead to sudden buckling failure. For the corresponding curves under other design decision variables, the same method can be used for robustness analysis.

[0102] In order to elaborate on the active processing function of the robust and reliable indicators, Figure 3 The corresponding curves when the design decision variables T = 15MPa and T = 18MPa are selected (see Figure 4 ) for a specific analysis. For the curves corresponding to different design decision variables, if the critical satisfaction values ​​of the mutation characteristic values ​​of the two are required to be the same during the design process, for example, let Δ c When 7.032 is taken, the robust reliability index corresponding to T = 15MPa is is 0.036, and the robust reliability index corresponding to T = 18MPa is 0.120. This shows that when the value of the design decision variable T increases from 15MPa to 18MPa, the variation range of the uncertainty parameters that the structure can allow increases from 0.036 to 0.120 (robustness increase). At this time, the structure corresponding to the design decision variable T = 18MPa has a higher tolerance for uncertainty parameters and can accept larger fluctuations in uncertainty parameters. Therefore, it can be considered that the support stability performance in this case is better and the reliability is higher. In actual engineering, when it is necessary to consider the potential impact of emergencies or other factors and improve the risk resistance of the structure, it is entirely possible to actively adjust the corresponding design decision variables to actively deal with the stability of the structure, making it insensitive to the dynamic changes of uncertainty parameters and minimizing the impact of potential risks. When the same robust reliability index is selected, for example, When 0.200 is taken, the critical satisfactory value Δ of the plate crack damage mutation characteristic value corresponding to T = 15MPa c The corresponding Δ is 0.776 when T = 18 MPa c is 3.055. When the variation range of the uncertainty parameters allowed by the structure is the same (both are ±20%), the minimum acceptable value of the mutation characteristic value corresponding to T = 15MPa is less than the minimum acceptable value of the mutation characteristic value at T = 18MPa. c =3.055, in order to maintain the stability of the support, the critical satisfaction value at T = 15MPa needs to be reduced from 3.055 to 0.776 (performance appreciation). When the design decision variable T = 18MPa, when the uncertainty parameter changes within the range of ±30%, the sudden characteristic value of the plate cracking failure is always greater than 1. At this time, the structure is in a stable state and no sudden buckling failure of the rock plate will occur; and when the design decision variable T = 15MPa, when the uncertainty parameter changes within the range of ±30%, there is a situation where the sudden characteristic value is less than 0, and the structure is at risk of sudden instability. In order to make the robust reliability index at T = 15MPa It is still 0.300, and the structure returns to a stable state. Then, the design decision variable, that is, the maximum horizontal support anchoring force that the anchor can provide, must be increased to T = 18MPa. This process reflects that the reliability method based on information gap non-probability has the advantage of quantitatively and actively dealing with stability performance. In actual engineering, it can achieve cost saving control under the premise of ensuring support stability performance.

[0103] Figure 4The robustness analysis of the proposed method focuses on the influence of the rock plate height a on the support stability performance. However, in actual modeling, the rock plate height a and the elastic modulus E are both used as uncertainty parameters. Therefore, in order to better illustrate the influence of the two uncertainty parameters on the support stability performance, the calculation results corresponding to the design decision variable t = 18MPa are selected to carry out sensitivity analysis on the two uncertainty parameters, and three cases are selected for calculation: (1) only considering the uncertainty of the elastic modulus E; (2) only considering the uncertainty of the rock plate height a; (3) considering the uncertainty of both the elastic modulus E and the rock plate height a. The results are shown in Figure 2. Figure 5 As shown by Figure 5 It can be seen that when only the uncertainty of the elastic modulus E is considered, the robust reliability index When the value of the plate crack damage mutation characteristic value increases from 0.050 to 0.150, the critical satisfactory value Δ c It decreased from 19.306 to 18.685, a decrease of 0.621. When only the uncertainty of the rock plate height a is considered, the robust reliability index It decreased from 13.059 to 5.231, a decrease of 7.828, which is obviously greater than 0.621 corresponding to the elastic modulus E. This shows that for the same variation range of uncertainty parameters, the influence of the rock plate height a on the support stability performance is greater than the influence of the elastic modulus E on it; for the robust reliability index From 0.050 to 0.150, the critical satisfactory value of the plate crack damage mutation characteristic value Δ c It decreased from 12.848 to 4.491, a decrease of 8.357, which is greater than the decrease corresponding to the rock slab height a. Therefore, it can be considered that the uncertainty influence of multiple parameters is greater than the uncertainty influence of a single parameter, which is consistent with the actual engineering situation.

