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

Abstract

The invention discloses a non-probabilistic reliability evaluation method and device for a deep roadway surrounding rock-support system, and belongs to the technical field of mine underground roadway engineering structures. The method comprises the following steps: constructing performance functions corresponding to instability states of a system consisting of deep roadway surrounding rock and supports; calculating an original response interval of the performance function; an optimized response interval is obtained; and constructing a reliability analysis and evaluation index of the surrounding rock-support system, and evaluating the overall reliability of the deep roadway surrounding rock-support system by using the reliability analysis and evaluation index of the system. The deep roadway surrounding rock-support system non-probabilistic reliability evaluation method and the deep roadway surrounding rock-support system non-probabilistic reliability evaluation device which comprehensively consider multiple types of instability states are established from the whole system consisting of the deep roadway surrounding rock and the support, so that the whole actual stability and safety condition of the deep roadway can be reflected more objectively and truly; the method can be applied to the technical field of system reliability analysis of mine underground roadway engineering structures.

Description

Technical Field

[0001] The present invention belongs to the technical field of the engineering structure of underground roadways in mines, and particularly relates to a non-probabilistic reliability evaluation method and device for a surrounding rock-support system of deep roadways. Background Art

[0002] When analyzing the stability of a surrounding rock-support system of deep roadways, although the traditional probabilistic reliability method has been relatively well developed, such methods rely on obtaining a large amount of statistical information on relevant uncertain variables. However, for the actual engineering of deep roadways, as the excavation depth continues to increase, it becomes more difficult to obtain sufficient statistical information on the uncertain variables of the surrounding rock-support system, resulting in the inapplicability of the traditional probabilistic reliability method. Based on this, by using the non-probabilistic reliability method, the uncertain variables in the surrounding rock-support system of deep roadways are characterized in the form of interval variables, that is, only the value range of the uncertain variables needs to be obtained to carry out the analysis, and thus the inherent defects in the traditional probabilistic reliability method can be effectively solved.

[0003] On the one hand, in the actual engineering application process of the existing interval non-probabilistic reliability method, the response interval of the objective function is calculated based on the interval mathematics principle. However, the current interval mathematics theory is not yet perfect, especially the interval expansion problem that is extremely likely to occur during the interval operation process, which seriously affects the calculation results of the interval non-probabilistic reliability method, resulting in the distortion of the reliability analysis conclusion and the inability to obtain the true non-probabilistic reliability analysis and evaluation index in the actual engineering of the surrounding rock-support system of deep roadways.

[0004] On the other hand, in the current interval non-probabilistic reliability analysis of the stability of the surrounding rock-support system of deep roadways, the analysis is often only carried out for its single instability state. However, for the system composed of the surrounding rock and support of deep roadways, the failure states that cause the overall instability of the system are not simply unique, and the multiple different instability states are not completely independent. The occurrence of any one of the instability states may lead to the overall instability and failure of the surrounding rock-support system. Therefore, it is necessary to comprehensively consider multiple different instability states in the surrounding rock-support system of deep roadways in order to obtain a true non-probabilistic reliability analysis and evaluation index that characterizes the overall surrounding rock-support system of deep roadways itself.

[0005] Therefore, it is really necessary to provide a non-probabilistic reliability evaluation method and device for a surrounding rock-support system of deep roadways to solve the problems raised in the above background art. Summary of the Invention

[0006] The purpose of the embodiments of the present invention is to provide a non - probabilistic reliability evaluation method and device for the surrounding rock - support system of deep roadway. Based on the existing interval non - probabilistic reliability method for describing uncertain variables, aiming at the interval expansion problem, the second - order interval Taylor expansion optimization technology is used to calculate the optimized response interval of the function of the instability state, and considering various instability states of the system composed of the surrounding rock and support of the deep roadway, the non - probabilistic system reliability theory is used to construct the system reliability analysis and evaluation index, and the non - probabilistic reliability evaluation of the overall surrounding rock - support system of the deep roadway is carried out, so as to solve at least one technical problem involved in the background technology.

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

[0008] On the one hand, the embodiments of the present invention provide a non - probabilistic reliability evaluation method for the surrounding rock - support system of deep roadway, including the following steps:

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

[0010] Step S2: According to the constructed function, use the interval theory to describe each uncertain variable, and use the traditional interval non - probabilistic reliability method to calculate the original response interval of the function.

