Computational Geotechnics — Summer 2022

Solve the following system by Gauss Jacobi method 6x + y + z = 105 4x +8y + 3z = 155 5x + 4y - 10z = 65

Explain Newton-Raphson method with suitable example.

Find a root of the equation x3 – 4x = 9 using the Bisection method in four stages.

Use 2nd order Range – Kutta method to find y (0.2), given that dy = 2x + dx y , y(0) = 1; (use ℎ = 0.1).

Explain False Position method with suitable example.

Explain Newton’s Raphson method with suitable example.

Use the Runge-Kutta method of fourth order to solve dy = 1 + y2 Subject to y(0) = 0, find y(0.2) and y(0.4). dx

Briefly explain Drucker-Prager theory.

Define discrete element method. How it is useful to the geotechnical engineering?

Explain application of FEM method for geotechnical engineering.

Explain Mohr-Coulomb theory.

Give difference between discrete modeling versus continuum modeling.

Explain in detail One- dimensional plasticity theory for understanding the behavior of soil.

Explain Terzaghi’s theory of 1-dimensional consolidation with assumptions.

Explain basic concept of discrete modelling.

Explain Modified Mohr Coulomb failure theory for shear strength? Sketch typical strength envelop for different type of soil.

Explain earth pressure coefficients based upon Lade-Duncan criterion.

Explain the flow through porous media.

Briefly explain 1-Dimentional consolidation.

Give detail explanation on various types of consolidation.

Differentiate between consolidation and compaction.

Explain consolidation mechanism through spring analogy theory.1

Explain consolidation in detail.

Asaturated clay layer of 4 m thickness takes 2 years for 50% primary consolidation when drained on both sides. Its coefficient of volume change m = 1.5 x 10-3 m2/kN. Determine the coefficient of v consolidation and coefficient of permeability. Assume γ = 10 kN/m3 w

Explain tri-axial test with neat sketch.