A geotechnical parameter displacement back analysis error propagation method and related equipment

Abstract

The present application provides a kind of geotechnical parameter displacement back analysis error propagation method and related equipment, grid model is established based on the working condition data and geological exploration data collected, and simulation displacement is obtained by solving;The sensitivity of rock-soil parameters in geological exploration data is analyzed using simulated displacement, to obtain the rock-soil parameters to be inverted;The error characteristics of each component in deformation monitoring data are quantified to obtain error distribution characteristics to generate observation sample sequence;Establish the prior probability density function and likelihood function of the rock-soil parameters to be inverted;Based on the observation sample sequence, likelihood function and prior probability density function, multiple back analysis calculations are performed on the rock-soil parameters to be inverted to obtain the posterior rock-soil parameter matrix, and the back analysis error propagation result of the study area is obtained based on the posterior rock-soil parameter matrix;It can accurately calculate and evaluate the influence of measurement error on inversion result and displacement prediction and risk assessment.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method and related equipment for back-analysis error propagation of geotechnical parameters displacement. Background Technology

[0002] In geotechnical engineering, displacement back analysis is a crucial method for correcting geotechnical parameters, and its results directly impact slope stability evaluation, engineering design optimization, and risk control decisions. Existing geotechnical parameter back analysis methods mainly fall into two categories: deterministic back analysis and probabilistic back analysis. Deterministic back analysis typically relies on least squares fitting or optimization algorithms, adjusting model parameters to achieve the best match between simulated and monitored displacements. Probabilistic back analysis, on the other hand, uses methods such as Bayesian inversion and Markov chain Monte Carlo to obtain the probability distribution of parameters, thereby quantifying the uncertainty of the parameters.

[0003] However, in actual monitoring, surface and subsurface displacements are inevitably affected by factors such as the accuracy of measuring instruments and external environmental disturbances, resulting in a certain degree of random error. Existing inverse analysis techniques generally assume that the measurement data has high reliability and often only use a fixed observation error variance in the likelihood function to characterize the measurement error. While these methods can reflect data noise to some extent, they cannot reveal the propagation law of measurement error in the inverse analysis process, nor can they accurately assess the impact of error on the final parameter inversion results.

[0004] Current error assessment methods rely heavily on linearized error propagation theory or covariance propagation methods. Traditional error propagation methods typically require first- or second-order Taylor expansions of the inverse analysis model, depending on the model's differentiability and linear approximation. While these methods are well-suited for simple models, in geotechnical parameter displacement inverse analysis, the inverse model integrates complex numerical calculations, black-box surrogate model relationships, and complex coupling relationships among multiple sub-models, exhibiting strong nonlinearity and even non-differentiability. This makes it difficult for linearized error propagation methods to accurately reflect the true error propagation characteristics, easily leading to significant biases. Summary of the Invention

[0005] This invention provides a method and related equipment for propagating errors in geotechnical parameter displacement inverse analysis, the purpose of which is to accurately calculate and evaluate the impact of measurement errors on inversion results, displacement prediction, and risk assessment.

[0006] To achieve the above objectives, the present invention provides a method for propagating errors in geotechnical parameter displacement back analysis, comprising:

[0007] Step 1: Collect working condition data, geological exploration data, and deformation monitoring data for the study area;

[0008] Step 2: Establish a grid model based on the working condition data and geological exploration data, and solve the grid model to obtain the simulated displacement;

[0009] Step 3: Use simulated displacement to perform sensitivity analysis on the soil and rock parameters in the geological exploration data to obtain the soil and rock parameters to be inverted;

[0010] Step 4: Based on the accuracy level of the monitoring instruments in the study area, on-site environmental interference, and installation conditions, quantify the error characteristics of each component in the deformation monitoring data to obtain the error distribution characteristics, and generate an observation sample sequence based on the error distribution characteristics.

[0011] Step 5: Establish the prior probability density function of the soil and rock parameters to be inverted based on geological exploration data, and construct the likelihood function based on deformation monitoring data, simulated displacement, and error distribution characteristics.

[0012] Step 6: Based on the observed sample sequence, likelihood function, and prior probability density function, perform multiple back-analysis calculations on the soil and rock parameters to be inverted to obtain the posterior soil and rock parameter matrix, and obtain the back-analysis error propagation results of the study area based on the posterior soil and rock parameter matrix.

