Introduction

During an explosive volcanic eruption, the fall out of tephra (ejected particles of all sizes) from the eruptive plume can lead to significant additional loading on roofs. Buildings close to an eruptive vent can sustain substantial damage or even collapse (e.g. Blong 2003; Jenkins et al. 2014; Hayes et al. 2019). Most recently, roof collapses occurred following the April 2021 eruption of La Soufrière on St Vincent (Lesser Antilles).

The key factors that are thought to influence the load transferred to the roof by a tephra deposit, are magma composition and vesicularity, the size distribution and shape of the grains, and properties of the roof (Fig. 1). Magma properties influence the density of individual grains, while their size distribution and shape influence packing (Estrada 2016; Landauer et al. 2020). Deposit density depends on both grain density and packing and can also increase substantially if the deposit is wet (e.g. Blong 1981; Macedonio and Costa 2012; Hayes et al. 2019; Williams et al. 2021). The size and intensity of the eruption impact the height of the volcanic plume (e.g. Bonadonna and Costa 2013; Suzuki et al. 2016; Cassidy et al. 2018) and atmospheric processes, including wind velocity and precipitation, influence the transport and deposition of particles (e.g. Petersen et al. 2012; Bonadonna et al. 2015; Poulidis et al. 2018). In turn, these factors affect the amount of tephra deposited at any location. The load on the roof depends on the bulk density and thickness of the deposit, but tephra thickness can be altered after deposition by drifting and sliding. These processes are influenced by tephra properties, such as the internal angle of friction and grain size distribution, as well as the material, shape and pitch of the roof and the coefficient of friction between the tephra and the roof (e.g. Hampton et al. 2015).

Fig. 1
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Key factors influencing the load transferred to the roof by a tephra deposit. Shaded factors are the focus of this study

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The aim of this study is to discuss and present the geomechanical properties of tephra relevant to roof loading. Understanding these properties is critical when assessing the vulnerability of buildings in areas at risk of tephra fall as they influence the additional load that is transferred to a roof and hence its likelihood of collapse. Estimating this additional loading is also important for building design, where building codes use a combination of historic records and experimental results to assess loads likely to occur within a building’s lifespan. Snow loading, which is fundamentally similar to loading from tephra in that it a granular air-fall deposit, is well characterised and routinely included in international design standards (e.g. British Standards Institution 2009; International Standards Organization 2013; American Society of Civil Engineers and Structural Engineering Institute 2017), but tephra fall is not routinely taken into account, and at the time of writing is not specifically considered in any international design standards or building codes.

This study forms part of a wider body of research investigating the potential of roof collapse by tephra loading with relevance to Ascension Island and the development of standards to account for tephra loads in building design. Ascension is a volcanically active UK Overseas Territory in the south Atlantic with an area of 98 km2 and ~ 780 residents. Because of Ascension’s remote location and exposure to potential volcanic hazards, buildings could be vulnerable to collapse from any future explosive activity. In addition, Ascension tephra deposits vary widely in grain size and composition (e.g. Winstanley 2020; Preece et al. 2021), making it an ideal location to investigate any variation in the geomechanical properties of tephra, and whether synthetic tephra can be used in lieu of natural material.

In order to undertake the required laboratory tests, large volumes of tephra are required and these are not always easily obtained from natural sources due to the hazards associated with near-source sampling following an eruption and the costs of transporting large volumes of samples. We therefore investigated whether synthetic tephra (of unknown composition, made from crushing and sieving commercially available volcanic aggregates) could be used to model the properties of naturally occurring deposits that are relevant when considering roof loads (bulk density, grain size distribution and internal angle of friction). By comparing synthetic tephra of a non-specific composition to published data and the results from tests conducted as part of this study on Ascension tephra, the possibility of using commercially available aggregate to generate the volumes of material required for large scale testing can be assessed.

We compiled published density and grain size data for deposits from 64 global eruptions, measured the grain size distributions (GSDs) of samples of pumice, scoria and ash from Ascension and selected representative GSDs for our synthetic samples. We then used shear box tests to measure the internal angle of friction of dry samples of both natural and synthetic material. The tests undertaken in this study were only performed on dry tephra and do not consider the saturated state of the deposit. Results for our synthetic samples matched well with both Ascension samples and published data from a wide range of eruptions; we can therefore be confident in using synthetic tephra to investigate the properties that control loading and sliding.

