A method of safety monitoring and measurement of overall frost heaving pressure of tunnel in seasonal frozen area
-
Guangyao Cui
Abstract
Antifreeze design, scientific operation, and maintenance of tunnels with broken surrounding rock in seasonal frozen areas are key factors that affect the safety of tunnel. According to a freezing damage treatment project, theoretical analysis, field monitoring, and numerical simulation are used to study the calculation method of the overall frost-heaving pressure of a tunnel with broken surrounding rock in the seasonal frozen area. Based on the overall frost-heaving model of the broken freeze–thawing lithosphere, a calculation method of the overall frost-heaving pressure of the horseshoe-shaped tunnel with broken surrounding rock in a seasonal frozen area is proposed. The results show that the management grading results based on the freezing depth of the surrounding rock on site are consistent with those based on the minimum safety factor of the lining structure, which indicates that the proposed method for calculating the overall frost-heaving pressure of broken surrounding rock tunnel and management standards for safety monitoring and measurement of tunnel linings can be applied to engineering practice. The research results can provide a reference for the calculation of frost-heaving pressure, operational safety, and prevention of freezing damages in tunnels with broken surrounding rock in a seasonal frozen area.
1 Introduction
Frozen soil refers to the rock and soil below 0℃ and containing ice, which can be generally divided into short-term frozen soil, seasonal frozen soil and permafrost [1]. China has the third largest area of frozen soil in the world, with seasonal frozen soil accounting for more than 50% of the land area [2]. In recent years, with the continuous and in-depth development of China’s transportation infrastructure, a large number of tunnels have emerged in seasonal frozen areas. In the seasonal frozen area, severe freezing damages were recorded in tunnels without antifreeze designs, seriously affecting the operation safety and the service life of the tunnel [3,4].
Frost-heaving pressure is generally considered to be the cause of freezing damages in tunnels in the seasonal frozen area, so it is of great significance to accurately calculate the frost-heaving pressure. The calculation models of frost-heaving pressure were first proposed in the 1970s, including the rigid ice model [5,6], the hydrodynamic models [7,8], and the segregation potential models [9,10,11]. After the 1990s, these models were developed and applied at a high speed with the advent of finite element software. In the twenty-first century, scholars and experts have conducted more in-depth and widely applied research on the frost-heaving pressure in the frozen area, mainly through laboratory tests and numerical simulations. For example, some have used laboratory tests to understand the mechanical behaviors of frozen soils under hydrostatic and shear paths [12,13,14,15]. Using a variety of assumptions, some have also modeled the behavior of frozen soils. For instance, evolutionary laws for tracking changes in porosity and volume during freezing have been proposed [16]. Kim et al. presented a model describing the progressive soil in frozen regions [15].
At present, there are three main models to calculate the frost-heaving pressure of tunnel in the seasonal frozen area: the frost-heaving model of the weathered layer with water, the frost-heaving model of stagnant water and the overall frost-heaving model of broken freeze–thawing lithosphere [17]. The overall frost-heaving model is mainly used to study the frost-heaving mechanism of the tunnel with broken surroundings rock in the seasonal frozen area. Lai et al. proposed the overall frost-heaving model of the tunnel and obtained the frost-heaving pressure and lining stress of the tunnel in the seasonal frozen area by using the corresponding principle of elastic viscoelasticity [18]. Feng et al. divided the surrounding rock of the whole tunnel into the non-frozen elastic area, frozen elastic area, frozen plastic area, and lining area, and established a new elastic-plastic calculation model of the surrounding rock of the tunnel in the seasonal frozen area [19]. Considering the comprehensive effects of non-uniform frost heaving, supporting strength and supporting time, Liu et al. deduced the elastic–plastic solution of tunnel frost-heaving pressure in the seasonal frozen area [20]. Liu et al. optimized the overall frost-heaving model by considering the comprehensive effect of the reduction of rock elastic modulus and the increase of porosity due to the freeze–thawing cycles [21].
To sum up, the current research on frost-heaving pressure is based on mechanical analysis. The tunnels are all circular sections, which is not consistent with the actual project. Moreover, there are few literature reports on the management standard for safety monitoring and measurement of existing railway tunnel structures in the seasonal frozen area. So, in the next section of the article, based on the overall frost-heaving model of the broken freeze–thawing lithosphere, the calculation equation of the overall frost-heaving pressure of the horseshoe-shaped tunnel is deduced. Then, in the third section, relying on the freezing damages treatment project in Yushuchuan Tunnel, the management standard for safety monitoring and measurement of existing railway tunnel structure in the seasonal frozen area are put forward and finally verified in the fourth section through field measurement and numerical simulation. The research results are of great significance to antifreeze design and operation safety of tunnels in seasonal frozen areas.
