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91 appropriate. Apply a 0.5 factor to the resulting seismic co- cific guidance on the minimum length of the anchors in efficient if 1 to 2 inches of average permanent movement can Figure 11.9.1-1. be accepted and conditions are such that they will develop. Otherwise use the kmax without further reduction. One of the key factors for the anchored wall is that each 5. Compute wall pressures using M-O equation for active anchor is load tested during the construction process. The pressure, the charts in Figures 7-11 and 7-12, or the gen- load test is used to confirm that the anchor will meet long- eralized limit equilibrium method. Estimate earth pres- term load requirements. The testing typically includes ap- sure for passive loading using charts in Figure 7-25 or plying from 1.5 to 2 times the design (working) load and the methodology published by Shamsabadi et al. (2007). monitoring creep of the anchor. Well-defined criteria exist Do not use the M-O equation for passive pressure. for determining the acceptability of the anchor during proof 6. Evaluate structural requirements using a suitable software or performance testing. package or through use of hand methods (for example, free earth support). Confirm that displacements are suffi- 7.9.2.1 Seismic Design Considerations cient to develop an active pressure state. 7. Check global stability under seismic loading using a limit The AASHTO LRFD Bridge Design Specifications provide equilibrium program such as SLIDE with the seismic coef- limited guidance for the seismic design of anchored walls. ficient modified for height effects. Assume that the critical Article 11.9.6 indicates that, "the provisions in Article 11.8.6 surface passes beneath the structural element. If the capac- shall apply." The referenced article deals with nongravity ity to demand ratio (that is, factor of safety) is less than 1.0, cantilever walls, and basically states that the M-O equations estimate displacements. should be used with the seismic coefficient kh = 0.5A. Various other methods also have been recommended for The generalized limit equilibrium approach can be used the seismic design of anchored walls: where soil conditions, seismic coefficient, or geometry warrant. In this analysis the contributions from the structural elements The FHWA report Geotechnical Earthquake Engineering need to be included in the evaluation of stability. Programs (FHWA, 1998a) presents an approach for walls anchored such as SLIDE allow incorporation of the structural element with a single deadman. This method suggests using the through the use of an equivalent reaction, where the reaction M-O equations to estimate the seismic active and passive of individual members is "smeared" to obtain an equivalent pressures. The design method recommends that the anchors two-dimensional representation. be located behind the potential active failure surface. This failure surface is flatter than that used for the static stabil- ity analysis. 7.9.2 Anchored Walls A more recent FHWA document Ground Anchors and The next class of walls is essentially the same as nongravity Anchored Systems (FHWA, 1999) provides discussions on cantilever walls; however, anchors are used to provide addi- the internal stability using pseudo-static theory and external tional support to the walls. Typically the anchors are installed stability. Again the approach is to use the M-O equations. when the wall height exceeds 20 feet, or sometimes even at less The document notes that, height if a steep backslope occurs above the wall or the wall use of a seismic coefficient from between one-half and two- supports heavy loads from a structure. The height of anchored thirds of the peak horizontal ground acceleration divided by walls can exceed 100 feet. gravity would appear to provide a wall design that will limit The anchored wall can be used in either cut or fill conditions. deformations in the design earthquake to small values acceptable for highway facilities. For fill conditions the reaction is usually provided by a The seismic active earth pressure is assumed to be uni- deadman anchor. This wall type is generally limited to use formly distributed over the height of the wall. at port facilities, where a single deadman anchor is used to For the grout tendon bond, considered a brittle element augment the capacity of the wall. While deadman can be of the system, the report suggests using the site-adjusted used for highway construction, particularly for retrofits, PGA with no reductions in the M-O equations to obtain other wall types, such as MSE or semi-gravity cantilever a peak force and that a factor of safety against brittle fail- walls, are usually more cost-effective for new walls. ure be 1.1 or greater. For cut slope locations, the wall uses one or more grouted For ductile elements (for example, tendons, sheet piles, anchors to develop additional capacity. Anchors are usu- and soldier piles) the seismic coefficient in the M-O ally installed at approximately 10-foot vertical spacing; method is 0.5 times the site-adjusted PGA. The Newmark horizontal spacing of the soldier piles is often 8 to 10 feet. method is used as the basis of this recommendation. For AASHTO LRFD Bridge Design Specifications provide spe- this condition the factor of safety should be 1.1 or greater.

