# Tectonic hazards/Seismic fitness

Seismic fitness or seismic sustainability is the ability of buildings and civil engineering structures to perform their basic operational functions with seismic risk limited to acceptable level.
Seismic fitness may be considered the paramount goal of earthquake engineering which is concerned with protecting society, the natural and the man-made environment from the earthquake hazards.
For any particular object and earth shaking intensity, seismic fitness is not universal. It depends on a particular type of challenge: e.g., the soil conditions, 3-D directions of shaking, possibility of tsunami and its magnitude, etc. Technically, earthquake engineering is the study of behavior of buildings and structures subject to seismic loading. To provide their seismic fitness, a structural engineer should:
* Understand the interaction between buildings or civil infrastructure and the ground.
* Foresee the potential consequences of strong earthquakes on urban areas and civil infrastructure.
* Design, construct and maintain structures to perform at earthquake exposure up to the expectations and in compliance with building codes.
A seismically fit structure does not necessarily has to be extremely strong or expensive. It just has to withstand the seismic effects while sustaining an acceptable level of damage.
The most powerful and budgetary tools for upgrading seismic fitness of buildings and structures are vibration control technologies and, in particular, base isolation.

## Seismic loading

Seismic load is one of the basic concepts of earthquake engineering which means application of an earthquake-generated agitation to a building or other structure. It happens at contact surfaces of a structure either with the ground, or with adjacent structures, or with gravity waves from tsunami. Seismic loading, which is the major challenge for seismic fitness, depends, primarily, on:
* Anticipated earthquake's parameters at the site
* Geotechnical parameters of the site
* Structure's parameters
* Characteristics of the anticipated gravity waves from tsunami (if applicable).
Ancient builders believed that earthquakes were a result of wrath of gods (e.g., in Greek mythology, the main "Earth-Shaker" was Poseidon) and, therefore, could not be resisted by humans. As knowledge of engineering has improved, however, architects and engineers have become better at building structures with proper seismic performance.

## Earthquake simulation

Earthquake simulation is a vibrational input that possesses essential features of a real seismic event. The very first earthquake simulations were performed by statically applying some horizontal inertia forces, based on scaled peak ground accelerations, to a mathematical model of a building. With the further development of computational technologies, static approaches began to give way to dynamic ones.
Dynamic experiments on building and non-building structures may be physical, like shake-table testing, or virtual, or hybrid ones. In all cases, to verify a structure's expected seismic performance, researchers prefer to deal with so called “real time-histories” though the last cannot be “real” for a hypothetical earthquake specified by either a building or by some particular research requirements.
Therefore, there is a strong incentive to engage an earthquake simulation, like, e.g., the earthquake simulating displacement time-history Cone presented on the left.
Earthquake simulations have been widely used in the research supported by The George E. Brown Network for Earthquake Engineering Simulation (NEES).
Sometimes, earthquake simulation is understood as a re-creation of local effects of a strong ground shaking.

## Seismic performance

Seismic performance is an execution of a structure's ability to sustain its due functions, such as safety and serviceability, at and after a particular earthquake exposure. A structure is, normally, considered safe if it does not endanger the lives and wellbeing of those in or around it by partially or completely collapsing. A structure may be considered serviceable if it is able to fulfill its operational functions for which it was designed.
Basic concepts of the earthquake engineering, implemented in the major building codes, assume that a building should survive The Big One (the most powerful anticipated earthquake) though with partial destruction. Drawing an analogy with a human body, it will have dislocated joints, fractured ribs, traumatized spine and knocked out teeth but be alive and, therefore, quite O.K. according to the prescriptive building codes. This situation is a major barrier to implementation of any structural innovations in the earthquake engineering technologies employing the seismic vibration control and, particularly, the most effective brands of base isolation.
However, alternative performance-based design approaches already exist and are implemented at earthquake engineering research. Some of them, for assessment or comparison of the anticipated seismic performance or for seismic performance analysis, use the Story Performance Rating R as a major criterion while the Seismic Performance Ratio (SPR) is used for a rather accurate prediction of seismic performance of a building up to the point of its state of severe damage.
Anyway, replacement of the present prescriptive design standards with the future codes of performance is not an easy task: most of the designers would be reluctant to accept any additional legal obligations.

