GRANMA manuscript No. (will be inserted by the editor)

Living Quicksand

Dirk Kadau1, Hans J. Herrmann1,2, Jos´eS. Andrade Jr.1,2, Ascˆanio Dias Ara´ujo2, Luiz Jos´eC. Bezerra3 and Luis P. Maia3

Abstract The image of quicksand merciless swallowing a mans can be swallowed or even sucked in, engineers of soil victim has inspired the fantasy of kids and helped writers mechanics have typically asserted that, since the density and moviemakers to get rid of evil figures. Is this really of sludge is larger than that of water, a person cannot possible? This is still disputed since till today it is not fully submerge [6]. The fluidization of a soil due to an even clear what quicksand exactly is. In soil mechanics, increase in ground water pressure which in fact is often the “quick-condition” is usually described as a liquefaction responsible for catastrophic failures at construction sites due to high water pressure essentially possible with any is called by engineers the “quick-condition” and can theo- soil. However, previous studies have detected anomalous retically happen to any soil [7–9]. Is this condition, which rheological properties from natural quicksand. Pushed by can be reproduced on rather short time scales, equivalent these contradicting points of view we set off to Len¸cois to the legendary quicksands? Another way of fluidization Maranhenses in North-East Brazil, where quicksands are can be vibrations either from an engine [10] or through an common, to investigate rheology and strength in situ. We earthquake [11]. Recently Khaldoun et al. [12] have stud- found that along very quiet drying lakes cyanobacteria ce- ied natural quicksand brought from a salt lake close to ment an impermeable crust above a suspension of grains. Qom in Iran. They found strong shear thinning behavior, Beyond a critical pressure, the crust fails releasing wa- and claim that the presence of salt is crucial. Their sam- ter from the collapsing colloidal structure and radically ples behaved similarly to artificial quicksand produced in changing the depth dependence of the shear strength from the lab and no strong memory effects have been reported. a constant to a linear function. The sedimenting solid frac- tion and the rapid increase of shear strength can indeed trap an intruder endangering his life if the basin is suffi- 2 ciently deep. As opposed to some previous studies, we find Experiments that this quicksand condition cannot be restored once it The Len¸cois Maranhenses is a natural park in the state has collapsed. Finally, we also show some preliminary re- of Maranh˜ao in the North-East of Brazil consisting of sults from a contact dynamics model specially designed to barchanoid dunes separated by lagoons (Fig. 1) that are mimic the living quicksand behavior. pushed inland by strong winds with a velocity of 4 to 8 meters per year [13]. It is well known for its beauty as well Key words. Granular matter, Contact Dynamics Simu- as the presence of quicksands in which vehicles have often lations, Distinct Element Method, Quicksand, Collapsible been trapped and oil companies have lost equipment. This soil, Biomaterial quicksand appears at the shore of drying lagoons after the rain season. These lagoons, placed amidst very clean sand, have no inlet or outlet and are exclusively filled by rain water. Their bottom is covered by a soft brown or green sheet of algae and cyanobacteria. 1 We investigated quicksand at Lat: 2o28.76’ S, Introduction Long: 43o03.53’ W. If the pressure on the surface is The nature and danger of quicksand has been disputed not higher than a given threshold value, namely pc = for a long time [1–5]. Despite widespread belief that hu- 10 − 20 kPa, it is even possible to walk on it and observe that the surface elastically deforms like a waterbed. These April 24, 2008 deformations visibly range over meters. If the pressure ex- Dirk Kadau, Hans J. Herrmann, Jos´eS. Andrade Jr., Ascˆanio ceeds pc, the surface starts to display a network of tensile Dias Ara´ujo, Luiz Jos´eC. Bezerra and Luis P. Maia cracks as seen in Fig. 2. Out of the cracks pours water. The object or person rapidly sinks inside, until reaching Institute for Building Materials, ETH H¨onggerberg, 8093 the bottom of the basin, which in our case could be up Z¨urich, Switzerland to one meter deep, and is then trapped within a consol- Departamento de F´ısica, Universidade Federal do Cear´a, 60451-970 Fortaleza, Cear´a, Brazil idated soil. Objects less than one meter long but lighter Labomar, Universidade Federal do Cear´a, Av. Aboli¸c˜ao 3207, than water like tables of wood are easily drawn inside and Meireles, 60165-081 Fortaleza, Cear´a, Brazil become nearly impossible to retrieve. We conclude that, if the basin is deeper than two meters which could possibly Correspondence to: [email protected] happen, a human being might perish. 2

120 field 1 (unpert.) field 2 (unpert.) 100 field 3 (unpert.) field 1 (pert.) field 2 (pert.) 80 field 3 (pert.)

