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Online 1. 15 years of reproducible research in computational harmonic analysis [2008]
 Donoho, David Leigh.
 Stanford, Calif. : Dept. of Statistics, Stanford University, [2008]
 Description
 Book — 1 online resource (27 pages)
 Also online at
Online 2. 2 x 2 kappa coefficients : measures of agreement or association [1987]
Online 3. 2 x 2 measures of association [1978]
 Kraemer, Helena Chmura.
 November 1978.
 Description
 Book — 1 online resource (29 pages)
 Also online at

Online 4. The 2 x k contingency table with ordered columns : how important to take account of the order?. [1985]
Online 5. 27year mortality in the Western Collaborative Group Study : construction of risk groups by recursive partitioning [1991]
 Carmelli, D.
 February 1991.
 Description
 Book — 1 online resource (35 pages) Digital: text file.
 Also online at

 Olkin, Ingram.
 Stanford, Calif. : Dept. of Statistics, Stanford University, 2000.
 Description
 Book — 1 online resource (14 pages)
 Also online at

Online 7. A Bayesian Approach to Seismic Hazard Mapping: Development of Stable Design Parameters [1978]
 Mortgat, CP (Author)
 March 1978
 Description
 Book
 Summary

The energy released by earthquakes propagates in the earth's crust as body and surface waves. The intensity and duration of shaking of structures located in the path of these waves depends upon the intensity and duration of the seismic ground motion along with the characteristics of the structure. Structural failures resulting in considerable damage and loss frequently occur because of these motions and inadequate seismic resistance of the structures. Earthquake engineers and planners often use the words risk and hazard interchangeably in their work. Seismic risk is regarded by many to be synonymous with seismic hazard. There is some danger in this ambiguity since these two words for seismic phenomenon have different meanings. Seismic hazard is defined as "expected occurrence of future adverse seismic event (earthquake)". Seismic risk is defined as "expected consequences of future seismic event". Consequences may be life loss, economic loss, function loss and damage. Loosely, it can be said that a seismic hazard involves "nature's punch" while a seismic risk involves interaction between "nature's punch" and human activity. The intensity and duration of future earthquake ground motions are random and can therefore be known only in the probabilistic sense of the likelihood of exceeding a given level during a given time period. (Rosenblueth and Esteva, 1966; Benjamin, 1968; Cornell, 1968). If economic planning and engineering design criteria are to be formulated on a rational basis,then it is necessary to have the best available estimates of these future ground motions. The best practical representation of earthquake loadings for a given geographical region is in the form of seismic hazard maps  where the earthquake effect is shown in terms of the most useful engineering parameters for design. Presently there is a great need for improvements in risk mapping techniques and in the description of the related engineering parameters. Therefore the present dissertation is divided in two parts. The first part concentrates on seismic hazard mapping which can be best defined as the exposure to seismic loading at a given location. This exposure is expressed in terms of an effect and the probability of its occurrence. The second part concentrates on a study of stable design parameters. Its general purpose is to provide a statistical and probabilistic view of the response of structures to earthquake excitation. The attention is focused on response parameters which have a direct engineering value.
The energy released by earthquakes propagates in the earth's crust as body and surface waves. The intensity and duration of shaking of structures located in the path of these waves depends upon the intensity and duration of the seismic ground motion along with the characteristics of the structure. Structural failures resulting in considerable damage and loss frequently occur because of these motions and inadequate seismic resistance of the structures. Earthquake engineers and planners often use the words risk and hazard interchangeably in their work. Seismic risk is regarded by many to be synonymous with seismic hazard. There is some danger in this ambiguity since these two words for seismic phenomenon have different meanings. Seismic hazard is defined as "expected occurrence of future adverse seismic event (earthquake)". Seismic risk is defined as "expected consequences of future seismic event". Consequences may be life loss, economic loss, function loss and damage. Loosely, it can be said that a seismic hazard involves "nature's punch" while a seismic risk involves interaction between "nature's punch" and human activity. The intensity and duration of future earthquake ground motions are random and can therefore be known only in the probabilistic sense of the likelihood of exceeding a given level during a given time period. (Rosenblueth and Esteva, 1966; Benjamin, 1968; Cornell, 1968). If economic planning and engineering design criteria are to be formulated on a rational basis,then it is necessary to have the best available estimates of these future ground motions. The best practical representation of earthquake loadings for a given geographical region is in the form of seismic hazard maps  where the earthquake effect is shown in terms of the most useful engineering parameters for design. Presently there is a great need for improvements in risk mapping techniques and in the description of the related engineering parameters. Therefore the present dissertation is divided in two parts. The first part concentrates on seismic hazard mapping which can be best defined as the exposure to seismic loading at a given location. This exposure is expressed in terms of an effect and the probability of its occurrence. The second part concentrates on a study of stable design parameters. Its general purpose is to provide a statistical and probabilistic view of the response of structures to earthquake excitation. The attention is focused on response parameters which have a direct engineering value.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 8. A Bayesian Geophysical Model for Seismic Hazard [1981]
 McCann Jr, MW (Author)
 May 1981
 Description
 Book
 Summary

Earthquakes are a manifestation of the earth's geologic development. Their occurrence has been a topic of concern to man for thousands of years. This led to the development of earthquake engineering which seeks to define the expected hazard due to earthquakes and to control and reduce the consequences of these events to man's environment. These goals entail two central ideas, that of seismic hazard and seismic risk. In earthquake engineering these concepts are defined as follows: seismic hazard is the "expected occurrence of future seismic events", and seismic risk is the "expected consequence to future seismic events." This report deals with seismic hazard and the methods by which it is described.
Earthquakes are a manifestation of the earth's geologic development. Their occurrence has been a topic of concern to man for thousands of years. This led to the development of earthquake engineering which seeks to define the expected hazard due to earthquakes and to control and reduce the consequences of these events to man's environment. These goals entail two central ideas, that of seismic hazard and seismic risk. In earthquake engineering these concepts are defined as follows: seismic hazard is the "expected occurrence of future seismic events", and seismic risk is the "expected consequence to future seismic events." This report deals with seismic hazard and the methods by which it is described.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
 Sohn, H (Author)
 199901
 Description
 Book
 Summary

