Qinghai-Tibet Plateau railway roadbed unfrozen soil area estimation and prediction method

Abstract

The invention relates to a method for estimating and predicting the unfrozen soil area of a Qinghai-Tibet Plateau railroad bed. The method comprises the following steps: S1, sorting environmental data and social economic data of the Qinghai-Tibet Plateau railroad bed; s2, estimation and prediction modeling of the unfrozen soil area of the railroad bed on the Tibet Plateau: constructing a Bayesian interlayer structure model according to seven parameters including soil type, temperature, rainfall, vegetation coverage, engineering construction, man-made heat source and railway operation, and estimating the unfrozen soil area; s3, updating the Bayesian parameters of the unfrozen soil area change trend model of the railway bed in the Qinghai-Tibet Plateau: for the seven Bayesian parameters, updating the prior distribution by using a Markov chain Monte Carlo-based method and then using the Bayesian theorem, and passing the posterior distribution; s4, constructing a Qinghai-Tibet Plateau railroad bed unfrozen soil area change trend model; and S5, making corresponding prevention and control measures according to a prediction result, and maintaining and managing a railway foundation. The method can improve the prediction precision and accuracy.

Description

Technical Field

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

[0002] The Qinghai-Tibet Plateau is a typical ecologically fragile area, which is extremely sensitive to human activities and climate warming. Once it is damaged, it is irreversible. Under the combined influence of global warming and human activities, the permafrost area of ​​the Qinghai-Tibet Plateau is in a state of continuous degradation, which is mainly manifested in the increase of ground temperature, the increase of active layer thickness and the melting of permafrost. The melting of permafrost, the increase of permafrost active layer thickness, the increase of permafrost temperature, and the increase of unfrozen area of ​​railway subgrade in the Qinghai-Tibet Plateau will eventually lead to the decrease of stability of engineering structures, the occurrence of roadbed subsidence, cracks and other diseases, which will seriously threaten the safety and stability of railway subgrades in the region. At the same time, a large number of roadbed diseases and potential risks are present during train operation, which makes the maintenance of Qinghai-Tibet Railway very difficult. Therefore, by accurately estimating the unfrozen area of ​​Qinghai-Tibet Railway, it is helpful to better understand and monitor the safety of railways, timely discover the trend 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 unfrozen area of ​​the Qinghai-Tibet Plateau railway embankment are time-consuming and labor-intensive in terms of data acquisition. Especially in the Qinghai-Tibet Plateau, the use of manual measurement methods has disadvantages such as low efficiency and high cost, and some field estimation methods may not be able to achieve high accuracy, especially in complex and changing natural environments. Methods that rely on remote sensing may be limited by factors such as the satellite's temporal resolution, spatial resolution, vegetation occlusion, and image quality, resulting in changes on smaller scales or short time scales that cannot be effectively monitored. In addition, since seasonal changes, climate anomalies, etc. may affect the actual condition of frozen soil, 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 unfrozen soil area of ​​the Qinghai-Tibet Plateau railway subgrade with improved precision and accuracy.

[0005] In order to solve the above problems, a method for estimating and predicting the unfrozen soil area of ​​the Qinghai-Tibet Plateau railway subgrade described in the present invention comprises the following steps:

[0006] S1 Qinghai-Tibet Plateau Railway subgrade environmental data and socio-economic data compilation;

[0007] S2 Estimation and prediction modeling of unfrozen soil area of ​​Qinghai-Tibet Plateau railway embankment:

[0008] 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:

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

[0011] 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;

[0012] S3 Bayesian parameter update of the Qinghai-Tibet Plateau railway subgrade unfrozen soil area change trend model:

[0013] 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;

[0014] S4 Construction of the model for the trend of unfrozen soil area change on the Qinghai-Tibet Plateau railway embankment:

[0015] The following unfrozen soil area change exploration model is constructed based on natural and human factors:

[0016]

[0017] 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;

[0018] S5 formulates corresponding prevention and control measures, maintenance and management of railway foundation according to the prediction results.

