J. Cent. South Univ. (2021) 28: 264-283

DOI: https://doi.org/10.1007/s11771-021-4601-5

Pre-evaluation on stability of proposed expressway embankment with existing geothermal regulation measures in permafrost regions

LUO Xiao-xiao(罗晓晓)^{1, 2}, MA Qin-guo(马勤国)^{1, 2}, JIANG Hai-qiang(姜海强)²

1. State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-environment and

Resources, Chinese Academy of Sciences, Lanzhou 730000, China;

2. State Key Laboratory of Subtropical Building Science, South China University of Technology,Guangzhou 510641, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2021

Abstract: Embankment stability is the primary problem for the expressway construction in permafrost regions. The proposed Qinghai-Tibet Expressway (QTE) is planned to construct along the Qinghai-Tibet Project Corridor. Confronted with harsh environmental condition and intense heat exchange between earth and atmosphere, it is necessary to predict and evaluate the stability of the proposed QTE. In this study, the factors affecting the embankment stability are analyzed firstly. And then, a scheme for the stability evaluation of the embankment is established. Finally, the evaluation scheme is used for the pre-evaluation of the stability for the proposed QTE with different geothermal regulation measures (GRMs). The results indicate that the influencing factors include climatic environment, permafrost property, engineering condition and geological condition, and among them, engineering condition and permafrost property are the main influence factors for embankment stability. The stability of the proposed QTE varies greatly in the different geomorphological regions. The application effect and contribution to embankment stability of the existing GRMs are different, and using GRMs cannot completely overcome the influence of various factors on expressway stability. In the construction process, different GRMs should be adopted depending on the geomorphological environment where the embankment is located to ensure the embankment stability.

Key words: permafrost; expressway embankment; influencing factor; stability evaluation; geothermal regulation measures

Cite this article as: LUO Xiao-xiao, MA Qin-guo, JIANG Hai-qiang. Pre-evaluation on stability of proposed expressway embankment with existing geothermal regulation measures in permafrost regions [J]. Journal of Central South University, 2021, 28(1): 264-283. DOI: https://doi.org/10.1007/s11771-021-4601-5.

1 Introduction

Frozen soil is composed of mineral particles, viscoplastic ice inclusion, liquid water and gaseous inclusions (water vapor and air). During the long-term evolution of frozen soil, the underground ice layers with the thickness of several meters or even tens of meters are formed [1, 2]. The construction of embankment disturbs the energy balance of natural surface, causing the underlying permafrost degradation, and further affecting the stability of embankment [3, 4]. Taking the Qinghai-Tibet Highway as example, the mean annual ground temperature of permafrost beneath embankment is about 30% higher than that of the natural site, and the thickness of active layer is 1.5-2.0 times deeper than that of the natural site [5]. Compared with ordinary highway, the construction of expressway accelerates the warming and thawing of frozen soil, because of the wider asphalt pavement, stronger heat absorption capacity and more severe engineering thermal disturbance [6, 7]. Therefore, although the Qinghai-Tibet Expressway (QTE) has been incorporated into the Chinese 12th Five-Year Plan, the sections at permafrost section (from Golmud to Lhasa) have been delayed due to the permafrost problem.

In order to prevent the underlying permafrost from degradation, various geothermal regulation measures (GRMs) are applied [8, 9]. Insulation board, awning, ventilated duct, crushed-rock layer and thermosiphon are widely used in warm permafrost regions. Field tests and numerical simulation results show that these measures can protect permafrost and improve embankment stability [10-12]. However, each measure is not perfect and has certain limitations in practice. For example, the insulation board cannot change the heat absorption trend caused by embankment construction [13], which is not conducive to the long-term stability of the embankment. Ventilated duct may bring heat energy into the embankment in warm seasons, and the cooling effect is poor in regions with high annual average ground temperature [14]. When the crushed-rock layer are laid at the bottom of embankment, the cooling effect in the center of embankment is limited by the embankment width [15]. And the wider the embankment is, the worse the cooling effect will be. When the crushed-rock layer is laid on the embankment slope, the cooling effect is easily disturbed by aeolian sand [16]. The cooling effect of thermosiphon is limited, and the embankment with thermosiphon is easy to encounter the secondary disasters [17]. In addition to the above-mentioned GRMs, a measure to reduce the thermal energy absorption by increasing the albedo of embankment surface has developed. The traditional methods are using white paving and covering with white coating, but their application is restricted by albedo measurement and visual vertigo caused by white pavement. As a method to calculate the albedo of embankment by the solar radiation absorption and reflection of the reference object is proposed [18, 19], the non-white paving and non-white coating are put forward [20, 21]. These new methods can effectively block solar radiation and free from glare problem. Even for the sunny slope of the embankment in permafrost regions, they can reduce and eliminate the asymmetry of the temperature field [22, 23]. Although the existing GRMs can maintain embankment stability to a certain extent, their application effect and contribution to embankment stability are different. Therefore, it is necessary to analyze the application effects of existing GRMs in detail and make classification.

For the proposed QTE planned to construct along the existing Qinghai-Tibet Project Corridor, its stability is related to geological and climatic conditions and the GRMs [24-26]. In this case, it is of great significance to establish a pre-evaluation scheme for the stability of the proposed QTE under different GRMs in different geomorphic regions. Common methods to evaluate the reliability and stability of engineering structure are genetic algorithm [27], BP neural network [28, 29], catastrophe progression method [30, 31], fuzzy reasoning method [32], and fuzzy comprehensive evaluation method [33]. Genetic algorithm is usually combined with reliability theory to analyze the reliability of engineering structure. The three operators of selection, intersection and variation are determined by experience, and the calculation process is cumbersome. For BP neural network and fuzzy reasoning method, a large number of data samples are required, and the more the samples are, the more accurate the evaluation results will be. Both catastrophe progression method and fuzzy comprehensive evaluation method are based on fuzzy membership function. Compared with the fuzzy comprehensive evaluation method, each index in catastrophe progression method is not needed to assign weights, but the maximum index number decomposed in each hierarchical structure cannot exceed four, which is not suitable for the stability evaluation of engineering structure with many influencing factors. For the expressway embankment in permafrost regions, there are many factors affecting its stability, and these factors are interrelated and have strong fuzziness. It is difficult to quantify these influence on expressway stability.

Thus, with the above analysis, in this paper, the factors affecting expressway stability in permafrost regions are analyzed firstly, and the hierarchical structure of the evaluation index is determined. Then, the fuzzy comprehensive evaluation model of expressway stability is established to predict and evaluate the stability of the proposed QTE with different GRMs. According to the forecast and evaluation results, the efficiency of the existing GRMs are considered, and some suggestions on the application of the GRMs are proposed for the proposed QTE in different landforms along the Qinghai-Tibet Project Corridor.

2 Analysis on factors affecting expressway stability in permafrost regions

Embankment stability in permafrost regions is mainly restricted by the thermal state of underlying permafrost. Thus, the factors that affect the embankment stability, except for the external load (vehicles, earthquakes) and the construction quality of the embankment itself, can be considered the factors that cause the degradation of the underlying permafrost. These factors can be classified into the categories of climatic environment, permafrost property, engineering condition and geological condition.

