Use of the Lognormal Distribution for Processing the Results of Mechanical Testing of Soils
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SOIL MECHANICS USE OF THE LOGNORMAL DISTRIBUTION FOR PROCESSING THE RESULTS OF MECHANICAL TESTING OF SOILS
UDC 624.131 V. I. Sheinin Gersevanov Research Institute of Bases and Underground Structures, Research Centre for Construction JSC, Moscow, Russia, *Corresponding author Email: [email protected].
The possibility of using the methods developed in modern applied statistics for determining the lower confidence limit for the mathematical expectation of lognormal experimental values of a mechanical characteristic of soil, i.e. its 'calculated value', is studied. Practical considerations are given regarding the relative benefit of using the lognormal distribution in data processing as opposed to the normal distribution generally assumed for test results, especially with a small number of tests and real coefficients of variation.
A generally accepted and recommended practice in the statistical analysis of the results of testing the mechanical properties of soils is based on the hypothesis of the normal probability distribution [1]. It is taken for granted that such a representation reflects a multiplicity of factors influencing each individual result, but in reality its advantage lies only in the relative simplicity of the procedure used for processing and obtaining the calculated values as opposed to other, physically more likely distribution laws. The shortcomings of approximating a real probability distribution by a Gaussian law − assumption of nonzero probability of physically nonexistent (negative) values, equiprobability of negative and positive deviations from center, and too rapid diminishment of the frequency of these deviations away from center − are ordinarily not taken into account, and whereas in [1] the possibility of using a lognormal distribution is at least permitted 'for larger variability of the characteristics', in handbooks on processing of test results obtained for materials such as concrete and hard rock [2, 3] the possibility of using distributions other than the normal distribution is not mentioned at all. At the same time, in mechanical engineering [4, 5] it is recommended that other continuous distributions, first and foremost, the lognormal distribution, be used. Specifically, "satisfactory correspondence of static and dynamic tests for plastic and mixed fracture as well as long-time static and fatigue tests to a lognormal distribution" is noted in [4]. The lognormal distribution is widely used in earth sciences [6, 7, and others]. In [8] it is stated: "It is entirely likely that in the future the lognormal distribution will be one of the most widely used distributions in applied statistics." This is determined also by the fact that the characteristics of natural or large-scale technological processes have obviously large (>0.3) relative variability metrics, which on the use of the Gaussian distribution can give results at variance with engineering experience. The use of non-Gaussian distributions, including lognormal, promotes the development of accessible computer programs that make i
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