2 Calculation method of frost-heaving pressure of tunnel in seasonal frozen area
2.1 Model assumption
The frost-heaving model of the horseshoe-shaped tunnel in the seasonal frozen area is shown in Figure 1. The red area represents the surrounding rock. The blue area represents the disturbed layer of freeze–thawing lithosphere. The orange area represents the weathered layer of freeze–thawing lithosphere. The green area represents the tunnel lining. The frost-heaving area of the tunnel cross-section is considered by the method of the equivalent rectangle. The weathered layer and the disturbed layer are jointly restrained by the lining and the surrounding rock, and then the expansion pressure, that is, the frost-heaving pressure, is generated for the lining and the surrounding rock. C w is the circumference of the center of the weathered layer. C wo is the outer circumference of the weathered layer. C wi is the inner circumference of the weathered layer. C d is the circumference of the center of the disturbed layer. C do is the outer circumference of the disturbed layer. C di is the inner circumference of the disturbed layer. C di is equal to C wo. And h, h 1, and h 2 are the thickness of lining, weathered layer and disturbed layer, respectively.
Frost-heaving model of horseshoe-shaped tunnel.
The model assumes that the frost-heaving pressure has the same effect on all directions in the space, and the weathered layer, the disturbed layer, the lining and the surrounding rock are elastically contacted, which conforms to the isotropic assumption and does not consider the coupling effect of the weathered layer and the disturbed layer.
2.2 Equation derivations
According to the frost-heaving model of a horseshoe-shaped tunnel, the freeze–thawing lithosphere of the horseshoe-shaped tunnel is composed of a weathered layer and a disturbed layer. When the freezing depth of the tunnel is less than the thickness of the weathered layer, only the frost heaving of the weathered layer is considered. When the freezing depth of the tunnel is greater than the thickness of the weathered layer, the joint frost heaving of the weathered layer and the disturbed layer is considered.
It is assumed that the frost-heaving pressure of the weathered layer after freezing is P 1, the frost-heaving pressure of the disturbed layer after freezing is P 2, and the frost-heaving pressure of the same layer is equal in all directions in space. The final frost-heaving pressure on the lining is P.
When the weathered layer is frost heaving, the displacement of the interface between the weathered layer and the lining is:
where K 1 is the equivalent elastic resistance coefficient of lining;
The displacement of the interface between the weathered layer and the disturbed layer is:
where K 3 is the elastic resistance coefficient of the disturbed layer.
Assuming that the longitudinal length of the tunnel is taken as the unit length, the volume of the weathered layer is:
The volume increment of the weathered layer after frost heaving is:
The relationship between volume expansion and volume increment of the weathered layer is as follows:
where α w is the frozen-heave factor of the weathered layer.
Substituting equations (3) and (4) into equation (5), it is concluded that the frost-heaving pressure produced by the weathered layer is:
When the disturbed layer is frost heaving, the displacement of the contact surface between the disturbed layer and the weathered layer is:
where K′ is the equivalent elastic resistance of lining and weathered layer.
Substituting equation (8) into equation (7), we can get:
The displacement of the contact surface between the disturbed layer and the original surrounding rock is:
where K 4 is the original elastic resistance coefficient of the surrounding rock;
The volume of the disturbed layer is:
The volume increment of the disturbed layer after frost heaving is as follows:
The relationship between the volume of the disturbed layer and the volume increment is as follows:
where α d is the frozen-heave factor of the disturbed layer.
According to equations (12) and (13), the frost-heaving pressure produced by the disturbed layer is as follows:
K 2 is the elastic resistance coefficient of weathered layer; C w is the center circumference of weathered layer; C wo is the outer circumference of weathered layer. C wi is the inner circumference of the weathered layer; C d is the circumference of the center of the disturbed layer; C do is the outer circumference of the disturbed layer. C di is the inner circumference of the disturbed layer; C di is equal to C wo; and h, h 1, and h 2 are the thickness of the lining, weathered layer and disturbed layer, respectively.
