In this chapter, the ultimate limit state of a system is considered by means of limit equilibrium, plasticity slip line method, limit analysis and DLO methods. The basic plasticity formulation for the slip line method is given, which is applied to some classical geotechnical problems. Following this, the three major geotechnical problems are unified under the extremum principle by the plasticity formulation. There is also discussion on the basic formulation for the DLO method and the limitations of the method or the commercial program.
Keywords: Axi-symmetric, Bearing capacity, DLO, Extremum, Lateral earth pressure, Limit equilibrium, Limit analysis, Plasticity, Slip line, Slope stability.