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Microcosm preparation and incubationLeaf litters were collected from Lilly-Dickey Woods, a mature eastern US temperate broadleaf forest located in South-Central Indiana (39°14′N, 86°13′W) using litter baskets and surveys for freshly senesced litter as described in Craig et al.52. Of the 19 species collected in Craig et al. (2018), we selected litter from 16 tree species with the goal of maximizing variation in litter chemical traits (Table S1). Litters were air-dried and then homogenized and fragmented such that all litter fragments passed a 4000 µm, but not a 250 µm mesh. Whereas leaf litters had a distinctly C3 δ13C signature of −30.1 ± 1.5 (mean, standard deviation), we used a 13C-rich (δ13C = −12.6 ± 0.4) soil obtained from the A horizon of a 35-yr continuous corn field at the Purdue University Agronomy Center for Research and Education near West Lafayette, Indiana (40°4′N, 86°56′W). The soil is classified as Chalmers silty clay loam (a fine-silty, mixed, superactive, mesic Typic Endoaquoll). Prior to use in the incubation, soils were sieved (2 mm) and remaining recognizable plant residues were thoroughly picked out. Soils were mixed with acid-washed sand—30% by mass—to facilitate litter mixing (see below) and to increase the soil volume for post-incubation processing. The resulting soil had a pH of 6.7 and a C:N ratio of 12.0.We constructed the experimental microcosms by mixing the 16 litter species with the 13C-enriched soil. Each litter treatment was replicated four times in four batches (i.e., 16 microcosms per species, 272 total microcosms including 16 soil-only controls). Two batches (C budget microcosms) were used to monitor CO2 efflux and to track litter-derived C into SOM pools, and two batches were used to quantify microbial biomass dynamics.Incubations were carried out in 50 mL centrifuge tubes modified with an O-ring to prevent leakage and a rubber septum to facilitate headspace sampling. To each microcosm, we added 5 g dry soil, adjusted moisture to 65% water-holding capacity, and pre-incubated for 24 h in the dark at 24 °C. Using a dissecting needle, 300 mg of leaf litter were carefully mixed into treatment microcosms and controls were similarly agitated. This corresponds to an average C addition rate of 27.1 ± 1.1 g C kg−1 dry soil among the 16 species. During incubation, microcosms were loosely capped to retain moisture while allowing gas exchange, and were maintained at 65% water-holding capacity by adding deionized water every week.Carbon budget in microcosmsRespiration was quantified with an infrared gas analyzer (LiCOR 6262, Lincoln, NE, USA) coupled to a sample injection system. Our first measurement was taken about 12 h after litter addition (day 1) and subsequent measurements were taken on days 2, 4, 11, 19, and 30 for both batches and on days 46, 64, 79, 92, 109, 128, 149, and 185 for the second batch. Prior to each measurement, microcosms were capped, flushed with CO2-free air, and incubated for 1–8 h depending on the expected efflux rate. Headspace was sampled with a gas-tight syringe and the CO2-C concentration was converted to a respiration rate (µg CO2-C day−1). Total cumulative CO2-C loss was derived from point measurements by numerical integration (i.e., the trapezoid method). To evaluate soil-derived CO2-C efflux, we measured δ13C in two gas samples per litter type or control on a ThermoFinnigan DELTA Plus XP isotope ratio mass spectrometer (IRMS) with a GasBench interface (Thermo Fisher Scientific, San Jose, CA). Isotopes were measured on days 1, 4, 11, 30, 64, 109, and 185. On each of these days, a two-source mixing model70 was applied to determine the fraction of total CO2-C derived from soil organic matter vs. litter:$$frac{{F}^{l}(t)}{F(t)}=frac{delta Fleft(tright)-,delta {F}^{c}(t)}{delta {C}_{l}-delta {F}^{c}(t)}$$
(1)
