Tunneling method multi-objective optimization method based on uncertain quantification and probabilistic risk assessment

Abstract

The application discloses a tunnel construction method multi-objective optimization method of uncertain quantification and probability risk assessment, belongs to the technical field of tunnel construction, and solves the problem of the limitation of the decision under complex geological conditions caused by the traditional tunnel construction method comparison and selection method which usually ignores the uncertainty of surrounding rock parameters and support failure probability; the application does not use a single fixed value, but regards the key surrounding rock parameters as random variables, simulates and calculates the vault settlement displacement data set and the maximum support stress data set under each compared and selected tunnel construction method, and calculates the support reliability index and the conditional failure probability of each compared and selected tunnel construction method, so that the spatial variability of the surrounding rock parameters and the failure probability of the support structure are simultaneously introduced into the tunnel construction method comparison and selection decision framework, a multi-objective optimization model containing the engineering construction period cost, the support failure probability and the reliability index is established, and the technical problem of the limitation of the traditional deterministic method in the decision under complex geological conditions is systematically solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel construction, in particular to a tunnel construction method multi-objective optimization method based on uncertain quantification and probability risk assessment. BACKGROUND

[0002] In tunnel engineering construction, the scientific comparison and selection of construction methods is the premise of safe and rapid tunnel construction. Due to the difference of geological environment, the diversity of tunnel cross-section size, the environmental restriction of construction site, the applicability of mechanical equipment matching and the restriction of construction period target, and on the basis of ensuring the stability of surrounding rock and construction safety, the comparison and selection of tunnel construction method is a typical multi-objective decision-making problem, which needs to consider the project progress, construction cost and resource efficiency.

[0003] The current tunnel construction method comparison and selection usually takes the surrounding rock classification system as the core basis, and through matching the support parameter design, supplemented by support deformation monitoring data, numerical simulation verification and engineering experience comprehensive decision. But there are still two problems in the actual construction process:

[0004] (1) Uncertainty of spatial distribution of surrounding rock parameters is not considered

[0005] The tunnel surrounding rock mechanical parameters show significant spatial variability and anisotropy characteristics. As the basis of support structure design, the uncertainty of surrounding rock parameters directly affects the safety and economy of support scheme. Simplifying the surrounding rock parameters as spatial mean value may cause deviation in support response evaluation.

[0006] (2) Single support failure evaluation index, without considering support failure probability

[0007] Although the traditional comparison and selection method considers multiple factors such as geological conditions and structural safety, it simplifies the support failure risk as deformation or safety factor threshold judgment, ignores probabilistic evaluation, and makes the support structure relatively conservative in the face of actual external factors. Tunnel deformation and safety factor are the core problems of tunnel engineering stability evaluation. When the support deformation approaches the critical value, its failure probability may increase significantly. The existing research has not established a quantitative correlation model of primary support deformation-failure probability. SUMMARY

[0008] In view of the above problems in the prior art, the present application provides a tunnel construction method multi-objective optimization method based on uncertain quantification and probability risk assessment, which solves the problem that the traditional tunnel construction method comparison and selection method has limitations in decision-making under complex geological conditions due to the neglect of uncertainty of surrounding rock parameters and support failure probability.

[0009] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0010] The application provides a tunnel construction method multi-objective optimization method for uncertain quantification and probability risk assessment, and comprises the following steps:

[0011] S1, determining multiple tunnel construction methods for comparison and selection based on a construction object and a construction constraint condition;

[0012] S2, collecting surrounding rock parameters and establishing a surrounding rock parameter model in a normal distribution, generating multiple parameter combinations based on the surrounding rock parameter model, simulating and calculating the vault settlement displacement and the maximum support stress of each parameter combination under each tunnel construction method for comparison and selection, and obtaining a vault settlement value displacement data set and a maximum support stress data set of each tunnel construction method for comparison and selection;

[0013] S3, calculating the support reliability index of each tunnel construction method for comparison and selection corresponding to each vault settlement value displacement data set;

[0014] S4, performing linear regression fitting on the vault settlement value displacement data set and the maximum support stress data set of each tunnel construction method for comparison and selection to obtain a linear regression fitting formula, and constructing a conditional failure probability of each tunnel construction method for comparison and selection based on the linear regression fitting formula of each tunnel construction method for comparison and selection;

[0015] S5, selecting an optimal tunnel construction method based on the support reliability index and the conditional failure probability of each tunnel construction method for comparison and selection and in combination with the construction period and the cost corresponding to each tunnel construction method for comparison and selection.

[0016] Further, the method for obtaining multiple parameter combinations is as follows:

[0017] S21, collecting samples and obtaining surrounding rock parameters through sample tests, and establishing a surrounding rock parameter model in a normal distribution based on the mean value and the standard deviation of each parameter in the surrounding rock parameters, wherein the surrounding rock parameters comprise an elastic modulus , a specific gravity , a surrounding rock internal friction angle and a cohesion ;

[0018] S22, generating multiple random parameter combinations from the surrounding rock parameter model through a Monte Carlo sampling method.

