X.11.1 General C.X.11.1
Prefabricated modular walls shall be designed for seismic loading except where conditions given in Article X.4 are satisfied or where allowed otherwise by the Owner.
Before conducting the seismic evaluation, the prefabricated modular wall shall be designed to meet all gravity and live load requirements in accordance with the provisions in Section 11 of the AASHTO LRFD Bridge Design Specifications.
The prefabricated modular wall develops resistance to seismic loads from both the geometry and weight of the wall section. The primary design issues for seismic loading are global stability, external stability (i.e., sliding, overturning, and bearing), and internal stability. External stability includes the ability of each lift within the wall to also meet external stability requirements. Interlocking between individual structural sections and the soil fill within the wall needs to be considered in this evaluation.
The starting point for the seismic design of the prefabricated modular wall is an acceptable static design, meeting the
requirements of the current AASHTO LRFD
Bridge Design Specifications. Once the static
design has been completed, the design is checked for seismic response.
As part of the seismic check, the performance expectations for the wall during the design seismic event should be determined through discussions with the Owner. Some of the factors that should be considered in determining performance expectations are summarized in Appendix AX.
X.11.2 Method of Analysis C.X.11.2
The prefabricated modular wall shall be analyzed to show that the wall can
The seismic design of the prefabricated modular wall generally involves the same
withstand seismic forces from seismic earth pressures and from inertial forces of the wall without excessive sliding or rotation of the wall and without exceeding stress limits within the structural system.
Either limit equilibrium or displacement methods shall be used to establish that performance during seismic loading meets design expectations.
seismic analyses as used for rigid and semi- rigid gravity walls described in Article X.7 of this section of the Specifications. The one significant difference is that the sliding and overturning stability at different levels within the modular wall also need to be confirmed. For these checks the earth pressure will differ not only because of the reduced height, but also because of different wave scattering effects.
The approach taken for prefabricated modular wall design in this Article involves the use of the simplified M-O equation, the wedge equilibrium method, or a generalized limit equilibrium method to estimate wall pressures. The contributions of any cohesion within the soil behind the wall should be accounted for in the earth pressure determination. Either the generalized limit
equilibrium or the figures in Appendix BX
can be used to account for these effects. An alternate approach involving the use of 2-dimensional finite element or finite difference computer programs is also acceptable. As noted for other walls, considerable skill and experience are required when using these numerical methods, particular when seismic loading is involved. Most often these numerical methods are suitable for special studies. Before using this alternate approach for seismic design of prefabricated modular walls, detailed discussions should take place with the Owner.
X.11.2.1 Seismic Earth Pressure C.X.11.2.1
Procedures given in Article X.7.2.1 shall be followed to determine the seismic earth pressure that will be imposed on the wall. Wall pressures shall be estimated at multiple heights behind the wall for use in external and internal stability checks.
The seismic coefficient used in the earth pressure computation shall be determined following the procedures described in Article X.4. Where small (e.g., 1 to 2 inch) permanent displacements are permissible
Prefabricated modular walls will often be constructed at locations where soil conditions preclude the use of the Mononobe-Okabe (M-O) equation. The cohesion in these soils has a significant effect on the earth pressure, which the M-O equation cannot capture in a simple relationship. In this situation the wedge equilibrium method or the generalized limit equilibrium method offers an alternative for estimating wall pressures. For those special conditions where the fill behind
during the design seismic event, a 50% reduction in the peak ground acceleration used in design shall be permitted. A reduction beyond 50% shall be allowed only with the Owner’s approval and with displacement analyses that show permanent displacements are within the Owner’s performance requirements.
the wall is a clean homogeneous granular material, the M-O equation for seismic active pressure can be used.
If soils are homogeneous but have a
cohesive content, the figures in Appendix BX
can be used to account for the cohesive contribution. See Article X.7.2.1.1 for addi- tional considerations relative to the deter- mination of seismic active earth pressures, including the contributions from cohesion.
Procedures for estimating the seismic coefficient to use in the generalized limit equilibrium, wedge equilibrium, or M-O equation are as described in Article X.7.2.2. A reduction in the peak seismic coefficient for wave scattering (kav) is permitted for wall
heights between 20 and 70 feet as discussed in Article X.4. Other provisions are as described in the commentary to Article X.7.2.1.
