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68 This chapter summarizes results of studies conducted for the seismic analysis and design of retaining walls. The primary objectives of these studies were to: â¢ Address limitations with current methods used to estimate seismic earth pressures on retaining walls. These limita- tions include difï¬culties in using the M-O equations for certain combinations of seismic coefï¬cient and backslope above the retaining structure or for backï¬ll conditions where soils are not cohesionless or are not uniform. â¢ Develop guidance on the selection of the seismic coefï¬cient used to conduct either a force-based or displacement-based evaluation of the seismic performance of retaining walls. There is considerable confusion in current practice on the selection of the seismic coefï¬cient, particularly for different wall types. â¢ Provide recommendations on methodologies to use for the seismic analysis and design of alternate wall types that can be used to develop LRFD speciï¬cations. The approach taken to meet these objectives involved using results from the ground motion and wave scattering studies discussed in the previous two chapters. Speciï¬cally, the ap- proach for determining ground motions and displacements summarized in Chapter 5 provides the information needed for a force-based design and for determining retaining wall displacements. The information in Chapter 6 is used for mod- ifying the site-adjusted PGA to account for wave scattering ef- fects. With this information two methodologies are provided for the seismic analysis and design of retaining walls. The ï¬rst involves use of the classic M-O equations, and the second uses a more GLE methodology for cases where the M-O pro- cedure is not applicable or where an estimate of retaining wall displacements is desired. 7.1 Current Design Practice Various wall types are commonly used for transportation systems. A useful classiï¬cation of these wall types is shown in Figure 7-1 (FHWA 1996), which uses terminology adopted in the AASHTO LRFD Bridge Design Specifications. The cut and ï¬ll designations refer to how the wall is constructed, not nec- essarily the nature of the earthwork (cut or ï¬ll) associated with the wall. For example, a ï¬ll wall, such as a MSE wall or a nongravity cantilever wall, may be used to retain earth ï¬ll for a major highway cut as illustrated in the representative Fig- ures 7-2 to 7-5 showing wall types. This becomes an impor- tant factor in the subsequent discussions related to external seismic stability of such walls. Current AASHTO LRFD Bridge Design Specifications address seismic design of retaining wall types as summarized in the following paragraphs: 1. Conventional gravity and semi-gravity cantilever walls (Article 11.6.5). The seismic design provisions cite the use of the M-O method (specified in Appendix A, Article A18.104.22.168) to estimate equivalent static forces for seismic loads. Reductions due to lateral wall movements are per- mitted as described in Appendix A (A22.214.171.124). 2. Nongravity cantilever walls (Article 11.8.6). Seismic design provisions are not explicit. Rather reference is made to an accepted methodology, albeit the M-O equations are sug- gested as a means to compute active and passive pressures provided a seismic coefï¬cient of 0.5 times the site-adjusted PGA is used. 3. Anchored walls (Article 11.9.6). Seismic design provi- sions are not explicit, and reference is made to M-O method for cantilever walls. However, Article A126.96.36.199 indicates that, For abutments restrained against lateral movement by tiebacks or batter piles, lateral pressures induced by inertia forces in the backfill will be greater than those given by the Mononobe-Okabe analysis. The discussion goes on to suggest using a factor of 1.5 in conjunction with site-adjusted PGA for design âwhere doubt exists that an abutment can yield sufficiently to mobilize soil strength.â C H A P T E R 7 Retaining Walls
69 Figure 7-1. Earth retaining system classification (after FHWA, 1996). Figure 7-2. Wall types (after FHWA, 1996).
70 Figure 7-4. MSE wallsâconstruction configurations. Completed MSE wall Geotextile wall Figure 7-3. MSE wall types (after FHWA, 1996).
71 4. MSE walls (Article 11.10.7). Seismic design provisions are very explicit and are deï¬ned for both external and internal stability. For external stability the dynamic component of the active earth pressure is computed using the M-O equa- tion. Reductions due to lateral wall movement are per- mitted for gravity walls. Fifty percent of the dynamic earth pressure is combined with a wall inertial load to evaluate stability, with the acceleration coefï¬cient modiï¬ed to ac- count for potential ampliï¬cation of ground accelerations. In the case of internal stability, reinforcement elements are designed for horizontal internal inertial forces acting on the static active pressure zone. 5. Prefabricated modular walls (Article 11.11.6). Seismic de- sign provisions are similar to those for gravity walls. 6. Soil-nail walls. No static or seismic provisions are currently provided in AASHTO LRFD Bridge Design Specifications. However, an FHWA manual for the design of nail walls (FHWA, 2003) suggests following the same general pro- cedures as used for the design of MSE walls, which involves the use of the M-O equation with modiï¬cations for iner- tial effects. The use of the M-O equations to compute seismic active and passive earth pressures is a dominant factor in wall design. Limitations and design issues are summarized in the follow- ing sections. Figure 7-5. Cut slope construction. 7.2 The M-O Method and Limitations The analytical basis for the M-O solution for calculating seismic active earth pressure is shown in Figure 7-6 (taken from Appendix A188.8.131.52 of the AASHTO LRFD Bridge Design Specifications). This ï¬gure identiï¬es the equations for seismic active earth pressures (PAE), the seismic active earth pressure coefficient (KAE), the seismic passive earth pres- sure (PPE), and the seismic active pressure coefficient (KPE). Implicit to these equations is that the soil within the soil is a homogeneous, cohesionless material within the active or passive pressure wedges. 7.2.1 Seismic Active Earth Pressures In effect, the solution for seismic active earth pressures is analogous to that for the conventional Coulomb active pres- sure solution for cohesionless backï¬ll, with the addition of a horizontal seismic load. Representative graphs showing the effect of seismic loading on the active pressure coefï¬cient KAE are shown in Figure 7-7. The effect of vertical seismic loading is traditionally neglected. The rationale for neglecting verti- cal loading is generally attributed to the fact that the higher frequency vertical accelerations will be out of phase with the horizontal accelerations and will have positive and negative contributions to wall pressures, which on average can rea- sonably be neglected for design.
72 Figure 7-7. Effect of seismic coefficient and soil friction angle on active pressure coefficient. Figure 7-8. Effect of backfill slope on the seismic active earth pressure coefficient using M-O equation, where CF = seismic coefficient. of 38Â° in a Ï = 35Â° material. The M-O solution increases sig- niï¬cantly if the seismic coefï¬cient increases to 0.25 for the same case, as the failure plane angle decreases to 31Â°. In prac- tice, however, as shown in Figures 7-3 to 7-5, the failure plane would usually intersect firm soils or rock in the cut slope behind the backfill rather than the slope angle defined by a purely cohesionless soil, as normally assumed during the M-O analyses. Consequently, in this situation the M-O solu- tion is not valid. A designer could utilize an M-O approach for simple non- homogeneous cases such as shown in Figure 7-10 using the following procedure, assuming Ï1< Ï2: Figure 7-6. M-O solution. Seismic Active Earth Pressure AEP H kv= â0 5 12. Î³ ( ) = K P AE PE Seismic Passive Earth Pressure 0 5. Î³ Ï Î¸ Î² Î¸ Î² H k Kv2 2 2 1â( ) = â â( ) PE AE where K cos cos cos cos sin sin cos co Î´ Î² Î¸ Ï Î´ Ï Î¸ Î´ Î² Î¸ + +( ) Ã â +( ) â â( ) + +( )1 i s cos cos cos cos i KPE â( ) â¡ â£â¢ â¤ â¦â¥ = â +( ) â Î² Ï Î¸ Î² Î¸ Î² Î´ 2 2 2 â +( ) Ã â +( ) â +( ) â +( ) â Î² Î¸ Ï Î´ Ï Î¸ Î´ Î² Î¸1 sin sin cos cos i i Î²( ) â¡ â£â¢ â¤ â¦â¥ â2 Î³ = unit weight of soil (ksf) H = height of wall (ft) Ï = friction angle of soil (Â°) Î¸ = arc tan (kh/(1 â kv))(Â°) Î´ = angle of friction between soil and wall (Â°) kh = horizontal acceleration coefï¬cient (dim.) kv = vertical acceleration coefï¬cient (dim.) i = backï¬ll slope angle (Â°) Î² = slope of wall to the vertical, negative as shown (Â°) Figure 7-8 shows the effect of backfill slope angle on KAE as a function of seismic coefficient, and illustrates the design dilemma commonly encountered of rapidly increasing earth pressure values with modest increases in slope angles. Fig- ure 7-9 indicates the underlying reason, namely the fact that the failure plane angle Î± approaches that of the backï¬ll slope angle Ï, resulting in an inï¬nite mass of the active failure wedge. For example, for a slope angle of 18.43Â° (3H:1V slope) and a seismic coefï¬cient of 0.2, the failure plane is at an angle
