Non-probabilistic robustness analysis method for rock tunnel supporting structure based on information defects

Abstract

The invention discloses a non-probabilistic robustness analysis method for a rock tunnel supporting structure based on information defects, and belongs to the technical field of tunnel engineering structure reliability design. The method comprises the following steps: quantitatively processing uncertainty parameters of surrounding rock of a rock tunnel by adopting a nested convex set model; deriving a performance function for describing the stability of the rock tunnel supporting structure based on a Duncan-Fama surrounding rock convergence function; constructing a robust function according to the relationship between the response value of the performance function and the critical value; defining the maximum fluctuation amplitude value of the allowable uncertain parameter change before the rock tunnel supporting structure is unstable as a robust reliable index; selecting a reasonable decision variable to obtain a change rule of a robust reliable index; and respectively carrying out sensitivity analysis on single-parameter fluctuation and multi-parameter combined fluctuation aiming at uncertainty parameters. According to the method, actual problems are analyzed and processed by adopting non-probability reliability, and the problem that uncertainty parameter data are seriously scarce in reliability analysis of the tunnel engineering structure is effectively solved.

Description

Technical Field

[0001] The invention belongs to the technical field of non-probabilistic reliability design of tunnel engineering structures, and in particular relates to a non-probabilistic robustness analysis method for a rock tunnel support structure based on information gaps. Background Art

[0002] In tunnel engineering, especially for deep tunnel engineering with more complex surrounding rock environment, it is usually difficult to collect a large enough amount of sample information due to the limitations of economic cost, environment and construction technology. This makes it difficult to obtain accurate statistical characteristics of uncertainty parameters (such as probability density function distribution form, variance and other data). This greatly limits the application of traditional probabilistic reliability methods based on random probability theory and mathematical statistics in the field of tunnel engineering.

[0003] In view of this actual engineering feature, further processing around uncertainty parameters from a "non-probabilistic" perspective and establishing a more objective reliability analysis method have become important issues that need to be addressed in this field. Summary of the invention

[0004] The purpose of the embodiment of the present invention is to provide a non-probabilistic robustness analysis method and system for a rock tunnel support structure based on information gaps, which analyzes and solves practical problems from the perspective of non-probabilistic reliability; based on the information gap theory, a nested convex set model is used to quantify and process uncertainty parameters, and a robust function is constructed based on a performance function that maintains the stability of the rock tunnel support structure. The robust reliability index is defined as the maximum fluctuation amplitude of the uncertainty parameter change that can be allowed before the rock tunnel support structure becomes unstable, and the characterization index is used to reflect the influence of the uncertainty parameter fluctuation on the reliability of the rock tunnel support structure, and a related analysis of the stability reliability of the rock tunnel support structure is carried out, thereby solving at least one technical problem involved in the background technology.

[0005] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0006] The embodiment of the present invention provides a non-probabilistic robustness analysis method for a rock tunnel support structure based on information gaps, comprising the following steps:

[0007] Step S1, using a nested convex set model to quantify the uncertainty parameters of the surrounding rock of the rock tunnel;

[0008] Step S2, deriving a performance function describing the stability of the rock tunnel support structure based on the Duncan–Fama surrounding rock convergence function;

[0009] Step S3, constructing a robust function according to the relationship between the response value and the critical value of the performance function;

[0010] Step S4, based on the constructed robust function, the maximum fluctuation amplitude value of the allowable uncertainty parameter change before the rock tunnel support structure becomes unstable is defined as a robust reliability index;

[0011] Step S5, selecting reasonable decision variables to obtain the variation law of robust reliability index, and providing a basis for judging the stability and reliability of rock tunnel support structure;

[0012] Step S6, performing sensitivity analysis of single parameter fluctuation and multi-parameter combination fluctuation for each uncertainty parameter.

