Rock-soil body anti-shear strength parameter probability back analysis method and system based on multi-source information fusion

Abstract

This invention provides a probabilistic inverse analysis method and system for shear strength parameters of soil and rock masses based on multi-source information fusion, relating to the field of geological hazard risk assessment technology. This invention integrates indoor experimental information, historical prior information, and vegetation age observation information for shear strength parameters. Through Bayesian updating and probabilistic inverse analysis methods, it obtains the final shear strength parameters, significantly reducing the uncertainty of these parameters. The accurate shear strength parameters of various soil and rock masses in deformable slopes output by this invention can be directly used for precise evaluation of slope stability, providing a reliable scientific basis for identifying potential instability and sliding locations and optimizing the design of support structures (such as anti-slide piles and anchors).

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of geological disaster risk assessment technology, and in particular to a probabilistic back analysis method and system for shear strength parameters of rock and soil based on multi-source information fusion. Background Technology

[0002] Geotechnical engineering involves various uncertainties, such as the inherent spatial variability of soil and rock parameters, measurement uncertainties, and model uncertainties. While traditional laboratory or field tests can obtain shear strength parameters of soil and rock, limitations imposed by internal and external factors such as geotechnical investigation costs and sampling sites often result in only very limited site information, such as laboratory or field test data. In practical geotechnical engineering applications, selecting appropriate shear strength parameters is one of the biggest challenges in slope stability evaluation. Directly utilizing limited field test data for inverse analysis of slope shear strength parameters has become a widely used method in the field of geotechnical engineering.

[0003] Methods for back analysis of shear parameters in soil and rock masses can be divided into two categories: 1) deterministic back analysis methods; and 2) probabilistic back analysis methods. To account for the uncertainty of soil and rock parameters, scholars both domestically and internationally have made significant progress in probabilistic back analysis considering this uncertainty in recent years. The most commonly used probabilistic back analysis method is the Bayesian method. Bayesian parameter back analysis can effectively account for the uncertainty of soil and rock parameters and overcome the limitation of limited indoor (field) test data in geotechnical engineering. However, current Bayesian back analysis methods use relatively limited observation information, which may not be able to accurately and reliably calibrate the soil and rock parameters of complex slopes. Therefore, how to effectively integrate multi-source information to conduct back analysis of the shear strength of soil and rock masses in complex deformable slopes has become a crucial problem that urgently needs to be solved. Summary of the Invention

[0004] This invention provides a probabilistic inverse analysis method and system for shear strength parameters of soil and rock mass based on multi-source information fusion, so as to at least partially solve the above-mentioned problems.

[0005] The first aspect of this invention provides a probabilistic inverse analysis method for shear strength parameters of soil and rock masses based on multi-source information fusion, the method comprising: Determine the potential instability mode of the deformable slope and obtain test data on the shear strength parameters of the soil and rock masses of the deformable slope, including slip zone soil, landslide deposits, strongly tilted rock masses, and weakly tilted rock masses; the shear strength parameters include: cohesion and internal friction angle; The test data of the shear strength parameters of the soil and rock mass were processed using the non-parametric Bootstrap method to obtain the corrected statistical characteristics and distribution information of the test parameters, which were used as test information. For each type of soil and rock mass, based on the shear strength parameter data of the corresponding soil and rock mass in similar historical engineering cases, the historical parameter statistical characteristics and historical parameter distribution information of the shear strength parameters are determined as prior information; Based on the prior information and the experimental information, the information is updated using Bayes' formula to obtain the posterior distribution information of the shear strength parameters of each soil and rock mass after the initial calibration. Dendrochronology was used to infer the stability of deformable slopes under historical extreme working conditions and obtain the corresponding stability coefficients as observation information. A slope stability calculation model for deformable bodies is constructed. Combining the surrogate model and the Bayesian probabilistic inverse analysis method, the posterior parameter distribution information is used as the new prior information. Based on the observation information, the shear strength parameters of various types of soil and rock masses are back-analyzed to obtain the final shear strength parameters.

[0006] A second aspect of this invention provides a probabilistic inverse analysis system for shear strength parameters of soil and rock masses based on multi-source information fusion, the system comprising: The test data acquisition module is used to determine the potential instability mode of the deformable slope and to acquire test data on the shear strength parameters of the soil and rock masses of the deformable slope, including slip zone soil, landslide deposits, strongly tilting rock masses, and weakly tilting rock masses; the shear strength parameters include: cohesion and internal friction angle; The test information determination module is used to process the test data of the shear strength parameters of the soil and rock mass using the non-parametric Bootstrap method to obtain the corrected statistical characteristics and distribution information of the test parameters, which are used as test information. The prior information determination module is used to determine the historical parameter statistical characteristics and historical parameter distribution information of each type of soil and rock mass based on the shear strength parameter data of the soil and rock mass in similar historical engineering cases, as prior information. The posterior parameter determination module is used to update the shear strength parameters of each soil and rock mass after the first calibration by Bayes' formula based on the prior information and the test information. The observation information determination module is used to infer the stability state of deformable slopes under historical extreme working conditions using dendrochronology, and obtain the corresponding stability coefficients as observation information. The inverse analysis module is used to construct a slope stability calculation model for deformable bodies. Combining the surrogate model and the Bayesian probabilistic inverse analysis method, the module uses the posterior distribution information as the new prior information and performs inverse analysis of shear strength parameters for various types of soil and rock masses based on the observation information to obtain the final shear strength parameters.

[0007] A third aspect of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When executed by the processor, the program implements the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in the first aspect of the present invention.

[0008] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in the first aspect of the present invention.

[0009] The fifth aspect of the present invention provides a computer program product, including a computer program / instruction, which is implemented by a processor as the steps in the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in the first aspect of the present invention.

[0010] This invention integrates indoor test information, historical prior information, and vegetation age observation information for shear strength parameters. Through Bayesian updating and probabilistic inverse analysis, it obtains the final shear strength parameters, significantly reducing their uncertainty. The precise shear strength parameters of each soil and rock mass in the deformable slope output by this invention can be directly used for detailed evaluation of slope stability, providing a reliable scientific basis for identifying potential instability points and optimizing the design of support structures (such as anti-slide piles and anchors).

[0011] In this embodiment of the invention, natural, rainstorm, and earthquake conditions are set to cover the conventional and extreme environments that slopes may actually face, making the calculation results more valuable for engineering reference.

[0012] In this embodiment of the invention, the instability risk of different potential sliding surfaces can be clearly identified by calculating the stability coefficients of different potential sliding surfaces, providing a clear target for protection decisions. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart of the steps of the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion provided in the embodiments of the present invention; Figure 2 This is a typical geological profile of a deformable slope, an exemplary case provided in this embodiment of the invention.

[0015] Figure 3 This is a schematic diagram of possible instability modes in different sections of the deformable slope provided in this embodiment of the invention; Figure 4 It is a probability density function of the mean and standard deviation of the natural cohesion of the landslide deposit in the exemplary case provided in the embodiments of the present invention; Figure 5 This is statistical distribution information of the natural shear strength of slip zone soil provided in the embodiments of the present invention; Figure 6 This is the statistical distribution information of shear strength of deformable slope landslide deposits provided in the embodiments of the present invention; Figure 7 This is statistical distribution information on the shear strength of rock mass in a deformable slope with strong tilting, provided in an exemplary case according to an embodiment of the present invention. Figure 8 This is statistical distribution information on the shear strength of weakly tilting rock mass in a deformable slope, provided in an exemplary case according to an embodiment of the present invention. Figure 9 The stability coefficients of the shallow layer accumulation proxy model and the stability calculation numerical model provided in the embodiments of the present invention are examples of this invention. F s Comparison of calculation results; Figure 10 This is an exemplary case of Markov chain sampling of shallow layer stacks provided in the embodiments of the present invention; Figure 11 This is an exemplary case of the a priori and posterior distribution of shear strength parameters of shallow layer deposits provided in the embodiments of the present invention; Figure 12 The stability coefficients of the surrogate model and the numerical model for stability calculation of slip zone soil, provided in the embodiments of the present invention, are examples of this invention. F s Comparison of calculation results; Figure 13 This is an exemplary case of Markov chain sampling results for slip zone soil provided in the embodiments of the present invention; Figure 14 This is an exemplary case of the prior and posterior distribution of the shear strength parameters of slip zone soil provided in the embodiments of the present invention; Figure 15 The stability coefficients of the surrogate model and the numerical model for stability calculation of the toppled and fractured rock mass provided in the embodiments of the present invention are as follows: F s Comparison of calculation results; Figure 16 This is an exemplary case of Markov chain sampling results of a toppled and broken rock mass provided in the embodiments of the present invention; Figure 17 This is an example of the a priori and posterior distribution of shear strength parameters of a toppled and fractured rock mass provided in the embodiments of the present invention; Figure 18 The stability coefficients of the surrogate model and the numerical model for stability calculation of the bottom boundary of the tilted deformable body, provided in the exemplary case of this invention, are given in the embodiments of the present invention. F s Comparison of calculation results; Figure 19 This is a sampled result of the Markov chain at the bottom boundary of the tilted deformable body, provided in an embodiment of the present invention. Figure 20 This is an example of the prior and posterior distribution of the shear strength parameters at the bottom boundary of a tilted deformable body provided in the embodiments of the present invention. Detailed Implementation

