Question: Development of a methodology to solve embedded walls following the free earth support method.

The objective of this project is the development of an automatic methodology to solve embedded walls following the free earth support method as explained in class. The problem can be generally described as an anchored sheet pile wall which is constructed to retain soil to a height h. The surface of the retained soil will be horizontal and level with the top of the wall.

All round pressure (kPa) 100 200 400 800
Deviatoric stress (kPa) 452 908 1810 3624

1. Plot the Mohr-Coulomb failure criterion in terms of the alternative criteria (s', t), (σ₁', σ_3') and (p', q) and obtain the shear strength parameters of the soil after a suitable linear best t analysis.

2. Following EC7, take a material factor of safety of Υm = 1.25 in order to reduce the shear strength parameters of the soil.

3. Display in a graph the distribution of eective vertical and horizontal stresses as a function of depth.

4. Display in a graph the residual moment and the anchored force as a function of the depth of penetration d. This graph will help you estimate the depth of penetration.

5. Determine accurately the penetration depth after solving the resulting algebraic cubic equation (you can use the bisection method, the secant method or the Newton-Raphson method).

Display a convergence curve along with a table showing the convergence of the method.

6. Determine accurately the force in the tie rod.

7. Display in a graph the distribution of the shear force diagram and the bending moment diagram in the embedded wall. See Figure 5(a).

8. Display in a graph the deformation of the embedded wall (for simplicity, considered it clamped at the bottom end). Select a suitable E
I constant for the embedded wall (you can use numerical integration if you wish). See Figure 5(b).

9. Display in a graph the anchor force and the depth of embedment as a function of the anchor location ho. See Figure 6.