[0013] Optionally, in step S1, the uncertain parameters include rock mass elastic modulus E, initial geostress p0, rock mass cohesion c, internal friction angle

[0014] Optionally, in step S1, a nested convex set model is used to quantify the uncertainty parameters of the surrounding rock of the rock tunnel, specifically including:

[0015] The rock mass elastic modulus E, initial ground stress p0, rock mass cohesion c, internal friction angle The average value of is taken as the nominal value of the four uncertainty parameters under non-probabilistic conditions, and the rock elastic modulus E, initial ground stress p0, rock cohesion c, internal friction angle The nested convex set quantization model is expressed as follows:

[0016]

[0017] In the formula, α is the uncertain parameter, which represents the uncertainty parameter E, p0, c, The fluctuation range of t and is the vector representation of the uncertainty parameters, and the scalar representation is the unknown true values ​​of the four uncertainty parameters and known nominal value

[0018] Optionally, in step S2, the control equation for stability analysis of rock tunnel support structure is obtained by Duncan–Fama surrounding rock convergence function, which is expressed as follows:

[0019]

[0020] Where R is the tunnel excavation radius; is the displacement around the tunnel; μ is the Poisson's ratio of the rock mass, p i For support resistance.

[0021] Optionally, in step S2, a performance function describing the stability of the rock tunnel support structure is derived, specifically including:

[0022] The maximum allowable convergence value of the ratio of the final radial displacement after surrounding rock excavation to the tunnel excavation radius As the critical value R c , the performance function R(p,u) describing the stability of rock tunnel support structure can be obtained through formula (2):

[0023]

[0024] In the formula, R c is the critical satisfaction value, which is equal to the maximum allowable convergence value of the ratio of the final radial displacement generated after surrounding rock excavation to the tunnel excavation radius It shows the maximum acceptable value of the performance function R(p,u) when the rock tunnel support structure does not become unstable.

[0025] Optionally, in step S3, constructing a robust function specifically includes:

[0026] When the uncertainty parameters E,p0,c, When the deviation between their respective nominal values ​​reaches the maximum, the maximum acceptable value of the ratio of the final radial displacement of the tunnel surrounding rock to the tunnel excavation radius can still be guaranteed to meet formula (4). Then, the robust function can be obtained, which is expressed as follows:

[0027]

[0028] In the formula, It is a robust and reliable indicator.

[0029] Optionally, step S5 specifically includes:

[0030] Select the support resistance p i As the decision variable, different support resistances p are analyzed. i The changing law of the robust reliability index and the interaction relationship between the robust reliability index and the selected critical satisfaction value are analyzed.

[0031] Optionally, in step S6, the influence of different uncertainty parameters on the robust reliability index under single parameter fluctuation is explored, including the following four situations: ① only considering the influence of rock elastic modulus E; ② only considering the influence of initial geostress p0; ③ only considering the internal friction angle ④Only consider the influence of rock cohesion c.

[0032] Optionally, in step S6, the uncertainty parameters E, p0, c, and The influence of different combinations of on the robust reliability indexes includes the following three combinations: ① two-parameter combination fluctuation; ② three-parameter combination fluctuation; ③ four-parameter combination fluctuation.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. The present invention adopts a nested convex set model to quantify and process uncertainty parameters to describe the dynamic changes of uncertainty parameters in the actual engineering of rock tunnel support structures. It proposes a robust reliability index calculation method and stability assessment criterion based on information gaps, which provides a new idea for the design of rock tunnel support structures from a non-probabilistic perspective and expands the application scope of non-probabilistic reliability analysis methods.

[0035] 2. The present invention proposes a corresponding robust reliability index of the rock tunnel engineering support structure by constructing a robust function. The index quantitatively represents the degree to which the reliability is affected by the change of uncertainty parameters and the sensitivity of the support structure stability to the change of uncertainty parameters.

[0036] 3. For robust reliability, the present invention can actively consider the impact of changes in uncertainty parameters on the stability of the support structure during the analysis process. By actively adjusting the decision variables in the performance function, the support structure can have the ability to actively resist changes in uncertainty parameters, thereby reducing the impact of uncertainty factors on the stability of the support structure.

