Lightweight Aggregate Concrete (LAC)
Chapter 1: Introduction
Aggregate and cement concrete drama a critical function in the civil technology where the building of constructions both for domestic and commercial intent is dependent upon the quality and scientific features of the concrete used as argued by Leif Berntsson Satish Chandra ( 2002 ) [ 1 ] . This is apparent from the fact that concrete is used in many applications apart from structural applications including insularity, make fulling etc…
In this study a critical analysis on the lightweight sum concrete ( LAC ) is presented to the reader. The research will supply a comprehensive penetration on the scientific facets environing LAC and the demand for utilizing LAC in structural applications.
1.2: Purpose and Aims
The purpose of this study is to show a critical analysis on the Lightweight Aggregate Concrete ( LAC ) and research on its structural applications and farther developments.
The above purpose is achieved by encompassing the study on the undermentioned aims
- To carry on a comprehensive overview on the Lightweight Aggregate Concrete ( LAC ) by supplying the history, definitions and economic factors environing the applications and usage of LAC in civil constructions.
- To supply a critical overview on the production of cement and its belongingss in the visible radiation of LAC and its application in civil constructions.
- To show a scientific analysis on the belongingss of LAC utilizing different composing stuffs including both the mechanical and chemical belongingss.
- To look into on the ordinances refering to LAC and their effects on a specific composing of LAC in a given geographical part.
- To look into on the LAC production and usage in Greece.
1.3: Research Scope
The presence of concrete in civil technology is thorough in nature and therefore the research range is limited to the composing of the LAC and its application in civil construction applications. The cardinal facets of the LAC and its industry in Greece is besides included in the range of the research although a planetary research on the LAC industry and ordinances refering to LAC is out of range of this undertaking.
The research range besides includes the probe of the general ordinances adhered in the Europe including the ACI-318 and design considerations in the visible radiation of Seismic Design.
1.4: Research methodological analysis
The nature of the research is dependent on the analysis and findings environing the LAC which is used in civil constructions. Since constructing a civil construction is non portion of the undertaking due to be and resource restraints, the research methodological analysis is strictly dependent on qualitative analysis utilizing secondary research informations. The qualitative attack to research in instances of the technology analysis is advised as a dependable attack as the findings from the research on the secondary resources are already published therefore supplying a validated beginning of information for analysis. This is farther justified by John W. Creswell ( 2002 ) [ 2 ] .
Hence the research methodological analysis in this study is qualitative research utilizing published resources including diaries, text books and scientific documents. The Internet is used as the chief hunt infinite for roll uping information to execute the qualitative analysis.
1.5: Chapter Overview
Chapter 1: Introduction
This is the current chapter where the reader is provided with a brief debut on the subject, research purpose and aims, range and methodological analysis. The chapter sets the phase for the overall research presented in the study.
Chapter 2: Literature Reappraisal
In this chapter a historic overview on the concrete and the usage of Lightweight Aggregate Concrete ( LAC ) is presented to the reader. This is so followed by the definition of the LAC and its application in the civil structural applications from a historic position. The chapter is concluded with an overview on the economic factors and benefits realised through the usage of the LAC in the civil construction applications with illustrations. The economic overview besides throws visible radiation on the cardinal facets of LAC that benefit the overall concrete composing in structural applications every bit good as supply a elaborate reappraisal of the assorted LAC composings used in the yesteryear during the initial phases of LAC’s usage in the building industry.
Chapter 3: Concrete Production
This chapter presents a elaborate overview on the modern concrete production techniques and the development of the production techniques over the old ages.
The two popular techniques used in the production viz. the rotary kiln and the sintering procedure with penetration on the fluctuations is presented to the reader in this chapter. Furthermore, the lightweight sum production and the cardinal production methods used in the commercial applications including the advantages associated are presented to the reader.
Chapter 4: LAC – Properties, Regulations and composing analysis based on geographics.
This chapter presents a critical analysis on the belongingss of LAC and the assorted combination of lightweight sum that is used in different classs of the building. The research throws visible radiation on the assorted composings of lightweight sum and their distinguishable characteristics that help accomplish the coveted benefits in a structural application. The chapter so presents a critical overview on the ordinances refering to the LAC followed by the composing analysis based on the stuffs that are available locally to a given geographical location. The chosen geographics for this research is Greece.