M-O method may be used, such as the well-known, graphical Culmann method illustrated in Figure 3-1. The principles of the Culmann wedge method have been incorporated in the Caltransâ computer program CT-FLEX (Shamsabadi, 2006). This program will search for the critical failure surface corre- sponding to the maximum value of PAE for nonuniform slopes and backï¬lls, including surcharge pressures. For uniform cohesive backfill soils with c and Ï strength parameters, solutions using M-O analysis assumptions have been developed, as discussed in Section 7.3. However, the most versatile approach for complex backfill and cut slope geometries is to utilize conventional slope stability programs, as described in Section 7.4. 7.2.2 Seismic Passive Earth Pressures The M-O equation for passive earth pressures also is shown in Figure 7-6. The seismic passive pressure becomes impor- tant for some wall types that develop resistance from loading of the embedded portion of the wall. If the depth of embed- ment is limited, as in the case of many gravity, semi-gravity, and MSE walls, the importance of the passive earth pressure to overall equilibrium is small, and therefore, using the static passive earth pressure is often acceptable. In the case of nongravity cantilever walls and anchored walls the structural members below the excavation depth depend on the passive earth pressure for stability and therefore the effects of seismic loading on passive earth pressures can be an important contribution. Work by Davies et al. (1986) shows that the seismic passive earth pressure can decrease by 25 per- cent relative to the static passive earth pressure for a seismic coefï¬cient of 0.4. This decrease is for a Ï = 35 degree material and no backslope or wall friction. 73 Figure 7-10. Application of M-O method for nonhomogeneous soil. Figure 7-9. Active failure plane angle based on M-O equation. 1. Calculate the active pressure PAE1 and active failure plane angle (Î±AE1) for the backï¬ll material. Graphs such as Fig- ures 7-8 and 7-9 may be used for simple cases. 2. If Î±AE1<Î±1/2, the solution stands and PAE1 gives the correct seismic active pressure on the wall. 3. If Î±AE1>Î±1/2, calculate the active pressure (PAE2) and active failure plane angle (Î±AE2) for the native soil material. For cohesive (c-Ï) soils, solutions described in Section 7.3 may be used. Also, calculate the active pressure (PAEi) for the given interface between two soils from limit equilibrium equations. The larger of PAEi and PAE2 gives the seismic ac- tive pressure on the wall. In most cases, the native soil cut will be stable, in which case it will be clear that the active pressure corresponding to the cut angle Î±1/2 will govern. For more complex cases in- volving nonuniform backslope proï¬les and backï¬ll/cut slope soils, numerical procedures using the same principles of the
Although the reduction in passive earth pressure during seismic loading is accounted for in the M-O equation for passive pressures (Equation A184.108.40.206-4 in AASHTO LRFD Bridge Design Specifications), the M-O equation for passive earth pressures is based on a granular soil and Coulomb failure theory. Various studies have shown that Coulomb theory is unconservative in certain situations. Similar to the M-O equation for active earth pressure, the M-O equation for passive earth pressure also does not include the contri- butions of any cohesive content in the soil. The preferred approach for passive earth pressure determination is to use log spiral procedures, similar to the preferred approach for gravity loading. Shamsabadi et al. (2007) have published a generalized approach that follows the log spiral procedure, while accounting both for the inertial forces within the soil wedge and the cohesive content within the soil. A key consideration during the determination of static passive pressures is the wall friction that occurs at the soil- wall interface. Common practice is to assume that some wall friction will occur for static loading. The amount of inter- face friction for static loading is often assumed to range from 50 to 80 percent of the soil friction angle. Similar guidance is not available for seismic loading. In the absence of any guidance, the static interface friction value often is used for seismic design. Another important consideration when using the seismic passive earth pressure is the amount of deformation required to mobilize this force. The deformation to mobilize the pas- sive earth pressure during static loading is usually assumed to be large, say 2 to 5 percent of the embedded wall height, depending on the type of soil (that is, granular soils will be closer to the lower limit while cohesive soils are closer to the upper limit). Only limited guidance is available for seismic loading (for example, see Shamsabadi et al., 2007), and there- fore the displacement to mobilize the seismic passive earth pressure is often assumed to be the same as for static loading. 7.3 M-O Earth Pressures for Cohesive Soils The M-O equation has been used to establish the appro- priate earth pressure coefficient (KAE) for a given seismic coefficient kh. Although it is possible to use the Coulomb method to develop earth pressure equations or charts that include the contribution of any cohesive content, the avail- able M-O earth pressure coefficient equations and charts have been derived for a purely cohesionless (frictional) soil where the soil failure criteria would be the Mohr-Coulomb failure criterion, parameterized by the soil friction angle, Ï. However, experience from limit equilibrium slope stability analyses shows that the stability of a given slope is very sensi- tive to the soil cohesion, even for a very small cohesion. 7.3.1 Evaluation of the Contribution from Cohesion Most natural cohesionless soils have some fines content that often contributes to cohesion, particularly for short-term loading conditions. Similarly, cohesionless backï¬lls are rarely fully saturated, and partial saturation would provide for some apparent cohesion, even for clean sands. In addition, it appears to be common practice in some states, to allow use of backï¬ll soils with 30 percent or more ï¬nes content (possibly contain- ing some clay fraction), particularly for MSE walls. Hence the likelihood in these cases of some cohesion is very high. The effect of cohesion, whether actual or apparent, is an impor- tant issue to be considered in practical design problems. The M-O equations have been extended to c-Ï soils by Prakash and Saran (1966), where solutions were obtained for cases including the effect of tension cracks and wall adhesion. Similar solutions also have been discussed by Richards and Shi (1994) and by Chen and Liu (1990). To further illustrate this issue, analyses were conducted by deriving the M-O equations for active earth pressures and extending it from only a Ï soil failure criterion to a generalized c-Ï soil failure criterion. Essentially, limit equilibrium analyses were conducted using trial wedges. The active earth pressure value (PAE) was computed to satisfy the condition of moment equilibrium of each of the combinations of the assumed trial wedge and soil shear strength values over the failure surface. The conï¬gurations of the trial wedges were varied until the relative maximum PAE value was obtained for various hori- zontal seismic coefï¬cient kh. The planar failure mechanism is retained in the analyses and is a reasonable assumption for the active earth pressure problem. Zero wall cohesion was assumed and tension cracks were not included. 7.3.2 Results of M-O Analyses for Soils with Cohesion Figure 7-11 and Figure 7-12 present active earth pressure co- efï¬cient charts for two different soil friction angles with differ- ent values of cohesion for horizontal backï¬ll, assuming no ten- sion cracks and wall adhesion. Within each chart, earth pressure coefï¬cients are presented as a function of the seismic coefï¬cient (kh,) and various values of cohesion (c). The c value was nor- malized by the product Î³ H where Î³ is the unit weight of soil and H is the wall height in the presented design charts. The following illustrates both the use and the importance of the cohesive contribution: 1. For a typical compacted backï¬ll friction angle of 40 degrees, the c/Î³ H would be about 0.083 and 0.167 for a slope height (H) of 20 feet and 10 feet, respectively (for a Î³ = 120 pcf in combination of a small cohesion value c = 200 psf). 2. From Figure 7-12 (for Ï = 40 degrees), it can seen that the resultant design force coefï¬cients Kae for a seismic coefï¬cient 74
75 Figure 7-11. Seismic coefficient charts for c- soils for 35. Figure 7-12. Seismic coefficient charts for c- soils for 40. kh = 0.3 would be (i) 0.4 for no cohesion; (ii) 0.25 for a wall height 20 feet with 200 psf cohesion, and (iii) be 0.1 for a wall height at 10 feet with 200 psf cohesion. 7.3.3 Implication to Design From this example, it can be observed that a small amount of cohesion would have a signiï¬cant effect in reducing the dynamic active earth pressure for design. The reduction for typical design situations could be on the order of about 50 per- cent to 75 percent. For many combinations of smaller kh con- ditions (which would be very prevalent for CEUS conditions) and also shorter wall heights, a rather small cohesion value would imply that the slope is stable and the soil capacity, in it- self, would have inherent shear strength to resist the inertial soil loading leading to the situation of zero additional earth pres- sure imparted to the retaining wall during a seismic event. This phenomenon could be a factor in explaining the good per- formance of retaining walls in past earthquakes. To illustration this, traditionally reduction factors on the order of about 0.5 have been applied to the site-adjusted PGA to determine the seismic coefï¬cient used in wall design. Wall movement is a recognized justiï¬cation for the reduction fac- tor as previously discussed. However, the wall movement con- cept may not be correct for retaining walls supported on piles, particularly if battered piles are used to limit the movement of the wall. In this case the contributions of a small amount of cohesion (for example, 200 psf) could effectively reduce the seismic coefï¬cient of a 20-foot tall wall by a factor of 0.5, thereby achieving the same effects as would occur for a wall that is able to move.
