A Calculation Model for the Loess Collapse Coefficient Considering Progressive Wetting, Dry Density, and Applied Vertical Pressure Calculation Model for Moisture-Induced Collapse of Loess Considering Three Factors: Overburden Pressure, Water Content and Density

In the arid and semi-arid landscapes of northern and northwestern China, a vast expanse of yellowish-brown earth known as loess covers nearly 6.6 percent of the country's land. This soil, formed by wind-blown dust over thousands of years, possesses a unique and precarious nature. In its natural, dry state, the particles are held together by weak bonds, creating a structure full of tiny, open pores that resembles a sponge made of dust. This structure is metastable, meaning it holds its shape only as long as it remains dry. However, when water infiltrates this soil while it is under the weight of buildings or the earth above it, those weak bonds dissolve. The soil structure suddenly collapses, the particles rearrange into a denser configuration, and the ground sinks. This phenomenon, known as wetting-induced collapse, poses a significant threat to infrastructure, causing foundations to settle unevenly, roads to buckle, and slopes to fail. Engineers have long sought a way to predict exactly how much a specific patch of this soil will sink when it gets wet, but the answer has remained elusive because the soil's behavior depends on a complex mix of factors: how wet it already is, how tightly packed the particles are, and how much pressure is pushing down on it.

A team of researchers from Xijing University and Shangluo University set out to untangle these interacting factors by studying loess from the Ili region in Xinjiang. They began by collecting soil samples from depths between 8 and 15 meters, a zone where the earth is often subjected to the weight of future construction. In the laboratory, they recreated the conditions loess might face in the real world. They took the dry soil, crushed it into a uniform powder, and then carefully mixed in precise amounts of water to create specimens with varying levels of moisture. They then compacted these mixtures into rings to achieve different densities, ranging from loose and airy to tight and heavy. Once prepared, these specimens were placed under a series of increasing vertical pressures, simulating the weight of a building or the overlying earth, ranging from 50 kilopascals up to a substantial 2000 kilopascals.

The critical moment in their experiment came when they flooded these pressurized specimens with water. As the water soaked in, the researchers measured exactly how much the soil shrank. They found that the amount of sinking, or the collapse coefficient, did not follow a simple, straight-line pattern. Instead, the soil's reaction was a dynamic dance of cause and effect. When the soil was very dry, adding a little water caused a dramatic collapse. As the initial water content increased, the soil became less sensitive to further wetting, and the amount of additional sinking decreased. Similarly, the density of the soil played a crucial role; looser soil with more empty space between particles collapsed much more violently than soil that had already been packed tightly.

Perhaps the most surprising discovery was how the soil reacted to the pressure pushing down on it. The researchers observed that the collapse did not simply increase as the pressure increased. Instead, the soil's tendency to collapse rose as the pressure went up to a certain point, reached a peak, and then began to decrease or stabilize at higher pressures. This meant that a soil layer might be highly prone to sinking under a moderate load but less so under a very heavy one, a nuance that simple models often miss. The team realized that to predict this behavior accurately, they could not look at water content, density, and pressure in isolation. They had to understand how these three factors worked together as a single, coupled system.

To capture this complexity, the researchers developed a new calculation model. They translated their physical measurements into a set of relationships that described how the collapse coefficient changed as the soil moved from a dry, loose state toward a wetter, denser one. They introduced a way to measure the "wetting parameter," which tracks how far the soil has progressed from its initial dry state toward being fully saturated. By testing their model against all their laboratory data, they found it could successfully predict the collapse behavior with a high degree of accuracy, capturing the non-linear rise and fall of the collapse coefficient as pressure changed. The model showed that as the soil became more saturated, the remaining potential for collapse steadily diminished, a trend that held true across the different densities they tested.

The true test of this model came when the researchers applied it to a real-world scenario. They took data from a massive field experiment conducted in the Ili region, where a 30-meter-thick layer of loess had been flooded to measure its total self-weight collapse. Using their new model, they calculated the expected sinking for each meter of that soil column, layer by layer, based on the natural water content and density found at each depth. The result was a predicted total settlement of 3330.71 millimeters. When they compared this to the actual measured settlement from the field test, which was 3520 millimeters, the difference was remarkably small—a relative error of just 5.38 percent. This close match demonstrated that the model could effectively translate simple, measurable soil properties into a reliable prediction of how much a foundation might sink.

The study concludes that while the model is specifically calibrated for the loess of the Ili region, it provides a powerful framework for understanding the mechanics of wetting-induced collapse. It moves beyond the idea that soil behavior is governed by a single factor, showing instead that the interplay between moisture, pore structure, and pressure creates a complex but predictable response. By accounting for the progressive nature of wetting, the model offers engineers a tool to estimate the risk of foundation failure more accurately, potentially preventing the costly and dangerous differential settlements that plague structures built on this fragile earth. The work confirms that with the right mathematical approach, the hidden instability of loess can be quantified, turning a geological hazard into a manageable engineering challenge.