University
stringclasses 19
values | Text
stringlengths 458
20.7k
|
|---|---|
ADE | An innovative indicator for determining the relative improvement upon a Best
Alternative to a Negotiated Alternative (BATNA) solution allows stakeholders to rapidly
assess how well a solution performs across multiple objectives and multiple objective
spaces. In addition, as the joint-Pareto solutions are Pareto optimal with respect to each
stakeholderβs individual problem formulation, this assists with arriving at a consensus on
a final compromise solution. This is because stakeholders do not have to compromise by
accepting a solution that is dominated in the objective space of their preferred formulation,
nor do they have to explore and analyse results of a single problem formulation with
aggregated or agreed upon objectives that do not necessarily reflect their values.
The approach was demonstrated on a multi-stakeholder catchment management
problem, requiring 16 different objectives from stakeholders to assess solutions. Eight
optimization formulations were solved to generate solutions to a best alternative scenario
and a collaborative scenario. From a set of solutions that were joint-Pareto optimal within
the collaborative scenario, a set of selected solutions were identified for further
consideration by stakeholders.
4.6 Acknowledgements
Research funding was provided by the University of Adelaide, and the Goyder Institute
for Water Research. The authors thank Dr. Dale Browne and e2DesignLab, Australia for
assistance with the case study data.
132 |
ADE | CHAPTER 5
Conclusion
Recently, the application of Water Sensitive Urban Design (WSUD) has demonstrated
an ability to mitigate the impacts of development on urban water supply security and
natural ecosystem health (Askarizadeh, Rippy et al. 2015). An increasingly popular
WSUD technique is urban stormwater harvesting (SWH), which incorporates stormwater
best management practices (BMPs) in systems used to intercept and capture, treat, store
and distribute surface stormwater runoff for later reuse. WSUD approaches, especially
SWH, can provide multiple benefits such as a reliable water supply for irrigation,
improvement in urban vegetation and amenity, and restoration of urban runoff quality and
quantity closer to pre-development levels (Fletcher, Mitchell et al. 2007). However,
optimizing WSUD systems to achieve these multiple objectives, which are often
conflicting, can make planning and design tasks more complex than traditional
stormwater management systems. Compounding this difficulty are the multiple possible
spatial scales at which BMPs can be distributed throughout a catchment, the large number
of different types of system components and interaction between components, and the
large number of decision options (e.g. size, type and location of BMPs) and therefore
large number of possible solutions. Consequently, many WSUD system planning and
design problems are suited to be formulated mathematically as multiobjective
optimization problems with large and complex solution spaces; which consist of a set of
planning or design decisions that need to be selected to maximize a set of objectives given
practical constraints.
While formal multiobjective optimization approaches, including the use of
metaheuristics linked with models to evaluate the objective function performance, may
be well suited to solving WSUD planning and design problems, their application also
presents a number of challenges. An optimization framework that considers all aspects of
the SWH system preliminary design problem is necessary to take into account multiple
objectives, different system components, the distribution of components throughout a
catchment and a formal optimization approach. In addition, to ensure the results of the
application of optimization approaches are trusted and used in practice, it is necessary to
adapt approaches to incorporate stakeholder input and facilitate negotiation between
133 |
ADE | multiple stakeholder groups with different preferences to encourage the adoption of a final
WSUD solution. In order to address these issues, three optimization frameworks using
multiobjective metaheuristic algorithms were introduced in this thesis, which are able to:
1) handle SWH systems preliminary design incorporating multiple objectives, different
types of system components, distribution of BMPs, and a large number of decision options
in a holistic fashion, 2) encourage the adoption of the results of optimization by
incorporating input from stakeholders in the problem formulation and evaluation using
portfolio optimization approach, and exploration of analysis of optimization results using
visual analytics, and 3) facilitate negotiation between a number of stakeholder groups,
each with different value sets and interests, through a innovative multi-stakeholder visual
analytics approach to identify, explore, analyse and select from jointly optimal solutions.
5.1 Research Contribution
The overall contribution of this research is the development of three optimization
frameworks for optimal WSUD systems planning and design using multiobjective
optimization algorithms. In the first framework, optimal SWH systems with components
distributed at the development scale are identified to maximize water quality
improvement and SWH capacity, at minimal cost, subject to practical limits on the
combination of BMPs within systems and pollution reduction requirements set by
regulators. The benefits of this framework are demonstrated using a real-world case study
based on a new housing development located north of Adelaide, South Australia. The
second framework produces optimal integrated catchment management plans consisting
of BMP projects for maximizing water quality improvement, SWH capacity, and urban
vegetation and amenity improvement at the regional scale and is applied to a real case
study for a major Australian city. The third framework incorporates the optimization
approach in the second framework into a multi-stakeholder optimization-visual analytics
framework to facilitate the selection of a solution to complex environmental planning
problems through negotiation between parties. This uses visual analytics considering
extremely large numbers (>10) of objectives and is applied to a sixteen objective multi-
stakeholder catchment management plan problem for a real case study for a major
Australian city.
134 |
ADE | The specific research contributions to address the objectives stated in the Introduction
are as follows:
1. A generic multiobjective optimization framework to assess trade-offs in spatially
distributed SWH system designs, featuring the Non-Dominated Sorting Genetic
Algorithm (NSGA-II) linked with an integrated stormwater model (eWater
MUSIC) and a lifecycle cost model, was developed in Paper 1. This framework
is able to identify SWH system designs that maximize trade-offs between water
quality, stormwater harvesting capacity and minimize lifecycle cost of BMPs and
water transfer infrastructure. A SWH systems design problem for a real case
study for a new housing development north of Adelaide, South Australia was
used to demonstrate the utility of the framework. The results demonstrate the
benefits of adopting Pareto optimal spatially distributed SWH systems identified
using the framework, compared with traditional designs with BMPs located at
the catchment-outlet. Results indicate that, where storage space is limited at the
catchment outlet, better harvested stormwater supply reliability as well as better
water quality improvement can be achieved by distributing capture, treatment,
and storage BMPs in an integrated SWH system.
2. A general multiobjective optimization framework for the selection of a portfolio
of BMPs for catchment management was developed in Paper 2. The framework
addresses the need for a decision support approach for the selection of BMPs that
considers numerous, possibly conflicting, performance criteria, handles a large
number of decision options and potential strategies, facilitates the identification
and representation of trade-offs between performance criteria, which develops
trusted strategies, within the limits of existing planning capacities. The approach
was applied to a case study catchment plan for a catchment authority in a major
coastal city in Australia. The results demonstrate the benefits of exploring full
portfolio solution trade-offs in a many-dimensional Pareto optimal front. A
comparison between the trade-off spaces of a lower dimensional water quality-
cost problem formulation (typical in previous catchment management plan
optimization studies) and the many-objective formulation, demonstrated that
low-objective formulations can result in Pareto optimal portfolios with low
performance in non-objective performance criteria. The study demonstrated that
the use of the visual analytics approach to explore combined optimization and
135 |
ADE | decision spaces could assist in overcoming institutionally influenced biases to
include particular projects or BMP technologies to demonstrate alternative
similar cost options to decision-makers.
3. A general optimization-visualisation framework that deals with multiple
stakeholders with multiple objectives, and encourages a negotiated outcome for
a portfolio optimization problem, was presented in Paper 3. The framework
addresses the need for a decision support approach for identifying solutions to
complex environmental problems that i) handles multiple stakeholder
formulations of the problem reflecting their interests and values, ii) enables
interactive exploration and analysis of possible solutions by stakeholders, iii)
encourages stakeholder trust in the final selected solution, and iv) facilitates a
final negotiated outcome. Improvements on existing multi-stakeholder
exploration approaches were developed. These include visualization of the full
trade-offs between extremely large numbers of objectives using multiple linked
parallel coordinate plots in a visual analytics package. Solutions were framed
within the plots to compare proposed solutions to a best alternative across
multiple objectives. This was done to facilitate negotiation by emphasising the
benefits gained and losses prevented through accepting a negotiated outcome.
This also highlights inequities between stakeholders and facilitates bargaining
when equitable outcomes are available. An innovative indicator for determining
the relative improvement upon a Best Alternative to a Negotiated Alternative
(BATNA) solution allows stakeholders to rapidly assess how well a solution
performs across multiple objectives and multiple objective spaces. In addition, as
the joint-Pareto solutions are Pareto optimal with respect to each stakeholderβs
individual problem formulation, this assists with arriving at a consensus on a final
compromise solution. The approach was demonstrated on a multi-stakeholder
catchment management problem, requiring sixteen different objectives from four
stakeholders to assess solutions. Eight optimization formulations were solved to
generate solutions to a best alternative scenario and a collaborative scenario.
5.2 Limitations
The limitations of this research are discussed below.
136 |
ADE | 1. The framework for a SWH preliminary design in Paper 1 considers harvesting and
water quality control functions, but not flood control functions as is the case in
many WSUD systems. The case study was selected to allow the water quality
control volumes in BMPs to be sized separately from any flood control
infrastructure dealing with greater than 1 in 1 year flood events.
2. The objective functions selected in Papers 1, 2, and 3 reflect commonly used
WSUD indicators of performance but additional objectives may also be important.
Where additional objectives are added to optimization problem formulations in
application of the framework this may require the use of multiobjective
metaheuristic algorithms that have been demonstrated to work on problems with
more than four objectives.
3. The utility of the proposed framework in Paper 1 has been demonstrated via the
development-scale case study, as its application enabled optimal solutions to be
identified within a given computational budget. However, application of the
framework will not necessarily support real-world decision making, particularly
in places where a large number of nodes in a system are possible, requiring orders
of magnitude more simulations and much longer model run-times.
4. Although economic factors (e.g., capital and maintenance costs of WSUD
components) have been included in the proposed frameworks, there is no
consideration of the sensitivity of the optimal WSUD systems obtained to different
cost assumptions. In particular, the long-term cost of maintenance to maintain
functional performance of WSUD assets, as well as uncertainty about these costs,
is a subject of ongoing research. For example, the cost model assumes a
proportional relationship between the size of BMPs and cost, however does not
take into account the amount of sediment captured in BMPs, which means smaller
BMPs may have underestimated costs compared with those estimated by a model
including associated costs to remove sediment to maintain functional
performance.
5. The water quality, stormwater harvesting and urban vegetation and amenity
values were not subjected to a sensitivity analysis to model inputs, therefore
optimization results should be tested further. In particular, to determine the
137 |
ADE | pollutant load reduction of a WSUD system in MUSIC it is typical practice to
simulate the system several times with a stochastic function for the pollutant wash-
off model in MUSIC switched on, and to then to calculate an average performance
value. This was not possible in the framework in Paper 1 due to limitations on run-
time. The stormwater harvesting performance of optimization solution should be
further tested using several climate scenarios as suggested in (Marchi, Dandy et
al. 2016).
6. The visualization method presented in Paper 3 has not yet been demonstrated in a
stakeholder workshop setting, and impacts of the real-world application are yet to
be tested and understood.
In the proposed frameworks, the WSUD systems are developed using one rainfall
pattern, whereas the harvesting performance is may be impacted by future climate
changes (although, Clark et al. 2015 have found climate change is not likely to be
critical to urban runoff when compared to increasingly dense urban development,
in South Australia). Demand for alternate water supplies (i.e. non-potable quality)
is also a critical variable that should be considered.
7. Notably, the optimization formulations in the case studies in Paper 2 and 3 do not
consider interaction between having a higher harvest capacity, which might allow
for more irrigation of green spaces.
5.3 Future Work
From the above limitations, some future studies are recommended below.
1. Future application of the framework in Paper 1, might consider an additional flood
control objective and linking a flooding model to the framework. This would be
possible through the use of metaheuristic algorithms that allow for multiple linked
models to evaluate multiple objectives.
2. As long model run-time and computational budget limited the size of case study
available to apply the framework in Paper 1, in addition to the model pre-emption
method employed, future studies could consider parallelization of model
simulations, surrogate modelling techniques, or additional optimization operators
138 |
ADE | to prevent simulation of inferior solutions that could reduce run-time further, as
discussed in Maier, Kapelan et al. (2014). This would permit larger WSUD
systems, additional decision options, scenarios including the impact of climate
change on optimal BMP placement, as well as consideration of solution robustness
and uncertainty analyses.
3. Future studies on the impact of climate changes on distributed systems of BMPs
used for stormwater harvesting should be investigated, as has been done for BMP
systems not including harvesting (Chichakly, Bowden et al. 2013).
4. As economic sensitivities, as well as other model parameter and objective function
sensitivities are important for real-world WSUD systems planning and design,
there is a need to take into account this factor in further studies. Furthermore, risk
management should be also addressed to evaluate the impact of maintenance cost
sensitives.
5. Adding more objectives to the optimization formulations could provide decision-
makers with even more insight into the performance trade-offs of optimal WSUD
systems. However, the number of solutions that represent Pareto front increases
exponentially with the number of objectives, making solutions representing
optimal trade-offs more difficult to identify, explore and analyse. Therefore,
metaheuristics that have been demonstrated to work on problems with high
numbers of objectives should be used to identify optimal solutions (e.g. BORG;
Hadka and Reed (2012)). Nonetheless, visual analytics approaches are particularly
useful for exploring and analysing optimization results of problems with large
number of objectives as demonstrated in Paper 3, in particular.
6. The optimization-visual analytics presented in Paper 3 should be tested in an
experimental workshop setting, to demonstrate its ability to facilitate the rapid
selection of compromise solutions.
7. The problem formulation in Paper 2 and 3 should consider synergistic (or
cannibalistic) interaction between objectives such as projects with higher
harvesting capacity, which may increase the irrigation capacity, thus increasing
green score of projects nearby.
139 |
ADE | Table B- 1 Detailed costings of stormwater harvesting components used to develop the model for LCCSWH [$] (Eqn. 8) in the case
study application of the optimization framework. Based on values in Inamdar (2014). SWH component cost values were adjusted
from 2012$ to 2016$, at 1% p.a (D. Browne, personal communication, 2016)
Underground Conc. Storage Stormwater pipes Control System Pump system Electricity
Volume Capital Cost Annual Capital Annual Capital Annual Capital Annual Annual NPV NPV Total Levelized
Supplied ($) Cost Cost Cost Cost Cost Cost Cost Capital Annual NPV cost
ML/yr ($/year) Cost ($/year) (2016$) ($/year) (2016$) ($/year) ($/year) Cost Cost (2016$) (2016$/ML)
($) (2016$) (2016$)
Pleasance Garden 5.6 191750 3020 49500 650 30000 1400 19180 5000 156 302221 128544 430765 6306
Ievers Reserve 5.6 153400 3020 65250 650 30000 1400 19428 5000 173 278962 128757 407719 5969
Batman Park 5.7 191750 3020 20925 650 30000 1400 19428 5000 173 272744 128757 401502 5775
Birrarung Marr Park 15.1 536900 3020 82620 650 30000 1400 39300 5000 864 716786 137443 854230 4638
Holland Park 18.5 920400 3020 47790 650 30000 1400 48190 5000 605 1088863 134188 1223051 5420
Clayton Reserve 26 767000 3020 151200 650 30000 1400 29102 5000 735 1016980 135822 1152802 3635
B-4 |
ADE | Equation ( D-3 )
where a sum of the cost of BMPs to capture and treat stormwater runoff, LCC [$]
BMP
(Equation (D-2)), and to transfer harvested water to a balancing storage for further
treatment and distribution, LCC [$] (Equation (D-3)) is applied with BMP
SWH i
representing the ith BMP in the candidate portfolio, N [integer] is the number of projects
in the portfolio, and TAC [$] is the total acquisition cost as a function of SA, the surface
area of BMP. M [$) is this the annual maintenance cost per unit surface area
i
PWF [fraction], for the establishment period, and PWF [fraction], for the
estab maint
remaining design life of system components, are the present worth factor for a series of
annual costs computed using an appropriate discount rate. ECF [fraction] is the
establishment cost factor (i.e., multiplier) for the annual maintenance cost M [$] during
the establishment period (typically 1-2 years) for each BMP. For BMPs with a stormwater
harvesting function, C [$], C [$], C [$], and C [$] are the capital
CapTank CapPipe CapControl CapPump
costs for required underground storage tank, control systems, pipes, and pump stations,
and C [$], C [$], C [$], and C [$] are the annual maintenance costs for
mTank mPipe mControl mPump
the tank, pipes, control systems, and pumps, and operating costs, respectively.
For the case study, the objective function for lifecycle cost of each portfolio, LCC [$],
,S
was calculated using (Equation (D-1) to (D-3)). The parameters for LCC [$] (Equation
BMP
(D-2) were estimated from cost schedules developed by Melbourne Water Australia
(2013) (Table D-1). A typical lifecycle period of 25 years, a discount rate of 6.5% per
year, an establishment cost factor of 3, and an establishment period of 2 years, were
adopted. The parameters for LCC [$] (Equation (D-3)) were estimated as follows. A
SWH
cost model for the total net present value (NPV) of stormwater harvesting components
was determined using regression (r2 = 0.814) between levelized lifecycle cost [$/ML] and
estimated annual volume supplied [ML/yr], using detailed costing data for six stormwater
harvesting projects derived by Inamdar (2014) (see Section 3.2.3.1). Thus, the lifecycle
cost of stormwater harvesting components from Equation (D-4) was calculated using the
following equation:
D-2 |
ADE | Equation ( D-5 )
where, [mass year-1] is the mean annual pollutant mass retained by BMPs in
each candifdΛ aβ° t(cid:181) eβ¦ kΒ· pΛ o rtfolio, N is the number of BMPs in a portfolio, Resid [mass year-1] is
i
the mean annual mass of pollutant leaving the ith BMPβs contributing catchment area, and
Source [mass year-1] is the mean annual mass of pollutant that reaches the ith BMPβs
i
catchment outlet in a post-development catchment baseline scenario without intervention.
Resid and Source should be determined using a stormwater quality assessment model
accepted by the catchment management authority (Coombes, Kuczera et al. 2002, Bach,
Rauch et al. 2014).
Total Nitrogen (TN) was the specific pollutant constituent adopted for the water quality
objective. The mean annual pollutant mass of TN retained by each candidate portfolio
was calculated based on the sum of average annual TN mass retained by individual BMPs
in a portfolio. The water quality improvement of each BMP (Source, - Resid ; Equation
i i
(D-5)) was assessed using the integrated catchment model, MUSIC version 6.1 (Model
for Urban Stormwater Improvement Conceptualization, (eWater 2009)), as suggested by
the CMA regulations. MUSIC is an integrated stormwater model that evaluates
rainfall/runoff and pollutant generation and transport, hydraulic and pollutant removal
performance of BMPs (Bach, Rauch et al. 2014). MUSIC algorithms simulate runoff
based on models developed by Chiew and McMahon (1999) and urban pollutant load
relationships based on analysis by Duncan (1999). An assessment of interactions between
BMPs was not deemed necessary because the contributing catchments of individual
BMPs were spatially mutually exclusive.
A.3 Stormwater Harvesting
Average annual supply capacity (Equation (D-6)) is adopted as an indicator of
stormwater harvesting performance. The supply stormwater harvesting objective function
is:
o
MAXIMIZE: fβ‘β°βββ¦Λ = (cid:135) Supplyk
k,-
D-4 |
ADE | Equation ( D-6 )
where Supply [volume] is the average annual stormwater harvested volume for the ith
i
BMP in a portfolio, and N [integer] is the number of projects in a portfolio.
Experts on stormwater harvesting from each LGA were asked to evaluate the
stormwater harvesting potential of BMPs within their jurisdiction. They estimated the
expected irrigation demand required by open spaces near each BMP, and the average
annual potential capacity to supply the demand. The estimates were based on procedures
specific to each LGA, and reflect the stormwater harvesting objective performance values
accepted by decision-makers.
