Relationships between Yield Acceleration and Static Factor of Safety

Abstract Pseudostatic limit equilibrium analysis can be used to understand of the effects of seismic accelerations on embankments, dams, and slopes. In particular, the yield acceleration, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k Subscript y" display="inline" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> , is used as an indicator of the horizontal acceleration required to cause instability. Because of the higher computational cost associated with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k Subscript y" display="inline" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> , analytical and numerical techniques to calculate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k Subscript y" display="inline" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> from the static factor of safety, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F Subscript s t" display="inline" overflow="scroll"> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> </mml:math> , are attractive. Once calculated, the yield acceleration is also a key input for many methods of evaluating slope displacement or deformation. This study shows that the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k Subscript y Baseline minus upper F Subscript s t" display="inline" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>y</mml:mi> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> </mml:math> relationship can be divided into effects related to geometry, shear strength, and ponded water. Validation by comparison to a large dataset of calculated values shows that the derived relationships accurately predict <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k Subscript y" display="inline" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F Subscript s t" display="inline" overflow="scroll"> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> </mml:math> , especially for relatively homogeneous slopes. Slopes with more complex geometry and/or more complex shear strength models showed lower accuracy and precision in the prediction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k Subscript y" display="inline" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> . Caution should be exercised when attempting to predict <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k Subscript y" display="inline" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F Subscript s t" display="inline" overflow="scroll"> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> </mml:math> for complex cross sections.