There have been increased economic and societal demands to periodically monitor the safety of structures against longterm deterioration, and to ensure their safety and adequate performance during the life span of the structures. In this work, a Bayesian probabilistic framework for damage detection is proposed for the continuous monitoring of structures. The idea is to search for the most probable damage event by comparing the relative probabilities for different damage scenarios. The formulation of the relative posterior probability is based on an output error, which is defined as the difference between the estimated vibration parameters and the theoretical ones from the analytical model. The Bayesian approach is shown (1) to take into account the uncertainties in the measurement and the analytical modeling, (2) to perform damage diagnosis with a relatively small number of measurement points and a few modes, and (3) to systematically extract information from continuously obtained test data. A branchandbound search scheme is devised to expedite the search for the most likely damage event without exhaustively examining all possible damage cases. As an alternative to modal vectors, loaddependent Ritz vectors are incorporated into the Bayesian framework. The following advantages of Ritz vectors over modal vectors are shown: (1) in general, loaddependent Ritz vectors are more sensitive to damage than the corresponding modal vectors, and (2) by a careful selection of load patterns, substructures of interest can be made more observable. Furthermore, a procedure to extract Ritz vectors from vibration test is proposed, and the procedure is successfully demonstrated using experimental test data. Data from vibration tests of civil structures indicate that the environmental effects such as temperature, traffic loading, humidity can often mask subtle structural changes caused by damage. A linear adaptive filter is presented to discriminate the changes of modal parameters due to temperature changes from those caused by structural damage or other environmental effects. Results based on the field vibration test of a bridge indicate that the filter can reproduce the temporal variability of the frequencies so that the thermal effects on the vibration parameters can be differentiated from other environmental effects or potential structural damage.
There have been increased economic and societal demands to periodically monitor the safety of structures against longterm deterioration, and to ensure their safety and adequate performance during the life span of the structures. In this work, a Bayesian probabilistic framework for damage detection is proposed for the continuous monitoring of structures. The idea is to search for the most probable damage event by comparing the relative probabilities for different damage scenarios. The formulation of the relative posterior probability is based on an output error, which is defined as the difference between the estimated vibration parameters and the theoretical ones from the analytical model. The Bayesian approach is shown (1) to take into account the uncertainties in the measurement and the analytical modeling, (2) to perform damage diagnosis with a relatively small number of measurement points and a few modes, and (3) to systematically extract information from continuously obtained test data. A branchandbound search scheme is devised to expedite the search for the most likely damage event without exhaustively examining all possible damage cases. As an alternative to modal vectors, loaddependent Ritz vectors are incorporated into the Bayesian framework. The following advantages of Ritz vectors over modal vectors are shown: (1) in general, loaddependent Ritz vectors are more sensitive to damage than the corresponding modal vectors, and (2) by a careful selection of load patterns, substructures of interest can be made more observable. Furthermore, a procedure to extract Ritz vectors from vibration test is proposed, and the procedure is successfully demonstrated using experimental test data. Data from vibration tests of civil structures indicate that the environmental effects such as temperature, traffic loading, humidity can often mask subtle structural changes caused by damage. A linear adaptive filter is presented to discriminate the changes of modal parameters due to temperature changes from those caused by structural damage or other environmental effects. Results based on the field vibration test of a bridge indicate that the filter can reproduce the temporal variability of the frequencies so that the thermal effects on the vibration parameters can be differentiated from other environmental effects or potential structural damage.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 10. A Comparison of Earthquake Building Code Regulations [1980]
 Egbert III, JT (Author)
 198005
 Description
 Book
 Summary

It is important to constantly review the building codes that are currently being used in order to determine what improvements might be made. For example, the formulae for obtaining base shear, lateral force distribution and building period are continually being evaluated. Each year design force levels increase in order to meet regulations which reduce the likelihood of failure in the event of an earthquake. Buildings must be constructed stronger and this may result in more structural redundancies, some of which may be unnecessary. When a change to a code is proposed, the effect of this change on the variety of structural shapes and systems must be considered. For example, a code change could affect a two or three story concrete shear wall building much differently than a twenty story steel frame high rise. Rather than randomly increasing design levels or altering code requirements a code change should first be examined for effects on a representative set of structures. This examination procedure is the subject of this work where the set of structures has been designed by current building codes and can be used for comparative purposes in evaluating the overall usefulness of a proposed change and its value to certain structural systems. The Seismology Committee of the Structural Engineers Association of Northern California (SEAONC) has studied a method which will standardize and simplify the procedure for examining the effect of proposed building code changes. The findings strongly indicate the need for the study of a typical or standard set of buildings which would include not only the general specifications for design of each building, but also several sets of completed designs done by use of the most widely used building codes of today. This proposal offers a simple procedure that can be utilized to compare the impact of a code change against a code with a known performance.
It is important to constantly review the building codes that are currently being used in order to determine what improvements might be made. For example, the formulae for obtaining base shear, lateral force distribution and building period are continually being evaluated. Each year design force levels increase in order to meet regulations which reduce the likelihood of failure in the event of an earthquake. Buildings must be constructed stronger and this may result in more structural redundancies, some of which may be unnecessary. When a change to a code is proposed, the effect of this change on the variety of structural shapes and systems must be considered. For example, a code change could affect a two or three story concrete shear wall building much differently than a twenty story steel frame high rise. Rather than randomly increasing design levels or altering code requirements a code change should first be examined for effects on a representative set of structures. This examination procedure is the subject of this work where the set of structures has been designed by current building codes and can be used for comparative purposes in evaluating the overall usefulness of a proposed change and its value to certain structural systems. The Seismology Committee of the Structural Engineers Association of Northern California (SEAONC) has studied a method which will standardize and simplify the procedure for examining the effect of proposed building code changes. The findings strongly indicate the need for the study of a typical or standard set of buildings which would include not only the general specifications for design of each building, but also several sets of completed designs done by use of the most widely used building codes of today. This proposal offers a simple procedure that can be utilized to compare the impact of a code change against a code with a known performance.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 11. A Computer Program for Nonstationary Analysis and Simulation of Stong Motion Earthquake Records [1984]
 Tilliouine, B (Author)
 March 1984
 Description
 Book
 Summary