When the freezing depth is less than the thickness of the weathered layer (h ≤ h 1), the frost-heaving pressure is completely generated by the weathered layer; that is, the frost-heaving pressure is:
When the freezing depth is greater than the thickness of the weathered layer (h ≥ h 1), the frost-heaving pressure is completely provided by both the weathered layer and the disturbed layer. At this time, the frost-heaving pressure is:
3 Management standards for safety monitoring and measurement of tunnel lining in seasonal frozen area
3.1 Overview of Yushuchuan tunnel
Yushuchuan Tunnel is located in the low mountains and hills of the Buerhaton River in China. The region has relatively large topographic fluctuation, with a relative elevation difference of about 132 m, and the vegetation is developed. The tunnel import mileage is DK237 + 624, and the export mileage is DK239 + 835. The total length of the tunnel is 2,211 m, and the maximum buried depth is about 158 m. The design speed of the tunnel is 250 km/h, and the clearance area above the top surface of the inner rail is 92 m2. The distance between the whole tunnel line is 4.6 m. The average annual temperature in the area where the tunnel is located is 4.6℃, the average temperature in January is −15.2℃, the extreme maximum temperature is 36.5℃, the extreme minimum temperature is −37.1℃, and the maximum freezing depth of the soil is 192 cm. The tunnel is insulated by steel corrugated plate insulation lining.
3.2 Safety analysis of tunnel structure
3.2.1 Calculation of overall frost-heaving pressure
Following the Code for Design of Metro GB50157-2013 [22] and the design data of the tunnel project, the secondary lining of the tunnel is made of C30 concrete with a thickness of 40 cm. The equivalent elastic resistance coefficient of the lining can be taken as 75 kPa/mm. Based on the Code for Design of Road Tunnel JTG D70-2004 [23], the elastic resistance coefficient of grade IV surrounding rock is 200–500 kPa/mm, and that of grade V surrounding rock is 100–200 kPa/mm. In light of the design data, the surrounding rock of the tunnel is grade IV, so the original elastic resistance coefficient of the surrounding rock can be taken as 500 kPa/mm. The weathered layer and disturbed layer are broken surrounding rock, which can be taken as grade V surrounding rock, so the elastic resistance coefficient of the weathered layer can be taken as 200 kPa/mm, and the elastic resistance coefficient of the disturbed layer can be taken as 150 kPa/mm. From the site survey, it can be shown that the frozen-heave factor of the weathered layer is 15%, and the frozen-heave factor of the disturbed layer is 4%. The actual freezing depth is 2–3 m. In terms of the frost-heaving model of the weathered layer with water, the thickness of the weathered layer can be taken as 100 mm. The thickness of the disturbed layer is the difference value between the actual freezing depth and the thickness of the weathered layer. The outer perimeter of the disturbed layer changes with its thickness. The inner perimeter of the weathered layer is 30.7 m, and the outer perimeter is 31.3 m.
The overall frost-heaving pressure of tunnel lining under different freezing depth is calculated respectively, as shown in Table 1.
Calculation results of overall frost-heaving pressure under different freezing depth
| Freezing depth/m | Frost-heaving pressure/MPa |
|---|---|
| 0.2 | 1.119 |
| 0.3 | 1.485 |
| 0.4 | 1.852 |
| 0.5 | 2.218 |
| 0.6 | 2.584 |
| 0.7 | 2.951 |
| 0.8 | 3.317 |
| 1.0 | 4.050 |
| 1.2 | 4.783 |
| 1.4 | 5.516 |
| 1.6 | 6.248 |
| 1.8 | 6.981 |
| 1.92 | 7.421 |
3.2.2 Analysis of calculation results
In this part, the finite element software ANSYS is used for modeling and analysis, and the calculation model is shown in Figure 2. The lining is simulated by BEAM element and considered as linear elasticity, and the surrounding rock is simulated by PLANE42 element. The structural internal pressures and safety factors of plain concrete lining and reinforced concrete lining under overall frost-heaving pressure at different freezing depths are calculated, respectively (Table 2).
Calculation model.
Minimum safety factor of tunnel structure with different freezing depth
| Freezing depth/m | Minimum safety factor of plain concrete lining | Minimum safety factor of reinforced concrete lining |
|---|---|---|
| 0.2 | 2.87 (pressure control) | 4.68(pressure control) |
| 0.3 | 2.11 (pressure control) | 3.39(pressure control) |
| 0.4 | 1.67 (pressure control) | 2.65 (pressure control) |
| 0.5 | 1.45 (pressure control) | 2.37 (pressure control) |
| 0.6 | 1.18 (pressure control) | 1.95 (pressure control) |
| 0.7 | 1.07 (pressure control) | 1.76 (pressure control) |
| 0.8 | 0.91 (pressure control) | 1.42 (pressure control) |
| 1.0 | 0.74 (pressure control) | 1.16 (pressure control) |
| 1.2 | 0.63 (pressure control) | 1.01 (pressure control) |
| 1.4 | 0.54 (pressure control) | 0.84 (pressure control) |
| 1.6 | 0.48 (pressure control) | 0.74 (pressure control) |
| 1.8 | 0.43 (pressure control) | 0.66 (pressure control) |
| 1.92 | 0.40 (pressure control) | 0.62 (pressure control) |
Following the Code for Design of Metro GB50157-2013 and the Code for Design of Road Tunnel JTG D70-2004, the safety factor of small eccentric compression member is:
And the safety factor of small eccentric compression member is:
where width of the section is expressed by b, and the width of the section is 1 m. The thickness of the section is expressed by H. Structural axial force is expressed by N. The ultimate compressive strength of concrete is expressed by R a . The ultimate tensile strength of concrete is expressed by R l . The safety factor is expressed by K. The longitudinal bending coefficient of components is expressed by ϕ. The influence coefficient of axial force eccentricity is expressed by α.