[0019] 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.

[0020] 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).

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] 1. The present invention is 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, the soil type, temperature, human activities, and parameter differences during function fitting are taken into account, thereby improving the accuracy of the estimation of the unfrozen soil area of ​​the Qinghai-Tibet Plateau railway subgrade.

[0023] 2. The present invention forms a function by coupling seven basic parameters describing permafrost degradation, focusing on linking temperature with soil type, rainfall, and elevation to achieve the estimation and prediction of the causes of permafrost degradation or the differences in environmental parameter thresholds, and then formulates corresponding railway subgrade permafrost protection measures based on the estimation results, providing support and suggestions for the management, transformation, and line selection of unfrozen subgrade of the Qinghai-Tibet Plateau railway.

[0024] 3. The present invention solves the problem of conditional probability distortion and improves the precision and accuracy of model prediction by introducing a truncated normal distribution to evaluate the performance of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0026] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0027] The present invention uses the Bayesian interlayer structure model to comprehensively consider multiple factors affecting the frozen soil area, including elevation, soil type, temperature, rainfall, human activities, etc., as well as the relationship between the individual 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 the estimation of the unfrozen soil area of ​​the Qinghai-Tibet Plateau railway subgrade.

[0028] A method for estimating and predicting the unfrozen soil area of ​​the Qinghai-Tibet Plateau railway embankment comprises the following steps:

[0029] S1 Qinghai-Tibet Plateau Railway roadbed environmental data and socio-economic data compilation:

[0030] Collect relevant environmental data and socio-economic data along the Qinghai-Tibet Plateau railway embankment, and determine the characteristic attribute variables that affect the change of frozen soil area under the railway embankment to establish a comprehensive spatial data set. Environmental data include vegetation coverage, temperature, rainfall, soil type, and climate change; socio-economic data include population density, artificial space lighting distribution, engineering construction, artificial heat sources, and railway operations.

[0031] From a preset railway subgrade frozen soil degradation feature database, multiple data consisting of the data feature vectors are obtained, and the multiple data obtained are respectively formed into a training sample set and a test sample set, and then further data discretization and normalization preprocessing are performed to eliminate the influence of unit and quantity level differences on the model.

[0032] The changes in the temperature field at the bottom of the railway embankment and near the foot of the slope are mainly caused by natural factors (including: soil type, temperature, rainfall, vegetation coverage, etc.) and human factors (including: engineering construction, artificial heat source, railway operation, etc.). Under the combined effect of these two factors, permafrost may warm up, thereby causing problems such as a reduction in the frozen soil area and the transformation of low-temperature frozen soil to high-temperature frozen soil. Under the dual influence of climate change and engineering load, permafrost roadbeds are prone to thawing deformation, longitudinal cracks and other problems, which seriously affect the service life and safety of the road. Therefore, the railway embankment frozen soil data adopted by the present invention is the average state under modern average conditions, and the obtained prediction results are based on the changes in the stable state of the existing railway embankment frozen soil.

[0033] The present invention collects temperature survey data of frozen soil areas along the Qinghai-Tibet Plateau railway observed and recorded in two time periods, 1991-1992 and 2007-2008. After normalization, 1991-1992 is determined as a model training data set, and 2007-2008 is determined as a model test data set.

[0034] S2 Estimation and prediction modeling of unfrozen soil area of ​​Qinghai-Tibet Plateau railway embankment:

[0035] 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:

[0036] area=V×logθ; logθ=logθ g1 +logθ g2 ;

[0038] 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 It is the intensity of frozen soil thawing caused by human factors, in MPa.

[0039] The specific process is as follows:

[0040] The present invention constructs a Bayesian interlayer structure model, determines the relationship and parameters of each layer, and estimates the annual unfrozen area (a potential or unobserved variable). In the present invention, for each year, a function based on the degradation rate of the frozen soil area after the logistic transformation is simulated, which is achieved by fitting a degradation function for each year's frozen soil area in a multi-layer Bayesian model framework, in which "natural factors" and "human factors" are used as variation effects (also often referred to as "random effects").

