Philippa Kaur

Survey sites and data collectionBenthic and fish surveys were conducted at randomly stratified sites throughout the entirety of the FRT by NOAA’s National Coral Reef Monitoring Program (NCRMP). Sites were categorized into three biogeographic regions, including Dry Tortugas (DRTO, n = 228), Florida Keys (FLKs, n = 322), and Southeast Florida (SEFL, n = 173) (Fig. 1). The Florida Keys were further classified into the following four sub-regions: Lower Keys (LK, n = 103), Middle Keys (MK, n = 46), Upper Keys (UK, n = 140), Biscayne (BISC, n = 33). Within each region/sub-region (except for SEFL), reefs were categorized according to reef types. For DRTO, this included bank, forereef, and lagoon reef sites. For the LK, MK, UK, and BISC, reef types were categorized as inshore, mid-channel, and offshore. Data were collected throughout the region in 2014, 2016, and 2018.Fish and benthic surveys were conducted in accordance with NCRMP methodologies34 (Table S2). The protocol used for the fish surveys was developed from a modified Reef Visual Census (RVC) method35 and was performed using a stratified random sampling design. Divers surveyed two 15 m diameter cylinders, spaced 15 m apart. Fish species were identified to the lowest taxonomic level for a period of five minutes. This was followed by an additional five minutes dedicated to recording species abundances and sizes (10 cm bins).Surveys were used to quantify the benthic cover at each site. The protocol for these surveys followed a standard line point-intercept sampling design. At each site, a 15 m weighted transect was draped along the reef surface. Surveyors recorded benthic composition at 15 cm intervals along the transect (i.e., 100 equidistant points). The benthic composition from these 100 points was then transformed to percent cover of ecologically important functional groups (scleractinian coral [species-specific], gorgonians, hydrocoral, CCA, macroalgae, turf algae, sponges, bare/dead substrate, sand/sediment).Carbonate budget analysisPlanar benthic surveys were adjusted to account for the three-dimensional complexity (i.e., rugosity) of each site using light detection and ranging (LiDAR) data (1 m horizontal resolution; 15 cm vertical resolution) from topobathymetric mapping surveys of the South Florida eastern coastline conducted by NOAA’s National Geodetic Survey. A 15 m x 15 m region of interest (ROI) was placed around the GPS coordinates of each site using ArcGIS Pro with 3D and Spatial Analyst extensions (ESRI). The ROI was then overlaid with existing multibeam echosounder (MBES) and LiDAR bathymetry data. Within the ROI, LiDAR was extracted using the Clip Raster function from ArcPy (ArcGIS’s python coding interface), and the Surface Volume tool was used to calculate the 3D surface area. Rugosity was calculated by dividing the 3D surface area by the 2D surface area of the ROI.The methodology for standardizing reef carbonate budgets to topographic complexity (i.e., rugosity) diverged from that of the ReefBudget approach by using site-specific rugosity rather than species-specific rugosity17. This was a necessary limitation of this analysis as transect rugosity at 1 m increments was not measured using the NCRMP benthic survey protocol. To ensure that reef topographic complexity was still accounted for, however, rugosity of the entire reef site, calculated from LiDAR bathymetry data, was used in this analysis. While rugosity of the site rather than of each benthic component, specifically for corals, can lead to an under or overestimation of carbonate production rates, we note that site and species rugosity (i.e., encrusting and massive coral morphologies) was low for the vast majority of sites and species surveyed, thereby reducing the probability of an under or overestimation.Reef carbonate budget analysis was performed following a modified version of the ReefBudget approach17. Coral carbonate production was derived from species-specific linear extension rates (cm year−1), skeletal density (g cm−3), coral morphology (branching, massive, sub-massive, encrusting/plating), and percent cover. Carbonate production by CCA and other calcareous encrusters was similarly calculated as a function of surface area, literature reported linear extension rates, and skeletal density17. Gross carbonate production at each survey site was measured as the sum total of carbonate production by all calcareous organisms found at each site and was standardized to site-specific reef rugosity.Gross