Introduction

Mass movements are recognized as complex processes that encompass a broad range of rates, mechanisms, and resulting magnitudes of livelihood and infrastructural damage (e.g., Petley 2012). While Highland and Bobrowsky (2008)’s typology offers a clear delineation of mass movement type—based on rates and penetration depths—the development of a similar classification scheme for their causes is more challenging, as multiple factors and their feedback including (but not limited to) rainfall, lithology, rock strength and fracturing, and slope are difficult to deconvolve in a consistent way globally (e.g., Petley 2012; Zhang et al. 2022).

This is especially true for ultraslow (i.e., < 1 cm year−1) soil creep, initially proposed by Davis (1892). Culling (1963) was the first to develop a model whereby porosity is “injected” due to various disturbances such as wetting and drying and bioturbation, leading to particle motion. The direct relationship between topographic slope and sediment flux governs almost all current landscape evolution models (e.g., Tucker and Hancock 2010). A dominant paradigm has been the significant role exerted by the activity of living organisms on hillslopes (“biogenic creep”: Pawlik and Šamonil 2018); yet Finlayson (1985) recognizes creep as “hav[ing] a multiplicity of causes with different combinations present in different areas …” Moreover, Deshpande et al. (2021) reject the “dogma” of biological disturbances, by demonstrating experimentally the indefinite creep of an undisturbed sandpile, at rates and styles comparable to natural hillslopes, suggesting that soil behaves in a creeping glass-like manner.

There has been renewed interest in interrogating the causes and mechanisms of creep as a result of three recent and interlocking developments. First, there has been an important improvement in the resolution to which creep rates can be measured—down to 10−6 ms−1 in the laboratory or 10−4 ms−1 in the field—using experimental techniques such as speckle images from expanded laser beam, and vibrating-wire extensometers (Mariotti et al. 2019; Deshpande et al. 2021). These advances have unmasked soil creep as the culprit behind much spectacular infrastructural damage: for instance, creep was recently revealed to cause 38–44% of burst water mains in the UK, leading to total economic costs “more than double” those related to faster mass movements in that country (Pritchard et al. 2014). Thirdly, increasing recognition of the number of catastrophic failures resulting from a sudden increase in downslope motion—a “slow-to-fast transition”—has motivated a need to enhance monitoring of creep rates in space and time in order to inform early-warning thresholds (e.g., Yao et al. 2021; Zhang et al. 2022).

Many studies that focus on this monitoring do so for discrete case studies, therefore concluding only that variations in creep rates come from Finlayson (1985)’s “multiplicity of causes.” Agliardi et al. (2020) coupled laboratory experiments on rockslide shear zone material with in situ observations to demonstrate that rates of soil creep in a region of northern Italy followed short-term pore fluid pressure variations, which modify the behavior of shear zones. Yao et al. (2021) consider several intrinsic soil properties (i.e., porosity, plasticity, organic, and clay mineral content) to be most significant in determining creep behavior over several parts of China. By contrast, other studies stress the importance of climatic and microclimatic controls (i.e., precipitation and slope aspect) on soil creep efficiency and hillslope evolution (e.g., Ben-Asher et al. 2017; Wen and Yuan 2022). Other extensive datasets on ground motion exist alongside precipitation, demonstrating its physical consequences for the strength of hillslope soils in terms of modulations in pore fluid pressure (e.g., Iverson and Major 1987; Angeli et al. 1996; Bernardie et al. 2014).

The purpose of this paper is therefore to answer an acknowledged open question (e.g., Finlayson 1985; Clarke et al. 1999): is it possible to deconvolve the processes governing the behavior of slow mass movements (i.e., both soil creep and slow-to-fast transitions) in a case-study-agnostic way—or must every site be treated differently? We approach this problem by conducting repeated (2015–2022) measurements to distinguish long-term creep rates from short-term disturbances. Four regions of the southern UK were chosen (Fig. 1; Table 1) for the monitoring to reflect four different bedrock lithologies; other workers have emphasized the important yet indirect role of parent lithology on which unstable hillslopes are formed, but do not offer direct lithological comparisons (e.g., Agliardi et al. 2020; Wen and Yuan 2022). Within these regions, long-term downslope ground movement was quantified, as well as local slope, precipitation, temperature, depth to bedrock, and soil properties including porosity and clay mineral content. We investigated the following:

