Ninth International Conference on Permafrost ... - IARC Research

A Hypothesis: A Condition of Growth of Thick Ice WedgesAnatoli BrouchkovTyumen State Oil and Gas UniversitySo-called Ice Complex or “edoma” in Siberia, whichrepresents extremely ice-rich and perennially-frozensediments with thick polygonal ice wedges, is formed interritories acting as terrestrial accumulation basins duringthe Pleistocene. It sometimes consists of more than 90% iceby volume. Simplifying, a decrease of temperature causessoil to shrink and cracks to form; then water seeps into thecracks in spring. It freezes and expands when it is chilledby permafrost. This cycle continues to enlarge the wedgesyear by year until the soil above the wedges is pushed upand finally almost disappears around. However, details ofthe mechanism of thermal contraction cracking and icewedge formation still remain unclear (French 1996). Ice isknown to be able to flow under loads, and it probably couldbe easier for ice to be pressed up than for soil. Why do weobserve the result of soil pushing up only, not ice, and whatis the mechanical condition of the process?Water freezing and expanding when it is chilled bypermafrost can be expressed by the Clapeyron equation.Stresses can be estimated approximately as 13.4 MPa pera decrease in negative temperature by 1°C. In the case ofmechanical equilibrium, if horizontal stresses σ zare equalin soil and ice, the heaving strain of about 9% of volumeof freezing water ε fis connected to mechanical compressionof frozen soil (dσ z*l fr/Е fr) and ice (dσ z*l ice/Е ice), being of l frand l icein size and having the strain modulus Е frand Е ice,respectively:dεf(1)dσz=lfr lice+E EfriceIf, for example, ε fis 0.0045 m as a result of freezing of0.05 m of water, l fr= 5 m and l ice= 0.5 m, and the long-tempcompression modulus Е fr= 20 MPa and Е ice= 50 MPa, thenstress σ z= 0.017 MPa. In many cases, the value of ε fis evenless then 0.05 m; for example 0.001–0.003 m only in Barrow(Black 1951), and 0.002–0.01 m in Kolyma plain (Berman1965). Due to higher modulus values, compression of soilreaches 4.33 and ice 0.17 mm consequently. The size of thedeformed soil area varies, for example, near Fairbanks in therange of 0.3–3 m (Pewe 1962). The lateral strains dependingon Poisson’s ratio will be less than compression, but probablythey will be more for soil than for ice. Stresses are small andperhaps unable to make considerable structural changes ofsoil mass. Repeating a thousand times, it results in ice wedgethickness of about 4 m. This is generally in agreement withthe point that soil is pushed up during ice wedge formation.However, it was found that soil layers at a certain distancefrom the ice wedge are almost not affected (Popov 1965).An area of high density of deformed soil should be createdon contact with an ice wedge to give space to ice, and thatarea should be gradually increased in size in accordance withan increase of wedge thickness. One reason for the deformedarea to remain small is the stress distribution in soil mass.The stresses are basically not equal and become smallerwith distance from an ice wedge. Using q/unit length on thesurface of a semi infinite soil mass, or if the excess stressis according to the Boussinesq equation (Ahlvin & Smoots1988), the stress can be found approximately:σ∆ σ ~ I(2)zz n zwhere n changes from about 1 to 2, I = influence factor forthe load, and z = distance from the ice wedge. Formula (1)should be adjusted then according (2). If horizontal stress σ z= 0.017 MPa near an ice wedge, it is about σ z= 0.004 MPaonly on distance of 2 m. Thus, stresses might be too smallto cause deformations far from the ice wedge, but they arebig enough to move soil particles and pore ice near the icewedge. Another reason for the deformed area to be small isperhaps because of gradual movement of attached ice soiltowards the surface together with ice caused by pressure andbuoyancy.Signs of diapirism and soil circulation are widespread inperiglacial areas (Hallet & Waddington 1991). Buoyancy canbe an effective driving force in the case of ice wedges dueto different densities of frozen soil (1.5–1.7 and more cm 3 /g)and ice (0.9–1 cm 3 /g). If the size of polygons are more thanor equal to the height of an ice wedge h, and the viscosity ofice η iis much less than the viscosity of the surrounding soilη s, the rate of vertical movement of an ice wedge wall υ willbe (Artyushkov 1969):2ρ ghυ ~ ∆ (3)ηswhere ∆ρ = difference of densities of soil and ice; g = gravityacceleration, 9.81 m/sec; η s= viscosity of surrounding soil,Pa*s. However, the assumption that the viscosity of ice isless than the viscosity of the surrounding soil is far frombeing acceptable: relationship is opposite. The ice viscositycan be assumed as 10 12 –10 13 Pa*s, and frozen soil viscosityas 10 10 –10 11 Pa*s. The buoyancy of an ice wedge and itsvertical movement z can still be found from the similarNavier-Stoks equation:2∆ρglv ~~ tz18η s(4)where t = time; l = width of ice wedge. If the width of the icewedge l = 1 m, and time t is 1000 years, then resurfacing ofice can reach about 1.5 m. That value of vertical movementmay change the shape of ice wedges drastically, especially insaline or high-temperature permafrost. Vertical orientation of33