Physical Modelling of Permafrost Warming in Rock Slopes

Physical modelling of permafrost warming in rock slopes

M.C.R. Davies & O. Hamza School of Engineering, University of Dundee, Dundee, Scotland, UK C. Harris School of Earth Sciences, Cardiff University, Cardiff, Wales, UK

ABSTRACT: An investigation into the influence on rock slope stability of warming permafrost has been conducted as part of the European PACE research programme into the effect of climate change on permafrost. This paper reports on the latest stage in this investigation. Failure mechanisms in jointed rock slopes containing ice- filled discontinuities were investigated in a series of geotechnical centrifuge model tests. As the temperature of the ice in the critical discontinuity increased, the shear strength of the joint reduced and some blocks forming the model slope became unstable. The results of the experiments help to identify mechanisms triggering failure of rock slopes in permafrost and are used to validate an analytical technique to assess the stability of rock slopes in these regions. The results of this study are also applicable for assessing the influence of anthropogenic activities on the stability of frozen rock slopes.

1 INTRODUCTION the shear strength of a simulated rock joint. In a series of laboratory direct shear box tests it was demonstrated As a result of measurement of permafrost temperatures that the shear strength of the ice-filled frozen joint is, in European Mountains – and other cold regions indeed, a function of both temperature and normal throughout the world – it is becoming clear that per- stress. However, when the results of the tests conducted mafrost is warming as a response to global climate on specimens with ice-filled joints were compared with change (Vonder Mühll et al. 1998, Vonder Mühll et al. control experiments in which the joint did not contain 2000). When assessing the stability of rock slopes ice, it was found that as the ice in the joint warms at cer- located in these cold regions in which the discontinu- tain temperatures and pressures, the ice-filled joint can ities contain ice it is generally assumed that this ice con- display less shear strength than an ice free joint. These tributes to maintaining stability (e.g. Bjerrum & Jørsbad results imply that, in slope stability assessment, if the 1968). Indeed, a reduction in rock slope stability with presence of ice in a joint is ignored (on the grounds that increase in ambient temperature has been attributed to ice will always add to shear strength and its absence rep- the loss of the stabilising influence of ice in joints when resents the most unstable conditions) then as ice in the it melts (e.g. Dramis et al. 1995). The phase change joint warms, conditions may arise where unexpected from ice to water has three potential effects. First, there failure could occur. The stability of such slopes may, is a loss of joint bonding, which is provided by ice/rock therefore, be more sensitive to changes in the thermal interlocking and “adhesion” of the ice to the rock. environment than previously envisaged. Second, the release of water may result in elevated water To test this hypothesis, Davies et al. (2001) used the pressures in the joint leading to a reduction in the effec- technique of geotechnical centrifuge modelling to tive pressure normal to the joint and, thus, a lowering of simulate the conditions of permafrost warming in its shear strength. Third, groundwater circulation may jointed rock slopes. Models of a slope with a simplified be re-established, further raising water pressures and geometry containing a single ice-filled discontinuity reducing shear strength. Although rock slope stability (i.e. a single potential sliding block) were constructed assessment techniques consider water pressures, they and permitted to warm during centrifuge operation. A do not take into account the effects of thermally induced range of slope angles and angles of inclination of the changes in ice properties. discontinuity were used in the models. The model The shear strength and stiffness properties of ice slopes were designed so that in the absence of ice in the are a function of temperature, e.g. Barnes et al. (1971), discontinuities they should have been stable (i.e. the Fish & Zaretsky (1997), and this will affect the shear angle of inclination of the discontinuity was lower capacity of a frozen rock joint. In order to quantify the than the angle of friction of the joint and, to prevent significance of such changes in material properties on the development of pore pressure in the joint as ice the stability of rock slopes containing ice-filled discon- melted, drainage paths were provided to remove water tinuities in the context of warming permafrost, Davies from the discontinuity). Nevertheless, in each case et al. (2000) investigated the influence of temperature on slope failure occurred whilst a large proportion of the

