Identification of rock and fracture kinematics in high Alpine rockwalls under the influence of altitude

. In alpine environments, tectonic processes, past glaciation and weathering processes fractured rock and prepare or trigger rockfalls, which are important processes of rock slope evolution and natural hazards. In this study, I quantify thermal-10 and ice-induced rock and fracture kinematics and place these in the context of their role in producing rockfall and climate change. I conducted laboratory measurements on intact rock samples, and installed temperature loggers and crackmeters at four rockwalls reaching from 2585 to 2935 m in elevation in the Hungerli Valley, Swiss Alps. My laboratory data shows that thermal expansion followed three phases of rock kinematics, which resulted in a hysteresis effect. In the field, control crackmeters on intact rock reflected these temperature phases and based on thermal expansion coefficients of these observed 15 phases, I modelled thermal stress. Model results show that thermal stress magnitudes were predominantly below rock strengths. Crackmeters across fractures revealed fracture opening during cooling and reverse closing behaviour during warming on daily scale. Elevation-dependent snow cover controlled the number of daily temperature changes and thermal stresses affecting both intact and fractured rock, while the magnitude is controlled by topographic factors influencing insolation. On seasonal scale, slow ice segregation induced fracture opening can occur within lithology-dependent temperature regimes called frost cracking 20 windows. Shear plane dipping controlled if fractures opened or closed irreversible with time due to thermal-induced block crawling on annual scale. Climate change will shorten snow duration and increase temperature extremes, therefore, will affect the number and the magnitude of thermal changes and associated stresses. Earlier snowmelt in combination with temperature increase will shift the ice-induced kinematic processes to higher altitudes. In conclusion, climate change will affect and change rock and fracture kinematics and, therefore, change rockfall patterns in Alpine environments. Future work should quantify


Introduction
Alpine environments are characterized by high relief due to the interaction of tectonic uplift, climate and erosion (e.g.Schmidt and Montgomery, 1995;Egholm et al., 2009;Whipple et al., 1999).Tectonics result in the fracturing of rock (Molnar et al., 2007) which promotes erosion.Glaciers eroded deep Alpine valleys (Harbor et al., 1988;Herman et al., 2015;Prasicek et al., laboratory tests to investigate the influence of thermal changes on rock kinematics.Furthermore, I installed control crackmeters and rock temperature loggers on intact rocks at four rockwalls reaching from 2585 to 2935 m in elevation to validate laboratoryderived rock deformation behaviour and to model thermal stresses.I installed crackmeters across fractured rock to quantify thermal-and ice-induced fracture kinematics and to identify their spatial variation along altitude.I analyse my observations in a geomorphic context and discuss the role of rock and fracture kinematics for preparing and triggering rockfall.

Research Area
The Hungerli Valley is a hanging valley located in the Turtmann Valley, Valais Alps, Switzerland (Fig. 1a).The geology is predominantly paragneiss, consisting of schistose quartz slate (Bearth, 1980).At the Rothorn (RH) the schistose quartz slate is intersected by aplite and at the Hungerlihorli (HH) by amphibolite (Bearth, 1980).The valley was shaped by past glaciations and regional ice sheet models suggest an ice cover up to 2800 m during Last Glacial Maximum (LGM; Kelly et al., 2004).In addition, cirque glaciation was abundant during LGM at the Rothorn (RH), Furggwanghorn (FH) and between Hungerlihorli (HH) and Brändjispitz (BS; Fig. 1c-d).During Little Ice Age, only the Rothorn cirque was ice-covered and is currently occupied by the remnants of the Rothorn Glacier (RG) that possessed a surface area of 0.053 km² and a length of 405 m in 2011 (Fischer et al., 2014).Rockwalls occur at elevations that range from 2500 up to 3300 m (Fig. 1b).The hanging valley (Fig. 1d) is occupied by several rock glaciers (Nyenhuis et al., 2005) and talus slopes (Otto et al., 2009).A sediment budget analysis showed that 1/5 of all stored deposits is derived from rockfall indicating a high rockfall activity (Otto et al., 2009).

