Philippa Kaur

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Present fire-climate classificationTo identify the different regions of the planet with suitable climatic conditions for fire activity, we compare the global distribution of climate indicators based on temperature and precipitation, with satellite-derived GFED4 burned area data21 (Fig. 1). Starting from four general climates (Tr-tropical, Ar-arid, Te-temperate and Bo-boreal) based on the Köppen–Geiger climate classification main categories22, we create four fire-prone classes using climate thresholds to define the patterns observed in Fig. 1. Each category is characterised by the element that boosts fire activity during the FS: low precipitation, high temperatures or a combination of both. The classification is made by contrasting the probability distribution of the climatic variables at data points associated with high fire activity vs. points with low fire activity within the main Köppen-Geiger categories (see Threshold Selection in Methods section for a detailed explanation).Fig. 1: Burned area observations and climate drivers.a 1996–2016 maximum annual burned area (BAmax) and monthly burned area time series for selected regions. b Average monthly precipitation percentage from the annual total for the fire season (PPFS). c Average monthly temperature anomaly from the annual mean for the fire season (TAFS).Full size imageThe environmental conditions associated with fire occurrence emerge more clearly in this comparison, yielding the different threshold sets in Table 1 that determine the fire-prone months at any location (the selection method is detailed in the Methods section). We define those years with at least 1-month meeting the thresholds, as fire-prone years (FPY). Depending on the number of FPY at each location, the categories of Table 1 are sub-divided into recurrent (r), occasional (o) and infrequent (i) (see Methods). The average number of fire-prone months during the FPY is defined as the potential FS length (PFSL), i.e., the season with climatic characteristics prone to fire activity.Table 1 Fire classification defining criteria.Full size tableFigure 2a depicts the global map of the burned areas classified according to the selected thresholds (Table 1). Savanna fires are responsible for the largest proportion of burned area on the global scale21. The FS in these areas is longer than in other climates (see Supplementary Fig. 1) and, despite savanna fires being also dependent on ignition patterns and human policies and practices, the FS is tied to a pronounced seasonal cycle of precipitation23,24,25, with fire occurring mainly during the dry part of the cycle. Because of this, the Tropical – dry season fire class (Tr-ds) coincides with the distribution of the tropical savanna climate. In Fig. 2, boreal fires are represented as hot season fires (Bo-hs) due to the large positive temperature anomaly existing in those locations during the FS (Fig. 1c). In fact, temperature variations explain much of the variability in boreal burned area26,27. Temperate fires are classified as dry and hot season (Te-dhs) because they affect regions where the dry season coincides with the warm season (Fig. 1b, c). Here, high temperatures and precipitation seasonality determine fire activity and inter-annual burned area variability, e.g., in Western North America28,29,30,31 and Southern Europe32,33. Fire activity in arid regions occurs during warm months, but the relation with precipitation is more complex. The FS is associated with a hot season in cooler (MAT  27.5 °C), the FS starts right at the beginning of the dry season (e.g., the Sahel, Supplementary Fig. 12) while where MATs are more moderate, between 18.5 and 27.5 °C, it takes longer to develop (e.g., Central Australia and the Kalahari desert, Supplementary Figs. 12 and 13). Due to the dependency between fires and the existence of fuel in arid climates, we named this class Arid fuel limited (Ar-fl). A more in-depth discussion about the definition of this fire-climate class can be found in the section entitled Threshold selection for each climate of the Supplementary Information.Fig. 2: Fire-prone region classification.a With observed burned area data as a reference: not classified (NC, white) and misclassified (C, black) areas with BAmax = 0 ha, unclassified (NC, grey) and classified (Tr-ds, Ar-fl, Te-dhs and Bo-hs) areas with BAmax  > 0 ha. Each class is subdivided into three subcategories depending on the recurrence of the fire-prone conditions: recurrent (r), occasional (o) and infrequent (i). b Present (1996–2016) fire-prone climatic regions. c Future (2070–2099) fire-prone climatic regions with shaded grey representing a  0 ha) or fireless (BA = 0 ha). This reveals a two-way relation between fires and climate: fires take place under specific climatic conditions, and most places with these climatic conditions are indeed fire-prone, which supports our earlier hypothesis. Fire activity is controlled by weather, resources to burn and ignitions, as represented through the fire regime triangle12,20. On broad temporal scales and large spatial scales, temperature and precipitation have an important impact on fire because these climate variables influence vegetation type and the abundance, composition, moisture content, and structure of fuels34. Although ignitions may be driving fires to a greater extent than temperature or precipitation at specific locations or events35, they do not seem to limit fire activity at coarse spatial and temporal resolutions, implying that where fuels are sufficient and atmospheric conditions are conducive to combustion, the potential for ignition exists, either by lightning or human causes13,20. For all these reasons, we can identify specific climates that are prone to fires.The areas classified as fire-prone in Fig. 2b comprise 99.26% of the observed global mean annual burned area in Supplementary Fig. 2. This percentage is above 85% for all four general climates (Supplementary Fig. 20). The percentage of land area with non-zero burned area data classified as fire-prone is 91.22%. Considering for each location only the obtained FPY, the percentage of the observed burned area classified is 90.36%. Furthermore, the PFS obtained in the fire-climate classification (Fig. 3b) also correlates well with the timing of observed fire incidence, as globally 87.91% of the observed mean burned area occurs during the identified months of PFS at classified fire-prone locations.Fig. 3: Potential fire season.a Future minus present potential fire season length (PFSL) difference in months (ΔPFSL). b Present potential fire season. c Future potential fire season.Full size imageUnclassified regions (in grey in Fig. 2a) correspond for the most part to those with the least burned area or those where agricultural practices modify the climatic seasonality of fires. In addition, as the classification is conceived from a climatic point of view, locations with fire activity associated with specific meteorological conditions that are not appreciable at the monthly temporal resolution, are probably not well identified. For example, a week of extremely high temperatures could be almost unnoticeable in the monthly mean temperature, but not in fire activity. Similarly, months with the same total precipitation may have different fire activity if the precipitation falls concentrated in a few days or is distributed throughout the month. Furthermore, the short temporal sampling period of the burned area data could also be influencing our results. Locations with long fire cycles may not be well represented in the data.Future fire-climate classificationA future fire-climate classification map is derived by applying the thresholds obtained in the present fire-climate classification to future climatology variables from multiple coupled model intercomparison project phase 5 (CMIP5) global circulation model (GCM) outputs, considering the RCP8.5 scenario (the worst-case climate change scenario of the CMIP5). Two contrasting approaches can be taken for analysing future fire activity, one that considers quick vegetation adaptation to the new climatic conditions, and another that does not. These two approaches clearly diverge in the boreal regions, where the biome (mainly