Effect of residual stresses on measurements by relief methods

Abstract

1. When the stresses in hard rocks are determined by the relief method (individual point measurements), the principal cause of the scatter of the results is residual stresses. The rms error of individual measurements characterizes the scatter. This value can be regarded as the residual stress level. 2. As the number of individual measurements increases the mean stress approaches the true value (\(\mathop {\lim }\limits_{n \to \infty } \bar \sigma _i = \sigma _{act} = const\)), the mean value of the residual stresses tends to zero (\(\mathop {\lim }\limits_{n \to \infty } \sigma _{i res} = 0\)), and the mean-square deviation of the individual measurements approaches a constant value characterizing the residual stress level (\(\mathop {\lim }\limits_{n \to \infty } S_{\sigma_i} = const\)) 3. The necessary number of measurements for stress determination by relief methods with a given degree of reliability and relative error depends on the ratio of level of residual stresses to that of the active loads (the residual stress induction coefficient K). The number of measurements must increase with this ratio. When K>1 the relative errors of the determination of σi, and the required number of measurements n, markedly increase.