# Structure and Strength of Artificial Soils Containing Monomineral Clay Fractions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Substrates

^{−3}), while sand particles were wet-sieved out. The silt was composed mainly from feldspars and quartz.

- goethite 71063-100G (Sigma-Aldrich, St Louis, MO, USA);
- kaolinite containing <5% illite and ~10% quartz,
- illite containing ~10% kaolinite and ~5% quartz,
- montmorillonite K10 (Sigma Aldrich Chemie GmbH, Steinheim, Germany);
- zeolite coming from a clinoptilolitic tuff deposit in Sokirnitsa, Ukraine [59] containing clinoptilolite as a dominant phase, ~10% stilbite and ~10% thomsonite.

#### Substrates Characteristics

^{−3}), were measured by helium pycnometry using an Ultrapycnometer 1000 system (Quantachrome Instruments, Boynton Beach, FL, USA) in five replicates.

^{−3}minerals in 1 dm

^{3}0.001 mol·dm

^{−3}KCl solution using a ZetaSizer Nano ZS instrument (Malvern Ltd., Leamington Spa, UK) apparatus in six replicates. The PSD of the silt was estimated using a laser diffraction method using a Malvern Mastersizer 2000 according to Ryzak and Bieganowski [60]. The zeta potential of the silt was not measured with the ZetaSizer because silt particles were too large and they sedimented in the electric field. Therefore, it was taken as the average of zeta potential values for feldspar and quartz at pH = 6.5 (this pH value located between pH of the silt-mineral pastes used for aggregates preparation) read from plots presented by Wang et al. [61], who measured the zeta potential of these minerals at various pH values.

_{N2}(m

^{2}·kg

^{−1}), and surface fractal dimensions, D

_{fracN2}, were estimated from low temperature nitrogen adsorption isotherms, relating the adsorbed amount a (kg·kg

^{−1}) to the relative adsorbate pressure p/p

_{0}(p (Pa) is the adsorbate equilibrium pressure and p

_{0}(Pa) is the saturated pressure of the adsorbate at the temperature of the measurement T (K)). The surface areas were calculated from the standard BET equation [62] and the nanopore fractal dimensions, D

_{fracN2}, from the slopes of the linear parts of the ln-ln plots of adsorption a vs. adsorption potential A = RTln(p

_{0}/p), where R is a universal gas constant, using the equation [63]:

_{fracN2}= 3(1 − 1/m). Alternatively, for 1/m > 1/3 the adsorption is governed by the capillary condensation mechanism and D

_{fracN2}= 3 − 1/m. The surface fractal dimension is 2 for flat, planar surfaces, and tends to 3 with increasing surface complexity and roughness.

_{0}using the Kelvin equation, assuming cylindrical shape of pores and zero solid-liquid contact angle:

_{0}) = 2γV

_{m}/rRT

_{m}is its molecular volume.

_{i}(r

_{i}), of the radii r

_{i}≤ r:

_{poreN2}(m

^{3}·kg

^{−1}), calculated as a difference of the volume of the liquid nitrogen accumulated in the material at a relative pressure corresponding to 30 nm pore and that corresponding to 2 nm pore), the pore size distribution function, Ξ(r), was obtained:

_{i}(r

_{i})/V

_{poreN2}is a volumetric fraction of particular pores, f(r

_{i}), calculated as:

_{i}) = f(r

_{i,av}) = Ξ (r

_{i+1})−Ξ (r

_{i})

_{i,av}denotes the arithmetic mean of r

_{i+1}and r

_{i}.

