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 引用本文: 丁洲祥. 一维渗透力与浮力[J]. 力学学报, 2017, 49(5): 1154-1162.
Ding Zhouxiang. ONE-DIMENSIONAL SEEPAGE FORCE AND BUOYANCY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1154-1162.
 Citation: Ding Zhouxiang. ONE-DIMENSIONAL SEEPAGE FORCE AND BUOYANCY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1154-1162.

## ONE-DIMENSIONAL SEEPAGE FORCE AND BUOYANCY

• 摘要: 为简化分析，针对一维渗流问题，研究提出了土力学中渗透力和浮力的两种推导方法，作为传统的宏观尺度孔隙水隔离体法的有益补充.弹性力学平衡微分方程、土力学Terzaghi有效应力方程和流体力学简化Bernoulli方程构成本文分析渗透力和浮力的3个基本方程.在基本方程基础上，容易推导出相应的骨架和孔隙水两种隔离体的平衡微分方程，从而在静力平衡范畴内揭示渗透力和浮力的内涵.单位体积饱和土体的渗透力，源于总水头压力的梯度，而浮力则源于位置水头压力在竖向的梯度，这两者统一于骨架或孔隙水的平衡微分方程.实际工程关注的有效应力计算问题，一般可以直接应用3个基本方程来确定；只有在简化条件下可按渗透力和浮力计算土体中有效应力分布规律.还讨论了若干研究热点问题，重点探讨了当前一种渗透力新定义j=wi在形式上的合理性以及在实际应用中可能存在的风险，并验证了一维渗透力的一种经典精细化表述结果中考虑渗流速度时间导数的严谨性.在土力学渗透力和浮力问题研究中应重视和正确应用Terzaghi有效应力方程.

Abstract: For the sake of simplicity, two methods of deriving seepage force and buoyancy associated with one-dimensional fluid flow in saturated soil were developed to give a uselful supplement to conventional macro-scale method of isolated pore fluid. To study the seepage force and buoyancy, three fundamental governing equations, namely, equilibrium differential equation in elasticity, Terzaghi's effective stress equation and simplified Bernoulli's equation in fluid mechanics, are utilized for the derivation of seepage force and buoyancy. Based on the fundamental governing equations, it is readily to derive the differential equations of equilibrium corresponding to the isolated soil skeleton and the isolated pore fluid, and hence, the connotation and nature of seepage force and buoyancy can be disclosed. The seepage force per unit volume of saturated soil arises from the gradient of fluid pressure in terms of total head. The buoyancy originates in the vertical component of gradient of fluid pressure in terms of position head. Both the seepage force and the buoyancy can be embodied in equilibirium differential equation with respect to skeleton or pore fluid of satured soil. In geotechnical practice, the three governing equations can be directly applied to the calculation of effective stress. Only in some simplified cases, the distribution of effective stress can be obtained using the seepage force and buoyancy. Additionally, some hot topics are also discussed in this study, and emphasis shall be put on the discussion on the rationality and the potential application risk of the new definition of seepage force, i.e., j=wi. The strictness of one classic formulation of seepage force in history was thoroughly validated when considering the derivative of seepage velocity with respect to time. It is noteworthy that in the study of seepage force and buoyance from the perspective of soil mechanics, the Terzaghi's effective stress equation shall be reasonably implemented with practical significance.

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