Climatic environment: Solar radiation is a direct heat source, and its variation determines the temperature fluctuation at the pavement surface and shallow layer of embankment. Air temperature is an important factor affecting the thermal stability of embankment. The cumulated positive temperature for air temperature (thawing index) is positively correlated with the annual maximum thawing depth of permafrost [34], which is closely related to the embankment stability. During rainy season, the humidity at embankment slope and shallow layer increases, and vertical seepage in soil accelerates the thawing of underlying frozen soil.

Permafrost property: Permafrost is sensitive to temperature, and its strength and carrying capacity reduce with the temperature increasing [35-37]. The higher the mean annual ground temperature of underlying permafrost is, the worse the embankment stability will be. The ice content in permafrost determines the warming and thawing rates of permafrost and the settlement of embankment from permafrost thawing [38, 39]. If the distributions of ice and ground temperature of the permafrost beneath the embankment are uneven, the depths of seasonal thawing will be unequal, forming differential deformation. Surface water and suprapermafrost water affect the distribution and development of permafrost beneath the embankment. If drainage is blocked, atmospheric precipitation accumulates at the low-lying areas, and connects to the suprapermafrost water, resulting in embankment toe being soaked [40]. The seasonal rising and descending of the groundwater cause the repetitive expansion and shrinkage of the soil, giving rise to mud-pumping and other embankment diseases [41]. Thawing settlement generally occurs in seasonal thawing layer, and the greater the depth of seasonal thawing, the greater the settlement deformation. Besides, the thickness of the permafrost is conductive to the embankment stability, and the larger the permafrost thickness is, the better the embankment stability will be.

Engineering condition: Roadbed height is an important factor for the embankment stability in permafrost regions [42-44]. The height is too low to achieve the thermal insulation effect of the embankment, but embankment with high height increases the heat absorption surface and additional load to foundation and causes the residual thawed layer in the first cold season after the embankment construction [42, 45]. Affected by the direction of the roadbed, the sunny slope receives more solar radiation, and the temperature at the sunny slope is relatively higher than that at the shady slope, which causes asymmetric thermal regime in embankment, and further promotes the uneven settlement and the formation of longitudinal cracks [39, 46]. Except for roadbed height, the width and the slope gradient both affect the thermal state of the underlying permafrost. The wider the pavement is, the greater the heat absorption intensity is, and the less likely the heat diffuses from both sides, forming heat gathering effect under the roadbed [6]. Compared with the integrated roadbed, the separated roadbed can alleviate the heat accumulation inside the embankment, and postpone the degradation of the underlying permafrost. In this case, if the slope is relatively gentle, it is conducive to the heat dissipation inside the embankment. Meantime, the gentle slope is not prone to collapse during the rainy season. However, if the distance between the two separated embankments is unreasonable, the thermal interaction between the two embankments will be caused [47]. Moreover, the separated embankment covers larger area than integrated embankment, which is unfriendly to the ecological environment along the Qinghai-Tibet Project Corridor. No matter which construction method is adopted, the necessary GRMs are indispensable. Monitoring datum from the Qinghai-Tibet Testing Expressway (QTTE) shows that the GRMs based on convective heat transfer theory not only effectively cool the underlying permafrost, but also produce a cold energy accumulation effect beneath the embankment [48]. With the increase of the service life, the structural performance of the embankment will be reduced. If the embankment is not timely repaired, various diseases such as looseness, pothole, crack, and ups and downs will occur.

Geological condition: Vegetation is the medium for energy exchange between the atmosphere and lithosphere, affecting the hydro- thermal circulation of underlying permafrost through reflection, scattering solar radiation, blocking wind and snow, also absorbing and retaining water. Vegetation deterioration can cause degradation of permafrost [49]. Restricted by altitude, ground temperature of the permafrost basically decreases and the thickness increases from the plain to the mountain. However, affected by the terrain, the ground temperature at low-lying section is low, and the seasonal frozen layer is relatively thick in those areas. The particle size, mineral and organic composition of skeleton soil in seasonal thawing layer affect hydrothermal processes in permafrost.

3 Establishment of comprehensive evaluation system

For the evaluation of embankment stability in permafrost regions, the method combining the advantages of the analytic hierarchy process and fuzzy comprehensive evaluation can appropriately reduce the randomness of subjective judgment and evaluation, and improve the reliability of the evaluation results.

3.1 Construction of analytic hierarchy process (APH) model

Evaluating the stability of the embankment in permafrost regions by the mothed of APH, the membership relation of the influencing factors should be determined firstly, and then these factors are disassembled into several levels from top to bottom. According to the above analysis results on influencing factors of embankment stability in permafrost regions, the hierarchical substructure model for expressway stability is established, as shown in Figure 1. This hierarchical substructure model consists of three levels including object hierarchy, rule hierarchy and factor hierarchy, and the elements in the factor hierarchy are the expressway stability evaluation indexes. The elements in rule hierarchy include climatic environment, permafrost property, engineering condition and geological condition. Climatic environment consists of three secondary-level influencing factors: mean annual solar radiation, mean annual air temperature and annual mean precipitation. Permafrost property includes five secondary level influencing factors: Permafrost type, seasonal thawing depth, permafrost thickness, mean annual ground temperature, surface water and groundwater. Engineering condition is composed of five secondary level influencing factors: Roadbed height, roadbed direction, GRM, roadbed section form, and service life. Geological condition is composed of three secondary level influencing factors: Vegetation coverage, active layer lithology and terrain.

Figure 1 Hierarchical substructure model for expressway stability in permafrost regions (GRM: Geothermal regulation measure)

3.2 Determination of weight of influencing factors

3.2.1 Construction of judgment matrix

The judgment matrix is the evaluation for objective factors. Each value in the matrix is a quantitative representation of the relative importance of each element. The relative importance of an element is usually marked by a number from 1 to 9 or its reciprocal. The larger the number is, the more important one factor is relative to another. Assuming that the element in the upper level in the hierarchical substructure model is A_i (i=1, 2,…, m) and the element in the lower level is B_n (n=1, 2, …, k), the relative importance of each element is determined by questionnaire survey, as shown in Table 1. According to the evaluation results, the judgment matrix is formed:

Table 1 Evaluation results

(1)

where b_ij represents the importance of the factor b_i relative to b_j and b_ij is determined as follows:

(2)

3.2.2 Calculation of weight value

After obtaining the judgment matrix, the weight value of each factor is calculated by using the sum and product method. The calculation steps are as follows:

First, the normalization of the judgment matrix B_n is carried out and the normalization matrixis obtained:

(3)

And then, the elements in each column of the normalized matrix are summed to obtain a vector W=[W₁, W₂, …, W_k], and the vector W is normalized to obtain the eigenvector

(4)

whereand each element in the eigenvector is the weight value of each factor in the same level.

3.2.3 Validation for rationality of weight value

In order to ensure the rationality of the weight value obtained by the judgment matrix, the consistency checking of the judgment matrix is performed. Firstly, it needs to calculate the maximum eigenvalue λ_max:

(5)

And then, the consistence proportional factor CR is proposed to perform the consistency test:

(6)

where CI is the consistency index and CI=(λ_max-k)/ (k-1); k is the number of influencing factors; RI is the mean random consistency index, and the values are shown in Table 2. When CR≤0.1, the judgment matrix is considered to be consistent and the weight is reasonable; otherwise, the judgment matrix needs to be readjusted.

