A method for estimating and predicting the unfrozen soil area of the Qinghai-Tibet Plateau railway subgrade

Abstract

The present invention relates to a method for estimating and predicting the area of unfrozen soil in the railway subgrade of the Qinghai-Tibet Plateau. The method comprises the following steps: S1, sorting out the environmental data and socioeconomic data of the railway subgrade of the Qinghai-Tibet Plateau; S2, estimating and predicting the area of unfrozen soil in the railway subgrade of the Qinghai-Tibet Plateau and establishing a model: constructing a Bayesian interlayer structure model with seven parameters including soil type, temperature, rainfall, vegetation cover, engineering construction, anthropogenic heat source, and railway operation, and estimating the area of unfrozen soil; S3, realizing the Bayesian parameter update of the change trend model of the area of unfrozen soil in the railway subgrade of the Qinghai-Tibet Plateau: for the seven Bayesian parameters, first using the method based on Markov chain Monte Carlo, and then using Bayes' theorem to update the prior distribution and passing through the posterior distribution; S4, constructing the change trend model of the area of unfrozen soil in the railway subgrade of the Qinghai-Tibet Plateau; S5, formulating corresponding prevention and control measures according to the prediction results, and maintaining and managing the railway subgrade. The present invention can improve the prediction accuracy and precision.

Description

Technical Field

[0001] The present invention relates to the technical field of natural disaster prediction, and particularly to a method for estimating and predicting the area of unfrozen soil of the railway subgrade on the Qinghai-Tibet Plateau. Background Art

[0002] The Qinghai-Tibet Plateau is a typical ecologically fragile area, extremely sensitive to human activities and climate warming, and once damaged, it cannot be restored. Affected by the combined effects of global warming and humidification and human activities, the permafrost area on the Qinghai-Tibet Plateau is in a continuous state of degradation, mainly manifested as rising ground temperature, increasing thickness of the active layer, and melting of the permafrost layer, etc. With the melting of the permafrost, the increase in the thickness of the active layer of the permafrost, and the rise in the permafrost temperature, the area of unfrozen soil of the railway subgrade on the Qinghai-Tibet Plateau increases, ultimately leading to a decline in the stability of engineering structures, the occurrence of diseases such as subgrade settlement and cracks, and further seriously threatening the safety and stability of the railway subgrade in this area. At the same time, a large number of subgrade diseases and potential risks appear during the operation of trains, resulting in great difficulty in maintaining the Qinghai-Tibet Railway. Therefore, by accurately estimating the area of unfrozen soil of the Qinghai-Tibet Railway, it is helpful to better understand and monitor the railway safety status, timely discover the trends and causes of permafrost degradation, deepen the understanding of the impact of land transportation on the ecological environment, and provide a scientific basis for the country to formulate reasonable road construction strategies.

[0003] However, the existing methods for estimating the area of unfrozen soil of the railway subgrade on the Qinghai-Tibet Plateau are time-consuming and laborious in obtaining data. Especially in the Qinghai-Tibet Plateau region, manual measurement has disadvantages such as low efficiency and high cost, and some field estimation methods may not be able to achieve high precision, especially in complex and ever-changing natural environments. And the methods relying on remote sensing may be limited by factors such as the time resolution, spatial resolution of satellites, vegetation occlusion, and image quality, resulting in the inability to effectively monitor the changes on a small scale or short time scale. In addition, due to seasonal changes, climate anomalies, etc. that may affect the actual situation of permafrost, the existing estimation techniques may not be able to comprehensively consider these factors. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for estimating and predicting the area of unfrozen soil of the railway subgrade on the Qinghai-Tibet Plateau with improved precision and accuracy.

[0005] To solve the above problems, a method for estimating and predicting the area of unfrozen soil of the railway subgrade on the Qinghai-Tibet Plateau according to the present invention includes the following steps:

[0006] S1 Organize the environmental data and socioeconomic data of the railway subgrade on the Qinghai-Tibet Plateau;

[0007] S2 Estimate and predict the area of unfrozen soil of the railway subgrade on the Qinghai-Tibet Plateau and establish a model:

[0008] Construct a Bayesian hierarchical structure model with seven parameters: soil type, temperature, rainfall, vegetation cover, engineering construction, anthropogenic heat source, and railway operation, and estimate the unfrozen soil area area according to the following formula:

