# Drawing the Failure Envelope & Mohr Circle for Soil w/ Given Properties

• EzaMoo
In summary, the failure envelope and Mohr circle are graphical representations of the strength and failure characteristics of soil. To draw these, properties such as cohesion, angle of internal friction, and stress values at failure are needed. The failure envelope is drawn by plotting shear and normal stress, while the Mohr circle is a circle with its center at the origin and a radius equal to the maximum shear stress. These provide valuable information for designing structures and identifying potential failure mechanisms.
EzaMoo

## Homework Statement

A*certain*soil*has*c’*=*12kPa*and*φ’*=*32°.*The*major*and*minor*principal*stresses*at*a*point*in*this*
soil*are*348*and*160*kPa*respectively,*and*the*pore*water*pressure*at*this*point*is*96*kPa.*Draw*
the*failure*envelope*and*the*Mohr*circle*and*determine*if*a*shear*failure*will*occur*at*this*point*in*
the*soil.*If*so,*determine*the*angle*between*the*failure*plane*and*the*plane*on*which*the*major*
principal*stress*acts.*

As attached.

## The Attempt at a Solution

As attached. But how do I know if failure has occurred?

#### Attachments

• mohrs.pdf
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## 1. What is the purpose of drawing the failure envelope and Mohr circle for soil?

The purpose of drawing the failure envelope and Mohr circle for soil is to visually represent the strength and failure characteristics of a soil sample. It helps engineers and scientists to analyze the behavior of soil under different stress conditions and determine its shear strength parameters.

## 2. What are the properties of soil needed to draw the failure envelope and Mohr circle?

The properties of soil needed to draw the failure envelope and Mohr circle include the cohesion (c), angle of internal friction (φ), and the normal stress (σ) and shear stress (τ) values at failure. These parameters can be obtained through laboratory tests such as direct shear or triaxial tests.

## 3. How is the failure envelope drawn for soil with given properties?

The failure envelope is drawn by plotting the shear stress (τ) on the y-axis and the normal stress (σ) on the x-axis. The cohesion (c) is represented by the intercept of the envelope on the y-axis, while the slope of the envelope is equal to the tangent of the angle of internal friction (φ). The envelope is then drawn as a straight line connecting the points at which the soil sample failed under different stress conditions.

## 4. What is the Mohr circle and how is it related to the failure envelope?

The Mohr circle is a graphical representation of stress conditions at a point in a soil sample. It is a circle with its center at the origin and a radius equal to the maximum shear stress (τmax). The failure envelope is tangent to the Mohr circle at the point of failure, and the angle between the envelope and the horizontal axis is equal to 2φ.

## 5. What information can be obtained from the failure envelope and Mohr circle for soil?

The failure envelope and Mohr circle provide important information about the strength and failure characteristics of soil under different stress conditions. This information can be used to design foundations, retaining walls, and other structures that rely on the strength of soil. It can also help to identify potential failure mechanisms and determine the stability of slopes and embankments.

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