Bi-layered architecture facilitates high strength and ventilation in nest mounds of fungus-farming termites

Study species and site

Odontotermes obesus is a fungus-farming termite species²¹ which makes cathedral-shaped, buttressed mounds⁹. It is widely distributed in India²¹ with mounds of several meters in height⁹. The study was conducted at the Indian Institute of Science Campus in Bangalore, India, which has a residual red soil formed from weathering of gneissic bedrock²². The soil is classified as inorganic clay of low plasticity and contains kaolinite and montmorillonite as dominant clay minerals, and quartz, mica and feldspar as non-clay mineral fractions²². It contains 43%, 34% and 23% of sand, silt and clay-sized fractions respectively²². For all analysis presented in this paper, the outermost region of termite mounds with surface conduits directly in contact with the atmosphere was considered as the buttress and the innermost region farthest away from the mound exterior was considered as the mound core. This was determined visually on a case to case basis based on the architecture of individual termite mounds (see Supplementary Fig. S1 online).

Strength of termite mound regions

To understand the scaling of strength with dimensions of mound samples, termite mound slices used by Kandasami et al.¹¹ were obtained and samples were cored out with diameters 2 cm, 2.5 cm and 3.5 cm and standard aspect ratio of 2²³. These were tested under unconfined compression in a micro Universal Testing Machine (micro UTM) at a displacement of 1 mm/min. The unconfined compressive stress (UCS) for these samples were not significantly different (see Supplementary Fig. S2 online) and were similar to values in Kandasami et al.¹¹ with samples of 6 cm × 3 cm (height: diameter) suggesting no effect of specimen dimension in strength testing; samples of small dimensions could therefore be used for further experiments. This validation was essential since it was not possible to get samples of 6 cm × 3 cm (height: diameter) dimensions from the buttress of the mound due to presence of pits in the mound walls (see Supplementary Fig. S1 online). Samples of 2 cm × 1 cm (height:diameter) were cored out from the core and buttress of the horizontal slices mentioned above. Depending on the availability of samples without channels/tunnels made by termites, 3 to 8 samples were cored out from each location, weighed and their densities were calculated. These samples acted as technical replicates. Samples were oven dried at 50 °C overnight since the mound slices from which they were derived had been stored under laboratory conditions. Samples were then tested under unconfined compression at 1 mm/min displacement and peak compressive stress recorded.

In order to obtain biological replicates, a drill was attached to a sampling tube (see Supplementary Fig. S3 online), and soil samples were obtained from the core and buttress of occupied mounds (N = 6 mounds). Drilling was carried out at 90 cm and 120 cm from the base (see Supplementary Fig. S3 online). Termites repaired the drilled section within 24 h. This method of sample collection, therefore, ensured minimal damage to the mounds. Samples were carefully transported in zip lock bags to minimise moisture loss, were cored to the dimensions 2 cm × 1 cm (height:diameter), were tested under unconfined compression at 1 mm/min displacement and the peak compressive stress was recorded. The in situ moisture content of soil from the core of the occupied mounds was 6–10% and that for the buttress was 0–4%. Some moisture loss was observed during sample testing, which was attributable to moisture loss occurring during sampling and testing.

Brazilian test for tensile strength of mound soil

To determine the tensile strength of termite mound soil, we performed a set of Brazilian or diametral compression tests wherein a disc of diameter 13.70 mm and thickness 6.60 mm²⁴ was subjected to compression (displacement rate = 1 mm/min) under displacement–controlled loading along its diametral plane. Due to the compression load, a tensile stress state develops in the specimen normal to the compressed diameter with peak values near the centre of the specimen (see details in Supplementary, see Supplementary Fig. S4 online). To avoid local failure at compressed ends due to stress concentration, a cushion arc subtending an angle 2α (12°) at the centre of the disc is used to distribute the load uniformly²⁵. With increase in axial displacement, the axial load increases to a peak where a crack initiates near the centre of the specimen and propagates towards the compressed ends instantly. The tensile strength corresponding to this peak load is calculated using σ_t = 2P/πDt where P is the peak compression load at failure or first drop in the load displacement curve, t is the thickness of the disc and D is the diameter of the disc²⁶.