[0013] Furthermore, the error distribution characteristics include Gaussian distribution characteristics and heavy-tailed distribution characteristics;

[0014] The expression for the characteristics of the Gaussian distribution is:

[0015] ;

[0016] in, Indicates error Gaussian distribution characteristics, Indicates error The mean, Indicates error Standard deviation;

[0017] The expression for the characteristics of the heavy-tailed distribution is:

[0018] ;

[0019] in, Indicates error The characteristics of the thick-tailed distribution. Indicates degrees of freedom. Indicates position parameters, Indicates the scale parameter. This represents the gamma function.

[0020] Furthermore, the expression for the prior probability density function of the soil and rock parameters to be inverted, based on geological exploration data, is as follows:

[0021] ;

[0022] in, Indicates the first Geotechnical parameters to be inverted The logarithm mean, Indicates the first Geotechnical parameters to be inverted The standard deviation of the logarithm, This indicates the number of soil and rock parameters to be inverted.

[0023] Furthermore, the expression for the likelihood function, constructed based on deformation monitoring data, simulated displacement, and error distribution characteristics, is as follows:

[0024] ;

[0025] in, This represents deformation monitoring data. Indicates simulated displacement. Indicates error The mean, Indicates error standard deviation This indicates the number of deformation monitoring data.

[0026] Furthermore, the expression for multiple inverse analysis calculations of the soil and rock parameters to be inverted, based on the observed sample sequence, likelihood function, and prior probability density function, is as follows:

[0027] ;

[0028] in, Indicates the first The expected value of the posterior probability density function of the soil and rock parameters obtained from the set of observation samples is: , Indicates the first The first group of observation sample sequences Post-hoc geotechnical parameters Represents the normalization factor. Represents the likelihood function. This represents the prior probability density function.

[0029] Furthermore, the posterior geotechnical parameter matrix is ​​as follows:

[0030] ;

[0031] in, Represents the posterior geotechnical parameter matrix. Indicates the first The first group of observation sample sequences Post-hoc geotechnical parameters.

[0032] The present invention also provides a device for propagating errors in back analysis of soil and rock parameter displacement, comprising:

[0033] The data acquisition module is used to collect working condition data, geological exploration data, and deformation monitoring data of the study area.

[0034] The solver module is used to build a mesh model based on working condition data and geological exploration data, and solve the mesh model to obtain the simulated displacement;

[0035] The analysis module is used to perform sensitivity analysis on the soil and rock parameters in the geological exploration data using simulated displacement, and to obtain the soil and rock parameters to be inverted.

[0036] The quantization module is used to quantify the error characteristics of each component in the deformation monitoring data according to the accuracy level of the monitoring instruments in the study area, the interference of the on-site environment, and the installation conditions, to obtain the error distribution characteristics, and to generate the observation sample sequence based on the error distribution characteristics.

[0037] The module is used to establish the prior probability density function of the soil and rock parameters to be inverted based on geological exploration data, and to construct the likelihood function based on deformation monitoring data, simulated displacement, and error distribution characteristics.

[0038] The inverse analysis module is used to perform multiple inverse analysis calculations on the soil and rock parameters to be inverted based on the observed sample sequence, likelihood function, and prior probability density function to obtain the posterior soil and rock parameter matrix, and to obtain the inverse analysis error propagation results of the study area based on the posterior soil and rock parameter matrix.

[0039] The present invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a method for propagating errors in the displacement analysis of geotechnical parameters.

[0040] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a method for propagating errors in the displacement inverse analysis of geotechnical parameters.

[0041] The above-described solution of the present invention has the following beneficial effects:

[0042] This invention establishes a grid model based on collected working condition data and geological exploration data, and solves the grid model to obtain simulated displacement. Sensitivity analysis is then performed on the soil and rock parameters in the geological exploration data using the simulated displacement to obtain the soil and rock parameters to be inverted. Based on the accuracy level of the monitoring instruments in the study area, on-site environmental interference, and installation conditions, the error characteristics of each component in the deformation monitoring data are quantified to obtain error distribution characteristics, and an observation sample sequence is generated based on these error distribution characteristics. A prior probability density function for the soil and rock parameters to be inverted is established based on the geological exploration data. Based on the deformation monitoring data, simulated displacement, and error distribution characteristics... The method involves constructing a likelihood function; performing multiple back-analysis calculations on the soil and rock parameters to be inverted based on the observed sample sequence, the likelihood function, and the prior probability density function to obtain the posterior soil and rock parameter matrix; and obtaining the back-analysis error propagation results for the study area based on the posterior soil and rock parameter matrix. Compared with existing technologies, this invention does not require linearization or differentiability assumptions for the back-analysis model, and can be directly applied to numerical inversion processes containing complex constitutive relations and strong nonlinear characteristics. When dealing with nonlinear models containing complex geological structures and multi-stage excavation, it can accurately calculate and evaluate the impact of measurement errors on inversion results, displacement prediction, and risk assessment.