taiga) is strongly conditioned by the low temperatures and where future temperature changes at the end of the 21st century will have a greater amplitude. It is expected that the boreal forest of these areas will not be immediately replaced by a temperate mixed forest where the average annual temperature exceeds the range of values typical of the taiga biome. Terrestrial vegetation compositional and structural change could occur during the 21st century where vegetation disturbance is accelerated or amplified by human activity, but equilibrium states may not be reached until the 22nd century or beyond36.Based on the assumption that during the future period (2070–2099) the vegetation will not be fully adapted to the new climatic conditions, and since the present Köppen–Geiger climate classification (on which we base our Tr, Ar, Te and Bo categories) closely corresponds to the different existent biomes22, we analyse only the projected changes in the specific fire-climate classification variables, maintaining the general division of Tropical, Arid, Temperate and Boreal regions as is in present climate conditions. The future fire-climate classification is shown in Fig. 2c.We note that we determine future fire activity from relationships of the latter with the present climate; however, these relationships might not be stationary. Our approach does not contemplate possible future changes in precipitation frequency if they are not noticeable in monthly precipitation amounts. Areas with the rising incidence of extreme precipitation events due to global warming37 may experience an increase in monthly precipitation but a decrease in rainy days, which may lead us to consider the conditions there less favourable for fire activity than they actually will be.Future changes in global fire activityModelled future fire-prone regions experience significant variations with respect to the present (Fig. 2b, c). Due to global warming, the Bo-hs fire class pertaining to boreal forests would spread over a larger area, reaching most of Northern Scandinavia and undergoing a southward and northward expansion in Canada, Alaska and Russia. This category may experience a percentual expansion of 47.0% according to our results. This expansion is more accentuated for the combination of the highest recurrence subcategories Bo-hs-r and Bo-hs-o, reaching a value of 111.5%.The conjunction of Te-dhs-r and Te-dhs-o fire classes of midlatitudes also undergoes a considerable expansion of 24.5% in the area (Fig. 2b, c). The most remarkable changes are expected in Southern China and Southern Europe. A large part of Europe transitions from an infrequent fire category to a more frequent fire category with Csa and Csb Mediterranean climates38.The Tr-ds fire classes with frequent fire-prone conditions in the Tropics presents fewer spatial changes (Fig. 2b, c), with a spatial contraction of 6.3%. The most important differences are found in South America. Some of the climate model results considered here indicate also that some parts of the Eastern Amazon rainforest will move from a non-fire class to Tr-ds fire class, as other studies have suggested39.The Arid fire-prone classes Ar-fl-r and Ar-fl-o would increase its area by 5.0%. Projected changes in the extent of this class are very sensitive to changes in annual precipitation, conducive to vegetation and fuel reduction or increment, thus there is significant uncertainty in the proximity of desert regions (Fig. 2c).Clearer conclusions can be drawn from the FPY and PFSL calculation (Figs. 3 and 4). The number of months meeting the set of conditions in Table 1 yields the estimated PFSL (Fig. 3b), and the number of years with at least 1-month meeting the thresholds, the FPY. In the boreal regions, we obtain a general lengthening of the PFS. The PFS of these areas is conditioned by temperature, so the amplified warming of Artic zones40 is expected to make the FS longer. Notwithstanding, in certain parts of Eastern Asia, the intense warming is counterbalanced by an increase of the precipitation in certain warm months (see Supplementary Figs. 21 and 22), leading to a slight shortening of our estimated PFS. There is evidence, however, that temperature increases may lead to drier fuels in the future despite the precipitation increase, thus augmenting fire risk, as some investigations have shown for Canada41. Our results agree in general with several other studies that have previously pointed towards an increase of the FSL in boreal areas1,17,42, even when some suggest a more pronounced lengthening in more northerly latitudes1,17. In terms of the frequency of years with fire-prone conditions, the conclusions are even clearer. A general increase of the FPY is observed, especially for northerly latitudes, where the differences reach values of more than +4 years per decade (Fig. 4a). This possible increase in fire activity in boreal areas may result in significant peatland combustion and a release of the large quantities of soil carbon that they store into the atmosphere43. These greenhouse gas emissions may create a positive feedback loop, leading to a further increase in temperature, which in turn will enhance boreal wildfire incidence and more peatland burning.Fig. 4: Fire-prone years.a Future minus a present number of years with at least one month classified as fire-prone per decade (ΔFPY). b Present fire-prone years per decade. c Future fire-prone years per decade.Full size imageThe Te-dhs fire class, corresponding to temperate climates, would also experience a general lengthening of the PFS (Fig. 3). A future precipitation decline may be especially significant in Southern Europe (Supplementary Fig. 21), associated with an increased anticyclonic circulation yielding more stable conditions44, while the temperature rise would be quite homogeneous among all Te-dhs fire-climate class areas. The FS drought intensification around the Mediterranean, together with the general warming (Supplementary Fig. 21), would lead to a lengthening of the PFS of around 2 months (Fig. 3a), but summer months could also experience this precipitation decline (Supplementary Fig. 22), meaning that the FS would be more severe. The Western US, which has already experienced over the last decades the lengthening of the FS45 and the increase of large fires46 and extreme wildfire weather47,48 due to climate change, may also experience an FS lengthening by the end of the 21st century. Some authors18,48,49,50 have studied projected fire future changes from other points of view (occurrence of very large fires, wildfire potential, etc.), finding also a general increase of fire severity by the end of the century in some of these Te-dhs fire regions. The interannual recurrence of fire-prone conditions will significantly increase in countries like France, Italy or Eastern China (Fig. 4a).The PFSL of the Tropical Tr-ds fire-climate class presents slight differences between present and future values (Fig. 3). Some areas of the Northern African savanna may experience a shortening of the PFS, while Southern Africa shows a lengthening. A dipole pattern of wetting in tropical Eastern Africa and drying in Southern Africa51 could be the reason for these future changes. There is a contrasting influence of ENSO in present African fire patterns52, which suggests that the future pattern of precipitation variations in Central Africa may be associated with ENSO future changes under climate change conditions53. Although the quantification of ENSO changes in a warmer climate is still an issue that continues to be investigated, an expansion and strengthening of ENSO teleconnections is confirmed by some authors53,54,55. The general increase in precipitation along all seasons in western equatorial Africa would lead to a significant decrease in the recurrence of interannual fire-prone conditions (Fig. 4a).Our results show that fire-prone areas in Temperate and especially Boreal climates are projected to undergo the most significant expansion and lengthening of the potential FS at the end of the XXI century driven by rising temperatures. In the Tropics, little change is expected in these respects. Notwithstanding, global warming is likely to make fire risk more severe mostly everywhere, and in particular in some regions such as Mediterranean Europe and the Eastern Amazon, where an important decrease in precipitation is also predicted during the PFS. More favourable fire conditions will potentially increment fire activity and burned areas in many places. In others, especially in the Tropics, increasing suppression efforts and a cease to agricultural and pastoral practices like vegetation clearing by fire, replaced by more intensive farming, could counteract the impact of a warmer climate. A reduction of these human-caused fires in the Tropics could bring global burned area down2, despite rising trends elsewhere, given the vast contribution of Tropical fires to the burned areas at the global scale (Fig. 1). More