Mobilization of cohesion could signiï¬cantly reduce seis- mic earth pressures to include such reductions in design prac- tice is not always straight forward due to uncertainties in es- tablishing the magnitude of the cohesion for compacted ï¬lls where mixed c-Ï conditions exist under ï¬eld conditions. This is particularly the case for cohesionless ï¬lls, where the degree of saturation has a signiï¬cant effect on the apparent cohesion from capillarity. From a design perspective, uncertainties in the amount of cohesion or apparent cohesion makes it difï¬cult to incorporate the contributions of cohesion in many situations, particularly in cases where clean backï¬ll materials are being used, regard- less of the potential beneï¬ts of partial saturation. However, where cohesive soils are being used for backï¬ll or where native soils have a clear cohesive content, then the designer should give consideration to incorporating some effects of cohesion in the determination of the seismic coefï¬cient. 7.4 GLE Approach for Determining Seismic Active Pressures To overcome the limitations of the M-O method for cases involving nonhomogeneous soils and complex backslope geometry, conventional limit-equilibrium slope stability com- puter programs may be used. The concept has been illustrated, in a paper by Chugh (1995). For the purpose of both evalu- ation of this approach and application to examples used for the recommended methodology (Appendix F), the computer program SLIDE (RocScience, 2005), a program widely used by geotechnical consultants, was used. The basic principle in using such programs for earth pres- sure computations is illustrated in Figure 7-13. Steps in the analysis are as follows: 1. Setup the model geometry, ground water profile, and design soil properties. The internal face of the wall, or the plane where the earth pressure needs to be calculated, should be modeled as a free boundary. 2. Choose an appropriate slope stability analysis method. Spencerâs method generally yields good results because it satisï¬es the equilibrium of forces and moments. 3. Choose an appropriate sliding surface search scheme. Circular, linear, multi-linear, or random surfaces can be examined by SLIDE and other commercial slope stabil- ity analysis programs. 4. Apply the earth pressure as a boundary force on the face of the retained soil. The location of the force is assumed at one-third from the base (1â3 H, where H is retained soil height) for static cases. For seismic cases the location can be reasonably assumed at mid height (0.5 H) of the retained soil. However, different application points between 1â3 H and 2â3 H from the base can be examined to determine the maximum seismic earth pressure. The angle of applied force depends on assumed friction angle between wall and soil. A horizontal load simulates a smooth wall, whereas a load inclined at Ï degrees indicates that the friction angle between wall and soil is equal or greater than internal fric- tion angle of the soil. 5. Change the magnitude of the applied load until a minimum ratio of C/D of 1.0 is obtained. The C/D ratio is equivalent to the factor of safety for the analyses. The force correspon- ding to a C/D ratio of 1.0 is equal to total earth pressure on the retaining structure. 6. Verify design assumptions and material properties by examining the loads on individual slices in the output. The program SLIDE was calibrated against M-O solutions by considering examples shown on Figures 7-14 and 7-15. The first set of figures shows the application of SLIDE for computing active earth pressure on a wall with horizontal backï¬ll. The two analyses in Figure 7-14A show the compu- tation of the active earth pressure for a homogeneous backï¬ll and seismic acceleration of 0.2g and 0.4g. The calculated re- sults are identical to results from the M-O equation. The two analyses in Figure 7-14B show computation of the active earth pressure for a case with nonhomogenous backfill. Fig- ures 7-15A and 7-15B show the similar analyses for a wall with sloping backfill. 7.5 Height-Dependent Seismic Design Coefficients Current AASHTO LRFD Bridge Design Specifications use peak ground acceleration in conjunction with M-O analysis to compute seismic earth pressures for retaining walls. Ex- cept for MSE walls where amplification factors as a function of peak ground acceleration are used, based on studies by Segrestin and Bastick (1988), the current approach makes no adjustments in assigned ground acceleration for wall height. Chapter 6 provides a fundamental approach for making these adjustments based on scattering analyses for elastic soils. To conï¬rm that the recommendations in Chapter 6 apply for sit- uations where there is an impedance contrast between foun- dation and ï¬lls, and the possible inï¬uence of nonlinear soil behavior, an additional set of analyses was performed. Results 76 Figure 7-13. Adoption of slope stability programs to compute seismic earth pressure (Chugh, 1995).
77 Figure 7-14A. SLIDE calibration analyses for horizontal backfill (homogeneous soil conditions). of these analyses are used with the results of the analyses in Chapter 6 to develop recommendations for height-dependent seismic design coefï¬cients. 7.5.1 Evaluation of Impedance Contrasts and Soil Behavior To examine the effects of impedance contrasts and nonlin- ear soil behavior on height effects, one-dimensional SHAKE91 (1992) analyses were undertaken and are documented in detail in Appendix G. The initial set of SHAKE analyses re- peated many of the parameters originally evaluated by Seg- restin and Bastick: â¢ 20-foot wall height. â¢ Three different shear wave velocities for soil supporting the wall (820 ft/sec; 1,200 ft/sec; and 3,300 ft/sec). Idriss mod- ulus and damping versus shearing strain curves for rock. â¢ Compacted backï¬ll within wall with Ï = 30 degrees and maximum shear modulus (Gmax) equal to 70 (Ïâ²m)0.5. The
78 Figure 7-14B. SLIDE calibration analyses for horizontal backfill (nonhomogeneous soil conditions). ternal stability evaluations in the AASHTO LRFD Bridge Design Specifications. Plots showing these comparisons are provided in Appendix G. These results show ampliï¬cation at the top of the wall, as well as maximum average acceleration along the wall height, similar to results from Segrestin and Bastick. However, the latter studies were limited to 20-foot high (6 meter) walls. Additional parametric studies were subsequently con- ducted to evaluate the effects of wall heights, impedance Seed and Idriss modulus and damping curves were used to represent shearing strain effects. â¢ Nine ground motions consistent with the discussions in Chapter 5, including the two used by Segrestin and Bastick. These studies were successfully calibrated against studies un- dertaken by Segrestin and Bastick (1988) for MSE walls, which forms the basis for MSE wall backï¬ll seismic coefï¬cients and ex-
79 Figure 7-15A. SLIDE calibration analyses for sloping backfill (homogeneous soil conditions). 7.5.2 Results of Impedance Contrast and Nonlinearity Evaluations Results of the studies summarized above and described in Appendix G generally follow trends similar to the wave scattering studies described in Chapter 6. However, based on a study of the results and to simplify the results for the development of recommended speciï¬cations and commen- contrasts, and accelerations levels, using the same SHAKE models: â¢ Response evaluated at wall heights of 20, 50, and 100 feet. â¢ The low-strain shear modulus changed to Gmax = 59 (Ïâ²m)0.5 to correspond to a relative density of 75 percent, which was judged to be more realistic. â¢ Nine ground motions used as noted above.
80 Figure 7-15B. SLIDE calibration analyses for sloping backfill (nonhomogeneous soil conditions). taries for the AASHTO LRFD Bridge Design Specifications, the use of a simple linear function to describe reductions in average height-dependent seismic coefficients, as shown in Figure 7-16, is recommended. Comparisons with the curves resulting from the height-dependent scattering studies also are noted in Figure 7-16. Curves in Figure 7-16 from Chapter 6 are for slightly differ- ent equivalent Î² values than shown for the simpliï¬ed approach. These values are 1.7, 1.1, and 0.4 for UB, mid, and LB spectral response, respectively. The differences in the Î² values explain the difference between the locations of the lines for the curves from Chapter 6 versus the simpliï¬ed straight-line functions.
