The effects of water flow and temperature on thermal regime around a culvert built on permafrost

Loriane Périer ,Guy Doré ,C.R.Burn

1.Laval University,Center for Northern Studies (CEN),1035 Avenue De la médecine,Québec,Canada G1A 0A6

2.Carleton University,Dept.of Geography and Environmental Studies Ottawa,Ontario,Canada K1S 5B6

1 Introduction

Permafrost is defined as ground (soil or rock) in which temperature is at or below 0 °C for at least two consecutive years (Van Everdingen,2005).In northern regions,climate warming and infrastructure construction both commonly lead to permafrost thaw.We have observed several stabilization problems close to culverts on the Alaska Highway in western Yukon,Canada.The free circulation of air and water through a culvert creates a high disturbance to the ground thermal regime near the structure.Where the permafrost is ice-rich,settlement may occur,causing culvert distortion,joint damage,and water circulation under the culvert.Two culverts on the Alaska Highway near Beaver Creek were instrumented to monitor their thermal regime.A thermal model has been developed with TEMP/W to evaluate the influence of several factors on the thermal regime.Existing knowledge about the influence of water temperature and flow on thermal regime surrounding culverts is limited,but experience teaches us that thaw depth is always greater under culverts than in the adjacent embankment because the air and water flowing through the pipe transfer heat to the ground (McGregoret al.,2010).The information gathered in this project will support the development of a design procedure for drainage systems around transportation embankments with low impact on permafrost.

2 Test sites

A first culvert was instrumented in early May 2013 at the Beaver Creek permafrost test site,on the Alaska Highway near the Canada/US border.The road is on warm,discontinuous permafrost that is potentially unstable as the mean annual ground temperature is higher than-2 °C.The soil is very sensitive to temperature variations,and if permafrost thaws the subgrade soil is subject to loss of bearing capacity and is susceptible to creep under loads imposed by the backfill.The highway test section has several experimental systems for mitigation of ground thermal effects,except where the culvert is located (Figure 1) (M-Lepage,2012).

Figure 1 Localization and description of test site

3 Instrumentation and method

Instrumentation installed in the culvert is illustrated in figure 2.Three thermistor probes were installed,two in the floor of the culvert near the entrance and exit,and one on the side of the culvert near the entrance.Each probe contained three thermistors which measured the soil temperatures underneath or beside the culvert.In addition,air temperature in the culvert was measured near the entrance.It was difficult to insert the probes into the packed and sometime frozen gravel fill around the culvert,so data collection was limited to 30 cm beyond the culvert wall.Measurements were made at the culvert wall and at distances of 15 and 30 cm into the fill.Temperatures were recorded every hour from May 24 to October 4.A short circuit occurred upstream during the first week and deleted records of air and soil temperatures in the side of the culvert.Probes under the culvert upstream and downstream provided data throughout the monitoring period.All thermistors were connected to two HOBO U30 data loggers;one was placed at the inlet and the other at the outlet of the culvert.

As shown in figure 3,a V-weir was installed 7 m upstream from the culvert inlet to measure the water flow into the culvert.A HOBO U20 pressuremeter was installed upstream of the weir to measure water pressure every hour,at the same time as atmospheric pressure was recorded near the culvert inlet on a barometer connected to a HOBO U30 data logger.The pressuremeter was at the base of a pipe inserted into the soil beside the weir.The difference between air and water pressure allowed assessing water height in the weir,making it possible to determine flow (Q) using equation(1)(Achouret al.,2003):

whereαis V-weir angle,gis gravitational acceleration andhis the water level passing in the V-weir.A thermistor was installed on the V-weir to measure water temperature entering the culvert.

Figure 4 shows a schematic diagram of the final installation of the culvert.The flow measurement system was successfully installed,but was damaged during the summer,affecting some of the data collected.Water flowed under the weir in mid-July 2013,because it was installed when the thaw depth was shallow.Temperature and flow data were recorded every hour from May 24 to July 11,2013.

Figure 2 Installation of instrumentation upstream and downstream (units:m)

Figure 3 Flow measurement system

Figure 4 Schematic diagram of the instrumentation at the culvert

4 Geothermal simulation with TEMP/W

The objective of our initial simulation was to calibrate a 2D thermal model using TEMP/W to the conditions of the reference embankment without a culvert.The ground at the site consisted mainly of silt topped with one meter of peat.The 4.5-m high embankment was made of granular fill.On site thermal properties were obtained from previous work at the site (De Grandpré,2011),and compared with properties estimated for site soil conditions obtained with the method proposed by C?té and Konrad (2005).The values used in the simulation are presented in table 1.