Our compiled dataset consisted of 1674 records of marine mammal records after removing duplicate reports. It included 660 reports of sightings, 59 reports of induced mortalities or hunting records, 240 reports of incidental mortalities, 632 unique stranding records (live / dead), and 83 records which could not be categorised because of incomplete information.SightingsA total of 660 opportunistic sightings (number of individuals, ni = 3299) were recorded throughout the Indian coastline between 1748 and 2017 (Fig. 1a, 2a, 3a). Sighting data on the east coast (species = 18, ni = 1105) was mostly restricted to Odisha and Tamil Nadu (representing 97% of total east coast sightings). On the west coast (ni = 1297), Maharashtra (ni = 549), Gujarat (ni = 248) and Karnataka (ni = 307) contributed to highest sighting records (representing 85% of total west coast sightings). Sightings from the islands also contributed to 24.85% of the dataset (Andaman & Nicobar Islands = 24.37%, Lakshadweep = 0.48%). Highest incidence of sightings was for DFP (ni = 1894) followed by dugongs (ni = 959), BW (ni = 58) and SBW (ni = 17).Figure 1Marine mammal records obtained from data compiled between years 1748 – 2017 along the east coast, west coast and the islands of India for the groups i.e., baleen whales (BW), dolphins and finless porpoise (DFP), sperm and beaked whales (SBW) and dugongs, given as color-coded stacked bars where (a) sighting records—records where live animals were sighted (b) induced mortalities—records where animals were reported hunted or killed or were driven ashore, (c) incidental mortalities—records where animals were found dead after entanglement in fishing nets or being struck by vessels and (d) stranding records—records where dead or live animals were found washed ashore, or floating near shore or stranded alive and were attempted for rescue.Full size imageFigure 2Marine mammal records obtained every year from the data compiled between years 1748–2017 along Indian coastline given as cumulative numbers for each group i.e., baleen whales (BW), dolphins and finless porpoise (DFP), sperm and beaked whales (SBW) and dugongs, as color-coded stacked bars, where (a) sighting records—records where live animals were sighted (b) induced mortalities—records where animals were reported hunted or killed or were driven ashore, (c) incidental mortalities—records where animals were found dead after entanglement in fishing nets or being struck by vessels and (d) stranding records—records where dead or live animals were found washed ashore, or floating near shore or stranded alive and were attempted for rescue.Full size imageFigure 3Bubble plots showing distribution of marine mammal records obtained from data compiled between years 1748–2017 along the Indian coastline for each group i.e., baleen whales (BW), dolphins and finless porpoise (DFP), sperm and beaked whales (SBW) and dugongs, as color-coded stacked bars, where (a) sighting—records where live animals were sighted (b) induced mortalities—records where animals were reported hunted or killed or were driven ashore, (c) incidental mortalities—records where animals were found dead after entanglement in fishing nets or being struck by vessels and (d) strandings—records where dead or live animals were found washed ashore, or floating near shore or stranded alive and were attempted for rescue. Size of the bubble indicates number of individuals. These maps were created using ArcGIS 10.5 (https://desktop.arcgis.com/en/arcmap/10.3/map/working-with-layers/about-symbolizing-layers-to-represent-quantity.htm).Full size imageInduced mortalitiesA total of 59 incidences (ni = 102) were recorded of marine mammals being hunted/ captured between the years 1748–2017 (Fig. 1b, 2b, 3b). The total number of animals hunted/ captured deliberately is similar along east coast (ni = 33), west coast (ni = 29) and islands (ni = 36). Out of all marine mammal species, 90% of the animals hunted at the east coast were dugong D. dugon (ni = 30, all from Tamil Nadu). On the west coast, records of hunting incidences of finless porpoise Neophocaena phocaenoides were highest (79% of total records on west coast, Goa ni = 17, Kerala ni = 4, Karnataka and Maharashtra ni = 1). In the islands (i.e., Andaman and Nicobar Islands), 94% of the hunting records were of dugongs (ni = 34).Incidental mortalitiesA total of 240 net entanglements (ni = 1356) were reported along the Indian coast between the years 1748 and 2017 (Fig. 1c, 2c, 3c). Similar counts of individuals entangled along east (ni = 670) and west coast (ni = 654) were obtained with low reporting from the islands (ni = 26). Fourteen species were reported entangled from both east and west coast with only 4 species recorded from the islands. D. dugon was found to be most frequently entangled along the east coast (63 incidences, ni = 594, contributing to 56% of the total numbers on east coast), followed by Tursiops sp. (11 incidences, ni = 14, 9% of the east coast dataset). On the west coast, Tursiops sp. was the most frequently entangled (18 incidences, ni = 117, contributing to 18% of the west coast dataset), followed by N. phocaenoides (17 incidences, ni = 34, contributing to 17% of the dataset). The total number of DFP being entangled from west coast (ni = 623) were higher than east coast (ni = 68). More dugong individuals were entangled along east coast (i.e., from Tamil Nadu; ni = 594) as compared to the west coast (i.e., Gujarat; ni = 3) and Islands (i.e., Andaman and Nicobar; ni = 19). D. dugon was the most frequently entangled species in the islands (19 incidences, ni = 19, contributing to 79% of the total numbers in islands dataset) followed by false killer whale Pseudorca crassidens (3 incidences, ni = 5, contributing to 12% of the islands dataset). Very few BW or SBW (11 incidences, ni = 11) were recorded accidently entangled throughout the Indian coastline.StrandingsMarine mammals stranding reports consisted of 91.93% dead (ni = 581) and 8.07% live strandings (ni = 51) (Figs. 1d, 2d, 3d). Considering mass strandings as strandings with ni  > 2 (excluding mother and calf;33,34), 8.5% of all reports were mass strandings (21 strandings, ni = 1054). Most of the records did not have information about the sex of the stranded animal (83%), the age class (88%) or the state of decomposition of the carcass (53%). Highest strandings were reported of dugongs (strandings = 190, ni = 228), followed by BW (strandings = 178, ni =  = 190), DFP (strandings = 157, ni =  = 552) and SBW (strandings = 47, individuals = 48). There were 54 incidences (ni = 54, 9% of total stranding data) where the animal was not identified reliably to include in either of the groups.Species composition and frequencies of strandings were different on east coast, west coast and in the islands (Fig. 1, Table 1). Twenty-two species were reported as stranded on the east coast with D. dugon as the most frequently stranded species (83 incidences, ni = 107, ~ 29% of all records), followed by Indo-Pacific humpback dolphin Sousa chinensis, (31 incidences, ni = 108, ~ 10% of all records). On the west coast, out of 20 species reported as stranded, Balaenoptera musculus was most frequent (28 incidences, ni = 29, ~ 12% of all records) followed by N. phocaenoides (23 incidences, ni = 39, ~ 10% of all records). In the islands, 13 species were reported as stranded, D. dugon (93 incidences, ni = 102, contributing to 77% of the total animals found on the islands) followed by strandings of sperm whale Physeter macrocephalus (8 incidences, ni = 8, contributing to 6% of the data; Table 1).

