Shear Strength of Soils

Summary

Saeed Hashemi's presentation delves into the critical geotechnical concept of soil's shear strength, essential for analyzing the stability of soil masses in structural engineering. It defines shear strength as the soil's resistance to failure and sliding, introduces the Coulomb failure criterion, and discusses how cohesion and friction angle affect soil strength. The presentation also covers the Mohr Circle for stress representation, the significance of effective stresses over total stresses, and the method to determine the failure envelope through testing. Lastly, it touches on the calculation of the failure plane's orientation, providing a comprehensive understanding of soil mechanics.

Takeaways

• 📚 Shear strength of soil is a fundamental concept in geotechnical engineering, defining the internal resistance of soil to resist failure and sliding.
• 🔍 Shear failure occurs when the shear stress equals the shear strength of the soil, leading to potential structural instability if not accounted for in construction.
• 🏗️ The safety of structures like buildings and bridges is closely tied to the shear strength of the soil they are built upon.
• 📏 Coulomb's failure criterion expresses the shear strength of soil as a linear function of the normal stress at failure, crucial for predicting soil behavior.
• 📐 The Mohr-Coulomb failure criterion introduces two parameters: cohesion (C) and the angle of internal friction (Φ), which are key to understanding shear strength.
• 🌐 Different soil types exhibit varying cohesion and friction angles, affecting their shear strength and resistance to failure.
• 📉 The relationship between shear stress and normal stress can be non-linear for some soils, indicating complexity in soil behavior.
• 🔄 The concept of effective stress is essential for considering underground pore pressure when analyzing soil stability.
• 🔍 Mohr's Circle is a graphical representation used to determine the state of stress in soil and to predict failure conditions.
• 🧪 Laboratory tests on soil specimens are necessary to plot Mohr's Circles and define the failure envelope, enhancing the accuracy of soil strength assessments.
• 📝 The orientation of the failure plane in soil can be calculated using the friction angle, providing insight into the direction of potential slips or collapses.

Q & A

What is the definition of shear strength of soil according to the presentation?

Shear strength of soil is defined as the internal resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it.

Why is understanding shear strength important in geotechnical engineering?

Understanding shear strength is crucial in geotechnical engineering because it helps analyze the stability of soil masses, which is essential for the safety of structures like buildings and bridges.

What is the Coulomb failure criterion mentioned in the presentation?

The Coulomb failure criterion is a linear function that expresses the shear strength of a soil at a point on a particular plane as a function of the normal stress at failure on the same point.

What are the two components of shear strength mentioned in the script?

The two components of shear strength are cohesive and frictional, which are represented by the soil's cohesion (C) and the angle of internal friction (Phi).

How does the angle of internal friction relate to the stability of soil?

The angle of internal friction (Phi) is related to the stability of soil because it represents the angle of repose at which the soil will naturally stand. A steeper angle indicates a firmer soil, which is more resistant to shear failure.

What is the significance of the Mohr Circle in the context of soil mechanics?

The Mohr Circle is significant in soil mechanics as it graphically represents the state of stress in a soil element and is used to determine the maximum shear stress and the orientation of the failure plane.

What is the role of effective stress in the analysis of soil failure?

Effective stress plays a critical role in the analysis of soil failure because it considers the influence of underground pore pressure. It is used to calculate the actual stress on the soil grains that can lead to failure.

How is the failure envelope determined using Mohr Circles?

The failure envelope is determined by conducting multiple tests on identical soil specimens and plotting the Mohr Circles for each test condition. The envelope is then drawn to represent the boundary of all possible failure conditions.

What does the orientation of the failure plane indicate in soil mechanics?

The orientation of the failure plane indicates the direction in which the soil is most likely to fail under a combination of shear and normal stresses, and it can be calculated as a function of the friction angle.

Why is it important to consider the effective stresses rather than total stresses when dealing with underground pore pressure?

Considering effective stresses is important when dealing with underground pore pressure because it accounts for the reduction in stress on the soil grains due to the presence of water or air in the soil pores, leading to a more accurate prediction of soil behavior.