### Seismic performance evaluation

Seismic or earthquake performance evaluation is a formal procedure to quantify the level of actual or anticipated seismic performance associated with the direct damage to an individual building subject to a specified ground shaking.
The best way to do it is to put a model that simulates the building structure on a shake-table that simulates the earth shaking and to watch what may happen next (if you have no time to stand out in the field and wait for a real earthquake to strike, which is called a field testing). Such kinds of experiments were performed still more than a century ago. Another way is to evaluate the earthquake performance analytically.
The very first earthquake simulations were performed by statically applying some horizontal inertia forces, based on scaled peak ground accelerations, to a mathematical model of a building. With the further development of computational technologies, static approaches began to give way to dynamic ones.
Traditionally, numerical simulation and physical tests have been uncoupled and performed separately. So-called hybrid testing systems employ rapid, parallel analysis using both physical and computational tests.

#### Concurrent performance testing

Concurrent performance testing is an effective and persuasive way of validation of new earthquake-protective building technologies. It may include both physical and virtual testings of two or more structural objects under the same conditions that simulate earthquake-like excitations. For illustration, please see the images presented below:
* PrintScreens of concurrent computer models animations.
* The final seconds of a concurrent shake-table testing.
* Comparative shake-table testing of two models.

### Seismic performance simulation

Earthquake or seismic performance simulation is meant to study effect of earthquakes on building structures and is a practical way of seeing a thing to happen without it actually taking place in the same way. There are research institutions just devoted to earthquake performance simulations, like, e.g., The George E. Brown, Jr. Network for Earthquake Engineering Simulation or NEES.

#### Physical seismic performance simulation

The best way to do it is to put the structure on a shake-table that simulates the seismic loads and watch what may happen next (if you have no time to stand out in the field and wait for a real earthquake to strike, of course). The earliest experiments like this were performed more than a century ago

#### Computational seismic performance simulation

Another way is to evaluate the earthquake performance analytically. The very first earthquake simulations were performed by statically applying some horizontal inertia forces, based on scaled peak ground accelerations, to a mathematical model of a building. With the further development of computational technologies, statics approaches began to give way to dynamics ones.

### Seismic performance analysis

Seismic performance analysis is an intellectual tool of earthquake engineering which breaks the complex topic into smaller parts to gain a better understanding of seismic performance of building and non-building structures. The technique as a formal concept is a relatively recent development. In general, seismic analysis is based on the methods of structural dynamics. For decades, the most prominent instrument of seismic analysis has been the earthquake response spectrum method which, also, contributed to the proposed building code's concept of today.
However, those response spectra are good, mostly, for single-degree-of-freedom structural systems. Numerical step-by-step integration, applied with the charts of seismic performance, proved to be a more effective method of performance analysis for the multi-degree-of-freedom structural systems with severe non-linearity and under a substantially transient process of earthquake type kinematic excitation or earthquake simulation.

## Research for earthquake engineering

Earthquake engineering research means both field and analytical investigation or experimentation intended for discovery and scientific explanation of earthquake engineering related facts, revision of conventional concepts in the light of new findings, and practical application of the developed theories.
The National Science Foundation (NSF) is the main United States government agency that supports fundamental research and education in all fields of earthquake engineering. In particular, it focuses on experimental, analytical, and computational research on design and performance enhancement of structural systems.
The George E. Brown, Jr. Network for Earthquake Engineering Simulation or NEES is created by the National Science Foundation to give researchers the tools to learn how earthquakes and tsunamis impact buildings, bridges, utility systems and other critical components of civil infrastructure.
The Earthquake Engineering Research Institute (EERI) is a leader in dissemination of earthquake engineering research related information both in the U.S. and globally.
A definitive list of earthquake engineering research related shake-tables around the world may be found in Experimental Facilities for Earthquake Engineering Simulation Worldwide. The most prominent of them is now E-Defense Shake Table in Japan.
The major earthquake engineering research activities worldwide are mostly associated with the following centers:
* Earthquake Engineering Research Institute (EERI)
* Earthquake Engineering Research Center
* Pacific Earthquake Engineering Research Center (PEER)
* John A. Blume Earthquake Engineering Center
* Consortium of Universities for Research in Earthquake Engineering (CUREE)
* Multidisciplinary Center for Earthquake Engineering Research (MCEER)
* Earthquake Engineering Research Projects of CSUN
* George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES)
* USGS Earthquake Hazards Program
* Office of Earthquake Engineering at Caltrans
* Earthquake Engineering Research Centre of Iceland
* Earthquake Engineering New Zealand
* Earthquake Engineering Research - Earthquake engineering research|research program by U.S. Army
* Canadian Research Centers and Research Groups on Earthquake Engineering
* Hyogo Earthquake Engineering Research Center
* Laboratory for Earthquake Engineering of NTUA
* Earthquakes and Earthquake Engineering in The Library of Congress
* International Institute of Earthquake Engineering and Seismology
* National Center for Research on Earthquake Engineering