[0009] area = V × logθ; logθ = logθ g1 + logθ g2 ;

[0010] Where: V is the frozen soil area, in km 2 ; logθ is the frozen soil degradation rate; θ is the frozen soil melting intensity, in MPa; θ g1 is the frozen soil melting intensity caused by natural factors, in MPa; θ g2 is the frozen soil melting intensity caused by anthropogenic factors, in MPa;

[0011] S3 Implementation of Bayesian parameter update for the unfrozen soil area change trend model of the Qinghai-Tibet Railway subgrade:

[0012] For the seven Bayesian parameters in the step S2, first use the method based on Markov chain Monte Carlo, and then use Bayes' theorem to update the prior distribution and obtain the posterior distribution;

[0013] S4 Construction of the unfrozen soil area change trend model for the Qinghai-Tibet Railway subgrade:

[0014] Construct the following unfrozen soil area change exploration model according to natural factors and anthropogenic factors:

[0015]

[0016] Where: π att represents the frozen soil change caused by natural factors under a certain type of frozen soil; π def represents the frozen soil change caused by anthropogenic factors under a certain type of frozen soil; π represents the frozen soil type, and 1, 2, and 3 are used to indicate three types of frozen soil: short-term frozen soil, seasonal frozen soil, and permafrost;

[0017] S5 Develop corresponding prevention and control measures based on the prediction results, and maintain and manage the railway foundation.

[0018] The environmental data in the step S1 includes vegetation coverage, temperature, rainfall, soil type, and climate change; the social and economic data includes population density, artificial space light distribution, engineering construction, anthropogenic heat source, and railway operation.

[0019] In the step S4, the frozen soil type is quantitatively described by a truncated normal distribution for the occurrence of frozen soil melting of the Qinghai-Tibet Railway subgrade, and the value range of the variable frozen soil type is limited between (1, 3).

[0020] The present invention has the following advantages compared with the prior art:

[0021] 1. Based on the characteristic attributes of the unfrozen soil area of the Qinghai-Tibet Plateau railway subgrade, by fitting a function for the unfrozen soil area in a multi-layer model framework, considering soil type, temperature, human activities, and parameter differences during function fitting, the accuracy of estimating the unfrozen soil area of the Qinghai-Tibet Plateau railway subgrade is improved.

[0022] 2. By coupling 7 basic parameters describing frozen soil degradation to form a function, which focuses on relating temperature to soil type, rainfall, and elevation to achieve the estimation and prediction of the causes of frozen soil degradation or differences in environmental parameter thresholds, and then formulating corresponding railway subgrade frozen soil protection measures based on the estimation results, providing support and suggestions for the treatment, transformation, and route selection of the unfrozen soil of the Qinghai-Tibet Plateau railway subgrade.

[0023] 3. By introducing the truncated normal distribution to evaluate the performance method of the model, the problem of conditional probability distortion is solved, and the accuracy and reliability of model prediction are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The following further details the specific embodiments of the present invention with reference to the accompanying drawings.

[0025] Figure 1 is the flow chart of the present invention. SPECIFIC EMBODIMENTS

[0026] The present invention comprehensively considers multiple factors affecting the frozen soil area by using the Bayesian interlayer structure model, including elevation, soil type, temperature, rainfall, human activities, etc., as well as the mutual relationships of respective independent variable factors, and establishes a flexible and adjustable interlayer structure model. Through the analysis and inference of multiple levels, the unfrozen soil area and development trend of the Qinghai-Tibet Plateau railway subgrade are accurately estimated, thereby improving the accuracy and reliability of estimating the unfrozen soil area of the Qinghai-Tibet Plateau railway subgrade.

[0027] A method for estimating and predicting the unfrozen soil area of the Qinghai-Tibet Plateau railway subgrade includes the following steps:

[0028] S1. Sorting out the environmental data and socioeconomic data of the Qinghai-Tibet Plateau railway subgrade:

[0029] Collecting the relevant environmental data and socioeconomic data along the Qinghai-Tibet Plateau railway subgrade, and determining the characteristic attribute variables affecting the change of the frozen soil area under the railway subgrade to establish a comprehensive spatial data set. The environmental data includes vegetation coverage, temperature, rainfall, soil type, and climate change; the socioeconomic data includes population density, artificial space light distribution, engineering construction, anthropogenic heat sources, and railway operation.