[0043] Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0045] Figure 2 This illustrates the trend of inversion result accuracy under the influence of random errors in deep displacement measurement in this embodiment of the invention. Figure 2 (a) shows the trend of the standard deviation of the elastic modulus. Figure 2 (b) shows the trend of the relative error percentage of the elastic modulus. Figure 2 (c) shows the trend of the standard deviation of cohesion. Figure 2 (d) shows the trend of the percentage change in the relative error of cohesion;

[0046] Figure 3 This is a schematic diagram of the structure of the soil and rock parameter displacement back analysis error propagation device in an embodiment of the present invention;

[0047] Figure 4 This is a schematic diagram of the structure of the terminal device in an embodiment of the present invention. Detailed Implementation

[0048] To make the technical problems, solutions, and advantages of this invention clearer, a detailed description will be provided below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0049] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a locking connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0050] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0051] This invention addresses existing problems by providing a method and related equipment for back-analysis error propagation of geotechnical parameters displacement.

[0052] like Figure 1 As shown, an embodiment of the present invention provides a method for propagating errors in back analysis of soil and rock parameter displacement, comprising:

[0053] Step 1: Collect working condition data, geological exploration data, and deformation monitoring data for the study area;

[0054] Step 2: Establish a grid model based on the working condition data and geological exploration data, and solve the grid model to obtain the simulated displacement;

[0055] Step 3: Use simulated displacement to perform sensitivity analysis on the soil and rock parameters in the geological exploration data to obtain the soil and rock parameters to be inverted;

[0056] Step 4: Based on the accuracy level of the monitoring instruments in the study area, on-site environmental interference, and installation conditions, quantify the error characteristics of each component in the deformation monitoring data to obtain the error distribution characteristics, and generate an observation sample sequence based on the error distribution characteristics.

[0057] Step 5: Establish the prior probability density function of the soil and rock parameters to be inverted based on geological exploration data, and construct the likelihood function based on deformation monitoring data, simulated displacement, and error distribution characteristics.

[0058] Step 6: Based on the observed sample sequence, likelihood function, and prior probability density function, perform multiple back-analysis calculations on the soil and rock parameters to be inverted to obtain the posterior soil and rock parameter matrix, and obtain the back-analysis error propagation results of the study area based on the posterior soil and rock parameter matrix.

[0059] In this embodiment of the invention, the working condition data includes: the excavation volume, excavation length, excavation depth, and excavation height range corresponding to each stage of slope excavation; slope geometric parameters, including slope gradient, step height, step width, and slope ratio; and boundary condition parameters related to the construction process. The working condition data is used to characterize the stress and deformation state of the slope under different construction conditions.

[0060] In this embodiment of the invention, the geological exploration data includes: topographic data and three-dimensional spatial coordinate information of the study area; rock mass zoning and rock mass quality classification results; soil and rock parameters corresponding to different rock mass types; spatial distribution of structural and tectonic planes and their soil and rock parameters. The working condition data and geological exploration data are used together to construct a grid model, determine the initial parameters of the model, and perform numerical simulation.

[0061] Deformation monitoring data is obtained through periodic automated deformation observation using a measurement robot, including GNSS displacement values, inclinometer displacement values, and pore water pressure values. In this embodiment of the invention, the mapping relationship between the soil and rock parameters to be inverted and the deformation monitoring data is as follows:

[0062]

[0063] in, A vector representing deformation monitoring data. Indicates the soil and rock parameters to be inverted. Represents the observation error vector. This represents quantified operational and environmental data, such as excavation stage, excavation depth, and rainfall. This represents a numerical simulation process based on a grid model.

[0064] In this embodiment of the invention, the finite element method or the finite difference method is used to solve the mesh model to obtain the simulated displacement.

[0065] It should be noted that the basic solution idea of ​​the finite element method is to divide the computational domain into a finite number of non-overlapping elements. Within each element, some suitable nodes are selected as interpolation points for the solution function. The variables in the differential equation are rewritten as linear expressions composed of the nodal values ​​of each variable or its derivative and the selected interpolation function. The differential equation is then solved discretically using the variational principle or the weighted residual method. In contrast, the finite difference method divides the solution domain into many grid points, uses the difference quotient to approximate the differential operation at each point, and then obtains the system of difference equations for the entire domain by substituting the boundary conditions and initial conditions.