3.3 Management standard for monitoring and measurement of tunnel lining
According to Code for Design of Road Tunnel JTG D70-2004, the minimum safety factor of plain concrete tunnel lining under pressure control is 2.0, and the minimum safety factor of reinforced concrete tunnel lining under pressure control is 1.7. Based on Table 2, the freezing depth of the surrounding rock of plain concrete tunnel lining shall not exceed 0.3 m, and that of reinforced concrete tunnel lining shall not exceed 0.7 m.
In order to reduce the occurrence of tunnel freezing damages as much as possible, ensure the operation safety of the existing railway tunnel, and realize the early warning and prevention of the existing railway tunnel freezing damages, we hereby establish the management standard for the safety monitoring and measurement of the existing railway tunnel structure in the seasonal frozen area, as shown in Figure 3 and Tables 3 and 4.
Management standard for safety monitoring and measurement of existing railway tunnel structure in seasonal frozen area: (a) plain concrete lining, (b) reinforced concrete lining.
Management standard for monitoring and measurement (plain concrete lining)
| Management level | Minimum safety factor | Freezing depth of surrounding rock | Construction condition |
|---|---|---|---|
| I | A < A 0 = 2.0 | U > U 0 = 0.30 m | Measures required |
| II | A 0 ≤ A ≤ 1.2A 0 | 0.26 m ≤ U ≤ 0.30 m | Enhanced monitoring, normal operation |
| III | 1.2A 0 ≤ A ≤ 1.4A 0 | 0.21 m ≤ U ≤ 0.26 m | Frequent monitoring, normal operation |
| IV | A > 1.4A 0 | U < 0.21 m | Routine monitoring, normal operation |
Management standard for monitoring and measurement (Reinforced concrete lining)
| Management level | Minimum safety factor | Freezing depth of surrounding rock | Construction condition |
|---|---|---|---|
| I | A < A 0 = 1.7 | U > U 0 = 0.70 m | Measures required |
| II | A 0 ≤ A ≤ 1.2A 0 | 0.58 m ≤ U ≤ 0.70 m | Strengthen monitoring and normal operation |
| III | 1.2A 0 ≤ A ≤ 1.4A 0 | 0.50 m ≤ U ≤ 0.58 m | Frequent monitoring, normal operation |
| IV | A > 1.4A 0 | U < 0.50 m | Routine monitoring, normal operation |
According to Figure 3 and Tables 3 and 4, we develop the monitoring frequency of surrounding rock temperature (Table 5).
Monitoring frequency of surrounding rock temperature
| Management level | Monitoring frequency and treatment measures |
|---|---|
| I | Take thermal insulation measures (such as spraying polyurethane thermal insulation materials, etc.) |
| II | Enhanced monitoring (the monitoring frequency is twice of level III), normal operation |
| III | Frequent monitoring (twice the monitoring frequency of level IV), normal operation |
| IV | Routine monitoring (monitor every 6–8 h), normal operation |
4 Field application and verification
4.1 On-site monitoring of surrounding rock temperature in Yushuchuan tunnel
4.1.1 Temperature measuring instrument
PT100 temperature sensor of class A was used for the temperature test. The temperature sensor was fixed on the 3-meter-long bar with adhesive tape, as shown in Figure 4. Each test section was provided with a temperature tester, and the tester components were placed in the case, and the case was fixed at the position of 1 meter above the tunnel wall foot. The exposed sensor wire was connected with the tester along the lining wall, and the wire was clamped vertically on the lining wall with a U-shaped line with a spacing of 15 cm.
Temperature measuring instrument: (a) temperature sensor; (b) test rod.
4.1.2 Monitoring arrangement
The monitoring section and monitoring point layout are shown in Figure 5. The temperature sensor of the lining structure was arranged on the inner surface and the middle of the secondary lining, the interface between the secondary lining and the primary support, and the interface between the primary support and the surrounding rock. The temperature sensors inside the surrounding rocks were arranged at equal intervals, and the interval is 70 cm.