Table 2 Mean random consistency index

3.2.4 Determination of weight

Based on the established APH model for expressway stability, the weight of various factors affecting the expressway stability in permafrost regions is calculated. The calculated results for the judgment matrix and weight refer to Appendix A.

3.3 Establishment of fuzzy comprehensive evaluation model

The fuzzy comprehensive evaluation model consists of three elements (U, V, R), and its application is divided into five steps:

1) Determine the influencing factor set U of the evaluation object, U={U₁, U₂, …, U_m}. The set U consists of affecting factor subsets U_i, U_i={U_i1, U_i2, …, U_ik} where k represents the number of factors in the subset U_i.

2) Determine the evaluation set V, V={V₁, V₂, …, V_n} where n is the number of evaluation levels. In this study. n takes 4 levels including stable level, basically stable level, less stable level, and unstable level.

3) Establish the single factor evaluation matrix R_i. In general, the influencing factor U_ij (i=1, 2, …, m; j=1, 2, …, k) has a certain fuzziness to each element in the evaluation set V. Using the appropriate membership function to evaluate the influencing factor U_ij, the fuzzy evaluation subset of each factor U_ij is obtained, which is presented as R_ij={r_ij1, r_ij2, …, r_ijn}. Therefore, the single factor evaluation matrix can be expressed as:

(7)

The determination method of the membership degree of quantitative and qualitative indicators refer to Appendix B for details.

4) Introduce the weight vector L_i (L_i=[l_i1, l_i2, …, l_ik]) of factor subset U_i, where l_ij≠0, and l_ij indicates that each factor of the evaluation factor set has different roles in the evaluation object. For the weight vector L_i and the single factor evaluation matrix R_i, fuzzy operation F_i=L_i○R_i is performed according to matrix product algorithm:

(8)

The weight vector L (L=[l₁, l₂, …, l_m]) of factor set U is introduced. The weighted vector L and the secondary fuzzy comprehensive evaluation matrix F=[F₁, F₂, …, F_m]^T are subject to the same fuzzy operation P=L○F to obtain the primary fuzzy comprehensive evaluation set P={p₁, p₂, …, p_n}.

5) Recommend the expressway embankment stability index. The value range of the stability index is [25, 100], and it is divided into four levels according to the equal steps, as quantization evaluation set V={100, 75, 50, 25} for expressway embankment stability. The primary fuzzy comprehensive evaluation result P is processed and the stability index Q=PV ^T is obtained. The larger the stability index, the more stable the expressway. In order to make the evaluation results easy to understand, the expressway embankment stability grades are divided by the stability index. The range of stability index values corresponding to each level is shown in Table 3.

Table 3 Evaluation standard for expressway stability

Based on a large number of references, and combined with the opinions of experts, the reference standards for the grading of each evaluation index in the fuzzy comprehensive evaluation model of expressway stability are given in Table 4.

4 Verification for evaluation model

Taking the expressway embankment with temperature-controlled ventilation as an example, the above evaluation model is verified. Designed and constructed in accordance with the Chinese expressway design standards, the embankment has been completed in September, 2009. The road height is 3 m; the width of the roadbed top surface is 13.0 m; the slope ration is 1:1.5; and the road direction is about 198° from north. The embankment is located in the southern part of the Beiluhe Basin which belongs to the piedmont alluvial-proluvial high plain landform with a surface vegetation coverage rate of 90%. The mean annual air temperature is about -3.58 °C; the mean annual solar radiation is 5760 MJ/m²; and the mean annual precipitation is about 450 mm. The runoff and drainage are developed. The maximum ice content is approximately more than 80% and the mean annual ground temperature range is -1.0- -0.5 °C. The area belongs to the high-temperature and ice-rich permafrost area. The depth of the permafrost table is approximately 1.84 m beneath the natural surface, and the permafrost thickness is 30 m. In addition, the geological data show that four soil layers are included within the depth of 20 m, i.e., sand soil (0-0.5 m), sandy loam (0.5- 5.0 m), sub-clay (5.0-7.0 m), and weathered mudstone (below 7.0 m).

Table 4 Grading standards of evaluation indexes

According to the above survey results and the calculation method for membership degree, each single factor evaluation matrix can be determined, and the corresponding weight subset is introduced to calculate the single factor fuzzy comprehensive evaluation set. Then, the primary fuzzy comprehensive evaluation set of embankment stability can be calculated, and the stability index of embankment is finally obtained to be 77.51. Refer to Appendix C for the calculation process of the fuzzy comprehensive evaluation set of embankment stability and embankment stability index.

According to the expressway stability index, the embankment is basically stable. Actually, the cracks appeared at the half of the roadbed near the sunny slope at the initial stage of construction (2010), and the crack depth was less than the thickness of the pavement surface (Figure 2). After repairing, no new cracks have appeared. The actual embankment is in stable state. This indicates that the evaluation result for the expressway stability by the fuzzy comprehensive evaluation model is consisted with the actual situation, and the model has certain reliability.

Figure 2 Photo of expressway embankment with temperature-controlled ventilation

5 Effectiveness evaluation of GRMs

The stability of the expressway embankment in permafrost regions is related to the GRMs. The most suitable GRM should be applied to ensure the embankment stability. This requires a clear understanding of the application effect of GRMs.

In the process of rehabilitation of the Qinghai-Tibet Highway in 2003, some GRMs were applied to improve embankment stability in some damaged sections. These countermeasures mainly included insulation board, thermosiphon, ventilation, crushed-rock interlayer, etc. For the terrible engineering environment, composite measures were used.

Based on the monitoring datum of ground temperature, deformation and disease of the Qinghai-Tibet Highway in the recent 13 years [50], the disease incidence of ordinary embankment and embankment with countermeasure is shown in Figure 3. The emergence of most diseases is concentrated within 2 to 5 years after the embankment construction. Compared with ordinary embankment, insulation board, thermosiphon, ventilation, crushed-rock interlayer and composite measure combining ventilation with crushed-rock interlayer can reduce the disease incidence of roadbed by 35%, 45%, 45%, 55% and 55%, respectively (Figure 4(a)). The effective rates of insulation board, thermosiphon, crushed-rock interlayer and ventilation in preventing and controlling disease are 60%, 70%, 80% and 70%, respectively. For the embankment with insulation board, the disease incidence in the early stages after construction ranges from 3% to 15%. Since the fourth year, the damage incidence has rapidly increased, and reached about 40% in the ninth year (Figure 4(b)). The high incidence period of disease is from the fourth to eighth year after construction, and the maximum annual disease incidence is 6.5% (Figure 4(c)). For the embankment with thermosiphon, the disease occurs rapidly in five years after construction. The annual disease incidence reached a maximum of 9% in the third year and was basically 0 after the sixth year (Figure 4(c)). Its disease sections account for 30% of the whole embankment (Figure 4(b)). The high incidence period of disease for the ventilated embankment is from the third year to the sixth year after construction. The annual disease incidence is about 5.5% during this period (Figure 4(c)). The annual disease incidence of embankment with crushed-rock interlayer is relatively small, less than 3%. Fortunately, the effective rate of the composite measure combining ventilation with crushed-rock interlayer in preventing and controlling disease rises to 80%. Although the application of countermeasures can effectively prevent embankment diseases to some extent, it cannot completely eliminate embankment disease (Figure 4(a)).

