Rock soil reliability analysis method and device, electronic equipment, medium and program product

Abstract

The invention relates to the technical field of rock-soil analysis, in particular to a rock-soil reliability analysis method and device, electronic equipment, a medium and a program product.The method comprises the steps that a performance function of a retaining wall is established to determine rock-soil body parameters and probability distribution information in an uncertain physical space; based on the probability distribution information, converting the rock-soil body parameters into an independent standard normal space so as to iteratively calculate rock-soil body parameter design points in the independent standard normal space; and the rock-soil body parameter design points are converted into an uncertainty physical space to calculate the reliability index and the failure probability of the retaining wall, and a rock-soil reliability analysis result is generated. The method can be suitable for calculation of the reliability index and the failure probability of the retaining wall in various scenes, has high flexibility and calculation efficiency, effectively meets the actual requirements of geotechnical engineering reliability analysis in different scenes, and provides more powerful guarantee for safe and stable operation of a geotechnical structure.

Description

Technical Field

[0001] The present application relates to the field of geotechnical analysis technology, and in particular to a geotechnical reliability analysis method, device, electronic equipment, medium and program product. Background Art

[0002] In the field of geotechnical engineering, geotechnical parameters generally show intricate correlations. For example, there is a general negative correlation between the shear strength index of soil, cohesion, and the internal friction angle. For reliability analysis and risk assessment in the field of geotechnical engineering, it is particularly important to build a model that accurately reflects the probabilistic characteristics of geotechnical parameters. However, the actual challenge is that the test data or experimental data obtained at the geotechnical engineering site are often very limited, which directly leads to the difficulty in comprehensively establishing a multivariate probability distribution model for geotechnical parameters, that is, facing the problem of incomplete probability information. Therefore, when conducting engineering reliability analysis, geotechnical engineers have to face the current situation of incomplete probability information, and instead rely on the unilateral probability description of geotechnical parameters and the limited knowledge of the correlation coefficients between these parameters to conduct risk assessment on this basis.

[0003] In related technologies, many researchers have combined Copula theory with Monte Carlo simulation to solve complex geotechnical engineering reliability analysis problems. The results show that the differences in different Copula functions in describing the correlation structure between geotechnical parameters directly lead to different distribution patterns of sample points generated under the same failure domain conditions, which in turn affects the final results of geotechnical structure reliability assessment. The essential root of this difference lies in the sensitivity of the Copula function to the number of samples in the failure domain and its unique sample generation mechanism. Specifically, some Copula functions may be more inclined to generate samples in the edge area of ​​the failure domain, while others may cover the entire failure domain more evenly. This uneven distribution of samples directly affects the results of reliability analysis. In addition, when this method is used for numerical simulation of implicit functional functions commonly used in actual engineering, its efficiency bottleneck gradually emerges. Implicit functional functions often involve complex physical processes and computational models, and each simulation requires a lot of computing resources. Therefore, under limited computing resources, this method may be difficult to efficiently complete the reliability analysis of geotechnical structures under low failure probability conditions, limiting its wide application in engineering practice.

[0004] A first-order reliability method based on the first-order Taylor series expansion of the performance function has attracted much attention. The first-order reliability method approximates the originally complex nonlinear performance function to a linear function by performing a first-order Taylor series expansion on the performance function at the design point, thereby greatly simplifying the calculation process of reliability assessment. This method not only effectively reduces the calculation cost, making it possible to perform fast and multiple reliability analysis under limited resources, but also, through reasonable approximation, it can often meet the accuracy requirements of reliability assessment in engineering practice while maintaining high accuracy. Specifically, the first-order reliability method gradually approaches the true failure probability of the geotechnical structure by iterating the design points of the geotechnical parameters. In each iteration, the position of the next design point is estimated according to the current calculation conditions, the first-order Taylor series expansion of the performance function is recalculated, and the estimated value of the design point is updated accordingly until the convergence condition is met.

[0005] However, when the Copula theory in related technologies is combined with the first-order reliability method, the design point iteration process may converge slowly or even diverge, resulting in low computational efficiency, and will cause the design point to fall into periodic and chaotic solutions with low stability. This severely limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis and needs to be solved urgently. Summary of the invention

[0006] The present application provides a geotechnical reliability analysis method, device, electronic device, medium and program product to solve the problems that when the Copula theory and the first-order reliability method in the related technology are combined, the design point iteration process may converge slowly or even diverge, the calculation efficiency is low, and the design point may fall into periodic and chaotic solutions, and the stability is not high, which seriously limits the application of the first-order reliability method based on the Copula theory in geotechnical engineering reliability analysis.

[0007] The first aspect of the present application provides a geotechnical reliability analysis method, comprising the following steps: establishing a functional function of a retaining wall to determine the geotechnical parameters and probability distribution information in an uncertain physical space; based on the probability distribution information, converting the geotechnical parameters to an independent standard normal space to iteratively calculate the geotechnical parameter design points in the independent standard normal space; converting the geotechnical parameter design points to the uncertain physical space to calculate the reliability index and failure probability of the retaining wall, and generating the geotechnical reliability analysis results.

[0008] Optionally, in one embodiment of the present application, the iterative calculation of the rock and soil parameter design points in the independent standard normal space includes: setting the design point allowable error and the initial rock and soil parameter design point; based on the initial rock and soil parameter design point, calculating the functional function value and gradient of the current iteration to calculate the rock and soil parameter design point and the quasi-Newton method BFGS matrix of the next iteration; judging whether the iteration converges, wherein if the iteration converges, then obtaining the rock and soil parameter design point within the allowable error range of the design point based on the rock and soil parameter design point and the BFGS matrix of the next iteration.

