The Destabilizing Effect of Glacial Unloading on a Large Volcanic Slope Instability in Southeast Iceland

Abstract

Since the turn of the 20th century, glacial thinning has been exposing volcanic mountain slopes around Iceland’s outlet glaciers. In the early 2000s, several slope instabilities appeared around the Svínafellsjökull outlet glacier in Southeast Iceland. The largest of these is located on a slope called Svarthamrar and is defined by a more than 2 km-long fracture system that separates the northernmost part of the mountain, south of Svínafellsjökull. Here we present updated glacier bed topography, a stratigraphical and structural assessment of the Svarthamrar slope, and quantify the destabilizing effect of glacial unloading from 1890 to deglaciated. Our results show that the slope was predisposed to instability by structural discontinuities and a strongly overdeepened glacial trough. Glacial unloading likely controlled the slope destabilization, potentially exacerbated by temporarily steeper hydraulic gradients due to rapid glacier thinning in the late 1990s and 2000s. The load of older landslide deposits on the glacier acts stabilizing on the slope. We propose that future glacial thinning will reduce the slope stability further, making it more susceptible to external triggers, and resulting in reactivation of the deformation and potential failure. Similar trends of destabilization can be expected for many slopes in Iceland and elsewhere.

1. Introduction

Global temperature rise since the beginning of the 20th century has led to glacial retreat across the planet [1,2,3]. As a result, retreating valley glaciers expose steep mountain slopes, which often adjust to the new conditions through slope processes [4,5]. Chronological clustering of landslide activity during and shortly after deglaciation in combination with temperature increase have been documented in studies from Scotland [6], Norway [7,8], and Iceland [9]. Whether, and how, a slope fails in these environments depends on the local combination of static (non-changing) boundary conditions, dynamic (changing over time) boundary conditions, and short-term triggering factor [10].

Static boundary conditions describe inherent characteristics of slope geology such as stratigraphy, physical rock mass properties and structural weaknesses. Short-term triggering factors cover any transient disturbances, such as seismic events, increased pore-water pressure due to extraordinary precipitation periods or excessive snowmelt, which critically reduce the slope stability [11]. Destabilizing changes of dynamic boundary conditions include temperature rise and increased average precipitation. These can have significant effects on glacier extent, mountain permafrost, and hydrology [12]. Glacial changes affect rock slope stability in several ways. Mechanical damage to the bedrock can occur due to glacial loading and unloading cycles [13,14,15]. Deglaciated slopes are exposed to atmospheric forces, which can lead to increased rates of mechanical weathering during the paraglacial period [16]. Rock slopes can also be critically weakened through weathering and progressive rock failure [17,18,19].

Glacier ice deforms by power law creep under their own mass or when an external stress is exerted [20]. When a large rock slope deforms into the side of a glacier, the ice will adjust through plastic deformation due to the density difference between the rock and glacier ice (ca. 3:1) [21,22]. Whether glacier deformation occurs in a plastic or brittle manner depends on the compressive strain rate caused by the protruding rock slope. Under low compressive strain rates (10⁻⁷–10⁻³ s¹) ice behaves in a plastic manner and at higher deformation rates (~>10⁻³ s¹) ice exhibits brittle behavior [21]. Therefore, it can be assumed that the shear strength of glacier ice has a neglectable stabilizing effect on rocks slopes that are deforming into the side of a glacier [23]. Consequently, the presence of glacier ice will not prevent deformation of an already critical rock slope but the elastic strength of ice at high strain rates may prevent the slope from rapid catastrophic failure [22,24]. Such glacier deforming slope movements have been described for example from New Zealand [22] and Switzerland [24].

Glacial unloading describes the reduction of glacier load, exerted on the subglacial slope, through thinning and retreat. For glacier marginal rock slopes that have not reached critical shear stresses to develop significant non-elastic deformation, glacial unloading may have a destabilizing effect [25].

Glaciers host confined aquifers, which are defined by the subglacial water pressure, which is controlled by the glacial overburden pressure [26,27]. Therefore, the maximum subglacial water pressure equals the glacial overburden pressure which represents the floatation limit of the ice. Subglacial water pressures at tidewater glaciers are often close to those values [26]. The water table within the surrounding bedrock is controlled by the water pressures in the adjacent glacier hosting valley. Hence, when the glacier thins, the glacial overburden pressure is reduced, which lowers the subglacial water pressure. That again increases the hydraulic gradient in the adjacent mountain slope temporarily, leading to lowering of the water table elevation over a certain timeframe and re-adjustment of the hydraulic gradient in the mountain. The time it takes for the water table to adjust depends on the hydraulic conductivity and other hydrological parameters [28,29,30]. In rock slopes, a steeper hydraulic gradient and/or higher water pressures generally reduce the slope stability [31].

Volcanic edifices are often susceptible to large slope failures due to relatively weak and chaotic rock assemblages [32]. Those can be mountain-scale volcanic debris avalanches triggered by volcanic activity (e.g., [33,34,35]) or classical rock slope failures (e.g., [12,36,37,38,39]).

Extensive landslide deposits are found in many formerly glaciated mountain valleys in Iceland (e.g., [40,41,42]). While glacial debuttressing is often described as a contributing factor in slope destabilization, the short-term effects of glacial unloading on adjacent slopes are still poorly understood.

In the early 2000s, the onset of a large slope instability was observed in the northern part of Mt. Svínafell in Southeast Iceland, on a slope called Svarthamrar. In this study we document the structural geology and stratigraphy of the Svarthamrar instability and put it in context with the geometry of the slope instability. We then model the slope stability for different potential failure surfaces across glacier scenarios to isolate and quantify the destabilizing effect of glacial unloading on the Svarthamrar slope instability (Figure 1).

Study Area

Iceland’s glaciers have lost about 16% of their mass between the end of the Little Ice Age (LIA), around 1890, and 2019 [43]. Most of that ice was lost at the outlet glaciers, some of which have thinned by more than 100 m and retreated by up to 8 km over that timeframe [44,45,46]. This ice loss is progressively exposing steep glacially eroded troughs, especially along the southern margin of the Vatnajökull Ice Cap.

Öræfajökull [63.999, −16.652] is a stratovolcano and Iceland’s highest mountain at 2110 m a.s.l. It hosts an ice cap which forms the southernmost part of the Vatnajökull Ice Cap (Figure 1). The Öræfajökull Ice Cap has several outlet glaciers to the west, south and east. One of these outlet glaciers on the volcano’s eastern flanks is called Svínafellsjökull. The valley sides are characterized by the steep mountain slopes of Mt. Hrútsfjall [64.051, −16.770] (1854 m a.s.l.), Mt. Hafrafell [64.035, −16.839] (1157 m a.s.l.) to the north, and Mt. Skarðatindur [64.008, −16.785] (1087 m a.s.l.)—Mt. Svínafell [63.982, −16.816] (893 m a.s.l.) massif to the south. On the northern flanks of this mountain, south of Svínafellsjökull, lies a slope named Svarthamrar [64.011, −16.815]. It consists of rugged cliffs in the lower parts and grades into a more plateau-like morphology higher up. On this mountain side lies the slope instability which is the focus of this study.

The Öræfajökull volcano lies outside of the active plate boundaries [47] and is therefore not directly affected by significant stresses from plate spreading, which means that large magnitude tectonic earthquakes are unlikely to occur [48]. However, significant seismic events associated with volcanic activity of Öræfajökull have been documented preceding the two historic eruptions of 1362 and 1727 AD [49] and during a phase of magmatic dyke intrusion between 2016 and 2018 [50]. Einarsson [49] documents that earthquake activity around Öræfajökull can produce ground acceleration that causes severe shaking and even collapses of housing structures. Therefore, earthquakes with a magnitude of up to 5 are realistic around Öræfajökull. 13 eruptions have been associated with Öræfajökull during the Holocene [51]. Realistic triggering factors around the volcano are therefore seismic activity [49], increased precipitation [52,53], extensive snowmelt [54], or ground deformation due to volcanic activity [50].