[0011] Step S3: Aiming at the interval expansion problem in the original response interval, use the second - order interval Taylor expansion optimization technology to calculate the upper and lower limits of the function, and obtain the optimized response interval.

[0012] Step S4: Comprehensively consider various instability states that may actually exist between the surrounding rock and support of the deep roadway, introduce the non - probabilistic system reliability theory, construct the surrounding rock - support system reliability analysis and evaluation index based on the optimized response interval, and use this system reliability analysis and evaluation index to evaluate the overall reliability of the surrounding rock - support system of the deep roadway.

[0013] On the other hand, the present invention also provides a non - probabilistic reliability evaluation device for the surrounding rock - support system of deep roadway that executes the non - probabilistic reliability evaluation method of the surrounding rock - support system of deep roadway, including the following steps:

[0014] A function construction module, which 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 describe each uncertain variable by using the interval theory according to the constructed functional function, and calculate the original response interval of the functional function by using the traditional interval non-probabilistic reliability method;

[0016] The response interval obtaining module is used to calculate the upper and lower limits of the functional function by using the second-order interval Taylor expansion optimization technology for the interval expansion problem in the original response interval, and obtain the optimized response interval;

[0017] The reliability evaluation module comprehensively considers various possible instability states that may actually exist between the surrounding rock and support of deep roadway, introduces the non-probabilistic system reliability theory, constructs the reliability analysis and evaluation index of the surrounding rock-support system based on the optimized response interval, and uses this system reliability analysis and evaluation index to evaluate the overall reliability of the surrounding rock-support system of deep roadway.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0019] (1) The present invention uses the second-order interval Taylor expansion optimization technology to calculate the upper and lower limits of the complex functional function belonging to the surrounding rock-support system of deep roadway, suppresses the disorderly expansion of the interval range by reducing the frequency of interval operation calls, so as to obtain the optimized response interval, avoiding the serious expansion phenomenon that is extremely easy to occur when the traditional interval non-probabilistic reliability method calculates the response interval of complex functional functions, and solving the engineering practical problem that the reliability analysis result is relatively rough due to interval expansion and it is difficult to effectively guide the non-probabilistic reliability assessment of the underground roadway structure in mines.

[0020] (2) By using the concept of system reliability, the present invention starts from the overall system composed of the surrounding rock and support of deep roadway, constructs a non-probabilistic analysis method for system reliability that comprehensively considers various instability states corresponding to the surrounding rock and support, overcomes the inherent defect that the existing non-probabilistic methods usually only carry out reliability assessment around a single instability state when applied to the technical field of underground roadway engineering structures in mines, and thus more objectively and truly reflects the overall actual engineering safety state of deep roadway.

[0021] (3) The non-probabilistic reliability assessment method and device for the surrounding rock-support system of deep roadway established by the present invention solve the serious interval expansion problem existing in the practical engineering application of the traditional interval non-probabilistic reliability method, and on this basis, carry out non-probabilistic system reliability analysis around the overall system composed of the surrounding rock and support of deep roadway, making it more efficient in calculation efficiency, more accurate in analysis results, and more in line with the actual situation of the overall system in engineering applications, thereby further expanding the applicable range of the non-probabilistic reliability method in the technical field of underground roadway engineering structures in mines. Description of the Drawings

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings, where:

[0023] Figure 1 It is a flowchart of the non-probabilistic reliability assessment method for the deep roadway surrounding rock - support system provided by the present invention;

[0024] Figure 2 It is a schematic diagram of the excavation and support structure of the deep roadway provided by the present invention;

[0025] Figure 3 It is a schematic diagram of the bolt structure of the deep roadway provided by the present invention. Specific embodiments

[0026] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0027] The terms "first", "second", etc. in the specification 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 used 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 more. In addition, "and / or" in the specification and claims means at least one of the connected objects, and the character " / " generally indicates an "or" relationship between the associated objects before and after.