How does the presentation suggest increasing the number of tests can improve the accuracy of the failure envelope?

The presentation suggests that increasing the number of tests allows for more Mohr Circles to be plotted, which leads to a more precise and detailed failure envelope, enhancing the understanding of soil behavior under various stress conditions.

Outlines

00:00

🏗️ Shear Strength of Soils and Failure Criteria

Saeed Hashemi introduces the concept of shear strength in soils, a fundamental aspect of geotechnical engineering. Shear strength is the internal resistance of soil to resist failure and sliding along any plane within it. It is crucial for analyzing the stability of soil masses and ensuring the safety of structures like buildings and bridges. The presentation explains that soils fail in shear under various stress combinations. The Coulomb failure criterion is discussed, which expresses the shear strength as a linear function of the normal stress at failure. The two components of shear strength—cohesion and friction—are highlighted, with examples of different soil types and their respective values. The importance of understanding shear strength for geotechnical engineering is emphasized.

05:02

📊 Mohr's Circle and Failure Envelope in Soil Mechanics

The second paragraph delves into the application of Mohr's Circle for understanding stress states in soil mechanics. It explains how different stress conditions can be represented by Mohr's Circles and how the failure envelope is determined by the intersection of these circles with the envelope. The concept of effective stress is introduced, which is necessary when considering underground pore pressure. The process of finding the failure envelope using Mohr's Circles involves testing identical soil specimens under varying stress conditions until failure occurs. The orientation of the failure plane is also discussed, showing how it can be calculated based on the friction angle. The presentation concludes with a practical example of how these principles are applied in geotechnical engineering to predict and prevent soil failure.

Keywords

💡Shear Strength

Shear strength refers to the internal resistance of a soil mass to resist failure and sliding along any plane within it. It is a fundamental concept in geotechnical engineering, as it determines the stability of soil masses under different stress conditions. In the script, shear strength is described as the force that prevents soil from failing under loading, such as in the case of an embankment or a footing. The importance of understanding shear strength is highlighted by the example of a grain elevator in Canada, where soil failure led to the collapse of the structure.

💡Shear Failure

Shear failure is the process by which a material, like soil, fails under shear stress. It is a critical concept in the script as it explains how and when soil can fail. The script mentions that when the shear stress at a point within the soil equals the soil's shear strength, failure occurs at that point. This concept is crucial for assessing the stability of structures built on soil, as it directly impacts the safety of those structures.

💡Coulomb's Failure Criterion

Coulomb's failure criterion is a principle used to predict the failure of a material under shear stress. It is named after the French engineer Charles Augustin de Coulomb and is central to the script's discussion on soil mechanics. The criterion is expressed as a linear function of the normal stress at failure and is used to determine the conditions under which soil will fail. The script explains that failure will occur at any point in the soil where the critical combination of shear and normal stresses develops, according to Coulomb's equation.

💡Friction Angle

The friction angle, also known as the angle of internal friction, is a measure of the resistance of a soil to deformation under load. It is a key component of the shear strength of soil, as explained in the script. The friction angle is defined as the angle of repose at which the soil remains stable. The script uses the friction angle to differentiate between firm and loose soils, with firm soils having a steeper angle of repose. This angle is integral to understanding how soil behaves under different stress conditions.

💡Cohesion

Cohesion is the force that holds particles of soil together, providing resistance to shearing forces. It is one of the two components of shear strength, as mentioned in the script. Cohesion is particularly important in soils like plastic clay, where it is the primary resistance against shear, with the script noting that in such cases, the friction angle is zero because there is no friction between the grains.

💡Effective Stress

Effective stress is the stress that acts on the soil skeleton, which is the arrangement of soil particles. It is a crucial concept in geotechnical engineering because it helps to determine the shear strength of soils. The script explains that when there is underground pore pressure, it is essential to calculate effective stresses to understand how soil will behave under load. Effective stress is used to draw Mohr's Circles and to determine the failure envelope.