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] This invention provides a probabilistic inverse analysis method for shear strength parameters of soil and rock masses based on multi-source information fusion, specifically, as follows: Figure 1 The diagram illustrates a flowchart of the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion, provided by an embodiment of the present invention. The method includes the following steps: S101, determine the potential instability mode of the deformable slope, and obtain test data on the shear strength parameters of the soil and rock mass of the sliding zone soil, landslide deposit, strongly tilted rock mass, and weakly tilted rock mass of the deformable slope.

[0018] The shear strength parameters include cohesion and internal friction angle.

[0019] To facilitate understanding, an exemplary case is provided in this embodiment of the invention to analyze the technical solution of the invention, such as... Figure 2 As shown, it illustrates a typical geological profile of the deformable slope in this exemplary case, where the yellow portion represents slip zone soil, the red portion represents landslide deposits, the blue portion represents strongly tilting rock mass, the purple portion represents weakly tilting rock mass, and the brown portion represents bedrock.

[0020] Specifically, in this case, the typical profile of the deformed slope shows a rear edge elevation of approximately 450m and a front edge elevation of 92m. The terrain is steep at the bottom and gentle at the top, with a gentle plateau at the rear edge. The tug-of-war height of the riverbank is approximately 4m, and the bedrock on the riverbank is heavily weathered. The typical profile shows that the deformed slope consists of six strata, namely Quaternary colluvial deposits (Q4...). col+dl Quaternary alluvial deposits (Q4) al Quaternary landslide deposits (Q4) delThe rock types include striped quartz schist (Sa2-6), thin-layered interbedded quartz schist (Sa2-5), grayish-black medium-thin layered banded mica schist (Sa3), and grayish-white medium-thick layered massive quartzite (Sa4). Under these conditions, the deformed slope exhibits four typical instability and sliding modes: instability of the slip zone within the shallow surface deposits, instability of the long slip zone, instability of the toppling fracture zone, and instability of the bottom boundary of the toppling deformation. Figure 3 As shown, it illustrates the possible instability modes in different sections of the deformed slope, where (a) represents instability of the shallow deposits; (b) represents instability along the long slip zone; (c) represents instability along the toppled fault zone; and (d) represents instability along the bottom boundary of the toppled deformed body.

[0021] In this embodiment of the invention, in step S101, the test data of the shear strength parameters of the soil and rock mass of the slip zone soil, landslide deposit, strongly tilting rock mass, and weakly tilting rock mass of the deformable slope are determined based on the following steps: S1, samples were taken from the slip zone soil, landslide deposits, strongly tilted rock mass and weakly tilted rock mass of the target deformable slope to obtain soil and rock samples.

[0022] Specifically, sampling can be conducted based on the actual site conditions. Referring to the relevant provisions for undisturbed soil sample collection in the "Standard for Geotechnical Testing Methods" (GB / T50123-2019), a cylindrical PVC pipe with an inner diameter of 95mm and a height of 110mm should be used for undisturbed soil sampling. The collected undisturbed soil samples should be immediately sealed with plastic wrap and transparent tape and brought back to the laboratory.

[0023] S2, for slip zone soil: Based on the undisturbed sample of slip zone soil, a rapid shear test was conducted to obtain test data on the shear strength parameters of the slip zone soil in its natural state and saturated state.

[0024] Specifically, the mechanical properties of the prepared soil and rock samples are tested, including direct shear tests in both natural and saturated states. The direct shear test is a method for directly shearing soil to obtain shear strength parameters, and includes three methods: rapid shear, consolidated rapid shear, and slow shear. Because this method is flexible and simple in terms of sample preparation and operation, it is often used in engineering practice and scientific research to directly obtain the mechanical parameters of slip zone soil. The principle is to first apply a pressure value in the normal direction, and then push the shear box at a constant speed to shear the sample. A stress ring can be used to measure the shear stress during the shearing process, and a dial gauge can be used to measure the horizontal displacement during the shearing process. The shear strength of the sample can be obtained from the relationship curve between shear stress and normal stress. Among the three test methods, the rapid shear test is more suitable for landslides under rapid loading conditions such as sudden instability and failure due to heavy rain or earthquakes.

[0025] In the exemplary case, a DJY-4L quadruple constant strain direct shear apparatus provided by the laboratory was used to conduct a rapid shear test on undisturbed slip zone soil samples. During the rapid shear test, four samples were sheared simultaneously at each test, with applied vertical stresses of 50 kPa, 150 kPa, 250 kPa, and 400 kPa, respectively. The shear rate was set to 0.8 mm / min, and the maximum shear displacement was 6 mm.

[0026] According to the standard "Standard for Geotechnical Testing Methods" (GB / T50123-2019), when conducting direct rapid shear tests on undisturbed samples, the highest shear stress value is taken as the peak strength of the rapid shear test. If the shear stress continues to increase after the shear displacement is 6 mm without a significant peak, then the shear stress at 6 mm is taken as the peak strength. Based on the relationship between shear strength and normal stress, the shear strength parameters of the slip zone soil in its natural and saturated states are obtained after data processing, as shown in Tables 1 and 2.

[0027] Table 1. Test values ​​of shear strength parameters of slip zone soil under natural conditions

[0028] Table 2. Test values ​​of shear strength parameters of slip zone soil under saturated state

[0029] Statistical results of experiments on the shear strength parameters of slip zone soil show that, under natural conditions, the average cohesion (c) of the slip zone soil is 45.35 kPa, and the internal friction angle is... φ The mean value is 27.55°. Under saturated conditions, the mean value of the cohesion c of the slip zone soil is 33.45 kPa, and the mean value of the internal friction angle is... φ The average value is 25.7°. Compared with the natural state, the cohesion of the saturated slip zone soil is reduced by 20%, and the internal friction angle is reduced by about 10%. It can be seen that the water content of the slip zone soil has a significant impact on shear strength, a greater impact on cohesion, and a smaller impact on the internal friction angle.

[0030] S3, for landslide deposits, strongly tilted rock masses, and weakly tilted rock masses: physical parameters of soil and rock samples are obtained through physical experiments and rock wave velocity tests, including natural unit weight, saturated unit weight, and longitudinal wave velocity; mechanical parameters of the rock are obtained through uniaxial tests and conventional triaxial tests, including uniaxial compressive strength, cohesion, internal friction angle, and elastic modulus; the GSI value is quantified by the surface characteristics and integrity coefficient of the rock mass structure; based on the Hoek-Brown strength criterion, combined with mechanical parameters, physical parameters, and GSI, test data of shear strength parameters of landslide deposits, strongly tilted rock masses, and weakly tilted rock masses are obtained.

