Damage-Based Assessment for Performance-Based Design and Analysis of Timber or Wood Structure Under Earthquake Load

This paper discusses the damage-based assessment for performance-based design and analysis of timber or wood structures under earthquake load. It explores different damage models and focuses on the Park-Ang Damage Model. The study aims to evaluate the performance of timber buildings using a damage-based approach and identifies the differences between force-based design, displacement-based design, and damage-based design in timber structures.

Damage-Based Assessment for Performance-Based Design and Analysis of Timber or Wood
Structure Under Earthquake Load
Submitted by:
Shreya Regmi
University of Melbourne

Abstract:
When an earthquake occurs, a lot of casualties and economic losses are experienced. The
structures used for the construction of the buildings determined a lot in regards to the extent of
loses which are experienced. The materials used for the construction of the structures can either
be steel, concrete, or timber, depending on the design. By definition, the damage of the
materials during earthquakes refers to the sudden or progressive deterioration, of the
mechanical strength of these materials when exposed to loading, chemical, or thermal effects.
Nonetheless, various models exist which helps in predicting these damages. They include
Displacement-Based Design (DBD): Forced-Based Design: and performance-based design. This
paper has, however, designed a new approach, damage based model, which is best suitable for
timber structures. In this paper, the recent numerical and experimental studies of timber
structures have been reviewed to find the probable gaps for future research.
Further, it has discussed some of the damage based models and narrowed down to the
Park-Ang Damage Model. The results indicate that the Park-Ang Damage Model is based on
hysteretic energy demands and normalized maximum displacements, usually in a linear form.
Thus, it is appropriate for the timber structures as it takes into consideration the cumulative
damage failure and the initial exceedance failure with regards to the determination of the
structural damage under earthquake.
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1. Introduction
Timber is originated from wood and is one of the oldest material used in the construction
industry, dating back the Stone Age Periods (Wood, 2017). Steel, timber and reinforced concrete
have been widely used in construction, but it has been understood that the confidence accorded
to timber structures is comparatively lower than the level of confidence granted to steel and
reinforced concrete structures (Miyake, Koshihara, Isoda, & Sakamoto, 2004). This is in terms of
the seismic response, and as such, the life cycle Costs of timber buildings is more than that of
concrete and steel buildings. However, the application of timber on structures has since
improved with the discovery of materials such as steel and concrete, resulting into development
of very modest structures.
The loads which are experienced by structures during an earthquake which originates
from ground acceleration forces of inertia is called the Seismic loads or Earthquake loads. The
magnitude of an earthquake depends on various factors like dynamic properties and mass of a
building, duration of an earthquake, intensity, and frequency of ground motion and the structures
and properties of soil that any structures are standing on. Regardless of the level of confidence
associated with timber buildings, research has indicated that these structures represent one of the
most significant investments human beings have ever made. In North America, research has
indicated that light frame buildings occupy about 80% to 90% (Folz & Filiatraut, 2005) of the
built environment, mainly because of the economics associated with timber. As with Japan, the
design of timber buildings is usually done according to seismic regulations, often revised after
several years. The design life of between 10 and 20 years has been the most significant, but
currently, most of the timber buildings were designed with the outdated specification. As with
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America, research has indicated that no proper seismic analysis has been done for the past 30
years, posing the country at significant anger when it comes to seismic activity.
Despite all the advantages of using timber as the primary construction material, it's
seismic response and behavior is yet to be understood fully. However, recent developments have
seen the seismic response of timber being thoroughly investigated. Hybrid buildings test, shaking
table tests and earthquake simulations, to mention a few, are some of the criteria that have come
to the fore when it comes to an understanding the seismic response of timber buildings.
Background
Steel is expensive while concrete has a significant carbon footprint on the planet. However, it is
understood that timber structures are some of the safest when it comes to occupancy protection.
