Monte Carlo-Based Reliability Assessment of Multiple Failure Modes in Truss Soil Retaining System Considering Soil Parameter Uncertainty

In the crowded cities of today, the ground beneath our feet is being dug up more often than ever. To build basements for skyscrapers or parking garages, engineers must carve deep holes into the earth, but the soil surrounding these holes wants to collapse inward. To stop this, they build retaining walls. One specific type, known as a soil truss system, uses a framework of triangular supports, piles driven into the ground, and a layer of sprayed concrete to hold the earth back. Designing these structures is a delicate balancing act. If the design is too weak, the wall could slide or break, causing a catastrophic collapse. If it is too strong, the project becomes unnecessarily expensive and wasteful.

For decades, engineers have relied on a method called deterministic design. This approach treats the soil as if it were a single, perfect material with fixed, known properties. They calculate the forces and apply a large safety factor—a buffer zone—to ensure the wall holds. However, real soil is never perfect. It varies from spot to spot, and the measurements taken during construction are never exact. This uncertainty means that a wall designed with a fixed safety factor might be far safer than needed in one location, or dangerously close to failure in another. To address this, researchers are turning to probabilistic methods, which treat soil properties as ranges of possibilities rather than single numbers, asking not just "will it hold?" but "what is the chance it will fail?"

In a recent study, researchers Sepehr Dousti and Ehsan Seyedi Hosseininia from Ferdowsi University of Mashhad applied this probabilistic thinking to the soil truss system. They wanted to understand how likely different parts of the structure were to fail under various conditions. Instead of assuming the soil was uniform, they used a powerful computer technique called Monte Carlo simulation. Imagine rolling a pair of dice thousands of times to see every possible outcome of a game; the researchers did something similar with the soil. They ran ten thousand virtual simulations, each time slightly changing the soil's strength and the weight of the load on top of the excavation. By doing this, they could map out the true probability of four specific failure modes: the entire wall sliding, the supporting piles breaking, the footings sinking, and the concrete skin cracking.

The study revealed that the weight of the load sitting next to the excavation, known as a surcharge, is a major driver of risk. When this load increases, the chance of the wall sliding grows significantly. The researchers found that the spacing between the triangular trusses also plays a critical role in sliding; wider gaps between supports make the system much more likely to slip. However, the story changes for the other parts of the structure. For the piles and footings, the risk of failure is highest in shallow excavations. As the hole gets deeper, the probability of these components failing stabilizes at a level where the design is essentially a coin toss, suggesting that the standard safety rules used today might be overly cautious for deep digs but insufficient for shallow ones.

One of the most surprising findings concerned the type of mathematical curve used to predict the soil's behavior. Engineers often assume soil properties follow a "normal" distribution, where most values cluster around an average. The researchers tested this against a "log-normal" distribution, which accounts for the fact that soil strength cannot be negative and often skews differently. They discovered that for sliding, piles, and footings, the log-normal model predicted a lower chance of failure than the normal model. This suggests that using the traditional normal distribution might lead engineers to design walls that are stronger than necessary, wasting money on materials that aren't needed. The only exception was the shotcrete, the sprayed concrete layer, where the trend reversed, and the log-normal model predicted a slightly higher risk.

The researchers also looked at how the soil's two main strength factors—its stickiness and its internal friction—work together. In the real world, these two properties are often linked; if the soil is stickier, it might also be more frictional. The study showed that this connection matters most when the load on the wall is light. In those quiet, low-stress situations, ignoring the link between these soil properties could lead to an inaccurate safety assessment. But when the excavation is deep or the load is heavy, this correlation becomes less important, and the system behaves in a more predictable way.

Ultimately, this work suggests that the old way of designing with a single, fixed safety factor is often too conservative, leading to designs that are safer than they need to be and therefore more expensive. By embracing the natural uncertainty of the soil and using these advanced simulations, engineers can create designs that are both safer and more economical. The study confirms that while the soil truss system is a robust solution for urban excavation, its reliability depends heavily on understanding the specific conditions of the site, the weight of the surrounding load, and the true nature of the soil's variability. This approach offers a clearer, more realistic path forward for building the deep foundations that modern cities require.