School of Engineering and Technology, (SET)

Geotechnical engineers are increasingly challenged to solve geotechnical problems using analytical solutions, numerical methods, and experimental methods. This course provides sound fundamental knowledge of solid mechanics and geomechanics, and introduces effective analytical solutions for practical problems.

This includes the theory of solid mechanics (such as stress and strain, linear elasticity), elastostatic plane problems, plasticity of soil (development of simple framework for soil plasticity and simple computer program), cavity expansion problems and applications of analytical solutions in tunnelling problems.

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I.                Mathematical Foundations
1.      Tensors & continuum mechanics
2.      Scalar & vectors
3.      Indicial notation
4.      Algebra of Cartesian tensors
5.      Matrices & determinants
6.      Linear equations & eigenvalue problems

II.              Stress & Strain Tensors
1.      Force distribution & stresses
2.      Stress vector & equations of motion
3.      Stress tensor
4.      Stationary shear stresses
5.      Octahedral shear stress & stress deviator
6.      Mohr’s circle for a plane tensor
7.      Strain tensor
8.      The so-called compatibility condition
9.      Cylindrical & spherical coordinates

III.            Linear Elasticity
1.      Strain energy function
2.      Orthotropic & isotropic elastic solids
3.      Solution schemes
4.      Basic unknowns: displacement
5.      Basic unknowns: stress/strain

IV.           Elastostatic Plane Problems
1.      Plane problems of isotropic elastic materials
2.      Airy function for isotropic plane problem
3.      Isotropic elastic plane problems in cylindrical coordinates
4.      2D problems in rectangular coordinates
5.      Displacement for a give biharmonic function
6.      Examples of infinite plane problems
7.      Solution of problems in elasticity by potentials: strain potential, Galerkin vector, Love’s strain function, Kelvin’s problem, Boussinesq’s problem, Cerruti’s problem, Neuber-Papkovich representation

V.             Plasticity
1.      Mathematical theory of plasticity
2.      A critical state model to interpret soil behaviour
3.      General stress-strain relation in CSM: application of CSM to Bangkok clay
4.      Behaviour of sand
5.      Simple methods for triaxial compression of sand: Yu, Li & Dafalias, Zienkiewicz et al.’ models

VI.           Cavity Expansion Problems
1.      Elastic cylinder
2.      Elastic-perfectly plastic cylinder

VII.         Analytical Solutions & Applications
1.      Porewater pressure, lining stress in drained tunnel
2.      Seepage force in drained tunnel
3.      Seismic-induced ovaling of circular tunnel lining
4.      Steady-state groundwater inflow into drained tunnel
5.      Circular opening in elastic-brittle-plastic rock
6.      Tunneling-induced ground movements in clays
Lecture Notes
Karasudhi, P. (1991), Foundations of Solid Mechanics, Kluwer Academic Publishers.

Chen, W.F., Mizuno, E. (1990), Nonlinear Analysis in Soil Mechanics, Elsevier.

Yu, H.S. (2000), Cavity Expansion Methods in Geomechanics, Kluwer Academic Publishers.

Davis, R.O., Selvadurai, A.P.S. (1996), Elasticity and Geomechanics, Cambridge University Press.

Budhu, M. (2000), Soil Mechanics & Foundations, John Wiley & Sons.
International Journal of Geomechanics, ASCE, USA
Canadian Geotechnical Journal, Canadian Geotechnical Society, Canada
Tunnelling and Underground Space Technology, Elsevier
The final grade will be computed according to the following weight distribution:

Mid-Semester Exam (20%)
Final Exam (50%)
Assignments (30%)

Open book exam.
SECTION NAME
A Dr. Avirut Puttiwongrak