FOS=1.5, FROM WHENCE YOU CAME?

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For earth dams, the most common requirement for static, long-term, steady-state slope stability is the 1.5 factor of safety.  Who says?  Where did that come from?  Let’s explore this a little.

Wikipedia says that according to Elishakoff the notion of factor of safety in engineering context was apparently first introduced in 1729 by Bernard Forest de Bélidorwho was a French engineer working in hydraulics, mathematics, civil, and military engineering in the 1700s.

Here’s a long one from Wikipedia.  “Appropriate design factors are based on several considerations, such as the accuracy of predictions on the imposed loads, strength, wear estimates, and the environmental effects to which the product will be exposed in service; the consequences of engineering failure; and the cost of over-engineering the component to achieve that factor of safety. For example, components whose failure could result in substantial financial loss, serious injury, or death may use a safety factor of four or higher (often ten). Non-critical components generally might have a design factor of two. Risk analysis, failure mode and effects analysis, and other tools are commonly used. Design factors for specific applications are often mandated by law, policy, or industry standards”.

Really makes you wonder how we got to FOS=1.5 for earthen dams, doesn’t it?

Wikipedia continues.  “Buildings commonly use a factor of safety of 2.0 for each structural member. The value for buildings is relatively low because the loads are well understood, and most structures are redundant. Pressure vessels use 3.5 to 4.0, automobiles use 3.0, and aircraft and spacecraft use 1.2 to 3.0 depending on the application and materials. Ductile, metallic materials tend to use the lower value while brittle materials use the higher values. The field of aerospace engineering uses generally lower design factors because the costs associated with structural weight are high (i.e., an aircraft with an overall safety factor of 5 would probably be too heavy to get off the ground). This low design factor is why aerospace parts and materials are subject to very stringent quality control and strict preventative maintenance schedules to help ensure reliability. A usually applied Safety Factor is 1.5, but for pressurized fuselage it is 2.0, and for main landing gear structures it is often 1.25”.

Okay, the FOS=1.5 is starting to make a little more sense if you consider that the cost to achieve a higher FOS can be considerable and (hopefully) the design, construction and operation are “subject to very stringent quality control and strict preventative maintenance schedules to help ensure reliability”.

According to Herza, Ashley and Thorp in “Factor of Safety? – Do we use it correctly?”, “The minimum acceptable FoS for dam design were anecdotally determined in the USA in mid-20th century by back-calculating the FoS of existing dams. It was found that the FoS of 1.5 provided sufficient contingency and was generally considered acceptable”.  Unfortunately, they don’t cite a reference.

In his Theoretical Soil Mechanics book, Terzaghi indicates that the safety factor should be set to 1.5 but offers no explanation for this figure.  I should imagine, therefore, that Terzaghi presumed that a dam would be the designed, constructed and operated with approaches that are “subject to very stringent quality control and strict preventative maintenance schedules to help ensure reliability”.