  • Jurassic limestone hillslopes, many of which exhibit characteristic sub-parallel step-like terracettes, in the Cotswold Hills, southwest UK: a region containing the highest concentration of landslides in Europe (Ackermann and Cave 1967; Paul 2014);

  • slopes developed on the Eocene-aged London clay, the stability of which having been debated for over 60 years, in the London Basin (e.g., Skempton and DeLory 1957; Vaughan and Walbancke 2009);

  • Devonian-aged sandstone hillslopes in the Black Mountains along the southern England-Wales border; and

  • relatively gentle slopes on peat, which blankets much of the igneous rocks of Dartmoor, southwest UK.

Fig. 1
figure 1

a Geological map of Devon, southwest UK. Small circles, British Geological Survey (BGS) landslides (Pennington et al. 2015); 1 and 2, peat soil investigation areas (Table 1); Ex, Exeter. b Digital elevation model for same area; black lines, slopes > 30°. c 2015–2022 precipitation for same area. d Mean annual temperature variation. e–h Same but for clay soil (study areas 3 and 4). Lo, London. i–l Same but for sandstone and limestone soils (study areas 5 and 6, and 7 and 8, respectively). Gl, Gloucester

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Table 1 Location, soil measurements, and mean annual downslope movement for peat, clay, sandstone, and limestone soils
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Methods

Figure 1 shows the study areas: for each soil parent lithology, two different UK regions were chosen for our measurements. These regions are denoted by the numbers on Fig. 1 and were chosen to capture as broad a variety of localities (in terms of slope, aspect, climate, depth to bedrock, and intrinsic soil properties) as possible within temporal, financial, and equipment constraints. Also shown on Fig. 1 are bedrock geology, topography and slope, mean precipitation over 2015–2022, computed from the 2ADPR product of the Global Precipitation Mission (Hou et al. 2014), mean annual temperature variation, extracted from the UK Met Office’s Integrated Data Archive System (Met Office 2012), and the coordinates of all mapped landslides (irrespective of rate of movement) in each study area (Pennington et al. 2015).

We used vibrating-wire extensometers (model 4435, Geokon, USA) to monitor downslope surface movement, and followed the procedure of Mariotti et al. (2019), who employed a similar piece of equipment to monitor creep rates in a marsh bank. The instruments measured the length of a 3-m-long and 2.5-cm-wide trench every 2 h, with a resolution of 0.02 mm and accuracy of 0.05 mm. These trenches extended either to 20 cm depth or to base soil, which was < 20 cm in two limestone localities (8 and 15 cm at Lst7-c and Lst8-a, respectively; Table 1) Within each soil lithological region (i.e., peat, clay, sandstone, limestone), one extensometer monitored ground movement continuously at one site from January 3, 2015, to December 24, 2022, while another was deployed at successive other sites for a duration of 1 year in turn (Table 1).

At the continuously monitored site, soil temperature was measured at six-hourly intervals in the top 1 cm of the trench, and 15-min precipitation was recorded using a co-located Davis Aerocone 0.2-mm automatic tipping bucket rain gauge, following the climatological recording procedure of Kirkby (1967). Soil porosity and clay mineral content (as the percentage of illite + montmorillonite + smectite + kaolinite) were measured using percolation testing (Danielson and Sutherland 1986) and X-ray diffraction (per Nayak and Singh 2007), respectively.

For each continuously monitored site, we then sought the simplest continuous relationship that would honor variations in ground movement as a function of temperature and/or precipitation. To do this, we formulated a joint inverse problem (e.g., Sambridge 1999) to minimize the misfit H between predicted and actual ground movements. A conjugate gradient method is used to minimize H; we sought a balance between data misfit and model smoothness, i.e., the simplest relationship that would fit the entire 2015–2022 time series reasonably well. We tested a suite of models in which the Lagrangian multiplier (i.e., regularization parameter), μ, was systematically varied in order to achieve such a balance (e.g., O’Reilly and Rueda 1992). This routine, which is essentially an extension of least-squares regression, is widely used to model other geophysical observables, such as seismic refraction and reflection data, and is described in detail elsewhere (e.g., Parker 1994). This process yielded the following simple objective functions for the peat and sandstone sites (final RMS misfit = 0.82 and 0.77, respectively):

$${v}_{p}={P}_{p}+\frac{1}{4}\text{ln}\left(\frac{{P}_{p}}{2}\right),$$
(1)
$${v}_{s}={-T}_{s}+\frac{1}{6}\text{ln}\left(\frac{{T}_{s}}{4}\right),$$
(2)

where vp and vs = ground movement of slopes where peat and sandstone, respectively, form the bedrock, Pp = co-located precipitation at the peat site, and Ts = co-located temperature at the sandstone site.

