Question

In formula (47.1) the total stress \(\sigma_{v}\) appears. Should that not be the effective stress \(\sigma_{v}^{\prime}\), because the shearing resistance of a soil is determined by the effective stresses and not by the total stresses?

Short answer

Answer: Formula (47.1) should use effective stress (\(\sigma_{v}^{\prime}\)) to calculate the shearing resistance of soil because it accurately represents the stress transmitted between soil particles and determines the shearing resistance.

Step-by-step solution

Understand the difference between total stress and effective stress

Total stress (\(\sigma_{v}\)) is the stress applied to the soil, including the weight of the soil and the stresses applied to the surface. Effective stress (\(\sigma_{v}^{\prime}\)) is the stress that is actually transferred through the soil particles, which is the total stress minus the pore water pressure. In other words, effective stress represents the intergranular stress or the stress transmitted between soil particles.

Know the relationship between effective stress and shearing resistance of the soil

The shearing resistance of a soil is influenced by its effective stress. When the effective stress increases, the contact between soil particles also increases, leading to greater shearing resistance. On the other hand, if the effective stress decreases, the contact between soil particles reduces, resulting in lower shearing resistance. Thus, effective stress plays a significant role in determining the shearing resistance of the soil.

Examine Formula (47.1) for Shearing Resistance

It is not provided, but let's assume that Formula (47.1) uses the total stress \(\sigma_{v}\). This implies that the shearing resistance depends on the total stress applied to the soil, which is not entirely accurate as we have seen that effective stress is the determining factor.

Conclusion - Use of Effective Stress

Based on our understanding of the concepts of total stress and effective stress, we can conclude that Formula (47.1) should use effective stress (\(\sigma_{v}^{\prime}\)) instead of total stress (\(\sigma_{v}\)). This is because the shearing resistance of the soil depends on the effective stress and not the total stress as it accurately represents the stress transmitted between soil particles.

Key concepts

Total Stress vs Effective Stress

Understanding the difference between total stress and effective stress is critical for students studying soil mechanics.

Total stress, denoted as \(\sigma_{v}\), encompasses all forces acting upon a given area of soil. This includes the weight of the overlaying soil itself, any structures on the surface, and additional loads that might be applied. In contrast, effective stress, represented as \(\sigma_{v}^{\prime}\), is the actual stress that contributes to soil strength and consolidation - it’s the 'usable' stress for soil particles.

The key to distinguishing between the two lies in the water within the soil pores. While total stress accounts for all factors, effective stress considers the pore water pressure that counteracts some of these forces. The formula for finding effective stress is:\[\sigma_{v}^{\prime} = \sigma_{v} - u\]where \(u\) is the pore water pressure. Effective stress is the engineer's focus because it directly influences the soil's structural stability and ability to support loads.

Shearing Resistance of Soil

The shearing resistance of soil is essentially its ability to resist deformation or failure under shear forces. It’s a critical factor in maintaining the stability of slopes, foundations, and retaining structures.

Shearing resistance is not a static property; it adjusts with changes in effective stress. To put it simply, as effective stress increases, soil particles tend to 'hug' each other more tightly. This results in a higher resistance against shearing forces. Consequently, when effective stress decreases, perhaps due to rising pore water pressure during saturation, particle contacts become less effective, reducing shearing resistance.

Therefore, when considering shearing resistance in any calculation or design, effective stress rather than total stress should be used to ensure accuracy. This is because it is the effective stress that determines how well the soil particles bear load without slipping past each other.

Stress Transmission in Soil Particles

Students often wonder how stress is actually transmitted through a seemingly loose and variable medium like soil. The concept of stress transmission in soil particles is crucial to the field of soil mechanics and foundational in understanding how structures interact with their ground.

Soil is made up of individual grains or particles that, though in contact, have spaces or 'pores' between them. When a load is applied to the surface, the force is transmitted down through these contacts from one particle to the next. The efficiency of this force transmission is significantly affected by the effective stress in the soil.

Higher effective stress means stronger particle contacts and better force transmission. This improved transmission directly translates to more substantial support for overlying structures and a more stable soil foundation. In contrast, lower effective stress implies weaker contacts and compromised force transmission, leading to potential settlement or failure.