169 joint (typically approximately 40% of its length) still contained ice. The results of the experiments con- 4 3 firmed the hypothesis arising from the results of the W laboratory shear tests and also enabled the validation of a method to assess quantitatively the reduction in stabil- h 2 ity of slopes containing ice-filled discontinuities with H warming permafrost. 1 The study presented in this paper extends the investi- β gation of Davies et al. (2001) by considering a more complex slope geometry. The motivation for this is α that whilst the earlier study demonstrated clearly the fundamental mechanisms associated with the warming of ice-filled discontinuities, the simple geometry used for the investigation might not represent the wider range Figure 1. Geometry of centrifuge model containing a sin- of field conditions. In particular, these are generally gle ice-filled discontinuity inclined at an angle, b, with three more complex because rock slopes frequently contain vertical joints (blocks forming slope are numbered 1 to 4). more than one set of discontinuities. When surface temperatures increase, heat is conducted into the slope LVDT resulting in the warming and eventual melting of ice along the discontinuity on which failure might occur. If as this process occurs the joint system permits closure along a length of the potential shear plane there will be a resulting increase in shear capacity that may be sufficient to avoid slope failure. This potentially + more complex mechanism was investigated in geo- + technical centrifuge model tests. 440 mm +

2 CENTRIFUGE MODEL TESTING

2.1 Model design 803 mm + Thermocouple location The stress-strain behaviour of rock joints is stress level dependent and can be highly non-linear. Therefore, to Figure 2. Cross-section of centrifuge model showing con- simulate the constitutive behaviour of such joints cor- struction and instrumentation. rectly it is necessary for prototype stress levels to be reproduced in a model (e.g. Schofield 1980). This slopes would be expected to be stable. The model slope, may be achieved by subjecting a 1/N scale model to of height H 0.365 m, was constructed in a centrifuge an elevated gravity field, N times the acceleration due strong box of internal dimensions 0.803 m long, 0.5 m to gravity (g) obtained by rotating the model in a large high and 0.6 m wide (Fig. 2). The prototype dimensions centrifuge. Centrifuge modelling laws indicate that of the model were, therefore, H 43.8 m and h 29 m. the time for conductive and advective heat transfer As can be seen from Figures 1 and 2, the potential slid- and diffusion processes – in the experiments reported ing zone contained three vertical discontinuities and herein the rates of temperature rise and pore pressure four potentially sliding blocks. Two model tests were dissipation, respectively – both scale as 1/N2. An expla- conducted for this geometry, one in which the discon- nation of the appropriate centrifuge modelling laws tinuity inclined at b 35° was ice-filled (the “frozen” for simulating cryogenic processes has been given else- model) and the other, which was a control experiment, where (e.g. Harris et al. 2000). in which the discontinuity contained no ice. Plane strain models were used to represent rock slopes using a model scale of 1/120 (i.e. at a centrifuge acceleration, N.g, of 120 g). The geometry selected 2.2 Configuration, preparation and for the models is shown in Figure 1, where the slope instrumentation of the models angle a 60° and the inclination of the discontinuity b 35°. The angle b was less than the angle of inter- To ensure consistency in joint roughness between mod- nal friction for the joint, which was obtained in a series els, Davies et al. (2001) developed a technique for con- of direct shear tests. Thus in the absence of ice the structing slopes from concrete having similar physical

