The mechanical work necessary to penetrate soil and extend a burrow depends on the failure mechanism of the soil, which varies with soil type, depth (Fig. 6(a); Dorgan, 2015), soil stiffness and toughness and organism size (Che & Dorgan, 2010; Dorgan, 2015; Ruiz et al., 2015). In cohesive soils, burrowing at shallow depths can be achieved through plastic rearrangement of soil grains and aggregates. At greater depths, organisms such as worms, clams and plant roots alternate radial expansion and axial elongation motions to extend burrows by fracture propagation and deformation-induced softening (Trueman, 1968; Abdalla et al., 1969; Greacen & Oh, 1972; Dorgan et al., 2005, 2007). This is typically achieved by applying radial stresses against the burrow walls, either through expansion of a body section near the burrow tip or through movement of mouthparts, which results in effective stress relaxation at the burrow tip (referred to as an open-mode discontinuity by Shin & Santamarina (2011)). In non-cohesive soils, burrowing at shallow depths can be enabled by ‘sand fluidisation,’ a process in which rapid shearing of soil induces a local flow failure due to soil contraction or generation of excess pore pressures. This process is used by several worms, shrimps, crabs and vertebrate organisms, including sandfish lizards and ocellated skinks (Trueman, 1970; Maladen et al., 2011; Sharpe et al., 2015; McInroe et al., 2018). At greater depths in sands, burrowers use similar behaviours as in cohesive sediments: they employ a dual-anchor system to apply normal forces to burrow walls with different regions of the body (Dorgan, 2018). Rather than causing fractures, these forces are likely to locally compact the surrounding soil and induce effective stress relaxation ahead of the tip. In addition, the radial expansion against the burrow walls increases the pressure against the organism's body, which provides an anchor to generate propulsion to penetrate the soil in the form of friction and bearing capacity (Trueman, 1968; Summers & O'Reilly, 1997; Dorgan, 2018). Organisms such as razor clams and other bivalves also soften the soil through fluid injection and dynamic expansion and contraction of their shell to increase local pore pressures (Trueman, 1968; Winter et al., 2012).

Fig. 6. Bio-inspired burrowing. (a) Schematic representation of strategies employed by burrowing organisms as a function of depth and grain size (from Dorgan (2015)). (b) Force chain map from DEM simulation of bio-inspired probe during self-burrowing showing mobilisation of tip resistance and anchor reaction (data from Chen et al. (2021)). (c) Comparison of length-to-diameter ratios for self-burrowing obtained from cavity expansion analyses for depths between 5 m and 40 m, showing agreement with dimensions of various clam species (data from Martinez et al. (2020)). (d) Burrowing-out curves of bio-inspired actuator showing the effect of sand relative density (D1, D2 and D3 correspond to different sand relative densities, data from Tao et al. (2019)). (e) Actuation strategies consisting of lateral head movement and body elongation employed by a burrowing soft robot (redrawn from Ortiz et al. (2019))

DEM simulations and laboratory experiments relating to bio-inspired self-burrowing probes for site characterisation have highlighted key aspects that enable penetration using the dual-anchor mechanism (Cortes & John, 2018; Huang & Tao, 2018; Khosravi et al., 2018; Chen et al., 2020, 2021; Huang & Tao, 2020). Radial expansion of a probe section develops anchorage forces and relaxes the contact forces ahead of the probe's tip, facilitating subsequent penetration (Fig. 6(b)). Cavity expansion simulations have been used to assess the upscaling potential of a dual-anchor mechanism in sandy, silty and clayey soils at different depths (Martinez et al., 2020). Results indicate that a probe consisting of a radially expanded anchor and a penetrating tip would require an anchor with a length of 2·0 to 4·5 times the tip diameter to generate sufficient anchorage forces, which is on the order of aspect ratios (length-to-diameter ratio, L/D) of various razor clam species (Fig. 6(c)). Other research has focused on developing prototypes for sensor deployment applications. For instance, Tao et al. (2019) and Huang et al. (2020) developed robot prototypes capable of burrowing out by employing an elongation-shortening mechanism inspired by razor clam locomotion. The authors showed that the robot's performance in dry sand depends on the relative density (Fig. 5(d)), the period of the expansion–contraction cycles and the soil–robot interface frictional interactions. Ortiz et al. (2019) developed a marine worm-inspired soft robot that employs two strategies: bi-directional bending of the head to remove and loosen soil and radial expansion of a body section to provide anchorage (Fig. 6(e)). Use of these techniques in constant-displacement experiments reduced the penetration resistance by up to 50% and allowed a tethered prototype to move horizontally through granular media.