Urban Vegetation and Amenity Improvement
The urban vegetation and amenity improvement indicator depends on stakeholder
interests, which may include maximizing vegetation and tree coverage and quality of
recreation spaces. Each project should be appraised and evaluated (scored) by vegetation
experts. The cumulative urban vegetation improvement objective function is:
o
MAXIMIZE: fΒΈΒ»β β o = (cid:135) Greenk
k,-
Equation ( D-7 )
where Green [integer]is a score, determined by expert assessment, attributed to the ith
i
project in a portfolio.
The βgreenβ scoreβ of individual projects (which is a weighted score of several
indicators, and was developed by the authors and agreed to be used as an optimisation
objective by consultants), use scores assigned by experts (see section 3.3) from each
LGA interviewed in a workshop session by consultants. The experts were asked to
answer the following questions about the BMP projects within their jurisdiction:
Answer βYesβ βNoβ or βMaybeβ to the following questions: 1) βwill native vegetation
increase at the site?β, 2) βwill tree cover increase at the site?β, and, 3) βwill the quality
of recreation spaces in the area increase?β. The total catchment βgreenβ score objective
function was:
(cid:137)
Greenk = βΛ,-ScoreΛ
D-5 |
ADE | Abstract
ABSTRACT
Terrorism has become a serious threat in the world, with bomb attacks carried out
both inside and outside buildings. There are already many unreinforced masonry
buildings in existence, and some of them are historical buildings. However, they do
not perform well under blast loading. Aiming on protecting masonry buildings,
retrofitting techniques were developed. Some experimental work on studying the
effect of retrofitted URM walls has been done in recent years; however, these tests
usually cost a significant amount of time and funds. Because of this, numerical
simulation has become a good alternative, and can be used to study the behaviour of
masonry structures, and predict the outcomes of experimental tests.
This project was carried out to find efficient retrofitting technique under blast loading
by developing numerical material models. It was based on experimental research of
strengthening URM walls by using retrofitting technologies under out-of-plane
loading at the University of Adelaide. The numerical models can be applied to study
large-scaled structures under static loading, and the research work is then extended to
the field of blast loading. Aiming on deriving efficient material models,
homogenization technology was introduced to this research. Fifty cases of numerical
analysis on masonry basic cell were conducted to derive equivalent orthotropic
material properties. To study the increasing capability in strength and ductility of
retrofitted URM walls, pull-tests were simulated using interface element model to
investigate the bond-slip relationship of FRP plates bonded to masonry blocks. The
interface element model was then used to simulate performance of retrofitted URM
walls under static loads. The accuracy of the numerical results was verified by
comparing with the experimental results from previous tests at the University of
Adelaide by Griffith et al. (2007) on unreinforced masonry walls and by Yang (2007)
on FRP retrofitted masonry walls. To study the debonding behaviours of retrofits
iv |
ADE | Chapter 1: Introduction
1. INTRODUCTION
1.1. BACKGOURND
The protection of structures against blast loads is a government research priority for
βSafeguarding Australiaβ against terrorism. Unreinforced masonry (URM)
construction, which is widely used in public buildings, is extremely vulnerable to
blast loads. An effective solution to mitigate blast effects on URM construction is to
strengthen the masonry using retrofit technologies. Hence, developing retrofit
technologies for URM construction is necessary and imperative.
Retrofit URM constructions are currently in their infancy around the world (Buchan
and Chen 2007; Davidson et al. 2005; Davidson et al. 2004b; Hamoush et al. 2001;
Romani et al. 2005; Tan and Patoary 2004; Urgessa et al. 2005; Ward 2004; Yang and
Wu 2007). Categories of available masonry retrofit include: conventional installation
of exterior steel cladding or exterior concrete wall, and new technologies such as
external bonded (EB) FRP retrofit technologies, catch systems, sprayed-on polymer
and/or a combination of these technologies (Davidson et al. 2005; Davidson et al.
2004b). However, most of the current research focuses on studying the behaviours of
retrofitted masonry walls under static, cyclic or seismic loading {Hamoush, 2001
#175;Malvar, 2007 #578;Silva, 2001 #512;Yang, 2007 #407}. Recently, blast tests
have been conducted to investigate retrofitting techniques to strengthen unreinforced
masonry (URM) walls against blast loading (Baylot et al. 2005; Carney and Myers
2005; Myers et al. 2004; Romani et al. 2005). Therefore, it is urgent to study the
behaviours of retrofitted URM walls under blast loading, and develop an efficient
retrofitting solution to enhance blast resistance of masonry structures.
1 |
ADE | Chapter 1: Introduction
The analyses of retrofitted masonry member against static, cyclic or seismic loading
have received considerable attention in recent years (Baratta and Corbi 2007;
Bastianini et al. 2005; El-Dakhakhni et al. 2004; ElGawady et al. 2006b; ElGawady et
al. 2007; Hamoush et al. 2002; Hamoush et al. 2001; Korany and Drysdale 2006;
Shrive 2006; Silva et al. 2001; Willis et al. 2006). Empirical, analytical and numerical
methods have been developed to estimate the response of retrofitted masonry under
quasi-static loads (Cecchi et al. 2004; Ceechi et al. 2005; ElGawady et al. 2006a;
Hamed and Rabinovitch 2007; Korany and Drysdale 2007a; Korany and Drysdale
2007b; Wu and Hao 2007a; Wu et al. 2005). The empirical method, which is based on
a collection of experimental data, is easy to use, but the accuracy of this method
depends on the test data available. Although analytical methods can perform quick
and reliable analysis, it is sometimes not possible to obtain analytical solutions due to
the complexity of the problems. The finite element method, which is widely used in
practical engineering, provides explicit and direct results.
The analysis of masonry members with retrofits subjected to blast loads is currently
still in its initial stages. For example, conventional design guidelines (American
Society of Civil Engineers (ASCE) 1997; American Society of Civil Engineers
(ASCE) 2007; Department of Defence (DoD) 1990) reference using a βSingle Degree
of Freedomβ (SDOF) model in the blast analysis and design of retrofitted masonry
member (Biggs 1964). Although the SDOF method is easy to implement and is
numerically efficient, it has a number of drawbacks. For example, it cannot capture a
variation in mechanical properties of a cross-section along the member, cannot
simultaneously accommodate shear and flexural deformations, and cannot allow
varying distribution of blast loading spatially and temporally. All of this is in contrast
to finite element analysis, where these accommodations are possible. Thus there is a
need to develop a finite element model to analyse the dynamic response of retrofitted
masonry members against blast loads.
2 |
ADE | Chapter 1: Introduction
1.2. SCOPE AND OBJECTIVES
The primary aim of this project is to establish numerical models to investigate the
behaviours of retrofitted URM walls under blast loading. To achieve this goal, there
were four milestones during the project:
1) Simulation of URM walls using homogenization technique. This
consists of: (a) building masonry basic cell (MBC), (b) identifying material
models for brick and mortar, and (c) deriving equivalent material
properties of masonry basic cell. The basic material properties of brick and
mortar were gained from material tests (Griffith et al. 2007). By simulating
the behaviours of MBC under various load statements, the equivalent
material properties were derived from the simulated stress-strain curves of
MBC. Based on the equivalent material properties, a three-dimensional
(3D) homogenized model was derived. This homogenized model was
validated in simulating full-scaled URM walls.
2) Developing bond-slip model by simulating pull-tests. The interface
bond/slip characteristics between FRP and masonry govern the
performance of retrofits. Aiming on gaining reliable results, the bond
behaviours should be simulated accurately. In this thesis, interface and
contact models were used in simulating pull-test including externally
bonded (EB) and near surface mounted (NSM), meaning accurate results
were obtained. The validated homogenized masonry models together with
reliable interface models between masonry and FRP were applied in the
simulation of full-scaled retrofitted URM walls under quasi-static loads.
3) Studying the behaviours of retrofitted URM walls subjected to blast
loading. The validated numerical models are extended to simulate
3 |
ADE | Chapter 1: Introduction
retrofitted masonry wall subjected to blast loading. Several types of
retrofitting techniques were tested. Parametric studies were conducted to
simulate masonry walls with different retrofitting techniques subjected to
blast loading and effective retrofits are found. A comparison of the
effectiveness of various retrofitted masonry walls was plotted.
4) Developing pressure-impulse (P-I) diagrams as design guideline. Based
on simulation results, two critical damage levels were identified for the
retrofitted masonry walls. As a type of design guideline, P-I diagrams were
developed, in which both the effect of pressure and impulse were well
considered.
1.3. THESIS OUTLINE
In Chapter 1, background, scope and objects of this project are introduced. The brief
summary of this thesis will be presented in the following content in this chapter.
Chapter 2 presents relevant literature on URM walls and retrofitted URM walls
subjected to blast loading. The commonly used retrofitting techniques on concrete and
masonry structures are summarized. The brief overview of methods on estimating
blast loading is described. Proposed methods, which were used to analyse behaviours
of masonry walls, are also introduced.
Chapter 3 presents homogenization approach. The equivalent material properties of
URM were derived from the behaviour of the constitutive materials (brick and mortar)
in a basic cell. The derived homogenized properties of the masonry basic cell were
used to simulate the performance of masonry under static loading. Results of the
simulation under static loading were validated by experiments. Both the distinct
4 |
ADE | Chapter 2: Literature Review
2. LITERATURE REVIEW
2.1. INTRODUCTION
Masonry walls are widely used in Australia, but are not commonly designed with blast
resistance in mind. In recent years, several retrofitting reinforced technologies have
been developed to strengthen reinforced concrete structures, which have been
extended to apply to unreinforced masonry (URM) structures. However, few
investigations have focused on strengthening URM walls to resist blast loads (Ward
2004).
This literature review summaries the damage to unreinforced masonry walls subjected
to blast loading, and examines the current available retrofitting technologies for
strengthening masonry structures. Examples of such technologies are near-surface
mounted FRP, external bonded FRP, sprayed-on polyurea and aluminium foam, all of
which are considered appropriate for strengthening URM walls. Since this project
focuses on studying the behaviours of URM walls under blast loading, methods of
estimating blast loading are presented. In addition, a review of primary techniques in
estimating the response of masonry walls under blast loading, especially the finite
element method, is provided. A review of some current design guidelines for blast
loading is also included in the following literature review.
2.2. BACKGROUND OF URM STRUCTURES
Unreinforced masonry (URM) construction is widely used in Australia, as it provides
a combination of structural and architectural elements. This method is attractive and
6 |
ADE | Chapter 2: Literature Review
durable, and provides effective thermal and sound insulation and excellent fire
resistance (Page 1996). However, it is found that URM construction is extremely
vulnerable to terrorist bomb attacks since the powerful pressure wave at the airblast
front strikes buildings unevenly and may even travel through passageways, resulting
in flying debris that is responsible for most fatalities and injuries. In order to protect
URM construction from airblast loads, an effective solution is to strengthen the
masonry using retrofitting technologies.
Old masonry construction is usually designed without considering the effects of
blast-resistance. In general design, masonry is considered to have little tensile strength.
For this reason, negative factors affecting the stability of masonry structures, such as
the crack and breathing phenomenon observed in blast events, have not been studied
widely. In Australia, a large number of buildings were constructed using masonry
without additional protection to resist blast events, as bomb attacks or explosive
accidents seldom happen in Australia. However, in recent years, with the rising threat
of terrorism, protection of many existing buildings, structures and facilities against
airblast loading is receiving more and more attention.
Some research on masonry structures against blast loading has been carried in recent
years. Baylot et al. (2005) studied the blast response of lightly attached concrete
masonry cell walls. Unretrofitted concrete masonry cell (CMU) walls and several
different types of retrofits were tested under blast loading, with results showing that
URM walls failed on light impulse and produced high velocity debris under high
impulse. The researchers also found that debris from failing masonry wall and
collapse are two main types of damage to URM wall subjected to blast loads. Because
of the different properties of the cells and mortar, URM walls have weak planes due to
the low tensile strength at each cell-mortar interface. The failures of masonry walls
under blast loads are likely to be localized. They produce damage from wall
fragments, which would injure the people behind the wall or destroy other structure,
and debris with high velocity will damage other nearby structures. Muszynski and
7 |
ADE | Chapter 2: Literature Review
Purcell (2003) tested four unretrofitted URM walls with different standoff distances.
All mortar joints failed, some masonry blocks spalled and breaching occurred under
high explosive detonations. Experiments (Davidson et al. 2005; Muszynski and
Purcell 2003) showed that cracking usually occurred on the inter surface of masonry
walls under light explosions, and appeared around breaching under high explosive
blasts. Catastrophic breaching or even collapse happened when explosion came to
high enough or the stand-off distances were small enough and wall failed in that case.
In summary, due to the shortcomings of masonry construction subjected to airblast
loading, it is necessary to find efficient retrofitting technologies, study the behaviours
of retrofitted URM walls under airblast loading, and develop an efficient mitigating
solution to enhance blast resistance of URM construction.
2.3. CONVENTIONAL METHODS FOR URM STRENGTHENING
An effective solution to mitigate blast effects on URM construction is to strengthen
the masonry using retrofit technologies. However, retrofit URM constructions are
currently in their infancy around the world (Buchan and Chen 2007; Davidson et al.
2005; Davidson et al. 2004b; Ward 2004). Categories of available masonry retrofit
include: conventional installation of exterior steel cladding or exterior concrete wall,
and new technologies such as external bonded (EB) FRP plating, metallic foam
cladding, sprayed-on polymer and/or a combination of these technologies (Davidson
et al. 2005; Davidson et al. 2004b; Schenker et al. 2008; Schenker et al. 2005).
2.3.1. Fibre Reinforced Polymers
Fibre reinforced polymers (FRP) have a variety of advantages over other materials,
such as lower density, high stiffness and strength, adjustable mechanical properties,
8 |
ADE | Chapter 2: Literature Review
resistance to corrosion, solvents and chemicals, flexible manufacturing and fast
application (Bastianini et al. 2005). They have been widely used in structural
repairing and seismic resistance, and in recent years some studies for explosion
resistance using FRP have been conducted. A variety of retrofitting technologies have
been used to strengthen reinforced concrete (RC) structures (i.e. beams and columns)
(Oehlers and Seracino 2004). Some of them have already been used to retrofit
masonry walls, for example, near surface mounted (NSM) FRP plates and externally
bonded (EB) FRP plates (Figure 2.1), which have high satisfactory performance and
wide usage for enhancing RC structures. These technologies have proven to be an
innovative and cost effective strengthening technique under out-of-plane static
loading for strengthening masonry walls.
Figure 2.1 Samples of EB & NSM FRP plates
Near-surface mounted (NSM) FRP plates, which have been successfully used for
strengthening concrete members, have been extended to retrofit masonry structures.
Some recent tests under cyclic loading (Liu et al. 2006; Mohamed Ali et al. 2006)
showed that the NSM plates can be used to strengthen RC structures with little loss of
ductility, and increase the overall shear capacity substantially. Two experiments
(Galati et al. 2006; Turco et al. 2006) showed that the NSM plates increased the
flexural capacity (from 2 to 14 times), strength, and ductility of URM walls
significantly. However, few studies on the behaviour of URM structures under blast
loading have been conducted.
9 |
ADE | Chapter 2: Literature Review
The key factor in increasing ductility and preventing the intrusion of wall fragments
into occupant areas is the ability to absorb strain energy (Davidson et al. 2004b).
Some recent experiments (Davidson et al. 2004b; Muszynski and Purcell 2003) on EB
retrofitting techniques indicated that the high stiff FRP materials, such as steel plate
and carbon fibre reinforced polymer (CFRP) used to retrofit masonry walls appeared
less effective than low stiff materials under blast loads. An experimental work
(Muszynski and Purcell 2003) tested air-entrained concrete (AEC) masonry walls
retrofitted with carbon fibre reinforced polymer (CFRP) and Kevlar/glass (K/G)
hybrid that is less stiff than CFRP. The residual displacements of CFRP structure were
higher than the K/G Hybrid structure, which indicated the low stiff material would
provide more ductility and absorb more strain energy, with bonding being another
critical factor. Externally boned techniques could be applied to strengthen masonry
walls, when retrofitting materials that balance stiffness, strength, and elongation
capacity become available. Therefore, GFRP appears a good option, as it is
cost-effective and easier to apply, compared with the rigid material such as CFRP and
steel plates.
Since the performance of FRP-strengthened URM walls is often controlled by the
behaviour of the interface between the FRP and masonry, it is very important to study
the bond-slip relationship in detail. Debonding could occur between the inter-surfaces
of high stiff FRP materials and masonry when structures are subjected to out-of-plane
loads. Stress concentration is also a problem if FRP is bolted on masonry walls.
Screws can be used to fix the FRP materials, but may become a significant hazard,
like debris, when subjected to blast loading. Therefore, it may not be a suitable for
application on masonry walls.
Strengthening techniques such as near-surface mounted (NSM) FRP plates and
externally bonded (EB) FRP plates have been used to increase the flexural strength of
masonry structures (Yang 2007). The behaviour at the interface between FRP and
masonry is an important consideration in the analysis and design of masonry
10 |
ADE | Chapter 2: Literature Review
retrofitted with EB and NSM plates. Pull tests, in which an FRP strip or plate is
bonded to a masonry prism and loaded in tension, are often used to study the
bond-slip relationship of FRP-to-masonry. In the last decade, considerable research,
including experimental, analytical and numerical approaches, has been conducted to
investigate the FRP-to-concrete bond behaviour (Al-Mahaidi and Hii 2007; Lu et al.
2006; Lu et al. 2007; Mosallam and Mosalam 2003; Neale et al. 2005; Oehlers and
Seracino 2004; Teng et al. 2006; Willis et al. 2004). Recently similar experimental
and analytical studies have been carried out in investigation of the FRP-to-masonry
bond behaviour (Yang 2007). However, little research has focused on numerical
simulation of the bond behaviour of masonry retrofitted by using EB glass FRP
(GFRP) strips and NSM carbon FRP (CFRP) plates.
2.3.2. Spray-on Polyurea
Spray-on polyurea is new technique using urea-based or polyurea-based coating
sprayed on the surface of masonry walls. It produces a tensile membrane, which
prevents spalls significantly. The material is cheap, but needs careful surface
preparation before application (Ward 2004). Polyurea has low stiffness, and Davidson
et al.βs study (2004b) demonstrated that it could enhance the flexural ability of URM
wall and reduce debris effectively. Coated and non-coated wall panels were tested to
establish the effectiveness of spray-on polyurea, with results showing that compared
with stiffer materials, polyurea can absorb strain energy and keep fragments within a
safe area. Further research (Davidson et al. 2005) found that stiff composite materials,
such as woven aramid fabrics or CFRP, can also reduce fragments effectively.
However, compared with polyurea, they are more expensive, which limits their
applicability. Baylot et al. (2005) studied debris hazard from masonry walls against
blast loads. Three types of retrofits (FRP, polyurea, steel) with different amount of
grout and reinforcement were tested to find the most effective retrofitting technology
for decreasing the degree of hazard under blast loads. The panels retrofitted by
11 |
ADE | Chapter 2: Literature Review
spayed-on polyurea performed well and succeeded in reducing the hazard level inside.
The previous tests indicated that spray-on polyurea can be an effective technique for
increasing the ductility of masonry walls.
2.3.3. Aluminium Foam
Aluminium foams are new, lightweight materials with excellent plastic energy
absorbing characteristics that can mitigate the effects of an explosive charge on a
structural system by absorbing high blast energy. The material behaves closely to that
of a perfect-plastic material in compression, which makes aluminium foam an
attractive choice for use in sacrificial layers for blast protection. Airblast tests on
aluminium foam protected RC structural members have been conducted recently and
it was found that aluminium foam was highly effective in absorbing airblast energy
and thus successfully protected RC structural members against airblast loads
(Schenker et al. 2008; Schenker et al. 2005). Due to its properties, it is believed that
aluminium foam would also be very effective in protecting of URM constructions
against airblast loads, although no tests have been performed. Since field airblast tests
are very expensive and sometimes not even possible due to safety and environmental
constraints, numerical simulations with a validated model provide an alternative
method for an extensive investigating the effects of aluminium foam in mitigating
airblast loads on the URM construction.