An effective geothermal simulation requires an accurate description of the soil stratigraphy and the initial thermal conditions.Soil temperature data for the embankment are available from the control section close to the culvert (see figure 1).In this section,thermistors are located at several different depths in the slope of the embankment (M-Lepage,2012).Ground temperatures at the control section have been recorded every four hours throughout the year.The maximum and minimum temperature profiles from the last full year of recording (2011),which is representative of the four years of available data,are presented in figure 5.

Table 1 Thermal properties

The surface thermal boundary condition was the record of ground temperatures 30 cm below the surface of the embankment obtained in 2011.This temperature series was used to drive all simulations reported in this paper.The initial ground temperature profile within and below the embankment was based on measured temperatures in the subjacent permafrost.These values were projected upward into the embankment and are presented as the orange line in figure 5.In the simulations,surface temperatures were varied through the monthly averages of temperatures recorded at 30-cm depth below the surface of the embankment.The dashed lines in figure 5 represent the simulated maximum and minimum values for ground temperatures in the embankment and the ground beneath,obtained to check calibration of the thermal model without a culvert.

Figure 5 Maximum and minimum temperatures simulated within the embankment and subjacent permafrost,compared with field measurements at the control section.Data for an embankment both with and without a culvert are presented

Once the model was calibrated,a culvert and insulation were introduced into the stratigraphy.The culvert was represented by a semi-circle,because the temperatures right and left of the culvert were assumed to be symmetrical and the conditions to be adiabatic.The same surface and stratigraphic boundary conditions were used,except for conditions in the culvert.Inside the culvert,imposed water temperatures corresponded to values reported by the thermistor installed on the surface at the bottom of the culvert.Variations of water temperatures for a year corresponded to recorded temperatures between May and October in the floor of the culvert.For the other months,the temperature at the bottom of the culvert was considered to be 0 °C.The air temperature in the culvert was simulated with monthly mean air temperatures from the weather station at the test site.The maximum and minimum temperatures obtained from this simulation are presented as dotted lines in figure 5.It can be observed that the culvert had a warming effect on the ground during summer,and a cooling effect in winter.

A closer examination of field and simulated ground temperatures is presented in figures 6 and 7.The orange lines represent field measurements at various times in June 2013,and black lines represent temperatures obtained from the TEMP/W model.The simulation was started in September.These figures present data from near the inlet and near the outlet of the culvert.Near the outlet,data were available to 15 cm below the culvert wall,while at the inlet measurements were made to a depth of 30 cm.

The culvert wall temperatures were similar at both ends of the structure,but at some specific dates,water temperature is warmer on the upstream side than on the downstream side showing that heat is transferred to the soil underneath the culvert during those dates.The effect of the insulation layer,only 20 cm below the culvert at the inlet,was not visible on the field data.Downstream,the temperature probe was not deep enough to be able to sense the presence of the insulation.In general,the model overestimates field measurements at 15-cm depth near the inlet,but at 30-cm the field measurements were several degrees higher than the simulation.We suggest that this may be due to water infiltration into the holes made during probe installation,and we expect that data collected in summer of 2014 will not show this effect.

Figure 6 Upstream in June 2013,under-culvert thermal regime

Figure 7 Downstream in June 2013,under-culvert thermal regime

5 Empirical relations

We have found that statistical relations are useful to establish a link between water temperatures at the weir (Tw),near the inlet (Ti),and flow (Q).These relations have enabled a sensitivity analysis of variations in flow rate and water temperatures at the weir on the thermal regime of the soil under the culvert.

Weekly average values ofTwandTifrom data collected in 2013 are presented in figure 8.The coefficient of determination (R2) for these data is 0.69,and the shape of the relation appears to be linear.

Figure 9 presents a logarithmic relationship betweenTiandQfor weekly average values.R2 is 0.56.

Flow values (Q) were transformed into logarithmic values in order to provide a linear relationship betweenTiandQand to obtain a multiple linear regression betweenTi,TwandQ.This relationship has two dependent variables,TwandQ,two coefficients,X1andX2,and a constant.The coefficient of multiple determination is 0.82,calculated from 48 daily observations.The statistical relation is:

In figure 10,Tipredicted by equation(2)is plotted against the corresponding field measurements.

