Terje Haukaas

Professor

Relevant Degree Programs

 

Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - Mar 2019)
Damage modelling for performance-based earthquake engineering (2016)

The overarching objective in this work is to advance damage modelling for performance-based earthquake engineering. To achieve this objective, this thesis provides a new vision, technique, and software framework for the assessment of seismic damage and loss to building components. The advent of performance-based earthquake engineering placed a renewed emphasis on the assessment of damage and monetary loss in structural engineering. Assessment of seismic damage and loss for decision making entails two ingredients. First, models that predict the detailed damage to building components; second, a probabilistic framework that simulates damage and delivers the monetary loss for the reliability, risk, and optimization analysis. This motivates the contributions in this thesis, which are summarized in the following paragraphs. First, a literature review is conducted on models, techniques and experimental studies that address component damage due to earthquakes. The existing approaches for prediction of the seismic damage, repair actions, and costs are examined. The objective in this part is to establish a knowledge bank that facilitates the subsequent development of probabilistic models for seismic damage. Second, a logistic regression technique is employed for developing multivariate models that predict the probability of sustaining discrete damage states. It is demonstrated that the logistic regression remedies several shortcomings in univariate damage models, such as univariate fragility curves. The multivariate damage models are developed for reinforced concrete shear walls using experimental data. A search algorithm for model selection is included. It is found that inter-story drift and aspect ratio of walls are amongst the most influential parameters on the damage. Third, an object-oriented software framework for detailed simulation of visual damage is developed. The work builds on the existing software Rt. Emphasis is on the software framework, which facilitates detailed simulation of component behaviour, including visual damage. Information about visual damage allows the prediction of repair actions, which in turn improves our ability to predict the time and cost of repair.

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Probabilistic models, methods, and software for evaluating risk to civil infrastructure (2012)

The fundamental objective in this thesis is to advance the state-of-the-art in the field of infrastructure risk analysis. To meet this objective, probabilistic models, methods, and software are developed and applied. The work is conducted within a new reliability-based approach, in which reliability methods are employed to compute risk. Risk, in this context, means the probability of exceeding monetary loss. Evaluating such probabilities requires probabilistic models for hazards, response, damage, and loss. This motivates the contributions in this thesis, which are summarized as follows: First, a new computer program, called Rt, is developed. It is tailored to conduct reliability analysis with many probabilistic models. It orchestrates the interaction of models by means of a new object-oriented software design. Each model and analysis algorithm is represented by an object. As a result, new models and algorithms are easily implemented without modifying existing code. Another novelty is the parameterization of uncertainties, decisions, and model responses. This has several implications; one being that, in each step of an analysis, only the models affected by new parameter realizations are evaluated. Another novelty is the computation of “direct differentiation” response sensitivities in a multi-model analysis. Second, a library of new probabilistic models are developed and implemented in Rt. The models are intended for use in regional seismic risk analysis. The library includes new models for location and magnitude of earthquakes, and response, damage, and loss of building. The library also features damage and loss models for entire regions. Third, the models are applied in a risk analysis for the Vancouver metropolitan region in Canada. The primary results are “loss curves” and “hazard curves,” which show the probability of exceeding loss and spectral acceleration, respectively. As another example of results, it is found that Richmond is the most vulnerable municipality. Finally, new sensitivity measures are developed to prioritize the allocation of resources to mitigate risk and to reduce model uncertainty. In particular, these measures identify the buildings whose retrofit yields the most reduction in regional risk. They also identify the models whose improvement yields the most reduction in uncertainty.

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Efficient finite element response sensitivity analysis and applications in composites manufacturing (2009)