Figure 3 Embankment diseases for highway in permafrost regions:

Figure 4 Disease incidence of embankment in different service life:

It can be seen that among the various countermeasures, the controlling efficiency of crushed-rock interlayer is relatively high, the thermosiphon and ventilations are in the middle, and the insulation board is lower. The composite measure can improve the controlling effect. In order to further clarify the effectiveness of various GRMs, according to operating principle, the GRMs are classified into six types including reducing solar radiation, releasing heat, controlling heat conduction, air convection heat exchange, composite measure and replacing roadbed with bridge. The principle, advantages and disadvantages of each GRM are summarized in Tables 5-9.

Investigation of embankment disease along the Qinghai-Tibet Highway manifests that the embankment diseases are mainly subsidence, uneven deformation and longitudinal cracking [34, 39] (Figure 3). The construction of embankment will change the thermal equilibrium state of the original surface. The asphalt pavement has a strong heat-absorbing effect, causing the thawing of underlying permafrost and forming a thawing layer. When the ice content of the underlying permafrost along the same section is different, there will be uneven deformation in the transverse direction of the embankment (Figure 3(a)), which can be aggravated by the uneven distribution of the ground temperature at both slopes of the embankment. The greater the transverse uneven deformation, the more easily the longitudinal cracks occur (Figure 3(b)). If the geological conditions of the underlying permafrost are different greatly in the longitudinal direction, the roadbed will have different deformation in different sections, which will cause the road surface undulating (Figure 3(c)).

Therefore, in order to ensure the long-term stability of highway, the underlying permafrost should be protected from degeneration firstly. Secondly, the uneven deformation caused by the temperature difference between the sunny and shady slope should be eliminated. And then, for the sections with quite different geological conditions, the overall cooling is achieved. Finally, the permafrost can be cooled rapidly. The above four strategic points are reflected in the application effect of the GRMs as follows: the rise of the permafrost table, the symmetrical distribution of ground temperature, the overall cooling of permafrost, and the rapid cooling. Based on the evaluation of the cooling performance of various GRMs in Tables 5-9, these GRMs are classified into three grades.

Table 5 Efficiency evaluation for countermeasures of reducing solar radiation

Table 6 Efficiency evaluation for countermeasures of releasing heat

Table 7 Efficiency evaluation for countermeasures of controlling heat conduction

Level I: It can protect permafrost immensely, overcome the asymmetrical distribution of the ground temperature, and achieve rapid, overall and uniform cooling of permafrost. These GRMs include the composite measure combining hollow concrete bricks and ventilated ducts, the composite measure combining thermosiphon, thermal insulation board and asymmetrical crushed-rock revetment, temperature-controlled ventilations, land bridge, etc.

Table 8 Efficiency evaluation for countermeasures of air convection heat exchange

Table 9 Efficiency evaluation for composite embankment and land bridge

Level II: It can better protect permafrost, but cannot completely overcome the asymmetrical distribution of the ground temperature. These GRMs include crushed-rock interlayer embankment, crushed-rock revetment embankment, U-shaped ripped-rock embankment, the composite measure combining crushed-rock interlayer and ventilated ducts, the composite measure combining thermosiphon with thermal insulation board, etc.

Level III: It can protect permafrost to some extent, but the application scope is limited. It may be unfriendly to the embankment engineering and environment. These GRMs include thermal insulation board, thermosiphons, expanded polystyrene blocks, foamed concrete, awnings, etc.

6 Pre-evaluation on stability of proposed QTE

The proposed QTE is to be built along the Qinghai-Tibet Project Corridor. Because of the wider asphalt pavement, expressway has stronger heat absorption than ordinary highway, which is more likely to cause the degeneration of the underlying permafrost and affect the stability of expressway. Therefore, it is necessary to predict and evaluate the stability of the QTE, so as to facilitate decision makers to make judgment.

Considering that the QTE has not yet been built, the engineering conditions such as roadbed direction, roadbed section form, and GRM cannot be got in detail, so the stability levels of roadbed height, roadbed direction, roadbed section form and service life are determined to be unstable in the calculation process. According to Refs. [73, 74], the mean annual solar radiation in most areas along the Qinghai-Tibet Project Corridor is greater than 6000 MJ/m², and even the mean annual solar radiation in the Hohxil Mountains and the most areas from Tanggula Mountains to the Ando- Liandaohe Highlands is more than 7000 MJ/m². In addition, affected by topography and precipitation, the mean annual solar radiation of local areas is relatively low. For example, the mean annual solar radiation of the Beiluhe Basin and Tongtianhe Basin are 5600 to 6000 MJ/m². Combined monitoring data [75, 76] with the monthly precipitation (http://data.cma.cn), the mean annual precipitation along the Qinghai-Tibet Project Corridor is obtained. Vegetation coverage is obtained based on geospatial data cloud (http://www.gsclond.cn). The remaining evaluation index related to the permafrost property is obtained by on-site investigations. Limited to the space of the paper, only some of the evaluation indexes of expressway stability along the Qinghai-Tibet Project Corridor are shown in Table 10.

The stability of the proposed QTE with different levels of GRMs is evaluated by the fuzzy comprehensive evaluation method mentioned above, and the evaluation results are shown in Table 11. According to the evaluation standard for expressway stability, it is believed that when the stability index Q is greater than 62.50, the expressway stability reaches the basically stable level and basically satisfies the stability of expressway (Table 3). The evaluation results of stability for expressway without any countermeasures indicate that, except that the expressway embankment in Tanggula Mountains is basically stable, the other sections along the Qinghai-Tibet Project Corridor are at the less stable level. In this case, it is necessary to take some countermeasures to improve the stability of the expressway embankment.

Table 10 Evaluation indexes of expressway stability along the Qinghai-Tibet Plain Corridor

According to Table 11, the stability of the proposed QTE at Kunlun Mountains, Hohxil Mountains, Fenghuo Mountains, and Taoerjiu Mountains can reach basically stable level by adopting the Level III GRMs. For the proposed QTE at West part of the Xidatan Valley, Chumarhe Plain, Tuotuohe Basin, Kaixinling Mountains, Jiebuqu Valley, and Ando-Liangdaohe Highlands, the stability of the embankment can attain the basic stability by adopting Level II GRMs. Due to the harsh permafrost environment, the Level I GRMs should be adopted to achieve the basic stability of the proposed QTE at Beiluhe Basin, Tongtianhe Basin and Buquhe Valley. In addition, even if Level I GRMs are adopted in all landform zones along the Qinghai-Tibet Project Corridor, the stability of the proposed QTE cannot reach the stable level. This indicates that even if the corresponding GRMs are taken for the expressway, it still cannot overcome the influence of the permafrost property, climatic environment, engineering condition and geological condition on the stability of expressway. The necessary maintenance during operation period is essential for the stability of expressway in permafrost regions.

7 Conclusions

In this paper, a fuzzy comprehensive evaluation model for embankment stability in permafrost regions is established, and through this evaluation model, the stability of the proposed expressway with different levels of geothermal regulation measures is pre-evaluated. The following conclusions are drawn:

1) The influence factors of embankment stability in permafrost regions include climatic environment, permafrost property, engineering condition and geological condition. Among them, engineering condition and permafrost property are the main influence factors for embankment stability.