[0019] Further, step S2 further comprises the following steps:

[0020] S23, obtaining 5 Gaussian nodes of each parameter in all parameter combinations and Gaussian weights corresponding to the Gaussian nodes by using a fifth-order Gaussian-Hermite integral method, and obtaining 5 actual engineering values of each parameter through the corresponding 5 Gaussian nodes;

[0021] S24, sequentially changing each parameter at the 5 actual engineering values through a multiplication dimension reduction method, while fixing the remaining parameters as their respective mean values, and obtaining 20 MDRM parameter combinations;

[0022] S25, respectively combine 20 groups of MDRM parameter combinations in each tunnel construction method for numerical simulation to obtain displacement response values and stress response values of each group of MDRM parameter combinations in each tunnel construction method; and the displacement response values and stress response values of each group of MDRM parameter combinations are respectively taken as the vault settlement displacement data set and the supporting maximum stress data set of each tunnel construction method.

[0023] Further, the calculation method of the supporting reliability index of each tunnel construction method comprises the steps of:

[0024] S31, establishing a vault settlement displacement response function based on the tunnel construction method , and its expression is:

[0025]

[0026] wherein, is the number of parameters in the surrounding rock parameter model; is the displacement response value when all parameters are mean values; , , , are univariate displacement response functions based on the multiplication dimension reduction method, respectively changing the elastic modulus , the unit weight , the internal friction angle of surrounding rock and the cohesion of the remaining parameters at the mean value;

[0027] S32, calculating the mean value and the second moment of , and their expressions are respectively:

[0028]

[0029]

[0030] wherein, , , and are the expected values of , , , , and are respectively obtained by multiplying each of the 5 displacement response values with the corresponding 5 Gaussian weights and summing them up;

[0031] S33, calculating the variance and the standard deviation of , and their expressions are respectively:

[0032] ,

[0033] S34, calculate the supporting reliability index .

[0034] Further, the method for constructing the conditional failure probability of each tunnel construction method includes the following steps:

[0035] S41, based on the linear regression fitting of the vault settlement value displacement data set and the supporting maximum stress data set of the tunnel construction method to be compared and selected, a linear regression fitting formula is obtained:

[0036]

[0037] wherein, is the supporting maximum stress; and are fitting coefficients; is the vault settlement value displacement; is the residual error, which is subject to a normal distribution with a mean of zero, ; is a normal distribution function; is the variance of the normal distribution;

[0038] S42, statistically analyze the tensile strength of the supporting material used in the tunnel construction method to be compared and selected , according to the mean and the variance of output the normal probability distribution of ;

[0039] S43, establish the safety margin of the tunnel construction method to be compared and selected , which is expressed as:

[0040]

[0041] wherein, safety is indicated by failure is indicated by

[0042] S44, construct the normal probability distribution of the safety margin under a given vault settlement value displacement , wherein, and the expressions of and are respectively:

[0043] ,

[0044] wherein, and They are respectively The conditional mean and conditional variance;

[0045] S45. Calculate the settlement and displacement of the fixed arch crown. Conditional reliability index ;

[0046] S46. Calculate the settlement and displacement of the fixed arch crown. The probability of failure under the following conditions :

[0047]

[0048] in, For a given crown settlement value The probability of support structure failure under certain conditions; This is the cumulative distribution function of the standard normal distribution.

[0049] Furthermore, step S5 further includes the following steps:

[0050] S51. Determine the allowable crown settlement displacement range of the construction object, and obtain the mean, maximum and minimum failure probabilities under each comparative tunnel construction method.

[0051] S52. A comprehensive score is calculated for each comparative tunnel construction method, and the comparative tunnel construction method with the highest comprehensive score is selected. The comprehensive score of the tunnel construction methods selected by comparison The expression is:

[0052]

[0053] ,

[0054] ,

[0055] in, , , and All are weighting coefficients; , , and The first Reliability index of the tunnel construction method for comparison The normalized indices of mean failure probability, duration, and cost; among them, , , and The first The reliability index, failure probability mean, construction period and cost of the compared tunnel construction methods; 、 、 、 The reliability index, failure probability, construction period and cost of all compared tunnel construction methods are respectively the maximum values; 、 、 and The reliability index, failure probability, construction period and cost of all compared tunnel construction methods are respectively the minimum values.

[0056] Further, the allowed vault settlement displacement interval of the construction object is 0.2% to 0.6% of the maximum allowed vault settlement displacement value.

[0057] The application discloses a tunnel construction method multi-objective optimization method based on uncertain quantification and probability risk assessment, and has the following beneficial effects:

[0058] 1. The application no longer uses a single fixed value, but regards key surrounding rock parameters as random variables, simulates and calculates vault settlement displacement data sets and supporting maximum stress data sets under each compared tunnel construction method, and calculates the supporting reliability index and conditional failure probability of each compared tunnel construction method, so that the spatial variability of surrounding rock parameters and the failure probability of supporting structures are simultaneously introduced into a tunnel construction method comparison and decision-making framework, a multi-objective optimization model including engineering construction period cost, supporting failure probability and reliability index is established, and the technical problem of decision-making limitations of a traditional deterministic method under complex geological conditions is systematically solved.

[0059] 2. The application adopts field sampling and test to determine the probability distribution of parameters, so that the established surrounding rock parameter model is closer to engineering practice, and a large number of random parameter combinations are generated by using a Monte Carlo sampling method, so that the possible value range and distribution of surrounding rock parameters can be fully covered, and the comprehensiveness and statistical significance of the probability evaluation result are ensured.

[0060] 3. The application adopts a five-order Gauss-Hermite integral and a multiplication dimension reduction method (MDRM), and only needs to be performed 20 times (numerical simulation calculation), so that the statistical moment results of hundreds of Monte Carlo simulations can be accurately approximated. This greatly overcomes the technical bottleneck of high cost and long time of traditional probability analysis, so that the method becomes efficient and feasible in actual engineering application.

