Frost Mitigation Techniques for Tunnels in Cold Regions: The State of the Art and Perspectives

Abstract

Tunnels located in cold regions are vulnerable to frost damage resulting from the special atmosphere, which directly threatens the safety of the tunnel structure and operation. Frost problems of tunnels in cold regions have not been fundamentally resolved. This paper reviews design theory and the frost mitigation techniques currently used in the design, construction and maintenance of cold region tunnels. The depths of freezing and thawing and frost heaving force are the key indexes of design theory. Insulation is the main design technology used to prevent frost heaving and thawing, and the active heating technology has also been applied in practice. In construction, reducing the heat of hydration and blasting by specific winter construction techniques can prevent tunnel freeze–thaw damages. In operation, the restoration of drainage systems, the reinforcement of structures and the reinstallation of freezing-prevention systems are effective measures to treat frost problems. Finally, some constructive suggestions and opinions are put forward to improve the service performance of tunnels.

1. Introduction

In China, 52.4% of 15,117 tunnels have suffered frost damage [1,2], and in Japan 38.2% of tunnels have suffered frost problems [3]. Tunnels in Gangwon province of South Korea are also affected by a number of frost problems [4]. Based on the maximum freezing depth and the monthly average temperature in January, the tunnel frost damage intensity can be divided into several levels in the seasonal freezing areas of the Northern Hemisphere. In a survey of 156 tunnels in China, Gao et al. [5] divided tunnels in cold regions into high-latitude tunnels and high-altitude tunnels. Frost problems include lining material deterioration, tunnel deformation and cracking, concrete spalling, seepage and icing [6,7,8,9,10,11,12]. Tunnel linings can deform and crack under frost heaving and are intensified by forced ventilation and inadequate drainage. In addition, when the thermal stress acting on the lining is greater than the tensile strength of the lining, many cracks are formed [8,10]. As a result, the lining cracking causes more leakage in a tunnel than usual. Icing occurs when the temperature inside a tunnel is below zero, which affects the structure and traffic safety of the tunnel. Tunnels need more security systems and equipment to better withstand cold weather and reduce casualties and prolonged disruptions to the transport system [13]. Although there are many related studies, many challenges related to frost problems remain in theory and practice [14,15,16]. In permafrost regions, the basic principles of design and construction are to protect the tunnel-surrounding rock and the tunnel entrance slope from warming and thawing [17].

More and more tunnels are being constructed in cold regions, with difficulties in construction and maintenance in practice. Firstly, a large number of references about cold region tunnels are collected and read. Secondly, these related and important references are classified into four collections based on design theory, techniques for frost problem mitigation in design, construction and maintenance. And then, past and present techniques of frost-problem mitigation in the design, construction and maintenance of cold-regional tunnels (Figure 1) are summarized. Finally, some new ideas and directions to solve these problems are put forwards.

2. Theory of Tunnel Design in Cold Regions

2.1. Freezing and Thawing Depth

The depth of the freezing and thawing of the surrounding rock affects the thermal stability of cold-region tunnels. Engineers and researchers are thus interested in the temperature of the surrounding rock. The thermal conductivity of the surrounding rock is one of the most important factors affecting the temperature distribution. The thermal conductivity is usually obtained in laboratory tests or using empirical formulas [18,19] (

Table 1. Thermal conductivity models.

Name	Formulas	Parameters	Reference
Physical model	$\begin{array}{l}{\lambda }_f=S_{rf}^{1/2}(1-n_f){\lambda }_s+n_f{S}_{rf}^{2/3}{\lambda }_i\\ +\left[\right(1-S_{rf})S_{rf}^{1/2}{n}_f+(1-S_{rf}^{1/2}\left)\right]{\lambda }_g\end{array}$ $\begin{array}{l}{\lambda }_u=S_{ru}^{1/2}(1-n_u){\lambda }_s+{\theta }_u{n}_u{S}_{ru}^{2/3}{\lambda }_w\\ +\left[\right(1-S_{ru})S_{ru}^{1/2}{n}_u+(1-S_{ru}^{1/2}\left)\right]{\lambda }_g\end{array}$	$n_f=\frac{1.09n_u}{1+0.09n_u}$ $S_{rf}=\frac{1.09S_{ru}}{1+0.09S_{ru}}$ $n_u=1-{\rho }_d/{\rho }_s$ $S_{ru}=\frac{W}{100}\frac{{\rho }_d}{n_u{\rho }_w}$ λf, λu refer to thermal conductivity under frozen and unfrozen states; n is the initial porosity of pore media; Sr is saturation degree; θu is volumetric unfrozen water; the subscript u and f refer to the unfrozen and frozen states, respectively; ρ is density, and subscript s and w refer to soil-rock particle and water, respectively; ρd is dry density; W is water content.	[20]
CK model	$\begin{array}{l}{\lambda }_f=({\lambda }_{sat\left(f\right)}-{\lambda }_{dry}){\lambda }_{rf}+{\lambda }_{dry}\\ {\lambda }_u=({\lambda }_{sat\left(u\right)}-{\lambda }_{dry}){\lambda }_{ru}+{\lambda }_{dry}\end{array}$	λf, λu refer to thermal conductivity under frozen and unfrozen states; λsat(f), λsat(u) refer to thermal conductivity of saturated soil under frozen and unfrozen states; λdry is thermal conductivity of dry soil; λrf, λru are thermal conductivity of frozen and unfrozen states for unsaturated soil which relate to the saturation degree.	[21]
Multiple linear regression model	$\begin{array}{l}{\lambda }_u=(1.913\pm 10.313)+(0.127\pm 0.118)w\\ +(0.869\pm 3.355){\rho }_d+(-7.110\pm 12.595)n\\ +(-2.076\pm 2.948)S_r\end{array}$ $\begin{array}{l}{\lambda }_f=(16.028\pm 14.954)+(0.042\pm 0.174)w\\ +(-4.581\pm 4.866){\rho }_d+(-17.448\pm 17.846)n\\ +(-0.882\pm 4.273)S_r\end{array}$	λf, λu refer to thermal conductivity under frozen and unfrozen states; ρd is dry density; w is water content; Sr is saturation degree; n is the initial porosity of pore media;	[19]

).

The depths of the freezing and thawing of the surrounding rock are easily determined if the temperature distribution of the surrounding rock is obtained. It is thus important to obtain the temperature distribution of the surrounding rock. The underground temperature field is affected by the ventilation, groundwater, and thickness of the secondary lining; i.e., the temperature distribution around a tunnel is affected by seepage, moisture transfer, the phase change, and air flow. It is therefore difficult to obtain the temperature distribution of the surrounding rock and tunnel structure. However, there are approximate analytical formulas and many numerical solutions.