The increasing need for a better understanding of the structural response to earthquake ground motion, has led to several structural analysis approaches. Among these, the equivalent static force approach and the response spectrum approach, although simple in concept and easy to implement, are known for not being accurate enough, especially if used for the design of very important and complex structures. To account for the nonlinear behavior of structures, the only reliable and accurate method is the socalled "time history" approach. In this method, a complete accelerationtime history of the earthquake record is used as an input to a structural model. The structural model is assumed to behave nonlinearly beyond the elastic limit. A finiteelement (two or three dimensional) soilstructure model is usually developed for this purpose. The response is obtained by numerical integration. Even though this method provides a sufficiently sophisticated and accurate model of the soil structural system, the input earthquake time history has considerable uncertainty. Therefore many researchers have developed analytical as well as numerical methods to simulate the earthquake time histories. Such models help to better understand the seismic phenomenon by itself and also give structural designers an option to evaluate the possible nonlinear response of their structures due to a family of simulated earthquakes. Several stationary and nonstationary models for earthquake simulation have been proposed (Cornell, 1964; Housner, 1964; Jennings, 1969; Ipek, 1980). It is generally recognized that due to the transient nature of the seismic input, a nonstationary simulation is far more reasonable, especially if one is dealing with nonlinear structural behavior, which is the case for strong ground motions. This program (Tilliouine, 1982) uses the concept of a physical spectrum (Mark, 1970). It can generate an ensemble of synthetic earthquakes having prescribed nonstationarities, both in the amplitude and frequency domains.
The increasing need for a better understanding of the structural response to earthquake ground motion, has led to several structural analysis approaches. Among these, the equivalent static force approach and the response spectrum approach, although simple in concept and easy to implement, are known for not being accurate enough, especially if used for the design of very important and complex structures. To account for the nonlinear behavior of structures, the only reliable and accurate method is the socalled "time history" approach. In this method, a complete accelerationtime history of the earthquake record is used as an input to a structural model. The structural model is assumed to behave nonlinearly beyond the elastic limit. A finiteelement (two or three dimensional) soilstructure model is usually developed for this purpose. The response is obtained by numerical integration. Even though this method provides a sufficiently sophisticated and accurate model of the soil structural system, the input earthquake time history has considerable uncertainty. Therefore many researchers have developed analytical as well as numerical methods to simulate the earthquake time histories. Such models help to better understand the seismic phenomenon by itself and also give structural designers an option to evaluate the possible nonlinear response of their structures due to a family of simulated earthquakes. Several stationary and nonstationary models for earthquake simulation have been proposed (Cornell, 1964; Housner, 1964; Jennings, 1969; Ipek, 1980). It is generally recognized that due to the transient nature of the seismic input, a nonstationary simulation is far more reasonable, especially if one is dealing with nonlinear structural behavior, which is the case for strong ground motions. This program (Tilliouine, 1982) uses the concept of a physical spectrum (Mark, 1970). It can generate an ensemble of synthetic earthquakes having prescribed nonstationarities, both in the amplitude and frequency domains.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
 Miller, SA (Author)
 September 2015
 Description
 Book
 Summary

Improved design measures for civil engineering materials are necessary to reduce the environmental impact of the built environment. Over the last century buildings have been one of the largest consumers of materials. Due to growing material demands in the construction industry associated with increased global population and economic demands, it is imperative that research on designing materials use sustainability metrics in conjunction with performance metrics. However, little research has been conducted on developing design methodologies to incorporate sustainability metrics in the field of sustainable civil engineering material design. Rather, most recent advances have been associated with comparative analyses of existing materials and typically lack consideration of usephase properties in the environmental impacts. By examining the influence of constituent properties on composite materials, this dissertation focuses on linking environmental impact, material durability, and composite constituent selection through a unique design method. The design procedure consists of three fundamental steps for improved material design: (1) consideration of a base domain of alternatives for composite constituents and characterization of these alternatives in terms of mechanical and timedependent properties through experimental testing; (2) environmental impact assessment and consideration of material improvements through life cycle analysis; and (3) application of mechanical and timedependent properties to environmental impact modeling to refine desired alternatives for assessment in step (1). This thesis applies the design method through application to a class of biobased composites, composed of a biosynthesized polymer and varying natural fibers, which offers a potentially lower environmental impact material option for the construction industry. In this research, characterization of mechanical properties and environmental impact properties of these composites as well as improvements in composite design were considered through manipulations in composite reinforcement and production techniques. By extending theories from mechanical design and life cycle analysis, initial property comparisons for the influence of these manipulations and for the influence of base units for comparison were made. To incorporate durability performance metrics, this research examined creep deformation behavior, which is a critical timedependent material property for structural load bearing applications and timedependent material serviceability. Creep behavior was incorporated into life cycle analysis and allowed for assessment of environmental impacts associated with material quantities needed to maintain necessary material functionality. The results of the design method proved effective: through an integration of the analyses conducted, desirable constituents can be selected and processing methods can be refined. While this research is applied to biobased composites, the principles developed are applicable to green engineering of any composite material. The iterative design procedure presented can act as a springboard to new research in improved analysis and design techniques for composites.
Improved design measures for civil engineering materials are necessary to reduce the environmental impact of the built environment. Over the last century buildings have been one of the largest consumers of materials. Due to growing material demands in the construction industry associated with increased global population and economic demands, it is imperative that research on designing materials use sustainability metrics in conjunction with performance metrics. However, little research has been conducted on developing design methodologies to incorporate sustainability metrics in the field of sustainable civil engineering material design. Rather, most recent advances have been associated with comparative analyses of existing materials and typically lack consideration of usephase properties in the environmental impacts. By examining the influence of constituent properties on composite materials, this dissertation focuses on linking environmental impact, material durability, and composite constituent selection through a unique design method. The design procedure consists of three fundamental steps for improved material design: (1) consideration of a base domain of alternatives for composite constituents and characterization of these alternatives in terms of mechanical and timedependent properties through experimental testing; (2) environmental impact assessment and consideration of material improvements through life cycle analysis; and (3) application of mechanical and timedependent properties to environmental impact modeling to refine desired alternatives for assessment in step (1). This thesis applies the design method through application to a class of biobased composites, composed of a biosynthesized polymer and varying natural fibers, which offers a potentially lower environmental impact material option for the construction industry. In this research, characterization of mechanical properties and environmental impact properties of these composites as well as improvements in composite design were considered through manipulations in composite reinforcement and production techniques. By extending theories from mechanical design and life cycle analysis, initial property comparisons for the influence of these manipulations and for the influence of base units for comparison were made. To incorporate durability performance metrics, this research examined creep deformation behavior, which is a critical timedependent material property for structural load bearing applications and timedependent material serviceability. Creep behavior was incorporated into life cycle analysis and allowed for assessment of environmental impacts associated with material quantities needed to maintain necessary material functionality. The results of the design method proved effective: through an integration of the analyses conducted, desirable constituents can be selected and processing methods can be refined. While this research is applied to biobased composites, the principles developed are applicable to green engineering of any composite material. The iterative design procedure presented can act as a springboard to new research in improved analysis and design techniques for composites.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 13. A Framework for RateIndependent Crystal Plasticity in the Finite Deformation Range [2014]
 Rahmani, H (Author)
 July 2014
 Description
 Book
 Summary

