PREDICTION OF FROST HEAVE INDUCED DEFORMATION OF DYKE KA-7 IN NORTHERN QUEBEC

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1 PREDICTION OF FROST HEAVE INDUCED DEFORMATION OF DYKE KA-7 IN NORTHERN QUEBEC J.-M. Konrad 1, M. Shen 1, R. Ladet 2 1. Dept. of Civil Engineering UniversitŽ Laval,QuŽbec, Canada, G1K 7P4 2. Hydro-QuŽbec, division Maintenance et sžcuritž des barrages, MontrŽal, QuŽbec, Canada Abstract KA-7 was built between 1978 and 1981 with first filling of the reservoir occuring in June The operating level of the reservoir was reached in September The effects of permafrost were noticed several years later, especially through significant deformations of the downstream face. The deformations were suggestive of solifluction lobes caused by cyclic frost heave and thaw settlement of the downstream shell consisting of compacted till. The paper focuses on the prediction of frost heave caused by the formation of ice lenses in the compacted till over several years of freezing and thawing leading to a progessive formation of permafrost, which, in turn, creates cumulative deformations. A model based on the segregation potential was used for one dimensional heat and mass transfer in association with temperature boundary conditions inferred from field data. The model showed that frost heaving of about 10 to 24 cm developed over 10 years using segregation potential values inferred from laboratory frost heave tests. Introduction Hydro-QuŽbec operates about 300 water retaining earth-structrures. Some of these structures are located in a northern environment, close to the 55th parallel where the annual mean temperature is -5 C. Such severe climatic conditions cause permafrost to develop within the earth-structures. This paper presents the results of frost heave predictions over several years of freezing and thawing at dyke KA-7, a homogeneous till embankment in which permafrost conditions were found in the downstream zones and in the toe drain. KA-7 is one of the 47 dykes of the Caniapiscau reservoir, which is in the most northerly region of the hydroelectric complex of James Bay (Figure 1). KA-7 was built between 1978 and 1981with first filling of the reservoir occuring in June The operating level of the reservoir was reached in September The effects of permafrost were noticed several years later, especially through significant deformations of the downstream face. The paper focusses on the prediction of frost heave caused by the formation of ice lenses in the compacted till over several years of freezing and thawing cycles. FROST-1D, a model based on the segregation potential is described and used for one dimensional heat and mass transfer for various scenarios of climatic history over a period of ten years. Description of KA-7 Dyke KA-7 is a homogeneous earth fill composed mainly of compacted till, 23 m high and 803 m long. The thickness of the till foundation varies between 6 m to 25 m from the right-hand to the left-hand abutment. Figure 2 depicts a cross-section of KA-7 and shows the internal drainage consisting of an inclined chimney drain connected to a horizontal downstream drain. Zone 1 (till) has an average fines content of about 21% and displays water contents varying between 5 and 12.5%. Placement dry unit weight was on average 21 kn/m 3. Zone 2B (filter) was a natural sand and gravel screened between 0-76 mm and mixed with crushed stone. Zone 2D (horizontal drain) consisted of crushed stone, 100 mm maximum. Zone 4A (rockfill for upstream protection) was erected with blocks between 68 and 1800 kg while the downstream protection consisted of crushed rock mm. The maximum reservoir level is m and the crest elevation is m. The upstream and downstream slopes are 2.5H:1V and 2.25H:1V, respectively. Observations TEMPERATURE EVOLUTION IN THE CREST Observations of temperature distribution beneath the crest from 1982 untill 1992 revealed the presence of permafrost at elevations and m in 1985, i.e. after J.-M. Konrad, M. Shen, R. Ladet 595

2 Figure 1: Location of Dyke KA-7. the third freeze-thaw cycle. The permafrost zone gradually aggraded until 1989 where it became stable and extended from elevations to m. The average temperature of this permafrost zone was -0.2 C, i.e. fairly warm permafrost. DEFORMATION OF DOWNSTREAM SLOPE Various phenomena related to frost action in the earth fill were observed from 1987 onwards, i.e., about 5 years after the end of construction. Longitudinal fissures near the right-hand abutment were detected in the crest between CH.8+76 and These fissures were 4 to 60 m long and 5 to 10 cm wide. Also, deformations of the downstream slope were first noticed in June 1989 between CH and at elevation m and in August 1992, deformations on the downstream face were recorded at elevations , , and m, respectively. The deformations were suggestive of solifluction lobes. It was difficult to estimate the magnitude of these movements because of the presence of large rock blocks on the downstream slope which masked the actual deformation of the underlying till embankment. However, since it was possible to notice large solifluction lobes despite these blocs, it was anticipated that the movements of the underlying till were significant (estimated to be about 30 cm) and warranted further study. Description of frost model FROST'1D is a PC-based user-friendly code which uses the finite element method to simulate frost heave and thermal regime in layered material systems and considers phase change and mass transfer using the segregation potential concept. FROST1D is also able to simulate complex construction procedures such as stage excavations and fill construction in individual lifts (Shen and Konrad, 1996). The model requires two equations for expressing the interrelationship between heat and mass transfer in 596 The 7th International Permafrost Conference

