Approximation Method for Evaluation of Strains and Forces in LTP Reinforcement of Embankments on Columns

This article presents a method of approximate finding of forces and strains resulting from the so-called membrane effect in the reinforcement of the transmission layer of embankments located on a soft soil improved by columns (rigid inclusions). The model task needed to determine the characteristic values in geosynthetic reinforcement supported on rigid columns was formulated. The reinforcement is treated as an isotropic membrane, in which the strains are determined using the formula for the length of the curve, i.e. it deviates from the assumptions of the small strain theory. Spatial problems are reduced to equivalent one-dimensional static tasks for analysis using the isotropic membrane theory. The closed form solution of this task exists only in the case of uniform load. For other types of loads, it is necessary to approximate the formula for the length of the curve occurring in the expression defining the strains in the membrane, e.g. using the Taylor series, and then solving the strongly non-linear equation in which the membrane tension force is unknown. The article presents the analysis of the effect of the length curve approximation with usage of the Taylor series on the accuracy of the results obtained. The presented analysis is very important from the point of view of standard engineering calculations needed to design the reinforcement of the transmission layer in the case of embankments located on soft soil reinforced with rigid inclusions.