[0028] Please refer to Figure 1 As shown, the embodiments of the present invention provide a non-probabilistic reliability assessment method for the deep roadway surrounding rock - support system, including the following steps:

[0029] Step S1, based on the interaction mechanism between the deep roadway surrounding rock and the support, construct the performance function corresponding to each instability state of the system composed of the deep roadway surrounding rock and the support;

[0030] Step S2, according to the constructed performance function, use the interval theory to describe each uncertain variable, and use the traditional interval non-probabilistic reliability method to calculate the original response interval of the performance function;

[0031] Step S3, for the interval expansion problem in the original response interval, the upper and lower limits of the performance function are calculated using the second-order interval Taylor expansion optimization technology to obtain the optimized response interval;

[0032] In step S4, the various possible unstable states of surrounding rock and support in deep tunnels are comprehensively considered, and the non-probabilistic system reliability theory is introduced. Based on the optimized response interval, the reliability analysis and evaluation index of the surrounding rock-support system is constructed. The reliability of the surrounding rock-support system of deep tunnels is evaluated using the system reliability analysis and evaluation index.

[0033] In step S1, the instability state includes three instability states: the anchor support force is too small, the surrounding rock deformation displacement is too large, and the plastic zone radius is too large.

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

[0035]

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

[0037] in:

[0038]

[0039] Wherein, c rm is the cohesion of the surrounding rock.

[0040] Among them, is determined by the following formula:

[0041]

[0042]

[0043] Wherein, ψ is the swelling angle; A i , B i , C i are intermediate variables introduced for the convenience of calculation; A, B, C are intermediate variables introduced for the convenience of calculation ; C1 and C2 are intermediate variable parameters introduced for the convenience of calculating A , B i , C i , A, B, C; i is a variable related to the internal friction angle ; N is an intermediate variable related to the swelling angle. ψ

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

[0045]

[0046] Wherein, (friction angle = peak internal friction angle = residual internal friction angle); c rm = c rmp = c cmr (cohesion = peak cohesion = residual cohesion); S θ is the radial spacing between bolts, and S z is the axial spacing between bolts.

[0047] It can be seen from the control effect of bolt support on the surrounding rock (see Figure 2 and Figure 3 ) that a certain supporting force needs to be provided inside the bolts to make the surrounding rock (corresponding to Figure 3 the number 2 therein) and the bolts (corresponding to Figure 2 and Figure 3 the number 1 therein) reach a balanced state together. However, due to the limitations of the bolt's own material, shape, size, etc., the maximum bolt force that the bolt itself can bear is limited, which is T max . If the bolt support is to play a role, it is necessary to ensure that the force exerted by the surrounding rock on the bolt does not exceed Tmax , that is, the function for the bolts in the deep roadway to maintain stability is obtained as:

[0048] G(X1) = T max -T ≥ 0;

[0049] That is:

[0050]

[0051] Meanwhile, when the surrounding rock and the support interact, the surrounding rock will deform. If the surrounding rock is to be stable, it is necessary to ensure that the displacement of the surrounding rock does not exceed the allowable value U lim , and the allowable displacement of the surrounding rock is related to the excavation radius r0. Thus, the function for the deep roadway corresponding to the deformation displacement of the surrounding rock is obtained as:

[0052] G(X2) = U lim -U / r0 ≥ 0;

[0053] That is:

[0054]

[0055] In addition, to ensure that behaviors such as the excavation process and the support application process can proceed normally, and the surrounding rock can interact with the support to reach a stable state after the support is completed, it is necessary to limit the radius of the plastic zone outside the surrounding rock after excavation. If the surrounding rock is not to be unstable, it is necessary to ensure that the value of the plastic zone radius does not exceed the allowable value λ lim , that is, the function for the deep roadway corresponding to the limitation of the plastic zone radius is obtained as:

[0056] G(X3) = λ lim -r p / r0 ≥ 0;

[0057] That is:

[0058]

[0059] In step S2, the value range of the uncertain variable is characterized by the midpoint of the interval and the interval radius, and it is standardized:

[0060] X = midrad(x, δx);

[0061] In the formula, X is the 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 function expression corresponding to the surrounding rock - support system of the deep roadway is very complex, the original response interval calculated in step S2 is prone to the problem of interval expansion, and the conclusion of reliability analysis is distorted. Furthermore, it is impossible to objectively and truly reflect the actual engineering state of the surrounding rock - support system of the deep roadway. Therefore, it is necessary to eliminate the interval expansion problem generated in the process of interval non - probability reliability calculation.

