The surface settlement during the tunneling process is becoming increasingly difficult to forecast as its surroundings become more and more erratic, and the maximal surface settlement raises risks posed suddenly by various uncertain factors. This paper proposes a novel approach to prediction of the surface settlement and analyzes the stability of tunnel construction. The dimensionless analysis and Buckingham’s π-theorem are adopted for this purpose, and some useful dimensionless quantities are found, which can be used to determine the surface settlement’s main properties. In this manner, the paper offers new ways of predicting surface settlement in various cases, and it sheds a new light on the tunnel’s design and safety monitoring.

Nanoparticles play an important role in nanofluids to enhance thermal conduction, and can be easily controlled by a magnetic force, so it can be widely used in nano/micro devices. This paper gives two mathematical models to describe the nanofluid flow, one is an approximate continuum model, in which the homotopy matching is used to deal the discontinuity between the fluid and nanoparticles, and the other is to use the conservation laws in a fractal space. The models give new physical insight into the particle fluid-flow.