Helgason and Duncan [55] describe the stratigraphy of Mt. Svínafell, just west of the study area and within the same mountain massif (Figure 1). Their study implies somewhat continuous stratigraphy up to the Svarthamrar slope instability. The lowest strata on the western part of the massif in Mt. Svínafell are reversely magnetized, sub-horizontal to horizontal sequences of tholeiitic lavas and red interbeds, with an approximate age of 4 million years (Upper-Gilbert magnetic chron). These rocks were formed prior to major glacial conditions in the area. By comparison of strata on both sides of Svínafellsjökull, i.e., in Mt. Hafrafell on the north side [56] and Mt. Svínafell on the south side [55], correlation has established that both sections have tholeiitic basalt lavas near the base that dip gently toward northwest. Glacial erosion has, however, caused considerably greater removal at Mt. Svínafell where the tholeiite lavas near the base at are overlain by much younger normally magnetized volcanic products of the Öræfajökull volcano which were dated to Brunhes age (<0.78 Ma) [55]. This sequence is up to 800 m thick. Glacial erosion and glacial marginal eruptions have shaped Mt. Svínafell to the state it is today. The Öræfajökull volcanics are characterized by sequences of massive phreatomagmatic tuffs and breccias and sub-aerially erupted basaltic and intermediate lavas, highlighting the changes between glacial and interglacial periods [55]. On the northern side of Mt. Svínafell, younger glacier-marginal and subaerially erupted volcanics were deposited on steep glacially eroded surfaces.

A previous study highlights a cluster of slope instabilities around Svínafellsjökull and discusses the morphology and deformation history of the Svarthamrar slope instability [25]. The largest of those instabilities is represented by over 200 sinkholes and a ca. 2 km long fracture that cuts across Mt. Svínafell and marks the visible extent (ca. 0.9 km²) of the Svarthamrar slope instability (Figure 1). Rotational or composite sliding of a minimum volume between 50 and 150 million m³ was suggested as a possible failure mechanism [25]. The up to 40-cm-wide main fracture started opening sometime between 2003 and 2007 which coincides with a period of rapid glacier thinning. Monitoring data shows that the slope deformed until 2018. Between 1994 and 2011 the glacier experienced the fastest thinning rates (~3 m/yr) since the end of the LIA. Thereafter, the glacier thinning in front of the Svarthamrar slope instability stopped, partly due to insulation after the deposition of a debris avalanche in 2013 [52]. The load of the debris (ca. 12 million t) reset the load on the subglacial slope to about 2007 values. The correlation between the onset of slope deformation during a phase of significant glacial thinning and the current stop of movement after a reduction of glacier thinning indicates that the Svarthamrar slope instability is likely somewhat controlled by the glacier load on the subglacial slope. In 2023 the debris still covered most of the glacier surface below the Svarthamrar slope instability. However, as the debris is being transported down-glacier at a rate of ca. 120 m/yr the glacier surface affected by surface ablation will gradually increase over the next years.

The slope morphology around Svarthamrar [25] and a bulky terminal moraine with an unusually high percentage of supraglacially transported material [57,58,59], suggest past landslide activity in the Svínafellsjökull catchment. Rock temperature measurements and regression show that permafrost is likely absent from the area and has thus no influence on the destabilization of the slope [25].

2. Methods

2.1. Geological and Structural Mapping

Geological field surveys were conducted in the summers of 2020–2022 to map structures, stratigraphy, and were correlated to previous work by Helgason and Duncan [55,56,60]. A Brunton compass clinometer was used to measure the dip and dip direction of discontinuities such as joints, erosional surfaces, and depositional horizons on suitable surfaces. Measurements of surfaces within dense and chaotic jointing, forming interlocking blocks in effusive volcanics, were neglected. Locations were recorded with a handheld GPS (Garmin S64). A handheld fluxgate magnetometer [61] was used to determine the polarization of volcanic rocks. Based on the magnetic polarity it was possible to distinguish Brunhes-aged volcanic rocks from older volcanics. The magnetic results were compared with the results in Helgason and Duncan [55] and Singer [62].

Since many parts of the study area are inaccessible, high-resolution drone imagery and photogrammetry was used to extrapolate stratigraphic units into steep terrain. The creation of the used 3D-mesh is described in Ben-Yehoshua et al. [25] and the data can be viewed at: https://v3geo.com/model/471 (accessed on 1 December 2024).

Three-dimensional (3D) mapping of structures was conducted with the MOVE suite (Version 2023.1, © Petex Limited, Guildford, UK) . In combination with recorded geological and structural information from the field, visible contacts and fractures were manually traced with 3D polylines. Those polylines were then interpolated by kriging to triangular irregular networks (TIN) surfaces. Within the software the poles for each triangle and averages for whole TIN surfaces were then computed. Poles from the measured and computed surfaces were plotted in stereonets with the Dips software (Version 7, © RocScience, Toronto, ON, Canada).

The stratigraphic units that were traced in 3D were then exported for 3D visualization in QGIS. Areas where it was not possible to infer units, due to sediment cover, were marked with the respective type of sediment.

To identify whether a dominant fracture orientation exists in the research area, structurally controlled lineations were mapped (Figure S1). Linear features longer than 10 m, independent of origin, stratigraphic unit, and orientation, were traced with polylines based on the DEM and RGB orthomosaic produced from drone photogrammetry [25] and a lidar DEM [63]. Mapped features include linear fractures such as dykes, canyons, ridges, and erosive structures on cliff sides.

2.2. Radio Echo Sounding and Glacier Bed

To improve glacier bed topography acquired by Magnússon et al. [64] an about 9 km long radio echo sounding (RES) profile was measured on Svínafelsjökull on October 4th, 2022 (Figure S2). The survey was conducted by three surveyors walking in line, with the front arm of the receiver antenna located between the first surveyor and the receiver unit (Blue System Integration Ltd., Vancouver, BC, Canada, see [65]), carried by the second surveyor who as well carried a differential GNSS (dGNSS) receiver. The third surveyor (in the back) carried the transmitter (5 MHz) 24 m behind the receiver. A recording interval of 3 s was used which corresponds to about one measurement every 2 m at typical walking speed. Each measurement point was assigned to a GNSS location (vertical and horizontal accuracy <0.5 m). The survey position corresponding to the location of the center point between the receiver and transmitter is assumed to be the location in the tracked dGNSS survey profile, 12 m (half antenna separation) in front of given transmitter position (third surveyor). The RES data was then 2D-migrated, and bedrock reflection traced as explained in Magnússon et al. [66]. Profile migration was carried out using a signal propagation velocity through the glacier (c_gl) of 1.68 × 10⁸ m s⁻¹. The c_gl value in temperate glaciers depends on density and water content of the ice. Generally, the depth average value of c_gl in the ablation area of Svínafellsjökull can be expected to be in the range of 1.6–1.7 × 10⁸ m s⁻¹ [67]. Bed reflections, detected during sharp turns, were excluded due to enhanced errors in the derived bedrock elevation at these locations [66]. The bedrock traces were exported as a list of X, Y, Z coordinates (Easting, Northing and bedrock elevation in meters above sea level), with 20 m length interval along survey profiles. This input was used for kriging interpolation of the bedrock in Surfer 23 (Version 26.1.216, © Golden Software, LLC, Golden, CO, USA), along with positions and corresponding elevation of the delineated glacier margin in 2011 within the bounds of the survey area.

