⚡ electrical engineering

Multiphysics-Informed Numerical Characterization of Bearing Behaviour in Sand–Clay Mixtures: Linking Clay Content, Strength–Stiffness Evolution, and Foundation Response

This study characterizes the non-monotonic bearing capacity of sand–clay mixtures by revealing a "resistance-deficit window" near 80% clay content where the decay of granular friction outpaces the mobilization of cohesive strength, a phenomenon validated through a comprehensive multiphysics framework combining analytical, limit-analysis, and finite-element methods.

Original authors: Muhammed Yeasin Arafat

Published 2026-08-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Muhammed Yeasin Arafat

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

The ground beneath our feet is rarely a single, uniform material. In many places, the soil is a complex mixture of coarse, gritty sand and fine, sticky clay. For engineers designing the foundations of buildings, bridges, and roads, understanding how these two materials behave together is a matter of safety and stability. Sand is strong because its grains lock together and resist sliding, a property that allows it to bear heavy loads. Clay, on the other hand, holds together through a sticky, cohesive force that develops when the fine particles are pressed against one another. When these two are mixed, the ground does not simply act like a blend of the two; instead, the way the soil carries weight shifts dramatically as the balance between sand and clay changes. The question is not just how much clay is present, but at what point the soil loses its ability to support a structure, and whether that weakest point happens when the mixture is half sand and half clay, or somewhere else entirely.

A researcher at the Bangladesh University of Engineering and Technology set out to map this hidden transition. They took soil from a developing area near Dhaka and created eleven distinct mixtures, ranging from pure sand to pure clay, with steps of ten percent clay added at each stage. Their goal was to trace how the strength and stiffness of the ground evolved as the sand skeleton was gradually replaced by a clay matrix. They did not rely on a single method to find the answer. Instead, they combined classical engineering formulas with advanced computer simulations that modeled the soil as a continuous material. They looked at how much pressure a standard two-meter-wide strip of foundation could hold before failing, and they also examined how much the ground would sink under that pressure. By running these tests across all eleven mixtures, they could watch the soil's behavior change in real time, from a friction-dominated state to a cohesion-dominated one.

The results revealed a surprising and non-linear story about how the ground fails. As the clay content increased, the soil's ability to resist sliding friction dropped sharply, while its sticky, cohesive strength began to rise. The researcher found that the soil's overall ability to hold a building did not simply decline in a straight line. Instead, it plummeted to a dangerous low point before climbing back up again. The weakest soil was not the one with the most clay, nor was it the one with the most sand. The lowest capacity occurred when the mixture contained eighty percent clay. At this specific point, the soil had lost almost all of its strong, sandy structure, but the clay had not yet built up enough sticky strength to fully compensate for that loss. This created a "resistance-deficit window," a vulnerable zone where the ground is weaker than it is in either of its pure forms.

This finding challenges a common assumption that the soil is weakest exactly when the two materials are equally balanced. The researcher discovered that the point where the sand's friction and the clay's stickiness contribute equally to the strength happens much earlier, at around fifty percent clay. However, the total strength of the ground continues to fall for another thirty percent of clay addition. The sand skeleton collapses quickly as clay fills the gaps between the grains, but the clay matrix takes longer to develop the full cohesive force needed to hold the load. It is only after the clay content reaches ninety to one hundred percent that the strength begins to recover, as the clay becomes the dominant material and its sticky properties take over completely.

The study used multiple methods to confirm this pattern, ensuring the result was not an artifact of a single calculation. They compared classical engineering equations with complex computer models that simulated the soil settling under a load. All methods agreed on the location of the weakest point: the eighty percent clay mixture. In the computer simulations, which measured how much pressure the soil could hold at a specific, small amount of settlement, the pressure dropped from over five hundred kilopascals in pure sand to just under three hundred kilopascals in the eighty percent clay mix, before rising again to over three hundred kilopascals in pure clay. The consistency across these different approaches gives engineers a clear picture of the danger zone.

The practical lesson for anyone building on mixed soils is that you cannot guess the strength of the ground just by looking at the percentage of sand or clay. A mixture that looks like it should be strong because it is mostly clay might actually be the weakest point in the entire range. The researcher emphasizes that the transition from a sandy, friction-based soil to a clay-based soil is not a smooth slide but a jagged path with a deep valley in the middle. To design safe foundations, engineers must test the specific mixture they are dealing with, rather than assuming it behaves like pure sand or pure clay. By identifying this specific composition where the ground is most vulnerable, the study provides a way to avoid the hidden trap of the resistance-deficit window, ensuring that structures are built on ground that is truly capable of holding them.

Technical Summary: Multiphysics-Informed Numerical Characterization of Bearing Behaviour in Sand–Clay Mixtures

Problem Statement
Natural foundation soils frequently exist as sand–clay mixtures where engineering behavior is governed not by the nominal percentage of fines, but by which fraction forms the load-bearing skeleton. In sand-dominated states, resistance relies on friction, interlocking, and dilation; as fines accumulate, they interrupt grain contacts and eventually form a cohesive matrix. This transition is non-linear and transitional rather than linear. A critical gap exists between material-scale mixture characterization and foundation-scale response: specifically, how the shift from a frictional skeleton to a cohesive matrix redistributes bearing resistance and whether the composition associated with minimum collapse capacity aligns with settlement-based foundation response.