[0031] Currently, reliable methods for obtaining rock mass mechanics parameters mainly include experimental methods, empirical analysis methods, numerical methods, and geophysical methods. Among these, the most accurate is the in-situ testing method. However, in-situ testing is constrained by geographical environmental factors, testing cycle, site conditions, and human and material resources, making it difficult to conduct large-scale experiments during the feasibility study stage of hydropower projects. To meet the needs of practical engineering, a method has gradually emerged that is based on indoor rock mechanics tests, comprehensively considering the influence of various factors such as rock mass quality grade, weathering, unloading degree, and stress state, and converting rock mechanics parameters into rock mass mechanics parameters after certain corrections. One of the most well-developed methods is the Hoek-Brown strength estimation method. This method is based on the Hoek-Brown strength criterion and uses the Geological Strength Index (GSI) to consider the influence of factors such as joints, fractures, and weathering on rock mass mechanics parameters, estimating rock mass mechanics parameters based on rock block mechanics parameters. Since E. Hoek proposed this method and gave a generalized range for GSI values, many scholars have conducted extensive research based on it, and the quantitative values ​​of GSI have become increasingly reasonable. Specifically, after collecting the main lithological samples from the deformed body on-site, standard cylindrical specimens with a diameter of 50 mm and a height of 100 mm were prepared. The basic physical and mechanical properties of the rock samples were tested in the laboratory according to the "Standard for Testing Methods of Engineering Rock Mass" (GB / T 50266—2013). Physical parameters such as the natural unit weight, saturated unit weight, and longitudinal wave velocity of the rock were measured through physical experiments and rock wave velocity tests. Mechanical parameters such as the uniaxial compressive strength, cohesion, internal friction angle, and elastic modulus of the rock blocks were measured through uniaxial tests and conventional triaxial tests. The test results are summarized in Table 3.

[0032] Table 3 Statistical Table of Test Results for Rock Physical and Mechanical Parameters

[0033] To reasonably determine the geological strength index of deformable rock masses in the study area, the surface characteristics of structural planes are used as lateral indicators, and the rock mass integrity coefficient is also considered. K v As a longitudinal indicator, quantification GSI The value of is determined. A survey and statistical analysis of the core samples retrieved from drilling in the study area is conducted, and representative core samples from deformed rock masses are selected. RQD The rock mass integrity coefficient is calculated using the following formula. K v。

[0034] (1) Based on the calculation results, compare GSI Value quantification table to determine the rock mass of each segment GSI value. mi The values ​​are as follows: Sa2-5 quartzite interbedded with quartz schist is 18, Sa2-6 quartz schist is 15, Sa-3 mica schist is 11, and Sa-4 quartzite is 20. The rock mass disturbance coefficient is determined based on the actual site conditions. D Because the construction of the Paimo rural road and exploration activities caused slight disturbance to the deformed rock mass, the value was taken as 0.3. Based on the above evaluation method, the rock mass strength parameters of each segment of the deformed rock mass were calculated.

[0035] In this exemplary case, the strength parameters of the rock mass of each segment of the deformable slope obtained by the Hoek-Brown estimation method were statistically analyzed, and the results are shown in Table 4.

[0036] Table 4. Statistical table of GSI strength parameters of rock mass in each segment.

[0037] S102, The non-parametric Bootstrap method is used to process the test data of the shear strength parameters of the soil and rock mass to obtain the corrected statistical characteristics and distribution information of the test parameters, which are used as test information.

[0038] In geotechnical engineering investigations, especially in the preliminary investigation phase of hydropower projects, it is common to encounter situations where the sample size for soil and rock mass test parameters is very small. This is because the number of soil and rock sampling tests is constrained by practical circumstances and economic conditions, making it impossible to obtain a large number of physical and mechanical parameters of the soil and rock mass. In actual engineering construction, small sample data (sample size) is typically used. n The mean and standard deviation of samples ≤ 30 are used to infer the statistical characteristics of soil and rock parameters. Due to the small sample size, there is a certain probability deviation between the statistical results and the true values, and they cannot accurately represent the true values ​​of soil and rock parameters. Directly applying the statistical results to slope stability evaluation and prevention engineering design will affect the accuracy of the results.

[0039] The nonparametric bootstrap method is a statistical approach that simulates and resamples experimental observation data to analyze the impact of its uncertainty, providing a new research tool for small-sample statistical inference problems. It can be used for statistical studies such as mean and variance estimation, regression analysis, and cross-validation. Through continuous improvement and development, the nonparametric bootstrap method has been widely applied in fields such as mechanical engineering, geotechnical engineering, and aerospace engineering in recent years. Compared with traditional statistical methods, the nonparametric bootstrap method uses the results of multiple repeated samplings to infer the distribution characteristics of the population's mean and standard deviation, effectively improving the estimation accuracy of confidence intervals and making the statistical characteristics of the population parameters more reasonable. This section will use the nonparametric bootstrap method to simulate the mean and standard deviation of the shear strength parameters of various soil and rock masses in a deformable body.

[0040] In statistical analysis of small samples, the Bootstrap method has proven to have irreplaceable advantages. Generally, a sufficiently large number of Bootstrap subsamples is needed to achieve good convergence in Bootstrap simulations. Related studies have shown that when... B =10 4 At that time, the mean and standard deviation of the Bootstrap subsamples converge well to the unknown distribution. F The overall mean and standard deviation. Therefore, this invention also uses... B =10 4 To simulate the mean and standard deviation of the sample.

[0041] Taking the landslide deposit cohesion sample X1 in its natural state obtained from the above exemplary case as an example (the other samples were analyzed using the same method), the Bootstrap sampling number was taken. B =10 4 The probability density functions for the Bootstrap sample mean and sample standard deviation of sample X1 are obtained as follows: Figure 4 As shown (where (a) represents the mean probability density function of the natural cohesion of the landslide deposit, and (b) represents the standard deviation probability density function of the natural cohesion of the landslide deposit), the mean and standard deviation of the Bootstrap sample mean are obtained as the mean and standard deviation of the distribution fitted to sample X1. Similarly, the mean and standard deviation of the test and estimated values ​​of the shear strength parameters of the other soil and rock masses can be obtained, and the calculation results are shown in Table 5.

[0042] Table 5. Mean and standard deviation of shear strength parameters of deformable soil and rock masses obtained by Bootstrap method simulation.

[0043] S103. For each type of soil and rock mass, based on the shear strength parameter data of the corresponding soil and rock mass in similar historical engineering cases, determine the historical parameter statistical characteristics and historical parameter distribution information of the shear strength parameters as prior information.

[0044] In the exemplary cases provided in the embodiments of the present invention, examples of toppling deformation bodies and landslides encountered in the construction of hydropower projects, mines, and highways in western China were collected and compiled through literature review. These examples involve the Yangtze River, Lancang River, Jinsha River, Yarlung Tsangpo River, Yalong River, Min River, and Yellow River basins. A total of 163 sets of shear strength parameters for rock and soil masses were obtained, including 63 sets of parameters for slip zone soil, 70 sets of parameters for toppling deformation bodies, and 30 sets of parameters for accumulated bodies, as shown in Tables 6-9.

[0045] Based on historical case statistics for the aforementioned soil and rock masses, a Kolmogorov-Smirnov (KS) distribution fitting test was conducted on several common distribution types to determine the most suitable distribution type. The test on these common distribution types revealed that the shear strength parameters of each soil and rock mass generally conform to a normal distribution, thus yielding a probability distribution model for the shear strength parameters of each soil and rock mass. The statistical results are shown in Table 10.

[0046] Table 6 Statistical Information on the Strength Parameters of Slip Zone Soil in Historical Landslides

[0047] Table 7 Statistical Information on Strength Parameters of Historical Deformed Bodies (Strongly Tilted Rock Mass)

[0048] Table 8. Statistical information on strength parameters of historically deformed bodies (weakly tilted rock masses)

[0049] Table 9 Statistical Information on Strength Parameters of Historical Landslide Accumulations

[0050] Table 10. Statistical table of shear strength parameters of various soil and rock masses in historical landslides and toppling deformed bodies obtained from literature collection.

[0051] S104. Based on the prior information and the test information, the information is updated using Bayes' formula to obtain the posterior distribution information of the shear strength parameters of each soil and rock mass after the initial calibration.

[0052] Because the mechanical properties of soil and rock masses are often influenced by factors such as lithology, rock mass structure, stratum dip angle, and structural plane orientation, the conditions and mechanical properties of rock masses are highly complex, resulting in certain variability in corresponding parameters. Shear strength parameters obtained from other engineering projects cannot accurately represent the mechanical properties of various soil and rock masses. Therefore, it is necessary to update and calibrate the collected prior information to make it more representative. Shear strength parameters of soil and rock masses obtained through laboratory tests and the Hoek-Brown estimation method are closer to the actual situation than the collected prior information. Therefore, in this embodiment of the invention, information collected from literature is used as prior information, and information obtained from experiments and field investigations is used as experimental information. A more reasonable probability distribution model of the shear strength parameters of various soil and rock masses is constructed using Bayesian update theory.

