Keywords: MathcadR, Eurocode 7, limit state design, retaining structures, reliability, first-order reliability method, optimization.

MathcadR moves beyond the capabilities of spreadsheets providing solutions expressively designed to document calculations. This paper presents some examples of a MathcadR implementation for geotechnical reliability-based analysis, concerning Eurocode 7 design methodology. Considering a well known classical calculation, the retaining structure sliding model, designed in MathcadR according to Eurocode 7, the first-order reliability method (FORM) is presented and a MathcadR implementation is performed considering correlated random variables with different distribution types. The Rackwitz-Fiessler equivalent normal transformation [1] or more efficiently an approach based on a derived simplified transformation, in conjunction with the MathcadR minimize function for optimization is used.

The first-order reliability method (FORM) is widely used worldwide in reliability analysis. Regardless of some recognized inadequacies, continuing interest is notorious: errors are acceptable in view of the large uncertainty in selecting the appropriate stochastic model and related parameters [2,3]. Two implementation methodologies in MathcadR are analyzed and the advantages of the second outlined: essentially, transformation is easier, but is also verified that the time required for implementation is quite similar and is not a relevant issue, mainly because MathcadR is a user friendly programming software.

The computation of the reliability index involves an iterative optimization process, and commonly used software packages are easily adapted to perform the optimization. For this purpose, spreadsheets have been widely used [4,5,6], but are difficult to audit or reuse: complex performance functions are not expressed in standard math notation and may contain errors that can decrease design quality. Furthermore, spreadsheets provide no support for advanced math calculations and substantial time and skills are required for programming.

MathcadR is a mathematical modelling package, so therefore does not exhibit such limitations and is better suited for implementing complex models: simultaneously solves and documents engineering calculations while reducing the risk of costly errors. MathcadR combines robust built-in functions with a unique and easy to use whiteboard interface, enabling knowledge capture, reuse and design verification, which results in improved product quality.

1

R. Rackwitz, B. Fiessler, "Structural Reliability Under Combined Random Load Sequences", Computers & Structures, 9(5), 489-494, 1978. doi:10.1016/0045-7949(78)90046-9

2

J. Huang, D.V. Griffiths, "Observations on FORM in a Simple Geomechanics Example", Structural Safety, 33(1), 115-119, 2011. doi:10.1016/j.strusafe.2010.10.001

3

R. Rackwitz, "Reliability Analysis-a Review and Some Perspectives", Structural Safety, 23(4), 365-395, 2001. doi:10.1016/S0167-4730(02)00009-7

4

B.K. Low, W.H. Tang, "Efficient Reliability Evaluation Using Spreadsheet", Journal of Engineering Mechanics, 123(7), 749-752, 1997. doi:10.1061/(ASCE)0733-9399(1997)123:7(749)

5

B.K. Low, W.H. Tang, "Reliability Analysis Using Object-Oriented Constrained Optimization", Structural Safety, 26(1), 69-89, 2004. doi:10.1016/S0167-4730(03)00023-7

6

B.K. Low, W.H. Tang, "Efficient Spreadsheet Algorithm for First-Order Reliability Method", Journal of Engineering Mechanics, 133(12), 1378-1387, 2007. doi:10.1061/(ASCE)0733-9399(2007)133:12(1378)

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