B.K. Low and C.I. Teh
School of Civil and Structural Engineering, Nanyang Technological University, Singapore
Wilson H. Tang
School of Civil Engineering, Hong Kong University of Science and Technology, Hong Kong, China
School of Civil and Structural Engineering, Nanyang Technological University, Singapore
Wilson H. Tang
School of Civil Engineering, Hong Kong University of Science and Technology, Hong Kong, China
An intuitive ellipsoidal perspective of the Hasofer-Lind reliability index in the original
space of the random variables is described. This alternative interpretation gave rise to a practical
approach for reliability analysis. The approach implements object-oriented constrained optimization
of multidimensional ellipsoids with ease and clarity in the ubiquitous spreadsheet platform.
It obtains the same result as the first order reliability method, but deals with the correlation matrix
in its original form without diagonalizing it. The performance functions can be implicit. Reliabilitybased
design via spreadsheet optimization is illustrated in two problems involving a semi-gravity
retaining wall and an anchored sheet pile wall. Multiple performance criteria are considered.
space of the random variables is described. This alternative interpretation gave rise to a practical
approach for reliability analysis. The approach implements object-oriented constrained optimization
of multidimensional ellipsoids with ease and clarity in the ubiquitous spreadsheet platform.
It obtains the same result as the first order reliability method, but deals with the correlation matrix
in its original form without diagonalizing it. The performance functions can be implicit. Reliabilitybased
design via spreadsheet optimization is illustrated in two problems involving a semi-gravity
retaining wall and an anchored sheet pile wall. Multiple performance criteria are considered.
The factors of safety used in civil engineering design do not explicitly account for the uncertainty
of the underlying parameters. A more rational approach is to evaluate the H-L second moment
reliability index that depends not only on the mean values of the parameters but also on their
scatters. An advantage of the invariant H-L index is that it avoids the ambiguities associated with
different formulations of the factor of safety when the performance function is nonlinear.
of the underlying parameters. A more rational approach is to evaluate the H-L second moment
reliability index that depends not only on the mean values of the parameters but also on their
scatters. An advantage of the invariant H-L index is that it avoids the ambiguities associated with
different formulations of the factor of safety when the performance function is nonlinear.
The deterministic design of a semi-gravity retaining wall using factors of safety are well discussed
in Lambe & Whitman (1979) and Craig (1997). Three failure modes need to be checked, namely
rotation about the toe of the wall, horizontal sliding along the base of the wall, and bearing capacity
failure of the soil beneath the wall under the inclined and eccentric resultant load derived from the
weight of the wall and the active earth thrust Pa acting on the back of the wall.
in Lambe & Whitman (1979) and Craig (1997). Three failure modes need to be checked, namely
rotation about the toe of the wall, horizontal sliding along the base of the wall, and bearing capacity
failure of the soil beneath the wall under the inclined and eccentric resultant load derived from the
weight of the wall and the active earth thrust Pa acting on the back of the wall.
References
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Low, B. K., Gilbert, R. B., and Wright, S. G. (1998). “Slope reliability analysis using generalized method of slices.” J. of Geotechnical and Geoenvironmental Engineering.
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