question archive Given the following results of a direct shear test, plot the test data and least squares best fit line
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Given the following results of a direct shear test, plot the test data and least squares best fit line. What is the soil cohesion (y intercept) and what is the tangent of the friction angle (slope)?
Specimen Normal Stress (psf) Shear Stress (psf)
1 200 450
2 400 520
3 600 590
4 1000 740
The soil cohesion is 375.43 psf and the tangent of friction angle is 0.363.
Step-by-step explanation
To solve for this, we must determine the "best fit line" for the given normal and shear tress data.
The "least square method" will yield the most accurate result. In order to do it we must follow the steps below;
Here is the solution following the steps shown above:
The slope of the line is 0.363 and the y -intercept is 375.43 psf. Therefore, the equation is y = 0.363x + 375.43.
Please see the attached file for the complete solution