[0009] Optionally, in one embodiment of the present application, the expression of the functional function may be, but is not limited to:

[0010] g=(W1R1+W2R2)-P a H0

[0011] Where W1 is the gravity of the triangular area of ​​the retaining wall, W2 is the gravity of the rectangular area of ​​the retaining wall, R1 is the force arm of the gravity of the triangular area of ​​the retaining wall at the toe of the wall, R2 is the force arm of the gravity of the rectangular area of ​​the retaining wall at the toe of the wall, P a is the active earth pressure, and H0 is the distance between the active earth pressure and the bottom of the wall.

[0012] Optionally, in one embodiment of the present application, the conversion formula of the rock and soil mass parameters may be, but is not limited to,:

[0013]

[0014] Among them, u is the rock and soil mass parameter in the independent standard normal space, u=[u c u φ ] T ,u c is the cohesion in the independent standard normal space, u φ is the internal friction angle in the independent standard normal space, the superscript “T” is the transpose of the vector, Φ -1 (·) is the inverse function of the standard normal distribution function and h(F c (c),F φ (φ); θ) is the conditional Copula function.

[0015] Optionally, in an embodiment of the present application, the calculation formula of the reliability index may be but is not limited to:

[0016]

[0017] Among them, β is the reliability index of the retaining wall, u * is the design point of the rock and soil mass parameters.

[0018] Optionally, in one embodiment of the present application, the expression for converting the geotechnical mass parameter design point into the uncertain physical space may be, but is not limited to,:

[0019]

[0020] Among them, x * is the design point of the rock and soil mass parameters, x * =[c * φ * ] T , c * is the cohesion design point in physical space, φ * is the design point of internal friction angle in physical space, F c -1 (·) is the inverse function of the cumulative distribution function of cohesion, F -1 (·) is the inverse function of the cumulative distribution function of the internal friction angle, is the inverse function of the conditional Copula function, and Φ(·) is the standard normal distribution function.

[0021] The second aspect of the present application provides a geotechnical reliability analysis device, including: a determination module, used to establish a functional function of a retaining wall to determine the geotechnical parameters and probability distribution information in an uncertain physical space; a calculation module, used to convert the geotechnical parameters to an independent standard normal space based on the probability distribution information to iteratively calculate the geotechnical parameter design points in the independent standard normal space; an analysis module, used to convert the geotechnical parameter design points to the uncertain physical space to calculate the reliability index and failure probability of the retaining wall, and generate the geotechnical reliability analysis results.

[0022] Optionally, in one embodiment of the present application, the calculation module includes: a setting unit for setting the allowable error of the design point and the initial rock and soil parameter design point; a calculation unit for calculating the functional function value and gradient of the current iteration based on the initial rock and soil parameter design point, so as to calculate the rock and soil parameter design point and the quasi-Newton method BFGS matrix of the next iteration; a judgment unit for judging whether the iteration converges, wherein if the iteration converges, the rock and soil parameter design point within the allowable error range of the design point is obtained based on the rock and soil parameter design point and the BFGS matrix of the next iteration.

[0023] Optionally, in one embodiment of the present application, the expression of the functional function may be, but is not limited to:

[0024] g=(W1R1+W2R2)-P a H0

[0025] Where W1 is the gravity of the triangular area of ​​the retaining wall, W2 is the gravity of the rectangular area of ​​the retaining wall, R1 is the force arm of the gravity of the triangular area of ​​the retaining wall at the toe of the wall, R2 is the force arm of the gravity of the rectangular area of ​​the retaining wall at the toe of the wall, P a is the active earth pressure, and H0 is the distance between the active earth pressure and the bottom of the wall.

[0026] Optionally, in one embodiment of the present application, the conversion formula of the rock and soil mass parameters may be, but is not limited to,:

[0027]

[0028] Among them, u is the rock and soil mass parameter in the independent standard normal space, u=[u c u φ ] T ,u c is the cohesion in the independent standard normal space, u φ is the internal friction angle in the independent standard normal space, the superscript “T” is the transpose of the vector, Φ -1 (·) is the inverse function of the standard normal distribution function and h(F c (c),F φ (φ); θ) is the conditional Copula function.

[0029] Optionally, in an embodiment of the present application, the calculation formula of the reliability index may be but is not limited to:

[0030]

[0031] Among them, β is the reliability index of the retaining wall, u * is the design point of the rock and soil mass parameters.

[0032] Optionally, in one embodiment of the present application, the expression for converting the geotechnical mass parameter design point into the uncertain physical space may be, but is not limited to,:

[0033]

[0034] Among them, x * is the design point of the rock and soil mass parameters, x * =[c * φ * ] T , c * is the cohesion design point in physical space, φ * is the design point of the internal friction angle in physical space, is the inverse function of the cumulative distribution function of cohesion, F -1 (·) is the inverse function of the cumulative distribution function of the internal friction angle, is the inverse function of the conditional Copula function, and Φ(·) is the standard normal distribution function.

[0035] The third aspect of the present application provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the geotechnical reliability analysis method as described in the above embodiment.

[0036] A fourth aspect of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned geotechnical reliability analysis method.

