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«A Design Guide for Earth Retaining Structures Hugh Brooks Civil & Structural Engineer John P. Nielsen Civil & Geotechnical Engineer Basics of ...»

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Earthquakes can occur anywhere. However, in the US the West Coast is most vulnerable as the Pacific tectonic plate, which covers the entire Pacific Rim, rotates counter-clockwise, northward along the West Coast, moving about an inch per year as it grinds past its boundary with the easterly North American plate. This movement is primarily along California’s infamous San Andreas Fault (so named for the community it passes near San Francisco) and is responsible for the numerous stress-relieving earthquake jolts occurring daily on the many associated faults.

In California there are over 400 measurable earthquakes each week Many are never felt (those under magnitude 3.0 are rarely felt). Fortunately, few cause damage. Some larger earthquakes in

California include:

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Note: Reports of earthquakes prior to 1935 use estimated Richter magnitudes.

Ironically, however, one of the largest earthquake events occurred mid-continent, near the town of Madrid on the Mississippi River midway between St. Louis and Memphis. Known as the New Madrid faults, there were a series of earthquakes in 1811-12 with estimated magnitudes of ≈ 7.7.

They were felt as far away as NYC and reportedly rang church bells as far away as Boston.

The largest recorded in North America: 1964, Alaska, 9.2 The largest earthquake ever recorded worldwide was in Chile in 1960 with a magnitude of 9.5.

More recently on 3/11/2011 off-shore Japan, magnitude 8.9.

The term “magnitude” as used in the above list, and in the media, was developed in 1935 by Caltech professor Charles Richter and colleagues and bears his name “Richter Scale”. They used data from a seismograph to describe a specific earthquake in terms of seismic energy released. It is a logarithmic scale (to the base 10) whereby a magnitude 5 earthquake releases about ten times

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the energy of that of a magnitude 4 (510 / 410 ≈ 10). This measure is popular with the media but does not have a direct correlation to ground acceleration that is used to determine the seismic force for the design of structures.

Prior to using the Richter Scale, the Mercalli Intensity Scale was developed, which classified earthquakes based upon their effect at the earth’s surface. It was developed by Guiseppe Mercalli in 1902 and described in a USGS pamphlet as shown below – the higher the number the more

severe the damage:

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The Richter magnitude scale, used mostly by the media and for general intensity comparisons, is now replaced by site-specific ground accelerations as explained in following sections. An excellent source of information on earthquakes, including hazard maps, is http://www.usgs.gov.

When is Seismic Design Required for Retaining Walls?

It depends upon what guides you. The evidence of earthquake damage to properly designed retaining walls is nearly non-existent, excluding waterfront walls where liquefaction occurred, and walls poorly designed for static loads. Based on the senior author’s observations and reviews of inspection reports from both the Northridge and Loma Prieta earthquakes, incidents of damage were not noted for walls properly designed for static loads. Building code changes are usually prompted by failures observed, such as that of wall-to-roof diaphragm connections on tilt-up buildings during the San Fernando earthquake of 1971 which prompted corrective code changes.

However, this does not seem to be the sequence for retaining walls because of the lack of failure evidence. It can, however, be argued that we have not yet experienced “the big one”, and more

6. EARTHQUAKE (SEISMIC) DESIGN Page 38 Basics of Retaining Wall Design may be learned from the Japan magnitude 8.9 earthquake of 3/10/2011. Whether the evidence supports it or not, (and the authors are not aware of results from seismic simulated tests on retaining walls) we are guided by IBC ’12 and ASCI 7-10 (or as modified or adopted by

jurisdictional codes):

Current Code Requirements in IBC ‘12

Here is IBC ‘12, 1613.1:

1613.1 Scope. Every structure, and portion thereof, including nonstructural components that are permanently attached to structures and their supports and attachments, shall be designed and constructed to resist the effects of earthquake motions in accordance with ASCE 7, excluding Chapter 14 and Appendix l1A. The seismic design category for a structure is permitted to be determined in accordance with Chapter 1613 or ASCE 7.

This clearly requires all “structures” to be designed for seismic loads. The question is whether a retaining wall which is unoccupied and not a risk to life safety (unless supporting a building), is considered such a “structure”? Or is it exempt as permitted by Exception 3: Agricultural storage structures intended only for incidental human occupancy?

However, the ASCE 7 cited by IBC ‘12, 1613.1, further states in the 2010 edition:

ASCE 7-10 chapter 15.6.1, Earth-Retaining Structures: “This chapter applies to all earthretaining structures assigned to Seismic Design Category D, E, or F (Note: these preclude Seismic Design Categories A, B, and C which are exempt from seismic design because SDS is less than 0.50 -- see following section for definition of SDS) The lateral pressure due to earthquake ground motion shall be determined in accordance with Chapter 11.8.3”. This latter Chapter states that if a geotechnical investigation report is required (often at the discretion of the building official) the report shall include “The determination of dynamic seismic lateral earth pressures on basement and retaining walls due to design earthquake ground motions”. 15.6.1 continues: “The risk category shall be determined by the proximity of the earth-retaining structure to other buildings and structures. If failure of the earth-retaining structure would affect the adjacent building or structure, the risk category shall not be less than that of the adjacent building or structure. Earth-retaining walls are permitted to be designed for seismic loads as either yielding or nonyielding walls. Cantilevered reinforced concrete or masonry retaining walls shall be assumed to be designed as simple flexural wall elements.” If a geotechnical investigation is required per IBC ‘12, 1803 such a report shall comply with IBC 1803.5.12. Note: that seismic design is not required for wall supporting less than six feet.