carbonate erosion for each survey-site was calculated as the sum total of erosion by four bioeroding groups: parrotfish, microborers, macroborers, and urchins. The calculations roughly followed the ReefBudget methodologies17 (Table 1). Parrotfish size frequency distributions from NCRMP surveys were multiplied by size and species-specific bite rates (bites min−1), volume removed per bite (cm3), and proportion of bites leaving scars to calculate total parrotfish erosion17. The substrate density (1.72 g cm−3) used in these calculations followed that of the ReefBudget protocol17. Microbioerosion was calculated from the percent cover of dead coral substrate, which was multiplied by a literature-derived rate17 of − 0.240 kg CaCO3 m−2 year−1. Macroboring was calculated as the percent cover of clionid sponges multiplied by the average erosion rate of all Caribbean/Atlantic clionid sponges17 (-6.05 kg CaCO3 m−2 year−1). External bioerosion by urchins was calculated using Diadema urchin abundance collected from the benthic surveys. Due to the lack of test size data from the NCRMP benthic surveys, urchin abundance was multiplied by the bioerosion rate of an average test sized36 (66 mm) Caribbean/Atlantic Diadema urchin (-0.003 kg CaCO3 m-2 year−1). While using an average test sized Diadema urchin for this analysis may have led to an under or overestimation of urchin erosion, the abundance of Diadema urchins measured in the surveys was minimal, as they appeared to be functionally irrelevant across the FRT.Model validationAs the survey methodologies and data sources employed in this analysis were modified from that of the standard ReefBudget approach17, we chose to validate our model through a fine scale temporal comparison of annual ReefBudget surveys conducted by NOAA at Cheeca Rocks (UK) to three nearby NCRMP sites used in our analysis. Since the NCRMP surveys were performed in 2014, 2016, and 2018, this study focused exclusively on these three survey years from the NOAA Cheeca Rocks dataset. Temporal trends related to reef growth/erosion were visually compared to see if survey types provided comparable results (SI Figure S6).Statistical analysisAll model calculations and statistical analyses were performed using R37 with the R Studio extension38. Generalized linear models (GLMs) were run on response variables involved in habitat production (i.e., net carbonate production, gross carbonate production, and gross carbonate erosion) to evaluate spatial trends related to reef development across sub-regions and reef types. Each GLM was performed with reef type being nested within sub-region. The best fit distribution for each variable was determined using the fitdistrplus R package39. Linear regression analysis was used to evaluate the relationship between net carbonate production and both live coral cover and parrotfish biomass. All plots were created using ggplot2 R package40 and edited for style with Adobe Illustrator41. More

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Automated tracking of four social insect speciesFifty queenright colonies were used in the tracking experiments (Table 1). Honeybee colonies (subspecies A. mellifera carnica) were housed in the campus apiary of the University of Lausanne. Colonies of L. niger were raised from single mated queens collected on campus. T. nylanderi colonies were collected from the University of Lausanne campus, and L. acervorum colonies collected from Anzeindaz, Switzerland. These four species were chosen because of their abundance and easy availability in Switzerland, and because they – or closely-related species – have previously been used as model systems for the study of spatial organisation in social insects20,21,23,27,44. The colony sizes used in our experiments (Table 1) fell within the natural range of sizes experienced by these species in nature, either as recently founded colonies (L. niger colonies are founded by a single queen and progressively grow from a few workers to mature sizes of up to 40,000 workers over the course of several years; new honeybee colonies are founded by swarms counting 2400–41,000 bees61) or as mature colonies (all colonies of T. nylanderi and L. acervorum used in our experiments were mature colonies collected whole from the field).In all species, a paper tag bearing a unique two-dimensional barcode was glued to the thorax of individuals to allow automated tracking of their movements (Fig. S1). In the ants, tagging of all individuals was performed in a single session two