[0037] The fifth aspect of the present application provides a computer program product, including a computer program, which, when executed, is used to implement the above-mentioned geotechnical reliability analysis method.

[0038] The embodiment of the present application can determine the parameters and probability information of the rock and soil in the physical space with uncertainty, calculate the design points of the rock and soil parameters in the independent standard normal space and convert them back to the physical space with uncertainty, thereby obtaining the reliability index and failure probability of the retaining wall, and then obtaining the reliability analysis results of the rock and soil. Therefore, the reliability of the rock and soil is analyzed based on the iHLRF-BFGS efficient iteration technology, and the design points of the rock and soil parameters can be accurately locked in only a few iterations. When facing highly complex nonlinear functional functions, its iteration process also shows extremely high stability, which effectively improves the stability and calculation efficiency of the present application, and has high adaptability in the face of different Copula function selections, and has extremely high practicality and scope of application, which can effectively meet the needs of rock and soil reliability analysis in different scenarios. Therefore, it solves the problem that when the Copula theory and the first-order reliability method in the related art are combined, the design point iteration process may converge slowly or even diverge, the calculation efficiency is low, and the design point will fall into periodic and chaotic solutions, the stability is not high, and the application of the first-order reliability method based on the Copula theory in the reliability analysis of geotechnical engineering is seriously limited.

[0039] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0041] Figure 1 A flow chart of a geotechnical reliability analysis method provided according to an embodiment of the present application;

[0042] Figure 2 A schematic diagram of a retaining wall according to an embodiment of the present application;

[0043] Figure 3 A schematic diagram of a design point iteration cloud diagram of a Gaussian Copula function according to an embodiment of the present application;

[0044] Figure 4 A schematic diagram of a design point iteration cloud diagram of a Plackett Copula function according to an embodiment of the present application;

[0045] Figure 5 A schematic diagram of a design point iteration cloud diagram of a Frank Copula function according to an embodiment of the present application;

[0046] Figure 6 This is a schematic diagram of the design point iteration cloud diagram of the No.16 Copula function of an embodiment of the present application;

[0047] Figure 7 This is a flow chart of a geotechnical reliability analysis method based on iHLRF-BFGS according to an embodiment of the present application;

[0048] Figure 8 It is a structural schematic diagram of a geotechnical reliability analysis device provided according to an embodiment of the present application;

[0049] Fig. 9 It is a schematic diagram of the structure of an electronic device provided according to an embodiment of the present application.

[0050] Reference numerals:

[0051] 10- geotechnical reliability analysis device: 100- determination module, 200- calculation module and 300- analysis module; 901- memory, 902- processor and 903- communication interface. DETAILED DESCRIPTION

[0052] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0053] The following describes the geotechnical reliability analysis method, device, electronic device, medium and program product of the embodiment of the present application with reference to the accompanying drawings. When the Copula theory and the first-order reliability method in the related technology mentioned in the above background technology are combined, the design point iteration process may converge slowly or even diverge, the calculation efficiency is low, and the design point will fall into periodic and chaotic solutions, and the stability is not high, which seriously limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis. The present application provides a geotechnical reliability analysis method, in which the geotechnical body parameters and probability information in the physical space with uncertainty can be determined, the geotechnical body parameter design points in the independent standard normal space are calculated and converted back to the physical space with uncertainty, thereby obtaining the reliability index and failure probability of the retaining wall, and then obtaining the reliability analysis result of the geotechnical. Thus, the geotechnical reliability is analyzed based on the iHLRF-BFGS efficient iteration technology, and the geotechnical parameter design points can be accurately locked in only a few iterations. When faced with highly complex nonlinear functional functions, the iteration process also shows extremely high stability, which effectively improves the stability and computational efficiency of this application, and is highly adaptable to the selection of different Copula functions, with extremely high practicality and scope of application, which can effectively meet the needs of geotechnical reliability analysis in different scenarios. Thus, the problem that when the Copula theory and the first-order reliability method in the related technology are combined, the iteration process of the design point may converge slowly or even diverge, the computational efficiency is low, and the design point may fall into periodic and chaotic solutions, and the stability is not high, which seriously limits the application of the first-order reliability method based on the Copula theory in the reliability analysis of geotechnical engineering.

[0054] Specifically, Figure 1 A flow chart of a geotechnical reliability analysis method provided in an embodiment of the present application.

[0055] like Figure 1 As shown in FIG. 1 , the geotechnical reliability analysis method includes the following steps:

[0056] In step S101, a function function of the retaining wall is established to determine the parameters and probability distribution information of the rock and soil mass in the uncertain physical space. The expression of the function function can be, but is not limited to, expressed as:

[0057] g=(W1R1+W2R2)-P a H0,

[0058] Where W1 is the gravity of the triangular area of ​​the retaining wall, W2 is the gravity of the rectangular area of ​​the retaining wall, R1 is the force arm of the gravity of the triangular area of ​​the retaining wall at the toe of the wall, R2 is the force arm of the gravity of the rectangular area of ​​the retaining wall at the toe of the wall, P a is the active earth pressure, and H0 is the distance between the active earth pressure and the bottom of the wall.