The resulting surface showed that the glacier bed on Svínafellsjökull is closer to represent a U-shaped valley than presented in Magnússon et al. [64], where the derived bed topography resembled a V-shaped valley. In that study the topography was interpolated based on un-migrated RES point measurements, which skews the result towards more V-shaped valleys, whereas in this study such limitations are avoided by tracing bed reflection from 2D migrated RES traversing Svínafellsjökull. The topography for the part of the glacier bed which was not covered by the new RES survey was created by assuming a continuous U-shaped topography in combination with the lowest topography line of the Svínafellsjökull bed [64] and the 2011 glacier margin [63]. The shallower topography of the marginal area was adopted from Magnússon et al. [64]. The interpolation of the new glacier bed elevation model was done with kriging in the MOVE suite (© Petroleum Experts, LLC). Afterwards, the updated glacial bed topography was merged with the 2011 lidar data [63].

2.3. Stability Modelling

By modelling the slope stability, we quantify the stability loss due to glacial unloading. Furthermore, it enables us to estimate the effect different physical rock mass properties, changes in groundwater table, and exerted seismic ground acceleration at different glacier thicknesses on the Factor of Safety (FOS). FOS is a measure of overall slope stability of a defined mass and is calculated as the ratio of resisting forces divided by driving forces [68]. When the driving forces exceed the resisting forces the FOS goes below 1.0, meaning that failure should occur. The aim of the modelling is not to reconstruct the slope perfectly or the current stability exactly, but rather to quantify the destabilizing effect of glacial unloading by calculating the FOS for different glacier scenarios.

To illustrate the FOS results as percentages of other scenarios we used the normalizing function (1):

$${FOS}_n={\displaystyle \frac{FOS\left(t\right)}{FOS\left(A\right)}}\times 100$$

(1)

where FOS(t) is the calculated FOS result of a certain scenario t relative to a baseline scenario FOS(A) and FOS_n is the ratio of the two. Based on FOS_n the normalized values were separated into percentage steps measuring the deviation from 100%.

Slope stability modelling was performed with the software Slide3 (© RocScience, LLC). Slide3 works with 3D models and applies the Limit Equilibrium Method (LEM) based on the limit plastic equilibrium that divides the failure mass into columns (80 × 80 columns in our model). Based on the input parameters the software calculates the forces affecting each column. Every run does 100 model iterations. The results of each column are then combined, and an overall FOS is calculated.

The 3D geological glacier-extent models were built by inserting triangulated surfaces of the mountain-and glacier bed topography into Slide3. These surfaces were derived from the described subglacial topography and lidar data [63] which was downsampled to a triangle side length of 100 m. The extent of the model includes the glacial trough of Svínafellsjökull and the surrounding mountain slopes.

2.3.1. Stratigraphic Units and Model Parameters

Based on the geological mapping (results chapter) the stratigraphy for the presented modelling approach was separated into two units (Figure 2 and Figure 3). The basement is made of Miocene, Pliocene and Matuyama age [55], basalt dominated, rocks (pre-Brunhes age (>780 ka) rocks—grey unit in Figure 2 and Figure 3). The overlying unit of Brunhes age rock that is dominated by hyaloclastite and tuffaceous breccias with intercalated subaerially erupted lavas and sediments.

For the material properties, the Brown–Hoek failure criterion [69] was applied to the rock masses. Therefore, the uniaxial compressive strength (UCS), the geological strength index (GSI) and the material constant for intact rock “m_i” must be defined. Since no laboratory tests on the rock masses have been performed and especially the quaternary unit is very heterogeneous, we used a range of UCS parameters from similar rocks from different literature and databases [70,71,72,73]. The same database was used for the applied rock densities (transformed into specific weight). The GSI value is a measure for the extent of rock fracturing and the joint surface quality [69]. GSI ranges for Brunhes, and pre-Brunhes age rocks were estimated by comparing observations from the field with the basic GSI chart (Figure 4c; chart explanation [69,74]. m_i values for the dominating rock types in these units (Brunhes-tuff and pre-Brunhes-basalt) were chosen from a database within the Slide3 software. We selected the lower limit of the m_i ranges due to the heterogeneity of the units.

As explained in the introduction, glacier ice will not resist a laterally intruding rock mass but rather adjust through plastic or brittle deformation [21]. To create this effect, the parameters controlling the shear strength of the ice must be reduced to a minimum, so that the only significant force exerted by the ice is the normal force of the glacier load on the subglacial slope. Based on these requirements we applied the Mohr-Coulomb failure criterion [75] and reduced the friction angle Φ and cohesion c both to 0.1. These parameters ensure neglectable shear strength within the glacier and enable us to isolate the effect of glacial unloading on the FOS.

The parameter ranges assigned in the model scenarios are outlined in

Table 1. The parameters applied for the modelling scenarios. Abbreviations and symbols: UCS—uniaxial compressive strength; GSI—Geological Strength Index; m_i—Hoek-Brown material parameter explained above; γ—Specific weight; c—cohesion; Φ—friction angle, k—seismic load coefficient; WT—water table scenario. γ—and UCS values were averaged for similar rock types from different databases [71,72,73,74]. The values for the material constant m_i were estimated by comparing field observations with data in the Slide3 software’s database.

	Pre-Brunhes Age Rocks				Brunhes Age Rocks				Glacier			Other Settings
Scenario	UCS [MPa]	GSI	mi	γ (kN/m3)	UCS [MPa]	GSI	mi	γ [kN/m3]	γ [kN/m3]	c [kPa]	Φ [°]	k	WT
A	50	20	17	28	10	20	13	26	9	0.1	0.1	0	A
B	110	35	17	28	50	40	13	26	9	0.1	0.1	0	A
C	50	20	17	28	10	40	13	26	9	0.1	0.1	0	A
D	50	20	17	28	50	40	13	26	9	0.1	0.1	0	A
E	50	20	17	28	50	20	13	26	9	0.1	0.1	0	A
F	50	35	17	28	10	20	13	26	9	0.1	0.1	0	A
G	50	35	17	28	50	20	13	26	9	0.1	0.1	0	A
H	50	35	17	28	50	40	13	26	9	0.1	0.1	0	A
I	110	20	17	28	10	20	13	26	9	0.1	0.1	0	A
J	110	20	17	28	10	40	13	26	9	0.1	0.1	0	A
K	110	20	17	28	50	40	13	26	9	0.1	0.1	0	A
L	110	20	17	28	50	20	13	26	9	0.1	0.1	0	A
M	110	35	17	28	10	20	13	26	9	0.1	0.1	0	A
N	110	35	17	28	10	40	13	26	9	0.1	0.1	0	A
O	110	35	17	28	50	20	13	26	9	0.1	0.1	0	A
P	50	35	17	28	10	40	13	26	9	0.1	0.1	0	A
AS0	50	20	17	28	10	20	13	26	9	0.1	16.7	0	A
AS1	50	20	17	28	10	20	13	26	9	0.1	16.7	0.01	A
AS2	50	20	17	28	10	20	13	26	9	0.1	16.7	0.05	A
AS3	50	20	17	28	10	20	13	26	9	0.1	16.7	0.1	A
BS0	110	35	17	28	50	40	13	26	9	0.1	16.7	0	A
BS1	110	35	17	28	50	40	13	26	9	0.1	16.7	0.01	A
BS2	110	35	17	28	50	40	13	26	9	0.1	16.7	0.05	A
BS3	110	35	17	28	50	40	13	26	9	0.1	16.7	0.1	A
WT-syn	50	20	17	28	10	20	13	26	9	0.1	0.1	0	WT-syn
WT-lag	50	20	17	28	10	20	13	26	9	0.1	0.1	0	WT-lag

and an overview of the individual modelled results are presented in Table S1A,B.