[0041] The degradation rate of frozen soil area of ​​railway embankment is estimated by fitting a functional form to the annual change of frozen soil area. The total area of ​​unfrozen embankment is then calculated based on the frozen soil degradation area.

[0042] The model used to describe the change in permafrost area combines seven change parameters, namely: 4 natural factors (soil type, temperature, rainfall, vegetation cover) and 3 human factors (engineering construction, artificial heat source, railway operation). These parameters correspond to the annual permafrost area degradation rate (y; annual permafrost degradation rate), y = (y g1 ,y g2 ), the element y of the vector for observing frozen soil changes is (y g1 ,y g2 ) as an independent Poisson model, in which the frozen soil changes caused by natural factors are y g1 , the change of frozen soil caused by human factors is y g2 .

[0043] The area of ​​frozen soil degradation is the sum of the area of ​​frozen soil degradation caused by natural factors and the area of ​​frozen soil degradation caused by human factors.

[0044] Because the operation of this model involves multiple variables, multiple dimensions, ranges, and units, it is necessary to constrain specific parameters, that is, normalize them 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 data set and the initial estimation model, and the estimation model of the degraded frozen soil area, that is, the estimation model of the unfrozen soil area, is obtained.

[0045] The total unfrozen area is calculated based on the frozen soil degradation area, and all the rates that cause frozen soil degradation are accumulated, that is: the annual unfrozen 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.

[0046] The present invention estimates the unfrozen area of ​​railway foundation based on historical data and probability inference. The unfrozen area and evolution trend of the Qinghai-Tibet Railway subgrade can be calculated using equations (5) and (6) respectively.

[0047] The data from 1991 to 1992 are used to verify the initial frozen soil area, which is represented by Vs; the frozen soil area from 2007 to 2008 is represented by V f represent.

[0048] Use the data from 1991-1992 to verify the following formula:

[0049] y gj |θ gj ~Poisson(θ gj ) …………(1)

[0050] Where: The change of frozen soil caused by natural factors is y g1 , the permafrost change caused by human factors is y g2 .

[0051] θ=(θ g1 ,θ g2 ) …………(2)

[0052] Where: θ is the thawing intensity of frozen soil, θ g1 is the intensity of frozen soil thawing caused by natural factors, θ g2 is the intensity of frozen soil thawing caused by human factors. The logarithmic random effect linear model is used to obtain these two types of frozen soil thawing intensities.

[0053] logθ g1 =Elevation+att h(g) +def a(g) ………(3)

[0054] Where: Elevation represents the elevation, and the elevation is used as a fixed change factor; att h(g) represents temperature, def a(g) Indicates rainfall.

[0055] logθ g2 =att a(g) +def h(g) ………(4)

[0056] Where: att a(g) Indicates engineering construction, def h(g) Indicates railway operation.

[0057] logθ=logθ g1 +logθ g2 ………(5)

[0058] Where: logθ is the permafrost degradation rate.

[0059] area=V×logθ……(6)

[0060] Where: area is the unfrozen area, V is the frozen area, and logθ is the frozen soil degradation rate (the sum of the frozen soil degradation rates caused by natural and human factors).

[0061] Assuming that Elevation conforms to the minimum information normal prior distribution (0, 0.0001), then

[0062] Elevation~Normal(0,0.0001)…………(7)

[0063] At this time, the changes in frozen soil caused by natural and human factors conform to the normal distribution:

[0064] att t ~Normal(μ att ,τ att ),def t ~Normal(μ def ,τ def ). …………(8)

[0065] Where: att t represents the natural factor under asymmetric central distribution, def t Indicates the human factors under asymmetric central distribution. Each t = 1, .., π, π represents the frozen soil type, and 1, 2, and 3 respectively indicate three frozen soil types: short-term frozen soil, seasonal frozen soil, and permanent frozen soil.

