tailieunhanh - SOIL MECHANICS - CHAPTER 10

Chương 10 FLOW NET 10,1 tiềm năng và chức năng dòng Hai chiều dòng chảy nước ngầm thông qua một đất đồng nhất thường có thể được mô tả khoảng một cách tương đối đơn giản bởi một mạng lưới dòng chảy, đó là một mạng lưới đường tiềm năng và các dòng suối. Các nguyên tắc sẽ được thảo luận một thời gian ngắn trong chương này. Tiềm năng nước ngầm, hoặc chỉ đơn giản là Φ, tiềm năng được định nghĩa như Φ = kh, (10,1) trong đó k là hệ số độ thấm (hoặc dẫn thủy lực), và h là. | Chapter 10 FLOW NET Potential and stream function Two dimensional groundwater flow through a homogeneous soil can often be described approximately in a relatively simple way by a flow net that is a net of potential lines and stream lines. The principles will be discussed briefly in this chapter. The groundwater potential or just simply the potential T is defined as T kh where k is the permeability coefficient or hydraulic conductivity and h is the groundwater head. It is assumed that the hydraulic conductivity k is a constant throughout the field. If this is not the case the concept of a potential can not be used. Darcy s law see can now be written as q - dx _ ỠT q - ã or using vector notation q -VT. In mathematical physics any quantity whose gradient is a vector field for example forces or velocities is often denoted as a potential. For that reason in groundwater theory T is also called the potential. In some publications the groundwater head h itself is sometimes called the potential but strictly speaking that is not correct even though the difference is merely the constant k. The equations indicate that no groundwater flow will flow in a direction in which the potential T is not changing. This means that in a figure with lines of constant potential these are denoted as potential lines the flow is everywhere perpendicular to these potential lines see Figure . The flow can also be described in terms of a stream function. This can best be introduced by noting that the flow must always satisfy the equation of continuity see . dw 0. dx dz 62 Arnold Verruijt Soil Mechanics 10. FLOW NET 63 This means that a function T must exist such that 1 T3 T2 2 T1 3 Figure Potential lines and Stream lines. qx - . dz z S-dx By the definition of the components of the specific discharge in this way as being derived from this function T the stream function the continuity equation is automatically satisfied as can be verified .