Non-probabilistic reliability evaluation method and device for deep roadway surrounding rock-support system

Abstract

This invention discloses a non-probabilistic reliability assessment method and apparatus for deep roadway surrounding rock-support systems, belonging to the technical field of underground roadway engineering structures in mines. The method includes the following steps: constructing the function functions corresponding to various instability states of the system composed of the surrounding rock and support of the deep roadway; calculating the original response interval of the function functions; obtaining the optimized response interval; constructing a reliability analysis and evaluation index for the surrounding rock-support system; and using this index to assess the overall reliability of the deep roadway surrounding rock-support system. This invention starts with the overall system composed of the surrounding rock and support of deep roadways, establishing a non-probabilistic reliability assessment method and apparatus for deep roadway surrounding rock-support systems that comprehensively considers multiple instability states. This more objectively and realistically reflects the actual stability and safety status of the deep roadway as a whole, and can be applied to the technical field of system reliability analysis for underground roadway engineering structures in mines.

Description

Technical Field

[0001] This invention belongs to the field of underground tunnel engineering structure technology, specifically relating to a non-probabilistic reliability assessment method and device for deep tunnel surrounding rock-support system. Background Technology

[0002] While traditional probabilistic reliability methods are well-established for analyzing the stability of rock-support systems in deep tunnels, they rely heavily on obtaining substantial statistical information on relevant uncertain variables. However, in practical deep tunnel engineering, as excavation depth increases, acquiring sufficient statistical information on the uncertain variables of the rock-support system becomes increasingly difficult, rendering traditional probabilistic reliability methods inapplicable. Therefore, a non-probabilistic reliability method is employed, representing uncertain variables in the rock-support system of deep tunnels as interval variables. This approach suffices to analyze the system by obtaining only the range of values ​​for the uncertain variables, effectively addressing the inherent limitations of traditional probabilistic reliability methods.

[0003] On the one hand, existing interval nonprobabilistic reliability methods are based on interval mathematical principles to calculate the response interval of the objective function in practical engineering applications. However, the current interval mathematical theory is not perfect. In particular, the interval expansion problem that is very easy to occur in the interval operation process seriously affects the calculation results of interval nonprobabilistic reliability methods, causing its reliability analysis conclusions to be distorted and unable to obtain the real nonprobabilistic reliability analysis and evaluation indicators in the actual engineering of deep roadway surrounding rock-support system.

[0004] On the other hand, current interval nonprobabilistic reliability analyses of the stability of deep roadway surrounding rock-support systems often only focus on a single instability state. However, for a system composed of both surrounding rock and support in deep roadways, the failure state leading to overall system instability is not simply unique, and the various instability states are not completely independent. The occurrence of any one of these instability states may lead to the overall instability and failure of the surrounding rock-support system. Therefore, it is necessary to comprehensively consider the various instability states in the deep roadway surrounding rock-support system in order to obtain a nonprobabilistic reliability analysis evaluation index that truly characterizes the overall stability of the deep roadway surrounding rock-support system.

[0005] Therefore, it is necessary to provide a non-probabilistic reliability assessment method and apparatus for deep tunnel surrounding rock-support systems to solve the problems mentioned in the background art. Summary of the Invention

[0006] The purpose of this invention is to provide a non-probabilistic reliability assessment method and apparatus for deep roadway surrounding rock-support systems. Based on existing interval non-probabilistic reliability methods for describing uncertain variables, and addressing the interval expansion problem, it employs second-order interval Taylor expansion optimization techniques to calculate the optimized response interval of the instability state function. Furthermore, it comprehensively considers multiple instability states of the system composed of deep roadway surrounding rock and support, and uses non-probabilistic system reliability theory to construct system reliability analysis and evaluation indicators. This allows for the comprehensive non-probabilistic reliability assessment of the deep roadway surrounding rock-support system, thereby solving at least one technical problem mentioned in the background art.

[0007] To solve the above-mentioned technical problems, the present invention is implemented as follows:

[0008] On one hand, embodiments of the present invention provide a non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems, comprising the following steps:

[0009] Step S1: Based on the interaction mechanism between the surrounding rock and support of the deep roadway, construct the functional functions corresponding to each instability state of the system composed of the surrounding rock and support of the deep roadway.