The analytical solution of the temperature distribution is difficult to obtain and is approximate. There are only a few solutions of the solutions which are based on differential equations of heat transfer. First lining, insulation, second lining, and surrounding rock including frozen or unfrozen zone are assumed to be different materials. However, the approximate analytical solutions have been obtained by different methods, such as the dimensionless and perturbative method [22], orthogonal and expansion theorem of the Bessel eigenfunction [23], superposition principle and the orthogonal expansion of the Bessel eigenfunction [24], Stehfest numerical inversion method [25], quasi-steady state assumption and integration [26], and so on.

Solving the temperature-distribution solution of a tunnel in a cold region is a complex problem that should include the heat transfer, coupling of the heat transfer and seepage, coupling of the heat transfer and heat convection between the air in the tunnel and surrounding rock, and the ice-water phase change (

Table 2. Differential equations of the temperature solution.

No.	Formulas	Parameters	Reference
1	$\begin{array}{l}{C}^{*}\frac{\partial T}{\partial t}=\frac{\partial }{\partial x}\left({\lambda }^{*}\frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left({\lambda }^{*}\frac{\partial T}{\partial y}\right)-C_w{\rho }_w\left(V_x^{*}\frac{\partial T}{\partial x}+V_y^{*}\frac{\partial T}{\partial y}\right)\\ S^{*}\frac{\partial H}{\partial y}=\frac{\partial }{\partial x}\left(K_x^{*}\frac{\partial H}{\partial x}\right)+\frac{\partial }{\partial y}\left(K_y^{*}\frac{\partial H}{\partial y}\right)\\ V_x^{*}=-K_x^{*}\frac{\partial H}{\partial x}\\ V_y^{*}=-K_y^{*}\frac{\partial H}{\partial x}\\ {\lambda }_f\frac{\partial T_f}{\partial n}-{\lambda }_u\frac{\partial T_u}{\partial n}=L\frac{ds\left(t\right)}{dt}\end{array}$	$C^{*}=\{\begin{array}{cc}\begin{array}{c}{C}_f\\ \frac{L}{2\Delta T}+\frac{C_f+C_u}{2}\\ C_u\end{array}& \begin{array}{c}T<(T_m-\Delta T)\\ (T_m-\Delta T)\le T\le (T_m+\Delta T)\\ T>(T_m+\Delta T)\end{array}\end{array}$ ${\lambda }^{*}=\{\begin{array}{cc}\begin{array}{c}{\lambda }_f\\ {\lambda }_f+\frac{{\lambda }_u-{\lambda }_f}{2\Delta T}(T-(T_m-\Delta T\left)\right)\\ {\lambda }_u\end{array}& \begin{array}{c}T<(T_m-\Delta T)\\ (T_m-\Delta T)\le T\le (T_m+\Delta T)\\ T>(T_m+\Delta T)\end{array}\end{array}$ $K_x^{*}=\{\begin{array}{cc}{\left(\frac{W_u}{W}\right)}^{\beta }{K}_x^u& T\le T_m\\ K_x^u& T>T_m\end{array}$ $K_y^{*}=\{\begin{array}{cc}{\left(\frac{W_u}{W}\right)}^{\beta }{K}_y^u& T\le T_m\\ K_y^u& T>T_m\end{array}$ The subscripts and superscripts f, u represent the frozen and the unfrozen states, respectively; T, C, λ are the temperature, volumetric heat capacity and thermal conductivity of surrounding rock, respectively; H, S, K are water head, water-supply degree, hydraulic conductivities, respectively; x, y refer to directions; ρ is density of water; s(t) is the phase front position; L is the latent heat per unit volume; n is the normal direction of phase front position; the phase change occurs in a range of temperatures T ± ΔT; W and Wu are the moisture content and the unfrozen water content; β is a constant, determined by experiments; Tm is frozen temperature of surrounding rocks; V is water filtration velocity; t is time.	[27,28]
2	$C\frac{\partial T}{\partial t}=\frac{\partial }{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left(\lambda \frac{\partial T}{\partial z}\right)$	T, C, λ are the temperature, volumetric heat capacity and thermal conductivity of surrounding rock, respectively; x, y, z refer to directions; t is time.	[29,30]
3	$\begin{array}{l}\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0\\ \frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}=-\frac{\partial p}{\partial x}+\frac{\partial }{\partial x}\left(\nu \frac{\partial u}{\partial x}\right)+\frac{\partial }{\partial y}\left(\nu \frac{\partial u}{\partial y}\right)+\frac{\partial }{\partial z}\left(\nu \frac{\partial u}{\partial z}\right)\\ \frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}=-\frac{\partial p}{\partial y}+\frac{\partial }{\partial x}\left(\nu \frac{\partial v}{\partial x}\right)+\frac{\partial }{\partial y}\left(\nu \frac{\partial v}{\partial y}\right)+\frac{\partial }{\partial z}\left(\nu \frac{\partial v}{\partial z}\right)\\ \frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}=-\frac{\partial p}{\partial z}+\frac{\partial }{\partial x}\left(\nu \frac{\partial w}{\partial x}\right)+\frac{\partial }{\partial y}\left(\nu \frac{\partial w}{\partial y}\right)+\frac{\partial }{\partial z}\left(\nu \frac{\partial w}{\partial z}\right)\\ C_a\frac{\partial T}{\partial t}+c_{a}u\frac{\partial T}{\partial x}+c_{a}v\frac{\partial T}{\partial y}+c_{a}w\frac{\partial T}{\partial z}=\frac{\partial }{\partial x}\left({\lambda }_a\frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left({\lambda }_a\frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left({\lambda }_a\frac{\partial T}{\partial z}\right)\end{array}$	u, v and w are flow velocities in the direction of x, y, z, respectively; p is effective pressure of air; T is air temperature; ν is kinematic viscosity coefficient for air; ca and λa are volumetric heat capacity and thermal conductivity for air, respectively; x, y and z are three directions in a rectangular coordinate system, respectively; t is time.	[31]
4	$\begin{array}{l}\overline{C}\frac{\partial T}{\partial t}=\frac{\partial }{\partial x}\left({\overline{\lambda }}_x\frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial z}\left({\overline{\lambda }}_z\frac{\partial T}{\partial z}\right)\\ \overline{C}=C+L{\rho }_w\frac{\partial {\theta }_w}{\partial T}\\ \overline{\lambda }=\lambda +L^2{\rho }_w{}^2{K}^{*}/T_k\end{array}$	T is temperature; t is time; x, z are two directions in a rectangular coordinate system, respectively; C and λ are heat capacity and thermal conductivity of soft rock, respectively; L is the latent heat; ρw is density of water; K* is comprehensive hydraulic conductivity; Tk is absolute temperature; θw is volume content of liquid water.	[32]
