1 Introduction

Fossilized diatoms are the amorphous silicate exoskeleton of plankton and algae. Due to their hollow and angular tooth-like outer surface and flat circular or cylindrical shapes (Fig. 1a), diatoms have high friction angles (between 32° and 43°—[29, 106], and an open hollow structure (with intra-particle porosity as high as 60–70%—[61]). These properties make fossilized diatoms unique among most mineral soil particles. In addition, the intra-particle porosity allows diatomaceous earth to store large amounts of water in natural environments (up to 460%—[17, 29]). The water trapping ability and high friction angle of fossilized diatoms yield high Liquid Limits (100 to 550%) and Plasticity Indices (30 to 500%) [29, 56, 96, 106]. Despite its ability to retain high amounts of water, diatomaceous earth shows volumetric stability when drying, as most water is stored inside the particles [77]. So, while the high friction angle and the volumetric stability hint at coarse-grained behavior, the high-water content and plasticity hint at fine-grained behavior of diatomaceous earth. To further confound the interpretation of diatomaceous earth behavior, Day [26] and Hong et al. [45] report compression indices of diatomaceous earth similar to those of fine-grained soils at low effective stresses. However, diatomaceous earth shows volumetric collapse when the fossilized diatoms crush at low effective stresses (in the low MPa range). In addition, the hydraulic conductivity of diatomaceous earth is higher than soils with similar porosity, Atterberg limits, and specific surface areas [92].

Fig. 1
figure 1

Scanning Electron Microscope (SEM) images of tested fine-grained soils: a diatomaceous earth, b silica flour, c kaolinite, and d montmorillonite

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Other researchers have also observed atypical responses in soils containing fossilized diatoms. For example, Bryant and Rack [16] and MacKillop et al. [64] documented that sediment layers with high fossilized diatom content tend to have higher over-consolidation stresses and porosity than deposits immediately above or below them. Furthermore, fossilized diatom deposits have low erosion potential [62, 65, 100], and good slope resistance [92] due to their high friction angle and low unit weight. Nevertheless, while diatomaceous earth tends to be susceptible to dynamic liquefaction [33], clayey soils with greater than 50% diatom content show an increase in the static and cyclic resistance at stresses lower than 600 kPa [106].

To properly quantify the diatoms’ contribution to soils’ behavior, researchers tried to estimate the fossilized diatom content in natural soils. Several methods are available: counting fossil particles from sediment samples [80], infrared absorption [24], X-ray diffraction [34], chemical analysis paired with a normative calculation [58], Teflon digestion bomb [31], and a variety of wet-chemical leaches [27, 32, 70, 71]. However, all these tests have limitations and accuracy problems, preventing their application in geotechnical engineering research and practice as they do not typically follow empirical correlations [26, 28, 64, 69, 92]. Researchers also tried to assess the differential characteristics of diatomaceous earth by sampling natural specimens or creating artificial ones. For example, researchers conducted tests to determine physical properties (i.e., particle size distributions, density, viscosity), index properties (i.e., Atterberg Limits), mechanical properties (compressibility, shear strength), and electrical properties [18, 19, 44, 75, 79, 108] by combining various fine soils and fossilized diatoms under more diverse conditions. Finally, Zuluaga-Astudillo et al. [110] just published a review of the state of art on the engineering behavior of diatomaceous earth. In their paper, they argued the importance of developing a new framework for assessing and classifying diatomaceous earth.

Despite their complex geotechnical properties, fossilized diatoms are applied in several industrial solutions (Table 1). For example, fossilized diatoms are used to remove bacteria and solids in water filters [20, 38, 53, 74, 81, 83, 98, 101]. In addition, soil stabilization, asphalt and plastic filler, concrete additives, friction-resistant matrices, and thermal insulation have all benefited from fossilized diatoms’ lightweight, hollow structure and shape [12, 35, 37, 49, 50, 60, 66, 68, 109]. Fossilized diatoms are also used for pest control as they dehydrate insects [1, 25, 82]. In addition, there are attempts to apply fossilized diatoms in energy fields to improve the discharge capacity of positive electrodes [47, 67].