Laboratory Measurements
To understand controlling factors of rock kinematics, I conducted laboratory measurements on air-dryed rock samples in a freezing chamber.For this purpose, I collected three approximately 0.4 m long, 0.15 m wide and 0.2 m high rock samples without visible evidence of weathering from talus slopes below rockwalls with lithologies ranging from aplite (AP, RW-1), amphibolite (AM, RW-2) to schistose quartz slate (QS, RW-3; in Fig. 1d).I assume that the rock samples are representative for the rockwall.On each rock sample (Fig. 2), two crackmeters were installed at the top (RD1) and at one side of the sample (RD2) to monitor rock deformation (RD) and rock top temperature (RTT) in 1 min intervals.The two Geokon crackmeters 4420-3 measured RD and automatically correct thermal expansion of the instrument.After temperature correction, the resolution of RD is below 0.00075 mm with an accuracy below 0.003 mm, while RTT is measured with an accuracy of ±0.5°C.
Two high-precision Greisinger thermistors connected to a Pt 100 temperature sensor (0.03°C accuracy) were used to monitor rock temperature in the center of the rock sample in 5 cm depth (RT5cm) and in 2 cm depth (RT2cm).To keep room temperature constant at low levels, the freezing chamber is located in a fridge that keeps the surrounding temperature at 8 to 10 °C.The freezing chamber itself consists of a custom-made Fryka cooler with a temperature-controlled (0.1°C accuracy) ventilation system to enable cooling of samples without thermal layering.The rock samples were cooled down from 10-14 °C to -8/9 °C RT2cm in 7-9 h.Then, I stopped cooling and enhanced a "natural" warming for 15 to 17 h until 8 °C RT2cm was reached.Based on the linear correlation, I derived the thermal expansion coefficient α: with L is crackmeter length, ∆RD is rock deformation change and ∆RT is rock temperature change.
Young modulus E and Poisson' ratio υ were derived using a Geotron ultrasonic generator USG40 in combination with Geotron preamplifier VV51 and 20 kHz sensors (Table 1).Seismic signals were recorded using a PICO oscilloscope and data analyzed using the software Geotron Lighthouse DW.Uniaxial compressive strength σu and tensile strength σt was measured (Table 1) in accordance to norms of the German Geotechnical Society by Mutschler (2004) and Lepique (2008).For a more detailed description of the seismic and mechanical tests see Draebing and Krautblatter (2019).

Field Measurements
To monitor fracture movement in the field, I installed three 0.4 m long Geokon Vibrating-Wire Crackmeters 4420-1-50 with resolution of 0.0125 mm and accuracy of 0.05 mm at RW-1 to RW-3 in 2016 (Fig. 3a-c).Instrumented rockwalls range from 2585 m (RW-3), 2672 m (RW-2) to 2935 m (RW-1) and are exposed in northwest (NW) to northeast (NE) direction (Fig. 1; Table 2).Rock strength of each rockwall was measured using a N-type Schmidt hammer following Selby (1980, Table 3).At RW-1, a 3.5 m long, 1.9 m wide and 2.1 m high aplite block was monitored (Fig. 3a).A slickenslide on top of the block indicates former movement of a previously above-laying block.The monitored block slides on a 20 to 40° inclined shear plane (J3 in Fig. 3a) into the valley with an identical angle than the slickenslide.The block is separated by a 10 to 70 mm wide crack of joint set 1 (J1) from a second 2.5 m long and 2.6 m high block.At RW-2, three blocks were monitored which are incorporated in a heavily fractured rockwall consisting of amphibolite.All monitored cracks possess an aperture between 1 and 2 mm (Table 1) and are dipping at 50° out of the rockwall (J2), however, the blocks are buttressed by adjacent blocks and the talus slope (Fig. 3b).RW-3 consists of schistose quartz slate and blocks are 0.3 to 1.5 m wide (Fig. 3c).Blocks are separated by 81° inclined and 30 to 50 mm wide cracks (J2), which were monitored.The schist cleavage is dipping at 22° into the rockwall.
To identify effects of different exposition, three more crackmeters were installed at RW-S at 2723 m in 2017 (Fig. 3d).RW-S is heavily fractured, which results in the occurrence of a high number of joint sets (Fig. 3d).The monitored blocks dip with an angle of 41° degrees into the rockwall (H2) and crack aperture range from 7.5 to 20 mm at Crack-2 to 45 to 135 mm at Crack-1 (Table 2).
All crackmeters were fixed by groutable anchors and half tubes protected the devices from snow load (Draebing et al., 2017a;Draebing et al., 2017b).At each rockwall, two crackmeters spanned cracks to monitor crack deformation (CD) and crack-top temperature (CTT).To validate rock deformation (RD) observed in the laboratory, one crackmeter was used as a control crackmeter and was fixed on intact bedrock without any cracks (Fig. 3).Due to snow load damage or technical failures, crackmeters had a different life span and the control crackmeter at RW-2 failed to record data completely.A 4-Channel Geokon data logger Lc2x4 recorded all data at each rockwall in 3h intervals between 1 September 2016 and mid-August 2017 and in 1h intervals from mid-August 2017 to 31 August 2019.Crackmeter data were temperature-corrected, residual uncertainty quantified and the existence of snow cover was deviated using daily standard deviation of CTT or RTT following the technique by Schmid et al. (2012).To analyse the overall fracture movement pattern (Bakun-Mazor et al., 2013), a monthly moving average of CD, RD, CTT and RTT was calculated.The thermal expansion coefficient of the control crackmeters was calculated based in Eq. 1.