[0063] For this reason, the functional function g(x) is now set as shown in the following formula:

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

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

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

[0067] Since the actual mathematical meaning of the Taylor expansion formula is to obtain the value of the point x + Δx by calculating the degree of deviation of the point x+Δx from the point x, therefore, the degree of deviation of the point [x - Δx,x + Δx] from the point x can be calculated by the Taylor expansion formula to obtain the optimized response interval of the functional function. For this reason, the upper limit G max and the lower limit G min of the functional function are calculated by using the second - order interval Taylor expansion optimization technology, and the optimized response interval [G min ,G max is obtained.

[0068] That is:

[0069]

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

[0071] where X is an uncertain variable; x is the interval mean of the uncertain variable X; is the operation symbol for partial derivative; n is a positive integer.

[0072] In step S4, the various possible instability states of both the surrounding rock and support in deep tunnels are comprehensively considered. A non-probabilistic system reliability theory is introduced, and a reliability analysis and evaluation index for the surrounding rock-support system is constructed based on the optimized response interval. This non-probabilistic system reliability analysis and evaluation index is used to evaluate the overall reliability of the deep tunnel surrounding rock-support system. The reliability analysis and evaluation index η for the deep tunnel surrounding rock-support system is expressed as follows:

[0073]

[0074] For the reliability analysis and evaluation index η of the surrounding rock-support system of deep tunnels, the corresponding solution calculation can be carried out by 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 in the deep tunnel surrounding rock-support system. When the load increases from 0 to L1, the component 1 fails. Then, the increase in load in the system will cause the component to enter the critical condition, which is defined as the first type of instability. j When , the force distributed to element i is ∑ j a ij R i , where a ij is the load L of component i j Utilization rate, if the component strength R i and each load increment satisfies a certain matrix {R}, then the element strength and incremental strength will satisfy {S}=[D]{R}, where [D] represents the ij It is constructed as the inverse matrix of the matrix, so the strength R of the deep tunnel surrounding rock-support system s , and the corresponding limit state equation of the instability state has the following relationship:

[0075] R s =∑ i S i =∑ i d i R i ;

[0076] M=∑ i d i R i -R=0;

[0077] Where: d i is a parameter related to load utilization; R is the external load borne by the system. Note that in the interval non-probabilistic reliability analysis, d iwill be regarded as an interval variable, and M is a non-linear equation. For each type of instability state, there will be a corresponding η. Considering that the deep roadway 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 roadway 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{η1, η2, η3, …, η n};

[0079] When η > 1, it is determined that the deep roadway surrounding rock - support system is overall stable and reliable; when η < 1, it is determined that the deep roadway surrounding rock - support system is overall unstable and unreliable; when η = 1, it is determined that the system is in a critical state overall.

[0080] The present invention also provides a non-probabilistic reliability evaluation device for the deep roadway surrounding rock - support system that executes the non-probabilistic reliability evaluation method of the deep roadway surrounding rock - support system, including the following steps:

[0081] A function function construction module, which is used to construct the function functions corresponding to the instability states of the system composed of the deep roadway surrounding rock and the support based on the interaction mechanism between the deep roadway surrounding rock and the support;

[0082] A raw response interval calculation module, which is used to describe each uncertain variable using interval theory according to the constructed function function, and calculate the raw response interval of the function function using the traditional interval non-probabilistic reliability method;

[0083] A response interval obtaining module, which is used to calculate the upper and lower limits of the function function using the second-order interval Taylor expansion optimization technique for the interval expansion problem in the raw response interval, and obtain the optimized response interval;

[0084] A reliability evaluation module, comprehensively considering various possible instability states that may actually exist between the deep roadway surrounding rock and the support, introducing the non-probabilistic system reliability theory, constructing a reliability analysis and evaluation index for the surrounding rock - support system based on the optimized response interval, and evaluating the overall reliability of the deep roadway surrounding rock - support system using this system reliability analysis and evaluation index.

[0085] The following uses specific embodiments to elaborate in detail on the non-probabilistic reliability evaluation method of the deep roadway surrounding rock - support system provided by the present invention.

[0086] The specific situation of the embodiment is as follows:

[0087] The excavation radius r0 of a certain deep roadway is 3.0 m. According to the in-situ 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 rmThe range is approximately [0.07 MPa, 0.13 MPa], the range of the elastic modulus E of the surrounding rock is taken as [300 MPa, 700 MPa], and the internal friction angle of the surrounding rock The range is [0.3840 rad, 0.6632 rad], and the value of the dilation angle ψ is approximately half of the friction angle That is [0.1970 rad, 0.3316 rad], and the excavation effect parameter β is taken as [0.2, 0.4].

