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Statistical Characterisation of Pore Morphological Evolution in Kaolinite under One-Dimensional Compression

This study statistically characterizes the nonlinear evolution of pore morphology in reconstituted Kaolinite under one-dimensional compression using a coupled SEM-MIP framework and PCA, establishing robust empirical regression models that link microstructural descriptors to macroscopic hydraulic and mechanical properties to support pore-informed constitutive modelling and machine learning applications.

Original authors: Rishabh Tiwari, Béatrice Anne Baudet, Matthew Richard Coop

Published 2026-07-27

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CC BY 4.0

Original authors: Rishabh Tiwari, Béatrice Anne Baudet, Matthew Richard Coop

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the ground beneath our feet not as a solid block of rock, but as a bustling, microscopic city made of tiny, flat clay tiles. In this city, the "buildings" are the clay particles, and the "streets" are the empty spaces, or pores, between them. When engineers build skyscrapers or dams, they need to know how this underground city behaves when heavy weights are placed on top of it. Does the city collapse? Do the streets get narrower? Does water stop flowing through the alleys? This is the world of soil mechanics, a branch of geotechnical engineering that tries to predict how the ground settles and drains under pressure. For a long time, scientists have been able to measure the big picture—how much the ground sinks or how fast water moves through it—but they've been like blindfolded architects guessing what the microscopic city looks like while it's being squashed. Understanding exactly how those tiny pores change shape is the missing link to building safer, more efficient structures.

This paper takes a deep dive into that microscopic city, specifically looking at a type of clay called kaolinite. The researchers acted like microscopic detectives, squashing samples of this clay under a controlled, one-dimensional squeeze (like pressing down on a stack of papers) with forces ranging from 100 kPa to a massive 6,000 kPa. They didn't just guess; they used two powerful tools to peek inside: a super-magnifying camera (Scanning Electron Microscopy, or SEM) to take 2D pictures of the pores, and a "mercury squeeze" test (Mercury Intrusion Porosimetry, or MIP) that forces liquid metal into the tiniest cracks to measure how wide the entrances are. By combining these methods, they tracked how the pores evolved from round, open rooms into long, narrow, and jagged corridors as the pressure increased.

The study found that as the clay gets squeezed, the pores don't just shrink; they fundamentally change their personality. At low pressure, the pores are somewhat round and scattered, like a crowd of people standing loosely in a park. As the pressure ramps up, the clay tiles (particles) rotate and flatten, forcing the pores to stretch out sideways, becoming long and thin. The researchers discovered that the "shape" of these pores is a secret code that tells us exactly how the soil will behave. They found a super-strong connection between a specific shape measurement called "solidity" (which measures how smooth or jagged a pore's edge is) and how fast the soil can drain water or how quickly it settles. In fact, the relationship was so strong that they could predict the soil's drainage speed just by looking at how jagged the pores were.

However, the paper also rules out a few simple ideas. It suggests that you can't just look at one single pore to understand the whole soil sample; the pores are too messy and varied. Instead, the "signature" of the pressure is hidden in the average shape and the spread of all the pores together. The authors also point out that while the changes happen gradually, they aren't perfectly predictable with simple straight-line math. The data is so complex and overlapping that if you wanted to use a computer to guess the pressure just by looking at the pores, you'd need a fancy, non-linear brain (like a neural network) rather than a simple calculator.

Ultimately, the researchers built a new set of mathematical "rules of thumb" (regression models) that link the microscopic shapes of the pores to the macroscopic behavior of the soil. They showed that as the pressure goes from 100 kPa to 6,000 kPa, the most common pore size shrinks by a whopping 81%, dropping from 0.73 µm down to 0.137 µm. The pores also get less round (circularity drops from about 0.62 to 0.48) and more stretched out (aspect ratio rises from 1.4 to 1.9). These numbers aren't just trivia; they provide a concrete, statistical map for engineers to build better computer models of the ground, ensuring that the foundations of our future cities are built on a solid understanding of the tiny, shifting world beneath our feet.

Technical Summary: Statistical Characterisation of Pore Morphological Evolution in Kaolinite under One-Dimensional Compression

Problem Statement
While the macroscopic mechanical behavior of clays under compression is well-described within the critical state framework (e.g., Cam Clay models), the physical mechanisms driving this behavior—specifically inter-aggregate pore collapse, fabric anisotropy development, and evolving hydraulic conductivity—operate at the pore and particle scales and remain incompletely characterized experimentally. Existing computational approaches, such as discrete element modeling, are constrained by a scarcity of rigorous experimental microstructural data. Furthermore, previous quantitative studies have largely focused on pore size distribution or particle arrangement, leaving a gap in the systematic quantification of pore shape descriptors and their empirical relationship to macroscopic mechanical parameters like stress, permeability, and the coefficient of consolidation.