Table 1 Engineering and scientific applications of diatoms and diatomaceous earth
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Given the difficulties in determining fossilized diatom content in natural soils, the purpose of this study is to provide a framework to better predict the engineering properties of natural soils containing a wide range of fossilized diatoms. In this study, we measured and documented the response of artificial mixtures of diatomaceous earth with three different fine-grained soils (i.e., silica flour, kaolinite, and montmorillonite). We used the results to identify how fossilized diatoms affect sediment behavior by targeting and comparing physical, electrical, and mechanical responses of particles with similar mineral composition but different particles shapes (including the presence of internal porosity—i.e., silica flour vs. fossilized diatoms), particles with similar particle sizes but different cation exchange capacities (i.e., kaolinite and montmorillonite vs. fossilized diatoms), and particles with different specific surface areas (i.e., silica flour, kaolinite and montmorillonite vs. fossilized diatoms). In addition, we evaluated how diatoms and mixtures respond to changes in pore fluid environments, high-stress conditions, and abrasion. These tests were employed to create differential responses for assessing the effect of diatom content in natural soils with low-cost and straightforward methodologies.

2 Materials

Mixtures of diatomaceous earth, silica flour, kaolinite, and montmorillonite soils were selected to include soils formed by particles of different sizes, shapes, mineralogies, specific surface areas, and surface charge densities. These mixtures provide a significant range in physical (i.e., Atterberg Limits and sedimentation), electromagnetic (i.e., electrical conductivity and dielectric permittivity), and mechanical (i.e., compression and abrasion responses) properties.

The source of freshwater diatomaceous earth was PREMA-GUARD, Inc. The particles have mostly centric (i.e., disk-type) and pennate (i.e., cylindrical) shapes [79, 110] with diameters ranging from 5 to 30 μm, lengths ranging from 10 μm to 50 μm, and internal openings ranging from 0.2 to 0.5 μm (Fig. 1a). Silica flour and diatoms have similar chemical compositions but without internal particle porosity. Premier Silica Inc. was the source of the tested silica flour. The silica flour passed the No. 325 sieve (44 µm opening—Fig. 1b). Kaolinite consists of successive 1:1 layers of gibbsite-silica sheets, and strong hydrogen bonds attach these sheet layers. As a result, the kaolinite has relatively low swell potential and Atterberg Limits. The tested kaolinite was purchased from Old Hickory Clay Company (Fig. 1c). Finally, 2:1 layers of silica-gibbsite-silica sheets form the montmorillonite clays. Cations and van der Waals forces weakly bonded the sheets. As a result, montmorillonite clays have high swell potential and Atterberg Limits (Fig. 1d). The physical properties of the soils used in this study are documented in Table 2.

Table 2 Basic properties of tested samples
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3 Methods

We used ASTM standards and other testing methodologies to assess the contribution of diatoms to physical, electrical, and mechanical properties. Table 3 summarizes all the tests performed and the type of material and fluid environments used. We did not test all material combinations in each testing methodology as we aimed to target different phenomena and mechanisms described in the following sections.

Table 3 Specimen conditions for each experiment
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3.1 Electromagnetic wave characterization

Electromagnetic (EM) waves capture the interaction and percolation of different volumetric phases in soils [87, 97, 102]. The EM properties of the specimens—electrical conductivity and dielectric permittivity—were measured as a function of diatom content, water content, and void ratio (as the effective stresses increase). We conducted these tests to evaluate the EM response of fine-grained soils and how the presence of diatoms influences these responses.

Soil specimens were tested with an HP 4192A Impedance Analyzer and the two-terminal electrode configuration (Fig. 2a). We used frequencies higher than 100 kHz to reduce electrode polarization effects, as Santamarina and Fratta [88] recommended. At the same time, we used small thickness/diameter ratios to minimize fringe effects [7, 36]. Finally, we converted the measured impedance values into real and imaginary components of the dielectric permittivity and electrical conductivity [36, 88, 89].

Fig. 2
figure 2

Setup for dielectric permittivity and electrical conductivity measurements. a Test configuration and electronic peripherals. b Cell for dry specimens (diameter d = 62.8 mm and height h = 4 mm specimen), and c cell for saturated specimens (d = 62.8 mm and h = 10 mm)

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3.2 Sedimentation behavior of fine-grained soil

The way fine-grained particles settle and aggregate is a function of the particles’ size and the fluid’s chemical properties [26, 63, 91]. Furthermore, the sedimentation fabric captures the effect of pore fluid, temperature, and pressure during formation [94, 95]. Therefore, we tested mixtures at 100:0, 75:25, 50:50, 25:75, and 0:100 ratios of montmorillonite-diatomaceous earth ratios under different pore fluids. The pore fluids included deionized water, 0.01 M, 0.1 M, and 1 M of NaCl solutions mixed with 2% by volume of fine-grained soils [39, 77]. These tests complemented earlier results of Palomino et al. [77] with kaolinite-diatoms mixtures.

