volume 2 issue 1 july 2013

Volume 2Issue 1July 2013

Scientific Journal of Civil Engimeering, Volume 2, Issue 1, July 2013

EDITORIAL Preface to the Second Volume, Issue 1 of the Scientific Journal of Civil Engineering (SJCE)

EDITOR – IN - CHIEF Prof. Ph.D. Darko Moslavac University Ss. Cyril and Methodius Faculty of Civil Engineering - Skopje Dear Readers,

The Scientific Journal of Civil Engineering (SJCE) was established in 2012. This effort, led by Faculty of Civil Engineering – Skopje creates opportunities for Faculty staff, postgraduate, doctoral students and all other experts which are involved in the broad field of civil engineering, to publish the results of their research activities for the general scientific and professional community.

Our goal is to improve and expand publications manifestations so that contributors with a serious interest may be included in the journal’s databases, thereby enhancing its status and recognition from the scientific community.

We would also like to address to our scientific colleagues from abroad to participate in the editorial board of the SJCE to expand the scope of the journal with assistance of our partners from abroad, especially those with which Faculty of Civil Engineering – Skopje has conducted long – term research and maintains working contacts.

The second volume includes 5 articles from the field of cartometry, transportation engineering, structural engineering, hydrology and neural networks. Two of them present original research results from doctoral thesis.

One of the greatest challenges in the coming issues will be the publications of a

special issue with a thematic section dealing with a complex matters in the field covered by the journal. I am very glad to announce the next special issue in which selection of articles from the Third Congress on Dams hold in Struga this year, will be presented.

We continue to invite all researchers, practitioners and members of the academic community to contribute through their articles to the development and maintenance of the quality of the SJCE journal. We are particularly pleased to publish the results of research, best practice, case studies, ideas for solutions of complex problems, proposals of innovations and the results of experience on important projects.

Sincerely Yours,

Prof. Ph.D. Darko Moslavac

July, 2013

Impressum

FOUNDER AND PUBLISHER

Faculty of Civil Engineering -Skopje Partizanski odredi 24, 1000 Skopje

EDITORIAL OFFICE

Faculty of Civil Engineering -Skopje Partizanski odredi 24, 1000 Skopje Rep. of Macedonia tel. +389 2 3116 066; fax. +389 2 3118 834 Email: [email protected]

EDITOR IN CHIEF

Prof. Ph.D. Darko Moslavac University Ss. Cyril and Methodius Faculty of Civil Engineering -Skopje Partizanski odredi 24, 1000 Skopje Rep. of MACEDONIA tel. +389 71 368 372; Email: [email protected]

ISSN: 1857-839X

EDITORIAL BOARD

Prof. Ph.D. Darko Moslavac University Ss. Cyril and Methodius, Rep. of Macedonia Prof. dr. sc. İbrahim Gurer Gazi University, Turkey Prof. dr Miodrag Jovanovic University of Belgrade, Rep. of Serbia Em.O.Univ.Prof. Dipl.-Ing. Dr.h.c.mult. Dr.techn. Heinz Brandl Vienna University of Technology, Austria Prof. dr. sc. Zalika Črepinšek University of Ljubljana, Slovenia Prof.dr.ir. J.C. Walraven Delft University of Technology, Netherland univ.dipl.ing.gradb. Viktor Markelj University of Maribor, Slovenia PhD, Assoc. Prof. Jakob Likar University of Ljubljana, Slovenia PhD,PE,CE Davorin KOLIC ITA Croatia Prof. dr. sc. Stjepan Lakušić University of Zagreb, Croatia Marc Morell Institut des Sciences de l’Ingénieur de Montpellier, France Prof. Ph.D. Miloš Knežević University of Montenegro Prof. Ph.D. Milorad Jovanovski University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Cvetanka Popovska University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Ljupco Lazarov University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Goran Markovski University Ss. Cyril and Methodius, Rep. of Macedonia

Prof. Ph.D. Zlatko Srbinovski University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Radojka Donceva University Ss. Cyril and Methodius, Rep. of Macedonia

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SJCE is published semiannually. All articles published in the journal have been reviewed. Edition: 200 copies SUBSCRIPTIONS Price of a single copy: for Macedonia (500 den); for abroad (10 EUR + shipping cost). BANKING DETAILS (MACEDONIA) Narodna banka na RM Account number: 160010421978815 Prihodno konto 723219 Programa 41

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Name: Gradezen fakultet Skopje

PRINT The journal is printed in Skopje by Pecatnica Goce Delcev

Impressum

FOUNDER AND PUBLISHER

Faculty of Civil Engineering -Skopje Partizanski odredi 24, 1000 Skopje

EDITORIAL OFFICE

Faculty of Civil Engineering -Skopje Partizanski odredi 24, 1000 Skopje Rep. of Macedonia tel. +389 2 3116 066; fax. +389 2 3118 834 Email: [email protected]

EDITOR IN CHIEF

Prof. Ph.D. Darko Moslavac University Ss. Cyril and Methodius Faculty of Civil Engineering -Skopje Partizanski odredi 24, 1000 Skopje Rep. of MACEDONIA tel. +389 71 368 372; Email: [email protected]

ISSN: 1857-839X

EDITORIAL BOARD

Prof. Ph.D. Darko Moslavac University Ss. Cyril and Methodius, Rep. of Macedonia Prof. dr. sc. İbrahim Gurer Gazi University, Turkey Prof. dr Miodrag Jovanovic University of Belgrade, Rep. of Serbia Em.O.Univ.Prof. Dipl.-Ing. Dr.h.c.mult. Dr.techn. Heinz Brandl Vienna University of Technology, Austria Prof. dr. sc. Zalika Črepinšek University of Ljubljana, Slovenia Prof.dr.ir. J.C. Walraven Delft University of Technology, Netherland univ.dipl.ing.gradb. Viktor Markelj University of Maribor, Slovenia PhD, Assoc. Prof. Jakob Likar University of Ljubljana, Slovenia PhD,PE,CE Davorin KOLIC ITA Croatia Prof. dr. sc. Stjepan Lakušić University of Zagreb, Croatia Marc Morell Institut des Sciences de l’Ingénieur de Montpellier, France Prof. Ph.D. Miloš Knežević University of Montenegro Prof. Ph.D. Milorad Jovanovski University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Cvetanka Popovska University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Ljupco Lazarov University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Goran Markovski University Ss. Cyril and Methodius, Rep. of Macedonia

Prof. Ph.D. Zlatko Srbinovski University Ss. Cyril and Methodius, Rep. of Macedonia Prof. Ph.D. Radojka Donceva University Ss. Cyril and Methodius, Rep. of Macedonia

ORDERING INFO

SJCE is published semiannually. All articles published in the journal have been reviewed. Edition: 200 copies SUBSCRIPTIONS Price of a single copy: for Macedonia (500 den); for abroad (10 EUR + shipping cost). BANKING DETAILS (MACEDONIA) Narodna banka na RM Account number: 160010421978815 Prihodno konto 723219 Programa 41

BANKING DETAILS (INTERNATIONAL) Corespond bank details: Deutsche Bundesbank Zentrale Address:Wilhelm Epstein strasse 14 Frankfurt am Main, Germany SWIFT BIC: MARK DE FF Bank details: National Bank of the Republic of Macedonia Address: Kompleks banki bb 1000 Skopje Macedonia SWIFT BIC:NBRM MK 2X IBAN: MK 07 1007 0100 0036 254

Name: Gradezen fakultet Skopje

PRINT The journal is printed in Skopje by Pecatnica Goce Delcev

3 | Page

content

Violeta Gjesovska Water Balance of VulneraBle HydroloGic SyStemS 7

Goran mijoski , andrej lepavcov tranSPort noiSe and meaSureS for Protection on motorWayS in tHe rePuBlic of macedonia 17

Blagoja markoski tHe metHodoloGy of tHe aPProXimatiVe diSPoSition of tHe actual Surface and Volume of tHe territory of tHe rePuBlic of macedonia 25

Silvana Petruseva neural netWorKS and tHeir aPPlication in ciVil enGineerinG. iSotHreSHold adaPtiVe netWorK (ian) 35

Sergey churilov, elena dumova-Jovanoska numerical modelinG of unreinforced and JacKeted maSonry BuildinGS 47

5 | PageSCIENTIFIC JOURNAL OF CIVIL ENGINEERING • Volume 2 • Issue 1 • July 2013

Scientific Journal of Civil Engineering • Volume 2 • Issue 1 • July 2013

Water balance model of vulnerable hydrological system 1 | P a g e

AUTHORS

Violeta Gjesovska Ph.D. Docent University Ss. Cyril and Methodius Faculty of Civil Engineering –Skopje [email protected]

Water Balance of Vulnerable Hydrologic Systems

Hydrologic systems, especially those of fresh water, are particularly vulnerable to the changes in water cycle components. Natural lakes are the largest reservoirs of fresh water and their ecosystems are highly impacted by the climate variability, climate change and human activities. The identification of causes and the assessment of the present state of aquatic ecosystems can be carried out through water balance modeling. This will enable prediction of their future state and water use planning.

Hydrologic modeling of water cycle components in natural lakes is presented in this paper. The water balance model has two modules dealing with evaporation and rainfall-runoff. The calibration and verification of the model is carried out on a case study - the Dojran Lake. In this study, the other water cycle components, such as water consumption and groundwater, were estimated by use of existing data and literature. The results are shown as comparison of the measured water levels and the computed ones. Concluding remarks and recommendations for future activities within the Dojran Lake watershed are also included.

Keywords: precipitation, evaporation, water use, water level, water balance

INTRODUCTION A vulnerable Hydrological System is a system that exhibits noticeable flora and fauna changes, as a result of water regime changes, induced by climate changes or by human activities. The identification of the causes and the assessment of the present state of the aquatic ecosystems can be carried out through water balance modeling.

A water balance applied to a particular control volume is an application of the law of conservation of mass. Achieving this will require the difference between the inflow and outflow rates across the control surface to be equal. Spatial water balance information provides the distribution of different components of the hydrologic cycle on a spatial basis. Spatial representation of these components requires geographic information system (GIS). Definition of the components in a water balance equation is rather a difficult assignment due to the large number of uncertainties and complex physical processes, which involve many stochastic variables. Water balance information provides the spatial – time distribution of different components of the hydrologic cycle. The water balance of Dojran Lake with its hydrological basin was determined in order to define dominant influences upon the conditions of the lake and the lake’s water fluctuations.

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Violeta Gjesovska

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2 | P a g e Water balance model of vulnerable hydrological system

BASIC WATERSHED CHARACTERISTICS Dojran Lake with its watershed is characterized as a hydrological vulnerable system. The cause of ecological catastrophe is the water level decrease in the last decade of the past century (1988÷2002). For the last decades, a progressive decrease of the water level of Dojran Lake has been recorded.

Dojran Lake is the smallest natural lake in R. Macedonia. The watershed of Dojran Lake is a closed hydrological system with natural inflow of water to the lake, but no natural outflow. Filling the lake is mainly from precipitation, from direct surface inflow and from underground inflow. In 2002, the Republic of Macedonia finished a project to build a system for bringing water from Gjavato wells near Vardar River with capacity of 1 m3/s. Consumption of water from the lake is present in the form of direct evaporation and usage of water from the Lake and its watershed for irrigation and water supply.