where (frac{{F}^{l}(t)}{F(t)}) is the fraction total CO2-C efflux [(F(t))] derived from litter [({F}^{l}(t))] at time (left(tright)), (delta Fleft(tright)) is the δ13C of the CO2 respired by each litter-soil combination, (delta {F}^{c}(t)) is the average δ13C of the CO2 respired by the control soil, and (delta {C}_{l}) is the δ13C of each litter type. These data were used to calculate cumulative soil-derived C efflux via numerical integration and, for each litter type, average soil-derived C efflux was subtracted from total cumulative CO2-C loss to determine cumulative litter-derived CO2-C loss.Carbon budget microcosms were harvested on days 30 and 185 to track litter-derived C into mineral-associated SOC at an early and intermediate stage of decomposition. To do this, we used a size fractionation procedure71,72 modified to minimize the recovery of soluble leaf litter compounds or dissolved organic matter in the mineral-associated SOC fraction. For each sample, we first added 30 mL deionized water, gently shook by hand to suspend all particles, and then centrifuged (2500 rpm) for 10 min. Floating leaf litter was carefully removed, dried for 48 h at 60 °C, and weighed; and the clear supernatant was discarded to remove the dissolved organic matter. The remaining sample was dispersed in 5% (w/v) sodium hexametaphosphate for 20 h on a reciprocal shaker and then washed through a 53 µm sieve. The fraction retained on the sieve was added to the floating leaf litter sample and collectively referred to as particulate SOC, while the fraction that passed through the sieve was considered the mineral-associated SOC. Both fractions were dried, ground, and weighed; and analyzed for C concentrations and δ13C values on an elemental combustion system (Costech ECS 4010, Costech Analytical Technologies, Valencia, CA, USA) as an inlet to an IRMS. As above, litter-derived C in the particulate and mineral-associated SOC was determined as follows:$$frac{{C}_{s}^{l}(t)}{{C}_{s}(t)}=frac{delta {C}_{s}left(tright)-,delta {C}_{c}(t)}{delta {C}_{l}-delta {C}_{c}(t)}$$
(2)
where ({C}_{s}(t)) is the total particulate or mineral-associated SOC content in the sample at time ((t)), ({C}_{s}^{l}(t)) is the litter-derived C in the soil, (delta {C}_{s}left(tright)) is the measured δ13C value for each soil fraction, (delta {C}_{c}left(tright)) is the average δ13C for each fraction in control samples, and (delta {C}_{l}) is the δ13C of each litter type. In a few cases, mineral-associated δ13C was slightly less negative in the treatment than in the control soil. In these cases, litter-derived mineral-associated SOC was considered zero.Total litter-derived SOC at each harvest date was calculated by subtracting the cumulative litter CO2-C from initial added litter C. The difference between this value and the sum of litter-derived particulate and mineral-associated SOC was considered the residual pool which we assume mostly represents water-extractable dissolved organic matter.Microbial biomass dynamics during incubationSample batches were harvested at days 15 and 100 to capture early- and intermediate-term microbial biomass responses to litter treatments. These times were selected to correspond with the middle of early and intermediate C budget microcosm incubations. We quantified microbial biomass as well as MGR, CUE, and MTR using 18O-labeled water73,74 as in Geyer et al.75.Microbial biomass C (MBC) was determined on two ~2 g subsamples using a standard chloroform fumigation extraction76. One subsample was immediately extracted in 0.5 M K2SO4 and one was fumigated for 72 h before extraction. After shaking for 1 h, extracts were gravity filtered through a Whatman No. 40 filter paper, and filtrates were analyzed for total organic C using the method of Bartlett and Ross77 as adapted by Giasson et al.78. The difference between total organic C in the fumigated and unfumigated subsamples was used to calculate MBC (extraction efficiency KEC = 0.45).To determine MGR, CUE, and MTR, we first pre-incubated two 0.5 g soil subsamples (one treatment and one control) for 2 d at 24 °C. Prior to this pre-incubation, samples were allowed to evaporate down to 53 ± 6% (mean, sd) water-holding capacity. After the pre-incubation, water was injected with a 25 µL syringe to bring each sample to 65% water-holding capacity. For one subsample, we used unlabeled deionized water. For the second