2.4. ESTIMATING RESPONSE OF MASONRY WALLS UNDER BLAST LOADING
2.4.1. Estimation of Blast Loading
(1) Empirical methods
The explosion considered here is a surface explosion with the charge placed about one
metre above the ground. Considering that a bomb attack is often carried out in a
12 |
ADE | Chapter 2: Literature Review
vehicle, which isolated from the ground, the ground shock can be diminished
(Luccioni et al. 2004). Henrych (1979) developed empirical formulae for estimating
the blast pressure history. In 2005, (Alia and Souli 2006; Remennikov and Rose 2005;
Wu and Hao 2005, Shi, 2007 #484) improved Henrychβs theory by enabling
calculation of the full pressure time history. The U.S. Army developed a blast-resistant
design manual TM-5-1300, which provides some empirical curves to predict blast
loads. However, the load time history is simplified as a triangle shape, and the load
rise period is ignored.
The typical simulated pressure shock wave time histories in the air are shown as
Figure 2.2, where T is the shock wave front arrive time, T is the rising time from
a r
arrival time to peak value, P is the peak pressure, and T is the decreasing time from
so d
peak to ambient pressure. The shock wave rises to the peak value suddenly (this
history is often ignored, as the rising time is very short), and then decreases back to
ambient value before entering a negative phase.
P (t)
s
P
so
T
a
P
o
T t
d
Figure 2.2 Typical free-air pressure time history
With a ground explosion in a free-air burst, a shock wave, having a hemispherical
front (Figure 2.3) is produced. The formulae for an explosion in a free-air can be used
for contact explosion, except that the charge weight must be substituted for half of the
13 |
ADE | Chapter 2: Literature Review
developed as an application of the code TM-5-855-1 (Headquarters 1986), and has
been incorporated into finite element programs AUTODYN and LS-DYNA
(Randers-Pehrson and Bannister 1997). Given charge weight and stand-off distance,
the blast history can be calculated automatically and applied to the surface of
specimens.
(3) Numerical simulation of explosion
For explosions in complex environments, in which shock waves travel through
complex routes or wave fronts impact on uneven surfaces, the previous methods do
not give reliable results. Therefore, numerical simulations were developed to cover
this shortcoming. In this method, the charge was simulated as a type of explosive
material. Air is modelled as fluid and could be coupled with the charge to get a more
accurate pressure history and numerical results. The whole process of explosion can
be presented, and complicated phenomena can be observed. Recently, some studies
(Alia and Souli 2006; Remennikov and Rose 2005; Wu and Hao 2005, Shi, 2007 #484)
were carried out using this method; however, there are some disadvantages which
should be noted. Firstly, the simulation involves a high number of calculations.
Therefore, blast at far stand-off distances becomes time-consuming. Secondly, the
application is complex, with some issues like the dimensions of the element closed to
the charge and near the concerned area, such as the contact surface between air and
specimens, requiring careful consideration. To have the negative phase of the pressure
history, the fast reduction of air pressure due to the leakage of gas may also be a
computing problem. Thirdly, equation of the gas should be modified to consider the
behaviour of the air under high temperature and high pressure, especially for a close
explosion.
15 |
ADE | Chapter 2: Literature Review
2.4.2. Finite Element Method
Numerical simulation is a cost-effective method for investigating the behaviour of
masonry structures. Compared with experiments, it gives better understanding of the
detailed process of events. The numerical simulation has become a widely used
method for investigating behaviours of structures under static or dynamic loading,
with a significant amount of research showing that it could produce considerable
coincidental results with experimental data. This section overviews the estimation of
blast loading, material properties for simulation, and some major numerical methods.
(1) Continuum model and discrete model
The continuum model considers the masonry material as a continuum medium, and is
applicable to analysing a large-scale masonry wall in some early investigations
(Anthoine 1995; De Buhan and De Felice 1997; Pegon and Anthoine 1997). Research
showed that after varying the bond pattern, neglecting the head joints, or assuming
plane stress states, reasonable estimates of the global elastic behaviour of masonry
were obtained. However, as Anthoine (1995) indicated, a careful examination of the
elastic stresses that develop in the different constitutive materials shows that the
situation might be quite different in the non-linear range (damage or plasticity). To
obtain reliable equivalent material properties of masonry material, homogenization is
critical in numerical analysis.
The discrete model has been developed to perform linear and nonlinear analyses of
masonry structures. It is computationally intensive, making it a time-consuming
method, and is therefore generally only suitable for simulating the fracture behaviours
of small specimens (Ma et al. 2001). In this study, the specimens are full-scaled
masonry walls made of cored brick and mortar joint. Therefore, to avoid the
calculating problem, the homogenized model is preferable, which is discussed in the
16 |
ADE | Chapter 2: Literature Review
following section.
(2) Homogenized model
The homogenization technique has been used in the past to derive the equivalent
material properties and failure characteristics for solid brick masonry. Considerable
research has been conducted in the last decade to investigate the complex mechanical
behaviour of solid brick masonry structures using various theoretical and numerical
homogenization techniques (Anthoine 1995; Luciano and Sacco 1997; Ma et al. 2001;
Milani et al. 2006a; Milani et al. 2006b; Wu and Ha 2006; Zucchini and Lourenco
2004). It has been shown that using homogenized material properties can give a
reliable estimate of masonry response under both static and dynamic loading.
However, substantially less computational time is required to perform the analysis of
masonry structures as compared with distinct model in which bricks and mortar joints
are separately discretized. Recently, the homogenization technique has been used to
derive equivalent material properties of hollow concrete block masonry (Wu and Hao
2007b), in spite of this, no study has been conducted to analyse the response of
masonry structure constituted by cored brick units jointed with mortar using the
homogenization technique. Due to the complex geometric properties of the cored
brick unit, it is very complicated and time consuming to use the distinct model to
perform the analysis on this kind of masonry structure. Therefore, it is of importance
if the equivalent material properties of this masonry structure can be derived.
As masonry is a composite structure constituted by bricks and mortar, using the
discrete method to compute large scale of masonry walls often requires a significant
amount of time. The homogenized technique, which is used to derive the behaviour of
the composite from geometry and behaviour of the basic cell, has been developed to
simplify the computation. Some homogenization models of URM structures subjected
17 |
ADE | Chapter 2: Literature Review
to blast loading has been investigated by researchers (Anthoine 1995; Cecchi and Di
Marco 2002; ElGawady et al. 2006a; Luccioni et al. 2004; Milani et al. 2006a; Wu
and Ha 2006; Zucchini and Lourenco 2004) in recent years.
Figure 2.4 Homogenization of Masonry Material (Wu and Ha 2006)
The homogenization approach is shown above in Figure 2.4. Determining the basic
cell is the first stage of homogenization. The basic cell contains all the geometric and
constitutive information of the masonry, and is modelled to calculate the equivalent
elastic constants and failure modes of masonry structures. Its volume depends on the
bonding formats and retrofitting modes. Header bond shown in Figure 2.4 is
commonly used for homogenization. More complex bond types require cells with
greater dimensions, which are divided into small elements to calculate the constants.
Some recent research (Cecchi et al. 2004; Ceechi et al. 2005) began to focus on
homogenizing CFRP retrofitted masonry structures. Firstly, the reinforcement and
masonry were homogenized separately, then the homogenization of reinforced
masonry was obtained by integrating the constitutive function of masonry and
reinforcement along the thickness of the wall (Ceechi et al. 2005). Moreover, the
authors developed a numerical finite element single-step homogenization procedure,
which can be used as an example for modelling retrofitted masonry walls.
18 |
ADE | Chapter 2: Literature Review
2.4.3. Design Guideline
According to previous studies, URM walls are weak, brittle, and have low ductility
under blast loading. In order to develop effective retrofitting technologies, major
damage levels should be studied, due to their significant hazard to occupants and
surrounding constructions. Some experimental tests have been done to investigate the
behaviour of URM walls under blast loads showing the major damage. Some
countries, such as the U.S. through its Department of Defence, developed a blast
evaluation guideline. Scaled distance is defined as R/W1/3, where R is the stand-off
distance and W is the TNT charge weight, which is used as a parameter by U.S. DoD
Code (1999) to evaluate the structural safety under blast loads. The safe scaled
distance is specified as 4.46 m/kg1/3 for unstrengthened buildings to ensure the
buildings are not destroyed. However, the description of damage level from U.S. DoD
Code is vague, and further research (Wu and Hao 2007a) has been done to fill in this
gap for concrete constructions. Wu and Hao (2007a) developed an improved approach
based on the U.S. DoD Code, which defined various performance levels, including
collapse. Besides the charge weight and stand-off distance, structural materials and
configurations are also two important parameters. However, some tests (Baylot et al.
2005) showed by increasing the charge weight, or decreasing the stand-off distance
other types of damage can be observed in addition to collapse, including cracks,
catastrophic breaching, and low and high velocity debris. Therefore, the development
of guidelines covering major damage levels for retrofitted masonry walls is necessary,
but due to a lack of experimental data, more research is required to achieve this goal.
2.5. SUMMARY
This literature review has considered the behaviours of URM walls under blast
loading, and was suggested that the retrofitting technologies can be applied to
19 |
ADE | Chapter 2: Literature Review
strengthen masonry constructions. Still, a suitable solution is required to provide the
better protection against all blast loads. According to published studies, existing
retrofitting technologies are efficient in providing protection to concrete and masonry
structures. Commonly used and newly developed retrofitting technologies on masonry
structures have been reviewed, including externally bonded FRP, near-surface
mounted FRP, spray-on polyurea and aluminium foam. It is found that previous
research primarily focused on studying behaviours of URM walls under static or blast
loading, or studied the FRP retrofitted URM walls under static loading or quasi-static
loading. Hence, more research on the retrofitted URM walls against dynamic loading,
such as blast loading, is needed.
To investigate the effectiveness of various retrofitting methods, the major damage
modes were identified. It is crucial to qualify the damage levels for developing the
design guideline, and it is expected that the previous damage levels and tests data
could be used to check the effectiveness of different retrofits. Finite element analysis
with blast loading calculated from a design code can be used to study the dynamic
behaviours of retrofitted masonry walls under blast loads. At present, there is no
industry guideline available for blast-resistant design of masonry structures, and it is
therefore expected that, this project will contribute to its development.
20 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
3. NUMERICAL SIMULATION OF URM WALLS USING THE
HOMOGENIZATION TECHNIQUE
3.1. INTRODUCTION
Homogenization techniques have been used to derive the equivalent material
properties of masonry for many years. However, no research has been conducted to
derive the homogenized model of the standard ten-core brick masonry wall,
commonly used in Australia. In this chapter, the homogenization technique was used
to model a three-dimensional masonry basic cell, which contains all the geometric and
constitutive information of the masonry wall, in a finite element program to derive its
equivalent mechanical properties. The detailed material properties of mortar and brick
were modelled using a numerical analysis. By applying different loading conditions
on the surfaces of a basic cell, stress-strain curves of the basic cell under various
stress states were simulated. Using the simulated stress-strain relationships, the
homogenized material properties and failure characteristics of the masonry unit were
derived. The homogenized 3D model was then utilized to analyse the response of a
masonry wall with and without pre-compression under out-of-plane loads (Griffith et
al. 2007). The same masonry wall was also analysed with distinct material modelling,
and the efficiency and accuracy of the derived homogenized model were
demonstrated.
3.2. HOMOGENIZATION PROCESS
Homogenization techniques can be used to derive the equivalent material properties
of a composite from the geometry and behaviour of the representative volume element.
21 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
Masonry is a composite structure constituted by bricks and mortar. Thus, the
homogenization technique can be used to derive the equivalent material properties of
masonry unit.
In this section, a highly detailed finite element model was used to model a
three-dimensional basic cell to derive the equivalent material properties for a
homogenous masonry unit. Various load cases were applied to the basic cell surfaces
to derive average stress-strain relationships of the homogenous masonry unit under
different stress states. The average elastic properties and failure characteristics of the
homogenous masonry unit are obtained from the simulated results. The numerical
results are verified from comparison to experimental results from previous tests
undertaken at the University of Adelaide, along with numerical results from
simulation using a distinct finite element model. The derived equivalent material
properties can be utilized to simulate large-scale masonry structures and predict their
failure modes under out-of-plane loading.
3.2.1. Homogenization Technique
Traditionally, laboratory tests are performed to obtain average stress and strain
relationships of a specimen, required to find the homogenized properties of composite
materials such as concrete with aggregates and cement. However, for masonry
structures, it is often too difficult to conduct the laboratory test. To overcome this
difficulty, the numerical homogenization method was used in this study to derive its
equivalent material properties. Figure 3.1 shows the homogenization process for a
basic cell, which contains all the geometric and constitutive information of the
masonry wall. The basic cell was modelled, separately, with individual components of
mortar and brick. Constitutive relations of the basic cell can be set up in terms of
average stresses and strains from the geometry and constitutive relationships of the
22 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
individual components. The average stress and strain (cid:3) and (cid:4) are defined by the
ij ij
integral over the basic cell as
1
(cid:3) (cid:6) (cid:5) (cid:3)dV
ij V V ij Eq. 3-1
1
(cid:4) (cid:6) (cid:5) (cid:4)dV
Eq. 3-2
ij V V ij
where V is the volume of the basic cell, (cid:3) and (cid:4) are stress and strain
ij ij
components in an element. By applying various displacement boundary conditions on
the surfaces of the basic cell, the equivalent stress-strain relationships of the basic cell
were established. In addition, the equivalent material properties of the basic cell were
derived from the simulated stress-strain curves. However, to simulate the performance
of the basic cell under different loading conditions in a finite element program, the
material properties of mortar and brick should be determined.
b. Basic cell c. Homogenization
a. Masonry sample
Figure 3.1 Homogenization of masonry material
3.2.2. Material Models for Brick and Mortar
In order to derive the equivalent inelastic material properties of the basic cell, reliable
23 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
then,
m(cid:7)1 2(cid:3)
(cid:9)(cid:6) and k (cid:6) c Eq. 3-8
3(m(cid:8)1) 3(m(cid:8)1)
The constants (cid:2) and k can be determined from the yield stresses in uniaxial tension
and compression.
Typical 10-core clay brick unit manufactured by Hallet Brick Ptd Ltd with nominal
dimensions of 230(cid:10)110(cid:10)76 mm3, as shown in Figure 3.3, was used in this study. The
detailed dimensions and locations of ten cores are also shown in Figure 3.3. The
mortar consisted of cement, lime and sand mixed in the proportions of 1:2:9, and the
10-core clay brick unit and a 10 mm thick mortar joint were used in this study. The
same material properties for bed and head joints were assumed.
A set of material tests were performed to gain the primary parameters for subsequent
simulations by Griffith (2007). The tests included bond wrench tests to gain flexural
tensile strength of the masonry, masonry unit beam tests to gain lateral modulus of
rupture of the brick units, and compression tests of a 5-layer-brick model to gain
compressive strength of the masonry and Youngβs modulus. Table 3.1 lists material
properties for mortar and brick. Details about the masonry properties are presented
elsewhere (Griffith et al. 2007).
110
25 42
230
Figure 3.3 Nominal dimensions of brick unit (mm)
Using material properties, the material constants (cid:2) and k in the above Drucker-Prager
25
67
02
52
02
52
02 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
strength model were derived, with their values listed in Table 3.1, and material
properties for brick and mortar were coded into a finite element program LS-DYNA
(LSTC 2007). The key parameters for using in simulations of masonry basic cell are
listed in Table 3.1.
Table 3.1 Material properties for brick and mortar
c E ,E (GPa) G (GPa) (cid:11) (cid:3)(MPa) (cid:3)(MPa) (cid:9) k (MPa)
c t c t c
brick 5.27 2.2 0.2 3.55 35.5 0.47 3.73
mortar 0.44 0.18 0.3 0.6 6.14 0.47 0.65
A general-purpose finite element program LS-DYNA was used in this study to
calculate the stress-strain relationships of the basic cell as shown in Figure 3.1b.
LS-DYNA provides a variety of material models for analysing masonry structures.
According to a previous research (Davidson et al. 2004a), four material models
perform well in simulating bricks under blast loading. The possible candidates are
βSoil and Foamβ, βBrittle Damageβ, βPseudo Tensorβ, and βWinfrith Concreteβ. The
material Soil and Foam is a cost-effective model with fewer inputs, and still gives
reliable results. The yield criterion of the material model βSoil and Foamβ is based on
Drucker-Prager strength theory as follows
(cid:12) (cid:13)
(cid:14)(cid:6) J (cid:7) a (cid:8)a p(cid:8)a p2 Eq. 3-9
2 0 1 2
where p is hydro pressure, which is equal to I /3. On yield surface, it has
1
(cid:12) (cid:13)
J (cid:7) a (cid:8)a p(cid:8)a p2 (cid:6)0 Eq. 3-10
2 0 1 2
Then, constants a , a and a in Soil and Foammodelare given by:
0 1 2
26 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
a (cid:6) k2
0
a (cid:6) (cid:7)6(cid:9)k Eq. 3-11
1
a (cid:6)9(cid:9)2
2
Considering the limited material properties and the efficiency of simulation, the βSoil
and Foamβ model in LS-DYNA was selected to model both brick and mortar in this
study, as the model is efficient and requires fewer inputs. The model simulates
crushing through the volumetric deformations, and a pressure-dependent flow rule
governs the deviatoric behaviour with three user-specified constants. Volumetric
yielding is determined by a tabulated curve of pressure versus volumetric strain as
shown in Figure 3.4 (LSTC 2007). The actual input constitutive relationships are
shown in Figure 3.5, and elastic unloading from this curve is assumed to be a tensile
cut-off. One history variable, the maximum volumetric strain in compression, is given.
If the new compressive volumetric strain exceeds the given value, loading is indicated.
When the yield condition is violated, the updated trail stresses are scaled back. If the
hydrostatic tension exceeds the cut-off value, the pressure and the deviatoric tensor
would be zeroed (Davidson et al. 2005; LSTC 2007).
Figure 3.4 Volumetric strain versus pressure curve for soil and crushable foam
model (LSTC 2007)
27 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
simulations of complex models, the equivalent tensile curve shows some ductility.
This is because individual elements did not fail at the same time under tension.
Therefore, there were always some elements that could carry loads until the specimen
was cut-through.
(1) Identification of inputs for numerical model
Although the key parameters have been already obtained from material tests, there are
still some parameters that have not yet been determined. For example, parameters
such as the bulk modulus were derived by numerical simulations, while key
parameters such as the shearing modulus and cut-off tensile strength were estimated
from the test results directly.
For common bricks and mortar, m (Eq. 3-7) equalled 10. Thus, for brick, a , a and a
0 1 2
equalled 2.82Γ1012, 4.76Γ1016 and 2.008. For mortar, a , a and a equal 4.16Γ1011,
0 1 2
1.83Γ106 and 2.008. The material card used in the analysis for βSoil and Foamβ is
listed in Table 3.2 with corresponding tabulated values. Values for the bulk unloading
modulus, volumetric strain values, and their corresponding pressures were estimated
from the results of Griffithβs tests (Griffith and Vaculik 2005) firstly, and then were
verified by simulating the compression of 5-layer-brick model.
Description of the input parameters is listed in Table 3.2. The shear modulus G was
E
calculated from Youngβs modulus by using formula G(cid:6) , and a ,a ,a were
2(1(cid:8)(cid:15)) 0 1 2
calculated from Eq.3-10. The unloading bulk modulus can be gained from test, and
must be greater than Youngβs modulus. However, in this study, trial simulations were
carried out to estimate the value of BULK, and it was found to be approximately 2.5
times greater than Youngβs modulus (1.8Γ1011 Pa). The experimental tensile strengths
were reported, ignoring the presence of the cores. Hence, for the detailed finite
element model, the test values were adjusted to account for the holes in the bricks.
