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Mohr Circle - Shear Strength of Soil, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering PDF Download

Mohr Circle

At any stressed point, three mutually perpendicular planes exist on which shear stress is zero. These planes are called principal planes. The normal stresses that act on these planes are called principal stress. The largest principal stress is called major principal stress (σ1), the lowest principal stress is called minor principal stress (σ3) and the third stress is called intermediate stress (σ2). The corresponding planes are called major, minor and intermediate plane, respectively. The critical stress values generally occur on the plane normal to the intermediate plane. Thus, only σ1 and σ3 are considered. Figure 9.2 shows an element and direction of σ1 and σ3. The major and minor principle planes are also shown. The major and minor principle planes are horizontal and vertical direction, respectively. The normal stress and shear stress at any plane making and angle q with horizontal can be determined analytically as:

\[\sigma={{{\sigma _1} + {\sigma _3}} \over 2} + {{{\sigma _1} - {\sigma _3}} \over 2}\cos 2\theta \]                           (9.3)

\[\tau={{{\sigma _1} - {\sigma _3}} \over 2}\sin 2\theta\]                       (9.4)

The stresses can be determined by graphically using Mohr Circle as shown in Figure 9.2. Mohr Circle is drawn in normal (σ) and shear (t) axis. The compressive normal stress is considered as positive. The shear stress that produces anti-clockwise couples on the element is considered as positive. The circle is drawn by taking O [(σ13)/2, 0] as center and (σ13)/2 as radius (as shown in Figure 9.2). Now from (σ3, 0) point draw a line parallel to AB plane. The line intersects the Mohr Circle at a point whose coordinates represents the normal and shear stress acting on AB plane [D(σ,  t)]. The A (σ3, 0) point is called pole or the origin of plane.

Mohr Circle - Shear Strength of Soil, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering


Fig. 9.1. Two particles/bodies in contact.

Mohr Circle - Shear Strength of Soil, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering

 Fig. 9.2. Mohr Circle.

The document Mohr Circle - Shear Strength of Soil, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering is a part of the Agricultural Engineering Course Soil Mechanics Notes- Agricultural Engineering.
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FAQs on Mohr Circle - Shear Strength of Soil, Soil Mechanics - Soil Mechanics Notes- Agricultural Engineering

1. What is Mohr Circle and how is it used in soil mechanics?
Ans. Mohr Circle is a graphical representation of the stress conditions at a point in a material. In soil mechanics, it is used to determine the shear strength of soil. By plotting the major principal stress and minor principal stress on a graph, the Mohr Circle allows engineers to analyze the shear strength parameters of soil, such as cohesion and angle of internal friction.
2. What factors affect the shear strength of soil?
Ans. Several factors influence the shear strength of soil. These include the soil's cohesion, which is the particle-to-particle attractive forces, and the angle of internal friction, which is the angle at which the soil particles can resist sliding or shearing. Other factors include the soil's moisture content, density, particle size distribution, and stress history.
3. How can the Mohr Circle be used to determine the shear strength of soil?
Ans. The Mohr Circle can be used to determine the shear strength of soil by analyzing the intersection point between the Mohr Circle and the Coulomb failure envelope. The Coulomb failure envelope represents the relationship between the shear stress and normal stress on a plane within the soil mass. By calculating the intercept and slope of the Coulomb failure envelope from the Mohr Circle, the shear strength parameters of the soil can be determined.
4. What is the significance of the angle of internal friction in soil mechanics?
Ans. The angle of internal friction is a critical parameter in soil mechanics as it represents the shear resistance of soil particles. It determines the maximum angle at which soil particles can resist sliding or shearing under applied stress. The angle of internal friction is used to calculate the shear strength of soil, design foundations, analyze slope stability, and determine the bearing capacity of soil.
5. How does the shear strength of soil impact agricultural engineering practices?
Ans. The shear strength of soil plays a crucial role in agricultural engineering practices. It affects the stability of slopes and embankments, the design of foundations for agricultural structures, and the selection of appropriate soil tillage and cultivation techniques. Understanding the shear strength of soil helps agricultural engineers make informed decisions regarding soil erosion control, irrigation system design, and soil compaction for optimal crop growth and productivity.
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