Chapter 5: Decision
This chapter reviews the aims of the research followed by supplying the decision to the study.
Chapter 2: Literature Reappraisal
2.1: Historical overview
Concrete, typically a mixture of sand, crushed rock and cement day of the months back to ancient history when ruddy calcium hydroxide was used as a cementing constituent in doing concrete ( Leif Berntsson Satish Chandra, 2002 ) . This makes it clear that the current mixtures of concrete have evolved over the historic periods to provide assorted technology demands with the developments in scientific discipline and the inventions in technology as argued by Leif Berntsson Satish Chandra ( 2002 ) . A classical illustration for the development of concrete since the ancient history is the usage of concrete by Romans in 300 BC when they found that blending a pink sand-like stuff which was volcanic ash they obtained from Pozzuoli with their normal lime-based concretes resulted in a far stronger stuff.
The history behind the usage of sum to do concrete mix day of the months back to every bit early as the early the Roman period when the Romans used advanced methods in fixing concrete mixes with different sum stuffs to accommodate the structural demands and strength. The classical illustrations for the above statement include the usage of lightweight sums as in the roof of the Pantheon, and embedded support in the signifier of bronze bars as argued by Leif Berntsson Satish Chandra ( 2002 ) . The engineering in concrete utilizing different sums every bit good as accounting for thermic and other physical qualities of re-enforcing stuffs to do concrete mixes that provide the coveted strength is apparent throughout history although the industrial revolution and the addition in the technology and the function of steel in the 20Thursdaycentury have increased the invention every bit good as developments around the engineering of doing the right concrete mix.
Concrete is non merely a critical component in the civil structural applications but besides a cardinal component in many other applications environing the building concern doing it one of the of import and most sought after merchandise in the technology concern itself as argued by Fu-Tung Cheng and Eric Olsen ( 2002 ) [ 3 ] . This is of course because of the fact that concrete is non merely a constituent in the building of civil constructions but besides a design ingredient in make up one’s minding upon the strength, truss and other physical elements that govern the stableness of a given edifice. This is besides justified in the statements of Leif Berntsson Satish Chandra ( 2002 ) .
The definition of cement in technology footings refers to pulverize stuffs which develop strong adhesive qualities when combined with H2O. This makes it clear that the cementing action of volcanic ash that was used to do concrete by the Romans autumn under the cement. It is farther apparent that concrete is referred to as a composite edifice stuff made from the combination of sum and cement binder.
From the above it is clear that the developments in the quality of cement and the innovation of Portland cement, gypsum plaster, etc… have a direct influence on the development of the concrete engineering although the aggregative constituent of the concrete composing plays an every bit of import function in assorted mixes of concrete that serve a coveted intent as argued by Leif Berntsson Satish Chandra ( 2002 ) .
Another component of greater significance to the development of concrete engineering in the recent old ages every bit early as the 1900s is the development of concrete boats during the 2nd universe war where the lightweight sum concrete played a critical function in the design and building of the ships itself as argued by Glenn A. Black ( 2004 ) [ 4 ] . It is besides interesting to observe that the importance of concrete has increased with the demand for refined and purpose specific concrete mixes where the function of concrete has been non merely to supply the structural support but besides the coveted strength at the needed physical conditions that is set in the given geographical location as argued by Glenn A. Black ( 2002 ) . The growing of the expanded clay and shale industry since the morning of the 20Thursdaycentury and the developments during the Second World War when the lightweight sum concrete utilizing clay and shale was used to build the war ships marked the accelerated growing of the usage of lightweight aggregative concrete as argued by Glenn A. Black ( 2004 ) .
2.2: Definition of lightweight sum
In order to specify the lightweight sum – the subject under research in this thesis, it is indispensable to show the basicss environing the lightweight sum. Hence this subdivision foremost presents a brief research on sum, its function in building as portion of the concrete mix and so travel towards the nucleus subject ( i.e. ) the definition of lightweight sum.
Aggregate is the footings used to jointly mention to the ingredients in doing a concrete mix that gives strength and texture to the overall concrete composing made of sand, cement and sum as argued by Glenn A. Black ( 2004 ) . Aggregate is the composite stuff of the concrete that is aimed to defy compressive emphasis doing it clear that the size, strength and weight of the aggregative stuffs are critical constituents for the overall efficiency of the concrete to pull off the compressive emphasis as argued by Glenn A. Black ( 2004 ) .