29 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
Aiming to simulate the compression test, a 5-layer-brick finite element model was
built as shown in Figure 3.8. The boundary conditions were set the same as the test,
and the results of stress and strain were obtained from the elements with the same
location of the gauges in the compression test.
The comparison of the test result and simulation result are presented in Figure 3.9.
Due to lack of test data in the plastic phase, the results were only compared in elastic
phase. From Figure 3.9, it can be found that the trend line of the simulation result
matches well with that of the test result, verifying the input material properties in Soil
and Foam model.
20.0
15.0
Test result
10.0
Simulation result
5.0
0.0
0 0.0001 0.0002 0.0003 0.0004
Strain
Figure 3.9 Stress-strain curves of the simulation and tests
3.2.3. Masonry Basic Cell and Convergence Tests
The first step of the homogenization process is to pick up masonry basic cell (Figure
3-1) with the common constitutive material properties form target masonry walls. The
basic cell should contain all the participant materials, constitute the entire structure by
periodic and continuous distribution, and also satisfy the requirement of minimum
32
)aPM(
ssertS |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
The masonry basic cell is a finely meshed. 8-node solid element, with 24 degrees of
freedom was used to represent the cell. Because the full integration of the element
may produce element locking problem, which makes the elements hard to deform, the
one-point integration element was used to get correct results. In this case, hourglass
energy was monitored to guarantee of the reliable results. Usually, the hourglass
energy is limited to 5% of total internal energy.
Convergence tests were conducted to determine the minimum number of elements
needed to achieve a reliable estimation. Theoretically, masonry basic cells with more
elements give more reliable results, but the calculation time for such a test is
significantly greater. Therefore, convergence tests were performed to choose an
efficient model. The finite element mesh used in the numerical model of the basic
cell is shown in Figure 3.10. As shown, the 10-core clay brick unit and mortar in the
basic cell were discretized into a number of solid elements. A convergence test on the
influence of element size on computational accuracy was carried out by halving the
size of the element for both brick and mortar while keeping loads on the basic cell
unchanged. This test was continued until the difference between the results obtained
with two consecutive element sizes was less than 5%. The test was performed by
applying simple elastic properties to the basic cells, and setting them under
compressive state. The boundary condition was set as vertical uniaxial compression,
the bottom was all fixed, and displacement through the Z axial was applied as loading
on the top.
Five models with different numbers of elements were tested, with the results
summarized in Table 3.4. The model with the largest number of elements (23750) was
considered to provide the most reliable result, and, as such, the results of the other
four models were compared with it. In this simulation, the average stress, strain and
Youngβs modulus of central elements were compared. From the results presented in
Table 3.4, it is concluded that all the models gave reliable results. Because of this, the
most effective model with 3560 elements for masonry basic cell was chosen.
34 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
Table 3.4 Average stress and strain of central elements
Model Stress (MPa) Strain (1Γ10-4) Youngβs Modulus (MPa) Difference
3560 -2.03 -5.30 3826 0.15%
5760 -2.03 -5.30 3829 0.25%
6144 -1.97 -5.16 3825 0.13%
10208 -2.01 -5.27 3823 0.07%
23750 -2.02 -5.30 3820
Because of the complex internal structure of the cored brick, it would be difficult to
build a model with less than 3000 elements. Moreover, the dimensions of elements
should be kept similar to ensure the reliability of results. Considering the influence of
this factor, models with fewer elements were not tested. Thus, 3560 eight-node solid
elements were used in the numerical model of the basic cell to achieve the reliable
estimation. The final numerical model used in the simulation is shown in Figure
3.10(a). Figure 3.10 (b) and (c) show two parts β bricks and mortar joint, and
containing 3560 elements totally.
3.2.4. Simulated Stress-Strain Relationships of the Masonry Basic Cell
The masonry basic cell was simulated under varieties of loading states to plot
stress-strain curves and derive the equivalent material properties. The loading states
include compression-compression, compression-tension, shearing, and
compression-tension-shearing. For compressive or tensile stress state, uniform
displacements were applied as compressive loading or tensile loading on the surfaces
of masonry basic cell.
To gain the equivalent material properties and yield surface, the response of the basic
cell under compressive-compressive, compressive-tensile, tensile-tensile,
35 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
compressive-shear and tensile-shear stress states were simulated. Over 50 cases were
simulated, and the calculated results are presented in Figure 3.11, Figure 3.12, and
Figure 3.13.
Figure 3.11 shows the typical stress-strain curves of the basic cell under uniaxial
compressive-compressive stress states. As shown in Figure 3.11a, the uniaxial
compressive strength in the Z direction is 15.7 MPa, which is quite close to the
experimental result of ultimate masonry compressive strength 16.0 MPa, carried out
by Griffith and Vaculik (2007). It was shown that the uniaxial compressive strengths
of the basic cell in the X and Y directions were 7.88 MPa and 7.39 MPa from the
simulation results of uniaxial compressive-compressive states in X and Y directions,
respectively. This indicated that the geometry of hollow bricks with ten cores reduced
the compressive strength of the basic cell in both X and Y directions significantly.
As the basic cell is under biaxial or triaxial compressive states, its strength
enhancement in the Z direction is not observed, although there are significant strength
enhancements in both X and Y directions. When the basic cell is under biaxial
compressive loads in the X and Z directions, as shown in Figure 3.11d, its maximum
compressive strength in the Z direction is 15.0 MPa, slightly smaller than its uniaxial
strength. The maximum strength in the Y direction is 24.8 MPa, which is much higher
than its uniaxial compressive strength. It is also shown in Figure 3.11f that the
maximum compressive strengths of the basic cell under triaxial compressive states in
X, Y and Z directions are 8.73, 17.4 and 13.8 MPa, respectively. In addition, the
compressive strength in the Z direction is slightly smaller than its uniaxial
compressive strength. It should be noted that due to different dimensions of the basic
cell in X, Y and Z directions, the ratios of the displacement must be set appropriately.
In the X and Z directions, as shown in Figure 3.11d, and in the X, Y and Z directions,
as shown in Figure 3.11f, the ratios are set to be 4:3 (u:w) and 4:2:3 (u:v:w) according
to the dimension of the representative element. This ensures that the strain ratios in Y
and Z directions and in X, Y and Z directions are about 1:1 and 1:1:1.
36 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
strength of the basic cell in the Z direction is much smaller than tensile strength of
mortar (0.6 MPa) as the volume of the cores is counted as part of the total volume of
the basic cell, as well as geometric size influence. The simulated results also indicate
that there is not a significant tensile strength enhancement in the Z direction when the
basic cell is under biaxial or triaxial tensile stress. In a tensile-compressive stress state,
the ultimate tensile strength slight increases and it can be observed from Figure 3.12e
that the basic cell fails owing to tensile strain before the compressive strength reaches
the maximum value. When the basic cell is in triaxial tensile states (see Figure 3.12f),
its tensile strengths in the X and Y directions are reduced, although there is a slight
increase in its tensile strength in the Z direction.
The representative stress-strain curves of the basic cell under the compressive-shear
and tensile-shear stress state are shown in Figure 3.13. The ultimate shear
strengths(cid:16) , (cid:16) and (cid:16) under pure shear condition are 0.78 MPa, 1.58 MPa and
zx zy yx
1.28 MPa, respectively. It is also shown in Figure 3.13b that under compressive-shear
stress state, the basic cell fails due to shear strain before the compressive strength
reaches the maximum value.
9.00E+05
0.788MPa 3.00E+06
2.07MPa
(cid:4)
zx
z (cid:3) (cid:3)
y xx 0.00E+00 z
u -0.0026 -0.0013 0 0.0013 0.0026
4.50E+05 w
u
-3.00E+06
x
u -6.00E+06
(cid:2) u
0.00E+00 xx w
0 (cid:3) 0.005 0.01 -9.00E+06 u:w=1:1
zx
ZX-Shearing ZX Z
(a) (b)
Figure 3.13 Stress-strain relation of the masonry basic cell in a shear stress state
39
)aP(
(cid:4)
xz |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
interlaminar normal direction and a single interlaminar shear direction. For the normal
component, failure can only occur under tensile loading and for the shear component,
the behaviour is symmetric around zero. There are two ways of applying a force to
enable a crack to propagate are identified in this model, being βMode I crackβ,
opening mode (Figure 3.17I, a tensile stress normal to the plane of the crack) and
βMode II crackβ, sliding mode (Figure 3.17II, a shear stress acting parallel to the
plane of the crack and perpendicular to the crack front).
I II
Figure 3.17 Smeared crack model under mode I and II
Two principle failure directions were specified for this model. Z axial was defined as
the normal direction, and an ultimate normal tensile stress was given as 0.85 MPa.
Due to torsion shear failure in bed joint, stepped failure was observed in the tests of
URM walls by Griffith et al. (2007).Therefore, XY was defined as the shear direction,
and a derived ultimate shear stress was given as 1.28MPa.
3.4. VALIDATION OF HOMOGENIZED MODEL
3.4.1. Experiments of Masonry Walls
Two short masonry walls were tested under uniform static loading by Griffith et al.
45 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
(2007). The experimental results were used to validate the numerical results. And the
configuration of this experiment is presented in Table 3.6. Bottom edges were
mortar bonded to the floor, and laterally supported by steel members, meaning, the
edge connection was considered as fixed. Steel angles were used to provide lateral
restrain on the top edges for both the wall with pre-compression and the wall without
pre-compression. Restrain of the vertical edges was carefully considered, due to its
significant effect on the results of two-way bending test. As shown in Figure 3.18,
return walls were used to support the main walls, and were restrained from rotation. A
uniform vertical pre-compression 0.1 MPa of stress was applied to the top of a short
wall.
Table 3.6 Wall geometry and boundary conditions (Griffith et al. 2007)
Wall Geometry and Support Conditions Pre-compression ((cid:3))
v
0.1 MPa
0 MPa
Front side
Return wall
Rear side
Figure 3.18 Short return walls used to stabilize walls
46 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
A uniform out-of-plane pressure was applied on the outside surface of the main wall.
Airbags were used to provide the static loading, and distribute the pressure uniformly.
Only the solid portions of the walls were acted on by airbags, meaning the opening
part did not carry any loads. The arrangement of the airbags is shown in Figure 3.19.
The load applied on the wall from the airbags was measured using load cells
positioned between the airbag backing board and the reaction frame. In addition, the
pressure acting on the wall surface was calculated by dividing the total load by the
area of the wall. Linear variable differential transformers (LVDT) were used to
measure displacements at different targets. The out-of-plane pressure applied to both
of the short walls reached 8.5KPa. Details about the experimental study can be found
in (Griffith et al. 2007).
1800Γ600
1800Γ600
1800Γ600
1800Γ600
Figure 3.19 Airbag arrangement
3.4.2. Simulation of Masonry Walls
The developed homogenized material model was used to simulate the response of an
unreinforced masonry (URM) wall under out-of-plane static loading, with and without
pre-compression 0.1 MPa in the vertical direction as shown in Figure 3.20. The wall
was 2.5m(cid:10)2.5m in dimension and had a concentrically positioned opening of
1.2m(cid:10)1.0m. The same masonry wall was also analysed with a distinct model in
which brick and mortar materials were discretized. The distinct model was built based
on the masonry basic cell, consisting of about 50 thousand elements. As this model
47 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
3.4.3. Experimental and Numerical Validation
The test data was used to verify the experimental results. The numerical verification
was achieved by comparing the simulation results of the distinct and homogenized
models with test data. Results of the pressure-displacement relationship and crack
patterns were compared with results from simulations of distinct models as
experimental validation.
Figure 3.22 shows the pressure-displacement relationship derived from tests and a
numerical simulation of the wall with and without pre-compression 0.1 MPa at a
target. As shown in Figure 3.22a, both the homogenized model and distinct model
give a good prediction of the URM wall response without pre-compression, as
compared with those obtained by experimental tests. However, with the same
computer system, the time required to obtain a solution using the distinct model was
20 hours, while only 4 minutes were needed for the simple homogenized model.
Again, similar responses were observed from the both models in comparison with the
test results with pre-compression 0.1 MPa, as shown in Figure 3.22b. The results of
the simulation with the smeared-crack model are also plotted in Figure 3.22b, and it
can be seen that the curves of the simulation and test match well. However, crack
patterns affect the section of curve where step cracks appear in the test. In the
simulation using the smeared-crack model, the crack pattern (Figure 3.24) was not as
accurate as in the distinct model. Therefore, from comparison of the
pressure-displacement curves, more stiffness was observed from the smeared-crack
model. With the same computer system, the calculation time for the smeared-crack
model was 15 minutes.
49 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
(a) without pre-compression (b) with pre-compression 0.1 MPa
Figure 3.22 Comparison of results from the short wall with and without
pre-compression test and simulation
By defining an ultimate strain for materials, elements can be removed during
simulation. In this way, cracks were simulated using a distinct model on URM walls
shown in Figure 3.23. Compared with test results, crack patterns match quite well in
these two cases. The cut-through cracks were not observed, indicating that the failure
of bricks was not accurately modelled in the numerical simulation.
It should be noted that although the homogenized model gives a reliable estimation of
the global response of URM wall to static loads in far less time than the distinct model,
it may yield inferior predictions of crack patterns of the URM wall compared with the
distinct model. This is because the weak mortar joints may significantly affect the
crack patterns. Figure 3.23 shows cracking patterns from tests with pre-compression
0.1 MPa in comparison with simulation of distinct model. The shading indicates the
displacement distribution normal to the plane of the wall. As shown, the distinct
model gives an accurate prediction of the crack patterns, whereas, the homogenized
model does not simulate crack patterns well. Therefore, for simulating local damage
of URM walls, the distinct model is a useful tool, although it is computational
intensive.
50 |
ADE | Chapter 3: Numerical Simulation of URM Walls by Using Homogenization Technique
3.5. CONCLUSIONS
This chapter presented numerical investigation of the ten-core brick URM wall using
the homogenization technique. The equivalent material properties of the masonry unit
such as the elastic moduli and failure characteristics were derived by numerical
simulation of a basic cell under various boundary conditions. The developed
homogenized model is then used to simulate the response of a URM wall with an
opening under static loading. It was found that the simulated results using the
homogenized model agree well with those obtained from the distinct model and test
results. However, far less time is required for a solution using the homogenized model
in comparison with distinct model. The developed homogenized model can be used to
simulate large-scale masonry structures under various loads. It is worth noting that
although the homogenized model has demonstrated its computational efficiency to
predict the global response of the URM wall, it may not give a good simulation of
local damage such crack patterns of the URM wall in comparison with the distinct
model.
52 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
4. SIMULATION OF FRP REPAIRED URM WALL UNDER
OUT-OF-PLANE LOADING
4.1. INTRODUCTION
The retrofitting of masonry structures with near-surface mounted (NSM) FRP plates
and externally bonded (EB) FRP plates has proven to be an innovative and cost
effective strengthening technique. The behaviour of such FRP-strengthened URM
walls is often controlled by the behaviour of the interface between the FRP and
masonry, which is investigated using a pull-test commonly. In modelling the
performance of the FRP retrofitted URM wall properly, the key step is to simulate
the interface behaviour between masonry and FRP retrofits.
Numerical methods have been used to simulate the interfacial behaviour of
FRP-to-concrete (Al-Mahaidi and Hii 2007; Lu et al. 2006; Lu et al. 2007). Usually,
there are two approaches to model debonding behaviour in FRP strengthened RC
members. One approach is to employ a layer of interface elements with
zero-thickness between the FRP and concrete element to simulate debonding failure.
Although the bond slip behaviour can be specified in the interface elements, it is not
a truly predictive model due to the zero thickness assumption for the interface
elements. The second approach is to use a thin layer of concrete elements adjacent to
the adhesive to simulate cracking and debonding failure. However, some research
has shown that it is difficult to use appropriate concrete models to simulate
debonding behaviour. Although the interfacial behaviour of FRP-to-concrete bond
has been studied in pull tests recently, few studies have been conducted to
investigate the bond-slip and load-displacement behaviour of the FRP-to-masonry
interface in pull tests.
53 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
In this Chapter, a numerical model will be used to simulate the response of the FRP
repaired URM wall under out-of-plane loads. The FRP-to-masonry interface is
modelled by a layer of interface elements or contact surface of zero thickness. The
interface element model and contact surface model were validated by simulating the
bond-slip behaviour of pull tests of both EB and NSM CFRP plate bonded to a
five-brick high masonry prism. The masonry prism in pull tests was modelled either
by the derived homogenized model or by the commonly used smeared crack model.
A distinct model was also employed to model masonry prism behaviour for a
comparison. The efficiency and accuracy of the homogenized model was verified
from simulation of the pull tests in comparison with the distinct model and the
smeared crack model. The homogenized model, together with the interface element
model, was then employed to simulate a severely damaged URM full-scale wall,
previously tested under reversed-cyclic loading, repaired with NSM CFRP plates
under out-of-loads. The smeared crack model was also used to model the response
of the FRP repaired URM wall. It was found that the simulated results predicted
using the homogenized model fitted well with test data.
4.2. MATERIAL MODELS IN SIMULATION
4.2.1. Masonry
The distinct model, homogenized model and smeared crack model validated in
Chapter 3 were used to model the performance of the 10-core clay brick masonry in
both pull tests and full scale wall under out-of-plane loading tests.
54 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
4.2.2. FRP Models
FRP composites, which are adhesively bonded to the masonry, can be modelled
using an elastic-brittle material model. Both CFRP and GFRP plates were used in
pull-tests. The reinforcing strips used in NSM pull-test were carbon fibre strip CFRP.
The width of the carbon FRP strip was 20mm, and the thickness was 1.2mm. The
material properties of CFRP were tested by Yang (2007) and the manufacture with
results shown in Table 4.1. The average values appear to be comparable with the
manufacturerβs data.
Table 4.1 Carbon FRP material properties (Yang 2007)
NOTE:
This table is included on page 55 of the print copy of
the thesis held in the University of Adelaide Library.
Table 4.2 GFRP material properties (Yang 2007)
NOTE:
This table is included on page 55 of the print copy of
the thesis held in the University of Adelaide Library.
The glass FRP (GFRP) material properties were determined based on the tensile test
performed by Yang (2007) and are summarised in Table 4.2. The average of rupture
55 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
strain was found to be approximately 11500 microstrain. The experimental values
for Youngβs modulus and strength of the GFPR strip are 19.3 MPa and 223 MPa,
respectively.
4.2.3. Bond-Slip Models
Adhesive material is used in practice to produce a continuous bond between the FRP
and masonry. It can help FRP strips to develop full performance by transferring
shear stress inside the layer of interface between FRP and masonry. Therefore, the
interface is the key component of FRP-to-masonry bond. The behaviour of interface
between the masonry and FRP is based on the strength properties of the epoxy
adhesive. The adhesive had tensile strength of 13.9 MPa and Youngβs modulus of
6.7 GPa. The tensile strength of the adhesive material is much greater than that of
masonry, hence, a failure surface was found in the masonry, but not in the adhesive
layer in experiments. Therefore, to achieve the goal of simulating the pull test and
studying the debonding behaviours, the interface consisting of the adhesive layer
and a thin masonry layer must be simulated accurately. The interface was modelled
using two methods in this study: a thin layer of interface element model and a
contact surface model.
Figure 4.1 illustrates the interface element model and contact surface model. As
shown in Figure 4.1a, the interface elements with a thickness of 1mm are adjacent to
FRP plates and masonry while the FRP plate and masonry are contacted directly in a
contact model as shown in Figure 4.1b. Since there is no thin layer of interface
elements in the contact surface model, the number of elements used model will be
reduced. Therefore, the contact model can be solved much more quickly.
