This article presents the outlines of the ground freezing works of the Line 14 extension project to the north of the Parisian subway in France. This project is one of the first in a long series of tunneling works managed by a company called Société du Grand Paris, which is in charge of the construction of approximately 200 km (124 miles) of tunnels and 68 subway stations around Paris. The subway lines will be opened, one by one, from 2020 to 2030. Package 3 of the Line 14-North project includes the creation of a subway station, three pedestrian accesses, a ventilation shaft and a 26 m- (85-ft) long rectangular tunnel linking the station and the shaft (Fig. 1).
This article focuses on the construction of the rectangular tunnel that joins the station and the shaft. The project will utilize artificial ground freezing due to a complex hydrogeotechnical context.
Presentation of the project
The tunnel. The rectangular tunnel is located 3.2 m (10.5 ft) under an active commuter train station (RER Line C) that was built in 1984 on deep concrete piles (Fig. 2).
The as-built position of the piles was only partially known at the beginning of the project, which required the excavation of a small gallery just above the RER-Line C (RERC).
Because Line 14 trains will circulate between the station and the shaft, the central pile (B11) was taken down and a section of the northern pile (B12) had to be reduced, as it extended beyond the external lining of the vertical wall. The southern pile (B3) will stay in its initial configuration.
At the center of the structure, two massive concrete beams were cast to transfer the loads onto concrete walls, requiring a hat-shape excavation line (Fig. 3). The tunnel was then divided into two cross sections:
- Section A-A: 8 m (26 ft) high by 14.5 m (47.5 ft) wide at each end of the tunnel.
- Section B-B: 11.2 m (36.7 ft) high by 14.5 m (47.5 ft) wide in the middle.
The transition from one section to the other is about 4 m (13 ft) (Fig. 3).
Geotechnical context. Most of the tunnel is excavated within the Beauchamp Sands formation, a geotechnical unit that includes three sublayers:
- Upper layer, consisting of fine sands or silts.
- Intermediate layer, which is much more clayey and can contain up to 30 percent fine particles (<2 μm).
- Lower layer, similar to the upper layer, but it is not in the tunnel’s path.
Beauchamp Sands were found up to the roof of section A-A and a marly-limestone formation (Saint-Ouen Limestone) in section B-B. This layer is basically a marl, with blocks of limestone reinforcing the ground.
A thin layer of very fractured limestone (Ducy limestone) divides the upper Beauchamp Sands and the Saint-Ouen limestone layer. Its thickness ranges from 40 cm to 1 m (15 in. to 3 ft).
The station is located under a former industrial site that has polluted the soil for several decades, leaving behind small quantities of hydrocarbons, which were found during initial investigations. The salt content was not significant enough to prevent the use of artificial ground freezing.
Hydrological context. The water level is located approximately 6 m (12 ft) above the tunnel’s crown, thus the ground is fully saturated.
Construction of the Clichy Station and the ventilation shaft completely modified the initial water flow trajectories, creating a north-south artificial channel under the RERC. The diaphragm walls created a dam effect with nearly 0.5 m (1.6 ft) of head difference between the north and the south piezometers. A secondary consequence of the dam effect was an increased flow speed underneath the RERC in the bottleneck created by the two shafts.
Chemical tracings were implemented during construction work to quantify the water flow speed and to confirm the feasibility of ground freezing. The hydrological study showed that flow speeds could be very high locally (20 m/day), which was due to the presence of the fractured Ducy limestone. However, the majority of the fluorescein was not detected even a few weeks after the injection, leading to the conclusion that the average water flow speed (< 0.5 m/day, < 1.6 ftpd) was low enough to practice artificial ground freezing.
Two hypotheses were made to explain the location of the largest flow speeds. One possibility was that there would be some heterogeneity in the soil-diaphragm wall interface. The other was that the Ducy limestone permeability had increased due to the washing out of its fracture filling. Indeed, during the drilling of the drains, the water was found to be charged with dark clay particles.