Meteo station, rock surface temperature and thermal stress modelling
Air temperature and snow depth data was derived from the meteo station Oberer Stelligletscher (2910 m) located 2.5 km SE of the research area in the Matter Valley (MeteoSwiss, 2019a).Probably due to snow cover above 3.5 m, there is a data gap from mid-January to end of February 2018.The temperature data gap was filled using air temperature adapted from near-by meteo station Grächen at 1605 m (MeteoSwiss, 2019b) by applying a linear correlation (r²= 0.85).To monitor rock surface temperature (RST), I installed four Maxim iButton DS1922 L temperature loggers with a nominal accuracy of ±0.5 °C in 10 cm deep boreholes following the measurement method by previous studies (e.g.Draebing et al., 2017a;Haberkorn et al., 2015).
The loggers recorded RST in 3h intervals between 1 September 2016 and 31 August 2019 (RW1-3) or between 1 September 2017 and 31 August 2019 (RWS), respectively.Due to the logger location in 10 cm depth, I determined snow cover duration using the uniform standard deviation threshold of <0.5 K for positive and negative RST in accordance to Haberkorn et al. (2015).I calculated daily rock temperature warming and cooling cycles ∆RT and applied the equation from Anderson and Anderson (2012) to model thermal stress σth: . (2)

Meteorological conditions and rock surface temperatures
At the meteo station at 2910 m, mean annual air temperature (MAAT) ranged from -0.6 °C in 2016/17, to -1.0 °C in 2017/18 and -1.1°C in 2018/19.Daily air temperatures fluctuated between -20 °C and 12 °C (Fig. 4a).After a short period of snow cover with snow depths up to 75 cm between November and December 2016, a second period of snow cover with snow depths up to 150 cm started in mid-January 2017 and lasted until mid-July 2017.Snow onset in the following year was delayed and started at the end of December 2017.Snow depths reached more than 350 cm and lasted until mid-August 2018.After approximately 2 months without snow, snow cover period started at the end of October 2018 and lasted until the end of July 2019 with snow depths up to 250 cm.Cooling periods lasted from mid-August to mid-January 2017, April 2018 or mid-February 2019 and mean monthly air temperature dropped to -12° C. The warming period lasted 4.5 to 7 months and reached a mean monthly air temperature of 6°C in mid-August.
Rock surface temperatures (RST) followed the annual and daily oscillation of air temperatures.At annual scale, RST of northexposed rockwalls ranged from -12.9 °C up to 13.4 °C for RW1, -5.6 °C up to 17.6 °C for RW2 and -7.0 °C up to 13.9 °C for RW3 (Fig. 4b-d).In contrast, the south-exposed logger at RWS recorded higher RST variations between -12 °C and 32 °C (Fig. 4e).At daily scale, the north-facing loggers measured small daily temperature variations up to 4 °C, whereas the southexposed logger recorded variations up to 16.5 °C.Snow cover attenuated daily temperature oscillations with expected high deviation between north-and south-exposed rockwalls.At north-facing rockwalls, snow cover onset was between October and November and lasted between 220 days and 251 days per year with only minor differences between RW1 to RW3 and individual years (Fig. 4b-d, Table 3).In contrast, snow onset was delayed to mid-February 2018 or snow cover was only sporadic in 2019, therefore, snow cover duration was reduced to 5to 80 days (Fig. 4e).
Nine to 23 min after stopping cooling, several crackmeters at all rock samples (AP RD2, AM RD2, QS RD1 and RD2) experienced a sudden rock deformation ranging from +0.004 mm to +0.0135 mm (transition phase; Fig. 4b, Fig, S2).Despite an increase of RTT from -7.3 to -5 °C, the QS sample and AP RD1 and AM RD1 showed a further rock contraction between -0.0016 mm and -0.0032 mm.The closing behaviour corresponded to the decrease of RT5 cm from -8.2 °C to -9.3 (Fig. 4b).
Applying laboratory derived thermal expansion coefficients (Table 1) for warming and cooling to Eq. ( 2) provides the daily thermal stresses within a rockwall.Daily thermal stresses reflected RST and were increased during snow-free periods in summer and decreased or absent during snow cover periods.Maximum stresses reached up to 2.9-3.0MPa at RW1, 6.8-7.2 MPa at RW2, 3.1-3.9MPA at RW3 and 15.4-20.1 MPa at RWS (Fig. 4b-e).