[0059] It can be understood that the functional function of the retaining wall can describe the stability state of the retaining wall, and the retaining wall can be used to support the rock and improve the stability of the rock. Based on this, when analyzing the reliability of rock and soil, the embodiment of the present application can first establish the functional function of the retaining wall, and the formula thereof can be, but is not limited to, expressed as:

[0060] g=(W1R1+W2R2)-P a H0,

[0061] Where g represents the functional stability of the retaining wall, W1 is the gravity of the triangular area of ​​the retaining wall, W2 is the gravity of the rectangular area of ​​the retaining wall, R1 is the force arm of the gravity of the triangular area of ​​the retaining wall at the toe of the wall, R2 is the force arm of the gravity of the rectangular area of ​​the retaining wall at the toe of the wall, P a is the active earth pressure, and H0 is the distance between the active earth pressure and the bottom of the wall.

[0062] The formula for the gravity W1 of the retaining wall triangle area can be, but is not limited to, expressed as:

[0063]

[0064] Among them, γ wall is the weight of the retaining wall, b is the length of the base of the retaining wall triangle area, and H is the height of the retaining wall; the formula for the gravity W2 of the retaining wall rectangle area can be, but is not limited to, expressed as:

[0065] W2=γ wall aH;

[0066] Where a is the length of the bottom side of the rectangular area of ​​the retaining wall;

[0067] The formula for the force arm R1 of the gravity in the triangular area of ​​the retaining wall at the toe of the wall can be expressed as, but not limited to:

[0068]

[0069] The formula for the force arm R2 of the rectangular area of ​​the retaining wall at the toe of the wall can be expressed as, but not limited to:

[0070]

[0071] Active earth pressure P a The formula can be expressed as but not limited to:

[0072]

[0073] Among them, γ is the weight of the backfill behind the retaining wall, c is the cohesion of the backfill behind the retaining wall, and φ is the internal friction angle of the backfill behind the retaining wall;

[0074] The formula for the distance H0 between the active earth pressure and the wall bottom can be, but is not limited to, expressed as:

[0075]

[0076] Figure 2 This is a schematic diagram of a retaining wall according to an embodiment of the present application. Figure 2 As shown, the retaining wall is located on hard clay, the back of the retaining wall is vertical and smooth, the height of the retaining wall is H = 5.5m, the bottom side length of the rectangular area of ​​the retaining wall is a = 0.4m, the bottom side length of the triangular area of ​​the retaining wall is b = 1.4m, and the weight of the retaining wall is γ wall =24kN / m 3 and the weight of the backfill behind the retaining wall γ=18kN / m 3 .

[0077] After the functional function of the retaining wall is established, the embodiment of the present application can determine the rock and soil parameters and their probability distribution information in the physical space with uncertainty.

[0078] Among them, the rock and soil parameters include but are not limited to cohesion c and internal friction angle φ; the probability distribution information includes but is not limited to the cumulative distribution function F of cohesion c (c) Cumulative distribution function of internal friction angle F φ (φ) and the Copula function C(F c (c),F φ (φ); θ), where θ is the Copula parameter, which can be obtained by inversely solving the Kendall rank correlation coefficient τ between cohesion and internal friction angle. The calculation formula can be, but is not limited to, expressed as:

[0079]

[0080] Table 1 is a statistical information table of cohesion c and internal friction angle φ in one embodiment of the present application, and the cumulative distribution function F of cohesion c (c) and the cumulative distribution function of the internal friction angle F φ (φ) can be uniquely determined by statistical information. Table 1 can be expressed as follows:

[0081] Table 1

[0082]

[0083] In the embodiment of the present application, four calculation conditions can be considered, namely, the Copula function C(F) between cohesion and internal friction angle c (c),F φ(φ); θ), four calculation cases including Gaussian Copula function, Plackett Copula function, Frank Copula function and No.16 Copula function can be considered. The Kendall rank correlation coefficient between cohesion and internal friction angle can be, but is not limited to, τ = -0.5.

[0084] After the inverse solution of the Kendall rank correlation coefficient τ, the formula of the Gaussian Copula function can be expressed as but not limited to:

[0085]

[0086] Among them, w1 is used to simplify the representation of F c (c), w2 is used to simplify the representation of F φ (φ), the Copula parameter can be taken as θ = -0.7071;

[0087] The formula of the Plackett Copula function can be expressed as, but not limited to:

[0088]

[0089] Among them, w1 is used to simplify the representation of F c (c), w2 is used to simplify the representation of F φ (φ), the Copula parameter can be taken as θ = 0.0877;

[0090] The formula of the Frank Copula function can be expressed as, but not limited to:

[0091]

[0092] Among them, w1 is used to simplify the representation of F c (c), w2 is used to simplify the representation of F φ (φ), the Copula parameter can be taken as θ = -5.7363;

[0093] No.16 The formula of the Copula function can be, but is not limited to, expressed as:

[0094]

[0095] Among them, w1 is used to simplify the representation of F c (c), w2 is used to simplify the representation of F φ (φ), the Copula parameter can be taken as θ = 0.0145.

[0096] The embodiments of the present application are highly adaptable to different Copula functions and can be applied to different structures. They are highly flexible and can meet the analysis needs of geotechnical reliability in a variety of scenarios.

[0097] Step S102: based on the probability distribution information, the geotechnical parameters are converted to an independent standard normal space to iteratively calculate the geotechnical parameter design points in the independent standard normal space. The conversion formula of the geotechnical parameters can be, but is not limited to, expressed as:

[0098]

[0099] Among them, u is the rock and soil mass parameter in the independent standard normal space, u=[u c u φ ] T ,u c is the cohesion in the independent standard normal space, u φ is the internal friction angle in the independent standard normal space, the superscript “T” is the transpose of the vector, Φ -1 (·) is the inverse function of the standard normal distribution function and h(F c (c),F φ (φ); θ) is the conditional Copula function.