subsample, enriched 18O-water (98.1 at%; ICON Isotopes) was mixed with unlabeled deionized H2O to achieve approximately 20 at% of 18O in the final soil water. Each sample was placed in a centrifuge tube (modified for gas sampling), flushed with CO2-free air, and incubated for 24 h. Headspace CO2 concentration was then measured, and samples were flash frozen in liquid N2 and stored at −80 °C until DNA extraction.DNA was extracted from each sample using a DNA extraction kit (Qiagen DNeasy PowerSoil Kit, Venlo, Netherlands) following the protocol described in Geyer et al. (2019) which sought to maximize the recovery of DNA. The DNA concentration was determined fluorometrically using a Quant-iT PicoGreen dsDNA Assay Kit (Invitrogen). DNA extracts (80 µL) were dried at 60 °C in silver capsules spiked with 100 µL of salmon sperm DNA (42.5 ng µL−1), to reach the oxygen detection limit, and sent to the UC Davis Stable Isotope Facility for quantification of δ18O and total O content.Microbial growth rate (MGR) was calculated following Geyer et al. (2019). Specifically, atom % of soil DNA O (at% ODNA) was determined using the two-pool mixing model:$${at} % ,{O}_{{DNA}}=,frac{left[left({at} % ,{O}_{{DN}A+{ss}}times {O}_{{DNA}+{ss}}right)-left({at} % ,{O}_{{ss}}times {O}_{{ss}}right)right]}{{O}_{{DNA}}},$$
(3)
where at% is the atom % 18O and ODNA+ss, ODNA, and Oss are the concentration of O in the whole sample, soil DNA, and salmon sperm, respectively. Atom percent excess of soil DNA oxygen (APE Osoil) was calculated as the difference between at% ODNA in the treatment and control samples. Total microbial growth in terms of O (Total O; µg) was estimated as:$${Total},O=frac{{O}_{{soil}}times ,{{APE},O}_{{soil}}}{{at} % ,{soil},{water}}$$
(4)
where at% soil water is the atom % 18O in the soil water. MGR in terms of C (µg C g−1 soil d−1) was calculated by applying conversion mass ratios of oxygen:DNA (0.31) and MBC:DNA for each sample, dividing by the soil mass, and scaling by the incubation time. Assuming uptake rate (Uptake) is equal to the sum of MGR and respiration, CUE and MTR were calculated by the following equations.$${CUE}=,frac{{MGR}}{{Uptake}},$$
(5)
$${MTR}=,frac{{MGR}}{{MBC}}$$
(6)
Data analysis for microcosm experimentLitter decay constants were calculated for each species using litter-derived CO2-C values to estimate litter mass loss over time. After it was determined that a single exponential decay model provided a poor fit, we fit litter decomposition data using the double exponential decay model:$$y=s{e}^{{-k}_{1}t}+(1-s){e}^{{-k}_{2}t}$$
(7)
where s represents the labile or early stage decomposition fraction that decomposes at rate k1, and k2 is the decay constant for the remaining late stage decomposition fraction.To reduce the dimensionality of litter quality and microbial indicators, indices were derived by principal component analysis (PCA; Fig. S1A, B) using the ‘prcomp’ function in R. The first axis of a PCA of decomposition parameters (s, k1, and k2) and litter chemical properties (soluble and AUR contents; AUR-to-N and C-to-N ratios; and the lignocellulose index [LCI]) was taken as a litter quality index. Whereas this index highly correlated with indicators of C quality (AUR, soluble content, and LCI), the second axis of this PCA correlated with C:N and AUR:N and was therefore taken as a second litter quality index representing variation in N concentration. The first axis of a PCA of MGR, CUE, and MTR was taken as a microbial physiological trait index.Bivariate relationships were examined using simple linear regressions on average species values at each harvest (n = 16). To examine relationships between microbial physiological traits and mineral-associated SOC, data from the early-term (day 15) and intermediate-term (day 100) microbial harvest were matched with early-term (day 30) and intermediate-term (day 185) C budget microcosms, respectively. In addition to examining total mineral-associated SOC formation, we also estimated the efficiency of litter C transfer into the mineral-associated SOC pool as the fraction of lost litter C (i.e., litter C lost as