During 1950’s,.an artificial channel was built in order to regulate the lake’s water level and control the water use on the Greek side. The controlled outflow of the water from the lake imposed a regime of oscillations of the water level in the lake at a limited level (max. 147.34 m a.s.l. and min.146.14 m a.s.l.). In 1988, the lake’s water level was at an altitude of 145.82 m a.s.l.,(0.32 cm under the minimum) the water surface area was 37.87 km2 and the water volume was 220 mil. m3. In the next period, the water level in the lake was rapidly decreased. In 2002, the water level was at an altitude of 141.33 m a.s.l.(4.51 m under the minimum altitude), the water surface area was 26.01 km2 and the water volume dropped to only 54 mil. m3.

The cause for the decrease of the water level in the lake are not clearly identified. These are located in the unfavourable hydrological conditions expressed through a longer dry period or uncontrolled usage of the water from the lake. The predominant factor influencing the conditions of the lake has still not been defined.

Figurе 1. Watershed of Dojran lake

Water balance model of vulnerable hydrological system




In literature, there are many studies which employed different tools and techniques in order to interpret a lake’s water level fluctuation and define the dominant factor for the decrease of the water level in the lake.

Primarily, the purpose of this study was to investigate whether the water level fluctuations of Dojran Lake were associated with the drought episodes in the region [8].

Statistic procedures were used in order to illustrate the strong relationship between the basic weather characteristics (precipitation and air temperature) and the lake level fluctuations [1], [5].

A very common method was the use of water budget models so as to explicate the lake level oscillation changes [3].

Other studies were focused on energy budget models in order to estimate the evaporation from the lake surfaces that led to changes in the water level [9].

Statistic procedures and other relevant techniques were used to investigate the influence of the drought on the lake water level [4].

The paper presents hydrologic modeling of water cycle components of Dojran Lake.

DATA USED IN THE STUDY Water balance modeling requires various types of data from different sources. Topography data (digital elevation model-DTM), meteorological (precipitation, air temperature, radiation, wind speed, relative humidity), hydrological (lake stage) and GIS layers (soils and watershed boundary) were used to conduct the analysis and study the effect of these variables on fluctuations of water levels in the lake as well as to calculate all the components of the water balance. Table 1 provides a summarized description of the types of data used in the study.

DEM with resolution 30x30 m was processed using grid GIS tools to determine the hydrologic parameters (watershed, flow accumulation and stream network), necessary for computing the upstream runoff inflow. Meteorological data (precipitation, air temperature, radiation, wind speed, relative humidity) are being recorded in a few meteorological stations in Greece (Muries, Ahmatovo, Evzoni, Policastro, Kukush, Sterna) and at one meteorological station in Macedonia (New Dojran).

Table 1: Summery of data used in the study

Type Data Year Resolution Stations

Topographic Digital elevation model, DEM 30 m

Geological Geological map

Used soils Corine Land Cover

Meteorological Precipitation 1951÷2010 1 station New Dojran

Air temperature 1951÷-2010 1 station New Dojran

Wind Speed 1961÷2008 1 station New Dojran

Relative humidity 1961÷2010 1 station New Dojran

Duration 1961÷2010 1 station New Dojran

Hydrological Lake stage 1951÷2010 1 station New Dojran

The precipitation was analyzed by using data on average monthly quantities of rainfall and average annual long-term rainfall quantities. The temperature regime was analyzed by use of data on average monthly and average annual long-term temperature.

Air temperature, wind speed, relative humidity and radiation data were used to estimate the evaporation from the water lake surface and its watershed.


Violeta Gjesovska

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WATER BALANCE METHODOLOGY The water balance of Dojran Lake is given by the following equation:

tt)t()t(t VIUV (1)

where: Vt and Vt+t are the volume of water in the lake at the start and at the end of time interval (t) , U(t) is the sum of all components entering the lake (inflow) and I(t) is the sum of all components leaving the lake (outflow) in time interval (t).

The inflow of Dojran Lake represents a set of components of precipitation that falls directly into the lake (Vp), surface inflow from the watershed (VQ) and water which is taken from the Gjavato system (Vpum) (after 2002). The outflow consists from components of

evaporation from the water lake surface (IE), evapotranspiration (IET) and the outflow from the lake (surface and underground outflow, water from the lake’s surface or underground water used for water supply or irrigation)(IQ). The unit of all components is the volume.

The equation of the water balance is:

ttQETE

pumQpt

V)III()VVV(V

(2)

Figure 2 shows the algorithm for the water balance model of Dojran Lake. The designations that are used in the algorithm have the following meaning: (P) is precipitations, (H) is water level of lake from “O” point (144,93 m.a.s.l), (A=f(H)) is the the lake surface area, (V=f(H)) is the volume of lake, (T) is air temperature, (U) is relative humidity, (W) is wind speed.

Figure 2. Algorithm for the water balance model

COMPONENTS OF WATER BALANCE

Precipitation

The components of precipitation that falls directly into the lake were calculated by the following relation:

2AA

PV ttt)t(p

(3)

where: ( )t(P ) is the sum of rainfall in time

(t), (Аt) and (Аt+t) are the water surface area at the start (t) and at the end (t+t) of time interval (t), respectively.





Underground inflow

Measured data on surface and underground inflow are not available. By using all the available data (topographical, geological and hydro geological) the underground inflow from the Macedonian side was estimated. According to the calculations, based on the size of aquifers (20÷30 m) and the filtration coefficient (k=10-5 m/s), the values of this component varied between (50÷60) l/s.

Runoff

The volume of surface inflow is calculated by using the following relation: VQ=Q.A, where (Q) is the actual direct runoff in (mm) or the effective precipitation (Q=Pe(t)), (A) is the area of the lake watershed. The runoff for the annual water balance is calculated using the Langbein model. The input data in this model (Model P-Q) are the air temperature and the precipitations. The precipitations due to the spatial imbalances are corrected by coefficient k=1.16. This value of coefficient was determined based on hypsometric curve of watershed and changes of amount of

precipitation in terms of altitude (on 100 m altitude, precipitations growing up for 50 mm). Figure 3 shows the algorithm for calculation of the annual runoff according Langbein. The designations that are used in the algorithm have the following meaning: (Tav.annual) and (Tav.monthly) are average annual and average monthly air temperature, ( annualP ), ( monthlyP ) are the annual and monthly sums of rainfall, (K) is temperature factor, Q/K=f(P/K) is relation developed by Langbein, (Qo) is average annual runoff, (Ks) is seasonal factor, (Qa) is improved assessment of annual runoff.

Effective precipitation, Pe(t)e =.P(t), is calculated by using the annual runoff coefficient (0.15), and the monthly runoff coefficient that is different for each monthTable 2 shows the monthly runoff coefficient 1 [according Blagoja Todorov,1977] and 2 (coefficient determined by calibration).

Figure 3. Algorithm for the rainfall-runoff model, Langbein model

Table 2: Monthly runoff coefficient

months I II III IV V VI VII VIII IX X XI XII η η1 0,15 0,18 0,35 0,36 0,25 0,15 0,05 0,04 0,05 0,07 0,10 0,12 0.15 η2 0,36 0,35 0,25 0,15 0,12 0,05 0,04 0,05 0,07 0,10 0,15 0,18 0.15

Gjavato system

The capacity of the Gjavato system for bringing water to the lake is 1m3/s, but it works with 30÷40% of its capacity.

Evaporation and evapotranspiration

The components of evaporation and evapotranspiration were calculated by using the heat balance method and the streamline


Violeta Gjesovska

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theory [Penman, 1950] as well as by using the empirical equation [Mayer, 1937].

Outflow

The volume of water usage for irrigation in Macedonia is 32,5 l/s or a total of 1,25 mil. m3/year, and 50 l/s or 1,576 mil. m3/year for water supply, [8]. Data on the surface and underground outflow, water usage directly from the lake, from the surface and the underground for water supply or irrigation on the Greek side of the watershed are not available.

Lake surface area and volume of lake

The data recorded on the Macedonian side and the measured data from the topographic map (1:5000) of the bottom of the lake on the Greek side were digitally processed and drawn as one curve for the lake surface area and one curve for the volume. The curve for the volume was used to estimate the lake’s water level (Z=f(t)).

Lake storage

The measured data on the water level at the water gage station in New Dojran were used for calculation of the water volume in Dojran Lake and calibration of the model of the water balance (source: UHMR-National Hydrometeorological Service of the Republic of Macedonia).

RESULTS AND DISCUSSION

The transformation model of the rainfall to surface runoff (rainfall-runoff model) was created simply by using the precipitation data from only one hydrological station (New Dojran) and the well-known topography of the drainage basin of Dojran lake. If one analyses the results obtained by two different models, it is apparent that the surface water flow coefficient gained with the Langbein model, which is 0.108 is lower compared to the coefficient of 0.15 acquired by using the effective rainfall method. The monthly coefficients of surface water flow were defined by calibrating the rainfall-runoff model (P-Q) and the measurement data on the lake’s water level. These monthly coefficients are useful when analysing the seasonal influence of the surface water flow. According to the results, these values of coefficients are the biggest in winter and spring and the smallest in summer

when the temperature of air and the evaporation are very high.

The values acquired with the Panman’s theory indicated that the annual evaporation sum of Dojran lake varied between 1056.34 mm in 1972 to 1412.68 in 1990, where the average evaporation sum for this period was 1205.5 mm. When employing, for the same purpose, the Mayer’s method, the results were 904.83 in 1974 and 2173.43 in 1988, respectively. In this case, the average annual evaporation sum was 1585.24 mm. The calculation showed that the annual evaporation sums were higher than the annual precipitation sums in the analysed period.

The components from the water balance model of the Dojran Lake watershed were defined at an annual, monthly and daily level (annual water balance, monthly water balance and daily water balance). However, in this paper, only the annual and monthly water balances are taken into account, analysed and discussed.

Using the water balance model, the water level in the lake was computed (annual water balance) in three variants for each year in the period 1961÷2008, and in three variants for each month (monthly water balance) of the period 1961÷2008. In each variant, different methods for calculation of the components of runoff or evaporation were used. Presented in Table 3 are the different variants and methods for calculation of the components.

The water balance model was used to investigate the influence of the underground inflow on changes of the water level of the lake. According to this research, the influence of this component is insignificantly small. This investigation was made in order to prove the correct choice of algorithm for the water balance model, recommended for a water balance model of a natural lake [7]

The results from the water balance model (water level changes in the lake) in different variants were compared, as well.

Figure 4 shows a comparison between the estimated and the observed average annual water level of Dojran Lake. Figure 5 shows a comparison between the estimated and the observed monthly water level of Dojran Lake.





Table 3: Variants of the water balance model

Components Variant 1 Variant 2 Variant 3

Annual water balance

(VP) Pannual Pannual Pannual

(VQ) VQ=Q.A

(Q according Langbein) VQ=(Pe(t) . A

(Pe(t) P(t)) VQ=Q.A

(Q according Langbein)

(VPum) 0,3 m3/s; (2002÷2008) 0,3 m3/s; (2002÷2008) 0,3 m3/s; (2002÷2008)

(IE) IE=E.Aav.

E according Penman) IE=E.Aav.


E according Mayer)

(IET) IET=ET.Aav.

ET according Penman) IET=ET.Aav.


ET according Penman)

(IQ) [2,82 mil.m3] [2,82 mil.m3] [2,82 mil.m3]

Monthly water balance

(VP) Pmonths. Pmonths. Pmonths.