[0100] After obtaining the rock and soil mass parameters and their probability distribution information in the physical space with uncertainty, the embodiment of the present application can then convert the rock and soil mass parameters into an independent standard normal space so as to iteratively calculate the design points of the rock and soil mass parameters in the independent standard normal space.

[0101] First, the geotechnical parameters in the physical space with uncertainty should be converted to the independent standard normal space. The conversion formula can be expressed as but not limited to:

[0102]

[0103] Among them, u is the rock and soil mass parameter in the independent standard normal space, u=[u c u φ ] T ,u c is the cohesion in the independent standard normal space, u φ is the internal friction angle in the independent standard normal space, the superscript “T” is the transpose of the vector, Φ -1 (·) is the inverse function of the standard normal distribution function and h(F c (c),F φ (φ); θ) is a conditional Copula function, and its formula can be, but is not limited to, expressed as:

[0104]

[0105] Next, the process of iterative calculation of design points of geotechnical parameters in independent standard normal space is explained.

[0106] Optionally, in one embodiment of the present application, calculating the design points of geotechnical parameters in an independent standard normal space includes: setting the allowable error of the design point and the initial design point of the geotechnical parameters; calculating the functional function value and gradient of the current iteration based on the initial design point of the geotechnical parameters to calculate the design points of the geotechnical parameters and the quasi-Newton method BFGS matrix of the next iteration; judging whether the iteration converges, wherein if the iteration converges, obtaining the geotechnical parameter design points within the allowable error range of the design point based on the design points of the geotechnical parameters of the next iteration and the quasi-Newton method BFGS matrix.

[0107] In other embodiments, after converting the geotechnical parameters in the physical space with uncertainty into the independent standard normal space, the present application can iteratively calculate the design points of the geotechnical parameters in the independent standard normal space. The specific steps can be expressed as follows:

[0108] (1) First, set the design point allowable error ε;

[0109] (2) Then, the number of iterations k is set to 1, and the geotechnical parameter design point of the first iteration is the initial geotechnical parameter design point u1, u1 = [u c1 u φ1 ] T =[0 0] T , where u c1 is the cohesion design point of the first iteration, u φ1 The design point of the internal friction angle of the first iteration and the BFGS matrix of the first iteration B1 = [1 0; 0 1];

[0110] (3) Calculate the performance function value g(u k ) and the gradient of the kth iteration where u k is the kth iteration geotechnical parameter design point, u k =[u ck u φk ] T ,u ck is the cohesion design point and u of the kth iteration φk is the design point of internal friction angle of the kth iteration;

[0111] (4) Calculate the design point u of the rock and soil mass parameters for the k+1th iteration k+1 , the formula can be expressed as but not limited to:

[0112] u k+1 =u k +λk d k ;

[0113] Among them, λ k is the iteration step size calculated by Armijo criterion, d k is the iteration direction, and its formula can be expressed as but not limited to:

[0114]

[0115] (5) Calculate the BFGS matrix B for k+1 iterations k+1 , the formula can be expressed as but not limited to:

[0116]

[0117] Among them, p k is the iterative increment of the design point, p k =λ k d k , z k is the iterative increment of the gradient of the Lagrangian function, and its formula can be, but is not limited to, expressed as:

[0118]

[0119] Among them, q k is the iterative increment of the uncorrected Lagrangian function gradient, and its formula can be, but is not limited to, expressed as:

[0120]

[0121] Among them, θ k is the correction factor, and its formula can be expressed as but not limited to:

[0122]

[0123] (6) The convergence criterion can be expressed as, but not limited to, the following formula:

[0124]

[0125] If the convergence criterion is satisfied and within the allowable error of the design point, let the design point u of the geotechnical mass parameter of the k+1th iteration be k+1 is the design point u of the rock and soil mass parameters in the independent standard normal space * , in, is the cohesion design point in the independent standard normal space, is the design point of the internal friction angle in the independent standard normal space; otherwise, if the convergence criterion is not satisfied, set the number of iterations k = k + 1 and return to step (3).

[0126] For example, in the embodiment of the present application, the allowable design point error ε=0.001 may be set; Figure 3 Schematic diagram of the design point iteration cloud diagram of the Gaussian Copula function of one embodiment of the present application, such as Figure 3 As shown, the design point of rock and soil parameters in the independent standard normal space can be u * =[-2.0188 -2.8668] T ; Figure 4 Schematic diagram of the design point iteration cloud diagram of the Plackett Copula function according to one embodiment of the present application. Figure 4 As shown, the design point of rock and soil parameters in the independent standard normal space can be u * =[-1.8233 -1.9979] T ; Figure 5 Schematic diagram of the design point iteration cloud diagram of the Frank Copula function of one embodiment of the present application, such as Figure 5 As shown, at this time, the design point u of the rock and soil parameter in the independent standard normal space is * =[-2.1426 -2.0696] T ; Figure 6 This is a schematic diagram of the design point iteration cloud diagram of the No. 16 Copula function of an embodiment of the present application, such as Figure 6 As shown, at this time, the design point u of the rock and soil parameter in the independent standard normal space is * =[-1.9780 -0.8441] T .

