Research on EPS application to very wide highway embankments in permafrost regions

YaHu Tian , JianHong Fang , YuPeng Shen

1. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

2. Qinghai Research Institute of Transportation, Xining, Qinghai 810008, China

1 Introduction

The construction of highway and railway embankments on permafrost may induce substantial disturbance in the heat and mass transfer balance between the ground surface and atmosphere, which results in more heat absorption in the embankments. This causes the temperature of the underlying permafrost to increase as the permafrost thaws, resulting in serious damage to embankments in the Qinghai-Tibetan Plateau due to thaw settlement. To prevent such damage, many techniques are utilized, such as embankment insulation, sun shields on the embankments, crushed-stone embankments, embankment ventilation pipelines, and installing thermosyphons in the embankments.In recent years these techniques have been developed in China and successfully used on the Qinghai-Tibetan Highway and Railway.

The G214 highway, currently being built from Gonghe County to Yushu City in Qinghai Province, is the first major highway to be constructed in permafrost regions in the Qinghai-Tibetan Plateau. It is about 435 km long, passing across the frozen soil regions; almost 200 km of it crosses high-temperature, unstable permafrost regions. The width of its embankments is 24 m in some zones. The annual mean temperature of the highway’s asphalt pavement on permafrost is about 6 °C higher than the annual mean air temperature, and about 3.5 °C higher than gravel pavement (Zhu, 1988). As the pavement width increases, the heat absorbed by asphalt pavement greatly increases, causing serious disturbances in the permafrost beneath the embankments and greater settlement of foundations, especially in high-temperature permafrost regions. The stability of very wide highway embankment in permafrost regions will be a new challenge after the construction of Qinghai-Tibetan Railway, because the technical standard of controlling of uneven deformation of pavement is stricter for the G214 highway.

One effective method for stabilizing the subgrade in permafrost regions is the utilization of thermal insulation material in the subgrade body at certain depths. This approach was first used in roadbed engineering on permafrost in the 1950s in Norway. Since the 1970s, EPS has been used as insulation in embankment engineering in America, Japan, and Canada (Gandahl, 1978; Johnson,1983; Olson, 1984). In China in 1970, a field test was conducted at the Fenghuoshan Experimental Station in Tibet to examine the efficiency of this countermeasure(Zhang and Yao, 1994). In 1992, another experimental section of thermal insulation was built on the Qinghai-Tibetan Highway (Shenget al., 2002). Liu and Tian(2002) and Wenet al.(2005) evaluated the EPS application to embankments of the Qinghai-Tibetan Railway.The results of these researches showed that the insulation functioned effectively.

The embankments of the G214 highway are being built differently from those on the Qinghai-Tibetan Railway, which has railway ballast on its embankment surfaces, and the Qinghai-Tibetan Highway, which has 8-m-wide embankments. Therefore, these embankment protection techniques may not be indiscriminately applied to the G214 highway. This paper assesses the design data and geologic and climate conditions of the G214 highway in permafrost areas, using two-dimensional finite element analysis of temperature fields for varying widths of highway embankments with insulation under current climate warming conditions. In this simulation study, the heights of the embankments are all 3.65 m and the widths are 12 m, 16 m, 18 m, 20 m,and 24 m. The evolutionary trends of embankment thermal regimes are analyzed and, finally, EPS application in a 24-m-width highway embankment in permafrost regions is evaluated. Our conclusions will hopefully be relevant and useful in the construction of the G214 highway.

2 Governing equations and finite element formulation

Assuming that no water infiltrates into the embankment and that water appears in the active layer, the 2-D heat conduction with phase change in the roadbed and base can be described as:

whereρrefers to soil density,сrefers to specific heat capacity of soil,trefers to time,λrefers to coefficient of heat conductivity, andTrefers to temperature.

For the problem of heat transfer with phase change in soil, the enthalpy transformation method has been proved to be effective. Enthalpy is the integral of specific heat of soil with respect to temperature:

Since enthalpy is a smooth function of temperature even in the phase change zone, it is therefore reasonable to interpolate the enthalpy rather than the heat capacity directly. By definition, it is:

This yields the following equation:

The physical domain can be divided into elements.By using the Galerkin residual weighted method for Equation(4), the following finite element matrices are obtained:

where:

in whichNiandNjrefer to element shape functions.

3 Computational domain

Based on the design specifications of the G214 highway and the actual embankment geometries, in our computations the height of embankment was 3.65 m and the slide slope was 1:1.5 (vertical to horizontal). During simulation calculation, five embankment widths were selected: 12 m, 16 m, 18 m, 20 m, and 24 m. The embankment was regarded as infinitely long with a constant cross section; thus, the heat conduction process could be modeled in two dimensions. Figure 1 shows the computational model and its dimensions. Part S1 is sand-gravel,Part S2 is gravel with fine inclusions, Part S3 is meadow soil and subclay, Part S4 is subclay with gravel, and Part S5 is weathered mudstone. The location of the EPS insulation was 1.65 m below the subgrade. The thermal parameters are given in Table 1. Given the symmetry of the left and right boundaries, the right side of the embankment was selected as the computational domain.During the calculation, 11 different cases were simulated,and they are summarized in Table 2.