Rockwall fracture kinematics
Crackmeters showed a decrease of snow duration with decreasing elevation.Crackmeters at RW1 located at 2935 m experienced 192 to 223 days of snow cover per year (Fig. 6).The number of snow-covered days was reduced to 69 and 73 days in 2016/17 at RW2 at 2672 m.Snow load damaged the equipment in the following years, which resulted in a data gap and incomplete measurement of snow cover duration.RW-3 at 2585 m showed between zero and nine days of snow cover and snow cover was limited to two days at Crack-2 in 2017/18 at the south-facing rockwall RWS.
All crackmeters experienced a cooling period (Phase 1 in Fig. 6) that ranged from September until mid-December to Mid-February.At RW1, the onset of snow cover controlled the end of the cooling period, only in 2016/17 cooling continued under snow cover.The cooling period was characterized by a crack opening (Table 4), which was between 0.22 and 0.53 mm at Crack-1 and between 0.04 and 0.09 mm at Crack-2 at RW1.At RW2, cracks opened between 0.09 mm at Crack-2 and 0.13 mm at Crack-1, while Crack-1 at RW3 revealed a crack opening between 0.15 and 0.33 mm.In contrast, Crack-2 at RW3 experienced a diverse crack deformation ranging from crack closing between 0.28 mm to 0.01 mm crack opening.At RWS, the cooling period was characterized by crack closing between 0.18 and 0.20 mm at Crack-1 and between 0.1 and 0.12 mm at Crack-2.
At RW1 and RW2, crackmeters experienced a slow warming below snow cover (Phase 2 in Fig. 6), which resulted in either crack opening or crack closing (Table 4).Crackmeters at RW1 experienced a crack deformation ranging from closing of 0.08 mm to crack opening of 0.07 mm.At RW2, cracks experienced a crack opening between 0.02 and 0.11 mm.At RWS, snow cover was absent during warming, however, Crack-2 experienced an opening of 0.16 mm, which was reversed by 0.13 mm during enhanced warming in 2017.RW1 and RW2 showed a period of predominantly crack closing during enhanced warming until snow cover completely melted (Phase 3 in Fig. 6).Crack-1 at RW1 experienced between 0.12 to 0.31 mm crack closing, while Crack-2 showed a diverse crack deformation ranging between 0.03 mm opening and 0.10 mm closing.At RW2, the crackmeters revealed crack closing between 0.15 and 0.29 mm.
All crackmeters experienced a warming period (Phase 4 in Fig. 6), which is characterized by both crack closing and crack opening (Table 4).At RW1, crackmeters revealed a crack opening between 0.05 and 0.12 mm.In contrast, RW3 showed a crack closing between 0.13 and 0.33 mm at Crack-1 and a crack deformation behaviour ranging from 0.07 crack opening to 0.24 mm crack closing at Crack-2.At RWS, the warming period is associated with crack opening between 0.00 and 0.14 mm.
In the 3-year period, RW1 experienced a crack opening between 0.45 and 0.51 mm.In contrast, RW3 showed an overall crack closing between 0.24 and 0.25 mm.Data at RW2 was limited to 2016/17 and cracks experienced no change or 0.1 mm closing.
RWS was characterized by crack closing in each year with a cumulative closing between 0.03 and 0.09 mm.
On a daily scale, cooling resulted in crack opening due to contraction of two rock blocks and warming in crack closing due to expansion of two rocks (Fig. 8).The peak of opening and closing between individual crackmeters can be different.Crackmeters at RW1 experienced daily CTT fluctuations in the range below 10°C and daily CD below 0.1 mm (Fig. 9) during snow-free periods.The fluctuations were increased up to 16°C and 0.11 mm at RW2, 23 °C and 0.26 mm at RW3 as well as 21°C and 0.32 mm at RW-S.