5	$\begin{array}{l}-q_i+q_v=c\rho \frac{\partial T}{\partial t}\\ q_i=-\lambda T_i\end{array}$	T is temperature; t is time; qi is heat flux density, i = 1, 2, 3; qv is volume heat source of rock and soil; c and λ are heat capacity and thermal conductivity; ρ is density.	[33]
6	$\begin{array}{l}{C}_{eq}\frac{\partial T}{\partial t}+\nabla [-{\lambda }_e\nabla T]+\left[\right(v_w\cdot \nabla \left){\left(\rho cT\right)}_w\right]=Q_e\\ \frac{\partial \left({\rho }_w{\theta }_w\right)}{\partial t}+\frac{\partial \left({\rho }_i{\theta }_i\right)}{\partial t}+\nabla \cdot \left[-\frac{{\rho }_w{k}_w}{{\mu }_w}(\nabla p_w+{\rho }_{w}g)-{\rho }_w(S{P}_0-D_r)\nabla T\right]={\rho }_{w}q\\ \frac{\partial {\theta }_i}{\partial t}=\frac{L_f{\rho }_w}{T}\cdot \frac{d{\theta }_w}{d{p}_w}\cdot \frac{\partial T}{\partial t}\end{array}$	$C_{eq}=\{\begin{array}{cc}{C}_a=C_1+{\rho }_w{L}_f\frac{\partial {\theta }_w}{\partial T}& T\le T_0\\ C_2& T>T_0\end{array}$ ${\lambda }_e=\{\begin{array}{cc}{\lambda }_1& T\le T_0\\ {\lambda }_2& T>T_0\end{array}$ $Q_e=\{\begin{array}{cc}{Q}_1& T\le T_0\\ Q_2& T>T_0\end{array}$ ${\mu }_w=661.2\times {(T-229)}^{-1.562}\times {10}^{-3}$ T is temperature; t is time; c and λ are heat capacity and thermal conductivity; subscripts 1, 2, refer to frozen zone and unfrozen zone; Q is the volumetric heat production generated (consumed) heat by heating (heat release) in unit body; ρw is the density of water; and Lf is the heat latent; νw is the seepage velocity of water; θw is volume content of liquid water; θi is volumetric ice content; ρi is the density of ice; μw is dynamic viscosity of water; kw is the permeability; pw is the water pressure; g is the gravity acceleration; SP0 is segregation potential; DT is heat diffusion rate under the action of temperature gradient; q is per unit volume.	[34]
7	$\begin{array}{l}{C}_1\frac{\partial T}{\partial t}+\nabla [-k_1\nabla T]=Q_{T1}\\ C_2\frac{\partial T}{\partial t}+{\rho }_w{L}_f\frac{\partial n\chi }{\partial t}+\nabla [-k_2\nabla T]=Q_{T2}\\ C_3\frac{\partial T}{\partial t}+\nabla [-k_3\nabla T]=Q_{T3}\end{array}$	$\begin{array}{l}{k}_1,k_2=n{\lambda }_w\chi +n{\lambda }_i(1-\chi )+(1-n){\lambda }_s\\ k_3=n{\lambda }_w+(1-n){\lambda }_s\\ C_1,C_2=n{\rho }_w{c}_w\chi +n{\rho }_i{c}_i(1-\chi )+(1-n){\rho }_s{c}_s\\ C_3=n{\rho }_w{c}_w+(1-n){\rho }_s{c}_s\end{array}$ T is temperature; t is time; ρw is the density of water; QTi, ki and Ci are the heat source, the thermal conductivity and the volumetric specific heat in the ith zone; subscripts 1, 2, 3 refer to frozen zone, freezing zone and unfrozen zone; Lf is the latent heat of water; χ is the unfrozen water volumetric content, χ* is the residual unfrozen water volumetric content at some lower reference temperature; a is a parameter to describe the rate of decay; Tc is the freezing point of water; n is the porosity; ρi and ρs are the densities of ice and skeleton, respectively; λw, λi and λs are the thermal conductivities of water, ice and skeleton, respectively; cw, ci and cs are the specific heats of water, ice and skeleton, respectively;	[35]
8	$\begin{array}{l}\nabla \cdot \left(\rho \mathit{u}\right)=0\\ \nabla \cdot \left(\rho \mathit{u}\right)\mathit{u}=\nabla \cdot [-p\mathit{I}+(\mu +{\mu }_t\left)\right]\times \left(\nabla \mathit{u}+{(\nabla \mathit{u})}^T-\frac{2}{3}(\nabla \cdot \mathit{u})\mathit{I}-\frac{2pk}{3}\mathit{I}\right)+S_m\\ \nabla \cdot \left(\rho c_p\mathit{u}{T}_a\right)=\nabla \cdot \left[\left({\lambda }_g+c_p\frac{{\mu }_t}{\mathit{P}{\mathit{r}}_T}\right)\nabla T_a\right]+Q_T\\ \{\begin{array}{c}\nabla \cdot \left(\rho k\right)\mathit{u}=\nabla \cdot \left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\nabla k\right]+{\mu }_{t}P\left(\mathit{u}\right)-\frac{2pk}{3}\nabla \cdot \mathit{u}-\rho \epsilon \\ \nabla \cdot \left(\rho k\right)\mathit{u}=\nabla \cdot \left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\nabla \epsilon \right]+\frac{C_{\epsilon 1}\epsilon }{k}\left[{\mu }_{t}P\left(\mathit{u}\right)-\frac{2pk}{3}\nabla \cdot \mathit{u}\right]-\frac{C_{\epsilon 2}\rho {\epsilon }^2}{k}\end{array}\end{array}$	$\begin{array}{l}{\mathit{S}}_{\mathit{M}}=\rho \mathit{X}- \frac{\partial }{\partial x}({\mu }^{’}\nabla \cdot \mathit{u})\\ P\left(\mathit{u}\right)=\nabla \mathit{u}:\left[\nabla \mathit{u}+{(\nabla \mathit{u})}^T\right]-2/3{(\nabla \cdot \mathit{u})}^2\\ {\mu }_t=\rho C_{\mu }{k}^2/\epsilon \end{array}$ u is the velocity of the airflow in the tunnel; ρ is the density of the airflow; p is the pressure; μ is the viscosity coefficient; I is the unit matrix; μt is the eddy viscosity coefficient; X is the body force along with coordinate axis orientation; μ’ is the second viscosity coefficient; Ta is the temperature of the airflow; cp is the specific heat of the airflow; λg is the conductivity of the airflow; PrT is the turbulence Prandtl number; QT is the heat source; where σk, σε, Cε1, Cε2 and Cμ are empirical constants, and their values areσk = 1.00, σε = 1.30, Cε1 = 1.44, Cε2 = 1.92 and Cμ = 0.07.	[36,37]
9	$\begin{array}{l}\frac{1}{a}\frac{\partial T}{\partial t}=\frac{{\partial }^{2}T}{\partial r^2}+\frac{1}{r}\frac{\partial T}{\partial r}+\frac{{\partial }^{2}T}{\partial x^2}(r\ge R,t>0)\\ \rho A{c}_p\left(\frac{\partial T_f}{\partial t}+v\frac{\partial T_f}{\partial x}\right)=hU(T_b-T_f)+q_s(t>0)\end{array}$	T is the temperature of the tunnel lining and surrounding rock; Tf is the wind temperature; r is the radial distance; a is the thermal diffusion coefficient; t is time; ρ is the density of the tunnel lining and surrounding rock; h is the convective heat transfer rate; Tb is the temperature of the tunnel wall; U is the perimeter of the cross section; qs is the equipment heating effect in the tunnel; cp is the constant-pressure specific heat capacity of the surrounding rock; A is the area of cross section.	[38]