Frozen body pattern. The frozen-body shape was designed to account for two primary constraints:
- The train station just above the tunnel: the frozen body had to remain open on top.
- The necessity to completely freeze the sandy layers: the uppermost freeze pipe had to be located in the Ducy limestone formation, 2.9 m (9.5 ft) from the RER base slab.
A U-shape frozen body was therefore designed, with a pipe spacing of 65 cm (26 in.) along the vertical sidewalls and 80 cm (31 in.) on the inverted vault. For geometrical reasons (location of the piles, lack of space in the ventilation shaft), local adaptations were made in the freeze pipe position plan (Fig. 4).
A total of 2,500 linear m (8,202 ft) of drilling was performed from both the station and the shaft:
- 1,709 m (5,606 ft) for 122 freeze pipes (61 per side), averaging 14 m in length.
- 450 m (1,476 ft) for 30 thermocouples. Sensors were placed every 2 m (6.5 ft) along the tunnel.
- 495 m (1,624 ft) for 34 drains: 19 to relieve water pressure inside the “U” during initial freezing and 15 to lower the water table at the top of the “U”.
In order to reduce water inflows inside the excavation area, tube-a-manchette injections were performed between the frozen body and the RER base slab. Several drains had to be installed to lower the water table because permeability criteria were not reached in the grouted area. These drains were active from the beginning of the excavations to the end of concreting works.
Mixed artificial ground freezing. The ground-freezing work took place in two stages:
- Initial freezing with liquid nitrogen N2 until the mechanical criteria were reached.
- Maintenance freezing with cooled brine (-35 °C). All pipes were therefore retrofitted with bigger tubes prior to excavation in order to ensure normal flow.
The transition from liquid nitrogen to brine was progressive and sequenced, which required that both circulate at the same time. A valve and a thermometer were installed at the head of each freeze pipe.
In order to maintain mechanical stability in zones where water flows were significant, there was a second switch from brine to liquid nitrogen during excavation works.
Ground freezing design
Frozen body characteristics — Ground freezing temperature. For this project, a frozen body was defined with a temperature at least equal to -10 °C. Frozen volumes for which temperatures were higher than -10 °C were neglected in the analysis, and frozen volumes for which temperatures were lower than -10 °C were considered to be as strong as if they were -10 °C.
This criterion was generally easy to reach except in the area at the top of the frozen sidewalls, where water inflows affected the freezing.
Ground characteristics. The frozen body’s mechanical and thermal characteristics were determined using particle size distributions following the methodology described by ISGF Working Group 1 in 1991. No laboratory tests were undertaken on frozen samples for this project, but the values were chosen in accordance with tests performed for a similar project nearby.
The ground characteristics used for the project are summarized in Table 1.
Minimum dimensions of the frozen body. The minimum frozen body shape was determined by the distance between the isothermal temperature -10°C and the nearest freeze pipe. The design was performed with a minimal thickness of:
- 80 cm (31 in.) on the vertical sidewalls.
- 60 cm (21 in.) on the inverted vault, which is much less stressed.
This defined the mechanical criterion, which was verified numerically using the RS2 2D software. The safety factor was defined as the ratio of the radius of the Mohr-Coulomb circle to the Mohr-Coulomb failure criteria. The FEM analysis concluded that the safety factor at each point of the frozen body ranged from 2 to 4 in the upper Beauchamp Sands, from 4 to 11 in the intermediate Beauchamp Sands and from 5 to 10 in the lower Beauchamp Sands. The global safety factor was much higher when considering the real thickness of the frozen body with its actual temperature distribution from -30 °C to 0 °C and the temperature-dependent mechanical properties.
Thermal analysis. A 2D finite elements analysis (FEA) was performed with CESAR v5 software (Fig. 5) to anticipate initial freezing time to reach the predefined mechanical criteria using nitrogen, which was around three days.
Additional durations were anticipated:
- Deviations of 2 percent added around one day (numerically calculated).
- Ground heterogeneity, particularly undetected clay lenses, could add another day.