Recommendations for seismic coefï¬cients to be used for earth pressure evaluations based on the simpliï¬ed straight line functions shown can be expressed by the following equations: where kmax = peak seismic coefï¬cient at the ground surface = Fpga PGA; and Î± = ï¬ll height-dependent reduction factor. For C, D, and E foundations soils where H = ï¬ll height in feet; and Î² = FvS1/kmax. For Site Class A and B foundation conditions (that is, hard and soft rock conditions) the above values of Î± should be increased by 20 percent. For wall heights greater than 100 feet, Î± coefï¬cients may be assumed to be the 100-foot value. Note also for practical purposes, walls less than say 20 feet in height and on very firm ground conditions (B/C founda- tions), kav â kmax which has been the traditional assumption for design. 7.6 Displacement-Based Design for Gravity, Semi Gravity, and MSE Walls The concept of allowing walls to slide during earthquake loading and displacement-based design (that is, assuming a Newmark sliding block analysis to compute displacements Î± Î²= + ( ) â[ ]1 0 01 0 5 1. . ( )H 7-2 k kav = Î± max ( )7-1 81 Figure 7-16. Simplified height-dependent scaling factor recommended for design. Figure 7-17. Concept of Newmark sliding block analysis (AASHTO, 2007). when accelerations exceed the horizontal limiting equilibrium yield acceleration) was introduced by Richards and Elms (1979). Based on this concept (as illustrated in Figure 7-17), Elms and Martin (1979) suggested that a design acceleration coefï¬cient of 0.5A in M-O analyses would be adequate for limit equilibrium pseudo-static design, provided allowance be made for a horizontal wall displacement of 10A (in inches). The design acceleration coefficient (A) is the peak ground acceleration at the base of the sliding wedge behind the wall in gravitational units (that is, g). This concept was adopted by AASHTO in 1992, and is reï¬ected in following paragraph taken from Article 11.6.5 of the 2007 AASHTO LRFD Bridge Design Specifications. Where all of the following conditions are met, seismic lateral loads may be reduced as provided in Article C11.6.5, as a result of lateral wall movement due to sliding, from values determined
using the Mononobe-Okabe method speciï¬ed in Appendix A11, Article A220.127.116.11: â¢ The wall system and any structures supported by the wall can tolerate lateral movement resulting from sliding of the struc- ture. â¢ The wall base is unrestrained against sliding, other than soil friction along its base and minimal soil passive resistance. â¢ If the wall functions as an abutment, the top of the wall must also be restrained, e.g., the superstructure is supported by slid- ing bearings. The commentary for this Article notes that, In general, typical practice among states located in seismically active areas is to design walls for reduced seismic pressures cor- responding to 2 to 4 inches of displacement. However, the amount of deformation which is tolerable will depend on the nature of the wall and what it supports, as well as what is in front of the wall. Observations of the performance of conventional cantilever gravity retaining walls in past earthquakes, and in particu- lar during the Hyogoken-Nambu (Kobe) earthquake in 1995, have identiï¬ed signiï¬cant tilting or rotation of walls in addition to horizontal deformations, reï¬ecting cyclic bearing capacity failures of wall foundations during earthquake loading. To accommodate permanent wall deformations involving mixed sliding and rotational modes of failure using Newmark block failure assumptions, it is necessary to formulate more complex coupled equations of motions. Coupled equations of motion may be required for evaluat- ing existing retaining walls. However, from the standpoint of performance criteria for the seismic design of new conven- tional retaining walls, the preferred design approach is to limit tilting or a rotational failure mode, to the extent possible, by ensuring adequate ratios of capacity to earthquake demand (that is, high C/D ratios) for foundation bearing capacity fail- ures and to place the design focus on performance criteria that ensure acceptable sliding displacements (that is lower C/D ratios relative to bearing or overturning). For weaker foundation materials, this rotational failure requirement may result in the use pile or pier foundations, where lateral seis- mic loads would be larger than those for a sliding wall. Much of the recent literature on conventional retaining wall seismic analysis, including the European codes of practice, focus on the use of Newmark sliding block analysis methods. For short walls (less than 20-feet high), the concept of a back- ï¬ll active failure zone deforming as a rigid block is reasonable, as discussed in the previous paragraph. However, for higher walls, the dynamic response of the soil in the failure zone leads to non-uniform accelerations with height and negates the rigid-block assumption. For wall heights greater than 20 feet, the use of height- dependent seismic coefficients is recommended to deter- mine maximum average seismic coefficients for active fail- ure zones, and may be used to determine kmax for use in Newmark sliding block analyses. In effect, this represents an uncoupled analysis of deformations as opposed to a fully coupled dynamic analysis of permanent wall deformations. However, this approach is commonly used for seismic slope stability analyses, as discussed in Chapter 8. The existing AASHTO LRFD Bridge Design Specifications use an empirical equation based on peak ground acceleration to compute wall displacements for a given wall yield acceler- ation. This equation was derived from studies of a limited number of earthquake accelerations, and is of the form: where ky = yield acceleration; kmax = peak seismic coefï¬cient at the ground surface; V = maximum ground velocity (inches/sec), which is the same as PGV discussed in this report; and d = wall displacement (inches). Based on a study of the ground motion database described in Chapter 5, revised displacement functions are recom- mended for determining displacement. For WUS sites and CEUS soil sites (Equation 5-8) For CEUS rock sites (Equation 5-6) where kmax = peak seismic coefï¬cient at the ground surface; and PGV = peak ground velocity obtained from the design spectral acceleration at 1 second and adjusted for local site class (that is, Fv S1) as described in Chapter 5. The above displacement equations represent mean values and can be multiplied by 2 to obtain an 84 percent conï¬dence level. A comparison with the present AASHTO equation is shown in Figure 7-18. 7.7 Conventional Gravity and Semi-Gravity Wallsâ Recommended Design Method for External Stability Based on material presented in the previous paragraphs, the recommended design methodology for conventional gravity and semi-gravity walls is summarized by the following steps: log . . log . logmax mad k k k ky y( ) = â â ( ) + â1 31 0 93 4 52 1 x max. log . log ( ) â ( ) + ( )0 46 1 12k PGV log . . log . logmax mad k k k ky y( ) = â â ( ) + â1 51 0 74 3 27 1 x max. log . log ( ) â ( ) + ( )0 80 1 59k PGV d V k g k ky= ( )( )â0 087 2 4. ( )max max 7-3 82
1. Establish an initial wall design using the AASHTO LRFD Bridge Design Specifications for static loading, using appro- priate load and resistance factors. This establishes wall dimensions and weights. 2. Estimate the site peak ground acceleration coefficient (kmax) and spectral acceleration at 1 second (S1) from the 1,000-year seismic hazards maps adopted by AASHTO (including appropriate site soil modification factors). 3. Determine the corresponding PGV from the correlation equation between S1 and PGV (Equation 5-11, Chapter 5). 4. Modify kmax to account for wall height effects as described in Figure 7-16 of Section 7.5. 5. Evaluate the potential use of the M-O equation to deter- mine PAE (Figure 7-10) as discussed in Section 7.2, taking into account cut slope properties and geometry and the value of kmax from step 3. 6. If PAE cannot be determined using the M-O equation, use a limit-equilibrium slope stability analysis (as described in Section 7.4) to establish PAE. 7. Check that wall bearing pressures and overturning criteria for the maximum seismic load demand required to meet performance criteria. If criteria are met, check for sliding potential. If all criteria are met, the static design is satisfac- tory. If not, go to Step 8. 8. Determine the wall yield seismic coefï¬cient (ky) where wall sliding is initiated. 9. With reference to Figure 7-19, as both the driving forces [PAE(k), kWs, kWw] and resisting forces [Sr(k) and PPE(k)] are a function of the seismic coefï¬cient, the determination of ky for limiting equilibrium (capacity to demand = factor of safety = 1.0) requires an interactive procedure, using the following steps: 10. Determine values of PAE as a function of the seismic co- efï¬cient k (<kmax) as shown in Figure 7-20a. 83 Figure 7-18. Comparison between all except CEUS-Rock and AASHTO correlations for PGV 30 kmax. Figure 7-19. Seismic force diagram on retaining wall. 11. Determine horizontal driving and resisting forces as a function of k (using spreadsheet calculations) and plot as a function of k as shown in Figure 7-20b. The values of ky correspond to the point where the two forces are equal, that is, the capacity to demand ratio against slid- ing equals 1.0. 12. Determine the wall sliding displacement (d) based on the relationship between d, ky/kmax, kmax, and PGV described in Section 7.6. 13. Check bearing pressures and overturning criteria to con- firm that the seismic loads meet performance criteria for seismic loading (possibly maximum vertical bear- ing pressure less than ultimate and overturning factor of safety greater than 1.0). 14. If step 13 criteria are not met, adjust footing dimensions and repeat steps 6-12 as needed. 15. If step 13 criteria are satisï¬ed, assess acceptability of slid- ing displacement (d).
From design examples and recognizing that static designs have inherently high factors of safety, a recommendation to eliminate step 7 and replace it by a simple clause to reduce the seismic coefï¬cient from step 6 by a factor of 50 percent (as in the existing AASHTO Speciï¬cations) would seem realistic. This is particularly the case since the new displacement func- tion gives values signiï¬cantly less than the present AASHTO Speciï¬cations. 7.8 MSE WallsâRecommended Design Methods The current AASHTO Speciï¬cations for MSE walls largely are based on pseudo-static stability methods utilizing the M-O seismic active earth pressure equation. In this approach dy- namic earth pressure components are added to static compo- nents to evaluate external sliding stability or to determine re- inforced length to prevent pull-out failure in the case of internal stability. Accelerations used for analyses and the concepts used for tensile stress distribution in reinforcing strips largely have been inï¬uenced by numerical analyses conducted by Segrestin and Bastick (1988), as described in Appendix H. (A copy of the Segrestin and Bastick paper was included in earlier drafts of the NCHRP 12-70 Project report. However, copyright restrictions precluded including a copy of the paper in this Final Report.) 7.8.1 Current Design Methodology In the past 15 years since the adoption of the AASHTO de- sign approach, numerous publications on seismic design methodologies for MSE walls have appeared in the literature. Publications have described pseudo-static, limit equilibrium methods, numerical methods using dynamic analyses, and model test results using centrifuge and shaking table tests. A comprehensive summary of much of this literature was pub- lished by Bathurst et al. (2002). It is clear from review of this literature that consensus on a new robust design approach suit- able for a revised design speciï¬cation has yet to surface due to the complexity of the problems and ongoing research needs. Over the past several years, observations of geosynthetic slopes and walls during earthquakes have indicated that these types of structures perform well during seismic events. The structures have experienced small permanent deformations such as bulging of the face and cracking behind the structure, but no collapse has occurred. A summary of seismic ï¬eld per- formance is shown in Table 7-1. The inherent ductility and ï¬exibility of such structures combined with the conservatism of static design procedures is often cited as a reason for the sat- isfactory performance. Nevertheless, as Bathurst et al. (2002) note, seismic design tools are needed to optimize the design of these structures in seismic environments. In the following sections, the current AASHTO design methods for external and internal stability are described, and recommendations for modiï¬cations, including a brief com- mentary of outstanding design issues, are made. 7.8.2 MSE WallsâDesign Method for External Stability The current AASHTO design method for seismic external stability is described in Article 18.104.22.168 in Section 11 of the Speciï¬cations, and is illustrated in Figure 7-21. The method evaluates sliding stability of the MSE wall under combined static and earthquake loads. For wall inertial load and M-O active earth pressure evaluations, the AASHTO method adopts the Segrestin and Bastick (1988) recommendations, where the maximum acceleration is given by: where A is peak ground acceleration coefï¬cient. However, as discussed in Appendix H, the above equation is conservative for most site conditions, and the wall height- dependent average seismic coefï¬cient discussed in Figure 7-16 in Section 7.5 is recommended for both gravity and MSE wall design. A reduced base width of 0.5H is used to compute the mass of the MSE retaining wall used to determine the wall inertial load PIR in the AASHTO method (Equation 22.214.171.124-3). The apparent rationale for this relates to a potential phase differ- ence between the M-O active pressure acting behind the wall and the wall inertial load. Segrestin and Bastick (1988) recom- mend 60 percent of the wall mass compatible with AASHTO, whereas Japanese practice is to use 100 percent of the mass. A study of centrifuge test data shows no evidence of a phase difference. To be consistent with previous discussion on non- gravity cantilever walls, height effects, and limit equilibrium methods of analysis, the total wall mass should be used to compute the inertial load. The AASHTO LRFD Bridge Design Specifications for MSE walls separate out the seismic dynamic component of the force behind the wall instead of using a total active force PAE as discussed in Section 7.4. Assuming a load factor of 1.0, the A A Am = â( )1 45. ( )7-4 84 Figure 7-20. Design procedure steps.
