Characteristic functions of regional soils: convergence

Whether from the perspective of engineering application of establishing $N{\text{ - }}{v_{\text{s}}}$ relationship curve in a region or as an essential part of regional soil characteristic theory, the number of arrays required for constructing scientific $N{\text{ - }}{v_{\text{s}}}$ function is an important problem, but this issue has not been involved before. The stability and convergence of $N{\text{ - }}{v_{\text{s}}}$ characteristic functions under different sample numbers are studied by using the random analysis of measured data, and the array thresholds for constructing $N{\text{ - }}{v_{\text{s}}}$ characteristic functions with different precisions are proposed. The measured data come from 9 regions in four countries, and there are 11 working conditions in total. The results of random analysis show that the $N{\text{ - }}{v_{\text{s}}}$ characteristic function is stable and convergent with the increase of the number of samples. The research shows that if the $N{\text{ - }}{v_{\text{s}}}$ array exceeds 50, 100, 200 and 800 in a region, the $N{\text{ - }}{v_{\text{s}}}$ characteristic functions with coefficients of variation less than 0.2, 0.15, 0.10 and 0.05 can be obtained respectively.