It is very useful to make clear the creep deformation phenomena of soft rocks. Because it is not only available to determine the support system after excavation, but also floor upheaval as well as destruction time by creep deformation could be estimated.
Therefore, the research on creep becomes much more important in the various fields of rock mechanics hereafter.
In this paper, in order to calculate creep deformation theoretically, Volterra's Integral Equation of 2nd kind is treated as follows.
(Equation in full paper)
In the research presented here the functional form of f(E,t,6') is assumed by intuition to be adopted to creep deformation- time curve. And the coefficients that are appeared in the equation will be determined by the experiment. Here, sandstone creep deformations were tested as examples.
Moreover, as the physical meanings of the coefficients are able to be estimated, it can be shown that this equation may have sufficient availability for calculation of creep deformation of rocks.
To estimate the creep deformation of soft rocks, there are usually two methods. One1 is the use of mechanical models and the other2 is the application of exponential functions. But the former is deficient to express the whole process of creep deformation and the latter has the comparative big difference between measrerd deformations and calculated ones, too.
The study has been executed to estimate the creep deformation process of rocks by dealing with Volterra's integral equations of 2nd kind whose functional form of kernel is conjectured by using that the curve between time and creep deformation has an inflection point. And by the experimental measurement using sandstone samples, the coefficients of kernel function are determined and at once their physical meanings are also investigated.
The integral equation of Volterra's 2nd type is shown by equation (1).
(Equation in full paper)
where, x(t) is an unknown function, g(t) is a known one and K(t, t') is a function called kernel which will be determined by the conditions of phenomenon concerned.
In the case treated here, as the functional form of kernel is unknown, the dealing procedure of the equation is much different. from ordinary solving methods of this equation. Therefore thinking of creep deformation phenomena and denoting E and t as strain and time respectively, following relations will be established, i.e.
(Equation in full paper)
Rock samples furnished to the experiments were taken from the sandstone strata of Wakanabe coal measures in Ishikari coal field in Hokkaido district.
As for the samples, usually they were taken from the boring cores which were drilled perpendicular to the bedding plane of strata. And they have, of course, the cylindrical forms whose diameter and length are 3 cm and 6 cm respectively. The circumference walls of the cylindrical samples were polished by the grindstone until the tolerance limit of diameter distortion attained to less than 0.05 mm. And the top and bottom surfaces of them were also ground by fine carborundum powder until the bias of the angles