Results

Table 1 details the coordinates of each site, the mean ground movement, and all other local measurements. Figure 2 displays, for 2015–2022, monthly averages of ground movement at the continuously monitored site for all four lithological groups, as a function of monthly means of precipitation and absolute temperature. This relatively coarse resolution was chosen (a) to focus on long-term (annual) variations in creep rates, which is the focus of this work; and (b) as diurnal temperature variations and individual rainfall events resulted in changes in ground deformation that were barely within extensometer measurement resolution (i.e., ± 0.02 mm).

Fig. 2
figure 2

a Mean monthly temperature (red line and axis), precipitation (blue bars and axis) variation, and measured downslope ground movement (black line and boxes) for peat soil locality peat1-a (Fig. 1; Table 1), 2015–2022. Dark gray dashed line, best-fitting inverse model. b Clay soil locality clay-4a. Black vertical lines, slope failure, followed by period of no slip measurements (light gray columns). c Sandstone soil locality Sst5-a. d Limestone soil locality Lst-7a

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Measured ground movement is a cumulative measure of deformation; the non-monotonicity of the curves suggests periods of elastic (i.e., reversible) deformation. Two best-fitting inverse models for peat and sandstone soils are also shown; the inverse procedure failed for clay and limestone soils. Periods following slope failure are also indicated, during which times monitoring of creep rates ceased as the extensometers were recovered and repaired. Figure 3 collates mean ground movements across all sites, as a function of local slope, soil porosity, depth to bedrock (i.e., regolith thickness), and clay mineral content.

Fig. 3
figure 3

Mean annual downslope movement (whiskers, one standard deviation), grouped by localities according to soil type (Table 1), as a function of a slope, b soil porosity, c depth to bedrock, and d percentage of clay minerals in soil

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Discussion and conclusions

We have marshaled multiple long-term time series of ground movements, temperature, precipitation, and extensive topographic and soil property data, to explore their relationships over four regions of the southern UK characterized by intense and frequent mass movements, but different parent lithologies.

Creep behavior varied greatly across the four different settings, from relatively rapid movements with dramatic annual variations (e.g., peat: mean ground movement over 2015–2022 = 0.12 ± 0.04 mm per month) to more modest downslope motion that changed little over annual cycles (e.g., limestone: 0.03 ± 0.01 mm). Five slope failures were recorded on clay and sandstone soils, leading to extended periods in which the extensometers were recovered and repaired. In the former case, an imminent slow-to-fast transition is suggested by sudden jumps in recorded ground movement immediately prior to failure, which occurred during the last three months of 2015, 2019, and 2020. Yao et al. (2021) report similar findings of a transition that spans a timescale of weeks, in response to prolonged rainfall episodes, culminating in slope failure. Zhang et al. (2022) also point to the singular role of sudden cloudbursts as a trigger for failure on creeping hillslopes.

Our simple inverse model sought to evaluate the capacity of climatological observables (i.e., temperature and rainfall, binned into monthly averages) to predict creep rates. For each bedrock lithological setting, we trialed the simplest model that might fit the entire ground movement time series reasonably well, either using temperature, rainfall, or a combination of the two, as an input. This approach failed for clay and limestone soils, implying that changes in climate do not govern creep behavior on these hillslopes. Moreover, the error-minimizing regression routine may not capture the entire suite of physical ingredients that underpin the main families of models of creeping hillslopes, e.g., viscous flow rules for stable creeping slides (Hu et al. 2020), Mohr-Coulomb, where pore fluid pressures are important (Bernardie et al. 2014), or rate-and-state friction that accounts for alternating slow-fast behavior (Handwerger et al. 2016). Many previous studies on landscape evolution modeling have posited a connection between soil flux and soil thickness, but several of the simple models presented typically integrate a velocity profile over depth (e.g., Braun et al. 2001; Anderson 2002; Furbish et al. 2009; Johnstone and Hilley 2015); our results (Fig. 3c) could further complicate these models and instead imply that the velocity at the top of the soil can also depend on thickness.