[0053] Using Bayesian update theory, the mean and standard deviation of cohesion and internal friction angle for each soil and rock mass are calculated. Taking the cohesion of slip zone soil as an example, its calculation method can be expressed as follows: (2) (3) In the formula: and The average value and standard deviation of the cohesion of soil and rock under natural conditions, obtained through literature collection and statistics, are the prior information. and This refers to the average value and standard deviation of the cohesion of soil and rock under natural conditions obtained through experimental methods, i.e., experimental information.

[0054] In the exemplary case, the shear strength parameters of historical landslides and toppling deformed bodies obtained from literature collection were used as prior information (Table 10), and the shear strength parameters of the deformed soil and rock mass simulated by the Bootstrap method (Table 5) were used as experimental information. The posterior probability density curves of the shear strength parameters of each soil and rock mass under natural conditions were constructed using the above method under small sample conditions. The results are as follows: Figures 5-8 As shown, Figure 5 The statistical distribution of shear strength of slip zone soil in its natural state is shown: cohesion (a); internal friction angle (b). Figure 6 The statistical distribution information of shear strength of landslide deposits on deformable slopes is shown. Figure 7 The statistical distribution information of shear strength of rock mass in a deformable slope with strong tilting is shown. Figure 8 The statistical distribution of shear strength of weakly tilting rock mass in deformable slopes is shown in Table 11.

[0055] Table 11 Statistical table of Bayesian update results for shear strength parameters of various soil and rock masses in the deformable body.

[0056] The Bayesian update results show that the standard deviations of the posterior distributions are significantly reduced compared to the prior distributions. This indicates that the uncertainty of each soil and rock mass parameter is significantly reduced after the Bayesian update, demonstrating that the Bayesian update method can reduce the uncertainty of input parameters and thus improve computational accuracy. Due to the variability of soil and rock properties, it is difficult to collect parameters for landslides and deformable bodies with completely identical or extremely similar geological conditions. Therefore, when the collected prior information cannot accurately represent the true characteristics of the parameter, it is essential to update and calibrate the prior information using experimental data.

[0057] S105 uses dendrochronology to infer the stability of the deformable slope under historical extreme conditions and obtain the corresponding stability coefficient as observation information.

[0058] Tree rings record changes in a tree's growth process under the influence of geomorphological processes such as natural disasters. If a deformable slope becomes unstable and fails, the trees within it may be damaged, exhibiting phenomena such as abrupt changes in tree rings, eccentric growth, tree scarring, root exposure, and the disappearance of surrounding trees. The corresponding anatomical features include the formation of reactive wood, changes in tree ring width, and callus formation. Analysis of tree ring anatomical features can determine the timing and frequency of landslide events. In addition to changes in tree ring width, the anatomical features of the tree's root cross-section can also be used to reconstruct the landslide process and displacement rate. Therefore, if a sufficient sample size can be obtained within the spatial scope of the study area, the spatial distribution data of trees affected by landslide events can be used to reconstruct the spatial characteristics of landslide events and landslide reactivation.

[0059] Among related technologies, three strategies have been proposed for determining the timing of landslides using dendromorphological research methods: ① First, determine the age of the oldest tree on the landslide body. If the trees began growing on the landslide body after the landslide occurred, the age of the oldest tree provides the minimum year the landslide occurred (this dating method is applicable when the tree settlement interval is known). ② Use the year in which growth inhibition began to form on trees on the landslide body affected by landslide activity but not dead (trees growing on the landslide edge or leading edge may survive the landslide) to determine the time of the landslide. ③ Use trees that died due to landslide activity for research. These dead trees can be cross-dated with locally surviving trees or existing local chronologies to determine the year of landslide activity. Only when it is confirmed that the trees died due to this landslide event can the age of the outermost ring of the tree be assigned to coincide with the time of this event.

[0060] In this embodiment of the invention, step S105 includes the following sub-steps: S1051. Based on tree sampling inside and outside the deformable slope, combined with dendrochronological analysis, the ages of trees inside and outside the deformable slope, radial growth characteristics of trees inside and outside the deformable slope, and changes in the growth rate of trees inside and outside the deformable slope were determined.

[0061] S1052, inferring the stability state of the deformable slope under historical extreme working conditions.

[0062] S1053, determine the corresponding stability coefficient based on the stability state and expert experience analysis.

[0063] In the above exemplary case, the tree species collected in the survey were mainly Lithocarpus ( Lithocarpus glaber Lithocarpus is widely distributed on deformed slopes.

[0064] The width of tree rings varies during tree growth due to environmental factors. Tree ring samples were collected from trees both inside and outside the deformed slope. Two core samples were drilled at approximately 1.3 m diameter at breast height (DBH) along different directions (perpendicular to the slope and parallel to the slope), resulting in a total of 50 core samples, 18 outside the deformed slope and 32 inside. The collected core samples were stored in clean sampling containers, with clear labeling of the relevant information.

[0065] Generally, tree ring width gradually widens during growth, peaking during the vigorous growth period, then slowly decreases, eventually stabilizing. This trend in tree ring width with increasing age is caused by the tree's physiological factors and is called the tree's growth trend. To more accurately reflect the response of tree radial growth to climatic factors, non-climatic information such as the tree's physiological growth trend needs to be removed. Therefore, this invention uses a modified negative exponential curve to detrend and standardize tree rings, resulting in a standardized chronology (STD) containing more climatic signals.

[0066] In the above exemplary case, the collected tree core samples were first measured annually using a LinTAB tree-ring width meter. Then, cross-dating was performed using the COFECHA program to obtain the tree age. However, this tree age is not the time when the tree began to grow, nor the time when it sprouted; it is merely the tree age at the sampling height. This is because field tree core sampling is not done at the base of the trunk, but at a height of 50-150 cm. The true age of the tree should be the age at the sampling height plus the time it took for the tree to grow from the base to the sampling height. Different tree species require different amounts of time to grow to the sampling height in different growing environments. Therefore, the tree age mentioned in this article is only the age of the tree at the sampling height, but in principle, this measured age is less than the tree's true age.

[0067] Analysis of 16 trees collected from the slope surface of the deformed body revealed that the oldest tree was 249 years old, while the youngest was only 32 years old. Eleven of these trees were over 73 years old, meaning they were presumably born before the 1950 earthquake. The age distribution of the trees exhibited a certain regularity, with older trees mainly distributed at the top and middle of the deformed body. This is primarily related to recent human activities; in areas with relatively flat terrain suitable for human activity, large trees were often felled to make way for roads or temporary construction sites; while older trees were typically found in steep, dangerous areas that were difficult to cultivate.

[0068] Observations of tree growth dynamics inside and outside the deformed structure revealed that after 1950, the growth of trees outside the deformed structure fluctuated dramatically and significantly, showing an overall downward trend; while the growth dynamics of trees inside the deformed structure remained relatively stable. The significant difference in tree growth trends between the inside and outside of the deformed structure after 1950 (P<0.05) suggests that earthquakes may have caused changes in the growth environment of trees inside and outside the deformed structure, thus inferring a high probability that earthquakes would trigger secondary disasters such as small-scale landslides on the outer slope of the deformed structure.

[0069] Landslides cause tree scarring, trunk tilting, broken branches, reduced branches, root damage, and exposure. These effects typically lead to decreased tree growth in the following years, resulting in narrow rings and impacting the tree's growth rate. Before 1950, the average growth rate of trees inside the landslide was 0.967 / a, while the average growth rate of trees outside the landslide was 0.927 / a. After 1950, the average growth rate of trees inside the landslide was 0.967 / a, while the average growth rate of trees outside the landslide was 1.13 / a. Before 1950, the difference in growth rate between trees inside and outside the landslide was not significant (P=0.41); after 1950, a significant difference in growth rate appeared (P<0.05), indicating that the growth of trees outside the landslide was affected after the 1950 earthquake, possibly due to secondary disasters such as small landslides caused by the earthquake impacting the growth of trees outside the landslide.

[0070] Based on tree-ring chronology and tree growth rate analysis, after 1950, the growth of most trees within the deformed body did not decrease; instead, it maintained a gradual growth trend. This result indicates that the growth of trees within the deformed body was almost unaffected by the earthquake, suggesting that the slope of the deformed body did not experience overall instability along the deep slip surface during the 1950 earthquake.