a. Baleen whales

Table 1 Number of stranding events reported for marine mammals between 1748–2017 in India from the east coast, the west coast and Lakshadweep and Andaman & Nicobar archipelagos.Full size tableA total of 178 BW strandings (ni = 190) were reported. Most species were unidentified (east coast ni= 27, west coast ni = 58, islands ni = 4; i.e., 47% of the data). Identified strandings comprised of 6 species (see Table 1), some of which were later found to be misidentification (no confirmed evidence for common Minke Whale Balaenoptera acutorostrata, Sei Whale Balaenoptera borealis and Fin Whale Balaenoptera physalus from Indian waters; MMRCNI, 2018). Higher number of strandings occurred on the west coast (ni = 126), as compared to east coast (ni = 60). The east and west coast reported all six species of BW, whereas only three species stranded on the islands. B. borealis (misidentified) was the most stranded species across the east coast (12 incidences, ni = 12, contributing to 11% of the data) whereas blue whale Balaenoptera musculus was the most frequent across the west coast (28 incidences, ni = 29, contributing to 11% of the data). Baleen whale strandings were rare in the islands (4 incidences, ni = 4).Forty-seven SBW strandings (ni = 48) were reported along the Indian coast. More SBW stranded on the east coast (ni = 23) as compared to the west coast (ni = 13) and the islands (ni = 12). P. macrocephalus was most frequently reported (70% of all SBW records, east coast ni = 20, west coast ni = 6, islands ni = 8).There were 157 strandings (ni =552) of DFP belonging to 14 species. Twenty-one of these events were mass strandings (ni  > 2). The largest mass stranding event (ni = 147) occurred of short-finned pilot whale Globicephala macrorhynchus along the west coast (Tamil Nadu). Higher number of DFP strandings were recorded from east coast (ni = 418) as compared to west coast (ni = 83) and the islands (ni = 51; Table 1). East coast received a higher diversity of stranded DFP (number of species = 11) as compared to west coasts (number of species = 9) and the islands (number of species = 3). S. chinensis was the most frequently stranded species along the east coast (31 incidences, ni = 108, contributing to 33% of the data) whereas N. phocaenoides was the most frequent along the west coast (23 incidences, ni = 39, contributing to 37% of the data; Table 1).

d. Dugongs

The current distribution of dugongs in India is in the shallow coastal waters of Gujarat, Tamil Nadu and Andaman & Nicobar Islands37,38. There are 190 stranding events recorded between the years 1893 and 2017. The highest number of stranded dugongs were recorded from Tamil Nadu (ni = 107) closely followed by Andaman and Nicobar Islands (ni = 102) and few records from Gujarat (ni = 19).Temporal stranding patternsOur analysis of temporal trends for the last 42 years (1975–2017) showed that the mean number of strandings along the Indian coast was 11.25 ± SE 1.39 / year. The number of stranding reports show an increasing trend for two decades after 1975, dropping between 1995 and 2004. We observed a distinct rise in strandings post 2005 (18.23 ± SE 2.98 / year) with the highest reports from 2015–17 (27.66 ± SE 8.51/year) (Fig. 4).

a. Baleen whales

Figure 4A beanplot of decadal trends in marine mammal stranding in India from data compiled between years 1975–2017. Data prior to 1975 was discontinuous over the years to be considered for decadal trends. The data for last decade considered here includes only two years (2015–17) where increased reporting is evident. The bold horizontal lines indicate the mean number of strandings in each decade whereas the smaller horizontal lines indicate stranding numbers recorded for each year within the decade.Full size imageOn the west coast, mean stranding rate throughout the years (1975–2017) was 0.0010 ± SE 0.0014 strandings/km, and a steady rise was observed in rate of reported strandings after 2010. A seasonal trend was observed as well, with a peak in the month of September (sr = 0.0061 ± SE 0.0016 strandings/km), i.e., towards the end of monsoon season, and lowest strandings were recorded in the month of June (sr = 0.0016 ± SE 0.006 strandings/ km) (Fig. 5).Figure 5Temporal patterns (annual and monthly stranding rates / 100 km of coastline) in strandings of marine mammal records obtained from data compiled between years 1975–2017 along east and west coast of India for each group where (a) annual stranding rate and (b) monthly stranding rate for baleen whales (BW); (c) annual stranding rate and (d) monthly stranding rate for dolphins and finless porpoise (DFP); (e) annual stranding rate and (f) monthly stranding rate for sperm and beaked whales (SBW) and (g) annual stranding rate and (h) monthly stranding rate for dugongs.Full size imageThe mean stranding rate of BW on the east coast through 1975–2017 was 0.0013 ± SE 0.0017 strandings/km, but no specific trends were observed according to years or seasons. Stranding rates of BW did not differ between east and west coast (Mann–Whitney U test, U = 390, U standardized = -0.025, p value  > 0.05).The stranding rates of SBW differed significantly along both the coasts (Mann Whitney U test, U = 192, U standardized = 0.0, p value  More

Detection and validation of high-quality jumbo phage binsDue to the large size of jumbo bacteriophage genomes, it is likely that they are present in multiple distinct contigs in metagenomic datasets and therefore require binning to recover high-quality metagenome-assembled genomes (MAGs) [28]. This has been shown for large DNA viruses that infect eukaryotes, where several recent studies have successfully employed binning approaches to recover viral MAGs [2, 3, 30]. Here, we used the same 1545 high-quality metagenomic assemblies [31] used in a recent study to recover giant viruses of eukaryotes [3], but we modified the bioinformatic pipeline to identify bins of jumbo bacteriophages. These metagenomes were compiled by Parks et al. [31] and included available metagenomes on the NCBI’s Short Read Archive by December 31, 2015 (see Parks et al. [31]). This dataset includes a wide variety of marine metagenomes (n = 469) including many non-Tara metagenomes (n = 165). We focused our benchmarking and distribution analyses on Tara data [29] because of the well-curated metadata and size fractions in this dataset. We first binned the contigs from these assemblies with MetaBat2 [32], which groups contigs together based on similar nucleotide composition and coverage profiles, and focused on bins of at least 200 kilobases in total length. We subsequently identified bins composed of bacteriophage contigs through analysis with VirSorter2 [33], VIBRANT [34], and CheckV [35] (see Methods for details).The occurrence of multiple copies of highly conserved marker genes is typically used to assess the level of contamination present in metagenome-derived genomes of bacteria and archaea [36]. Because bacteriophage lack these marker genes [37], we developed alternative strategies to assess possible contamination in our jumbo phage bins. Firstly, we refined the set of bins by retaining those with no more than 5 contigs that were each at least 5 kilobases