days before the beginning of the experiment, whilst in the bees, newly-emerged workers (one-day-old or less) were tagged every 3 days over the 21 days prior to the beginning of the experiment (Supplementary Note 1).Tagged colonies were kept in glass observation nests with a single entrance (internal nest dimensions, A. mellifera: 69 × 45 × 4 cm, L. niger: 70 × 40 × 8 mm; L. acervorum: 63 × 42 × 2 mm, T. nylanderi: 63 × 42 × 1.5 mm). The honeybee observation nests also included a 64 × 44 cm wooden frame enclosing a double-sided wax comb containing honey, pollen, and developing brood20. Bees were free to move between both sides of the comb. In all species, individuals were allowed to freely exit and enter the nest. Ants were provided with ad libitum food (Drosophila, sugar solution) and water in a foraging arena, while bees foraged on natural resources outside. Both the ant and honeybee observation nests were exposed to diurnal cycles of temperature and light (Supplementary Note 1).High resolution digital video cameras operating at two frames per second were used to identify the location and orientation of each tag across successive images22. All colonies were continuously tracked for three days, which corresponded to the inter-cohort time in the honeybee colonies. The trajectories of each worker, and the physical contacts between workers (Fig. S18 and Supplementary Note 14) were extracted using an existing software pipeline62.Building bipartite site-visit networksTo quantify the spatial preferences of individual ants and bees, the interior of the nest was discretised into a regular hexagonal lattice (Fig. 1a, b). Because the worker body lengths of our four study species span an order of magnitude (from ~ 1.5 mm for T. nylanderi to ~ 15 mm for A. mellifera), the width of the hexagonal bins were defined as 1/4 of the mean worker body-length.To characterise the spatial preferences of different individuals to different parts of the nest, we counted the number of times ({n}_{i}^{s}) that each individual i visited each hexagonal site s. A visit by individual i to site s began when i crossed the border into s, and was terminated when i crossed the border out of s, regardless of the amount of time spent inside. To prevent stationary individuals located on the border between two adjacent sites from rapidly accumulating many single-frame visits to the two sites, successive visits to a same site were only counted when at least 20s elapsed between the end of the previous visit and the start of the next.The site-visit data were used to construct a bipartite network, in which individuals (layer 1) were connected by undirected edges to the sites (layer 2) they visited (Fig. 1c, d). Because individuals typically made multiple visits to the same sites, each edge i–s was weighted according to the total number of times individual i visited site s, that is, ({n}_{i}^{s}).Partitioning site-visit networks into modulesThe extent to which the site-visit networks were partitioned into discrete ‘modules’ (i.e., set of workers with similar space-use patterns and the set of sites that they exhibit strong ties to) was assessed using the DIRTLPAwb+ algorithm for partitioning weighted bipartite networks39. This algorithm searches for the partition that maximises the number and strength of the links within modules, whilst minimizing connections between modules. The number of modules was not specified a priori by the user, but was identified by the algorithm. All site-visit networks had positive modularity (Fig. S3), indicating that they could be partitioned into a set of well-separated modules (Figs. 1e–h, S2, and S4–S5). The modules in each partition were then assigned functional labels according to the following rules. First, the module whose sites were on average closest to the nest entrance was labelled ‘forager’ module. Second, the module or modules with the greatest spatial overlap with the brood pile in the ant colonies or the broodnest(s) in the honeybee colonies were labelled ‘nurse’ module(s). After defining the forager and nurse modules, the remaining modules (if any) were labelled as follows. If there was only one module remaining after identifying the nurse and forager modules, as was typically the case in honeybee colonies, it was labelled ‘peripheral’. If there were two modules remaining, as was typically the case in ant colonies, then the module whose sites were on average closer to the nest borders (i.e., to the periphery of the nest) was labelled ‘peripheral’, and