[0071] S106. Construct a slope stability calculation model for deformable bodies. Combine the surrogate model and Bayesian probabilistic inverse analysis method. Using the posterior distribution information as the new prior information, and based on the observation information, perform inverse analysis of shear strength parameters for various types of soil and rock masses to obtain the final shear strength parameters.

[0072] Specifically, a representative profile of the deformable slope can be selected, and a stability calculation model of the representative profile can be constructed in Geo-Studio software. To ensure rapid extraction of stability coefficients during the calculation process, an interface program between the stability calculation model and MATLAB is established to realize data interaction between the two, providing a physical and mechanical model foundation for stability evaluation. Addressing the computationally intensive nature of probabilistic inverse analysis, an adaptive global Kriging surrogate model method is introduced to construct an explicit functional relationship between the input parameters (cohesion and internal friction angle) and the model output (stability coefficients) of the stability calculation model. The optimal parameter configuration scheme that balances computational efficiency and accuracy is also investigated. After the surrogate model is constructed, Bayesian inverse analysis can be performed based on the computationally efficient surrogate model, thereby improving computational efficiency.

[0073] A probabilistic inverse analysis method is used to establish the shear resistance parameters of soil and rock mass based on the stability state of deformable bodies in past historical periods (such as the stability state under the maximum rainstorm conditions in the past few decades, the stability state of deformable bodies in high-intensity earthquakes, etc.). The posterior parameter distribution information updated in step S104 is used as the new prior information, and the stability state of deformable bodies is used as the observation information. Probabilistic inverse analysis is performed to obtain its posterior distribution, which further improves the accuracy of parameter estimation and provides a statistical basis for the evaluation of deformable body stability.

[0074] In this embodiment of the invention, step S106 includes the following sub-steps: S1061, based on the surrogate model, construct an explicit functional relationship between the input parameters and the output of the stability calculation model. The input parameters include cohesion and internal friction angle, and the model output is the stability coefficient.

[0075] S1062, the surrogate model generates initial sample points for input parameters through Latin hypercube sampling, and constructs an initial surrogate model based on the initial sample points and the corresponding stability coefficients.

[0076] S1063: Use hybrid adaptive sequential sampling to generate candidate sample points as the sample pool for newly added samples; calculate the quality parameters of the candidate sample points, select the sample points corresponding to the maximum quality parameters as newly added sample points, incorporate them into the initial sample set to form a new training sample set, and retrain the surrogate model. Continue iterating until the pre-set convergence criteria are met to obtain the stability calculation model.

[0077] S1064, Based on the stability calculation model and the observation information, a new posterior distribution of shear strength parameters for various types of soil and rock masses is determined using the Bayesian probabilistic inverse analysis method.

[0078] S1065, the new posterior distribution is sampled using the adaptive differential evolution Metropolis algorithm, and the final shear strength parameters are obtained based on the Markov chain samples.

[0079] Due to the complexity of the geological environment and formation mechanism of rock and soil masses, their mechanical properties inevitably exhibit significant variability. Let random variables be denoted as... To account for uncertainties in shear strength parameters ( , m (where the number of random variables is a factor), based on Bayes' theorem, prior information about given parameters can be obtained from observed data. d Update and obtain parameters The posterior distribution can be expressed as: (4) In the formula, For random variables The prior distribution; For random variables The posterior distribution of; Let be the likelihood function.

[0080] Due to the complexity of slope stability calculation models, calculating the posterior distribution in equation (4) using traditional analytical methods is very difficult. Using Monte Carlo Markov Chain (MCMC) sampling techniques is an effective way to solve this problem. The Differential Evolution Adaptive Metropolis Algorithm (DREAM) is a multi-chain MCMC method. This method employs... N The Markov chains are computed in parallel to generate proposed samples through differential evolution, and then the Metropolis criterion is used to determine whether to accept the candidate samples.

[0081] The specific calculation steps of the DREAM algorithm can be summarized as follows: 1) Generate random variables based on their prior distribution. The initial sample of the Markov chain is denoted as Subscript 1 indicates t = 1, which is the first sample in the Markov chain, superscript i Indicates the first i Chains, in total A chain, where N is usually 2. m , m The dimension of the random variable. Initial sample. The size is .

[0082] 2) When hour: First, regarding the first A chain of chains is used to generate candidate samples through mutation operations according to the following formula: (5) In the formula, This represents the number of Markov chain logs used to generate candidate samples. , ,when j =1,2, , , n =1,2, , hour . Elements in ε are sampled from ε and ε respectively. m Dimensional uniform distribution U (- c , c )and m 3D normal distribution N (0, c* );in c It is a positive number less than 1, with a typical value of 0.1. c* It is a positive number that is much smaller than the posterior distribution width, such as 10. -6 Jump rate Depends on the number of heteropair pairs and the number of parameters to be updated together The calculation formula is as follows: (6) Based on crossover probability CR (The value range is [0, 1]) Determine whether to accept the sample; the calculation formula is as shown in equation (7): u A random number that is uniformly distributed in the range [0, 1]. The initial value is m .

[0083] (7) The Metropolis acceptance rate was calculated according to equation (7). : (8) according to Determine whether to accept candidate samples, if If the random number is greater than a uniformly distributed [0, 1], then the candidate sample is accepted. Conversely, if they do not accept it, then Outlier chains are removed using the interquartile range statistic method.

[0084] Finally, outlier chains are detected and convergence is assessed. Convergence diagnostic values ​​are calculated. If all parameter dimensions satisfy If the chain does not break, the calculation stops; otherwise, the chain evolution continues.

[0085] The Kriging model not only possesses global and local statistical properties, but also fully considers the distribution information of variables, thus enabling it to better analyze trends in known information. It has been widely used in fields such as materials science, geotechnical engineering, and aerodynamics.

[0086] The Kriging model is a kernel interpolation method based on the assumption of a stationary random process, comprising a regression model and random error. The Kriging model outputs variables... G The relationship between (θ) and the input variable θ is expressed as: (9) In the formula, L (θ) represents G The trend surface function (θ) can be directly set as a constant for a standard Kriging model; This represents a stationary random process that follows a normal distribution. N (0, Its covariance is: (10) In the formula, Indicates the variance value; It is a correlation kernel function, which can be set to linear, exponential, or Gaussian kernel functions. Among them, the Gaussian kernel function is the most commonly used, and is expressed as: (11) In the formula, m The dimension of a random variable. Let S represent the model coefficients to be determined. Based on the training sample set S and the corresponding response set Y, the unknown parameters in equations (9), (10), and (11) can be solved using maximum likelihood. After obtaining the values ​​of these unknown parameters, the Kriging model can be used to predict the response value of any new sample point. G (θ) and variance. In this embodiment of the invention, the inverse analysis calculation uses a surrogate model constructed by the DACE toolbox to calculate the stability. Based on the sample set and its corresponding response set, the Kriging model master function of the DACE toolbox is used. dacefit The proxy model can then be constructed. The main function is as follows: (12) In this function, S is the sample set; Y is the response set corresponding to S; regr For the function handle of the regression model; corr The function handle for the relevant function; theta 0 represents the initial guess value for the relevant function parameters; lob and upb For parameters theta The lower and upper limits. Secondly, based on the output. dmodel The structure (containing parameters related to the surrogate model) uses a prediction function. predictor This can replace the stability calculation model to achieve the result output: (13) In this function, dmodel for dacefit The parameter structure of the surrogate model for function fitting; Y represents the input parameter value; Y represents the response value of the proxy model. MSE The estimated prediction variance reflects the accuracy of the predicted values.

[0087] The hybrid adaptive sampling strategy first generates a small number of initial sample points in the entire sample space. Then, it selects new sample points using a sampling strategy and adds them to the initial sample set to retrain the surrogate model. After the new surrogate model is trained, it again uses the sampling strategy to select new sample points and add them to the sample set to continue training the surrogate model. This process is iterated until the surrogate model reaches the expected accuracy. In this method, new sample points are selected by maximizing the quality parameter of each candidate sample, calculated using the following formula: (14) In the formula: D j This is the minimum Euclidean distance between the initial sampling point and the newly added sample point. This term ensures that the samples are uniformly distributed throughout the space. σ j ’2 The prediction variance for each candidate point, i.e., in equation (13) MSE .