[0061] 4. The application provides a specific means for quickly and accurately calculating the supporting reliability index based on the multiplication dimension reduction method MDRM and the first order second moment method (FOSM), the index comprehensively reflects the overall influence of the uncertainty of surrounding rock parameters on the stability of supporting structures, and provides clear and quantitative basis for preliminary reliability comparison of different construction methods.

[0062] 5、The present application can accurately calculate the real-time failure probability of the supporting structure under a specific deformation by establishing a linear fitting relationship between the supporting stress and the vault settlement and introducing conditional probability analysis, which is a dynamic and more precise risk management method compared with the traditional static safety factor evaluation.

[0063] 6、The present application can flexibly reflect the emphasis of different projects on safety, construction period or cost by adjusting the weight coefficient, so that the optimization result can better meet the individualized needs of the owner, and the universality and flexibility of the method are enhanced.

[0064] 7、The present application can ensure that the failure probability is at a controllable low risk level and avoid the waste of economic cost caused by excessive control of deformation by setting the vault settlement displacement interval, which reflects the optimal balance between safety and economy. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 It is a flowchart of the tunnel construction method multi-objective optimization method of uncertain quantification and probability risk assessment;

[0066] Figure 2 It is a tunnel rock distribution map;

[0067] Figure 3 It is a cross-sectional schematic diagram of the tunnel using double-side wall guide pit method, nine-part block temporary support method and nine-part rock column method;

[0068] Figure 4 It is a Monte Carlo simulation frequency and MDRM probability distribution fitting diagram of the double-side wall guide pit method;

[0069] Figure 5 It is a Monte Carlo simulation frequency and MDRM probability distribution fitting diagram of the nine-part block temporary support method;

[0070] Figure 6 It is a Monte Carlo simulation frequency and MDRM probability distribution fitting diagram of the nine-part rock column method;

[0071] Figure 7 It is a vault settlement displacement and maximum supporting stress fitting distribution diagram of the double-side wall guide pit method;

[0072] Figure 8 It is a vault settlement displacement and maximum supporting stress fitting distribution diagram of the nine-part block temporary support method;

[0073] Figure 9 It is a vault settlement displacement and maximum supporting stress fitting distribution diagram of the nine-part rock column method;

[0074] Figure 10 It is a conditional failure probability fitting diagram of the double-side wall guide pit method, nine-part block temporary support method and nine-part rock column method;

[0075] Figure 11 is a curve fitting diagram of the bending moment, axial force and displacement variation of the nine-part rock column method;

[0076] Figure 12 is a total ground settlement diagram in the construction process of the nine-part rock column method;

[0077] Figure 13 is a cross-section ground settlement diagram of the monitoring point in the construction process of the nine-part rock column method. DETAILED DESCRIPTION

[0078] The specific embodiments of the present application are described below to facilitate the understanding of the present application for those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0079] Example 1

[0080] Reference Figure 1 , a tunnel construction method multi-objective optimization method for uncertain quantification and probability risk assessment is provided, comprising the following steps:

[0081] S1, determining a plurality of compared and selected tunnel construction methods based on construction objects and construction constraint conditions.

[0082] S2, collecting surrounding rock parameters and establishing a surrounding rock parameter model in normal distribution, generating a plurality of parameter combinations based on the surrounding rock parameter model, simulating and calculating the vault settlement displacement and maximum support stress of each parameter combination under each compared and selected tunnel construction method, and obtaining the vault settlement value displacement data set and the maximum support stress data set of each compared and selected tunnel construction method.

[0083] Specifically, step S2 further comprises the following steps:

[0084] S21, obtaining surrounding rock parameters by collecting samples on site and testing the samples, and establishing a surrounding rock parameter model in normal distribution based on the mean and standard deviation of each parameter in the surrounding rock parameters, the surrounding rock parameters including elastic modulus , unit weight, internal friction angle of surrounding rock and cohesion .

[0085] S22, generating a plurality of random parameter combinations from the surrounding rock parameter model by the Monte Carlo sampling method.

[0086] S23, obtain 5 Gaussian nodes and Gaussian weights corresponding to each parameter in all parameter combinations by using a five-order Gaussian-Hermite integral method, and obtain 5 actual engineering values of each parameter through the corresponding 5 Gaussian nodes;

[0087] S24, obtain 20 groups of MDRM parameter combinations by sequentially changing each parameter on the 5 actual engineering values through the multiplication dimension reduction method while fixing the remaining parameters as their respective mean values;

[0088] S25, respectively, perform numerical simulation on the 20 groups of MDRM parameter combinations in each tunnel construction method to be compared and selected, and obtain the displacement response value and stress response value of each group of MDRM parameter combinations under each tunnel construction method to be compared and selected; the displacement response value and stress response value of each group of MDRM parameter combinations are respectively taken as the vault settlement displacement data set and the support maximum stress data set of each tunnel construction method to be compared and selected.

[0089] By using the five-order Gaussian-Hermite integral and the multiplication dimension reduction method (MDRM), only 20 times of numerical simulation calculation are required to approach the statistical moment results of hundreds or thousands of Monte Carlo simulations with high precision. This greatly overcomes the technical bottleneck of high calculation cost and long time consumption of traditional probability analysis, making the method efficient and feasible in practical engineering applications.