170 properties to granite. This involved casting blocks form- acquisition system they were accelerated to the test ing the slope in moulds of the appropriate geometry and acceleration of 120 g. As expected, the control slope internal roughness. In the study reported herein, a simi- remained stable following acceleration to 120 g. This lar process was used to form the slopes. The only differ- provided confirmation that shear stresses acting on ence was that the faces of the blocks, which formed the the inclined plane were not sufficient to shear off part vertical joints, were cast against a flat steel plate, whilst of the concrete asperities; which might result in a sig- the faces forming the inclined discontinuity were cast nificant reduction in the angle of friction of the joint. against a sheet of profiled steel. This resulted in blocks Therefore, if the ice-filled discontinuity in the frozen which had smooth vertical faces (to minimise inter- slope was permitted to close during thawing, since the block friction) and an inclined face with a regular pat- angle of dip of the discontinuity was less than the tern of asperities of height 0.55 mm, wavelength 5 mm measured friction angle for the joint, then the slope and roughness angle 20°, which fall within the range of would remain stable. values observed in the field (e.g. Hoek & Bray, 1981). The air temperature of the centrifuge chamber was To form the ice-filled joints, the concrete blocks approximately 24°C and, since this was higher than forming the two sides of the joint were fixed together the temperature of the frozen model, heat was trans- with the peaks of the asperities in contact, three of the ferred to the slope during the period between transfer four sides were sealed and then water was introduced of the centrifuge package from the thermostatically from the fourth, care being taken to ensure that the air controlled room to the stage in the experiment when in the joint was replaced by water. The blocks were the centrifuge reached the test acceleration of 120 g. then placed in a thermostatically controlled room set at The temperature distribution measured in the slope at a temperature of 12°C. Although this process does this stage in the experiment, Figure 3a, indicates that, not reproduce exactly field conditions where ice in although at this time surface temperatures on the crest joints forms under pressure (Tharp, 1987) and is of the slope were as high as 10°C, the temperature anisotropic, it permitted formation of joints with throughout almost the entire region adjacent to the repeatable properties. This was considered to be inclined discontinuity was less than zero. appropriate for the generic nature of the experimental Movement of the frozen slope, recorded by the study. For the control experiment it was required that LVDTs, after the model had reached the test accelera- the joint be closed fully and, therefore, the model was tion (120 g) is shown in Figure 4. The first large dis- assembled with the peaks of one side of the joint in placement recorded by LVDT 1 following 13 minutes contact with the troughs of the other. of testing (corresponding to 4.3 months at prototype The blocks forming the slope had a width of 0.165 m, scale) indicates clearly the moment the bottom block permitting three sets of blocks to be used to form the (Block 1 in Figure 1) failed. After this stage, the plots slope. The two outer sets provided insulation to the for LVDT 2 and LVDT 3 indicate failure of the two central set to ensure that the heat transfer processes in central blocks (Blocks 2 and 3), following 28 minutes this set was two-dimensional (in order to achieve a uni- and 31 minutes of testing respectively. However, as form temperature across the width of the inclined dis- can be seen from the data of LVDT 4, the top block continuity). Smooth vertical joints between the inner (Block 4) remained stable although there was a clo- and outer sets of blocks provided drainage paths to per- sure of the joint of approximately 0.29 mm. mit melt water to escape – thus preventing a build up of Figure 3b shows the temperature distribution, pore pressures. The model containing the ice-filled obtained from the thermocouples, in the model at the joint was assembled in a temperature-controlled room point of failure of Block 1. At this stage the tempera- and brought to an equilibrium temperature of 12°C ture in the region of the discontinuity at the base of prior to being transferred to the centrifuge for testing. this block was estimated to be below 0°C (with a mea- The temperature distribution within the central set of surement precision of 0.5°C) along approximately blocks forming the slope was monitored using thermo- 15% of its length. The measurements of LVDT 1 couples cast into the blocks or placed on the surface (Fig. 4), show that there was insignificant movement once the model was assembled as appropriate. In total of this block as the ice warmed and eventually melted 16 thermocouples were used. The displacement of these along much of the joint. This suggests that failure blocks was monitored using four linear voltage dis- occurred because there was insufficient movement to placement transformers (LVDT). The locations of the close the joint and, therefore, increase the shear strength thermocouples and the LVDTs are shown in Figure 2. above the critical value. Additionally, since only a small proportion of the joint beneath Block 1 remained 2.3 Experimental results frozen prior to failure, despite the provision of drainage paths, excess porewater pressures resulting from the Following transfer of the models to the centrifuge melting ice might have contributed to lowering the and connection of the instrumentation to the data effective stress in the joint and hence its shear strength.

171 respectively. Collapse of these blocks resulted, therefore, from the level of shear stresses along the discontinuity at the base of the block exceeding the available shear capacity of the ice-filled joint. At the point of failure of the third block, temperatures lower than 0°C were recorded along only approximately 5% of the discontinuity beneath the uppermost block in the slope, Block 4. The data for LVDT 4 shows there was partial closure of this joint and that this was sufficient to provide the required shear strength along this discontinuity to prevent failure occurring.