[0127] Step S103, converting the geotechnical parameter design points into the uncertain physical space to calculate the reliability index and failure probability of the retaining wall and generate the geotechnical reliability analysis results. The expression for converting the geotechnical parameter design points into the uncertain physical space can be, but is not limited to,:

[0128]

[0129] Among them, x * is the design point of rock and soil parameters, x * =[c * φ * ] T , c * is the cohesion design point in physical space, φ * is the design point of the internal friction angle in physical space, is the inverse function of the cumulative distribution function of cohesion, F -1 (·) is the inverse function of the cumulative distribution function of the internal friction angle, is the inverse function of the conditional Copula function, and Φ(·) is the standard normal distribution function.

[0130] The calculation formula of the reliability index can be expressed as:

[0131]

[0132] Among them, β is the reliability index of retaining wall, u * It is the design point of rock and soil parameters.

[0133] As a possible implementation method, after calculating the design points of the rock and soil mass parameters in the independent standard normal space, the embodiment of the present application also needs to convert the design points of the rock and soil mass parameters in the independent standard normal space into a physical space with uncertainty. The conversion formula can be, but is not limited to, expressed as:

[0134]

[0135] Among them, x* is the design point of rock and soil parameters in physical space, x * =[c * φ * ] T , where c * Design points and φ for cohesion in physical space * is the design point of the internal friction angle in physical space, is the inverse function of the cumulative distribution function of cohesion, F φ -1 (·) is the inverse function of the cumulative distribution function of the internal friction angle, is the inverse function of the conditional Copula function, Φ(·) is the standard normal distribution function

[0136] In the embodiment of the present application, the geotechnical parameter design point in the physical space corresponding to the Gaussian Copula function can be x * =[5.1189 17.4157] T , the design point of geotechnical parameters in the physical space corresponding to the Plackett Copula function can be x * =[5.5195 16.577] T , the design point of geotechnical parameters in the physical space corresponding to the Frank Copula function can be x * =[4.8805 17.9204] T And the design point of the rock and soil parameters in the physical space corresponding to the No.16 Copula function can be x * =[5.2000 17.2450] T .

[0137] After obtaining the corresponding rock and soil parameter design points in the target physical space, the embodiment of the present application can calculate the reliability index and failure probability of the retaining wall.

[0138] Among them, the formula of the reliability index β of the retaining wall can be expressed as but not limited to:

[0139]

[0140] Failure probability of retaining wall P f The formula can be expressed as but not limited to:

[0141] P f =Φ(-β).

[0142] Finally, we can get the reliability index β = 3.5063 and failure probability P corresponding to the Gaussian Copula function. f =2.2717×10 -4 , the reliability index β corresponding to the Plackett Copula function is 2.7048 and the failure probability P f =3.4172×10 -3 , the reliability index β corresponding to the Frank Copula function is 2.9790 and the failure probability P f =1.4461×10 -4 , the reliability index β corresponding to the No.16 Copula function is 2.1506 and the failure probability P f =1.5754×10 -2 .

[0143] The reliability analysis results of the geotechnical structure can be generated based on the reliability index and failure probability of the retaining wall. For example, when the reliability index of the retaining wall is high and the failure probability is low, the geotechnical reliability is high; when the reliability index of the retaining wall is low and the failure probability is high, the geotechnical reliability is low. It should be noted that the corresponding reliability analysis results generated by the reliability index and failure probability of the retaining wall can be set or adjusted by professional and technical personnel in this field according to actual conditions. This is only an exemplary description without specific limitation.

[0144] In the case where the Copula function has a significant impact on the reliability index and failure probability of the retaining wall, the embodiment of the present application can seamlessly adapt to various complex and changeable related structures through the high flexibility of the present application, providing an effective tool for related research and development. This deepens engineers' understanding of how the uncertainty of geotechnical parameters and their correlation subtly affect the reliability of geotechnical structures, and greatly enhances the risk prediction ability in the early stage of geotechnical structure design; it helps engineers to formulate more accurate and effective construction strategies to flexibly respond to various challenges caused by uncertain factors during the construction process, thereby ensuring the overall safety and stability of geotechnical engineering.

[0145] The present application is described in detail below with reference to a specific embodiment.

[0146] Figure 7 FIG. 1 is a flow chart of a geotechnical reliability analysis method based on iHLRF-BFGS according to an embodiment of the present application. Figure 7 As shown:

[0147] Step S701, establishing a functional function of a retaining wall;

[0148] Step S702, determining rock and soil mass parameters and their probability distribution information in a physical space with uncertainty;

[0149] Step S703, converting the rock and soil parameters in the physical space with uncertainty into an independent standard normal space;

[0150] Step S704, iteratively calculating the design points of rock and soil mass parameters in the independent standard normal space;

[0151] Step S705, converting the design points of rock and soil mass parameters in the independent standard normal space into a physical space with uncertainty;

[0152] Step S706, calculating the reliability index and failure probability of the retaining wall.