Monitoring layout: (a) layout of monitoring section, (b) layout of monitoring points.
4.1.3 Data acquisition
The tunnel temperature data were transmitted through the wireless acquisition system. Each section is equipped with a wireless bridge. The data were transmitted to the 4 G route set at the hole through the wireless bridge, and the wireless transmission was realized through the 4 G signal.
4.2 Numerical simulation
Taking Yushuchuan Tunnel as the background, the finite element software ANSYS is used to establish the calculation model. The safety factor of tunnel structure is calculated and analyzed by simulating the frost-heaving force of surrounding rock through the change of ambient temperature. The field-measured mileage is used for calculation, as shown in Table 6, and the material thermodynamic parameters are shown in Table 7.
Calculation condition
| Working condition | Mileage | Type of lining | Time of data collection | Ambient temperature in tunnel/℃ | Freezing depth/m | Whether there is insulation lining |
|---|---|---|---|---|---|---|
| 1 | K353 + 089 | Plain concrete | 04:00, January 16, 2019 | −7.60 | 0.25 | Yes |
| 2 | K352 + 783 | Reinforced concrete | 04:00, January 16, 2019 | −8.37 | 0.25 | No |
| 3 | K352 + 183 | Plain concrete | 04:00, February 10, 2019 | −17.29 | 0.35 | Yes |
| 4 | K352 + 033 | Reinforced concrete | 04:00, December 27, 2018 | −17.45 | 0.45 | No |
Material thermodynamic parameters
| Material category | Density (kg/m3) | Thermal conductivity W/mK | Specific heat at constant pressure J/kg K | Modulus of elasticity (GPa) | Poisson’s ratio |
|---|---|---|---|---|---|
| Surrounding rock | 2,300 | 1.5 | 840 | 20 | 0.3 |
| Tunnel lining | 2,500 | 1.8 | 1,390 | 28 | 0.2 |
| Polyurethane | 50 | 0.024 | 2,500 | 0.06 | 0.3 |
| Corrugated steel plate | 7,800 | 50 | 450 | 206 | 0.25 |
4.3 Comparative analysis and verification
After the modeling was completed, the safety factor of the lining structure was calculated by referring to equations (17) and (18), and the safety factor envelope was drawn in Figure 6.
Safety factor envelope diagram: (a) working condition 1, (b) working condition 2, (c) working condition 3, and (d) working condition 4.
The minimum safety factor of each working condition was extracted, and then, the monitoring measurement management standard was graded using Tables 3 and 4, and the grading result was compared with the field-measured freezing depth, as shown in Table 8.
Comparative analysis of results
| Working condition | In-situ monitoring | Numerical simulation | |||
|---|---|---|---|---|---|
| Freezing depth | Management level | Minimum safety factor | Management level | ||
| 1 | Plain concrete (with insulation lining) | 0.25 | Ⅲ | 2.58 | Ⅲ |
| 2 | Reinforced concrete (without insulation lining) | 0.25 | IV | 3.91 | IV |
| 3 | Plain concrete (with insulation lining) | 0.35 | I | 1.96 | I |
| 4 | Reinforced concrete (without insulation lining) | 0.45 | IV | 2.65 | IV |
It can be seen from Table 8 that the management and classification results based on the monitoring data of the surrounding rock freezing depth of four mileage sections of Yushuchuan Tunnel are consistent with the management and classification results based on the minimum safety factor of the numerical simulation lining structure. It shows that the calculation method of the overall frost-heaving pressure and the management standard for safety monitoring and measurement of tunnel lining can be applied to engineering practice.
5 Conclusions
In this article, based on the frost-heaving model of the weathered layer with water and the overall frost-heaving model of the broken freeze–thawing lithosphere, a new method for calculating the overall frost heaving of the horseshoe-shaped tunnel in the broken surrounding rocks of the seasonal frozen area. However, as the coupling effects of the weathered layer and the disturbed layer are not taken into account, the model generates model errors and future research could be optimized in this direction.
Based on the freezing damages treatment project of the Yushuchuan tunnel, the article uses the method of the overall frost pressure of a horseshoe-shaped tunnel in the broken surrounding rocks of the seasonal frozen area to calculate the freezing depth and finds that the minimum safety factor of the concrete lining decreases with increasing freezing depth. This law can be used to establish the management standard for monitoring and measurement of the existing railway tunnel structure in the seasonal frozen area.