[0066]

[0067] Formula (9) indicates that when the natural factors and human factors are set to 0, the frozen ground does not melt.

[0068] μ att ~Normal(0,0.0001),μ def ~Normal(0,0.0001),

[0069] τ att ~Gamma(0.1,0.1),τ def ~Gmama(0.1,0.1).…………(10)

[0070] In order to ensure the accuracy of the formula, the hyper-prior of the effects of frozen ground thawing caused by natural factors and human factors in formula (10) is modeled independently, and it is stipulated that μ represents natural factors and τ represents human factors, both of which conform to the location parameter of the minimum information distribution and the gamma distribution;

[0071] η=(μ att ,μ def ,τatt ,τ def ) …………(11)

[0072] Where: η represents other potential factors that can cause frozen soil thawing.

[0073] S3 Bayesian parameter update of the Qinghai-Tibet Plateau railway subgrade unfrozen soil area change trend model:

[0074] For the seven Bayesian parameters in step S2, the Markov Chain Monte Carlo-based method was first used, and then the Bayesian theorem was used to update the prior distribution and the posterior distribution (1,000 iterations on three chains).

[0075] For the spatiotemporal distribution and trend model of frozen ground thawing, the Bayesian update of the parameter probability distribution was performed, the convergence of the chains was checked to ensure that they were all within 0.001 around 0, and the mixing of all chains was visually assessed.

[0076] The posterior distribution of the coefficients is summarized by their median and the 95% highest posterior density interval HPDI (i.e., the narrowest posterior interval containing 95% of the probability mass, corresponding to the coefficient value most consistent with the data). Coefficients of model covariates are considered significant when their 95% HPDI does not contain zero, indicating that there is strong enough confidence to report the effect as positive or negative.

[0077] S4 Construction of the model for the trend of unfrozen soil area change on the Qinghai-Tibet Plateau railway embankment:

[0078] The following unfrozen soil area change exploration model is constructed based on natural and human factors:

[0079]

[0080] 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 changes 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 respectively indicate three types of frozen soil: short-term frozen soil, seasonal frozen soil, and permafrost.

[0081] The specific process is as follows:

[0082] Because the basis of the railway subgrade unfrozen soil area prediction model in the present invention is a Bayesian hierarchical model, the present invention is divided into two layers, namely, natural factors and human factors to construct an unfrozen soil area change exploration model.

[0083] Because permafrost area decline is often attributed to multiple mechanisms, different datasets and methods are used to best link patterns identified in long-term data to known potential drivers of permafrost degradation.

[0084] In order to reduce the excessive shrinkage caused by the stratified model, the frozen soil foundation is divided into three types based on the frozen soil type: short-term frozen soil, seasonal frozen soil, and permafrost. π is used to represent the frozen soil type, and 1, 2, and 3 are used to indicate the three frozen soil types respectively.

[0085] Each soil type is determined by a vector of prior probabilities, specified using a Dirichlet distribution with parameter π att and π def The minimum information model (1,1,1) but can obviously include (possibly subjective) prior information π att and π def The vector is used to represent the prior chance, and then the effects of natural factors and human factors on each type of frozen soil foundation of the railway are modeled. Therefore, the models of observable variables and remain unchanged, while the models of other hyperparameters are as follows: Formulas (13) and (14), assuming that each frozen soil type has two potential unobservable variables, namely, the natural factor variable grp att (π) and the human factor variable grp def (π), due to grp att (π) and grp def The value of (π) is unknown, and using the noncentral t distribution (nct), the following formula is essentially equivalent to defining a mixed model of the effects of permafrost degradation under natural and human activities.

[0086] The following model is validated using the results from 2007-2008:

[0087]

[0088] Where: π att represents the change of frozen soil caused by natural factors under a certain type of frozen soil, π def Indicates the changes in permafrost caused by human factors under a certain type of permafrost.