[0088] According to the on-site survey data, the relevant support parameters are as follows: The elastic modulus E of the bolt b Is 210 GPa, the diameter D of the bolt b Is 25 mm, the length L of the bolt is 3 m, and the installation vertical and horizontal spacing S θ 、S z Are both 1 m.

[0089] According to the iterative calculation results of the relevant expressions, p0 is taken as 0.0208 MPa.

[0090] Table 1 lists the value-taking situations of the above-mentioned deterministic parameters, as well as the interval ranges of the values of other uncertain variables and the corresponding results after standardized processing.

[0091] Table 1 Parameter value-taking table of the surrounding rock–support system of deep roadway

[0092]

[0093]

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

[0095] Table 2 Response intervals of intermediate variables

[0096]

[0097]

[0098] Table 3 Original response intervals of performance functions

[0099] State function Original response interval <![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] From the above data, it can be seen that especially in the response interval corresponding to the function G(X1), there is a serious interval expansion in its calculation results, resulting in the distortion of the calculated data, and its results have lost the reference significance, so it cannot be used as the reference basis for constructing the reliability analysis and evaluation index of the surrounding rock - support system of this project in the follow-up.

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

[0102] Table 4 Optimized response intervals of intermediate variables

[0103]

[0104]

[0105] Table 5 Optimized response intervals of the function

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

[0107] As can be seen from Table 5, the optimized interval values are within the range of the original response interval, indicating that this algorithm can optimize the response interval.

[0108] Based on step S4, according to 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 and evaluation indexes for the above three types of instability states are obtained as: η1 = 15.5474, η2 = 1.20132, η3 = 2.29109 respectively. Further, the non-probabilistic reliability analysis and evaluation index η of the surrounding rock - support system of this deep roadway can be obtained as η = min{15.5474, 1.20132, 2.29109} = 1.20132 > 1. Therefore, the conclusion is drawn that this deep roadway is stable and reliable, and the design of its corresponding surrounding rock - support system meets the requirements.

[0109] It should be noted that in this article, the term "including", "containing" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or also includes elements inherent in such a process, method, article or device. Without further limitations, an element defined by the statement "including a..." does not exclude the existence of another identical element in the process, method, article or device including that element.

[0110] 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 a 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 also be added, omitted, or combined. Additionally, the features described with reference to certain examples may be combined in other examples.

[0111] 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 of the present invention and the scope protected by the claims, and all of them fall within the protection scope of the present invention.

Claims

1. A non-probabilistic reliability assessment method for the surrounding rock-support system of deep roadway, characterized in that It includes the following steps: Step S1: Based on the interaction mechanism between the surrounding rock and support of deep roadway, construct the function functions corresponding to the instability states of the system composed of the surrounding rock and support of deep roadway. Step S2: According to the constructed function functions, use the interval theory to describe each uncertain variable, and use the traditional interval non-probabilistic reliability method to calculate the original response interval of the function functions. Step S3: Aiming at the interval expansion problem in the original response interval, use the second-order interval Taylor expansion optimization technique to calculate the upper and lower limits of the function functions, and obtain the optimized response interval. Step S4: Considering comprehensively various possible instability states that may actually exist between the surrounding rock and support of deep roadway, introduce the non-probabilistic system reliability theory, construct the reliability analysis and evaluation index of the surrounding rock-support system based on the optimized response interval, and use this system reliability analysis and evaluation index to evaluate the overall reliability of the surrounding rock-support system of deep roadway.

2. The non-probabilistic reliability assessment method for the deep roadway surrounding rock - support system according to claim 1, characterized in that, In Step S1, the instability states include three types of instability states: too small bolt supporting force, too large surrounding rock deformation displacement, and too large plastic zone radius.