in length to reduce the possibility that spurious contigs were put together. Secondly, we assessed the possibility that two strains of smaller phages with similar nucleotide composition may be binned together by aligning the contigs in a bin to each other. Bins that had contigs with high sequence similarity across the majority of their lengths were discarded (Supplementary Fig. 1). Thirdly, we discarded bins if their contigs exhibited aberrant co-abundance profiles in different metagenomes (see Supplementary Methods). To generate these co-abundance profiles, we mapped reads from 225 marine metagenomes provided by Tara Oceans [29] onto the bins. Coverage variation between contigs was benchmarked based on read-mapping results from artificially-fragmented reference genomes present in the samples (See Methods for details). Only bins with coverage variation below our empirically-derived threshold were retained. Using this stringent filtering, we identified 85 bins belonging to jumbo bacteriophages. These bins ranged in length from 202 kbp to 498 kbp, and 31 consisted of a single contig, while 54 consisted of 2–5 contigs (Supplementary Fig. 2).To assess global diversity patterns of jumbo bacteriophages, we combined these jumbo phage bins together with a compiled database of previously-identified jumbo phages that included all complete jumbo Caudovirales genomes on RefSeq (downloaded July 5th, 2020), the INPHARED database [14], a recent survey of cultivated jumbo phages [6], the Al-Shayeb et al. study [4], and marine jumbo phage contigs from metagenomic surveys of GOV 2.0 [26] (60 jumbo phages), ALOHA 2.0 [38] (8 jumbo phages), and one megaphage MAG recovered from datasets of the English Channel [39]. Ultimately, we arrived at a set of 244 jumbo phages, including the 85 bins, that were present in at least one Tara Oceans sample (min. 20% genome covered, see Methods) or deriving from a marine dataset (i.e. ALOHA, GOV 2.0) which we analyzed further in this study and refer to as marine jumbo phages. Statistics on genomic features can be found in Supplementary Dataset 1.Marine jumbo phages belong to distinct groups with diverse infection strategiesBecause bacteriophages lack high-resolution, universal marker genes for classification, such as 16S rRNA in bacteria, phages are often grouped by gene content [40, 41]. Here, we generated a bipartite network that included the 85 bins of jumbo phages with a dataset of available Caudovirales complete genomes in RefSeq (3012 genomes; downloaded July 5th, 2020) and the full set of reference jumbo phages described above. To construct the bipartite network, we compared proteins encoded in all the phage genomes to the VOG database, and each genome was linked to VOG hits that were present (Fig. 1, Supplementary Dataset 2, see Methods for details). To identify groups of phage genomes with similar VOG profiles, we employed a spinglass community detection algorithm [42] to generate genome clusters. Similar methods have recently been used to analyze evolutionary relationships in other dsDNA viruses [41]. The marine jumbo phages of this study clustered into five groups that included both jumbo and non-jumbo phage genomes (Fig. 2a). We refer to these five clusters as Phage Genome Clusters (PGCs): PGC_A, PGC_B, PGC_C, PGC_D, and PGC_E. These PGCs included cultured phages and metagenome-derived jumbo phages found in various environments (i.e. aquatic, engineered) and isolated on a diversity of hosts (i.e. Firmicutes, Proteobacteria, Bacteroidetes) (Fig. 2b, c). Of the marine jumbo phages, 135 belonged to PGC_A, 11 to PGC_B, 90 to PGC_C, 7 to PGC_D, and 1 to PGC_E (Fig. 1b). In addition to this network-based analysis, we also examined phylogenies of the major capsid protein (MCP) and the terminase large subunit (TerL) encoded by the marine jumbo phages and the same reference phage set examined in the network (Fig. 1c, d). With the exception of PGC_A, the marine jumbo phages that belong to the same PGC appeared more closely related to each other than those belonging to different clusters. The polyphyletic placement of jumbo phage PGCs in these marker gene phylogenies is consistent with the view that genome gigantism evolved multiple times, independently within the Caudovirales [6].Fig. 1: Bipartite network and marker gene analyses of jumbo phages.a Network with marine jumbos and references as nodes and edges based on shared VOGs. Marine jumbo phage nodes are colored by PGC as detected with spinglass community detection analysis, other nodes are in gray. Edges and VOG nodes have been omitted to more clearly represent the pattern of phage clustering. Node size corresponds to the natural log of genome length in kilobases. b Barchart of the number of members in each PGC. PGCs with marine jumbo phages are denoted with a star and the number of marine jumbo phages in that PGC. Proportion of marine jumbo phages in that PGC is colored. Phylogenies of TerL (c) and MCP (d) proteins with references and bins. Inner ring and branches are colored by the 5 PGCs that marine jumbo phages belong to. Navy blue circles in the outer ring denote marine jumbo phages.Full size imageFig. 2: Statistics of the Phage Genomes Clusters (PGCs).a Boxplot of genome length in each network cluster (x-axis is PGC number). Star denotes PGC with a marine jumbo phage and the color matches the PGC letters of Fig. 1. b Stacked barplot of the metagenome environment from which each phage derives from in each PGC (x-axis). Reference (yellow) are cultured phages, in black are the bins of jumbo phages from this study. c Stacked barplot of the host phylum of the RefSeq cultured phages in each cluster; metagenomic phages are in gray.Full size imageWe then compared functional content encoded by the marine jumbo phages in the PGCs to identify functional differences that distinguish these groups. PGC_E was excluded from this analysis because this genome cluster contained only a single jumbo phage. Collectively, most genes of the marine jumbo phages could not be assigned a function (mean: 86.60%, std dev: 7.01%; Supplementary Dataset 3), which is common with environmental viruses [43, 44]. Genes with known functions primarily belonged to functional categories related to viral replication machinery, such as information processing and virion structure (Fig. 3a), and these genes drove the variation between the genome clusters of marine jumbo phages (Fig. 3b). A recent comparative genomic analysis of cultivated jumbo phages was able to identify three types of jumbo phages that are defined by different infection strategies and host interactions (referred to as Groups 1–3) [6]. We cross-referenced our PGCs and found that PGCs B, C, and D of this study corresponded to Groups 1, 2, and 3, respectively, suggesting that these genome clusters contain phages with distinct infection and replication strategies. PGC_A corresponded to multiple groups, indicating that this genome cluster contains a particularly broad diversity of phages.Fig. 3: Functional predictions of PGCs.a Functional categories for genes encoded by jumbo phages averaged by PGC. b Heatmap of proportion of genomes in each PGC that contain the listed genes. Listed genes were selected