TANGENT-MODULI Sự khác biệt trong hành vi đất trong quá trình nén và chịu cắt cho thấy riêng biệt nhấn mạnh và biến dạng thành hai phần, mô tả nén, và cắt một mô tả. Điều này sẽ được trình bày trong chương này. Dilatancy sẽ được bỏ qua, ít nhất là ban đầu. | Chapter 13 TANGENT-MODULI The difference in soil behavior in compression and in shear suggests to separate the stresses and deformations into two parts one describing compression and another describing shear. This will be presented in this chapter. Dilatancy will be disregarded at least initially. Strain and stress The components of the displacement vector will be denoted by ux uy and uz. If these displacements are not constant throughout the field there will duy uy dy. . . . A J . ItAy . . . . . . Ay .. LUx Ax d uy A Ỉ . uy ax Ax u x Ax . x Figure Strains. be deformations or strains. In Figure the strains in the x y-plane are shown. The change of length of an element of original length Ax divided by that original length is the horizontal strain xx. This strain can be expressed into the displacement difference see Figure by xx duxỊdx. The change of length of an element of original length Ay divided by that original length is the vertical strain yy. Its definition in terms of the displacement is see Figure yy duy dy. Because ux can increase in y-direction and uy in x-direction the right angle in the lower left corner of the element may become somewhat smaller. One half of this decrease is denoted as the shear strain xy y xy 1 dux dy duy dx . Similar strains may occur in the other planes of course with similar definitions. 79 Arnold Verruijt Soil Mechanics 13. TANGENT-MODULI 80 In the general three dimensional case the definitions of the strain components are dux 1 dux duy ị e . 1 ị duz 1 ỡuz dux All derivatives duxỊdx duxỊdy etc. are assumed to be small compared to 1. Then the strains are also small compared to 1. Even in soils in which considerable deformations may occur this is usually valid at least as a first approximation. The volume of an elementary small block may increase if its length increases or it width increases or its height increases. The total volume strain is the sum of the strains in the three coordinate .