3 ANALYSIS OF THE INFLUENCE OF ICE TEMPERATURE ON SLOPE STABILITY

Using the temperature dependent strength parameters for the ice-filled joint obtained from direct shear box tests by Davies et al. (2000) in a simple wedge analysis it is possible to analyse the effect of temperature of the ice on the stability of the frozen slope (Davies et al. 2001). The results of the shear box tests indicate that the Coulomb line for a frozen joint may be represented by,

tmax c(T) s tan d(T ) (1) where c(T ) and d(T ) are temperature dependent parameters, which represent the intercept of the line with the tmax axis and the gradient of the line, respec- Figure 3. Isotherms showing the temperature distribution in tively. Where pressure melting occurs, resulting from a the model (°C): (a) model accelerated to 120 g; (b) at failure lowering of the freezing point of water, the strength of the first block – Slope B-1 frozen model (a 60°, parameters of the joint revert to those of the unfrozen b 35°). joint. Incorporating Equation 1 into the classical equation for the factor of safety, Fs, of a potentially sliding block yields, 2.0 LVDT 1 cT()⋅−ll ( W cosbd u )tan () T F (2) LVDT 2 s W sin b 1.0 LVDT 3 LVDT 4 where ᐉ length of the base of the block that is frozen; b inclination of the discontinuity; u average water 0.0 pressure in the discontinuity; and W weight of the LVDTLV DT 3 LVDTLV DT 4 potentially sliding block per unit width. LVLVDT DT 2

Displacement, mm Taking the average temperature of the ice along the -1.0 LVDTLV DT 1 base of a block at the point of failure and assuming there are no excess pore pressures, it is possible to obtain the calculated factor of safety, F , for Blocks 1, -2.0 s 0102001 30 40502 and 3 at failure using Equation 2. Ice was present Time, minutes along a significant proportion of the failure plane for Blocks 2 and 3 at failure. At this point the calculated Figure 4. Displacement of the slope following accelera- factors of safety for these two blocks are predicted to tion to 120 g, Slope B-1 frozen model (a 60°, b 35°). be 0.97 and 1.30 respectively. The calculated value for Block 3 is greater than unity indicating that the block Temperature measurements indicated that at the should have been stable. However, examination of point of failure of Blocks 2 and 3 the proportion of LVDT 3 and LVDT 4 in Figure 4 indicates: (i) that as the discontinuities at the base of the blocks where Block 3 began to move more rapidly following the fail- the temperature was below 0°C was 77% and 100% ure of Block 2, Block 4 moved down approximately

172 Table 1. Data used in stability analyses and calculate values of the factor of safety of each block. Blocks 123 4 Length (ᐉ), m 9.60 9.36 15.24 14.88 Frozen length1, % 15 77 100 2 T, °C 1.00 1.43 1.49 7.6 W, kN/m width 696 2916 3324 1081 c(T), kPa 54.85 106.54 114.79 0.00 tan d(T) 0.20 0.26 0.27 0.93 Factor of Safety2 0.49 0.97 1.30/0.983 1.334

1 Proportion of failure surface containing ice at failure. 2 Calculated at point of failure for each block except Block 4. 3 Calculated assuming contribution from Block 4. 4 Calculated at point of failure of Block 3.

0.1 mm, and (ii) Block 4 did not continue to move modeling, and simple geotechnical analysis has been once Block 3 had failed. This implies that Block 4 was conducted to investigate the effect of rise in ambient resting against Block 3 prior to the failure of the latter temperature on the stability of rock slopes containing block and, therefore, the shear stress acting on the ice-filled discontinuities. The centrifuge model tests inclined discontinuity beneath Block 3 was greater were conducted both to investigate the potential fail- than that resulting from Block 3 alone. If the shear ure mechanisms in rock slopes located in permafrost stress acting beneath Block 3 is increased to account regions that might occur as a result of increasing mean for the weight of Block 4 acting down the slope then annual temperatures and to validate a method for the predicted factor of safety for Block 3 reduces to analysis. 0.98. Once Block 3 had failed, closure of the joint Centrifuge experiments were conducted on models beneath Block 4 increased its shear stress capacity. with two sets of discontinuities (i.e. four blocks). Since When Block 3 failed there was negligible ice in the the dip of the discontinuity representing the potential joint at the base of Block 4. Therefore, using ᐉ length failure plane, b, in the model slopes was less than the of base of the block in Equation 2 and assuming full angle of friction of the rock joint – and shear stresses joint closure, the predicted factor of safety for this imposed on the shear plane resulting from the weight block is 1.33. In the absence of joint closure and with of the blocks did not degrade the shear stress capacity ice present along only 15% of the base of Block 1 the of the discontinuity – failure did not occur in the factor of safety is calculated to be 0.49. unfrozen model. However, failure was observed in the A summary of the parameters used in the analyses “frozen” model which had identical geometry but with is given in Table 1, together with the calculated values an ice-filled rock joint. Measurement of temperatures of factors of safety. These predicted results are in gen- throughout the profile of the frozen model revealed a eral agreement with the experimental observations variation in temperature along the discontinuity indi- indicating that, in the absence of sufficient closure cating that some of the ice in the joints melted prior to pressure, a jointed rock slope that is stable when there failure and that there was a variation in strength in the is no ice in the joints and is also stable when the ice in ice that remained. Displacement data revealed that there the joints is at low temperatures may become unstable was sufficient closure of the rock joint during warming as the ice warms. This reinforces and extends the find- to prevent failure of one of the blocks forming the slope. ings of earlier studies (i.e. Davies et al. 2000, Davies The analysis, which incorporates the findings of et al. 2001) which showed that the factor of safety of element tests conducted to improve understanding of an ice-filled joint can be significantly less than that of the fundamental mechanics of ice-filled rock joints dur- an unfrozen joint. ing shearing (Davies et al. 2000), provides a means for interpretation of the mechanisms associated with the warming of ice-bonded discontinuities and may be 4 CONCLUSIONS used to inform the assessment of the long term stability of rock slopes in permafrost regions (Harris et al. An investigation involving both laboratory experi- 2001). Although this study was conducted in the con- ments, using the technique of geotechnical centrifuge text of climate change, warming can also result from