The modern twenty-four hours concrete utilizations Portland cement as the cementing component and the sum that is held together by the cement and H2O to plan concrete for different grades of strengths, lastingness, heat & A ; sound insularity, and H2O stringency as argued by Glenn A. Black ( 2004 ) . This makes it clear that the sum is the critical constituent of the concrete that attributes to observe merely the strength and quality of the concrete but besides dictates the nature of the applications and the extent to which invention in technology can be taken to. The cardinal physical quality of the sum is the compressive strength that it can back up for a given composing.
The lightweight sums that are researched in this study typically attribute to up to 80 lbs per square inch which is used chiefly applications that demand lightweight concrete by virtuousness of the placement or for the support, insularity etc. specific gravitation is another critical component in depicting the quality of sum as the specific gravitation off the substance is straight relative to its emphasis and squeezability factors as argued by Glenn A. Black ( 2004 ) . A typical combination and most popular in the building industry for the sum is the crushed rock and sand mix at different sizes and squeezability that are used in high demand building structural applications as argued by Glenn A. Black.
Hence sum in concrete is defined as the constituent of concrete that attributes to the strength, lastingness, squeezability and insularity properties to back up the coveted building application.
Glenn A. Black ( 2004 ) says “The term “ Lightweight Aggregate ” describes a scope of particular usage sums that have an evident specific gravitation well below normal sand and crushed rock which were at one clip used in about all concrete” .
From the above it is clear that the lightweight sum is one of the critical elements that makes concrete flexible and various to do the overall structural design and specifications as to run into the building demands as argued by Leif Berntsson Satish Chandra ( 2002 ) . It is besides interesting to observe that the lightweight sum in the concrete that is made utilizing light weight stuffs besides provide an appreciable degree of squeezability every bit good as possess strength that can be defined based on the composing therefore doing it a versatile and cost effectual procedure in the production procedure itself.
The scope of lightweight sum is extended in nature from highly light stuffs used for insularity and non-structural concrete all the manner to expanded clays and shales used for structural concrete. This makes it clear that the lightweight sum in the concrete is chiefly aimed to accomplish high degree of physical stableness and squeezability through efficaciously using the physical qualities of the aggregative stuffs. This is farther justified in the statements of Leif Berntsson Satish Chandra ( 2002 ) who argues that the lightweight sum in the concrete is a major measure towards invention in the field of technology itself.
The strength and the air trapped in each single atom of the constituents of the aggregative stuffs are reciprocally relative to each other therefore doing it clear that in order to derive lightweight aggregate the sum of air trapped in the single atoms must be high therefore doing it clear that the strength of the concrete therefore obtained is low. The above relationship stated provides the counsel to guarantee the balance between the air trapped and the strength required in the concrete mix therefore doing the overall lightweight sum concrete customisable to run into the structural demands of the application on manus.
Lightweight Aggregate Concrete Spectrum
The concrete spectrum ensuing from the usage of the lightweight sum is highly diverse in nature runing from really lightweight sum concrete up to high strength sums dedicated for specific bespoke applications as argued by Glenn A. Black ( 2004 ) .
The ace lightweights scope of aggregative concrete that are derived from Vermiculite and Perlite are the capable of presenting weights every bit low as 15 to 20 lbs per three-dimensional pes therefore doing it clear the application of lightweight sums in the technology concern provides a diverse scope of applications for concrete.
The natural sums, Pumice and Scoria for illustration can be used to do concrete deliberation at approximately 25 to 30 lbs per three-dimensional pes and extended every bit high as 65 lbs per three-dimensional pes as argued by Glenn A. Black ( 2004 ) . Furthermore, the usage of coal clinkers and expanded shale, clay and slate sums produced utilizing rotary kiln method can present weights in a varying scope from 75 to 120 lbs per three-dimensional pes.
Another popular production method for this scope of sums includes the sintering where the weights are delivered typically runing from 90 to 120 lbs per three-dimensional pes.
The high terminal applications of aggregative concrete include the production of sums capable of presenting weights up to 150 lbs per three-dimensional pes utilizing the air-cooled scoria sums and the hard-rock sums such as sand and crushed rock and crushed rock, which produce conventional concretes as mentioned by Glenn A. Black ( 2004 ) .