Table 11 Evaluation results on stability of expressway with different levels of GRMs

2) GRM is the main engineering condition affecting embankment stability. Existing GRMs can protect permafrost to a certain extent, but their cooling efficiency is different. In terms of embankment disease controlling efficiency, the strategy of air convection heat exchange is high, the strategy of discharging heat is middle, and the strategy of controlling heat conduction is low. The composite measure combining two or more GRMs can significantly improve the controlling efficiency of embankment diseases.

3) The method of combining analytic hierarchy process and fuzzy comprehensive evaluation can effectively evaluate the stability of expressway in permafrost regions, and make reasonable pre-evaluation on the stability of the proposed expressway.

4) For the proposed QTE, the embankment stability cannot be guaranteed without any countermeasures in most regions. The selection of GRMs is closely related to the geographical environment for the embankment. In general, high level GRMs should be adopted in warm permafrost regions, while low level GRMs can be adopted in high-altitude mountainous regions. The GRMs cannot completely overcome the potential embankment disease. Necessary maintenance is the key to maintain the stability of expressways in permafrost regions.

Appendix A

The calculated results for the judgment matrix and weight of rule hierarchy and the factor hierarchy (permafrost property, engineering condition, geological condition climatic environment) are shown in Table A1 and Tables A2-A5, respectively.

Appendix B

The membership degree of quantitative indexes can generally be determined by the method of the ascending or descending semi-trapezoid function and linear trigonometric function. According to the numerical relationship between quantitative index and evaluation object, quantitative index can be divided into positive and negative indexes. Different types of indexes have different membership function curves (Figure B1). For positive indexes, such as permafrost thickness and vegetation coverage in this study, the larger the value, the higher the evaluation object level. But for negative indexes, such as seasonal thawing depth and mean annual ground temperature, the larger the value, the lower the evaluation object level. The membership degree of positive indexes under different evaluation levels can be calculated by Eqs. (B1)-(B4). The calculation method for membership degree of negative index is similar to that of positive index, and can be obtained by Figure B1(b), which is not specifically listed here:

(B1)

(B2)

(B3)

(B4)

where r_ij1, r_ij2, r_ij3 and r_ij4 are the membership degrees of factor U_ij at different evaluation levels; x is the actual value of the factor; C₁, C₂, C₃ and C₄ are the grading standards of evaluation levels. For level interval only containing the upper limit or the lower limit, the grading standard directly takes the limit value, but for level interval containing both the upper and lower limits, the standard takes the median of the upper and lower limits.

Table A1 Judgment matrix and weight of evaluation index for rule hierarchy

Table A2 Judgment matrix and weight for permafrost property

Table A3 Judgment matrix and weight for engineering condition

Table A4 Judgment matrix and weight for geological condition

Table A5 Judgment matrix and weight for climatic environment

Since the normal distribution function can reasonably indicate the fuzzy relation between an index and each evaluation level, a set of appropriate values with normal distribution characteristics are used as the fuzzy relation set of qualitative indexes in this study, namely single factor evaluation set. Table B1 shows the single factor evaluation set of qualitative indexes at different evaluation levels, which can be directly used for single factor evaluation.

Figure B1 Fuzzy membership degree function curves:

Table B1 Reference table of single factor evaluation set of qualitative indexes

Appendix C

Equations (C1)-(C4) present the calculation process of the fuzzy comprehensive evaluation set for permafrost property, engineering condition, geological condition and climatic environment, respectively:

(C1)

(C2)

(C3)

(C4)

The primary fuzzy comprehensive evaluation set is expressed as follows:

(C5)

The expressway stability index: Q=[0.4498, 0.2411, 0.2667, 0.0445] [100, 75, 50, 25]^T=77.51.

Contributors

LUO Xiao-xiao established the models, predicted the stability and wrote the first draft of manuscript. MA Qin-guo provided the ideas and edited the draft of the manuscript. JIANG Hai-qiang analyzed the calculated results.

Conflict of interest

LUO Xiao-xiao, MA Qin-guo, and JIANG Hai-qiang declare that they have no conflict of interest.

References

[1] CHENG Guo-dong. The mechanism of repeated-segregation for the formation of thick layered ground ice [J]. Cold Regions Science and Technology, 1983, 8(1): 57-66. DOI: 10.1016/0165-232X(83)90017-4.

[2] ZHAO Lin, DING Yong-jian, LIU Guang-yue, WANG Shao-ling, JIN Hui-jun. Estimates of the reserves of ground ice in permafrost regions on the Tibetan Plateau [J]. Journal of Glaciology and Geocryology, 2010, 32(1): 1-9. (in Chinese)

[3] PENG Hui, MA Wei, MU Yan-hu, JIN Long. Impact of permafrost degradation on embankment deformation of Qinghai-Tibet Highway in permafrost regions [J]. Journal of Central South University, 2015, 22(3): 1079-1086. DOI: 10.1007/s11771-015-2619-2.

[4] LIN Zhan-ju, NIU Fu-jun, LUO Jing, LU Jia-hao, LIU Hua. Changes in permafrost environments caused by construction and maintenance of Qinghai-Tibet Highway [J]. Journal of Central South University, 2011, 18(5): 1454-1464. DOI: 10.1007/s11771-011-0861-9.

[5] MA Wei, NIU Fu-jun, MU Yan-hu. Basic research on the major permafrost projects in the Qinghai-Tibet plateau [J]. Advances in Earth Science, 2012, 27(11): 1185-1191. (in Chinese)

[6] YU Qi-hao, FAN Kai, YOU Yan-hui, GUO Lei, YUAN Chang. Comparative analysis of temperature variation characteristics of permafrost roadbeds with different widths [J]. Cold Regions Science and Technology, 2015, 117: 12-18. DOI: 10.1016/j.coldregions.2015.05.002.

[7] MA Tao, TANG Tao, HUANG Xiao-ming, WANG Hao. Numerical analysis on thermal regime of wide embankment in permafrost regions of Qinghai–Tibet Plateau [J]. Journal of Central South University, 2016, 23(12): 3346-3355. DOI: 10.1007/s11771-016-3400-x.

[8] CHENG Guo-dong, SUN Zhi-zhong, NIU Fu-jun. Application of the roadbed cooling approach in Qinghai- Tibet railway engineering [J]. Cold Regions Science and Technology, 2008, 53(3): 241-258. DOI: 10.1016/ j.coldregions.2007.02.006.

[9] LIU Ming-hao, LI Guo-yu, NIU Fu-jun, LIN Zhan-ju, SHANG Yun-hu. Porosity of crushed rock layer and its impact on thermal regime of Qinghai-Tibet Railway embankment [J]. Journal of Central South University, 2017, 24(4): 977-987. DOI: 10.1007/s11771-017-3500-2.

[10] YU Qi-hao, NIU Fu-jun, PAN Xi-cai, BAI Yang, ZHANG Ming-yi. Investigation of embankment with temperature- controlled ventilation along the Qinghai-Tibet Railway [J]. Cold Regions Science and Technology, 2008, 53(2): 193-199. DOI: 10.1016/j.coldregions.2007.07.002.