This thesis presents the development, implementation, and application of response sensitivities in numerical simulation of composite manufacturing. The sensitivity results include both first- and second-order derivatives. Such results are useful in many applications. In this thesis, they are applied in reliability analysis, optimization analysis, model validation, model calibration, as well as stand-alone measures of parameter importance to gain physical insight into the curing and stress development process. In addition to novel derivations and implementations, this thesis is intended to facilitate and foster increased use of response sensitivities in engineering analysis. The work presented in this thesis constitutes an extension of the direct differentiation method (DDM). This is a method that produces response sensitivities in an efficient and accurate manner, at the one-time cost of deriving and implementing sensitivity equations alongside the ordinary response algorithm. In this thesis, novel extensions of the methodology are presented for the composite manufacturing problem. The derivations include all material, geometry, and processing parameters in both the thermochemical and the stress development algorithms. A state-of-the-art simulation software is developed to perform first-order sensitivity analysis for composite manufacturing problems using the DDM. In this software, several novel techniques are employed to minimize the computational cost associated with the response sensitivity computations. This sensitivity-enabled software is also used in reliability, optimization, and model calibration applications. All these applications are facilitated by the availability of efficient and accurate response sensitivities.The derivation and implementation of second-order sensitivity equations is a particular novelty in this thesis. It is demonstrated that it is computationally feasible to obtain second-order sensitivities (the “Hessian matrix”) by the DDM for inelastic finite element problems. It is demonstrated that the direct differentiation approach to the computation of first- and second-order response sensitivities becomes increasingly efficient as the problem size increases, compared with the less accurate and less efficient finite different approach.

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Performance-based earthquake engineering with the first-order reliability method (2008)

Performance-based earthquake engineering is an emerging field of study that complements the prescriptive methods that the design codes provide to ensure adequate seismic performance of structures. Accounting for uncertainties in the performance assessments forms an important component in this area. In this context, the present study focuses on two broad themes; first, treatment of uncertainties and the application of the first-order reliability method (FORM) in finite-element reliability analysis, and second, the seismic risk assessment of reinforced concrete structures for performance states such as, collapse and monetary loss. In the first area, the uncertainties arising from inherent randomness (“aleatory uncertainty”) and due to the lack of knowledge (“epistemic uncertainty”) are identified. A framework for the separation of these uncertainties is proposed. Following this, the applicability of FORM to the linear and nonlinear finite-element structural models under static and dynamic loading is investigated. The case studies indicate that FORM is applicable for linear and nonlinear static problems. Strategies are proposed to circumvent and remedy potential challenges to FORM. In the case of dynamic problems, the application of FORM is studied with an emphasis on cumulative response measures. The limit-state surface is shown to have a closed and nonlinear geometric shape. Solution methods are proposed to obtain probability bounds based on the FORM results. In the application-oriented second area of research, at first, the probability of collapse of a reinforced concrete frame is assessed with nonlinear static analysis. By modelling the post-failure behaviour of individual structural members, the global response of the structure is estimated beyond the component failures. The final application is the probabilistic assessment of monetary loss for a high-rise shear wall building due to the seismic hazard in the Cascadia subduction zone. A 3-dimensional finite-element model of the structure with nonlinear material models is subjected to stochastic ground motions in the reliability analysis. The parameters for the stochastic ground motion model are developed for Vancouver, Canada. Monetary losses due to the damage of structural and non-structural components are included.

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Master's Student Supervision (2010-2017)
Probabilistic cost models for lifecycle design of buildings (2017)

This thesis presents a collection of numerical models that predict the total lifetime cost of buildings. Different models are developed for different phases in the life of a building, i.e., extraction and manufacturing of materials, construction, operation, hazards, demolition, and recycling. Models forecast direct costs, environmental impact costs, and human health costs related to each such phase. The variability in the parameters that enter the cost models is addressed using random variables. The estimate of the total cost of a building can be used in future work to optimize the structural design.Despite powerful new optimization algorithms, the answer to what is holistically the optimal choice of materials, dimensions, and configurations is often unanswered in practice. One reason is that developers, architects, users, and societies may have different objectives, ranging from the cost of construction to aesthetic appeal and environmental impact. Another problem is the lack of unbiased models to predict the costs and benefits that matter to private and public stakeholders. Thus, concerns such as environmental impacts and cost of potential earthquakes are rarely quantified in an explicit and comprehensive manner. This issue is addressed in this thesis through the development of a collection of unified probabilistic cost models for a broad range of costs and benefits. The models proposed in this thesis are implemented in a computer program for simulation of building behaviour.