3. The non-probabilistic reliability assessment method for the deep roadway surrounding rock - support system according to claim 2, characterized in that The function function corresponding to too small bolt supporting force is expressed by the following formula: Wherein, X1 is an uncertain vector composed of uncertain variables involved in the function; T is the calculated value of the bolt support force; T max is the maximum allowable value of the bolt support force; E b is the elastic modulus of the bolt; A b is the cross-sectional area of the bolt; r0 is the excavation radius of the roadway; ρ is the sum of the bolt length L and the excavation radius r0 of the roadway; r is the distance from a point on the bolt length direction to the center of the roadway section; U r represents the displacement occurring when the distance from a point on the bolt length direction to the center of the roadway section is r; and are respectively the final displacements at the tail end and the front end of the bolt; and are respectively the initial displacements at the tail end and the front end of the bolt.

4. The non-probabilistic reliability assessment method for the deep roadway surrounding rock-support system according to claim 3, characterized in that The function function corresponding to too large surrounding rock deformation displacement is expressed by the following formula: Wherein, X2 is an uncertain vector composed of uncertain variables involved in the function; U lim is the allowable value of the surrounding rock deformation displacement; U is the radial displacement of the surrounding rock along the roadway after excavation; E is the elastic modulus of the surrounding rock; v is the Poisson's ratio of the surrounding rock; σ0 is the hydrostatic pressure of the surrounding rock; p s is the support resistance; p cr is the critical pressure; r p is the radius of the plastic zone.

5. The non-probabilistic reliability assessment method for the surrounding rock-support system of deep roadway according to claim 4, characterized in that The function function corresponding to too large plastic zone radius of the surrounding rock is expressed by the following formula: where X3 is an uncertain vector composed of uncertain variables involved in the performance function; λ lim is the allowable value of the plastic zone radius of the surrounding rock after excavation; N c is the uniaxial compressive strength; is a variable related to the internal friction angle ; β is an empirical parameter reflecting the excavation effect.

6. The non-probabilistic reliability assessment method of the deep roadway surrounding rock - support system according to claim 1, characterized in that In Step S2, the value interval of the uncertain variable is characterized by the interval midpoint and interval radius.

7. The non-probabilistic reliability assessment method for the deep roadway surrounding rock - support system according to claim 6, characterized in that, In step S3, the optimized response interval [G min , G max is expressed by the following formula: where X 0 = [x1 x2, x3, …, x n ; X is an uncertain variable; x is the interval mean of the uncertain variable X; is the operation symbol for partial derivative; g(·) is the objective function obtained by using the second-order interval Taylor expansion optimization technique; n is a positive integer.

8. The non-probabilistic reliability assessment method for the deep roadway surrounding rock-support system according to claim 7, characterized in that, In Step S4, the reliability analysis and evaluation index η of the surrounding rock-support system is expressed by the following formula:

9. The non-probabilistic reliability assessment method for the deep roadway surrounding rock - support system according to claim 8, characterized in that, In Step S4, using the non-probabilistic system reliability analysis and evaluation index to evaluate the overall reliability of the surrounding rock-support system of deep roadway specifically includes: The non-probabilistic system reliability evaluation index η is expressed by the following formula: η = min{η1, η2, η3, …, η n}; When η > 1, it is determined that the overall surrounding rock-support system of deep roadway is stable and reliable; when η < 1, it is determined that the overall surrounding rock-support system of deep roadway is unstable and unreliable; when η = 1, it is determined that the system as a whole is in a critical state.

10. A non-probabilistic reliability assessment device for a deep roadway surrounding rock - support system that implements the non-probabilistic reliability assessment method of the deep roadway surrounding rock - support system described in any one of claims 1 - 9, characterized in that, It includes the following steps: Function function construction module, which is used to construct the function functions corresponding to the instability states of the system composed of the surrounding rock and support of deep roadway based on the interaction mechanism between the surrounding rock and support of deep roadway. Original response interval calculation module, which is used to describe each uncertain variable using the interval theory according to the constructed function functions, and calculate the original response interval of the function functions using the traditional interval non-probabilistic reliability method. Response interval obtaining module, which is used to calculate the upper and lower limits of the function functions using the second-order interval Taylor expansion optimization technique for the interval expansion problem in the original response interval, and obtain the optimized response interval. Reliability evaluation module, considering comprehensively various possible instability states that may actually exist between the surrounding rock and support of deep roadway, introducing the non-probabilistic system reliability theory, constructing the reliability analysis and evaluation index of the surrounding rock-support system based on the optimized response interval, and using this system reliability analysis and evaluation index to evaluate the overall reliability of the surrounding rock-support system of deep roadway.

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