[0088] In this embodiment of the invention, a computational model is established in Geo-Studio based on a typical geological profile model of a deformable slope. Specifically, the potential sliding surfaces—the slip zone within the shallow deposit, the long slip zone, the toppling fracture zone, and the bottom boundary of the toppling deformation—are used for back analysis.

[0089] Using the posterior information of the shear strength parameters of each rock and soil mass of the deformable slope updated in step S104 as prior information, and based on the stability observation characteristics of the ecological vegetation of the deformable slope, the stability coefficients of the deformable body under extreme rainstorm and earthquake conditions are assumed respectively. The cohesion and internal friction angle of each potential sliding surface are calculated using the Bayesian probabilistic inverse analysis method. The probabilistic inverse analysis process for each potential sliding surface is basically the same.

[0090] Specifically, assuming that the deformable slope is subjected to the maximum rainfall conditions in recent decades and earthquake conditions with intensity IX to X, the shallow surface stability coefficient and the overall stability coefficient of the deep slip zone are used as observation information to conduct back analysis on the cohesion and internal friction angle of the shallow surface deposits under the rainfall condition and the cohesion and internal friction angle of the deep slip zone under the earthquake condition.

[0091] A back analysis of the cohesion and internal friction angle of the shallow deposit was conducted under a heavy rainfall condition. According to data from the area where the deformed slope is located, the maximum cumulative rainfall over the past few decades was 178 mm in 24 hours, 257 mm in 48 hours, and 292 mm in 72 hours. In this back analysis, the seepage of the deformed body under this heavy rainfall condition was first analyzed using the SEEP / W module in Geo-Studio. The heavy rainfall conditions were set as follows: 0-1 days, rainfall intensity 178 mm / d; 1-2 days, rainfall intensity 79 mm / d; 2-3 days, rainfall intensity 35 mm / d, lasting for a total of three days. The stability analysis was performed using the SLOPE / W module, which automatically searched for the critical slip surface of the shallow deposit and calculated its stability coefficient.

[0092] Using seismic intensities IX to X, a back analysis was conducted on the cohesion and internal friction angle of the deep slip zone. Multiple potential sliding surfaces exist within the deformed slope. Based on relevant specifications and discussions with experts, when performing the back analysis of the shear strength parameters of the deep slip zone, it was assumed that under this extreme seismic condition, the stability coefficient of the deformed body with a long slip zone as the sliding surface would be... F s =1.05, stability coefficient when the toppling fracture zone is the sliding surface. F s =1.10, stability coefficient when the bottom boundary of the tilting deformation is the sliding surface. F s=1.15. According to the horizontal peak ground acceleration (PGA) zoning values ​​and the PGA-intensity correlation table (Table 12) given in the "China Seismic Ground Motion Parameter Zoning Map" (GB18306-2015), when the seismic intensity is greater than or equal to IX, the corresponding PGA is greater than or equal to 0.4g. Given that existing data cannot accurately determine the specific value of the PGA experienced by the deformable slope in the 1950 historical earthquake, for conservative reasons, the horizontal PGA is taken as 0.4g when performing the back analysis of the shear strength parameters of the deep slip zone of the deformable slope. According to the "Code for Design of Slope of Hydropower Project" (NB / T20512-2021) and the "Code for Seismic Design of Hydraulic Structures of Hydropower Project" (NB35047-2015), when the quasi-static method is used to calculate the seismic effect, when the seismic intensity is greater than or equal to VIII, both horizontal and vertical seismic actions should be taken into account. The representative value of vertical seismic acceleration is 2 / 3 of the representative value of horizontal seismic acceleration, the coincidence factor is 0.5, and the reduction factor ζ=0.25.

[0093] Table 12 Comparison of Peak Ground Acceleration and Seismic Intensity

[0094] The Kriging surrogate model is used to approximate the cohesion. c and internal friction angle φ With stability coefficient F s The response relationship between them reduces the computational cost of Bayesian probabilistic inverse analysis. To capture the approximate global response behavior of the stability calculation model across the entire range, 20 initial sample points are generated through uniform sampling. Based on the range of values ​​of the random variable, its upper and lower bounds are determined, and 100 candidate sample points are generated using Latin hypercube sampling (LHS) as the sample pool for newly added samples. The stability coefficient corresponding to each initial sample point is calculated using the Geo-Studio model, thereby constructing the initial Kriging surrogate model based on the initial sample points of the random variable and the corresponding stability coefficients. Finally, the sample space is expanded by a hybrid adaptive sequential sampling method, and the quality parameters of the candidate sample points are calculated using Equation (14). The sample point corresponding to the maximum value of the quality parameter is selected as the newly added sample point and included in the initial sample set to form a new training sample set. The surrogate model is then retrained and iterated continuously until the pre-set convergence criterion is met.

[0095] To verify the accuracy of the surrogate model, 30 additional test sample points were generated using LHS. The stability coefficients for each test sample point were calculated using both the Geo-Studio model and the surrogate model, and then the deterministic coefficients were used. R 2 To evaluate the predictive quality of the proxy model. Figure 9 The stability coefficients of the surrogate model and the numerical model for stability calculation of shallow aggregates are shown. F s Comparison of calculation results. It can be seen that the Kriging surrogate model constructed using this method yields very good results with the numerical model for stability calculation, indicating that the surrogate model can be used to replace the numerical model for stability calculation, reducing computational costs and improving computational efficiency.

[0096] Statistical information on the cohesion and internal friction angle of historical landslide deposits in their natural state was collected as prior information, i.e. μ c = 57.10 kPa, σ c = 26.53 kPa; μ φ = 30.10°, σ φ = 5.13°, representing the stability coefficient of shallow-surface deposits under this rainstorm condition. F s =1.05 is used to update prior information based on observed information. The Markov chain number is set to 4, and the maximum sample size is 100,000. The DREAM algorithm is used to sample the posterior distribution, and the results are as follows. Figure 10 and 11 As shown. Figure 10 The sampling performance of the Markov chain is shown, and it can be found that the Markov chain moves actively in the posterior space, indicating that the Markov chain has excellent sampling performance. Figure 11 The cohesion of shallow-layer deposits is given. c and internal friction angle φ Comparison of posterior and prior probability densities. As shown in the figure, the posterior distribution intervals for cohesion and internal friction angle are significantly narrower than the prior distribution intervals, indicating a significant reduction in uncertainty. Based on the Markov chain sample, the cohesion is obtained... c and internal friction φ The means of the posterior distributions were 50.01 kPa and 25.81°, respectively, with standard deviations of 25.04 kPa and 2.35°. Statistical results show that the means of the posterior distributions for both cohesion and internal friction angle decreased to some extent, indicating that the prior distributions overestimated cohesion and internal friction angle.

[0097] Based on the age determination of some trees within the deformable slope, it can be proven that the slope was basically stable during the 1950 earthquake. Therefore, when conducting the back analysis of the shear strength parameters of the deep potential sliding surface of the deformable body, the stability coefficient of the slope during the 1950 earthquake is used as the baseline. F s=1.05 is used as stability observation information to construct a likelihood function for Bayesian inference.

[0098] When performing back analysis of the shear strength parameters of the slip zone on a deformable slope, the method is the same as that used in the back analysis of shallow deposits. First, an initial stability analysis model is established in Geo-Studio, and seismic loads are input (horizontal seismic coefficient is 0.1; vertical seismic coefficient is 0.033). During the back analysis, the cohesion of the slip zone soil obtained from the first Bayesian update is used. c and internal friction angle φ This will serve as the prior information for this inverse analysis, namely μ c = 44.19 kPa, σ c = 7.27 kPa; μ φ = 27.34°, σ φ =1.13°. Based on experience and experimental results, the shear strength of the underwater portion is taken as 85% of that in the natural state. A Kriging surrogate model is established based on the stability analysis numerical model, with a stability coefficient... F s =1.05 is used to update prior information based on observed information. With the same number of Markov chains and size, the DREAM algorithm is used to sample the posterior distribution. The accuracy of the surrogate model calculation is shown in [reference needed]. Figure 12 The results of the inverse analysis are shown below. Figure 13 and 14 Based on the Markov chain sample, the cohesion of the long slip zone can be obtained. c and internal friction angle φ The means of the posterior distributions were 43.87 kPa and 27.14°, respectively, with standard deviations of 7.24 kPa and 0.95°. Statistically, the prior distributions slightly overestimated cohesion and the angle of internal friction.