[0066] This invention employs the finite difference method for numerical simulation. The governing equations of geotechnical mechanics problems are typically described in the form of partial differential equations. The finite difference method, by discretizing the differential operators, transforms the governing equations in the continuous domain into a system of algebraic equations, thereby enabling the numerical solution of the deformation and stress evolution process of geotechnical masses. The calculation process includes the following steps:

[0067] 1. Determination of computational domain and geometric modeling: The scope of the computational domain is determined based on the working condition data and geological exploration data, and a three-dimensional geometric model reflecting the slope topography, layered structure and excavation range is established. The computational domain covers the main deformation-affected areas, and the boundary settings meet the numerical stability requirements far away from the excavation area.

[0068] 2. Spatial discretization: The solution domain is divided into a finite number of polyhedral elements using a spatial discretization strategy. Each element is connected by nodes to form a finite difference computational grid. The solution domain is represented by the set of all element nodes.

[0069] 3. Assignment of physical property parameters and constitutive relations: Based on geological exploration data, assign corresponding soil and rock parameter values ​​to different rock mass zones and structural surface units, and select corresponding constitutive models for each unit to describe the mechanical response characteristics of soil and rock under external load and unloading conditions.

[0070] 4. Initial and boundary conditions are set: Initial stress and gravity fields are applied throughout the computational domain, and displacement or mechanical constraints are set at the model boundaries to eliminate rigid body motion and simulate the actual engineering boundary environment.

[0071] 5. Difference approximation and discrete equation construction: Taylor expansion formulas are established at each grid node. Using central difference, forward difference, or backward difference methods, the spatial and temporal derivatives in the control equations are approximated by algebraic difference expressions, thereby constructing node equilibrium equations and forming a global discrete equation system.

[0072] 6. Simulation of loading and excavation process: Based on the loading data, a multi-stage construction process is defined. By unloading or deleting the excavation area units at the corresponding stages, the step-by-step excavation behavior in the actual project is simulated. The support or reinforcement conditions are updated synchronously at each stage to reflect the influence of the construction sequence on the slope mechanical response.

[0073] 7. Iterative solution and convergence determination: The discrete equation system is solved iteratively, and the nodal displacements, stresses and strain states are updated in each calculation step; the convergence of the calculation is determined by indicators such as unbalanced forces, residuals or displacement increments, and the current stage of calculation ends when the preset convergence criteria are met.

[0074] 8. Simulated displacement extraction and result output: After the calculation is completed in each working condition stage, the simulated displacement results are extracted from the specified node or monitoring position to form a simulated displacement sequence corresponding to the deformation monitoring data in terms of spatial location and time stage.

[0075] Specifically, this embodiment of the invention uses orthogonal experimental design and simulated displacement to perform sensitivity analysis on soil and rock parameters in geological exploration data, determining the soil and rock parameters to be inverted as internal friction angle, elastic modulus, and cohesion. The specific steps include:

[0076] 1. Determine the set of candidate parameters and their range. Based on geological exploration data and engineering experience, select the rock mass and structural surface soil parameters that may affect slope deformation as the set of candidate parameters, and set multiple discrete level values ​​for each candidate parameter. Each level value is determined by the recommended value and its upper and lower limits given in the exploration report.

[0077] 2. Determine the response quantity and experimental index. The simulated displacement output by the numerical model is used as the response quantity, and the experimental index is determined at the same time. In this example, the experimental index is the simulated displacement of the key monitoring points.

[0078] 3. Construct orthogonal test tables and test scheme sets. Based on the number of candidate soil and rock parameters and the number of levels for each parameter, select matching orthogonal tables to form a set of parameter combination test schemes; each test scheme corresponds to a set of candidate parameter level combinations.

[0079] 4. Numerical solution to obtain simulated displacement: Input the parameter combination of each test scheme into the mesh model, and solve the problem based on the same boundary conditions and working condition data to obtain the corresponding simulated displacement results;

[0080] 5. Calculate the influence of parameters. For each candidate parameter, statistically analyze its simulated displacement at different levels and perform variance analysis. Calculate the influence of each geotechnical parameter through hypothesis testing. The higher the influence of the geotechnical parameter, the higher its sensitivity to displacement, that is, the more significant its influence on deformation.