the remaining module labelled ‘intermediate’. In some cases, the DIRTLPAwb+ algorithm identified five or more modules (9.0% of all iterations across all species and colonies). In these cases, the supernumerary modules never contained more than 1 or 2 individuals, and as they could not be unequivocally assigned using our labelling scheme, they were left unclassified for these iterations.Validating network modulesAs a network constructed by a purely random process could exhibit apparent modular structure by chance, we tested whether the discovered modules represent statistically significant entities. To do so, we produced 1000 null model random networks for each observed network using an established permutation method for bipartite networks63 (Supplementary Note 2). Comparisons between the maximum modularity of the observed networks with that of the corresponding random networks showed that, in all four species, the observed modularity was significantly greater than expected by chance (Fig. S3).Constructing worker task profilesA unique labour profile for each ant and each honeybee was constructed by estimating the activity of each worker in the following four tasks:1. Entrance guarding: workers were classed as guarding when they were (i) within two body lengths of the entrance, (ii) roughly facing the entrance, i.e., with a body alignment diverging from the direct heading to the entrance by no more than π/2 radians, and (iii) ‘on station’ at the entrance, as defined by trajectory coordinates with an associated first passage time (ref. 64; time taken for the individual to pass beyond a circle centred on its current location with a radius of two body-lengths) in excess of 500s.2. Patrolling: workers were classed as patrolling65 when they were (i) active, and (ii) ‘roaming’, as defined by first passage times of More

These authors contributed equally: Yannick Garcin, Enno Schefuß, Greta C. Dargie, Simon L. LewisAix Marseille University, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, FranceYannick Garcin & Ghislain GassierInstitute of Geosciences, University of Potsdam, Potsdam, GermanyYannick GarcinMARUM—Center for Marine Environmental Sciences, University of Bremen, Bremen, GermanyEnno SchefußSchool of Geography, University of Leeds, Leeds, UKGreta C. Dargie, Bart Crezee, Dylan M. Young, Andy J. Baird, Paul J. Morris & Simon L. LewisSchool of Geography and Sustainable Development, University of St Andrews, St Andrews, UKDonna Hawthorne, Ian T. Lawson & George E. BiddulphIFP Energies Nouvelles, Earth Sciences and Environmental Technologies Division, Rueil-Malmaison, FranceDavid SebagInstitute of Earth Surface Dynamics, Geopolis, University of Lausanne, Lausanne, SwitzerlandDavid SebagFaculté des Sciences et Techniques, Université Marien Ngouabi, Brazzaville, Republic of the CongoYannick E. Bocko & Y. Emmanuel Mampouya WeninaÉcole Normale Supérieure, Université Marien Ngouabi, Brazzaville, Republic of the CongoSuspense A. IfoÉcole Normale Supérieure d’Agronomie et de Foresterie, Université Marien Ngouabi, Brazzaville, Republic of the CongoMackline MbembaFaculté de Gestion des Ressources Naturelles Renouvelables, Université de Kisangani, Kisangani, Democratic Republic of the CongoCorneille E. N. Ewango & Joseph Kanyama TabuFaculté des Sciences, Université de Kisangani, Kisangani, Democratic Republic of the CongoCorneille E. N. EwangoInstitut Supérieur Pédagogique de Mbandaka, Mbandaka, Democratic Republic of the CongoOvide Emba & Pierre BolaSchool of Geography, Geology and the Environment, University of Leicester, Leicester, UKGenevieve Tyrrell, Arnoud Boom & Susan E. PageSchool of Water, Energy and Environment, Cranfield University, Bedford, UKNicholas T. GirkinBritish Geological Survey, Centre for Environmental Geochemistry, Keyworth, UKChristopher H. VaneInstitute of Earth Sciences, University of Lausanne, Lausanne, SwitzerlandThierry AdatteNEIF Radiocarbon Laboratory, Scottish Universities Environmental Research Centre (SUERC), Glasgow, UKPauline GulliverSchool of Biosciences, University of Nottingham, Nottingham, UKSofie SjögerstenDepartment of Geography, University College London, London, UKSimon L. Lewis More

