Abstract: The natural element method (NEM) is a newly coming meshless method, of which the shape function possesses both the characteristics of the meshless methods and the advantages of traditional finite element method, so it’s a most promising numerical method for geotechnical problems. The basic theory and the characteristics of NEM are addressed; and then some detailed application examples in geotechnical engineering are discussed. The Goodman element is introduced into the NEM to model the discontinuity; the general principle and detailed implementation are identical to those in FEM. How to model the infinite or semi-infinite problems using NEM, is discussed too. The coupling of NEM and FEM or IEM is seamless, because the NEM shape function satisfies the property of linear interpolation between adjacent boundary nodes. So the solving ability is enhanced by the coupling. Numerical examples show the rationality of scheme presented above.

Key words: meshless method, natural element method, discontinuity, Goodman elements, infinite elements