The tensile strength was estimated for samples extracted from different cross-sections at varying heights. For each cross section of the mound, several tests were performed (slice A2: n for buttress = 3, n for core = 3; slice A4: n for buttress = 2, n for core = 3; slice A7: n for buttress = 1, n for core = 3). The strength among these tests did not vary significantly (see “Results”).

Stability analysis of termite mounds

Slope stability analysis was performed on termite mounds to examine the effect of varying soil density and strength along the radial direction. Two geometrical models, triangular and trapezoidal, of the slope were used in this analysis (see Supplementary Fig. S5 online). The finite element method was used to perform slope stability analysis using a strength reduction factor. The advantage of using finite element-based slope stability analysis is that it does not require any à priori assumption of the failure surface^27,28. The termite mound slope was modelled as an axisymmetric domain with an isotropic, homogeneous, linear elastic perfectly plastic Mohr–Coulomb material. The axisymmetric domains were discretized with six noded triangular elements with reduced integration to obtain the global stiffness matrix (see Supplementary Fig. S5 online). Discretization is a prerequisite for performing slope stability analysis using the finite element method. The termite mound was discretized into triangular elements, force balance was performed on each element and the results obtained from individual elements were integrated to obtain the overall slope stability of the mound. The bases of these domains were kept fixed for finite element analysis (soil below the termite mound was not considered). The finite element simulations were performed in Plaxis 2D software. As observed from uniaxial compression test data and density calculations, the strength and density of the mound soil varied in radial directions; to accommodate this variation four sets of model parameters were used (Table S1) for outer buttress, inner buttress, outer core, and inner core (see Supplementary Fig. S5 online). The parameters for inner core and outer buttress were the average of their values along the height of the specimen. For outer core and inner buttress, density and cohesion were linearly interpolated between the inner core and outer buttress. The tensile strength was considered to be constant throughout the domain as obtained in our Brazilian test results using samples from the abandoned mound. Since the soil density is comparable between occupied and abandoned mounds and the cementation is also expected to be the same, the tensile strength is expected to be similar between occupied and abandoned mounds.

Cohesive strength (c) for slope stability analysis is half of the average uniaxial compressive strength. Friction (ϕ) and dilation (ψ) angle were set to zero as the termite soil is predominantly clayey. The parameters used for slope stability analysis are provided in Table S1 online.

In the strength reduction factor method, strength parameters were continuously reduced until slope failure occurred. This method involves the reduction of strength by a strength reduction factor in a step-by-step procedure. The factor of safety corresponds to a stable strength reduction factor over a number of successive steps given that the slope failure is achieved in these steps²⁸. A slope failure is identified by a contiguous surface/curve at the plastic limit (or pre-identified failure shear strain) whose end points lie at the boundary of the slope. The strength reduction factor at failure is approximately equal to the factor of safety as defined in limit equilibrium methods^29,30.

Porosity distribution from computed tomography

X-ray computed tomography (XCT) was performed on samples (of diameter ~ 1.3 mm, aspect ratio of one) extracted from buttress and core at different heights for analysing the distribution of pores within mound soil. From the reconstructed XCT data, the scanned volume was segmented into two phases, air voids and termite mound soil, using thresholds corresponding to air–soil gray-level intensity cutoff. A typical slice of scanned volume data is presented in Fig. S6 (see Supplementary Fig. S6 online) along with a binarized image corresponding to air–soil gray level intensity cutoff. In order to obtain the distribution of porosity from the binarized volume data, a probing cube of 101 voxels (~ 1.3 mm) was traversed along all the interior voxels within the specimen with the cube residing completely in the specimen. The size of the pores within the cube is estimated as

Porosity of all interior voxels was determined and frequencies of pore sizes were plotted for core and buttress of slices A2, A4 and A7 (Fig. 4). A total of 18 samples were scanned for this analysis (3 samples each for core and buttress within each slice). The pore sizes were divided into 1,000 bins between 0 and 1 mm for plotting. Any attempt towards reduction in the number of bins (say 500, 250, 200, 125, 100, 50, … bins) led to loss of information and statistical significance between core and buttress (see “Statistical analysis”).

