First-Order Rate Equations in Geotechnical Engineering

Abstract

First-order rate equations model physical or chemical processes in which the rate of approach to an end condition is proportional to the departure from that condition. Relationships were defined and tested with geotechnical problems including the prediction of end values for consolidation and for settlement from limited data. Solutions were obtained by substituting trial end values to obtain linearity of a prescribed relationship. The method does not require a thorough understanding of the mechanisms involved, but only that they be consistent and asymptotic to an end value. The mandatory linear relationship cannot be obtained if these criteria are not met, for example, for linear elastic behavior. First-order rate equations are discontinuous and overlap at behavioral boundaries such as that between primary and secondary consolidation. They also suggest a separate stage involving the loss of structure during consolidation of a quick clay. Settlement predictions are in close agreement with data from a grain elevator and from the Kansai International Airport, Japan. Other applications include defining minimum void ratios in fine-grained soils and determining a zero-flow liquid limit value.