(VQ) VQ=(Pe(t) . A

Pe(t)e =.Pmonth)

VQ=(Pe(t) . A Pe(t)e =

.Pmonth) VQ=(Pe(t) . A

Pe(t)e =.Pmonth)

(VPum) 0,3 m3/s; (2002÷2008) 0,3 m3/s; (2002÷2008) 0,3 m3/s; (2002÷2008)

(IE) IE=E.Aav.



E according Mayer)

(IET) IET=ET.Aav.



ET according Penman) (IQ) [0,15 mil.m3] [0,15 mil.m3] [0,15 mil.m3]

140

141

142

143

144

145

146

147

148

149

150

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

Time-t [year]

Altit

ude-

Z [m

.a.s

.l.]

observedvariant 1variant 2variant 3

Figure 4. Annual water level of Dojran Lake


Violeta Gjesovska

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140

141

142

143

144

145

146

147

148

149

1500 12 24 36 48 60 72 84 96 108

120

132

144

156

168

180

192

204

216

228

240

252

264

276

288

300

312

324

336

348

360

372

384

396

408

420

432

444

456

468

480

492

504

516

528

540

552

564

576

Time-t [months]

Altit

ude-

Z [m

.a.s

.l.]

.

ObservedVariant 1Variant 2Variant 3

1960

1970

1980

1990

2000

2008

Figure 5. Monthly water level of Dojran Lake

The comparison between the calculated and the measured water level shows that the error of the annual water balance model was 0,02 ÷ 1,0 m before 1988 and maximum 5,5 m; 5,8 and 5,46 m (for different variants) after 1988 year. The cause for the errors in the period from 1961 to 1965 is the average value of the components. In the period 1965 to 1988, the causes for errors can be related to the unknown regulation regime of the artificial channel. The causes for errors in the water balance model for the period after 1988 are not clearly noted. The causes can be associated with the uncontrolled use of the water from the lake (mainly on the Greek side). The hydrometeorological analysis of the available historical data on the studied area shows seasonal variability in the hydrological response. Correlations between average annual air temperature and water level and average precipitation and water level are not very strong.

The water balance model for Dojran Lake and its watershed was applied using data from the measurements done on the Macedonian side only. The value of the outflow on the Greek side of the watershed was not available. The difference between the volume of the simulated and the observed water level was defined in the same way as the value of these components. The maximal difference is in 2002 (200 mil. m3 or 5.5 m).

The instability of the monthly water balance model (3th variant) was located in the model of evaporation according to the Mayer’s theory (very high value of evaporation).

CONCLUSION Presented in this paper is an investigation of methodologies for establishment of a water balance model and hydrological modeling of water cycle components in natural lakes. The concluding remarks and the recommendation for future activities are based on analysis of the results from the water balance model of Dojran Lake.

Dojran lake is mainly filled by precipitation, direct surface inflow and underground inflow. The components of the water balance model were estimated by use of existing data and hydrological models. The surface inflow was defined mainly by using precipitation data and watershed characteristics (rainfall-runoff model). By hydrological analysis, it can be concluded that the changes of the water level of the lake took place after the changes of the value of precipitation. The component of underground inflow was estimated by use of the existing data on the hydrogeological characteristics of the watershed (on the Macedonian side only). The obtained results indicate that the water balance model is not sensitive to this component. The most important parameter of the water balance of





Dojran Lake is the evaporation. The models used for calculation of this component showed that the annual evaporation sums were higher than the annual precipitation sums in the analysed period.

Defining the components of the water balance model is recommended to be done by use of data on precipitations and all factors related to the watershed on both Macedonian and Greek side.

Finally, upgrading the collaboration between Macedonia and Greece is necessary for using and managing the water recourse in watershed of Dojran Lake.

REFERENCES

[1] Bonacci, O., Popovska, C. 2006. Dojransko jezero [Dojran Lake]. Hrvatska Vodoprivreda 158: 14-21 (in Croatian)

[2] Gesovska, V. 2012. Voden bilans na hidroloshki ranlivi sistemi [Water Balance of Vulnerable Hydrologic Systems]. Doctoral thesis, University of Ss. Cyril and Methodius, Faculty of Civil Engineering, Skopje, Macedonia (in Macedonian)

[3] Manley, R., Spirovska, M., Andovska, S. 2008. Water balance model of Lake Dojran. BALWOIS 2008, Ohrid Macedonia (published online at http://balwois.com/2008, reference number 960)

[4] Myronidis, D., Stathis, D., Ioannou, K., Fotakis, D. 2012. An Integration of Statistics Temporal Methods to Track the Effect of Drought in a Shallow Mediterranean Lake, Water Resource Management 26:4587–4605 DOI 10.1007/s11269-012-0169-z

[5] Popovska, C., Bonacci, O., 2006. Ecohydrology of Dojran Lake, Conference on Water Observation and Information System for Decision Support BALWOIS 2006, Ohrid, Macedonia

[6] Popovska, C., Bonacci, O., 2007. Ecohydrology of Dojran Lake, NATO Science for Peace and Security Series-C: Environmental Security, Proceedings of the NATO Advance Research Workshop on Dangerous Pollutants (Xenobiotics) in Urban Water Cycle, Lednice, Czech

Republic, pp. 151-160, Published by Springer-Verlag GmbH

[7] Popovska C., Gesovska V., Donevska K., 2004: Hydrology, Faculty of Civil Engineering, Skopje, Macedonia (in Macedonian)

[8] Skoklevski, Z. 2003. Водите на Дојранското езеро и човекот [Dojran Lake Waters and Man]. Water Economy Institute of RM, Skopje, Macedonia (in Macedonian)

[9] Stojov, V. 2011. Master thesis-Климатски и антропогени влијанија врз водните резерви на тектонските езера [Climatic and Anthropogenic Impacts on Water Reserves of Tectonic Lakes]. University of Ss. Cyril and Methodius, Faculty of Civil Engineering, Skopje, Macedonia (in Macedonian).


Violeta Gjesovska

14 | Page



Transport Noise and Measures for Protection on Motorways in the Republic of Macedonia 1 | P a g e

AUTHORS

Goran Mijoski Assist. Prof. PhD „Ss. Cyril and Methodius“ University

Faculty of Civil Engineering - Skopje [email protected]

Andrej Lepavcov Assist. Prof. PhD „American College“ University Faculty for Architecture and Design – Skopje

[email protected]

TRANSPORT NOISE AND MEASURES FOR PROTECTION ON MOTORWAYS IN THE REPUBLIC OF MACEDONIA

Noise has a great influence on the environment and represents a serious problem because it contributes to a significant reduction of the quality of people’s lives. Among factors that influence the envronment, noise is on the very top, along with air and water pollution. It is very important to point out that noise has an adverse influence not only on the environment, but also on drivers and passengers. Special accent in the paper is put on noise caused by motor traffic- the so called traffic noise, which is dependant on the surface characteristics of pavements.

Keywords: noise, pavement surface, tires, measures for noise protection, acoustic barrier.

1. INTRODUCTION

The sound represents a kind of energy that gets transferred through sound waves that the human ear can detect (range of sound pressure from 0 to 120 [dB], but the human ear can detect sound in the range from 20 [Hz] to 20 [kHz]), while noise is defined as all the unwanted sound that we hear. Noise has its physical properties: intensity, range and time changes that are measured by specific units. The intensity is measured in decibels [dB], the range of frequencies [Hz], and the time changes of duration are measured in seconds [s], or parts of a second. Most sources of noise from everyday life can be represented as: point and linear sources. The sound from point sources spreads monotonously in all directions, while the sound of linear sources spreads cylindrically. Noise coming from road traffic, represents a linear source of sound (Fig. 1).

Figure1. Sources of noise: a) point source and b) line source

Noise has a major impact on the environment and poses a serious problem because it contributes to a significant reduction in the quality of people’s lives. Among the effects on the

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2 | P a g e Transport Noise and Measures for Protection on Motorways in the Republic of Macedonia

environment, noise is at the very top, along with air and water pollution. Noise affects people in the form of harassment and diseases associated with stress, and also has an impact on communication and concentration. Also, it may cause reduced sleeping and stress, contributes to higher blood pressure and heart disease. Noise of 80 dB is traumatic (work performance, sleep), while physiological changes occur within noise of 65 dB. The impact of noise on animals is expressed by obstacles in communication, migration and reproduction. The conducted surveys in the EU countries showed that nearly 20% or about 80 million inhabitants live and work in areas where the noise level is higher than 65 dB, and approximately 170 million inhabitants live and work in the so-called "Gray zones" in which the noise level ranges between 55 and 65 dB. Based on the conducted tests, the European Union recognized noise as a problem and published Directive 2002/49/EC [1]. As common sources of noise, the following can be specified: construction activities, road and railway infrastructure, airport or helipad, street infrastructure, parking (open or closed - in an object), buildings for sports and other events, buildings for accommodation and residence of people (neighborhood), household appliances, racing tracks, amusement parks, shooting grounds and other. Based on the conducted surveys and types of noise resulting from different sources, it has been concluded that the greatest percentage of 81% goes to noise caused by traffic called transport noise, while only 19% of noise is a result of other noise sources (industry, construction and noise from activities in spare time). There are three types of transportation noise: the noise from road, rail and air traffic [2]. The distribution, or the share of individual types of traffic in the total 81% noise caused by traffic - transport noise in major urban areas is shown in the circular diagram given in Fig. 2.

Figure 2. Diagram of percentage share of various noise sources

Noise as a serious problem should be considered in all stages of the transport system, from design, construction, maintenance, to reconstruction. The noise that comes from transport affects millions of people and, in many cases, requires competent authorities to assure reduction of noise from transport, to improve or completely restore people’s quality of life. The noise impact on the quality of life can be very significant especially in the case of expansion of the transport systems. That is why there is a greater need for noise control and why noise in the field of transport is constantly increasing.

2. NOISE ON PAVEMENT SURFACES

Any source of sound can be described thanks to the combined ranges, amplitudes and time history. The range reveals the frequency content of the sound. Fig. 3 shows an example of a continuous range of a consistent motorway traffic, where you can see that the most dominant frequency range is between 200 and 2000 Hz [7].

Figure 3. Example of a range from transport noise on motorway

People do not hear equally well at all frequencies. They are perfectly able to hear frequencies from 20 to 20,000 Hz (though sensitivity at higher frequencies decreases with age), whereat the hearing is the most sensitive from about 1,000 to 6,300 Hz.

2.1. Influential factors of transport noise

Noise caused by motor traffic called transport noise is the result of interaction between motor vehicles and the pavement surface. Changes of the interaction lead to changes in the level of noise. It depends on the intensity, type,


TrAnsPorT noise And MeAsures for ProTecTion on MoTorwAys in The rePubLic of MAcedoniA Scientific Journal of Civil Engineering • Volume 2 • Issue 1 • July 2013


structure and speed, while in respect to the road, it depends on the type, the conditions of the pavement surface and the longitudinal slope. Noise caused by a motor vehicle in motion, can be divided into (Fig. 4):

- noise created by the engine when

working („engine“ noise); - noise generated by the interaction of

tyres from the vehicle and the pavement surface, when the vehicle is passing through the media - air („rolling“ noise) and

- noise which is the result of air turbulence that occurs when the vehicle moves („aerodynamic“ noise).