[0153] According to the geotechnical reliability analysis method proposed in the embodiment of the present application, the geotechnical parameters and probability information in the physical space with uncertainty can be determined, the geotechnical parameter design points in the independent standard normal space can be calculated and converted back to the physical space with uncertainty, thereby obtaining the reliability index and failure probability of the retaining wall, and then obtaining the reliability analysis results of the geotechnical. Therefore, the geotechnical reliability is analyzed based on the iHLRF-BFGS efficient iteration technology, and the geotechnical parameter design points can be accurately locked in only a few iterations. When facing highly complex nonlinear functional functions, its iteration process also shows extremely high stability, which effectively improves the stability and calculation efficiency of the present application, and is highly adaptable to the selection of different Copula functions, with extremely high practicality and scope of application, which can effectively meet the needs of geotechnical reliability analysis in different scenarios. As a result, the problem that when the Copula theory and the first-order reliability method in the relevant technology are combined, the design point iteration process may converge slowly or even diverge, the calculation efficiency is low, and the design point may fall into periodic and chaotic solutions, and the stability is not high, which seriously limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis, etc.

[0154] Next, the geotechnical reliability analysis device proposed according to the embodiment of the present application is described with reference to the accompanying drawings.

[0155] Figure 8 It is a schematic diagram of the structure of the geotechnical reliability analysis device of an embodiment of the present application.

[0156] like Figure 8 As shown, the geotechnical reliability analysis device 10 includes: a determination module 100 , a calculation module 200 and an analysis module 300 .

[0157] The determination module 100 is used to establish a functional function of the retaining wall to determine the parameters and probability distribution information of the rock and soil mass in the uncertain physical space;

[0158] A calculation module 200, for converting the geotechnical mass parameters into an independent standard normal space based on the probability distribution information, so as to iteratively calculate the geotechnical mass parameter design points in the independent standard normal space;

[0159] The analysis module 300 is used to convert the geotechnical parameter design points into the uncertainty physical space to calculate the reliability index and failure probability of the geotechnical material of the retaining wall and generate the geotechnical reliability analysis results.

[0160] Optionally, in one embodiment of the present application, the calculation module 200 includes: a setting unit, a calculation unit and a judgment unit.

[0161] Among them, the setting unit is used to set the design point allowable error and the initial rock and soil parameter design point;

[0162] A calculation unit, used for calculating the performance function value and gradient of the current iteration based on the initial geotechnical parameter design point, so as to calculate the geotechnical parameter design point and the quasi-Newton method BFGS matrix of the next iteration;

[0163] The judging unit is used to judge whether the iteration converges, wherein if the iteration converges, the geotechnical parameter design point within the allowable error range of the design point is obtained based on the geotechnical parameter design point of the next iteration and the BFGS matrix.

[0164] Optionally, in one embodiment of the present application, the expression of the functional function may be, but is not limited to:

[0165] g=(W1R1+W2R2)-P a H0,

[0166] Where W1 is the gravity of the triangular area of ​​the retaining wall, W2 is the gravity of the rectangular area of ​​the retaining wall, R1 is the force arm of the gravity of the triangular area of ​​the retaining wall at the toe of the wall, R2 is the force arm of the gravity of the rectangular area of ​​the retaining wall at the toe of the wall, P a is the active earth pressure, and H0 is the distance between the active earth pressure and the bottom of the wall.

[0167] Optionally, in one embodiment of the present application, the conversion formula of the geotechnical mass parameters may be, but is not limited to,:

[0168]

[0169] Among them, u is the rock and soil mass parameter in the independent standard normal space, u=[u c u φ ] T ,u c is the cohesion in the independent standard normal space, u φ is the internal friction angle in the independent standard normal space, the superscript “T” is the transpose of the vector, Φ -1 (·) is the inverse function of the standard normal distribution function and h(F c (c),F φ (φ); θ) is the conditional Copula function.

[0170] Optionally, in one embodiment of the present application, the calculation formula of the reliability index may be, but is not limited to,:

[0171]

[0172] Among them, β is the reliability index of retaining wall, u * It is the design point of rock and soil parameters.

[0173] Optionally, in one embodiment of the present application, the expression for converting the geotechnical mass parameter design point to the target physical space may be, but is not limited to,:

[0174]

[0175] Among them, x * is the design point of rock and soil parameters, x * =[c * φ * ] T , c * is the cohesion design point in physical space, φ * is the design point of the internal friction angle in physical space, is the inverse function of the cumulative distribution function of cohesion, F -1 (·) is the inverse function of the cumulative distribution function of the internal friction angle, is the inverse function of the conditional Copula function, and Φ(·) is the standard normal distribution function.

[0176] It should be noted that the above explanation of the embodiment of the geotechnical reliability analysis method is also applicable to the geotechnical reliability analysis device of this embodiment, and will not be repeated here.

[0177] According to the geotechnical reliability analysis device proposed in the embodiment of the present application, the geotechnical parameters and probability information in the physical space with uncertainty can be determined, the geotechnical parameter design points in the independent standard normal space can be calculated and converted back to the physical space with uncertainty, thereby obtaining the reliability index and failure probability of the retaining wall, and then obtaining the reliability analysis results of the geotechnical. Therefore, the geotechnical reliability is analyzed based on the iHLRF-BFGS efficient iteration technology, and the geotechnical parameter design points can be accurately locked in only a few iterations. When facing highly complex nonlinear functional functions, its iteration process also shows extremely high stability, which effectively improves the stability and calculation efficiency of the present application, and is highly adaptable to the selection of different Copula functions, and has extremely high practicality and scope of application, which can effectively meet the needs of geotechnical reliability analysis in different scenarios. As a result, the problem that when the Copula theory and the first-order reliability method in the relevant technology are combined, the design point iteration process may converge slowly or even diverge, the calculation efficiency is low, and the design point may fall into periodic and chaotic solutions, and the stability is not high, which seriously limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis, etc.