following equation (Equation 126.96.36.199-2) is used to deï¬ne the seismic dynamic component of the active force: where Î³s = soil unit weight; and H = wall height. The use of the symbol PAE is confusing, as the seismic dy- namic increment is usually defined as ÎPAE. Whereas it is not immediately evident how this equation was derived, it P A HAE m s= 0 375 2. ( )Î³ 7-5 is assumed that use was made of the approximation for KAE suggested by Seed and Whitman (1970), namely: where KA = static active pressure coefï¬cient; and KAE = total earthquake coefï¬cient. Hence using the AASHTO terminology, ÎPAE = (0.75 Am) Ã 0.5 Î³sH2 = 0.375Am Î³s H2 K K kAE A h= + 0 75. ( )7-6 85 1 Reinforced Earth Co., 1990, 1991, 1994; 2 Collin et al., 1992; 3 Eliahu and Watt, 1991; 4 Stewart et al., 1994; 5 Sandri, 1994; 6 Sitar, 1995; 7 Tatsuoka et al., 1996; 8 Ling et al., 1997; 9 Ling et al., 1989; 10 Ling et al., 2001 Table 7-1. Summary of seismic field performance of reinforced soil structures (Nova-Roessig, 1999).
Note that the Seed and Whitman (1970) simplified ap- proach was developed for use in level-ground conditions. If the Seed and Whitman simplification was, in fact, used to develop Equation (7-6), then it is fundamentally appropri- ate only for level ground conditions and may underesti- mate seismic earth pressures where a slope occurs above the retaining wall. For external stability, only 50 percent of the latter force increment is added to the static active force, again reflecting either a phase difference with inertial wall loads or reflect- ing a 50 percent reduction by allowing deformation potential as suggested for cantilever walls. In lieu of the above, the rec- ommended approach for MSE walls is a design procedure similar to that for gravity and semi-gravity walls (Section 7.6), where a total active earthquake force is used for sliding sta- bility evaluations. It also is noted that the AASHTO LRFD Bridge Design Spec- ifications suggest conducting a detailed lateral deformation analysis using the Newmark method or numerical modeling if the ground acceleration exceeds 0.29g. However, as dis- cussed for gravity and semi-gravity walls, due to the inherently high factors of safety used for static load design, in most cases yield seismic coefï¬cients are likely to be high enough to min- imize potential sliding block displacements. 86 Figure 7-21. Seismic external stability of a MSE wall (AASHTO, 2007).
7.8.3 MSE WallsâDesign Method for Internal Stability The current AASHTO design method for seismic internal stability is described in Article 188.8.131.52 of Section 11 of the AASHTO Specifications, and is illustrated in Figure 7-22. The method assumes that the internal inertial forces gener- ating additional tensile loads in reinforcements act on an active pressure zone assumed to be the same for the static loading case. A bilinear zone is defined for inextensible re- inforcements such as metallic strips and a linear zone for extensible strips. Whereas it could reasonably be anticipated that these active zones would extend outwards for seismic cases, as for M-O analyses, numerical and centrifuge mod- els indicate that the reinforcement restricts such outward movements, and only relatively small changes in location are seen. The internal inertial force in the AASHTO method is cal- culated using the acceleration Am defined in Section 7.8.2 for the external stability case. As previously discussed, the ac- celeration equation used for external stability evaluations is too conservative for most site conditions, and the use of the wall-height dependent average seismic coefficient concept discussed in Section 7.5 is recommended. In the AASHTO method, the total inertial force is distributed to the reinforcements in proportion to their effective resistant lengths Lei as shown on Figure 7-22. This approach follows the ï¬nite element modeling conducted by Segrestin and Bastick (1988), and leads to higher tensile forces in lower reinforce- ment layers. This is the opposite trend to incremental seismic loading used by AASHTO for external stability evaluations based on the M-O equation. In the case of internal stability evaluation, Vrymoed (1989) used a tributary area approach that assumes the inertial load carried by each reinforcement layer increases linearly with height above the toe of the wall for equally spaced reinforcement layers. A similar approach was used by Ling et al. (1997) in limit equilibrium analyses. This concept would suggest that longer reinforcement lengths could be needed at the top of walls with increasing accelera- tion levels, and the AASHTO approach could be unconserv- ative. In view of this uncertainty in distribution that has been widely discussed in the literature, a suggested compromise is to distribute the inertial force uniformly within the reinforce- ment. In essence, this represents an average of the tensile load 87 Figure 7-22. Seismic internal stability of a MSE wall (AASHTO, 2007).
distribution from the existing AASHTO approach with that determined using the tributary area of strips in the inertial active zone. A computer program MSEW (ADAMA, 2005) has been developed and is commercially available to design MSE walls using the current AASHTO LRFD Bridge Design Specifica- tions. An application of the program to design a representa- tive wall is provided in Appendix I, where the older allowable stress design (ASD) speciï¬cations are compared to the LRFD specifications. A modest seismic coefficient of 0.1 is used for design. Slightly longer reinforcing strips are needed for the LRFD design, and seismic loading does not impact the de- sign. The suggested recommendations to modify the seismic design procedure (acceleration coefficients and tensile load distribution) cannot be directly incorporated in the program, but changes to the source code could be made with little effort, and the design impact of the changes examined by studying several examples. The work plan in Chapter 4 identiï¬ed a methodology in- volving the application of limit equilibrium programs for as- sessing internal stability of MSE walls. In particular the com- puter programs, SLIDE and ReSSA (Version 2), were going to be used to conduct detailed studies. After performing a limited evaluation of both programs, the following concerns were noted relative to their application to AASHTO LRFD Bridge Design Specifications: 1. Since static and seismic design methodologies should desir- ably be somewhat consistent, the adoption of such programs for seismic design means that a similar approach should be used for static design. This would require a major revi- sion to the AASHTO static LRFD design methodology. 2. Whereas the use of ReSSA (Version 2) for static analyses has been compared successfully to FLAC analyses by Leshchinsky and Han (2004), similar comparisons have not been identified for seismic loading problems. Such comparisons would provide more conï¬dence in the use of a limit equilibrium program to simulate the mechanics of loading. In particular the main concern is the distribution of seismic lateral forces to reinforcing strips from the limit equilibrium analyses. It would be of value if in future cen- trifuge tests, for example, strips could be instrumented to measure loads during seismic loading. In view of the these concerns, adoption of limit equilibrium analyses is not currently recommended for MSE internal sta- bility analysis, although future research on their potential application is warranted. Deformation design approaches are not identiï¬ed for inter- nal stability in the AASHTO Speciï¬cations. Such methods are complex as they involve sliding yield of reinforcing strips or possible stretch in the case of geosynthetic grids or geotextiles. Methods range from more complex FLAC computer analy- ses to simplified methods based on limit equilibrium and Newmark sliding block analyses. Bathurst et al. (2002) sum- marizes a number of these methods. Approaches based on limit equilibrium and Newmark sliding block methods are also described, for example, by Ling et al. (1997) and Paulsen and Kramer (2004). Comparisons are made in the latter two papers with centrifuge and shaking table test results, with some degree of success. However, the explicit application of these performance-based methods in the AASHTO LRFD Bridge Design Specifications at the present time is premature. 7.9 Other Wall Types Three other wall types were considered during this Project: (1) nongravity cantilever walls, (2) anchored walls, and (3) soil nail walls. The treatment of these walls has been less detailed than described above for semi-gravity and MSE walls. Part of this reduced effort is related to the common characteris- tics of the nongravity cantilever, anchored, and soil nail walls to the walls that were evaluated. The following subsections provide a summary of the recommended approach for these wall types. 