[0081] 6. Determine the soil and rock parameters to be inverted, and select parameters with high sensitivity as the soil and rock parameters to be inverted; keep the parameters with low sensitivity or insignificant impact on the response as prior fixed values ​​or use engineering experience values, so as to reduce the dimensionality of the inversion analysis and improve the stability and calculation efficiency of the inversion.

[0082] It should be noted that, in order to reduce computational costs and improve computational efficiency during error propagation calculations, this embodiment of the invention uses a long short-term memory network as a surrogate model for the grid model, and uses a particle swarm optimization algorithm to optimize the hyperparameters of the surrogate model in order to improve the accuracy of the surrogate model. The inputs of the surrogate model are six geotechnical parameters, excavation stage, excavation volume, excavation depth, excavation length and slope ratio, and the output is the simulated displacement corresponding to the surface and underground stations.

[0083] Specifically, based on the accuracy level of the monitoring instruments in the study area, on-site environmental interference, and installation conditions, the error characteristics of each component in the deformation monitoring data are quantified to obtain the error distribution characteristics, including:

[0084] Based on the accuracy level of the monitoring instruments in the study area, the interference of the on-site environment, and the installation conditions, the mean and standard deviation of the error of each component in the deformation monitoring data are calculated to obtain the mean and standard deviation of the error.

[0085] The error distribution characteristics are determined using the mean and standard deviation of the error.

[0086] Specifically, error distribution characteristics include Gaussian distribution characteristics and heavy-tailed distribution characteristics;

[0087] For example, under normal circumstances, deformation monitoring data only contains random errors, which follow a Gaussian distribution. The Gaussian distribution characteristics are expressed as follows:

[0088] ;

[0089] in, Indicates error Gaussian distribution characteristics, Indicates error The mean is usually set to 0. Indicates error The standard deviation is used to determine the accuracy of the corresponding monitoring instrument.

[0090] When the observation environment is harsh and the deformation monitoring data may contain outliers or gross errors, the Gaussian distribution often underestimates the probability of extreme errors. In such cases, a heavy-tailed distribution is usually used to model the error, thus obtaining the heavy-tailed distribution characteristics, expressed as:

[0091] ;

[0092] in, Indicates error The characteristics of the thick-tailed distribution. Degrees of freedom The smaller the value, the easier it is for larger errors to occur. When this distribution converges to a Gaussian distribution, it is usually... To simulate deformation monitoring data containing gross errors, This represents the position parameter and the mean of the corresponding error. The conversion formula between the scale parameter and the standard deviation of error is as follows: , This represents the gamma function.

[0093] In this embodiment of the invention, it is assumed that the deformation monitoring error follows a Gaussian distribution, and its mean and standard deviation are determined by the accuracy of the monitoring instrument and the on-site conditions. The observation sample sequence is generated by random sampling.

[0094] Using the simulated displacement obtained from the numerical simulation of the corrected mesh model as the true value of the observation, in each sampling process, a set of error samples is randomly generated according to the Gaussian distribution, and these error samples are superimposed on the corresponding simulated displacements, thus obtaining a set of observation samples with random noise. By repeating the above random sampling and superposition process, a set of observation samples with random noise is generated. Group observation sample sequence Each sample group represents one possible actual observation scenario.

[0095] Specifically, the expression for the prior probability density function of the soil and rock parameters to be inverted, based on geological exploration data, is as follows:

[0096] ;

[0097] in, Indicates the first Geotechnical parameters to be inverted The logarithm mean, Indicates the first Geotechnical parameters to be inverted The standard deviation of the logarithm, This indicates the number of soil and rock parameters to be inverted;

[0098] Among them, the Geotechnical parameters to be inverted logarithm mean The calculation formula is:

[0099]

[0100] No. Geotechnical parameters to be inverted The standard deviation of the logarithm The calculation formula is:

[0101]

[0102] , They represent the first Geotechnical parameters to be inverted The mean and standard deviation.

[0103] Specifically, the expression for the likelihood function, constructed based on deformation monitoring data, simulated displacement, and error distribution characteristics, is as follows:

[0104] ;

[0105] in, This represents deformation monitoring data. Indicates simulated displacement. Indicates error The mean, Indicates error standard deviation This indicates the number of deformation monitoring data.

[0106] Specifically, the expression for multiple inverse analysis calculations of the soil and rock parameters to be inverted, based on the observed sample sequence, likelihood function, and prior probability density function, is as follows:

[0107] ;

[0108] in, Indicates the first The expected value of the posterior probability density function of the soil and rock parameters obtained from the set of observation samples is: , Indicates the first The first group of observation sample sequences Post-hoc geotechnical parameters Represents the normalization factor. Represents the likelihood function. This represents the prior probability density function.