56 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
(a) Interface element method (b)Contact surface method
Figure 4.1 Interface elements model and contact model
For the interface element model, the interface was modelled as a thin layer of
elements with thickness of 1 mm. The interface element behaved like an isotropic
elastic material. The strength criterion of the interface material was dominated by
debonding failure, i.e., shear failure. The post-failure process of the interface
elements was controlled by fracture energy, which can be determined from the
shear-slip curve. Figure 4.2a shows the experimental local bond-slip curves from
pull tests, which can be idealised as a bi-linear bond-slip model as shown in Figure
4.2b (Yang 2007). Both shear debonding failure and tensile failure dominate the
strength criterion of the thin layer interface material. The post-failure process of the
interface material is controlled by shear fracture energy and tensile fracture energy,
which equals to the area under the curves as shown in Figure 4.3a, and can be
estimated by the local bond-slip models in pull tests. The relationship between shear
stress and local slip can be identified by defining the ultimate stress (cid:7), the
f
corresponding slip at peak shear stress, (cid:8) , and slip at zero shear stress, (cid:8). The shear
1 f
fracture energy was estimated according to the average value of the areas under
experimental bond-slip curves in a previous study (Yang 2007). (cid:3) is assumed to be
ft
the tensile strength of brick units and tensile fracture energy rate G = 13.2J/m2,
ft
(cid:3) =3.55MPa (Seracino et al. 2007). The inputs of (cid:7) and G will vary with different
ft f f
retrofitting techniques. It was found that for the NSM model, the maximum shear
strength was 14.5 MPa, and shear fraction energy was 5000N/m. For EB model, the
maximum shear strength and shear fraction energy were found to be 5.87MPa and
57 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
were used in the near surface mounted specimen. In the testing, the bottoms of the
specimens were fixed, and a tensile load was applied to the top of FRP strips until
debonding occurred. The load and strains along FRP strips were recorded in these
pull tests as shown in Figure 4.5. The local bond-slip curves and global
load-displacement curves were estimated from the recorded data. Figure 4.6 shows
debonding failed along the FRP strips within masonry, while the adhesive material
was undamaged. Therefore, the interface between masonry and FRP strip was the
key component. Coding the material models for FRP, masonry and the interface
into a finite element program LS-DYNA, the interface element model and contact
surface model were validated by simulating the bond behaviours of EB GFRP and
NSM CFRP plates to masonry in the pull tests.
aluminium
PIC
grip strain
restraining
gauge
FRP EB steel plate
position
strip
strain
gauges
quick
masonry
drying
prism
paste
(a) EB (b) NSM
Figure 4.5 Pull-test specimens
(a) Detached glass FRP strip (b) failed surface of brick prism
Figure 4.6 GFRP fully debonding failure
61 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
4.3.2. Distinct Models
A distinct model for masonry introduced in Chapter 3 was used in the simulation of
the pull tests. Figure 4.7 shows distinct numerical models of NSM and EB pull-tests.
The top surface of the masonry block was fixed in the vertical direction to model the
restraint plate, and the bottom of the model was fixed in all degrees of freedom. The
tensile load in the numerical model was applied on the top of FRP strips by the
displacement control method until debonding occurred. Both CFRP and GFRP were
modelled using an elastic-brittle material model. Rupture of FRP plates was
controlled using principle strain values in this study. Both the interface element
model and contact surface were used to model the interface between FRP and
masonry prism in the simulation.
Gauge
(a) EB pull test (b) NSM pull test
Figure 4.7 Distinct numerical models of NSM and EB pull-tests
Figure 4.8 shows the local bond-slip relationships from experiments and numerical
simulation of the pull tests using interface element method. As shown in Figure 4.8a,
the interface element model gave good predictions of the local bond-slip relationship
62 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
EB GFRP model NSM CFRP model
Figure 4.13 Crack patterns
It should be noted that although both the interface element method and contact
surface method gave reliable estimations of local bond-slip relationships and global
load-displacement curves for NSM and EB FRP retrofitted models in pull tests, the
time spent in contact model is less than that in interface element model, due to its
simple stress transference process. In the models with same number of elements, the
contact model saved approximately 50% to 80% calculation time, indicating this
model is more efficient than NSM and EB retrofitted members. Moreover, compared
with the interface element model, there is less limitation in meshing geometric
models, and thus numerical models can be further simplified to save more
calculation time. However, the contact surface model may not yield reasonable
predictions of debonding failure mechanism of the pull tests as good as the interface
element model due to the zero thickness of the interface.
4.3.3. Homogenized Model and Smeared Crack Model
The homogenized model derived in Chapter 3 for masonry together with the elastic
material model for FRP and interface element model were coded into the finite
element program LS-DYNA to simulate the bond behaviours of EB GFRP and NSM
CFRP plates to masonry in pull tests. Figure 4.14a and Figure 4.14b show the
66 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
homogenized models of pull-tests of NSM CFRP plates and EB GFRP strips bonded
to two five-brick high masonry prisms. In order to check the reliability and
computational efficiency of the homogenized model in the numerical simulation, the
same pull tests were also analysed with the distinct model and the smear crack
model.
(a) Homogenized model of EB pull test (b) Homogenized model of NSM pull test
Figure 4.14 Homogenized models of pull tests
Figure 4.15 shows the local bond-slip relationships from experiments and numerical
simulation of the pull tests using the homogenized model and the distinct model. It
can be observed in Figure 4.15a that both the homogenized model and the distinct
model gave good predictions of the local bond-slip relationship for the EB GFRP
strip at 56 mm below the top surface as compared with those obtained from pull
tests. More accurate results were observed from the simulated local bond-slip
relationships of NSM CFRP plate at 20.5 mm below the top surface from pull tests
in comparison with the test results as shown in Figure 4.15b. Figure 4.16 shows the
corresponding global load-displacement curves from the numerical simulation and
test data, where it can be seen that numerical results from the homogenized model
and distinct model agreed reasonably well with test data. It should be noted that
although the layout of the five-brick high masonry prism in Figure 4.14a was
different from that of basic cell shown in Figure 4.14b, the simulation demonstrated
67 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
that both models gave good results, indicating that the homogenized model derived
from basic cell of masonry in Chapter 3 can also be used to simulate EB GFRP and
NSM CFRP plates to five-brick high masonry prism.
6.00E+06
Test 1.50E+07
Distinct model Test
Homogenized model Distinct model
4.00E+06 1.00E+07 Homogenized model
2.00E+06 5.00E+06
0.00E+00 0.00E+00
0 0.0005 0.001 0.0015 0 0.0005 0.001 0.0015 0.002
Slip (m) Slip (m)
(a) EB GFRP retrofitted model (b) NSM CFRP retrofitted model
Figure 4.15 Comparison of results of local bond-slip relationships in pull tests
6.00E+04
2.40E+04
4.00E+04
1.60E+04
Test Test
8.00E+03 Distinct model 2.00E+04 Distinct model
Homogenized model
Homogenized model
0.00E+00 0.00E+00
0 0.0005 0.001 0.0015 0 0.0005 0.001 0.0015 0.002
Displacement (m) Displacement (m)
(a) EB GFRP retrofitted model (b) NSM CFRP retrofitted model
Figure 4.16 Comparison of results of load-deflection curves in pull tests
The same local bond-slip relationships in the above pull tests were also simulated
using the smear crack model. Figure 4.17 shows a comparison of the simulated
results using the smeared crack model and the distinct model with the test data. It
can be observed that the smear crack model also predicted the local bond-slip
relationships for both NSM and EB FRP plates bonded to masonry prisms very well.
Figure 4.18 shows a comparison of global load-displacement curves in a pull test
68
)aP(
sserts
raehS
)N(
daoL
)aP(
sserts
raehS
)N(
daoL |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
using the smear crack model and distinct model. As shown, reasonable predictions
were obtained for both FRP strips or plates bonded to masonry prisms in pull tests.
6.00E+06
1.50E+07
Test
Test
Distinct Model
Distinct model
4.00E+06 Smeared crack model
1.00E+07 Smeared crack model
2.00E+06 5.00E+06
0.00E+00 0.00E+00
0 0.0005 0.001 0.0015 0 0.0005 0.001 0.0015 0.002
Slip (m) Slip (m)
(a) EB GFRP retrofitted model (b) NSM CFRP retrofitted model
Figure 4.17 Comparison of results of local bond-slip relationships in pull tests
2.40E+04 6.00E+04
1.60E+04 4.00E+04
Test
Test
8.00E+03 2.00E+04 Distinct model
Distinct model Smeared crack model
Smeared crack model
0.00E+00 0.00E+00
0 0.0005 0.001 0.0015 0 0.0005 0.001 0.0015 0.002
Displacement (m) Displacement (m)
(a) EB GFRP retrofitted model (b) NSM CFRP retrofitted model
Figure 4.18 Comparison of results of load-deflection curves in pull tests
It should be noted that while distinct, smeared crack and homogenized models all
gave reliable estimates of local bond-slip and global load-displacement for pull tests,
the solution time varied significantly. In the same pull test simulation, the
homogenized model could save about 75% and 90% calculation time, in comparison
with the smear crack model and the distinct model. This is shown in Figure 4.19,
and indicates that the homogenized model is the most efficient to model NSM and
EB plates bonded to masonry prisms in pull tests. It should also be noted that
although both the homogenized model and smear crack model gave accurate
69
)aP(
sserts
raehS
)N(
daoL
)aP(
sserts
raehS
)N(
daoL |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
prediction of results of pull tests with far less time compared with the distinct model,
it may not yield reasonable prediction of debonding failure mechanism of the pull
tests as good as the distinct model because the weak mortar joints may significantly
affect the debonding process.
80
Distinct model
Homogenized model
60
Smeared crack model
40
20
0
Simulation of pull tests
Figure 4.19 Comparison of computing time with different models in pull tests
4.4. APPLICATION OF THE NUMERICAL MODELS FOR FRP
REPAIRED URM WALLS UNDER OUT-OF-PLANE LOADING
The above validated numerical models were coded into the finite element program
LS-DYNA to simulate the response of two FRP repaired URM walls (with window
openings), under reversed-cyclic loading. The two walls were repaired, respectively,
with NSM CFRP plates and EB GFRP strips and tested under two-way monotonic
out-of-plane bending with pre-compression 0.1 MPa in the vertical direction. The
same tests were also analyzed with the smear crack model for a comparison. Figure
4.20 shows the damaged URM wall with opening repaired with two NSM CFRP
strips with 20 mm wide x 1.4 mm thick symmetric fixed in vertical direction. The
wall configurations and existing crack patterns in the experimental study were also
illustrated in Figure 4.20. Figure 4.21 shows the damaged URM wall repaired with
70
)emit
tinu(
emit
noitaluclaC |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
five EB 77 mm wide x 2.0 mm thick prefabricated GFRP strips spaced at 500 mm,
with two strips also placed adjacent to the window opening. The details of existing
crack patterns are depicted in Figure 4.21 and the experimental setup of the two FRP
repaired damaged URM walls were shown in Figure 4.22. In these experimental
tests, airbags were used to apply lateral pressure onto the FRP strengthened URM
wall specimens to simulate out-of-plane load induced by earthquakes. The load
applied on the wall using the airbags was measured using load cells positioned
between the airbag backing board and the reaction frame and the pressure acting on
the wall surface was calculated by dividing the total load by the area of the wall.
Linear variable differential transformers (LVDT) were used to measure
displacements at different targets. Strain gauges were placed on the FRP plates at
different points to record stress-strain curves. Details about the experimental study
can be found in (Yang 2007).
V1 V2
SG0
SG8
SG1
SG7
SG6 SG2
SG3
SG5
SG4
289 1922 289
650 1200 650
Strain Gauge LVDT
(a) Crack patterns (b) Locations of two NSM plates
Figure 4.20 Configuration of the damaged URM wall repaired with two NSM
plates
71
041
015
006
007
009
001
002
059
052
064
009
0052 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
V1 V2 V3 V4 V5
SG1 SG4 SG11 SG18 SG25
SG5 SG12 SG19 SG26
SG6 SG13 SG20 SG27
SG2 SG7 SG14 SG21 SG28
LVDT 1 LVDT 2 LVDT 3
SG8 SG15 SG22 SG29
SG9 SG16 SG23 SG30
SG3 SG10 SG17 SG24 SG31
1550 500 500 500 500
Strain Gauge LVDT
(a) Crack patterns (b) Locations of five EB strips
Figure 4.21 Configuration of the damaged URM wall repaired with five EB
strips
(a) NSM FRP repaired URM wall (b) EB FRP repaired URM wall
Figure 4.22 Experimental setup for the FRP repaired damaged URM wall
Figure 4.23 shows the numerical models for the two FRP repaired URM walls. Both
the homogenized model and smear crack model were used to model the behaviour of
masonry. The validated interface element models in the above section were used to
model the behavious of the bond-slip of FRP-to-masonry interface for NSM and EB
retrofitting. In the numerical model, existing crack patterns of the two specimens
tested under reversed-cyclic loading, shown in Figure 4.20a and Figure 4.21a, were
modelled as contact surfaces between different parts of masonry as shown in Figure
4.23. Friction ratio of cracks on the contact surfaces can range from 0.7 to 2.5
(Willis et al. 2004). Since the post-static test cracking patterns on the damaged
specimens were generated by the reversed-cyclic loading, the friction coefficient of
72
023
013
013
013
013
013
013
023
0052 |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
5.00E+03
4.00E+03
3.00E+03
2.00E+03 Cyclic test
Static test
Simulation cf=0.7
1.00E+03
Simulation cf=0.9
Simulation cf=1.3
0.00E+00
0 0.01 0.02 0.03 0.04
Displacement (m)
Figure 4.25 Simulation of the last part of load-displacement curve with various
coefficients of friction
Figure 4.26 shows load-displacement curves from tests and numerical simulations at
the target using the homogenized model and the smear crack model. As shown in
Figure 4.27, both the homogenized model and smear crack model gave good
predictions of the NEM CFRP repaired URM wall response as compared with those
obtained by experimental tests. The distribution of maximum strains along the two
EB GFRP plates obtained from numerical simulation using the homogenized model
and smear crack model was in comparison with test data as shown in Figure 4.28. As
shown, the homogenized model gave a more accurate prediction than the smear
crack model. Similar responses were observed from the both models in comparison
with the test results of EB GFRP plates repaired URM long wall as shown in Figure
4.29. It should be noted that with the same computer system the time spent for the
smeared crack model to solve the problem was much more than for the simple
homogenized model.
74
)aP(
erusserp
ecaF |
ADE | Chapter 4: Simulation of FRP Repaired URM Walls under Out-of-plane Loading
10 Test 10 Test
HCoommpoogseinteiz deadm maoged eml odel Smeared crack model
8 8
6 6
4 4
V1 V2 V3 V4 V5
V1 V2 V3 V4 V5
2 2
0 1550 INSIDEFAC50 E0 500 500 500 0 1550 INSIDEFAC50 E0 500 500 500
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Deflection (mm) Deflection (mm)
Figure 4.29 Simulation of EB repaired URM wall using the homogenized model
and smear crack model
4.5. CONCLUSIONS
Pull tests have been simulated using a contact model and interface element model in
the finite element program LS-DYNA. It was found that both the contact model and
interface element model gave a reasonable prediction of local bond-slip relationships
and global load-deflection curves for both NSM and EB FRP plates to masonry in
pull tests. However, less time was required to obtain a solution using the contact
model in comparison with interface element model. The contact surface model may
not simulate debonding failure mechanism of the pull tests as well as the interface
element model due to its zero thickness.
The homogenized model, smear crack model and distinct model have been used to
analyse the response of FRP plated masonry prisms in pull tests. It was found that
far less time was spent using the homogenized model in comparison with distinct
model and smear crack model. The homogenized model and smear crack model
together with the interface element model were used to simulate two seriously
damaged URM walls retrofitted with NSM and EB plates under out-of-plane loads.
The homogenized model has again demonstrated its computational efficiency to
predict global response of the two FRP repaired URM walls.
77
)aPk(
erusserP
023013013013013013013023
)aPk(
erusserP
023013013013013013013023 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
5. MITIGATION OF BLAST EFFECTS ON RETROFITTED
URM WALLS
5.1. INTRODUCTION
Unreinforced masonry (URM) construction is extremely vulnerable to terrorist bomb
attacks since the powerful pressure wave at the airblast front strikes buildings
unevenly and may even travel through passageways, resulting in flying debris that is
responsible for most fatalities and injuries. One way to protect URM construction
from airblast loads is to strengthen the masonry or to enhance its ductility. Categories
of available masonry retrofit include conventional installation of exterior steel
cladding or exterior concrete walls, externally bonded FRP plating, metallic foam
cladding, spray-on polymer and/or a combination of these technologies (Davidson et
al. 2005; Davidson et al. 2004b). However, limited research has been conducted to
investigate retrofitting techniques to strengthen unreinforced masonry (URM) walls
against airblast loading (Baylot et al. 2005; Carney and Myers 2005; Eamon et al.
2004; Myers et al. 2004; Ward 2004). Therefore, it is necessary to study the
behaviours of retrofitted URM walls under airblast loading, and develop efficient
retrofit solutions to enhance blast resistance of URM construction.
This chapter presents the results of numerical studies that were conducted to
investigate the effectiveness of structural retrofit of URM walls by external bonded
(EB) FRP plating, aluminium foam cladding, spray-on polymer and/or a combination
of these technologies. A distinct model was used to model the performance of
masonry, and the Drucker-Prager strength model verified in Chapter 3 was used to
simulate the behaviour of mortar and bricks for masonry structures. An elastic-brittle
material model was employed to model the FRP material. The interface element
78 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
model described and validated in Chapter 4 was used to model the
βpartial-interactionβ behaviours between the URM wall and the various retrofit
materials. The aluminium foam was modelled by a nonlinear elastoplastic material
model which was validated by test data from the manufacturer (CYMAT 2003). The
spray-on polyurea and steel skin for aluminium foam was simulated using
elastoplastic model. The material model βMAT_MODIFIED_HONEYCOMBβ in
LS-DYNA (Whirley and Englemann 1991) program was used to simulate the
performance of aluminium foam protected URM walls subjected to airblast loads.
Parametric studies were carried out to investigate the respective efficiency of different
retrofitting technologies. Pressure-impulse (P-I) diagrams were used to assess damage
levels of the retrofitted URM walls under airblast loads.
5.2. MATERIAL MODELS IN THE SIMULATION
Distinct model for masonry derived in section Β§3.2.2, and FRP models introduced in
section Β§4.2.2 were used to build models of retrofitted URM walls. With regard to
debonding failure due to tension at the interface between the masonry and the bonded
retrofit material, tensile failure was employed into the interface element model varied
in Chapter 4. Thus, material models for spray-on polyurea, and aluminium foam were
introduced in this section.
5.2.1. Material Model for Spray-on Polyurea
Spray-on polyurea is a type of low-stiffness polymer without any fiber reinforcement.
Davidson et al. (Davidson et al. 2005; Willis et al. 2004) who tested spray-on
polyurea retrofitted concrete masonry walls, reported that the polyurea provided a
high level effectiveness of migration against blast by abosribng strain energy and
79 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
preventing fragmentation. Compared with stiffer material such as CFRP, it provides a
cost-effective solution, and is easy to apply. The material model
MAT_PLASTIC_KINEMATIC developed for plastic material in LS-DYNA was used
to simulate the spray-on polyurea. It was modelled as an elastoplastic material with
material properties obtained from Davidsonβs tests as summarized in Table 5.1. The
failure strain for eroding elements was set as 89% (Davidson et al. 2005).
Table 5.1 Material properties of spray-on polyurea (Davidson et al. 2005)
NOTE:
This table is included on page 80 of the print copy of
the thesis held in the University of Adelaide Library.