[0090] S3, calculate the support reliability index of each tunnel construction method to be compared and selected through each vault settlement value displacement data set.

[0091] S4, perform linear regression fitting on the vault settlement value displacement data set and the support maximum stress data set of each tunnel construction method to be compared and selected to obtain a linear regression fitting formula, and construct the conditional failure probability of each tunnel construction method to be compared and selected based on the linear regression fitting formula of each tunnel construction method to be compared and selected.

[0092] S5, based on the support reliability index and the conditional failure probability of each tunnel construction method to be compared and selected, and combined with the corresponding construction period and cost, select the optimal tunnel construction method.

[0093] Specifically, the calculation method of the support reliability index of each tunnel construction method to be compared and selected includes the following steps:

[0094] S31, establish a vault settlement displacement response function based on the tunnel construction method to be compared and selected , the expression of which is:

[0095]

[0096] wherein, is the number of parameters in the surrounding rock parameter model, which is 4; is the displacement response value when all parameters are mean values; , , , Based on the aforementioned multiplicative dimensionality reduction method, the elastic modulus is varied while keeping the remaining parameters at their mean values. Severe internal friction angle of surrounding rock and cohesion The univariate displacement response function. To better illustrate, let's take... For example, To be in a fixed , , While being the mean The arch settlement displacement values ​​obtained by varying the values ​​across five actual engineering projects include: , ; For the first An actual engineering value, To and The corresponding crown settlement displacement value.

[0097] S32, Calculation mean and second moment Their expressions are as follows:

[0098]

[0099]

[0100] in, , , and They are respectively , , , The expected values ​​are obtained by multiplying each of the five displacement response values ​​by the corresponding five Gaussian weights and then summing them. To better illustrate this, let's take... For example, The expression is:

[0101]

[0102] in, The elastic modulus obtained based on the fifth-order Gauss-Hermitian integral method is the first... Gaussian weights.

[0103] S33, Calculation variance and standard deviation Their expressions are as follows:

[0104] ,

[0105] S34. Calculate the support reliability index .

[0106] Support reliability index It is used to assess whether the entire "surrounding rock-support" system will become unstable and fail. It represents the overall ability of each comparative tunnel construction method to control the deformation of the surrounding rock. The higher the index, the stronger the ability of the corresponding comparative tunnel construction method to maintain the stability of the surrounding rock under uncertain geological conditions.

[0107] As a further embodiment, the method for constructing the conditional failure probability of each comparative tunnel construction method includes the following steps:

[0108] S41. Based on the comparison and selection of tunnel construction methods, the data sets of crown settlement and displacement and the data sets of maximum support stress are used to obtain the linear regression fitting formula:

[0109]

[0110] in, The maximum stress required for support; and All are fitting coefficients; This represents the displacement due to the settlement of the arch crown. The residuals follow a normal distribution with a mean of zero. ; It is a normal distribution function; The variance of the normal distribution is used to represent random fluctuations.

[0111] S42. Statistical analysis and comparison of the tensile strength of support materials used in tunnel construction methods. ,according to mean and variance Output normal probability distribution .

[0112] S43. Establish a safety margin for comparing tunnel construction methods. Its expression is:

[0113]

[0114] in, Indicates safety. Indicates invalidity;

[0115] S44. Construct the displacement of the given crown settlement value. Safety margin normal probability distribution wherein, and are respectively:

[0116]

[0117]

[0118] wherein, and are respectively conditional mean and conditional variance of

[0119] S45, calculate the conditional reliability index under the vault settlement value displacement

[0120] conditional reliability index is used to quantify how the failure probability of the supporting structure dynamically evolves with the increase of deformation, and to ensure that even under the most unfavorable deformation displacement, the strength failure risk of the supporting structure of all compared tunnel construction methods is controllable.

[0121] S46, calculate the conditional failure probability under the vault settlement value displacement

[0122]

[0123] wherein, is the probability of failure of the supporting structure under the condition of a given vault settlement value , that is, under the condition that the vault settlement value is , the probability that the supporting stress exceeds the material strength ; is the cumulative distribution function of the standard normal distribution.

[0124] As a further scheme of the embodiment, step S5 can further include the following steps:

[0125] S51, determine the allowed vault settlement displacement interval of the construction object, and obtain the mean value, maximum value and minimum value of the failure probability under the condition of each compared tunnel construction method.

[0126] In the embodiment, the allowed vault settlement displacement interval of the construction object is 0.2% to 0.6% of the maximum allowed vault settlement displacement value.

[0127] S52, score each compared tunnel construction method comprehensively, and select the compared tunnel construction method with the highest comprehensive score, wherein the comprehensive score of the first compared tunnel construction method is expressed as: ​​​​​​​

[0128]

[0129] ,

[0130] ,

[0131] wherein, , , and are weight coefficients; , , and are the normalized indexes of the reliability index, the mean value of failure probability, the construction period and the cost of the i-th tunnel construction method, respectively; wherein, , , and are the reliability index, the mean value of failure probability, the construction period and the cost of the i-th tunnel construction method, respectively; , , , are the maximum values of the reliability index, the failure probability, the construction period and the cost among all the tunnel construction methods, respectively; , , and are the minimum values of the reliability index, the failure probability, the construction period and the cost among all the tunnel construction methods, respectively. By adjusting the weight coefficients, the emphasis on safety, construction period or cost of different projects can be flexibly reflected, so that the optimization results can better meet the individual needs of the owners, and the universality and flexibility of the method are enhanced. In summary, the beneficial effects of the present scheme are:

[0132] The present scheme no longer uses a single fixed value, but considers the key surrounding rock parameters as random variables, simulates the arch crown settlement displacement data set and the maximum support stress data set under each tunnel construction method, and calculates the support reliability index and conditional failure probability of each tunnel construction method, so as to simultaneously consider the spatial variability of surrounding rock parameters and the failure probability of support structure into the tunnel construction method selection decision framework, establish a multi-objective optimization model containing engineering construction cost, support failure probability and reliability index, and systematically solve the technical problems of decision-making limitations of traditional deterministic methods under complex geological conditions.