Figure 4. Types of noise The distance from the site of the source, and the density of traffic on the road (depending on their rank: motorways, national or regional), also significantly affect noise reduction [8]. If we have heavy traffic – continuous (Line source), doubling the distance from the site of the source, the noise is reduced by 3dB, and with less traffic - single passage of vehicles (Point source), doubling of distance from the source site, the noise is reduced by 6 dB (Fig. 5).

Figure 5. Impact of traffic density and distance from the source of traffic noise

The sound that comes from motorway traffic, a distance of about 90 meters (300 feet) from motorways, nearly always presents a noise level of 60 dB (A) (Fig. 6) [7].

Figure 6. Examples of noise sources

2.1.1. Impact of transport noise from pavement surface

The results of measurements of noise during movement on a pavement surface of asphalt concrete, show that the noise from the rolling of the tyre in direct speed, is the source of noise which is predominant in lightweight, and in heavy vehicles. This shows that such noise is primarily dependent on the structural features of the pavement surface (depth of micro and




macrotexture) and bumps or evenness of the pavement surface expressed by the „International Roughness Index“ (IRI [m/km]) as a parameter. The greatest impact on noise is exerted by the pavement surface and the traffic. Pavement surface influences noise through the following factors: roughness and conditions of the surface. The influence of the depth of the roughness of the pavement surface (Fig. 7) mostly depends on:

- the selected type of the wearing

asphalt layer (in terms of graininess and composition of the asphalt mixture);

- impacts from construction; - as well as additional measures taken

in the exploitation of roads (procedures thinning the road).

Figure 7. Roughness of the pavement surface

It has been found that there is a proportional dependence between the depth of the surface roughness and the pavement surface, or by increasing the depth of the pavement surface roughness, there takes place a linear increase of the noise and vice versa, by reducing the roughness, the noise from the interaction with the tyres is reduced. However, it is important to note that reducing roughness reduces the stability of vehicles and the satisfying of the requirements for traffic safety. Roads with the so-called "positive" texture, make higher noise than those with "negative" texture (Fig. 8).

Figure 8. Interaction between the texture of the pavement surface and the tyres

Also, it has been determined that the emission of noise on concrete pavement surfaces (with final wearing layers) is greater than that on pavement surfaces of asphalt wearing layers. The influential factor on the increase of noise is the final layer of the road, depending on the method of calculation. According to the German (Tab. 1) or French method (Tab. 2), its impact is different.

Type of pavement surface D4 (dBA)

Asphalt 0

Rough asphalt and concrete 1

Rough concrete (blistered) 1,5 - 2

Table 1. Increase in the level of noise depending on the pavement surface (German method)

Type of pavement surface Dpavement (dBA)

New asphalt or cement concrete pavement 0

Coarse grained asphalt 2

Flat rocky coating, worn cement concrete pavement 3

Table 2. Increase in the level of noise depending on the pavement surface (French method)

Additional external factors that affect

noise are the situation on the pavement surface, or the evenness, the unevenness, the dimensions and the geometric elements of the alignment (longitudinal and cross slope, the horizontal and vertical curvature of the route),



TrAnsPorT noise And MeAsures for ProTecTion on MoTorwAys in The rePubLic of MAcedoniA



then the emerging deformations, its polishing, whether the pavement surface is dry or wet (Tab. 3) and other.

Wearing layer

Condition of the road

Driving speed (km/h)

60 80 100

Noise in [dB (A)]

Asphalt Dry 70 75 79

Wet 80 82 84

Concrete Dry 73 78 82

Wet 80 82 84

Table 3. Average values of measured noise ont asphalt and concrete vehicular structures for specific road situations

From Table 3, it can be seen that [5]: - the level of noise increases with

increasing speed of movement and moisture on the road;

- pavement structures with wearing concrete layer are louder when the road is dry, while in wet conditions of the wearing layer of the road, the advantage of asphalt pavements as quieter is lost;

- increasing the speed of driving , the condition of the driving surface as an impact on noise decreases.

2.1.2. Impact on transport noise from the speed of movement

It is important to note that, during movement of vehicles with low speed, the engine noise is greater than the interaction between the vehicles and the driving surface. During the movement of vehicles with greater speed than 30 km/h (for cars) and 40 km/h (for heavy vehicles), noise due to tyre rolling down the road becomes significant, and at speeds exceeding 50 km/h, it becomes dominant. It can be concluded that, on the roads where vehicles are traveling at high speeds - motorways (up to 130 km/h), the dominant noise is the one that is created due to the

interaction between the wheels of the vehicle and the pavement surface, while the noise produced by the operation of the motor vehicles becomes negligible [3]. The type or category of vehicles has an impact on noise, wherefore it is necessary to have a data bank not only on the size of traffic, but also on the category of vehicles that move along a specified road. Therefore, precise calculations are done dividing vehicles into several categories (Fig. 9), not just two (light and heavy vehicles).

Figure 9. Emission level data as a function of speed for five vehicle types

2.1.3. Impact on transport noise from tires

Noise caused by tyres depends on several factors including: the internal pressure in the tires, the depressed area and the type of tread of the tyre.The high impact of tyres on noise is seen in the fact that the worn tread of the tire due to greater land area, together with the tyre pavement surface, is creating more noise. It should be noted that noise from tyres is greater in the case of trucks, while in cars, it becomes dominant at high speeds. By applying new technologies in the manufacturing of automobile tyres, and designing the type of tread of the tyre, some brands in the manufacturing of tyres produced the so called „Silent“ tires (Fig. 10), that produce much less noise during the interaction between the tyres and the pavement surface in the case of the same type of a pavement surface and the same prevailing conditions on it [9].




Figure 10. Typical features of a tyre

3. PROTECTION MEASURES AGAINST ROAD TRAFFIC NOISE Many of us are facing road traffic noise on motorways in our everyday lives, although the most affected are the people who live, work or attend school near a motorway or road with heavy traffic. Measures for protection against noise are divided into four groups (of which the first measure is the primary measure, while the remaining three are secondary measures) as follows:

- Measures to reduce noise at the source; - Measures to reduce the spread of noise

between the source and the place of reception (This measure is applied in cases when it is impossible to reduce the noise level at the source within the prescribed limits, and it has to be done in one of two ways: the first is an intervention at the place of emission by placing various types of barriers for protection from noise and the second is planning and managing the area near the road);

- Protection against noise at the site of emission (This type of measure is applied when the previous two cannot be applied and includes the use of sound insulation and paying close attention to the design of buildings near the road) and

- Taking economic measures and adopting appropriate regulations.

The first measure to reduce noise at the source, or reducing the noise that occurs as an interaction between the tyres of the vehicle and the pavement surface involves: reduction of the speed of movement, choosing the type of pavement surface, quality maintenance of roads and vehicles, etc.(Tab. 4)

Measure of protection against noise

Effects of the measure

[dB]

The engine of the vehicle

3 – 5

Reduction of speed 2 – 8

Driving surface 2 – 5

Traffic Management 2 – 4

Diverting traffic 5 – 10

Behaviour of drivers 0 – 5

Table 4. Effect of the measure to reduce noise at the source

The most common type of noise reduction on motorways is setting up a sound wall or sound barrier with wall shape, designed to reduce noise to 10 dB (A). These walls are built to lie longitudinally on the motorway, blocking the visual path from the view of the people who live along it. There are many different types of materials (plastic, stone, wood, metal, glass and other) and structures to reduce noise depending on the available space, acceptance by the population and durability. In order to be effective, the set barriers along roads must satisfy several criteria including: good ability to absorb sound, mechanical resistance and stability, resistance to frost and action of salt from winter road maintenance, fire resistance, and satisfying aesthetic criteria, i.e., matching the surrounding. There are two types of barriers (Fig. 11): reflecting (they reject sound waves without reducing their intensity) and absorbing (they absorb part of the sound energy and emit a sound wave of a reduced intensity) [10].

Figure 11. Types of barriers: a) absorbing, b) reflecting



TrAnsPorT noise And MeAsures for ProTecTion on MoTorwAys in The rePubLic of MAcedoniA



4. PROTECTION FROM NOISE IN THE REPUBLIC OF MACEDONIA Although not yet member of EU, the Repbulic of Macedonia adopted an appropriate legal regulation for protection from noise several years ago [4] [6]. In the past, until recently, protection from transport noise on the roads (motorways, national and regional roads) of the Republic of Macedonia was not given proper attention. The first protective walls – barriers were built during the construction of the ring road around the Skopje city. Acoustic barriers were implemented, both absorbing and reflecting. Absorbing barriers are made of aluminum, perforated on one side, filled with mineral wool (Fig. 12), while reflecting barriers are made of plastic and are transparent (Fig. 13). The reason for the lack of commitment to protection against noise, probably lies in the insufficient funding of road construction, and the non-existence of systematic monitoring of noise on roads during explotation. Other types of protection (applying the „Silent“ roads, etc.) have not been applied to the road network in Macedonia yet.

Figure 12. Protection against noise with absorbtive acoustic barrier on a motorway

Figure 9. Protection against noise with reflective acoustic barrier on a motorway

5. CONCLUSIONS

In addition to the measures of traffic organization, lowering of the noise level can be achieved by proper selection, design and content of the pavement surface. Near the populated areas, particular attention should be paid to elimination of bumps and providing good connections between the final and the lower layers of the road structure as well as avoiding deformation of the parts of intense breaking and departure from places.

Expansion joints of cement-concrete pavements need to be constructed in such a way not to cause additional impacts on noise.

One of the main factors to be considered in spatial arrangement is the pollution with noise because it significantly affects people’s health.

The competent departments dealing with roads, have to introduce the following activities in their practice:

- Planning and management of

noise; - Assessment of harmful effects on

humans and the environment; - Preparation of strategic noise

maps and - Preparation of action plans.

The implementation of these measures

will result in better protection from transport noise.




6. REFERENCES [1] Directive 2002/49/EC of European Parliament

and of the Council Releating to the Assessment and Management of Environmental Noise (Official Journal of the European Communities, L189/12, 2002)

[2] European Commission: Green Paper - Future Noise Policy, Brussels, 1996th

[3] European Commission Working Group 5: Inventory of Noise Mitigation Methods (Brussels, 2002)

[4] Law on Protection against Noise in the Environment (Official Journal of The Republic of Macedonia, No.79, Skopje, 2007)

[5] Mijoski G. „Integral Approach to the Evaluation of Attributes and Indicators of Pavement Surface“, doctoral dissertation, 2010.

[6] Rules for Application of Noise Indicators, Additional Indicators of Noise, Method of Measuring Noise and Methods of Assessment Indicators for Noise in the Environment (Official Journal of The Republic of Macedonia, No.107, Skopje, 2008)

[7] Rochat JL: Transportation Noise Issue, Chapter 19 (Handbook of transportation engineering, USA 2004)

[8] Rasmussen R., Bernhard R., Sandberg U., Mun E.: The Little Book of Quieter Pavements (U.S. Department of Transportation - Federal Highway Administration, Washington DC, USA, july 2007, p. 37)

[9] Yokohama Tyre Catalogue: AVS dB Decibel V550 - (2010)

[10] Watts GR: Traffic Noise Barriers (TRL Annual Rewiev, 1995)




The Methodology of the Approximative Disposition of the Actual Surface and Volume of the Territory of the Republic of Macedonia 1 | P a g e

AUTHORS

Blagoja Markoski

PhD, Associate Professor

“Ss. Cyril and Methodius” University

Faculty of Natural Sciences and Mathematics

Institut of geography

Skopje

[email protected]

THE METHODOLOGY OF THE APPROXIMATIVE DISPOSITION OF THE ACTUAL SURFACE AND VOLUME OF THE TERRITORY OF THE REPUBLIC OF MACEDONIA

On maps, surfaces of territories are naturally shown in horizontal direction. However, because of the extensive uneveness of terrains, there is a need for solving the problem of establishing the real surface of a concrete territory (in this case, the surface of the Republic of Macedonia). The goal is to assess (at least roughly) the actual size of the physical surface of the terrain and to use the very same size for analysis of the outspread of other natural objects in the areas (the outspread of forests, grass areas, possibilities for development of farming, etc.).