In this study we present a framework for the stressstrain analysis of polycrystalline materials subjected to quasistatic and isothermal loading conditions. We focus on rateindependent crystal plasticity as the primary micromechanism in the plastic deformation of crystalline aggregates. This deformation mechanism is modeled by a nonlinear stressstrain relationship and multiple linearly dependent yield constraints. Convergence problems induced by linear dependency of constraints is one of the challenges in modeling rateindependent crystal plasticity. Failure to converge at a single crystal level can cause numerical stability problems when modeling larger scales such as boundary value problems. In this work we first build a stress point model based on the ‘ultimate’ algorithm in the infinitesimal deformation range. Since this algorithm solves the stressstrain response analytically, the model is unconditionally convergent. Numerical examples are presented to demonstrate the numerical stability of the algorithm and the significance of considering crystal microstructure in modeling the plastic deformation of single crystals. To investigate the overall elastoplastic behavior of crystalline solids at scales larger than a single crystal, the stress point model at the infinitesimal deformation range is implemented in a nonlinear finite element code. Several boundary value problems are presented to demonstrate the numerical stability of the finite element model and also the effect of considering crystal microstructure on predicting the macroscale elastoplastic behavior of crystalline solids. We next formulate crystal plasticity in the finite deformation range. This formulation, which is based on the theory of distribution and strong discontinuity concepts, considers both material and geometric nonlinearity in the plastic deformation of crystals. We propose exact and approximate stress point algorithms to solve the presented framework. To find the set of linearly independent slip systems, we follow the same idea as the `ultimate' algorithm. The presented numerical examples demonstrate that the simplified approximate algorithm is accurate. The examples also indicate the significant impact of geometric nonlinearity on the stressstrain response of single crystals. We derive a framework to analyze the onset and configuration of localization in crystalline solids at infinitesimal and finite deformation ranges. The presented examples demonstrate that geometric nonlinearity has a significant impact on the localization analyses of crystalline solids.
In this study we present a framework for the stressstrain analysis of polycrystalline materials subjected to quasistatic and isothermal loading conditions. We focus on rateindependent crystal plasticity as the primary micromechanism in the plastic deformation of crystalline aggregates. This deformation mechanism is modeled by a nonlinear stressstrain relationship and multiple linearly dependent yield constraints. Convergence problems induced by linear dependency of constraints is one of the challenges in modeling rateindependent crystal plasticity. Failure to converge at a single crystal level can cause numerical stability problems when modeling larger scales such as boundary value problems. In this work we first build a stress point model based on the ‘ultimate’ algorithm in the infinitesimal deformation range. Since this algorithm solves the stressstrain response analytically, the model is unconditionally convergent. Numerical examples are presented to demonstrate the numerical stability of the algorithm and the significance of considering crystal microstructure in modeling the plastic deformation of single crystals. To investigate the overall elastoplastic behavior of crystalline solids at scales larger than a single crystal, the stress point model at the infinitesimal deformation range is implemented in a nonlinear finite element code. Several boundary value problems are presented to demonstrate the numerical stability of the finite element model and also the effect of considering crystal microstructure on predicting the macroscale elastoplastic behavior of crystalline solids. We next formulate crystal plasticity in the finite deformation range. This formulation, which is based on the theory of distribution and strong discontinuity concepts, considers both material and geometric nonlinearity in the plastic deformation of crystals. We propose exact and approximate stress point algorithms to solve the presented framework. To find the set of linearly independent slip systems, we follow the same idea as the `ultimate' algorithm. The presented numerical examples demonstrate that the simplified approximate algorithm is accurate. The examples also indicate the significant impact of geometric nonlinearity on the stressstrain response of single crystals. We derive a framework to analyze the onset and configuration of localization in crystalline solids at infinitesimal and finite deformation ranges. The presented examples demonstrate that geometric nonlinearity has a significant impact on the localization analyses of crystalline solids.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 14. A Generalized SemiMarkov Process for Modeling Spatially and Temporally Dependent Earthquakes [1993]
 Lutz, KA (Author)
 199307
 Description
 Book
 Summary