From the above it is clear that the sums that lie in the lower terminal of the weight that have lower compressive strength are used chiefly for insularity intents whilst those in the in-between spectrum are used for insularity and filling. The high terminal of the lightweight sum concrete spectrum are used in a broad scope of structural applications that demand high compressive strengths every bit good as efficient direction of weight as argued by Glenn A. Black. The concrete spectrum for the lightweight sum concrete is presented in the figure below
Fig 1: Lightweight Aggregate Concrete Spectrum
( Beginning: Glenn A. Black ( 2004 ) ,Lightweight Concrete history, Applications and Economics,Indiana University )
2.3: Economicss environing lightweight Aggregate Concrete
The cardinal facets of Lightweight Aggregate Concrete that attribute to the economical and structural benefits derived through the structural applications utilizing LAC include the undermentioned
2.3.1:Fire opposition– Resistance to fire is one of the critical elements that is expected in concrete to guarantee that the fire opposition and the structural stableness of the civil construction is maintained through the usage of aggregative concrete as argued by John P. Ries and Thomas A. Holm ( 2006 ) [ 5 ] . The fire opposition of lightweight sum is higher compared to the typical concrete sum chiefly because of the fact that the aggregative stuffs composing the lightweight sum have lower thermic conduction, lower coefficient of thermic enlargement as argued by John P. Ries and Thomas A. Holm ( 2006 ) . The fact that the aggregative stuffs possess built-in fire resistant belongingss is the cardinal component that is emphasised and strengthened in instance of the lightweight aggregates where the aforesaid heat opposition belongingss help accomplish higher fire opposition. It is besides interesting to observe that the built-in fire stableness of sum is high and in instance of the lightweight sum it is at a heat of over 2000 grades Fahrenheit.
As it is stated in the “ACI 216 “ Standard Method for Determining fire Resistance of
Concrete and Masonry Construction Assemblies ” , when slab thickness is determined by fire opposition and non by structural standards ( Goists, waffle slabs e.g. ) , the superior public presentation of lightweight concrete, will cut down the thickness of slabs ensuing in significantly lower concrete volumes” , ( John P. Ries and Thomas A. Holm, 2006 ) .
From the above it is clear that the fire opposition belongingss of the lightweight sum straight contributes to the overall structural stableness and the decrease in the volume occupied by the concrete in the structural applications. This justifies the various nature of the lightweight sum therefore enabling it to be used in advanced structural applications as argued by John P. Ries and Thomas A. Holm ( 2006 ) .
2.3.2: Service Life of the Structure– The service life of the construction is another critical component that is used as step of economic usage in instance of measuring the concrete and the aggregative efficiency against the capital invested as argued by John P. Ries and Thomas A. Holm ( 2006 ) . Glenn A. Black ( 2004 ) further provinces that the lastingness of lightweight sum is high and the life of the constructions constructed utilizing lightweight sum prove to hold higher life lastingness. The historical grounds to warrant the aforesaid include popular constructions likeThe Port of Cosa –built about 273 B.C. where the builders used lightweight concrete made out of natural volcanic stuffs,The Pantheonthat was finished in 27 B.C that incorporates concrete changing in denseness from underside to exceed of the dome and the most popular Amphitheater, built in 75 to 80 A.D. where the foundations were cast as lightweight concrete utilizing crushed volcanic lava as argued by John P. Ries and Thomas A. Holm ( 2006 ) . From the above statements it is apparent that the lastingness of the constructions designed utilizing the lightweight concrete is extended in nature.
Looking into the more modern illustrations to warrant the service life of the lightweight sum used in concrete for building include the lightweight concrete ships built by the American Emergency Fleet Corporation during the First World War. The compressive strengths of the concrete used were in the scope of 5000 pounds per square inch ( 35 MPa ) obtaining a unit weight of 110 lb/ftJ ( 1760 kg/mJ ) or less utilizing the rotary kiln produced expanded shale and clay sum as identified by John P. Ries and Thomas A. Holm ( 2006 ) . The service of these lightweight concrete boats during the universe wars and their subsequent in the merchandiser ships warrant the lastingness and service life of the lightweight sum used in concrete building applications. Furthermore, the fact that the higher degree of air trapped in the atoms make the submergence efficient in instance of the marine applications makes lightweight sum as a natural pick for the Marine applications although the usage of lightweight concrete extends to commercial structural applications in many Bridgess across the United States of America where the structural efficiency and stableness on Bridgess that were deemed unserviceable due to hapless burden bearing capablenesss was improved through the usage of lightweight aggregative concrete as argued by John P. Ries and Thomas A. Holm ( 2006 ) . Furthermore, the critical component that attributes to the service life of the lightweight concrete is the heat opposition, opposition to environmental corrosion and its lightweight that reduces the burden on the construction doing its service life longer than the typical concrete applications.