Methods

To ensure our test samples were representative of natural deposits, we compared them to published GSDs from global mafic, intermediate and silicic eruptions (listed in Table 1), focusing on proximal samples (≤ 10 km from source) to enable comparison with GSDs of samples from Ascension. The Ascension samples were sieved to 4 φg (63 μm) diameter, with smaller particles analysed by dynamic image analysis (British Standards Institution 2006) using a Microtrac CAMSIZER® X2. These samples comprised trachytic ash, lithic-rich and lithic-poor trachytic pumice (Preece et al. 2021) and coarse-grained and fine-grained basaltic scoria (Winstanley 2020) from five locations shown in Fig. 2.

Table 1 Published grain size distribution (GSD), size and magma composition for eruptions with published GSDs ≤10 km from source, used in Fig. 3
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Fig. 2
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Map of Ascension Island showing the locations of tephra samples used in this study

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Bulk densities for dry deposits were compiled from published data for 61 eruptions at 33 volcanoes (detailed in the Appendix). These cover small to large eruptions (VEI 2–7), with mafic to silicic magma compositions, and include both proximal-medial (< 50 km from source) and distal (≥ 50 km from source) values.

Test samples were created by crushing commercially available volcanic material using a Proctor compactor to obtain a range of grain sizes. The aggregates comprised mafic ‘volcanic lava filtration gravel’ and silicic ‘pumice gravel’ and ‘pumice crush’ from Specialist Aggregates Ltd. Samples were then sieved to 4 φg (63 μm) and finer grain sizes were analysed using the CAMSIZER® X2. The coarse (≥ − 4 φg, ≤ 16 mm) and fine (≥ 1 φg, ≤ 2 mm) test GSDs were selected to be consistent with published global data and the Ascension deposits. For each test, samples were oven dried and the sample mass and volume were measured and density calculated, to ensure that test densities were consistent with our dataset of published values.

Shear box tests were used to measure the internal angle of friction of the test samples. These tests represent stress along a shear plane, as described in BS 1377–7 (British Standards Institution 1990) and use the Mohr-Coulomb equation. For dry samples (with no fluid pore pressure) the equation can be written as:

$$\tau =\sigma\;\tan\;{\varphi}_f+c$$
(1)

where τ is the shear stress at failure along a plane, σ is normal stress, φf is the internal angle of friction, and c is cohesion.

For each test, the sample was loaded into the shear box and a normal force applied via a load plate. For the small shear box, this force came from calibrated weights added to a lever arm; for the large shear box, weights were added directly to the load plate for normal forces < 1 kN, and via a pneumatic loading system for forces ≥1 kN. The equivalent normal stress, σ, was calculated from stress = force/area. The shear box consisted of an upper and lower section which were gradually moved relative to each other. The shear force required to move the sections was measured using a proving ring. Values were recorded throughout the test and used to calculate the equivalent shear stress, τ. Horizontal and vertical displacement in the sample were also recorded using Linear Variable Differential Transformers (LVDT). The test finished when the shear force peaked or reached a plateau, as this represented the maximum shear stress in the sample before failure. Tests were carried out at different normal stresses (σ) and plotted against corresponding values of shear stress (τ). The internal angle of friction of the sample (φf) is the gradient of the best fit line through the data points on a σ vs τ plot (Eq. 1).

To minimise any scale effects, BS 1377–7 specifies that the largest grain size in the sample must be ≤ one tenth of the specimen height in the shear box. We used small shear box tests (sample size 100 × 100 × 20 mm) for samples ≤2 mm in diameter and large shear box tests (sample size 300 × 300 × 160 mm) for samples ≤16 mm in diameter. We conducted tests at normal stresses of 3–35 kPa, representing deposit depths for our test samples of ~ 50–220 cm. These depths can lead to roof failure depending on the density of the deposit (Blong 1984; Jenkins et al. 2014).