[0099] When performing back analysis on the shear strength parameters of the toppled and fractured rock mass of the deformed slope, the water-surface portion of the deformed body is based on the cohesion of the strongly toppled rock mass obtained in the first update. c and internal friction angle φ As prior information, i.e. μ c = 171.55 kPa, σ c =48.92 kPa; μ φ = 29.14°, σ φ = 4.13°. Similarly, the strength of the underwater deformed rock mass is 85% of its natural state. A Kriging surrogate model is established, with a stability coefficient...F s =1.10 updates prior information based on observed information. Using the same number of Markov chains and their sizes, the DREAM algorithm is employed to sample the posterior distribution. For the surrogate model's computational accuracy, see [link to relevant documentation]. Figure 15 The results of the inverse analysis are shown below. Figure 16 and 17 Based on the Markov chain sample, the cohesion of the tilting fracture zone can be obtained. c and internal friction angle φ The means of the posterior distributions were 161.34 kPa and 28.10°, respectively, with standard deviations of 45.47 kPa and 2.16°. Statistically, compared to the prior distributions, the posterior distributions for both cohesion and internal friction angle decreased to varying degrees, while their standard deviations increased. This indicates that the prior distributions overestimated cohesion and internal friction angle.

[0100] When performing back analysis of the shear strength parameters of the bottom boundary of the deformable body at the slope collapse, the water-surface portion of the deformable body is based on the cohesion of the weakly collapsed rock mass obtained in the first update. c and internal friction angle φ As prior information, i.e. μ c = 167.88 kPa, σ c =52.27 kPa; μ φ = 29.39°, σ φ = 4.23°. The strength of the underwater deformed rock mass is 85% of its natural state. A Kriging surrogate model is established, using the stability coefficient... F s =1.15 is used to update prior information based on observed information. The same number of Markov chains and their sizes are set, and the DREAM algorithm is used to sample the posterior distribution. See [link to surrogate model calculation accuracy] for details. Figure 18 The results of the inverse analysis are shown below. Figure 19 and Figure 20 Based on the Markov chain sample, the cohesion at the bottom boundary of the tilted deformable body can be obtained. c and internal friction angle φ The means of the posterior distributions were 172.55 kPa and 30.32°, respectively, and the standard deviations were 51.39 kPa and 3.60°, respectively. Statistically, the posterior distributions of both cohesion and internal friction angle showed a rightward shift, with an increase in the means, indicating that the prior distributions underestimated cohesion and internal friction angle. The standard deviations of both distributions decreased to some extent, suggesting a reduction in uncertainty.

[0101] The back analysis results of the shear strength parameters of each potential sliding surface of the deformable slope show a significant shift in the mean of the posterior distribution of each parameter. This indicates that during parameter back analysis, prior information is continuously calibrated through observation, making the back analysis results closer to reality. Simultaneously, the standard deviations of the posterior distributions of each parameter have decreased to varying degrees, demonstrating that back analysis can reduce parameter uncertainty and improve the reliability of stability calculations.

[0102] The results show that through Bayesian inverse analysis, prior information is effectively updated based on observational information, further reducing uncertainty and bringing the results closer to reality. If prior information is directly used to calculate the stability coefficient of the deformable body, the result will differ significantly from the actual situation, leading to unreliable calculations. In the early stages of geotechnical engineering investigations, when field experiments are not yet fully conducted and accurate mechanical parameters are difficult to obtain, probabilistic inverse analysis can be used to obtain reasonable mechanical parameters for the soil and rock mass.

[0103] In this embodiment of the invention, the method further includes the following steps: S100, based on the geological conditions, deformation characteristics and monitoring information of the deformable slope, determine the potential instability mode of the deformable slope.

[0104] S107, based on the final shear strength parameters of various types of soil and rock, determines the stability coefficient information of deformable slopes under different instability modes.

[0105] S108, Determine the stability of the deformable slope based on the stability coefficient information.

[0106] In this embodiment of the invention, before performing step S101, the potential instability mode of the deformable slope can be determined based on the geological conditions, deformation characteristics and monitoring information of the deformable slope in the target study area. Different instability modes correspond to different potential slip zones (e.g., instability of shallow deposits, instability along long slip zones, instability along toppling fault zones, instability along the bottom boundary of the deformable body, etc.).

[0107] Therefore, based on different instability modes, the shear strength parameters of the corresponding soil and rock masses can be back-analyzed using multi-source information (historical prior information, experimental information, vegetation observation information, etc.) (steps S101~S106 above) to obtain the final shear strength parameters. Based on the final shear strength parameters, the stability coefficients of each instability mode under different working conditions are calculated to evaluate the stability of the deformable slope.

[0108] Specifically, based on recommendations from relevant standards such as the "Code for Design of Slopes in Hydropower Projects" (NB / T10512-2021), the MP method within the rigid body limit equilibrium method is adopted to calculate the stability of deformable slopes, using Geo-Studio as the calculation software. The basic calculation principles are referenced from the "Code for Design of Slopes in Hydropower Projects" (NB / T10512-2021).

[0109] In this embodiment of the invention, when performing stability calculations, based on actual field investigation conditions and previous research results on the relationship between long-term strength and peak strength of slip zone soil and rock mass, a reduction is made based on the posterior mean of the back analysis. For the slip zone soil, the field findings indicate that the slip zone soil is relatively dense, therefore, the ratio of its long-term strength to peak strength is taken as 0.85, i.e. c value and tan φ Each value is reduced by 0.85; for deformed rock masses, the ratio of long-term strength to peak strength is taken as 0.9; the parameters of the underwater part are based on experience and are reduced by 85% of the parameters under natural conditions. The calculated values ​​of rock and soil strength parameters in the embodiments of this invention are shown in Table 13.

[0110] Table 13 Values ​​of Calculation Parameters for Potential Slip Surface Strength of Deformable Slopes

[0111] According to historical rainfall data of the study area, in the calculation of the stability of the deformable slope, different combinations of rainfall intensity and duration were adopted to set up three rainstorm conditions, and the stability coefficient of the deformable slope was calculated after the rainfall.

[0112] Based on the horizontal peak ground acceleration (PGA) zoning values ​​and the PGA-intensity comparison table given in the "China Seismic Ground Motion Parameter Zoning Map" (GB18306-2015), when calculating the stability of deformable slopes, different seismic intensities are considered, and one seismic condition is set up to calculate the stability coefficient of deformable slopes under the seismic condition.

[0113] Stability calculations employed rigid body limit equilibrium theory, using a geological model of the deformable slope as a foundation. Stability calculation models for each profile of the deformable slope were constructed in Geo-Studio. Based on field investigations and analysis of survey data, the causal mechanisms of toppling deformation and potential instability failure modes were summarized, revealing the coexistence of multiple deformation failure modes. Therefore, in stability calculations, the toppling slip zone (long slip zone), toppling fracture zone, and toppling deformation bottom boundary of each zone were used as potential sliding surfaces to calculate the stability coefficients of each zone under different working conditions.

[0114] In the above exemplary case, based on the determined physical and mechanical parameters of each rock and soil mass of the deformable body, the Geo-Studio software was used to perform stability calculations on different potential sliding surfaces of each section of the deformable body slope under different working conditions based on the limit equilibrium method. The calculation results are shown in Table 14.

[0115] Table 14 Statistical Table of Calculation Results of Deformable Body Slope Stability under Different Working Conditions

[0116] In this embodiment of the invention, the stability state of each zone of the deformable slope under different working conditions can be divided according to the table of slope stability state in Section 6.5 of the "Code for Engineering Geological Investigation of Slopes of Hydropower Projects" (NB / T 10513-2021).