In the context of establishing surfaces, the problem of setting the volume of the physical body of a given territory over the surface of the reference ellipsoid was established, as well (in this case, the volume of the Republic of Macedonia). This enables getting information about the size of mines and mineral capacities, information useful for comparison, etc.

This paper shows the corresponding mathema-tical methods for solving this particular problem. They are mainly based on previous data on the size of surfaces according to the hypsometric belts of the territory of the Republic of Macedonia.

Keywords: Cartometry, measurement of surfaces, measurement of volume, territory of the Republic of Macedonia.

INTRODUCTION

The problem of defining a surface area on a map is solved in the domain of cartometry, in the frames of ratio accuracy and application of cartographic projection. During surface measur-ements, a territory is measured in a horizontal state. The actual (real) surface area of a given territory is somewhat larger in size due to its uneven surface (highlands, recesses, inclination, etc.). Accordingly, there arises the

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2 | P a g e The Methodology of the Approximative Disposition of the Actual Surface and Volume of the Territory of the Republic of Macedonia

need for some scientific and economic means to solve the problem of determining the actual size and volume of an actual territory. The theoretical and methodological approach were applied for average surface estimation of the territory of Macedonia in accordance with the previously determined surfaces of the hypsometric belts with an equidistance of 100 m. The degree of accuracy tightly depends on the applied ratio and equidistance during the surface determination of the hypsometric belts.

PROBLEMS AND METHOD PROCEDURES

Problem

The subject of scientific research was the establishment of the real surface and volume of the Earth’s physical surface of a concrete territory (in this case, the territory of the Republic of Macedonia). The data were based on the cartometric network of the surfaces of the hypsometrical belts presented on a map to the scale 1:200000, but with quotients of correction brought down to the accuracy referring to the scale of 1:2500. Accordingly, it was reasonable to expect a corresponding approximate value of the size of the surface and volume of the Earth’s physical territory of the Republic of Macedonia.

Outlining the problem is more of a theoretical methodological aspect with the aim of applying the problem in cartometric study of smaller territories where maps with larger ratios and smaller equidistance of hypsometric belts can be used.

Method Procedure To solve the outlined problem of determining the actual surface and volume of the Earth’s physical surface of the territory of Macedonia, the following methods were applied: cartographic methods;

mathematical and statistical methods;

geographic methods.

METHODOLOGY OF WORK The methodological procedure of defining the real surface and volume of the Earth’s physical surface of a concrete terrain globally assumes:

cartometric study of the surfaces of hypso-metrical belts;

definition of the interval of hypsometrical belts according to given equidistance and angle;

definition of the diagonal part of the hypsometrical layers (hypotenuse c) for the purpose of calculation of the real surface;

definition of the volume of the hypso-metrical belts according to given surface and equidistance.

These outlined elements were subject to further processing and application for the territory of Macedonia.

Hypsometric Belts Planning

The surface of the hypsometrical belts was defined according to the well-known equation for defining the surface with the help of a map to concrete scales. In other words:

PuP kn *2 (1)

where:

Pn - surface in nature

u2 - scale (surface scale factor)

Pk - surface on a map Comment:

The accuracy of the surface is closely dependant on the volume of the scale, i.e., the bigger the scale, the bigger the accuracy. The set problem has a function tendency to have less equidistances.

In the case of the Macedonian territory taken as an example, the previously calculated surfaces of the hypsometric belts were considered with an equidistance of 100 m, calculated for different landforms and summed up for the entire territory of Macedonia.

The calculated surfaces of the hypsometric belts were therefore the starting basis in defining the methodology of the actual surface and volume of the Earth’s physical surface and geographic body of Macedonia.

Defining the Interval of Hypsometric Belts Depending on the structure and the slope of a terrain, the interval of hypsometrical belts may


The MeThodoLoGy of The APProxiMATive disPosiTion of The AcTuAL surfAce And voLuMe of The TerriTory of The rePubLic of MAcedoniA



be of a different size. However, if both the surface of the hypsometrical belts and the equidistance are known, the method of defining the interval is based on solving a right triangle so that the equidistance is one known side of the triangle and there is one known angle. According to the prevailing slopes of the terrain, the slope angle on the upper part of the side a (in other words, the equidistance e) is randomly given, in which way the conditions for defining the other side of the triangle and the hypotenuse are created. The above-mentioned is obtained by using the following equations:

tgab * (2)

(in this case, b is the average interval i) and

cosac (3)

Figure 1 . Solving a right angle triangle

Note:

Further down, the value of e will be used in the formula – an equidistance as an exchange of leg a, and i - interval as an exchange of leg b.

Comment:

In the Macedonian case, an average 200 slope terrain contingent was used.

The known surface of the concrete hypsomet-rical belt was divided by the set length of side b, in other words, interval i, so that the length of the hypsometrical belt was logically obtained.

iP

a xp (4)

where:

a - length of the hypsometrical belt

xpP - surface of the hypsometrical belt

i - interval (average width of the hypsomet-rical belt)

Figure 2. Definition of the surface elements of a declined hypsometric belt

Defining a Declined Hypsometric Belt Since the size of hypotenuse c was established with the previously discussed method, there was the possibility of defining the diagonal surface of the hypsometrical belt by using the following equation:

acPkp (5)

where:

kpP - diagonal surface of the hypsometrical belt a - length of the hypsometrical belt c - hypotenuse of the right triangle

The overall real surface of the whole territory is equal to the sum of the diagonal surfaces of all the hypsometrical belts. In other words:

rkpnkpkp PPPP 21 (6) where:

1kpP -diagonal surface under the slope of the first hypsometrical belt

2kpP -diagonal surface under the slope of the second hypsometrical belt

kpnP -diagonal surface under the slope of the n-th hypsometrical belt

rP -overall real surface

Defining the Volume of the Hypsometric Layer Defining the volume of an uneven body is a very complicated task. However, as a basis for

Hypsometric belt

Hypsometric layer




the solution to the problem, the sizes were taken according to the hypsometrical belts. The method consists of calculating the cumulative values of the size of the surface of each hypsometrical layer starting with the highest hypsometrical belts to the lowest one. In other words:

nPPPPP 321 (7)

P -overall cumulative surface of the territory

1P -surface of the highest hypsometrical belt

2P -surface of the second hypsometrical belt

nP -surface of the n-th hypsometrical belt. Using the established values of the surfaces of the separate hypsometrical layers and the equidistance, i.e., equation:

ePvn (8)

where,

nv -volume of a certain hypsometrical layer

e -equidistance of the hypsometrical layer

P -overall cumulative surface of the territory

The volume of each hypsometrical layer can be calculated separately. If the calculated data are summed up,

vvvv n 21 (9)

where,


The overall volume of the Earth’s physical surface of a concrete territory (in this case, the approximate values for the Republic of Macedonia were taken into account as an example) can be obtained, disregarding the volume of the diagonal parts of the hypso-metrical belts. These parts of the problem are solved using the value of equidistance-e (one of the sides of the triangle-a), interval-i (the second side of the triangle-b) and length of the lower hypsometrical belt-a in the following equation yielding the volume of cuboids.

aiev (10) where,

a -length of the hypsometrical belt

I -interval (average width of the hypsomet-rical belt)

e -equidistance of the hypsometrical layer

Since it is the matter of the volume of the diagonal part, the volume of the square is divided by 2. In other words:

2aievxn

(11)

where,

xnv -volume of a diagonal body on a concrete hypsometrical layer

The values are added to each concrete hypsometrical layer. In other words:

111 xvvV

222 xvvV

xnnn vvV (12) where,

nV -overall volume of a concrete hypsomet-rical layer

The sum of volumes of hypsometrical layers is the overall volume of the geographical body on the concrete territory between the highest and the lowest point. In other words, the problem is solved by using the following equation:

VVVVV n ...321 (13)

where,

V -overall volume of a geographical body (the subject of study)

In this case, it was the total volume of the geographic body of the territory of Macedonia taken as an example.

RESULTS Table forms were outlined based on the previously established methodology and using the hypsometric surface data for the Mace-donian territory. The presented values refer to the slope surface of the hypsometric belts and the sum surface of the whole territory, such as the volume of the hypsometric layers, the

blagoja Markoski





cumulative volume of the scale set hypsometric layers, the volume of the slope part of the hypsometric belts and the total volume of the geographic body of the territory.

The approximate surface and volume data for the territory of Macedonia are given in Table 1.

From the data outlined in the table, it can be seen that, for an assumed 200 average slope of the land, the actual slope surface of the territory of Macedonia is 32270.7 km2. The data cannot be taken as completely accurate but it can be assumed that the value is much closer to the real physical surface than the horizontal projection surface, which is 25713 km2 .

From the data presented in the above table, it is obvious that the territory of the Republic of Macedonia has a volume of 23032.274 km3 (Table 2).

DISCUSSION Defining the actual surface of a given territory with all its uneven surfaces and defining the volume of a specific geographic body (mountain, valley, regions, etc) is a very complex task. However, the procedure can be solved theoretically only if certain conditions are met. One condition is to calculate the surface of the territory using the hypsometric belts on a topographic map. The applied solutions will be more precise if one uses maps of a larger ratio, where the relief map has contours with smaller equidistance. It will be more precise if one works on smaller geographic objects with clearly defined geomorphological (morphostructural) objects where the slope of the land is much simpler.

Table 1. An outline of hypsometric belt surfaces in horizontal state and the actual surface of the territory of Macedonia.

Item no.

Hypsometric belt surface

P km2

Interval

leg (log b)

For angle b=a*tg700

а=е=100m

Hypsometric belt length

km

Hypotenuse c length

km

Slope surface of

hypsometric belts km2

А B А / B C (А / B)*C

1 0.5 0.122 4.098361 0.158 0.647541

2 4 0.122 32.78689 0.158 5.180328

3 6.4 0.122 52.45902 0.158 8.288525

4 19.1 0.122 156.5574 0.158 24.73607

5 35.6 0.122 291.8033 0.158 46.10492

6 62.9 0.122 515.5738 0.158 81.46066

7 88.6 0.122 726.2295 0.158 114.7443

8 142.6 0.122 1168.852 0.158 184.6787

9 187.4 0.122 1536.066 0.158 242.6984

10 258.6 0.122 2119.672 0.158 334.9082

11 328.4 0.122 2691.803 0.158 425.3049

12 446.9 0.122 3663.115 0.158 578.7721

13 564.7 0.122 4628.689 0.158 731.3328




14 700.6 0.122 5742.623 0.158 907.3344

15 898.7 0.122 7366.393 0.158 1163.89

16 1065.8 0.122 8736.066 0.158 1380.298

17 1300.9 0.122 10663.11 0.158 1684.772

18 1570.8 0.122 12875.41 0.158 2034.315

19 1767.4 0.122 14486.89 0.158 2288.928

20 1932.5 0.122 15840.16 0.158 2502.746

21 2098.9 0.122 17204.1 0.158 2718.248

22 2582.8 0.122 21170.49 0.158 3344.938

23 2389.0 0.122 19581.97 0.158 3093.951

24 2050.2 0.122 16804.92 0.158 2655.177

25 1985.7 0.122 16276.23 0.158 2571.644

26 1675.1 0.122 13730.33 0.158 2169.392

27 572.6 0.122 4693.443 0.158 741.5639

28 181.2 0.122 1485.246 0.158 234.6689

32270.72

Source:

Markoski B. (1992) Cartographic Study of Hypsometric Structures of Population Displacement in Macedonia. PhD. Dissertation – script, Ss. Cyril & Methodius University, page 1– 625, Skopje (in Macedonian).

