The two aspects of the research on the multi-scale problems in engineering of rock and concrete include:

1) To establish the strain gradient theory of rock and concrete which contains defects (voids), micro-cracks or crystal lattices; to study the phenomena of the localization of deformation which lead to the failure of the structure; to establish new fracture and fatigue theory of rock and concrete. The above research has significant applications in the investigations of the large-scale engineering projects such as tunnel, bedrock, tall building, dam and groyne.

2) In rock and concrete engineering, many problems such as the foundation of group pickets, group anchor, group scupper of decompression and well of oil extraction are multi-scale problems. To solve these problems using finite element method, a large number of degree of freedoms are required to guarantee the transition between the meshes with different density. Given the computational resources and methods available now, it is extremely difficult to solve the problems. Therefore the second aspect of this research is to construct new methods of assembling different domains to eliminate constraints in the transition region of the finite element mesh and to establish the theory of structural cell element for the applications in the large-scale computations of the problems in rock and concrete engineering.