Question

The total, neutral and effective vertical stresses (in t/m\(^2\)) at a depth of \(5\) m below the surface of a fully saturated soil deposit with saturated density of \(2\) t/m\(^3\) would, respectively, be

• A. \(5,\;5\text{ and }10\)
• B. \(5,\;10\text{ and }5\)
• C. \(10,\;5\text{ and }10\)
• D. \(10,\;5\text{ and }5\)

Hint:

Remember Terzaghi's effective stress principle: \[ \boxed{\sigma=\sigma'+u} \] or equivalently, \[ \boxed{\sigma'=\sigma-u.} \] For saturated soils, \[ u=\gamma_wz. \]

Answer 1

The Correct Option is D

Concept: For a saturated soil, \[ \boxed{\sigma=\gamma_{sat}z} \] \[ \boxed{u=\gamma_wz} \] \[ \boxed{\sigma'=\sigma-u} \] where \[ \sigma=\text{Total stress}, \] \[ u=\text{Pore water pressure}, \] \[ \sigma'=\text{Effective stress}. \]

Step 1: Calculate the total stress. Given, \[ \gamma_{sat}=2\;\text{t/m}^3,\qquad z=5\;\text{m}. \] Therefore, \[ \sigma = 2\times5 = 10\;\text{t/m}^2. \]

Step 2: Calculate the neutral stress. For water, \[ \gamma_w=1\;\text{t/m}^3. \] Hence, \[ u = 1\times5 = 5\;\text{t/m}^2. \]

Step 3: Calculate the effective stress. \[ \sigma' = 10-5 = 5\;\text{t/m}^2. \] Thus, \[ \boxed{\sigma=10,\qquad u=5,\qquad \sigma'=5\;\text{t/m}^2.} \] Therefore, the correct option is \[ \boxed{(D)\;10,\;5\text{ and }5.} \]