💡Mohr's Circle

Mohr's Circle is a graphical representation used to determine the state of stress at a point within a material. It is a fundamental tool in soil mechanics, as depicted in the script. The script describes how Mohr's Circles can be used to represent different stress states and to find the failure envelope by plotting shear stress versus normal stress. The circles are used to predict soil failure by comparing the stress state to the failure envelope.

💡Failure Envelope

The failure envelope is a graphical representation of the conditions under which a soil will fail. It is derived from a series of tests and is a key concept in understanding soil stability. The script explains that failure envelopes are drawn using Mohr's Circles, and that they represent the maximum shear stress a soil can withstand for different normal stresses. The failure envelope is essential for predicting soil behavior under various loading conditions.

💡Deviatoric Stress

Deviatoric stress, also known as the difference between the principal stresses, is the stress that causes distortion or shearing in a material. In the script, it is mentioned in the context of increasing the stress on soil specimens until failure occurs. The script explains that as deviatoric stress increases, the Mohr's Circle becomes larger until it touches the failure envelope, indicating failure.

💡Orientation of Failure Plane

The orientation of the failure plane refers to the angle at which a soil mass fails under a combination of shear and normal stresses. This concept is important for understanding the direction of soil movement during failure. The script provides a formula to calculate this angle as a function of the friction angle. The orientation of the failure plane is crucial for predicting the behavior of soil during construction projects and natural events like landslides.

Highlights

Shear strength of soils is a fundamental concept in geotechnical engineering.

Shear strength is the internal resistance of soil to resist failure and sliding along any plane.

Soils generally fail in shear under different combinations of stresses.

Shear strength is critical for analyzing the stability of soil masses and the safety of structures.

Shear failure occurs when shear stress equals the soil's shear strength at a point within the soil mass.

Coulomb's failure criterion expresses shear strength as a linear function of normal stress at failure.

The Mohr-Coulomb failure criterion includes cohesion (C) and the angle of internal friction (Φ).

Friction angle can be defined as the angle of repose of the soil.

Shear strength has two components: cohesive and frictional.

Different soil types have varying values of cohesion and friction angle.

The relationship between shear stress and normal stress can be non-linear for some soil types.

Higher values of cohesion and friction angle result in higher shear strength of soil.

The Mohr's Circle represents any stress state and can be used to define the failure envelope.

Effective stresses must be considered when there is underground pore pressure.

The orientation of the failure plane can be calculated based on the friction angle.

Laboratory tests are necessary to determine the failure envelope using Mohr's Circles.

The number of tests influences the precision of the failure envelope.

The maximum shear stress and normal stress at failure can be calculated from effective principle stresses.