The geometry of the prefabricated modular wall is such that determination of the passive earth pressure at the face of the wall can usually be ignored. For those cases where the wall is embedded more than a few feet, the passive pressure for seismic loading should also be determined and used in the stability analyses. Procedures described in Article X.7.2.1.2 can be used to determine the passive earth pressure.
X.11.2.2 Wall Displacement Analysis C.X.11.2.2
Displacements shall be estimated using one of the procedures given in Article X.4 for cases where (1) the C/D ratio for global stability is less than 1.0 or (2) the amount of sliding allowed by the Owner can exceed 1
to 2 inches, thereby supporting a kmax
reduction factor of greater than 50%.
For critical structures identified by the Owner, the displacements estimated from the equations in Article X.4 shall be multiplied by 2 to obtain an 84% confidence level.
The displacement estimate for the prefabricated modular wall can be made by following the steps outlined in Article X.7.2.2 of the Specifications.
X.11.3 Design Requirements C.X.11.3
The prefabricated modular wall shall be designed to meet global stability, external stability, and internal stability requirements as set forth in this Article. Earth pressures and displacement evaluations discussed in the preceding Articles shall be used as input for these analyses.
The seismic performance of the prefabricated modular block wall should be conducted following the same general procedures as used for the rigid and semi- rigid gravity wall, as described in Article X.7.3.
The primary difference for this wall type relative to a rigid or semi-rigid gravity wall is that sliding and overturning can occur at various heights between the base and top of the wall, as this class of walls typically uses gravity to join sections of the wall together.
The interior of the wall is normally filled with soil, and this provides both additional weight and shear between structural elements. The contributions of the earth, as well as the batter on the wall, need to be considered in the analysis.
X.11.3.1 Global Stability C.X.11.3.1
Procedures given in Article X.7.3.1 shall be used to check global stability. The results of these analyses shall demonstrate that the capacity-to-demand ratio is greater than 1.0. If the capacity-to-demand ratio is less than 1.0, displacements shall be estimated or the wall shall be redesigned to meet the capacity-to-demand requirements.
The global stability check needs to consider failure surfaces that pass through the wall section, as well as below the base of the wall. The check on stability at mid level must consider the contributions of both the soil within the wall and any structural interlocking that occurs for the particular modular wall type.
When checking stability at the mid level of a wall, the additional shear resistance from interlocking of individual structural members will depend on the specific wall type. Usually interlocking resistance is provided by the wall supplier. The interlocking forces are often such that the critical load case becomes external and internal stability rather than global stability within the wall height.
X.11.3.2 External Stability C.X.11.3.2
The external stability of the prefabricated modular wall shall be evaluated to show that the prefabricated wall section meets sliding, overturning, and bearing stability requirements. The sliding
The evaluation of external stability will be similar to procedures described in Article X.7.3.1 with the additional provision that checks need to be performed at different heights within the wall, as discussed above
and overturning requirements shall be satisfied for both the entire wall, as well as individual levels within the wall.
The ratio of capacity-to-demand shall be greater than 1.0 using the following resistance factors:
Sliding: 1.0
Overturning: 1.0
Toe Bearing: 0.67
Earth pressures defined previously shall be used in the external stability assessment. If the ratios identified are not satisfied, the prefabricated modular wall shall be re-sized to meet the required capacity-to-demand ratios.
for global stability. These additional checks need to consider the capacity from interlocking structural members of the wall relative to each other. Careful review of the particular wall type will be required to evaluate these forces.
When evaluating sliding and overturning stability at varying heights within the wall, the seismic wall pressure needs to be adjusted for scattering effects if scattering adjustments are included in the analyses. Generally, the scattering factor decreases as the wall height above the elevation of interest decreases. For evaluations where the height of the wall above the elevation is 20 feet or less, the scattering coefficient should be 1.0.
X.11.3.3 Internal Stability C.X.11.3.3
Internal stability of the prefabricated modular wall shall be evaluated for maximum moments and shears developed during sliding, overturning, and bearing for load and resistance factors provided in Article X.6.. Design requirements shall be consistent with the Owner’s performance expectations for Extreme Event I.
This class of walls is typically involves proprietary wall systems comprised of wall segments that interlock. The interlock is often through gravity connections, but mechanical systems can also be used. In most cases it will be necessary to require the wall vendor to provide submittals showing that the wall will meet the Owner’s performance objectives under the imposed seismic loads.
For these design checks, the earth pressure determined from Article X.11.2.1 should be used by the vendor with the required resistance factors, the soil bearing capacity, and the soil sliding resistance to show internal stability.