[0133]

[0134] The present scheme no longer uses a single fixed value, but considers the key surrounding rock parameters as random variables, simulates the arch crown settlement displacement data set and the maximum support stress data set under each tunnel construction method, and calculates the support reliability index and conditional failure probability of each tunnel construction method, so as to simultaneously consider the spatial variability of surrounding rock parameters and the failure probability of support structure into the tunnel construction method selection decision framework, establish a multi-objective optimization model containing engineering construction cost, support failure probability and reliability index, and systematically solve the technical problems of decision-making limitations of traditional deterministic methods under complex geological conditions. ​​

[0135] Embodiment 2

[0136] This embodiment is a further extension based on Embodiment 1, which aims to take Chongqing Rail Transit No. 10 Central Park East Station as an example to illustrate the specific implementation of the scheme, and the unmentioned parts refer to Embodiment 1 or the prior art.

[0137] This embodiment takes Chongqing Rail Transit No. 10 Central Park East Station as an example.

[0138] Chongqing Rail Transit No. 10 Central Park East Station is located on the east side of Central Park in the Gongang New City of Yubei District, adjacent to Tongmao Avenue, and is laid out in the east-west direction along Tongmao Avenue. The station mileage is K38+189.995~K38+405.995, the maximum excavation width of the station body is 25.54m, the height is 21.62m, the total excavation area is 468.55m2, the overburden thickness is 20.93m, and the design form of straight wall combined with circular arch is adopted.

[0139] The tunnel along the stratum lithology is mainly composed of medium-thick layered sandy mudstone with purple-brown to purple-red color, occasionally mixed with gray, grayish green sandstone and grayish white limestone, and the bonding force between layers is relatively weak. The rock mass structure surface is mainly affected by tectonic fissures. The rock stratum distribution and tunnel cross section are shown in REF _Ref14168 \h Figure 2 .

[0140] The original design adopts the double-side wall pilot tunnel method, which is complex in process and difficult to meet the time limit. The surrounding rock in the construction process is single, mainly sandy mudstone, and the overall surrounding rock condition is good.

[0141] Through step S1 and according to the actual situation on site, a nine-part block temporary support excavation method is proposed, and the nine-part rock column excavation method is selected as a comparison, as shown in Figure 3 , Figure 3 wherein a, b and c are double-side wall pilot tunnel method, nine-part block temporary support method and nine-part rock column method respectively.

[0142] Specifically, the double-side wall pilot tunnel method divides the large cross-section station according to the upper, middle and lower, left, middle and right division principle, and sets up vertical and horizontal temporary supports to maintain the stability of tunnel excavation. However, in the construction, the area of ① and ② parts is too small, which is not conducive to mechanical construction, and the process conversion is complex, the construction period is long, the excavation height of ⑦ part is high, which needs blasting construction, and there are safety hazards.

[0143] Specifically, the nine-part block temporary support method reduces the block space of ⑦ part, and at the same time reduces the block space above the inverted arch of ⑤ and ⑥ to realize manual excavation and reduce the disturbance to the surrounding rock. The block area of ①, ②, ⑧ and ⑨ is increased to facilitate on-site mechanized construction. At the same time, the horizontal temporary support is cancelled to speed up the construction progress.

[0144] Specifically, the nine rock column method cancels all temporary supports while not changing the block space and excavation sequence of the nine-part temporary support method.

[0145] The basic constraint conditions in the method comparison are as follows:

[0146] (1) The vault settlement should not exceed 15 mm, the supporting system tensile stress should not exceed 1.42 MPa, and the compressive stress should not exceed 20 MPa.

[0147] (2) For the tunnel stability requirement, the safety factor index needs to meet the support reliability index β≥3.0, and the β error is ≤5%.

[0148] (3) Under the premise of ensuring the safety of tunnel construction, the use of resource cost is controlled, and the main body construction of the tunnel is completed within the original planned period of one year.

[0149] Step S2, a surrounding rock parameter model showing a normal distribution is established by sampling the surrounding rock parameters on site, a plurality of parameter combinations are generated based on the surrounding rock parameter model, the vault settlement displacement and the maximum support stress of each parameter combination are simulated and calculated under each compared tunnel method, and the vault settlement value displacement data set and the maximum support stress data set of each compared tunnel method are obtained.

[0150] The surrounding rock parameters are modeled using a normal distribution, as shown in Table 1.

[0151] Table 1 Probability distribution of surrounding rock parameters

[0152]

[0153] The five Gauss nodes of each parameter in all parameter combinations and the Gauss weights corresponding to the Gauss nodes are obtained by using the five-order Gauss-Hermite integration method, as shown in Table 2.