2.3.2. Slip Surfaces

Since the geometry of the incipient slip surface is unknown, hypothetical surfaces were created based on the mapped extent of the main fracture on the surface of the slope [25]. A rotational failure surface was chosen since the majority of known large rock slope failures in Iceland occurred rotational [39,40,76,77]. The horizontal extent (ca. 2 km) of the main fracture, cutting several lithological units along a vertical range of at least 400 m suggests that the instability penetrates deep into the bedrock. The fracture dimensions were used to create a boundary towards the south in Slide3 to calculate potential slip surfaces that would result in a comparable fracture pattern. Using the LEM favorable spline surfaces were calculated by the software of which four were chosen to represent different extents of the involved rock mass. Spline surfaces have been found to be more realistic representations of failure surfaces than spherical or ellipsoidal geometries [78,79]. The constructed slip surfaces all facilitate rotational movement and are illustrated as SL1 to 4 in Figure 2. The following rock volumes are involved in the tested failure surfaces: SL 1 = 547.4 × 10⁶ m³, SL 2 = 268.4 × 10⁶ m³, SL 3 = 178.5 × 10⁶ m³, and SL 4 = 97 × 10⁶ m³. The volume of SL 4 lies withing the minimum volume range suggested by Ben-Yehoshua et al. [25].

2.3.3. Glacier Scenarios

Eight different scenarios were built with the described bed topography but varying glacier thicknesses (Figure 2 and Figure 3) and extents from 1890 to completely deglaciated. Since there was only minimal glacier lowering between 2011 and 2013 the pressure of the 2013 debris avalanche of 70.11 kN/m² [25] was added to the 2011 glacier surface to create the 2013 glacier scenario (Formula (2)). The surface of the mountain side was updated based on the post 2013 debris avalanche DEM [80]. For the 2011-50 m and 2011-100 m scenarios the 2011 glacier surface was lowered by 50 and 100 m respectively (Figure 2). These scenarios aim to represent potential future glacier surfaces within a similar scale as in the time from 1890 to 2011. In the last scenario the valley is entirely deglaciated and hosts a lake which has the same level as the 2011 pro-glacial lake runoff.

The pressure was calculated with the mass of the 2013 debris avalanche (12.16 × 10⁶ t) distributed evenly on the glacier area covered 1.7 × 10⁶ m² [25]:

$$P={\displaystyle \frac{F}{A}}={\displaystyle \frac{M\times g}{A}}$$

(2)

where P is the pressure, F is the load of the debris, M is the mass of the debris, g is the gravitational acceleration (9.81 m s⁻²), and A is the glacier area covered by the landslide debris.

2.3.4. Water Surfaces

The location of the water table within the slope has a significant effect on the slope stability. However, there is no information on the water pressures within the glacier or in the surrounding bedrock. Therefore, the following water tables and confined aquifers are based on the minimum and maximum values for the glacier. To isolate the effect of glacial unloading on the different physical property scenarios (A–P) the calculations were performed with a minimum water table (WT-A in Figure 2) that is defined by the elevation of the pro-glacial lake. The elevation of the pro glacial lake is controlled by the lake runoff at 88 m a.s.l.

To assess the effect of the groundwater table being controlled by the subglacial water pressures on the FOS we assume a certain hypothetical hydraulic gradient within the bedrock that somewhat follows the topography (WT-syn in Figure 2). Between glacier scenarios the water table is adjusted at the same rate as the glacier thinning rate. In scenario WT-lag (Figure 2) the effect of transiently high hydraulic gradients due to a lag of water table adjustment during rapid glacier thinning on the FOS is calculated. If the hydrological conditions in the area allow for such a lag it most likely occurred during the period of rapid glacier thinning between 1994 and 2011. For the WT-lag scenarios, a 10-year-lag of the water table in the bedrock for the 2003, 2011, and 2013 scenarios was assumed. 10 years may be exaggerated for this setting; however, the timeframe was chosen to highlight the potentially destabilizing effect of such a hydraulic lag. Seasonal variations of groundwater level might be substantial [27,81] but are not considered in these calculations. Since the subglacial water pressures adjust with the glacier thinning, a steeper hydraulic gradient is achieved for scenarios 2003, 2011, and 2013. The scenarios (WT-syn and WT-lag) show the same glacier elevation scenarios but with a hypothetical, unconfined water table in the bedrock and a confined water table within the glacier, just below the floatation limit. For WT-lag a datapoint at the year 2020 was added where we assume the same glacier level as 2011/2013 but with adjusted water table. To calculate the elevation of the hydraulic head at the floatation level of the glacier the following Formula (3) was applied:

$$h_p=h\times {\displaystyle \frac{{\rho }_i}{{\rho }_w}}$$

(3)

where h_p is the maximum hydraulic head relative to the valley floor, h is the maximum glacier thickness, ρ_i is the density of ice (900 kg × m⁻³), and ρ_w is the density of water (1000 kg × m⁻³). Based on this the maximum h_p can be expected at 90% of the thickness of glacier. The glacier elevation was therefore lowered by the difference between h and h_p and assigned as a confined water table within the glacier. Since the presented setup is a simplified experiment to test the sensitivity of the FOS to the described processes seasonal variations in sub-glacial water pressure or short-term changes in pore-water pressure due to rainwater infiltration were not considered.

2.3.5. Seismic Scenarios

Seismic activity up to magnitude 5 was deemed realistic in association with magma movements within the volcanic system of Öræfajökull. Since the research area lies on the flanks of Öræfajökull (Figure 1) and only ca. 6 km away from the volcano’s caldera rim, seismic activity at the caldera is likely to affect the unstable slope. To test the sensitivity of the FOS to seismic activity, several seismic load coefficients (k) were applied to Scenarios A and B (AS 0–3 and BS 0–3, Table 1). The seismic load coefficient is a dimensionless coefficient which represents an additional component of vertical and horizontal load on a rock mass created by the ground acceleration during a seismic event. The relation for a maximum seismic coefficient is described as the ratio (4):

$$k_{max}={\displaystyle \frac{PGA}{g}}$$

(4)

where k_max is the highest possible seismic load coefficient during a seismic event, PGA is the peak ground acceleration at site, and g is the gravitational acceleration. Higher k values represent stronger ground acceleration. The local PGA is not only related to the energy released by an earthquake (magnitude) but also by the ground type, distance to the hypocenter, and topography. Modelling experiments were conducted with the values for k of 0.01, 0.05 and 0.1 [48,82,83]. For simplicity reasons we applied the same k value to the horizontal (k_h) and vertical component (k_v).

Since seismic acceleration involves fast-loading conditions, the glacier is likely to behave as a brittle material and would resist the deformation with a certain shear strength. Therefore, for the seismic scenarios, we apply the internal friction μ = 0.3 for ice at −2.5 °C [21] which is converted to a friction angle Φ = 16.7° in the Mohr-Coulomb failure criterion (5):

$$\Phi =arctan\left(\mu \right)$$

(5)

3. Results

3.1. Geology and Important Structures

The stratigraphy in the research area is a complex arrangement of subaerially- and subglacially erupted volcanics and occasional clastic sediments, these are cross-cut by ten erosive horizons (Figure 5a and Figure 6). The stratigraphy was separated into Brunhes-aged rocks and pre-Brunhes-aged rocks. This separation was conducted by measuring the polarization of volcanic rocks across the stratigraphy. The Brunhes age volcanics are dominated by subglacially erupted tuffs, breccias and hyaloclastites, with intermittent subaerial lavas of basaltic and intermediate composition with exclusively normal polarization. The Brunhes age rocks were separated into older (with dyke intrusions) and younger (no dyke intrusions) units. The pre-Brunhes age rocks are dominated by subaerially erupted basaltic lavas with occasional sedimentary interbeds. The polarity of the lavas within this unit alternates several times between reverse and normal polarities showing that this stratigraphy was deposited before the Brunhes age. The jointing within most subaerially erupted lavas across the unstable slope form tightly interlocking blocks (Figure 4a), whereas the hyaloclastites and tuffaceous breccias usually form less jointed, massive units (Figure 4b). Due to numerous erosive horizons and heterogeneity across the study area, four logs were established (Figure 5 and Figure 6). All logs share the same basement unit which extends across the study area. The basement unit consists of fine-grained lavas between 2–10 m thick separated by red sedimentary interbeds (Figure 4a). Most lavas are fine grained and occasionally, sparsely phyric. The basement lavas dip gently (2–6°) towards to west and northwest.