_{poreN2}(m), was calculated as:

#### 2.2. Preparation of Artificial Soil Aggregates

#### The Aggregates Characteristics

^{−5}m·s

^{−1}was registered for ten replicates of each aggregate. The average breakage curve for each aggregate was calculated from at least six breakage curves being most similar among ten experimental replicates. Reasons of the breakage curves selection are explained in the Supplementary Materials. From the average braking curves the dependence of the compression stress, σ (MPa), (load divided by the aggregate cross section area) versus strain, ΔL/L (relative aggregate deformation, equal to piston displacement divided by the aggregate height) was calculated. From the slope of the linear parts of the above dependence the Young’s modulus, E (MPa), was derived. As found by Horabik and Jozefaciuk [48], for aggregates prepared from kaolinite and 10–50 µm silt, the dependence of the compressive strength at breakage, σ

_{max}(MPa) (maximum compression) on mineral percentage could be satisfactorily fitted to a Langmuir-type function. The same function to describe the dependencies of both the maximum compression and the Young’s modulus on mineral percentage, M%, for the studied aggregates was used:

_{max}or E and C and k are constants.

_{(BD)}(cm

^{3}·g

^{−1}), were calculated.

^{−3}µm) using the Autopore IV 9500 porosimeter (Micromeritics, Norcross, GA, USA) for three replicates of each aggregate. The intrusion volumes were measured at stepwise increasing pressures allowing to equilibrate at each pressure step. The maximum deviations between the mercury intrusion volumes were not higher than 6.2% and they occurred mainly at low pressures (largest pores). The volume of mercury V

_{MIP}(m

^{3}·kg

^{−1}) intruded at a given pressure P (Pa) gave the pore volume that can be accessed. The intrusion pressure was translated on equivalent pore radius R

_{MIP}[m] following the Washburn [64] equation:

_{m}cosα

_{m}/R

_{MIP}

_{m}is the mercury surface tension, α

_{m}is the mercury/solid contact angle (taken as 141.3° for all studied materials) and A is a shape factor (equal to 2 for the assumed capillary pores).

_{MIP}vs. R

_{MIP}, a normalized pore size distribution, χ(R

_{MIP}), was calculated and expressed in the logarithmic scale [65]:

_{MIP}) = 1/V

_{MIP}

_{,max}dV

_{MIP}/dlog(R

_{MIP}),

_{MIP}

_{,max}is the maximum amount of the intruded mercury (at the highest pressure).

_{MIP}

_{,max}may be treated as the total volume of material pores accessible by mercury.

_{MIP}), the average pore radius, R

_{MIPav}, was calculated from:

_{MIPav}= ∫R

_{MIP}χ(R

_{MIP}) dR

_{MIP}.

^{2}V

_{MIP}/d(logR

_{MIP})

^{2}= 0

_{ia}, was taken as the volume of mercury intruded into the pores of lower radii than PT (at higher pressures than this corresponding to PT) and the average intrinsic pore radius, R

_{ia}, (radius of pores smaller than PT) was calculated from Equation (10) in the same way as R

_{MIPav}, placing V

_{ia}instead of V

_{MIP}

_{,max}in Equation (9).

_{fracMIP}, was calculated from the slope of the linear part (if any) of the dependence of log(dV/dR

_{MIP}) against logR

_{MIP}[68]:

_{fracMIP}= 2 − slope

## 3. Results and Discussion

#### 3.1. Properties of the Substrates

^{2}·g

^{−1}depending on a degree of crystallinity of the mineral. Possibly, the zeolite used in this paper had a low degree of crystallinity, or it decreased under long-term immersion in water during sedimentation. The extent of the surface area does not correlate with the mineral particle dimension, indicating a marked contribution of internal surfaces into the total surface of the minerals. All materials but the goethite exhibit negative surface potential at the experimental conditions. The most negative zeta potential has montmorillonite, and the least negative-illite.

^{3}·g

^{−1}) to the material volume (cm

^{3}·g

^{−1}). The material volume was calculated as a sum of micropore volume (V

_{poreN2}) and the volume of the solid phase (equal to 1/SPD). The third one is a ratio of the average pore diameter, d

_{poreN2}, to the average particle diameter of the material, d

_{particle}. Since the latter two values were very small, they are expressed as percents.