3.3 Atterberg limits

Fine-grained soils gradually increase their volume when the water content increases and the consistency transitions from solid to semi-solid, plastic, and liquid. Shrinkage Limit, Plastic Limit, and Liquid Limit capture these transitions [72, 84, 105]. We used the Fall Cone Test (80-g mass with a 30° steel cone—[103, 107] to determine the undrained shear strength as an alternative to the Casagrande cup’s Liquid Limit measurements. In the Fall Cone Test, the Liquid Limit is the water content corresponding to an undrained shear stress of 1.7 kPa. The water content that yields an undrained shear strength of 170 kPa defines the Plastic Limit [41]. We also measured the Shrinkage Limit (i.e., a measure of the water content at which a fine-grained soil volume starts increasing) to establish the volumetric stability of different soils and the effect of the internal porosity in the diatoms. We followed the procedure described in the ASTM D4943 standard [6] with the modification to allow for different NaCl concentrations to help evaluate the sensitivity of the tested soils under different chemical environments.

3.4 Abrasion and confined compression tests

The Los Angeles Test assesses the abrasion resistance of aggregate materials. Particles degrade by grinding as the material tumbles in a 711-mm diameter and 508-mm long hollow steel drum rotating at 30 to 33 rpm filled with twelve 48-mm diameter steel balls (ASTM C131 [2]). The Los Angeles Tests ran for 1, 4, 12, and 24 h on pure samples of dry diatomaceous earth, silica flour, kaolinite, and montmorillonite. After each testing time, we measured Atterberg Limits and grain size distribution and took scanning electron microscope (SEM) images to assess their abrasion responses.

Finally, we evaluated particle crushing using oedometer tests (ASTM D2435 [3] with modified specimen dimensions) while monitoring how the stress–strain behavior changes with diatom content [21, 43, 55, 57]. We tested dry mixtures of 0%, 33%, 67%, and 100% diatomaceous earth with kaolinite and silica flour with vertical stress ranging from 100 kPa to 8 MPa. We aim to assess the contribution of diatoms on particle crushing. Mercury Intrusion Tests [5] captured the pore size distribution changes with increasing compression stresses.

4 Test results and interpretation

4.1 Permittivity properties

The properties and distribution of solid and fluid phases affect soils’ permittivity. Mixture models represent the contribution of the different phases in particulate media [48, 87, 90]:

$$\varepsilon_{m}^{\prime \beta } = \left( {1 - n} \right) \cdot \varepsilon_{p}^{\prime \beta } + \theta_{v} \cdot \varepsilon_{l}^{\prime \beta } + \left( {n - \theta_{v} } \right) \cdot \varepsilon_{g}^{\prime \beta }$$
(1)

where εi’ is the relative dielectric permittivity of the mixture (m), solid particles (p), liquid (l) and gas (g), n is the porosity, θv (= n·Sr) is the volumetric water content, and Sr is the degree of saturation. The characteristic mixing factor β is a function of these phases’ relative interactions and arrangement to the direction of the applied electric field. When the layering is aligned parallel to the direction of the electric field, the characteristic mixing factor β is close to 1; when the layering is perpendicular to the direction of the electric field, the β becomes −1; and β is 0.5 for isotropic two-phase media [23, 48, 87]. For common natural soils, the characteristic mixing factor β varies between 0.3 and 0.6.