). Lai derived governing differential equations of the coupled problem of temperature and seepage fields with a phase change from the theory of heat transfer and seepage [27,28]. Zhang and Zhang obtained the finite element formulae of three-dimensional temperature fields with a phase change using Galerkin’s method based on the governing differential equations of the temperature field [29,30]. Lai presented a three-dimensional calculation model of the coupled problem according to the basic theories of heat transfer, geocryology, and fluid mechanics, taking the coupled problem of the heat transfer of the surrounding rock and the heat convection between the air in the tunnel and the surrounding rock into account [31]. Yang introduced a common numerical method of solving the moisture and heat coupling for the soft rock of tunnels in cold regions [32]. Zhang developed a program including the latent heat of a change in phase based on the finite difference method and internal FISH language of FLAC3D2.1 [33]. Tan established governing equations for a thermohydro coupling model according to the basic law of water flow and heat transfer in porous media under freeze/thaw conditions, adopting the theory of continuum mechanics, thermodynamics, and the segregation potential [34]. Tan obtained the temperature field distribution with an ice-water phase change occurring in porous media by adjusting the parameters of the unfrozen water contents of the frozen zone, freezing zone, and unfrozen zone [35]. Tan presented an adaptive finite element method based on a standard k-ε turbulence model, wall function, and thermal function [36]. Tan developed a temperature field model that includes temperature control equations of the surrounding rock, air temperature field control equations of the tunnel, and wind flow control equations of the turbulence field [37]. Zhou developed an unsteady-state finite-difference numerical model to study heat convection between the air and the tunnel wall and the heat transfer in the surrounding rock and at interfaces between different materials in the structure of the tunnel according to unsteady-state finite-difference equations for heat transfer and heat convection [38]. Jin developed a heating element to study the temperature of groundwater at the backfill of the tunnel lining [39].

2.2. Frost Heaving Force

Freeze-thaw cycles often damage the surrounding rock and supporting structures. It is thus important to obtain the stress acting on the surrounding rock and supporting structures. Lai obtained the effect of the frost heaving force on the stress acting on the tunnel lining using a mathematical mechanical model of the coupled problem of temperature, seepage, and stress fields with a phase change [27]. Lai assumed that there was a viscoelastic frozen zone between the elastic lining and elastic unfrozen zone far from the lining. They then obtained the lining stresses of cold-region tunnels through numerical inversion of the Laplace transform [40]. On this basis, Lai assumed that frozen soil is viscoplastic and obtained the time stress response of tunnels [41]. Gao obtained the elastic stress in the surrounding rock and plastic zone that was determined by Kastner. Their analytical solution showed that the hardening effect of the plastic zone cannot be ignored because the frost heave parallel to the freezing direction is greater than that perpendicular to the freezing direction [42]. Feng divided the surrounding rock into the unfrozen elastic zone, frozen elastic zone, support zone, and frozen plastic zone, which conforms to the ideal elastoplastic model and the Mohr–Coulomb yield criterion. They established an analytical elastoplastic solution for the stress [43]. Feng presented an analytical calculation of a tunnel model under unequal compression, which included an excavation model and frost heaving model. They obtained the total stress and deformation of the lining and surrounding rock through the superposition of the results of the two models [44]. Huang established a statistical damage constitutive model, assuming that the micro-unit strength satisfies the Weibull distribution and maximum-tensile-strain yield criterion [45]. They then obtained the stress of the surrounding rock and lining using elastic and plastic theory.

The frost heaving force is an important load in a cold-region tunnel and has attracted much attention from engineers and researchers (

Table 3. Formulas for the frost heaving force.

