Limit analysis of supporting pressure in tunnels with regard to surface settlement

The proliferation of Hoek-Brown nonlinear failure criterion and upper bound theorem makes it possible to evaluate the stability of circular tunnels with an original curved collapsing mechanism. The arch effect of shallow circle tunnel is not taken into consideration so that the mechanical characteristics can be easily described. Based on the mechanism, the upper bound solution of supporting pressure of tunnels under the condition of surface settlements and overloads on the ground surface is derived. The objective function is formed from virtual work equations under the variational principle, and solutions are presented by the optimum theory. Comparisons with previous works are made. The numerical results of the present method show great agreement with those of existing ones. With regard to the surface settlement and overloads, the influence of different rock parameters on the collapsing shape is analyzed.

Numerical study of vortex breaker optimization in a first stage oxygen tank

One of the crucial factors affecting the carrying capacity of the cryogenic liquid launch vehicle is the effective volume of the tank.Theoretical and experimental investigations on vortex breaker mechanisms have proposed promising schemes applied in the oxygen tank of the liquid-propellant launch vehicle to ensure the normal operation of the engine.In this paper,the liquid surface profile functions of the laminar core when the vortex generates were derived based on the Rankine vortex model.The dimensionless residual volume V/d3 and the Froude number were applied to compare the theoretical prediction of critical height with the actual simulation data of liquid oxygen.This comparison method can improve the model’s accuracy.The efficiency of different basic shapes of vortex breakers was tested by conducting CFD modelling on a non-vertical outflow tank under a specific operating condition.Simulation results suggest negligible effects of heat transfer and surface tension.A circular plate is considered the optimal vortex breaker shape in traditional vertical outflow tanks,while a higher optimize efficiency was discovered in the half baffle basic shape in a non-vertical outflow tank by comparing the dimensionless residual volume and flow coefficient.A 34.26%reduction in flow resistance of half baffle breaker can be reached when applying a twenty-degree outlet pipe chamfering setting compared to a zero-degree chamfer.Considering practical operating limitations,it is concluded that a vortex breaker mechanism in a half baffle basic shape with a radius of 2.5d and a height of 4/d is the optimal scheme,which is suitable for all types of tanks.Its optimization efficiency of the residual volume reduction is about 56.68%compared to a nobreaker installation case.Lastly,a general equation based on CFD simulation for predicting the residual volume under a certain outflow velocity was proposed:V=d3yaFr0:3,which trend is consistent with that of mathematical prediction V=d3yaFr1=3.This consistency proves the accuracy and applicability of optimization strategy in this paper.