Figure 3a, b shows the relative real and imaginary effective permittivity at 10 MHz as porosity increases. When the soil is dry, the effect of the interaction between multiple phases disappears with the absence of water (i.e., β = 1 in Eq. 1), and the response becomes a simple linear combination of the contribution of the volumetric phases. So, the solid particles’ real and imaginary effective permittivity can be determined when the measurements extrapolate to zero porosity. The 10-MHz relative dielectric permittivity for the diatom particles is εm* = 6.22—j·0.44, for silica flour particles is εm* = 4.32—j·0.14, and for kaolinite particles is εm* = 6.16—j·0.68. We expected that diatoms and silica flour particles would have yielded similar values (within the range of the reported real relative permittivity for silica—between 3.6 and 4.5—[13, 46]). Either the biological origin of the diatoms or, most likely, the water still entrapped within the internal porosity of diatoms contributes to the greater estimated real and imaginary dielectric permittivity [59]. The imaginary permittivity is highest in kaolinite and the lowest in silica flour (Fig. 3b). The imaginary effective relative permittivity includes the effect of surface conduction, which should be most significant for kaolinite, even at low water contents [73, 85, 89]. We also estimated the effective electrical conductivity of diatomaceous earth σ = 3.57·10–7 S/m, silica flour σ = 3.07·10–7 S/m, and kaolinite σ = 3.80·10–7 S/m (Fig. 3c). Again and as expected, these values are slightly higher for kaolinite.

Fig. 3
figure 3

Electromagnetic measurements of dried fine-grained soils: a real relative permittivity, b imaginary effective permittivity at 10 MHz as a function of porosity, and c effective electrical conductivity as a function of frequency for oven-dry fine-grained soils

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Figure 4 documents the increase of real relative permittivity as a function of volumetric water content at 10 MHz. The characteristic mixing factor β was estimated by fitting Eq. 1 to the data in Fig. 4. We used the real relative permittivity estimated for the different solid phases (Fig. 3a). A value of the parameter β close to 1 indicates that the particle arrangement is parallel to the electric field (i.e., low orientational polarization is favored). In contrast, β = 0.5 indicates an isotropic structure (Fig. 4a). The kaolinite and silica flour yield β = 0.53 and β = 0.32 (Fig. 4c, d), respectively; these values are within the range reported for natural soils (0.3 to 0.6). Results show that diatomaceous earth’s parameter β = 0.82 is consistent with a lower orientational polarization (Fig. 4a, b). In addition, the dielectric permittivity does not increase smoothly with increasing volumetric water content in all three soils (Fig. 4b–d). Changes in the slope of the curves indicate transitions from unsaturated to saturated conditions at volumetric water contents of θv = 0.49 for silica flour, θv = 0.51 for kaolinite, and θv = 0.70 for diatomaceous earth. The internal porosity of diatoms explains the greater volumetric water content in diatomaceous earth. Finally, Fig. 4e documents the complex interaction between electrical conductivity and volumetric water content in the three tested soils. As the volumetric water content increases after reaching full saturation, the deionized water displaces the solid phase, surface conduction decreases, and low conduction of the liquid phases reduces the overall conductivity of the soils [11, 51, 86].

Fig. 4
figure 4

a Conceptual description of particle arrangement factor β (Eq. 1). 10 MHz real relative permittivity of fine-grained soils vs. volumetric water content for b diatomaceous earth, c silica flour, and d kaolinite specimens. e Electrical conductivity of soils vs. volumetric water content

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The real and imaginary relative effective permittivities in saturated mixtures change with decreasing volumetric water content as the effective vertical stress increases from 100 to 600 kPa (Fig. 5). Higher diatom contents yield increasing permittivity values because diatoms allow for high water contents (i.e., water permittivity is higher than other phases in the mixtures). However, mixes with kaolinite show greater orientational polarization and surface conductance than silica flour [89]. So, the real and imaginary permittivities are higher in kaolinite mixtures than in other mixtures at the same volumetric water content. Conversely, the permittivity difference between kaolinite and silica flour mixtures decreases with increasing diatom content.

Fig. 5
figure 5

Evolution of the effective real and imaginary relative permittivities of saturated fine-grained soil mixes with diatoms as the effective vertical stress increases during compression tests

