Lateral earth pressure loadings are applied in various states—specifically, active, at-rest, and passive states. The state of pressure to be considered varies with the wall type.
Yielding Walls. Yielding walls are free to translate or rotate about their top or base. For such walls, the lateral earth pressure may be computed assuming active conditions and wedge theory. In general, the lateral displacement at the top of a rigid wall of height H necessary to develop the active state varies from 0.001H in dense cohesionless soils to as much as 0.004H in loose cohesionless soils. For clay soils, a greater displacement on the order of 0.01H to 0.02H, for stiff and soft soils, respectively, is necessary to develop an active state. See Figs. 8.7 and 8.8.
Thus, it is noted that the amount of displacement necessary to develop active pressure can vary, say, for a 20-ft-high (6 m) wall, from less than И in (6 mm), in a dense cohesionless material, to as much as 5 in (125 mm), in soft clay. Clearly, the backfill material selected at any location plays a major role in the earth pressure for which a wall must be designed.
Restrained Walls. Restrained walls are walls that are fixed or partially restrained against translation or rotation. Lateral earth pressures are computed assuming at-rest conditions using the following relationship:
P =
P° 2
where P0 = resultant of at-rest earth pressure, kips/ft (N/mm)
7 = unit weight of soil or rock, kips/ft3 (kN/m3)
H = wall height, ft (mm)
K0 = at-rest pressure coefficient
This latter condition may occur naturally at walls that are not totally freestanding—for example, at the junction of the wingwall at bridge abutments—or the condition may occur by design. Examples include locations where the lateral deflection cannot be tolerated because it retains a structure, or a heavily reinforced concrete counterfort wall, which is sensitive to settlement, located on material susceptible to settlement, especially differential settlement. In the latter case the designer must evaluate options that may include, depending upon the depth of the material that will settle, (1) removal and replacement, (2) deep foundations to adequate bearing material, or (3) selection of a different wall type, if conditions permit, that will be more tolerant to the potential for the differential settlement.
Should some force be present that tends to push the wall into the earth mass it is intended to retain—which therefore develops a resistance to slip on the failure plane or a resistance to the lateral displacement needed to mobilize the active pressure state—a condition known as passive pressure develops. The lateral earth pressure for which the wall must be designed increases significantly, as much as 10 times, and requires special attention. See Fig. 8.9 for a qualitative depiction of the relative lateral displacement.
Rigid Walls. For the case of rigid walls, which involves wall translation or rotation “into the backfill,” the movement necessary to develop passive earth pressure behind the wall varies from 0.020H to 0.060H for cohesionless soils, dense to loose, respectively. Also, for stiff to soft cohesive soils, the lateral displacement will vary from 0.020H to 0.040H. It is obvious that passive earth pressures can be developed in these defined conditions. Certainly, the best way for the designer to account for these pressures is to avoid them wherever possible and practical, alleviating the conditions under which such pressures develop. This brief discussion is intended only to generate an awareness in the designer that such conditions can be created. An example would be dead-man type anchorages tying the wall top into solid materials or outside the failure plane of the wedge, thus preventing the movement necessary for development of the active pressure state.
