Trong những chương trước, các mối quan hệ của các dòng chảy của nước ngầm và áp lực các chất lỏng, hoặc người đứng đầu nước ngầm, đã được thảo luận, trong hình thức của pháp luật Darcy. Về nguyên tắc dòng chảy có thể được xác định nếu phân phối của áp lực hoặc đầu được biết đến. Để dự đoán hoặc tính toán phân phối áp lực của pháp luật Darcy trong chính nó là không đủ. Một nguyên tắc thứ hai là cần thiết, được cung cấp bởi các nguyên tắc bảo toàn khối lượng. Nguyên tắc. | Chapter 8 GROUNDWATER FLOW In the previous chapters the relation of the flow of groundwater and the fluid pressure or the groundwater head has been discussed in the form of Darcy s law. In principle the flow can be determined if the distribution of the pressure or the head is known. In order to predict or calculate this pressure distribution Darcy s law in itself is insufficient. A second principle is needed which is provided by the principle of conservation of mass. This principle will be discussed in this chapter. Only the simplest cases will be considered assuming isotropic properties of the soil and complete saturation with a single homogeneous fluid fresh water . It is also assumed that the flow is steady which means that the flow is independent of time. Flow in a vertical plane Suppose that the flow is restricted to a vertical plane with a cartesian coordinate system of axes x and z. The z-axis is supposed to be in upward vertical direction or in other words gravity is supposed to act in negative z-direction. The two relevant components of Darcy s law now are q - fr dx qz - h- dz Conservation of mass now requires that no water can be lost or gained from a small element having dimensions dx and dz in the x z-plane see Figure . In the x-direction water flows through a vertical area of magnitude dy dz where dy is the thickness of the element perpendicular to the plane of flow. The difference between the outflow from the element on the right end side and the inflow into the element on the left end side is the discharge dx dy dz. dx In the z-direction water flows through a horizontal area of magnitude dx dy. The difference of the outflow through the upper surface and the inflow through the lower surface is dQz dx dy dz. dz y 49 Arnold Verruijt Soil Mechanics 8. GROUNDWATER FLOW 50 V C dz qx qx jxx dx dx Figure Continuity. The sum of these two quantities must be zero and this gives after division by dx dy dz 0. 8 2 The validity of this equation the .
