Experimental and numerical investigation on heap formation of granular soil sparsely cemented by bacterial calcification

Highlights

• The shape of a heap formed by granular materials is investigated experimentally and theoretically.

• A biocementation technique is used for partially cementing the grains.

• Effect of partial cementation is captured numerically through clumping of the grains.

• The present Discrete element Model is capable of capturing the shapes of the heaps.

• A polynomial curve is prescribed for the definition of the shape.

Abstract

Bacterial cementation can be a pathway to sustainable cementation in soil mounds as it consumes miniscule amount of energy in comparison to engineered cement. Bacteria cement grains through progressive formation of inter-granular bridges. This study presents a numerical framework to model the sparsely cemented granular heaps. A rigorous experimental program has been presented to observe the relationship between the level of cementation and the shapes of heap. A discrete element model (DEM) for sparsely cemented grains has been developed. The extent of cementation is modelled through random clumping of grains. It is observed that DEM is capable to capture the effect of cementation through grain clumping. A parametric study of the grain size distribution, internal friction angle, shape of clumps and the extent of cementation has been performed. The results show that friction angle, grain size distribution and grain clumping have considerable effect on the shape of heap. A cubic polynomial is able to capture the shape of heap reasonably well. The results will be useful for predicting the profile of sparsely cemented granular heaps.

Introduction

With climate change, frequency of extreme weather events such as storms and floods is on the rise[1]. It poses new engineering challenges to the countries like Australia where 80% of the population lives within 50 kms from the coastline [2]. Study of heaps of natural granular materials such as sand, silt and clay is important for the solution of problems such as protection coasts against waves, river banks against currents, embankments against soil liquefaction pressure[3]. Renourishment of beaches and river banks with a soil mound (Fig. 1) is gaining popularity over other invasive forms of protection such as groynes or rock armours due to their aesthetic acceptability and minimal effect on the native flora and fauna[4]. These mounds need to be designed for optimal performance against destabilising forces such as waves, currents and hydrostatic pressures. The loose grains form a heap characterized by their grain size distribution and internal angles of friction [5].

Granular heaps comprising loosely packed grains have long been studied through experimental and theoretical approaches [6]. It is observed that grain properties such as inter-granular friction [[7], [8], [9]] grain shape [[10], [11], [12]], and grain size distribution [[13], [14], [15], [16]] influence the shape of heap. When the frictional resistance is not sufficient to resist the destabilising forces, additional resistance against motion must be created. Often, a small dose of cement is added to the granular media resulting in some grains clumping together. The clumping increases resistance to motion by 1) grain interlocking, and 2) inter-grain cohesion. However, addition of cement can be toxic to the native flora and fauna. Moreover, engineered cement consumes vast amounts of energy and emits large quantities of CO₂ [17]. Annual production of Portland Cement makes up around 6% of all anthropogenic greenhouse gas emissions [18]. In the nature, on the other hand, clumping of grains is observed due to bio-geo-chemical processes in sand heaps, especially when it is moist for a substantial period of time [19]. In contrast to the engineered clumping, natural clumping is non-toxic and devoid of environmental hazards. Nature might therefore offer clues towards sustainable stabilisation of sand heaps.

Recently, researchers have developed a natural cementation technology through microbially induced calcium carbonate precipitation (MICP) as an alternative to cement binders [20,21]. In this process, bacterial enzymes are utilised to nucleate calcium carbonate as the cementing material [21]. The technology has been applied in a number of engineering problems such as stabilisation of road bases [22], fortification of rammed earth[23] and sustainable bricks [24]. Significant advancement in the process has been made, which has been discussed elsewhere[25]. However, the process of biostabilisation of soil is fundamentally different from that of the engineered cement binders. Our research proved that biocementation is initiated when bacterial cells secure themselves in the grooves of the substrate such as sand[26]. They act as nucleation sites for the growth of calcium carbonate crystals (Fig. 2a). The crystals grow to form mesocrystals (Fig. 2b) and then the mesocrystals grow to bridge neighbouring particles, thus achieving cementation (Fig. 2c). We have been able to estimate the degree of cementation through a quantitative energy dispersive X-ray scan (Fig. 2d). Thus, biocementation grows in layers with initiating from a plethora of nucleation sites dictated by the concentration of microbial cells.

A pressing research need in the advancement of biocementation is detailed knowledge of granular media behaviour under varying degrees of partial cementation. In particular, a model is needed to predict: (i) the location and degree of cementation, and (ii) the consequent influence of varying partial degrees of cementation on the mechanical response of the material. Emergence of the discrete element method (DEM) has facilitated the numerical modelling of inter-granular interactions. It is noted that a minimum number of grains must be used for the DEM to capture the desired phenomenon [27]. The limitation of DEM in modelling non-spherical grains is overcome through imposition of rigidity condition among a group of spheres arranged in the desired shape [28]. Using DEM, particle shape [29], size [30] and frictional behaviour [31] of granular assemblages have been investigated. Development of public domain codes for DEM, such as YADE, has made the technique freely available to researchers [32]. Triaxial test condition has been simulated through imposition of pressure boundary conditions [33]. The bonded granular systems have been modelled by introducing a cohesive bond between the grains [34,35]. Some reports on using DEM for modelling bio-cemented samples are available [36,37]. In all these investigations, an average homogenous inter-grain cohesive strength has been assumed to represent the degree of cementation. The averaged cohesive strength is adjusted through trial and error to achieve results close to that obtained from experiments. In these cases the stress-strain behaviour of sand columns is predicted through DEM. Use of DEM for prediction of the shape of heap for sparsely cemented material is not reported hitherto. DEM is especially equipped to model the formation of a heap as it is able to incorporate inter-granular friction, sliding, rolling and movements of grains that is several orders of magnitude higher than the grain sizes. Moreover, cementation can be introduced through clumping of grains.

In this paper, we report an experimental and numerical investigation on sand that is sparsely cemented. MICP has been performed on loose sand to bind the grains partially; only a small fraction grain are bonded forming clumps. Consequently, the grains can still move freely to form a heap. The process of formation of heap, especially with partial grain bonding, has been numerically modelled for the first time. The experimental and the numerical results have been compared. Both the experimental and numerical results have been utilised in developing a polynomial fit for the shapes of the heaps based on the basic geometric parameters. The expression is useful to determine the degree of cementation required to obtain the target shape of heap.