[0109] In this embodiment of the invention, the geotechnical parameters to be inverted are based on the observed sample sequence, likelihood function, and prior probability density function. The subsequent inverse analysis yielded the following posterior geotechnical parameter matrix:

[0110] ;

[0111] in, Represents the posterior geotechnical parameter matrix. Indicates the first The first group of observation sample sequences Post-hoc geotechnical parameters.

[0112] Specifically, the back-analysis error propagation result for the study area, based on the posterior geotechnical parameter matrix, involves discretizing the posterior geotechnical parameters of a specific column in the matrix and then calculating their estimated values. The expression is as follows:

[0113]

[0114] in, Indicates the first Post-hoc geotechnical parameters The estimated value, Indicates discretization, This indicates that the mean value is being calculated.

[0115] The present invention further illustrates the method using the excavation of the left bank slope of Baihetan as an example:

[0116] Based on the data in the geological exploration report, a mesh model of the excavated slope on the left bank of Baihetan was established in FLAC3D, and the simulated displacement was calculated using the finite difference method.

[0117] Sensitivity analysis of soil and rock parameters was performed using orthogonal test method. The soil and rock parameters to be inverted were determined to be elastic modulus E(V), E(Ⅳ1), E(Ⅳ2) and cohesion c(V), c(Ⅳ1), c(Ⅳ2).

[0118] The available deformation monitoring data comes from eight prism observation stations, which are used to conduct periodic automated deformation observations using a measurement robot. In addition, there is a four-point displacement gauge underground. Three surface displacement measuring points (TP1-1, TP1-2, TP1-3) and one deep displacement measuring point (M1-1) are selected for inversion.

[0119] The Long Short-Term Memory Network was trained using a dataset generated by numerical simulation, and the hyperparameters of the model were optimized using the Particle Swarm Optimization algorithm to obtain a surrogate model, which improved the accuracy of the surrogate model. The input of the surrogate model is six geotechnical parameters, excavation stage, excavation volume, excavation depth, excavation length and slope ratio, and the output is the calculated displacement corresponding to the surface and underground monitoring stations.

[0120] Determine the distribution type of the observation error of the field monitoring instrument, i.e., Gaussian distribution;

[0121] Set the number of test samples for a single Monte Carlo simulation. ;

[0122] Generate using random sampling algorithms For the observation sample sequence with random noise, based on the instrument accuracy requirements, five different random errors were designed for surface displacement observation: 1 mm, 2 mm, 3 mm, 5 mm and 10 mm; for deep displacement observation, four random errors were designed: 0.25 mm, 0.5 mm, 1 mm and 2 mm.

[0123] The six parameters to be inverted all follow a log-normal distribution and are independent of each other. The expression for their prior probability density function is as follows:

[0124] ;

[0125] Establish the likelihood function:

[0126] ;

[0127] in, and Indicates the system at the 1st The moment of the first Observations and surrogate model calculations at each location, This represents the standard deviation of the corresponding observation error.

[0128] Determine the prior means and standard deviations of the elastic moduli E(V), E(Ⅳ1), E(Ⅳ2) and cohesion c(V), c(Ⅳ1), c(Ⅳ2) based on the values ​​generated in step 2. For each set of observation samples, a likelihood function is established and inverse analysis is performed.

[0129] Multiple inverse analysis calculations are performed on the soil and rock parameters to be inverted based on the observed sample sequence, likelihood function, and prior probability density function.

[0130] Since the inversion calculation in this case is highly nonlinear and cannot obtain an analytical solution, the multi-chain Markov Monte Carlo algorithm (DREAM algorithm) is used to solve the posterior geotechnical parameters.

[0131] This process is repeated 2000 times, ultimately yielding a posterior geotechnical parameter matrix consisting of 2000 sets of posterior geotechnical parameters. The resulting error propagation is as follows: Figure 2 As shown, Figure 2 This study demonstrates the changing trend of inversion accuracy under the influence of random errors in deep displacement measurements. The inversion accuracy of rock mass parameters decreases with increasing deep measurement errors, consistent with the influence of surface displacement measurement errors. When the error is within the range of 0.25-1 mm, the relative error percentage (REP) of both elastic modulus and cohesion remains below 2%, indicating a relatively small impact of the error. However, when the random error reaches 2 mm, the inversion accuracy decreases significantly, with the maximum REP of elastic modulus increasing to 2.9% and the maximum REP of cohesion reaching as high as 7.1%. These results indicate that when the error reaches 2 mm, the impact on inversion accuracy begins to intensify significantly, and the sensitivity of cohesion parameters to random errors in deep observations remains higher than that of elastic modulus; 10 mm and 2 mm are the minimum accuracy requirements for surface and deep displacement measurement instruments, respectively.