Log 1 [64.017, −16.794 to 64.0103, −16.7983] (Figure 5 and Figure 6) lies on the eastern segment of the Svarthamrar slope instability and covers a vertical range of 520 m. The basement unit described above is exposed at the bottom of the log (Figure 4a). Thick deposits of the LIA lateral moraine from Svínafellsjökull and talus obscure about 100 m of the stratigraphy (question mark in Figure 6 Log 1). On top of this moraine a few layers of normally and reversely polarized, phaneritic basalt lava are exposed. These are crosscut by a boundary, above which a thin layer of diamictite containing striated clasts in a silty matrix was mapped. Above the diamictite lies a massive, tuffaceous breccia with a rust-colored matrix and steep bedding (~60°) towards north. This unit extends about 100 m vertically and hosts a dense network of dyke and sheet intrusions. Above lies an up to 50 m thick diamictite with horizontally aligned, partly striated clasts. The conglomerate transitions into a finer grained, horizontally bedded sandstone with angular clasts. On top of this unit a basaltic lava flow was deposited. At about 730 m a.s.l. this lava flow is eroded and overlain by a massive, about 80 m thick, orange-brown hyaloclastite. The highest unit in this log is a succession of subaerial lavas of basaltic and potentially intermediate composition that form an up to 60 m tall near-vertical cliff. The entire stratigraphy of Log 1 is affected by dyking.

Log 2 [64.0152, −16.8094 to 64.0095, −16.8056] (Figure 5 and Figure 6) is located east of the center of the instability and spans a vertical range of 520 m. The lowermost part is covered by glacial till from the lateral moraine, but the same basement unit as seen in Logs 1, 3 and 4 can be inferred with high confidence. At around 500 m a.s.l. a sequence of basaltic lavas of 2 to 8 m thickness is exposed. These are cut off at an erosional boundary overlain by a grey diamictite layer containing striated clasts. Above, steeply bedded tuffaceous breccia was deposited which is overlain by a ca. 40 m thick diamictite unit with striated clasts. An erosive contact separates this unit from a ca. 120 m thick unit of tuffaceous breccia with rust-colored matrix (Figure 4b). At about 780 m a.s.l. a 1 m thick diamictite with striated clasts separates the underlying tuffaceous breccia from a finer grained, lighter colored tuffaceous breccia. This is overlain by a thin layer of red scoria followed by a unit of aphanitic, platy lava.

Log 3 [64.0138, −16.8203 to 64.0087, −16.8143] (Figure 5 and Figure 6) is located about 400 m west of Log 2. The top of the basement unit is limited by an erosive contact which is overlain by up to 15 m-thick, highly lithified diamictite with sub angular-subrounded, boulder sized clasts in a fine-grained matrix. Above this lies a sequence of basaltic lavas with varying phenocryst content and layer thicknesses between 2 and 5 m. Both normal and reverse polarity was measured in different lavas across this unit. Occasional thin, sandy interbeds are found between the lava layers. It is cross-cut by an erosional boundary and overlain by a 1-m-thick layer of diamictite with striated clasts. On top lies a fine-grained clay- and silt stone that contains horizontal sand layers that gradually transition to a massive, ca. 50 m thick sandstone with horizontal horizons of angular clasts. The material is highly solidified and forms vertical walls with rectangular jointing. The sand grains consist of glassy and altered particles. Above this layer is another diamictite layer of ca. 3 m thickness that includes up to 50 cm diameter, striated clasts. A sequence of 2–6 m thick, phaneritic, basaltic lavas with varying magnetic polarization are deposited on top. This unit was traced across to Log 2 and likely Log 1. Separated by a 0.5–1 m thick layer of diamictite with striated clasts, lies a unit of ca. 70 m-thick, massive, tuffaceous breccia with a yellow-rust-colored matrix that also can be traced to Log 2. Dyke intrusions were observed throughout the log up to the erosive contact that demarks this unit. This contact is overlain by a diamictite with striated clasts and grey silty matrix. A massive, ca. 100 m thick, fine grained tuffaceous breccia overlies the diamict (which can also be traced to Log 2). This unit is overlain by a thin layer of red scoria followed by the platy lava as described on top of Log 2. aphanitic, platy lava.

Log 4 [64.0107, −16.8306 to 64.0065, −16.8257] (Figure 5 and Figure 6) is located on the westernmost part of the Svarthamrar slope instability. The top of the basement unit is limited by a 1 m thick diamictite with striated clasts, overlain by fine grained hyaloclastite with distinct bedding dipping at 25–35° towards the northwest. This unit becomes more massive higher up and transforms into a tuffaceous breccia with chaotically distributed palagonized clasts. This unit is overlain by cube-jointed, sparsely phyric, basaltic lavas that form vertical cliffs further west. The uppermost unit is the same as described in Log 2 and 3. In this log, all units overlying the basement are normally polarized and dyke intrusions are absent.

The diamictites with striated clasts across all logs and the highly solidified diamictite at the bottom of log 2 are interpreted as tillites deposited during glacial erosive periods. These horizons are daylighting with dip angles between 10° and 30°. Even though these erosive horizons were generally easier to excavate with a geologic hammer than the over- and underlying layers, no signs of shear or other deformation were noticed along these horizons.

3.2. Structural Observations

The subaerial lavas in the study area generally form tightly interlocking blocks (Figure 4a) or plates, with weathered joint surfaces. Red interbeds are usually more easily eroded than the lavas. Subglacially erupted materials (tuffaceous rocks and hyaloclastites) are also softer and less fractured than the subaerial lavas.

The ca. 2-km-long southernmost alignment of sinkholes and bedrock fractures (Figure 5) was inferred to have an underlying connected fracture system which is here referred to as the “main fracture”. The sinkholes are usually elongated depressions where sediment collapsed into underlying fractures (Figure 7a,c). In most cases there is fresh debris on the slopes of the sinkholes with no or collapsed vegetation. At the bottom of some sinkholes a bedrock fracture is exposed (e.g., Figure 7c). Bedrock fractures in the area don’t exhibit a vertical offset and instead only show horizontal opening (e.g., Figure 7d). The main fracture is between 20 and 50 cm wide, extends ca. 2 km across the entire Brunhes age stratigraphy over a vertical range of at least 400 m. Due to sediment cover on the east and west side of the main fracture it was not possible to trace the fracture down into the pre-Brunhes age rocks.

The bedrock fracture in Figure 7c strikes at 35° (dipping 75°) whereas the general alignment of sinkholes in this area strikes at 95°. This observation suggests that the western part of the main fracture consists, at least partly, of en-echelon fractures that form aligned sinkholes on the surface.

The easternmost segment of the main fracture can be traced into the steep cliff (orange surface with yellow boundary in Figure 6). Tracing the lineation of the bedrock fracture and interpolating the resulting 3D-line with kriging to a surface, yields a dip of 73° towards an azimuth of 154°. Indicating that this segment of the fracture is dipping in the opposite direction to the slope, resembling what had been observed on the western side of the main fracture.

