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DISPLACEMENT CALCULATION FOR GRAVITY RETAINING WALL UNDER
EARTHQUAKE LOADING
Sliding Displacement
Traditionally, sliding displacement of a gravity retaining wall is calculated using Newmark's (1965)
sliding block method. Using the concept of a yield or threshold acceleration, relative displacement
between a rigid wall and the ground beneath will accumulate from the instant the ground acceleration
exceeds the threshold until the block and the ground have the same velocity again. For design purpose,
Franklin and Chang (1977) analyzed a number of historic earthquake records to develop "standardized"
sliding displacements as a function of the ratio of threshold to peak acceleration.
The sliding block approach was modified and extended by Richards and Elms (1979) for the design of
gravity retaining walls. A design envelope based on Franklin and Chang's standardized displacements
was proposed to estimate the displacement of gravity walls, defined by
where
V 2
d = 0.087—(N/A)" 4 (2.1)
A
d - displacement of a gravity wall in inches
V = peak velocity of the design earthquake in inch/sec
N = threshold acceleration for sliding in in/sec 2 , and
A = peak lateral ground acceleration in in/sec 2
Rotational Displacement
For a gravity retaining wall, the displacement can also be caused by the rotation of the wall. A rotating
block method was introduced by Zeng and Steedman (2000) to calculate such displacement. Similar to
sliding block method, when the threshold acceleration for rotating is exceeded, a wall will start to rotate.
Rotational displacement will accumulate until the angular velocity of rotation is dropped to zero. The
important influential parameters on the angle of rotation are: peak acceleration, number of significant
cycles, and the frequency of base motion. This approach was developed further to calculate coupled
rotating and sliding displacement.
Gravity Retaining Wall with Saturated Backfill
Both the sliding and rotating block methods are used mainly for retaining walls with dry backfill. If the
soil around the wall is saturated such as in the case of a quay wall, the calculation become too complex
for these analyses to be used. Firstly, there are hydrodynamic pressures on both sides of the wall. The
calculation of hydrodynamic pressure on the seaside is quite straightforward for a rigid wall by using the
Westergaard's (1933) theory. However, the calculation of hydrodynamic pressure on the backfill side is