[0037] 4. The present invention is particularly suitable for tunnel projects where it is difficult to obtain sufficient data on uncertainty parameters and where information on uncertainty parameters is severely lacking. In traditional interval theory methods, the premise is that the upper and lower limits of uncertainty parameters must be clearly known, and the fluctuation amplitude of uncertainty parameters in actual tunnel projects also changes dynamically, that is, the upper and lower limits of uncertainty parameters are also uncertain. The method in the present invention directly guides engineering design analysis by studying the fluctuation amplitude of uncertainty factors, and has a lower starting point for uncertainty factor information requirements. It only needs to consider the fluctuation of uncertainty factors within a certain amplitude, avoiding the difficulty of obtaining clear upper and lower limits, and is more suitable for actual underground projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] 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:

[0039] Figure 1 A flowchart of a non-probabilistic robust reliability analysis method for a rock tunnel support structure based on information gaps provided by an embodiment of the present invention;

[0040] Figure 2 The auxiliary monotonicity discrimination curve diagram (p) of the relationship curve between the performance function and the uncertainty parameter provided by the embodiment of the present invention i=0MPa, E =3966.13MPa);

[0041] Figure 3 A diagram showing the calculation results of robust reliability at different supporting forces provided by an embodiment of the present invention;

[0042] Figure 4 A comparative analysis diagram of robust reliability when the support force provided in the embodiment of the present invention is 0.2MPa and 0.4MPa;

[0043] Figure 5 A comparison diagram of single parameter fluctuation sensitivity analysis provided by an embodiment of the present invention (p i =0.2MPa);

[0044] Figure 6 A comparison diagram of the dual-parameter combination volatility sensitivity analysis provided by an embodiment of the present invention (p i =0.2MPa);

[0045] Figure 7 (a) to (f) are comparison diagrams of sensitivity analysis of dual-parameter combination fluctuations and corresponding single-parameter fluctuations provided in an embodiment of the present invention (p i =0.2MPa);

[0046] Figure 8 A comparison chart of sensitivity analysis between three-parameter combination fluctuation and two-parameter combination fluctuation provided in an embodiment of the present invention (p i =0.2MPa);

[0047] Fig. 9 A comparison chart of sensitivity analysis between four-parameter combination fluctuation and two-parameter combination fluctuation provided in an embodiment of the present invention (p i =0.2MPa);

[0048] Fig.10 A comparison chart of sensitivity analysis between four-parameter combination fluctuation and three-parameter combination fluctuation provided in an embodiment of the present invention (p i =0.2MPa). DETAILED DESCRIPTION

[0049] 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.

[0050] 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.

[0051] See also Figure 1 As shown, an embodiment of the present invention provides a non-probabilistic robustness analysis method for a rock tunnel support structure based on information gaps, comprising the following steps:

[0052] Step S1, using a nested convex set model to quantify the uncertainty parameters of the surrounding rock of the rock tunnel;

[0053] Step S2, deriving a performance function describing the stability of the rock tunnel support structure based on the Duncan–Fama surrounding rock convergence function;

[0054] Step S3, constructing a robust function according to the relationship between the response value and the critical value of the performance function;

[0055] Step S4, based on the constructed robust function, the maximum fluctuation amplitude value of the allowable uncertainty parameter change before the rock tunnel support structure becomes unstable is defined as a robust reliability index;

[0056] Step S5, selecting reasonable decision variables to obtain the variation law of robust reliability index, and providing a basis for judging the stability and reliability of rock tunnel support structure;

[0057] Step S6, performing sensitivity analysis of single parameter fluctuation and multi-parameter combination fluctuation for each uncertainty parameter.

[0058] In step S1, the uncertainty parameters specifically include the rock mass elastic modulus E of the rock mass surrounding the rock tunnel, the initial ground stress p0, the rock mass cohesion c, the internal friction angle

[0059] The nested convex set model is used to quantify the uncertainty parameters of the surrounding rock of rock tunnels, including:

[0060] The rock mass elastic modulus E, initial ground stress p0, rock mass cohesion c, internal friction angle The average value of is taken as the nominal value of the four uncertain parameters under non-probabilistic conditions, and the rock elastic modulus E, initial ground stress p0, rock cohesion c, internal friction angle The nested convex set quantization model is expressed as follows:

[0061]

[0062] In the formula, α is the uncertain parameter, which represents the uncertainty parameter E, p0, c, The fluctuation range of t and is the vector representation of the uncertainty parameters, and the scalar representation is the unknown true values ​​of the four uncertainty parameters and known nominal value

[0063] In step S2, the control equation for stability analysis of rock tunnel support structure is obtained by the Duncan–Fama surrounding rock convergence function, which is expressed as follows:

[0064]

[0065] Where R is the tunnel excavation radius; is the displacement around the tunnel; μ is the Poisson's ratio of the rock mass, p i For support resistance.

