MOHR'S CIRCLE BASICS AND TUTORIALS LINKS

MOHR'S CIRCLE BASIC DEFINITION AND INFORMATION LINKS
What Is Mohr's Circle? The Purpose Of Mohr's Circle


The shear strength of soil is generally characterized by the Mohr–Coulomb failure criterion. This criterion states that there is a linear relationship between the shear strength on the failure plane at failure (τff) and the normal stress on the failure plane at failure (σff) as given in the following equation:
                            τff = σff tanφ + c
where φ is the friction angle and c is the intrinsic cohesion. The strength parameters (φ, c) are used directly in many stability calculations, including bearing capacity of shallow footings, slope stability, and stability of retaining walls. The line defined by Eq. (17.1) is called the failure envelope.


A Mohr’s circle tangent to a point on the failure envelope (σff, τff) intersects the x-axis at the major and minor principal stresses at failure (σ1f, σ3f). For many soils, the failure envelope is actually slightly concave down rather than a straight line.

For a comprehensive review of Mohr’s circles and the Mohr–Coulomb failure criterion, see Lambe and Whitman [1969] and Holtz and Kovacs [1981]. But more online resource, below are links to articles that best explain and gives example on the application of Mohr's Circle:

Mohr's Circle Calculator
Given the stress components sx, sy, and txy, this calculator computes the principal stresses s1, s2, the principal angle qp, the maximum shear stress tmax and its angle qs. It also draws an approximate Mohr's cirlce for the given stress state. Continue reading...

Mohr's Circle for 2-D and 3-D Stress Analysis
After the data for the Mohr's circle are input, press the button "Draw", then the Mohr's circle can be created; press the button "fill", the Mohr's circle are created and filled with red color. If the Mohr's circles are too small, press the button "size 1" or "size 2" to enlarge them. Whenever the data for the Mohr's circle are modified, press "Draw" or "fill" button to get modified Mohr's circle. Besides, the paramters for the Mohr's circle and calculated principal stresses and maximum shear stress are given too. Continue reading...

Mohr's Circle Information
Mohr's circle, named after Christian Otto Mohr, is a two-dimensional graphical representation of the state of stress at a point. The abscissa, , and ordinate, , of each point on the circle are the normal stress and shear stress components, respectively, acting on a particular cut plane with a unit vector  with components. Continue reading...

ROCKS USED IN CONSTRUCTION STRENGTH CLASSES BASICS AND TUTORIALS

ROCKS USED IN CONSTRUCTION STRENGTH CLASSES BASIC INFORMATION
What Are The Strength Classes Of Rocks Used In Construction?


Based on the scale effects and geological conditions discussed in the previous sections, it can be seen that sliding surfaces can form either along discontinuity surfaces, or through the rock mass. The importance of the classification is that in essentially all slope stability analysis it is necessary to use the shear strength properties of either the discontinuities or of the rock mass, and there are different procedures for determining the strength properties as follows:

• Discontinuity shear strength can be measured in the field and the laboratory.
• Rock mass shear strength is determined by empirical methods involving either back analysis of slopes cut in similar geological conditions, or by calculation involving rock strength indices.

As a further illustration of the effects of geology on shear strength, relative strength parameters for three types of discontinuity and two types of rock mass are shown on the Mohr diagram. The slope of these lines represents the friction angle, and the intercept with the shear stress axis represents the cohesion

A description of these conditions on Figure 4.7 is as follows:

Curve 1 Infilled discontinuity: If the infilling is a weak clay or fault gouge, the infilling friction angle (φinf ) is likely to be low, but there may be some cohesion if the infilling is undisturbed.

Alternatively, if the infilling is a strong calcite for example, which produces a healed surface, then the cohesive strength may be significant.

Curve 2 Smooth discontinuity: A smooth, clean discontinuity will have zero cohesion, and the friction angle will be that of the rock surfaces (φr). The friction angle of rock is related to the grain size, and is generally lower in fine grained rocks than in coarse-grained rocks.

Curve 3 Rough discontinuity: Clean, rough discontinuity surfaces will have zero cohesion, and the friction angle will be made up of two components. First, the rock material friction angle (φr), and second, a component (i) related to the roughness (asperities) of the surface and the ratio between the rock strength and the normal stress.

As the normal stress increases, the asperities are progressively sheared off and the total friction angle diminishes.

Curve 4 Fractured rock mass: The shear strength of a fractured rock mass, in which the sliding surface lies partially on discontinuity surfaces and partially passes through intact rock, can be expressed as a curved envelope. At low normal stresses where there is little confinement of the fractured rock and the individual fragments may move and rotate, the cohesion is low but the friction angle is high.

At higher normal stresses, crushing of the rock fragments begins to take place with the result that the friction angle diminishes. The shape of the strength envelope is related to the degree of fracturing, and the strength of the intact rock.

Curve 5 Weak intact rock: Rocks that are composed of fine grained material that has a low friction angle. However, because it contains no discontinuities, the cohesion can be higher than that of a strong intact rock that is closely fractured. The range of shear strength conditions that may be encountered in rock slopes clearly demonstrates the importance of examining both the characteristics of the discontinuities and the rock strength during the site investigation.