## Seismic vibration control

Seismic vibration control is a set of technical means aimed to mitigate seismic impacts in building and non-building structures to achieve their targeted seismic fitness. All seismic vibration control devices may be classified as passive, active or hybrid where:
* passive control devices have no feedback capability between them, structural elements and the ground;
* Active control devices incorporate real-time recording instrumentation on the ground integrated with earthquake input processing equipment and actuators within the structure;
* hybrid control devices have combined features of active and passive control systems.High-rise with Multi-Frequency Quieting Building System.
When ground seismic waves reach up and start to penetrate a base of a building, their energy flow density, due to reflections, reduces dramatically: usually, up to 90%. However, the remaining portions of the incident waves during a major earthquake still bear a huge devastating potential.
After the seismic waves enter a superstructure, there is a number of ways to control them in order to sooth their damaging effect and improve the building's seismic performance, for instance:
* to dissipate the wave energy inside a superstructure with properly engineered seismic dampers;
* to disperse the wave energy between a wider range of frequencies,;
* to reflect, diffract, and dissipate seismic waves in a process of their vertical propagation with the help of elevated building foundation;
* to absorb the resonant portions of the whole wave frequencies band with the help of so called tuned mass dampers.
Devices of the last kind, abbreviated correspondingly as TMD for the tuned (passive), as AMD for the active, and as HMD for the hybrid mass dampers, have been studied and installed in high-rise buildings, predominantly in Japan, for a quarter of a century.
To increase the shielded range of forcing frequencies, the concept of Multi-Frequency Quieting Building System (MFQBS) was developed.
However, there is quite another approach: partial suppression of the seismic energy flow into the superstructure known as seismic or base isolation.
For this, some pads are inserted into or under all major load-carrying elements in the base of the building which should substantially decouple a superstructure from its substructure resting on a shaking ground. The first evidence of earthquake protection by using the principle of base isolation was discovered in Pasargadae, a city in ancient Persia, now Iran: it goes back to VI century BC.

### Base isolation

Base isolation or seismic isolation is a collection of special units in a building resting on its foundation to provide separation of the building from the shaking ground thus improving its seismic performance.
From the very beginning, the theory of base isolation rested on two pillars: heavy damping and frequency separation. Unfortunately, nobody paid any attention that the heavy damping was a sort of a strong connection between a substructure and superstructure, and that the idea of decoupling them with the help of such connections was of no good. Anyway, to virtually test-drive any design concept of base isolation, some online help is available now.
Base isolation system consists of isolation units with or without isolation components, where:
1. Isolation units are the basic elements of base isolation system which provide the mentioned separation effect to a building structure.
2. Isolation components are the connections between isolation units and other parts of the building having no separation effect of their own.
Some famous base-isolated buildings are presented below:
* Pasadena City Hall, California, U.S.
* San Francisco City Hall, California, U.S.
* Salt Lake City/County Building, Utah, U.S.

