# Bio-inspired burrowing mechanics

## Simulation of penetration and burrowing processes (FEM and SPH)

We have developed a modeling approach that can be used to simulate anchor penetration and pull out at reasonable computational cost. The Smooth Particle Hydrodynamics (SPH) method is used to simulate the soil close to the penetration zone where large deformation of soil takes place, while the portions of the model where only small strain is expected (i.e., probe and far-field soil) are simulated by the Finite Element Method (FEM). The FEM+SPH method was verified against analytical and numerical solutions of stress distributions under a shallow foundation, displacement fields during slump tests, and stress and strain fields during biaxial compression tests.

## Mechanics of ant nests

We extracted 3-D digital twins of Florida Harvester ant structures from a nest cast in situ and simulate the stress and displacement fields around that nest with the Finite Element Method (FEM). Stress invariants around the main shaft are compared to those around idealized geometric representations of that shaft, i.e. helixes with a fixed pitch angle and a uniform elliptical cross-section. Helical structures made of circular cross-sections and horizontally oriented elliptical cross-sections interact in a way that reduces the risk of tension failure and distributes the shear stress more evenly. One can show that in addition to the extra stability that they offer and the lower risk of tensile or shear failure that they exhibit, helical shafts have the advantage of requiring less power to excavate than straight sub-vertical shafts

## Influence of plant root growth on soil microstructure and strength

We study of the influence of plant root growth on the density of a granular soil. Our collaborators at L3SR established a protocol to obtain reproducible samples of sand with a sprouting seed. Maize and chickpea roots are grown in tubes filled by pluviation with Hostun sand. Root development and induced soil micro-structural changes are imaged every 24 hours by x-ray tomography for 7 days. The acquired images are processed and trinarized into separate phases (soil, root, voids). This allows measuring the evolution of soil porosity during root growth to be measured. Eventually, a sub-volume of soil around a root tip is defined after 7 days of growth and the evolution of porosity in that volume is characterized in reverse chronological order. The root does not affect the soil local porosity nor the topology of the root system at a distance larger than ten times the diameter of the main root. The evolution of local porosity is not fully understood at this stage, but it is reproducible.

## Root-like cavity expansion at shallow depth

In plant roots, water uptake increases the turgor pressure inside the root cells, which pushes cell membranes against stiff cell walls. Roots thus expand radially, leading to a decrease in soil compressive stress ahead of the tip, allowing for root axial growth. Plant roots can be seen as pressurized vessels that adapt their shape to soil mechanical response, thus probing soil properties. In general, the deformation patterns and failure mechanisms of pressurized cavities at shallow depth are of relevance to many geotechnical applications, including tunneling and horizontal directional drilling. That is why we conducted an experimental study of a reduced-scale pressurised cavity under geostatic stress, in order to measure the effect of cavity length, vertical stress and soil density on soil deformation and failure. x-ray computed tomography was used to acquire images of the system at key stages of the cavity inflation process. A closed shaped failure region developed around the cavities, beyond which, shear planes of elliptic paraboloid shape formed, extending from the bottom of the cavities all the way to the free surface. The plane strain assumption did not hold beyond the central portion of the longest cavity tested (L = 6D). The volumetric strain and porosity changes inside the shear bands showed significant dilation in dense specimens, but contraction in loose specimens. The average orientation and the thickness of the shear bands were in agreement with those found in the literature for passive arching mechanisms (anchoring). The orientation of the principal strains around the cavity follows catenary shapes, similar to those displayed in active trapdoor mechanisms.

## Machine learning – based estimation to blowout susceptibility around pressurized cavities

The need to solve complex problems that still do not have a closed form analytical solution is one of the challenges of current practice, including the susceptibility estimation of cavity blowout during horizontal directional drilling (HDD). Computational tools and high frequency data acquisition in conjunction with machine learning open up new opportunities to create tools that can aid in the understanding and design of these problems. We propose the use of a predictor function, calibrated with a pool of numerical simulations that can predict the susceptibility of blowout of a cavity, given a fixed geometrical and stress configuration based on the mechanical parameters of the soil the cavity is embedded in; results using k-means clustering (for classification) and support vector machines (SVM) to create the predictor function, showed and accuracy of about 87% in predicting the blowout susceptibility.

## Design of Horizontal Directional Drilling alignment by Ant Colony Optimization (ACO)

Horizontal Directional Drilling (HDD) is a trenchless method that consists in drilling an inclined and curved bore from an entry point to an exit point. In practice, HDD is designed iteratively by trial and error, to minimize the cost under geometric and mechanical constraints. Here, we optimize the drill path with continuous implementations of an Ant Colony Optimization (ACO) algorithm that sets the depth of the alignment and its entry and exit angles as the design parameters to optimize, to ensure minimal drill path length (cost), avoid collapse or instability (mechanical constraints) and remain in the construction domain (geometric constraint). We compare the ACO results to the drill paths designed in practice in two different scenarios: one in which the entry and exit points are fixed, and one in which the geometry of the central segment is constrained. Results show that ACO can be used to automate the otherwise time-consuming design process while minimizing the drill path length and the costs associated to it.