#### 3.2. Mechanical Properties of the Aggregates

#### 3.3. Structural Properties of the Aggregates

#### 3.4. Relations between Mechanical and Structural Properties of the Aggregates

_{max}) to present everything in a single figure. The dependencies of the above defined scaled values (Y/Y

_{max}) of parameters characterizing the studied aggregates on mineral percentage are shown in Figure 11. Because the maximum strength and the Young’s modulus of 100% illite aggregates did not follow the general trends, these values were not taken to the calculation of the average values of the respective two parameters. A reason of such anomalous behavior of illite is for us not clear. Possibly in the cake and in the aggregates of platy illite particles the input of face-to-face blocky structures prevails over edge-to face (cardhouse) ones. The blocky structures resist the pressure more strongly than the cardhouse ones.

_{EXT}, should be reached, as well. Assuming that the minerals fill the silt pores as agglomerates which have the same bulk density as pure (100%) mineral aggregates, the BD

_{EXT}and the percentage of the mineral at BD

_{EXT}, M%

_{(BD EXT)}, were calculated. The M%

_{(BD EXT)}values are: 35.3% (kaolinite), 28.2% (montmorillonite), 28.1% (zeolite), 39.8% (illite) and 33.3% (goethite). All these values are markedly lower than 64%, at which the maximum shear strength occurred. The theoretical maximal bulk densities at the moment when all silt pores are filled by the mineral agglomerates, BD

_{EXT}, are: 2.13 (kaolinite), 1.92 (montmorillonite), 1.91 (zeolite), 2.29 (illite) and 2.06 g·cm

^{−3}(goethite). All these values are markedly higher than bulk densities of particular aggregates measured at all mineral concentrations. Since the above considerations are valid only when the silt skeleton structure remains unaltered, one can conclude that quite different structures are formed during silt-minerals aggregation processes. Most probably direct contacts between the skeleton grains disappear because the mineral particles push them away from each other. It is also possible that the structure of mineral agglomerates joining the silt grains is different from the structure of pure mineral aggregates.

#### 3.5. Relations between Mechanical Properties of the Aggregates and Properties of the Mineral Particles

_{σ}constant in the Langmuir-type fit of the maximum stress against mineral percentage may be interpreted in terms of particle binding energy, as mentioned by Horabik and Jozefaciuk [48]. One can say that particle binding energy increases with specific surface, pore volume and porosity of the mineral particles. It seems rational because the latter parameters govern the amount of water adsorbed on the surface at low moistures (the aggregates were studied at low relative water pressures) and the cohesion forces between particles depend on the amount of water. The energy of particle binding seems to decrease with increasing zeta potential that appears to be connected with particles repulsion. However, the electric repulsion forces should have no significant role at low moistures where the electric double layer is suppressed to a great extent and the electric charge of particles is screened by a tight layer of counterions. As can be read from adsorption isotherms of various minerals presented by Jozefaciuk and Bowanko [73] the minerals hold around two monomolecular layers of water molecules at 60% moisture, at which our aggregates were studied. The electric repulsion should be more pronounced at higher moistures.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Representative SEM photographs of the surfaces of the broken aggregates composed from pure materials. The names of the materials are written within the respective pictures. The scale bar for silt is 100 µm and for all the minerals it is 10 µm (drawn only in illite picture).

**Figure 3.**Dependence of the compressive stress on the relative deflection for the studied aggregates. The names of the materials are written within the respective pictures. Note different lengths of the units in different plots.

**Figure 4.**Dependencies of the maximum stress (

**a**) and the Young’s modulus (

**b**) of the studied aggregates on the mineral concentration. Dashed lines are the best fits of the experimental data to the Langmuir-type equation (Equation (7)). The best fit of the Young’s modulus for goethite does not include the point for 64% of this mineral (the fit including all points is drawn with solid line). The labels of the points for given mineral are the same in both plots.

**Figure 5.**Relative root mean square errors for the approximation of the measured data by the Langmuir-type equation for all studied aggregates together.