Cyclic thermal rock deformation
Cyclic thermal stresses can result in thermal fatigue that breakdown rock and is an important component of mechanical weathering.In my laboratory tests, I can differentiate thermal cycles into three phases: (1) cooling phase, (2) transition phase, (3) warming phase.The (1) cooling phase was characterized by rock contraction with thermal coefficients α (Table 1), which are in the order of previous thermal expansion coefficients for quartz minerals (Siegesmund et al., 2008) or rock samples (Ruedrich et al., 2011;Skinner, 1966).After stopping cooling and enhancing a natural warming of the rock samples, the (2) transition phase started (Fig. 5a-b).Some crackmeters experienced a sudden rock deformation due to rapid rock response to warming, while other crackmeters even on the same rock sample showed further rock contraction (Fig. S1-2).The contraction behaviour corresponded to decreasing RT5 cm, while RTT was already increasing as a response to warmer air temperature.
Therefore, the transition phase is characterized by a temperature difference between rock surface (RTT) and rock depth (RT5cm), which is a result of the slow speed of heat conduction.While the rock surface (RTT) was warming and rock was expanding, the overall rock kinematics was still controlled by cooling of the rock interior and associated contraction.The (3) warming phase was characterized by rock expansion (Fig. 4 and 5) with thermal expansion coefficients that are slightly different from the cooling (Table 1).Therefore, thermal cycles showed a hysteresis effect, which was previously observed on other lithologies (Ruedrich et al., 2011).
The control crackmeters demonstrated that snow cover controls the occurrence of daily temperature cycles, and associated rock expansion during warming and contrary rock contraction during cooling.Daily temperature changes affected the upper 0.21 to 0.42 m assuming a 12 h temperature cycle and a thermal diffusivity between 1 and 2 mm s -2 typical for metamorphic rocks (Vosteen and Schellschmidt, 2003;Cermák and Rybach, 1982).These rock depths correspond to daily temperature cycles in rockwalls observed in previous studies (Gunzburger and Merrien-Soukatchoff, 2011;Anderson, 1998).On annual scale, thermal changes affected 4 to 8 m and, therefore, the entire instrumented rock blocks assuming a half-year cycle and thermal diffusivities typical for metamorphic rocks.Rock temperature boreholes in the Alps suggest heat propagation to similar depths (Phillips et al., 2016a;PERMOS, 2019).Control crackmeters revealed identical phases of thermal-induced rock deformation as laboratory measurements including hysteresis effects.The hysteresis effect was amplified at RW-1, where rock blocks are between 2 and 4 times larger than rock blocks at the other rockwalls (Fig. 3).A larger rock block size results in a longer heat transfer by conduction and increases the transition phase, therefore, I interpret the increase of the hysteresis effect as a result from block size and an effect of scale.The observed differential thermal expansion in combination with different response during transition phase results in mechanical stresses able to breakdown rock that will be discussed in Chapter 5.3.