This has been significantly attributed to the ratio of the weight to strength, which, as research has
indicated, is very high (Van Der Lindt, Pei, Liu & Fikiatraut, 2010). Moreover, there is the fact
that timber structures efficiently dissipate the energy from an earthquake because one of their
properties is nonlinear ductility. This nonlinear ductility proper, coupled with the ability to
dissipate earthquake energy, may also at times result in the destruction that may not conform to
design standard.
In its first test, the NEES project focused on a two-story building. This building has been
considered as a benchmark for all the seismic response tests and analysis that are being
conducted at present. In line with this, the experiment tried to focus on building configuration
and the response to seismic activity. Elements such as joints, bracing, and frame design are all
essential in the design of a building in a seismic prone region.
The shaking tables test has been of vital importance when it comes to seismic response
understanding. In line with this, the Building Research Institute has developed three proposals to
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improve the performance of timber structures. The first proposal is that of a composite structure
whose timber elements are supported by elements made from other materials. There is also the
aspect of joints and their importance to the overall building stability. These joints are a
conjunction of timber and other structural elements. Finally, there is the design of the general
building. Designing a hybrid structure made up of wood and the other construction materials
such as reinforced concrete is one of the viable proposals. All in all, various tests are being
conducted to come up with timber buildings that will be able to withstand shock waves, in line
with the performance-based criteria of building design.
Objective
The main objective of this study is to
1. Evaluate the performance of timber buildings by using a damage-based approach under
earthquake loads.
This paper identifies different damage models for concrete, steel, and timber structures. The
damage-based approach regarding the performance of timber buildings, when subjected to
earthquake loads, has been evaluated.
In this technique, the damping of the single degree of freedom and secant stiffness
determines the structure. By extension, this design relies on attaining a specific limit state of
displacement, ether characterized by non-structural drift limits or material strain limits
characterization by this design helps in preventing multiple problems associated with The
force-based design, (FBD) since the initial stiffness is employed in the determination of
elastic period.
Aims
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1. To explore how to shift from the displacement-based procedure to the damage-based
procedure
2. What we have to do to move from the displacement-based procedure to the damage-
based procedure and what is the current status.
3. To explore the existing damage models?
4. To explore the types of data sheets required for various damage models
To examine the types of systems or dynamic structural models required
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LITERATURE REVIEW
Recent numerical and experimental research works
In 2016. An earthquake series occurred in Kumamoto, after which a comprehensive assessment
including over 2500 houses was done in the area. For the buildings that were constructed after
the 200 building standard law, there was extensive destruction to the structural as well as non-
structural constituents. Later on, the results obtained from this scenario was adopted by
researchers in conducting a vulnerable building type test in 2017 on a Japanese conventional post
and beam wood townhouse. The methodology applied was a shake table testing, and the results
obtained resonated with the theoretical information on the place. (Kotaro Sumida1 et al., 2014)
In 2009, a shake table test was also used in Miki, Japan oma light wood frame building. The
experiment was aimed at validating the significance of midrise light-frame wood buildings in
regards to great earthquakes. From the multiple tests conducted, a detailed damaged inspection
was carried out, and from the results, there was excellent building performance irrespective of
slight damage.
Hao et al., Conducted a numerical analysis on the model suitable for estimation of damage on
timber as a result of seismic loads. The colleagues employed park-and damage model, in
connection to an incremental dynamic analysis based technique. Further, they carried an
experimental test to be able to forecast the likely degree of damage to the wood frames when
exposed to earthquakes. From the results obtained, displacement aloe does not offer reliable
information on the seismic performance for the timber structures.
Hao et al. Conducted a reliability-based methodology for the prediction of damage and seismic
performance in wood frame buildings. The duo used a comparative analysis method, which
included a damage-based limit state criterion and displacement-based criterion. The results
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obtained by the researchers indicated that damage based criterion results into a more realistic
performance as well as offering a viable approach for the assessment of the seismic vulnerability
for the wood frame fittings. Besides, this resulted in easy predicted of the earthquakes hence,
enhancing loss estimation analysis and mitigation.