Experiment results and regression modelThe simulation experiment results based on the design scheme are presented in Table 4, including 24 analysis factors and 7 zero-point experiments for estimating the errors. Quadratic multiple regression analysis of the results in Table 4 was performed using the Design-Expert software, and the regression models between the influencing factors and evaluation indices were established as follows:$$ Y_{{1}} = {1767.57} – {64.29}X_{{1}} + {117.46}X_{{2}} + {324.46}X_{{3}} + {107.87}X_{{4}} – {21.81}X_{{1}} X_{{2}} + {17.94}X_{{1}} X_{{3}} – {41.44}X_{{1}} X_{{4}} + {16.69}X_{{2}} X_{{3}} – {41.19}X_{{2}} X_{{4}} + {73.56}X_{{3}} X_{{4}} + {23.2}{X_{{1}}^{{2}}} – {82.42}{{X_{{2}}}^{{2}}} – {13.17}{{X_{{3}}}^{{2}}} – {53.67}{{X_{{4}}}^{{2}}} $$$$ Y_{{2}} = {1968.14} + {636.42}X_{1} + {34.42}X_{2} + {66}X_{3} + {115.17}X_{{4}} + {28.63}X_{{1}} X_{{2}} + {9.13}X_{{1}} X_{{3}} – { 45.87}X_{{1}} X_{{4}} + {1}0X_{{2}} X_{{3}} + {30.5}X_{{2}} X_{{4}} – {1.75}X_{{3}} X_{{4}} + {55.03}{X_{{1}}^{{2}}} – {8.1}{{X_{{2}}}^{{2}}} – {72.72}{{X_{{3}}}^{2}} + {61.03}{{X_{{4}}}^{{2}}} $$Table 4 Experiment schemes and results.Full size tableThe relationship between the actual values of the efficiency of conveying-soil and the distance of throwing-soil and the predicted values of the regression model is shown in Fig. 7. It can be seen from Fig. 7 that the actual values are basically distributed on the predicted curve, consistent with the trend of the predicted values, and linearly distributed.Figure 7Scatter plot. (a) Scatter plot of actual and predicted distance of throwing-soil. (b) Scatter plot of actual and predicted efficiency of conveying-soil.Full size imageVariance analysis and discussionThe F-test and analysis of variance (ANOVA) were performed on the regression coefficients in the regression models of the evaluation indices Y1 and Y2, and the results are shown in Table 5. According to the significance values P of the lack of fitting in the regression models of the objective functions Y1 and Y2 in Table 5, PL1 = 0.1485  > 0.05 and PL2 = 0.2337  > 0.05 (both were not significant), indicating that no loss factor existed in the regression analysis, and the regression model exhibited a high fitting degree.Table 5 ANOVA results of regression model.Full size tableAccording to the ANOVA, the significance values P of each influencing factor in the test could be determined28. For the evaluation index Y1, the factors X1, X2, X3, X4, X3X4, X22, X42 had extremely significant influences, while the factors X1X4, X2X4 had a significant influence. For the evaluation index Y2, the factors X1, X3, X4, X1X4, X12, X32, X42 had extremely significant influences, and the factors X2, X1X4 had a significant influence. Within the level range of the selected factors, according to the F value of each factor as shown in Table 5, the weight of the factors affecting the efficiency of conveying-soil is feeding speed  > helix angle of auger  > rotating speed of auger  > slope angle. And the weight of the factors affecting the distance of throwing-soil is slope auger  > rotating speed of auger  > feeding speed  > helix angle of auger.In addition, it is obvious that there are interactions between the feeding speed and rotating speed of the auger, slope auger and rotating speed of auger, helix angle of the auger and rotating speed of the auger on the efficiency of conveying-soil Y1. For the distance of throwing-soil Y2, there is an interaction between the slope angle and the rotating speed of the auger.Analysis of response surfaceThe fitting coefficient of the efficiency of conveying-soil is R2 = 0.9714, R2adjust = 0.9263, R2pred = 0.8082, the difference between R2adjust and R2pred is less than 0.2. The fitting coefficient of the distance of throwing-soil is R2 = 0.9873, R2adjust = 0.9742, R2pred = 0.9355, the difference between R2adjust and R2pred is smaller than 0.2. It is indicated that the response surfaces of the two models established have good consistency and predictability for the experimental results29.The response surface is created directly using the Design-Expert software. After entering the data, select “Analysis” module. In the “Model-Graph” menu bar, select “3D-surface” to switch to the 3D view. To express the interactive influence of each factor on the efficiency of conveying-soil Y1 and distance of the throwing-soil Y2, the above two quadratic regression equations of the evaluation indices were subjected to the dimensionality reduction treatment. Two of the factors was set to level 0, while the other two underwent interaction effect analysis to study the influence law on the evaluation indices Y1 and Y2, and the corresponding response surfaces were generated, as illustrated in Fig. 8.Figure 83D response diagram effect of evaluation indices. (a) Effect of interaction