Variance of mechanical precompression stress in graphic estimations using the Casagrande method and derived mathematical models

Mechanical precompression stress is a yardstick for the strength and compressibility of soils. The default method for the estimation of precompression stress is the graphic method according to Casagrande. It involves a subjective perception by the engineer who not only determines the point of the highest curvature visually, but decides also which points are to be used for generating the virgin compression line. In order to avoid such subjective approaches, mathematical models for the determination of precompression stress have been developed emanating from the Casagrande method. These models estimate the smallest radius of the curvature based on the minimum of the second numerical derivative. The paper has the aim to quantify the variance of subjectivity implied by the person executing the graphic method, the variance of different model approaches and the accuracy of the latter in handling the graphic values. Additionally we wanted to investigate the effect of different parameters on the ordinate of the diagram and the effect of the first load step on the precompression stress. To understand these relationships, stress/bulk density functions and stress/void ratio functions measured on 13 sites were analysed by five experienced but independent engineers and by use of three mathematical models. an errors of precompression stress estimations by the different testers were 0.01–0.12 and by the models 0.10–0.87 on a logarithmic scale. Expressed in kPa, increasing mean errors were observed with rising precompression stress, due to delogarithmization. For the graphical determination, they reached approx. 10–20 kPa at precompression stress levels of 60–150 kPa in typical subsoils; this means 15% on average. The handling of graphically obtained values by help of mathematical models disclosed considerable deviations between them. In the logarithmic variant, the mean absolute errors varied from 0.09 (9 kPa) to 0.40 (30 kPa) and the determination coefficients from 0.71 to 0.96. Another influence on the level of precompression stress has been observed when different variables were plotted on the ordinate of the graph. The graphically obtained values of precompression stress and those shown in the dry bulk density graph exceed the values calculated on the basis of the void ratio by the factor 1.2–1.5. Furthermore, it can be stated that in soil-compression tests with an initial load of 25 kPa higher precompression stress values were obtained than with lower initial loads (5 kPa), if the precompression values were low.