Just east of the easternmost segment of the main fracture, a vertical offset of ca. 15 m between lava layers of pre-Brunhes age is visible (Figure 7b and Figure 6, pink plane) which continues west into the direction of the Svarthamrar slope instability. The interpolated surface dips at 52° towards 7° azimuth. The vertical offset does not continue into overlying Brunhes-aged rocks, indicating that the deformation along the fault plane occurred before the deposition of the younger volcanics. Tracing the fault to the east it aligns with the steeply eroded north face of Mt. Skarðatindur.

North of the main fracture numerous smaller sinkholes and bedrock fractures occur within the unstable slope (Figure 5), indicating recent bedrock fracturing within the area of the Svarthamrar slope instability. The sediment cover across the Svarthamrar slope varies in thickness but is often more than 1 m thick, which prevents tracing the entire extent of the underlying bedrock fracture network. Inferred lines along the sinkholes (Figure 5) indicate that a fracture network is present on the slope. No large-scale morphological deformation features such as antiscarps, were observed on the slope. All tension cracks in this area are dipping 70–90°. Often the dip direction is towards the south, the opposite direction to the Svarthamrar slope.

At a smaller unstable rock slope west of the Svarthamrar slope instability a ca. 185 m long and up to 50 cm wide bedrock fracture cuts the basement lavas vertically (Figure 7d location in Figure 1). Rocks thrown into the fracture were heard bouncing between the sides of the crack for up to 9 s suggesting a depth of at least 50–100 m. The presence of this bedrock fracture shows that the harder basement lavas can form deep, vertical fractures.

Bedrock lineations were mapped across the study area in Brunhes- and pre-Brunhes-aged rocks to identify a potential tendency of the bedrock to form failures of all scales in a certain direction. Figure 5c shows that there is a clear distribution of bedrock lineations in both Brunhes and pre-Brunhes-aged rocks. The majority of lineations in both units are distributed along a strike of 60–80° which aligns with the eastern segment of the main fracture. The strike of the western part of the main fracture aligns better with the strike of the fault (Figure 7b and pink plane in Figure 6).

3.3. Modelling Results

The calculated FOS values from all stability model runs can be reviewed in Table S1A,B.

3.3.1. Scenarios A–P

The modelling results of scenarios A to P (Table 1) with a constant water table WT A (Figure 2) show that the FOS for all pre-defined slip surfaces decreases as the glacier is thinning (Figure 8). However, the range of FOS reduction is different between the respective slip surfaces and only lasts as long as the slip surface extends below the glacier surface. Once the glacier surface has thinned below the extent of the slip surface there is no further destabilizing effect from glacial unloading (SL3 and SL4 in Figure 8). The resulting trendlines cluster in three general groups of FOS values based on the input values (Table 1). Scenarios with stronger rock mass properties generally have higher FOS values and weaker rock mass properties have lower calculated FOS values (Table S1A,B). For SL 1–3 the physical properties of the pre-Brunhes basement unit are controlling the calculated FOS more and for SL 4 (the shallowest) the strength parameters of the Brunhes age rocks have a bigger impact on the FOS. The rock strength parameters have a bigger impact on the resulting FOS than the selection of slip surfaces. Figure 8 shows clearly that the trendlines of the same slip surfaces follow an almost identical trend.

The additional load of the 2013 debris avalanche deposits on the glacier increases the FOS compared to the 2011 scenario (

Table 2. Mean relative FOS reduction for the slip surfaces (SL 1–4) due to glacial unloading of the glacier, seismic scenarios (k) for scenarios A and B (white), and water table scenarios WT-syn (light grey) and WT-lag (bold and dark grey). The rows of the glacier scenarios 1890 to “no glacier” show the FOS loss (%) relative to the respective 1890 scenario. The values of the seismic scenarios (k) are relative to the respective glacier scenarios without applied seismic coefficient (Figure 9b).

Glacier Scenario	SL1	SL2	SL3	SL4
1890	0	0	0	0
1994	−6.8	−8.3	−6.2	−4
2003	−9.5	−11.3	−8.3	−5.4
2011	−12.4	−14.6	−10.6	−6.8
2013	−11.6	−14.3	−9.7	−6.4
2013-50 m	−18	−19.9	−13.3	−7.9
2013-100 m	−23	−24.2	−15.4	−8
no glacier	−35.6	−31.8	−16.6	−8
k = 0.01	−1.8	−2.5	−2.4	−2.2
k = 0.05	−8.2	−10.9	−10.9	−9.7
k = 0.1	−14.8	−19.3	−19.4	−17.5
1890	0	0	0	0
1994	−2.9	−3.0	−0.1	3.4
2003	−2.8	−2.6	1.3	5.2
2003	−3.8	−4.4	−0.8	3.2
2011	−4.4	−4.3	0.5	4.1
2013	−3.6	−3.3	2.1	4.4
2011	−3.0	−2.0	2.9	6.0
2013	−2.1	−1.1	4.4	6.4
2011-50 m	−5.0	−2.0	5.7	5.3
2011-100 m	−6.4	−1.9	7.5	5.3
no glacier	−13.6	−3.4	9.1	5.3

). Compared to the overall loss of FOS across all glacier scenarios this stability increase is small (0.3–0.8%) but nevertheless, the FOS is reset to values that occurred in the late-2000s.

To analyze how the different applied physical properties affect the FOS reduction, the calculated results were normalized relative to the 1980 FOS results and transformed into percentage (Equation (1)). All normalized results from A–P (Table S1A,B) of the same slip surface and glacier scenario are similar within a standard deviation of 0.45%, indicating that the resulting trendlines have the same function within this uncertainty. The average normalized results from scenarios A–P are plotted as dashed lines in Figure 9a which shows their range of the FOS reduction. Reducing the glacier thickness has the smallest effect on the shallowest SL4 (dashed line with triangle markers), which only experiences about 8% FOS loss from 1890 to the 2011-50 m glacier scenarios and then stabilizes. A slightly steeper trendline was calculated for SL3 (dashed line with square markers) which loses about 16% between the 1890 and 2011-100 m glacier scenarios and then stabilizes. SL2 and SL1 have comparably steep gradients, and both become deglaciated between the last two scenarios with a total FOS loss of 31.8% and 35.6%, respectively.

3.3.2. Seismic Acceleration

All glacier scenarios applied with the weakest and strongest rock mass property scenarios (A and B) were modelled with seismic coefficients k as 0.01, 0.05, and 0.1 representing increasing strengths of ground acceleration. The relative FOS reduction compared to the non-seismic scenario is consistent within 2% standard deviation for the respective seismic loads throughout the different glacier scenarios (Table S1A,B). The average values are presented in Figure 9a and Table 2. The higher the applied seismic coefficient (stronger ground acceleration) the more the FOS reduction compared to the non-seismic scenario. Applying a seismic coefficient of 0.01 reduces the FOS by 1.8–2.5% depending on which slip surface is affected. A seismic coefficient of 0.05 reduces the FOS by 8.2–10.9% and a seismic coefficient of 0.1 reduces the FOS by 14.8 to 19.4% depending on the slip surface (Table 2).

3.3.3. Scenarios WT-syn and WT-lag

The FOS results from glacier thinning-synchronous water table adjustment (WT-syn) and of a 10-year-lag of water table adjustment during rapid thinning (WT-lag) are presented in Figure 10. It shows that for S3 (black) and S4 (blue) the FOS increases throughout the glacial thinning, due to the lowering of the water table. For SL1 and SL2 the overall FOS decreases throughout the deglaciation.