[0066] In step S2, a performance function describing the stability of the rock tunnel support structure is derived, which specifically includes:

[0067] The maximum allowable convergence value of the ratio of the final radial displacement after surrounding rock excavation to the tunnel excavation radius As the critical value R c , the performance function R(p,u) describing the stability of rock tunnel support structure can be obtained through formula (2):

[0068]

[0069] In the formula, R c is the critical satisfaction value, which is equal to the maximum allowable convergence value of the ratio of the final radial displacement generated after surrounding rock excavation to the tunnel excavation radius. It shows the maximum acceptable value of the performance function R(p,u) when the rock tunnel support structure does not become unstable.

[0070] In step S3, a robust function is constructed, which specifically includes:

[0071] When the uncertainty parameters E,p0,c, When the deviation between their respective nominal values ​​reaches the maximum, the maximum acceptable value of the ratio of the final radial displacement of the tunnel surrounding rock to the tunnel excavation radius can still be guaranteed to meet formula (4). Then, the robust function (i.e., the optimal planning problem) can be obtained, which is expressed as follows:

[0072]

[0073] In the formula, It is a robust and reliable indicator.

[0074] In step S5, the support resistance p is selected i As the decision variable, different support resistances p are analyzed. i The changing law of the robust reliability index and the interaction relationship between the robust reliability index and the selected critical satisfaction value are analyzed.

[0075] In step S6, sensitivity analysis of single parameter fluctuation and multi-parameter combined fluctuation is carried out for each uncertainty parameter, specifically including:

[0076] The influence of different uncertainty parameters on robust reliability indicators under single parameter fluctuation is explored, including the following four situations: ① only considering the influence of rock elastic modulus E; ② only considering the influence of initial geostress p0; ③ only considering the internal friction angle ④Only consider the influence of rock cohesion c.

[0077] To explore the impact of different combinations of uncertain parameters on robust reliability indicators under multi-parameter combination fluctuations, there are three combinations: ① two-parameter combination fluctuations; ② three-parameter combination fluctuations; ③ four-parameter combination fluctuations.

[0078] The non-probabilistic robustness analysis method for rock tunnel support structure based on information gap provided by the present invention is described in detail with reference to specific embodiment 1.

[0079] Example 1

[0080] According to the non-probabilistic reliability analysis method of the rock tunnel support structure based on information gap provided by the present invention, the following is verified and stability designed through engineering case data and theoretical formulas. The nominal values ​​of some parameter values ​​and uncertain parameters of a rock tunnel project are as follows:

[0081] The rock mass Poisson's ratio μ is 0.316, the rock mass cohesion c is 0.65 MPa, and the rock mass internal friction angle is The average value is 31.0°, the average value of initial geostress p0 is 3.0MPa, and the average value of rock elastic modulus E is 3966.13MPa.

[0082] Step S1, using a nested convex set model to quantify the uncertainty parameters of the surrounding rock of the rock tunnel;

[0083] The rock mass elastic modulus E, initial ground stress p0, rock mass cohesion c, internal friction angle The average value of is taken as the nominal value of the four uncertain parameters under non-probabilistic conditions, and the rock mass elastic modulus E, initial ground stress p0, rock mass cohesion c, internal friction angle The nested convex set quantization model is expressed as follows:

[0084]

[0085] In the formula, α is the uncertain parameter, which represents the uncertainty parameter E, p0, c, The fluctuation range of t and is the vector representation of the uncertainty parameters, and the scalar representation is the unknown true values ​​of the four uncertainty parameters and known nominal value

[0086] Step S2, obtaining a performance function describing the stability of the rock tunnel support structure based on the Duncan–Fama surrounding rock convergence function;

[0087]

[0088] In the formula, R c is the critical satisfaction value, which is equal to the maximum allowable convergence value of the ratio of the final radial displacement generated after surrounding rock excavation to the tunnel excavation radius It shows the maximum acceptable value of the performance function R(p,u) when the rock tunnel support structure does not become unstable.