2.3.3: Economic sustainability
John P. Ries and Thomas A. Holm ( 2006 ) argue that the structural applications in the modern yearss are judged against the cost, functionality, aesthetics or a combination of these as argued by John P. Ries and Thomas A. Holm ( 2006 ) . This makes it clear that the costs associated with the building of the construction every bit good as the running costs associated with care, infinite and fix are the critical elements that attribute to the pick of a given concrete mix over another. The lightweight sum that is used in the LAC is higher in costs compared to the typical concrete mix as argued by John P. Ries and Thomas A. Holm ( 2006 ) . This is of course because of the demand to bring forth the concrete mix utilizing stuffs of alone physical belongingss and the extent of research and development involved with the overall design of the building application. Alongside, the cost is treated as the cardinal component in instance of commercial execution of building applications preponderantly because of the fact that the step on the returns in footings of return on investing is attributable when compared against the costs associated with the building of the construction.
John P. Ries and Thomas A. Holm ( 2006 ) say that although the capital involved with the building of lightweight constructions is high, the fact that the low care costs and costs associated with other back uping constructions during the buildings like the decrease in steel, girders and besides the decrease in the slab thickness will equilibrate the costs with the production of the LAC concrete mix itself. This farther justifies that the economic sustainability where the return on the investing and the optimal pick for building is accomplishable utilizing lightweight sum as argued by John P. Ries and Thomas A. Holm ( 2006 )
The statements of Glenn A. Black ( 2004 ) that the lightweight sum besides has the benefit of lower degree of care and negligible fixs associated due to its lastingness features farther justify that the effectivity of the lightweight sum in accomplishing economic sustainability is high. Hence the lightweight sum is extremely recommended in the building of critical structural applications like Bridgess and commercial edifice where the burden bearing is high and the infinite is a critical component to salvage costs.
2.3.3: Energy ingestion and energy nest eggs– The Energy Performance of Buildings Directive of the European Union is a classical illustration for the justification that the composing of the concrete and the belongingss of the constituents consisting the construction of constructing commercial and domestic contribute straight to the overall energy ingestion as argued by John P. Ries and Thomas A. Holm ( 2006 ) . This is farther justified in the statements of Sarah Gaventa ( 2006 ) [ 6 ] where the writer has justified that the concrete mix and the design of the overall construction to accommodate the structural demands have a direct impact on the energy ingestion. Alongside, the heat immune belongingss of the lightweight sum and the ability to pin down higher sum of air within the atoms consisting the sum further do the lightweight sum to be able to run into the warming and chilling demands in a given construction as argued by Sarah Gaventa ( 2006 ) . It is besides interesting to observe that the energy public presentation efficiency in the edifice particularly in the West where a major part of the energy is used for heating intents justify that the concrete mix and the aggregative composing to do the concrete mix are critical for the successful energy nest eggs in the edifices as argued by Sarah Gaventa ( 2006 ) .
The lastingness, stableness and other physical belongingss including the squeezability of an aggregative stuff property to the ability of the concrete used in the edifice to retain heat therefore cut downing the ingestion of energy for interior warming intents as argued by Sarah Gaventa ( 2006 ) .
It is besides a good known fact that the decrease in the concrete denseness increases the thermic opposition therefore doing it clear that the lightweight sum will increase the thermic opposition due to the lower specific gravitation of the aggregative composing that reduces the denseness of the concrete used in the building of the construction. A typical illustration is the concrete denseness of 90lb/cubic pes will hold a opposition ( R value ) of 0.26/inch whilst the R value for a denseness of 135lb/cubic pes is about 0.10/inc therefore doing it clear the energy efficiency is greatly increased through the usage of lightweight sums as argued by John P. Ries and Thomas A. Holm ( 2006 ) .