Sitespecific hazard estimation requires the modeling of the occurrences of earthquakes on any faults with the potential to impact the site. Previous earthquake occurrence models have assumed either spatial independence or temporal independence or both. However, for large magnitude earthquakes (approximately moment magnitude 6:5 and above) occurring infrequently on long faults, evidence indicates that the assumptions of temporal and spatial independence are not valid. A new fault behavior model incorporating temporal and spatial dependence is needed to estimate sitespecific hazard in areas subject to such earthquakes. This research develops an earthquake occurrence model that is a generalized semiMarkov process (GSMP) and allows for the simulation of the fault behavior through time. The fault is discretized into short cells; the model traces through time the slip accumulated on each cell and the amount of slip release on each cell due to earthquake occurrences. The size of each simulated earthquake is related to the amount of slip that is released. In order to apply the model to a fault, the following data must be known for each cell along the entire length of the fault: the slip rate, the mean and standard deviation of the earthquake interarrival times, and the time of the last earthquake. Additionally, the time of the last earthquake that ruptured the entire fault must be known. The model can then simulate the sizes and locations of earthquakes occurring along the fault for the time period of interest. Application of the model to the northern San Andreas fault (the portion of the fault that ruptured in 1906) implies that there are two distinct processes at work. The North Coastsection generates large earthquakes (approximately moment magnitude 7.7 to 8.1), and the South Santa Cruz Mountains segment generates somewhat smaller earthquakes (approximately moment magnitude 6.8 to 7.4). The San Francisco Peninsula segment represents a transition between these two behaviors. The model is relatively insensitive to the cell size chosen, to the distribution chosen to model the times between earthquakes triggering at a given place on the fault, and to the choice of a segmentation model that subdivided the San Francisco Peninsula segment. The moment magnitude of the largest earthquakes simulated are sensitive to the slip rate. The results for individual segments are highly sensitive to the mean interarrival times, but the aggregate results are much less sensitive. This research develops an earthquake occurrence model that is appropriate for estimating hazard due to large, spatially and temporally dependent earthquakes. Because smaller magnitude earthquakes can also be important in seismic hazard analysis, however, this model must be combined with another designed to model lower magnitude seismicity (perhaps a Poisson model) in order to estimate the total sitespecific hazard.
Sitespecific hazard estimation requires the modeling of the occurrences of earthquakes on any faults with the potential to impact the site. Previous earthquake occurrence models have assumed either spatial independence or temporal independence or both. However, for large magnitude earthquakes (approximately moment magnitude 6:5 and above) occurring infrequently on long faults, evidence indicates that the assumptions of temporal and spatial independence are not valid. A new fault behavior model incorporating temporal and spatial dependence is needed to estimate sitespecific hazard in areas subject to such earthquakes. This research develops an earthquake occurrence model that is a generalized semiMarkov process (GSMP) and allows for the simulation of the fault behavior through time. The fault is discretized into short cells; the model traces through time the slip accumulated on each cell and the amount of slip release on each cell due to earthquake occurrences. The size of each simulated earthquake is related to the amount of slip that is released. In order to apply the model to a fault, the following data must be known for each cell along the entire length of the fault: the slip rate, the mean and standard deviation of the earthquake interarrival times, and the time of the last earthquake. Additionally, the time of the last earthquake that ruptured the entire fault must be known. The model can then simulate the sizes and locations of earthquakes occurring along the fault for the time period of interest. Application of the model to the northern San Andreas fault (the portion of the fault that ruptured in 1906) implies that there are two distinct processes at work. The North Coastsection generates large earthquakes (approximately moment magnitude 7.7 to 8.1), and the South Santa Cruz Mountains segment generates somewhat smaller earthquakes (approximately moment magnitude 6.8 to 7.4). The San Francisco Peninsula segment represents a transition between these two behaviors. The model is relatively insensitive to the cell size chosen, to the distribution chosen to model the times between earthquakes triggering at a given place on the fault, and to the choice of a segmentation model that subdivided the San Francisco Peninsula segment. The moment magnitude of the largest earthquakes simulated are sensitive to the slip rate. The results for individual segments are highly sensitive to the mean interarrival times, but the aggregate results are much less sensitive. This research develops an earthquake occurrence model that is appropriate for estimating hazard due to large, spatially and temporally dependent earthquakes. Because smaller magnitude earthquakes can also be important in seismic hazard analysis, however, this model must be combined with another designed to model lower magnitude seismicity (perhaps a Poisson model) in order to estimate the total sitespecific hazard.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 15. A Method for Earthquake MotionDamage Relationships with Application to Reinforced Concrete Frames [1996]
 Singhal, A (Author)
 199610
 Description
 Book
 Summary