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4.2 Sedimentation tests

Sedimentation tests indirectly assess the effect of pore fluid on the fabric formed by soils as they settle in a liquid environment [78]. Figure 6a shows the volume change as a function of time for a 50%/50% diatomaceous earth/montmorillonite mixture in a 0.01 M NaCl solution. In these tests, as the particles settle, they flocculate or aggregate forming different fabrics. The volume of the sedimented material at the bottom of the column decreases gradually as the effective stress increases and the solid skeleton consolidates. Sedimentation tests continued until the sedimentation volume no longer changed. The time to reach the final sedimented volume is longer with the higher proportion of montmorillonite and lower NaCl concentrations. This response is expected for soils with lower coefficients of consolidation [14, 52]. Also, the final height of the settled material is a function of the thickness of the diffuse double layer \(\vartheta \propto \sqrt {\left[ {\varepsilon_{{_{l} }}^{\prime } \cdot T/\left( {c_{0} \cdot z} \right)^{2} } \right]}\) (where ϑ is the diffused double layer thickness, εl’ is the relative permittivity of the pore fluid, T is the absolute temperature, c0 is the fluid concentration, and z is the ion valence), and final fabric of the sedimented soil. The higher NaCl concentration in the solution reduces the thickness of the diffuse double layer, and the final sedimentation volume also decreases. This effect is most significant in the montmorillonite and becomes less relevant as diatom content increases in the mixture (Fig. 6b). However, for NaCl concentrations of 1.0 M, the final sedimented volume was practically independent of all soil mixtures. The diffused double layer became much thinner, and the mixture behaved like coarse-grained soils. Palomino et al. [76] indicated that when the NaCl concentration increases, the final fabric of the mixture transitions from being controlled by the chemistry to a simple geometric effect. During this transition, the impact of electrical charges on the edges and faces reduces (especially for the thin montmorillonite particles). Then, the diffused double layer shrinks, and the volume decreases as the particles flocculate in the form of edge-to-edge or face-to-face [23, 52, 76, 89].

Fig. 6
figure 6

a Sedimentation evolution for 50% diatoms and 50% montmorillonite mixture in 0.01 M NaCl pore fluid. b Final sediment volume for diatomaceous earth and montmorillonite mixtures in different NaCl concentration pore fluid solutions

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4.3 Atterberg limits of fine-grained soil under varying pore fluid salt concentration

Figure 7 presents the Atterberg Limits of the silica flour, kaolinite, and montmorillonite mixtures as a function of the diatom content and the NaCl concentration in the pore fluid. Again, there are clear trends in the results. The Atterberg limits of diatomaceous earth specimens are insensitive to changes in the NaCl concentration. Despite the diatoms’ high specific surface area, their low surface charge density results in thin diffused double layers that do not change with dissolved salts [30]. Still, diatomaceous earth shows higher Liquid Limits than kaolinite and silica flour as diatom’s internal porosity stores most of the water.

Fig. 7
figure 7

Atterberg limits of soil mixtures as a function of diatom content and NaCl concentrations. The volume change of the mixture tends to transition from the Liquid Limit to the Shrinkage Limit

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Montmorillonite clays have large net negative charge density (about 20 to 50 times larger than kaolinite—[15]) and large specific surface area (400 to 800 m2/g—[89]), and relatively weak van der Waal forces binding the particle layers. As a result, montmorillonite attracts large amounts of water and yields high Liquid Limits (about 300 with deionized water). In addition, the diffuse double layer of montmorillonite dramatically decreases with increasing NaCl concentration. Consequently, the Liquid Limit decreases from over 300 for deionized water to 95 for 1 M NaCl solution (Fig. 7 and Table 4). However, the Plastic Limits do not depend on the pore fluid NaCl concentration. Of the materials tested here, montmorillonite specimens show the most significant volume change when the water content decreases from the Liquid Limit to the Shrinkage Limit (volume change ranges from 84% for deionized pore fluid to 56% for 1 M NaCl pore fluid—Figs. 7 and 8).

Table 4 Atterberg Limits results for three fine-grained soils and mixtures with different NaCl pore fluid concentrations
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Fig. 8
figure 8

Formation of cracks during volume change in different fine-grained soils

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While the Liquid Limit is highest for the montmorillonite specimen, the Shrinkage Limit is highest for diatomaceous earth, as documented in Fig. 7. This response results from montmorillonite adsorbing large quantities of water on the particles’ outer surfaces and interlayer spaces. Then, as the water content decreases, the montmorillonite shrinks. On the other hand, as diatoms absorb large quantities of water in their internal porosity when the water leaves the intra-porous, the diatomaceous earth does not change its volume. Therefore, the Shrinkage Limit in diatomaceous earth is larger than those for montmorillonite and kaolinite, as increasing amounts of water are needed for diatomaceous earth to change its volume. Furthermore, since water removal in diatomaceous earth does not result in significant volume changes, shrinking and cracking are minimal when transitioning from the Liquid Limit to the Shrinkage Limit (Fig. 8).