Ants efficiently excavate stable nest structures in different soil types. For instance, Soga (2011) provided comparisons of the energy efficiency of the excavation using tunnel-boring machines (TBMs) with that of ant tunnelling. TBMs were reported to have efficiencies between two and four orders of magnitude lower than ant tunnelling (1·7 × 10⁷ to 4·4 × 10⁸ J/m³ in rock and sand for the former and 1·2 × 10⁴ to 7·9 × 10⁵ J/m³ in sand for the latter). Field and laboratory studies have shown that ant excavation habits and performance, and resulting nest architecture, change with soil type and conditions. X-ray CT observations on fire ant colonies showed that nest depth depends on particle size and water content (Monaenkova et al., 2015). The most stable tunnels were excavated at intermediate water contents (Fig. 7(a)), implying that the increasing strength provided by the capillary forces allowed for creation of more stable tunnels. Yamamoto et al. (2019) performed two-dimensional and three-dimensional (3D) experiments on monolayer and multilayer soil deposits. Changes in particle size and density did not significantly influence tunnel diameter, but excavation rates and volume of excavated soil were greater in soils with lower density and smaller particle sizes. Espinoza & Santamarina (2010) revealed the role of different interparticle forces on the excavation ability of ants and the stability of ant tunnels. Analytical results show that the ant mandible pulling force is expected to be greater than the combined particle weight and electrical and capillary forces for particles smaller than fine gravels (Fig. 7(b)). Fig. 7(c) presents a synthesis of the results, showing the effect of grain size and degree of saturation on the tunnel stability and excavation performance of ants. Antlions and wormlions are also efficient at excavating in both coarse- and fine-grained soils. These animals dig cone-shaped traps to hunt prey; antlions use a spiral digging strategy whereas wormlions use a central digging strategy (Tuculescu et al., 1975; Franks et al., 2019). Research has shown that the angles of the antlion and wormlion traps are close to the angle of repose and that the soil within the trap slopes is close to the critical state (Botz et al., 2003, Büsse et al., 2020). The instability of these slopes, along with sand throwing by the predators, creates avalanches that make prey slide and fall to the bottom of the trap.

Fig. 7. Ant tunnel excavation and stability: (a) effect of particle size and water content on the depth of fire ant nests, showing an optimal water content for tunnel stability (D = nest depth, d = mean particle size, W = water content; adapted from Monaenkova et al. (2015)); (b) interparticle forces as a function of particle size (t = distance between particles, ω = water content) (adapted from Espinoza & Santamarina (2010)); (c) geometrical and geomechanical control of ants’ digging behaviour highlighting restrictions imposed by the limited ant mandible force and tunnel instability (M = mandible size, d = mean particle size) (adapted from Espinoza & Santamarina (2010))

Soil conditions affect the growth, establishment and natural selection of plants. Plants, in turn, influence soil properties such as chemical composition and internal structure, and can contribute to increased erosion and landslide resistance. Plant and tree roots grow in many different conditions, from clays and soils rich in organic materials (e.g. crops, cypress trees) to sandy substrates (e.g. palm trees and dune grasses) to rocky terrains (e.g. juniper trees). The characteristics of the root system, as well as its interactions with the soil, including the penetration resistances, root architecture and anchorage capacity, are a function of the plant species and soil and environmental conditions (e.g. Grime, 1977; van Noordwijk & De Willigen, 1987; Bengough & Mullins, 1990; Bengough & McKenzie, 1997; Barthélémy & Caraglio, 2007).

Savioli et al. (2014) performed FEM simulations of root growth in non-cohesive soil. These simulations monitored the radial effective stresses and volumetric strains while a root-shaped cavity was expanded (Fig. 8(a)). Radial expansion increased the radial effective stress along the sides of the root (shown in cooler shades) and decreased the stress at the root tip (shown in warmer shades). While volumetric strains were dilative overall, the dilation zone was largest at the root tip. These results suggest that the relaxation of stresses and decrease in density at the tip may facilitate soil penetration, especially in stiff and strong soils, in agreement with Shin & Santamarina (2011).