To compare φf values for the test tephra to natural samples, small shear box tests were also used to determine the internal friction angle for the Ascension ash (≤ 2 mm) samples. The sample volumes of pumice and scoria were too small to enable large shear box tests to be carried out on these materials.

Results

Near-source GSDs

Published proximal GSDs vary widely, even for eruptions with similar magma compositions (Fig. 3a-c for mafic (basalt, ≤ 52% SiO2), intermediate (basaltic andesite—andesite, 52–63% SiO2) and silicic (dacite—rhyolite, > 63% SiO2) eruptions detailed in Table 1). The Ascension deposits (Fig. 3d) also show coarse to fine GSDs. When all the GSDs are plotted together (Fig. 4) there is a large overlap and, for these proximal deposits, magma composition does not seem to control GSD. The coarse and fine GSDs of the test tephra (also shown on Fig. 4) were selected to be representative of both published data and the Ascension Island samples. The coarse test distribution is at the finer end of the published range of GSDs; however, a maximum grain size of 16 mm was chosen because of size constraints of the laboratory equipment, and because we are interested in the properties of the bulk deposit rather than properties of individual large clasts.

Fig. 3
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Grain size distributions for proximal (≤ 10 km from source) samples from published data (Table 1) from a) mafic eruptions, b) intermediate eruptions and c) silicic eruptions. d Presents trachytic pumice and ash, and basaltic scoria samples from Ascension Island

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Fig. 4
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Summary of published grain size distributions (GSDs) for eruptions listed in Table 1 and presented in Fig. 3, plus GSDs for the Ascension samples and the test samples used in this study

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Deposit densities

Deposit densities compiled from published data reveal a range of values from ~ 400 to 1500 kg m− 3 for all magma compositions. For individual eruptions, where proximal/medial and distal bulk densities are reported separately, distal values are usually higher, likely indicating higher grain density and/or more efficient packing of finer grains. For some eruptions e.g. Fuego 1973 (Rose et al. 2008) textural variation in the deposits results in both low and high proximal to medial bulk densities. There is more variability in the density for low to medium silica content materials and some high silica samples have lower bulk densities. However, when the dataset is taken as a whole, there are no clear trends relating to magma composition, eruption size or distance from source (Figs. 5 and 6). Densities of the (dry) test samples are within the range of values found in the published data, as shown in Table 2.

Fig. 5
figure 5

Variation of bulk density with magma composition. Values are for proximal-medial samples (< 50 km from source), distal samples (≥ 50 km from source) or the whole deposit. Dotted lines indicate a range of values was reported. Proximal-medial and distal values from the same eruption are linked by a solid green line

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Fig. 6
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Variation of bulk density with eruption size (VEI). Values are for proximal-medial samples (< 50 km from source), distal samples (≥ 50 km from source) or the whole deposit. Dotted lines indicate a range of values was reported. Proximal-medial and distal values from the same eruption are linked by a solid green line

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Table 2 Dry densities of test samples, and published data listed in the Appendix. Coarse and fine grain size distributions are shown in Fig. 4
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Peak stress and internal angle of friction

Results from the shear box tests (Figs. 7 and 8) reveal that after initial compaction, the synthetic samples dilated and shear stress reached a peak value. In comparison, the Ascension ash samples compacted throughout the tests (negative vertical displacement) and shear stress reached a plateau rather than peaking. No breaking or crushing of the grains was observed, with changes in volume achieved by rearrangement of deposit packing.

Fig. 7
figure 7

Results of small shear box tests for particles ≤2 mm, horizontal displacement vs shear stress (left column) and horizontal vs vertical displacement (right column). a Synthetic pumice, b Synthetic scoria, c Ascension ash. These tests are limited by the maximum amount of travel available for the sample in the shear box. The rate of change of shear stress vs time has been examined and this shows the rate of change peaking early in the test and then subsiding to alternate between small positive and negative values oscillating around 0. Therefore, we are confident that the peak shear stress value measured is representative

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Fig. 8
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Results of large shear box tests for particles ≤16 mm, horizontal displacement vs shear stress (left column) and horizontal vs vertical displacement (right column). a Synthetic pumice, b Synthetic scoria

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On plots of normal stress vs peak shear stress, for both pumice and scoria the coarse and fine GSDs plot on the same line (Fig. 9). The friction angles (φf), calculated using Eq. (1), are very similar for the test samples and the Ascension ash, at between 35.8 and 36.5° (Table 3). These results suggest that the internal angle of friction is independent of both tephra composition and grain size at the low normal stresses of these tests.