We also calculate the porosity of the whole specimen by the following relation

The porosity measurements for buttress and core at different cross sections are listed in Table 1.

Air permeability of mound soil

To understand the functional significance of the differences in density and strength on the gaseous permeability of termite mound samples, one sample each from the core and buttress at different heights from the abandoned mound was examined (see Supplementary Fig. S1 online). Samples were also obtained from the core and buttress of six occupied mounds by drilling at 0.9 and 1.2 m heights from the base of the mounds. Samples of dimensions 2 cm × 1 cm (height:diameter) were cored and inserted inside custom-made glass T-tubes. The samples were sealed inside the tubes with a commercial adhesive. The adhesive was allowed to dry and harden for 24 h before permeability testing. To ensure that all air flow can be attributed to the permeability of the mound samples alone, it was confirmed that the adhesive itself is impermeable to air in the range of air pressures tested. The set-up used for testing the permeability of termite mound soil was modified from King et al.⁴. The glass T-tubes with the samples were attached to a source of synthetic air (80% N₂, 20% O₂, 0% RH) and the flow rate was regulated using mass flow controllers Alicat MFC-100 and Alicat MFC-500 in the range 10–100 sccm (standard cubic centimetres per minute) and 100–500 sccm, respectively. The corresponding pressure was measured using a custom-made 14,000 Pa MEMS (micro-electronic measurement sensor) pressure transducer (0.28% full scale error) (see Supplementary Fig. S7 online). Air flow velocity vs. pressure graphs were plotted for samples from occupied and abandoned mounds. The pressures recorded in our experiment fell beyond the full scale error suggesting that they are not due to measurement error and thus reflect a real phenomenon.

Statistical analysis

We analysed the data using the software package R version 3.3.3 (2017-03-06). Data were tested for normality using the Shapiro–Wilk test. For the data on the scaling of strength in termite mound soil, Mann–Whitney U tests were performed followed by Bonferroni corrections. For the unconfined compressive strength data obtained from the abandoned mound, no significant interactions were found; therefore, a type II analysis of variance (ANOVA)³¹ was performed using the model: Compressive Strength ~ Height + Region  by employing the Anova function in the car package where Compressive Strength denotes peak compressive strength for each sample, Height refers to distance of each slice of the termite mound from the base (A2–A7; Fig. 1 and see Supplementary Fig. S1 online), and Region denotes the region within a slice (core vs. buttress; see Supplementary Fig. S1 online). For compressive strength data from the occupied mound, unpaired t tests were performed to check for differences between core and buttress at 90 cm and 120 cm from the base of the mound. Type II analysis of variance (ANOVA) was performed using the model: Tensile Strength ~ Height + Region by employing the Anova function in the car package where Tensile Strength denotes the tensile strength for each sample (see details in “Methods” and Supplementary; see Supplementary Fig. S4 online), Height refers to distance of each slice of the termite mound from the base (A2, A4, A7; see Supplementary Fig. S1 online), and Region denotes the region within a slice (core vs. buttress; see Supplementary Fig. S1 online). Data for porosity distribution in termite mound wall were analysed using a Kolmogorov–Smirnov (KS) test. Pore size distribution of core and buttress were compared for slices A2, A4 and A7 individually. The actual pore size values were compared using unpaired Mann–Whitney U tests for slices A2, A4 and A7 individually. Since the sample sizes in all these cases were very large, random subsamples were also taken and were subjected to unpaired Mann–Whitney U tests; results showed that the difference between core and buttress remained significant even when the sample was reduced to 1/128th of its original size (only results from original sample size and reduction to 1/128th of sample sizes are shown). Any further reduction would not have provided a representative sample.

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