based on containing a known function and having a variance between the PGCs above 0.2. Dendrogram was generated based on hierarchical clustering in pheatmap.Full size imageThe second largest phage cluster with marine jumbo phages, PGC_B, consists of 238 phages (11 (4.6%) marine jumbo phages, including 10 bins generated here), and included cultured phages of Group 1, which is typified by Pseudomonas aeruginosa phage PhiKZ. Supporting this correspondence with Group 1, all marine jumbo phages of PGC_B encoded the same distinct replication and transcription machinery, including a divergent family B DNA polymerase and a multi-subunit RNA polymerase (Fig. 3b, Supplementary Dataset 3). These marine jumbo phages also encoded a PhiKZ internal head protein, and they uniquely encoded shell and tubulin homologs which has recently been found in PhiKZ phages to assist in the formation of a nucleus-like compartment during infection that protects the replicating phage from host defenses [18, 19]. Although we could not confidently predict hosts for the 11 metagenomic marine jumbo phages in this PGC_B (Supplementary Dataset 1), the cultured phages of this genome cluster infect pathogenic bacteria belonging to the phyla Proteobacteria (178 phages) and Firmicutes (6 phages) (Fig. 2c), implicating a potential host range for marine jumbo phages in PGC_B.The next largest phage genome cluster, PGC_C, comprised of 156 phages total (90 marine jumbo phages (57.7%); 4 bins generated from this study) and included reference jumbo phages in Group 2 (31, 19.9%) which are typified by Alphaproteobacteria and Cyanobacteria phages. Likewise, the host range of other cultured phages in PGC_C support the Group 2 correspondence, either infecting Cyanobacteria (139 phages) or Proteobacteria (4 phages) (Fig. 2c). Furthermore, all 3 marine metagenomic phages in PGC_C for which hosts could be predicted were matched to Cyanobacteria hosts (Supplementary Dataset 1). Functional annotations of PGC_C marine jumbo phages revealed nearly all encode a family B DNA polymerase (97.8% of phages) and the photosystem II D2 protein (PF00124, VOG04549) characteristic of cyanophages (90% of phages) (Fig. 3b). This PGC included the reference Prochlorococcus phage P-TIM68 (NC_028955.1), which encodes components of both photosystem I and II as a mechanism to enhance cyclic electron flow during infection [45]. This suggests that an enhanced complement of genes used to manipulate host physiology during infection may be a driver of large genome sizes in this group. Additionally, most of the PGC_C marine jumbo phages encoded lipopolysaccharide biosynthesis proteins (76%), which have been found in cyanophage genomes that may induce a “pseudolysogeny” state, when infected host cells are dormant, by changing the surface of the host cell and preventing additional phage infections [6] (Supplementary Dataset 3). Taken together, most marine jumbo phages of PGC_C likely follow host interactions of jumbo cyanophages, such as potentially manipulating host metabolism by encoding their own photosynthetic genes and potentially inducing a pseudolysogenic state.Finally, phages of PGC_D totaled at 47 phages, of which 7 were marine jumbo phages generated in this study (14.9%). This group included Group 3 jumbo phages (15, 31.9%), which is primarily distinguished by encoding a T7-type DNA polymerase but is not typified by a particular phage type or host range. Supporting this grouping, all marine jumbo phages in this study encoded a T7 DNA polymerase which belongs to family A DNA polymerases (Fig. 3b, Supplementary Dataset 3). Most of the other genes distinctively encoded by the marine jumbo phages in this group included structural genes related to T7 (T7 baseplate, T7 capsid proteins), a eukaryotic DNA topoisomerase I catalytic core (PF01028), and DNA structural modification genes (MmcB-like DNA repair protein, DNA gyrase B). Hosts of metagenomic marine jumbo phages in PGC_D could not be predicted (Supplementary Dataset 1); however, cultured Group 3 jumbo phages in PGC_D all infect Proteobacteria, primarily Enterobacteria and other pathogens.The largest of the phage genome clusters, PGC_A, contained 469 phages, including 135 marine jumbo phages (63 bins from this study). This genome cluster contained the largest jumbo phages, such as Bacillus phage G (498 kb) and the marine megaphage Mar_Mega_1 (656 kb) recently recovered from the English Channel [39]. Unlike other PGCs, PGC_A contained mostly metagenomic phages (401, 85%, Fig. 2b, c). Considering PGC_A contains the largest jumbo phages (Figs. 1b, 2a), the vast genetic diversity in this PGC might explain why few genes were found to distinguish this group. Of the genes unique to PGC_A, only one was present in at least half of the phages (51.9%), which was a Bacterial DNA polymerase III alpha NTPase domain (PF07733). The host ranges of cultured phages from this PGC further reflect the large diversity of this group and included a variety of phyla and genera that can perform complex metabolisms or lifestyles, such as the nitrogen-fixing Cyanobacteria of the Nodularia genus isolated from the Baltic Sea (accessions NC_048756.1 and NC_048757.1) and the Bacteroidetes bacteria Rhodothermus isolated from a hot spring in Iceland (NC_004735.1) [46]. Because this group contains an abundance of metagenome-derived genomes that encode mostly proteins with no VOG annotation (Supplementary Dataset 2), it is possible that it includes several distinct lineages that could not be distinguished using the community detection algorithm of the bipartite network analysis.Relative abundance of jumbo bacteriophages across size fractionsTo explore the distribution of the marine jumbo phages in the ocean, we first examined the size fractions in which the jumbo phages were most prevalent. To remove redundancy for the purposes of read mapping, we examined the 244 jumbo phages at the population-level ( >80% genes shared with >95% average nucleotide identity [24]), corresponding to 142 populations (11 unique to this study, corresponding to 47 bins). We then mapped Tara Oceans metagenomes onto the 142 jumbo phage populations, and 102 of these populations could be detected [min. 20% of genome covered], resulting in 74 populations in PGC_A, 2 in PGC_B, 22 in PGC_C, 3 in PGC_D, and 1 in PGC_E. Out of the 225 Tara Oceans metagenomes examined, 213 (94.6%) contained at least one jumbo phage population (median: 7, Supplementary Dataset 4). Jumbo phages were more frequently detected in samples below 0.22 µm ( More