[0154] Table 2 Gauss-Hermite integration method

[0155]

[0156] Steps S21-S25 obtain the MDRM parameter combinations, and the vault settlement displacement is obtained by simulating and calculating the displacement response, as shown in Table 3.

[0157] Table 3 MDRM parameter combinations and their displacement responses

[0158]

[0159] The average value and standard deviation of the tunnel displacement of the original double-sided wall pilot tunnel method calculated by step S3 is 11.03 mm and 3.47 mm, the reliability index is 3.18, the Monte Carlo simulation obtains 1.2142, and the error is 1.25%. The average value and standard deviation of the tunnel displacement of the nine-part block method is 13.16 mm and 3.58 mm, the reliability index is 3.68, the Monte Carlo simulation obtains 1.2875, and the error is 1.39%. The average value and standard deviation of the tunnel displacement of the nine-part rock column method is 12.25 mm and 3.23 mm, the reliability index is 3.79, the Monte Carlo simulation obtains 1.3376, and the error is 1.35%. The results show that MDRM can accurately quantify the influence of the uncertainty of surrounding rock parameters on the tunnel displacement, and the reliability of the model is verified. At the same time, the reliability index of the nine-part rock column method (3.79) > the nine-part block method (3.68) > the double-sided wall pilot tunnel method (3.18), the numerical values are all greater than the safety threshold, and the nine-part rock column method has the highest reliability, indicating that it has the lowest risk of structural failure under the condition of surrounding rock parameter fluctuation.

[0160] In order to verify that the five-order Gaussian-Hermite integration and multiplication dimension reduction method (MDRM) adopted in the scheme can accurately approximate the statistical moment results of hundreds of Monte Carlo simulations (MCS), the present embodiment is verified with reference to Figures 4-6 The probability distribution graphs of MCS and MDRM of the three construction methods show that the MCS and MDRM of the three construction methods are highly consistent. The double-sided wall pilot tunnel method has slight differences near the mean value, and the nine-part block method and the nine-part rock column method are highly consistent. The three construction methods have differences at the left limit displacement, but they are all within a safe and controllable range, which also verifies the balanced ability of MDRM in calculation efficiency and accuracy.

[0161] Through step S4, the support failure probability of different construction methods is quantified by conditional probability. The linear regression fitting graph of the displacement data set and the maximum stress data set of the arch crown settlement value in each compared tunnel construction method is referenced in Figures 7-9 Table 4.

[0162] Table 4 Condition failure probability table of construction method

[0163]

[0164] In the allowed arch crown settlement interval, the arch crown settlement value is taken as the abscissa, and the conditional failure probability is taken as the ordinate to draw the conditional probability curve of the tunnel support system of each compared tunnel construction method, with reference to Figure 10 .

[0165] In this embodiment, the limit stress exceeding probability of more than 0.8 is taken as the high risk threshold, and 0.2% to 0.6% is selected as the limit relative displacement control interval in combination with the engineering surrounding rock characteristics and deformation control requirements. The interval corresponds to the vault settlement value of the limit relative displacement of 12 to 36 mm, which meets the maximum vault settlement of the project. Meanwhile, the displacement interval that is too small (<0.2%) needs to be strengthened, which increases the cost, and the large interval (>0.6%) leads to a sharp increase in failure probability. Therefore, 0.2% to 0.6% is selected as the probability risk assessment interval.

[0166] In the limit relative displacement control interval of 0.2% to 0.6%, the slope of the failure probability curve of the three construction methods reflects the rate of support stress growth with the vault settlement. It can be seen from the following formula that the greater the slope, the greater the stress increment caused by the unit settlement, and the higher the sensitivity of the support structure to deformation. Figure 10 It can be seen from the following formula that the greater the slope, the greater the stress increment caused by the unit settlement, and the higher the sensitivity of the support structure to deformation. Figure 10 According to the slope change of the middle curve in the control interval, it can be seen that the slope of the nine-part rock column method is the largest, and the nine-part temporary support is the lowest, but the nine-part rock column method can still maintain the conditional failure probability of less than 0.8 at the limit relative displacement value of 0.6%. Meanwhile, at the limit relative displacement value of 0.6%, the support failure probability of the nine-part rock column method increases from 0.32 to 0.42 compared with the nine-part temporary support method, but the difference is within the safety tolerance. The above data model analysis shows that the three construction methods can meet the engineering construction.

[0167] In addition, in terms of construction period and resource efficiency, the nine-part rock column method shortens the construction period to 9.5 months by canceling the temporary support and optimizing the partition space, which improves the efficiency by 20.8% compared with the original scheme, and reduces the material and labor costs by 25% to 30%. In summary, the nine-part rock column method is the optimal construction method that takes into account safety and efficiency.

[0168] As a further scheme of this embodiment, the specific support stress of the nine-part rock column method is analyzed. Specifically, during the construction of the tunnel, the lining support structure is in direct contact with the surrounding rock, and the bending moment and axial force cloud diagrams of the support structure are extracted to analyze the stress changes of the initial concrete structure during the tunnel excavation. After the initial concrete support is completed, the axial force is evenly distributed in the horizontal direction, mainly distributed in the inverted arch and the haunch. The axial force mainly distributed in the inverted arch is compressive stress, with a maximum value of 90.624 , and the axial force mainly distributed in the haunch is tensile stress, with a maximum value of 2170.29 . The axial force is distributed in the right upper haunch and the left lower haunch and in the inverted arch in the vertical direction. The axial force mainly distributed in the inverted arch is compressive stress, with a maximum value of 222.1424 , and the axial force mainly distributed in the right upper haunch and the left lower haunch is tensile stress, with a maximum value of 1522.50 .