In this article, four mileage sections of the Yushuchuan tunnel are selected for comparative analysis by using the method of field temperature monitoring and numerical simulation. The results show that the management and classification results based on the monitoring data of the surrounding rock freezing depth of four mileage sections of the Yushuchuan tunnel are consistent with the management and classification results based on the minimum safety factor of the numerical simulation lining structure. This shows that the calculation method of the overall frost-heaving pressure and the existing tunnel lining safety monitoring management standard can be applied to engineering practice.
-
Funding information: This work was supported by the National Natural Science Foundation of China (Grant Numbers: 52178378).
-
Author contributions: Cui and Xiong – conceptualization; Cui – methodology; Cui and Xiong – investigation; Cui – data curation; Cui and Xiong – writing – original draft preparation; Xiong – writing – review and editing; Cui – project administration; Cui – funding acquisition.
-
Conflict of interest: The authors declare no competing interest.
-
Ethical approval: The conducted research is not related to either human or animal use.
-
Data availability statement: All data generated or analyzed during this study are included in this published article.
References
[1] Zhang FL, Zhu ZW, Fu TT, Jia JX. Damage mechanism and dynamic constitutive model of frozen soil under uniaxial impact loading. Mech Mater. 2020;140:103217. 10.1016/j.mechmat.2019.103217.Suche in Google Scholar
[2] Lai YM, Xu XT, Dong YH, Li SY. Present situation and prospect of mechanical research on frozen soils in China. Cold Reg Sci Technol. 2013;87:6–18. 10.1016/j.coldregions.2012.12.001.Suche in Google Scholar
[3] Gambino GF, Harrison JP. Rock engineering design in frozen and thawing rock: Current approaches and future directions. Procedia Eng. 2017;191:656–65. 10.1016/j.proeng.2017.05.229.Suche in Google Scholar
[4] Martinez AR, Roubinet D, Tartakovsky DM. Analytical models of heat conduction in fractured rocks. J Geophys Res-Solid Earth. 2014;119(1):83–98. 10.1002/2012JB010016.Suche in Google Scholar
[5] Gilpin RR. A model for the prediction of ice lensing and frost heave in soils. Water Resour Res. 1980;16(5):918–30. 10.1029/WR016i005p00918.Suche in Google Scholar
[6] O’Neill K, Miller RD. Exploration of a rigid ice model of frost heave. Water Resour Res. 1985;21(3):281–96. 10.1029/WR021i003p00281.Suche in Google Scholar
[7] Harlan RL. Analysis of coupled heat-fluid transport in partially frozen soil. Water Resour Res. 1973;9(5):1314–23. 10.1029/WR009i005p01314.Suche in Google Scholar
[8] Jame Y-W, Norum DI. Heat and mass transfer in a freezing unsaturated porous medium. Water Resour Res. 1980;16(4):811–9. 10.1029/WR016i004p00811.Suche in Google Scholar
[9] Konrad J-M, Morgenstern NR. A mechanistic theory of ice lens formation in fine-grained soils. Can Geotech J. 1980;17(4):473–86. 10.1139/t80-056.Suche in Google Scholar
[10] Konrad J-M, Morgenstern NR. The segregation potential of a freezing soil. Can Geotech J. 1981;18(4):482–91. 10.1139/t81-059.Suche in Google Scholar
[11] Konrad J-M, Morgenstern NR. Frost heave prediction of chilled pipelines buried in unfrozen soils. Can Geotech J. 1984;21(1):100–15. 10.1139/t84-008.Suche in Google Scholar
[12] Beier NA, Sego DC. Cyclic freeze–thaw to enhance the stability of coal tailings. Cold Reg Sci Technol. 2009;55(3):278–85. 10.1016/j.coldregions.2008.08.006.Suche in Google Scholar
[13] Esmaeili-Falak M, Katebi H, Javadi A. Experimental study of the mechanical behavior of frozen soils - A case study of tabriz subway. Period Polytech-Civil Eng. 2018;62(1):117–25. 10.3311/PPci.10960.Suche in Google Scholar
[14] Esmaeili-Falak M, Katebi H, Javadi AA. Effect of freezing on stress-strain characteristics of granular and cohesive soils. J Cold Reg Eng. 2020;34(2):05020001. 10.1061/(asce)cr.1943-5495.0000205.Suche in Google Scholar
[15] Kim SY, Hong W-T, Lee J-S. Silt fraction effects of frozen soils on frozen water content, strength, and stiffness. Constr Build Mater. 2018;183:565–77. 10.1016/j.conbuildmat.2018.06.187.Suche in Google Scholar
[16] Multon S, Sellier A, Perrin B. Numerical analysis of frost effects in porous media. Benefits and limits of the finite element poroelasticity formulation. Int J Numer Anal Methods Geomech. 2012;36(4):438–58. 10.1002/nag.1014.Suche in Google Scholar
[17] Luo Y, Chen J. Research status and progress of tunnel frost damage. J Traffic Transp Eng (Engl Ed). 2019;6(3):297–309. 10.1016/j.jtte.2018.09.007.Suche in Google Scholar
[18] Lai Y, Hui W, Ziwang W, Songyu L, Xuejun D. Analytical viscoelastic solution for frost force in cold-region tunnels. Cold Reg Sci Technol. 2000;31(3):227–34. 10.1016/S0165-232X(00)00017-3.Suche in Google Scholar