Differences between force-based design, displacement-based design, and damage-based
design in timber structures
Forced-Based Design:
This design is grounded on the determination of base shear force, which is a consequence of
dynamic earthquake movement using the buildings elastic period or an acceleration response
spectrum. This design approximates the effect of dynamic loading caused by earthquakes by
applying static loads with magnitudes and directions. As a result of dynamic loading,
concentrated lateral force occur in all the building floors, where the mass concentration exists.
Strong lateral forces are more significant at a higher elevation of the structure. Therefore, lateral
displacement and lateral force are maximum at the structure top. Most of the structure uses
similar static lateral forces procedure which is available in most design codes for modeling these
effects in a structure. The modeling is done by directly placing a force at each story level
(ElAttar, Zaghw & Elansary, 2012)
Displacement-Based Design (DBD):
DBD approach calculates the base shear force based on displacement response spectrum. This
approach is one of the most straightforward analysis design analysis methods of the multi-degree
of freedom structures. Here, the equivalent damping of an equivalent single degree of freedom
structures and secant stiffness characterizes the structure is characterized by the (ElAttar, Zaghw
& Elansary, 2012). The structure in this technique is defined by the secure rigidity and equal
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damping of a similar single degree of freedom structure. This approach of the design is about
attaining a specific shift limit state, which can be defined by non-structural drift limits or
material strain limits which are gotten from design codes present in the design level seismic
intensity.
Damage-based design model
A damage based design model makes it very easy to monitor the structural health of a
building. Nonetheless, there exists limited research information on the same. The damage based
model identifies the problem at the very initial stages using a technology that relies on fiber
optics and sensors. There exist various ways in which the damage-based design is achieved, for
instance: the use of several natural frequency shifts, also modifications in the modal properties.
In this approach, one sensor usually acts as an actuator to produce the stress waves, which gets
propagate in the timber structure surface, while the other sensors detect the stress was which are
being propagated. Cracks and other defects will thus induce an extra attenuation on the stress
wave, which is being propagated and the model since the defects by the aid of w wavelet-packet-
based damage index. So far, one of the commonly adopted damage models by researchers is the
park-and index model. The reason behind this is as a result of the model consideration of
cumulative damage failure and exceedance failure in regards to defining the structural damage
that is under earthquake. Further, this model allows for consideration of the effects resulting
from the load sequence and load path on the damage.
Proposed design
Park-Ang Damage Model:
The Park-Ang index model has been identified as one of the most common inference points
when it comes to the damage of reinforced concrete. In identifying the structural damage that is
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caused by an earthquake, the Park- Ang model is exhaustive in terms of the cumulative damage
failure and moreover, can define the first exceedance failure of any reinforced concrete building.
In line with the damage that is caused to reinforced concrete elements, the Park and Ang model
is based on hysteretic energy demands and normalized maximum displacements, usually in a
linear form (Bazan & Sasani, 2004). The formula used in this expression is defined as follows:
Where ∆max is the displacement in a maximum form that is in demand during the process of chic
displacement.
∆u is the capacity of maximum displacements that is only available during monotonic
loading.
Eh refers to the hysteretic demand of energy during the process of cyclic displacement.
F y refers to yield strength.
Finally, Beta is used as a weighing factor, finding and estimating the relationship between the
accumulative damage and the energy dissipation process.