Compared to WT-syn the values of WT-lag (dashed lines) show about 2% lower FOS values for all slip surfaces during the time of rapid glacier thinning between 1995 and 2011 and subsequent alignment of the trendlines as the thinning rate declined (Figure 10). During this period a “window” of lower FOS values is created due to the temporarily steeper hydraulic gradient in the mountain slope (Figure 2).

Compared to the FOS trends of the slip surfaces without water table adjustment (Figure 9a) the FOS trend of WT-syn decreases less (SL1 and SL2) or reverses and FOS values increase with decreasing glacier thickness (SL3 and SL4).

4. Discussion

4.1. Geology and Important Structures

The bed topography below Svínafellsjökull (Figure 2 and Figure S2) shows an, for Icelandic valleys, atypical, strongly overdeepened trough [64,84] which extends below 200 m below sea level. The geological and structural assessment revealed that the Svarthamrar slope instability affects rocks that originate from ice-volcano interaction, as well as subaerially erupted lavas. Ten, partly cross-cutting, erosive horizons with tillites, most likely originate from past glacial erosion. Most of these surfaces are dipping towards Svínafellsjökull and are overlain by subglacial and subaerial volcanics. This indicates that the glacier has been periodically active throughout the Brunhes age. This interpretation agrees with observations by Helgason and Duncan [55,60] further west on the mountain. Repeated glacial activity confined to a valley has been linked to overdeepening of glacial troughs [85] which is associated to a higher likelihood of slope instability [86] and [references within]. This atypical valley geometry might be a contributing factor why there is currently a cluster of slope instabilities and generally more signs of past landslide activity in the valley [25,52,57]. Along the inclined till horizons no signs of deformation were observed, showing that the slope instability does not follow these discontinuities. Based on the main fracture’s vertical and horizontal extent (400 m and 2 km respectively) and the fact that it cuts across the mapped stratigraphic units (Figure 5), it is likely 100’s of meters deep. This is further supported by other paraglacial landslide sites in similar geological locations in Iceland, where the headscarp has formed a 200–300 m tall, near-vertical wall [39,76,87].

The observation that the eastern segment of the main fracture strikes in the same direction as the overall tendency of rock failures in the research area (Figure 5c) and the western segment strikes in the same east-west orientation as the described normal fault (Figure 7b, pink plane in Figure 5b), indicates that the slip surface is somewhat controlled by inherent structures. Since the vertical offset along the normal fault was not observed in higher parts of the stratigraphy this discontinuity is likely an old tectonic feature that may be gravitationally reactivated [88]. The fault orientation aligns eastwards with the steeply eroded north face of Mt. Skarðatindur (Figure 1) indicating that failures along this weakness shaped the geometry of the mountain slope. A failure within the Svarthamrar slope instability could therefore occur along this discontinuity.

The absence of large-scale morphological deformation features across the Svarthamrar slope instability suggests that the deformation at the time of this study has not exceeded a stage of tension crack formation. However, a “one-foot-wide, bottomless crack” resembling parts of the main fracture on Svarthamrar was present on Mt. Innstihaus [63.658, −19.566] in South Iceland, before a large paraglacial rock avalanche and subsequent outburst flood occurred [39]. Ben-Yehoshua et al. [25] hypothesize that rock slope failures in Icelandic volcanic edifices occur after small-scale and short-term pre-failure deformation compared to what has been observed elsewhere [89]. Thiele et al. [90] modelled that volcanic edifices intruded by volcanic dyke networks tend to fail more suddenly since peak stresses are concentrated on dyke networks rather than on larger rock masses. Since intersecting dyke intrusions were observed in many parts of the Svarthamrar slope instability and dykes are ubiquitous to Iceland’s central volcanos this could explain limited pre-failure deformation. More research is, however, necessary to evaluate this theory in the context of Icelandic landslides.

4.2. Scenarios A–P and Seismic Acceleration

Ben-Yehoshua et al. [25] proposed that thinning of Svínafellsjökull to some extent controls the destabilization and deformation of the Svarthamrar slope instability and that the slope is currently at an equilibrium, indicated by a halt of deformation. Since glacier mass balance models predict the glacier to thin throughout the next decades [91], a simplified geological model (Figure 2 and Figure 3) was used in our study to test the destabilizing effect of glacial thinning and groundwater adjustment in the surrounding mountain slopes. As the applied model only accounts for the unloading of the glacier and no other additional forces that the ice may exert on the slope, the FOS reduction can be considered as minimum estimate.

For the scenarios A–P a constant minimum water table (WT-A) was applied to isolate the effect of the glacial unloading (Figure 2). The results from scenarios A–P show that the removal of the glacial load from the slope has a significant effect on the slope stability (Figure 9a). The FOS values calculated range between 3.7 and 1.45, indicating that the modelled slope should be stable for all glacier scenarios. However, the slope was deforming from the mid-2000s to 2018 [25], suggesting that the FOS was approaching 1. Since scenarios A–P did not account for structural weaknesses, and only considered the minimum water table elevation (WT A—Figure 2), overestimated FOS values are reasonable.

The results show that the absolute slope stability is dictated by the material properties, however, the relative reduction of FOS due to glacial unloading behaves identical for the individual slip surfaces independent of rock mass properties (within the selected parameter range). The depth and geometry of the slip surface seems to be the main controlling factor. The results furthermore show that seismicity has a strong impact on the slope stability with up to almost 20% reduction of FOS at an average ground acceleration of 0.1 g (k = 0.1) (Figure 9b). Due to the proximity to the caldera (6 km), high frequency shaking can be expected in the study area which would result in parts of the slope instability moving in opposite directions, reducing the additional seismic load significantly [92]. This effect would reduce the destabilizing effect of a seismic event. Seismic amplification due to topography, material contrasts and internal fracturing, on the other hand, could increase the ground acceleration locally [92,93]. Our calculations show that seismic events can cause significant lowering of the FOS, but more detailed modelling work is necessary to quantify the effect better.

To visualize the FOS trends from a current perspective the results of scenarios A–P were normalized relative to the 2013 glacier scenario (Figure 11a), which approximately reflects the current (2024) glacier dimensions. Slope deformation occurred during glacier retreat from the mid-2000s to 2018 [25] suggesting that the slope was approaching a FOS of 1.0. Due to the simplified model, the exact glacier thickness where a FOS of 1.0 would be reached is unknown. However, a hypothetical threshold of FOS_h = 1.0 was placed closely below the 2011 glacier scenario of all trendlines (Figure 11a) to illustrate the increased susceptibility of the slope to external triggers as the glacier thins. The area with red gradient indicates a period of pre-failure slope deformation starting at mid-2000s glacier thicknesses. The 2013 scenario includes the load of the 2013 debris avalanche on the glacier, which slightly increases the FOS. Whether the slope will cross the FOS_h = 1.0 line with future thinning depends on the geometry and depth of the slip surface. If the slip surface is rather shallow (e.g., SL4) the threshold might not be crossed but if the instability extends deeper, then the FOS_h = 1.0 line is crossed. The figure illustrates that, along with glacial thinning, the slope becomes more susceptible to triggering factors such as short-term increase of pore water pressure (precipitation or snowmelt) or seismic activity. The model results show that seismic load of a certain strength or the increase of the ground water table over a certain interval reduces the FOS a constant relative amount throughout the glacial thinning scenarios. E.g. while a seismic event that occurred at a greater glacial thickness may not have any effect on the slope, the same seismic event at a lower glacier surface could reduce the FOS below values of 1.0. The same is likely for increased pore-water pressures due to extreme or prolonged periods of rain.

The calculated relative FOS reduction of SL 1, 2 and 3 generally agree with results from Affliction glacier, British Columbia, Canada where the glacier had completely retreated away from a large instability in a volcanic edifice. Here, a 15% reduction of FOS since the LIA was calculated [12].