All things considered, a duration for initial freezing of approximately five days was anticipated.
In addition to the anticipation of initial freezing duration, the FEA simulations enabled:
- An estimate of nitrogen consumption and of the thermal power necessary to maintain brine at – 35 °C. A total value of 2,000 m3 and a minimum thermal power of 150 kW were anticipated. The thermal power was split in two units but for practical reasons, a total power of 210 kW was installed on site.
- An increase in probe spacing over the inverted vault, which ensured that the mechanical criterion on the frozen inverted vault and on the vertical frozen sidewalls was reached more or less at the same time.
Phasing. The phasing of the work was dictated by the buoyancy of the U-shaped frozen body, which would generate vertical constraints on the RER invert (base slab). The tunnel’s excavation was divided into six sections. Three sections in the lower part were excavated first and were backfilled after the formwork was cast, which created a working platform for the excavation of the three upper sections (Fig. 6).
Temporary support design. Because of the creep behavior of ice, the strength of the frozen body decreases with time. Heavy steel ribs (HEM 220 and HEM 200) were installed every meter as temporary support together with a 27-cm thick layer of fiber-reinforced shotcrete. Rib size was dictated by the rectangular shape of the galleries. Moreover, due to the geometrical constraints to drill the freeze pipes, the space between the frozen body and the excavation line was quite limited.
Given the poor characteristics of the upper Beauchamp sands (c = 0 kPa) and of Saint-Ouen limestone, sheet piles were installed at the crown of the lower galleries and at the transition from the short section to the high section (sections AA and BB in Fig. 3), which was very difficult due to the presence of hardened limestone. In addition, jacks were used to redistribute loads from the sidewalls of gallery No. 1 when excavating gallery No. 2 (Fig. 7).
Initial freezing sequence. To cope with the significant water circulations previously described, a solution could have been to grout the Ducy limestone, since the clay filling was removed from the fractures. However, this was not feasible within the schedule. Instead, the initial freezing with liquid nitrogen was sequenced, taking into account the critical water flow speed required to close the space between freeze pipes using liquid nitrogen, which is around 20 m/day (65 ftpd) (Andersland, 2003).
To avoid the bottleneck effect in the Ducy limestone that would appear if the sands and marls were frozen first, the ground freezing was sequenced in three steps (Fig. 8). The Ducy limestone was frozen first (Fig. 8-a), thus redirecting water circulation above and below the frozen ground wall. The closure of the flow in the Ducy limestone was verified through regular temperature monitoring and by using drains located at the center of the frozen shell. The rest of the U-shaped shell was then frozen with liquid nitrogen (Fig. 8-b).
Finally, the central inverted vault was frozen with liquid nitrogen initially, and with brine for maintenance (Fig. 8-c). The goal was to strengthen the upper Beauchamp sands — a geotechnical unit without any cohesion — and to close off the shell, creating a watertight “box” for the excavation of galleries 1 to 3. However, the freezing of this horizontal line generated significant heave of the RERC station, and was abandoned prior to excavation works.
Thermal erosion test. Two drain lines were placed on either side of the gap between the upper freeze pipes and the bottom slab of RERC, to capture water seepage before it entered the tunnel. These drains were also used to reduce the volume of water that would flow over the U-shaped shell.
One concern was the risk of thermal erosion due to water flow from the top of the U shape, which could have caused a reopening of the Ducy limestone fractures. This, in turn, would have increased flow speed in the Ducy limestone because of the dam effect created by the frozen U shape, further hindering closing the fractures. Given the risks involved, an erosion test was conducted after the switch to temperature maintenance using brine.
The erosion test consisted of discharging the drains located inside the “U,” thus artificially causing water flow over the arms of the “U.” Temperatures in the frozen body were monitored for three weeks. No increase was observed, even at higher brine temperatures (up to T brine = -28 °C tested). This demonstrated the robustness of the frozen body against external water flow (and thermal erosion).
A full tank of liquid nitrogen was nonetheless kept on site to switch back to liquid nitrogen cooling if necessary.