No.	Formulas	Parameters	Reference
1	$\begin{array}{c}{P}_b=\frac{1}{\Delta }\left\{{\epsilon }_0(1+{\mu }_2)\right\}\left[\frac{(1+{\mu }_2)(c^2+b^2-2{\mu }_2{c}^2)}{E_2(c^2-b^2)}+\frac{(1+{\mu }_3)}{E_3}\right]\\ -\left[{\epsilon }_0(1+{\mu }_2)+\frac{(1+{\mu }_3)}{E_3}{P}_0\right]\times \frac{2(1-{\mu }_2{}^2)c^2}{E_2(c^2-b^2)}\end{array}$	$\begin{array}{c}\Delta =\frac{(1+{\mu }_1)(1+{\mu }_2)[2{\mu }_1{b}^2-(b^2+a^2\left)\right](c^2+b^2-2{\mu }_2{c}^2)}{E_1{E}_2(b^2-a^2)(c^2-b^2)}-\frac{{(1+{\mu }_2)}^2(b^2+c^2-2{\mu }_2{b}^2)(c^2+b^2-2{\mu }_2{c}^2)}{E_2{}^2(c^2-b^2)}\\ +\frac{(1+{\mu }_1)[2{\mu }_1{b}^2-(b^2+a^2\left)\right](1+{\mu }_3)}{E_1{E}_3(b^2-a^2)}+\frac{4{(1-{\mu }_2{}^2)}^2{c}^2{b}^2}{E_2{}^2(c^2-b^2)}-\frac{(1+{\mu }_2)(1+{\mu }_3)(b^2+c^2-2{\mu }_2{b}^2)}{E_2{}^2{(b^2-a^2)}^2}\end{array}$ ${\epsilon }_0=\frac{1}{3}\alpha \left(W-W_u\right)$ W and Wu are the water content and the unfrozen water content of the surrounding rock, respectively; α is the volumetric expansion per unit volume when water is frozen to ice. The subscripts 1, 2, 3 refer to the lining, the frozen surrounding rock and the unfrozen surrounding rock, respectively; E and μ are the elastic modulus and Poisson’s ratio, respectively; Pb is frost heave force; P0 is the initial geostress; a is the inner diameter of circle lining; b, c are the inner diameter and outer diameter of frozen surrounding rock.	[40]
2	$P=\frac{\alpha t}{2\left({\Delta }_m+{\delta }_m\right)}$	P is frost heave force; α is frost heaving ratio of water, α = 0.09; t is the depth of water body; Δ is the average displacement of each point of lining when 1 MPa frost heaving force acts on it; δ is the average displacement of each point of surrounding rock when 1 MPa frost heaving force acts on it.	[46]
3	$P=\frac{\alpha t\left(K_{lm}+K_{im}\right)\left(K_{rm}+K_{im}\right)}{2\left(K_{lm}+2K_{im}+K_{rm}\right)}$	P is the frost heave force; α is the frost heaving ratio of ice; t is the depth of water body; Krm is the average of elastic resistance coefficient of surrounding rock; Klm is the average of elastic equivalent coefficient of lining; Kim is the average of elastic equivalent coefficient of ice.	[47]
4	$P_e=\frac{\left[\beta n{S}_{r}u-n\left(1-S_r\right)\right]K_s{K}_i}{K_s{S}_r+K_i}H\left[u-\chi \right]$	$u=\frac{m_i}{m_i+m_w}$ $H\left[u-\chi \right]=\{\begin{array}{cc}0& u\le \chi \\ 1& u>\chi \end{array}$ $\chi =\frac{1-S_r}{\beta S_r}$ mi is the quality of ice; mw is the quality of unfrozen water; u is frozen water ratio; n is porosity; Sr is saturation degree; β is volume expansion coefficient when water is changed into ice; Ki, Ks are the bulk modulus of ice and rock skeleton, respectively.	[48]
5	$\begin{array}{c}{P}_b=\left\{2D_1(1-{\mu }_{ц})\frac{{\Delta }_c}{c}-\left[D_3+D_2+D_1\left(1-2{\mu }_{ц}\right)\right]\frac{{\Delta }_b}{b}\right\}/\\ \{\left\{\frac{a^2+b^2\left(1-2{\mu }_{\mathsf{{\rm I}}}\right)}{\left(b^2-a^2\right)}\frac{(1+{\mu }_{\mathsf{{\rm I}}})}{E_{{}_{\mathsf{{\rm I}}}}}+2\left[D_1+D_2(1-2{\mu }_{ц})\right]\cdot \frac{1+{\mu }_{ц}}{E_{ц}}\right\}\cdot \\ \left[D_3+D_2+D_1\left(1-2{\mu }_{ц}\right)\right]-\frac{8D_1{D}_2{(1-{\mu }_{ц})}^2(1+{\mu }_{ц})}{E_{ц}}\}\end{array}$	$D_1=\frac{c^2}{2(c^2-b^2)}$$D_2=\frac{b^2}{2(c^2-b^2)}$$D_3=\frac{E_{ц}(1+{\mu }_{\text{Ш}})}{2E_{\text{Ш}}(1+{\mu }_{ц})}$ ${\Delta }_b=\frac{b\left(1-2{\mu }_{ц}\right)\left(k-1\right)\eta }{2(1-{\mu }_{ц})\left(k+2\right)}\left(\ln b-\frac{1}{2}\right)+\frac{C_1}{2}b+\frac{C_2}{b}$ ${\Delta }_c=\frac{c\left(1-2{\mu }_{ц}\right)\left(k-1\right)\eta }{2(1-{\mu }_{ц})\left(k+2\right)}\left(\ln c-\frac{1}{2}\right)+\frac{C_1}{2}c+\frac{C_2}{c}$ a is the inner diameter of circle lining; b, c are the inner diameter and outer diameter of frozen surrounding rock; Ⅰ, Ⅱ, Ⅲ refer to lining, frozen surrounding rock, unfrozen surrounding rock, respectively; E is elastic modulus; μ is Poisson’s ratio.	[26,50]
6	$q_{\max }=B_3(1-B_4^h)P_b$$q_1=B_1{q}_{\max }$ $q_2=B_2{q}_{\max }$	B1, B2, B3, B4 are the parameters of frost heave force distribution; Pb is frost heave force of equivalent circle tunnel; h is the buried depth of tunnel; qmax is the load acting on arch foot.	[51]

). Lai assumed that there is a viscoelastic frozen zone between the elastic lining and elastic unfrozen zone far from the lining. They then obtained the frost forces of cold-region tunnels through the numerical inversion of the Laplace transform [40]. Wang simplified the calculation of the force generated by frost heaving behind the lining structure using numerical results [46]. Fan obtained the frost heaving force using the equivalent elasticity coefficient for a hard-rock cold tunnel [47]. Kang obtained the distributions of unfrozen, freezing, and frozen zones around a cold-region tunnel according to the conditions of occurrence of frost heaving strains. They then applied the frost heaving force in the form of pore pressure in their calculation [48]. Tan presented a model that is based on a thermo-hydro-mechanical damage (THMD) coupling mechanism and includes not only the effects of the volumetric strain on the temperature field, seepage field, and stress field but also the effects of the frost heave pressure and freeze–thaw cycles on the integrity of the rock mass [49]. The analytical solution for the anisotropic frost heaving force of a cold-region tunnel has been obtained using the non-uniform frost heaving coefficient k [26,50]. Adopting a constant ratio of frost heaving forces between a curved-wall lining and round lining, Huang obtained the frost heaving force acting on the curved-wall linings of different frost region tunnels by modifying the analytical solution of the frost-heaving force acting on a round tunnel [51].

2.3. Classifications of the Surrounding Rock and Cold Regions

Reasonable classifications of the surrounding rock and cold regions could provide guidance in the design of tunnels in cold regions. According to the effects of the frost heaving susceptibility of the rock and fissure filling, grade of the rock mass, rock porosity, and groundwater recharge conditions, Xia divided rock masses into two groups according to the frost heaving susceptibility of the rock. In the case of rocks that are not susceptible to frost heaving, frost heaving mainly occurs because of the freezing of field water in pores and fissures [52]. In the case of rock susceptible to frost heaving, the frost heaving is affected by water migration during freezing (

Table 4. Classification of frost-heave susceptibility for rock mass.

Frost-Heave Susceptibility of Rock Mass		Grades of Surrounding Rock	Porosity	Supply Condition of Groundwater	Frost Heaving Ratio	Frost Heave Characteristic
Rock	Fissure Filler
No frost-heave susceptibility	No frost-heave susceptibility (or no Fissure filler)	I~V	<5	Open condition	<0.13	No
			5~20.5		0.13~0.47	Weak
			20.5~37		0.47~0.80	Less strong
			>37		0.80~1.60	Strong
No frost-heave susceptibility	Frost-heave susceptibility	IV	<7.5	Open condition	0.13~0.47	Weak
			7.5~23.5		0.47~0.80	Less strong
			>23.5		0.80~1.60	Strong
		V	<9		0.47~0.80	Medium
			9~49.5		0.80~1.60	Less strong
			>49.5		>1.60	Strong
Frost-heave susceptibility	Frost-heave susceptibility	IV	<4.5	Open condition	0.13~0.47	Weak
			4.5~15		0.47~0.80	Less strong
			15~39		0.80~1.60	Strong
			>39		>1.60	Severe
		V	<5.5		0.47~0.80	Less strong
			5.5~31		0.80~1.60	Strong
			>31		>1.60	Severe

).

