What Are the Effective and Total Deviator Stresses in Saturated Silty Clay?

[db725]

Urgent Question Soil Mechanics -- Please Help

Homework Statement

A saturated over-consolidated silty clay is estimated to have the effective strength parameters

c'=5 kPa
∅'=25 kPa

A specimen of the silty is mounted into a triaxial cell and full consolidated to 400 kPa with a cell pressure of 500 kPa and a back pressure of 100 kPa. With the drainage then turned off, the specimen is slowly loaded axially failure. At failure, the porewater pressure was measured to be 160 kPa and the diameter of the specimen was calculated to be 103.47 mm.

Estimate

1. the effective deviator stress at failure (σ1'-σ3')
2. the total deviator stress at failure (σ1-σ3), and
3. the load which would be needed to be applied to the loading piston to cause failure.

Homework Equations

σ1=σ'1+u

deviator stress =deviator load/area

The Attempt at a Solution

cell pressure =500 kPa, back pressure=100 kPa, σ3= 500-100=400 kPa

u(failure)=160 kPa

Area at failure = (∏ x diameter^2)/4=(∏x103.47^2)/4=8408.50 mm^2

1. Deviator stress= deviator load/area= (400 x 10^3)/8408.50=47.57 kPa

σ'3 at failure = 400-160=240 kPa

σ'1 at failure= σ'3 +deviator stress = 240 +47.57=287.57 kPa

2. σ1=σ1'+u=287.57+160=447.57 kPa σ3=σ3'+u =240+160=400 kPa

3. Not sure how to do this. Was thinking of drawing the mohr circles using the previous calculations. However I feel like there is something wrong with the above as when I sketched the mohr circles I got a strange circle.

I would greatly appreciate any help on this question as I am getting prepared for a final exam in my engineering degree. My exam is in 2 days and I would really like to know if I am on the right track or not. Thanks in advance.

 

[KataKoniK]

it is important to approach problems in a systematic and logical manner. Here are some steps you can take to solve this problem:

1. First, make sure you understand the given information and what is being asked. The problem gives you the effective strength parameters of the soil, the conditions under which the specimen was tested, and the measurements taken during the test. You are asked to estimate the effective and total deviator stresses at failure, as well as the load needed to cause failure.

2. Next, review the equations and concepts related to effective and total stresses, deviator stress, and porewater pressure. Make sure you understand how these values are calculated and what they represent.

3. Then, start by calculating the effective deviator stress at failure. This can be done by using the given information on the cell pressure, back pressure, and porewater pressure, as well as the formula for deviator stress. Make sure your units are consistent.

4. Next, use the effective deviator stress to calculate the effective principal stresses at failure. This can be done using the Mohr-Coulomb failure criterion, which states that the failure occurs when the deviator stress equals the effective cohesion plus the effective stress multiplied by the effective friction angle. Make sure your units are consistent.

5. Once you have the effective principal stresses, you can use them to calculate the total principal stresses at failure. This can be done by adding the porewater pressure to the effective principal stresses.

6. Finally, to calculate the load needed to cause failure, you can use the formula for deviator stress and rearrange it to solve for the deviator load. This load should be applied to the loading piston, so make sure you use the correct area in your calculation.

7. Once you have completed all the calculations, make sure to double check your units and final answers to ensure they are correct.

I hope this helps you in solving the problem. Remember to approach it step by step and use the equations and concepts you have learned in your studies. Good luck on your exam!