between X1 and X2 on efficiency of conveying-soil. (b) Effect of interaction between X2 and X4 on efficiency of conveying-soil. (c) Effect of interaction between X3 and X4 on efficiency of conveying-soil. (d) Effect of interaction between X3 and X4 on distance of throwing-soil.Full size imageIt can be seen in Fig. 8a, when the slope angle was constant, the efficiency of conveying-soil increased with the rotating speed of the auger to a certain value, then the efficiency increase changed more gently. The reasons for this phenomenon are described as follows. On the one hand, the greater the kinetic energy of the soil when leaving the original position, and the thinner the soil was cut, resulting in the smaller the probability of blockage in the spiral blade space. On the other hand, the centrifugal force of soil arriving at the pit mouth is greater, so it does not obstruct in the pit mouth. However, if the rotation speed of the auger was too high and the soil layer cut was too thin, the subsequent soil’s driving effect to the front would be weakened, or even the flow would be interrupted, so the vertical rising speed of the soil would be reduced. When the rotational speed of the auger was constant, the efficiency of conveying-soil decreased with the increase of slope and then slightly increased. With the increase of slope, the time of slope cutting process increased, and there was more soil backfilling on the side of high altitude, which leaded to the reduction of soil discharge efficiency. However, with the increase of slope, the amount of soil slide at the pit mouth was increased, improving the efficiency of soil discharge. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the rotating speed than in that of the slope angle, indicating that the rotating speed of auger X4 had a more significant influence than the slope angle X1.As can be seen in Fig. 8b, when the helix angle of the auger was fixed, the efficiency of conveying-soil continued to increase with the increase of the rotation speed. When the rotating speed of auger was fixed, the efficiency of conveying-soil increased with the increase of the helix angle and tends to decrease when it reached a certain value. The spiral blades space was the channel of soil movement. This phenomenon was caused by the increase of the gap between the two spiral blades with the increase of the helix angle of the auger, the soil was not easy to produce blockage. Meanwhile, the movement distance of soil was shorter, and the soil with higher kinetic energy was discharged more quickly from the pit. When reaching the pit mouth, the angle of soil throwing was larger and the soil backfilling rate was reduced. However, if the helix angle of auger was too large, the upward support ability and friction of the spiral blade surface to the soil would be reduced. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the helix angle than the rotating speed of the auger, indicating that the helix angle of the auger X2 had a more significant influence than the rotating speed of the auger X4.When the feeding speed was fixed, the efficiency of throwing-soil continued to increase with the increase of the rotating speed. When the rotating speed of auger was fixed, the efficiency of the throwing-soil with the increase of the feeding speed (see in Fig. 8c). The phenomenon was caused by the faster the feeding speed of the auger, the thickness of soil cut per unit time increased. Furthermore, the subsequent driving force of soil increased, and the soil kinetic energy increased. However, in the actual production, excessive feeding speed would cause soil blockage on the surface of spiral blades. The reason is due to in the simulation process, the soil would not stop moving because of blockage. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the rotating speed than in that of the feeding speed, indicating that the rotating speed of auger X4 had a more significant influence than the feeding speed X3.When the slope was fixed, the distance of the throwing-soil increased with the increase of rotation speed of the auger, and the increase amplitude increased gradually, as shown in Fig. 8d. The reason for this phenomenon was that the soil had more kinetic energy when it left its original position and the centrifugal force it received when it reaching the pit mouth is greater. When the rotation speed was too low, the soil layer was thin and the subsequent soil driving force was insufficient, resulting in the soil mass per unit area at the pit