Study on nonlinear dynamics of non-isothermal flow in broken rock

The special physical environment with the high groundstress, high ground temperature, high karst hydraulic pressure, and intensemining disturbance`` in deep broken rocks, determines that their mechanicsystem is a complicated nonlinear dynamical one. Given a relative stablestress field, the flow in broken rock can be considered as a non-isothermalone, and the dynamical mechanism on the instability of non-isothermal flowin broken rock is analyzed by the theory of bifurcation and catastrophe ofnonlinear science.(1) According to the energy equations of the fluid and the solid, the energyconstitutive equation on non-isothermal flow in the broken rock isdeveloped, and combining with the continuity equation, kinetic equation andthe state equation of the flow, the one-dimensional nonlinear dynamicalequations of non-isothermal flow in broken rock are established.(2) Using these equations and boundary conditions, the dimensionless steadystates of the flow system are obtained by using Mathcad software. It isindicated that the obtaining of the steady states for the non-isothermalflow system is much more difficult than that for the isothermal flow systemand there are analytical solutions of steady states in isothermal flowsystem, while for the non-isothermal flow system, its analytical solutionsof steady states can not be obtained.(3) The branch figure of the steady states of flow velocity for thenon-isothermal flow system is drawn by the numerical analysis and comparedwith the isothermal flow, both the limited equilibrium point correspondingto the non-isothermal seepage field and the parameter value when thehysteresis appears all have an offset.(4) The stability of the steady states is analyzed by the iteration methodof successive lower relaxation, and the non-isothermal flow system has asaddle-node bifurcation and a fold catastrophe. But its catastrophe positionexist a rightward deviation, and the absolute value of the limited parameterb decreases a magnitude, so the catastrophe is apt to take place in thenon-isothermal flow dynamical system , namely, even if the breakingphenomenon is not very serious, the fold catastrophe may take place possiblyin the non-isothermal flow system.