[0010] Step S2: Based on the constructed function, use interval theory to describe each uncertain variable, and use the traditional interval nonprobabilistic reliability method to calculate the original response interval of the function.

[0011] Step S3: For the interval expansion problem in the original response interval, the upper and lower limits of the function function are calculated using the second-order interval Taylor expansion optimization technique to obtain the optimized response interval.

[0012] Step S4: Taking into account the various possible instability states of both the surrounding rock and the support in deep roadways, a non-probabilistic system reliability theory is introduced. Based on the optimized response interval, a reliability analysis and evaluation index for the surrounding rock-support system is constructed. This system reliability analysis and evaluation index is then used to assess the overall reliability of the deep roadway surrounding rock-support system.

[0013] On the other hand, the present invention also provides a non-probabilistic reliability assessment device for a deep roadway surrounding rock-support system that performs the aforementioned non-probabilistic reliability assessment method, comprising the following steps:

[0014] The function construction module is used to construct the function corresponding to each instability state of the system composed of the surrounding rock and support of the deep roadway based on the interaction mechanism between the surrounding rock and support of the deep roadway.

[0015] The original response interval calculation module is used to calculate the original response interval of the function based on the constructed function, using interval theory to describe each uncertain variable, and using traditional interval nonprobabilistic reliability methods.

[0016] The response interval acquisition module is used to calculate the upper and lower limits of the function function by applying the second-order interval Taylor expansion optimization technique to solve the interval expansion problem in the original response interval, and obtain the optimized response interval.

[0017] The reliability assessment module comprehensively considers the various possible instability states of both the surrounding rock and the support in deep roadways. It introduces a non-probabilistic system reliability theory, constructs a reliability analysis and evaluation index for the surrounding rock-support system based on the optimized response interval, and uses this system reliability analysis and evaluation index to assess the overall reliability of the deep roadway surrounding rock-support system.

[0018] Compared with the prior art, the advantages of this invention are as follows:

[0019] (1) This invention uses second-order interval Taylor expansion optimization technology to calculate the upper and lower limits of the complex function of the surrounding rock-support system of deep roadways. By reducing the frequency of interval operation calls, the disorderly expansion of the interval range is suppressed, thereby obtaining its optimized response interval. This avoids the serious expansion phenomenon that is very easy to occur when the traditional interval non-probabilistic reliability method calculates the response interval of complex function. It solves the practical engineering problem that the reliability analysis results are relatively rough due to interval expansion, which makes it difficult to effectively guide the implementation of non-probabilistic reliability assessment of underground roadway structures in mines.

[0020] (2) By applying the concept of system reliability, this invention starts from the system as a whole composed of the surrounding rock and support of deep roadways, and constructs a non-probabilistic analysis method for system reliability that comprehensively considers the various instability states of the surrounding rock and support. This overcomes the inherent defect of existing non-probabilistic methods in the field of underground roadway engineering structure technology, which usually only focus on the reliability assessment of a single instability state. This makes the method more objective and realistic in reflecting the actual engineering safety status of the entire deep roadway.

[0021] (3) The non-probabilistic reliability assessment method and device for deep roadway surrounding rock-support system established by the present invention solves the serious interval expansion problem of traditional interval non-probabilistic reliability method in actual engineering application. On this basis, non-probabilistic system reliability analysis is carried out around the system composed of deep roadway surrounding rock and support, making it more efficient in calculation, more accurate in analysis results, and more in line with the actual situation of the system as a whole in engineering application, thereby further expanding the scope of application of non-probabilistic reliability method in the field of underground roadway engineering structure technology. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. 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 effort, wherein:

[0023] Figure 1 A flowchart of the nonprobabilistic reliability assessment method for the deep tunnel surrounding rock-support system provided by the present invention;

[0024] Figure 2 A schematic diagram of the deep tunnel excavation and support structure provided by the present invention;

[0025] Figure 3 A schematic diagram of the deep tunnel anchor structure provided by the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] The terms "first," "second," etc., used in the specification and claims of this invention are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0028] Please see Figure 1 As shown, this embodiment of the invention provides a non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems, comprising the following steps:

[0029] Step S1: Based on the interaction mechanism between the surrounding rock and support of the deep roadway, construct the functional functions corresponding to each instability state of the system composed of the surrounding rock and support of the deep roadway.