mouth was light and then the kinetic energy was small. When the rotating speed of auger was fixed, the distance of the throwing-soil increased continuously with the increase of the slope. As the slope increased, the time of soil swipe down process increased and then the rolling distance on the slope increased. Further analysis demonstrated that the response surface for Y2 changed more rapidly in the direction of the slope angle than in that of the rotating speed of auger, indicating that the slope angle X1 had a more significant influence than the rotating speed X3.Comprehensive optimal designAs relative importance and influencing rules of various experimental factors on evaluation indexes were different from each other, evaluation indexes should be taken into comprehensive consideration30. The optimization equation is obtained by the Design-Expert software multi-objective optimization method with Y1 and Y2 as the optimization objective function.$$25le {X}_{1}le 45$$$$10le {X}_{2}le 22$$$$0.04le {X}_{3}le 0.1$$$$30le {X}_{4}le 120$$$${{Y}_{1}}_{mathrm{max}}({X}_{1},{X}_{2},{X}_{3},{X}_{4})$$$${{Y}_{2}}_{min}({X}_{1},{X}_{2},{X}_{3},{X}_{4})$$In practice, the best combination of parameters needs to be selected according to the terrain slope. When the slope was fixed, the Design-Expert software was applied to optimize and solve the above mathematical model. The optimal combination of working parameters affecting the efficiency of conveying-soil Y1 and distance of throwing-soil Y2 for the auger were obtained and are shown in Table 6. If the ground preparation was required before the digging operation, the digging parameters can be designed according to values of Group 6 in Table 6.Table 6 Optimal parameter combinations of several terrain slopes.Full size tableDisturbance of soilA soil disturbance is defined as the loosening, movement and mixing of soil caused by an auger passing through the soil16. In the interface of the EDEM Analyst, add a “Clipping plane” to show the movement of the auger inside the pit. The kinetic energy, soil particle velocity vector, and velocity value of soil particles is observed when the auger in the middle of the soil bin31,32, as shown in Fig. 9.Figure 9The disturbance of the soil effect by spiral blade.Full size imageThe soil was lifted to the surface and then dropped to the lower side. In addition to the volume occupied by the spiral blades, the disturbed area also included the out-of-pit disturbed area caused by the compression of the cutting end of the spiral blade, as shown in the lower left corner of the auger.The kinetic energy and velocity of soil decreased firstly and then increased along the opposite direction of the auger feeding. The cutting end of the auger and the soil-throwing section occurred in the region with high kinetic energy and velocity. This was because the maximum kinetic energy was obtained at the cutting end of the auger, which was gradually consumed in the process of rising. After reaching the dumping end, the soil lost the restraint of the pit wall. When the centrifugal force of soil lost the reaction force, the kinetic energy of soil increased. Too much kinetic energy, however, can cause the soil to spread too far, causing subsequent trouble. The kinetic energy of the soil at the cutting end was related to the rotational speed of the auger. The spiral angle affected the angle between the force and gravity, and then the kinetic energy consumption in the process of soil increased.Verification experimentsTo verify the accuracy of the optimization model for auger working, as well as to evaluate the rationality of the working parameter combination optimized by the virtual experiment, performance verification tests were carried out on the EDEM software. According to the optimized process parameter setting test (as shown in Table 6), the relative error between the theoretical value and the experimental value was obtained. The verification test results are summarized in Table 7. The average relative errors of the efficiency of conveying-soil and the distance of throwing-soil between the Theoretical value and text value were only 4.4%, 9.1%. The simulation model is fairly accurate. The field performance verification experiments were carried out in slope. Figure 10 illustrates the field test and working conditions.Table 7 Results and comparison of validation test.Full size tableFigure 10Operation diagram at the experiment site.Full size image More

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