Progressive irreversible rock movement
In overhanging steep rock cliffs, thermal stresses can propagate fractures and trigger rockfall (Collins and Stock, 2016;Stock et al., 2012).Exfoliation joints warm differentially (Guerin et al., 2019) and thermal bowing results in fracture propagation parallel to the rockwall (Collins and Stock, 2016).In fractured rock, daily and annual thermal cycles result in rock contraction with fracture widening during cooling and rock expansion during warming with fracture closing (Fig. 11b; Cooper and Simmons, 1977;Draebing et al., 2017b).My data showed that crack opening and closing occurred on a daily scale (Fig. 8).
The magnitude of this crack deformation depends on the magnitude of temperature change and was increased at RWS and RW3, which experienced much higher daily temperature changes (Fig. 9).The data demonstrated that the number of daily temperature changes per year (Fig. 9 and Fig. S5) is controlled by the duration of snow cover.Snow cover insulates the ground (Zhang, 2005) and decreases daily thermal changes (Fig. 10; Luetschg and Haeberli, 2005;Draebing et al., 2017b), therefore, rockwalls at lower elevations (e.g.RW3) or south-exposed rockwalls (e.g.RWS) experienced a shorter snow cover duration (Table 2) and a higher frequency of thermal cycles than higher-elevated rockwalls with longer snow cover (e.g.RW2-3).
On seasonal scale, several crackmeters experienced a slow crack opening during negative CTT that suggest the influence of ice (Fig. 11c).Matsuoka (2001Matsuoka ( , 2008) ) observed rapid crack opening during freeze-thaw cycles in spring or autumn that suggest volumetric expansion as the trigger of crack opening.In contrast, I observed a slow crack opening lasting between 1.5 to 2 months at RW2 in 2017 (Fig. 6b and Fig. 7c-d), 3 to 3.5 months at Crack-2 at RWS in 2018 (Fig. 6d and Fig. 7h), and 5 to 5.5 months at Crack-2 at RW1 in 2017 and 2019 (Fig. 6a and Fig. 7b).The opening occurred in a CTT range between -5 to -3.3°C at RW2, between -8 and -3.6°C at RWS and -9 to -1°C at RW1.These temperature ranges are within the frost cracking window from -8 to -3 °C suggested by Anderson (1998) or in the range of laboratory observed frost cracking windows of aplite, amphibolite and schist quartz slate (Draebing and Krautblatter, 2019).The temporal trajectories of the affected cracks showed that crack opening occurred during warming within the negative temperature range (Fig. 7b-d.h), therefore, a purely thermal response of the rock would result in rock expansion and crack closing.In addition, a transition phase as observed in the laboratory or at control crackmeters can be excluded, thus, the transition phase is associated with temperature changes from warming to cooling or reverse, which were absent during these crack opening phases.Therefore, I interpret the observed crack opening as a result of ice segregation and subsequent closing because of ice relaxation.Cracks can infill with ice by refreezing of meltwater, ice infill growth slowly with time by cryosuction (Weber et al., 2018;Draebing et al., 2017b) and build up ice pressure and stresses in a subcritical range (Draebing and Krautblatter, 2019), which induce slow fracture opening (Draebing and Krautblatter, 2019;Draebing et al., 2017b).
On annual scale, thermal-induced crack opening and closing can be reinforced by cryogenic processes (Hasler et al., 2012), can propagate fractures (Ishikawa et al., 2004) and can result in irreversible rock movement (Weber et al., 2017).Previous studies focussed on toppling rock blocks (Ishikawa et al., 2004) or provided no information on the failure type (Hasler et al., 2012;Weber et al., 2017).Due to the tectonic setting, the observed blocks are located on a shear plane dipping out of the slope (RW1-2, Fig. 3 a) or dipping into the slope (RW3, RWS; Fig. 3b-d).Gunzburger et al. (2005) observed daily non-permanent block movement and suggested that thermal changes can induce rock creep along shear planes.On non-buttressed blocks located on shear planes dipping out of the slope (RW1), crackmeters recorded annual and overall crack opening indicating that the lower located block in Figure 3 a is creeping slope downwards with an annual rate of 0.11 to 0.24 mm a -1 (Table 4).The majority of the creeping occurred during the cooling phase (Phase 1 in Fig. 6a), which was characterized by 0.22 to 0.53 mm opening of Crack-1 at RW1.This opening was slightly reversed at Crack-1 and extended at Crack-2 by ice segregation during phase 2. In Phase 3, the closing pattern reversed most of the previous crack opening.The warming phase 4 induced a crack opening, which is contrary to expected crack closing.Bakun-Mazor et al. ( 2020) identified thermally-induced wedging as a cause of crack opening during warming.The rock contracts during cooling and a wedge within the fracture sinks into the cooling-induced gap and causes a crack opening during warming induced thermal expansion.A wedge was not visible at Crack-1 and the annual opening exceed the crack opening during the warming phase 4. Therefore, I interpret the crack opening as irreversible thermal-induced block movement.
In contrast to RW1, all other block are located on shear planes dipping into the rockwall or buttressed by other blocks (Fig. 3b-d).The cooling phase resulted in crack opening at RW2 and Crack-1 at RW3 and the opening was reversed during the warming phase 4 resulting in an irreversible annual (RW2-3) and overall closing (RW3).Crack closing at Crack-2 at RW3 and RWS occurred during the cooling period and was not completely reversed during the warming period resulting in an annual and overall crack closing (Table 4).In summary, thermal induced crack deformation caused an irreversible block movement along the shear plane into the rockwall (Fig. 11e).