3 Figure 2: Cross section of KA-7. soils. For the case in which the convection in the soil is neglected, the heat transfer equation may be written as C T * T Q t = æ ö çl + xè x ø where C* denotes the enthalpy per unit volume (J/ Cm 3 ); l is the temperature dependent thermal conductivity (W/m C); T is the soil temperature ( C); x is the depth (m); Q is the internal heat source (W/m 3 ). The latent heat of phase change in soils is released at a discrete temperature (OÕNeill, 1983), Tf, without any artificial spreading of phase front, i.e: sd( f ) C * = C+ L T -T where L s denotes the latent heat of fusion per unit volume of soil (J/m 3 ); C is the volumetric heat capacity depending on temperature (J/ Cm 3 ), and d is the Dirac delta function. For mass transfer, only the liquid water flow driven by a pressure gradient in the unfrozen water phase is considered in the FROST'1D. The rate of mass transfer is approximated using the segregation potential at near thermal steady state, SP t, defined as the ratio of frost heave rate to the overall temperature gradient in the frozen fringe: [1] [2] dh SPt = æ ö è dt ø æ dt ö è dx ø f The advantage of using SP t to characterize the freezing soil is that it is not necessary to make any assumptions on hydraulic conductivity, temperature and suction within the frozen fringe since SP t is simply the ratio of two directly measurable quantities. Conditions simulated The problem of solifluction lobe development is in fact a 3-dimensional problem. Using a one-dimensional prediction model cannot yield accurately the magnitude of the slope displacements. However, it may give a qualitative assessment of the severity of the deformations in the slope by enabling the visualization of the evolution of the thermal conditions with each freezethaw cycle and the magnitude of accumulated heave with time for a horizontal surface. The case of an inclined surface with identical soil properties will include a downslope movement associated with gravity resulting in soil accumulation which has a height larger than the accumulated heave predicted for the case of a horizontal surface. The soil conditions at the downstream face of KA-7 consisted of 0.9 m of rockfill over 9.0 m of till placed on a 2.0 m thick sand layer underlain by a 4.0 m thick lodgement till on top of the bedrock with the physical parameters for each zone indicated in Table 1. Laboratory frost heave tests indicated that the till from [3] J.-M. Konrad, M. Shen, R. Ladet 597

4 Figure 3: Results of simulation with FROST1D for case (a). Figure 6: Results of simulation with FROST1D for case (d). Figure 4: Results of simulation with FROST1D for case (b). Figure 7: Results of simulation with FROST1D for case (e). the James Bay area was frost-susceptible at low overburden pressure (Konrad and Morgenstern, 1983). In the simulations, the following relationships was used: - Pe SP = 112e 17 mm 2 / o C d t pressure in Mpa. with Pe= overburden At Caniapiscau, the average air freezing index is about 3500 C d while the thaw index is about 1300 C d. Several cases were studied in order to investigate the influence of climatic history: Figure 5: Results of simulation with FROST1D for case (c). a) 10 years of freeze-thaw with average conditions; b) 3 average winters, 2 cold winters, 5 average winters; c) 3 average winters, 2 cold winters, 3 average winters, 2 cold winters; d) 4 average winters, 1 very cold winter, 5 average winters; 598 The 7th International Permafrost Conference

5 Table 1. Soil properties Table 2. Summary of frost heave after 10 freeze-thaw cycles Conclusion At Caniapiscau where the average freezing index is 3500 C.d, permafrost conditions within a homogeneous earth-structure were noticed after several years of operation. A simple one-dimensional frost heave model using the segregation potential as input to the coupled heat and mass transfert mechanisms has shown that surface frost heave for horizontal layers was of the order of 10 to 24 cm depending on climate history over a ten year period. The largest frost heave values were obtained by including two very cold winters during this 10 year period. Acknowledgments e) 4 average winters, 1 very cold winter, 2 average winters, 1 very cold winter, 2 average winters; The authors would like to thank Hydro-QuŽbec and particularly the managerial office of Secteur Caniapiscau for the permission to publish this paper. Results of simulations The results of the simulation of case (a) are presented in Figure 3. The light coloured zone shows the permafrost condition existing at the end of summer in each of these years. It took three freeze-thaw cycles to establish a thin permafrost zone which increases with subsequent cycles. The upper part of Figure 3 shows also the evolution of surface heave according to the corresponding ground surface temperature input also shown on the same graph. The results for cases (b) to (e) are presented on Figures 4 to 7 using the same format which incidentally is the output format given by FROST-1D. Table 2 summarizes the value of permanent surface heave after 10 freezethaw cycles for each case. It appears from these simulations that surface heave is very sensitive to the occurrence of very cold winters. Close examination of permafrost conditions for each case reveals that frost heave accumulates as the lowest frost front progresses progressively into unfrozen soil with each freezing cycle. On the other hand, stable permafrost tables such as in cases (a), (b) and (d) yield fairly stable frost heave values. References Konrad, J.-M. and Morgenstern N.R. (1983). Frost-susceptibility of soils in terms of their segregation potential. Proceedings 4 th International Conference on Permafrost. pp OÕNeill, K. (1983). Fixed mesh finite element solution for cartesian two-dimensional phase change. Journal of Energy Resources Technology, ASME, 105, Shen, M. and Konrad, J.-M. (1996). Dam construction in northern environment: A numerical study. 8th International Specialty Conference on Cold Regions Engineering, ASCE. pp J.-M. Konrad, M. Shen, R. Ladet 599