Mechanism And Mathematical Model Of Frost Heave In Unsaturated Coarse-grained Soil Subgrade Of High-Speed Railway In Cold Regions

Infrastructure construction in cold regions is the hot topic in engineering construction in China.However,the frost heave occurred in the subgrade of the high-speed railway with the coarse-grained fills affects the performance of high-speed railway and scientifically challenges the traditional theories for frost heave.The existing frost heave theories are for the frost heave in fine-grained soils induced by the liquid water transfer.The coarse-grained soils are generally considered as frost non-susceptible soils.Hence,the traditional frost heave theories are difficult to explain the frost heave occurred in the subgrade of high-speed railway with the coarsegrained fills.The hypothesis that the frost heave in coarse-grained soils is caused by vapour transfer has been attracted much attention,but little experimental or numerical evidence has been reported thus far.A series of frost heave tests was carried out to reveal the frost heave mechanism of coarse-grained soils by the one-dimensional frost heave apparatus and the X-ray microCT device.A frost heave model was presented considering the vapour transfer.The program PCHeave was updated to realize the numerical simulation for the frost heave in unsaturated coarse-grained soils.Finally,the freezing process of subgrade of high-speed railway was simulated using PCHeave.A comparative analysis of the amount of frost heave with and without considering vapour transfer revealed that the vapour flux accounted for approximately 60% of the recharge volume inducing frost heave.The main conclusions were drawn as follows:(1)A series of laboratory tests were carried out using the self-developed frost heave apparatus.The results show that considerable frost heave occurs in coarse-grained soils with zero fine content while the specimen is subjected to only vapour supply.The observed frost heave in the 6 cm-high coarse-grained soils with a particle size of 2.0-5.0 mm reached 5.56 mm and 8.30 mm after the specimens were frozen for 168 h and 336 h,respectively.It revealed that vapour transfer is the main mechanism of frost heave in unsaturated coarse-grained soils.These tests reveal that frost heave increases at first and then decreases with increasing initial water content in coarse-grained soils.Increasing the temperature gradient can facilitate vapour flow in soil.A ramped freezing mode facilitates a notably higher external water inflow than that under a one-step freezing mode and leads to a greater frost heave amount.Uniform and large soil pores facilitate vapour transfer and the formation of thicker ice lens in the coarse-grained soils,which results in a greater value of frost heave.(2)The characteristics of ice lens were observed by the X-ray Micro-CT tests,and the ice content was calculated in layers by the digital image technology.Under the constant temperature gradient,only one horizontal freezing zone containing segregated ice and saturated pore ice rather than layered ice lens in the frozen soil was observed.The highest volumetric ice content was more than 60% near the freezing front,which shows that a segregated ice forms.Under a stepwise decrease in temperature,ice lenses distributed in layers are formed in the frozen soil.The largest volumetric ice contents at each freezing zone were more than 60%.The distribution of ice lens in frozen coarsegrained soils are different from those in frozen fine-grained soils.(3)Based on the existing of frozen fringe,a mathematical expression for the neutral stress was given,and a neutral stress criterion for the initiation of ice lens was established: when the neutral stress within the frozen fringe is equal to the overburden pressure,a new ice lens initiates.The energy balance equations and mass balance equations were given,which considering the full phase change of vapour-waterice.The equations for the hydraulic gradient and vapour diffusion coefficient were determined.Finally,a frost heave model for unsaturated soil considering the vapour transfer was presented.The frost heave model is promising for engineering applications because it just needs a few simple parameters with obvious physical meaning to predict the frost heave and the frozen depth.(4)The PCHeave program was updated based on the presented frost heave model,which can calculate the frost heave and the frozen depth and simulate the growth of ice lens in one-dimensional multi-layered soils.The predicted results of frost heave and frost depth show good agreement with the measured values of laboratory experiments.The proposed model can reasonably reflect the process of frost heave in coarse-grained soils.The effects of overburden pressure,temperature boundary,particle size distribution and unfrozen water content on the frost heave of unsaturated coarse-grained soils induced by vapour transfer were also analysed by PCHeave.(5)The frost heave deformation of embankment was monitored on site during the operation period.The frost heave was both about 8 mm in2019-2020 at the Haerbin-Mudanjiang Railway K225 and MudanjiangSuifenhe Railway K401,which mainly occurring within the 1.5 m depth of the subgrade.The frost heave mechanism of subgrade of highspeed railway was analysed by the presented model.It was found that vapour flux accounted for approximately 60% of the total external intake water.Vapour flow is the leading cause of the frost heave in subgrade of high-speed railway with the coarse-grained fills.The results of this study theoretically supplement the traditional theories of frost heave,which can provide theoretical support and scientific guidance for the construction of high-speed railway in cold regions.