Table 2. An outline of hypsometric layer volume for Macedonia

Item no.

Hypsometric scale

Hypsometric belt surface

km2nP

Hypsometric layer

cumulative surface km2

Equi-

distan-ce

e=0.1

km

Hypsometric layer volume

km3

nv

Slope Hypsomet-

ric layer volume км2

xnv

Hypsomet-ric layer

total volume km2

nV

Cumulative volume of Macedonia

km3

1 2700-2753 0.5 0.5 0.1 0.05 0.025 0.075 0.075

2 2600-2700 4.0 4.5 0.1 0.45 0.20 0.65 0.725

3 2500-2600 6.4 10.9 0.1 1.09 0.32 1.41 2.135

4 2400-2500 19.1 30.0 0.1 3.00 0.96 3.96 6.095

5 2300-2400 35.6 65.6 0.1 6.56 1.78 8.34 14.435

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6 2200-2300 62.9 128.5 0.1 12.85 3.14 15.99 30.425

7 2100-2200 88.6 217.1 0.1 21.71 4.42 26.13 56.555

8 2000-2100 142.6 359.7 0.1 35.97 7.13 43.10 99.655

9 1900-2000 187.4 547.1 0.1 54.71 9.37 64.08 163.735

10 1800-1900 258.6 805.7 0.1 80.57 12.93 93.50 257.235

11 1700-1800 328.4 1134.1 0.1 113.41 16.42 129.83 387.065

12 1600-1700 446.9 1581.0 0.1 158.10 22.34 180.44 567.505

13 1500-1600 564.7 2145.7 0.1 214.57 28.23 242.80 810.305

14 1400-1500 700.6 2846.3 0.1 284.63 35.03 319.66 1129.965

15 1300-1400 898.7 3745.0 0.1 374.50 44.93 419.43 1549.395

16 1200-1300 1065.8 4810.8 0.1 481.08 53.29 534.37 2083.765

17 1100-1200 1300.9 6111.7 0.1 611.17 65.04 676.21 2759.975

18 1000-1100 1570.8 7682.9 0.1 768.29 78.54 846.83 3606.805

19 900-1000 1767.4 9449.9 0.1 944.99 88.37 1033.36 4640.165

20 800-900 1932.5 11382.4 0.1 1138.24 96.62 1234.86 5875.025

21 700-800 2098.9 13481.3 0.1 1348.13 104.94 1453.07 7328.095

22 600-700 2582.8 16064.1 0.1 1606.41 129.14 1735.55 9063.645

23 500-600 2389.0 18453.1 0.1 1845.31 119.45 1964.76 11028.405

24 400-500 2050.2 20503.3 0.1 2050.33 102.51 2152.84 13181.245

25 300-400 1985.7 22489.0 0.1 2248.90 99.28 2348.18 15529.425

26 200-300 1675.1 24164.1 0.1 2416.41 83.75 2500.16 18029.585

27 100-200 572.6 24736.7 0.1 2473.67 28.63 2502.30 20531.885

28 46-100 181.2 24917.9 0.1 2491.79 9.06 2500.85 23032.735

- TOTAL 24917.8 217868.9 - 21786.89 1245.845 23032.274 -

Source:

Markoski B. (1992) Cartographic Study of Hypsometric Structures of Population Displacement in Macedonia. PhD. Dissertation – script, Ss. Cyril & Methodius University, page 1–625, Skopje (in Macedonian).

According to such set conditions, certain forms are established to determine the hypsometric belt surface and perform cartographic surface measurements on hypsometric belts. More over, the interval of the hypsometric belts (with a previously set equidistance and slope angle)

and the slope of the hypsometric belts (hypotenuse c) are determined in order to calculate, more precisely, the actual surface and define the volume of the hypsometric belts according to the previously given area and equidistance.




In accordance with the applied methodology, calculations were made to outline the paramet-ers of the territory of Macedonia. Several calculations that were carried out show that the actual territory of Macedonia covers 32270,72 km2 at an angle of 200 (instead of the surface of 25713 km2 calculated in horizontal projection) and that the volume of the geographic body is 23032,274 km3.

The presented data cannot be taken as absolutely correct, but there is evidence of obtained relevant data and values that are much closer to the real physical surface. Therefore, one can only talk about surface volumes which are roughly the size of the actual physical land.

Such solutions have an applicative value as to more correct dimensioning of a territory, especially for the crop real estate registry (agricultural land, forests, pastures, etc.)

SUMMARY The subject of the scientific research was establishment of the real surface and volume of the Earth’s physical surface of a concrete territory (in this case, the territory of the Republic of Macedonia). The data were based on the cartometric network of the surfaces of the hypsometrical belts on a map to the scale of 1:200000, but with quotients of correction brought down to the accuracy referring to scales of 1:2500. Accordingly, it was reasonable to expect a corresponding approxi-mate value of the size of the surface and volume of the Earth’s physical territory of the Republic of Macedonia.

The methodological procedure of defining the real surface and volume of the Earth’s physical surface of a concrete terrain, globally assumes:

cartometric study of the surfaces of hypso-metrical belts;

definition of the interval of the hypsomet-rical belts according to given equidistance and angle;

definition of the diagonal part of the hypso-metrical layers (hypotenuse c) for the purpose of calculating the real surface;

definition of the volume of the hypsomet-rical belts according to given surface and equidistance.

The surface of the hypsometrical belts is defined according to the well-known equation for defining the surface with the help of a map to concrete scales. In other words:

PuP kn *2 (14) Depending on the structure and the slope of the terrain, the interval of the hypsometrical belts may have a different size. However, if both the surface of the hypsometrical belts and the equidistance are known, the method of defining the interval is based on solving a right triangle so that the equidistance is one known side of the triangle and there is one known angle. According to the prevailing slopes of the terrain, the slope angle on the upper part of the side a (in other words, the equidistance e) is randomly given, in which way the conditions for defining the other side of the triangle and the hypotenuse are created. The above-mentioned is obtained by use of the following equations:

tgab * (15)

(in this case, b is the average interval i) and

cosac (16)

The known surface of the concrete hypso-metrical belt is divided by the set length of side b, in other words, interval i, whereat the the length of the hypsometrical belt is logically obtained.

iP

a xp (17)

Since the value of the size of hypotenuse c was established by the previously discussed method, there was the possibility of defining the diagonal surface of the hypsometrical belt according to the following equation:

acPkp (18) The overall real surface of the whole territory is equal to the sum of the diagonal surfaces of all the hypsometrical belts. In other words:

rkpnkpkp PPPP 21 (19) Defining the volume of an uneven body is a considerably complicated task. However, as the basis for the solution to the problem, the sizes were taken according to the hypsomet-rical belts. The method consists of calculating cumulative values of the size of the surface of each hypsometrical layer starting with the

blagoja Markoski





highest hypsometrical belts to the lowest one. In other words:

nPPPPP 321 (20) Using the established values of the surfaces of the separate hypsometrical layers and the equidistance by the following equation:

ePvn (21) Тhe volume of each hypsometrical layer can be calculated separately. If the calculated data are summed up,

vvvv n 21 (22) Тhe overall volume of the Earth’s physical surface of a concrete territory (in this case, the approximate values for the Republic of Mace-donia were taken into account as an example) can be obtained, disregarding the volume of the diagonal parts of the hypsometrical belts. These parts of the problem are solved using the value of equidistance-e (one of the sides of the triangle-a), interval-i (the second side of the triangle-b) and length of the lower hypsometrical belt-a in the subsequent equa-tion that yields the volume of cuboids:

aiev (23) Because this is the matter of the volume of the diagonal part, the volume of the square is divided by 2. In other words:

2aievxn

(24)

The values are added to each concrete hypsometrical layer. In other words:

111 xvvV

222 xvvV

xnnn vvV (25) The sum of the volumes of the hypsometrical layers is the overall volume of the geographical body on the concrete territory between the highest and the lowest point. In other words, the problem is solved by the following equation:

VVVVV n ...321 (26)

Symbols:

Pn -surface in nature,

u2 -scale (surface scale factor),

Pk -surface on map

a -length of the hypsometrical belt

xpP -surface of the hypsometrical belt i -interval (average width of the hypsometri-

cal belt)

kpP -diagonal surface of the hypsometrical belt c -hypotenuse of the right triangle

1kpP -diagonal surface under the slope of the first hypsometrical belt

2kpP -diagonal surface under the slope of the second hypsometrical belt

kpnP -diagonal surface under the slope of the n-th hypsometrical belt

rP -overall real surface P -overall cumulative surface of the territory

1P -surface of the highest hypsomet. belt

2P -surface of the second hypsomet. belt

nP -surface of the n-th hypsometrical belt


hsP -surface of a hypsometrical layer e -equidistance of the hypsomet. layer

xnv -volume of a diagonal body on a concrete hypsometrical layer

nV -overall volume of a concrete hypsome-trical layer

V -overall volume of a geographical body

REFERENCES

[1] Blagoev B. (1981) Statistics – General Statistics of Methodology, Ss. Cyril & Methodius University, page 1 – 497, Skopje (in Macedonian).

[2] Kolchkovski D. (2004) Physical Geography of Macedonia, p. 1-273, Skopje (in Macedonian).

[3] Markoski B. (1992) Cartographic Study of Hypsometric Structures of Population Displacement in Macedonia. PhD. Paper – script, Ss. Cyril & Methodius University, page 1– 625, Skopje (in Macedonian).

[4] Markoski B. (2010) The Methodology of the Approximative Disposition of the Actu-al Surface and Volume of the Territory of the Republic of Macedonia, Proceedings, Fourth Congress of the Macedonian Geographers, Dojran 7-10 October 2010, Macedonian Geographical Society,Skopje.




[5] Markoski B. (2003) Cartography, Geo-map, p. 1-411, Skopje, (in Macedonian).

[6] Markoski B. (2004) Cartographic Defining and Differentiating Mountain Space Com-plex in Macedonia. Geographic Bulletin, Institute of Geography, p. 25-34, Skopje. (in Macedonian).

[7] Markoski B. (1995) Space Hypsometry and Macedonian Demography – Cartogra-phic Method. Macedonian Thesaurus, p. 1-316, Skopje, (in Macedonian).

[8] State Geodesy Office. (1982) Cadastre Records. Skopje, (in Macedonian).

[9] Milevski I., Markoski B., Gorin S., Jova-novski, M. (2009) Application of Remote Sensing and GIS in Detection of Potential Landslide Areas, Proceedings of the International Scientific Meeting “Geogra-phy and Sustainable Development”, Ohrid.

