Q: ASCE 7-10 Section 11.8.3 and 2012 IBC Section 1803.5.12 require inclusion of dynamic seismic lateral earth pressures on basement and retaining walls of structures assigned to Seismic Design Category (SDC) D, E, or F due to design earthquake ground motions. However, those documents do not specify the methods for calculating these pressures. How do we determine the dynamic seismic lateral earth pressure on basement or retaining walls?

A: You are correct that ASCE 7-10 and the 2012 IBC do not specify any methods for calculating increase in lateral earth pressures due to seismicity. 2012 IBC Section 1803.5.12, in conjunction with Section 1803.1, requires that dynamic seismic lateral earth pressure be provided by the registered design professional preparing the geotechnical investigation report. For the registered design professional, discussion and guidance regarding different approaches for determining seismic lateral pressures can be found in Part 3 of the 2009 NEHRP Provisions in Resource Paper 12, titled "Evaluation of Geologic Hazards and Determination of Seismic Lateral Earth Pressures." All three parts of the 2009 NEHRP Provisions can be downloaded for free from here.

Q: Okay, so the resource paper you mentioned above provides guidelines and equations for determining seismic lateral earth pressures. But are those pressures and loads at ASD level or Strength/LRFD level?

A: The seismic lateral pressures and loads are most commonly calculated at ASD level, just like the static active pressure values. The pressure level (ASD or LRFD) should be verified with the registered design professional providing the values. 

Q: Should we multiply the forces from seismic lateral earth pressure values by the factor (Ie/R), like we do when determining seismic base shear for a building? What about the Redundancy Factor, ρ?

A:  The lateral earthquake loads on retaining walls should be multiplied by the Importance Factor, Ie per ASCE 7-10 Section 15.4.1.1, which requires that the importance factor be at least equal to that determined from ASCE 7-10 Table 1.5-2. ASCE 7-10 Section 15.6.1, Earth Retaining Structures, includes requirements on how to determine Risk Category of a retaining wall for this purpose. A basement wall is part of a building, and consequently, its Ie should be the same as that used for the building itself.

The IBC and ASCE 7 do not specifically address the application of the Response Modification Factor, R, for basement walls or retaining walls. It is our opinion that the lateral earth pressures should not be divided by R. The R-factor is used to account for energy dissipation and inelastic deformation capacity of a structure. In the case of lateral earth pressure, even though the resource paper cited above (as well as ASCE 7-10 Section 15.6.1) talks about "Yielding Walls," the walls are not actually yielding in the structural sense. The term "Yielding Wall" only means that the walls "can move sufficiently to develop minimum active earth pressures." The paper goes on to say: "Note that in this context, yielding refers to permanent displacement of the wall as a result of the seismic event and does not mean that stresses within the structural system were exceeded. The amount of movement to develop minimum active pressure is very small. A displacement at the top of the wall of 0.002 times the wall height is typically sufficient to develop the minimum active pressure state."

It is also our opinion that the Redundancy Factor, ρ, should be 1.0 for basement walls and retaining walls, because the idea of redundancy does not really apply to walls designed for out-of-plane forces. Item 9 under ASCE 7-10 Section 12.3.4.1 (Conditions Where Value of ρ is 1.0) includes "Design of structural walls for out-of-plane forces, including their anchorage." The same logic can be extended to retaining walls as well. See also ASCE 7-10 Section 15.6, Exception: ρ = 1.

Q: For the purpose of the load combination equations, is the seismic lateral earth pressure considered a load due to lateral earth pressure, H, or an earthquake load, E?

A:  Section C11.8.3 of the expanded seismic commentary to ASCE 7-10 says the following:

Evaluation of Dynamic Seismic Lateral Earth Pressures. The dynamic lateral earth pressure on basement and retaining walls during earthquake ground shaking is considered to be an earthquake load, E, for use in design load combinations. This dynamic earth pressure is superimposed on the preexisting static lateral earth pressure during ground shaking. The preexisting static lateral earth pressure is considered to be an H load.

However, please note that E in ASCE 7 is determined at strength level, and consequently has a load factor of 1.0 on it in the strength design load combinations and 0.7 in the ASD load combinations. Seismic lateral earth pressures, on the other hand, are typically computed at ASD level. Therefore, we cannot use the same load factors as those used on E. It is our opinion that the above statement from the expanded commentary means that the seismic part of the earth pressure needs to be considered only in those load combinations that include E, but the load factor for strength design should be 1.4 and for ASD should be 1.0. Note the suggested strength design load factor of 1.4 is different from the load factor used on H, which is 1.6. This is because ASCE 7-10 applies a load factor of 0.7 on E for reducing it to ASD level. Our recommended factor of 1.4 is simply the reciprocal of 0.7.