Soil Mechanics Simulator

The Mohr-Coulomb failure criterion defines the shear strength of the soil. Failure occurs when the shear stress on a plane reaches a value that depends linearly on the normal stress on that same plane.

Where $\tau_f$ is the shear stress at failure, $c$ is the cohesion (soil's "stickiness"), $\sigma$ is the normal stress, and $\phi$ is the internal friction angle. In the simulator, $c$ and $\phi$ are set by their respective sliders.

Terzaghi's bearing capacity equation calculates the ultimate pressure a shallow foundation can support before a shear failure mechanism develops in the underlying soil.

Here, $q_u$ is the ultimate bearing capacity, $\gamma$ is the soil unit weight, $D_f$ is the foundation depth, $B$ is the foundation width, and $N_c$, $N_q$, $N_\gamma$ are bearing capacity factors that depend only on the friction angle $\phi$. The simulator solves this when you adjust the geometry and soil strength parameters.

Shallow Foundation Design: This is the direct application. Every house, building, or bridge pier resting on footings or rafts requires a bearing capacity check to prevent catastrophic sinking and a settlement analysis to ensure doors won't jam and pipes won't crack from differential movement.

Slope Stability Analysis: The same Mohr-Coulomb failure criterion is used to assess the risk of landslides. Engineers analyze potential failure planes within a slope to calculate a factor of safety, helping to design safe road cuts, embankments, and open-pit mines.

Retaining Wall Design: The lateral earth pressure exerted on a retaining wall, which determines how thick and deep the wall must be, is derived directly from the soil's shear strength parameters (cohesion and friction angle) visualized in the simulator.

Construction Planning: Predicting consolidation settlement over time is critical for large infrastructure projects like embankments for highways or pre-loading of port terminals. It informs how much surcharge to apply and how long to wait before building the final structure.

First, note that cohesion and internal friction angle are not determined independently. While the simulator lets you adjust them with separate sliders, in real soil—especially cohesive soil (clay)—the internal friction angle φ can be an apparent value. There's the concept of the "effective internal friction angle φ'" used in effective stress analysis and the "φ=0" approach used in total stress analysis. For example, a simplified method evaluating stability of soft clay using only cohesion c with "φ=0" is often used. After learning about the two extremes of sandy soil (high φ, low c) and clay layers (low φ, high c) with the tool, consider how both parameters interact in intermediate soils like "silt" or "sandy clay".

Next, Terzaghi's formula is not a "universal solution". It assumes a continuous footing (strip foundation). For square or circular isolated footings, you need to apply shape factors. For instance, the bearing capacity of a square footing with width B=2m is about 1.3 times that of a continuous footing with the same width. Also, the formula assumes ideal conditions of homogeneous, horizontal soil. In reality, soil is layered, and inclined loads or seismic forces may act. Use the "ultimate bearing capacity" obtained from the tool for understanding the basic concept and for parameter sensitivity analysis (to see which factors are influential).

Finally, understand the limitation that the "consolidation time" calculation is based on a one-dimensional model. The tool uses Terzaghi's one-dimensional consolidation theory; once the drainage distance H (e.g., half the clay layer thickness for double drainage) is determined, the settlement time history can be calculated. However, in the field, vertical drains like sand drains are installed to shorten the drainage path and accelerate consolidation. You can confirm in the tool that reducing the "drainage distance" dramatically shortens consolidation time—this is precisely one of the theoretical bases for ground improvement.