[0169] When the tunnel cross-section is excavated by the nine-part rock column method, the initial support is completed immediately after the upper, middle and lower three pilot holes on both sides of the tunnel surrounding rock are excavated. At this stage, the stress of the tunnel cross-section mainly depends on the initial support of the upper, middle and lower small sections on both sides and the support of the middle rock column, which may lead to instability of the surrounding rock and large deformation. However, the deformation of the surrounding rock is small and still within the safe range, as shown by the axial force of the lining. The maximum positive bending moment in the horizontal direction is located at the haunch of the arch on both sides, with a maximum value of 162.753 , and the maximum negative bending moment is located at the springing of the tunnel cross-section, with a maximum value of 368.808 . The maximum positive bending moment in the vertical direction is located at the two sides of the inverted arch, with a maximum value of 179.762 , and the maximum bending moment is located at the springing of the tunnel cross-section, with a maximum value of 301.585 .

[0170] During the independent construction of the two pilot holes, the initial support is easily subjected to concentrated compression at the haunch and wall foot regions under the radial pressure of the surrounding rock, while the arch springing is locally subjected to tension due to the deformation of the surrounding rock. After the middle rock column is excavated and the initial support is completed, the overall stiffness of the structure is improved, and the bending moment distribution presents the characteristics of "mainly compression and bending, and local tension". The horizontal bending moment appears in the positive and negative bending moment transition zone in the tunnel rock column region, indicating that the middle support bears part of the horizontal thrust and relieves the stress concentration of the two pilot holes. The vertical bending moment is subjected to compression at the crown and inverted arch, which is consistent with the stress characteristics of the "arch effect" of the tunnel structure. The numerical results of the tensile region in the middle and lower parts of the side wall show that it does not exceed the safety limit.

[0171] The nine-part rock column method simplifies the construction process by eliminating temporary support, and the lag construction of the middle rock column realizes the secondary release of the surrounding rock stress and the gradual ring of the support structure. The distribution characteristics of the bending moment graph dominated by compressive stress show that the initial support effectively bears the surrounding rock load during the entire construction process, verifying the feasibility of the method.

[0172] Bending moment, axial force-displacement curve Figure 11 , Figure 11a, b, c and d in the figure are the bending moment-vertical displacement graph, the bending moment-horizontal displacement graph, the axial force-vertical displacement graph and the axial force-horizontal displacement graph, respectively. The displacement change presents a phased change characteristic of rapid growth-tending to stability. The rapid growth stage corresponds to the initial excavation of the pilot tunnel, the stress change period of the initial support not being closed, and reflects the local stress concentration of the initial support and the temporary bearing state. The stable stage reaches the safety state of system balance due to the excavation of the middle rock pillar and the closure of the initial support into a ring, and the coordinated convergence of the displacements of multiple parts indicates that the overall stress of the support structure is uniform.

[0173] According to the optimization results of the construction method, the construction method is changed to the nine-rock-pillar method, and the surface settlement and vault deformation in the construction process are referenced from Figure 12 and Figure 13 .

[0174] For the surface settlement, the surface settlement amount is 5.4 mm after the completion of the excavation of the pilot tunnels on the left and right sides of the tunnel, and the final surface settlement is 8.2 mm. In the rock pillar excavation stage, the side pilot tunnels have been completely penetrated, and the main pressure of the surrounding rock is borne by the support structure and the unexcavated rock mass. After the rock pillar is removed, the original surrounding rock pressure is redistributed, which causes the surrounding rock deformation to intensify, thereby causing the settlement amount to suddenly increase. As can be seen from Figure 13 , in the rock pillar excavation stage, the surface settlement presents a similar "V" shape change trend, indicating that when relying on the rock pillar self-bearing system, the direct unloading of the excavation area leads to significant local settlement, but the coordinated action of the support system and the unexcavated rock mass limits the spread of the settlement to both sides. It is proved that the nine-rock-pillar method has the ability to actively share the load and reduce the deformation of the surrounding rock.

[0175] The final vault settlement is 12.5 mm. Before the rock pillar is excavated, the change trend of the vault settlement is highly similar to that of the surface settlement. After the rock pillar is excavated, the vault loses part of the direct support, and the initial settlement rate accelerates, but through the timely bearing of the subsequent support and the step-by-step excavation strategy of the rock pillar, the settlement increase rate gradually slows down until it reaches the maximum value.

[0176] In summary, the above monitoring shows that the nine-rock-pillar method effectively controls the deformation of the surrounding rock through the coordinated action of step-by-step excavation and reserved rock pillars. The maximum vault settlement is 12.5 mm, which does not exceed the safety threshold. It is proved that the nine-rock-pillar method, while optimizing the construction process and reducing the dependence on temporary support, takes into account the stability of the surrounding rock and the construction efficiency, further demonstrating the adaptability of the nine-rock-pillar method.

[0177] Although the specific embodiments of the application are described in detail with reference to the drawings, it should not be understood as limiting the scope of protection of the present application. Various modifications and variations made by those skilled in the art within the scope described in the claims are still within the scope of protection of the present application.

