Research on forecasting model of sandstone deformation rate during sine wave loading segment under the lag effect

Abstract

To reduce data variance caused by individual differences of different samples, a new experimental method is proposed by loading and unloading the axial forces with different frequencies and different waves of a certain load amplitude to the same rock sample without damaging it. Lag time segments are defined and fractionized into segments I and II. Criterions for segmentation, definitions of relevant parameters and empirical analysis are also offered afterwards. In the course of sinusoidal loading, the serious peak value dislocation of the displacement variation rate and the loading rate is defined as peak dislocation. Meanwhile, the definition of the apparent tangent modulus is put forward and the linear relation between it and the vertical force in the frequency of 0.1, 0.2, 0.5 Hz sinusoidal loading segment is confirmed to be ever-present on the basis of the test data. Then the calculating formula of the deformation rate in non-lag time is deduced. It is thus suggested that the deformation rate should be codetermined by the loading rate df/dt and instant load f(t), which well explains the peak dislocation of the time-variable curve peak value of dl/dt and deformation rate of df/dt. Finally the lag time derivation model is established and by comparing the calculated values with the measured ones, it is demonstrated that the above formula offers a better simulation of the sandstone deformation rate in the sinusoidal loading segment, with the load amplitude being 96 kN and the frequency ranging from 0.1 Hz to 0.5 Hz.