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92 A global check on stability also is recommended. Simi- ficient seems justified. If this reduction is, however, accepted, lar to the approach in Geotechnical Earthquake Engi- then careful consideration needs to be given to the stiffness of neering, the anchor zone should be outside the flattened the wall-anchor system to confirm that the elongation of the failure surface. anchor strand or bar and the stiffness of the wall are such that Another FHWA document Design Manual for Permanent several inches of movement can occur. Ground Anchor Walls (FHWA, 1998b) has a slight varia- While the methodologies for the seismic design of anchored tion on the above methods. First, the method suggests using walls seem to lack guidance on a number of topics, the FHWA 1.5 times the site-adjusted PGA, but notes that Caltrans has documents note that anchored walls have performed well dur- been successful using a 25 percent increase over the normal ing past seismic events. It was noted that of 10 walls inspected apparent earth pressures. The justification for the lower after the 1987 Whittier earthquake and the 1994 Northridge loads is related to the test loads that are applied (133 per- earthquake, wall performance was good even though only one cent times Load Group VII); these loads are higher than in 10 walls inspected was designed for earthquake loading. would be obtained using the AASHTO approach. Since the seismic loads are applied for a short period of time, the 7.9.2.2 Seismic Design Methodology document suggests not increasing the soldier piles or wall facing for the seismic forces. For external stability the re- The following approach is suggested for design of anchored port identifies a deformation-based approach used at the retaining walls: time by Caltrans. This method is based on the Makdisi and Seed (1978) charts for computing deformations. 1. Perform static design following the AASHTO LRFD Bridge Whitman (1990) in a paper titled, "Seismic Design and Design Specifications. Behavior of Retaining Walls," presents a methodology 2. Establish the site peak ground acceleration coefficient (kmax) that accounts for the increased support from the anchor and spectral acceleration S1 at 1 second from the 1,000-year as the wall deforms. In the Whitman approach, a limit equi- AASHTO maps, including appropriate site soil modifica- librium analysis is conducted with a program such as SLIDE. tion factors. The anchor lock-off load is modeled as an external force 3. Determine the corresponding PGV from correlation equa- oriented along the axis of the anchor (that is, typically tions between S1 and PGV (provided in Chapter 5). 10 to 20 degrees). The yield acceleration is determined, and 4. Modify kmax to account for wall-height effects as described then the deformation is estimated using a Newmark chart. in Section 7.6. Do not use 1.5 factor given in the current This deformation results in elongation of the anchor tendon AASHTO Specifications, unless the wall cannot be allowed or bar, which results in an increased reaction on the wall to deflect. (that is, = PL/AE). Analyses are repeated until there is 5. Compute wall pressures using the M-O equation for active compatibility between the deformations and the anchor pressure, the charts in Figures 7-11 and 7-12, or the gener- reaction. The final force is then checked against capacity of alized limit equilibrium method. Apply a factor of 0.5 if the tendon and grouted anchor. 1 to 2 inches of average permanent movement are accept- able and the stiffness of the wall and anchor system (that is, With one exception, the documents summarized here do = PL/AE) will allow this movement. If 1 to 2 inches are not suggest amplification within the zone between the retain- not tolerable or cannot develop, then use the full seismic ing wall and the anchors. One reference was made to the use coefficient. Estimate earth pressure for passive loading of an amplification factor identical to that used for the seis- using Figures 7-23 to 7-25 or the equations developed by mic design of MSE walls [that is, Am = (1.45 - A)A]. No basis Shamsabadi et al. (2007). for this increase was provided. Most references do suggest 6. Use the same pressure distribution used for the static pres- that the location of the anchors be moved back from the wall sure distribution. For the resulting load diagram, check to account for the flattening of the active zone during seismic loads on tendons and grouted anchors to confirm that the loading. The potential that the pressure distribution behind seismic loads do not exceed the loads applied during per- the anchored walls changes during seismic loading is not cur- formance or proof testing of each anchor. Confirm that rently addressed. the grouted anchors are located outside the seismic active The most significant uncertainty appears to be whether pressure failure wedge. to use the peak seismic coefficient, or a value that is higher 7. Check global stability under seismic loading using a limit or lower than the peak. Arguments can be made for higher equilibrium program such as SLIDE with the seismic coef- values based on amplification effects. However, if several ficient modified for height effects. Assume that the critical inches of movement occur as demonstrated by the example surface passes beneath the structural element. If the capac- problem in Appendix J, a reduction in the peak seismic coef- ity to demand ratio is less than 1.0, estimate displacements.