Recent earthquakes have shown their devastating effects on structures. Damage to structures has significant socioeconomic consequences. Before the occurrence of an earthquake, planners can use estimates of structural damage to predict the likely extent of building damage, economic loss, and number of casualties. Immediately after an earthquake, damage estimates can be used by emergency response planners to assess the vulnerability of a structure to aftershocks and to decide whether the building is safe to enter or not. Postearthquake rehabilitation decisions require estimates of structural damage to decide whether to repair or to demolish a damaged structure. Structural damage to buildings can be estimated by using seismic site hazard along with relationships between earthquake ground motion severity and structural damage. This dissertation deals only with the latter relationships. These relationships are most frequently described in the form of conditional probability distributions of damage at specified ground motion intensities. These motiondamage relationships are usually expressed in terms of fragility curves and damage probability matrices. The development of fragility curves and damage probability matrices requires the characterization of the ground motion and the identification of the different degrees of structural damage. This study presents a systematic approach for developing motiondamage relationships that does not rely either on heuristics or on empirical data. Instead, the probability of damage is estimated by quantifying the response of a structure subjected to a significant ensemble of ground motions with a wide range of parameter variations. The quantification of the structural response also includes the variability in structural parameters. For this purpose, a Monte Carlo simulation approach is used to determine the probabilities of structural damage, and the ensemble of ground motions is generated using an appropriate model for ground motion simulation. The models for ground motion simulation include the stationary Gaussian model with modulating functions and the autoregressive moving average (ARMA) models. The Latin hypercube technique is used to increase the efficiency of the Monte Carlo simulation. The approach developed in this study is then applied to obtain fragility curves and damage probability matrices for reinforced concrete moment resisting frames. Reinforced concrete frames are divided into three classes based on the number of stories in the frames. These include low rise concrete frames that are 13 stories tall.mid rise frames that are 47 stories tall. and high rise frames that are 8 stories or taller. The ground motion for these three classes of frames is characterized by the average spectral acceleration over period bands corresponding to the three classes of frames. Sample structures for the three classes of frames are used to develop the motiondamage relationships. Parametric studies are performed to assess the effect of geometric variations in the performance of concrete frame structures. The Bayesian technique is presented that enables the incorporation of observed damage data with the motiondamage relationships. Using damage data from the Northridge earthquake. the fragility curves for low rise frames are updated. It is found that the synthetic fragility curves. obtained by the Monte Carlo simulation, provide the best estimates of the updated probabilities of the different damage states for these frames. The uncertainty associated with the motiondamage relationships is presented in terms of confidence bounds on the fragility curves.
Recent earthquakes have shown their devastating effects on structures. Damage to structures has significant socioeconomic consequences. Before the occurrence of an earthquake, planners can use estimates of structural damage to predict the likely extent of building damage, economic loss, and number of casualties. Immediately after an earthquake, damage estimates can be used by emergency response planners to assess the vulnerability of a structure to aftershocks and to decide whether the building is safe to enter or not. Postearthquake rehabilitation decisions require estimates of structural damage to decide whether to repair or to demolish a damaged structure. Structural damage to buildings can be estimated by using seismic site hazard along with relationships between earthquake ground motion severity and structural damage. This dissertation deals only with the latter relationships. These relationships are most frequently described in the form of conditional probability distributions of damage at specified ground motion intensities. These motiondamage relationships are usually expressed in terms of fragility curves and damage probability matrices. The development of fragility curves and damage probability matrices requires the characterization of the ground motion and the identification of the different degrees of structural damage. This study presents a systematic approach for developing motiondamage relationships that does not rely either on heuristics or on empirical data. Instead, the probability of damage is estimated by quantifying the response of a structure subjected to a significant ensemble of ground motions with a wide range of parameter variations. The quantification of the structural response also includes the variability in structural parameters. For this purpose, a Monte Carlo simulation approach is used to determine the probabilities of structural damage, and the ensemble of ground motions is generated using an appropriate model for ground motion simulation. The models for ground motion simulation include the stationary Gaussian model with modulating functions and the autoregressive moving average (ARMA) models. The Latin hypercube technique is used to increase the efficiency of the Monte Carlo simulation. The approach developed in this study is then applied to obtain fragility curves and damage probability matrices for reinforced concrete moment resisting frames. Reinforced concrete frames are divided into three classes based on the number of stories in the frames. These include low rise concrete frames that are 13 stories tall.mid rise frames that are 47 stories tall. and high rise frames that are 8 stories or taller. The ground motion for these three classes of frames is characterized by the average spectral acceleration over period bands corresponding to the three classes of frames. Sample structures for the three classes of frames are used to develop the motiondamage relationships. Parametric studies are performed to assess the effect of geometric variations in the performance of concrete frame structures. The Bayesian technique is presented that enables the incorporation of observed damage data with the motiondamage relationships. Using damage data from the Northridge earthquake. the fragility curves for low rise frames are updated. It is found that the synthetic fragility curves. obtained by the Monte Carlo simulation, provide the best estimates of the updated probabilities of the different damage states for these frames. The uncertainty associated with the motiondamage relationships is presented in terms of confidence bounds on the fragility curves.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 16. A Method for Structural Safety Evaluation under MainshockAftershock Earthquake Sequences [1993]
 Sunasaka, Y (Author)
 199307
 Description
 Book
 Summary