7.9.1 Nongravity Cantilever Walls These walls include sheet pile walls, soldier pile and lagging walls (without anchors), and secant/tangent pile walls. Each of these walls is similar in the sense that they derive their resist- ance to load from the structural capacity of the wall located below the ground surface. The heights of these walls typically range from a few feet to as high as 20 to 30 feet. Beyond this height, it is usually necessary to use anchors to supplement the stiffness capacity of the wall system. The depth of the wall below the excavation depth is usually 1.5 to 2 times the height of the exposed wall face. 184.108.40.206 Seismic Design Considerations The conventional approach for the seismic design of these walls is to use the M-O equations. Article C11.8.6 of the AASHTO LRFD Bridge Design Specifications indicates that a seismic coefficient of kh = 0.5A is to be used and that wall inertial forces can be ignored. In this context A is the peak ground acceleration for the site based on the AASHTO haz- ard map and the site classiï¬cation. The use of the 0.5 factor implies that the wall is able to move, although this is not ex- plicitly stated. As discussed in previous sections, the original development of the 0.5 factor assumed that the wall could move 10A (in inches), which could be several inches or more and which would often be an unacceptable condition for this class of walls. 88
Most nongravity cantilever walls are flexible and there- fore the customary approach to static design is to assume that active earth pressure conditions develop. The amount of movement also will be sufï¬cient to justify use of the M-O equation for estimating seismic active earth pressures. How- ever, rather than the 0.5 factor currently given in the AASHTO Specifications, it is suggested that the wave scattering fac- tors described in Section 7.5 of this chapter be used. For typical nongravity cantilever walls, which have a height of 25 feet or less, this means that the factor will range from 0.8 to 0.9 rather than 0.5. The decision whether to use the 0.5 factor currently given in AASHTO will depend on the amount of permanent move- ment of the nongravity cantilever wall that is acceptable dur- ing the design seismic event. If the structural designer reviews the design and agrees that average permanent wall movements of 1 to 2 inches at the excavation level are acceptable, the seis- mic coefï¬cient used for design (after reducing for scattering effects) can be further reduced by a factor of up to 0.5. The acceptability of the 0.5 factor is based on several considerations: â¢ Allowable stresses within the wall are not exceeded during the earthquake and after the earthquake, since there is likely to be at least 1 to 2 inches of permanent wall move- ment at the excavation level. â¢ Weather conditions at the site will allow several inches of outward movement to develop. If pavements, sidewalks, or protective barriers prevent outward movement of 1 to 2 inches, then the reduction of 0.5 would not seem to be appropriate. â¢ Aesthetics of the wall after permanent movement are ac- ceptable. Often there will be some rotation with the move- ment at the excavation line, resulting in a wall that is lean- ing outward. This wall may be structurally acceptable but it may result in questions whether the ï¬ll is falling over. â¢ Movement at the excavation level or at the top of the wall, which will likely be at least 1 to 2 several inches because of rotation, do not damage utilities or other infrastructure located above or below the wall. Another important consideration is the characteristics of the soil being supported. Nongravity cantilever walls are normally constructed using a top-down method, where the structural support system is installed (that is, sheet pile or soldier pile) and then the earth is excavated from in front of the structural members. In many cases the natural soil behind the wall will have some cohesive content. As discussed in Section 7.3, the active earth pressure can be significantly re- duced if the soil has a cohesive component. If site explorations can conï¬rm that this cohesive component exists, then it makes sense that the design method accounts for this effect. One important difference for this class of walls relative to gravity walls and MSE walls is that the capacity of the wall depends on the passive pressure at the face of the structural unit: either the sheet pile or the soldier pile. For static loading, the passive pressure is usually estimated from charts as shown in Article 220.127.116.11 of the AASHTO LRFD Bridge Design Speci- fications. For soldier piles the effective width of the structural element below the base of the wall is assumed to be from 1 to 3 pile diameters to account for the wedge-shape form of soil reaction. The upper several feet of soil are also typically ne- glected for static passive earth pressure computation. This is done to account for future temporary excavations that could occur. In view of the low likelihood of the excavation occur- ring at the time of the design earthquake, this approach can be neglected for seismic load cases. Under seismic loading a reduction in the seismic passive pressure occurs. This reduction can be estimated using M-O equation for passive pressures (Equation A18.104.22.168-4). How- ever, as noted earlier in this chapter, the M-O equation for passive earth pressures is based on a granular soil and Coulomb failure theory. Various studies have shown that Coulomb theory can be unconservative in certain situations. The M-O equation also does not include the contributions of any cohe- sive content to the soil. Similar to the previous discussion for active pressures, the effects of cohesion on the passive earth pressure have been found to be signiï¬cant. As an alternative to the M-O passive pressure equation, the seismic passive earth pressure can be estimated using the charts in Figures 7-23 through 25. These charts show the relationship between KPE and kh as a function of the normalized soil cohe- sion. The charts were developed using log spiral procedures, following the methodology published by Shamsabadi et al. (2007). The interface friction for these charts is 0.67 Ï. Proce- dures described by Shamsabadi et al. can be used to estimate the seismic passive coefï¬cient for other interface conditions. Significant deformation is required to mobilize the pas- sive pressure, and therefore, for static design, the resulting passive pressure coefï¬cient is often reduced by some amount to control deformations. For static loading the reduction is usually 1.5 to 2. In the absence of specific studies showing otherwise, this same reduction may be appropriate for the seismic loading case in a limit equilibrium analysis, to limit the deformation of the nongravity cantilever. This approach would be taken if using the computer programs SPW 911 or SWALSHT. Alternately, a numerical approach, such as followed within the computer program PY WALL (Ensoft, 2005) can explicitly account for the displacement through the use of p-y springs. Programs such as L-PILE and COM624 also can be used to make these analyses, although appropriate consideration needs to be given to the development of p-y curves. These programs are not specifically set up for evaluating seismic response 89
Figure 7-25. Seismic passive earth pressure coefficient based on log spiral procedure (cont.) (c soil cohesion, soil total unit weight, and H is height). but can be used to evaluate seismic performance by intro- ducing appropriate soil pressures and reactions consistent with those expected to occur during a seismic event. Appen- dix K describes a study that was part of the NCHRP 12-70 Project that demonstrates the use of the general beam-column approach to evaluate nongravity cantilever retaining walls under seismic loading. Included within the Appendix K dis- cussion are recommendations on p- and y-multipliers to de- velop p-y curves for continuous (sheet pile) retaining walls. 22.214.171.124 Seismic Design Methodology The following approach is suggested for design of non- gravity cantilever walls: 1. Perform static design following the AASHTO LRFD Bridge Design Specifications. 2. Establish the site peak ground acceleration coefï¬cient (kmax) and spectral acceleration S1 at 1 second from the 1,000-year maps adopted by AASHTO (including appropriate site soil modiï¬cation factors). 3. Determine the corresponding PGV from correlation equa- tions between S1 and PGV (provided in Chapter 5). 4. Modify kmax to account for wall-height effects as de- scribed in Section 7.6. Include cohesion component as 90 Figure 7-23. Seismic passive earth pressure coefficient based on log spiral procedure (c soil cohesion, soil total unit weight, and H is height). Figure 7-24. Seismic passive earth pressure coefficient based on log spiral procedure (cont.) (c soil cohesion, soil total unit weight, and H is height).