Methodology
The study employs a coupled Scanning Electron Microscopy (SEM) and Mercury Intrusion Porosimetry (MIP) framework to analyze reconstituted kaolinite, selected for its simple mineralogy and well-defined platelet structure.

Specimen Preparation: Saturated specimens were prepared at an initial water content of $1.25w_L$ to eliminate initial fabric effects. They underwent one-dimensional consolidation in an oedometer across seven stress stages ranging from 100 kPa to 6,000 kPa.
Preservation: To prevent fabric alteration during drying, specimens were preserved via ultra-rapid freeze-drying.
MIP Analysis: Used to determine pore entrance throat diameters (0.0055–350 µm) and track pore population shifts, acknowledging the "ink-bottle effect" where MIP measures throat rather than body dimensions.
SEM Imaging: High-resolution imaging was conducted on vertical and horizontal cross-sections. From these images, four dimensionless pore shape descriptors were extracted using ImageJ: Circularity, Roundness, Aspect Ratio, and Solidity. Pore orientation was analyzed via $\theta$ -PDF plots.
Statistical Analysis: The study utilized Principal Component Analysis (PCA) on the full descriptor dataset to identify variance modes and developed empirical regression models linking pore descriptors to vertical effective stress ( $\sigma'_v$ ), coefficient of consolidation ( $C_v$ ), and permeability ( $k$ ).

Key Results

Macroscopic Behavior: The kaolinite exhibited a well-defined oedometric normal compression line (NCL) with a compression index $C_c \approx 0.37$ . Permeability decreased by two orders of magnitude ( $5 \times 10^{-9}$ to $2 \times 10^{-11}$ m/s) as stress increased from 100 to 6,000 kPa.
Morphological Evolution:
- Size: MIP peak pore entrance diameter decreased by 81% (from 0.73 µm to 0.137 µm), with the most rapid reduction occurring between 400 and 2,000 kPa.
- Shape: Pores became progressively more elongated and irregular. The peak aspect ratio increased from ~1.4 to ~1.9, while mean circularity decreased from ~0.62 to ~0.48.
- Solidity: Distributions shifted toward lower values with increasing right-skewness, indicating the development of concave, crack-like pore boundaries at high stresses.
- Orientation: Pore orientation evolved from an initially isotropic distribution to a highly anisotropic state with preferred alignment perpendicular to the loading axis (horizontal), intensifying up to 2,000 kPa before showing signs of micro-shear localisation at higher stresses.
Statistical Findings (PCA): Three principal components accounted for 80.5% of the total variance: PC1 (44.8%) representing pore size, PC2 (22.0%) representing shape, and PC3 (13.7%) representing boundary complexity. The PCA scatter plot showed continuous, overlapping shifts rather than discrete clustering, suggesting a nonlinear evolution of pore morphology with stress.
Regression Correlations: Strong empirical relationships were established between pore descriptors and macroscopic parameters:
- Solidity showed the strongest correlation with the coefficient of consolidation ( $C_v$ ) via a logarithmic fit ( $R^2 = 0.98$ ) and with permeability ( $k$ ) via a power-law fit ( $R^2 = 0.97$ ).
- Aspect Ratio showed the strongest fit against vertical effective stress ( $\sigma'_v$ ) ( $R^2 = 0.93$ ).
- The regression forms (exponential for stress, logarithmic for $C_v$ , power-law for $k$ ) align with theoretical expectations regarding clay compression lines and hydraulic tortuosity.

Significance and Claims
The authors claim that this study provides a statistically rigorous basis for linking microstructural pore morphology to macroscopic mechanical behavior in clays. Key contributions include:

Quantitative Framework: The establishment of regression models that link pore shape descriptors (particularly solidity) to $C_v$ and $k$ , extending beyond previous studies that focused primarily on pore size.
Methodological Validation: The demonstration that a coupled SEM-MIP approach, when cross-validated, can reliably characterize pore evolution and remove image artifacts, providing a reproducible methodology for clay characterization.
Constitutive Modeling: The results offer a quantitative experimental basis for "pore-informed" constitutive modeling. The authors suggest that the independence of size, shape, and orientation modes (revealed by PCA) supports their use as complementary state variables in future models.
Machine Learning Potential: The overlapping nature of the PCA data suggests that linear classifiers are insufficient for stress-state discrimination; instead, the dataset is suitable for training non-linear machine learning models (e.g., neural networks) to predict stress states from microstructural data.

The paper concludes that these findings establish structured datasets suitable for machine learning applications and provide a foundation for future work on natural structured clays and non-destructive in-situ characterization.

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