Temperature monitoring and frozen wall thickness evaluation. Chains of thermocouples were installed in dedicated boreholes (Fig. 4). The longitudinal spacing between each individual thermocouple was set at 2 m (6.5 ft).
To ensure that the mechanical criteria were verified for the duration of the tunneling work, the position of the -10 °C isotherm had to be extrapolated from the temperature measured at each sensor point.
The hypothesis on temperature distribution was logarithmic, following Sanger and Sayles’s equation (Sanger 1979). The temperature distribution was calculated with:
with r the running coordinate, R the distance between the sensor and the freeze pipe surface, r0 the freeze pipe radius (external), T0 the temperature of the sensor (e.g. -10 °C), Tf.tube the freeze pipe temperature (e.g., brine temperature).
Once all the freeze pipes and temperature sensor pipes were drilled, their 3D position was measured and entered in a 3D CAD model. The analysis of this 3D CAD model had the following objectives:
- To measure the real distance R between each sensor and the closest freeze pipe, deviations are included. This is a sensitive input to the Sanger and Sayles formula (R).
- To verify the spacing between each pipe maximum deviations of 40 cm (15.7 in.) were recorded. This implied a longer initial freezing time for the sections of the shell with wider spacing. Additional freeze pipes were installed to correct wider spacing and selected boreholes from the ventilation shaft were prolonged to compensate for significant deviations of drillings originating from the station.
An automated alert system was installed in order to ensure safety in the thickness of the frozen wall during the duration of artificial ground freezing. The temperature was recorded every 15 minutes and uploaded onto a web application for data gathering and plotting. Threshold temperatures were defined and notifications were automatically sent when the threshold temperatures were reached.
The temperature/thickness criteria were defined considering the overlap of two circular isotherms as the thickness of the frozen wall (Fig. 10). Because this approach does not take into account the relative influence of the freeze pipes, which tend to smoothen the overlap, the specified criteria were conservative:
- Design criteria: thickness 0.8 m (2.6 ft) in diameter at -10 °C.
- Alert threshold: Isotherm -2 ° C at 0.75 m (2.4 ft) from the cold source = overlap of 0.4 m (1.3 ft).
- Alarm threshold: Isotherm -2 °C at 0.65 m (2.1 ft) from the cold source = overlap of 0.2 m (0.65 ft).
The goal of the alert and alarm thresholds was to safeguard the continuity of the ice wall over the full duration of the project in order to ensure water tightness. The geometric thresholds were transformed into temperature thresholds, using the Sanger and Sayles formula for each sensor, depending on the distance between each sensor and the closest freeze pipe.
These thresholds were used to drive the active freezing phase. Temporary thresholds, defined using a lower Tf.tube temperature of -80 °C (i.e., the exhaust temperature of nitrogen) were used during the liquid nitrogen sequences. The switch to brine took place after all temperature measurements passed under the liquid nitrogen threshold, thus reducing frost heave and nitrogen consumption at the same time.
Uplift due to frost heave. Freezing-related frost heave in soil is the result of two different processes, which are associated with the ground’s hydraulic conductivity and texture. In very permeable grounds, frost heave is unlikely to occur since water dilation during the phase change from water to ice pushes away liquid water toward the unfrozen parts, thus absorbing the dilation.
The freezing front advance speed depends on the freezing temperature. There is a critical ground hydraulic conductivity threshold at which the water does not have time to escape the freezing front before being frozen. For ground with hydraulic conductivity lower than this critical value, frost heave is possible and is a function of the initial water content being frozen (thus dilated) minus the part of the water that can migrate toward the unfrozen parts. This occurs in fine sands, such as clayey Beauchamp sands.
