Graphical methods can sometimes be advantageously used to design sheet pile retaining walls especially for cases of complex or irregular loading. The lateral pressure distribution is first determined by the methods previously outlined. The maximum bending moment and the anchor pull are then determined by application of
the graphical methods. The wall and the corresponding pressure diagram is divided into a number of equal panels or sections as shown in Figure 32. The resultant earth pressure on each panel is replaced by an equivalent concentrated force acting through the center of the section and drawn to a convenient scale. The method for the design of anchored and cantilevered walls differs slightly and will be discussed separately below.
Cantilevered Wall (Tường tự do- Không neo)
Once the wall has been divided and the equivalent forces determined, a vector diagram or string polygon is constructed (Figure 32) as follows. On a horizontal base line, commencing at the right, the successive force vectors for each panel from the point of zero pressure to the bottom of the wall are laid off end to end i.e., the passive equivalent forces. The theoretical depth of the sheet piling is unknown; therefore, arbitrary depth must be chosen. A pole 0 is then selected at a distance from the base line equal to
Once the wall has been divided and the equivalent forces determined, a vector diagram or string polygon is constructed (Figure 32) as follows. On a horizontal base line, commencing at the right, the successive force vectors for each panel from the point of zero pressure to the bottom of the wall are laid off end to end i.e., the passive equivalent forces. The theoretical depth of the sheet piling is unknown; therefore, arbitrary depth must be chosen. A pole 0 is then selected at a distance from the base line equal to
Selected scale of the moments / (scale of the equivalent forces * scale of lengths )
The moment scale is selected so as to give a convenient size of drawing. The successive equivalent active force vectors above the point of zero pressure are laid off end to end on a horizontal line originating at the pole 0 and extending to the right. From pole 0 lines are drawn to the ends of all the passive load vectors and from the right hand edge of the passive load line to the ends of all the active load vectors. This procedure is relatively simple and is illustrated in Figure 32.
The moment diagram is then drawn as follows. Starting at the top of the piling at point 0', the line 0'-1' in the moment diagram is drawn parallel to line A-l of the vector diagram, intersecting the first or top load line of action at point 1'; from point 1' line 1'-2' is then drawn parallel to line A-2 of the vector diagram intersecting the second load line of action at 2'. The process is continued through all sections including both active
and passive lines.
Anchored Walls (Tường có neo)
The vector diagram or string polygon may also be used to design anchored walls by use of the simplified equivalent beam method. The vector diagram is drawn as shown in Figure 33. On a horizontal line commencing at the right, the successive loads for the sections from the bottom to the top of the equivalent beam are laid off end to end. The pole distance is selected as for cantilevered walls. The moment diagram is constructed exactly as in the cantilevered case starting at the bottom of the equivalent beam.
The line drawn for the top section of the moment diagram is projected back to intersect the line of action of the anchor pull at A'. From A' a straight line is then drawn to the starting point 0'. This straight line is the base line of the moment diagram and its inclination depends on the position of 0 in the vector diagram. The line A-O in the vector diagram is drawn through 0 parallel to A'-0' and gives the magnitude of the anchor tension and the equivalent reaction at the point of zero pressure. The maximum bending moment is found by scaling the maximum horizontal distance from A'-0' to the curve in the moment diagram. The total depth of penetration is obtained from the equation:
(Source: Steel sheet piling Design Manual )