**Figure 6.**Representative SEM images of the surfaces of broken silt-illite aggregates with different concentrations of the mineral. The scale bar shown for 2% illite is valid for all other images.

**Figure 7.**Representative SEM images of the surfaces of broken silt-goethite aggregates with different concentrations of the mineral. The scale bar shown for 2% goethite is valid for all other images.

**Figure 8.**High magnification SEM images of the surfaces of aggregates containing 4% of illite (

**a**) and 4% of goethite (

**b**). In contrast to the illite particles, individual particles of goethite are located upon the surfaces of the silt particles.

**Figure 9.**Dependencies of pore volume on pore radius derived from mercury intrusion porosimetry. The names of the materials are written within the respective pictures. Note different lengths of the y-units in different plots.

**Figure 10.**Pore size distribution functions showing frequency, f(R), of the occurrence of pores of various radii, R. The names of the materials are written within the respective plots. Since curves for 0% of each mineral are hardly visible in the respective plots, the common curve (SILT) is depicted also (0% of each mineral = pure silt).

**Figure 11.**Dependence of the scaled values of parameters characterizing the studied aggregates (Y/Y

_{max}) on mineral percentage. Here Y is a value of a particular parameter at a given mineral content and Y

_{max}is the maximum value of this parameter. The parameters Y (listed in the legend) are: BD—bulk density, σ

_{max}—maximum stress, E—Young’s modulus, D

_{mip}—pore surface fractal dimension, V

_{MIP,}

_{max}—pore volume (from mercury intrusion), V

_{(BD)}—pore volume (from bulk density), V

_{ia}—intraaggregate pore volume, R

_{MIP av}—average pore radius (from MIP), R

_{ia}—intraaggregate pore radius, PT—penetration threshold. The Y/Y

_{max}values are averages for all aggregates. 100% illite aggregate is excluded from the calculation of the average Young’s modulus and average maximum stress.

**Figure 12.**Dependence of the maximum stress on the scaled values, Y/Y

_{max}, of parameters characterizing the studied silt-minerals aggregates containing 2–64% of the minerals. Here Y is a value of a particular parameter at a given mineral content and Y

_{max}is the maximum value of this parameter. The parameters Y in the legend from top to bottom are: BD—bulk density, D

_{MIP}—pore surface fractal dimension, V

_{MIP,}

_{max}—pore volume (from mercury intrusion), V

_{ia}—intraaggregate pore volume, V

_{(BD)}—pore volume (from bulk density), PT—penetration threshold, R

_{ia}—intraaggregate pore radius, R

_{MIP av}—average pore radius (from MIP), E—Young’s modulus. The Y/Y

_{max}and maximum stress values are averages for all aggregates.

Silt | Kaolinite | Montmorillonite | Zeolite | Illite | Goethite | Max SD% | Min SD% | ||
---|---|---|---|---|---|---|---|---|---|

S_{N2} | m^{2}·g^{−1} | 1.7 | 14.4 | 225.2 | 26.1 | 145.5 | 12.5 | 5.9 S | 0.62 G |

d_{particle} | µm | 15.0 | 0.66 | 0.58 | 0.51 | 0.49 | 0.39 | 44.4 K | 2.56 G |

ζ | mV | −45 | −35.4 | −51.5 | −45.5 | −23.2 | 12.1 | 10.7 G | 1.35 M |

V_{poreN2} | mm^{3}·g^{−1} | 0.7 | 6.6 | 119 | 16.5 | 52.5 | 40.5 | 4.9 I | 0.18 M |