[11] WEN Zhi, SHENG Yu, MA Wei, QI Ji-lin, WU Ji-chun. Analysis on effect of permafrost protection by two-phase closed thermosyphon and insulation jointly in permafrost regions [J]. Cold Regions Science and Technology, 2005, 43(3): 150-163. DOI: 10.1016/j.coldregions.2005.04.001.

[12] DONG Yuan-hong, PEI Wan-sheng, LIU Ge, JIN Long, CHEN Dong-gen. In-situ experimental and numerical investigation on the cooling effect of a multi-lane embankment with combined crushed-rock interlayer and ventilated ducts in permafrost regions [J]. Cold Regions Science and Technology, 2014, 104-105: 97-105.

[13] WEN Zhi, SHENG Yu, MA Wei, QI Ji-lin. Evaluation of EPS application to embankment of Qinghai-Tibetan railway [J]. Cold Regions Science and Technology, 2005, 41(3): 235-247. DOI: 10.1016/j.coldregions.2004.11.001.

[14] LAI Yuan-ming, WANG Qiu-sheng, NIU Fu-jun, ZHANG Ke-hua. Three-dimensional nonlinear analysis for temperature characteristic of ventilated embankment in permafrost regions [J]. Cold Regions Science and Technology, 2004, 38(2, 3): 165-184. DOI: 10.1016/ j.coldregions.2003.10.006.

[15] ZHANG Ming-yi. Study on long-term thermal stability of air cooled subgrade in permafrost regions [D]. Lanzhou: Cold and Arid Regions Environmental and Engineering Research Institute, The Chinese Academy of Sciences. 2007. (in Chinese)

[16] YU Wen-bing, LIU Wei-bo, CHEN Lin, YI Xin, HAN Feng-lei, HU Da. Evaluation of cooling effects of crushed rock under sand-filling and climate warming scenarios on the Tibet Plateau [J]. Applied Thermal Engineering, 2016, 92: 130-136. DOI: 10.1016/j.applthermaleng.2015.09.030.

[17] YU Fan, ZHANG Ming-yi, LAI Yuan-ming, LIU Yong-zhi, QI Ji-lin, YAO Xiao-liang. Crack formation of a highway embankment installed with two-phase closed thermosyphons in permafrost regions: Field experiment and geothermal modelling [J]. Applied Thermal Engineering, 2017, 115: 670-681. DOI: 10.1016/j.applthermaleng.2017.01.001.

[18] QIN Ying-hong, TAN Kang-hao, LIANG Jia. Theory and procedure for measuring the albedo of a roadway embankment [J]. Cold Regions Science and Technology, 2016, 126: 30-35. DOI: 10.1016/j.coldregions.2016.03.005.

[19] TAN Kang-hao, QIN Ying-hong, LIANG Jia, PANG Ru-yue, LI Yun-feng. Theory and application of measuring the albedo of crushed-rock layer embankment in permafrost regions [J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(1): 254-260. (in Chinese)

[20] LEVINSON R, AKBARI H, REILLY J C. Cooler tile-roofed buildings with near-infrared-reflective non-white coatings [J]. Building and Environment, 2007, 42(7): 2591-2605. DOI: 10.1016/j.buildenv.2006.06.005.

[21] BANESHI M, MARUYAMA S, KOMIYA A. Comparison between aesthetic and thermal performances of copper oxide and titanium dioxide nano-particulate coatings [J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2011, 112(7):1197-1204. DOI: 10.1016/j.jqsrt.2010.08.032

[22] QIN Ying-hong, TAN Kang-hao, YANG Hai-feng, LI Fang-hua. The albedo of crushed-rock layers and its implication to cool roadbeds in permafrost regions [J]. Cold Regions Science and Technology, 2016, 128: 32-37. DOI: 10.1016/j.coldregions.2016.05.004.

[23] QIN Ying-hong, HILLER J E. Understanding pavement- surface energy balance and its implications on cool pavement development [J]. Energy and Buildings, 2014, 85: 389-399. DOI: 10.1016/j.enbuild.2014.09.076.

[24] WANG Shao-ling, MI Hai-zhen. The change of permafrost under roadbed with asphalt pavement along the Qinghai-Tibet highway [J]. Journal of Glaciology and Geocryology, 1993, 15(4): 566-573. (in Chinese)

[25] LIU Jian-kun, TONG Chang-jiang, FANG Jian-hong. Inductions of geotechnical engineering in cold area [M]. Beijing: China Railway Press, 2005. (in Chinese)

[26] JIN Hui-jun, WANG Shao-ling, YU Qi-hao, WU Qing-bai, WEI Zhi. Regionalization and assessment of environmental geological conditions of frozen soils along the Qinghai-Tibet Engineering Corridor [J]. Hydrogeology & Engineering Geology, 2006, 33(6): 66-71, 137. (in Chinese)

[27] QI Chang-qing, WU Qing-bai, SHI Bin, TANG Chao-sheng. Reliability analysis of thawing settlement of permafrost subgrade based on genetic algorithm [J]. Rock and Soil Mechanics, 2006, 27(8): 1429-1432, 1436. (in Chinese)

[28] QI Chang-qing, WU Qing-bai, SHI Bin, WU Ji-min, YU Jin. Application of BP neural network on deformation prediction for permafrost embankment [J]. Hydrogeology & Engineering Geology, 2007, 34(4): 27-30. (in Chinese)

[29] MIAO Jiang-long, CHEN Xi, LV Yan-nan, WANG Dong- yong. Prediction on deformation and reliability of subgrade of Qinghai-Tibet Railway based on BP neural network method [J]. Journal of Natural Disasters, 2018, 27(4): 83-89. (in Chinese)

[30] CAO Wei, SHENG Yu, QIN Ying-hong, LI Jing, WU Ji-chun. An application of a new method in permafrost environment assessment of Muli mining area in Qinghai-Tibet Plateau, China [J]. Environmental Earth Sciences, 2011, 63(3): 609-616. DOI: 10.1007/s12665-010-0728-7.

[31] ZHAO Hong-ting, WU Qing-bai, ZHANG Zhong-qiong, HOU Yan-dong. Assessment of cooling effect of the crushed rock embankment based on catastrophe progression method [J]. Chinese Journal of Rock Mechanics and Engineering. 2019, 38(8): 1686-1695. (in Chinese)

[32] HUO Ming, CHEN Jian-bing, ZHU Dong-peng, ZHANG Jin-zhao. Study of early warning on roadbed diseases of Qinghai-Tibet highway in permafrost regions [J]. Rock and Soil Mechanics, 2010, 31(1): 331-336. (in Chinese)

[33] CAO Wei, CHEN Ji, ZHANG Bo, WU Ji-chun, LI Jing, SHENG Yu. Fuzzy evaluation of the effect of rubble roadbed engineering in permafrost regions along the Chaidaer-Muli Railway in Qinghai Province [J]. Journal of Glaciology and Geocryology, 2015, 37(6): 1555-1562. (in Chinese)

[34] ANDERSLAND O B, LADANYI B. Frozen ground engineering [M]. New Jersey: John Wiley and Sons, 2004.

[35] WU Zi-wang, LIU Yong-zhi. Frozen subsoil and engineering [M]. Beijing: China Ocean Press, 2005. (in Chinese)

[36] ZHOU Zhong, LIU Zhuang-zhuang, YANG Hao, GAO Wen-yuan, ZHANG Cheng-cheng. Freeze-thaw damage mechanism of elastic modulus of soil-rock mixtures at different confining pressures [J]. Journal of Central South University, 2020, 27(2): 554-565. DOI: 10.1007/s11771- 020-4316-z.