Yuan and Lai divided surrounding rock into freezing-thawing surrounding rock and permafrost surrounding rock [53]. Each of these classes were then divided into two subclasses according to the freezing-thawing sensitivity of the rock (

Table 5. Classification of surrounding rock in cold regions.

State of Water Content	Freezing Index /°C·d	Freeze-Thaw Sensitivity	Classification	Subclassification	Phenomenon
Watery	200~2000	Sensitive	Freeze-thaw surrounding rock	Sensitive freeze-thaw surrounding rock	The freeze–thaws happen with the seasons in surrounding rock. The frost heaving, relaxation and thermal collapse act on lining. The freezing and thermal erosion of the mix of water and particles act on back of lining.
		Insensitivity		Insensitive freeze–thaw surrounding rock	There is no seasonal frost heaving in surrounding rock. There are no frost heaving materials behind lining. But there is only freeze–thaw of fissure water and collection water of it.
	>2000	Sensitive	Permafrost surrounding rock	Sensitive permafrost surrounding rock	Although the surrounding rock is sensitive to freezing and thawing, it is always freezing. The thickness of frozen circle would be changed with seasons. Most of the frost heaving force is borne by the frozen circle itself.
		Insensitivity		Insensitive permafrost surrounding rock	The surrounding rock is not sensitive to freezing and thawing. The surrounding rock is always freezing. The fissure water is changed to ice in surrounding rock. The tunnel structure is not affected by the frost heaving force
No water	—	—	—	—	—

).

Gao, following a survey of 156 tunnels in China, suggested that tunnels in cold regions be separated into tunnels of low latitude and tunnels of high altitude [5]. They classified five sub-regions according to the average temperature in the coldest month and the frost depth (

Table 6. Sub-regions of tunnels in cold regions.

Zone ID	Average Temperature in the Coldest Month/°C	Frost Depth/m	Characteristics of Frost Problems
Ⅰ	−5~0	0.15~0.5	No frost problems
Ⅱ	−5~−10	0.5~1.0	There is a small amount of water seepage and icing in some parts of the tunnel, which will not affect the traffic.
Ⅲ	−10~−15	1.0~1.5	There is ice on the wall and pavement of tunnel, which affects driving speed.
Ⅳ	−15~−25	1.5~2.5	There is a lot of ice on the wall and pavement of the tunnel, which affects driving safety. Human or mechanical de-icing is required to ensure access and safety.
Ⅴ	≥−25	>2.5	There is a large amount of ice on wall and pavement of the tunnel; the drainage ditch is completely frozen. Traffic is interrupted.

).

3. Techniques for Frost Problem Mitigation in Tunnel Design

There are many freeze–thaw problems in cold-region tunnels because the temperatures of surrounding rock and structures are susceptible to ambient temperatures [54], especially near the tunnel entrance/exit [55]. Generally, tunnels that suffer frost heaving are located in seasonally frozen areas. The durability of lining materials is affected by freeze–thaw cycles. Permafrost tunnels face thermal disturbance and refreezing due to a large amount of heat generated in construction, such as the heat generated by machines and blasting, and the hydration heat of cast-in-situ concrete lining and shotcrete. Field observations have shown that the thermal disturbance depth is about 30 m (Figure 2) and the thermal disturbance area undergoes warming, cooling, and super cooling [56]. As such, permafrost tunnels should reduce the thawing area in construction and accelerate refreezing in operation.

3.1. Frost Heaving Prevention

3.1.1. Insulation Layer

Thermal insulation materials can control frost heaving by reducing the freezing depth of the surrounding rock of tunnels in seasonally frozen regions. An insulation layer is usually installed on the inner surface of the lining (Figure 3, “Insulation layer (a, black)”) or between the preliminary lining and the secondary lining (Figure 3, “Insulation layer (b, red)”). Both installations have advantages and disadvantages. The insulation layer is easier to break for the former than the latter. If the insulation layer is broken, it is easier to replace for the former than the latter. Thermal insulation efficiency and reduction for the influence of temperature stress on the secondary lining are better for the former than the latter. In addition, there is an off-wall insulation installation referred to in reference [57]. There is a small distance between the insulation layer and the lining when the insulation layer is installed on the surface of the lining. A close air layer is formed between the insulation layer and lining, and it is another insulation layer. There is currently no consensus on the optimal installation, with some believing that the former installation is better [58,59,60,61] and others believing that the latter is better [62]. Depending on the environmental conditions, an insulation layer is usually installed at a specified length from the entrance/exit to the middle of tunnels. For example, an insulation layer was installed 600 m from the entrance and 400 m from the exit to the middle in Galongla tunnel [34,36,37], while an insulation layer was installed 796 m from the east entrance and 786 m from the west entrance toward the middle of Dongnanli tunnel [63]. The basic principle is that the installation length of the insulation layer is generally determined based on the location where the surrounding rock is not frozen in the cold season. The installation length of the insulation layer is largely affected by the ground temperature, inlet wind speed and temperature, atmospheric temperature and ground thermal conductivity [64,65]. Some valuable and specific stipulations are in Technical Specifications for Design and Construction of Highway in Seasonal Frozen Soil Region [66]. Practice has shown that the installation location and length of the insulation layer requires further research considering environmental, geological, hydrological and climatic conditions.

There are many kinds of insulation materials, such as phenolic, polyurethane, polystyrene, high-pressure polyethylene, rubber materials, rock wool, and more. Important material parameters include cold tolerance, thermal conductivity, water absorption, and compressive strength (

Table 7. Performance of insulation materials.

Performance	Phenolic	Polyurethane	Polystyrene	High Pressure Polyethylene	Rubber–Plastic	Rock Wool
Cold tolerance (°C)	−180	−110	−80	/	−40	−60
Thermal conductivity W/(m·K)	0.02~0.033	0.022~0.036	0.033~0.04	0.029~0.035	0.031~0.036	0.033~0.064
Water absorption (kg/m3)	0.02	0.03	0.2	0.02	0.3	<2
Compressive strength (MPa)	0.216	0.127	0.107	0.033	0.03	0.107

), and their cold tolerance is less than the lowest temperature in common cold seasons. Both the thermal conductivity and compressive strengths of phenolic and polyurethane are less than other insulation materials. Their insulation effects are optimal and relatively difficult to crush. Freezing resistance of phenolic and polyurethane is better than the other insulation materials because of their small water absorption [67,68,69].