[0089] Step S3, constructing a robust function according to the relationship between the response value and the critical value of the performance function;

[0090] The definition of robustness means that when the uncertainty parameters E, p0, c, When the deviation between their respective nominal values ​​reaches the maximum, the maximum acceptable value of the ratio of the final radial displacement of the tunnel surrounding rock to the tunnel excavation radius can still be guaranteed to meet equation (8). Therefore, the following optimal planning problem can be obtained:

[0091]

[0092] Formula (9) is also the robust function obtained in step S3.

[0093] Step S4, based on the constructed robust function, the maximum fluctuation amplitude value of the allowable uncertain parameter change before the rock tunnel support structure becomes unstable is defined as a robust reliability index;

[0094] The left side of equation (9) It is a robust and reliable indicator.

[0095] Step S5, selecting reasonable decision variables to obtain the variation law of robust reliability index, and providing a basis for judging the stability and reliability of rock tunnel support structure;

[0096] Select the support resistance p iAs the decision variable, different support resistances p are analyzed. i The variation law of the robust reliability index under the condition of , and the interaction relationship between the robust reliability index and the selected critical satisfaction value. The value of , firstly, we need to optimize equation (9):

[0097] (1) Inner layer optimization: to make it less than or equal to Always established, only needs The maximum value of the performance function, that is, the monotonic relationship between the performance function and the uncertainty parameter needs to be discussed. From formula (7), it can be directly judged that the performance function is a monotonic decreasing function of the rock mass elastic modulus E; analysis Figure 2 Each curve can be obtained, the performance function is the uncertainty parameter c, is a monotonically decreasing function of the uncertainty parameter p0.

[0098] (2) Outer optimization: defined by robustness, requiring uncertainty parameters E,p0,c, When the deviation between E,p0,c, and their respective nominal values ​​reaches the maximum, the rock tunnel support structure remains stable. Combined with the monotonicity provided by the inner layer optimization, when E,p0,c, The offsets are and When , the offset of each uncertainty parameter reaches the maximum, and the performance function reaches the maximum value at this time.

[0099] Now we focus on the uncertainty effect of p0 and give the decision variable support resistance p i =0, 0.2, 0.4, 0.6MPa when the corresponding calculation results, such as Figure 3 As shown. Figure 3 The following conclusions can be drawn from the analysis:

[0100] Watch alone Figure 3 From each curve we can see:

[0101] First, as the maximum acceptable value of the ratio of radial displacement to excavation radius R c Increase (i.e. The more relaxed the value is), the more robust and reliable the index is. The larger the value, according to the definition of robust reliability index, it indicates that the initial ground stress p0 can be allowed to fluctuate in a larger range under the premise of tunnel stability, and the less sensitive the tunnel stability performance is to the fluctuation of uncertainty parameters. It can be concluded that the tunnel is more reliable or has strong robustness. In actual engineering, the maximum acceptable value of the ratio of radial displacement to excavation radius is

[0102] R cThe gradual increase of means that the restrictions on maintaining the stability of the tunnel during design are looser, so its stability is naturally less affected by the fluctuation of uncertain parameters, which is in line with actual engineering.

[0103] Then, according to Figure 3 A preliminary analysis of the tunnel stability can be performed. i = 0.2MPa, when the maximum acceptable value R c When it is 0.156, the corresponding robust reliability index is It means that the fluctuation range of the initial geostress p0 is ±25%, that is, the allowable fluctuation range of p0 is [2.25MPa, 3.75MPa], which means that p0 fluctuates within this range and the tunnel can still maintain a stable state. c When the value is 0.109, the calculated robust reliability index is This extreme case indicates that the initial geostress p0 does not fluctuate, that is, there is no deviation between the true value and the nominal value of the initial geostress p0. At this time, any slight fluctuation in p0 will affect the stability of the tunnel. In other words, to ensure stability, p0 cannot change even within a very small range, which is obviously unrealistic from an engineering point of view. From the perspective of robustness, it can be considered that the stability of the tunnel is very sensitive to the change of uncertainty parameters, and its reliability or robustness is poor. At this time, the design parameters should be adjusted in time to deal with the risk of instability.