CO2, recovered in the mineral-associated SOC fraction, or in the residual pool) retained in the mineral-associated SOC. Path analyses were used to evaluate the hypothesis that microbial physiological traits mediate the effect of litter quality on mineral-associated SOC formation and mineral-associated and particulate SOC decay. We hypothesized that the litter quality index would be positively associated with the microbial physiological trait index (representing faster and more efficient microbial growth) and microbial physiological traits would, in turn, be positively associated with the rate and efficiency of mineral-associated SOC formation. We expected that this mediating pathway would reduce the direct relationship between litter quality and SOC. This analysis was conducted using the LAVAAN package79 to run path analyses for total litter-derived mineral-associated SOC, mineral-associated SOC formation efficiency, and soil-derived mineral-associated and particulate SOC for both early and intermediate stage harvests. All analyses were performed using R version 3.5.2.Field study design and soil samplingWe worked in the Smithsonian’s Forest Global Earth Observatory (ForestGEO) network80 in six mature U.S. temperate forests varying in climate, soil properties, and tree community composition (Fig. 1a): Harvard forest (HF; 42°32′N, 72°11′W) in North-Central Massachusetts, Lilly-Dickey Woods (LDW; 39°14’N, 86°13’W) in South-Central Indiana, the Smithsonian Conservation Biology Institute (SCBI; 38°54′N, 78°9′W) in Northern Virginia, the Smithsonian Environmental Research Center (SERC; 38°53′N, 76°34′W) on the Chesapeake Bay in Maryland, Tyson Research Center (TRC; 38°31′N, 90°33′W) in Eastern Missouri, and Wabikon Lake Forest (WLF; 45°33′N, 88°48′W) in Northern Wisconsin, USA. Land use history across the six sites consisted mostly of timber harvesting which ceased in the early 1900s. Soils are mostly Oxyaquic Dystrudepts at HF, Typic Dystrudepts and Typic Hapludults at LDW, Typic Hapludalfs at SCBI, Typic or Aquic Hapludults at SERC, Typic Hapludalfs and Typic Paleudalfs at TRC, and Typic and Alfic Haplorthods at WLF. Further site details are reported in Table S5.Each site contains a rich assemblage of co-occurring arbuscular mycorrhizal (AM)- and ectomycorrhizal (ECM)-associated trees (Table S6), which we leveraged to generate environmental gradients in factors hypothesized to predict microbial physiological traits within each site. Specifically, the dominance of AM vs. ECM trees within a temperate forest plot has been shown to be a strong predictor of soil pH, C:N, inorganic N availability, and litter quality52,53,54. We established nine 20 × 20 m plots in each of our six sites in Fall 2016 (n = 54) distributed along a gradient of AM- to ECM-associated tree dominance. Plots were selected to avoid obvious confounding environmental factors. Where possible, we established our nine-plot gradient in three blocks (5 cm) at HF, which was removed before coring. Samples were also collected at 5–15 cm depth for soil texture analysis. We sampled from an inner 10 × 10 m square in each plot to avoid edge effects. All samples from the same plot were composited, sieved (2 mm), picked free of roots, subsampled for gravimetric moisture (105 °C), and air-dried, or refrigerated (4 °C) until analysis for microbial physiological variables and N availability.Soil propertiesWe determined several physicochemical properties known to predict mineral-associated SOC. We measured soil pH (8:1 ml 0.01 M CaCl2:g soil) and soil texture using a benchtop pH meter and a standard hydrometer procedure82, respectively. Organic matter content was high in some upper surface soils, so plot-level soil texture was determined from 5 to 15 cm depth samples. We quantified oxalate-extractable Al and Fe pools (Alox and Feox) in all soil samples as an index of poorly crystalline Al- and Fe-oxides83, which is one of the strongest predictors of SOM content in temperate forests84. Briefly, we extracted 0.40 g dried, ground soil in 40 mL 0.2 M NH4-oxalate at pH 3.0 in the dark for 4 h before gravity filtering and refrigerating