Transcripts

hello everybody my name is Saeed hashemi

today I'm going to give you a short

presentation about sheer strength of

soils which is one of the most important

basics of geotechnical engineering

here is the outline of my today's

presentation first I'm going to

introduce the sheer strength of soils

and Define the shear failure concept

then I'll explain the more coulomb

failure Criterion and finally I'll

explain the sheer parameters related to

these Criterion

okay what is the shear strength of the

soil Shear strength is defined as the

internal resistance per unit area that

the soil Mass can offer to resist

failure and sliding along any plane

inside it in fact various studies showed

that soils generally fail in Shear under

different combination of stresses as you

can see in this figure

if at the point on any plane within a

soil Mass which is under loading such as

these embankment or this street footing

the shear stress becomes equal to the

shear strength of the soil then failure

will occur at that point therefore we

need this knowledge to analyze the

stability of soil masses

so in case of constructing any structure

such as a building or a bridge the

safety of that structure closely depends

on the sheer strength of the soil

as you can see in this photo

under footing soil fail in this grain

elevator in Canada and then the

structure collapsed while it had no

problem in its building elements such as

beams or columns

we know that soil is a material

comprised of discrete mineral grains and

decayed organic matter along with

intergranular gases and liquids as shown

here

when the shear stress along this surface

reaches the shear strength of the soil

failure happens in case of a Shear

failure the soil grains which is here

slide over each other along the failure

surface

and crushing of cranes won't occur if

the soil is not Consolidated actually

these two photos are examples of sheer

failure due to Landslide phenomenon

originally the sheer strength of a soil

at a point on a particular plane was

expressed by coulomb as a linear

function of the normal stress at failure

on the plane at the same point and this

function as you can see here Tau f is

the maximum shear stress the soil can

take without failure under normal stress

Sigma thus failure will occur at any

point in the soil where the critical

combination of shear and normal stresses

develops also as you can see in this

graph

the state of stress in two Dimensions

can be shown on a plot of shear stress

versus versus normal stress Sigma in

this graph derived C

is the cohesion of the soil and Phi here

which is this angle

it will be the angle of internal

friction or friction angle actually a

friction angle can be defined as the

angle of repose which the soil still is

naturally so a firm soil will have a

steeper angle of reposed than a loose

one

as I mentioned before Shear strength has

two components cohesive and frictional

in this slide you can see the different

values of cohesion and friction angle

for different soil types for example in

case of pure gravel there is no cohesion

between the grains and C is zero and the

shearing resistance is developed only by

inter particle forces by Phi or in case

of plastic clay which is shown here the

only parameter that resists against the

shear is cohesion and Phi is zero

because there is no friction between the

grains it should be noted that the

relationship between Tau

and sigma

can be non-linear for some soil types

and finally you should notice that the

higher the values C and Phi higher the

shear strength of a soil

okay more circles

any stress State can be represented by

coulomb equation as I mentioned before

and also a more more Circle which is

here or here

can be defined by the total or effective

principle stresses Sigma 1 dash and

sigma 3 Dash

we can draw in more circles for

different test conditions for example in

if the combination of stresses touches

the failure envelope the element will

fail as shown here and for element X

but in case of element y the more Circle

as you can see here will not touch the

envelope and element remains safe

in this element element y with applying

the Delta Sigma stress after the

hydrostatic estrus condition more Circle

becomes larger and with this stress

condition that we have in here the soil

elements does not fail why because the

more circle is located within the

failure envelope but please note that

more circles cannot extend to the area

above the envelope because when it

touches the envelope here this is the

failure envelope the element fails and

it is not possible to pass this line

in this slide you can see that with

increasing the Delta Sigma or deviatoric

stress more Circle becomes larger

until touches the failure envelope and

the sample fails at exactly this point

it should be mentioned that the shear

stress in a soil element can be resisted

only by the skeleton of the soil grains

so we need to consider the effective

stresses if we have underground pore

pressure so in this case we have to

calculate the effective stresses and

then we can draw the more Circle as you

can see in here instead of the more

Circle that we have we can have with the

total stresses and also the center of

the Mohr Circle and also the maximum

shear stress can be calculated by these

two simple equations if you wanna if we

have the sigma V and sigma H according

to our experimental test then we can

derive the sigma Dash Sigma V Dash and

sigma H dash and then we can draw our

more Circle easily

uh for finding the failure envelope by

more circles we need to test several

identical specimens in the first stage

we need to apply the hydrostatic stress

condition to the specimen and in the

second stage we will increase the the

butyric stress or vertical stress to the

specimens until the specimen failed so

with each test we will have one more

Circle so we need at least at least

three more circles to be able to draw

our failure envelope and in case of

total stress and in case of having

underground pore pressure then we have

to calculate the effective stresses

from the total stresses and then we can

draw our

more circles but in terms of Sigma Dash

and then we can draw our failure

envelope easily but keep in mind that

with increasing the number of tests we

can have more precise failure envelope

and finally the last slide is about the

orientation of failure playing as you

can see here the orientation of failure

play in a soil element which failed due

to the combination of shear stress and

normal stress as well can be calculated

as a function of a friction angle it's

equal to 45 degrees plus Phi over 2.

actually this angle Theta can be also

shown on more Circle which is two times

Theta

and the stresses at failure points Tau F

and sigma F Dash can be calculated as a

function of effective principle stresses

Sigma 1 dash and sigma 3 Dash so we can

calculate these two stresses based on

the applied stresses that we had

recorded in the experimental test in the

laboratory

I hope you enjoyed the presentation and

thank you so much for your attention