However, as with the parameters used in the analysis, it is still a challenge finding the variable
∆u, regardless of the experimental data that is available on cyclic displacement. This led Park to
develop a procedure that was based on the experimental results of monoclinic loading to identify
the parameter. This, nevertheless, required a proper statistical procedure. As with the weighting
factor, it can easily be determined by taking
into consideration the cyclic displacements
that have been experimentally
estimated for building elements such as beams and columns and incorporating ∆you through
regression analysis. The weighting factor is defined by various characteristics of the building
elements such as the ratio of shear span to the depth, the normalized axial force, and the ratio of
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reinforcement as in the volumetric transverse and tensile perspectives. Nevertheless, Park
identified variations of about 0.6 in the beta coefficient and 0.54 in the displacement index
(Bazan & Sasani, 2004)
Park-Ang Damage Index Based on Effective Energy Dissipation
By definition, effective energy dissipation is the hysteric energy loss of the structural damage
when the damage is at the non-elastic stage. For instance, longitudinal steel bars deflection, the
concrete cracking, and the crush of cover concrete. The hysteric dissipation results in the
damage of the reinforced concrete columns. This damage can only be determined conclusively
when the useful energy is included during the calculation of the damage. Besides, the influence
of load sequence and displacement amplitude on structure damage is also reflected upon by the
effective energy dissipation. However, the energy limit of Park-Ang damage index does not
differentiate whether structure damage is caused by the input energy and consequently excludes
the factorization of the structural damage from the displacement amplitude. Analyzing the
operational energy dissipation ratio present in the effective hysteric energy dissipation, an e1
factor is introduced, which influences the overall energy dissipation on the damaged structure.
The equation below illustrates this phenomenon. :
Where, ei is the effective energy dissipation factor, obtained in the below equation
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.
Mathematically, the expression for δu is shown below.
Experimental Verification of the Park-Ang Damage Index
To validate the Park-Ang Damage Index effectively, we will refer to 6 experiments conducted by
different groups shown in the table below
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From the results obtained by this study, the park-ang model has a mean value closer to 1 and
smaller scatter.
The Park-Ang Damage Index Based on Load Sequence.
Considering the influence of the concrete column and load sequence into account, the equation
for the criterion is shown below.
Where, si is the load sequence factor, which is given by the following relationship.
Park-Ang damage model for timber when exposed to earthquake loads.
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The shaking Tables Test
It forms the foundation of other seismic tests, including the NEES wood frame program and the
CUREE-Caltech wood frame project. Nevertheless, these seismic projects consist of various
phases which are imperative for the eventual seismic response analysis. To begin with, there is
the aspect of the test models. According to the Japanese, these models are a representation of the
structures that have been in existence for the past 30 to 40 years (Isoda, Okada, Kawai, &
Yanaguchi, 2016). The design of the test model considered the Y direction to be higher in length
than the X direction, but the height of the building limited to two storeys. Other factors that are
taken into consideration during the design of the test model include the weight and the ratio of
the strength to the weight in both the X and Y directions.
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After the design of the test model, the next phase of testing is subjecting the model to motion. In
the analysis, several models are used. These models may have the same properties, but there is
usually a difference when it comes to the input motion. Nevertheless, considering the three axes,
one of the models is usually subjected to motion in the X direction, the second model subjected
to motion in the Y direction while the third model subjected to motion in both the X and Y
directions. The final model is subjected to a motion on the three directions. All these are an
indication of the type of motions that a building may be subjected to in earthquake periods. The
motions used are based on parameters acquired during recent earthquakes. The R, as well as the
T components that are usually obtained during earthquake motion, are the input parameters in
such an analysis (Van Der Lindt, Pei, Pryor, Shimizu & Isoda, 2014).
Finally, the seismic response of the timber structures is based on FEM analysis and matrices. The
use of a truss element in the analysis is also allowed, with the final goal being the estimation of
the dynamic force balance. As such, some parts of the analysis may be based on specific
assumptions. However, the FEM used in such an analysis is usually three dimensional, as per the
dimensions of the models used.
METHODOLOGY
To comprehend the response of timber buildings to earthquakes, the capstone test has been one
of the most default. In line with this, the capstone test is based on the ground motions that were
witnessed in Northridge in the year 1994 (Van Der Lindt & Gupta, 2006).
To develop a full comprehension of the damage that can be caused to a timber building, the study
focused on drift results. Other factors such as forces usually require a more intensive study with
some literature focusing on this specific aspect of timber building seismic response.