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The fuel transportation system in British Columbia : attributes and vulnerabilities (2016)

Disasters can, and do lead to widespread disruption, often crippling transportation systems in complex ways. Transportation systems need to be designed not only to operate on an ordinary day; they need to be designed to respond to man-made and natural disasters. Proactive planning can allow transport to resume service, and deal with crises, as quickly as possible post-disaster. This thesis provides information to assist in the development of plans and protocols for emergency scenarios. Coastal communities throughout British Columbia (BC) are heavily dependent on maritime transportation for the supply of fuel, food, and other critical resources. Vancouver Island only has an estimated 3 days’ worth of food and fuel stored on the island. Without sufficient storage, or a means of producing these resources, coastal communities are highly vulnerable to maritime disruption. If transportation systems are disrupted for an extended period, communities can experience shortages to supply. This can lead to communities losing power, operations, and critical resources for survival. Through interviews and interactive workshops with industry stakeholders, this study brings forth issues and limitations within fuel transportation in BC. Current transportation systems are potentially ill equipped to deal with large-scale events with some response plans fragmented, and the decision-making infrastructure at times ad hoc. Improving a system’s preparedness through identification of hazards, and educating the industry could significantly aid the system’s response and revitalization post-disaster. Through review of current systems and plans, this thesis highlights persistent concerns within the system and begins to explore ways to improve the resilience of fuel distribution in BC. Through analyzing mitigation options, the validity of pro-active planning can be seen. The concerns and recommendations from this thesis could lay the foundation for building a more resilient system capable of executing effective emergency response.

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Force transfer around openings in CLT shear walls (2015)

During an earthquake, shear walls can experience damage around corners of doors and windows due to development of stress concentration. Reinforcements provided to minimize this damage are designed for forces that develop at these corners known as transfer forces. In this thesis, the focus is on understanding the forces that develop around opening corners in cross laminated timber (CLT) shear walls and reinforcement requirements for the same.In the literature, four different analytical models are commonly considered to determine the transfer force for design of wood-frame shear walls. These models have been reviewed in this thesis. The Diekmann model is found to be the most suitable analytical model to determine the transfer force around a window-type opening.Numerical models are developed in ANSYS to analyse the forces around opening corners in CLT shear walls. CLT shear walls with cut-out openings are analysed using a three-dimensional brick element model and a frame model. These models highlight the increase in shear and torsion around opening corners due to stress concentration. The coupled-panel construction practice for CLT shear walls with openings is analysed using a continuum model calibrated to experimental data. The analysis shows the increase in strength and stiffness of walls, when tie-rods are used as reinforcement. Analysis results also indicate that the tie-rods should be designed to behave linearly for optimum performance of the wall.Finally, a linear regression model is developed to determine the stiffness of a simply-supported CLT shear wall with a window-type opening. This model provides insight into the effect of various geometrical and material parameters on the stiffness of the wall. The process of model development has been explained, which can be improved further to include the behaviour of anchors.

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Reliability-based design optimization using DDM enabled finite elements (2015)

Rts is a risk-based structural optimization, multi-platform computer program that incorporates uncertainty into structural analysis with the utilization of random variable parameters. The major contribution to this thesis is that Rts now has the capability to perform reliability-based design optimization using Finite Element Method (FEM) analytical sensitivities. Analytical gradients are exact, more efficient, and convergence is achieved more rapidly in gradient- based optimization methods when compared to finite difference sensitivity methods. For this thesis, I have derived and implemented both nodal and material analytical gradients throughout the Rts framework starting at the finite element level up through to the optimization level. The Reliability-Based Design Optimization (RBDO) model stream includes an FEM model, a COST model, a RISK model with built-in First-Order Reliability Model (FORM), and the orchestrating RBDO model. A program wide Direct Differentiation Method (DDM) framework was additionally established that provides efficient analytical gradient calculations throughout the model stream. The FEM elements implemented consist of the Bilinear-Mindlin four node and nine node plate elements. An academic COST model was created to showcase the multi-model capabilities of Rts and the ability to calculate DDM dependencies of downstream models. Additionally, a RISK model was implemented that incorporated a built-in FORM model with gradient-history capabilities and in-model DDM dependency calculations; the RISK measure used is the mean cost. The RBDO model was also built upon to include DDM capabilities and downstream model integration. Finally, two reliability-based design optimization examples were implemented using both nodal and material sensitivities. The thickness and width of a timber cantilever beam was optimized with respect to mean cost taking into account deflection damage and construction cost.