[0132] This invention establishes a grid model based on collected working condition data and geological exploration data, and solves the grid model to obtain simulated displacement. Sensitivity analysis is then performed on the soil and rock parameters in the geological exploration data using the simulated displacement to obtain the soil and rock parameters to be inverted. Based on the accuracy level of the monitoring instruments in the study area, on-site environmental interference, and installation conditions, the error characteristics of each component in the deformation monitoring data are quantified to obtain error distribution characteristics, and an observation sample sequence is generated based on these error distribution characteristics. A prior probability density function for the soil and rock parameters to be inverted is established based on the geological exploration data. Based on the deformation monitoring data, simulated displacement, and error distribution characteristics... The likelihood function is constructed; based on the observed sample sequence, the likelihood function, and the prior probability density function, multiple back-analysis calculations are performed on the soil and rock parameters to be inverted to obtain the posterior soil and rock parameter matrix, and the back-analysis error propagation results of the study area are obtained based on the posterior soil and rock parameter matrix. Compared with the prior art, the embodiments of the present invention do not require linearization or differentiability assumptions for the back-analysis model, and can be directly applied to numerical inversion processes containing complex constitutive relations and strong nonlinear characteristics. When dealing with nonlinear models containing complex geological structures and multi-stage excavation, it can accurately calculate and evaluate the impact of measurement errors on inversion results, displacement prediction, and risk assessment.

[0133] Corresponding to the soil and rock parameter displacement back analysis error propagation method described in the above embodiments, such as Figure 3 As shown, this embodiment of the invention also provides a soil and rock parameter displacement back analysis error propagation device 100, which includes:

[0134] The data acquisition module 101 is used to collect working condition data, geological exploration data and deformation monitoring data of the study area.

[0135] The solver module 102 is used to establish a grid model based on working condition data and geological exploration data, and to solve the grid model to obtain the simulated displacement.

[0136] Analysis module 103 is used to perform sensitivity analysis on the soil and rock parameters in the geological exploration data using simulated displacement, and to obtain the soil and rock parameters to be inverted.

[0137] The quantization module 104 is used to quantify the error characteristics of each component in the deformation monitoring data according to the accuracy level of the monitoring instrument in the study area, the interference of the on-site environment, and the installation conditions, to obtain the error distribution characteristics, and to generate an observation sample sequence based on the error distribution characteristics.

[0138] Module 105 is used to establish the prior probability density function of the soil and rock parameters to be inverted based on geological exploration data, and to construct the likelihood function based on deformation monitoring data, simulated displacement, and error distribution characteristics.

[0139] The inverse analysis module 106 is used to perform multiple inverse analysis calculations on the soil and rock parameters to be inverted based on the observed sample sequence, likelihood function, and prior probability density function to obtain the posterior soil and rock parameter matrix, and to obtain the inverse analysis error propagation results of the study area based on the posterior soil and rock parameter matrix.

[0140] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0141] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0142] This invention also provides a terminal device, such as... Figure 4 As shown, the terminal device D10 of this embodiment includes: at least one processor D100 ( Figure 4 The diagram shows only one processor, a memory D101, and a computer program D102 stored in the memory D101 and executable on the at least one processor D100. When the processor D100 executes the computer program D102, it implements the above-described method for propagating errors in the displacement analysis of geotechnical parameters.

[0143] The terminal device D10 can be a desktop computer, laptop, handheld computer, server, server cluster, or cloud server, etc. This terminal device may include, but is not limited to, a processor D100 and a memory D101. Those skilled in the art will understand that... Figure 4 This is merely an example of terminal device D10 and does not constitute a limitation on terminal device D10. It may include more or fewer components than shown in the figure, or combine certain components, or different components, such as input / output devices, network access devices, etc.

[0144] The processor D100 can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0145] In some embodiments, the memory D101 may be an internal storage unit of the terminal device D10, such as a hard disk or memory of the terminal device D10. In other embodiments, the memory D101 may be an external storage device of the terminal device D10, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the terminal device D10. Furthermore, the memory D101 may include both internal and external storage units of the terminal device D10. The memory D101 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory D101 can also be used to temporarily store data that has been output or will be output.