Nevertheless, to measure the peak intensity drift, there should be an average estimation of the
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displacements obtained from the optical tracking system. According to the study, these
displacements were 7 in number. The displacements are usually specific and are unrepresented
the motion that is witnessed in each diaphragm of the building. The torsional response of the
building is also a factor that should be observed during the analysis because it is usually a
variable that is dependent on the international drift of the sheer walls of the building (Panc,
Risiwosky, Pei, & Van Der Lindt, 2015).
Nevertheless, after each testing procedure, inspection plays a pivotal role in the eventual analysis
and conclusion. That stated, a team that may be composed of around 40 individuals inspects the
capstone building, with each quadrant of the building storeys requiring proper inspection. These
groups of people are mandated with the responsibility of measuring the cracks that have been
developed during the tests, with the eventual goal to determine how they have been propagated.
This involves the use of tip markets that are typical to seismic tests.
DAMAGE MODELS USED FOR CONCRETE, STEEL AND TIMBER STRUCTURES
Timber Models
The three construction materials have different properties, mainly in terms of elasticity and
fracture behavior. That stated, the models used in identifying the seismic response of timber are
dependent on the three-dimensional finite element method (Folz & Filiatraut, 2004). Fracture and
the pattern of cracking tend to be dependent on the intensity of an earthquake and as such,
models focus on the X, Y, and Z dimensions of destruction. The masses that are identified at
each floor level are essential input parameters to the model, and so are other parameters such as
the bending stiffness. The appropriate damage model for timber structures is the Park-Ang
Damage Model. As detailed above, Park-Ang Damage Model is based on hysteretic energy
demands and normalized maximum displacements, usually in a linear form. This model is
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determined by getting the product of load sequence factor and the effective energy dissipation
factor. It is appropriate for the timber structures since it takes into consideration the cumulative
damage failure and the initial exceedance failure with regards to the determination of the
structural damage under earthquake. It also has a minimum mean value, which overall influences
the seismic parameters (lasting time, frequency spectrum, and amplitude) which determines the
structure damage. This makes it the mostly applied damage model by researchers. However, we
also realize that apart from being the only model which relies on deformation and energy
dissipation, there are few damage models for timber.
Steel Models
The model of analysis depends on the test frame experiment. The test frame is a steel building of
standard column, stud and beam dimensions. Nevertheless, in the pre-analysis phase, damages
that are strategically placed at the beams and columns are used to determine the changes in the
shapes of nodes. In line with this, there is the use of simulation models that are dependent on the
input of white noise. Therefore, the model uses the comparative study of changes in the
properties of the white noise and the node properties to identify the destroyed location of a steel
building.
Steel structures are ductile, and often would undergo plastic deformation, before the occurrence
of failure and damage. The suitable damage model for the steel structures is the Ductile Damage
Model. This model concentrate on the aspects of crack initiation, damage propagation, as well as
the ductile fracture behavior of notched specimens. Finite element analysis and continuum
damage mechanics are employed in the prediction of ductile damage.
Concrete models
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Concrete is an elastic and isotropic material whose damages occur as a result of extensions.
These damages reduce the stiffness of multiple components, and the damaged material will
eventually become anisotropic or lose its isotropic features. In isotropic models, the initial
number of the symmetry planes and direction are not affected by the damage. Hence implying
that the medium used does not matter. The appropriate damage models for the concrete
structures are thus isotropic damage model and anisotropic Damage Model.
Isotropic damage model,
The equation below represents the damage
The scalar variable D Represents the damage, and the evolution takes place when the extension
deformation becomes more significant than the reference value. For instance
Where εi is a principal deformation component, being its positive part, i. e.:
Considering the thermodynamic principles
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here D. = dD/dt , i. e., D time derivative; F( ) is written in terms of and defined continuous
and positive.
where DT and DC are given by:
Anisotropic Damage Model.