1803.5.12 Seismic Design Categories D through F. For structures assigned to Seismic Design Category D. E or F the geotechnical investigation required by Secai 1803.5.11 shall also

include all of the following as applicable:

1. The determination of dynamic seismic lateral pressures on foundation walls and retaining supporting more than 6 feet (1.83 m) of backfill height due to design earthquake ground motions

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Bottom line: Check with the local building authority for code applicability and interpretation, and with the geotechnical engineer for their recommendations applicable to retaining walls.

Seismic Design Background Determining with some rationale how seismic forces act on retaining walls is complex and impeded by diverse opinions, differing theoretical assumptions, and in-situ tests that don’t match theoretical approaches. Researchers acknowledge the complexity of this task as code-writers try to mandate minimum design guidelines for public safety.

This effort is difficult for two reasons. As stated earlier, unlike buildings where we can learn from failures, reports of damage to reasonably well designed retaining walls (that were not designed, considering seismic forces) are nearly non-existent (waterfront walls and liquefaction conditions excluded) therefore there is little to observe and analyze to suggest design remedies.

And as opinioned above, many question the need for adding seismic forces to static-designed retaining walls, considering both performance history and factors of safety incorporated into the design of walls. Secondly, and compounding the dilemma, as stated above many of the theoretical approaches to determine seismic forces on retaining walls each relies upon differing assumptions that yield differing results, and to in-situ and laboratory tests that didn’t perform as theory predicted.

6. EARTHQUAKE (SEISMIC) DESIGN Page 40 Basics of Retaining Wall Design In past years “pseudo-static” (that is, using a static force to simulate a dynamic force) analyses were conducted for which the inertial effects of ground shaking were represented by a lateral force, which then made the problem solvable using statics. That force was usually set equal to

0.15W, where 0.15 was assumed to be the effective horizontal ground acceleration and W the “rigid body mass” portion of the backfill. The line of action of the force was assumed to act through the center of gravity the rigid soil mass. Factors greater than 0.15 might have been used based upon a consideration of the “importance” of the wall (now codified as the Importance Factor).

The practice of assuming a static equivalent horizontal ground acceleration factor is now largely replaced with a “site acceleration” based upon site specific spectral analyses. The concept of spectral analysis, whereby the design acceleration is based upon the characteristics and period of a structure, was introduced in the 30’s and codified in the 40’s. Accelerations for retaining walls, which are generally considered “short period” structures (less than 0.2 seconds), use a design acceleration given for 2% damping with a 10% chance of being exceeded in 50 years. This sitespecific Peak Ground Acceleration (PGA) derived from a Maximum Considered Earthquake (MCE), is given by the geotechnical consultant or can be obtained by maps in IBC ‘12 or ASCE 7-10 (they are the same), or directly from www.usgs.gov.

The pseudo-static approach is useful when analyzing a wall for stability – overturning, soil bearing, and sliding – but does not give the distribution of seismic lateral force incrementally on the stem. Resolving this deficiency is discussed in following sections.

Mononobe-Okabe Analysis The well known and frequently cited Mononobe-Okabe equation (M-O) is an adaptation of the Coulomb equation to account for seismic forces. The Coulomb equation (discussed in Chapter 5, Forces and Loads on Retaining Walls) can be used to determine the lateral force on a retaining wall from earth pressure but does not include the inertial force that the soil backfill impacts on a retaining wall during an earthquake. One of several solutions to this problem, taking into account both horizontal and vertical ground accelerations, are the M-O equations that provide seismic coefficients for active and passive pressure (KAE and KPE respectively). The development of this widely accepted work is based on an original work by Japanese professors Mononobe and Okabe in 1926-29.

Many investigations of dynamic forces on retaining walls are reported in the technical literature.

One of the most important and influential was an ASCE paper titled Design of Earth Retaining Structures for Dynamic Loads, by Seed and Whitman, the results from which were presented at a 1970 Cornell University conference. In that paper they also cite the pioneering studies by Mononobe and Okabe. Another contribution was a later ASCE paper by Robert Whitman titled, Seismic Design and Behavior of Gravity Retaining Walls in 1990. That paper considered the lateral force to be derived from an inverted triangular wedge of soil behind the wall. SeedWhitman proposed a simplified equation, based upon the Mononobe and Okabe theory, for the combined static and seismic factor, which they termed KAE, to be applied to this wedge acting against the wall. This adaptation of the Coulomb equation to calculate the total (seismic and static) pressure, introduced the variable , which is defined as the angle whose tangent is the  kh  ground acceleration ( = tan-1 1 k  ), resulted in the M-O equation we now use (See Appendix  v I for definitions of kh and kv). We note that if the acceleration variable  is excluded from the MO equation it reverts to the familiar Coulomb equation.

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