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The formula for calculating allowable bearing capacity, represented as qa, is derived from consideration of the net allowable pressure that an underlying soil can withstand. The correct formula relates the net pressure (qnet) to a factor of safety (FS) to ensure that the applied loads do not exceed the soil's strength.
Specifically, allowable bearing capacity is derived by dividing the net bearing pressure by the factor of safety. The factor of safety acts as a mitigative measure, allowing for uncertainties in soil behavior, material properties, and potential variations in loading conditions. By using this relationship, the final value obtained for allowable bearing capacity (qa) provides a more conservative estimate intended to prevent failure or excessive settlement of the structure.
In practical applications, engineers assess the existing conditions of the soil and the loads that will be applied to it. With these values, employing the correct formula facilitates safe and effective design, enhancing both safety and longevity of the construction.
The other choices each represent different concepts or misapplications of the relationship between net pressure, bearing capacity, and safety factors, which is why they would not be correct in this context.