[0030] Obtain multiple data composed of the above-mentioned data feature vectors from a preset database of the degradation characteristics of frozen soil in railway subgrades. After forming the obtained multiple data into a training sample set and a test sample set respectively, further perform preprocessing of data discretization and normalization to eliminate the influence of units and quantity level differences on the model.

[0031] The changes in the temperature field near the lower part and the toe of the railway subgrade are mainly caused by two aspects: natural factors (including soil type, temperature, rainfall, vegetation coverage, etc.) and human factors (including engineering construction, human heat sources, railway operation, etc.). Under the combined action of these two types of factors, permafrost may warm up, leading to problems such as a decrease in the area of permafrost regions and the transformation of low-temperature permafrost to high-temperature permafrost. Under the dual influence of climate change and engineering loads, permafrost subgrades are prone to problems such as thaw settlement deformation and longitudinal cracks, seriously affecting the service life and safety of the road. Therefore, the frozen soil data of the railway subgrade adopted in the present invention is the average state under modern average conditions, and the obtained prediction results are based on the changes in the existing stable state of frozen soil in railway subgrades.

[0032] The present invention collates the temperature survey data of the permafrost regions along the Qinghai-Tibet Railway observed and recorded during two time periods from 1991 to 1992 and from 2007 to 2008. After normalization, 1991 - 1992 is determined as the model training data set, and 2007 - 2008 is the model test data set.

[0033] S2 Estimation and prediction modeling of the unfrozen soil area of the Qinghai-Tibet Railway subgrade:

[0034] Construct a Bayesian interlayer structure model with 7 parameters including soil type, temperature, rainfall, vegetation coverage, engineering construction, human heat source, and railway operation, and estimate the unfrozen soil area area according to the following formula:

[0035] area = V × logθ; logθ = logθ g1 + logθ g2 ;

[0036] In the formula: V is the area of frozen soil, with the unit of km 2 ; logθ is the degradation rate of frozen soil; θ is the thawing intensity of frozen soil, with the unit of MPa; θ g1 is the thawing intensity of frozen soil caused by natural factors, with the unit of MPa; θ g2 is the thawing intensity of frozen soil caused by human factors, with the unit of MPa.

[0037] The specific process is as follows:

[0038] The present invention constructs a Bayesian interlayer structure model to determine the relationships and parameters of each level, and estimates the area of unfrozen soil each year (a latent or unobserved variable). In the present invention, for each year, a function based on the degradation rate of the frozen soil area after logical transformation is simulated, which is achieved by fitting a degradation function for the frozen soil area each year separately in the framework of a multi-layer Bayesian model, where "natural factors" and "human factors" are used as varying effects (also often referred to as "random effects").

[0039] Estimate the degradation rate of the frozen soil area of the railway subgrade by fitting a functional form separately for the change in the frozen soil area each year. Then calculate the total area of the unfrozen subgrade based on the degraded frozen soil area.

[0040] The model used to describe the change in the frozen soil area incorporates seven varying parameters, namely: 4 in natural factors (soil type, temperature, rainfall, vegetation cover) and 3 in human factors (engineering construction, anthropogenic heat source, railway operation). These parameters correspond to the degradation rate of the frozen soil area each year (y; the annual frozen soil degradation rate), y = (y g1 , y g2 ), and the elements y of the vector observing the frozen soil change, y = (y g1 , y g2 ) are used as independent Poisson models, where the change in the frozen soil caused by natural factors is y g1 , and the change in the frozen soil changed by human factors is y g2 .

[0041] The degraded frozen soil area is the sum of the degraded frozen soil area caused by natural and human factors and the degraded frozen soil area caused by human factors.

[0042] Because this model involves multiple variables, multiple dimensions and ranges, and units during operation, specific parameters need to be constrained, that is, normalized to [0, 1]. For the convenience of calculation, the function is converted into a logarithmic function. The following formula is used to estimate the parameters in the model training dataset and the initial estimation model, and thus an estimation model for the degraded frozen soil area, that is, an estimation model for the unfrozen soil area, is obtained.

[0043] Calculate the total area of the unfrozen soil based on the degraded frozen soil area, and accumulate all the rates causing the degradation of the frozen soil, that is: the annual unfrozen soil area is defined as the frozen soil area multiplied by the frozen soil degradation rate to obtain the unfrozen soil area. The unfrozen soil area is represented by area, the frozen soil area is represented by V, and the frozen soil degradation rate is represented by logθ, that is, area = V × logθ.