appropriate. Apply a 0.5 factor to the resulting seismic co- efficient if 1 to 2 inches of average permanent movement can be accepted and conditions are such that they will develop. Otherwise use the kmax without further reduction. 5. Compute wall pressures using M-O equation for active pressure, the charts in Figures 7-11 and 7-12, or the gen- eralized limit equilibrium method. Estimate earth pres- sure for passive loading using charts in Figure 7-25 or the methodology published by Shamsabadi et al. (2007). Do not use the M-O equation for passive pressure. 6. Evaluate structural requirements using a suitable software package or through use of hand methods (for example, free earth support). Conï¬rm that displacements are sufï¬- cient to develop an active pressure state. 7. Check global stability under seismic loading using a limit equilibrium program such as SLIDE with the seismic coef- ï¬cient modiï¬ed for height effects. Assume that the critical surface passes beneath the structural element. If the capac- ity to demand ratio (that is, factor of safety) is less than 1.0, estimate displacements. The generalized limit equilibrium approach can be used where soil conditions, seismic coefï¬cient, or geometry warrant. In this analysis the contributions from the structural elements need to be included in the evaluation of stability. Programs such as SLIDE allow incorporation of the structural element through the use of an equivalent reaction, where the reaction of individual members is âsmearedâ to obtain an equivalent two-dimensional representation. 7.9.2 Anchored Walls The next class of walls is essentially the same as nongravity cantilever walls; however, anchors are used to provide addi- tional support to the walls. Typically the anchors are installed when the wall height exceeds 20 feet, or sometimes even at less height if a steep backslope occurs above the wall or the wall supports heavy loads from a structure. The height of anchored walls can exceed 100 feet. The anchored wall can be used in either cut or ï¬ll conditions. â¢ For ï¬ll conditions the reaction is usually provided by a deadman anchor. This wall type is generally limited to use at port facilities, where a single deadman anchor is used to augment the capacity of the wall. While deadman can be used for highway construction, particularly for retroï¬ts, other wall types, such as MSE or semi-gravity cantilever walls, are usually more cost-effective for new walls. â¢ For cut slope locations, the wall uses one or more grouted anchors to develop additional capacity. Anchors are usu- ally installed at approximately 10-foot vertical spacing; horizontal spacing of the soldier piles is often 8 to 10 feet. AASHTO LRFD Bridge Design Specifications provide spe- ciï¬c guidance on the minimum length of the anchors in Figure 11.9.1-1. One of the key factors for the anchored wall is that each anchor is load tested during the construction process. The load test is used to confirm that the anchor will meet long- term load requirements. The testing typically includes ap- plying from 1.5 to 2 times the design (working) load and monitoring creep of the anchor. Well-defined criteria exist for determining the acceptability of the anchor during proof or performance testing. 126.96.36.199 Seismic Design Considerations The AASHTO LRFD Bridge Design Specifications provide limited guidance for the seismic design of anchored walls. Article 11.9.6 indicates that, âthe provisions in Article 11.8.6 shall apply.â The referenced article deals with nongravity cantilever walls, and basically states that the M-O equations should be used with the seismic coefï¬cient kh = 0.5A. Various other methods also have been recommended for the seismic design of anchored walls: â¢ The FHWA report Geotechnical Earthquake Engineering (FHWA, 1998a) presents an approach for walls anchored with a single deadman. This method suggests using the M-O equations to estimate the seismic active and passive pressures. The design method recommends that the anchors be located behind the potential active failure surface. This failure surface is ï¬atter than that used for the static stabil- ity analysis. â¢ A more recent FHWA document Ground Anchors and Anchored Systems (FHWA, 1999) provides discussions on the internal stability using pseudo-static theory and external stability. Again the approach is to use the M-O equations. The document notes that, use of a seismic coefï¬cient from between one-half and two- thirds of the peak horizontal ground acceleration divided by gravity would appear to provide a wall design that will limit deformations in the design earthquake to small values acceptable for highway facilities. The seismic active earth pressure is assumed to be uni- formly distributed over the height of the wall. â For the grout tendon bond, considered a brittle element of the system, the report suggests using the site-adjusted PGA with no reductions in the M-O equations to obtain a peak force and that a factor of safety against brittle fail- ure be 1.1 or greater. â For ductile elements (for example, tendons, sheet piles, and soldier piles) the seismic coefficient in the M-O method is 0.5 times the site-adjusted PGA. The Newmark method is used as the basis of this recommendation. For this condition the factor of safety should be 1.1 or greater. 91
A global check on stability also is recommended. Simi- lar to the approach in Geotechnical Earthquake Engi- neering, the anchor zone should be outside the ï¬attened failure surface. â¢ Another FHWA document Design Manual for Permanent Ground Anchor Walls (FHWA, 1998b) has a slight varia- tion on the above methods. First, the method suggests using 1.5 times the site-adjusted PGA, but notes that Caltrans has been successful using a 25 percent increase over the normal apparent earth pressures. The justiï¬cation for the lower loads is related to the test loads that are applied (133 per- cent times Load Group VII); these loads are higher than would be obtained using the AASHTO approach. Since the seismic loads are applied for a short period of time, the document suggests not increasing the soldier piles or wall facing for the seismic forces. For external stability the re- port identiï¬es a deformation-based approach used at the time by Caltrans. This method is based on the Makdisi and Seed (1978) charts for computing deformations. â¢ Whitman (1990) in a paper titled, âSeismic Design and Behavior of Retaining Walls,â presents a methodology that accounts for the increased support from the anchor as the wall deforms. In the Whitman approach, a limit equi- librium analysis is conducted with a program such as SLIDE. The anchor lock-off load is modeled as an external force oriented along the axis of the anchor (that is, typically 10 to 20 degrees). The yield acceleration is determined, and then the deformation is estimated using a Newmark chart. This deformation results in elongation of the anchor tendon or bar, which results in an increased reaction on the wall (that is, Î = PL/AE). Analyses are repeated until there is compatibility between the deformations and the anchor reaction. The ï¬nal force is then checked against capacity of the tendon and grouted anchor. With one exception, the documents summarized here do not suggest ampliï¬cation within the zone between the retain- ing wall and the anchors. One reference was made to the use of an ampliï¬cation factor identical to that used for the seis- mic design of MSE walls [that is, Am = (1.45 â A)A]. No basis for this increase was provided. Most references do suggest that the location of the anchors be moved back from the wall to account for the ï¬attening of the active zone during seismic loading. The potential that the pressure distribution behind the anchored walls changes during seismic loading is not cur- rently addressed. The most significant uncertainty appears to be whether to use the peak seismic coefficient, or a value that is higher or lower than the peak. Arguments can be made for higher values based on amplification effects. However, if several inches of movement occur as demonstrated by the example problem in Appendix J, a reduction in the peak seismic coef- ï¬cient seems justiï¬ed. If this reduction is, however, accepted, then careful consideration needs to be given to the stiffness of the wall-anchor system to conï¬rm that the elongation of the anchor strand or bar and the stiffness of the wall are such that several inches of movement can occur. While the methodologies for the seismic design of anchored walls seem to lack guidance on a number of topics, the FHWA documents note that anchored walls have performed well dur- ing past seismic events. It was noted that of 10 walls inspected after the 1987 Whittier earthquake and the 1994 Northridge earthquake, wall performance was good even though only one in 10 walls inspected was designed for earthquake loading. 188.8.131.52 Seismic Design Methodology The following approach is suggested for design of anchored retaining walls: 1. Perform static design following the AASHTO LRFD Bridge Design Specifications. 2. Establish the site peak ground acceleration coefï¬cient (kmax) and spectral acceleration S1 at 1 second from the 1,000-year AASHTO maps, including appropriate site soil modiï¬ca- tion factors. 3. Determine the corresponding PGV from correlation equa- tions between S1 and PGV (provided in Chapter 5). 4. Modify kmax to account for wall-height effects as described in Section 7.6. Do not use 1.5 factor given in the current AASHTO Specifications, unless the wall cannot be allowed to deflect. 5. Compute wall pressures using the M-O equation for active pressure, the charts in Figures 7-11 and 7-12, or the gener- alized limit equilibrium method. Apply a factor of 0.5 if 1 to 2 inches of average permanent movement are accept- able and the stiffness of the wall and anchor system (that is, Î = PL/AE) will allow this movement. If 1 to 2 inches are not tolerable or cannot develop, then use the full seismic coefï¬cient. Estimate earth pressure for passive loading using Figures 7-23 to 7-25 or the equations developed by Shamsabadi et al. (2007). 6. Use the same pressure distribution used for the static pres- sure distribution. For the resulting load diagram, check loads on tendons and grouted anchors to conï¬rm that the seismic loads do not exceed the loads applied during per- formance or proof testing of each anchor. Conï¬rm that the grouted anchors are located outside the seismic active pressure failure wedge. 7. Check global stability under seismic loading using a limit equilibrium program such as SLIDE with the seismic coef- ï¬cient modiï¬ed for height effects. Assume that the critical surface passes beneath the structural element. If the capac- ity to demand ratio is less than 1.0, estimate displacements. 92