Furthermore, as mixtures increase their diatom content, their Shrinkage Limits increase. The influence of diatomaceous earth is most significant in the mixes with montmorillonite (Fig. 7). In addition, we observed that shrinkage cracks in the montmorillonite mixture for all tested pore fluids became thinner or disappeared when mixed with diatoms.

The reduction of shrinkage with the presence of diatoms has important engineering implications. For example, while montmorillonite clays have low hydraulic conductivity, they tend to shrink when drying or when subjected to salt-soluble pore fluids. This shrinking creates cracks and pathways through which leachate can more easily seep. Then, the addition of diatomaceous earth could improve the performance of landfill caps and liners. That is, shrinkage cracks in clay liners triggered by the reduction in moisture or the increase in chemical concentration may be controlled by adding diatoms. Furthermore, while diatoms may increase the hydraulic conductivity of the clay mixture, they also create a more stable structure, reducing volume change and improving the reliability of cap and liner systems.

The changes in pore fluids and the mixtures’ diatom content shift the position of the soils on the Casagrande’s Plasticity chart. Kaolinite and silica flour increase their Liquid Limit with the addition of diatoms (Fig. 9a). However, increasing NaCl pore fluid concentration does not affect the classification of kaolinite (clay-like behavior) and silica flour (silt-like behavior) mixtures. However, increasing the NaCl concentration in the pore fluid causes a transition in the montmorillonite response towards a kaolinite-type behavior. As a result, increasing the NaCl concentration in the pore fluid in the montmorillonite shifts its behavior by reducing the plasticity of the mixtures (Fig. 9b). Finally, Fig. 9c documents how the Atterberg Limits of silica flour, kaolinite, and montmorillonite change as a function of diatomaceous earth content when deionized water is the pore fluid. Silica flour mixtures (with similar mineralogy to those of the fossilized diatoms) increase in Liquid Limit and Plasticity Index as the water is absorbed internally by the diatom particles. However, as the diatomaceous earth content increases, kaolinite and montmorillonite show more complex behavior. The mixtures of kaolinite and montmorillonite cross the line “A” in Casagrande’s Plasticity chart when the diatom content is 33% and 70%, respectively. The mixture transitions from clay-like behavior to a more silt-like response at those points. As kaolinite is less plastic than montmorillonite, the relative quantity of diatoms needed for this transition are smaller. Then, the transition becomes even more pronounced as the diatomaceous earth content increases.

Fig. 9
figure 9

The response of soil mixtures under different chemical environments and increasing diatoms content. a As the NaCl concentration in the solution increases, kaolinite and montmorillonite become less plastic, while diatom and silica flour do not change their plasticity. b Adding diatom increases the Liquid Limit in kaolinite and silica flour mixes; however, it reduces the Liquid Limit in montmorillonite. The pore fluid in these tests is deionized water

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4.4 Physical properties of abraded and crushed fine-grained soils

4.4.1 Abrasion

We measured the Atterberg Limits of soil mixtures after completing the Los Angeles abrasion and oedometer tests. We evaluated the effect of intra and interparticle porosity changes on index properties after particle degradation and crushing. The fine-grained soil particles were abraded in the Los Angeles Test machine during increasing times (from 1 to 24 h.) Table 5 and Fig. 10 summarize these results. We measured the shift in grain size distribution using the hydrometer test.

Table 5 Mean particle size d50 of each fine-grained subjected to the Los Angeles abrasion and oedometer test
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Fig. 10
figure 10

Effect of abrasion on the fine-grained soil particles. High-resolution SEM images comparing natural and abraded specimens after 24 h of Los Angeles test for a diatomaceous earth, b silica flour, c kaolinite, and d montmorillonite

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The pre and after-Los Angeles Tests’ mean particle size d50 showed a decrease from 8.3 to 2.7 μm for diatomaceous earth, from 13.3 to 5.0 μm for silica flour, and from 0.8 to 0.3 μm for montmorillonite. However, the mean particle size of kaolinite appeared to increase from 2.4 to 35.6 μm. During the abrasion process, diatomaceous earth’s physical and mechanical properties are the most affected among the soils tested: Liquid and Plastic Limits decreased from 130 to 57 and 99 to 40, respectively (Table 6). These changes are due to the reduction of internal porosities angularity of the particles (Fig. 10a—[40]). As a result, the diatomaceous earth, classified initially as MH in the Casagrande’s Plasticity Chart, shifts to ML as particles undergo the abrasion process (Fig. 11).

