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Mohr's circle is used to determine which principal stresses will produce this combination of shear and normal stress, and the angle of the plane in which this will occur. According to the principle of normality the stress introduced at failure will be perpendicular to the line describing the fracture condition.
The Mohr circle is used to find the stress components and , i.e., coordinates of any point on the circle, acting on any other plane passing through making an angle with the plane . For this, two approaches can be used: the double angle, and the Pole or origin of planes.
Different values of friction angle can be defined, including the peak friction angle, φ' p, the critical state friction angle, φ' cv, or residual friction angle, φ' r. c' = is called cohesion , however, it usually arises as a consequence of forcing a straight line to fit through measured values of (τ,σ') even though the data actually falls ...
The Swedish Slip Circle method assumes that the friction angle of the soil or rock is equal to zero, i.e., = ′. In other words, when friction angle is considered to be zero, the effective stress term goes to zero, thus equating the shear strength to the cohesion parameter of the given soil.
The shear strength of soil is primarily due to interparticle friction and therefore, the shear resistance on a plane is approximately proportional to the effective normal stress on that plane. [3] The angle of internal friction is thus closely related to the maximum stable slope angle, often called the angle of repose.
The measure of ∠AOB, where O is the center of the circle, is 2α. The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that intercepts the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.
Expressions in terms of cohesion and friction angle [ edit ] Since the Drucker–Prager yield surface is a smooth version of the Mohr–Coulomb yield surface , it is often expressed in terms of the cohesion ( c {\displaystyle c} ) and the angle of internal friction ( ϕ {\displaystyle \phi } ) that are used to describe the Mohr–Coulomb yield ...
The angle is computed by computing the trigonometric functions of a right triangle whose vertices are the (external) homothetic center, a center of a circle, and a tangent point; the hypotenuse lies on the tangent line, the radius is opposite the angle, and the adjacent side lies on the line of centers.