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Fritz Jooste Administrator Posts: 6
8/24/2020
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This post gives an example of the accuracy of the Rubicon Online Tools' Layered Elastic Theory (LET) algorithm. This algorithm is coded in the C# language specifically for Rubicon Toolbox online tools and can handle any number of layers, although generally Rubicon Toolbox online tools restrict you to between 6 and 8 layers depending on the tool you are using.
In this post, we show how the Rubicon Toolbox Online Tools LET Algorithm compares with other well-established and proven algorithms. Specifically, we use the example on page 120 to 122 of Huang's book on Pavement Analysis and Design. Please note that the example provided here is from the First Edition of Huang's book.
The pavement structure used in Huang's analysis is given in the figure below. Note that Huang only provides Imperial units and thus there is a degree of rounding error in the conversion of thicknesses and stiffness values and - more importantly - in the conversion of stresses and strains between these two unit systems. Huang's results are reported only in Imperial units with one or two decimal rounding.
In Huang's example, a rather complex load configuration is assumed. The load configuration is given below, with evaluation positions numbered and indicated in red dots. For each of the four evaluation positions, stresses and strains are evaluated at the bottom of the asphalt layer (depth 151.9 mm) and at the top of the subgrade (457.02 mm).
In Huang's book, stresses, strains and deflections are provided at each evaluation position for the Kenlayer and ELSYM5 algorithms. Huang shows that Kenlayer's results are generally within 2% of those of the older, more established ELSYM5 algorithm.
In the table below, we compare the results obtained with Rubicon Toolbox's Stress-Strain calculator with those given by Huang for ELSYM5. Please note that results had to be converted from SI Units (which are used in Rubicon Toolbox), to Imperial Units. Some errors due to rounding can therefore be expected. We present the comparison of results in three tables: (a) Vertical Deflection; (b) Strains; and (c) Principal Stresses:
The "% Difference" column values were calculated using the ELSYM5 results as base value. Positions where the % difference is above 2% are highlighted in red. A discussion of these results follows below the three tables.
Table (a): Vertical Deflection
Table (b): Strains
Table (c): Principal Stresses
Discussion:
The three tables above shows a close agreement between the Rubicon Online Tools LET Algorithm and the results given by the ELSYM5 algorithm. In most cases, the differences are below 2%, similar to the comparison between Kenlayer and ELSYM5 reported by Huang.
In the case of strain comparisons, two locations (positions 1 and 3, top of the subgrade) have horizontal tensile strains that differ by 7.4% and 8.6% respectively. The reason for this deviation is not known, but comparisons between the (also well established) WESLEA algorithm suggested less than 1% difference between the Rubicon Online Tools algorithm and the WESLEA algorithm.
It is suspected that these differences represent edge cases where small differences between the inputs used by Huang for ELSYM5, and here with the Online Tools, have a significant impact on the results. We believe the weaker correspondence is due to these differences in setup/input assumptions, combined with conversion of printed values, rather than an algorithmic error. It should also be noted that tensile strains at the top of the subgrade are not commonly used in mechanistic analyses.
In the case of Principal Stresses, most results are close to or below 2%. One value, at the top of the subgrade, position 2, has a difference of 5.7%. This higher difference is believed to be a result of the rounding issues related to conversion of results between unit systems. Again, when comparing the results of the Rubicon Online tools with WESLEA, differences are below 1%.
edited by on 8/24/2020
edited by on 10/17/2023
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