[0178] Fig. 9 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device may include:

[0179] A memory 901 , a processor 902 , and a computer program stored in the memory 901 and executable on the processor 902 .

[0180] When the processor 902 executes the program, the geotechnical reliability analysis method provided in the above embodiment is implemented.

[0181] Furthermore, the electronic device further comprises:

[0182] The communication interface 903 is used for communication between the memory 901 and the processor 902 .

[0183] The memory 901 is used to store computer programs that can be executed on the processor 902 .

[0184] The memory 901 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0185] If the memory 901, the processor 902 and the communication interface 903 are implemented independently, the communication interface 903, the memory 901 and the processor 902 can be connected to each other through a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig. 9 Only one thick line is used in the diagram, but this does not mean that there is only one bus or only one type of bus.

[0186] Optionally, in a specific implementation, if the memory 901, the processor 902 and the communication interface 903 are integrated on a chip, the memory 901, the processor 902 and the communication interface 903 can communicate with each other through an internal interface.

[0187] The processor 902 may be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0188] An embodiment of the present application also provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the above-mentioned geotechnical reliability analysis method is implemented.

[0189] The embodiment of the present application also provides a computer program product, including a computer program, which can run computer instructions. When the computer instructions are executed by a processor, the geotechnical reliability analysis method provided in the embodiment of the present application is implemented.

[0190] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0191] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0192] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0193] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purpose of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or N wirings (electronic devices), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically by optically scanning the paper or other medium and then editing, interpreting or processing in other suitable ways as necessary and then storing it in a computer memory.

[0194] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above embodiment, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented by hardware, as in another embodiment, it can be implemented by any one or a combination of multiple of the following technologies known in the art: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0195] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0196] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0197] The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A geotechnical reliability analysis method, characterized in that: The following steps are involved: Establish the functional function of the retaining wall to determine the parameters and probability distribution information of the rock and soil mass in the uncertain physical space; Based on the probability distribution information, the rock and soil mass parameters are converted into an independent standard normal space to iteratively calculate the rock and soil mass parameter design points in the independent standard normal space; The geotechnical parameter design points are converted into the uncertain physical space to calculate the reliability index and failure probability of the retaining wall and generate the geotechnical reliability analysis results.

2. The method according to claim 1, characterized in that The iterative calculation of the geotechnical mass parameter design points in the independent standard normal space includes: Set the design point allowable error and initial geotechnical parameter design point; Based on the initial geotechnical mass parameter design point, calculating the performance function value and gradient of the current iteration to calculate the geotechnical mass parameter design point and the quasi-Newton method BFGS matrix of the next iteration; Determine whether the iteration converges, wherein if the iteration converges, obtain the geotechnical parameter design point within the allowable error range of the design point based on the geotechnical parameter design point of the next iteration and the BFGS matrix.

3. The method according to claim 1, characterized in that The expression of the functional function is: g=(W1R1++W2R2)-P a H0 Where W1 is the gravity of the triangular area of ​​the retaining wall, W2 is the gravity of the rectangular area of ​​the retaining wall, R1 is the force arm of the gravity of the triangular area of ​​the retaining wall at the toe of the wall, R2 is the force arm of the gravity of the rectangular area of ​​the retaining wall at the toe of the wall, P a is the active earth pressure, and H0 is the distance between the active earth pressure and the bottom of the wall.

4. The method according to claim 1, characterized in that: The conversion formula of the rock and soil mass parameters is: Among them, u is the rock and soil mass parameter in the independent standard normal space, u=[u c u φ ] T ,u c is the cohesion in the independent standard normal space, u φ is the internal friction angle in the independent standard normal space, the superscript "T" is the transpose of the vector, Φ -1 (·) is the inverse function of the standard normal distribution function and h(F c (c),F φ (φ); θ) is the conditional Copula function.

5. The method according to claim 1, characterized in that The calculation formula of the reliability index is: Among them, β is the reliability index of the retaining wall, u * is the design point of the rock and soil mass parameters.

6. The method according to claim 1, characterized in that The expression for converting the geotechnical mass parameter design point into the uncertain physical space is: Among them, x * is the design point of the rock and soil mass parameters, x * =[c * φ * ] T , c * is the cohesion design point in physical space, φ * is the design point of the internal friction angle in physical space, is the inverse function of the cumulative distribution function of cohesion, F -1 (·) is the inverse function of the cumulative distribution function of the internal friction angle, is the inverse function of the conditional Copula function, and Φ(·) is the standard normal distribution function.

7. A geotechnical reliability analysis device, characterized in that: include: A determination module is used to establish the functional function of the retaining wall to determine the parameters and probability distribution information of the rock and soil mass in the uncertain physical space; A calculation module, used for converting the rock and soil mass parameters into an independent standard normal space based on the probability distribution information, so as to iteratively calculate the design points of the rock and soil mass parameters in the independent standard normal space; The analysis module is used to convert the geotechnical parameter design points into the uncertain physical space to calculate the reliability index and failure probability of the retaining wall and generate the geotechnical reliability analysis results.

8. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the geotechnical reliability analysis method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the geotechnical reliability analysis method as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed, it is used to implement the geotechnical reliability analysis method as described in any one of claims 1-6.

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