In the experimental investigation of eight materials, polyurethane foam was the optimal insulation material [70]. Thickness and thermal conductivity are the most important design parameters of the insulation layer [59], which are greatly affected by the burial depth, boundary conditions, phase transition, tunnel ventilation conditions, and ground thermal conductivity [71,72,73]. Polyurethane foam board (with a thickness of 3 cm), aluminum silicate fiberboard (2 cm), polyurethane foam board (3 or 4 cm), aluminum silicate fiberboard (3 or 4 cm), and polyphenolic foam board (4 cm) are reasonable selections for Zhegu Mountain tunnel [74]. In reality, different thicknesses have been used in different tunnels because of different environmental conditions and insulation layer materials (

Table 8. Thickness of the insulation layer used in some tunnels.

No.	Tunnel Name	Material	Thermal ConductivityW/(m.k)	Thickness (cm)	Preference	Remarks	The Minimum Temperature
1	-	Air & polyurethane foam	/	/	[76]	Reasonable	/
2	-	Hard polyurethane board	0.0207	3	[77]	Reasonable	/
3	Galongla tunnel	Flolic	0.025	6	[34,37]	Reasonable	−30.1 °C
4	-	PU rigid polyurethane foam board	0.02	4	[58]	Unreasonable	/
5	-	Air, phenolic foam	0.0259, 0.021	5	[63]	Reasonable	/
6	-	Air & polyurethane foam board	/	/	[78]	Reasonable	/
7	Yuximolegai tunnel	Hard polyurethane board	0.024	5	[79]	Reasonable	−29.5 °C
8	Huapiling Tunnel	Hard polyurethane board	0.024	5	[61]	Reasonable	−34.1 °C
9	-	FLOLIC	0.025	5	[80]	Reasonable	/
10	Four-season cross-country skiing tunnel	Polyurethane	0.03	5	[60]	Reasonable	−6 °C

). An insulation layer with a thickness of 5 cm is often used in tunnels, and the most commonly used insulation material is hard polyurethane board. How to simply obtain the reasonable parameters of insulation materials will be a hot spot in the future research. Additionally, new environmentally friendly insulation materials with optimal durability should be studied and applied [75].

3.1.2. Heating and Other Measures

Heating is another way to alleviate frost problems of drainage ditches and entrance/exit structures. Geothermal energy, electrical heating, and hot-water supplies have been adopted for heating. The geothermal energy of the surrounding rock in the middle of a tunnel has been used to heat the ditch and lining at the entrance of Linchang tunnel (Figure 4) [81,82,83]. Lai et al. [84] showed that the combination of electric heat tracing (Figure 4) and insulation was a feasible and effective way to prevent frost damage. Heating from the back of the lining was another effective method to prevent freezing damage [39,85]. Additionally, thermal insulation doors (Figure 5) and snow shelters (Figure 6) have been used to increase the air temperature in tunnels in seasonally frozen areas. In-situ test results have revealed that thermal insulation doors are better than snow shelters in preventing frost damage [86,87]. All technologies have advantages and disadvantages (

Table 9. Comparison of advantages and disadvantages of different technologies.

Techniques		Advantages	Disadvantages	Ways to Improve
Heating	Geothermal energy	Highly effective, sustainable developmental strategy, low-carbon green, cheap	Efficiency gradually decreases. It is not universal, and some places do not have the conditions to utilize geothermal heat.	Heat compensation, improve heat conversion efficiency
	Electric heating	Extremely effective	Expensive, energy consumption. There is no power transmission line in remote areas, and only wind or solar energy can be used. It is inconvenient to repair the damaged heating circuit.	Improve the durability of circuit materials and laying methods.
	Hot water	Extremely effective	Expensive, energy consumption. Water pipes are easy to crystallize and block. It is inconvenient to repair the damaged hot water circuit.	Improve the durability of circuit materials and laying methods. Use auxiliary technology to eliminate pipeline crystallization.
Thermal insulation doors		Highly effective, cheap, low-carbon green	Inconvenient, limited warming.	Automatic sensing, automatic opening or closing of the door
Snow shelters		Effective, cheap, low-carbon green	Poor durability. Low heating efficiency.	Improve durability of materials
Thermosyphon		Low carbon green, strong heat transfer ability, safety and economy	Expensive, poor durability	Improve durability of materials

).

3.2. Anti-Thawing Measures

During the construction and operation of tunnels in permafrost regions, engineers need to maintain the frozen state of the surrounding rock of tunnels. An insulation layer is therefore used to reduce heat transfer into the surrounding rock [88]. The layout of the insulation layer in a permafrost tunnel is similar to that in a seasonally frozen tunnel (Figure 3). The most important influencing parameters of the insulation layer are thermal conductivity and thickness [29]. An insulation layer with a thermal conductivity of 0.03 W m⁻¹ °C⁻¹ and a thickness of 5 cm was used for Fenghuoshan and Kunlunshan tunnels, and there were no seasonally thawing zones [89,90,91]. Xia et al. [92] obtained an analytical formula for the thickness of the thermal-insulation layer of a permafrost tunnel. Li et al. [93] presented a coupled heat–water model to optimize the parameters of the thermal insulation layer. A thermosyphon was used to prevent permafrost from thawing in part of a permafrost tunnel with small buried depth (Figure 7) [17,94,95]. The thermosyphon technology is a device that uses the conversion convection cycle of liquid and vapor phases to achieve heat transfer [96]. It is a device that uses natural cold energy without external power. It has the characteristics of strong heat transfer ability, small heat transfer temperature difference, low starting temperature, good temperature uniformity, one-way heat transfer, safety and economy. Until now, there are relatively few permafrost tunnel projects, and the accumulated engineering experience is limited. To this end, it is necessary to address the scientific prediction and long-term field monitoring of the thermal field of frozen surrounding rock under climate change and operation conditions.

3.3. Anti-Icing Measures

Icing is one of the main disaster risks faced by tunnels in cold regions [11]. It occurs in different parts of a tunnel in winter, such as the drainage system, the tunnel portal road, and the lining surface. Drainage tunnels are useless in permafrost tunnels but have been used for sluicing and drainage in unstable frozen and unstable local permafrost tunnels [97]. To prevent the water in drainage pipes from freezing, the ring drain pipes were wrapped with a striped insulating layer at the back of the lining and extended below the road [98]. Tattersall et al. [99] designed a heavy-gauge corrugated liner plate in the form of an arch with an insulation layer. Heating equipment was installed along the roads to melt the ice and snow at the tunnel portals. For example, Lai et al. [78] installed the heating cables in the structural layer of a road. A waterproof and ripped-rock layer was laid between two clay layers for insulation and preventing leakage during the construction of Kunlun mountain tunnel. This measure can prevent the water from icing in the tunnel [33,100]. There is little icing in cold tunnels if the waterproofing system and drainage system work well [101].