#### Antifriction and Multi-Step Base Isolation

Antifriction and Multi-Step Base Isolation (AF&MS BI), also called Shock Evader, is relatively recent type of seismic vibration control. In spite of the fact that the first attempts to isolate buildings from potentially shaky ground were made thousands years ago, the modern concept of seismic isolation (flexible mounting + damping) is foreign for earthquake engineering: it has not been inherited, it has been borrowed from the mechanical engineering.
Though the concept is working perfectly in all sorts of vehicles, in seismic isolation everything is not so smooth because the conditions in both cases are quite different.
In a car, for instance, the working stresses in auto parts are far below their ultimate bearing capacity. Therefore, some overloads associated with heavy damping are of no practical importance here. Another matter is a building structure: during a strong earthquake, it is intended to perform at the near-to-collapse level and, therefore, any extras can become crucial for its safety.
However, there is an alternative to the contradictory damping mechanism of those base isolators. It can be found in the utmost lessening the damping and substituting its positive, mitigating quality with any sort of tuning-out mechanism which satisfies the following requirements:
* Let the earth move its way.
* Prevent resonant amplifications.
* Restore the structure in its pre-earthquake position on the foundation.
It is not the building, it is the earth that should be vibrating if the building is supported on the ideal isolation system. Any attempt to reduce a relative displacement of the superstructure with respect to the base will inevitably result in additional transmission of earthquake energy into the building.
This new concept has been embodied in Shock Evader or, which is the same, in the Antifriction and Multi-Step Base Isolation (AF&MS BI) that incorporated the merits of the traditional flexible mounting but without its drawback - a compulsory damping mechanism.

#### Earthquake protector

Earthquake protector is a type of base isolation intended for protection of building and non-building structures against potentially damaging lateral impact of strong earthquakes.
Heavy damping mechanism sometimes incorporated in vibration control technologies and, particularly, in base isolation devices, may be considered a valuable source of suppressing vibrations thus enhancing a building's seismic performance. However, for the very pliant systems such as base isolated structures, with a relatively low bearing stiffness but with an high damping, the so-called "damping force" may turn out the main pushing force at a strong earthquake. This finding created a theoretical ground in earthquake engineering for a damping-disengaged base isolation technology called Earthquake protector.
A shake-table video of concurrent shake-table experiments with two identical and kinematically equivalent to their 12-story prototype building models is presented at. The right model there rests on Earthquake Protectors, while the left one, caught at the time of its crash, is fixed to the shake-table platen.
Analytical software called EPET or Earthquake Performance Evaluation Tool enables concurrent virtual experiments on the same building models with any sliding type of base isolation, including Earthquake protector, and without.

#### Elevated building foundation

Elevated building foundation (EBF) is a kind of seismic base isolation technology which is made a major part of a building superstructure. It is made to protect the building's superstructure against damage from the shaking caused by an earthquake.
This goal can be met with the right building materials, size, and setup of EBF for the building site and local soil conditions.
As a result of multiple wave reflections and diffractions, as well as energy dissipation of the seismic waves as they move up through the EBF, any movement of seismic wave energy into the building superstructure will be decreased, which will lower seismic loads and improve seismic performance of the structure.
In other words, the building does not shake as much because it is sitting on the elevated building foundation, and will probably take less damage from the earthquake.

#### Friction pendulum bearing

Friction pendulum bearing (FPB) is another name of Friction pendulum system (FPS). It is based on three conceptual pillars:
* articulated friction slider;
* spherical concave sliding surface;
* enclosing cylinder for lateral displacement restraint.
Snapshot with the link to video clip of a shake-table testing of FPB system supporting a rigid building model is presented at the right.

#### Simple roller bearing

Simple roller bearing or Earthquake-protective building buffer is a simplified version of a base isolation device called earthquake protector which is intended for protection of various building and non-building structures against potentially damaging lateral impacts of strong earthquakes.
This metallic bearing support may be adapted, with certain precautions, as a seismic isolator to skyscrapers and buildings on soft ground. Recently, it has been employed under the name of Metallic Roller Bearing for a housing complex (17 stories) in Tokyo, Japan.

### Seismic damping

When seismic waves start to penetrate a base of building structure, seismic dampers can decrease their damaging effect and improve the building's seismic performance. Some samples of seismic dampers design and implementation are presented in the images below:
* Heavy damping Lead rubber bearing being tested at the UCSD facility.
* Tuned mass damper in Taipei 101, the world's second tallest skyscraper.
* Pyramid-shaped skyscraper to prevent buildings' resonant amplifications.

#### Dry-stone walls control

People of Inca civilization were masters of the polished dry-stone walls, called ashlar, where blocks of stone were cut to fit together tightly without any mortar. The Incas were among the best stone masons the world has ever seen, and many junctions in their masonry were so perfect that even blades of grass could not fit between the stones.
Peru is a highly seismic land, and for centuries the mortar-free construction proved to be apparently more earthquake-resistant than using mortar. The stones of the dry-stone walls built by the Incas could move slightly and resettle without the walls collapsing which should be recognized as an ingenious passive vibration control technique employing both the principle of energy dissipation and that of suppressing resonant amplifications.