[37] QU Yong-long, NI Wan-kui, NIU Fu-jun, MU Yan-hu, CHEN Guo-liang, LUO Jing. Mechanical and electrical properties of coarse-grained soil affected by cyclic freeze- thaw in high cold regions [J]. Journal of Central South University, 2020, 27(3): 853-866. DOI: 10.1007/s11771- 020-4336-8.

[38] YU Fan. Investigation on settlement mechanism of roadway embankments in permafrost regions [D]. Lanzhou: Cold and Arid Regions Environmental and Engineering Research Institute, The Chinese Academy of Sciences. 2013. (in Chinese)

[39] CHOU Ya-ling. Study on shady-sunny effect and the forming mechanism of the longitudinal embankment crack in permafrost [D]. Lanzhou: Cold and Arid Regions Environmental and Engineering Research Institute, The Chinese Academy of Sciences. 2008. (in Chinese)

[40] GUO Yan-wei, LI Sheng-tao, GENG Xin. Main water disasters and hydrogeological mechanisms on Qinghai-Tibet Highway (Kunlun Mountain pass to Wudaoliang) [J]. Subgrade Engineering, 2012(6): 45-48. (in Chinese)

[41] FAN Ji-jiao, LI Sheng-tao, ZHANG Sen-qi, WANG Xiu- ming, LI Rong. Main water disasters and hydrogeological mechanism in Kunlun mountain-Qingshui river section of Qinghai-Tibet engineering corridor [J]. Geotechnical Investigation & Surveying, 2012, 40(1): 43-48, 90. (in Chinese)

[42] WU Zi-wang, ZHU Lin-nan, GUO Xing-min, WANG Xiao- yang, FANG Jian-hong. Critical height of the embankment in the permafrost regions along the Qinghai-Kangding highway [J]. Journal of Glaciolgy and Geocryology, 1998, 20(1): 3-5. (in Chinese)

[43] ZHANG Ming-yi, ZHANG Jian-ming, LAI Yuan-ming. Numerical analysis for critical height of railway embankment in permafrost regions of Qinghai-Tibetan plateau [J]. Cold Regions Science and Technology, 2005, 41(2): 111-120. DOI: 10.1016/j.coldregions.2004.09.001.

[44] ZHANG Jian-ming, ZHANG Jin-zhao, LIU Yong-zhi. Study on the reasonable embankment height of Qinghai-Tibet Railway in permafrost regions [J]. China Railway Science, 2006, 27(5): 28-34. (in Chinese)

[45] MA Qin-guo, LAI Yuan-ming, WU Dao-yong, LIAO Meng-ke. Analysis of critical height of railway embankment in permafrost region [J]. China Railway Science, 2015, 36(6): 8-15. (in Chinese)

[46] ZHANG Lu-xin, YUAN Si-cheng, YANG Yong-ping. Mechanism and prevention of deformation cracks of embankments in the permafrost region along Qinghai-Xizang Railway [J]. Quaternary Sciences, 2003, 23(6): 604-610. (in Chinese)

[47] MA Qin-guo, LAI Yuan-ming, WU Dao-yong. Analysis of temperature field of high grade highway embankment in permafrost regions [J]. Journal of Central South University (Science and Technology), 2016, 47(7): 2415-2423. (in Chinese)

[48] YU Qi-hao, MU Yan-hu, YUAN Chang, MA Wei, PAN Xi-cai. The cold accumulative effect of expressway embankment with a combined cooling measure in permafrost zones [J]. Cold Regions Science and Technology, 2019, 163: 59-67. DOI: 10.1016/j.coldregions.2019.04.009.

[49] CHANG Xiao-li, JIN Hui-jun, WANG Yong-ping, ZHANG Yan-lin, ZHOU Gang-yi, CHE Fu-qiang, ZHAO Yu-mei. Influences of vegetation on permafrost: A review [J]. Acta Ecologica Sinica, 2012, 32(24): 7981-7990. (in Chinese)

[50] WANG Shuang-jie, JIN Long, MU Ke, ZHU Dong-peng, CHEN Dong-gen, DONG Yuan-hong. Distresses and countermeasures of highway subgrade in plateau permafrost regions [J]. Engineering Sciences, 2017, 19(6): 140-146. (in Chinese)

[51] YU Qi-hao, PAN Xi-cai, CHENG Guo-dong, HE Nai-wu. An experimental study on the cooling mechanism of a shading board in permafrost engineering [J]. Cold Regions Science and Technology, 2008, 53(3): 298-304. DOI: 10.1016/j.coldregions.2007.07.003.

[52] REGEHR J D, MILLIGAN C A, MONTUFAR J, ALFARO M. Review of effectiveness and costs of strategies to improve roadbed stability in permafrost regions [J]. Journal of Cold Regions Engineering, 2013, 27(3): 109-131. DOI: 10.1061/(ASCE)CR.1943-5495.0000054.

[53] CHEN Ji, HU Ze-yong, DOU Shun, QIAN Ze-yu. Yin–Yang Slope problem along Qinghai–Tibetan Lines and its radiation mechanism [J]. Cold Regions Science and Technology, 2006, 44(3): 217-224. 10.1016/j.coldregions.2005.12.001.

[54] CHEN Ji, XU Shun-hua, DOU Shun, ZHANG Lu-xin. Observation and study of cooling radius of heat pipes in swampy permafrost regions along Qaidar-Muli Railway [J]. Journal of Glaciology and Geocryology, 2011, 33(4): 897-901. (in Chinese)

[55] YU Qi-hao, PAN Xi-cai, CHENG Guo-dong, HE Nai-wu. Study on main influential factors on ventilated embankment and corresponding measures [J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(S1): 3045-3051. (in Chinese)

[56] SHENG Yu, MA Wei, WEN Zhi, ZHANG Ming-yi. Analysis of difference in thermal state between south faced slope and north faced slope of railway embankment in permafrost region [J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(17): 199-203. (in Chinese)

[57] QIN Ying-hong, ZHANG Jian-ming. A review on the cooling effect of duct-ventilated embankments in China [J]. Cold Regions Science and Technology, 2013, 95: 1-10. DOI: 10.1016/j.coldregions.2013.07.005.

[58] YU Qi-hao, CHENG Guo-dong, NIU Fu-jun. The application of auto-temperature-controlled ventilation embankment in Qinghai-Tibet Railway [J]. Science in China Series D-Earth Sciences, 2004, 47(1): 168-176. DOI: 10.1360/04zd0019.

[59] FAN Kai. Research on the deformation control and the stability techniques of highway embankment in high altitude and cold regions [D]. Lanzhou: Cold and Arid Regions Environmental and Engineering Research Institute, The Chinese Academy of Sciences. 2015. (in Chinese)

[60] AHMED S, RIAZ A K. Temperature monitoring and compressibility measurement of a tire shred embankment: Winnipeg, Manitoba, Canada [J]. Transportation Research Record Journal of the Transportation Research Board, 2002, 1808(1): 67-75. DOI: 10.3141/1808-08.