Fig. 9
figure 9

Peak shear stress vs normal stress for synthetic pumice and scoria and Ascension Island ash. Open markers indicate small shear box tests for particle diameters ≤2 mm, filled markers indicate large shear box tests for particle diameters ≤16 mm

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Table 3 Internal angle of friction from shear box tests for synthetic pumice and scoria and Ascension Island ash
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Discussion

Near-source grain size distribution data

Typically GSDs of deposits become finer with increasing distance from the vent, as larger particles fall out close to source and finer particles remain in the plume (Koyaguchi and Ohno 2001a). However, the GSD of a proximal deposit depends on many factors which influence the eruption, transport and sedimentation of tephra. The magma fragmentation process influences the total grain size distribution of the erupted products (e.g. Kueppers et al. 2006; Cashman and Rust 2016), while sedimentation is affected by particle aggregation (e.g. Mueller et al. 2018; Rossi et al. 2021), plume dynamics (e.g. Scollo et al. 2017) and atmospheric conditions (e.g. Genareau et al. 2019; Poulidis et al. 2021). Our results reflect this complexity as eruptions of similar compositions show a wide range of near-source GSDs, while there is a large overlap between samples with different compositions and from eruptions of different sizes. The Ascension samples are not fresh (with last known eruptions ≥500 y ago) and may have been reworked, however, the Ascension GSDs are consistent with the published data for proximal samples from 11 eruptions (Table 1).

Deposit densities

Bulk density is influenced by both the density of individual grains, degree of saturation and the deposit packing. The latter depends on grain size distribution as this affects the extent to which voids between coarser grains can be filled by finer particles. A small number of eruptions have published data on both proximal/medial and distal bulk densities, with some having higher distal values (e.g. Thorarinsson and Sigvaldason 1972; Walker 1980; Todde et al. 2017), likely due to distal deposits having a higher crystal content or higher pumice density, as smaller particles have a relatively lower proportion of vesicles. However, this pattern is not followed for all eruptions (e.g. Thorarinsson 1954; Rose et al. 2008), particularly where the range of proximal densities is wide. Uncertainties with these data include the impact of changes over time, both short-term (compaction) and long-term (weathering), as well as the different methods used to measure deposit density. As noted in the introduction, tests in this study were only performed on dry samples, and the degree of saturation may add further uncertainly. The wide range of reported bulk densities and the lack of a clear trend relating to magma composition, eruption size or distance from source suggest these factors alone cannot reliably be used to estimate tephra loading.

Properties of synthetic samples

The GSDs and internal angles of friction of our synthetic samples matched well with the natural samples from Ascension for the grain sizes we considered (≥ − 4 φg, ≤ 16 mm) and the densities of the synthetic samples (412–1532 kg m− 3) lie within the range of published deposit densities. These important findings provide confidence that we can use synthetic samples to test the geomechanical behaviour of tephra deposits and so avoid the difficulties and costs associated with collecting and transporting natural samples.

Internal angle of friction

In plots of peak shear stress vs normal stress, results for coarse and fine GSDs plotted on the same line for both synthetic pumice and scoria (Fig. 9). This suggests that the friction angle is independent of grain size at the low normal stresses likely to be experienced in roof loads, where field surveys indicate that collapse can occur at ~ 1–10 kPa (Jenkins et al. 2014). This contrasts with results at higher normal stresses (> 100 kPa) where the internal angle of friction has been shown to vary with grain size (e.g. Hamidi et al. 2009; Mostefa Kara et al. 2013; Alias et al. 2014). At higher normal stresses the largest grains may provide a greater barrier to movement than found in our study.