Among these other models, there are many location-specific variations that attest to the fundamental difficulty of characterizing creeping soils and slow mass movements. However, our empirical results suggest that precipitation variation alone is strongly predictive of creep rates on peat soil slopes (Eq. 1). Finlayson (1981) argues that the high organic content of these soils (typically > 60%) and very high porosity values (up to 0.86: Fig. 3b) render them even more expansive than the more widely studied clay soils. Long et al. (2022) agree on the fundamental role of wet-dry cycles in driving creep on peat soils, while acknowledging a paucity of data. They also suggest that monitoring pore water pressure and permeability changes with strain and time could complement creep measurements, which, unusually, show little correlation with slope (all our peat soil slopes were recorded as < 5°). For the sandstone soil slope, by contrast, our inverse scheme was only successful when temperature variations alone were considered to govern creep behavior (Eq. 2). Our best-fitting model is highly smoothed but can be exploited to predict creep rates in the absence of empirical data post-failure (Fig. 2c). In this setting, slope movement was greatest when mean monthly temperatures were < 0 °C, implying the significance of freeze-thaw cycles. Wen and Yuan (2022) report on the disintegration of a similar sandstone in Yunan Province, China, during repeated freeze-thaw cycles, reducing subgrade strength, and enhancing soil creep rates. However, this region also experienced important annual and daily wet-dry cycles that simultaneously affected creep behavior. We did not investigate the possibility of a time lag between temperature/precipitation perturbations and creep response, which depend on intrinsic soil properties such as grain size distribution and clay content, and could represent a future extension to the work presented here (e.g., Johnstone and Hilley 2015).

We were unable to produce any satisfactory models of limestone and clay soil creep as a function of climatological variables: not “satisfactory” in that a balance between model smoothness and data RMS misfit could not be achieved, so optimization could not take place (cf. O’Reilly and Rueda 1992; Parker 1994). Instead, we note the positive correlation between regolith thickness and ground movement for thin limestone soils, and similar positive correlations between slope and clay mineral content, and ground movement, for clay soils (Fig. 3).

The results in Fig. 3c suggest a viscous-flow type of behavior; fruitful future modeling effort might therefore lie in a viscous fluid formulation (cf. Angeli et al. 1996). Soil porosity did not appear to exert any control on creep in any sites. Skempton and DeLory (1957) considered all slopes formed over London clay flatter than 10° to be fundamentally stable; this finding was contradicted by later work, which identified pore pressure equilibration, slope angle, and the presence of hitherto undetected shear zones within the soil to be the dominant controls on creep rates and the presence and timing of slow-to-fast transitions (e.g., Vaughan and Walbancke 2009). The depths reported in Fig. 3c are from soil to bedrock, except for the London clay localities, where numerous shear bands were encountered, which have demonstrated geotechnical consequences, e.g., dramatic reductions in undrained shear strength (Pantelidou and Simpson 2007; Linde-Arias et al. 2017).

For our limestone sites, those with the thinnest soil layers (~ 0.1 m; Table 1) experienced the lowest rates of long-term creep: this behavior is shared with sandstone soils. In oolitic limestones and some sandstones, thinner soils are associated with a more abrupt mechanical transition to bedrock, which has been suggested to decouple slow (< 1 cm year−1) long-term soil creep rates from potentially more rapid movement (e.g., cambering) in bedrock (Ackermann and Cave 1967; Paul 2014).

In summary, we have presented long-term records of soil creep at four regions of the southern UK characterized by intense mass movement activity. We have used co-located climatological, topographic, and intrinsic soil measurements to identify that parent lithology must be considered in the first instance when seeking to decouple the “multiplicity of causes” that govern soil creep behavior. Lithology sets the pace of creep indirectly by dictating hillslope repose angles and soil composition and thickness. Annual and daily cycles in rainfall and temperature may instead set the tempo of creep—especially in peat and sandstone soils, where our simple inverse modeling scheme was successful—and may also dictate rapid accelerations in surface movement that might precede slope failure. Fruitful future work would include measuring creep rates at different depths in order to obtain local creep profiles (cf. Moeyersons 1988), as well as conducting additional long-term measurements over other bedrock lithologies and climate regimes.