[0089]

[0090] In the formula: In the formula: nct represents asymmetric central distribution, v represents the degree of freedom, v = 4; att t and def t It indicates that the changes of frozen soil caused by natural factors and human factors conform to the asymmetric central distribution, grp(t) represents the unobservable variable; each t = 1,..,π,π represents the frozen soil type, and 1, 2, and 3 respectively indicate three types of frozen soil: short-term frozen soil, seasonal frozen soil, and permanent frozen soil. μ represents natural factors, τ represents human factors, Indicates the changes of frozen soil caused by natural factors and Changes in permafrost caused by human factors, It indicates the changes of frozen soil caused by natural factors when human factors remain unchanged. It refers to the changes caused by human factors while natural factors remain unchanged.

[0091] Formula (14) is derived from formula (13), which is a mixed model of frozen soil changes caused by natural and human factors.

[0092]

[0093] Where: att t Indicates the changes in frozen soil mainly caused by natural factors, def t represents the permafrost change mainly caused by human factors, nct represents asymmetric central distribution, v represents the degree of freedom, v = 4; π att represents the change of frozen soil caused by natural factors under a certain type of frozen soil, π def It indicates the changes of frozen soil caused by human factors under a certain type of frozen soil; each t=1,..,π,π represents the frozen soil type, and 1, 2, and 3 respectively indicate three types of frozen soil: short-term frozen soil, seasonal frozen soil, and permafrost. Indicates that natural factors cause certain types of frozen soil changes and Certain types of frozen ground changes caused by human factors, It indicates a certain type of frozen soil change caused by natural factors when human factors remain unchanged. It refers to a certain type of frozen soil change caused by human factors while natural factors remain unchanged.

[0094]

[0095] Formulas (15) and (16) represent the truncated normal distribution (trunc) of short-term frozen soil and permafrost, respectively. According to the location and scale parameters of the asymmetric central distribution (nct), if the frozen soil thawing state is different under natural and human factors according to different frozen soil types, it is likely to show a slow frozen soil thawing rate, but the scale and location parameters of the frozen soil thawing of the Qinghai-Tibet Railway subgrade may be different. Therefore, the frozen soil type can be used to quantitatively describe the occurrence of frozen soil thawing of the Qinghai-Tibet Railway subgrade using the truncated normal distribution (trunc). k represents the variable frozen soil type, and the value range of the variable frozen soil type is limited to (1, 3).

[0096]

[0097] Formula (17) shows that seasonal frozen soil conforms to the normal distribution.

[0098]

[0099] Formula (18) indicates Both use the minimum information gamma distribution.

[0100] S5 formulates corresponding prevention and control measures based on the prediction results, and maintains and manages the railway foundation:

[0101] If the railway subgrade in the study area continues to degrade at the current permafrost degradation rate, the melting of the permafrost beneath the subgrade may cause greater settlement and deformation of the railway subgrade. Therefore, the model test data set of the present invention is used to verify the estimation model of the unfrozen area of ​​the railway subgrade in the study area, and corresponding permafrost protection measures are formulated based on the estimation results. In the construction and maintenance of railway projects, high-power forced cooling measures should be adopted to reduce the ground temperature. At the same time, combined with the anti-freeze-thaw measures of the railway line, freeze-thaw monitoring and subgrade filling verification results, engineering countermeasures and suggestions are proposed for reference and guidance of railway subgrade survey, design and construction in the permafrost area of ​​the Qinghai-Tibet Plateau in the future.

[0102] At the same time, the model was verified using historical data of unfrozen railway subgrade area measured in 1991-1992 and 2007-2008 to ensure the model's prediction ability and accuracy. At the same time, it was adjusted according to the specific geological and geomorphological conditions of different regions to adapt to the prediction of unfrozen railway subgrade area 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; θg1 is the permafrost thawing intensity caused by natural factors, unit MPa; θg2 is the permafrost thawing intensity 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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