Welcome to the HOT  TOPIC in Earthquake Engineering # 8 !
By Valentin Shustov
      Earthquake design procedures and those of structural evaluation for the earthquake insurance industry have been totally incompatible. One of the main reasons for this is obvious: the insurance industry is exclusively performance oriented while the seismic design is, mostly, not .
     The earthquake loss estimation is usually performed in terms of a Damage Ratio, or a ratio of the earthquake damage dollar amount to the total value of the building. For a long time it was associated with a collection of mass inventory data and was based, mostly, on experts' opinions. It looks, therefore, more like an art than a science. 
     A considerable step forward was made lately, with the completion of project called HAZUS (1997) offering a fully computerized procedure for loss estimation. However,  inconsistencies in the direct physical damage evaluation still require major improvements. 
    Motion-Damage Relationships of the HAZUS have two basic deficiencies: 
    1. They are not written in the building code language and, therefore, cannot be adequately quantified for a computerized design and analysis. 
    2. Those relationships are based, at least partially, on experts' judgments valid for an average construction. Besides, they are most applicable for a statistically large number of facilities.
   On the contrary, a Damage Ratio Charts Method or DRCM is based on a consistent quantitative analysis targeting a prediction of the damage ratios and employs a limited number of well-understood structural and earthquake related parameters (Shustov, 1997). It establishes a direct theoretical relationship between the standard structural design procedure and the expected damage characteristics required by insurers. The method is easy and user-friendly: its application, supported by a site-specific evaluation, will not take more than a few days.
    System of sampling buildings per DRCM is based on the following quantitative characteristics
     a) Quality Factor  Rw of the building structural system, which is understood, irrespective of any reevaluations, as a degree the system can be allowed to go to beyond the elastic range. 
     b) Number of stories  N
     c) Specific Lateral Stiffness  Ke/m  of the ground story where  Ke  is the aggregate lateral stiffness of the story and m is its lumped mass. The  Ke  value corresponds to the elastic range of horizontal deformations of the vertical or horizontal load carrying elements, whichever is less.
Story Performance Rating R (Shustov, 1994) may be used as a fundamental criterion: R = v/ve where v  is an actual or calculated inter-story drift and ve  is a drift at the assumed elastic limit of deformation (Topic 7). The ultimate allowable value of  R  will occur when  R = Rw = vu/v  where Quality Factor  Rw is understood as the ratio of the ultimate allowable story drift vu  that can be tolerated by the structure without a collapse to the maximum elastic story drift ve.
    Ratio R / Rw  called a Seismic Performance Ratio controls the anticipated losses due to a seismic exposure. It is not the sole possible measure of seismic performance. However, in a majority of cases it is the most important one which would determine the Damage Ratio D.R.
    How to relate physical damage to economic losses may constitute a separate topic. Meantime, as the first degree of approximation, the following formula may apply: D.R. = 0.3(R/Rw)3100 %. The formula is represented graphically above and it demonstrates that when  R/Rw  (the current building standards' moment of truth: Demand equals Ultimate Capacity),  D.R. = 30 %. When R value reaches 1.5 Rw, the building's losses approach its replacement value.
Damage Ratio Charts (DRC)  is a graphical environment that introduces a new, streamlined way of organizing a valuable information on the anticipated performance of buildings. DRC contours connect the points of the equal D.R. in the domain of Rw   and   Ke/m  coordinates. 
R/Rw  depends upon the type of structure, number of stories, and earthquake intensity. Due to this, a system of DRC is needed to account for a wide variety of design configurations.
     Such system constitutes a matrix called a DRCSystem. An element of the matrix, or a DRC, represents a family of  damage ratio isograms. Unlike HAZUS 97, the DRCS introduces all variety of different building types with the help of the single parameter Rw
   Implementation of Damage Ratio Charts Systems will decrease a need in lengthy preliminary computations and will make unnecessary some costly services of risk management engineers.
 Shustov, V., 1994, "Energy Absorbing Technique: Challenge of Proportioning", Proc. 3rd Int'l 
 Conf. on Structures under Shock and Impact, Madrid, Spain. 
 HAZUS 97, 1997, Loss Estimation Product Package, developed by RMS under contract to 
 NIBS funded by FEMA, Washington, DC. 
 Shustov, V., 1997, "Future Seismic Codes and Earthquake Insurance", Proc. 66th Annual 
 SEAOC Convention, San Diego, CA.
Your questions on this page may be emailed to: valentin.shustov@csun.edu. You may also visit Dr.Shustov's Home Page  or CME research Web Page  or  "HOT TOPICS".
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  This page was last updated on 30 March 2000