[19] Feng Q, Jiang BS, Zhang Q, Wang LP. Analytical elasto-plastic solution for stress and deformation of surrounding rock in cold region tunnels. Cold Reg Sci Technol. 2014;108:59–68. 10.1016/j.coldregions.2014.08.001.Suche in Google Scholar
[20] Liu WW, Feng Q, Fu SG, Wang CX. Elasto-plastic solution for cold-regional tunnels considering the compound effect of non-uniform frost heave, supporting strength and supporting time. Tunn Undergr Space Technol. 2018;82:293–302. 10.1016/j.tust.2018.08.054.Suche in Google Scholar
[21] Liu HY, Yuan XP, Xie TC. A damage model for frost heaving pressure in circular rock tunnel under freezing-thawing cycles. Tunn Undergr Space Technol. 2019;83:401–8. 10.1016/j.tust.2018.10.012.Suche in Google Scholar
[22] MOHURD (Ministry of Housing and Urban-Rural Development). China national standards: Code for design of metro GB50157-2013. MOHURD: China Architecture & Building Press, Beijing; 2013.Suche in Google Scholar
[23] MOT (Ministry of Transport of the People’s Republic of China). China National Standards: Code for Design of Road Tunnel JTG D70-2004. MOT: China Communications Press, Beijing; 2004.Suche in Google Scholar
© 2023 the author(s), published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
Artikel in diesem Heft
- Research Articles
- Vibrational wave scattering in disordered ultra-thin film with integrated nanostructures
- Optimization of lead-free CsSnI3-based perovskite solar cell structure
- Determination of the velocity of seismic waves for the location of seismic station of Zatriq, Kosovo
- Seismic hazard analysis by neo-deterministic seismic hazard analysis approach (NDSHA) for Kosovo
- Ultimate strength of hyper-ellipse flanged-perforated plates under uniaxial compression loading
- Development of an adaptive coaxial concrete rheometer and rheological characterisation of fresh concrete
- Synthesis and characterization of a new complex based on antibiotic: Zirconium complex
- Exergy–energy analysis for a feasibility trigeneration system at Kocaeli University Umuttepe Campus
- Transient particle tracking microrheology of plasma coagulation via the intrinsic pathway
- Analysis of complex fluid discharge from consumer dispensing bottles using rheology and flow visualization
- A method of safety monitoring and measurement of overall frost heaving pressure of tunnel in seasonal frozen area
- Application of isolation technology in shallow super-large comprehensive pipe galleries in seismically vulnerable areas with weak soils
- Application of the ramp test from a closed cavity rheometer to obtain the steady-state shear viscosity η(γ̇)
- Research on large deformation control technology of highly weathered carbonaceous slate tunnel
- Tailoring a symmetry for material properties of tellurite glasses through tungsten(vi) oxide addition: Mechanical properties and gamma-ray transmissions properties
- An experimental investigation into the radiation-shielding performance of newly developed polyester containing recycled waste marble and bismuth oxide
- A study on the fractal and permeability characteristics of coal-based porous graphite for filtration and impregnation
- Creep behavior of layered salt rock under triaxial loading and unloading cycles
- Research and optimization of tunnel construction scheme for super-large span high-speed railway tunnel in poor tuff strata
- Elongational flow mixing: A novel innovative approach to elaborate high-performance SBR-based elastomer compounds
- The ductility performance of concrete using glass fiber mesh in beam specimens
- Thickened fluids classification based on the rheological and tribological characteristics
- Strength characteristics and damage constitutive model of sandstone under hydro-mechanical coupling
- Experimental study of uniaxial compressive mechanical properties of rough jointed rock masses based on 3D printing
- Study on stress distribution and extrusion load threshold of compressed filled rock joints
- Special Issue on Rheological Behavior and Engineering Stability of Rock Mass - Part II
- Seismic response and damage mechanism of tunnel lining in sensitive environment of soft rock stratum
- Correlation analysis of physical and mechanical parameters of inland fluvial-lacustrine soft soil based on different survey techniques
- An effective method for real-time estimation of slope stability with numerical back analysis based on particle swarm optimization
- An efficient method for computing slope reliability calculation based on rigorous limit equilibrium
- Mechanical behavior of a new similar material for weathered limestone in karst area: An experimental investigation
- Semi-analytical method for solving stresses in slope under general loading conditions
- Study on the risk of seepage field of Qiantang River underground space excavated in water-rich rheological rock area
