A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plast...A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.展开更多
In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience ...In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience to analyze the stability, which is unsafe in the project. To find a solution of the phreatic surface which is convenient to put into use and in accordance with the practice, the article, based on Boussinesq equation, infers analytic solutions suitable to the water level at different ratios and achieves an analytic solution equation through fitting curves. The correctness of the equation is also proved by the experiments of sand and sand-clay models and the inaccuracy of empirical generalization is analyzed quantitatively. The calculation results show that the inaccuracy through the method of experiential generalizing is so large that the designers should be awake to it.展开更多
Under barometric pressure, groundwater flow in well-aquifer systems is a kind of hydromechanical coupling problem. Applying the flux boundary conditions on borehole wall and water pressure equilibrium conditions insid...Under barometric pressure, groundwater flow in well-aquifer systems is a kind of hydromechanical coupling problem. Applying the flux boundary conditions on borehole wall and water pressure equilibrium conditions inside and outside the borehole wall under barometric pressure （BP）, an analytic solution to well-water level changes has been proposed in this paper. The formulation shows that the BP coefficients increase with time and tend to BP constant. The Change of BP coefficients over time depends only on the ratio of transmissivity （T） to the well radius squared （ r2, ） , and has nothing to do with the change in BP. The BP constant only relates to aquifer loading efficiency （B）, and has nothing to do with the aquifer transmissivity and well radius. The BP coefficients＇ change over time in the analytic formulation is consistent with the analysis of measured data from the Nanxi wells. Based on the BP coefficient changes over time, a parameter estimation method is suggested and discussed in its application to the estimation of the aquifer BP constant （or B） and transmissivity by using the Nanxi well data.展开更多
To realize the accurate control of water hammer in pipes by valve stroking, based on basic differential equations of water hammer subjected to initial and boundary conditions, the traveling solution of wave equations ...To realize the accurate control of water hammer in pipes by valve stroking, based on basic differential equations of water hammer subjected to initial and boundary conditions, the traveling solution of wave equations in finite region was applied to the linear water hammer problem. With the given velocity function at the valve and the introduction of curve integration independent of integral path, the exact analytic solution of dimensionless water hammer pressure was obtained in the course of valve closing. Based on the definition of eigen wave height, optimal eigen wave height and observation time, the control goal of water hammer pressure and the judgment rule of the optimal eigen wave height were determined, then the optimal velocity function in the calculated example was derived, which can reduce the water hammer pressure maximally. According to this function, a valve closing program was set, and the optimal control of water hammer could be realized.展开更多
An analytic approximation method known as the homotopy analysis method(HAM)is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large f...An analytic approximation method known as the homotopy analysis method(HAM)is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large floating structure(VLFS)on the surface of deep water.A convergent analytical series solution for the plate deflection is derived by choosing the optimal convergencecontrol parameter.Based on the analytical solution the efects of diferent parameters are considered.We find that the plate deflection becomes lower with an increasing Young’s modulus of the plate.The displacement tends to be flattened at the crest and be sharpened at the trough as the thickness of the plate increases,and the larger density of the plate also causes analogous results.Furthermore,it is shown that the hydroelastic response of the plate is greatly afected by the high-amplitude incident wave.The results obtained can help enrich our understanding of the nonlinear hydroelastic response of an ice sheet or a VLFS on the water surface.展开更多
A mathematical model for salt transport by a cylindrical root in an infinite extent of soil is derived and solved analytically by asymptotic matching of the inner and outer solutions. By asymptotic analysis it is show...A mathematical model for salt transport by a cylindrical root in an infinite extent of soil is derived and solved analytically by asymptotic matching of the inner and outer solutions. By asymptotic analysis it is shown that the salt solution uptake by a single cylindrical root in the absence of competition does not influence the overall salt concentration in the soil even when the soil moisture concentration is less than full saturation.展开更多
基金Project(50969007)supported by National Natural Science Foundation of ChinaProject(GJJ13753)supported by the Scientific and Technological Research Fund,Department of Education,Jiangxi Province,China
文摘A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.
文摘In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience to analyze the stability, which is unsafe in the project. To find a solution of the phreatic surface which is convenient to put into use and in accordance with the practice, the article, based on Boussinesq equation, infers analytic solutions suitable to the water level at different ratios and achieves an analytic solution equation through fitting curves. The correctness of the equation is also proved by the experiments of sand and sand-clay models and the inaccuracy of empirical generalization is analyzed quantitatively. The calculation results show that the inaccuracy through the method of experiential generalizing is so large that the designers should be awake to it.
基金supported by special funds for Public Welfare Scientific Research of Ministry of Science and Technology,PRC(200808055)Scientific Research Project of Education Department,Hebei Province(Z2009104),China
文摘Under barometric pressure, groundwater flow in well-aquifer systems is a kind of hydromechanical coupling problem. Applying the flux boundary conditions on borehole wall and water pressure equilibrium conditions inside and outside the borehole wall under barometric pressure （BP）, an analytic solution to well-water level changes has been proposed in this paper. The formulation shows that the BP coefficients increase with time and tend to BP constant. The Change of BP coefficients over time depends only on the ratio of transmissivity （T） to the well radius squared （ r2, ） , and has nothing to do with the change in BP. The BP constant only relates to aquifer loading efficiency （B）, and has nothing to do with the aquifer transmissivity and well radius. The BP coefficients＇ change over time in the analytic formulation is consistent with the analysis of measured data from the Nanxi wells. Based on the BP coefficient changes over time, a parameter estimation method is suggested and discussed in its application to the estimation of the aquifer BP constant （or B） and transmissivity by using the Nanxi well data.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 50478025 and 50506009) the 46th China Postdoctoral Science Foundation(Grant No.20090460912)
文摘To realize the accurate control of water hammer in pipes by valve stroking, based on basic differential equations of water hammer subjected to initial and boundary conditions, the traveling solution of wave equations in finite region was applied to the linear water hammer problem. With the given velocity function at the valve and the introduction of curve integration independent of integral path, the exact analytic solution of dimensionless water hammer pressure was obtained in the course of valve closing. Based on the definition of eigen wave height, optimal eigen wave height and observation time, the control goal of water hammer pressure and the judgment rule of the optimal eigen wave height were determined, then the optimal velocity function in the calculated example was derived, which can reduce the water hammer pressure maximally. According to this function, a valve closing program was set, and the optimal control of water hammer could be realized.
基金supported by the National Natural Science Foundation of China (Grant No. 11072140)
文摘An analytic approximation method known as the homotopy analysis method(HAM)is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large floating structure(VLFS)on the surface of deep water.A convergent analytical series solution for the plate deflection is derived by choosing the optimal convergencecontrol parameter.Based on the analytical solution the efects of diferent parameters are considered.We find that the plate deflection becomes lower with an increasing Young’s modulus of the plate.The displacement tends to be flattened at the crest and be sharpened at the trough as the thickness of the plate increases,and the larger density of the plate also causes analogous results.Furthermore,it is shown that the hydroelastic response of the plate is greatly afected by the high-amplitude incident wave.The results obtained can help enrich our understanding of the nonlinear hydroelastic response of an ice sheet or a VLFS on the water surface.
文摘A mathematical model for salt transport by a cylindrical root in an infinite extent of soil is derived and solved analytically by asymptotic matching of the inner and outer solutions. By asymptotic analysis it is shown that the salt solution uptake by a single cylindrical root in the absence of competition does not influence the overall salt concentration in the soil even when the soil moisture concentration is less than full saturation.