Fig. 8. Soil penetration by plant roots. (a) Numerical results of radial root growth showing relaxation of radial stresses (warm colours) and dilation (warmer colours) at root tip (from Savioli et al. (2014)). (b) X-ray CT scan of root system growing in sand showing particle displacements (from Anselmucci et al. (2021)). (c) Comparison of work during straight and circumnutative penetration showing greater efficiency of circumnutative penetration (ρ = soil density, α = angle amplitude of circumnutations, T =  period of circumnutations, from Del Dottore et al. (2018)). (d) Schematic diagram showing root growth process, indicating successive cells growing in the meristematic region (MR) and shifting over time into the mature region (from Sadeghi et al. (2014)). (e) Root-like device for soil penetration. As the deposition head (DH) rotates, it deposits a filament around the outer surface (from Sadeghi et al. (2014)). (f) Root-inspired burrowing device that combines root tip extension and soil fluidisation to decrease penetration resistances (from Naclerio et al. (2018)). A full-colour version of this figure can be found on the ICE Virtual Library (www.icevirtuallibrary.com)

The influence of the soil properties and condition on the growth of a root system has been largely investigated in the field of plant science (e.g. Bengough & Mullins, 1990; Atwell, 1993). However, the root growth process alters the in situ state of stresses, fabric and moisture conditions, which in turn can influence the mechanical behaviour of the soil. Anselmucci et al. (2021) performed in vivo X-ray CT of seeds growing in coarse and fine sand of varying density (Fig. 8(b)). Their X-ray CT data analysed with digital image correlation (DIC) measured the evolution of the soil strain field and showed that the sand grains are mainly displaced in the same direction as root elongation for distances equivalent to two mean particle diameters.

During growth, plant roots perform oscillatory, semi-circular movements called circumnutations (Mullen et al., 1998). Although the role of circumnutation in plant root growth is still debated, recent findings by Taylor et al. (2021) indicate that circumnutation is critical for seedling establishment in rocky soil because they facilitate growth past obstacles. Del Dottore et al. (2018) hypothesised that these movements can decrease penetration resistance. The authors validated this hypothesis experimentally by comparing the resistances mobilised and work needed for straight, vertical penetration and penetration performed with circumnutations by an artificial probe. Results show that circumnutations decrease penetration resistance and work across a range of soil densities (Fig. 8(c)). Prototypes of burrowing robots have focused on decreasing the penetration resistance to enable deeper soundings and more efficient operations (e.g. Del Dottore et al., 2018). Sadeghi et al. (2014) developed a device inspired by root growth in which new material is added behind the tip as it advances. This mimics the root growth process, where cells split and slough as they mature (Fig. 8(d)). This significantly reduces frictional resistance along the root sides, leaving only the penetration resistance to overcome, and can result in a 70% decrease in energy consumption compared to conventional penetration. Fig. 8(e) presents a series of images of this root-inspired robot. Naclerio et al. (2018) developed a soft self-burrowing robot that combines the bio-inspired principle of plant root growth by way of tip extension with air-induced fluidisation (Fig. 8(f)). The authors report a reduction in penetration resistance of 10× relative to vertical pseudo-static penetration and demonstrate 50 cm deep growth into real sand in less than 20 s.

Many fish bury themselves to ambush prey and evade predators. Some fish, like the sand lance, burrow by diving head-first into the substrate while undulating their bodies. Researchers have not observed sand fluidisation to reduce penetration resistances. Instead, Bizarro et al. (2016) proposed that the spacing of the scale bands interacts with the grain size of the substrate to produce reduced frictional forces between the fish and the sand. In flatfish, body size and undulation frequency affect burial performance (McKee et al., 2016). These authors developed a physical model of a flatfish to isolate the effect of undulation on burial speed. Their results suggest there is an optimal range of undulation frequency (5–10 Hz) that allows for the most efficient burial, suggesting that generation of excess pore water pressures due to cyclic loading occurs. Pacific sandfish have been hypothesised to use a modified two-phase respiratory pump to force water into the substrate during burial to liquefy it and decrease burial resistances (Macdonald et al., 2014).

Although snakes lack limbs, they move efficiently in a variety of environments including sand dunes, trees, forest litter, prairie grasslands and oceans. Their ventral scales are aligned transversely along their underbelly (Fig. 9(a)) and the frictional interactions between the scales and the substrate control the snake's locomotive performance. Several studies have shown that snakes rely on directional friction for locomotion, where the ‘cranial’ friction coefficient is greater than the ‘caudal’ friction coefficient (Fig. 9(b)). Gray & Lissmann (1950) measured the friction coefficient between dead snakes and various textured surfaces, obtaining values of 1·22 in the cranial direction and 0·49 in the caudal direction for sandpaper. Marvi et al. (2013) also measured friction coefficients between 40% and 250% greater in the cranial than caudal direction for three snake species (Fig. 9(c)). In addition to the asymmetric geometry of the scales, nano-scale features called denticles within each scale (Fig. 9(d)) contribute to frictional anisotropy at a smaller scale (e.g. Hazel et al., 1999; Baum et al., 2014). A comparative study by Rieser et al. (2021) indicates that the structure of the denticles directly influences the locomotor performance of snakes, such as sand-inhabiting sidewinders.

