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74 Although the reduction in passive earth pressure during 7.3.1 Evaluation of the Contribution seismic loading is accounted for in the M-O equation for from Cohesion passive pressures (Equation A11.1.1.1-4 in AASHTO LRFD Most natural cohesionless soils have some fines content Bridge Design Specifications), the M-O equation for passive that often contributes to cohesion, particularly for short-term earth pressures is based on a granular soil and Coulomb loading conditions. Similarly, cohesionless backfills are rarely failure theory. Various studies have shown that Coulomb fully saturated, and partial saturation would provide for some theory is unconservative in certain situations. Similar to the apparent cohesion, even for clean sands. In addition, it appears M-O equation for active earth pressure, the M-O equation to be common practice in some states, to allow use of backfill for passive earth pressure also does not include the contri- soils with 30 percent or more fines content (possibly contain- butions of any cohesive content in the soil. The preferred ing some clay fraction), particularly for MSE walls. Hence the approach for passive earth pressure determination is to use likelihood in these cases of some cohesion is very high. The log spiral procedures, similar to the preferred approach for effect of cohesion, whether actual or apparent, is an impor- gravity loading. Shamsabadi et al. (2007) have published a tant issue to be considered in practical design problems. generalized approach that follows the log spiral procedure, The M-O equations have been extended to c- soils by while accounting both for the inertial forces within the soil Prakash and Saran (1966), where solutions were obtained for wedge and the cohesive content within the soil. cases including the effect of tension cracks and wall adhesion. A key consideration during the determination of static Similar solutions also have been discussed by Richards and passive pressures is the wall friction that occurs at the soil- Shi (1994) and by Chen and Liu (1990). wall interface. Common practice is to assume that some wall To further illustrate this issue, analyses were conducted by friction will occur for static loading. The amount of inter- deriving the M-O equations for active earth pressures and face friction for static loading is often assumed to range from extending it from only a soil failure criterion to a generalized 50 to 80 percent of the soil friction angle. Similar guidance c- soil failure criterion. Essentially, limit equilibrium analyses is not available for seismic loading. In the absence of any were conducted using trial wedges. The active earth pressure guidance, the static interface friction value often is used for value (PAE) was computed to satisfy the condition of moment seismic design. equilibrium of each of the combinations of the assumed trial Another important consideration when using the seismic wedge and soil shear strength values over the failure surface. passive earth pressure is the amount of deformation required The configurations of the trial wedges were varied until the to mobilize this force. The deformation to mobilize the pas- relative maximum PAE value was obtained for various hori- sive earth pressure during static loading is usually assumed zontal seismic coefficient kh. The planar failure mechanism is to be large, say 2 to 5 percent of the embedded wall height, retained in the analyses and is a reasonable assumption for the depending on the type of soil (that is, granular soils will be active earth pressure problem. Zero wall cohesion was assumed closer to the lower limit while cohesive soils are closer to the and tension cracks were not included. upper limit). Only limited guidance is available for seismic loading (for example, see Shamsabadi et al., 2007), and there- 7.3.2 Results of M-O Analyses for Soils fore the displacement to mobilize the seismic passive earth with Cohesion pressure is often assumed to be the same as for static loading. Figure 7-11 and Figure 7-12 present active earth pressure co- efficient charts for two different soil friction angles with differ- 7.3 M-O Earth Pressures ent values of cohesion for horizontal backfill, assuming no ten- for Cohesive Soils sion cracks and wall adhesion. Within each chart, earth pressure The M-O equation has been used to establish the appro- coefficients are presented as a function of the seismic coefficient priate earth pressure coefficient (KAE) for a given seismic (kh,) and various values of cohesion (c). The c value was nor- malized by the product H where is the unit weight of soil coefficient kh. Although it is possible to use the Coulomb and H is the wall height in the presented design charts. method to develop earth pressure equations or charts that The following illustrates both the use and the importance include the contribution of any cohesive content, the avail- of the cohesive contribution: able M-O earth pressure coefficient equations and charts have been derived for a purely cohesionless (frictional) soil 1. For a typical compacted backfill friction angle of 40 degrees, where the soil failure criteria would be the Mohr-Coulomb the c/ H would be about 0.083 and 0.167 for a slope height failure criterion, parameterized by the soil friction angle, . (H) of 20 feet and 10 feet, respectively (for a = 120 pcf in However, experience from limit equilibrium slope stability combination of a small cohesion value c = 200 psf). analyses shows that the stability of a given slope is very sensi- 2. From Figure 7-12 (for = 40 degrees), it can seen that the tive to the soil cohesion, even for a very small cohesion. resultant design force coefficients Kae for a seismic coefficient