In order to find the slide-resistant capability of the subgrade steps in gravity-type anchorages of suspension bridges

the slip-line theory for plane strain problem of perfect plasticity is applied to derive the differential equations of the slip-lines for geotechnical materials satisfying Mohr-Coulomb failure criterion. Then

upper and lower limits of the slide-resistance of the subgrade step are developed by using the theorem of limit analysis

unlike the Rankine passive earth pressure

the proposed method takes account of the vertical pressure on the top face of the step

caused by the self-weight of the anchorage

and the friction between anchorage and the subgrade. Comparison with the finite element solutions shows that the actual slide-resistance lies between the lower and upper limits

and the resistance is greater than the lower limit by about 18%. At failure

the slip-band passes through the front end of the anchorage step; and the longer the horizontal length of the step

the higher the slide-resistance. Thus

the lower bound solution can be used to safely estimate the minimum slide-resistance of the subgrade step. The upper and lower limits of the slide-resistance of a multi-stepped subgrade can be expressed

respectively

as the summations of those values from constituent steps. However

due to the rigid rotation of the anchorage and the eccentric compression on the subgrade top

not all of the steps come into full play

and instead most slide-resistance comes from the first subgrade step. When it is near to the maximum load

the first subgrade step takes approximately 80% of the total slide-resistance

with remaining subgrade steps almost quitting work. It is shown that the lower limit of the slide-resistance of the multi-stepped anchorage is higher than maximum frictional force between anchorage and subgrade. Incorporation of the slide-resistance of the vertical step make the anti-slide stability factor of the anchorage increase by about 70%

and the actual slide-resistance of the entire multi-stepped subgrade is much greater than the horizontal component of the ultimate cable tension. In design stage

the slide-resistance of the multi-stepped subgrade can be estimated safely as the sum of those from the first and the second subgrades.