173 anthropogenic processes, such as construction activity, Dramis, F., Govi, M., Guglielmin, M. & Mortara, G. 1995. and the results of this study are also applicable for the Mountain permafrost and slope instability in the assessment of risk in this context. The development of Italian Alps: the Val Pola Landslide. Permafrost and a more sophisticated analysis incorporating tempera- Periglacial Processes 6: 73–82. ture prediction resulting from both changes in mean Fish, A.M. & Zaretsky, Y.K. 1997. Ice Strength as a function of hydrostatic pressure and temperature. CRREL Rep. annual temperature or anthropogenic activity forms 97-6. part of the continuation of this study. Harris, C., Davies, M.C.R. & Etzelmüller, B. 2001. The assessment of potential geotechnical hazards associ- ACKNOWLEDGEMENT ated with mountain permafrost in a warming global climate, Permafrost and Periglacial Process 12: 145–156. This research was undertaken as part of the European Harris, C., Rea, B. & Davies, M.C.R. 2000. Geotechnical Union research project “Permafrost and Climate in centrifuge modeling of gelifluction processes: valida- Europe (PACE)” (DGXII Contract ENV4-CT97-0492). tion of a new approach to periglacial slope studies. Annals of Glaciology 31: 417–421. Hoek, E. & Bray, J. 1981. Rock slope engineering. London: REFERENCES Institution of Mining and Metallurgy. Schofield, A.N. 1980. Cambridge Geotechnical Centrifuge Barnes, P., Tabor, D. & Walker, J.C.F. 1971. The friction operations, 20th Rankine Lecture. Géotechnique and creep of polycrystalline ice. Proc. Roy. Soc. Lond. 30(3): 227–269. A. 324: 127–155. Tharp, T.M. 1987. Conditions for crack propagation by Bjerrum, L. & Jørsbad, F. 1968. Stability of rock slopes in frost wedging. Geological Society of America Bulletin Norway. Norwegian Geotechnical Institute Publication 99: 94–102. 79. Vonder Mühll, D., Delaloye, R., Haeberli, W., Hölzle, M. & Davies, M.C.R., Hamza, O., Lumsden, B.W. & Harris, C. Krummenacher, B. 2000. Permafrost Monitoring 2000. Laboratory measurement of the shear strength Switzerland PERMOS, annual report 1999/2000. of ice filled rock joints. Annals of Glaciology 31: Vonder Mühll, D., Stucki, T. & Haeberli, W. 1998. Borehole 463–467. temperatures in Alpine permafrost: a ten year series. Davies, M.C.R., Hamza, O. & Harris, C. 2001. The effect Proc. Seventh International Conference on Perma- of rise in mean annual temperature on the stability of frost, Yellowknife, Canada: 1089–1095. rock slopes containing ice filled discontinuities. Permafrost and Periglacial Process 12: 137–144.

174