[0146] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0147] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0148] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a method for propagating errors in the displacement inverse analysis of geotechnical parameters.

[0149] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to a building device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0150] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for propagating errors in back analysis of soil and rock parameters displacement, characterized in that, include: Step 1: Collect working condition data, geological exploration data, and deformation monitoring data for the study area; Step 2: Establish a grid model based on the working condition data and the geological exploration data, and solve the grid model to obtain the simulated displacement; Step 3: Use the simulated displacement to perform sensitivity analysis on the soil and rock parameters in the geological exploration data to obtain the soil and rock parameters to be inverted; Step 4: Based on the accuracy level of the monitoring instruments in the study area, on-site environmental interference, and installation conditions, quantify the error characteristics of each component in the deformation monitoring data to obtain the error distribution characteristics, and generate an observation sample sequence based on the error distribution characteristics. Step 5, based on the geological exploration data, establish the expression for the prior probability density function of the soil and rock parameters to be inverted as follows: ； in, Indicates the first Geotechnical parameters to be inverted The logarithm mean, Indicates the first Geotechnical parameters to be inverted The standard deviation of the logarithm, This indicates the number of soil and rock parameters to be inverted; Based on the deformation monitoring data, the simulated displacement, and the error distribution characteristics, the expression for the likelihood function is as follows: ； in, This represents deformation monitoring data. Indicates simulated displacement. Indicates error The mean, Indicates error standard deviation Indicates the quantity of deformation monitoring data; Step 6: Based on the observed sample sequence, the likelihood function, and the prior probability density function, perform multiple inverse analysis calculations on the soil and rock parameters to be inverted to obtain the expression for the posterior soil and rock parameter matrix: ； in, Indicates the first The expected value of the posterior probability density function of the soil and rock parameters obtained from the set of observation samples is: , Indicates the first The first group of observation sample sequences Post-hoc geotechnical parameters Represents the normalization factor. Represents the likelihood function. This represents the prior probability density function; The back-analysis error propagation results of the study area are obtained based on the posterior geotechnical parameter matrix.

2. The method for propagating errors in back analysis of soil and rock parameter displacement according to claim 1, characterized in that, The error distribution characteristics include Gaussian distribution characteristics and heavy-tailed distribution characteristics; The expression for the Gaussian distribution characteristics is: ； in, Indicates error Gaussian distribution characteristics, Indicates error The mean, Indicates error Standard deviation; The expression for the heavy-tailed distribution characteristic is: ； in, Indicates error The characteristics of the thick-tailed distribution. Indicates degrees of freedom. Indicates position parameters, Indicates the scale parameter. This represents the gamma function.

3. The method for propagating errors in back analysis of soil and rock parameter displacement according to claim 1, characterized in that, The a posteriori geotechnical parameter matrix is ​​as follows: ； in, Represents the posterior geotechnical parameter matrix. Indicates the first The first group of observation sample sequences Post-hoc geotechnical parameters.

4. A device for propagating errors in back analysis of soil and rock parameter displacement, characterized in that, The apparatus for using the geotechnical parameter displacement back analysis error propagation method as described in any one of claims 1-3 includes: The data acquisition module is used to collect working condition data, geological exploration data, and deformation monitoring data of the study area. The solver module is used to establish a grid model based on the working condition data and the geological exploration data, and to solve the grid model to obtain the simulated displacement. The analysis module is used to perform sensitivity analysis on the soil and rock parameters in the geological exploration data using the simulated displacement, so as to obtain the soil and rock parameters to be inverted. The quantization module is used to quantify the error characteristics of each component in the deformation monitoring data according to the accuracy level of the monitoring instruments in the study area, the interference of the on-site environment, and the installation conditions, to obtain the error distribution characteristics, and to generate an observation sample sequence based on the error distribution characteristics. The construction module is used to establish the prior probability density function of the soil and rock parameters to be inverted based on the geological exploration data, and to construct the likelihood function based on the deformation monitoring data, the simulated displacement, and the error distribution characteristics. The inverse analysis module is used to perform multiple inverse analysis calculations on the soil and rock parameters to be inverted based on the observed sample sequence, the likelihood function, and the prior probability density function to obtain the posterior soil and rock parameter matrix, and to obtain the inverse analysis error propagation results of the study area based on the posterior soil and rock parameter matrix.

5. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the geotechnical parameter displacement back analysis error propagation method as described in any one of claims 1 to 3.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the geotechnical parameter displacement back analysis error propagation method as described in any one of claims 1 to 3.

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