d_{poreN2} | nm | 5.79 | 5.94 | 6.22 | 2.61 | 6.24 | 4.98 | 5.1 Z | 0.39 M |

SPD | g cm^{−3} | 2.70 | 2.62 | 2.52 | 2.33 | 2.74 | 4.11 | 0.18 G | 0.03 S |

D_{fracN2} | - | 2.25 | 2.55 | 2.58 | 2.62 | 2.70 | 2.63 | 1.6 S | 0.7 K |

P | % | 0.2 | 1.7 | 23.1 | 3.7 | 12.6 | 14.3 | - | - |

Q | % | 0.04 | 0.9 | 1.07 | 0.51 | 1.27 | 1.28 | - | - |

_{N2}—specific surface area (from nitrogen adsorption), d

_{particle}—average particle diameter, ζ—zeta potential, V

_{poreN2}—volume of 10–30 nm micropores, d

_{poreN2}—average pore diameter, SPD—solid phase density, D

_{fracN2}—surface fractal dimension, P—volumetric porosity (fraction of pores), Q—average pore diameter to average particle diameter ratio. Two last columns show maximum and minimum standard deviations (SD) expressed as percents, followed by the first letter of the material for which particular value of SD occurred. The standard deviations are not presented for data calculated from average numerical values.

**Table 2.**Numerical values of C and k constants providing the best fits of the experimental data to the Langmuir-type equation (Equation (7)) for the dependencies of the maximum stress, σ

_{max}, and Young’s modulus, E, on minerals percentage presented in Figure 4.

Data | Constant * | Kaolinite | Monmorillonite | Zeolite | Illite | Goethite |
---|---|---|---|---|---|---|

σ_{max} | C_{σ}, MPa | 3.0 | 4.1 | 6.2 | 11.6 | 1.1 |

k_{σ} | 0.010 | 0.031 | 0.022 | 0.017 | 0.042 | |

E | C_{E}, MPa | 272 | 362 | 424 | 393 | 55 |

k_{E} | 0.013 | 0.064 | 0.043 | 0.116 | 0.771 |

Material | MIN % | σ_{max} MPa | E MPa | BD gcm^{−3} | V_{MIP,}_{max}cm ^{3}g^{−1} | V_{(BD)}cm ^{3}g^{−1} | V_{ia}cm ^{3}g^{−1} | R_{MIPav}µm | D_{fracMIP}– | PT µm | R_{ia}µm |
---|---|---|---|---|---|---|---|---|---|---|---|

Silt | 0.08 | 28.5 | 1.377 | 0.321 | 0.356 | 0.213 | 4.380 | 2.24 | 4.772 | 3.64 | |

Kaolinite | 2 | 0.10 | 26 | 1.389 | 0.317 | 0.350 | 0.167 | 3.956 | 3.07 | 4.336 | 2.79 |

4 | 0.14 | 26.6 | 1.425 | 0.288 | 0.331 | 0.146 | 3.303 | 3.22 | 4.336 | 2.50 | |

8 | 0.27 | 30.7 | 1.465 | 0.252 | 0.312 | 0.207 | 2.252 | 3.51 | 3.633 | 1.59 | |

16 | 0.41 | 41.7 | 1.521 | 0.251 | 0.286 | 0.196 | 1.004 | 3.99 | 1.966 | 0.73 | |

32 | 0.66 | 70.9 | 1.700 | 0.217 | 0.215 | 0.175 | 0.248 | 3.33 | 0.444 | 0.18 | |

64 | 1.19 | 127 | 1.676 | 0.198 | 0.219 | 0.119 | 0.065 | 4.54 | 0.054 | 0.03 | |

100 | 0.92 | 110.6 | 1.533 | 0.268 | 0.271 | 0.139 | 0.061 | 4.68 | 0.054 | 0.03 | |

Illite | 2 | 0.32 | 73.7 | 1.406 | 0.320 | 0.341 | 0.185 | 4.036 | 2.87 | 4.336 | 2.97 |

4 | 0.72 | 143 | 1.410 | 0.297 | 0.339 | 0.206 | 3.888 | 3.15 | 4.336 | 3.10 | |

8 | 1.33 | 195.7 | 1.487 | 0.270 | 0.303 | 0.114 | 2.280 | 3.41 | 2.176 | 1.22 | |