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Review, implementation and demonstration of dynamic analysis and ground motion models (2015)

Dynamic structural analysis in recent years has gained importance due to increasing need to design structures for seismic resistance and also meet different performance demands. Also, structures are becoming more complex and it is difficult to accurately simulate their dynamic behavior using static analyses. With the advent of better computational capacity, engineers have been adopting computer programs for design and analyses of buildings. Making use of the advancement in computation and the need for dynamic analyses, tools required for dynamic analyses are implemented in a software called Rts. Rts is the next version of Rt, a computer program for risk and reliability analysis. For dynamic analyses it is required to have a ground motion input which can either be selected from existing databases of ground motion records or be generated as synthetic ground motions. If using actual ground motions it is required to modify them so that they match the anticipated hazard level. To overcome the limitation of scarcity of ground motion records, synthetic ground motion models can be used. To accomplish this in Rts, a synthetic ground motion model is implemented. The dynamic analysis algorithm and the ground motion models are implemented using object oriented programming. These implementations can be seen as a stepping stone to develop a computer program that would be robust and closely simulate the behavior of structures. It also forms the platform for future research for performance based earthquake engineering design and reliability analysis.

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Risk minimization in Rts, with application to FFTT timber construction (2015)

The risk posed to a structure from an earthquake may be minimized by changing the design characteristics of the structure to determine the optimal design. A risk measure, the mean value of the cost functions in this thesis, can be determined using reliability methods to construct a loss curve. This formulation includes the effect of uncertainty in all aspects of the cost, including construction and repair given an event. This risk model also requires no prior information to determine the mean cost and does not define a discrete “failure,” instead using a continuum of possible outcomes in determining the mean of the cost functions. The optimization model allows for different search directions and step sizes in the search for the minimum cost, with steepest descent and BFGS search directions currently implemented. These analyses are performed using the Rts software, which has the capability of performing the optimization, risk, and reliability analyses on input structural models.The functionality of risk minimization is demonstrated with two example structures, with the framework provided for a third. The first is an example previously solved in Rt, which confirms functionality of the implementations in Rts. The second model uses an analytical model of a single-storey timber-steel hybrid frame, which utilizes the novel structural “Finding the Forest Through the Trees” (FFTT) design concept that has been proposed in Vancouver and studied at UBC. The minimum mean cost of this structure, subject to the cost functions and structural simplification, was determined by optimizing two decision variables that represent the fundamental geometry of the frame. Optimization of this frame converged to one point throughout many analyses, utilizing both the steepest descent and BFGS search methods. Finally, the framework for a future 6-storey FFTT example was developed. This example is inspired from modern tall timber design concepts, which are discussed in a literature review and demonstrates unique features within Rts, including the deep parameterization and nested model structure.

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Diaphragm stiffness in wood-frame construction (2013)

This thesis presents an investigation of the in-plane stiffness of wood-frame diaphragms. Studying the stiffness of the diaphragm is important since it affects the distribution of lateral loads to shear walls. In order to determine the force in each shear wall, it is common to classify a diaphragm as either flexible in engineering design. Wood-frame diaphragms have generally been treated as flexible, which distributes the lateral loads using the straightforward “tributary area” approach. The accuracy of this assumption is investigated in this study. A detailed numerical model is developed for the study of the in-plane behaviour of wood-frame diaphragms. The model is validated with full-scale diaphragm tests, which has not been done so far for other diaphragm models in previous studies. As such, the model can be used as a “virtual laboratory” to predict the in-plane behaviour of wood-frame diaphragms with various configurations. A simplified model is developed based on the detailed diaphragm model to be used in the building analysis. The simplified model consists of “truss units”, which can be calibrated using analytical methods. In previous studies, wood-frame diaphragms were generally simplified as beam or spring models, where individual calibration is required for diaphragms with various configurations. Compared with these models, the simplified model developed here is obtained as an assembly of truss units, thus the number of calibration times can be considerably reduced. A case study of a one-storey wood-frame building is conducted to investigate the distribution of lateral loads to shear walls under different diaphragm flexibility conditions. It is found that the wood-frame diaphragm in this work is rather rigid, but is found that the distribution of lateral loads to the shear walls is strongly dependent on the relative stiffness of the diaphragm and the shear walls.