5.2.2. Material Model for Aluminium Foam
Aluminium foams are new, lightweight materials with excellent plastic energy
absorbing characteristics that can mitigate the effects of an explosive charge on a
structural system by absorbing high blast energy. The typical behaviour of aluminium
foam in uniaxial compression is illustrated in Figure 5.1 (CYMAT 2003). As shown,
the material closely resembles to that of a perfect-plastic material in compression that
makes aluminium foam attractive for use in sacrificial layers for blast protection.
Airblast tests on aluminium foam protected RC structural members have been
conducted recently what it was found that aluminium foam was very effective to
absorb airblast energy (Schenker et al. 2008; Schenker et al. 2005). Due to these
results, it was believed that aluminium foam would also be very effective for
protection of URM construction against airblast loads although no tests have been
performed. Since field airblast tests are very expensive and sometimes not even
possible to conduct due to safety and environmental constraints, numerical
80 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
simulations with a validated numerical model was used here to provide an alternative
method for investigating the effectiveness of aluminium foam to mitigate airblast
loads on URM construction.
NOTE:
This figure is included on page 81 of the print copy of
the thesis held in the University of Adelaide Library.
Figure 5.1 Schematic stress- strain curve of aluminium foam (CYMAT 2003)
Aluminium foam sheets have a natural directionality, and the numbering convention
of material directions is shown in Figure 5.2. As noted above, it has the ability to
dissipate energy as a cellular solid due to very early onset of plastic yielding and large
plastic deformation capability as shown in Figure 5.1. To model the real anisotropic
behaviour of the aluminium foam, a nonlinear elastoplastic material model (LSTC
2007) was used separately for all normal and shear stresses. For the uncompacted
material, the trial stress components in the local coordinate system are updated
according to
(cid:3)n(cid:8)1trial (cid:6)(cid:3)n (cid:8)E $(cid:4) Eq. 5-1
ij ij ij ij
where E is elastic moduli varying from their initial values to the fully compacted
ij
values at V, linearly with the relative volume V (defined as the ratio of the current
f
volume to the initial volume):
E (cid:6) Eu (cid:8)&(E(cid:7)Eu) Eq. 5-2
ij ij ij
in which Eu is elastic/shear modulus in uncompressed configuration,
ij
81 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
5.3.2. URM Walls
Parametric studies were carried out to estimate the response of the URM walls against
airblast loads with a scaled distance increment of 0.01 m/kg1/3. It was found that the
critical scaled distance to prevent the URM wall from collapse is 9.0 m/kg1/3. For
URM walls under smaller blast loading (i.e. Z (cid:2) 9 m/kg1/3), damage was due to a
combination of growing shear cracks and tensile cracks in mortar joints,
demonstrating like step-like cracks as shown in Figure 5.9a. However, URM walls
were observed to collapse immediately as shown in Figure 5.9b when subjected to
larger blast loading (e.g. Z = 4 m/kg1/3), and shear failure was found near supports.
The performance of non-retrofitted URM walls under blast loads was used as a
βcontrolβ case for comparison purposes.
Front side
Front side
(a) Z=9 m/kg1/3 (b) Z=4 m/kg1/3
Figure 5.9 Performance of URM wall under different blast loads
5.3.3. NSM CFRP Retrofitted URM Walls
The NSM CFRP technique for the retrofitted URM walls against blast loading was
considered first. CFRP plates were applied vertically or horizontally (Figure 5.10) on
88 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
the URM wall which was simply supported at its four edges. Blast loading at different
scaled distances was applied on the front surface of the wall. Simulation results are
shown in Figure 5.11. It was found that maximum blast loads for the vertical or
horizontal NSM CFRP retrofitted walls to resist are at scaled distances of 9 m/kg1/3.
The failure models were similar as that of the URM wall. Under light impulse, the
tensile and shear failure models were observed in mortar. Step-like cracks were seen
and due to the FRP strips, more cracks were found in the central part of the rear side
of the wall due to the tensile failure of the mortar. For the horizontal NSM CFRP
retrofitted wall, mortar closed to the CFRP strips was damaged due to tensile failure,
and horizontal cracks in the mortar were observed near the CFRP strips that reduced
the integrity by separating the wall into several pieces. Debonding failure happened
near the edges of the vertical NSM CFRP retrofitted wall, and the wall lost the
enhancement from NSM CFRP strips in early stage. Compared with the behaviour of
URM wall under same blast loading, the vertical or horizontal NSM CFRP retrofits do
not increase the load capacity. Therefore, the NSM CFRP retrofitted technique is not
considered as a suitable method to retrofit URM walls against blast loading, even if
the wall is subjected to light impulse.
Rear side Rear side
(a)Vertically NSM CFRP (b)Horizontally NSM CFRP
retrofitted masonry wall retrofitted masonry wall
(Note: 2500mm Γ 2500mm wall with four 1.2mm Γ 20mm CFRP plates)
Figure 5.10 NSM CFRP retrofitted URM walls
89 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
Rear side Rear side
Figure 5.11 Debonding failure of NSM CFRP retrofitted URM walls
5.3.4. EB CFRP or GFRP Retrofitted URM Walls
The EB FRP retrofitting technique was selected next. Figure 5.12a shows four
100mmΓ2mm GFRP plates applied on the rear surface of URM wall. Numerical
simulation results are illustrated in Figure 5.13. As shown, when scaled-distance Z (cid:2)
5.0 m/kg1/3, step-like cracks were distributed on the most portions of rear surface of
the wall, and the debonding of FRP plates was found around the cracks. The GFRP
plates still carried loads, and the retrofitted URM wall was kept under light damage
level, on which little debonding was observed (Figure 5.13). Some local failure of
masonry was seen in the centre of the wall with the debonding failure level at Z = 5.0
m/kg1/3, and wall failure level was observed at Z = 4.7 m/kg1/3. Local failure of the
masonry was found at the portion of wall without being covered by GFRP plates. It
was observed that once the debonding area exceeds 10% of the whole bonded area,
the retrofitted walls begin to lose the protection from the FRP retrofits. Thus, the
relevant scaled-distance and impulse were defined as critical values of the debonding
failure level. The debonding patterns are shown Figure 5.13. The combined effect of
horizontal plus vertical GFRP plates was then investigated by applying four vertical
and four horizontal GFRP plates with dimension of 100mmΓ2mm on the rear surface
of the URM wall as shown in Figure 5.12b. The scaled-distance of wall failure level is
at 4.3 m/kg1/3 (see Figure 5.14), therefore, the additional GFRP plates on the rear
90 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
A comparison of effectiveness of EB GFRP retrofitted URM walls against blast
loading is shown in Figure 5.17. It is observed that GFRP applied on both surfaces
provides the best protection by increasing the capability of blast-resistance to 464%
compared with unretrofitted URM wall. However, it may not be cost-effective due to
increase of cost for the additional layer of FRP sheets.
CFRP retrofitting on URM wall was also investigated. Figure 5.18 shows the URM
wall retrofitted by four CFRP plates with dimension of 50mmΓ1.2mm on the rear
surface subjected to blast loading. The simulation results shows that debonding
occurred at a scaled distance of 9 m/kg1/3 and wall failure occurs at the scaled distance
of 6 m/kg1/3. Thus, the CFRP retrofitting does not increase substantially the blast
resistance capability of URM wall.
I. Debonding failure II. Wall failure
Z=9 m/kg1/3, Z=6 m/kg1/3,
Impulse=0.852MPa~(cid:19)(cid:22) Impulse=1.211MPa~(cid:19)(cid:22)
Rear side Rear side
Figure 5.18 EB CFRP retrofitted URM walls (4 plates)
For the walls with CFRP plates bonded on the entire rear surface (Figure 5.19a), wall
failure occurred at a scaled distance of 3.5 m/kg1/3 (see Figure 5.20), indicating that
entire surface CFRP retrofitting is similarly effective compared with the four vertical
94 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
EB CFRP plate retrofitted wall. However, when a layer of CFRP was added to the
entire front surface (Figure 5.19b), the wall failed at a scaled distance of 3.3 m/kg1/3,
and debonded at scaled distance of 3.7 m/kg1/3, as shown in Figure 5.21. Protection
effectiveness of the various EB CFRP retrofits was compared in Figure 5.22, which
shows that the effectiveness of blast resistance increases with more CFRP plates. The
CFRP installed on both entire sides of the walls provides the best protection to the
wall, however, compared with the wall retrofitted only on the entire rear side, the
effectiveness was not improved double. The Therefore, CFRP retrofitted on front side
is not a cost-effective protection.
(a) Fully applied on rear side (b)Fully applied on two sides
Figure 5.19 EB CFRP retrofitted URM walls on entire surface
Light damage I. Debonding failure II. Wall failure
Z<4 m/kg1/3 Z=4 m/kg1/3 Z=3.5 m/kg1/3
Rear side Rear side Rear side
Figure 5.20 Fully EB CFRP retrofitted URM walls on back surface
95 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
500%
464%
URM wall
400% 382%
EB GFRP (v4)
355%
EB GFRP (v4+h4)
296%
300% EB GFRP (fully, inside) 265%
221% 221% EB GFRP (v4, 2sides)
200% EB GFRP (fully, 2sides)
142% EB CFRP (v4)
100% EB CFRP (fully, inside)
100%
EB CFRP (fully, 2sides)
0%
EB FRP retrofitted URM walls
Figure 5.23 Comparison of EB FRP retrofitted URM walls
5.3.5. Spray-on Polyurea Retrofitted URM Walls
A parametric study was carried out to investigate the effectiveness of spray-on
polyurea as obviers. The spray-on polyrea retrofitted URM wall was used to study the
relationship between the thickness of spray-on polyrea and deflection of the wall at
scaled-distance 3 m/kg1/3 and 4 m/kg1/3. The polyurea was applied on both surfaces of
the wall and the results are plotted in Figure 5.24. It was found that the thickness
influences the effectiveness of the retrofit, with thicker spray-on polyurea giving
better protection.
The blast mitigation effectiveness of a layer of 15mm spray-on polyurea was applied
to the rear surface of the URM wall is shown in Figure 5.25. In the simulation, the
debonding failure was identified by the eroded bricks on the rear surface of the
masonry wall. Once the debonding area of eroded surface exceeds about 10% of the
entire bonding surface, the mitigation effect begins to decrease seriously. Figure 5.25
shows two failure modes for the retrofits observed in the simulations. Under great
pressure, the polyurea would be mutilated closed to supports. Shown in Figure 5.26,
local failure and debonding failure were observed. Debonding failure started from the
97
sllaw
MRU
no
stiforter
fo
ssenevitceffE |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
Local failure of the
spray-on polyurea
Local failure of the
masonry around the
center of the wall
Debonding failure Front side
Figure 5.26 Local failure of the spray-on polyurea and masonry (vertical section)
The results for polyurea sprayed on the both surfaces is shown in Figure 5.27. It was
observed from the simulation results, that the polyurea on the front surface can
enhence the wall by abosorbing more strain energy. It was found that the key factor
influencing the effectiveness of the retrofits is energy absorbing capability. A
comparison of the effectiveness of spray-on polyurea is shown in Figure 5.28. The
wall retrofitted by a layer of 15mm spray-on polyurea on its rear surface absorbed
three times more impluse energy than the unretrofitted URM wall. The increase of
impulse ratio was 859% for the wall retrofitted by spray-on polyurea on both surfaces,
indicating that by increasing the ductility, the masonry wall can survive much higher
blast impluses.
I. Debonding failure II. Wall failure
Z=3.3 m/kg1/3, Impulse=3.257MPa~(cid:19)(cid:22) Z=2.3 m/kg1/3, Impulse=7.322MPa~(cid:19)(cid:22)
Rear side Rear side
Figure 5.27 Two sides 15mm spray-on polyurea retrofitted URM walls
99 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
1000%
858.95%
URM wall
800%
Inside sprayed- on polyurea
retrofitted URM wall
600% Two sides retrofitted spray-on
polyurea URM wall
400% 326.84%
200%
100.00%
0%
URM wall and Retrofitted URM wall
Figure 5.28 Comparison of energy absorption of the spray-on polyurea
retrofitted walls
5.3.6. Aluminium Foam Protected URM Walls
Parametric studies were also conducted to study the response of URM walls
retrofitted with a layer of aluminium foam sheet (thickness of 40 mm) covered by two
1.5mm steel sheets on the front surface (Figure 5.29). For a scaled distance of more
than 4 m/kg1/3 as shown in Figure 5.30a, the protected URM wall suffered only light
damage. Once the scaled distance reached 3.3 m/kg1/3, the aluminium foam sheet
began to be damaed, and debonding between the steel sheets/masonry interface was
found as shown in Figure 5.30b, which demonstrates that the aluminium foam sheet
absorbs the airblast energy and mitigates blast effects on the URM wall, even though
the URM wall is still kept under light damage condition. The aluminium foam
protected URM wall collapsed as shown in Figure 5.30c as the scaled distance reaches
2.3 m/kg1/3. Once the URM wall retrofitted with a layer of a layer of 40mm thick
aluminium foam on the both surfaces in Figure 5.31a, debonding failure between the
aluminium foam and steel sheets/URM wall did not occur until the scaled distance
reached 2.3 m/kg1/3 as shown in Figure 5.31b. URM wall failure only occured when
100
etamitlu
no
desab
oitar
eslupmI
llaw
MRU
fo
eslupmi |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
Furthermore, different types of aluminium foam sheets can have great influence on its
blast energy absorption capacity. Tables 5.3 and Table 5.4 list the material properties
for A356SiC030 and A356SiC020 aluminium foams. Parametric sttudies were
conducted to investigate how the material properties of aluminium foam sheets
(keeping all the other material properties constant) affect the blast energy absorption
capacity on URM walls. Figure 5.34 shows different densities of aluminium foam
sheets on the mitigation of blast effects of URM walls. The corresponding response of
the aluminium foam protected wall is compared in Figure 5.36. As shown, the higher
the density, the smaller the response, that is, the more effective it mitigates blast
effects on URM wall. Figure 5.35 shows how thickness of aluminium foam sheets
influence mitigation of blast effects on the URM wall and corresponding response of
the aluminium foam protected URM walls are compared in Figure 5.37, where it can
be seen that the larger the thickness, the smaller the response. Figure 5.38 plots the
energy absorption of the aluminium foam retrofitted front wall with different density
and thickness. As before, the higher density and thicker foam layers absorb more
energy.
Table 5.3 Properties of A356SiC030 aluminium foam
Density (kg/m3) 300 Elastic modulus in a direction (GPa) 0.300
Youngβs modulus of al (GPa) 71.0 Elastic modulus in b direction (GPa) 0.460
Poissonβs ratio 0.33 Elastic modulus in c direction (GPa) 0.575
Yield stress of al (GPa) 0.322 Shear modulus (GPa) 1.0
Compressive strength (MPa) 2.4 Densification Strain (%) 72
Table 5.4 Properties of A356SiC020 aluminium foam
Density (kg/m3) 200 Elastic modulus in a direction (GPa) 0.185
Youngβs modulus of al (GPa) 71.0 Elastic modulus in b direction (GPa) 0.200
Poissonβs ratio 0.33 Elastic modulus in c direction (GPa) 0.270
Yield stress of al (GPa) 0.322 Shear modulus (GPa) 0.2
Compressive strength (MPa) 1.2 Densification Strain (%) 80
103 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
transferred to the wall by absorbing more of the blast energy. However, the remaining
impulse acted on the masonry wall was still too great for the soft retrofits. Therefore,
a strong rear support was expected to work best with the aluminium foam. Thus, a
layer of 5mm thick steel sheet was applied on the rear surface of the wall. The steel
sheet on the rear surface provided better support, allowing the aluminium foam to
absorb more energy. A comparison of effectiveness for the URM walls protected by
aluminium foam and the combined retrofits is shown in Figure 5.42. The combination
of aluminium foam with steel plate performed better than all other combinations,
except the double-sided aluminium foam sheet retrofit.
II. Debonding damage I. Wall failure
Z=3.3 m/kg1/3, Impulse=3.257MPa~(cid:19)(cid:22) Z=2 m/kg1/3, Impulse=10.05MPa~(cid:19)(cid:22)
Rear side Rear side
Figure 5.39 Combination of aluminium foam with spray-on polyurea
II. Debonding damage I. Wall failure
Z=2.3 m/kg1/3, Impulse=7.322MPa~(cid:19)(cid:22) Z=1.95 m/kg1/3, Impulse=11.13MPa~(cid:19)(cid:22)
Rear side Rear side
Figure 5.40 Combination of aluminium foam and steel plates
106 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
diagram, damage levels for aluminium foam protected URM walls should be defined.
For URM wall, the ultimate deflection at instability (cid:8) is predicted by using a one-way
u
vertical bending theory derived by Willis (Willis et al. 2004),
(cid:28) (cid:3) (cid:8)0.25,gh(cid:25)
( (cid:6)t(cid:26)(cid:26) 1(cid:7) v (cid:23)(cid:23) Eq. 5-13
u (cid:27) f (cid:24)
mc
where t is the thickness of the URM wall, (cid:3) is the pre-compressive stress, (cid:9) is the
v
density of the URM, g is the acceleration due to gravity, h is the height of wall, and
f is the ultimate compressive stress of mortar. The relationship of f and f is
mc mc mt
expressed as follows (MacGregor 1988),
f (cid:6)0.53 f Eq. 5-14
mt mc
where f is the ultimate tensile stress of mortar. The material properties used in this
mt
study are presented in Table 5.5, which gives an ultimate deflection of the
2500mm(cid:10)2500mm(cid:10)110mm URM wall was estimated to be 108mm based on Eq.
5-13. The ultimate deflection of 108mm was used as the failure criterion for the URM
wall, and was also used to decide the failure mode of the foam protected URM walls.
Figure 5.43 shows P-I diagram for the URM wall based on the above failure criterion.
500
400
300
URM wall
200
100
0
0 1000 2000 3000 4000 5000
I (KPa.ms)
Figure 5.43 P-I diagram for URM walls against airblast loads
108
)aPK(
P |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
Table 5.5 Material properties of URM wall
(cid:127)(cid:8)(cid:128)(cid:129)<(cid:130)(cid:19)3) g (m/s2) f (Mpa) t (mm) (cid:9)(cid:8)(cid:128)(cid:131)(cid:132)(cid:4)(cid:133) h (mm)
mt
1800 9.8 0.614 110 0 2500
Rear side Rear side Rear side
(a) Before deforming (b) Compacted aluminium (c) Debonding between
foam prior to debonding foam and steel sheet
Figure 5.44 Deformation process of aluminium foam protected URM wall
(vertical section)
For aluminium foam protected URM walls, two damage levels are defined: Level 1
foam debonding failure, and Level 2, as an URM wall failure. Debonding between
foam and steel sheets/masonry walls will occur when the ultimate deflection of an
URM wall exceeds the debonding deflection. Since the elastic modulus of steel sheet
is much greater than masonry, debonding begins to occur between the foam and steel
sheets rather than between the foam and the masonry. When the debonding area
exceeds 10% of the bonding area between foam and steel sheets, the aluminium foam
began to damage. Thus, it affects the retrofit effectiveness greatly and characterized as
debonding failure, that is, the damage Level 1. Figure 5.44 shows the debonding
109 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
failure process of aluminium foam protected URM wall. When a foam protected
URM wall is subjected to airblast loads, the foam and the steel sheet will initially
deform together with the URM wall (see Figure 5.44b). However, as the deformation
of the URM wall increases, debonding occurs between the foam and steel sheets as
shown in Figure 5.44c. When the ultimate deflection of the foam protected URM wall
reaches 108 mm, it reaches the Damage Lever 2, that is, URM wall failure. Table 5.6
characterizes damage levels for aluminium foam protected URM walls under airblast
loads.
Table 5.6 Damage levels for aluminium foam protected URM wall
Damage level Description Performance
I. Debonding The debonding area exceeds Failure of foam happens. Steps
failure 10% of the bonding area cracks can be observed in
between foam and steel sheets, mortar joints.
aluminium foam begin to
disintegrate.