Fig. 9. Biological strategies for directional friction in snakeskin: (a) photograph of ventral scales of a milk snake (scale bar corresponds to 1 cm, from Hu et al. (2009)); (b) schematic diagram of cranial and caudal shearing directions; (c) friction coefficient (μ) measurements for different snakes in the cranial and caudal directions; (d) scanning electron microscopy images of denticles within a snake scale (arrow points towards snake's tail and scale bar is 2 μm long, from Baum et al. (2014))

Researchers have investigated the development of direction-dependent friction resistances at soil–structure interfaces for applications such as deep foundations, soil anchors and soil nails and landfill liner systems. Martinez et al. (2019), Stutz et al. (2019), O'Hara & Martinez (2020) and Huang & Martinez (2020) performed monotonic and cyclic interface shear tests between sand and surfaces inspired by 3D scans of snakeskin, showing that shearing in the cranial direction mobilised larger interface shear resistances than shearing in the caudal direction. Differences of from 25 to 90% were observed during monotonic and cyclic shearing (Figs 10(a) and 10(b), respectively). Huang & Martinez (2021) examined the effect of normal effective stress, overconsolidation ratio and shearing velocity on the interface shear behaviour between clay and snakeskin-inspired surfaces and concluded that the response has a smaller direction dependence as compared to the interfaces with sand. Martinez et al. (2018), O'Hara & Martinez (2020) and Martinez & O'Hara (2021) also investigated the effect of snakeskin-inspired surface texturing on the performance of model piles during centrifuge load tests. The results indicate a difference in installation forces of 48% and pullout forces of 128%, where loading in the cranial direction consistently led to greater frictional resistances (Fig. 10(c)).

Fig. 10. Directional friction in load transfer across soil–structure interfaces. (a) Monotonic and (b) cyclic interface shear tests on snakeskin-inspired surface and sand showing the larger stress ratio and friction angle mobilised during cranial shearing (data from O'Hara & Martinez (2020)); δ, interface friction angle. (c) Centrifuge load tests on snakeskin-inspired piles highlighting the greater forces mobilised during cranial installation and pullout (data from O'Hara & Martinez (2020))

Research on the anchorage mechanisms of root systems has been performed in the fields of plant biology, soil science and geotechnical engineering. This research has highlighted several factors that contribute to anchorage capacity and load transfer, including architecture (i.e. level of branching and branching angle), root stiffness and soil shear strength (e.g. Coutts, 1983; Gray & Ohashi, 1983; Ennos, 1993; Stokes et al., 2000; Fourcaud et al., 2003; Gregory, 2006; Hamza et al., 2007; Mickovski et al., 2007). Investigations focused on developing bio-inspired technologies for foundation and anchorage systems have involved field, centrifuge and laboratory experiments and numerical simulations. For instance, Burrall et al. (2020) performed field vertical pullout tests on fruit trees with three different rootstock types (Lovell, Marianna and Myrobalan), which differ in their architectural characteristics. The results, shown in Fig. 11(a), indicate that the rootstock type had an important influence on the initial stiffness, peak capacity and softening of the pullout force–vertical displacement curves. The pullout performance of the root systems was calculated to be one to two orders of magnitude more efficient in terms of material use than business-as-usual alternatives such as micropiles and spread footings. Laboratory tests by Mallett et al. (2018) provided further insight into the effect of root architecture on the soil deformation around root analogues in sand. X-ray CT scans reveal the formation of shear bands within the sand whose location depends on the root internal angle (Fig. 11(b)). The geometry of the sand slip surface was generally conical in shape; however, its size and orientation changed with the root angle. Aleali et al. (2020) applied a multifaceted bio-inspiration approach to generate design ideas for deep foundations with greater shaft resistance than conventional cylindrical piles. Their design incorporates biological strategies such as a flexible but incompressible core, a longitudinally split shell that allows lateral expansion for anchorage and lateral root-type anchoring elements. FE modelling of the bio-inspired laterally expansive pile shows significant advantages in terms of greater confining pressure and load-carrying capacity compared to conventional piles.