until analysis (within 2 w) on an atomic-adsorption spectrometer (Aanalyst 800, Perkin Elmer, Waltham, MA, USA), using an acetylene flame and a graphite furnace for the atomization of Fe and Al, respectively.We quantified potential net N mineralization rates as an index of soil N availability. One 5 g subsample per plot was extracted immediately after processing by adding 10 mL 2 M KCl, shaking for 1 h, and filtering through a Whatman No. 1 filter paper after centrifugation at 3000 rpm. A second subsample from each plot was incubated under aerobic conditions at field moisture and 23 °C for 14 d before extraction. Extracts were frozen (−20 °C) until analysis for NH4+-N using the salicylate method and for NO3−-N plus NO2−-N after a cadmium column reduction on a Lachat QuikChem 8000 flow Injection Analyzer (Lachat Instruments, Loveland, CO, USA). Potential net N mineralization rates (mg N g dry soil−1 d−1) were calculated as the difference between pre- and post-incubation inorganic N concentrations.Microbial biomass dynamics in field plotsMicrobial biomass carbon and microbial physiological traits were quantified within 10 days of collection as described above, with four minor differences. First, 30 g soil subsamples were covered with parafilm and pre-incubated for 2 d near the field soil temperature measured at the time of sampling (16.5 °C for WLF and HF, and 21.5 °C for LDW, TRC, SCBI, and SERC). Second, for CO2 analysis, samples were placed in a 61 mL serum vial crimped with a rubber septum. Third, DNA concentrations were determined using a Qubit dsDNA BR Assay Kit (Life Technologies) and a Qubit 3.0 fluorometer (Life Technologies). Fourth, 14.5 g subsamples were used for microbial biomass analysis.Soil organic matter characterization in field plotsMineral-associated SOC was quantified as in the microcosm experiment, but without a pre-fractionation leachate removal step. We additionally measured soil amino sugar concentrations to estimate microbial necromass contributions to SOM. Amino sugars are useful microbial biomarkers because they are found in abundance in microbial cell walls, but are not produced by higher plants and soil animals19. Moreover, amino sugars can provide information on the microbial source of necromass. For example, glucosamine (Glu) is produced mostly by fungi whereas muramic acid (MurA) is produced almost exclusively by bacteria61,85. Amino sugars were extracted, purified, converted to aldononitrile acetates, and quantified with myo-inositol as in Liang et al.86. We used the concentrations of Glu and MurA to estimate total, fungal, and bacterial necromass soil C using the empirical relationships reported in Liang et al.8.$${Bacterial},{necromass},C,=,{MurA},times ,45$$
(8)
$${Fungal},{necromass},C,=,({mmol},{GluN},{-},2,times ,{mmol},{MurA})times ,179.17,times ,9$$
(9)
Leaf litter and fine roots in field plotsIn Fall 2017, we collected leaf litter on two sample dates from four baskets deployed in the inner 10 × 10 m of each plot. Litter was composited by plot, dried (60 °C), sorted by species, weighed, and ground. We performed leaf litter analyses on at least three samples of each species at each site —unless a species was only present in one or two plots— to get a site-specific mean for each species. Some non-dominant species were not included in these analyses because an insufficient amount of material was collected. Fine roots ( 0.5). Feox and Alox were correlated above this threshold and final models were selected to contain only Feox based on AIC. Residuals were screened for normality (Shapiro-Wilk), heteroscedasticity (visual assessment of residual plots), and influential observations (Cook’s D). Based on this, MGR, MTR, and mineral-associated SOC were natural log transformed. For all mixed models, we centered and standardized predictors (i.e., z-transformation) so that the slopes and significance levels of different predictors could be compared to one another on the same axis88. 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

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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