Chapter 3: Concrete Production
The production of concrete mix utilizing the sum is achieved through the commixture of the sum, sand and cement with right sums of H2O to bring forth the concrete mix of the necessary strength. The concrete commixture is dependent upon the quality of the sum every bit good as the cement used to accomplish the coveted denseness, strength and squeezability of the concrete for the structural application. In this chapter a critical overview on the cement production followed by the production methods for lightweight sums is presented to the reader.
3.2: Cement Production
The chief ingredient for the production of cement is limestone of changing chemical composings that are freely available in the preies as argued by Sarah Gaventa ( 2006 ) . The lime rock is processed and farther chemicals are added to derive the cement of the necessary strength and squeezability. The undermentioned explains the production procedure briefly
The natural limestone of changing chemical combinations is foremost collected to fix the natural mix where the limestone is assorted with minerals of minerals incorporating Ca oxide, Si oxide, aluminum oxide, ferrous oxide, and Mg oxide. This mixture is prepared to a all right mixture which forms the natural mix for a typical Portland cement. This is so blended to organize the natural blend where the natural mix is formulated to a really tight chemical preparation to derive the coveted strength from the finished green goods of the cement as argued by Sarah Gaventa ( 2006 ) .
The natural blending procedure is conducted in a manner where the comparative content of each oxide in the chemical composing is kept changeless throughout the production procedure in order to guarantee that the belongingss of the concluding merchandise is non altered. It is besides argued by Sarah Gaventa ( 2006 ) really little alterations to the Ca content in the natural mix may take to big alterations in the ratio of alite to belite in the cinder, and to matching alterations in the cement ‘s strength-growth features ( Sarah Gaventa, 2006 ) . This makes it clear that the effectual control of the natural mix is critical for the production of consistent quality cement to run into the demands of the structural application.
The following phase is the preparation of the cinder where the blend natural mixture is put through a complex chemical reaction procedure in a big cement kiln with temperature increasing over the length of the cylinder as argued by Sarah Gaventa ( 2006 ) . The concluding merchandise of the procedure is called cinder which is the concluding merchandise of the cement produced in the solid signifier at the coveted chemical combination. This is so put through a cement crunching procedure where the cinder that is produced is assorted with little sums of Ca sulfate to crunch the cement to the desired coarseness in order to back up the structural application.
Sarah Gaventa ( 2006 ) further argues that the major constituents that decide on the strength and quality of cement include the undermentioned
- Blast Furnace Slag
The Blast Furnace Slag is one of the critical elements in lending to the stableness of the chemical reaction in the cement kiln as argued by Sarah Gaventa ( 2006 ) . Another interesting component with the blast furnace scoria is the fact that the effectual usage of the scoria in the cement production procedure besides allows to command the specific gravitation of the cement when assorted with aggregative and H2O to organize concrete every bit good as the ability to make the coveted strength of the cement concrete through the right combination of limestone and gypsum.
The schematic of the cement production procedure is presented in the fig 2 below.
Fig 2: Cement production Schematic
( Beginning: hypertext transfer protocol: //www.cimnat.com.lb/Production/Model.gif )
3.3: Sum production
The aggregative production is the following critical component in the lightweight concrete readying as the lightweight sum is one of the major elements that must be produced at a higher degree of preciseness in order to guarantee the coveted degree of strength and specific gravitation are achieved as argued by John P. Ries and Thomas A. Holm ( 2006 ) .
The rotary kiln method is a traditional method of production which is popular since 1946 as argued by Glenn A. Black ( 2004 ) . The procedure of the production involves the application of heat to shale, clay and slate under controlled conditions. The conditions include the force per unit area and other features that trigger chemical reactions in order to accomplish the preferable specific gravitation and denseness of the sum constituent which is so land to the needed coarseness as argued by Glenn A. Black ( 2004 ) .
The sintering method every bit good as the rotary kiln method typically use the similar base natural stuff that comprise of a extremely silicious clay or shale that exhibits a bloating characteristic which is achieve through gas-forming minerals which release gas on exposure to the desired degree of heat as argued by Glenn B. Black ( 2004 ) . It is besides interesting to observe that the readying of the sum is dependent upon the extent to which the force per unit area and the external temperature is controlled that set the temperature-based chemical reactions as argued by Glenn A. Black ( 2004 ) .