4.3. Interpretation of WT-syn and WT-lag

With the scenarios WT-syn we calculate the sensitivity of FOS to water table changes that are controlled by changing subglacial water pressures due to glacial unloading (Figure 11b). Therefore, the results are a combination of the above-described destabilizing effect of glacial unloading and the stabilizing effect of a lowering groundwater table [27,81]. For SL 1 and 2 the destabilizing effect of glacial unloading exceeds the stabilizing effect of water table lowering resulting in overall FOS reduction during deglaciation. For SL 3 and 4 the stabilizing effect of the water table lowering exceeds the effect of glacial unloading resulting in overall FOS increase as a result of glacial thinning (Figure 9a). This indicates that shallow slip surfaces become more stable as the glacier thins and water table lowers, whereas deeper seated slip surfaces experience destabilization. However, the overall FOS reduction of SL 1 and 2 in WT-syn is small compared to the reduction experienced in scenarios A–P (Figure 9a). For WT-lag was assumed that, during rapid glacier thinning between 1995 and 2011, the water table in the surrounding slopes was lagging 10 years behind the subglacial water pressures, creating temporarily higher hydraulic gradients in the slope. The results show that such a lag creates a transient instability period of reduced FOS values. Thus, the faster the glacier thinning rate or the lower the hydraulic conductivity, the steeper the hydraulic gradient and the more pronounced the window. However, when the glacier thinning slows down or halts the hydraulic gradient has time to adjust which leads to an increase of FOS (Figure 10). This adjustment ends this “instability window”.

Figure 11b shows the results of SL 1 and 2 in the WT-syn and WT-lag scenarios normalized to the 2013 glacier scenario with water tables of WT-syn (Figure 2) which roughly reflects 2024 glacier conditions. Just like in Figure 11a, this visualization illustrates the course the FOS experiences during deglaciation from a current perspective. Future glacier thinning may lead SL 1 to cross the hypothetical failure threshold (FOS_h = 1) while SL 2 mostly stabilizes with continued deglaciation. The overall susceptibility to external triggers increases with future glacier retreat in WT-syn and WT-lag for SL 1 and 2 (Figure 11b) but decreases for SL 3 and 4 (Figure 9 and Figure 10).

In all calculations the additional load of the 2013 debris avalanche increased the FOS. It is reasonable that the halt in deformation, observed at the Svarhamrar slope instability since 2018, results from a combination of: 1. stagnation of the glacier surface, 2. additional load of the 2013 debris avalanche, and 3. normalization of the hydraulic gradient within the slope after a period of rapid thinning followed by several years of stagnation. As the debris is being transported down-glacier over the coming decade and glacier thinning will gradually start again [52], the Svarthamrar slope instability will likely destabilize further. Slope deformation observations in relation to future thinning of Svínafellsjökull are crucial to make a statement about the failure potential of the slope.

4.4. Wider Implications

The scenarios A–P (Figure 8, Figure 9 and Figure 11a), where a simplified minimum water table was applied, are somewhat comparable to glaciers with low subglacial water pressures and low water tables in surrounding rock slopes. This is mostly the case for well drained valley glaciers [94] or locations in the high alpine [16]. Our results suggest that such slopes are generally more sensitive to glacial unloading since the stabilizing effect of water table lowering likely plays a less important role. Scenarios WT-syn and WT-lag on the other hand reflect maximum estimates of subglacial water pressures [26]. Since the frontal margin of Svínafellsjökull is floating and annual precipitation is high on the upper slopes of Öræfajökull volcano (up to 10,000 mm/yr water equivalent according to Crochet et al. [95], high subglacial water pressures and high water tables in surrounding slopes are likely. The FOS evolution of glacier marginal rock slopes at comparable Icelandic outlet glaciers (e.g., Kvíárjökull [63.948, −16.482], Skaftafellsjökull [64.039, −16.899], Fjallsjökull [64.030, −16.434]) or similar settings elsewhere (e.g., Alaska, Patagonia, Greenland) are likely a result of the combination of destabilization due to glacial unloading and stabilization due to groundwater table lowering. Such slopes may be affected by an “instability window” during and shortly after phases of rapid thinning when elevated hydraulic gradients are present. The theoretical existence of such a “window” has widespread implications on how glacier retreat rates relate to paraglacial landslide hazard and how the post-glacial landslide distribution is put in context with paleo groundwater levels. In our reconstructed case the effect of the instability window only reduces the FOS by 2% but longer periods of rapid retreat, especially in bedrock with low hydraulic conductivity, would lead to a much more pronounced effect. Future work using long term hydrological and glaciological observations such as in Hugentobler et al. [27,81] are necessary to evaluate and quantify this effect better. We calculate that the stability of the deepest slip surface (SL1) decreases in all scenarios which indicates that the overall stability of paraglacial slopes is reduced due to glacial thinning, whereas instabilities with shallower slip surfaces stabilize as the glacier thins below the slip surface. Since all presented results show FOS values clearly above 1.0 can be hypothesized that glacial unloading alone is insufficient to cause failure, even in weak rocks (e.g., Scenario A). Therefore, preexisting structural weaknesses are necessary to enable slope instabilities, such as observed at Svarthamrar.

Numerous potential destabilizing effects, such as changing thermal regime [96], increasing surface erosion [4], and progressive rock fracturing [15] may accompany the deglaciation of rock slopes. In this research we isolate the direct effect of the removal of the glacial load on a glacier-marginal rock slope without taking the other factors into account. While glacier ice most likely cannot withstand a large lateral rock slope that has reached failure conditions [22], our calculations show that unloading can decrease the overall stability of rock slopes which haven’t reached failure conditions yet and make them more susceptible to external triggers.

5. Conclusions

Geological analysis indicates that the Svarthamrar slope was predisposed to instability by structural discontinuities and a strongly overdeepened glacial trough. The destabilization, however, is driven by glacial unloading but also potentially reduced by ground water lowering in the slope which is controlled by the subglacial water pressures. Absolute factor of safety values depend on the rock strength parameters, but the relative destabilizing effect of glacial unloading depends mostly on the geometry and depth of the slip surfaces. The deeper the slip surface reaches below the glacier, the greater the relative effect of glacier unloading. Throughout deglaciation deep slip surfaces become more susceptible to external triggering such as seismic events, heavy- or prolonged precipitation, excessive snowmelt or volcano deformation, whereas more shallow slip surfaces located higher up on the slope are likely to stabilize. The additional load of the 2013 debris avalanche on the glacier has a slight stabilizing effect. The same effect is likely to be the case at other debris covered glaciers. Renewed, gradual onset of glacial thinning while the debris cover is being transported down-glacier is likely to continue the destabilizing trend. A “paraglacial hydrologic lag window” during and shortly after rapid glacier thinning is a potential explanation to why the slope deformed during a period of rapid thinning between 1995 and 2011 and then stabilized by 2018. Such periods of increased instability during rapid retreat may have important implications on how glacier retreat rates and the concept of debuttressing have been associated with slope instability and highlight the importance of better hydrological understanding of the paraglacial slopes.

The modelled effect of glacial unloading affects all deglaciated or deglaciating slopes to some degree. However, our findings suggest that bedrock of a similar composition is strong enough to withstand the destabilizing effects of glacial unloading, but in combination with structural weaknesses and overdeepened glacial troughs, the slope gradually becomes more susceptible to instability. This study further highlights the interplay of slope destabilization due to glacial unloading and the counteracting slope stabilization resulting from decreasing water pressures because of lowering overburden pressure of the thinning glacier. Therefore, to better protect communities in the downstream areas of deglaciating rock slopes, it is important to understand the local structural settings of paraglacial slopes, the glacier thinning rates and hydrologic conditions.