A series of three direct shear tests has been conducted on a certain saturated soil. Each test was performed on a 2.375-inch dia
meter, 1.00-inch tall sample. The results of these tests are as follows:
Test Number Normal Stress Shear Stress
1 2435 1656
2 4870 3571
3 7305 4578
Determine the friction angle and cohesion intercept.
Test Number Normal Stress Shear Stress
1 2435 1656
2 4870 3571
3 7305 4578
Determine the friction angle and cohesion intercept.
1 answer:
Answer:
Go to explaination for the details of the answer.
Explanation:
Angle of friction (friction angle) is a measure of the ability of a unit of rock or soil to withstand a shear stress. It is the angle (φ), measured between the normal force (N) and resultant force (R), that is attained when failure just occurs in response to a shearing stress (S).
The cohesion intercept is a used when we want to describe the shear strength soils. The definition is mainly derived from the Mohr-Coulomb failure criterion and it is used to describe the non-frictional part of the shear resistance which is independent of the normal stress.
Please check attachment to Determine the friction angle and cohesion intercept.
You might be interested in
Answer:
(a) The mean time to fail is 9491.22 hours
The standard deviation time to fail is 9491.22 hours
(b) 0.5905
(c) 3.915 × 10⁻¹²
(d) 2.63 × 10⁻⁵
Explanation:
(a) We put time to fail = t
∴ For an exponential distribution, we have f(t) =
Where we have a failure rate = 10% for 1000 hours, we have(based on online resource);
e^(1000·λ) - 0.1·e^(1000·λ) = 1
0.9·e^(1000·λ) = 1
1000·λ = ㏑(1/0.9)
λ = 1.054 × 10⁻⁴
Hence the mean time to fail, E = 1/λ = 1/(1.054 × 10⁻⁴) = 9491.22 hours
The standard deviation = √(1/λ)² = √(1/(1.054 × 10⁻⁴)²)) = 9491.22 hours
b) Here we have to integrate from 5000 to ∞ as follows;
(c) The Poisson distribution is presented as follows;
p(x = 3) = 3.915 × 10⁻¹²
d) Where at least 2 components fail in one half hour, then 1 component is expected to fail in 15 minutes or 1/4 hours
The Cumulative Distribution Function is given as follows;
p( t ≤ 1/4) .