Claims

1. A tunneling method multi-objective optimization method for uncertain quantification and probabilistic risk assessment, characterized in that, The method comprises the following steps: S1, determining a plurality of tunnel construction methods based on the construction object and the construction constraint condition; S2, collecting surrounding rock parameters and establishing a surrounding rock parameter model in normal distribution, generating a plurality of parameter combinations based on the surrounding rock parameter model, simulating and calculating the vault settlement displacement and the maximum support stress of each parameter combination under each tunnel construction method to obtain a vault settlement displacement data set and a maximum support stress data set of each tunnel construction method; The method for obtaining the plurality of parameter combinations comprises the following steps: S21, collect samples and obtain surrounding rock parameters through tests, and establish a surrounding rock parameter model in normal distribution based on the mean and standard deviation of each parameter in the surrounding rock parameters, the surrounding rock parameters including elastic modulus , specific gravity , internal friction angle of surrounding rock , and cohesion ; S22, generating a plurality of random parameter combinations from the surrounding rock parameter model by a Monte Carlo sampling method; S23, obtaining 5 Gaussian nodes of each parameter in all parameter combinations and the Gaussian weight corresponding to the Gaussian nodes by a fifth-order Gaussian-Hermite integral method, and obtaining 5 actual engineering values of each parameter through the corresponding 5 Gaussian nodes; S24, changing each parameter on the 5 actual engineering values in turn by a multiplication dimension reduction method, and fixing the remaining parameters as their mean values to obtain 20 MDRM parameter combinations; S25, respectively performing numerical simulation on the 20 MDRM parameter combinations in each tunnel construction method to obtain the displacement response value and the stress response value of each MDRM parameter combination under each tunnel construction method; and taking all displacement response values and all stress response values of each MDRM parameter combination as the vault settlement displacement data set and the maximum support stress data set of each tunnel construction method; S3, calculating the support reliability index of the corresponding tunnel construction method through each vault settlement displacement data set; S4, performing linear regression fitting on the vault settlement displacement data set and the maximum support stress data set of each tunnel construction method to obtain a linear regression fitting formula, and constructing the conditional failure probability of each tunnel construction method based on the linear regression fitting formula of each tunnel construction method; S5, selecting the optimal tunnel construction method based on the support reliability index and the conditional failure probability of each tunnel construction method, and combining the corresponding construction period and cost.

2. The tunneling method multi-objective optimization method of uncertain quantification and probabilistic risk assessment according to claim 1, characterized in that, The method for calculating the support reliability index of each tunnel construction method comprises the following steps: S31、Based on the comparison and selection of tunnel construction method to establish vault settlement displacement response function The expression is: wherein, is the number of parameters in the surrounding rock parameter model; is the displacement response value when all parameters are mean values; , , , are univariate displacement response functions based on the multiplication dimension reduction method, respectively varying the elastic modulus , the unit weight , the internal friction angle and the cohesion of the surrounding rock while fixing the rest of the parameters at the mean values, respectively. S32, compute the mean of and the second moment whose expressions are respectively: wherein , , and are the expected values of , , , , respectively. S33, calculating of variance and standard deviation whose expressions are respectively: ， ； S34、calculating a support reliability index .

3. The tunneling method multi-objective optimization method of uncertain quantification and probabilistic risk assessment according to claim 2, characterized in that, The method for constructing the conditional failure probability of each tunnel construction method comprises the following steps: S41, performing linear regression fitting on the vault settlement displacement data set and the maximum support stress data set of the tunnel construction method to obtain a linear regression fitting formula: wherein, is the maximum stress supported; and are fitting coefficients; is the displacement of the crown settlement value; is the residual, which is normally distributed with mean zero, ; is the normal distribution function; is the variance of the normal distribution; S42, statistical analysis of tensile strength of supporting materials used in tunnel construction methods , according to the mean and variance of the output normal probability distribution ; S43、establish the safety margin of the compared tunnel construction method The expression is: wherein, represents safety, represents failure; S44, constructing a given vault settlement value displacement under the safety margin of the normal probability distribution where, and the expressions are respectively: ， wherein and are respectively the conditional mean and conditional variance of S45, calculating the vault settlement value displacement under the condition of reliability index ; S46, calculate the vault settlement value displacement under the condition of failure probability : wherein, is the probability of failure of the supporting structure under the given vault settlement value ; and is the cumulative distribution function of the standard normal distribution.

4. The tunneling method multi-objective optimization method of uncertain quantification and probabilistic risk assessment according to claim 3, characterized in that, Step S5 further comprises the following steps: S51, determining the allowed vault settlement displacement interval of the construction object to obtain the mean value, the maximum value and the minimum value of the failure probability under each tunnel construction method; S52, score each tunnel construction method comprehensively, and select the tunnel construction method with the highest comprehensive score, the first comprehensive score of the tunnel construction method The expression is: ， ， in, , , and All are weighting coefficients; , , and The first Reliability index of the tunnel construction method for comparison The normalized indices of mean failure probability, duration, and cost; among them, , , and The first The reliability index, mean failure probability, construction period, and cost of each tunnel construction method were compared. , , , These represent the maximum values ​​of reliability index, failure probability, construction period, and cost among all the tunnel construction methods selected. , , and These represent the minimum values ​​of reliability index, failure probability, construction period, and cost among all the tunnel construction methods selected.

5. The tunneling method multi-objective optimization method of uncertain quantification and probabilistic risk assessment according to claim 4, characterized in that, The allowed vault settlement displacement interval of the construction object is 0.2% to 0.6% of the maximum allowed vault settlement displacement value.

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