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Design parametersA new type of Debris-flow grille dam is proposed to be built with a height of 8 m. Column section 500 mm × 700 mm, spacing 5000 mm. The cross section of the beam is 400 mm × 300 mm, and the spacing is 4000 mm. The section steel adopts I-steel 45a, the spacing is 250 mm. The counterfort wall is 300 mm thick and 6500 mm high. Pile foundation adopts manual digging pile, pile by 1000 mm, 5000 mm deep. The concrete is C30; Stressed bar is HRB335; Stirrups is HRB300; Stay Cable is 3 (emptyset) s15.2. The design size of the anchor piers is shown in Fig. 12. In the Figure where (T = 2 times 10^{5} N); (L_{l} = 8500;{text{mm}}); (E_{l} = 1.95 times 10^{5} ;{text{N/mm}}^{2}); (A_{l} = 420;{text{mm}}); (D_{e} = 1000;{text{mm}}); (L_{m} = 1200;{text{mm}}); (E_{e} = 3.0 times 10^{4} ;{text{N/mm}}^{2}); (H = 1000;{text{mm}}); (mu = 0.2); (E = 20;{text{N/mm}}^{2}). The parameter of gully bed soil is shown in Table 1.Figure 12The parameters of anchor piers.Full size imageTable 1 The parameters of gully bed soil.Full size tableAnalysis of results(1) The effect of the elastic modulus and Poisson’s ratio of the surrounding soil on the displacement deformation of the anchor-pulling system.The elastic modulus (E) and Poisson’s ratio (mu) are important parameters for calculating the displacement deformation of soil. They have something to do with both the properties of materials and the stress level. To analyze the effect of the physical parameter variation of the surrounding soil on the displacement deformation of the anchor-pulling system, we can study changing the elastic modulus and Poisson’s ratio. The variation range of the elastic modulus is 15–45 N/mm2, and the variation range of Poisson’s ratio is 0.15–0.25.Figure 13 shows the variation curve in which the displacement deformation increases with the elastic modulus of the soil around the anchor pier. We can see that as the elastic modulus of the soil around the anchor pier increases, the displacement deformation decreases gradually. When the elastic modulus is in the range of 15–35 N/mm2, the curve is steep, and the decrease in deformation is apparent. After 35 N/mm2, the curve becomes smooth, and the decrease in deformation tends to be stable.Figure 13The effect of the elastic modulus E(15–45 N/mm2) of the surrounding soil on the displacement of the anchor-pulling system.Full size imageIn Fig. 14, the displacement deformation increases linearly with Poisson’s ratio of the soil around the anchor pier. However, the total impact is not large. From calculation, the variation of elastic modulus of the soil around the anchor pier has nothing to do with elastic deformation of the stayed cable ((S_{1} )), but mainly influences relative shear displacement between anchor piers and the surrounding soil ((S_{2} )) and the compression performance of the soil on the front of anchor piers ( (S_{3} )). where ((S_{2} )) accounted for 89% and (left( {S_{3} } right)) accounted for 11%. When the Poisson ratio increases, the displacement deformation also increases. Poisson’s ratio has the greatest influence on the relative shear displacement ((S_{2} )) of the anchor pier and soil, accounting for approximately 96.4%. The design parameters should be selected correctly during design. The influence of parameters on the deformation of anchor system is analyzed by using control variable method. The influence of a single variable on the results can be intuitively obtained. However, the elastic modulus E and Poisson ‘ s ratio (mu) of rock and soil are not independent. Therefore, Matlab is used to analyze the influence of the two aspects on the deformation of the tensile anchor system, and the results are shown in Fig. 15. It can be seen from Fig. 15 that the influence of elastic modulus E on the deformation of tensile anchor system is much greater than that of Poisson’s ratio (mu). And the variation of the curve is basically the same, so the interaction between the two is weak.Figure 14The effect of Poisson’s ratio (mu)(0.15–0.26) of the surrounding soil on the displacement of the anchor-pulling system.Full size imageFigure 15Influence of elastic modulus E (15–45 N/mm2) and Poisson’s ratio (mu left( {0.15 – 0.26} right)) on deformation of anchor system.Full size image(2) The effect of the design parameters of anchor piers on the displacement deformation of the anchor-pulling system.The design parameters of anchor piers include the equivalent width (D_{e}), length (L_{m}) and height (H). Different design parameters have varying effects on the displacement deformation of the anchor-pulling system. Keep other parameters unchanged and let ( D_{e} ) vary in 0.5–1.5 m, (L_{m}) vary in 0.6–2.0 m, and (H) vary in 0.5–1.5 m. Analyzing their effect on the displacement deformation of the anchor-pulling system, the results are shown in Figs. 16 and 17.Figure 16The effect of equivalent width (D_{e})(500–1500 mm) on the displacement of the anchor-pulling system.Full size imageFigure 17The effect of equivalent length (L_{m})(600–2000 mm) on the displacement of the anchor-pulling system.Full size imageAs illustrated in Figs. 16 and 17, the effects of the design parameters of the anchor piers on the displacement deformation of the anchor-pulling system are almost the same. As the size increases, the displacement deformation gradually decreases, and the front section decreases quickly, while the rear section becomes gradually smooth. Here, the equivalent width (D_{e}) and length (L_{m}) mainly affect the compression performance of the soil on the front of anchor piers (left( {S_{3} } right)). The anchor piers can be seen as rigid bodies where horizontal displacement takes place. Increasing the size means increasing the contact area between the anchor pier and soil body. With this increase, the compression performance of the soil on the front of the anchor piers decreases. However, the effect of the height (H) on the displacement deformation of the anchor-pulling system is the contribution to the relative shear displacement between the anchor piers and the surrounding soil ((S_{2} )). When (H) grows, ((S_{2} )) grows accordingly. However, theoretically, the larger the effect of the size, the better it is. Because of the constraint of topographic conditions, construction conditions and economic benefits in practical engineering, it is necessary to choose the best size. the anchor pier provides enough anchor force and saves all kinds of resources. The best design dimensions suggested are (D_{e}) = 1.2 m–1.8 m, (L_{m}) = 1.5 m–2.5 m, and (H) = 1.0 m–1.6 m.It can be seen from Fig. 18 that the width (D_{e}) and the height (L_{m}) of anchor pier influence each other greatly. When (D_{e}) is 600 mm, with the increase of (L_{m}), the deformation of tension anchor system will first decrease and then increase. When (D_{e}) is greater than 800 mm, with the increase of (L_{m}), the deformation of tension anchor system will continue to decrease. And with the increase of (L_{m}), the decreasing trend is more obvious. When (L_{m}) is 500 mm, with the increase of the height of the anchor pier (D_{e}), the deformation of the anchor system will increase first. When (L_{m}) is greater than 800 mm, with the increase of (D_{e}), the deformation of the anchor system will continue to decrease. But the decreasing trend is not much different.Figure 18Influence of Anchor Pier Width (D_{e} left( {500 – 1500;{text{mm}}} right)) and Anchor Pier Height (L_{m} left( {600 – 2000;{text{mm}}} right)) on Deformation of Anchorage System.Full size imageThe numerical validationThe establishment of the finite element modelWhen the finite element model of the anchor-pulling system and surrounding soil is created, the constitutive model of the surrounding soil uses the Mohr–Coulomb elastoplastic model. The anchor pier and surrounding soil use eight