In silts, another process takes greater importance: cryogenic suction. At the freezing fringe, free water freezes at 0 °C (in the absence of solutes), but adsorbed water freezes at lower temperatures due to the intermolecular forces between the grains and the water (Khakimov, 1957). This effect also exists in coarser soils such as sands, but the consequences are negligible due to the lower specific surface area. In silts, the specific surface area is large, and the adsorbed water content is not negligible compared with the free water. The presence of liquid water at temperatures below fusion temperature implies a contraction of water, which leads to a pressure decrease known as suction. To cancel this suction effect, liquid water is drawn toward the freezing fringe until the pressure is high enough for the phase change to occur. This process leads to a constant increase in water content.
During the initial freezing of the “U” with liquid nitrogen, a degree of displacement of the pile standing on barrette B11 was measured. This was the result either of frost heave under the tip of B11, or of an upward friction force due to frost heave along the barrette. In any case, the frost heave occurred because the water could not escape from the less permeable Beauchamp sands as a consequence of the fast advance of the freezing front during initial freezing with liquid nitrogen (-196 °C to -80 °C). When the coolant was switched to brine at a higher temperature (-35 °C to -28 °C), the frost heave stopped.
The upward force created by frost heave and transmitted by the barrette caused an uplift of the central part of the RERC and also had the secondary effect of unloading the ground located under the RERC base slab.
The uplift continued during initial freezing of the horizontal line, which acted as a forepoling umbrella, but the heave did not stop when switching the refrigerant to brine. In this case the frost heave process was continuous, probably influenced by the silt content in the Saint-Ouen limestone and the continuous water inflow under RERC.
Several adjustments were tested without any noteworthy effects on the uplift: a full opening of the lateral drains to reduce water inflows, an increase of the brine temperature, and stopping brine flow in the umbrella freeze pipes. The only solution was to abandon the frozen umbrella and actively melt it. When forepoling was necessary, it was implemented using flat sheet piles.
The major steps of the freezing project are presented in Fig. 11.
Maintenance with liquid nitrogen. In September 2018, the caution threshold was reached on a sensor located near the diaphragm wall of the ventilation shaft. This occurred as the lower lateral section was being concreted. The increase in temperature was associated with several factors:
- The proximity to the shaft and ventilation air-fluxes.
- The recent concreting of the tunnel abutment. During the 48 hours following shotcrete placement, heat emission from concrete hydration increased the temperatures up to 7 °C in the thermocouple probes located 50 cm from the excavation line.
- A warmer initial ground temperature in this particular area, probably due to water circulation under the RERC station. This last factor had been identified at the start of the project.
The corrective measures triggered by reaching the threshold were to decrease brine temperature and fully open the drains. But they were not sufficient to stop the warmup and to refreeze the frozen wall. The decision was made to switch to liquid nitrogen maintenance.
Liquid nitrogen maintenance was reintroduced using intermittent injections (for four to eight hours per night, depending on energy needs). A specific threshold was put in place to ensure the mechanical criteria were always verified and triggered an injection of liquid nitrogen N2. After a period of adjustment and calibration with the dynamic temperature response of the ground, the injections were performed during the night to limit interactions with the civil works.
After a few weeks of intermittent liquid nitrogen injections, another upward shift in the RERC was measured. Pile P8, located on top of barrette B3, started to lift because of a difference in heat flux at the proximity of the shafts and along the axis of the RERC. As stated above, the external heat flux (air convection) increased as it approached the diaphragm walls. Given that the freeze pipes were coaxial with an input flux from the center pipe and a return (and heat exchange with the ground) in the annulus space, the coldest part of the freeze pipe was its tip. In order to verify the mechanical temperature criteria at every point of the frozen shell, the intermittent injections of liquid nitrogen were triggered based on the temperature sensors closest to the diaphragm wall (warmer part). The cold removal along the freeze pipe created a much larger wall thickness along the axis of the RERC, whereas the wall thickness barely met the mechanical criteria close to the diaphragm walls.
By December 2018, the frozen wall had expanded just under the RERC base slab causing the uplift. The problem was solved by cutting the central pipe of the freeze pipe to half its initial length. This reduced heat removal at the tip of the freeze pipes and increased it closer to the diaphragm wall. This effectively stopped the frost heave (Fig. 12).
