What Is a Safety Factor Safety Factors in Soil . . . Explaining the Safety . . . Safety Factors in Soil and Explaining the Safety . . . A Similar Explanation . . . Pavement Engineering: Acknowledgments Theoretical Explanation of Main Reference Home Page Empirical Data Title Page Afshin Gholamy 1 and Vladik Kreinovich 2 ◭◭ ◮◮ Departments of 1 Geological Sciences and 2 Computer Science ◭ ◮ University of Texas at El Paso afshingholamy@gmail.com, vladik@utep.edu Page 1 of 8 Go Back Full Screen Close Quit
What Is a Safety Factor 1. What Is a Safety Factor Safety Factors in Soil . . . • Models are approximations to reality. Explaining the Safety . . . Explaining the Safety . . . • To describe a complex real-life process by a feasible A Similar Explanation . . . model: Acknowledgments – we find the most important factors affecting the Main Reference process and Home Page – we model them. Title Page • The ignored factors are smaller than the factors that ◭◭ ◮◮ we take into account; however: ◭ ◮ – they still need to be taken into account Page 2 of 8 – if we want to provide guaranteed bounds for the desired quantities. Go Back • To take these small factors into account, engineers mul- Full Screen tiply the results of the model by a constant. Close • This constant is known as the safety factor . Quit
What Is a Safety Factor 2. Safety Factors in Soil and Pavement Engineer- Safety Factors in Soil . . . ing: Empirical Data Explaining the Safety . . . • In many applications, a safety factor is 2 or smaller. Explaining the Safety . . . A Similar Explanation . . . • However, in soil and pavement engineering, the situa- Acknowledgments tion ia different. Main Reference • Researchers compared: Home Page – the resilient modulus predicted by the correspond- Title Page ing model and ◭◭ ◮◮ – the modulus measured by Light Weight Deflectome- ◭ ◮ ter. Page 3 of 8 • This comparison showed that: Go Back – to provide guaranteed bounds, Full Screen – we need a safety factor of 4. Close • How can we explain this? Quit
What Is a Safety Factor 3. Explaining the Safety Factor of 2: Reminder Safety Factors in Soil . . . • Let ∆ be the model’s estimate. Explaining the Safety . . . Explaining the Safety . . . • When designing the model, we did not take into ac- A Similar Explanation . . . count some factors. Acknowledgments • Let’s denote the effect of the largest of these factors Main Reference by ∆ 1 . Home Page • The factors that we ignored are smaller than the one Title Page we took into account, so ∆ 1 < ∆, i.e., ∆ 1 ∈ [0 , ∆]. ◭◭ ◮◮ • We do not have any reason to assume that any value ◭ ◮ from the interval [0 , ∆] is more frequent than others. Page 4 of 8 • Thus, it makes sense to assume that ∆ 1 is uniformly Go Back distributed on [0 , ∆]. Full Screen • Then, the average value of ∆ 1 is ∆ / 2. Close • The next smallest factor ∆ 2 is smaller than ∆ 1 . Quit
What Is a Safety Factor 4. Explaining the Safety Factor of 2 (cont-d) Safety Factors in Soil . . . Explaining the Safety . . . • The same arguments shows that its average value of ∆ 2 is ∆ 1 / 2, i.e., ∆ 2 = 2 − 2 · ∆. Explaining the Safety . . . A Similar Explanation . . . • Similarly, ∆ k = 2 − k · ∆. Acknowledgments • Hence the overall estimate is Main Reference ∆ + ∆ 1 + . . . = ∆ + 2 − 1 · ∆ + . . . + 2 − k · ∆ + . . . = 2∆ . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 5 of 8 Go Back Full Screen Close Quit
What Is a Safety Factor 5. A Similar Explanation for the Safety Factor of 4 Safety Factors in Soil . . . • Empirical data shows that for soil and pavement engi- Explaining the Safety . . . neering, 2 is not enough. Explaining the Safety . . . A Similar Explanation . . . • This means that ∆ 1 should be larger than our esti- Acknowledgments mate ∆ / 2: ∆ 1 ∈ [∆ / 2 , ∆]. Main Reference • In this case, the average value from this interval is Home Page ∆ 1 = (3 / 4) · ∆ . Title Page ◭◭ ◮◮ • Similarly, we get ∆ 2 = (3 / 4) 2 · ∆, ∆ k = (3 / 4) k · ∆ and thus, ◭ ◮ ∆+∆ 1 + . . . +∆ k + . . . = ∆ · (1+3 / 4+ . . . +(3 / 4) k + . . . ) = Page 6 of 8 Go Back ∆ / (1 − 3 / 4) = 4∆ . Full Screen Close Quit
What Is a Safety Factor 6. Acknowledgments Safety Factors in Soil . . . This work was supported in part by the US National Sci- Explaining the Safety . . . ence Foundation grant HRD-1242122 (Cyber-ShARE). Explaining the Safety . . . A Similar Explanation . . . Acknowledgments Main Reference Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 7 of 8 Go Back Full Screen Close Quit
7. Main Reference What Is a Safety Factor Safety Factors in Soil . . . • M. Mazari, E. Navarro, I. Abdallah, and S. Nazarian, Explaining the Safety . . . Explaining the Safety . . . “Comparison of numerical and experimental responses A Similar Explanation . . . of pavement systems using various resilient modulus Acknowledgments models”, Soils and Foundations , 2014, Vol. 54, No. 1, Main Reference pp. 36–44. Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 8 of 8 Go Back Full Screen Close Quit
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