[0030] Step S2: Based on the constructed function, use interval theory to describe each uncertain variable, and use the traditional interval nonprobabilistic reliability method to calculate the original response interval of the function.

[0031] Step S3: For the interval expansion problem in the original response interval, the upper and lower limits of the function function are calculated using the second-order interval Taylor expansion optimization technique to obtain the optimized response interval.

[0032] Step S4: Taking into account the various possible instability states of both the surrounding rock and the support in deep roadways, a non-probabilistic system reliability theory is introduced. Based on the optimized response interval, a reliability analysis and evaluation index for the surrounding rock-support system is constructed. This system reliability analysis and evaluation index is then used to assess the overall reliability of the deep roadway surrounding rock-support system.

[0033] In step S1, the instability states include three types: insufficient anchor bolt support force, excessive surrounding rock deformation displacement, and excessive plastic zone radius.

[0034] Combined Figure 2 and Figure 3 As shown, for ease of analysis, the surrounding rock is considered as an isotropic medium existing in a natural stress field and subjected to net water pressure. Based on the MC yield criterion and the plastic flow law, three state characteristic functions are derived, expressed as follows:

[0035]

[0036] In the formula, T is the calculated value of the anchor bolt support force; T max E represents the maximum allowable value of the anchor bolt support force. b A represents the elastic modulus of the anchor bolt. b ρ is the cross-sectional area of ​​the anchor bolt; r0 is the excavation radius of the roadway; ρ is the sum of the anchor bolt length L and the excavation radius r0; r is the distance from a point along the anchor bolt length direction to the center of the roadway cross-section; U r This represents the displacement that occurs when a point along the length of the anchor bolt is a distance r from the center of the roadway cross-section. and These are the final displacements at the tail end (r = ρ) and the front end (r = r0) of the anchor bolt, respectively. and ρ represents the initial displacement at the tail end (r = ρ) and the front end (r = r0) of the anchor bolt, respectively; U represents the radial displacement of the surrounding rock along the roadway after excavation; ν represents the Poisson's ratio of the surrounding rock; E represents the elastic modulus of the surrounding rock; σ0 represents the hydrostatic pressure of the surrounding rock; p s For support resistance; p cr The critical pressure; r p N is the radius of the plastic band; c Uniaxial compressive strength; It is related to the internal friction angle The relevant variables; β is an empirical parameter reflecting the mining effect.

[0037] in:

[0038]

[0039] In the formula, c rm It represents the cohesion of the surrounding rock.

[0040] in, It is determined by the following formula:

[0041]

[0042]

[0043] In the formula, ψ is the expansion angle; A i B i C i For ease of calculation The intermediate variables introduced, A, B, and C, are for ease of calculation. The intermediate variables introduced, C1 and C2, are for the convenience of calculating A. i B i C i Intermediate variable parameters introduced from A, B, and C; It is related to the internal friction angle Relevant variables; N ψ This is an intermediate variable related to the expansion angle.

[0044] Wherein, p0 needs to satisfy the following equation:

[0045]

[0046] In the formula, (Friction angle = Peak internal friction angle = Residual internal friction angle); c rm =c rmp =c cmr (Cohesion = Peak Cohesion = Residual Cohesion); S θ S is the radial spacing between anchor bolts. z This refers to the axial spacing between the anchor bolts.

[0047] The control effect of anchor bolt support on the surrounding rock can be seen (see...) Figure 2 and Figure 3 The anchor bolt needs to provide a certain supporting force to keep the surrounding rock (corresponding to) Figure 3 The number 2 in the text is related to the anchor bolt (corresponding to the number 2 in the text). Figure 2 and Figure 3 The number 1 in the equation reaches a state of equilibrium together with the anchor rod itself. However, due to limitations imposed by the anchor rod's material, shape, and size, the maximum anchor force that the anchor rod can withstand is limited, which is T. max To ensure the effectiveness of the rock bolt support, the force exerted on the rock bolt by the surrounding rock must not exceed T.max That is, the function that enables the anchor bolts in deep roadways to remain stable is:

[0048] G(X1)=T max -T≥0;

[0049] Right now:

[0050]

[0051] Meanwhile, when the surrounding rock interacts with the support, the surrounding rock will deform. To stabilize the surrounding rock, the displacement of the surrounding rock must not exceed the allowable value U. lim Since the allowable displacement of the surrounding rock is related to the excavation radius r0, the function function corresponding to the deformation displacement of the surrounding rock in the deep tunnel can be obtained as follows:

[0052] G(X2)=U lim -U / r0≥0;

[0053] Right now:

[0054]

[0055] Furthermore, to ensure the smooth operation of excavation and support processes, and to guarantee a stable interaction between the surrounding rock and the support after support is completed, it is necessary to limit the radius of the plastic zone around the excavated surrounding rock. To prevent rock instability, the radius of the plastic zone must not exceed the allowable value λ. lim That is, the function corresponding to the plastic zone radius limitation for deep roadways is:

[0056] G(X3)=λ lim -r p / r0≥0;

[0057] Right now:

[0058]

[0059] In step S2, the range of values ​​for the uncertain variable is characterized by the midpoint and radius of the interval, and then standardized.

[0060] X = midrad(x, δx);

[0061] In the formula, X is an uncertain variable, and x and δx are the interval mean and interval radius of the uncertain variable X, respectively.

[0062] In step S3, since the functional expression corresponding to the deep roadway surrounding rock-support system is very complex, the original response interval calculated in step S2 is prone to interval expansion, which distorts the reliability analysis conclusion and fails to objectively and realistically reflect the actual engineering state of the deep roadway surrounding rock-support system. Therefore, it is necessary to eliminate the interval expansion problem generated in the interval non-probabilistic reliability calculation process.

[0063] Therefore, the function g(x) is defined as follows:

[0064] g(x)=G(X1,X2,X3,X4,..,X n );

[0065] Calculate the value of the function g(x) g(X) 0 and the first derivative value and second derivative value

[0066] In the formula X 0 = [x1,x2,x3,…,x n ];j,k∈[1,2,…,n].

[0067] Since the practical mathematical meaning of the Taylor expansion is to obtain the value of point x+Δx by calculating the degree of deviation of point x+Δx from point x, the optimal response interval of the function can be obtained by calculating the degree of deviation of point [x-Δx, x+Δx] from point x using the Taylor expansion. Therefore, the upper limit G of the function is calculated using the second-order interval Taylor expansion optimization technique. max and lower limit G min The optimized response range [G] is obtained. min G max ].

[0068] That is:

[0069]

[0070] In the formula, X 0 = [x1x2,x3,…,x n ]; j,k,l,m∈[1,2,…,n]; j≠k, l≠m;

[0071] In the formula, X is an uncertain variable; x is the interval mean of the uncertain variable X; The operator for finding partial derivatives; n is a positive integer.

[0072] In step S4, considering the various possible instability states of both the surrounding rock and support in deep roadways, a non-probabilistic system reliability theory is introduced. Based on the optimized response interval, a reliability analysis and evaluation index for the surrounding rock-support system is constructed. This non-probabilistic system reliability analysis and evaluation index is then used to assess the overall reliability of the deep roadway surrounding rock-support system. The reliability analysis and evaluation index η of the deep roadway surrounding rock-support system is expressed by the following formula:

[0073]

[0074] For the reliability analysis and evaluation index η of the surrounding rock-support system in deep roadways, the corresponding solution calculation can be carried out using the load increment method. The analysis process is briefly described as follows: using L1 to L n There are n load increments representing n types of instability states in the deep tunnel surrounding rock-support system. When the load increases from 0 to L1, component 1 fails. Then, for each subsequent increase in load, a component is about to enter a critical condition, which is defined as the first type of instability state. Analysis shows that when the load increases to L... j At that time, the force distributed on element i is ∑ j a ij R i , where a ij For element i, the load L j The utilization rate, assuming the component strength R i If each load increment satisfies a certain matrix {R}, then the element strength and incremental strength will satisfy {S}=[D]{R}, where [D] represents the sum of the values ​​of a and b. ij Constructing the inverse matrix of the matrix, thus determining the strength R of the deep tunnel surrounding rock-support system. s The following relationship exists between the limit state equations corresponding to this instability state and the equations:

[0075] R s =∑ i S i =∑ i d i R i ;

[0076] M = ∑ i d i R i -R = 0;

[0077] In the formula: d i Here, is a parameter related to load utilization; R is the external load borne by the system. Note that in interval nonprobabilistic reliability analysis, d iWe will treat this as an interval variable, and M as a nonlinear equation. For each type of instability state, there will be a corresponding η. Considering that the deep tunnel surrounding rock-support system is actually a series system, the occurrence of one type of instability state can lead to the overall instability of the deep tunnel surrounding rock-support system. Therefore, the reliability analysis and evaluation index η of the surrounding rock-support system can be expressed as:

[0078] η=min{eta1, eta2, eta3,..., eta n};

[0079] When η > 1, the deep tunnel surrounding rock-support system is determined to be stable and reliable as a whole; when η < 1, the deep tunnel surrounding rock-support system is determined to be unstable and unreliable as a whole; when η = 1, the system is determined to be in a critical state as a whole.

[0080] The present invention also provides a non-probabilistic reliability assessment device for a deep roadway surrounding rock-support system, which performs the aforementioned non-probabilistic reliability assessment method for the deep roadway surrounding rock-support system, comprising the following steps:

[0081] The function construction module is used to construct the function corresponding to each instability state of the system composed of the surrounding rock and support of the deep roadway based on the interaction mechanism between the surrounding rock and support of the deep roadway.

[0082] The original response interval calculation module is used to calculate the original response interval of the function based on the constructed function, using interval theory to describe each uncertain variable, and using traditional interval nonprobabilistic reliability methods.

[0083] The response interval acquisition module is used to calculate the upper and lower limits of the function function by applying the second-order interval Taylor expansion optimization technique to solve the interval expansion problem in the original response interval, and obtain the optimized response interval.

[0084] The reliability assessment module comprehensively considers the various possible instability states of both the surrounding rock and the support in deep roadways. It introduces a non-probabilistic system reliability theory, constructs a reliability analysis and evaluation index for the surrounding rock-support system based on the optimized response interval, and uses this system reliability analysis and evaluation index to assess the overall reliability of the deep roadway surrounding rock-support system.

[0085] The non-probabilistic reliability assessment method for the deep tunnel surrounding rock-support system provided by the present invention will be described in detail below with specific embodiments.

[0086] The specific details of the implementation example are as follows:

[0087] The excavation radius r0 of a deep tunnel is 3.0m. Based on the on-site engineering rock mass classification and physical and mechanical parameter evaluation, the Poisson's ratio v of the surrounding rock in the excavation area is 0.2, and the cohesion c of the surrounding rock is... rmThe range is approximately [0.07MPa, 0.13MPa], the elastic modulus E of the surrounding rock is taken as [300MPa, 700MPa], and the internal friction angle of the surrounding rock is... The range is [0.3840 rad, 0.6632 rad], and the value of the expansion angle ψ is approximately equal to the friction angle. Half of that is [0.1970rad, 0.3316rad], and the mining effect parameter β is taken as [0.2, 0.4].

[0088] Based on the on-site survey data, the relevant support parameters are as follows: anchor bolt elastic modulus E b The pressure is 210 GPa, and the anchor diameter D is... b The anchor bolt is 25mm thick, with a length L of 3m and an installation spacing S. θ S z All are 1m.

[0089] p0 is taken as 0.0208 MPa based on the iterative calculation result of the relevant expression.

[0090] Table 1 lists the values ​​of the deterministic parameters mentioned above, as well as the range of values ​​for other uncertain variables and the corresponding standardized results.

[0091] Table 1. Parameter values ​​for the surrounding rock and support system in deep roadways.

[0092]

[0093]

[0094] After obtaining the range of uncertain variables as shown in Table 1, the original response intervals of each functional function can be calculated using the interval operation rules in interval mathematics. In this example, the response intervals of each functional function are calculated using MATLAB programming. Some intermediate variables and original response intervals are shown in Tables 2 and 3.