The thermal conductivity of EPS is 0.03 W/(m·°C).The specific heat capacity and density are 1,400 J/(kg·°C)and 40 kg/m3, respectively.

Figure 1 Illustration of computational model

Table 1 Soil properties

Table 2 Summary of simulated cases

4 Boundary and initial conditions

According to Zang and Wu (1999) and Fu (2011),and referencing Figure 1, the temperatures at the native surfaces AB and EF vary per the following formula:

The temperatures at the side slopes BC and DE change as follows:

The temperatures at pavement surface CD change as follows:

wherethrefers to time (hour).

The lateral boundaries (AH and FG) are assumed to be adiabatic. The temperature gradient at the bottom boundary HG is 0.03 °C/m.

5 The influence of width of embankment without insulation

Initially, the location of the permafrost table was 2.45 m under the natural surface. Based on the calculation results, when the widths of the uninsulated embankments were 12 m and 24 m, the permafrost tables at the center of the embankments were 2.86 m and 3.67 m, respectively, at 10 years after the construction. Their isotherms are shown in Figures 2a and 2b. Figure 2a shows that the maximum thaw depth increases less for the 12-m-wide uninsulated embankment, but the temperature of the permafrost at 4.5-m to 13-m depth beneath the native surface increases obviously and a high-temperature core occurs. Figure 2b shows that the maximum thaw depth increases more for the 24-m-wide uninsulated embankment and the zone of the high-temperature core is larger.These results indicate that for asphalt highway pavement in permafrost regions, the wider the uninsulated embankment is, the more severely the permafrost is disturbed.

Figure 2 Simulated isotherms of the embankments on October 1, 10 years after the construction(a) width of the embankment = 12 m; (b) width of the embankment = 24 m

With the passage of time and increased climate warming, at 30 years after construction the maximum thaw depths below the centers of the 12-m-wide and 24-m-wide embankments would increase 1.0 m and 3.5 m, respectively, compared to the depth of the natural permafrost table. Figures 3a and 3b show that the zones of high temperature are increasingly larger. These results indicate that, in permafrost regions, the effect of thermal aggregation on asphalt pavement is more obvious when highway embankments are wider.

Figure 3 Simulated isotherms of the embankments on October 1, 30 years after the construction(a) width of the embankment = 12 m; (b) width of the embankment = 24 m

6 The influence of width of embankment with 0.1-m-thick EPS

Figure 4 shows the predicted maximum thaw depths for 12-m-, 16-m-, 18-m-, 20-m-, and 24-m-wide embankments with 0.1-m-thick EPS over 30 years. It can be seen that when the width of embankment with 0.1-m-thick EPS is less than 20 m, the permafrost tables below the center of the embankments all are uplifted to different extents 10 years after the construction. After that, the maximum thaw depth begins to increase gradually. When the widths of embankments are 12 m, 16 m,18 m, 20 m, and 24 m, the permafrost tables below the center of embankment are 1.60 m, 2.49 m, 3.06 m, 3.76 m, and 5.40 m, respectively, under the natural surface 30 years after the construction. This is because there is heat accumulation under the insulation, which may cause the permafrost temperature to increase. Consequently, in permafrost regions, the wider a highway embankment is,the poorer the insulation efficiency is. When the width of an embankment is more than 16 m, 0.1-m-thick EPS might not maintain the stability of the highway.

Figure 4 The predicted maximum thawing depth below the center of embankments with 0.1-m-thick EPS

7 The influence of the insulation layer thickness

Figure 5 shows the predicted maximum thaw depths for 24-m-wide embankments with different thicknesses of EPS: the maximum thaw depth decreases in increments as the thickness of the insulation increases. When the thicknesses of insulation are 0.1 m, 0.15 m, 0.2 m,0.25 m and 0.3 m, the permafrost tables below the center of embankment are 5.40 m, 4.26 m, 3.31 m, 2.74 m and 2.10 m, respectively, under the natural surface 30 years after the construction. This demonstrates that the insulation should be more than 25 cm thick in order to maintain the stability of a 24-m-wide embankment. However,consideration of other factors such as the structural rationality of the embankment and high engineering costs;it might not be feasible to install EPS insulation in 24-m-wide embankments of the G214 highway in permafrost regions.

8 Conclusions

Based on the numerical results and analysis, we can conclude:

1) The effect of thermal aggregation on asphalt pavement in permafrost regions is more obvious when a highway embankment is wider, which may cause the permafrost table to decline severely.

2) The wider the embankment of a highway is, the thicker is the insulation necessary to maintain the embankment stability in permafrost regions. On the G214 highway, the insulation thickness should be more than 25 cm for 24-m-wide embankments. However, considering other factors such as the structural rationality of the embankments and high engineering costs, it might not be feasible to install EPS insulation in 24-m-wide embankments of the G214 highway in permafrost regions when the height of the embankments is less than 3.65 m.

Figure 5 The predicted maximum thawing depth below the centers of 24-m-wide embankments insulated with EPS

The authors wish to acknowledge the support provided by the Fundamental Research Funds for the Central Universities (No. 2011JBZ009), the National Natural Science Foundation of China (No. 41271072 and No.41171064), and the Open Fund of the Qinghai Research Institute of Transportation (No. 20121208).

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