[0044] The present invention estimates the area of unfrozen soil of the railway foundation based on historical data and probabilistic inference. In the present invention, the unfrozen area and the evolution trend of the frozen soil of the Qinghai-Tibet Railway subgrade can be calculated by equations (5) and (6) respectively.

[0045] Verify with the data from 1991 - 1992, and use Vs to represent the initial permafrost area; use V to represent the permafrost area in 2007 - 2008. f Represent.

[0046] Verify the following formula with the data from 1991 - 1992:

[0047] y gj |θ gj ~Poisson(θ gj ) ………(1)

[0048] In the formula: the change in permafrost caused by natural factors is y g1 , and the change in permafrost caused by human factors is y g2 .

[0049] θ = (θ g1 , θ g2 ) ………(2)

[0050] In the formula: θ is the permafrost thawing intensity, θ g1 is the permafrost thawing intensity caused by natural factors, and θ g2 is the permafrost thawing intensity caused by human factors. And use the log - random - effect linear model to obtain these two permafrost thawing intensities.

[0051] logθ g1 = Elevation + att h(g) + def a(g) ………(3)

[0052] In the formula: Elevation represents the elevation, and take the elevation Elevation as a fixed change factor; att h(g) represents the temperature, and def a(g) represents the rainfall.

[0053] logθ g2 = att a(g) + def h(g) ………(4)

[0054] In the formula: att a(g) represents the engineering construction, and def h(g) represents the railway operation.

[0055] logθ = logθ g1 + logθ g2 ………(5)

[0056] In the formula: logθ is the permafrost degradation rate.

[0057] area = V × logθ ………(6)

[0058] where: area is the unfrozen soil area, V is the frozen soil area, and logθ is the frozen soil degradation rate (the sum of the frozen soil degradation rates caused by natural and human factors).

[0059] Assume that Elevation follows the least informative normal prior distribution (0, 0.0001), then

[0060] Elevation ∼ Normal(0, 0.0001) ………(7)

[0061] At this time, the changes in frozen soil caused by natural and human factors follow a normal distribution:

[0062] att t ∼ Normal(μ att , τ att ), def t ∼ Normal(μ def , τ def ). ………(8)

[0063] where: att t represents the natural factors under the asymmetric center distribution, and def t represents the human factors under the asymmetric center distribution. For each t = 1,.., π, π represents the frozen soil type, and 1, 2, 3 are used to indicate three types of frozen soil: short-term frozen soil, seasonal frozen soil, and permafrost.

[0064]

[0065] Equation (9) indicates that when the natural and human factors are set to 0, the frozen soil foundation does not melt.

[0066] μ att ∼ Normal(0, 0.0001), μ def ∼ Normal(0, 0.0001),

[0067] τ att ∼ Gamma(0.1, 0.1), τ def ∼ Gmama(0.1, 0.1). ………(10)

[0068] To ensure the accuracy of the formula, the hyperprior of the frozen soil melting effect caused by natural and human factors in formula (10) is independently modeled. It is stipulated that μ represents the natural factors and τ represents the human factors, and both follow the location parameter of the least informative distribution and the gamma distribution;

[0069] η = (μ att , μ def , τatt , τ def ) ………(11)

[0070] In the formula: η represents other potential factors that can cause the thawing of frozen soil.

[0071] S3 Bayesian parameter update implementation for the unfrozen soil area change trend model of the Qinghai-Tibet Plateau railway subgrade:

[0072] For the 7 Bayesian parameters in step S2, first use the method based on Markov Chain Monte Carlo, and then use Bayes' theorem to update the prior distribution, and pass through the posterior distribution (1,000 iterations on three chains).

[0073] For the spatio-temporal distribution and change trend model of frozen soil thawing, Bayesian update of the parameter probability distribution, check the convergence of the chains to ensure that they are all within 0.001 near 0, and visually evaluate the mixing of all chains.

[0074] The posterior distribution of the coefficients is summarized by their median and 95% highest posterior density interval HPDI (i.e., the narrowest posterior interval containing 95% of the probability mass, corresponding to the coefficient values most consistent with the data). When the 95% HPDI of the coefficients of the model covariates does not contain zero, they are considered important, indicating that there is strong enough confidence to report a positive or negative effect.