[0104] Comparing and analyzing different curves can get more information. Figure 3 Medium i =0.2MPa and p i = 0.4MPa, and then we will discuss it in more depth. Figure 4 ,observe Figure 4 We can get:

[0105] In the robust and reliable index When the same, Figure 4 When the reliability index is selected as 0.5, the decision variable support force p i = The maximum acceptable value R of the ratio of radial displacement to excavation radius corresponding to the 0.2MPa curve c =0.211 and p i = R corresponding to the 0.4MPa curve c =0.179. This shows that if the uncertainty parameter initial ground stress p0 is allowed to fluctuate within the range of ±50%, the maximum acceptable value R c=0.179, in order to maintain the original stability of the tunnel, when the support force drops to 0.2MPa, the maximum acceptable value must be relaxed to R c =0.211, which is called Performance Premium. Conversely, in the design calculation process, if the maximum acceptable value is reduced in order to improve the stability of the tunnel or because the designer is too conservative about the project (in this embodiment, R c From 0.211 to 0.179), it is necessary to increase the support force (in this embodiment, p i This shows that the robust reliability index obtained by the Information-Gap robust reliability model can actively adjust the numerical value of the decision variable (the support force in this embodiment) according to the fluctuation range of the uncertainty parameter (such as the "need" uncertainty parameter p0 to fluctuate within the range of ±50% of the nominal value in this embodiment) and the maximum acceptable value for maintaining tunnel stability.

[0106] The maximum acceptable value R required in the design calculation c When the same, Figure 4 When the maximum acceptable value is 0.136, the decision variable support force p i = Robust reliability index of the ratio of radial displacement to excavation radius corresponding to the 0.2MPa curve And p i =0.4MPa curve corresponds to This shows that when the decision variable p i When the uncertainty parameter initial geostress p0 increases from 0.2MPa to 0.4MPa, the allowable fluctuation range of the uncertainty parameter initial geostress p0 will increase from 0.15 to 0.267, which is called Robustness Premium. As the allowable fluctuation range of the tunnel for the uncertainty parameter initial geostress p0 increases, the stability of the tunnel also increases. The more reliable the tunnel, the stronger its robustness. This is in line with engineering practice, that is, the tunnel tends to be safer after increasing the support force. This is reflected in the engineering design calculation, which can be achieved by quantitatively and actively adjusting the decision variable (in this embodiment, the support resistance p i ), reduce the impact of uncertainty parameters on tunnel stability, that is, reduce the sensitivity of tunnel stability to fluctuations in uncertainty parameters, thereby ensuring tunnel safety, stability and reliability.

[0107] Step S6, performing single parameter and multi-parameter sensitivity analysis on the uncertain parameters.

[0108] First, the influence of different uncertainty parameters on the robust reliability index is considered in the case of single parameter fluctuation, including the following four cases: ① only considering the influence of rock elastic modulus E; ② only considering the influence of initial ground stress p0; ③ only considering the internal friction angle ④ Only consider the influence of rock mass cohesion c. Draw the corresponding maximum acceptable value of the ratio of radial displacement to excavation radius and the robust reliability index Function curve to Figure 5 ,analyze Figure 5 We can get:

[0109] When robust reliability index When the values ​​of and increase from 0.1 to 0.4 at the same time, the maximum acceptable value R of the ratio of radial displacement to excavation radius under the influence of each uncertainty parameter alone c This indicates that the value of the adjusted robust reliability index increases, that is, the fluctuation range of the allowed uncertainty parameter becomes larger. This "tolerant" behavior is manifested in the tunnel support structure, that is, if the support force is not increased, the maximum acceptable value R of the tunnel to maintain stability must be increased. c , that is, a more relaxed selection of the critical value of tunnel failure, which is in line with the actual engineering situation. When the increased values ​​are the same, the maximum acceptable value R of the ratio of radial displacement to excavation radius under the influence of each uncertainty parameter alone is c The increase value is different, from Figure 5 The uncertain parameters obtained are rock elastic modulus E, initial ground stress p0, internal friction angle The R of the rock mass cohesion c corresponding to each case c Value-added information is shown in Table 1.

[0110] Table 1 Corresponding increments of each uncertainty parameter

[0111]

[0112] This shows that different uncertainty parameters have different influences on tunnel stability, and the rock mass elastic modulus E and initial ground stress p0 have the greatest and similar influences, followed by the internal friction angle. Finally, there is the rock mass cohesion c. In actual engineering, when only a single uncertain factor is considered, the stability of the tunnel support structure is most sensitive to the fluctuation of the rock mass elastic modulus E and the initial ground stress p0, followed by the internal friction angle Finally, there is the rock mass cohesion c. This conclusion can guide the design process of actual tunnel engineering, that is, giving priority to the uncertainty of the rock mass elastic modulus E and the initial ground stress p0, so as to minimize their influence on the stability performance of the surrounding rock support structure.

