For the first patern, elastic dynamics is adopted to study the steady state rolling contact, elastic dynamics incorporating with rigid dynamics is adopted to study the non-steady state. For the steady state, the analytical solution is obtained, and for the non-steady state, the variational formulation to solve the problem numerically is derived For the later patern, the function type friction coefficient is introduced. On the basis of the quasi-stastic theories of constant friction coefficients, both the exact theory and the simplified theory of the function type friction coefficient are established, the computer programms for both the theories are also made out. Using the function type friction coefficient, Shen-Hedrick-Elkins theory's application range is extended to large creepage .

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Then the weak formulation of the control equations considering the contact constraint conditions has been developed. Combined the Lagrange multiplier and penalty function methods, the augmented Lagrangian method is used to treat the contact constraint and solved the non-linear and non-smooth problems of the mechanical response perfectly. A finite element model has been applied for the test project of the reinforced slope and to study the mechanism of the interaction of the soil and reinforced material.

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It analyses the characterization of typical type curve and the influential factor of well-test curve ,which includes non-dimensional offsetting, non-dimensional length of horizontal welk equivalency pressure point, interporosity flow coefficient, storativity ratio and the boundary condition.

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