Structures are frequently subjected to sequences of mainshock and aftershocks during their life. Strong aftershocks have been known to cause extensive structural damage and losses of human lives and property in addition to the damage and losses of the mainshock. It is clear that aftershocks are crucial to structural safety in the event of earthquakes. A procedure for evaluating the structural safety under mainshockaftershock earthquake sequences is described. This procedure consists of 3 steps:(1) simulation of the mainshockaftershock earthquake sequences, (2) calculation of ground motions at the structural site, and (3) calculation of the structural damage. At step (1), we assume that the probability density of interarrival times of mainshocks is Weibull or exponentially distributed according to the earthquake data near the site. In addition, the magnitudes of mainshocks are assumed to be exponentially distributed. Then the number and the magnitude of aftershocks depend on the magnitude of the mainshock. The magnitudes of aftershocks are modeled by an exponential distribution. At step (2), we assume that epicenters of earthquakes are uniformly distributed along active faults. Then we calculate the response spectra of ground motions with magnitudes calculated in steps (1) and epicenters using the Joyner and Boor (1982) spectral attenuation equation. The time histories of ground motions are then simulated using the duration independent envelope function proposed by Tung et ale (1992). At the final step (3), we obtain structural damage which can be calculated by nonlinear analysis of structure. The structural safety during the mainshockaftershock sequences is estimated from the cumulative damage index from the complete sequences. The proposed damage estimation method is applied to the overpass of Highway 101 at Painter Street in Rio Dell, California. The structure is modeled as a single degree of freedom system. A probabilistic occurrence model of the mainshockaftershock sequence is developed according to the earthquake data near Eureka. The average and standard deviation of damage index of the structure are estimated using the proposed simulation procedure. Based on the results from this simulation, it is observed that the cumulative damage from the mainshockaftershock sequences is found to be significantly higher than the damage obtained if only mainshocks are included in the analysis. Thus, consideration of the aftershock sequences in the damage model plays an important role in the computation of damage indices and should be considered in all damage analysis.
Structures are frequently subjected to sequences of mainshock and aftershocks during their life. Strong aftershocks have been known to cause extensive structural damage and losses of human lives and property in addition to the damage and losses of the mainshock. It is clear that aftershocks are crucial to structural safety in the event of earthquakes. A procedure for evaluating the structural safety under mainshockaftershock earthquake sequences is described. This procedure consists of 3 steps:(1) simulation of the mainshockaftershock earthquake sequences, (2) calculation of ground motions at the structural site, and (3) calculation of the structural damage. At step (1), we assume that the probability density of interarrival times of mainshocks is Weibull or exponentially distributed according to the earthquake data near the site. In addition, the magnitudes of mainshocks are assumed to be exponentially distributed. Then the number and the magnitude of aftershocks depend on the magnitude of the mainshock. The magnitudes of aftershocks are modeled by an exponential distribution. At step (2), we assume that epicenters of earthquakes are uniformly distributed along active faults. Then we calculate the response spectra of ground motions with magnitudes calculated in steps (1) and epicenters using the Joyner and Boor (1982) spectral attenuation equation. The time histories of ground motions are then simulated using the duration independent envelope function proposed by Tung et ale (1992). At the final step (3), we obtain structural damage which can be calculated by nonlinear analysis of structure. The structural safety during the mainshockaftershock sequences is estimated from the cumulative damage index from the complete sequences. The proposed damage estimation method is applied to the overpass of Highway 101 at Painter Street in Rio Dell, California. The structure is modeled as a single degree of freedom system. A probabilistic occurrence model of the mainshockaftershock sequence is developed according to the earthquake data near Eureka. The average and standard deviation of damage index of the structure are estimated using the proposed simulation procedure. Based on the results from this simulation, it is observed that the cumulative damage from the mainshockaftershock sequences is found to be significantly higher than the damage obtained if only mainshocks are included in the analysis. Thus, consideration of the aftershock sequences in the damage model plays an important role in the computation of damage indices and should be considered in all damage analysis.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 17. A Methodology for Nonlinear SoilStructure Interaction Effects Using TimeDomain Analysis Techniques [1992]
 Borja, RI (Author)
 199206
 Description
 Book
 Summary

The dynamic response of rigid foundations on an elastoviscoplastic halfspace is investigated in the context of nonlinear finite element (FE) analysis. A deviatoric viscoplastic theory with a linear combination of isotropic and kinematic hardening is used to model the soil constitutive response. Largescale nonlinear FE computations are made feasible by the use of a composite NewtonPOG iteration technique, which requires the factorization of the consistent tangent operator no more than once during the solution process. Timedomain analyses are used to investigate the nonlinear responses of vertically oscillating circular, square, and rectangular foundations to harmonic loads, using two and threedimensional FE modeling. It is shown that for low frequency excitations, resonance is created which amplifies the motion of the foundation at amplitudes well above those obtained at the zerofrequency leveL In addition, horizontal, rocking, and torsional vibration modes of strip and square foundations are considered using the same methodology developed for vertically oscillating foundations. The foundation responses for horizontal, rocking, and torsional modes are characterized by increased vibrational amplitudes due to material stiffness degradation. Furthermore, one or more resonance frequencies are created which resemble those observed for vertically oscillating finitesize foundations. Nonlinear soil effects are shown to be dominant over a wide range of excitation frequencies for foundations vibrating in torsional and horizontal modes. In contrast, nonlinear soil effects are shown to be dominant over a much narrower range of excitation frequencies for the vertical and rocking modes.
The dynamic response of rigid foundations on an elastoviscoplastic halfspace is investigated in the context of nonlinear finite element (FE) analysis. A deviatoric viscoplastic theory with a linear combination of isotropic and kinematic hardening is used to model the soil constitutive response. Largescale nonlinear FE computations are made feasible by the use of a composite NewtonPOG iteration technique, which requires the factorization of the consistent tangent operator no more than once during the solution process. Timedomain analyses are used to investigate the nonlinear responses of vertically oscillating circular, square, and rectangular foundations to harmonic loads, using two and threedimensional FE modeling. It is shown that for low frequency excitations, resonance is created which amplifies the motion of the foundation at amplitudes well above those obtained at the zerofrequency leveL In addition, horizontal, rocking, and torsional vibration modes of strip and square foundations are considered using the same methodology developed for vertically oscillating foundations. The foundation responses for horizontal, rocking, and torsional modes are characterized by increased vibrational amplitudes due to material stiffness degradation. Furthermore, one or more resonance frequencies are created which resemble those observed for vertically oscillating finitesize foundations. Nonlinear soil effects are shown to be dominant over a wide range of excitation frequencies for foundations vibrating in torsional and horizontal modes. In contrast, nonlinear soil effects are shown to be dominant over a much narrower range of excitation frequencies for the vertical and rocking modes.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 18. A Modular, Wireless Damage Monitoring System for Structures [1998]
 Straser, EG (Author)
 August 1998
 Description
 Book
 Summary