Active thawing and settlement control. Given the underpinning of barrette B11 to the L14 tunnel, some adjustments were needed to limit differential ground settlements between B11 (fixed point, attached to L14N), B3 (lateral friction deactivated at the height of the tunnel) and B12 (lateral friction deactivated on one side of the barrette at the height of the tunnel).
With artificial freezing, some extra-lateral support was provided to B3 and B11 due to increased frozen soil properties. Three sources of settlement are considered in thawed soil:
- Decreased soil properties during thawing.
- Redistribution of bearing capacity between lateral friction and tip resistance due to the structural modifications of B3 and B12.
- Heave/thaw settelments.
In order to avoid differential settlements, the top slab of the L14 tunnel was mounted on jacks, with the possibility to move the slab up or down to follow the movements of B3 and B12. This implied that the adjustment gap could not be concreted over until settlement was stabilized and the jacks were no longer needed.
When the ground was frozen, at the level of the adjustment gap, the ground water was retained by the frozen ground, the temporary support and the waterproofing membrane. During thawing and when support was necessary, a drainage system was put in place to prevent water from damaging the waterproofing membrane, involving the management of exhaust water at a very late stage of the works, such as electrified rail installation.
In order to accelerate soil settlement after the civil works were completed, the ground was actively thawed using warm brine (+30 °C to +55 °C) circulating through the brine distribution network, which created holes in the frozen shell. The thawing process was associated with a loss in ground resistance, especially after heaving had occurred. Some localized increases in water content pockets may have remained after heaving and needed to dissipate for the ground to regain resistance properties close to its initial state.
The presence of the barrettes was beneficial, as they helped transmit the vibrations of the trains into the ground, which participated in the reorganization of the grains. However, grain reorganization can occur only if the melted water is connected with the free ground water (e.g., melted water is not locked into a frozen ground pocket). This configuration would have delayed grain reorganization, and thus ground settlement, until after the whole ground was melted. This was avoided by sequencing active thawing from the top of the “U” to its base; creating a water evacuation “chimney” along the axis of the pipes (Fig. 13).
A new temperature distribution model was developed for monitoring purposes. Numerical modeling showed that the freezing front at the end of active freezing was hardly affected by active thawing. Indeed, in order to thaw, the frozen ground needs to collect energy, mainly the latent heat of fusion. As this energy is provided by the center of the frozen body, a melting front develops inside the frozen body, using all the energy provided by the active warming for latent heat. In contrast, the outer melting front can gain energy only from the surrounding ground (natural thawing).
Numerical modeling also showed that the temperature distribution in the thawed ground could be considered linear from the imposed freeze pipe temperature to the 0 °C isotherm. This enabled monitoring of the thawing process using the temperature sensors.
Some drains were equipped with manometers that followed the piezometric head under the tunnel until it reached a value compatible with the external water level. Total melting was achieved in three months with brine temperatures of up to +50 °C. The temperature in the ground at the end of melting was stabilized around +35 °C to ensure no ice pockets remained.
Artificial ground freezing was necessary to realize the Line 14 tunnel under the train station base slab. The open shape of the frozen ground led to two concurrent constraints. On the one hand, the train station uplift was mitigated by warmer brine temperature. On the other hand, colder brine temperatures were necessary to respect the mechanical criterion and ensure safety in a complex geotechnical and hydraulic context. Because of significant water flows above the frozen body, liquid nitrogen was locally used to maintain the frozen body thickness during the second part of excavation works. The 16-month period of construction work finally ended with artificial thaw during two months.
Andersland, O.B. et al. 2003. Frozen Ground Engineering (2nd ed.). Reston: ASCE.
ISGF Working Group 1. 1991. Testing methods for frozen soils. Beijing, 2, 493-502.
Khakimov, Kh.R. 1957. Artificial Freezing of Soils Theory and Practice. Moscow: Academy of Science of the USSR.
Sanger, F.J. & Sayles, F.H. 1979. Thermal and rheological computations for artificially frozen ground construction. Engineering Geology, 13: 311-337.