Table 6 Atterberg Limits after Los Angeles abrasion and oedometer tests
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Fig. 11
figure 11

Shifts in the Casagrande Chart as abrasion time during Los Angeles Tests and particle crushing in the oedometer test

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Furthermore, the silica flour shifts its response from ML toward the transitional CL-ML type when the soil is placed under more extended Los Angeles Test periods (Fig. 10b, Fig. 11). During the abrasion process, the Atterberg Limits of silica flour decrease due to a decrease in the angularity in the particles [54, 93] even when the mean particle size became smaller (Table 5—[40, 99]). However, those changes are minor and do not change from ML classification (Fig. 11). The Atterberg Limits of montmorillonite also decreased after 24 h. of abrasion time (Table 6). However, these changes cannot be explained just by the grain size changes or the particles’ angularity. During the Los Angeles Test, we hypothesize that the abrasion process increases the time needed for the montmorillonite particles to hydrate fully. If the particles are not completely hydrated, the Liquid Limits will appear to decrease relative to the unabraded particles. Alternately, the masses of Fe and Al increased in the montmorillonite (as determined by X-ray refraction tests—Tables 6 and 7). So, we further hypothesize that adding free cations to the particles’ surfaces contributes to the decrease in the measured Atterberg Limits. Our results indicate that montmorillonite gradually transitions from CH to MH as the Los Angeles Test time increases.

Table 7 Soils’ chemical composition during increasing Los Angeles Abrasion testing times
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In contrast, abrasion appears to increase the mean particle size of kaolinite from 2.4 μm to 35.6 μm when measured using the hydrometer analysis (Table 5, Fig. 10c). The SEM images show that while kaolinite booklets break during the abrasion, individual particles press and bond together by the abrasion process, forming larger face-to-face aggregates. The dispersant used in the hydrometer test appears ineffective in completely separating these aggregates, resulting in larger particle sizes. Accordingly, the Liquid Limit decreases with increasing abrasion time, and the classification shifts from CH to ML (from just above the “A” line to just below the “A” line) after 24 h of abrasion (Fig. 11).

4.4.2 Compression

Figure 12 shows the SEM images of diatomaceous earth during increasing oedometer vertical effective stresses. Particle crushing was observed as the effective vertical stress increased, gradually shifting diatoms’ physical and mechanical properties to behave more like silica flour (Fig. 11). Figure 13a presents the log of effective stress vs. void ratio results for diatomaceous earth, silica four, kaolinite, and selected mixtures during confined compression tests. The tested materials have different compression indices and initial void ratios; each mix represents a different soil type. The measured compression index increases with a higher initial void ratio and greater diatomaceous earth content. The compression index remains relatively constant during loading until about 2 MPa vertical stress. Then, there is a sudden increase in the compression index (Fig. 13a). However, there is no change in the compression index in silica flour and kaolinite specimens with no diatom content. The difference in this mechanical response is due to the crushing of diatom particles (that occurs between 2 and 4 MPa—Fig. 13a). Beyond 4 MPa, the compression index appears to stabilize again, as most fossilized diatoms have already been crushed. This behavior was also confirmed by observing that the increase in the compression index is greater with increasing diatom content (Fig. 13b).

Fig. 12
figure 12

Effect of oedometer stress on the fossilized diatom particles as documented by SEM images: a 1 MPa, b 2 MPa, c 4 MPa, and d 8 MPa vertical effective stress

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Fig. 13
figure 13

a Effect of oedometer stress on the compression index for different combinations of fine particles percentage. b Compression index at 150 kPa and 3 MPa vertical effective stress for soil specimens with diatom content

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4.5 Evaluation of porosity changes

