1.6. Total Stress Mohr’s Circles

Changing σ3 allows several tests of this type to be conducted on various clay specimens. The shear strength parameters (c and ϕ) can now be determined by plotting Mohr’s circle at failure, as shown in figure and drawing a common tangent to the Mohr’s circles. This is the Mohr-Coulomb failure envelope. (Note: For normally consolidated clay, c≈0).

This chunk discusses how varying the confining pressure (σ3) during triaxial tests permits the evaluation of different soil specimens. By plotting the Mohr’s Circle at the point of failure, engineers can identify the shear strength parameters called cohesion (c) and the angle of internal friction (ϕ). The Mohr-Coulomb failure envelope is a critical concept, representing the relationship between shear stress and normal stress at failure. Notably, for normally consolidated clays, the cohesion is approximately zero, which simplifies the analysis.

Think of Mohr's Circle like a balancing act on a seesaw. As you change the weight on one side (σ3), you need to see at what point the seesaw tips (failure) and how it relates to the weight distribution (c and ϕ). Just as a seesaw will tip differently based on the weights used, the Mohr’s Circle shows us how soils fail under different stress conditions.

This total stress failure envelope is defined by the equation s=ccu+σtanϕcu, Where ccu and ϕcu are the consolidated-undrained cohesion and angle of friction respectively (Note: ccu≈0 for normally consolidated clays).

This chunk introduces the total stress failure envelope equation. Here, 's' represents the shear stress at failure, 'ccu' is the cohesion of the soil, and 'ϕcu' is the angle of internal friction in consolidated-undrained conditions. Understanding this equation is crucial for assessing soil stability, especially in scenarios without drainage. The note that ccu is approximately zero for normally consolidated clays is essential, as it highlights that these types of soils behave differently compared to well-consolidated soils.

Imagine you are pushing a book across the table. The force needed to push the book represents the shear stress. The roughness of the table surface is akin to cohesion. In this scenario, knowing how much force (shear stress) is needed at different angles helps us understand how easily the book will move – reflecting what engineers do with soil using the total stress failure envelope.

Similarly, effective stress Mohr’s circles at failure can be drawn to determine the effective stress failure envelopes. They follow the relation expressed in equation.

This section mentions the effective stress Mohr’s circles, which are used to determine the effective stress conditions in soils at failure. The effective stress is critical in geotechnical engineering, as it accounts for the pore water pressures acting within the soil and helps predict how it will behave under load. The specific equations are important to derive these envelopes, although the exact equations aren't included here.

Think of effective stress like the pressure you feel when you push down on a sponge submerged in water. The sponge (soil) feels a certain amount of weight (effective stress) from above, but the water inside (pore pressure) pushes back, affecting how the sponge reacts. Understanding this relationship is essential in preventing soil failure and ensuring structures remain stable.

For unconsolidated-undrained triaxial tests, Major principal total stress=σ3=Δσf=σ1, Minor principal total stress =σ3.

This section clarifies the conditions for unconsolidated-undrained tests where the total stresses are described. Here, major principal total stress equates the applied stress and the total stress conditions, indicating that the soil undergoes failure without any consolidation or drainage. These conditions are essential for understanding soil behavior immediately after a disturbance.

Consider a balloon filled with water. If you puncture the balloon quickly (applying stress), the pressure inside (total stress) is immediately released, and the water squirts out without any chance for the water to escape slowly. This is similar to what happens in unconsolidated-undrained tests where conditions dictate an instant reaction to applied stresses.

The pore water pressure parameter B in soft saturated soils is 1, so u=σ3+A(σ1−σ3). The value of the pore water pressure parameter A at failure will vary with the type of soil.

This chunk explores pore water pressure in saturated soils and how it is accounted for during triaxial tests. The pore water pressure parameter impacts how the soil responds to additional stress. When the parameter B is equal to 1, we have a simplified relationship that emphasizes the interaction between confining pressure (σ3) and the shear stresses. The variability of parameter A indicates that soil types respond differently under similar conditions, which is important for geotechnical design.

Think of pore water pressure like a sponge soaking up water. As more water is absorbed, the pressure within the sponge increases, changing how easily it can deform. The equations describing this pressure help engineers predict how soils will behave under stress, just like knowing how much water a sponge can hold helps you understand its limitations.

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