The assumption for this model is that concrete is under the category of materials which are
initially unimodular, and isotropic, but upon being damaged, they begin to present different
behaviors in compression and tension. This model is about equivalence energy between the
continuous medium and damaged medium. The equation below illustrates the model.
where f1(D1, D4, D5) = D1 - 2 f2(D4, D5) and f2(D4, D5) = 1 - (1-D4) (1-D5).
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EXPERIMENTAL STUDY OF TIMBER STRUCTURE
In the experimentation of timber structures and their seismic response, a model is usually
developed to identify the structural elements and their response. In line with this, there is the
numerical model formulation that is used to identify the response of the various elements.
Nevertheless, the first consideration is the structural orientation of the various elements of the
building. That stated, the numerical model is focused on the following distinctive elements: the
shear walls, the floors, the roof diaphragm, and the partition walling. As with the foundation, it is
assumed to be rigid. This is also the case when it comes to the flooring and roofing elements.
Moreover, there is the assumption that is based on the kinetics of the building. The assumption is
that the coordinates of the building model are global. This result in the transformation of the
entire building structure into the first quadrant of the coordinate system. It also means that the
origin of the system serves as the degree of freedom for each of the diaphragm, meaning each
diaphragm requires three degrees of freedom. This, in turn, means that the eventual outpost
requires two transformations of the original matrix and on top of that, there is also one rotation
(Morita, Teshigawara, Isoda, & Hamamoto, 2001).
To identify the load in each node and the reactions, the stiffness matrix, as well as the loading
vector, needs to be established. This is because the external forces from the earthquake can be
transformed to act on any part of the diaphragm (Van Der Lindt, 2005). Working with the origin
of the transformation, the forces of inertia, as well as those that restore balance, are easily
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identified. This means that each reaction can be identified meaning that the timber elements can
be designed in terms of joints, strength to improve the durability and resistance to earthquake
seismic waves.
GAP BETWEEN THE EXISTING STUDY OF DAMAGE-BASED MODEL OF TIMBER
STRUCTURES AND COMPARE IT WITH STEEL AND CONCRETE STRUCTURE.
 Lack of numerical and experimental information,
There is limited information in regards to the statistical and experimental information of the
existing study of a damage-based model of timber structures. This has resulted in a big gap for
the timber structures, which has influenced its application on various platforms. The numerical
and experimental information would be much easier to handle and implementation of the model
for the timber structures.
 limited proposed Seismic damage indices
There are limited proposed Seismic damage indices. These indices are widely used to envisage
possible damage. Additionally, they influence the decisions related to the reoccupation of
buildings that are damaged during an earthquake.
 Insufficient formulas incorporating the Non-linearity of timber structures
From previous studies, timber behaves differently when exposed to a various structural load, thus
dissipates a lot of energy. The present formulas do not take into consideration this factor, hence
creating a gap in the damage-based model of timber.
COMPARISON OF THE CONCRETE, STEEL, AND TIMBER
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There exist multiple information for the behavior of steel, concrete, and timber when exposed to
various structural loads. However, timber tends to behave differently when exposed to a various
structural load, thus dissipates a lot of energy.
Conclusion
A new approach, damage based model, which is best suitable for timber structures have
been developed in this research. Over the past years, usage of timber structures has been on the
rise as a result of its less expensive costs. However, during earthquakes, mostly timber structures
are bound to be grossly affected, prompting a design based on damage- approach to help in
curving the problem. The Park-Ang Damage Model is based on hysteretic energy demands and
normalized maximum displacements, usually in a linear form. Hence, making it appropriate for
the timber structures. By extension, this model takes into consideration the cumulative damage
failure and the initial exceedance failure with regards to the determination of the structural
damage under earthquake. Contrarily, the gaps between the existing study of a damage-based
model of timber structures including the lack of numerical and experimental information, limited
proposed damage-indices, as well as non-linearity of the timber make the research a little bit
complex. Hence, there is a need to consider the advanced analysis of the methods used in this
research to develop design codes for timber buildings that are exposed to different conditions of
earthquake loads.
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