nodes as oparametric elements, such as solid45, of which the basic grid unit is cubic units. When the grid is divided, the grid between the anchor pier and the surrounding soil contact is dense. The LINK10 unit is used to simulate cables, which have a bilinear stiffness matrix. It can simulate not only tensile bar units but also compressed bar units. For example, when the pull-up option is used alone, if the unit is under pressure, its stiffness disappears, so it can be used to simulate the relaxation of cables or chains. This feature is very significant for the static problem of wire rope, which uses a unit to simulate the entire cable. It can also be used for dynamic analysis with inertial or damping effects when the needed relaxation unit should pay attention to its performance rather than its movement. The soil is homogeneous. The soil physical parameters and structure design parameters are consistent with the theoretical calculation parameters mentioned above. The tensile force of the cable is exerted on the nodes as a force. The top surface of the model is free, and the normal displacements of the remaining faces are constrained such that the displacements are zero. The contact of the anchor pier and surrounding soils is a rigid-flexible surface-to-surface contact element to reflect the interaction. The surface of the anchor pier is regarded as the “target” surface, and the surface of the soil body is regarded as the “contact” surface. The coefficient of friction and normal penalty stiffness are 0.35 and 0.15, respectively. The scope of interaction between the anchor pier and the surrounding soil in the model is taken as 15 m × 11 m × 12 m, referring to past experience in engineering and the research data of the effect scope that the related anchors have had on the soil. The values of the model geometric parameters and physical and mechanical parameters are the same as in “Design parameters” section. The finite element model is shown in Fig. 19.Figure 19Finite element model of the anchor-pulling system and surrounding soil.Full size imageResearch on finite element model gridIn order to verify the convergence of numerical simulation, the soil was divided into three different mesh sizes. Condition 1 is fine finite element meshing. The stress nephogram of condition 1 is shown in Fig. 20. Condition 2 is medium finite element mesh. The stress nephogram of condition 1 is shown in Fig. 21. Condition 3 is coarse finite element mesh. The stress nephogram of condition 1 is shown in Fig. 22. See Table 2 for specific grid division.Figure 20Condition 1 stress cloud diagram.Full size imageFigure 21Condition 1 stress cloud diagram.Full size imageFigure 22Condition 1 stress cloud diagram.Full size imageTable 2 Mesh size of three working conditions.Full size tableIt can be seen from the stress nephogram of the three working conditions that the thicker the grid is, the greater the displacement of the anchor system is. The maximum displacement difference between condition 2 and condition 3 is 2.6%; the maximum displacement of condition 1 is 17% different from that of condition 2. The finer the mesh, the more accurate the numerical simulation results. But with the increase in computing time. It can be seen from Table 2 that the maximum iteration of condition 1 is 10 times, and the result will converge. The maximum iterations of condition 2 and 3 only need 7 times, and the results can converge.The calculation resultsFigure 23 and Fig. 24 are the displacement nephograms of the soil around the anchor piers for 100 kN and 400 kN, respectively. The soil displacement increases with increasing load, the affected area will increase and become uniform, and the area under load will also increase. The soil within the range of 1–3 m around the anchor pier is greatly affected, accounting for 80% of the total force. The soil around the anchor pier should be reinforced, and the anchoring force should be enhanced in the design.Figure 23Displacement fringe of soil around the anchor piers for 100 kN.Full size imageFigure 24Displacement fringe of soil around the anchor piers for 400 kN.Full size imageIn order to further study the influence of anchorage pier size on the displacement and deformation of anchorage system, finite element models with different sizes are established by finite element method. The stress nephogram is shown in Figs. 25, 26 and 27.Figure 25Top 800 mm, bottom 800 mm anchor pier stress nephogram.Full size imageFigure 26Top 1000 mm, bottom 1000 mm anchor pier stress nephogram.Full size imageFigure 27Top 800 mm, bottom 1000 mm anchor pier stress nephogram.Full size imageFrom Figs. 25, 26 and 27, it can be seen that when the anchor pier is rectangular, the deformation of the tensile anchor system decreases with the increase of the size of the anchor pier, but the degree is small. When the anchor pier is trapezoidal, the material is small, but the deformation is more ideal than the rectangular. It can be seen that reasonable selection of anchor pier size is crucial, not blindly increase the size of anchor pier.Figure 28 shows that the displacement of the soil around the anchor pier increases with increasing load, and the added value is obvious at approximately 2–3 mm. Figure 29 shows that the increase in load has a great effect on the soil in front of the anchor pier. As the load increases, the compressive deformation of the soil gradually increases. As the distance from the anchor pier increases, the displacement of the soil decreases, and the scope of influence gradually decreases. The displacement of the soil tends to be stable beyond 4–5 m from the anchor pier.Figure 28The displacement of soil around anchor pier.Full size imageFigure 29The horizontal displacement of soil along cable axis.Full size imageComparison of theoretical calculation and numerical simulation results at the time of load variationTo verify the correctness of the theoretical calculation, we compare the theoretical calculation with numerical simulation results of displacement deformation of anchor-pulling system under different pulling force of stayed cable. The results are shown in Fig. 30, see Table 3 for data.Figure 30Comparison of theoretical calculation and numerical simulation results.Full size imageTable 3 Comparison between theoretical calculation and numerical simulation.Full size tableAs seen from Fig. 30, the theoretical and numerical simulation results are consistent, showing a linear growth trend. The slope difference of the two straight lines is approximately 5%, which meets the accuracy requirements of geotechnical engineering. As the restraint effect of the surrounding soil on the anchor pier is not fully considered, the theoretical calculation result is too large. The deformation of anchor (left( {S_{1} } right)) in displacement deformation is the same, and the relative shear displacement (left( {S_{2} } right)) of the anchor pier and the soil and the compressive deformation ((S_{3} )) of the soil at the front end of the anchor pier are 1.25 times and 1.08 times the numerical simulation results, respectively. The change in (left( {S_{2} } right)) in the calculation results is large and should be taken into account in the design. More