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In-plane stiffness of cross-laminated timber floors (2012)

This study investigates the in-plane stiffness of CLT floor diaphragms and addresses the lateral load distribution within buildings containing CLT floors. In practice, it is common to assume the floor diaphragm as either flexible or rigid, and distribute the lateral load according to simple hand calculations methods. Here, the applicability of theses assumption to CLT floor diaphragms is investigated. There is limited number of studies on the subject of in-plane behaviour of CLT diaphragms in the literature. Many of these studies involve testing of the panels or the connections utilized in CLT diaphragms. This study employs numerical modeling as a tool to address the in-plane behaviour of CLT diaphragms. The approach taken to develop the numerical models in this thesis has not been applied so far to CLT floor diaphragms. Detailed 2D finite element models of selective CLT floor diaphragm configurations are generated and analysed in ANSYS. The models contain a smeared panel-to-panel connection model, which is calibrated with test data of a special type of CLT connection with self-tapping wood screws. The floor models are then extended to building models by adding shearwalls, and the lateral load distribution is studied for each building model. A design flowchart is also developed to aid engineers in finding the lateral load distribution for any type of building in a systematic approach. By a parametric study, the most influential parameters affecting the in-plane behaviour of CLT floor diaphragm and the lateral load distribution are identified. The main parameters include the response of the CLT panel-to-panel connections, the in-plane shear modulus of CLT panels, the stiffness of shearwalls, and the floor diaphragm configuration. It was found that the applicability of flexible or rigid diaphragm assumptions is primarily dependent on the relative stiffness of the CLT floor diaphragm and the shearwalls.

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Probabilistic models of damage and repair cost for reinforced concrete structural members (2011)

The context of this thesis is performance-based engineering, in which the prediction of damage is a central theme. In contrast with traditional structural engineering, which focuses on forces and displacements, performance-based engineering entails the consideration of seismic consequences in terms of direct and indirect cost of damage to structures. To account for unavoidable uncertainties in such predictions, a probabilistic approach is adopted in this thesis. Specifically, a methodology is proposed that is based on reliability analysis in conjunction with probabilistic models. The phrase “unified reliability analysis” is employed to describe the approach. Although the framework of models generally includes hazard, structure, and consequence models, it is the damage models that are of particular concern in this thesis. In a novel approach, the visual damage at the structural component level is predicted. Importantly, such models predict “physical quantities” of damage. This is done because it is recognized that repair action selection is the central link between the predicted damage and its associated direct and indirect costs. Hence, in order to predict the repair cost and time associated with seismic events, this study puts forward damage models that are directly utilized to predict the repair action. In turn, this leads to probabilistic estimates of seismic loss by summing contributions from the components in the structure. The probabilistic model development follows a Bayesian framework. This approach builds on linear regression theory and explicitly accounts for uncertainties. Specifically, the coefficients in the linear regression models are random variables. The probabilistic models developed in this thesis facilitate the unified reliability analysis that ultimately determines final loss probabilities. This thesis describes the overall methodology, which is generic and applicable to a wide range of structural components, and applies it to reinforced concrete components. This specific application includes the development of a probabilistic model of crack length in reinforced concrete shear walls.

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A probabilistic approach for estimating environmental impacts over the life cycle of buildings (2010)

There is increased awareness and concern regarding human activities with high environmental impacts caused by the construction, operation, maintenance and decommissioning of the built environment. The work presented in this thesis helps predict holistically the environmental impact indicators of different building design options. A probabilistic framework, applicable to multiple building function types, is proposed to estimate the environmental metrics of energy, water and global warming potential. The environmental impact indicators are studied at varying resolutions of data quality. The proposed framework differs from alternate tools by explicitly accounting for uncertainty through the use of random variables in its models. The modeling approach emphasizes greater transparency of the environmental impact intensity values that relate known information about the building, such as material quantities, with respective environmental impacts. Explicit environmental impact models are presented for each of the building’s life cycle phases, including extraction, manufacture, on-site construction, operation, maintenance, and end of life. The methodology is then demonstrated by analyzing a sample residence in Ontario. The environmental impacts associated with the entire life cycle of the building are reported and possible improvements to the methodology are identified. The ability to analyze the probability of exceeding an environmental impact threshold is a feature of this work that is useful in the refinement of environmental performance rating systems. The general lack of public information about the environmental impact of the manufacturing of building components in North America, as well as uncertainty about component replacement frequency and the building service life continue to pose a challenge for environmental impact analysis. However, this thesis presents a new probabilistic framework in which this uncertainty is explicitly identified and addressed.

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