tailieunhanh - SOIL MECHANICS - CHAPTER 33

Nhấn mạnh có thể có trong đất được giới hạn bởi các tiêu chí thất bại Mohr-Coulomb. Sau Rankine (1857), tình trạng này sẽ được sử dụng trong chương này để xác định các giá trị hạn chế đối với những căng thẳng nằm ngang, và sự căng thẳng hệ số K. bên Vì lý do đơn giản cân nhắc sẽ được giới hạn trong đất khô đầu tiên. Sự ảnh hưởng của nước lỗ rỗng sẽ được điều tra sau này. . | Chapter 33 RANKINE The possible stresses in a soil are limited by the Mohr-Coulomb failure criterion. Following Rankine 1857 this condition will be used in this chapter to determine limiting values for the horizontal stresses and for the lateral stress coefficient K. For reasons of simplicity the considerations will be restricted to dry soils at first. The influence of pore water will be investigated later. Mohr-Coulomb As seen before see Chapter 20 the stress states in a soil can be limited with a good approximation by the Mohr-Coulomb failure criterion. This Figure Mohr-Coulomb. criterion is that the shear stresses on any plane are limited by the condition T Tf c ơ tan Ộ where c is the cohesion and Ộ is the angle of internal friction. The criterion can be illustrated using Mohr s circle see Figure . so that ơ xx ơzz If it is assumed that ơzz and ơxx are principal stresses and that ơzz is known by the weight of the load and the soil it follows that the value of the horizontal stress ơxx can not be smaller than indicated by the small circle and not larger than defined by the large circle. The ratio between the minor and the major principal stress can be determined by noting see Figure that the radius of Mohr s circle is 2 ơi Ơ3 and that the location of the center is at a distance 2 ơi ơ3 from the origin. It follows that for a circle touching the envelope sin Ộ 2 ơi Ơ3 1 ơi ơ3 c cot Ộ 181 Arnold Verruijt Soil Mechanics 33. RANKINE 182 1 sin ộ cos ộ ------ --7 Ơ1 2 c --. 1 sin ộ 1 sin ộ This relation has been derived before in Chapter 20. The two coefficients in this equation can be related by noting that cos ộ a 1 sin2 ộ ạ 1 sin ộ 1 sin ộ 1 sin ộ 1 sin ộ 1 sin ộ 1 sin ộ 1 sin ộ This means that equation can be written as Figure Ratio of principal stresses. where Ơ3 Kaơi 2cy K 1 sin ộ Ka -------- ---. 1 sin ộ Apart from the constant term 2cựKa there appears to be a given ratio of the minor and the major principal .