Monitoring the performance of civil structures has recently become an area of great activity in both the research community and public sector. With the significant negative impact that extreme events and long term deterioration can have on the built environment, monitoring of civil structures holds promise as a way to provide critical information for near realtime condition assessment. This information can be used in the prudent allocation of emergency response resources after earthquakes and for identification of incipient damage in structures experiencing longterm deterioration. There is an economic and societal need to improve the response and condition assessment capabilities immediately following earthquakes and to extend the useful life of current infrastructure. To meet this need, the research in this study aims to provide an information system, consisting of a hardware, software, and system level solution. The vast majority of published work on monitoring civil structures has focused on developing algorithms to advance the detection and diagnosis of damage to structures. An equally important task is the establishment of a flexible hardware platform capable of near realtime data acquisition. Many of the existing monitoring algorithms and strategies assume a sophisticated hardware infrastructure. Such an assumption ignores the issues of upfront cost, cost to benefit ratio, system installation, and lifecycle operation and maintenance. This study has developed an inexpensive and flexible instrumentation system based on embedded systems and wireless networks to meet the needs of the structural monitoring community. The approach has been to determine the desired qualities of a structural monitoring system and design the hardware and software to facilitate damage detection. The vision of this study is realized in the prototype Sensor Unit; a wireless, modular, and battery powered data acquisition device.
Monitoring the performance of civil structures has recently become an area of great activity in both the research community and public sector. With the significant negative impact that extreme events and long term deterioration can have on the built environment, monitoring of civil structures holds promise as a way to provide critical information for near realtime condition assessment. This information can be used in the prudent allocation of emergency response resources after earthquakes and for identification of incipient damage in structures experiencing longterm deterioration. There is an economic and societal need to improve the response and condition assessment capabilities immediately following earthquakes and to extend the useful life of current infrastructure. To meet this need, the research in this study aims to provide an information system, consisting of a hardware, software, and system level solution. The vast majority of published work on monitoring civil structures has focused on developing algorithms to advance the detection and diagnosis of damage to structures. An equally important task is the establishment of a flexible hardware platform capable of near realtime data acquisition. Many of the existing monitoring algorithms and strategies assume a sophisticated hardware infrastructure. Such an assumption ignores the issues of upfront cost, cost to benefit ratio, system installation, and lifecycle operation and maintenance. This study has developed an inexpensive and flexible instrumentation system based on embedded systems and wireless networks to meet the needs of the structural monitoring community. The approach has been to determine the desired qualities of a structural monitoring system and design the hardware and software to facilitate damage detection. The vision of this study is realized in the prototype Sensor Unit; a wireless, modular, and battery powered data acquisition device.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 19. A Nonstationary Probablilistic Model for Pore Pressure Development and Site Response Due to Seismic Excitation [1987]
 Wang, JN (Author)
 198708
 Description
 Book
 Summary

A complete probabilistic analysis for pore pressure development in layered horizontal soil deposits based upon nonstationary random vibration theory is developed in this study. This analysis includes: (1) Modeling the earthquake ground motions; (2) performing a response analysis; and (3) application of a probabilistic pore pressure generation model. By means of this complete analysis, a set of seismic fragility curves can be constructed such that the probability of liquefaction at any depth within a given soil profile can be expressed as a function of the Root Mean Square{RMS) of acceleration and duration of the earthquake excitation. The random vibration method developed herein provides an alternative approach to conventional deterministic equivalent uniform cycle methods for evaluating liquefaction potential. In modeling the earthquake ground motions, a frequency independent amplitudemodulating function is introduced to describe the nonstationarity in intensity content. The amplitudemodulating function is a simple twoparameter trigonometric function developed in a normalized form for both duration and intensity. Frequency content of the earthquake ground motion is characterized through the normalized TajimiKanai power spectral density function{PSD), which is fully described by a damping parameter and a frequency parameter. Statistics on the parameters describing the amplitudemodulating and PSD functions are evaluated from past earthquake records. Response analysis is performed assuming the seismic excitation to consist of one dimensional vertically propagating shear waves. Incorporating random vibration theory, the response analysis produces timedependent power spectral
A complete probabilistic analysis for pore pressure development in layered horizontal soil deposits based upon nonstationary random vibration theory is developed in this study. This analysis includes: (1) Modeling the earthquake ground motions; (2) performing a response analysis; and (3) application of a probabilistic pore pressure generation model. By means of this complete analysis, a set of seismic fragility curves can be constructed such that the probability of liquefaction at any depth within a given soil profile can be expressed as a function of the Root Mean Square{RMS) of acceleration and duration of the earthquake excitation. The random vibration method developed herein provides an alternative approach to conventional deterministic equivalent uniform cycle methods for evaluating liquefaction potential. In modeling the earthquake ground motions, a frequency independent amplitudemodulating function is introduced to describe the nonstationarity in intensity content. The amplitudemodulating function is a simple twoparameter trigonometric function developed in a normalized form for both duration and intensity. Frequency content of the earthquake ground motion is characterized through the normalized TajimiKanai power spectral density function{PSD), which is fully described by a damping parameter and a frequency parameter. Statistics on the parameters describing the amplitudemodulating and PSD functions are evaluated from past earthquake records. Response analysis is performed assuming the seismic excitation to consist of one dimensional vertically propagating shear waves. Incorporating random vibration theory, the response analysis produces timedependent power spectral  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series
Online 20. A Preliminary Investigation of the Dynamic Response of the Imperial County Services Buildings During the October 15, 1979 Imperial Valley Earthquake [1981]
 Pauschke, JM (Author)
 January 1981
 Description
 Book
 Summary

On October 15, 1979 during the Imperial Valley earthquake, the Imperial County Services Building, located in El Centro, California, became the first extensively instrumented building to sustain significant structural damage induced by seismic loads. This report presents a preliminary assessment of the dynamic behavior of this building based on the vibration data recorded prior to (ambient), during, and after (ambient) the October 15, 1979 earthquake. The thirteen building and the three nearby free field records obtained during this earthquake are analyzed in detail in the time and frequency domains to trace the nonlinear response.
On October 15, 1979 during the Imperial Valley earthquake, the Imperial County Services Building, located in El Centro, California, became the first extensively instrumented building to sustain significant structural damage induced by seismic loads. This report presents a preliminary assessment of the dynamic behavior of this building based on the vibration data recorded prior to (ambient), during, and after (ambient) the October 15, 1979 earthquake. The thirteen building and the three nearby free field records obtained during this earthquake are analyzed in detail in the time and frequency domains to trace the nonlinear response.  Collection
 John A. Blume Earthquake Engineering Center Technical Report Series