Methodology
The study employs a "composition–property–response" framework using a source soil from the Purbachal New Town Project in Bangladesh. Eleven mixtures were prepared with clay contents ranging from 0% to 100% in 10% increments. The methodology integrates experimental characterization with three distinct numerical and analytical approaches applied to a common 2 m surface strip-footing problem:

Material Characterization: Index properties (liquid limit, plasticity index), effective strength parameters ( $c'$ , $\phi'$ ), and stiffness descriptors ( $E_{50ref}$ , $E_{oedref}$ , $E_{urref}$ , $K_0$ , dilation angle $\psi$ ) were determined for all mixtures.
Analytical and Limit Analysis: Classical bearing capacity equations (Vesic, Hansen, Meyerhof, Terzaghi-type) were evaluated using the measured strength parameters. Additionally, limit-analysis-informed bounds (FELA and UBLA) were constructed using literature-based $N_\gamma$ values to bracket collapse loads.
Finite Element Method (FEM): A custom, independent nonlinear plane-strain FEM solver was implemented using an elastic-perfectly plastic Drucker–Prager model with non-associated flow. The model simulated displacement-controlled loading up to $s/B = 10\%$ , with the primary comparison criterion set at $s/B = 3\%$ to represent mobilized bearing pressure rather than ultimate collapse.

Key Contributions

Mechanistic Partitioning: The study decomposes total bearing resistance into cohesive ( $c'N_c$ ) and self-weight/frictional ( $\frac{1}{2}\gamma B N_\gamma$ ) components to trace the internal transfer of load-bearing dominance.
Identification of a "Resistance-Deficit Window": The research identifies a specific composition interval where granular resistance has largely decayed before cohesive resistance fully compensates, leading to a non-monotonic bearing capacity curve.
Cross-Method Validation: The work validates the consistency of collapse-oriented methods (analytical and limit analysis) with settlement-based continuum modeling (FEM) across a full spectrum of soil compositions, despite the methods representing different physical quantities (limit state vs. mobilized state).

Results

Strength Evolution: As clay content increased from 0% to 100%, the effective friction angle ( $\phi'$ ) declined continuously from 41.22° to 14.28°, while effective cohesion ( $c'$ ) increased from 0 to 34.03 kPa. Notably, $c'$ remained stagnant between 70% and 80% clay while $\phi'$ continued to drop.
Non-Monotonic Capacity: All collapse-oriented methods (Vesic, Hansen, Meyerhof, Terzaghi, FELA, UBLA) identified a minimum bearing capacity at 80% clay.
- Vesic capacity dropped from 2165.8 kPa (0% clay) to a minimum of 258.3 kPa (80% clay), representing an 88.1% reduction, before recovering to 401.4 kPa at 100% clay.
- The FEM mobilized pressure at $s/B = 3\%$ followed the same trend, decreasing from 545.0 kPa to 288.6 kPa (80% clay) and recovering to 352.2 kPa (100% clay).
The Resistance-Deficit Window: The partitioning analysis revealed that cohesive and frictional contributions became comparable (equal share) at approximately 50% clay. However, the total capacity minimum was delayed until 80% clay. This 50–80% interval constitutes a "resistance-deficit window" where the loss of the high-friction sand skeleton outpaces the development of the cohesive clay matrix.
Methodological Consistency: While absolute pressure values differed between collapse-based methods and the FEM (due to stiffness and settlement constraints), the trend consistency was high. Pearson correlations with the Vesic series ranged from 0.947 (FEM) to 0.998 (Hansen). All methods agreed on the location of the minimum capacity (80% clay).

Significance and Claims
The paper claims to provide a mechanics-based interpretation of foundation behavior in mixed-grained soils, moving beyond simple correlations with clay content. The primary significance lies in demonstrating that the point of minimum foundation capacity does not coincide with the point where cohesive and frictional resistances are equal. Instead, a "lag" exists where the granular advantage is lost before the cohesive matrix is strong enough to compensate.

The author asserts that for mixed-grained soils, relying on end-member properties (pure sand or pure clay) or fines percentage alone is insufficient and potentially dangerous for design. The proposed framework offers a reproducible way to identify the "vulnerable state" (the resistance-deficit window) where the foundation is most susceptible to failure. The study emphasizes that the agreement among diverse methods regarding the location of the transition is more informative than numerical coincidence in absolute values, highlighting the fundamental shift in the governing failure mechanism across the composition range.

Limitations
The author notes that the study relies on a single property state per mixture without replicate uncertainty analysis. The FEM model utilizes a simplified elastic-perfectly plastic Drucker–Prager approximation without hardening, anisotropy, or coupled hydro-mechanical effects. The limit analysis benchmarks were derived from literature values rather than independent solver runs. Consequently, the conclusions are specific to the material and loading idealization presented, serving as a diagnostic framework rather than a universal empirical threshold.

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