[0075] S4 Construction of the unfrozen soil area change trend model of the Qinghai-Tibet Plateau railway subgrade:

[0076] Construct the following unfrozen soil area change exploration model according to natural factors and human factors:

[0077]

[0078] In the formula: π att represents the frozen soil change caused by natural factors under a certain type of frozen soil; π def represents the frozen soil change caused by human factors under a certain type of frozen soil; π represents the frozen soil type, and 1, 2, and 3 are used to indicate three types of frozen soil: short-term frozen soil, seasonal frozen soil, and permafrost.

[0079] The specific process is as follows:

[0080] Because the basis of the unfrozen soil area prediction model of the railway subgrade in the present invention is a Bayesian hierarchical model, the present invention is divided into 2 layers, that is, a unfrozen soil area change exploration model is constructed according to natural factors and human factors.

[0081] Since the shrinkage of the frozen soil area is usually attributed to multiple mechanisms, different data sets and methods are used to best link the patterns identified in the long-term data with the known potential driving factors of frozen soil degradation.

[0082] To reduce the over - shrinkage caused by the hierarchical model, based on the type of frozen soil, the frozen soil foundation is divided into three types: short - term frozen soil, seasonal frozen soil, and permafrost. Let π represent the type of frozen soil, and use 1, 2, and 3 to indicate the three types of frozen soil respectively.

[0083] Each soil type depends on a vector of prior probabilities, and π is specified using a Dirichlet distribution with parameters. att and π def The minimum - information - content model (1, 1, 1) of, but obviously π can contain (possibly subjective) prior information att and π def The vector is used to represent the prior chance, and then the effects of each frozen soil foundation of the railway under the action of natural factors and human factors are modeled. Therefore, the model of the observable variable is invariant, and the models of other hyperparameters are as follows in formulas (13) and (14). Assuming that each type of frozen soil has two potential unobservable variables, namely the natural - factor variable grp att (π) and the human - factor variable grp def (π), since the values of grp att (π) and grp def (π) are unknown, the non - central t distribution (nct) is used. Essentially, the following formula defines a mixed model of the degradation effect of frozen soil under natural and human activities.

[0084] Verify the following model using the results from 2007 - 2008:

[0085]

[0086] In the formula: π att represents the change in frozen soil caused by natural factors under a certain type of frozen soil, and π def represents the change in frozen soil caused by human factors under a certain type of frozen soil.

[0087]

[0088] In the formula: In the formula: nct represents the non - central t distribution, v represents the degrees of freedom, v = 4; att t and def t represent that the changes in frozen soil caused by natural factors and human factors conform to the non - central t distribution, and grp(t) represents the unobservable variable; for each t = 1,.., π, π represents the type of frozen soil, and 1, 2, and 3 are used to indicate the three types of frozen soil respectively: short - term frozen soil, seasonal frozen soil, and permafrost. μ represents the natural factor, and τ represents the human factor. represents the change in frozen soil caused by natural factors and The permafrost changes caused by human factors, represent the permafrost changes caused by natural factors without the change of human factors, represent the changes caused by human factors without the change of natural factors.

[0089] Formula (14) is derived from formula (13), which is a mixed model of permafrost changes caused by natural and human factors.

[0090]

[0091] In the formula: att t represents the permafrost changes mainly caused by natural factors, def t represents the permafrost changes mainly caused by human factors, nct represents the asymmetric center distribution, v represents the degree of freedom, v = 4; π att represents the permafrost changes caused by natural factors under a certain type of permafrost, π def represents the permafrost changes caused by human factors under a certain type of permafrost; for each t = 1,.., π, π represents the permafrost type, and 1, 2, 3 are used to indicate three types of permafrost: short-term permafrost, seasonal permafrost, and permafrost. represents the permafrost changes of a certain type caused by natural factors and the permafrost changes of a certain type caused by human factors, represents the permafrost changes of a certain type caused by natural factors without the change of human factors, represents the permafrost changes of a certain type caused by human factors without the change of natural factors.

[0092]

[0093] Formulas (15) and (16) respectively represent two truncated normal distributions (truncated normal distriution, trunc) of short-term permafrost and permafrost. According to the position and scale parameters of the asymmetric center distribution (nct), if the permafrost melting state is different under natural and human factors according to different permafrost types, it is very likely to show a slow permafrost melting rate, but only the scale and position parameters of the permafrost melting of the Qinghai-Tibet Railway subgrade may be different. Therefore, the occurrence of permafrost melting of the Qinghai-Tibet Railway subgrade by permafrost type can be quantitatively described by the truncated normal distribution (trunc), k represents the variable permafrost type, and the value range of the variable permafrost type is restricted between (1, 3).

