tailieunhanh - SOIL MECHANICS - CHAPTER 6

Darcy LUẬT 6,1 hydrostatics Như đã đề cập trong chương trước, phân phối căng thẳng trong nước ngầm ở phần còn lại sau các quy tắc của hydrostatics. Chính xác hơn, nó có thể được tuyên bố rằng trong trường hợp không có dòng chảy nhấn mạnh trong chất lỏng trong môi trường xốp phải đáp ứng các phương trình cân bằng trong các hình thức ∂ p = 0, ∂ x ∂ p = 0, ∂ y ∂ p + γw = 0 . ∂ z | Chapter 6 DARCY S LAW Hydrostatics As already mentioned in earlier chapters the stress distribution in groundwater at rest follows the rules of hydrostatics. More precise it can be stated that in the absence of flow the stresses in the fluid in a porous medium must satisfy the equations of equilibrium in the form dp dx dp dy dp dz 0 0 Yw 0- x Figure Equilibrium of water. Here it has been assumed that the z-axis is pointing in vertically upward. The quantity Yw is the volumetric weight of the water for which Yw 10 kN m3. It has further been assumed that there are no shear stresses in the water. This is usually a very good approximation. Water is a viscous fluid and shear stresses may occur in it but only when the fluid is moving and it has been assumed that the water is at rest. Furthermore even when the fluid is moving the shear stresses are very small compared to the normal stress the fluid pressure. The first two equations in mean that the pressure in the fluid can not change in horizontal direction. This is a consequence of horizontal equilibrium of a fluid element see Figure . Equilibrium in vertical direction requires that the difference of the fluid pressures at the top and bottom of a small element balances the weight of the fluid in the element . Ap YwAz. Here Az represents the height of the element. By passing into the limit Az 0 the third equation of the system follows. The value of the volumetric weight Yw in the last of eqs. need not be constant for the equations to be valid. If the volumetric weight is variable the equations are still valid. Such a variable density may be the result of variable salt contents in the water or variable temperatures. It may even be that the density is discontinuous for instance in case of two different fluids separated by a sharp interface. This may happen for oil and water or fresh water and salt water. Even in those cases the equations correctly express equilibrium of the fluid. In soil