Thermal stress in concrete blocks of dams with consideration of creep

Abstract

Various aspects of thermal stresses in concrete hydraulic structures have been investigated and reported by a number of authors [1][2][3][4], buc many problems of calculating thermal stresses in concrete masses still do not have a satisfactory solution.Consideration of creep of concrete is one such problem. A concrete mass during construction represents an inhomogeneous system whose mechanical and rheological characteristics are functions of coordinates. In such systems the Arutyunyan principle [5] for determining thermal stresses wi=h consideration of creep is inapplicable, and it is necessary =o solve =he initial equaEions of the theory of creep of concrete. The B. E. Vedeneev All-Union Scientific-Research Institute of Hydraulic Engineering (VNIIG) has developed a method for calculating thermal stresses (in an exact formulation in the sense of consideration of creep) in a concrete mass consisting of one block located on an elastico-creep foundation. A discussion follows.I. Computation of Thermal Stress in a Concrete Block Working Jointly with an Elastic Foundation in the Form of a Half-Strlp (Fig. I). This model of the foundation adequately describes the working of a block placed on a foundation consisting of an old block.In addition, it reflects with sufficient accuracy the condition of cons=rut=ion of =he mass on a fractured rock foundation [6, 7].We will make the substitution x -x,/L, then x will vaz> in the interval (--i, i). We will introduce also notations which will be used later .rm_.~h.L. U,=y/h. The temperature field of t:he mass is assumed co be expressed in the form Tr y, t)'=Zco(0Qr y) if=l, 2),where the index i = 1 pertains to the block and the index i = 2 to the foundation. By means of an appropriate linear combination of functions of the type of Eq. (i) we can describe the majority of real temperature fields in concrete masses. The inEegrodifferentlal equations for the creep-stress function have the form t &&fr (0 ~ 0~r i) (t. ~) d, =--='/) '~T c~; (t) (i = 1. 2), (2) (t)--J 'r where E~ i) = E (i) in the case of plane stress; E! i) = E(i)/(1-~(i)=), plane strain; c~ (i) -oE(i), plane stresses; a(xi) = ~(i)(1 + v(i)), plane strain; v(i) is Poisson's ratio (i ---Xl, ;). The stresses are expressed in terms of the function F(i) (t) by the equations , 7 Fig. i. Schematic of calculated region. I) Concrete block; 2) rock formation.