60 (KPa) τ 40 a) 20

0 0 20 40 60 80 h(cm)

Fig. 3. Dependence of the shear strength τ on depth h be- fore (empty symbols) and after (circles) the collapse of the quicksand for three different quicksand fields in Len¸cois Maran- henses. The shear strength has been measured with a vane rheometer [15]. In the perturbed case (i.e., before the collapse), b) the solid line corresponds to the best fit to the data from all fields of the linear function τ = ah with a = 1.2 ± 0.1 kPa/cm. Fig. 1. In (a) we show a photograph of the dune field at the The shear strength of the unperturbed quicksand (i.e., before ≈ Len¸cois Maranhenses (Maranh˜ao state, North-East of Brazil) the collapse), however, is approximately τ 5.4 kPa until where lagoons like the one shown in (b) form during the rainy reaching the bottom of the basin. season between two adjacent dunes and dry out thereafter. The “living quicksand” is usually found at the shores of these lagoons. The collapse of the quicksand is irreversible. We conclude that it is not possible to understand this quicksand by only investigating samples in the lab. One has to study it in situ because the sampling itself does already destroy the metastable quicksand condition. Measurements have been performed by partially cov- ering the quicksand fields with light wood plates. This enabled us to walk on the surface of unperturbed and per- turbed quicksand areas without provoking any significant changes on the structure of the system. In Fig. 3 we show the dependence of the shear strength τ on the depth be- fore and after the collapse of the system, measured for three different quicksand fields in Len¸cois Maranhenses. In the unperturbed case, our results indicate that τ re- mains approximately constant at τ ≈ 5.4 kPa up to the bottom of the quicksand basin where it then shows a rapid increase with depth. The collapsed material, on the other Fig. 2. Typical quicksand bed at the shore of a drying la- hand, shows a linear increase of the shear strength with goon in Len¸cois Maranhenses (Maranh˜ao state, North-East of depth, τ(h) = ah, with a ≈ 1.2 kPa/cm. We conclude Brazil). Beyond a threshold pressure pc, the crust of the quick- from our measurements that the quicksand is essentially sand breaks in a brittle way leaving a network cracks, and the a collapsing suspension of grains with depth independent material collapses. The maximum penetration depth for the static viscosity. After the collapse, it becomes essentially human body was not greater than one meter. a soil with shear strength governed by the Mohr-Coulomb friction criterion. Two questions arise: What produces the impermeable Once the crust has broken, water and solid phase segre- crust enclosing the fluid bubble and how is this crust gate. This explosion of excess pore-water and repacking of formed? We investigated the material of the bottom of the sand grains has been discussed by several authors (see [14] lake, forming the crust and constituting the interior of the and Refs. therein). The remaining soil shows pronounced bubble physically, chemically and biologically. As shown in shear thinning behavior similar to the one reported in Fig. 4, the most visible finding was the huge amount of liv- Ref. [12] and releases a gas when strongly agitated. The ing merismopedia, cylindrospernopsis and other cyanobac- original status of a crust with waterbed motion can not be teria as well as of diatomacea of various types (e.g., frus- recovered neither artificially nor after waiting a long time. tulia) and other eukaryotes. They constitute the largest 3

