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Using gelatin as an analogue for sediment (on the basis of its similar mechanical properties)1,2,4 and polarized light to visualize the burrow around N. virens, we investigated whether these worms burrow by crack propagation. Gelatin is birefringent, which enables its stress to be analysed5 during burrowing.

We found that the edges of the burrow were visible and that they showed evidence of a discoidal crack, which was held open by the dorsal and ventral surfaces of the animal (Fig. 1a, b). The arc of the crack extends laterally beyond the setae and anteriorly to the tips of the antennae. Visualization of stress fields by photoelastic stress analysis (for methods, see supplementary information) reveals a force exerted dorsoventrally by eversion of the animal's pharynx against the relatively flat wall of the crack (Fig. 1c).

Figure 1: The crack-shaped burrow around the annelid worm Nereis virens in polarized light.
figure 1

a, Anterior view in crosspolarized light, showing the longer axis of the discoidal crack, which is parallel to the setae, and showing the dorsal and ventral surfaces against the gelatin substrate; the shape of the burrow follows the line encircling the crack. b, Dorsal view in crosspolarized light, showing the shape of the burrow around the animal. c, Side view in circularly polarized light, showing the stress field dorsal and ventral to the worm, and the crack extending anteriorly.

According to linear elastic fracture mechanics, the stress intensifies at the crack tip, propagating it when the critical stress intensity is reached1,6. Here, the everted pharynx acts as a wedge, with the radial force intensified at the tip of the crack, which propagates, allowing the animal to move forward (Fig. 2). The crack's aspect ratio (T/W in Fig. 2) is a function of the material properties of the sediment (the critical stress intensity and Young's modulus). Expansion of a subterminal body portion has previously been considered as an anchor7; we infer instead that a terminal or subterminal lateral expansion acts as a wedge in elastic mud.

Figure 2: Scheme showing dorsal view of crack shape and lateral oblique views of crack propagation during burrowing.
figure 2

Arrows extending vertically from the crack indicate forces. The worm everts its pharynx and exerts a force normal to the direction of movement (1), which causes the crack to propagate, releasing energy (2). The worm then retracts the pharynx and moves forward into the crack (3) before repeating the cycle (4). W is the longer axis of the discoidal crack; T, the shorter.

We measured the maximum force required to propagate a crack as 0.023±0.002 newtons (mean±s.e.m.; n=5), which is less than 10% of the ‘radial’ force of 0.6 N that is exerted by a worm against an aquarium wall3. Sediment behaves like an elastic solid that deforms under stress, as evidenced by acoustic8 and bubble-growth experiments1. The relatively small forces exerted by growing bubbles in sediment are well predicted by linear elastic fracture mechanics from the mechanical properties of the medium1. According to the theory of elasticity, a closer, rigid boundary necessitates greater force for a given displacement, resulting in substantial effects of nearby rigid walls on burrowers.

Crack propagation may also be a likely mechanism of movement for burrowers from several other marine phyla. For example, clams and echinoids, which are both found in muddy sediments, could exploit their wedge-like shape — and some echinoids have been reported to push directly into the frontal sediment, rather than excavating it, and to move through the sediment by means of a repeated rocking motion, unlike more globular, excavating echinoids living in sands9. Gammarid amphipods could exploit their resemblance to oblate bubbles1,2, and subterminal expansions in earthworms indicate that they may burrow, and roots grow10, by an analogous mechanism.

Burrowing by crack propagation also bears on bioturbation, the movement of sediment grains and fluids by living organisms. Bioturbation models have generally ignored the polymeric matrix that leads to elastic behaviour and that keeps sediment grains in the same relative position to each other, instead considering particles as separate, “randomly wandering” elements11. But cracks open new surfaces from which animals can feed, leading to unsteady release and uptake of solutes. Crack propagation focuses stresses at the propagating crack tip. These stresses are probably the highest experienced by sediments after their deposition and bear on issues such as the permanence of clay–grain associations and the mechanical protection of organic material from decay.