[0104] On the basis of the above sensitivity analysis, the influence of the uncertainty of the rock plate height a and the elastic modulus E on the support stability performance is comprehensively considered. The values ​​of the design decision parameter T are 15, 18, 21, 24, and 27 MPa, respectively. The results are as follows: Figures 6 to 9 As shown, it shows the design decision variable T, robust reliability index and the critical satisfactory value of the plate crack damage mutation characteristic value Δ c The changing rules among the three, such as vertical stress σ P =45MPa, first determine the minimum acceptable value of the plate crack damage mutation characteristic value Δ according to the design specification requirements c , and then according to the robust reliability index Change, from Figures 6 to 9 The corresponding design decision variable T is selected to meet the requirements of structural resistance uncertainty, so as to achieve the purpose of actively dealing with the stability performance of the support. Figures 6 to 9It can be seen that as the vertical stress increases, the curve gradually shifts to the right, and the critical satisfaction value corresponding to the same design decision variables and robust reliability index continues to decrease. The combined rock plate structure gradually becomes unstable with the increase of vertical stress, which is consistent with the phenomenon that the plate cracks and spalling first appear in the project, and then cause severe rock dynamic failure. At this time, if the ability of the structure to resist the dynamic changes of uncertain parameters is to be improved, it is necessary to actively increase the design decision variables, that is, the support force to meet the requirements of support stability performance.

[0105] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0106] In addition, it should be noted that the scope of the methods and systems in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved. For example, the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0107] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A non-probabilistic robust reliability analysis method for plate crack support in a deep-buried hard rock chamber, characterized in that: The steps include: Step S1, focusing on the sudden buckling failure of the layered composite rock slab during the slab cracking process of the deep-buried hard rock chamber, a mechanical mutation model of the layered composite rock slab failure under the slab cracking mode is constructed using the mutation theory. The total potential energy V of the layered composite rock slab under the slab cracking mode is equal to the sum of the load potential energy W and the strain energy U, which is expressed by the following formula: Where U i is the strain energy of the i-th rock plate, W Pi is the vertical load potential energy of the i-th rock slab, W Ni is the horizontal load potential energy of the i-th rock slab; in: Where D i is the bending stiffness of the i-th rock plate, a is the height of the rock plate, ω0 is the deflection at the center of the height direction of the rock plate, and is the maximum deformation of the rock plate before failure; σ P is the vertical stress, b i is the thickness of the i-th rock plate, T is the maximum horizontal support anchoring force that the anchor rod can provide; in: b i =b1+(i-1)d (6) In the formula, E is the elastic modulus of the rock plate, u is the Poisson's ratio of the rock plate, assuming that the thickness of the rock plate follows an arithmetic progression, b1 is the thickness of the first rock plate, and d is the plate thickness increment; Step S2, in view of the actual engineering characteristics that the statistical data of uncertainty parameters that cause plate cracking failure in deep hard rock chambers are severely scarce, a nested convex set model for quantitatively characterizing uncertainty parameters is established by using information-deficient non-probability theory; Step S3, based on the mechanical catastrophe model, construct the performance function of support stability under the slab cracking mode of the deep-buried hard rock chamber. The mechanical catastrophe model is expressed by the following formula: Δ=8m 3 +27n 2 (8)In the formula, m and n are control variables; in: The performance function of support stability under the slab cracking mode of deep-buried hard rock chamber is constructed, including: The mutation characteristic value Δ of the layered composite rock slab is used as the criterion for judging whether the structure is stable, the rock slab thickness a and the rock slab elastic modulus E are used as uncertainty parameters to form the uncertainty vector u=[a,E], and the maximum horizontal support anchoring force T that the anchor can provide is used as the design decision variable. The performance function R(q,u) for ensuring support stability under the slab cracking mode of the deep buried hard rock chamber can be obtained, which is expressed by the following formula: R(q,u)=Δ| [T,(a,E)] ≥Δ c (12) In the formula, Δ c is the critical satisfactory value of the mutation characteristic value, which is the minimum acceptable value of the performance function R(q,u) when the combined rock plate structure does not undergo instability mutation; Step S4, constructing a robust function according to the relationship between the output response value of the performance function and the critical satisfaction value; Step S5, based on the constructed robust function, the maximum fluctuation range of the allowable uncertainty parameter change when meeting the stability performance requirements of the chamber support in the plate cracking mode is defined as a robust reliability index; Step S6, based on the robust reliability index, select the support design decision variables to provide a basis for judging the stability and reliability of the deep-buried hard rock chamber support.

2. The method according to claim 1, characterized in that: In step S2, the nested convex set model is expressed as follows: In the formula, α is an uncertain parameter, which represents the gap between the unknown true value and the known nominal value of the uncertainty parameter, and reflects the fluctuation range of the uncertainty parameter; and They correspond to the known nominal values ​​of the rock plate thickness a and the rock plate elastic modulus E in the uncertainty parameters respectively.

3. The method according to claim 2, characterized in that In step S4, the robust function is expressed as follows: In the formula, It is a robust and reliable indicator.

4. The method according to claim 3, characterized in that The method also includes step S7, in which the support stability reliability analysis method based on non-probability of information gap is verified by using the mechanical mutation model of layered combined rock slab failure under the slab cracking mode of deep-buried hard rock chamber.

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