[0094]

[0095] Formula (17) indicates that seasonal permafrost conforms to the normal distribution.

[0096]

[0097] Formula (18) represents All use the minimum information gamma distribution.

[0098] S5 formulates corresponding prevention and control measures according to the prediction results, and maintains and manages the railway foundation

[0099] If the railway subgrade in the study area continues to degrade at the current permafrost degradation rate, the thawing of the underlying permafrost may cause greater settlement deformation of the railway subgrade. Therefore, the estimation model of the unfrozen area of the railway subgrade in the study area is verified using the model test dataset of the present invention, and corresponding permafrost protection measures are formulated according to the estimation results. In the construction and maintenance of railway engineering, high-power forced cooling measures should be adopted to reduce the ground temperature. At the same time, combined with the anti-freezing and thawing measures of the railway line, the results of freeze-thaw monitoring and subgrade filler verification, engineering countermeasures and suggestions are put forward for reference and guidance in the future exploration, design and construction of railway subgrades in the permafrost region of the Qinghai-Tibet Plateau.

[0100] At the same time, the historical data from 1991 to 1992 and the measured unfrozen area of the railway subgrade in 2007-2008 are used to verify the model to ensure the prediction ability and accuracy of the model. At the same time, it is adjusted according to the specific geological and geomorphic conditions in different regions to adapt to the prediction of the unfrozen area of railway subgrades in different regions and improve its universality and application scope.

Claims

1. A method for estimating and predicting the unfrozen soil area of ​​the Qinghai-Tibet Plateau railway embankment, comprising the following steps: S1 Qinghai-Tibet Plateau Railway subgrade environmental data and socio-economic data compilation; S2 Estimation and prediction modeling of unfrozen soil area of ​​Qinghai-Tibet Plateau railway embankment: The Bayesian interlayer structure model was constructed based on seven parameters, namely soil type, temperature, rainfall, vegetation cover, engineering construction, anthropogenic heat source, and railway operation, and the unfrozen soil area was estimated as follows: area=V×logθ;logθ=logθ g1 +logθ g2 ; Where: V is the frozen ground area, unit km 2 ; logθ is the permafrost degradation rate; θ is the permafrost thawing intensity, unit: MPa; θ g1 is the intensity of frozen soil thawing caused by natural factors, unit: MPa; θ g2 is the intensity of frozen soil thawing caused by human factors, unit: MPa; S3 Bayesian parameter update of the Qinghai-Tibet Plateau railway subgrade unfrozen soil area change trend model: For the 7 Bayesian parameters in step S2, first use a Markov Chain Monte Carlo method, then use the Bayesian theorem to update the prior distribution, and then use the posterior distribution; S4 Construction of the model for the trend of unfrozen soil area change on the Qinghai-Tibet Plateau railway embankment: The following unfrozen soil area change exploration model is constructed based on natural and human factors: Where: π att Indicates the changes of frozen soil caused by natural factors under a certain type of frozen soil; π def It indicates the change of frozen soil caused by human factors under a certain type of frozen soil; π indicates the type of frozen soil, and 1, 2, and 3 indicate three types of frozen soil: short-term frozen soil, seasonal frozen soil, and permafrost; S5 formulates corresponding prevention and control measures, maintenance and management of railway foundation according to the prediction results.

2. The method for estimating and predicting the unfrozen soil area of ​​the Qinghai-Tibet Plateau railway subgrade according to claim 1, characterized in that: The environmental data in step S1 include vegetation coverage, temperature, rainfall, soil type, and climate change; the socio-economic data include population density, artificial space lighting distribution, engineering construction, artificial heat sources, and railway operations.

3. The method for estimating and predicting the unfrozen soil area of ​​the Qinghai-Tibet Plateau railway subgrade according to claim 1, characterized in that: In step S4, the frozen soil type uses a truncated normal distribution to quantitatively describe the occurrence of frozen soil thawing on the Qinghai-Tibet Railway subgrade, and limits the value range of the variable frozen soil type to between (1, 3).

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