16 | 2.39 | 221.5 | 1.578 | 0.222 | 0.265 | 0.116 | 1.581 | 3.71 | 2.176 | 0.76 | |

32 | 4.42 | 318 | 1.715 | 0.191 | 0.215 | 0.160 | 0.594 | 4.04 | 1.777 | 0.43 | |

64 | 6.03 | 354 | 1.881 | 0.140 | 0.165 | 0.108 | 0.095 | 4.20 | 0.657 | 0.03 | |

100 | 8.86 | 510 | 1.860 | 0.138 | 0.173 | 0.056 | 0.013 | 4.51 | 0.003 | 0.00 | |

Montmorillonite | 2 | 0.11 | 31.1 | 1.389 | 0.307 | 0.349 | 0.209 | 3.756 | 2.55 | 4.336 | 2.97 |

4 | 0.29 | 61.4 | 1.381 | 0.325 | 0.353 | 0.189 | 3.567 | 2.55 | 4.336 | 2.41 | |

8 | 0.72 | 90.2 | 1.434 | 0.304 | 0.325 | 0.205 | 2.449 | 2.37 | 3.633 | 1.70 | |

16 | 1.33 | 226.4 | 1.545 | 0.251 | 0.273 | 0.151 | 0.521 | 2.38 | 0.801 | 0.26 | |

32 | 2.40 | 251.7 | 1.536 | 0.254 | 0.272 | 0.162 | 0.219 | 3.38 | 0.540 | 0.10 | |

64 | 2.57 | 273.9 | 1.374 | 0.318 | 0.341 | 0.245 | 0.111 | 3.42 | 0.249 | 0.05 | |

100 | 2.11 | 236.2 | 1.016 | 0.503 | 0.512 | 0.362 | 0.066 | 3.43 | 0.205 | 0.05 | |

Zeolite | 2 | 0.11 | 36.1 | 1.377 | 0.332 | 0.355 | 0.178 | 4.241 | 2.56 | 4.336 | 3.18 |

4 | 0.13 | 40.1 | 1.385 | 0.331 | 0.349 | 0.206 | 3.531 | 2.86 | 4.336 | 2.55 | |

8 | 0.55 | 72.3 | 1.431 | 0.325 | 0.324 | 0.265 | 2.608 | 3.16 | 4.336 | 2.16 | |

16 | 1.83 | 214.7 | 1.563 | 0.228 | 0.260 | 0.168 | 0.575 | 4.14 | 2.176 | 0.27 | |

32 | 2.96 | 255 | 1.726 | 0.177 | 0.190 | 0.097 | 0.089 | 4.16 | 0.079 | 0.05 | |

64 | 3.43 | 298.3 | 1.465 | 0.270 | 0.275 | 0.177 | 0.083 | 4.18 | 0.079 | 0.05 | |

100 | 2.53 | 247.9 | 1.096 | 0.472 | 0.483 | 0.361 | 0.070 | 4.66 | 0.079 | 0.05 | |

Goethite | 2 | 0.15 | 35.6 | 1.424 | 0.301 | 0.335 | 0.204 | 3.324 | 3.09 | 4.336 | 2.24 |

4 | 0.19 | 40 | 1.457 | 0.303 | 0.321 | 0.179 | 3.006 | 2.97 | 3.939 | 1.81 | |

8 | 0.26 | 45.3 | 1.519 | 0.255 | 0.298 | 0.153 | 2.054 | 3.16 | 3.633 | 0.92 | |

16 | 0.41 | 51.6 | 1.629 | 0.244 | 0.264 | 0.186 | 0.705 | 2.87 | 2.176 | 0.37 | |

32 | 0.66 | 54.7 | 1.888 | 0.189 | 0.200 | 0.150 | 0.138 | 3.78 | 0.249 | 0.08 | |

64 | 0.82 | 121 | 1.717 | 0.289 | 0.293 | 0.148 | 0.093 | 3.84 | 0.071 | 0.06 | |

