Fig. 2. Ice column growth under no groundwater flow (u=0m/s) in the GWS (granite weathered soil). (a) Temperature distribution during freezing using brine (Tpipe = -30℃, freeze-pipe spacing S=1m), (b) Ice saturation around freeze-pipes
Fig. 3. Ice wall closure time tclose,u=0 with adjacent pipes arranged in a row in the absence of groundwater flow (u=0m/s) (blue circle = numerical study; red-dot line = Eq. (6) (Sanger and Sayles, 1979); black-solid line: modified S&S equation (Eq. (7))
Fig 4. Ice column growth under groundwater velocity u=0.17m/s (top→bottom). (a) Temperature distribution over time during freezing using brine (Tpipe = -30℃, freeze-pipe spacing S=1m), (b) Ice saturation around freeze-pipes
Fig. 5. Ice column growth under groundwater velocity u=0.35m/s (top→bottom). (a) Temperature distribution over time during freezing using brine (Tpipe = -30℃, freeze-pipe spacing S=1m), (b) Ice saturation around freeze-pipes
Fig. 6. Ice column growth under groundwater velocity u=0.37m/s (top→bottom). (a) Temperature distribution over time during freezing using brine (Tpipe = -30℃, freeze-pipe spacing S=1m), (b) Ice saturation around freeze-pipes
Fig. 8. Comparison of critical groundwater velocity for ice wall integrity: blue circle = numerical study; red-dot line = Sanger and Sayles (1979); black-solid line = modified S&S equation (Eq. 9) (dpipe=10cm)
Fig. 9. Comparison of ice-wall closure time between Eq. (10) and numerical results
Fig. 10. Non-uniform ice column in the heterogeneous soil with groundwater flow (Andersland and Ladanyi, 2004)
Fig. 11. Evolution of Ice column growth (blue, boundary of T=0℃) and temperature distribution (red plane) with no groundwater flow (i=0)
Fig. 12. Evolution of Ice column growth (blue, boundary of T=0℃) and temperature distribution (red plane) under groundwater hydraulic gradient i=0.045 (thickness of yellow line represents relative groundwater velocity)
Fig. 13. Comparison of ice-wall closure time between single homogenous systems (“Sand”, “WGS”) and WGS-Sand-WGS layered system (“Layer”)
Fig. 1. (a) Temperature field around the tunnels from AGF with groundwater flow (Pimentel et al., 2012), (b) Effect of more permeable layer around the frozen body under groundwater flow (Sres, 2009)
Fig. 7. (a) Effect of groundwater velocity (u) and freeze-pipe spacing (S) rate on ice wall formation time (dpipe=10cm). (b) Relationship between groundwater flow (u) and freeze-pipe diameter (dpipe) for ice wall formation time (S=1.0m)
Table 1. Soil properties for numerical analysis
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