Altitudinal effects on rock and fracture kinematics and implications for rock stability
Thermal changes are an important climatic factor inducing stresses responsible for mechanical weathering (Eppes and Keanini, 2017).Thermal stresses cause subcritical cracking (Eppes et al., 2016) and propagate fractures (Eppes et al., 2010;Eppes and Keanini, 2017).In alpine rockwalls, thermal changes result in deformation of rocks (Guerin et al., 2020;Collins and Stock, 2016) and induced stresses can decrease the strength of stability-relevant rock bridges (Guerin et al., 2019) and can trigger rockfall (Stock et al., 2012;Collins and Stock, 2016).Applying the observed thermal coefficients and recorded RST in 10 cm depth to the thermal stress model by Anderson and Anderson (2012) demonstrated that thermal stresses occurred during snowfree periods and during periods of thin snow cover before snow achieved sufficient height to insulate the rock surface (Phillips, 2000;Luetschg and Haeberli, 2005).Modelled thermal stresses represent maximum values, thus, the equation (2) assumes isotropic material and an equal volumetric expansion in every direction.Occurring rock types possess cracks and schist planes, which results in anisotropy ranging between 0.05 for amphibolite, 0.06 for aplite and 0.55 for schistose quartz slate (Draebing and Krautblatter, 2019).Therefore, modelled stresses for schistose quartz slate are potentially overestimated.Stresses will concentrate at crack tips and widen cracks (Eppes and Keanini, 2017), however, stress calculation requires knowledge on crack geometry which is not available.The applied model provides a quantitative measure of stress levels and demonstrates that stresses occurring at RW1-3 are below tensile strengths and compressive strengths of in-situ rock (Table 1).Thermal stresses are not exceeding rock strength and are subcritical in sensu Eppes and Keanini (2017), however, the cyclicity of thermal stresses progressively weakens rock (Eppes et al., 2016).Schmidt hammer values showed high values between 63 ±4.8 and 71.8 ±2.5 for RW1-2, which consist of high-strength aplite and amphibolite (Table 1), therefore, these values suggest minor weathering near the surface.In contrast, rockwalls with schistose quartz slate revealed lower rebound values with RWS had lower (31.4 ±2.4) values than RW3 (39.4 ±4.2).This could be a result of higher modelled thermal stresses at RWS compared to RW3 (Fig. 4).However, thermal processes are not acting isolated and other weathering processes including mechanical, chemical and biological weathering can be responsible for the observed decrease in rock strength (Viles, 2013b;Eppes and Keanini, 2017).As soon cracks are existent, daily thermal changes induce fracture kinematics that can widen cracks (Fig. 10b).
My data demonstrated that snow cover controls the number of daily crack deformation (Fig. 8 and Fig. S5).According to Bender et al. (2020), the changes of snow duration is elevation dependent and locations in Valais above to 2500 m will experience a shortening of the snow season of approximately 10 % by 2035, 17 % by 2060 and 25 % by 2085.Temperature extremes and variability (Schär et al., 2004;Gobiet et al., 2014) will increase in the future.Therefore, the number and the magnitude of thermal stresses will increase in the future, which could be amplified if climate becomes wetter (Eppes et al., 2020).Consequently, thermal stresses will play a more important role in preparing and triggering rockfall in the future.
Cryogenic processes can cause fracture movement (Draebing et al., 2017b) and produces subcritical stresses that are below tensile strengths of rocks (Draebing and Krautblatter, 2019).These stresses occur in a wide temperature range between -15 and -1°C according to field measurements (Girard et al., 2013;Amitrano et al., 2012), numerical models (Walder and Hallet, 1985) and laboratory tests (Draebing and Krautblatter, 2019).My data showed the occurrence of cryogenic induced opening and closing at several crackmeters (Fig. 7b-d, 7h).The slow opening in combination with the temperature regime suggests that ice segregation is the driving process behind the observed crack opening.This opening can progressively weaken rockwall strength and potentially triggers rock slope failure as observed at Piz Kesch in winter 2014 (Phillips et al., 2016b).The length of the temperature window enabling ice segregation increases with altitude but is modulated by insulating snow cover.Climate change will shorten the snow duration by an earlier meltout date (Bender et al., 2020) and increase air and ground temperatures (Bender et al., 2020;Gobiet et al., 2014), therefore, the time period of temperature windows enabling ice segregation will decrease.This will affect especially rockwalls located at lower elevations, therefore, cryogenic processes and triggered rockfall will be shifted to higher elevations.At higher-elevations, the climate-changed induced changes of the temperature regime will also affect permafrost rockwalls, decrease rockwall stability (Draebing et al., 2014;Krautblatter et al., 2013) and increase rockfall activity due to increased thawing (Ravanel et al., 2010;Ravanel and Deline, 2010) amplified by temperature extremes (Gruber et al., 2004b;Ravanel et al., 2017).
Plastic deformation of fractures contributes to the preparation of rockfalls (Gunzburger et al., 2005).Previous studies demonstrated that thermal-induced crack deformation causes irreversible displacement of rock blocks (Weber et al., 2017;Hasler et al., 2012).Gunzburger et al. (2005) and do Amaral Vargas et al. (2013) suggested that thermal changes can cause rock creep along shear planes.My data demonstrates that rock blocks creep with a direction depending on shear plane dipping.
Dipping out of the rockwall results in creeping that increases fracture opening (RW1, Fig. 10d) and can trigger rockslide processes.In contrast, dipping into the rockwall causes fracture closing (RW3, RWS; Fig. 10e).My observed blocks will not be released as rockfall, however, the observed mechanism can trigger a wedge failure in more steeper and overhanging rockwalls that are more susceptible to rockfall (Matasci et al., 2017).Several studies indicated that thermal-induced stresses can affect rock slopes up to 100 m depth (Gischig et al., 2011b) and affect deep-seated gravitational slope deformations (Gischig et al., 2011a;Rouyet et al., 2017;Watson et al., 2004).Therefore, thermal changes can decrease rock slope stability with time (preparatory factor) and potentially cause landsliding (triggering factor).