100 | 0.72 | 66.6 | 1.403 | 0.456 | 0.469 | 0.261 | 0.097 | 3.87 | 0.079 | 0.06 | |

Max SD% | - | 51.3 | 33.3 | 0.7 | 5.3 | - | 13.3 | 6.6 | 5.4 | 10.0 | 5.1 |

- | G4 | G4 | S | G4 | - | G2 | Z2 | S | G2 | S | |

Min SD% | - | 12.1 | 3.4 | 0.1 | 2.1 | - | 4.6 | 2.9 | 2.0 | 4.3 | 1.8 |

- | I100 | M64 | I100 | I100 | - | Z64 | M64 | Z64 | M64 | I64 |

_{max}—maximum stress, E—Young’s modulus, BD—bulk density, V

_{MIP,}

_{max}—total pore volume (from mercury intrusion), V

_{BD}—pore volume (from bulk density), V

_{ia}—intraaggregate pore volume, R

_{MIPav}—average pore radius, D

_{fracMIP}—pore surface fractal dimension, PT—penetration threshold, R

_{ia}—average intraaggregate pore radius. The last rows show maximum and minimum standard deviations (SD) expressed as percents. Below them the first letter of the mineral component and its percentage in the aggregate for which particular value of SD occurred are shown. The standard deviations are not presented for data calculated from average numerical values.

**Table 4.**Coefficients of determination (R

^{2}) for linear fits between parameters characterizing aggregate strength and mineral particles properties. Only R

^{2}values higher than 0.5 were taken into account. The sign preceding the R

^{2}value is the sign of the slope of the respective linear fit.

Parameter | S_{N2} | d_{particle} | ζ | V_{poreN2} | d_{poreN2} | D_{fracN2} | P | Q |
---|---|---|---|---|---|---|---|---|

C_{σ} | - | −0.7 | - | - | - | +0.99 | - | - |

k_{σ} | 0.53 | - | −0.51 | +0.69 | - | - | +0.64 | - |

C_{E} | - | −0.89 | - | - | - | - | - | - |

k_{E} | - | −0.59 | - | - | - | +0.80 | - | - |

σ_{max} | - | −0.55 | +0.56 | - | - | +0.93 | - | - |

E | - | −0.69 | - | - | - | +0.95 | - | - |

_{σ}and k

_{σ}) and for the dependencies of the Young’s modulus on minerals percentage (C

_{E}and k

_{E}). σ

_{max}—maximum stress for pure minerals aggregates; E—Young’s modulus for pure minerals aggregates. Properties of mineral particles (see Table 1) from left to right: S

_{N2}—specific surface area; d

_{particle}—particle diameter; ζ—zeta potential; V

_{poreN2}—volume of 2–30 nm pores; d

_{poreN2}—average pore diameter; D

_{fracN2}—surface fractal dimension; P—volumetric porosity, Q—pore diameter to particle diameter ratio.

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**MDPI and ACS Style**

Jozefaciuk, G.; Skic, K.; Adamczuk, A.; Boguta, P.; Lamorski, K.
Structure and Strength of Artificial Soils Containing Monomineral Clay Fractions. *Materials* **2021**, *14*, 4688.
https://doi.org/10.3390/ma14164688

**AMA Style**

Jozefaciuk G, Skic K, Adamczuk A, Boguta P, Lamorski K.
Structure and Strength of Artificial Soils Containing Monomineral Clay Fractions. *Materials*. 2021; 14(16):4688.
https://doi.org/10.3390/ma14164688

**Chicago/Turabian Style**

Jozefaciuk, Grzegorz, Kamil Skic, Agnieszka Adamczuk, Patrycja Boguta, and Krzysztof Lamorski.
2021. "Structure and Strength of Artificial Soils Containing Monomineral Clay Fractions" *Materials* 14, no. 16: 4688.
https://doi.org/10.3390/ma14164688