#### Building elevation control

Building elevation control is a valuable source of vibration control of seismic loading. Thus, pyramid-shaped skyscrapers, continue to attract attention of architects and engineers because such structures promise a better stability against earthquakes and winds.
Besides, the elevation configuration can prevent buildings' resonant amplifications due to the fact that a properly configured building disperses the shear wave energy between a wide range of frequencies.
Earthquake or wind quieting ability of the elevation configuration is provided by a specific pattern of multiple reflections and transmissions of vertically propagating shear waves, which are generated by breakdowns into homogeneity of story layers, and a taper. Any abrupt changes of the propagating waves velocity result in a considerable dispersion of the wave energy between a wide ranges of frequencies thus preventing the resonant displacement amplifications in the building.
Tapered profile of a building is not a compulsory feature of this method of structural control. A similar resonance preventing effect can be also obtained by a proper tapering of other characteristics of a building structure, namely, its mass and stiffness. As a result, the building elevation configuration techniques permit an architectural design that may be both attractive and functional.

#### Hysteretic damper

Hysteretic damper is intended to provide better and more reliable seismic performance than that of a conventional structure at the expense of the seismic load energy dissipation. There are four major groups of hysteretic dampers used for the purpose, namely:
   * Fluid viscous dampers (FVDs)
   * Metallic yielding dampers (MYDs)
   * Viscoelastic dampers (VEDs)
   * Friction dampers (FDs)
Each group of dampers has specific characteristics, advantages and disadvantages for structural applications.

#### Lead rubber bearing

Lead Rubber Bearing or LRB is a hybrid of base isolation employing a property of heavy seismic damper. It was invented by William Robinson, a New Zealander. Heavy damping mechanism incorporated in vibration control technologies and, particularly, in base isolation devices, is often considered a valuable source of suppressing vibrations thus enhancing a building's seismic performance. However, for the rather pliant systems such as base isolated structures, with a relatively low bearing stiffness but with a high damping, the so-called "damping force" may turn out the main pushing force at a strong earthquake. The video shows a Lead Rubber Bearing being tested at the UCSD Caltrans-SRMD facility. The bearing is made of rubber with a lead core. It was a uniaxial test in which the bearing was also under a full structure load. Many buildings and bridges, both in New Zealand and elsewhere, are protected with lead dampers and lead and rubber bearings.

#### Springs-with-damper base isolator

Springs-with-damper base isolator installed under a three-story town-house, Santa Monica, California is shown on the photo taken prior to the 1994 Northridge earthquake exposure. It is a base isolation device conceptually similar to Lead Rubber Bearing.
One of two three-story town-houses like this, which was well instrumented for recording of both vertical and horizontal accelerations on its floors and the ground, has hardly survived a severe shaking during the 1994 Northridge earthquake and left valuable recorded information for the further study. In sense of average peak accelerations, the building performed at that time 21% worse than its non-isolated hypothetical counterpart.

#### Tuned mass damper

Typically, the tuned mass dampers, a kind of seismic vibration control technology, are huge concrete blocks mounted in skyscrapers or other structures and moved in opposition to the resonance frequency oscillations of the structures by means of some sort of spring mechanism.
Taipei 101 skyscraper depicted on the left needs to withstand typhoon winds and earthquake tremors common in its area of the Asia-Pacific. For this purpose, a steel pendulum weighing 660 metric tons that serves as a tuned mass damper was designed and installed atop the structure. Suspended from the 92nd to the 88th floor, the pendulum sways to decrease resonant amplifications of lateral displacements in the building caused by earthquakes and strong gusts.

