Coal Age Magazine - For nearly 100 years, Coal Age has been the magazine that readers can trust for guidance and insight on this important industry.
Issue link: https://coal.epubxp.com/i/277753
The method of engineering design is the process of choosing the appropriate components to make a functional structure that is sufficiently safe. Engineering design typically involves an iterative, purely deterministic approach where a multitude of inputs are adjusted until the optimal design is reached. This deterministic approach to assess safety and durability general- ly results in a factor of safety (FS) value, as calculated by: The factor of safety is a very easy calculation to perform in many circumstances, and it is very easy to interpret the results. If the strength of a component or a structure is greater than the stress expected to be applied to the component or structure, then the factor of safety will be greater than one and the com- ponent or structure is not expected to fail. However, if the s t r e s s e x e r t e d o n t h e c o m p o n e n t o r s t r u c t u r e e x c e e d s t h e strength, then the factor of safety will be less than one and the component or structure is expected to fail. F o r t h e d e t e r m i n i s t i c a p p r o a c h t o b e u s e d , i t m u s t b e assumed that the exact inputs are known. If the exact inputs are known, then the exact solution can be determined. The deter- ministic approach is a very simple approach to engineering design. The greatest strength of a deterministic factor of safety calculation is also its greatest weakness: it is extremely simple. Because of its simplicity, the deterministic approach to factor of safety calculations is completely lacking in uncertainty quantification. Uncertainty quantification is an important practice in all engineering practices. This is especially true when regarding g e o t e c h n i c a l e n g i n e e r i n g . A h i g h l e v e l o f u n c e r t a i n t y i s involved with engineering geotechnical structures. A common method of skirting the issue of uncertainty quantification is to t a k e a c o n s e r v a t i v e a p p r o a c h t o d e s i g n . T h e c o n s e r v a t i v e approach involves underestimation of the strengths and/or overestimation of the stresses in an attempt to guarantee a safe design. Using a conservative approach for engineering design does not guarantee safety, can lead to overdesign of compo- nents and structures, and removes meaning from the term fac- tor of safety by introducing intentionally arbitrary inputs. This conservative approach has led to design standards that r e q u i r e f a c t o r s o f s a f e t y f o r e l e v a t o r s t o b e a s h i g h a s 1 1 . Elevators must be overdesigned to some degree because of the likelihood of misuse and the dire consequences of failure, but many engineering structures do not require the overdesign that is typically present. Intentionally designing to a factor of safety much greater than 1 indirectly admits the fault in the determin- istic approach while bypassing more meaningful and less arbi- trary alternatives. Probabilistic Approach A probabilistic approach to engineering design can be a superior alternative to a deterministic approach. Instead of considering one value for each input in an engineering design calculation, a probabilistic approach allows for a distribution of values for each input parameter. A distribution is used rather than a single value to represent the uncertainty or variability in the data. With a dis- tribution of inputs, the output will also take the form of a distri- bution. This distribution of outputs leads to the greatest strength of the probabilistic analysis, which is a meaningful result. m i n e d e s i g n B Y B E N F A H R M A N A N D E R I K W E S T M A N Probabilistic Approach to Coal Pillar Design Performing a probabilistic study rather than a deterministic one is a relatively easy way to quantify the uncertainty in an engineering design Figure 2: Example of output distribution of factor of safety. Figure 1: Example of probability distributions of stress and strength. 30 www.coalage.com March 2014 CA_pg30-33_V2_CA_pg46-47 3/12/14 8:44 AM Page 30