Values of the internal angle of friction were very similar for pumice and scoria (36.5° and 35.8 ° respectively) suggesting that the friction angle is also independent of magma composition and deposit density. This implies that any internal sliding of the deposit will be consistent across a range of different compositions and grain sizes, at least for the compositions and GSDs tested here. This in turn is important, as tests at one GSD could provide information about the friction angle of other GSDs. However, these results should be confirmed by laboratory sliding tests.

The peak shear stresses for the volcanic ash from Ascension Island were lower than values for the synthetic samples at similar normal stresses. The ash also compacted throughout the tests, whereas the synthetic samples mainly showed dilatory behaviour after initial compaction. This is thought to be due to the natural sample having a higher proportion of very fine grains, which more easily reorganised and compacted into void spaces between the larger grains when stresses were applied. However, despite these differences in behaviour, the angle of friction of the Ascension ash (36.4°) was similar to the synthetic samples (36.5° and 35.8 °) and consistent with values for a range of volcanic rocks at similar normal stresses (Heap and Violay 2021). This indicates that this friction angle is applicable across different tephra compositions and grain sizes, including the synthetic deposits.

The angle of repose and the internal angle of friction (φf) may not be the same, as the failure plane is constrained when φf is determined using shear box tests. However, they are both related to the frictional properties of the grains. Tests on a range of granular materials (with maximum grain size ~ 6 mm) found that the angle of repose after consolidation closely matched the internal friction angle and was independent of grain size distribution (Metcalf 1966). This suggests that our results are relevant when considering the minimum roof pitch at which tephra will slide.

Relevance to tephra loading on roofs

The load transferred to a roof depends on the depth and density of a tephra fall deposit. Our results show that bulk density varies widely, even within a single eruption, and cannot be reliably estimated from magma composition or eruption size. Hence when assessing building vulnerability or designing new buildings to withstand tephra fall it is important to understand the range of loads likely to be experienced. This study has considered mafic and silicic deposits, with low to high bulk densities and coarse and fine GSDs and so our results are likely to be relevant when considering roof loading from future eruptions. However, our dataset should be supplemented where possible with relevant data from historic eruptions.

Limitations

This work only considered dry tephra and the addition of water would change the properties of the deposit considerably. Deposit densities have been reported to increase by 45–100% following rain (Blong 1981; Macedonio and Costa 2012; Hayes et al. 2019; Williams et al. 2021) and further work is needed to consider how water affects bulk densities and friction angles. As our shear box tests were limited to grains ≥ − 4 φg (≤ 16 mm), we did not consider how larger particles may affect the internal angle of friction within a deposit. Aspects other than simple gravitational sliding (e.g. drifting) may also change the distribution of material on a roof and these also need further investigation. In order to understand more about tephra sliding behaviour and how this impacts the load transferred to a roof, the effect of roof properties, for example, material and pitch, must also be considered. This should be the focus of future work that will allow development of standards to account for tephra loads in building design and risk analysis.

Conclusions

We combined published data and experimental results to investigate key geomechanical properties of tephra: bulk density, grain size distribution and internal angle of friction. These properties influence roof loading and are therefore important when assessing the vulnerability of buildings to collapse.

Published tephra deposit densities and near-source grain size distributions (≤ 10 km) vary widely but there are no clear trends when considering eruptions of different compositions and sizes that can be used when assessing vulnerability.

Our laboratory experiments revealed that, at the low normal stresses likely to be experienced in roof loads (≤ 35 kPa), values of the internal angle of friction were very similar across all our tests (35.8° - 36.5°). As the friction angle influences deposit sliding behaviour, this suggests that any internal sliding of the deposit will be consistent across a range of different magma compositions, deposit densities and grain sizes.

We have shown that synthetic tephra samples, made from crushing and grading volcanic aggregates, can be used to represent natural tephra deposits in tests of geomechanical properties relevant to roof loading, regardless of eruption type or composition. This is of particular importance given the difficulty of sourcing the required volumes of natural tephra.

We considered deposits with a wide range of magma compositions, densities and grain size distributions and so we have provided an envelope of values for parameters relevant to roof loading (Tables 2 and 3), in which future eruptions are likely to sit.