[10] Milevski, I., Markoski, B., Jovanovski, M. and Gorin, S. (2010) Landslide Risk Mapping by Remote Sensing and GIS in Gevgelija-Valandovo Basin. Geologica Balcanica, No39, Sofia, BAS, pp.255.

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Neural Networks and Their Application in Civil Engineering. Isothreshold Adaptive Network (IAN) 1 | P a g e

AUTHOR

Silvana Petruseva Ph.D. Assistant Professor Ss. Cyril and Methodius University Faculty of Civil Engineering (Department of Mathematics) – Skopje [email protected]

NEURAL NETWORKS AND THEIR APPLICATION IN CIVIL ENGINEERING. ISOTHRESHOLD ADAPTIVE NETWORK (IAN) Artificial neural networks (ANN) have been found to be powerful and versatile computational tools for many different problems in civil engineering over the past 2 decades. They have proved useful for solving certain types of problems, which are too complex, or too resource-intensive nonlinear problems to tackle using more traditional computational methods, such as the finite element method. ANN-s are intelligent tools, which have gained strong popularity in a large array of engineering applications such as pattern recognition, function approximation, optimizati – on, forecasting, data retrieval, automatic control or classification, where conventional analytical methods are difficult to pursue, or show inferior performance.

A review of some problems in civil engineering that were successfully solved by using neural networks is presented in this paper. A general introduction to neural networks (NN), their basic features and learning methods is given. A particular architecture- the Isothreshold Adaptive Network (IAN) and its ability to solve some problems in civil engineering, is also presented.

Keywords: artificial neural network (ANN), Isothreshold Adap-tive Network (IAN), pattern recognition.

INTRODUCTION Neural Networks have made a remarkable contribution to the advancement of various fields of endeavor and have become very popular for data analysis over the past 2 decades. Their application in the civil engineering field is considered in this paper.

Neural networks are intelligent systems that are based on simplified computing models of the biological structure of the human brain, whereas the systems based on traditional computer logic require comprehensive programming in order to perform a given task. ANN-s are suitable for multivariable applications where they can easily identify interactions and patterns between inputs and outputs. ANN models do not require complicated and time consuming finite element input file preparation for routine design applications. They are able to infer important information for the task, which is being solved by them, if data that is representative of the underlying process to be implemented, is provided.

Neural networks have a self-learning ability, which is particularly useful where comprehensive models that are required for conventional computing methods are either too large or too complex to represent accurately, or simply doesn’t exist at all.

624:004.822


silvana Petruseva Scientific Journal of Civil Engineering • Volume 2 • Issue 1 • July 2013

2 | P a g e Neural Networks and Their Application in Civil Engineering. Isothreshold Adaptive Network (IAN)

The highly connected, distributed nature of neural networks also provides a high degree of generalization capability and noise immunity.

The first journal article on neural network application in civil engineering was published in 1989.Since then, many articles on NN appli-cation in different areas of civil engineering like structural engineering, management, environ-mental and water resources engineering, tra - ffic, geotechnical and geomechanical enginee-ring, have been published [4]. In the next section, ANN architectures, their basic characteristics and types are introduced. In the subsequent text, a particular type of a neural network - Isothreshold Adaptive Array (IAN) and its ability to solve some civil engineering problems, is presented.

Artificial Neural Networks – general overview

The functioning and the survival of intelligent systems depends on their system for processing information. The nervous system is the system for processing information in biological systems. It consists of the brain, as the central processing system for processing information and a set of sensors. The basic information element in biological systems is the neuron or the neural cell. There are billions of such processors in the brain. They are distributed, work simultaneously and cooperate. The neuron processors make the microstructure, the material basis of the biological intelligence.

An approach to research of artificial intelligence is motivated by this observation and deals with the concepts of artificial neuron and artificial neural network, as the microstructure of artificial (synthetic) intelligence [8].

Artificial neural networks are among the most attractive approaches to investigation of artificial intelligence. The research in this direction began in 1940 and continued with different intensity in different periods of time. After a stagnation in the seventies of the last century, this area experienced a renaissance in the second half of the 1980ties.

The area of artificial neural networks is distinctively interdisciplinary. Sciences like physiology, neurology, mathematics, physics, philosophy, biology, computer science,

engineering, intermingle with each other in their efforts to build an intelligent system based on the concept of artificial neural network.

There are several aspects that make this area attractive. Three of them are:

relation with biological neural networks;

relation with the concept of parallel distributed processing;

relation with the concept of learning and self-organization.

Artificial neurons are inventions that are inspired by the anatomy and physiology of biological neurons. Figure 1 presents the morphology of a human neuron. It is assumed that the neuron is of an electrical nature – it has an electrical potential in respect to the environment. This electrical potential is changed due to external influences. The neuron has several inputs through which it receives electrical impulses, and only one output through which it sends an electrical impulse in the environment.

Modeling of a neuron can be a very complex task. It involves the following key notions:

body of the neuron (soma);

axon – output neural strand through which it sends signals to other neurons;

dendrites - growths of the soma which form a dendritic canopy;

synapses – places in dendrites or soma where the neuron receives signals from other neurons; synapses are connections with other neurons;

cumulative postsynaptic potential (SPP) is a cell potential, which is formed due to the cumulative synergistic influence of synaptic potentials;

synaptic influence (weight): synapses have different influence on the formation of SPP. Some of them have a positive influence (excitation), while some have a negative effect (inhibition). Every synapse has its “weight” in the formation of SPP;


neurAL neTworks And Their APPLicATion in civiL enGineerinG. isoThreshoLd AdAPTive neTwork (iAn)Scientific Journal of Civil Engineering • Volume 2 • Issue 1 • July 2013


threshold of the neuron excitation: minimal SPP needed for the triggering of an output signal from the neuron;

presynaptic processing: processing of the biosygnals by direct connection of the axon with the synapses, before the potential is transmitted to the soma of the neuron;

neural network: the structure of the connected neurons.

On the basis of these elements, the ma-thematical model of an artificial neuron can be defined. Figure 2 shows such an element [8]. It

is assumed that the neuron is in some neural network with n neurons and that it potentially receives signals from each neuron, including from itself.

Signals that travel through the whole network at one moment in time can be described by the following vector

x=(x1, x2, …., xn)

In general, they are real numbers, but for the purpose of simplicity, they are taken as binary numbers.

These signals can form pre-synaptic connections

Figure 1. Example of a neuron morphology




Figure 2. Mathematical model of an artificial neuron

in front of each neuron. These connections define an arbitrary non-memory function, which is often one of the following two functions: pre-synaptic inhibition, or pre-synaptic sensitization denoted by ai. These signals form an input vector in the j-th neuron aj =(a1j, a2j, a3j,….., anj ). Each of these inputs is accompanied by the weight of the connection, whereat the weights form the following vector

wj =(w1j, w2j, w3j,….., wnj )

The set of weights of synapses from all neurons represents the memory of the network. The memory is most frequently presented by a memory matrix W=(w1, w2,….,wj,…wn).

Very often, for the purpose of simplicity in modeling, the pre-synaptic network is not taken into account, whereat vector aj is equated with vector x.

The threshold of the j-th neuron is denoted by j , which can be changed. For the purpose of

simplicity of mathematical manipulations, weight woj is associated with the threshold.

The output of the neuron is generated in two steps: first, SPP is computed

ij

n

iijj waSPP

1

and after that, the activation level of the neuron

)( jojj wSPPfb

which is communicated to the environment as an output signal xj=bj which travels through the network and is a potential input signal for all neurons, is computed. In the above formula, function f is called activation function.

Different mathematical models are used for this function. The most frequently used are presented in figure 3.

00

)(xifxif

xf

a)

xifxifxxif

xf )(

b)

)1,0(1)(

xeaxf

or )1,0()()( xtghxf

silvana Petruseva


neurAL neTworks And Their APPLicATion in civiL enGineerinG. isoThreshoLd AdAPTive neTwork (iAn)



c)

Figure 3. Some types of activation functions

Parallel distributed processing is the most significant aspect of information processing with neural networks. This aspect is stressed out by the definition of ANN given in the subsequent text.

An artificial neural network is a parallel distributed information structure, which consists of processing elements (which may have a local memory and perform local operations for information processing) connected with signal channels called interconnections. Each processing element has one output which branches into many side connections. The output signal may be of any mathematical type. Each processing in the elements is local, i.e., it depends only on the input signals and the memory values of the element.[17]

Figure 4.Laminated representation of a one-layer network.

Other researchers have noticed that the most interesting fact is that ANN can memorize information without deleting the old one [30]. This definition, in fact, stresses the neural network as an associative memory. Parallel associative memory processing is an inherent characteristic of biological neural networks, for example, the brain. Investigating in this direction, researchers are looking for ANN that will have the characteristics of the brain, i.e., they are trying to model the processing of the information in the brain (brain-style processing).

The architecture of ANN can be interpreted in two ways: laminated and matrix. Figure 4 shows a laminated representation of a one-layer network.

A laminated representation of a three-layer net is given in figure 5. It is a network without a feedback connection (feedforward network). Some networks have feedback connections (feedback network).

Three-layer networks are usually used for more complex nonlinear mappings. The middle level is called the “hidden” network level, in addition to the input and output level. It has been shown that any nonlinear function can be realized by a three-layer network. These networks are therefore the most general.




Figure 5. A three-layer feedforward network (laminated representation)

Learning methods of ANN

Functionally, all ANN-s are “vector mappers” that accept a feature input vector from one data space and produce from it an associated feature output vector from another data space. Inside the network, the data pass between computational elements along weighted connections. Because the data that emerge from the network change as the connection weights change, ANN can “learn “ to produce the desired output by adjusting the magnitudes of their weights. Here, the primary interest is focused on how different phenomena of learning can be represented by the aid of the “synaptic weight” concept. The problem of learning in ANN has been present since the 50ties of the last century and is connected with the name Rosenblatt [27].The network that he proposed and called Perceptron is very much of a current interest in the area of learning at microstructure level. Writing data in neural associative memories is through modification of the previously stored information in the synaptic weights, not by its overwriting. Therefore, the term learning is added to the process of storing of the information in these memories. Generally, the process of learning is considered as any change of the state of the memory. Mathematically, it can be described as follows:

0dtdW

learning

Appropriate adjustments of weights in the network are determined by the computational elements themselves, using learning rules that should minimize some type of a cost function. Each computational element works to improve its own performance. The parallel distributed processing gives ANN the ability to learn complex mappings without having to specify a priori functions and rules required by conventional computing methods. The user needs only to select the correct type of net-work and the most appropriate data representation (input feature vectors) for the problem being solved.