Figure 8 Correlation between Ti and Tw

Figure 9 Correlation between Ti and Q

6 Sensitivity analysis

A sensitivity analysis was conducted forTiusing equation(2)and varying both flow and temperature of the water in the weir.The flow rate for May 26 to July 11 was varied with respect to field measurements.For the rest of the season,flow was extrapolated from the relation between dailyQand time presented in figure 11.

Figure 11 Flow (Q) as function of time

The flow was assumed to decline steadily after July 11.Equation(3)presents this relation:

Table 2 shows the effect of changes inQof ±10%onTifor specific days in the monitoring period.Equation(2)does not yield a great change inTi,and so a small effect of the simulated changes was anticipated.The new values forTiwere inserted in the TEMP/W model and the effects of these changes were observed.The results are presented in figure 12,but they confirmed little change in ground temperatures.

An analysis of change in sensitivity to water temperatures at the weir was conducted by varying the values by ±10% of the temperature.These values were obtained for May 26 to July 11 from field measurements.For the rest of the season,values forTwwere obtained from a relation betweenTwand air temperatureTaas measured by Environment Canada at Beaver Creek.This relation is presented in figure 13 and summarized in equation(4).

Table 3 shows the sensitivity ofTito changes inTwas simulated for the initial part of the season.When these values and others for the rest of the season were implemented in TEMP/W,there was a recognizable change in ground temperatures beneath the culvert.This variation is presented in figure 14.

Figure 12 Simulation of ground temperature near the culvert wall with variation in Q

Figure 13 Tw as function of Ta

Table 2 Decrease and increase flow

A final simulation with TEMP/W was conducted without insulation in the stratigraphy below the culvert.The importance of insulating the culvert is significant,and the change in thaw depth was greater than any effect of changes in flow or water temperature.As presented in figure 15,the thaw depth is about 30 cm with insulation,and about 120 cm without insulation.

Figure 14 Simulation on Tw

Figure 15 Simulation without insulation

7 Discussion and conclusions

Culverts induce significant thermal disturbances to highway embankments in permafrost regions because they introduce heat from flowing water and surface air into the ground.An operational culvert in the Beaver Creek test section was instrumented in early summer of 2013 and some of the data obtained at the site was used to conduct a modeling exercise on the ground thermal regime around the culvert.Field installation was limited by the practical consideration of installing thermistor probes into the ground adjacent to the culvert from within the structure.As a result it was not possible to insert probes more than 30 cm into the adjacent packed fill.Later in the summer,we were able to instrument more extensively at a site where a culvert was being constructed,and so we are in the process of obtaining more extensive data from the fill beside the new culvert.These data will be incorporated into the project simulations as they become available.

The thermal model is considered to be reasonably reliable because it was calibrated successfully using the extensive data set available from the Beaver Creek Test Site.Measured thaw penetration beneath the culvert in summer of 2013 was not replicated well,but we consider that this is likely due to the disturbance to monitoring sites introduced during equipment installation.We anticipate that a closer correspondence will be available from data in summer of 2014.

We consider that the thermal impact of the culvert is likely to be a function of the temperature of water entering the culvert and the flow rate,because these variables control the temperature at the culvert wall and the quantity of heat introduced to the culvert.A relation was obtained between the water temperature 7 m inside the culvert and both water temperature outside the culvert and flow into the structure.The relation demonstrates that in-culvert water temperature is dominantly a function of the temperature of the water flowing into the structure,and varies little with flow rate.

A sensitivity analysis on the effect of these variables on the ground thermal regime was also conducted as part of this study.As anticipated,changes in flow altered the ground temperatures around the culvert very little,but water temperatures had a noticeable effect on the ground thermal regime.We are conscious that the relations used to drive the sensitivity analysis are based on only a partial account of seasonal conditions.Conditions in the rest of the season were approximated using relations derived from local environmental data,but we expect to refine the model with a full season’s information from 2014.

We do not expect fundamental changes in the structure of the derived relations,but we anticipate developing a function to simulate the change in water temperature through the culvert,in order to estimate,using the thermal model,the thermal effect of the culvert throughout its length in the embankment.

Table 3 Tw decrease and increase

The authors would like to thank the reviewers for their suggestions,Transport Canada for financial support,and Yukon Highways and Public Works for their support,logistics and assistance during instrumentation at the new Beaver Creek Culvert and information regarding the rules for construction of culverts in Yukon.Finally,the authors thank the research team and Arquluk students for assistance during installation and discussion in the laboratory.

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