Find a real root of the equation x3- cosx = 0 using the Newton-Raphson method correct to three decimal places starting from x = 1.0
[3 marks]Explain Bisection method with suitable example.
[4 marks]Solve the following system by Gauss Jacobi method. 20x+y-2z = 17, 3x+20y-z = -18 and 2x-3y+20z = 25
[7 marks]Explain False Position method with suitable example.
[3 marks]Enlist the types of boundary conditions. Explain Disichlet conditions.
[4 marks]Use fourth order Runge-Kutta method to find y(0.2) with h=0.1, given that 10 dy = x2+y2, y(0)=1. dx
[7 marks]Use second order Runge-Kutta method of solve initial value problem y’= -y, where y(0)=1 for x = 0.2 and x = 0.412
[7 marks]Differentiate between discrete modeling versus continuum modeling.
[3 marks]Briefly explain Drucker-Prager theory.
[4 marks]Explain One-dimensional (1D) plasticity theory.
[7 marks]Briefly explain continuum modeling.
[3 marks]Briefly explain discrete element method (DEM).
[4 marks]Explain Mohr-Coulomb theory.
[7 marks]Briefly explain soil constitutive model.
[3 marks]Explain the flow through porous media.
[4 marks]Explain earth pressure coefficients based upon Lade-Duncan criterion.
[7 marks]Differentiate between elastic models and plastic models.
[3 marks]Give the importance of boundary value problems in geotechnical engineering.
[4 marks]What is classical plasticity? Explain general framework of classical plasticity.
[7 marks]Define following terms: 1. Immediate Settlement 2. Primary Consolidation 3. Secondary Consolidation
[3 marks]Asaturated clay layer of 5 m thickness takes 1.5 years for 50% primary consolidation when drained on both sides. Its coefficient of volume change m is 1.5 x 10-3 m2/kN. Determine the coefficient of consolidation (m2/yr) v and coefficient of permeability (m/year). Assume γ = 10 kN/m3 w
[4 marks]Explain Tri-axial Test. OR1
[7 marks]Enlist the assumptions made in Terzaghi’s theory of 1-dimensional consolidation.
[3 marks]Spring analogy to explain consolidation theory.
[4 marks]Alaboratory specimen of clay 30 mm thick drained at top as well as bottom, has taken 400 second to reach 40% consolidation. When the pressure increased from 80 kN/m2 to 160 kN/m2. The initial void ratio was 0.85 and the final void ratio due to increasing of the load was 0.50. Determine coefficient of permeability.
[7 marks]