[0095] Table 2 Response range of intermediate variables

[0096]

[0097]

[0098] Table 3 Original Response Range of Function

[0099] State function Original response range <![CDATA[G(X1)]]> 1.0e+9*[-0.0886,2.1545] <![CDATA[G(X2)]]> [-0.1317,0.0068] <![CDATA[G(X3)]]> [-5.0416,1.7588]

[0100] As can be seen from the above data, especially the response interval corresponding to the function G(X1), the calculation results have undergone severe interval expansion, resulting in data distortion and loss of reference value. Therefore, it cannot be used as a reference for the subsequent construction of reliability analysis and evaluation indicators for the surrounding rock-support system of this project.

[0101] To eliminate the severe interval expansion problem generated in the above calculation process, the state function is optimized using the second-order interval Taylor expansion optimization technique. Based on step S3, the optimized response intervals of the intermediate variables after the second-order interval Taylor expansion optimization are shown in Table 4, and the optimized response intervals of the function are shown in Table 5.

[0102] Table 4 Optimization Response Range for Intermediate Variables

[0103]

[0104]

[0105] Table 5 Optimized Response Range of Functionality

[0106] State function Response range <![CDATA[G(X1)]]> [126.686,144.103] <![CDATA[G(X2)]]> [0.000291009,0.00318207] <![CDATA[G(X3)]]> [0.396865,1.00164]

[0107] As shown in Table 5, the optimized interval values ​​are within the range of the original response interval, indicating that the algorithm can optimize the response interval.

[0108] Based on step S4 and the optimized state function response interval results described in step S3, the non-probabilistic reliability index... Based on the theory described in step S4, the non-probabilistic reliability analysis evaluation indices for the three types of instability states are obtained sequentially as follows: η1 = 15.5474, η2 = 1.20132, and η3 = 2.29109. Therefore, the non-probabilistic reliability analysis evaluation index for the deep roadway surrounding rock-support system is η = min{15.5474, 1.20132, 2.29109} = 1.20132 > 1. Thus, it is concluded that the deep roadway is stable and reliable, and its corresponding surrounding rock-support system design meets the requirements.

[0109] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0110] Furthermore, 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, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than 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.

[0111] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems, characterized in that, Includes the following steps: Step S1: Based on the interaction mechanism between the surrounding rock and support in deep roadways, for three types of instability states—insufficient anchor bolt support force, excessive surrounding rock deformation displacement, and excessive radius of the plastic zone of the surrounding rock—functional functions are constructed for each instability state of the system composed of the surrounding rock and support in deep roadways. The functional function corresponding to insufficient anchor bolt support force is expressed by the following formula: ； In the formula, This is an uncertain vector composed of uncertain variables involved in the functional function; This is the calculated value of the anchor bolt support force; This represents the maximum allowable value of the anchor bolt support force. The elastic modulus of the anchor bolt; The cross-sectional area of ​​the anchor bolt; The radius of the tunnel excavation; Anchor bolt length With the tunnel excavation radius sum; It is the distance from a point along the length of the anchor bolt to the center of the roadway cross-section; This indicates that the distance from a point along the length of the anchor bolt to the center of the roadway cross-section is... The displacement that occurs at that time; and These are the final displacements at the tail end and the front end of the anchor bolt, respectively. and These are the initial displacements at the tail end and the front end of the anchor bolt, respectively. Step S2: Based on the constructed function, use interval theory to describe each uncertain variable, and use the traditional interval nonprobabilistic reliability method to calculate the original response interval of the function. Step S3: For the interval expansion problem in the original response interval, the upper and lower limits of the function function are calculated using the second-order interval Taylor expansion optimization technique to obtain the optimized response interval. Step S4: Taking into account the various possible instability states of both the surrounding rock and the support in deep roadways, a non-probabilistic system reliability theory is introduced. Based on the optimized response interval, a reliability analysis and evaluation index for the surrounding rock-support system is constructed. This system reliability analysis and evaluation index is then used to assess the overall reliability of the deep roadway surrounding rock-support system.

