tailieunhanh - SOIL MECHANICS - CHAPTER 34

Từ lâu trước khi các phân tích của Rankine Coulomb nhà khoa học Pháp đã trình bày một lý thuyết về hạn chế trạng thái căng thẳng trong đất (năm 1776), mà vẫn còn có giá trị lớn. Lý thuyết này cho phép xác định những căng thẳng trên một cấu trúc giữ lại cho các trường hợp áp lực đất chủ động và thụ động. Phương pháp này dựa trên giả định rằng đất không cùng máy bay trượt thẳng | Chapter 34 COULOMB Long before the analysis of Rankine the French scientist Coulomb presented a theory on limiting states of stress in soils in 1776 which is still of great value. The theory enables to determine the stresses on a retaining structure for the cases of active and passive earth pressure. The method is based upon the assumption that the soil fails along straight slip planes. Active earth pressure For the active case a retreating wall the procedure is illustrated in Figure . It is assumed that in case of a displacement of the wall towards the left a triangular wedge of soil will slide down along a straight slip plane. Figure Active earth pressure. The angle of the slope with the vertical direction is denoted by Ớ. It is also assumed that at the moment of sliding the weight of the soil wedge is just in equilibrium with the forces on the slip surface and the forces on the wall. For reasons of simplicity it is assumed at least initially that the force between the soil and the wall Q is directed normal to the surface of the wall . shear stresses along the wall are initially neglected. In later chapters such shear stresses will be taken into account as well. The purpose of the analysis is to determine the magnitude of the force Q. The principle of Coulomb s method is that it is stated that the wall must be capable of withstanding the force Q for all possible slip planes. Therefore the slip plane that leads to the largest value of Q is to be determined. The various slip planes are characterized by the angle 3 and this angle will be determined such that the maximum value of Q is obtained. The starting point of the analysis is the weight of the soil wedge W per unit width perpendicular to the plane shown in the figure W 2yh2 tan 3. This weight must be balanced by the horizontal force Q horizontal because the wall has been assumed to be perfectly smooth and the forces N and T on the slip plane. The direction of the shear force T is .