Fig. 11. Anchorage of natural and analogue root systems: (a) force–displacement curves during vertical pullout test of Lovell, Marianna and Myrobalan rootstocks where the Myrobalan rootstocks mobilise the largest pullout forces (data from Burrall et al. (2020)); (b) shear strain (e_shear) maps within soil from X-ray CT scans during vertical pullout tests on root analogues where the location of the shear band depends on the root branching angle (from Mallett et al. (2018))

Trees and plants take up moisture from the soil through their roots, which then evaporates from their leaves (evapotranspiration). This water removal from soil increases the soil suction (e.g. Blight, 2003; Hemmati et al., 2012), and is sometimes referred to as ‘hydraulic reinforcement’. Researchers have quantified the suction magnitude and the influence zone size for different plant and tree species, concluding that vegetation increases both the suction magnitude developed during drying as well as that maintained during wetting (e.g. Ng et al., 2013). Other researchers have shown that vegetation can alter the soil-water retention curve (Leung et al., 2015a) and reduce the hydraulic conductivity and infiltration rate in soils (e.g. Leung et al., 2015b). Engineering analyses have confirmed the beneficial effects of vegetation on slope stability (Gray & Sotir, 1996). For instance, Switala & Wu (2018) showed through FEM simulations that slope displacements during rainfall were significantly smaller on vegetated slopes than on bare slopes (Fig. 12(a)). In addition, the authors showed that slope horizontal displacements were smaller when both mechanical reinforcement by roots and increase in suction by evapotranspiration were considered (Fig. 12(b)).

Fig. 12. Mass and thermal transport. (a) Contours of horizontal displacements, u, after 100 h of rainfall obtained from FEM simulation of a non-vegetated slope and a slope with mechanical root reinforcement and evapotranspiration. (b) Comparison of slope horizontal displacements for non-vegetated and vegetated cases where mechanical reinforcement and evapotranspiration reduce the slope movements (from Switala & Wu (2018)). (c) Leaf venation (LV) network connecting 15 discrete population centroids in Metro Atlanta (from Patino-Ramirez & Arson (2020)). (d) Photograph of Macrotermes michaelseni termite mound and cross-section in Namibia showing multi-scale porosity (height of mound is about 5 ft (1·52 m))

The problem of connecting a central node to a set of spatially scattered points is common to many natural and artificial systems of all scales and levels of complexity. In engineering, this is common in distribution networks (e.g. public transportation, water and gas distribution). Patino-Ramirez & Arson (2020) evaluated a leaf venation (LV) algorithm for designing bio-inspired infrastructure transportation networks employing Runion's algorithm (Runions et al., 2005). This algorithm generates venation systems that grow out a stem in a finite domain that contains a given distribution of auxin sources. Auxin is a growth hormone that dictates the direction of growth of venation segments. Patino-Ramirez & Arson (2020) modelled the city of Atlanta metropolitan area with the stem representing the intersection of two Metropolitan Atlanta Rapid Transit Authority (MARTA) metro lines and the auxin sources representing population centroids (Fig. 12(c)). Results indicate that leaf-inspired models can perform similarly to or better than computer-intensive optimisation algorithms in terms of network cost and service performance, which could facilitate the design of engineering transportation and resource distribution networks.

The nest and mound superstructures built by colonies of fungus-farming termites (Fig. 12(d)) are efficient at controlling internal ventilation, which helps regulate internal heat and humidity (Turner & Soar, 2008; Katariya et al., 2018; Vesala et al., 2019). The mound is porous across nano-, micro- and macro-scales, with the tunnel structure within the mound constituting the macro-scale pores (Turner, 2005). Air is brought up through the nest as a result of diurnal temperature oscillations, where it mixes with spent air and gases such as carbon dioxide, then rises into the mound where it is dissipated through the mound material to the atmosphere (King et al., 2015). Turner & Soar (2008) indicated that gas exchange with the atmosphere is controlled by convection in the main tunnel, mixed convection and diffusion in the millimetre-scale tunnels and diffusion through the micro- and nano-pores. Relative to the atmospheric temperature, the mound's internal temperature is from 10 to 15°C warmer during the night and from 10 to 15°C cooler during the day largely due to the large thermal capacity of the soil surrounding the nest (Turner & Soar, 2008; also Bardunius and Lingwall, personal communication, 2020). The mound is constructed by the termites from locally available soils around the nest (Jouquet et al., 2004), where termites employ only the fine fractions of soil at moisture contents between the liquid and plastic limits (Kandasami et al., 2016). In addition, organic material in the soil is essential for effective cohesion of transported soil pellets (Zachariah et al., 2017).