Mercury intrusion tests assess the change in the pore size distribution of the diatomaceous earth with increasing compression stresses. As the effective vertical stress increases from 0 to 2 MPa, the interparticle porosity decreases as the distance between particles decreases and a few diatoms crush (Fig. 14). As a result, the pore fraction percentage at pore diameters 0.013, 0.18, and 0.35 µm increased linearly up to 2 MPa, and the 0.77-µm pore diameter decreased without changing the fraction percentage. When particles rearrange, pore fractions change even with minor particle crushing [45]. However, subtle but essential changes occur when the effective vertical stress increases beyond 2 to 4 MPa, and particle crushing occurs. As the particles crush between 2 and 4 MPa, the pore diameters fraction percentage of 0.013, 0.18, and 0.35 µm significantly increase. The decrease in mean particle size d50 also indicates that particle crushing occurs as the stress in the diatomaceous earth increases from 2 to 8 MPa (Table 5).

Fig. 14
figure 14

Mercury-intrusion determined pore fractions as a function of the pore diameter from diatomaceous earth specimens collected during confined compression tests

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4.5.1 Particle breakage discussion

When diatomaceous earth particles break under compressive stresses, they lose their ability to store water within the particles, and the Atterberg Limits decrease (Table 7). In contrast, the Liquid Limits of kaolinite and silica flour specimens are unaffected by increased compression stresses. Furthermore, particles smaller than 0.074 mm are not typically susceptible to breakage during compression [57]. Silica flour particles require about 30 MPa for particle crushing [55]. However, due to their unique hollow structure, the diatoms are susceptible to breakage even when particles are smaller than 0.074 mm and below 30 MPa. Hamm et al. [42] found that diatoms can support a force of about 750 μN before they break. For a 3-MPa isotropic effective stress, we calculated forces of 276 μN would cause crushing in a simple cubic packing of particles of diameter d = 8.3 μm, void ratio e = 2.4, and coordination number cn = 8 [89]. Besides, in the case of soils containing diatoms, physical properties may change during compression, requiring attention to the effect of high stresses on the engineering properties of diatomaceous earth or soils containing diatoms in geotechnical engineering projects.

5 Conclusions

Fossilized diatoms in artificial fine-grained soil mixtures influence the overall behavior of soils. This study attempted to answer the question: What percentage of diatomaceous earth in a fine-grained soil mixture will control the overall properties? Our results show that simple physical and index tests capture the effect of fossilized diatoms in soils:

  • While diatomaceous earth and silica flour particles have similar mineral compositions, the estimated 10-MHz relative dielectric permittivity at zero porosity of fossilized diatoms is similar to the dielectric permittivity of kaolinite. This is because the water entrapped in the hollow structure of diatoms increases the measured permittivity above the permittivity of the silica flour. Furthermore, higher fossilized diatom contents in saturated mixtures yield higher permittivities for similar void ratios than other fine-grained soils.

  • Sedimentation volumes of fine-grained soils decrease with higher diatoms content and NaCl concentration in the pore fluid. The sedimented volumes are controlled mainly by the thickness of the diffuse double layer in the different mixtures. Fossilized diatoms form a thin diffuse double-layer thickness that is insensitive to changes in the salt concentration of the pore fluid. In contrast, the thickness of the diffused double layer of clay mineral particles reduces with salt concentrations in the pore fluid.

  • Atterberg Limits results show that mixtures with high diatom content retain high quantities of water even under high NaCl-concentration pore fluids: diatoms store most pore fluid in their hollow structure. So, their response is independent of the chemical concentration in the pore fluid. Furthermore, diatomaceous earth does not shrink when drying, improving the mixture stability when mixed with other fine-grained soils. So, adding diatoms might benefit landfill liners and caps where chemical leachates and drying conditions tend to crack and deteriorate their performance.

  • The internal porosity of diatoms is easily affected by abrasion and particle crushing, decreasing the water storage ability of fossilized diatoms. Then, when fossilized diatoms are abraded and crushed, Liquid and Plastic Limits fall, and the compression index increases.

All our results indicate the feasibility of simple physical, electromagnetic, and mechanical tests to characterize the presence of fossilized diatoms and assess their unique effect on the behavior of both natural and artificial soils. Furthermore, these tests provide insight into the pros (i.e., high friction angle and volumetric stability under water content changes and high-concentration electrolyte environments) and cons (i.e., potential collapse under relatively low compression stresses and low abrasion resistance) of using soils with diatom content in geotechnical and geoenvironmental engineering projects.