II. Wall failure Protected URM wall reaches Foam definitely fails, and wall
its maximum blast resistant collapses. Almost all the
capability. Ultimate deflection mortar joints are damaged.
of foam protected URM wall
exceeds the critical deflection
108mm.
In this study, damage levels for foam protected URM walls are identified using energy
absorption ratio method. The total input energy from a blast impulse is converted into
kinetic energy, with the elastic strain energy primarily stored by steel cover sheets,
and inelastic deformation strain energy stored by crushing and plastic deformation of
masonry and aluminium foam. At the end of the blast event, the retrofitted walls get
steady, with most of the input energy being converted to deformation energy stored as
internal energy mainly by wall and aluminium foam. Under small impulses, the ratio
of energy absorbed by the foam and URM wall (as shown in Figure 5.45) is roughly
constant since the foam and the steel sheet deform together with the URM wall.
Under greater impulses, the aluminium foam is compacted, and the steel sheets may
110 |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
also start to debond from the foam. The starting debonding point was defined as
Damage Level 1 as shown in Figure 5.45. Further increasing the impulse cause more
and more energy to be absorbed by the foam due to more foam cells rupturing until
the wall reaches Damage Level 2, as shown in Figure 5.45. At Damage Level 2, the
ratio of the energy absorbed by foam reaches a maximum so that it is easily identified
in the curves in Figure 5.45 and Figure 5.46. Further impulse increases cause the
aluminium foam to be destroyed and the URM wall to collapse. Similar phenomena
were observed in the EB FRP plates (Figure 5.47) and spray-on polyurea (Figure 5.48)
retrofitted URM walls.
Wall collaps
Critical deflection 108mm
Residual deflection of wall
Impulse
Damage Level 1 Damage Level 2
External Work (100%)
Wall failure
Energy Absorbed by Al-foam
Al-foam
failure Energy absorbed by wall
Impulse
Figure 5.45 Determination of Damage Levels based on energy absorption ratio
111
llaW
fo
noitcelfeD
laudiseR
)%(
oitar
ygrenE
debrosbA |
ADE | Chapter 5: Mitigation of Blast Effects on Retrofitted URM Walls
3000
URM 2Foam -level1
1Foam -level1 EB - GFRP - level1
2500 EB-CFRP- level1 Spray-on Polyurea β level 1
2000
125kg TNT 512kg TNT 1000kg TNT
1500
1000
500
0
0 500 1000 1500 2000 2500
I (KPa.ms)
Figure 5.59 P-I diagrams for retrofitted URM walls at damage level I
5.5. CONCLUSIONS
The performance of URM walls protected by various types of retrofitting technologies
was simulated numerically in this study. The numerical results indicate that the
aluminium foam is the most effective technique for mitigation of blast effects on
URM walls. This is because the foam absorbs more blast energy compared with the
other retrofitting techniques considered in this study. It was also found that both
thickness and density of aluminium foam sheets greatly influences mitigation
effectiveness against blast loads on URM walls. Damage levels were defined based on
a collapse failure mechanism and energy absorption method. P-I diagrams for EB FRP,
spray-on polyurea and aluminium foam protected URM walls based on the simulated
results.
118
)aPK(
P |
ADE | Chapter 6: Conclusions and Recommendations
6. CONCLUSIONS AND RECOMMENDATIONS
6.1. SUMMARY AND CONCLUSIONS
Masonry buildings exhibit the vulnerability of poor blast-resistant capacity with little
ductility. Aiming to find effective strengthening solutions to enhance masonry walls
against explosion, this project focused on studying the performance of retrofitting
techniques, such as EB FRP and NSM FRP, which have been widely use to strengthen
concrete structures, because of its light weight, high strength and durability. However,
the performance of the EB and NSM strips retrofits on masonry walls against blast
loading was poor. This research showed that, such retrofits failed in shear or bending
between strips. Hence, several other new materials, such as spray-on polyurea and
aluminium foam, were also studied for mitigation of blast effect. These retrofitting
systems were much more efficient.
To study the bonding behaviours between masonry and retrofits, bond-slip models
coded in LS-DYNA were used, and compared with pull tests for validation. Stress-slip
curves and load-displacement relationship were compared, from which it was found
the bond-slip model worked well. A homogenized model which performs efficiently
was derived for simulating full scaled retrofitted masonry walls under out-of-plane
loading. The models based on test data were verified with test results, and
load-displacement curves and strain distribution along the height were compared.
Results from the homogenized model matched well with experimental results. It was
found that the homogenized model could represent the elastic and plastic behaviours
of masonry walls. However, it did not give accurate results for post-failure zone.
The numerical models developed in this study were applied to simulate the behaviours
119 |
ADE | Chapter 6: Conclusions and Recommendations
of retrofitted masonry wall under blast loading. To increase ductility of the wall, a
new technique known as spray-on polyurea was employed in this study. It was found
that the capability of absorbing stain energy was the key factor that influenced
performance. A new energy absorbing material, aluminium foam, was applied to the
masonry walls. To investigate the effectiveness of different types of retrofitting
materials, two critical damage levels were defined. Based on simulation results,
debonding failure level and wall failure level were identified and then extended to
greater range of pressure and impulse relationship. Thus, pressure-impulse diagrams
for various retrofitting techniques were developed.
It should be noted that the numerical models and developed P-I diagrams were based
on one layer of brick masonry wall with thickness of 110 mm, and panel dimensions
of 2500mm Γ 2500mm. The performance of the retrofits will vary if the thickness or
dimensions are changed, especially for the aluminium foam protected masonry walls.
If applying the aluminium foam material on stronger masonry wall, the retrofits
would likely perform better by enhancing its capability of absorbing energy. The
study provides a general approach for simulating the retrofitted masonry walls.
However, further research on derived dimensionless P-I diagrams are recommended,
which can be applied to wide range of masonry structures.
In summary, it can be conducted that FRP material on masonry used against
earthquake loads may not have the same performance in blast environments. The
ability to absorb strain energy is important for protecting masonry walls against blast
impulses. Further studies should be conducted that focus on the new materials.
6.2. RECOMMENDATIONS FOR FURTHER RESEARCH
Based on the studies described herein, some related aspects requiring further research
120 |
ADE | Chapter 6: Conclusions and Recommendations
have become apparent, namely,
1. Material models for bricks and mortar could be improved to consider
microscopic material failures and the effect of strain rate. This would mean
more accurate results could be obtained, the relationship between retrofits and
masonry would be more reliable, and accurate local failure could be observed in
simulation.
2. The bond-slip model in current research is efficient, but could be improved by
extending to transfer 3-D stress and strain between masonry and retrofits to
simulating the physical behaviours accurately. The reasons behind different
types of debonding failures could be further studied in simulation.
3. Experiments on masonry and retrofitted masonry walls under blast loading are
required to verify the numerical models. Some phenomena such as local failure
at different locations which influence the debonding failure should be checked
using test results. Moreover, the P-I diagrams should be validated using
experimental data.
4. Dimensionless P-I diagrams are required for design purposes. More data would
be required to qualify the damage levels, and other failure modes would also be
observed which should be considered in guidelines.
5. Investigation into retrofitted masonry walls under close bursts or explosions at
small stand-off distances is deemed to be worthwhile and results could be
included in P-I diagrams to improve design guidelines.
121 |
ADE | Notations
NOTATIONS
A = area perpendicular to the principal strain direction
a = shear failure surface constants in Drucker-Prager model
0-2
E =modulus of elasticity
E =compressive modulus of elasticity
c
E =tensile modulus of elasticity
t
E = elastic moduli of aluminium foam
ij
Eu = elastic/shear modulus in uncompressed configuration
ij
E =equivalent moduli of elasticity
f = ultimate compressive stress of mortar
mc
f = ultimate tensile stress of mortar
mt
G = Elastic shear modulus
G = fracture energy release rate in smeared crack model
c
G = shearing fracture energy release rate in bond-slip model
f
G = tensile fracture energy release rate in bond-slip model
ft
G =fracture energy release rate of mode I in smeared crack model
I
G =fracture energy release rate of mode II in smeared crack model
II
g = acceleration due to gravity
h = height of the masonry wall
I = impulse of blast loading
I = first invariant of the stress tensor
1
J = second invariant of the deviatoric stress tensor S
2 ij
k = material constant in Drucker-Prager model
P = airblast over pressure
P = ambient over pressure
o
P = reflected pressure
r
P = peak value of incident pressure
so
122 |
ADE | ~ i ~
Abstract
The recovery of sulphuric refractory gold requires pre-treatment of the material for the
liberation of gold particles from sulphide-bearing minerals (mainly pyrite). This pre-treatment
is expensive and can increase significantly the total processing cost. However, for low-grade
materials stockpiled for a long period of time, this cost can be reduced if the material naturally
oxidised. When exposed to air and water, the pyrite in the stockpiles can be oxidised
spontaneously. Over a prolonged period of time, this process may result in partial or complete
oxidation of the contained pyrites, which may enable gold extraction by direct cyanide
leaching and reduce the need for pre-treatment, hence increase the profitability of reclaiming
the gold from the stockpiled material. The aim of this research is to investigate the possibility
that the natural oxidation of pyrites in stockpiles of refractory gold-bearing materials may
facilitate gold recovery without pre-treatment.
To solve this problem, pyrite oxidation under stockpile conditions was studied and two
models were developed to predict the level of pyrite oxidation in stockpiles. The first model
describes the oxidation rate of pyrite grains under unsaturated conditions and/or circum-
neutral to alkaline pH environments, in which a diffusion barrier develops on the fresh pyrite
surface during the reaction. This reaction rate model was derived using the shrinking core
model and it incorporates the effects of oxygen concentration, temperature and degree of
water saturation on the reaction. The second model is a coupled multi-component numerical
model that can simulate the pyrite oxidation in three-dimensional stockpiles together with
related processes such as oxygen transport and heat transfer. This numerical model includes
the reaction rate model as one of its components and the simulation incorporates the above-
mentioned factors as well as other stockpile properties such as size distributions of rock
fragments and pyrite grains. The outputs from the numerical model include oxygen
concentration, temperature distribution, air velocity field, pyrite oxidation level and, more
importantly, the oxidation profile of pyrite grains, which is an essential input for the
estimation of gold recovery without pre-treatment. The application of these models was
demonstrated in this research using a case study of the Kapit Flat stockpile on Lihir Island in
Papua New Guinea. The simulation results were compared with those measured for samples
taken from the stockpile and an acceptable estimation of the level of pyrite oxidation was
obtained after calibrating the model. The models developed in this research have been
demonstrated to provide a practical solution framework for estimating the level of pyrite
oxidation in refractory gold-bearing stockpiles so that the recovery of gold without pre-
treatment can be evaluated. |
ADE | ~ vii ~
Declaration
I certify that this work contains no material which has been accepted for the award of any
other degree or diploma in my name, in any university or other tertiary institution and, to the
best of my knowledge and belief, contains no material previously published or written by
another person, except where due reference has been made in the text. In addition, I certify
that no part of this work will, in the future, be used in a submission in my name, for any other
degree or diploma in any university or other tertiary institution without the prior approval of
the University of Adelaide and where applicable, any partner institution responsible for the
joint-award of this degree.
I acknowledge that copyright of published works contained within this thesis resides with the
copyright holder(s) of those works. I also give permission for the digital version of my thesis
to be made available on the web, via the Universityβs digital research repository, the Library
Search and also through web search engines, unless permission has been granted by the
University to restrict access for a period of time.
I acknowledge the support I have received for my research through the provision of an
Australian Government Research Training Program Scholarship. |
ADE | ~ ix ~
Acknowledgements
I gratefully acknowledge Newcrest Mining Limited for the sponsorship of my PhD stipend. I
would like to acknowledge Minerals Council Australia for awarding a research scholarship.
Undertaking this PhD has been a challenging and life-changing experience for me and I could
not make it this far without the support I received from many people.
I wish to express great gratitude to my supervisors, Professor Peter A. Dowd and Associate
Professor Chaoshui Xu, for inspiring me pursuing a PhD degree and providing me with massive
support during my study. I am grateful for their guidance and encouragement that have
inspired me to self-challenge. It was such a wonderful journey working with them and I have
gained a lot from it.
I also want to thank Ms Karyn Gardner, the principal geologist of Newcrest Mining Limited at
the time, for providing data and arranging my visit to the mine site. I thank my lovely
colleagues; they make my time at the school so enjoyable.
I wish to thank my group members and friends, Dr Zhihe Wang, Miss Yusha Li and Dr Changtai
Zhou, not only for inspiring me in technical discussions/research collaborations, but also for
their lovely company at my leisure time. I also thank a dear friend, Miss Wanjun Qiu, for her
lovely company during these years of study and work in Adelaide.
I wish to thank my parents for their love and support that enable me to pursue what I want.
Finally, a big thank to my fiancΓ© Mr Long Tan, who always backs me up in whatever I do and
supports me getting through the challenging and self-growing years of my life. |
ADE | ~ 2 ~
This section provides a brief description of the research background, a review of the literature
related to the research problem, the research objectives and a summary of the research
conducted to address the problem.
Research background
This project was initiated and funded by Newcrest Mining Limited. The company owns 100%
the Lihir gold mine located on Aniolam Island, Papua New Guinea. Lihir is a refractory pyrite
gold deposit and ore processing requires pre-treatment to oxidise the pyrite in order to
release the gold particles encapsulated within the pyrite crystal, after which gold can be
extracted by conventional cyanide leaching. The pre-treatment method at Lihir is pressure
oxidation, with four parallel autoclaves installed, providing currently an ore processing
capacity of 15 Mt per year (Newcrest Mining Limited, 2020). At the Lihir mine, the processing
of high-grade and medium-grade ores are prioritised while low-grade ores have been sent to
long-term stockpiles for later processing. The stockpiled material is classified as a measured
mineral resource with a total tonnage of about 83 Mt at an average grade of 1.9 g/t (Newcrest
Mining Limited, 2020). From laboratory tests on samples taken from the stockpiles, it was
found that the pyrite had naturally oxidised to varying degrees due to long-term exposure to
the atmosphere, and variable gold recoveries can be achieved from the partially oxidised
materials via direct cyanide leaching. This has increased interest in understanding more about
the level of pyrite oxidation within the stockpiles and investigating the value proposition of
recovering gold without pre-treatment enabling the stockpiles to be reclaimed at a lower
processing cost. The first step in assessing this potential is to estimate the distribution of the
level of pyrite oxidation within the stockpiles, which is the aim of the research reported in this
thesis. This estimation requires a detailed understanding of two components of the oxidation
process. The first is the rate of pyrite oxidation under the various conditions that may exist
within a stockpile, and the second is the quantification and simulation of the influences of
physical and chemical processes that affect the pyrite oxidation. The following literature
review focuses on these two particular components: the oxidation reaction of pyrite and the
numerical modelling of pyrite oxidation in rock piles.
Pyrite oxidation: surface reaction and kinetics
Pyrite oxidation is of wide interest in many research fields including mineral metallurgy,
environmental science and geochemistry. The conditions under which pyrite oxidation is
induced or occurs vary significantly from one application to another. For example, in
metallurgy, the oxidation of pyrite, as a part of the metal extraction process, is often set up
under extreme chemical and physical conditions such as high pressure with high oxidant
concentration in order to achieve a high reaction rate. However, in the environmental context,
pyrite oxidation can occur spontaneously at a much lower rate under natural conditions,
which often causes long-term environmental issues such as acid mine drainage (AMD) that
require control and remediation. For these reasons, pyrite oxidation has been studied
extensively under different conditions and in different contexts. In this thesis, the review of
pyrite oxidation is confined to pyrite oxidation in stockpiles under natural environmental
conditions. |
ADE | ~ 3 ~
1.2.1 Atmospheric oxidation of pyrite
In the natural environment, pyrite oxidation can occur spontaneously when exposed either
to atmospheric water and oxygen or to aqueous water and dissolved oxygen (DO). In the long
term, atmospheric oxidation of pyrite is a slower process than aqueous oxidation of pyrite.
The pyrite surface is often passivated after a fresh pyrite surface is oxidised and an oxidation
layer is formed (Chandra and Gerson, 2010).
Eggleston et al. (1996) used scanning tunnelling microscopy (STM) to observe the initial
oxidation of a pyrite surface in air and the results show that oxidation proceeds by extending
oxidized patches. They proposed a reaction mechanism in which oxidation proceeds via
Fe2+/Fe3+ cycling. The oxidation is initiated by electron transfer from pyrite-Fe2+ to O , leading
2
to the formation of ferrous oxide (Fe2+), which is further oxidised to Fe3+. As electron transfer
from oxide-Fe2+ to O is more energetically favourable than from pyrite-Fe2+ to O , pyrite-Fe2+
2 2
is preferentially oxidized by Fe3+ in the oxidation product, which causes the extension of the
oxidized area to adjacent unreacted areas. In Eggleston et al. (1996), this process was
modelled using a Monte Carlo approach based on the assumption that the probability of Fe2+
oxidation is positively proportional to the number of nearest-neighbour oxidized sites (Fe3+),
which successfully reproduced the surface image observed using scanning tunnelling
microscopy (STM). Similar mechanisms were also proposed in SchaufuΓ et al. (1998) and de
Donato et al. (1993).
Studies have shown that sulphate is the major oxidation product formed on the pyrite surface
after prolonged exposure to the atmosphere (Buckley and Woods, 1987; SchaufuΓ et al., 1998;
Todd et al., 2003) and the product is largely identified as iron sulphate Fe (SO ) (de Donato
2 4 3
et al., 1993; Todd et al., 2003). Iron-containing oxidation products also include iron oxy-
hydroxide FeOOH, iron hydroxide Fe(OH) and ferrous iron oxide FeO as identified in these
3
studies, although opinions differ on which is the most prolific. Based on the evidence given in
de Donato et al. (1993), elemental sulphur S0 and polysulphide may also be present on the
oxidized pyrite surface.
Jerz and Rimstidt (2004) studied the rate of pyrite oxidation in moist air (96.7% fixed relative
humidity) at 25Β°C under different oxygen partial pressures. The rate of oxidation was
determined by taking the time derivative of the oxygen consumption (in moles) which was
found to be approximately linearly proportional to the square root of time. The rate of oxygen
ππ
consumption ( in mol.m-2.sec-1) was determined as:
ππ‘
ππ
= 10β6.6π0.5π‘β0.5 (1-1)
ππ‘
where p is the partial pressure of oxygen (atm) and t is the reacting time (sec).
This relationship was derived from data measured over a period of about 30 days. The authors
compared the experimental results with those of aqueous oxidation and found that the rate
of pyrite oxidation in moist air is slightly faster at the beginning of the reaction and then slows |
ADE | ~ 4 ~
significantly, approaching the aqueous oxidation rates reported by humidity cell studies. Jerz
and Rimstidt (2004) attributed the slowing of the oxidation rate to the development of a
solution film around the pyrite surface due to hygroscopic oxidation products absorbing water
from the surrounding vapour as this solution film slows down oxygen diffusion from the air
interface to the pyrite surface and hence limits the oxidation reaction. Based on this
mechanism, they derived a theoretical rate formula which is of the same form as the empirical
rate formula of Eq. (1-1). However, the coefficient in their theoretical rate formula, given the
oxygen solubility and diffusivity in solutions, is about four orders of magnitude larger than
that given in Eq. (1-1). Jerz and Rimstidt (2004) attributed this discrepancy in coefficients to
the possibility that oxygen diffusion in the thin solution film can be much slower than that in
bulk solution. Nevertheless, the empirical rate formula of Eq. (1-1) provides a good fit to the
experimental data and captures the rate decreasing trend for pyrite oxidation during the
initial 30 days.
