Rocks, as well as optically sensitive and equivalent materials used to model them, can be divided into two types, according to the character of their deformation in time [i]. The first type includes rocks and materials for which under constant load the creep deformation tends to a definite finite limit; the second type includes rocks and materials for which in these conditions the creep deformation increases without limit.An Abelian kernel [2] is recommended for the analytical representation of the creep of rocks and materials in the Boltzmann--Volterra form. Kuznetsov [3] gives an exhaustive discussion of how to find the parameters of such a kernel from experimental data.If we are concerned withlong time intervals, an Abelian kernel represents unbounded creep, i.e., the second type of rocks and materials.The creep of rocks and materials of the first type is conveniently represented by means of the D-function of Rabotnov [4], for which a suitable analytical apparatus of transformations has been developed. In this connection the problem of determining the parameters of these functions from the experimental data arises.To solve this, we start with the usual form of the Boltzmann--Volterra relation,where o(t) and e(t) are the stress and strain at time t reckoned from the start of loading of the body; E, instantaneous modulus of elasticity; L(t --T), difference creep kernel; and I, some parameter.
According to [4], L depends on ~ and ~ and takes the form
) ~w~ (~, t --~) = (t --r)~ ~., (t L (t (2)
= r[(n+ t) (i + ~)][where the translator has used W to represent the Russian letter ~ in order to avoid confusion with E, the instantaneous modulus of elasticity].Processing the experimental data by means of Eq. (2) is a complicated problem [5], because it involves integral transformations of the experimental functions; moreover, the values obtained for the parameters do not have reasonable physical significance.If we consider the creep kernel in form (2), we must bear the following points in mind. I) Normalization of Rabotnov's function depends on 8, t lira !w~(~, t--r)dr = t2) The dimensions of B depends on a, being equal to [time] -(x+~)3) The values of a and 8 are negative for all real materials. Attempts to make this point clear have had the result that some authors place minus signs in front of ~ and B on the right-hand side of Eq. (2), whereas Rabotnov places plus signs.Thus the same quantities have been assigned different senses.4) The expression for the creep curve contains the quantity (~ + i), not ~ by itself. It is desirable that the creep kernel should contain this quantity, which can be determined A. A. Skochinskii Institute of Mining, Lyubertsy. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. i,