Conclusion
Thermal-induced rock deformation can cause fracture movement and thermal stresses able to breakdown rock.Cyclic thermal rock deformation follows a cooling and warming phase with different thermal expansion coefficients.The transition between these phases are characterised by both rock contraction and expansion and thermal cycles show a hysteresis effect observed in the laboratory and the field.Snow cover controls the number of daily temperature changes, while topographic factors influencing insolation (e.g.aspect) controls the magnitude of temperature changes.Months-long slow crack opening occurred within a temperature range between -9 and -1°C suggested that ice segregation caused slow fracture opening reversed by ice relaxation.Depending on the dipping of shear planes, thermal changes on annual scale causes rock creeping that widen or shorten fracture aperture.Cycles of thermal-and ice-induced crack opening and closing can progressively weaken rockwalls and trigger rockfall.Climate change will shorten snow duration and increase temperature extremes, therefore, will affect the number and the magnitude of thermal changes and associated stresses.However, an earlier snowmelt in combination with temperature increase will decrease the occurrence of ice segregation and will shift the frost favouring temperature regime to higher altitudes.Therefore, climate change will change the frequency, magnitude and the location of thermal and ice-induced stresses and will change the spatial variation of rockfall in alpine environments in the future.4).

Figure 2 :
Figure 2: (a) Cooling chamber with aplite sample from RW-1.(b) Schematic illustration of the sensors at the rock samples.Rock deformation (RD) was measured by two crackmeters.Thermistors record rock-top temperature (RTT) for temperature correction of RD.Two temperature sensors measured rock temperature in 2 cm (RT2cm) and 5 cm (RT5cm) depth.

Figure 3 :
Figure 3: (a) Three crackmeters were attached on two large (>2 m) aplite blocks at RW-1 at 2935 m.(b) At RW-2 at 2672 m, two crackmeters were installed on densely fractures amphibolite blocks.Crackmeters monitor CD and RD of schistose quartz slate (c) at RW-3 at 2585 and (d) at RW-S at 2723 m.

Figure 4 :
Figure 4: (a) Air temperature and snow depth from meteo station Oberer Stelligletscher plotted for the period from September 2016 to August 2019.Rock surface temperatures (red lines) and mean 10-day RST (dark red line) recorded by iButtons installed at (b) RW1, (c) RW2, (d) RW3 and (e) RWS.Thermal stress was modelled using minimum α (light blue lines), mean α (blue lines) and maximum α (dark blue lines) Grey rectangles highlight the data gap filled with modelled air temperatures in (a) and snow cover (be).Numbers represent measured Schmidt hammer rebound values R.

Figure 5 :Figure 6 :
Figure 5: Laboratory crackmeter measurements of rock samples.(a) Rock-top temperature (RTT), rock temperature (RT) and rock deformation (RD) of crackmeter 1 and 2 plotted versus time for the schistose quartz slate sample (QS).(b) Rock deformation plotted versus rock-top temperature or rock temperature for crackmeter 2 of QS.Numbers indicate the timing of the beginning of the cooling period (black dot), end of the cooling period (black rectangle) and beginning of the warming period (black triangle).Arrows 655

Figure 7 :
Figure 7: Monthly mean crack deformation plotted versus monthly mean crack-top temperature for individual crackmeters.Red 675

Figure 9 :
Figure 9: Daily crack deformation plotted versus daily crack-top temperature for (a) RW1, (b) RW2, (c) RW3 and (d) RWS in 2018/19.Numbers n indicate the number of daily cycles, NA highlights incomplete measurements during the period due to instrument failure.For results of all periods, see Fig. S5 in the supplementary information.

Figure 10 :
Figure 10: Conceptual illustration of (a) thermal-induced rock kinematics, (b) thermal-induced fracture kinematics, (c) ice-induced fracture kinematics, (d) thermal-induced rock creeping on a shear plane dipping out of the rockwall and (e) thermal-induced rock kinematics on a shear plane dipping into the slope.Insets in (a) and (b) show daily temperature oscillation below snow cover and without snow cover.