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Numerical study on thermal regimes beneath canal in permafrost zones with different geological conditions
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摘要: 多年冻土区水利工程的建设和运营会对下伏多年冻土产生显著热影响，且不同冻土条件下影响程度明显不同。以高海拔多年冻土区某渠道工程为背景，在考虑冻融土体内水分迁移、冰水相变及土体未冻水含量与温度非线性关系基础上，构建了冻融土体水-热耦合数学模型。利用该模型，开展了气候变暖背景下，渠道多年冻土地基热状况长期演化规律模拟预测，并考虑多年冻土年平均地温（TMAGT）和体积含冰量（iv）的影响。结果表明，当多年冻土含冰量为少冰（iv≤10%）时，渠道垂向和横向热侵蚀显著，运营50年后渠道下部和岸坡下30 m范围已无多年冻土。当T MAGT为−0.5 ℃时，自岸坡向外约10 m范围内下部多年冻土已退化，而当T MAGT为−1.0和−1.5 ℃时，岸坡下部仍有多年冻土分布。随着含冰量的增加，多年冻土热惰性显著增加。当多年冻土含冰量由少冰（iv≤10%）增加至多冰（10%<iv≤20%）、富冰（20%<iv≤30%）时，即使在T MAGT为−0.5 ℃时，运营50年后渠道下部仍有多年冻土存在，但是自渠道中心形成了一个“锅底状”的融化盘。在过水和气候变暖因素作用下，渠底和坡脚多年冻土表现为自上而下的退化模式，而岸坡和天然场地多年冻土退化表现为活动层的缓慢下移和上限附近多年冻土的缓慢升温。Abstract: In permafrost regions, construction and operation of hydraulic projects will exert considerable thermal impact on underlying permafrost, and its degree will be different at locations with different permafrost geological conditions. Taking a canal in a high altitude permafrost zone as an example, a water-thermal coupled mathematical model for freeze-thaw soils was established in this study. The water migration, ice-water phase change and nonlinear relationship between unfrozen water content and temperature in freezing soils were considered in the model. Using this model, the long-term evolution of the thermal conditions of permafrost subgrade under the canal in the context of climate warming was numerically investigated, and the influences of the mean annual ground temperature (MAGT) and ice content (iv) of the permafrost subgrade were considered. The results show that when the permafrost is ice-poor (iv < 10%), both the vertical and lateral thermal erosions of the canal are significant. After 50 years of the excavation, there is no permafrost under the mid-bottom and bank slope of the canal. When the MAGT is −0.5 ℃, the permafrost under the canal has degraded within about 10 m from the bank slope outward. When the MAGTs are −1.0 or −1.5 ℃, there is still permafrost under the bank slope of the canal. With the increase in iv, the thermal inertia of permafrost increases significantly. When the iv increases from ice-poor to ice-rich (20% < iv ≤ 30%), there is still permafrost existing under the canal in 50th year after the excavation even when the MAGT is −0.5 ℃. However, a thawed layer shaped as a pot-bottom develops beneath the canal. Under the impacts of climate warming and water thermal erosion, the permafrost beneath the canal experiences significant downward degradation, or quick descend of the permafrost table. Only under the impacts of climate warming, the permafrost beneath the slope of canal and the natural ground surface experiences a slow descent of the permafrost table and slight warming of the top permafrost layer.
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Key words:
- canal /
- permafrost /
- ground temperature /
- ice content /
- numerical simulation
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图 2 开挖1年后天然场地不同深度地温实测与模拟对比
Figure 2. Field observed and numerical simulated temperature profiles at natural ground after the canal construction
图 3 不同年平均地温条件下渠道开挖后第50年10月15日地基温度场
Figure 3. Temperature fields of permafrost subgrades with different MAGTs on October 15, 50 years after the canal construction
图 4 不同含冰量下渠道开挖后第50年10月15日地基温度场
Figure 4. Temperature fields of permafrost subgrades with different ice contents on October 15 of the 50th year after the canal construction
图 5 渠道开挖后20年内渠道不同位置地温曲线
Figure 5. Temperature profiles at different locations within 20 years after the canal construction
表 1 土体热物理参数
Table 1. Physical-thermal parameters of soil layers
土体名称 λu/(W·m−1·℃−1) λf/(W·m−1·℃−1) Cu/(J·m−3·℃−1) Cf/(J·m−3·℃−1) a b 砂砾土 1.91 2.61 2.41×106 1.86×106 10.67 0.57 粉质黏土 1.13 1.58 2.88×106 2.23×106 6.9 0.47 强风化泥岩 1.47 1.82 2.09×106 1.84×106 9.3 0.52 土体名称 α/m−1 θr θs Ks/(m·s−1) ρ/(kg·m−3) Ls/(J·m−3) 砂砾土 3.28 0.01 0.44 2.4×10−7 1800 2.31×107 粉质黏土 2.60 0.02 0.35 3.3×10−8 1600 6.51×107 强风化泥岩 2.30 0.02 0.25 1.2×10−8 1700 3.77×107 
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表 2 不同含冰类型土的热物理参数
Table 2. Physical-thermal parameters of frozen soils with different ice contents
含冰类型 ρd/(kg·m−3) W/% λf/(W·m−1·℃−1) Cf/(J·m−3·℃−1) λu/(W·m−1·℃−1) Cu/(J·m−3·℃−1) 少冰冻土 1 660 20 1.38 2.21×106 1.24 2.68×106 多冰冻土 1 540 25 1.58 2.23×106 1.13 2.88×106 富冰冻土 1 280 35 1.67 2.20×106 1.09 2.99×106
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表 3 不同含冰类型土的视比热容
Table 3. Apparent specific heat of frozen soils with different ice contents
单位：J·kg−1·℃−1 含冰类型 −25~−10 ℃ −10~−5 ℃ −5~−3 ℃ −3~−2 ℃ −2~−1 ℃ −1~−0.5 ℃ −0.5~−0.2 ℃ −0.2~0 ℃ 0~25 ℃ 少冰冻土 1 108 1 666 2 620 6 849 6 872 12 472 38 505 1 338 1 344 多冰冻土 1 158 1 693 2 650 6 726 6 758 12 141 37 137 68 372 1 466 富冰冻土 1 275 1 771 2 742 6 550 6 596 11 598 34 750 187 588 1 730
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