A soil sample is subjected to a triaxial stress state with a major principal stress of 300 kPa, an intermediate principal stress of 200 kPa, and a minor principal stress of 100 kPa. Determine if the soil will yield according to the Mohr-Coulomb criterion, given that the soil has a friction angle of 30 degrees and a cohesive strength of 50 kPa.

To determine if the soil will yield according to the Mohr-Coulomb criterion, we need to construct the Mohr's circle for the given triaxial stress state and check if the circle intersects the failure envelope defined by the friction angle and cohesive strength of the soil.

Given: Major principal stress (σ₁) = 300 kPa Intermediate principal stress (σ₂) = 200 kPa Minor principal stress (σ₃) = 100 kPa Friction angle (ϕ) = 30 degrees Cohesive strength (c) = 50 kPa

Find the center of the Mohr's circle: The center of the Mohr's circle is located at the average of the major and minor principal stresses. Center = (σ₁ + σ₃) / 2 = (300 kPa + 100 kPa) / 2 = 200 kPa

Find the radius of the Mohr's circle: The radius of the Mohr's circle is equal to half the difference between the major and minor principal stresses. Radius = (σ₁ - σ₃) / 2 = (300 kPa - 100 kPa) / 2 = 100 kPa

Plot the Mohr's circle on a graph, using the center and radius calculated.

Plot the failure envelope on the graph: The failure envelope is a line that represents the Mohr-Coulomb failure criterion. It has a slope equal to the tangent of the friction angle (tan(ϕ)) and intercepts the y-axis at the cohesive strength (c).

The equation of the failure envelope is: τ = σ * tan(ϕ) + c

For this case, with a friction angle of 30 degrees and a cohesive strength of 50 kPa, the equation becomes: τ = σ * tan(30°) + 50 kPa

Plot the failure envelope line on the graph.Check if the Mohr's circle intersects the failure envelope: If the Mohr's circle intersects the failure envelope, it means that the soil will yield according to the Mohr-Coulomb criterion. If there is no intersection, the soil will not yield.

By analyzing the graph, if the Mohr's circle intersects or touches the failure envelope, the soil will yield according to the Mohr-Coulomb criterion. If there is no intersection or contact between the circle and the envelope, the soil will not yield.

Please note that without a specific value for the shear strength parameters (ϕ and c) of the soil, it is not possible to provide a definitive conclusion regarding the yield behavior of the soil.