[61] WANG Ai-guo, MA Wei, WU Zhi-jian. Study on influence of sand-and-gravel layer thickness upblock-stone railway embankment on cooling effect of frozen-soil foundation [J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(13): 2333-2341 (in Chinese)

[62] WU Qing-bai, CUI Wei, LIU Yong-zhi. The cooling effect of U-type crushed rock embankment on permafrost [J]. Journal of Glaciology and Geocryology, 2010, 32(3): 532-537. (in Chinese)

[63] WU Qing-bai, ZHAO Hong-ting, ZHANG Zhong-qiong, CHEN Ji, LIU Yong-zhi. Long-term role of cooling the underlying permafrost of the crushed rock structure embankment along the Qinghai-Xizang Railway [J]. Permafrost and Periglacial Processes, 2020, 31(1): 172-183. DOI: 10.1002/ppp.2027.

[64] WU Jun-jie, MA Wei, SUN Zhi-zhong, WEN Zhi. In-situ study on cooling effect of the two-phase closed thermosyphon and insulation combinational embankment of the Qinghai-Tibet Railway [J]. Cold Regions Science and Technology, 2010, 60(3): 234-244. DOI: 10.1016/ j.coldregions.2009.11.002.

[65] YUAN Chang, YU Qi-hao, YOU Yan-hui, GUO Lei. Formation mechanism of longitudinal cracks in expressway embankments with inclined thermosyphons in warm and ice-rich permafrost regions [J]. Applied Thermal Engineering, 2018, 133: 21-32. DOI: 10.1016/j.applthermaleng.2017.12. 118.

[66] ZHANG Ming-yi, LAI Yuan-ming, DONG Yuan-hong. Three-dimensional nonlinear analysis for the cooling characteristics of crushed-rock interlayer embankment with ventilated duct along the Qinghai-Tibet Expressway in permafrost regions [J]. Journal of Cold Regions Engineering, 2010, 24(4): 126-141. DOI: 10.1061/(ASCE)CR.1943-5495. 0000018.

[67] DONG Yuan-hong, LAI Yuan-ming, LI Jing-bo, YANG Yu-gui. Laboratory investigation on the cooling effect of crushed-rock interlayer embankment with ventilated ducts in permafrost regions [J]. Cold Regions Science and Technology, 2010, 61(2, 3): 136-142. DOI: 10.1016/ j.coldregions.2010.01.012.

[68] ZHANG Ming-yi, ZHANG Xi-yin, LI Shuang-yang, WU Dao-yong, PEI Wan-sheng, LAI Yuan-ming. Evaluating the cooling performance of crushed-rock interlayer embankments with unperforated and perforated ventilation ducts in permafrost regions [J]. Energy, 2015, 93: 874-881. DOI: 10.1016/j.energy.2015.08.059.

[69] ZHANG Ming-yi, LAI Yuan-ming, WU Qing-bai, YU Qi-hao, ZHAO Tao, PEI Wan-sheng, ZHANG Jian-ming. A full-scale field experiment to evaluate the cooling performance of a novel composite embankment in permafrost regions [J]. International Journal of Heat and Mass Transfer, 2016, 95: 1047-1056. DOI: 10.1016/ j.ijheatmasstransfer. 2015.12.067.

[70] QIAN Jin, YU Qi-hao, JIANG Zi-qiang, GU Wei, YOU Yan-hui. Experiment on convective and cooling process of macrovoid hollow concrete brick layer [J]. China Journal of Highway and Transport, 2011, 24(3): 8-15. (in Chinese)

[71] XIAO Jian-zhang, LAI Yuan-ming, ZHANG Xue-fu, YU Wen-bing, ZHANG Shu-juan. Three-dimensional temperature character analysis the land bridge on the Qinghai-Tibet Railway [J]. Journal of Glaciology and Geocryology, 2004, 26(4): 426-434. (in Chinese)

[72] NIU Fu-jun, LIN Zhan-ju, LU Jia-hao, LIU Hua. Study of the influencing factors of roadbed settlement in embankment-bridge transition section along Qinghai-Tibet Railway [J]. Rock and Soil Mechanics, 2011, 32(S2): 372-377. (in Chinese)

[73] LI Ren, ZHAO Lin, DING Yong-jian, WU Tong-hua, XIAO Yao, XIN Yue-fei, SUN Lin-chan, HU Guo-jie, ZOU De-fu, JIAO Yong-liang, QING Yan-hui. Variation characteristics of global radiation over the Tibetan Plateau during the past 40 years [J]. Journal of Glaciology and Geocryology, 2012, 34(6): 1319-1327. (in Chinese)

[74] ZHOU Bing-rong, LI Feng-xia, YAN Liang-dong, ZHANG Hai-jing, HE Yong-qing. Research on model of solar radiation estimation in Qinghai Province [J]. Chinese Journal of Agrometeorology, 2011, 32(4): 495-499.

[75] LU Chun-xia, WANG Ling, XIE Gao-di, LENG Yun-fa. Altitude effect of precipitation and spatial distribution of Qinghai-Tibetan Plateau [J]. Journal of Mountain Science, 2007, 25(6): 655-663. (in Chinese)

[76] ZHU Xi-de, LI Lin, QIN Ning-sheng, ZHOU Lu-sheng, WANG Qing-chun. Studies on climatic variation and anomaly types of the annual precipitation over Qinghai- Tibetan Plateau [J]. Scientia Meteorologica Sinica, 2003, 23(4): 452-459. (in Chinese)

(Edited by ZHENG Yu-tong)

中文导读

多年冻土区现有地温调控措施作用下高速公路路基稳定性预评价

摘要：多年冻土区高速公路建设的主要问题是路基的稳定性。面对恶劣的环境条件和地表与大气之间强烈的热交换，有必要对多年冻土区拟建青藏高速公路的稳定性进行预测和评价。首先，分析影响路基稳定性的因素。然后，在此基础上建立路基稳定性评价方案。最后，利用该评价方案对不同地热调节措施条件下拟建青藏高速公路的稳定性进行预评价。结果表明，影响因素包括气候环境、冻土性质、工程条件和地质条件，其中工程条件和冻土性质是影响路基稳定的主要因素。在不同的地貌区域，拟建青藏高速公路的稳定性差异很大。现有地温调控措施的应用效果和对路基稳定性的贡献不同，采用地温调控措施不能完全克服各种因素对高速公路稳定性的影响，应根据路基所处的地貌环境采用不同的地温调控措施，以保证路基的稳定。

关键词：多年冻土；高速公路路基；影响因素；稳定性评价；地温调控措施

Foundation item: Project(2019QZKK0905) supported by the Second Tibetan Plateau Scientific Expedition and Research (STEP) Program, China; Project(41901074) supported by the National Natural Science Foundation of China; Project(2020A1515010745) supported by the Natural Science Foundation of Guangdong Province, China; Project(SKLFSE201810) supported by the Open Fund of the State Key Laboratory of Frozen Soil Engineering, China; Project(2019MS119) supported by the Fundamental Research Funds for the Central Universities, China

Received date: 2020-03-21; Accepted date: 2020-08-07

Corresponding author: MA Qin-guo, PhD, ResearchAssistant; Tel: +86-20-87114016; E-mail: maqinguo@lzb.ac.cn; ORCID: https:// orcid.org/0000-0002-4131-233X