[0113] Then consider the case of multi-parameter combination fluctuations, which have the following three combinations: ① two-parameter combination fluctuations; ② three-parameter combination fluctuations; ③ four-parameter combination fluctuations.

[0114] The maximum acceptable value of the ratio of radial displacement to excavation radius and the robust reliability index corresponding to the dual-parameter combined fluctuation form Function curve comparison chart, such as Figure 6 As shown, analysis Figure 6 We can get:

[0115] When robust reliability index When the values ​​of and increase from 0.1 to 0.4 at the same time, the maximum acceptable value R of the ratio of radial displacement to excavation radius under the combined influence of each set of dual parameter combinations c This indicates that the value of the adjusted robust reliability index increases, that is, the fluctuation range of the allowed uncertainty parameter becomes larger. This "tolerant" behavior is manifested in the tunnel support structure, that is, if the support force is not increased, the maximum acceptable value R of the tunnel to maintain stability must be increased. c , that is, a more relaxed selection of the critical value of tunnel failure, which is in line with the actual engineering situation.

[0116] Now let's compare and discuss the two-parameter combination and the two uncertainty parameters that make it up. Figure 7 shown.

[0117] analyze Figure 7 From the six figures in af, we can get the maximum acceptable value R of the ratio of radial displacement to excavation radius under the joint action of two parameters compared with the corresponding two uncertainty parameters acting alone when the robust reliability index increases by the same value. c The greater the added value, the more likely it is that the dual parameters have a greater impact on the stability of the tunnel support structure than the single parameter, which is in line with engineering practice.

[0118] Table 2 Corresponding value-added of dual parameter combinations

[0119]

[0120] From Table 2, we can see that different dual parameter combinations have different influences on the stability of the tunnel support structure. The combined effect is the greatest, so if only two uncertain parameters are considered in the design, the initial ground stress p0 and the internal friction angle should be selected. combination, so as to better maintain the stability of the tunnel support structure.

[0121] The maximum acceptable value of the ratio of radial displacement to excavation radius and the robust reliability index corresponding to the three-parameter combination fluctuation form Function curve comparison chart, such as Figure 8 The corresponding value-added information table is shown in Table 3:

[0122] Table 3 Corresponding value-added of three parameter combinations

[0123]

[0124] analyze Figure 8 From Table 3, it can be seen that different combinations of three parameters have different influences on the stability of the tunnel support structure. The combined effect of the rock mass cohesion c is the greatest, so if the three uncertain parameters are taken into account during the design, the initial ground stress p0, the internal friction angle The combination of the three parameters and the rock mass cohesion c can ensure the stability of the tunnel support structure under the most unfavorable conditions. The three-parameter combination has a greater impact on the stability of the tunnel support structure than the two-parameter combination.

[0125] The maximum acceptable value of the ratio of radial displacement to excavation radius and the robust reliability index corresponding to the four-parameter combination fluctuation form Function curve comparison chart, such as Fig. 9 , Fig.10 The corresponding value-added information table is shown in Table 4:

[0126] Table 4 Corresponding value-added of four parameter combinations

[0127]

[0128] analyze Fig. 9 , Fig.10 As shown in Table 4, when the four parameters are combined, the influence of uncertainty parameters on the stability of the tunnel support structure is greatly improved compared with the two-parameter combination and the three-parameter combination. The maximum acceptable value R c Compared with the three-parameter combination, the added value is nearly doubled, which means that the sensitivity of tunnel reliability to the fluctuation of uncertainty parameters is greatly improved, which is in line with engineering practice. Compared with the single parameter acting alone, when the maximum acceptable value R of the ratio of radial displacement to excavation radius is c When the four parameters are the same, the robust reliability index corresponding to the combination of This also reflects that due to the complex rock environment in which the tunnel project is located and the lack of research on various mechanisms, a large number of uncertain parameters have been generated. Under the joint action of various uncertain parameters, the impact on tunnel stability has increased exponentially, making the original results of stability analysis based on a single parameter or a small number of combined parameters may not be reliable. Therefore, in the actual design calculation, more attention should be paid to analyzing the joint action of uncertain parameters to ensure tunnel safety.