[0117] Based on the same inventive concept, embodiments of the present invention also provide a probabilistic inverse analysis system for shear strength parameters of soil and rock masses based on multi-source information fusion, the system comprising: The test data acquisition module is used to determine the potential instability mode of the deformable slope and to acquire test data on the shear strength parameters of the soil and rock masses of the deformable slope, including slip zone soil, landslide deposits, strongly tilting rock masses, and weakly tilting rock masses; the shear strength parameters include: cohesion and internal friction angle; The test information determination module is used to process the test data of the shear strength parameters of the soil and rock mass using the non-parametric Bootstrap method to obtain the corrected statistical characteristics and distribution information of the test parameters, which are used as test information. The prior information determination module is used to determine the historical parameter statistical characteristics and historical parameter distribution information of each type of soil and rock mass based on the shear strength parameter data of the soil and rock mass in similar historical engineering cases, as prior information. The posterior parameter determination module is used to update the shear strength parameters of each soil and rock mass after the first calibration by Bayes' formula based on the prior information and the test information. The observation information determination module is used to infer the stability state of deformable slopes under historical extreme working conditions using dendrochronology, and obtain the corresponding stability coefficients as observation information. The inverse analysis module is used to construct a slope stability calculation model for deformable bodies. Combining the surrogate model and the Bayesian probabilistic inverse analysis method, the module uses the posterior distribution information as the new prior information and performs inverse analysis of shear strength parameters for various types of soil and rock masses based on the observation information to obtain the final shear strength parameters.

[0118] Based on the same inventive concept, embodiments of the present invention also provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the steps in the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in any of the above embodiments.

[0119] Based on the same inventive concept, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps in the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion described in any of the above embodiments.

[0120] Based on the same inventive concept, embodiments of the present invention provide a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps in the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in any of the above embodiments.

[0121] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0122] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, embodiments of the present invention can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0123] The above provides a detailed description of the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion provided by the present invention. Specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A probabilistic inverse analysis method for shear strength parameters of soil and rock masses based on multi-source information fusion, characterized in that, The method includes: Determine the potential instability mode of the deformable slope and obtain test data on the shear strength parameters of the soil and rock masses of the deformable slope, including slip zone soil, landslide deposits, strongly tilted rock masses, and weakly tilted rock masses; the shear strength parameters include: cohesion and internal friction angle; The test data of the shear strength parameters of the soil and rock mass were processed using the non-parametric Bootstrap method to obtain the corrected statistical characteristics and distribution information of the test parameters, which were used as test information. For each type of soil and rock mass, based on the shear strength parameter data of the corresponding soil and rock mass in similar historical engineering cases, the historical parameter statistical characteristics and historical parameter distribution information of the shear strength parameters are determined as prior information; Based on the prior information and the experimental information, the information is updated using Bayes' formula to obtain the posterior distribution information of the shear strength parameters of each soil and rock mass after the initial calibration. Dendrochronology was used to infer the stability of deformable slopes under historical extreme working conditions and obtain the corresponding stability coefficients as observation information. A slope stability calculation model for deformable bodies is constructed. Combining the surrogate model and the Bayesian probabilistic inverse analysis method, the posterior parameter distribution information is used as the new prior information. Based on the observation information, the shear strength parameters of various types of soil and rock masses are back-analyzed to obtain the final shear strength parameters.

2. The probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion according to claim 1, characterized in that, The method further includes: Based on the geological conditions, deformation characteristics, and monitoring information of the deformable slope, the potential instability modes of the deformable slope are determined. Based on the final shear strength parameters of various types of soil and rock, the stability coefficient information of deformable slopes under different instability modes is determined; The stability of the deformable slope is determined based on the stability coefficient information.

3. The probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion according to claim 1, characterized in that, The test data of shear strength parameters of soil and rock masses in slip zone soil, landslide deposits, strongly tilting rock masses, and weakly tilting rock masses of deformable slopes were determined based on the following steps: Sampling was conducted on the slip zone soil, landslide deposits, strongly tilting rock mass and weakly tilting rock mass of the target deformable slope to obtain soil and rock samples. For slip zone soil: Based on undisturbed slip zone soil samples, rapid shear tests were conducted to obtain test data on the shear strength parameters of slip zone soil in its natural and saturated states; For landslide deposits, strongly tilted rock masses, and weakly tilted rock masses: physical parameters of soil and rock samples were obtained through physical experiments and rock wave velocity tests, including natural unit weight, saturated unit weight, and longitudinal wave velocity; mechanical parameters of the rock samples were obtained through uniaxial compression tests and conventional triaxial tests, including uniaxial compressive strength, cohesion, internal friction angle, and elastic modulus; the GSI value was quantified by the surface characteristics and integrity coefficient of the rock mass structure; based on the Hoek-Brown strength criterion, combined with mechanical parameters, physical parameters, and GSI, test data of shear strength parameters for landslide deposits, strongly tilted rock masses, and weakly tilted rock masses were obtained.

4. The probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion according to claim 1, characterized in that, Dendrochronology was used to infer the stability state of deformable slopes under historical extreme conditions, and the corresponding stability coefficients were obtained, including: Based on tree sampling inside and outside the deformed slope, combined with dendrochronological analysis, the ages of trees inside and outside the deformed slope, radial growth characteristics of trees inside and outside the deformed slope, and changes in growth rate of trees inside and outside the deformed slope were determined. Inferring the stability state of deformable slopes under historical extreme working conditions; The corresponding stability coefficients are determined based on the stability state and expert experience analysis.

5. The probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion according to any one of claims 1-4, characterized in that, A slope stability calculation model for deformable bodies is constructed. Combining a surrogate model and Bayesian probabilistic inverse analysis, and using the posterior distribution information as new prior information, inverse analysis is performed on the shear strength parameters of various types of soil and rock masses based on the observed information, including: Based on the surrogate model, an explicit functional relationship between the input parameters and the output of the stability calculation model is constructed. The input parameters include cohesion and internal friction angle, and the model output is the stability coefficient. The surrogate model generates initial sample points for the input parameters through Latin hypercube sampling, and constructs an initial surrogate model based on the initial sample points and the corresponding stability coefficients. Candidate sample points are generated using hybrid adaptive sequential sampling, which serves as the sample pool for newly added samples. The quality parameters of the candidate sample points are calculated, and the sample points corresponding to the maximum quality parameters are selected as newly added sample points. These are then included in the initial sample set to form a new training sample set. The surrogate model is retrained and iterated continuously until the pre-set convergence criteria are met, resulting in a stability calculation model. Based on the stability calculation model and the observation information, a new posterior distribution of shear strength parameters for various types of soil and rock masses is determined by Bayesian probabilistic inverse analysis. The new posterior distribution is sampled using the adaptive differential evolution Metropolis algorithm, and the final shear strength parameters are obtained based on the Markov chain samples.

6. A probabilistic inverse analysis system for shear strength parameters of soil and rock masses based on multi-source information fusion, characterized in that, The system includes: The test data acquisition module is used to determine the potential instability mode of the deformable slope and to acquire test data on the shear strength parameters of the soil and rock masses of the deformable slope, including slip zone soil, landslide deposits, strongly tilting rock masses, and weakly tilting rock masses; the shear strength parameters include: cohesion and internal friction angle; The test information determination module is used to process the test data of the shear strength parameters of the soil and rock mass using the non-parametric Bootstrap method to obtain the corrected statistical characteristics and distribution information of the test parameters, which are used as test information. The prior information determination module is used to determine the historical parameter statistical characteristics and historical parameter distribution information of each type of soil and rock mass based on the shear strength parameter data of the soil and rock mass in similar historical engineering cases, as prior information. The posterior parameter determination module is used to update the shear strength parameters of each soil and rock mass after the first calibration by Bayes' formula based on the prior information and the test information. The observation information determination module is used to infer the stability state of deformable slopes under historical extreme working conditions using dendrochronology, and obtain the corresponding stability coefficients as observation information. The inverse analysis module is used to construct a slope stability calculation model for deformable bodies. Combining the surrogate model and the Bayesian probabilistic inverse analysis method, the module uses the posterior distribution information as the new prior information and performs inverse analysis of shear strength parameters for various types of soil and rock masses based on the observation information to obtain the final shear strength parameters.

7. The probabilistic inverse analysis system for shear strength parameters of soil and rock mass based on multi-source information fusion according to claim 6, characterized in that, The system also includes: The potential instability mode determination module is used to determine the potential instability mode of the deformable slope based on the geological conditions, deformation characteristics and monitoring information of the deformable slope. The stability coefficient determination module is used to determine the stability coefficient information of deformable slopes under different instability modes based on the final shear strength parameters of various types of soil and rock masses. The stability determination module is used to determine the stability of the deformable slope based on the stability coefficient information.

8. An electronic 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 probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in any one of claims 1-5.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in any one of claims 1-5.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps in the probabilistic inverse analysis method for shear strength parameters of soil and rock mass based on multi-source information fusion as described in any one of claims 1-5.

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