For cases where M-O equations are not appropriate, such as for some combinations of a steep back slope and high site- adjusted PGA or if the soil behind the wall simply cannot be represented by a homogeneous material, then the generalized limit equilibrium methodology should be used to estimate the seismic active earth pressure. This pressure can be either distributed consistent with a static pressure distribution and the wall checked for acceptability, or the deformation approach recommended by Whitman (1990) can be used to evaluate the forces in the vertical structural members, anchor tendons, and grouted zone. 7.9.3 Soil Nail Walls These walls are typically used where an existing slope must be cut to accommodate a roadway widening. The slope is re- inforced to create a gravity wall. These walls are constructed from the top down. Each lift of excavation is typically 5 feet in thickness. Nails are installed within each lift. The spacing of the nails is usually about 4 to 5 feet center-to-center in both the vertical and horizontal direction. The nail used to reinforce the slope is high strength, threaded steel bar (60 to 75 ksi). Each bar is grouted in a hole drilled into the soil. The length of the bar will usually range from 0.7 to 1.0 times the ï¬nal wall height. Most soil nail walls currently are designed using either of two computer programs, SNAIL, developed and made avail- able by Caltrans, and GOLDNAIL, developed and distributed by Golder and Associates. These programs establish global and internal stability. 184.108.40.206 Seismic Design Considerations The seismic design of soil nail walls normally involves deter- mining the appropriate seismic coefï¬cient and then using one of the two computer programs to check the seismic loading case. The AASHTO LRFD Bridge Design Specifications currently does not have any provisions for the design of soil nail walls. However, FHWA has a guidance document titled Soil Nail Walls (FHWA, 2003) used for soil nail wall design. This doc- ument has a section on the seismic design of these walls. Key points from the seismic discussions are summarized below: â¢ Soil nail walls have performed very well during past earth- quakes (for example, 1989 Loma Prieta, 1995 Kobe, and 2001 Nisqually earthquakes). Ground accelerations during these earthquakes were as high as 0.7g. The good perfor- mance is attributed to the intrinsic ï¬exibility. These obser- vations also have been made for centrifuge tests on model nail walls. â¢ Both horizontal and vertical seismic coefficient can be used in software such as SNAIL. A suggestion is made in the FHWA guidance document to use the same amplifi- cation factor used for MSE walls, that is, Am = (1.45 â A)A. The basis of using this equation is not given, other than the FHWA report indicates that performance of the soil nail wall is believed to be similar to an MSE wall. â¢ The seismic coefficient for design ranges from 0.5 Am to 0.67 Am. This reduction is based on tolerable slip of 1 to 8 inches with most slip of 2 to 4 inches. The possibility of performing Newmark deformational analysis is noted for certain soil conditions and high ground accelerations. â¢ The M-O equation is used to estimate the seismic active pressure acting on the wall. Reference is made to the angle of the failure plane for seismic loading being different than static loading. â¢ Mention is made of the limitations of the M-O procedure for certain combinations of variables, in particular when the backslope is steeper than 22 degrees and does not cap- ture many of the complexities of the system. â¢ A detailed design example based on the recommended approach is presented. The earlier FHWA report Geotechnical Earthquake Engi- neering (FHWA, 1998a) also provides some discussion on the design of soil nail walls. It mentions use of (1) the amplifi- cation factor, Am = (1.45 â A)A and (2) for external stability using 0.5 times the site-adjusted PGA, as long as the wall can tolerate 10 A (inches displacement) where A is the peak ground acceleration. This document also references using a seismic design coefï¬cient of 0.5A to check seismic bearing capacity stability. Limitations and assumptions for this approach are discussed in Appendix G. Procedures used to evaluate the external or global stability of the soil nail wall during seismic loading will be the same as those described previously for evaluating the seismic per- formance of semi-gravity walls and MSE walls. The uncer- tainty with this wall type deals with the internal stability. The computer programs currently used in practice, SNAIL and GOLDNAIL, use pseudo-static, limit equilibrium methods to determine stresses in the nail. Checks can be performed to determine if pullout of the nail, tensile failure, or punching failure at the wall face occur. For the seismic loading case, the increased inertial forces are accounted for in the analysis. Similar to the internal stability of MSE walls, the mechanisms involved in transferring stresses from the soil to the nails and vice versa are complex and not easily represented in a pseudo- static, limit equilibrium model. In principle it would seem that some signiï¬cant differences might occur between the seismic response of the soil nail wall versus the MSE wall. The primary difference is that MSE walls are constructed from engineered ï¬ll whose properties are well deï¬ned, whereas nail walls are constructed in natural soils characterized by variable properties. Part of this difference 93
also relates to the angle of the nail. Most nails are angled at 10 to 20 degrees to the horizontal in contrast to the horizon- tal orientation of the reinforcement within the MSE wall. This would likely stiffen the soil nail wall relative to the MSE wall, all other conditions being equal. From a design standpoint, it also is not clear if seismic forces are adequately modeled by the pseudo-static approach currently taken. These issues need to be further evaluated during independent research efforts. Many nail walls will be located in areas where there is a co- hesive content to the soil into which the nails are installed. For these sites the effects of cohesion on the determination of seismic earth pressure coefï¬cients, as discussed in Section 7.3, should be considered. 220.127.116.11 Seismic Design Methodology Based on material presented in the previous paragraphs, the recommended design methodology is summarized by the following steps: 1. Establish an initial wall design using the computer pro- gram SNAIL or GOLDNAIL for static loading, using ap- propriate load and resistance factors. This establishes wall dimensions and weights. 2. Establish the site peak ground acceleration coefï¬cient (kmax) and spectral acceleration S1 at 1 second from the 1,000-year maps adopted by AASHTO (including appropriate site soil modiï¬cation factors). 3. Determine the corresponding PGV from correlation equations between S1 and PGV (provided in Chapter 5). 4. Modify kmax to account for wall height effects as described in Section 7.6. Use the modiï¬ed kmax in the SNAIL or GOLDNAIL program. If the wall can tolerate displace- ments, use the SNAIL or GOLDNAIL program to estimate the yield acceleration, ky. Use the yield acceleration to esti- mate displacements following the procedures in Chapter 5. Note that both computer programs also provide an evalu- ation of global stability, and therefore, it is not necessary to perform an independent global stability analysis with a limit equilibrium program such as SLIDE. 7.10 Conclusions This chapter summarizes the approach being recommended for the seismic design of retaining walls. Force-based methods using the M-O equations and a more generalized displacement- based approach were evaluated. The methodologies intro- duce new height-dependent seismic coefï¬cients, as discussed in Chapters 5 and 6 and further refined in Section 7.5 for these analyses. Results of the work completed for retaining walls includes charts showing the effects of cohesion within the soil on the seismic earth pressure coefï¬cients that were developed. These effects can result in a 50 percent reduction in the seismic active earth pressure; however, it may be difï¬cult in some cases to conï¬dently rely on this beneï¬t. In view of current uncertain- ties, the designer needs to consider the implications of over- estimating the effects of cohesion on the seismic active and passive earth pressures. Two wall types were considered in detail during this study: (1) semi-gravity walls and (2) MSE walls. â¢ The proposed approach for gravity walls uses either the M-O seismic active earth pressure equation, the charts in Figures 7-11 and 7-12, or the generalized limit equilibrium method to determine seismic active forces. These forces are used to conduct bearing, overturning, and sliding stability checks. A key question that still exists for this type of wall is whether inertial forces from the soil above the heel of a semi-rigid gravity wall (for example, Figure 7-10 in this report) is deï¬ned by the entire soil mass times the seismic coefï¬cient or some lesser value. â¢ The MSE design methodology includes a critical review of the existing AASHTO guidance, including internal stabil- ity, and then identiï¬es a step-by-step approach for evalu- ating stability. Reference is made to the need to change ex- isting software to handle this approach. Questions also still exist on the distribution of stresses within the reinforce- ment strips during seismic loading. Three other wall types were considered to lesser extents: nongravity cantilever walls, anchored walls, and soil nail walls. The design approach for each of these walls also used the re- sults of work presented in previous sections and chapters. â¢ For nongravity cantilever walls, the M-O method is believed to be an appropriate method to determine seismic active pressures as long as there is ï¬exibility in the wall and the soil behind the wall is primarily cohesionless. Otherwise, charts in Figures 7-11 and 7-12 or a generalized limit equi- librium method can be used to estimate the seismic active earth pressure. The seismic coefficient used for design can be reduced by a factor of 0.5 as long as 1 to 2 inches of average permanent deformation at the excavation level are acceptable. A structural engineer should make this evalua- tion. Checks on wall deï¬ections also should be made to conï¬rm that the basic assumptions associated with wall displacement are being met. Seismic passive pressures should be determined using a log spiral approach, such as suggested by Shamsabadi et al. (2007). â¢ In the case of the anchored wall, either a limit equilibrium procedure or a displacement based procedure suggested by 94
Whitman can be used. Seismic active earth pressures for the limit equilibrium approach can be estimated using the M-O equation, charts in Figures 7-11 and 7-12, or the gen- eralized limit equilibrium approach. Soils must be homo- geneous and cohesionless if using the M-O equation while the generalized limit equilibrium method can accept com- binations of soil conditions. The seismic coefï¬cient for these analyses can be reduced by 50 percent as long as 1 to 2 inches of average permanent movement are acceptable and as long as anchor tendons and grouted zones are not overstressed. The Whitman displacement-based approach accounts for changing anchor tendon forces during seismic loading and appears to represent the fundamental mecha- nisms that occur during seismic response of this wall type. However, the additional effort to make these evaluations may not be warranted in areas where seismicity is low, and the normal performance and proof testing of the anchors provides sufï¬cient reserve capacity. â¢ Soil nail walls can be treated as semi-gravity walls from an external stability standpoint. In most cases seismic coefï¬- cients can be reduced by 0.5 since this type of wall can usu- ally tolerate several inches of permanent movement. For internal stability there are still questions on the distribu- tion of seismic forces to the nails within the reinforced zone and whether the current models adequately account for these distributions. Additional research is still required to evaluate these questions. In a number of areas it was apparent that signiï¬cant deï¬- ciencies exist with current design methodologies. These de- ï¬ciencies reï¬ect the complexity of the overall soil-structure interaction problem that occurs during seismic loading. The nature of these deï¬ciencies is such that for several of the wall types (for example, MSE, anchored, and soil nail) independent research efforts involving speciï¬c model and prototype testing will be required to fully understand the mechanisms involved in seismic loading. While there is considerable work to be done, past expe- rience also suggests that many of these wall types have per- formed well during relatively high seismic loading, despite having either no provisions for seismic design or a very sim- ple analysis. In most cases this good performance occurred when walls were ï¬exible or exhibited considerable ductility. More problems were observed for rigid gravity walls and non- gravity cantilever walls, often because of the lack of seismic design for these walls. The methodologies suggested in this chapter should help improve the seismic performance of these walls in the future. 95