## Seismic design

Seismic design is based on authorized engineering procedures, principles and criteria meant to provide seismic fitness of structures subject to earthquake exposure. Those criteria are only consistent with the contemporary state of the knowledge about seismic fitness of structures. Therefore, a building design which exactly follows seismic code regulations does not guarantee safety against collapse or serious damage.
The price of poor seismic design may be enormous. Nevertheless, seismic design has always been a trial and error process whether it was based on physical laws or on empirical knowledge of the structural performance of different shapes and materials.
To practice seismic design, seismic analysis or seismic evaluation of new and existing civil engineering projects, an engineer should, normally, pass examination on Seismic Principles which, in the State of California, include:
* Seismic Data and Seismic Design Criteria
* Seismic Characteristics of Engineered Systems
* Seismic Forces
* Seismic Analysis Procedures
* Seismic Detailing and Construction Quality Control
To build up complex structural systems, seismic design largely uses the same relatively small number of basic structural elements (to say nothing of vibration control devices) as any non-seismic design project.
Normally, according to building codes, structures are designed to "withstand" the largest earthquake of a certain probability that is likely to occur at their location. This means the loss of life should be minimized by preventing collapse of the buildings.
Seismic design is carried out by understanding the possible failure modes of a structure and providing the structure with appropriate strength, stiffness, ductility, and configuration to ensure those modes cannot occur.

### Seismic design requirements

Seismic design requirements depend on the type of the structure, locality of the project and its authorities which stipulate applicable seismic design codes and criteria. For instance, California Department of Transportation's requirements called The Seismic Design Criteria (SDC) and aimed at the design of new bridges in California incorporate an innovative seismic performance based approach.
The most significant feature in the SDC design philosophy is a shift from a force-based assessment of seismic demand to a displacement-based assessment of demand and capacity. Thus, the newly adopted displacement approach is based on comparing the elastic displacement demand to the inelastic displacement capacity of the primary structural components while ensuring a minimum level of inelastic capacity at all potential plastic hinge locations.
In addition to the designed structure itself, seismic design requirements may include a ground stabilization underneath the structure: sometimes, heavily shaken ground breaks up which leads to collapse of the structure sitting upon it. The following topics should be of primary concerns: liquefaction; dynamic lateral earth pressures on retaining walls; seismic slope stability; earthquake-induced settlement.
Nuclear facilities should not jeopardize their safety in case of earthquakes or other hostile external events. Therefore, their seismic design should be based on criteria far more stringent than those applied to the non-nuclear facilities

## Earthquake-resistant construction

Earthquake construction means implementation of seismic design to enable building and non-building structures to live through the anticipated earthquake exposure up to the expectations and in compliance with the applicable building codes.
Design and construction are intimately related. To achieve a good workmanship, detailing of the members and their connections should be, possibly, simple. As any construction in general, earthquake construction is a process that consists of the building, retrofitting or assembling of infrastructure given the construction materials available.
The destabilizing action of an earthquake on constructions may be direct (seismic motion of the ground) or indirect (earthquake-induced landslides, soil liquefaction and waves of tsunami).
A structure might have all the appearances of stability, yet offer nothing but danger when an earthquake occurs. The crucial fact is that, for safety, earthquake-resistant construction techniques are as important as quality control and using correct materials. Earthquake contractor should be registered in the state of the project location, bonded and insured.
To minimize possible losses, construction process should be organized with keeping in mind that earthquake may strike any time prior to the end of construction.
Each construction project requires a qualified team of professionals who understand the basic features of seismic performance of different structures as well as construction management.

## Seismic fitness quantification

Story Performance Rating R may be used as a fundamental criterion of seismic fitness: R = v/v$_e$ where v is an actual or calculated inter-story drift and v$_e$ is a drift at the assumed elastic limit of deformation. The ultimate allowable value of R will occur when R = R$_w$ = v$_u$/v$_e$ where Quality Factor R$_w$ is understood as the ratio of the ultimate allowable story drift v$_u$ that can be tolerated by the structure without a collapse to the maximum elastic story drift v$_e$.
Ratio R/R$_w$ 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/R$_w$) 100 %. The formula demonstrates that when R/R$_w$ (the current building standards' moment of truth: Demand equals Ultimate Capacity), D.R. = 30%. When R value reaches 1.5 R$_w$, the building's losses approach its replacement value.
There is, also, the Damage Ratio Charts Method which is based on a consistent quantitative analysis targeting a prediction of damage ratios and employs a limited number of well-understood structural and earthquake related parameters. It establishes a direct theoretical relationship between the standard structural design procedure and the expected damage characteristics required by insurers.