Reliability-based design applied to retaining walls

Figure_1_NormalssHgwalllaf'dgsoilabx*meanStDevnx6241090(x*, in radians)180.41.8f'26.4279226418353.5-2.4490.17453292521.57079632680.46125426460.2711223156d15.5341644182202-2.233ca99.999998906110015-0.000Correlation matrixKaPaf'10.800.3978291423128.896642095d0.810ca001f'dcaForceArmMomentPav34.52018656561.862.136335818W1100.80.933333333394.08W257.61.692.16PerFn1bPerFn2192.9201865656248.376335818-0.00000011482.49155.8118300646Overturning modeSliding modePah124.18816796642248.3763359328

SM

Figure_1_Normals

laaHbAdhesion caStiff clayW1W2Soil: unit weight g angle of friction f'Boxed cells contain equations=SQRT(MMULT(TRANSPOSE(nx),MMULT(MINVERSE(crmat),nx)))Ctrl + Shift, then Enterd+a-90Fig. 1. Reliability analysis of overturning failure mode and sliding mode, for correlated normal random variables, using Microsoft Excel spreadsheet.This workbook is provided by B. K. Low, author of "Reliability-based design applied to retaining walls", Geotechnique, Vol. 55, No. 1, 63-75, 2005. The aim is to allow hands-on experience and to enhance understanding of the reliability approach.This Excel file is for hands-on reliability analysis of Figure 1 of the paper.Steps for hands-on reliability analysis involving correlated normalsOverturning mode: (1) Copy mean column (cells L3:L5), and paste onto x* column (cells K3:K5). This initializes the x* values. (2) Click Tools\Solver, with settings shown below as explained in the paper. Solve.

(3) The reliability index b obtained by Solver is 2.491 (cell K15) for overturning mode. The design point is defined by the solution values in the x* column (cells K3:K5).

Sliding Mode:(1) Copy mean column (cells L3:L5), and paste onto x* column (cells K3:K5).(2) Click Tools\Solver, change settings as shown below, then click Solve.

(3) Solution: cells K3:K5, N3:N5, K15 and M15 will show values like those in the insert.A separate Excel file provides the reliability-based design shown in Fig. 7 of the paper.Select this

and change to:

$M$15