- Numerical analysis of the impact of excavation for undercrossing Yellow River tunnel on adjacent bridge foundations
- Deformation rules of deep foundation pit of a subway station in Lanzhou collapsible loess stratum
- Development of fiber compound foaming agent and experimental study on application performance of foamed lightweight soil
- Monitoring and numerical simulation analysis of a pit-in-pit excavation of the first branch line of Lanzhou Metro
- CT measurement of damage characteristics of meso-structure of freeze-thawed granite in cold regions and preliminary exploration of its mechanical behavior during a single freeze-thaw process
Artikel in diesem Heft
- Research Articles
- Vibrational wave scattering in disordered ultra-thin film with integrated nanostructures
- Optimization of lead-free CsSnI3-based perovskite solar cell structure
- Determination of the velocity of seismic waves for the location of seismic station of Zatriq, Kosovo
- Seismic hazard analysis by neo-deterministic seismic hazard analysis approach (NDSHA) for Kosovo
- Ultimate strength of hyper-ellipse flanged-perforated plates under uniaxial compression loading
- Development of an adaptive coaxial concrete rheometer and rheological characterisation of fresh concrete
- Synthesis and characterization of a new complex based on antibiotic: Zirconium complex
- Exergy–energy analysis for a feasibility trigeneration system at Kocaeli University Umuttepe Campus
- Transient particle tracking microrheology of plasma coagulation via the intrinsic pathway
- Analysis of complex fluid discharge from consumer dispensing bottles using rheology and flow visualization
- A method of safety monitoring and measurement of overall frost heaving pressure of tunnel in seasonal frozen area
- Application of isolation technology in shallow super-large comprehensive pipe galleries in seismically vulnerable areas with weak soils
- Application of the ramp test from a closed cavity rheometer to obtain the steady-state shear viscosity η(γ̇)
- Research on large deformation control technology of highly weathered carbonaceous slate tunnel
- Tailoring a symmetry for material properties of tellurite glasses through tungsten(vi) oxide addition: Mechanical properties and gamma-ray transmissions properties
- An experimental investigation into the radiation-shielding performance of newly developed polyester containing recycled waste marble and bismuth oxide
- A study on the fractal and permeability characteristics of coal-based porous graphite for filtration and impregnation
- Creep behavior of layered salt rock under triaxial loading and unloading cycles
- Research and optimization of tunnel construction scheme for super-large span high-speed railway tunnel in poor tuff strata
- Elongational flow mixing: A novel innovative approach to elaborate high-performance SBR-based elastomer compounds
- The ductility performance of concrete using glass fiber mesh in beam specimens
- Thickened fluids classification based on the rheological and tribological characteristics
- Strength characteristics and damage constitutive model of sandstone under hydro-mechanical coupling
- Experimental study of uniaxial compressive mechanical properties of rough jointed rock masses based on 3D printing
- Study on stress distribution and extrusion load threshold of compressed filled rock joints
- Special Issue on Rheological Behavior and Engineering Stability of Rock Mass - Part II
- Seismic response and damage mechanism of tunnel lining in sensitive environment of soft rock stratum
- Correlation analysis of physical and mechanical parameters of inland fluvial-lacustrine soft soil based on different survey techniques
- An effective method for real-time estimation of slope stability with numerical back analysis based on particle swarm optimization
- An efficient method for computing slope reliability calculation based on rigorous limit equilibrium
- Mechanical behavior of a new similar material for weathered limestone in karst area: An experimental investigation
- Semi-analytical method for solving stresses in slope under general loading conditions
- Study on the risk of seepage field of Qiantang River underground space excavated in water-rich rheological rock area
- Numerical analysis of the impact of excavation for undercrossing Yellow River tunnel on adjacent bridge foundations
- Deformation rules of deep foundation pit of a subway station in Lanzhou collapsible loess stratum
- Development of fiber compound foaming agent and experimental study on application performance of foamed lightweight soil
- Monitoring and numerical simulation analysis of a pit-in-pit excavation of the first branch line of Lanzhou Metro
- CT measurement of damage characteristics of meso-structure of freeze-thawed granite in cold regions and preliminary exploration of its mechanical behavior during a single freeze-thaw process