2. The non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems according to claim 1, characterized in that, The function corresponding to excessive deformation and displacement of the surrounding rock is expressed by the following formula: ； In the formula, This is an uncertain vector composed of uncertain variables involved in the functional function; This represents the allowable value for deformation and displacement of the surrounding rock. This refers to the radial displacement of the surrounding rock along the tunnel after excavation; The elastic modulus of the surrounding rock; Poisson's ratio of the surrounding rock; The hydrostatic pressure of the surrounding rock; For support resistance; The critical pressure; The radius of the plastic band is denoted as .

3. The non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems according to claim 2, characterized in that, The function corresponding to an excessively large radius of the plastic zone in the surrounding rock is expressed by the following formula: ； In the formula, This is an uncertain vector composed of uncertain variables involved in the functional function; This refers to the allowable radius of the plastic zone in the surrounding rock after excavation. Uniaxial compressive strength; It is related to the internal friction angle Relevant variables; Empirical parameters to reflect the excavation effect.

4. The non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems according to claim 1, characterized in that, In step S2, the range of values ​​for the uncertain variable is characterized by the midpoint and radius of the range.

5. The non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems according to claim 4, characterized in that, In step S3, the optimized response range It can be expressed as follows: ； ； In the formula, ; ; ; ; It is an uncertain variable; Uncertain variables The interval mean; The operator for finding partial derivatives; The objective function is obtained using the second-order interval Taylor expansion optimization technique; It is a positive integer.

6. The non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems according to claim 5, characterized in that, In step S4, the reliability analysis and evaluation index of the surrounding rock-support system is determined. It can be expressed as follows: 。 7. The non-probabilistic reliability assessment method for deep tunnel surrounding rock-support systems according to claim 6, characterized in that, In step S4, the reliability of the deep roadway surrounding rock-support system is evaluated using non-probabilistic system reliability analysis evaluation indicators, specifically including: Reliability evaluation index for nonprobabilistic systems It can be expressed as follows: ； when At that time, it was determined that the overall stability and reliability of the surrounding rock and support system in the deep roadway were good; when At that time, it was determined that the overall stability and unreliability of the surrounding rock and support system in the deep roadway was due to the situation. When this occurs, the system as a whole is determined to be in a critical state.

8. A non-probabilistic reliability assessment device for a deep roadway surrounding rock-support system, which implements the non-probabilistic reliability assessment method for a deep roadway surrounding rock-support system according to any one of claims 1-7, characterized in that, Includes the following steps: The function construction module is used to construct function functions corresponding to each instability state of the system composed of the surrounding rock and support in deep roadways, based on the interaction mechanism between the surrounding rock and support. This is done for three types of instability states: insufficient anchor bolt support force, excessive surrounding rock deformation displacement, and excessive radius of the plastic zone of the surrounding rock. The function corresponding to insufficient anchor bolt support force is expressed by the following formula: ； In the formula, This is an uncertain vector composed of uncertain variables involved in the functional function; This is the calculated value of the anchor bolt support force; This represents the maximum allowable value of the anchor bolt support force. The elastic modulus of the anchor bolt; The cross-sectional area of ​​the anchor bolt; The radius of the tunnel excavation; Anchor bolt length With the tunnel excavation radius sum; It is the distance from a point along the length of the anchor bolt to the center of the roadway cross-section; This indicates that the distance from a point along the length of the anchor bolt to the center of the roadway cross-section is... The displacement that occurs at that time; and These are the final displacements at the tail end and the front end of the anchor bolt, respectively. and These are the initial displacements at the tail end and the front end of the anchor bolt, respectively. The original response interval calculation module is used to calculate the original response interval of the function based on the constructed function, using interval theory to describe each uncertain variable, and using traditional interval nonprobabilistic reliability methods. The response interval acquisition module is used to calculate the upper and lower limits of the function function by applying the second-order interval Taylor expansion optimization technique to solve the interval expansion problem in the original response interval, and obtain the optimized response interval. The reliability assessment module comprehensively considers the various possible instability states of both the surrounding rock and the support in deep roadways. It introduces a non-probabilistic system reliability theory, constructs a reliability analysis and evaluation index for the surrounding rock-support system based on the optimized response interval, and uses this system reliability analysis and evaluation index to assess the overall reliability of the deep roadway surrounding rock-support system.

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