### Documentation and verification of STRES3D, Version 4.0; Yucca Mountain Site Characterization Project [report]

M.I. Asgian, C.M. St. John, M.P. Hardy, R.R. Goodrich
1991 unpublished
STRES3D is a thermomechanical analysis code for predicting transient temperatures, stresses and displacements in an infinite and semi-infinite, conducting, homogeneous, elastic medium. The heat generated at the sources can be constant or decay exponentially with time. Superposition is used to integrate the et fect of heat sources distributed in space and time to simulate the thermomechanical effect of placement of heat generating nuclear waste cannisters in an underground repository. Heat
more » ... ository. Heat sources can be defined by point, lines or plates with numerical integration of the kernal point source solution used to develop the line and plate sources. STRES3D is programmed using FORTRAN77 and is suitable for use on micro or larger computer systems. This report was prepared under WBS Element 124232. Numerical Integration: Line and ?late Heat Sources The solutions for line and plate heat sources are computed in STRES3D by numerical integration of the solution for a point heat source. The numerical integration technique utilized in the computations is the Gauss-Legendre quadrature (Carnahan, et al., 1969) . With this integration procedure, the integration interval is subdivided into unequally spaced integration points, none of which are located at the ends of the integration interval. 3"he function to be integrated is evaluated ,_ at each of the integration points and is assigned a weight of one or less. The integral of the function is proportional to the sum of the products of the weights and the values of the functic, ns at the integration points: This integration would be appropriate for a line source extending from z = a to z -b. For a plate source the necessary double integral becomes: The values of the weighting functions, w" depend on n, the order of integration. For second order integration, i.e., for n = 2, the three weighting factors are .5556, .8889, and .5556. The corresponding locations of the integration points (Gauss points) for second order integration are at points at [+. 3873 * (integration interval) + midpoint of intc",Trationinterval] and at the midpoint of the integration interval. The Gauss-Legendre quadrature gives the exact solution for functions which are polynomials of order (2n+ l) or less, where n is the order of integration. The error, thus, is of the order O(A2"), where A is the point spacing. The functions which describe the temperatures, stresses, and displacements due to point heat sources are not polynomials. As recorded in Section 1.3.1, the functions consist of products .amdsums of exponential functions, error functions, logarithmic functions, polynomials, and inverse trigonometric functions. Despite this complexity, they may be approximated piecewise as polynomials. Hence, the temperatures, stresses, and displacements due to a line heat source can be found from the weighted values of the point solutions at integration points along the line. The locations of the points and the weights assigned to the point solutions are those prescribed by the Gauss-Legendre procedure. Similarly, the functions which describe the perturbations due to an areal heat source can be found from an evaluation of the point source functions at prescribed points over the surface of the source. Thus, the basic routines for computing the heat flow, stresses, and deformations are identical for point, line, and areal sources. - Application and Assumptions ,_ Application of the code to a problem implies accepting a number of approximations and simplifications. The more important of these are: • the rock mass is continuous, homogeneous and linearly elastic, and has properties that are stress, temperature, and time independent; 1-15 i