a b

c d Fig. 4. Examples of bacteria found in the samples of the “quicksand”: (a) diatomaceae frustulia, (b) a typical colony of merismopedia, (c) cylindrospernopsis racibovskii, and (d) eu- karyote. fraction of mass besides the silicates of the sand. Still wa- ter and tropical weather conditions provide them an ideal environment. When the lake dries, they form the quite (a) (b) (c) elastic and rather impermeable crust which hinders fur- Fig. 5. Three different moments during the penetration pro- ther water from evaporating and which therefore just stays cess of an intruder into a loose cohesive packing. Before the below in the bubble. The cementing of soils by cyanobac- penetration in (a) we show the unperturbed granular network teria and other algae has in fact already been reported in generated by contact dynamics [18–20]. In (b) we see the de- previous studies [16,17]. We can therefore conclude that structive effect caused by the movement of the intruder, while this quicksand is a living structure. We also would like to in (c) it finally stops to remain buried under a collapsed mass point out that we found no salt in the water which means of grains. that the presence of salt is not a necessary condition to get quicksand, as opposed to the finding of Ref. [12]. show a typical simulation of this process. As depicted, the penetration of the disk causes the partial destruction of 3 the porous network and the subsequent compaction of the Simulation disassembled material. We observe the creation of a chan- In order to illustrate our point that objects lighter than nel (Fig. 5b) which finally collapses over the descending water can be swallowed in the quicksand by the mech- intruder. At the end of the penetration process (Fig. 5c), anism described above, we also perform computational the larger disk is finally buried under the loose debris of simulations with a model specially built to represent the small particles. Since the collapse takes place in a rather physics of an object being pushed inside and subsequently short time scale compared to the formation of the quick- removed from a fragile granular structure. sand, we assume that no new cohesive bonds are build up In our model simulation, we consider a system with instantaneously and that broken cohesive bonds will not width and initial height of 51 and 180 particle diameters, have time to recover during penetration. respectively, where periodic boundary conditions are ap- Our simulations show that the density of the original plied in the horizontal direction. The unperturbed quick- packing is roughly two thirds that of the compacted mate- sand is modeled as a granular network consisting of co- rial below which the intruder remains trapped. One should hesive disks put together through the contact dynamics also note that the constant force applied to the disk must technique [18,19] and a ballistic deposition process driven exceed a certain value to allow for penetration, otherwise by gravity, as described in Ref. [20] and shown in Fig. 5a. the object will stay above the surface, in agreement with After the settlement of all particles, the cohesive forces our field experiments. The snapshots shown in Figs. 5a-c between them are tuned to the point in which a barely have been obtained from model calculations with an ap- stable structure of grains is assured. This accounts for the plied force that is slightly above the penetration thresh- slowly drying process of the lakes that results in a tenuous old. The further increase of the force does not lead to any network of grains, like in a house of cards. In our model substantial changes in these pictures. the surrounding pore water is not explicitly considered but To be compatible with our experimental observations, is taken into account as a buoyant medium, thus reducing the forces necessary to introduce and remove again the the effective gravity acting onto the grains. disk should be rather different. Indeed, our results indi- We then proceed with the simulation by pushing a cate that, if we allow for the cohesive bonds in the mate- large disk of low density (half of the grain density) at rial to be completely restored after penetration, the force constant force into the granular structure. In Fig. 5 we strength needed to remove the intruder disk after the pen- 4 etration process can be as much as up to three times higher 16. A. Danin. Plant species - diversity and plant succession in than the pushing force. a sandy area in the northern negev. J. Arid Env., 167:409– 409, 1978. 17. A. Danin. Plant adaptions in desert dunes. J. Arid Env., 4 21, 1991. Conclusion 18. M. Jean and J. J. Moreau. Unilaterality and dry friction in the dynamics of rigid body collections. In Contact Me- In summary, the “living quicksand” studied here can be chanics International Symposium, pages 31–48, Lausanne, described as a suspension of a tenuous granular network 1992. Presses Polytechniques et Universitaires Romandes. of cohesive particles. If perturbed, this unusual suspen- 19. J. J. Moreau. Some numerical methods in multibody dy- sion can drastically collapse, promoting a rapid segrega- namics: application to granular materials. Eur. J. Mech. tion with water, to irreversibly bury the intruder object. A-Solid, 13:93–114, 1994. Our simulations indicate that in the worst condition, one 20. D. Kadau, G. Bartels, L. Brendel, and D. E Wolf. Pore could need a force up to three times one’s weight to get stabilization in cohesive granular systems. Phase Transit., out of such morass. Fortunately basins deeper than the 76:315–331, 2003. human size seem very rare.

5 Acknowledgement We thank Sarah Springman for lending us her equipment and CNPq, CAPES, FUNCAP, FINEP, the Volkswagen- stiftung and the Max Planck Prize for financial support.

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