4. Tunnel Construction Techniques for Frost Problem Mitigation

Permafrost tunnels are often excavated through drilling and blasting. The stability of the surrounding rock is affected by the thermal disturbance in permafrost regions [102]. If permafrost tunnels are not supported, the thawing depth of the surrounding rock increases over time [103]. Finally, the thawing depth of the surrounding rock exceeds the upper limit of the natural permafrost ground [104]. The plastic area around the tunnel excavation profile and the tensile stress of the lining increases with increase of the thawing depth [105]. After the permafrost tunnel is completed, the thawing depth decreases by refreezing [89]. The freeze–thaw cycles of the thermal disturbance zone are harmful to the surrounding rock and structures. Control methods are thus adopted to reduce the generation of heat. For example, dynamite enwrapped in water or saltwater and brine mud is used in blasting holes [106,107]. The start date of construction is also important for permafrost tunnels. The best time for construction is when the atmospheric temperature is below zero [88]. However, there is no construction thermal disturbance for seasonally frozen tunnels. It is necessary to ensure that there is no gap between the waterproof board and concrete surface or insulation board in seasonally frozen tunnels, because there is more load acting on the lining than usual if there is water to freeze behind the lining. The peeling resistance between the waterproof board and concrete surface or insulation board should be increased as much as possible [108]. If grouting is used in construction, the materials must solidify rapidly, have early strength, and be suitable for sub-zero temperatures [109]. The requirements for construction quality and grouting material are thus high. When transporting and maintaining in winter, the insulation of concrete and shotcrete should be guaranteed. The construction of a permafrost tunnel is thus difficult.

5. Tunnel Maintenance Techniques for Frost Problem Mitigation

The most effective countermeasures to deal with frost damage are the restoration of drainage systems, the reinforcement of structures, and the reinstallation of freezing-prevention systems [6,7,9,110]. For example, the drainage pipes are wrapped with XPS-plates to ensure that the water in pipes does not freeze [6]. An anti-water layer and an anti-freezing layer have been constructed between an old concrete lining and newly added concrete lining [110]. Scaffold rapid construction, corrugated-slide installation, corrugated-plate fixed safety measures, and a corrugated plate combined with a spontaneous bubble polyurethane surface treatment have been adopted [91]. Reasonable parameters of grouting materials and grouting techniques can prevent and control water leakage [111]. The durability and rapid maintenance of materials need to be addressed in future research.

The sufficient and necessary condition for icing is the presence of water. Water may be from groundwater, rainfall, or the melting of ice and snow. Grouting is one of the most effective and popular methods for preventing icing. For example, there is a lot of icing on the road and lining surface in a tunnel (Figure 8) in Xinjiang. Based on investigation and test, the maximum snow thickness is 1.5 m and the maximum frost depth is 1.5 m in the tunnel site, where annual average temperature is 4.7 °C. There was no ice after being treated by grouting (Figure 9). However, it will take time to verify the long-term effectiveness of this approach.

There is much frost damage near the entrance/exit of a tunnel especially when the tunnel is partly open-cut. Open-cut tunnels are often built after earth-rock excavation based on the design. An open-cut tunnel is buried by backfilling once it is completed. The backfill at the top of an open-cut tunnel is usually lost under the influence of freezing-thawing, rain, and wind (Figure 9). Changes in atmospheric temperature and seasonal frost heaving of backfill can easily damage the structure. Structures should be buried with backfill until their depths reach the lower freezing limit. The practice of tunnel engineering in cold regions focuses on the frost problems of main structures and does not pay sufficient attention to the frost problems of auxiliary structures, such as the freeze–thaw problems of the drainage ditch at the top of a tunnel entrance and side slope, and the structural defects and durability of the snow shelter. These problems also affect the operation and security of tunnels.

6. Summary

Tunnels in cold regions can suffer freezing and thawing damage because of changes in atmospheric temperature. Theories of tunnel design in cold regions and current techniques for frost problem mitigation in the design, construction, and maintenance of tunnels are reviewed in this paper. The main problem faced by permafrost tunnels is the melting of surrounding rock, which is frost heaving and icing in cold regions. The severity of these problems is determined by the ambient temperature, initial ground temperature, groundwater, and ventilation conditions. Under the background of global warming, the problem of permafrost degradation is becoming prominent. The risks of permafrost tunnels will increase, and the corresponding risk assessment and preventive measures need to be strengthened. For seasonally frozen regions, extreme hot weather and extreme cold weather are also increasing, and the freezing and thawing cycle intensity of tunnel entrance/exit will increase. Additionally, the durability of surrounding rock and lining under large temperature difference also needs to be strengthened.

The freezing and thawing depth and frost heaving force are the most important parameters in the design of tunnels in cold regions. Existing theoretical research and technologies on the frost heaving force and temperature field of tunnels in cold regions have helped solve some problems in practice, but there remain theoretical and technical problems in practice that need to be further studied. As examples: (1) The theory is difficult to understand and use, so it needs to be simplified. (2) The atmospheric parameters at a tunnel site are not usually available because there is no atmosphere observation station. Therefore, this paper proposes to establish atmospheric observation points in the tunnel site area. (3) It is not clear which of the formulas is the most reasonable and how it can be used in design; the theoretical formulas need to be classified. (4) More verification cases need to be carried out. Finally, (5) It is not clear how to adapt to changes in the natural and operating environments, including climate warming.

Techniques for frost problem mitigation in tunnel design include the installation of an insulation layer, heating system, thermal insulation gate, snow shelter, and thermosyphon. An insulation layer is the most commonly adopted option. The reduction of hydration heat and blasting heat is an effective way of decreasing thermal disturbances in the construction of permafrost tunnels. Five issues relating to the mitigation of the freeze–thaw problem need to be addressed: (1) The service life of insulation materials, thermal insulation gates, and snow shelters are not widely verified and the materials that have the same service life as tunnels should be developed. (2) Energy saving techniques and new energy techniques need further research, because the heating systems are expensive and require electricity, which is sometimes unavailable. (3) Effective measures for reducing thermal disturbances and guaranteeing the quality of construction in winter require further study. (4) An evaluation index system of tunnel frost damage is required for further investigation. (5) How to rank the frost damage to new and old tunnels is a difficult problem to solve.

As for the maintenance of tunnels in cold regions, the restoration of the drainage system, the reinforcement of structures, and the reinstallation of freezing-prevention systems are the most effective treatments. In terms of the quality of maintenance, it is necessary to understand the underlying reasons of frost problems, to carry out maintenance as soon as possible to reduce the traffic interruption, and to improve the bonding between new and old materials that have experienced many freeze–thaw cycles.

In addition, the development of new construction materials and grouting materials for cold environments is an important way to improve the service performance of tunnels in cold regions in the future.