The initial rate of pyrite oxidation in air has been measured in previous works. A comparison
of the measured rates published in the literature can be found in Jerz and Rimstidt (2004),
which showed a range from 10-8.7 to 10-6.5 O -mol/m2/s (or 10-9.2 to 10-7.0 FeS -mol/m2/s). LeΓ³n
2 2
et al. (2004) measured the rate of pyrite oxidation in the atmosphere in a desiccator at 20Β°C
and a rate of 10-9.3 FeS -mol/m2/s at day three was determined using sulphate as the reaction
2
progress variable. The reaction rate after 84 days was measured to be 10-10.4 FeS -mol/m2/s,
2
twelve times less than the initial reaction rate.
1.2.2 Aqueous oxidation of pyrite
The aqueous oxidation of pyrite can be described by the reaction sequence from Eq.(1-2) to
Eq.(1-5) which were proposed by Singer and Stumm (1970) in the context of acid mine
drainage. According to Singer and Stumm (1970), Eq.(1-2) is the initiator reaction for pyrite
oxidation, where pyrite is oxidized by oxygen and ferrous ion is released. Eq.(1-3) shows that
ferrous iron released from the reaction of Eq.(1-2) is oxidized to ferric ion by oxygen and the
generated ferric ion can further oxidize pyrite and thus produce more ferrous ion (Eq.(1-4)).
Hence, reactions described in Eq. (1-3) and Eq.(1-4) form the propagation process in acid mine
drainage. In the reaction of Eq.(1-5), ferric ion hydrolyses and precipitates as ferric hydroxide
when the pH is greater than about 3.
2Feπ +7π +2π» π β 2πΉπ2++4ππ 2β+4π»+ (1-2)
2 2 2 4
4πΉπ2++π +4π»+ β 4πΉπ3+ +2π» π (1-3)
2 2
Feπ +14πΉπ3++8π» π β 15πΉπ2++2ππ 2β+16π»+ (1-4)
2 2 4
πΉπ3++3π» π β πΉπ(ππ») +3π»+ (1-5)
2 3
This reaction sequence accounts for the observed aqueous oxidation products including
ferrous ion, ferric ion and sulphate. However, other oxidation products have also been
identified during the oxidation process. Lowson (1982) reported thiosulphate (π π2β),
2 3 |
ADE | ~ 5 ~
sulphite (ππ2β) and elemental sulphur (π0) in the aqueous oxidation of pyrite. Hiskey and
3
Shlitt (1982) pointed out that, depending on the exact reaction conditions, intermediates such
as thiosulphate, sulphite, dithionate and dithionite may also be formed in the overall reaction
of pyrite decomposition. On a pyrite surface, Nicholson et al. (1990) identified a ferric oxide
layer after oxidation in a carbonate-buffered solution. Mycroft et al. (1990) conducted
experiments for electrochemical oxidation of pyrite, where polysulphide and elemental
sulphur were detected. Karthe et al. (1993) investigated the pyrite surface after 30 minutes
of oxidation in solution over a pH range of 4 to 10 and found that iron hydroxy-oxide was
formed on the pyrite surface. Bonnissel-Gissinger et al. (1998) and Todd et al. (2003) also
studied pyrite surface oxidation in solution over a wide pH range of 2.5 - 12 and 2-10
respectively. The former found that when pH<4, O-H group, iron-deficient composition and
Fe (hydr)oxide presented on the pyrite surface with ferrous ion and sulphate released in
solution, while at higher pH, ferrous ion disappeared and the surface was covered by Fe
(hydr)oxide. However, Todd et al. (2003) found that ferric (hydroxy) sulphate is the main
product on the pyrite surface under acidic and neutral conditions and, when pH>4, Fe oxy-
hydroxide starts to occur. Under the most alkaline conditions, goethite and FeOOH were
formed which completely covered the pyrite surface.
Bailey and Peters (1976) suggested an overall stoichiometry for pyrite oxidation that includes
the formation of both sulphate and elemental sulphur, shown in Eq.(1-6), where the amount
of produced ferric iron and sulphate are represented by the undetermined parameters x and
y respectively.
Feπ +(0.5+1.5π¦+0.25π₯)π +(π¦β1β0.5π₯)π» π
2 2 2
β (1βπ₯)πΉπ2++π₯πΉπ3++π¦ππ 42β+(2βπ¦)π+(2π¦βπ₯ (1-6)
β2)π»+
In their analysis of the reaction mechanism of aqueous pyrite oxidation, Rimstidt and Vaughan
(2003) suggested that the formation of the final S-product depends on pH with nearly 100%
sulphate formation in low pH environments and substantial amounts of thiosulphate and
other S-products in high pH environments. Nevertheless, for simplification, the stoichiometry
of Eq. (1-2) for pyrite oxidation with oxygen and water as the primary reactants has often
been used in calculations and modelling of the reaction kinetics of pyrite oxidation.
The reaction sequence shown in Eq.(1-2) to Eq.(1-4) also suggests that both oxygen and ferric
ion are oxidants in pyrite oxidation. Assuming that ferric ion can only be produced via
oxygenation of Fe2+ (Eq.(1-3)), which is mostly true in natural systems, pyrite oxidation by Fe3+
(Eq.(1-3) and Eq.(1-4)) is stoichiometrically equivalent to pyrite oxidation by O (Eq.(1-2)). In
2
other words, pyrite oxidation always corresponds to the consumption of oxygen, irrespective
of whether pyrite is directly oxidised by oxygen or by ferric ion. Considering oxygen as the
ultimate oxidant and ferric ion as an intermediate one, the reactions in Eq.(1-2) to Eq.(1-4)
represent two reaction pathways for pyrite dissolution. The first is a direct pathway where
pyrite is directly oxidised by molecular oxygen as shown in Eq.(1-2) and the other is an indirect
pathway where pyrite is indirectly oxidised by oxygen via Fe2+/ Fe3+ cycle (Eq.(1-3) and |
ADE | ~ 6 ~
Eq.(1-4)). For the indirect pathway, the intermediate ferric ion is subject to loss due to
hydrolysis (Eq.(1-5)) when the pH is greater than about 3. The hydrolysis of ferric ion
corresponds to extra consumption of oxygen in the overall system in addition to pyrite
oxidation.
For the prediction of the level of pyrite oxidation, it is important to understand the overall
kinetics of pyrite oxidation under natural conditions, which depends on the kinetics of each
reaction pathway and their relative roles during the reaction. The roles of oxygen and ferric
ion in pyrite oxidation have been discussed in many studies. Singer and Stumm (1970) and
Moses et al. (1987) suggested that ferric ion, not oxygen, is the dominant oxidant that oxidises
pyrite directly. This was inferred from their findings that the oxidation by ferric ion alone
(Eq.(1-4)) is much faster than the oxidation by molecular oxygen (Eq.(1-2)). Moses and
Herman (1991) observed dramatic loss of ferrous ion in solution that cannot be explained only
by the oxidation of ferrous ion. They attributed this significant loss to the adsorption of
ferrous ion on the pyrite surface and noted that the adsorption of ferrous ion is preferred to
that of ferric ion. This adsorption of ferrous ion blocks the direct attack of both dissolved
oxygen (DO) and ferric ion on the pyrite surface. As a consequence, DO cannot oxidise pyrite
directly and the rate of pyrite oxidation is limited by the rate at which the adsorbed ferrous
ion can be oxidised by DO. Based on these findings, Moses and Herman (1991) suggested that
the oxidation of pyrite is predominantly via the indirect pathway through the Fe2+/Fe3+ cycle.
This model was extended in Eggleston et al. (1996) as part of the reaction mechanism
proposed for atmospheric oxidation of pyrite surfaces.
On the contrary, Williamson and Rimstidt (1994) argued that the oxidation by ferric ion
produced from the oxygenation of ferrous iron is not significant at pH = 2. This was based on
the observation in Smith (1970) that the oxidation rate with ferrous ion removed (using an
externally cycled batch reactor where amberlite cation exchange resins were placed in-line)
was the same. In addition, McKibben and Barnes (1986), in their kinetic study of pyrite
oxidation with oxygen, show that the oxidation rate does not depend on pH values when it is
in the range of 2-4, indicating that the variation of ferric ion concentration in solution, due to
solubility change with pH, does not affect the oxidation rate. Williamson et al. (2006) provided
a quantitative comparison of iron transformation rates in these reactions in the context of
AMD and concluded that the oxidation of pyrite (by either oxygen or ferric iron), rather than
the oxidation of ferrous iron, is the rate-determining step in both the initiating stage and the
propagation of AMD.
Under abiotic conditions, the rate of ferric ion regeneration is slow, hence the ferric ion
concentration in solution is in a range that is insignificant for the surface oxidation of pyrite.
In this case, as discussed in Williamson et al. (2006), the pyrite oxidation rate is predominantly
determined by the DO concentration. However, under microbial conditions, the rate of ferric
ion regeneration from ferrous ion oxygenation can be significantly boosted by bacteria
catalysis. Hence, the overall rate of pyrite oxidation is controlled not only by oxygen
concentration, but also by the microbial condition. Further discussion on the effect of bacteria
can be found in Section 1.3.5. |
ADE | ~ 7 ~
1.2.3 Kinetics and reaction rate formula for pyrite oxidation with oxygen
Empirical reaction rate formulas for pyrite oxidation with dissolved oxygen have been derived
by McKibben and Barnes (1986) and Williamson and Rimstidt (1994). In McKibben and Barnes
(1986), the rate formula was derived for the aqueous oxidation of pyrite by dissolved oxygen
at 30Β°C and low pH values of 2β4. Their regression analysis of the initial oxidation rates
measured under two oxygen partial pressures (0.21 atm and 1 atm) showed that the reaction
rate is of the order of 0.5 with respect to DO concentration. The pH dependency was also
examined, and the results show that the oxidation rate is independent of pH over the range
of 2 β 4. Eq.(1-7) was obtained based on their analysis in which the unit of the oxidation rate
is in moles-pyrite cm-2 min-1.
π
= β10β9.77π0.5
π π,π 2 π2
(1-7)
Note: the original equation for the rate of oxidation with DO in McKibben and
Barnes (1986) has a coefficient of 10-6.77, which does not match the reaction rate
data or the stated rate unit of moles pyrite cm-2.min-1. The rate formula cited
here is corrected according to the original rate data published in their paper.
Williamson and Rimstidt (1994) compiled the rate data in Smith (1970), McKibben and Barnes
(1986), Nicholson et al. (1988) and Moses and Herman (1991), and derived a rate formula for
pyrite oxidation with DO. Their derived rate formula is applicable over the pH range of 2β10
and DO concentration of 10-6 β 10-1 molar. The rate of pyrite destruction (molΒ·m-2Β·s-1) is
determined as:
0.5(Β±00.04)
π
π = 10β8.19(Β±0.1) π·π
(1-8)
0.11(Β±0.01)
π
π»+
Similar to the rate formula derived in McKibben and Barnes (1986), the rate of pyrite oxidation
with DO was also found to be a half order with respect to DO concentration. But over the pH
range of 2β10, the oxidation rate is pH-dependent with negative fractional order with respect
to H+ concentration.
In addition to the empirical rate formulas mentioned above, theoretical rate formulas have
also been derived based on the proposed reaction mechanisms for pyrite oxidation in several
published studies. Table 1-1 lists some of the theoretical rate formulas proposed for pyrite
oxidation with DO. These theoretical rate equations were designed to capture the reaction
mechanism rather than to capture the apparent reaction rate, hence the coefficients in these
equations were rarely measured. Since the detailed reaction mechanisms of pyrite oxidation
are of less concern for the research problem in this work, these studies are not reviewed in
detail. Readers interested in this specific research topic are referred to the review papers by
Murphy and Strongin (2009) and Chandra and Gerson (2010). |
ADE | ~ 8 ~
Table 1-1: Theoretical rate equations derived for pyrite oxidation with dissolved oxygen
Reaction mechanism/
Theoretical rate equation
Reference
rate-determining step
Mathews and Robins ππΉππ πΎ [π ]0.5 Adsorption isotherm of
2 = πΎπ΄ 2 π2
(1974) ππ‘ 1+πΎ [π ]0.5 oxygen on pyrite surface
2 π2
Bailey and Peters ππΉππ π πΎ π
πππ[ 2] = πΎ + πππβ‘[ 2 π2 ] Electrochemical control
1
(1976) ππ‘ π +π 1+πΎ π
π π 3 π2
Holmes and π [π»+]β0.18 π [π ]
π = πΉππ2 ( π2 2 )1/2 Electrochemical control
Crundwell (2000) πΉππ 2 14πΉ π
πΉππ2
Effects of other factors on the pyrite reaction rate
1.3.1 Effect of temperature
The temperature dependence of the reaction rate can be generally described by the
Arrhenius equation:
π = π΄πβ
π
πΈ
π π (1-9)
where π is the reaction rate constant, πΈ is the activation energy of the reaction, π
is the gas
π
constant, π is the absolute temperature and π΄ is the pre-exponential factor.
The measured activation energy πΈ for pyrite oxidation published in the literature varies
π
significantly. Smith (1970) measured the rate of aqueous pyrite oxidation under temperatures
from 25Β°C to 45Β°C and an πΈ of 64 KJΒ·mol-1 was obtained. In the experiment described in
π
McKibben and Barnes (1986), the activation energy for the temperature range of 20Β°C to 40Β°C
was determined to be 56.9 KJΒ·mol-1. Nicholson et al. (1988) determined an activation energy
of 88 KJΒ·mol-1 for the temperature range of 3Β°C to 25Β°C. At 60Β°C, however, the magnitude of
the reaction rate is less than expected based on this activation energy, suggesting a much
smaller activation energy near a temperature of 60Β°C. Schoonen et al. (2000) measured the
activation energy of pyrite oxidation for the pH range of 2 to 6 by increasing the temperature
in steps from 23Β°C to 46.3Β°C during reactions. They found that the activation energies depend
on the pH value and can vary as much as 40 KJΒ·mol-1 with different reaction progress variables.
The averaged activation energy over the pH range was found to be from 50 to 64 KJΒ·mol-1,
depending on the reaction progress variable, which is in good agreement with previous
studies. In ChiriΘΔ and Schlegel (2017), the activation energy for pyrite oxidation was
measured for the pH range of 1 to 5 with the temperature range of 25Β°C to 40Β°C and the
reported πΈ varied from 19.1 to 56.8 KJΒ·mol-1.
π
Nicholson et al. (1988) suggested that the variation in the measured activation energy at
different temperatures is due to a change of the relative controlling mechanism from surface
reaction to oxygen diffusion as temperature increases. In their experiments of pyrite |
ADE | ~ 9 ~
oxidation in carbonate-buffered solution, an oxidised layer was formed on the pyrite surface
and oxygen diffusion through the oxidised layer was a part of the reaction process. Both the
surface reaction and the diffusion of O through the oxidised layer can be affected by
2
temperature. The apparent activation energy is more of a reflection of the controlling process
which gradually changes from the surface reaction to the oxygen diffusion as temperature
increases. As discussed in Nicholson et al. (1988), oxygen diffusion has a much smaller
activation energy than that of the surface reaction, hence at the high temperature of 60Β°C,
the apparent activation energy decreases. Lasaga (1984) suggested that the diffusion-
controlled reaction would have an activation energy close to 20 kJΒ·mol-1.
1.3.2 Effect of water content
The rate of pyrite oxidation can be very different under different water conditions. Smith
(1970) conducted a series of experiments to observe the rate of pyrite oxidation in both the
liquid phase and the vapour phase at different relative humidity. It was found that the rate of
pyrite oxidation in the vapour phase increases with relative humidity and this increase can be
accelerated by raising the reaction temperature. A comparison of the overall rates under 100%
relative humidity and under liquid conditions (100% water saturation) shows that the rate of
pyrite oxidation is slightly faster in the latter condition. The same conclusion can be drawn by
comparing the rate of pyrite oxidation in moist air (Jerz and Rimstidt (2004) with that in
solution (e.g., Nicholson et al. (1990); Williamson and Rimstidt (1994)). However, rates
measured in the initial reaction stage (a few minutes into the reaction) display the opposite
trend as can be seen in Jerz and Rimstidt (2004).
LeΓ³n et al. (2004) studied the effect of water saturation on the rate of pyrite oxidation. The
results show that the rate increases as water saturation decreases from 95% to 25%. The
highest reaction rate is at 25% while the reaction rate is lowest at 0.1% (sample was placed in
a desiccator). Field observations of pyritic mine tailings in Elberling et al. (2000) also show
that the oxidation rate of pyrite is much faster in well-drained sites than that in wet sites.
Overall, the highest oxidation rate is achieved under partially saturated conditions followed
by the reaction rate in the fully saturated condition. The reaction rate in moist air is slightly
slower than that in the fully saturated condition and decreases further as air humidity
decreases. The reaction rate in the dry state (e.g. in a desiccator) is the lowest.
1.3.3 Effect of impurities
Lehner et al. (2007) studied the effect of impurities on the rate of pyrite oxidation using an
electrochemical approach. Natural arsenian pyrite and synthetic pyrite doped with As, Co or
Ni and undoped pyrite were investigated in the study. It was found that pyrite with As is more
reactive than pyrite with other impurity types while pyrite containing no impurities is least
reactive. In addition, the electric current density increases when As concentration increases,
indicating that the rate of pyrite oxidation increases with increasing As concentration.
Blanchard et al. (2007) conducted a Density Functional Theory (DFT) study on arsenic
incorporation into FeS and suggested that the presence of arsenic accelerates pyrite
2
dissolution. |
ADE | ~ 10 ~
Lehner and Savage (2008) conducted mixed flow and batch experiments to measure the
oxidation rate of pyrite synthesized with different impurities at different concentrations. The
results show that, statistically, pyrite with impurities has higher reactivity. However, Lehner
and Savage (2008) suggested that, in environmental modelling applications, the effect of
impurities on pyrite oxidation is probably less significant compared with the effects of other
influencing factors.
1.3.4 Effect of specific surface area
Pyrite samples from various sources may have different morphologies and hence the specific
surface area may vary significantly even for similar particle size distributions. Consequently,
the reaction rate measured for various samples will differ from one to another. For example,
Pugh et al. (1984) found that the reaction rate of framboidal pyrite is much faster than that
of massive pyrite because the specific surface area of the former is approximately ten times
larger than that of the latter. They also found that the relationship between the reaction rate
of different samples and their specific surface area (m2.g-1) is approximately linear. Nicholson
et al. (1990) studied the relationship between the rate of pyrite oxidation (per mass sample)
and particle size, and suggested that, at early reaction times, the reaction rate is linearly
proportional to the inverse grain diameter and, at later reaction times, is linearly proportional
to the square of the inverse grain diameter.
In many published studies, the reaction rate was reported not as the reaction rate per mass
sample, but as the reaction rate per surface area, referred to as the surface reaction rate. This
is the rate used in this work when referring the pyrite oxidation rate as applied in the
discussions and formulas listed in Section 1.2.1 and Section 1.2.3. For measurement, the
surface reaction rate is obtained by dividing the reaction rate measured per mass sample by
the specific surface area. Thus, discrepancies are expected among the surface reaction rates
derived in different studies where the surface area was obtained using different methods.
In some studies, the surface area was measured using the BET (Brunauer, Emmett and Teller)
method, which includes the pore size distribution and is based on the physical adsorption of
gas molecules on solid surfaces. In other studies, the specific surface area was calculated from
particle size, by multiplying the number of particles per gram of sample by the spherical area
of a single particle, as shown in Eq. (1-10) (Nicholson et al., 1988):
6
π΄ =
π ππ (1-10)
where A is the specific surface area per unit mass of sample, π is the mass density and π is
s
the particle diameter. This method assumes that the spherical particles have smooth surfaces
whereas the BET method takes the micro-morphology of the surface into consideration.
These different approaches yield results that usually differ by a factor of two to four, and in
some cases, the BET measured surface area can be up to 20 times larger than the calculated
surface area for the same pyrite sample. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.