[0129] 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.

[0130] 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.

[0131] 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 robustness analysis method for rock tunnel support structure based on information gap, characterized in that: The steps include: Step S1, using a nested convex set model to quantify the uncertainty parameters of the surrounding rock of the rock tunnel; Step S2, deriving a performance function describing the stability of the rock tunnel support structure based on the Duncan–Fama surrounding rock convergence function; Step S3, constructing a robust function according to the relationship between the response value and the critical value of the performance function; Step S4, based on the constructed robust function, the maximum fluctuation amplitude value of the allowable uncertainty parameter change before the rock tunnel support structure becomes unstable is defined as a robust reliability index; Step S5, selecting reasonable decision variables to obtain the variation law of robust reliability index, and providing a basis for judging the stability and reliability of rock tunnel support structure; Step S6, performing sensitivity analysis of single parameter fluctuation and multi-parameter combination fluctuation for each uncertainty parameter.

2. The method according to claim 1, characterized in that In step S1, the uncertain parameters include rock mass elastic modulus E, initial geostress p0, rock mass cohesion c, internal friction angle 3. The method according to claim 2, characterized in that In step S1, the nested convex set model is used to quantify the uncertainty parameters of the surrounding rock of the rock tunnel, specifically including: The rock mass elastic modulus E, initial ground stress p0, rock mass cohesion c, internal friction angle The average value of is taken as the nominal value of the four uncertainty parameters under non-probabilistic conditions, and the rock elastic modulus E, initial ground stress p0, rock cohesion c, internal friction angle The nested convex set quantization model is expressed as follows: In the formula, α is the uncertain parameter, which represents the uncertainty parameter E, p0, c, The fluctuation range of t and is the vector representation of the uncertainty parameters, and the scalar representation is the unknown true values ​​of the four uncertainty parameters and known nominal value 4. The method according to claim 3, characterized in that In step S2, the control equation for stability analysis of rock tunnel support structure is obtained by the Duncan–Fama surrounding rock convergence function, which is expressed as follows: Where R is the tunnel excavation radius; is the displacement around the tunnel; μ is the Poisson's ratio of the rock mass, p i For support resistance.

5. The method according to claim 4, characterized in that In step S2, a performance function describing the stability of the rock tunnel support structure is derived, which specifically includes: The maximum allowable convergence value of the ratio of the final radial displacement after surrounding rock excavation to the tunnel excavation radius As the critical value R c , the performance function R(p,u) describing the stability of rock tunnel support structure can be obtained through formula (2): In the formula, R c is the critical satisfaction value, which is equal to the maximum allowable convergence value of the ratio of the final radial displacement generated after surrounding rock excavation to the tunnel excavation radius. It shows the maximum acceptable value of the performance function R(p,u) when the rock tunnel support structure does not become unstable.

6. The method according to claim 5, characterized in that In step S3, a robust function is constructed, which specifically includes: When the uncertainty parameters E,p0,c, When the deviation between their respective nominal values ​​reaches the maximum, the maximum acceptable value of the ratio of the final radial displacement of the tunnel surrounding rock to the tunnel excavation radius can still be guaranteed to meet formula (4). Then, the robust function can be obtained, which is expressed as follows: In the formula, It is a robust and reliable indicator.

7. The method according to claim 6, characterized in that Step S5 specifically includes: Select the support resistance p i As the decision variable, different support resistances p are analyzed. i The changing law of the robust reliability index and the interaction relationship between the robust reliability index and the selected critical satisfaction value are studied.

8. The method according to claim 7, characterized in that In step S6, the influence of different uncertainty parameters on the robust reliability index under single parameter fluctuation is explored, including the following four situations: ① only considering the influence of rock elastic modulus E; ② only considering the influence of initial ground stress p0; ③ only considering the internal friction angle ④Only consider the influence of rock cohesion c.

9. The method according to claim 8, characterized in that In step S6, the uncertainty parameters E, p0, c, and The influence of different combinations of on the robust reliability indexes includes the following three combinations: ① two-parameter combination fluctuation; ② three-parameter combination fluctuation; ③ four-parameter combination fluctuation.

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