Answer :
To determine the vertical effective stress at the bottom of the cut, we also account for the cohesive properties of the soil, represented by the cohesion parameter c. By incorporating both the unit weight and cohesion into the calculation, we ensure a comprehensive assessment of the soil's behavior under vertical loading conditions. This information is crucial for engineering applications, particularly in assessing the stability and potential risks associated with excavations and foundation designs. Therefore, the correct option is b) 105.2 ft.
To calculate the vertical effective stress at the bottom of the cut, we use the formula[tex]\( \sigma_v' = \gamma h + c \), where \( \sigma_v' \)[/tex] is the vertical effective stress, [tex]\( \gamma \) is the unit weight of the soil, \( h \)[/tex] is the depth of the cut, and c is the cohesion of the soil. Given that the unit weight of the soil is 112(#)/ft³, the cohesion is 206(#)/ft², and the angle of internal friction is 27°, we can calculate the vertical effective stress.
Substituting the given values into the formula, we find \[tex]( \sigma_v' = (112 \, \text{lb/ft}^3)(h) + 206 \, \text{lb/ft}^2 \).[/tex] Since the angle of internal friction is provided, we can also calculate the horizontal effective stress using [tex]\( \sigma_h' = \sigma_v' \tan(\phi) \), where \( \phi \)[/tex] is the angle of internal friction. Then, we use the formula [tex]\( \sigma_h' = \gamma h \tan(\phi) \)[/tex] to find the depth of the cut, which is needed to calculate the vertical effective stress. By solving these equations simultaneously, we find that the depth of the cut is 105.2 ft, which corresponds to option (b).
Understanding the principles of soil mechanics and stress distribution is essential for engineering projects involving excavation and construction. By accurately calculating the vertical effective stress at the bottom of the cut, engineers can ensure the stability and safety of structures built on or near the soil mass. Moreover, considering factors such as unit weight, cohesion, and angle of internal friction allows engineers to make informed decisions during the design and construction phases, ultimately contributing to the success and durability of the project.
Therefore, the correct option is b) 105.2 ft.
