Experimental Test of Least-Squares Strain Gage Calculation Using Twinned Calcite
The least-squares strain is computed from calcite twin lamellae in cylinders of Indiana limestone experimentally shortened from 0 to 8.5 percent at 1.0-kb confining pressure, room temperature, and a constant strain rate of 10 −4 /sec. The best fit to the experimental results is obtained by using the inner width of the thick twins and setting the ratio between thin twin width and thick twin width at 0.5. The sum of deviations from the experimental axial strains for the best fitting strain magnitudes is only 0.52 strain in percent. The average accuracy is to within 27 percent of the experimental value. The average angle difference between the experimental and computed principal axes is 6.5°. The calculation technique is considered to be confirmed by these results. Results of the Conel (1962) technique and the version of it modified by Spang and Chappie (1969) are compared to the experimental results. Both techniques produce nearly the same agreement between principal axis directions as the least-squares method does. However, they underestimate the strain magnitudes by factors of 3.6 and 3.0, respectively. The principal axes produced by a numerical dynamic analysis of the data are essentially parallel to the computed principal strain axes.