The methods of learning in ANN are divided into: learning with a teacher, learning without a teacher and implementation of both types of learning [8].

learning with a teacher (supervised learning)

Learning with a teacher assumes an existing external teacher and/or global information by which the following is solved: when to stop learning, how long and how often each association during the process of training is to be shown and the assessment of the error. There are several types of this kind of learning. Some of them are:

silvana Petruseva




a) stochastic learning – this type of learning uses random processes and energy function for adjusting the weights. The stochastic learning makes random change of the weights, computes the energy function and maintains the changes of the weights according to some criteria. The Hopfield network [19,20] is of this kind. It can be used for pattern recognition, classification and detection of anomalies in data. b) reinforcement learning – Here, the weights are adjusted for a good performed action. The signal from the teacher is a scalar value, which only tells how much the undertaken action from the “learner” is good or bad, but it doesn’t say which is the desired action. The simplest equation that describes this learning is:

)( jiij raw where r is the scalar

value provided from the environment, ai is the signal from the i-th neuron, j is the threshold of the reinforcement of the j-th output element and is the constant that regulates the speed of learning. c) error correction learning – with this learning, the weights are adjusted proportionally to the difference between the desired (given by the teacher) and the received value from each neuron of the output layer. This is presented

as follows:

)( jjiij bcaw where cj

is the desirable value, bj is the received value from the j-th output neuron, ai is the signal of the i-th neuron, wij is the weight of the connection between the i-th and the j-th neuron, is a parameter that regulates the speed of learning. It was for a long time that the problem of learning with an external teacher was how to train the neurons which are not in the output layer, i.e., those which do not give direct output whereat the error that they make can

The connection weights are initially selected randomly. The inputs propagate forward through each layer, to emerge as outputs. The errors between these outputs and the correct answers are then propagated backward through the network and the connection weights are individually adjusted so as to reduce the error. After many examples are propagated through the network several times, the mapping function is “learned” with some tolerable error. This network is used for data modeling, classification, image compression, forecasting, speech and pattern recognition [18].

learning without a teacher (unsupervised learning)

When the network adapts to its information environment without intervention, the learning is called unsupervised learning. There are several kinds of this type of learning, like correlation learning, competitive learning [15] or hedonistic learning [22]. The concept of learning without a teacher can be realized also by the assumption of an existing variable in the system representing the “satisfaction” of the system during learning in the process of solving some task. With this concept, the system tends to maximize this variable. In this way, there is an “inner teacher“, who “tells” the system that the “variable of satisfaction” should be maximized. In that way, the neural network becomes self-organized. It modifies its behavior to achieve the desired state, which according to some criteria, means internal satisfaction. An example of such a neural network is the CAA neural network [9,11], which implements consequence learning and genetic concepts. Some modifications of this network are given in [26]. Kohonen maps [23] are also self-organized systems, which can be used for pattern recognition, classification and data compression.

not be seen. This problem was solved in the 80ties with the “back propagation algorithm” (BP). This enabled a new renaissance of the research related to ANN. The term “back propagation network” refers to a multilayered, feed-forward neural network trained by using an error back propagation algorithm [31,35,25,28]. The nodes between successive layers are connected by links, each of which transmits a weight that describes the strength of that connection quantitatively.

Some ANN applications in civil engineering

Optimization problems

Some successful applications of ANN in civil engineering are considered further in the text.

Optimization of large and complex engineering systems is particularly challenging in terms of convergence, stability and efficiency.




NN computing can also be used for optimization. Berke at al. (1993) proposed an optimum design of aerospace structural components by using a neural network. Adeli and Park (1995 a) presented a model of neural dynamics for optimal design of structures by integrating the penalty function model and the neuro-dynamic concept. Tashakori and Adeli (2001) presented an optimal (minimum weight) design of space trusses made of cold formed steel shapes using the neuro-dynamic model of Adeli and Park (1996) The model was used to find the minimum weight design for several space trusses commonly used as roof structures in long span commercial buildings and canopies, including a large structure with 1548 members, with excellent convergence results.

Mohamed et al. (1995) formulated the problem of optimal allocation of available yearly budget for bridge rehabilitation and replacement projects among a number of alternatives as an optimization problem using the Hopfield network (Hopfield 1982,1984). Senouci and Adeli (2001) presented a mathematical model for resource scheduling considering project scheduling characteristics, including precedence relationships, multiple-crew strategies and time-cost trade-off. The new model considers total project cost minimization. The model is solved by using the neural dynamics optimization model of Adeli and Park (1996). Adeli and Wu (1998) presented a regularization neural network model for estimating the cost of a construction project. The model is applied to estimate the cost of reinforced concrete pavements as an example. The new model is based on a solid mathematical foundation, making the cost estimation more reliable and predictable.

Geotechnical engineering

Core penetration test (CPT) measurements are frequently used to find the soil strength and stiffness parameters needed for design of foundations. Goh (1995) demonstrated the application of the BP algorithm in correlation with various experimental parameters and evaluation of CRT calibration chamber test data. Juang and Chen (1999) presented neural network models for evaluation of the liquefaction potential of sandy soils. The use of NN in predicting the collapse potential of soils was discussed by Juang et al. (1999). Basher (2000) proposed the NN as an alternative in modeling the constitutive hysteresis behavior of soils with high accuracy.

Isothreshold Adaptive Network

(IAN)

Presented further is the Isothreshold Adaptive Network (IAN) [9,10], which represents a supervised neural network, which can be used for any kind of problem that can be reduced to recognizing shapes or classification. It has been very successfully used for recognizing patterns (symbols) with 100% accuracy, speech and situations in controlling robots. In civil engineering, it can be used for solving any problem of recognizing or classification of any kind of objects.

Many authors have successfully used neural networks for some classification problems in civil engineering. For example, for pavement classification, Eldin and Senouci (1995) used the NN algorithm for condition rating of roadway pavements. Cal (1995) used an algorithm for soil classification based on three primary factors: plastic index, liquid limit water capacity and clay content. Attoh-Okine (2001) used a self-organizing map for grouping pavement condition variables such as thickness and age of pavement, average annual daily traffic, alligator cracking, wide cracking, potholing and rut depth to develop a model for evaluation of pavement conditions. V. Venayagamoorthy, D. Allopi and G.K. Venayagamoorthy (2004) proposed an intelligent technique using a neural network to classify different types of road pavement structures, which is essential in estimating bearing capacities and load equivalency factors of pavements under different loadings. IAN can also be used for such and similar problems.

The Isothreshold Adaptive Network is an advice-taking system, which receives advice from some kind of a teacher or reference model as to how to perform in a given situation during the process of learning. During the process of interaction, a cooperative game will take place between the teacher and the learner, whose goal will be to transfer the reference knowledge of the teacher to the knowledge base of the learner.

Consequence driven teaching

The most well-known paradigm in the study of this type of a system is the pattern classification paradigm. In this paradigm, there is a given set of prototype patterns x={x1,x2,…xN}, and a set of classes U={U1,…,Un}, N>=n.

silvana Petruseva




The vector of features representing the i-th pattern is given by xi=( xi

1,…,,xim). Uk is a scalar

representing the k-th class. The teacher usually shows the patterns and advices an association between a pattern and a class. The pattern used for teaching the learner constitutes the training set. In addition to the training set, an examination set is used during the learning process. It is a set of patterns used for testing the knowledge of the learner. The test set can be the same as the training set. Sometimes, the given set of prototypes is divided into two sets, whereat one serves as a training set, while the other is used as an examination (test) set. The third set of interest in this process is the exploitation set, which is used when the learner is launched as a pattern classification device in some decision making process, when the teacher is not present. The training set is chosen to be a representative subset of the exploitation set.

The two basic types of learner-teacher communication during the teaching process are: open loop and close loop type of communication.

In the open loop communication, the teacher produces pairs (pattern, class). After several iterations, an examination process is introduced. It is usually assumed that the sequence of all training pairs, the so called teaching sequence, can be produced an infinite number of times.

In the closed-loop communication, the teacher interleaves the teaching and examination trials. The teaching trial is introduced only if needed. This trial is a consequence sensitive event. It appears only as a consequence of erroneous classification produced by the learner. Here, the teaching sequence is shown a finite number of times.

In the case of advice taking systems it is assumed that the learning process is divided into trials, i.e., steps in which all relevant variables between the learner and the teacher are interchanged. There is a temporal relationship between the interface variables. Usually, the sequence of events is: X, Y, r, (U), i.e., situation (X) is shown, an answer (Y) is received, an evaluation (r) is given and advice (U) is provided, if needed.

Architecture and learning rule of IAN

IAN is a greedy policy classifier, which uses the maximum selector as the decision device for classifying input situations. It computes the neural potential (activation functions) g1,g2,…, ..,gn of each neuron at the output layer and chooses the one with the maximal value. So, the output of a greedy policy classifier is computed as y=argmax{ g1,g2,…,,gn}, which produces number i if the i-th activation function has the maximal value. Figure 6 shows the greedy policy learner, IAN. Two architectural features should be observed in this case.

First, the teacher’s signal is not received at the neural soma, as it is usually assumed in the Multilayer perception. Here, the teaching signal is a part of the synaptic input. The teaching input sensitizes the situation input. This type of a synapse is known as the Kandel’s synapse. The teaching inputs are controlled by signal r, which has control over the teaching process. Signal r determines whether a sensitization signal is eligible.

Figure 6. a) Isothreshold Adaptive Network (Drawing software by Rich Sutton, 1980)




b) Adaptive array representation of the Isothreshold Adaptive Network

Second, IAN provides a neural mechanism for the maximum selector device. The neural units are represented as consisting of two parts, the postsynaptic potential forming part (soma and dendritic tree) and the threshold–computing part. The threshold computing part has a common value for all networks. The value of the threshold is equal to the maximal value of the neural potentials produced in the considered set of neurons. Symbolically:

},...,max{ 1 ngg ,

where is a common threshold, and gi (i=1,..n) are neural potentials computed from the neural units as gi=wi

Tx.

Given that the common threshold is the maximal value of all the neural potentials and using the standard rule y=sgn1(wTx- ) (where sgn1(.) gives 1 for non-negative values, and 0 otherwise) in producing the neural output, the inherent neural maximum selector is obtained. Only a neuron with the maximal potential will have a potential equal to the threshold and will produce the output. None of the neurons will have a potential greater than the threshold potential.

The IAN can grow by attaching other neurons to the threshold part and the dendritic tree. Each new neuron in the network adds to the ability for recognition of a new pattern class.The learning rule used in the development of the adaptive array shown in figure 6 is a three-component learning rule:

)()()()( trtUtXtW ,

where X is the input not recognized in the previous trial, U is the advising input showing the class in which the pattern should be classified, and r is the penalty for X being not recognized [9].

In fact, the problem of recognizing, or classifying is reduced to comparing the elements of the input vector in the neural network (which represents the object which has to be classified or recognized) and the elements of the vectors which represent the classes of objects (which are almost learned). The vector - representative of some class, which is the nearest to the input vector, is the class in which the object belongs. In this way, it can be said that the object is recognized or classified in the appropriate class.

The most relevant attributes of the objects to be classified should be chosen in order to effectuate an accurate and efficient procedure of recognizing.

CONCLUSION

Some ANN applications in civil engineering are shown in this paper. A general introduction to ANN-s, their basic features and methods of learning is given. A particular architecture is presented, namely, the Isothreshold Adaptive Network, as a general classifier, which has been used successfully for pattern recognition in several practical applications and can also

silvana Petruseva


neurAL neTworks And Their APPLicATion in civiL enGineerinG. isoThreshoLd AdAPTive neTwork (iAn)



be used for each problem in civil engineering that can be reduced to pattern recognition or classification.

From many applications of ANN-s, it is evident that they can be applied successfully to many civil engineering problems and that, in many cases, they perform better than the conventional methods. They are suitable particularly for problems that are too complex to be modeled and solved by classical mathematics and conventional procedures.

Future development of neural networks is certainly undeniably connected with their application in practice.

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[2] Adeli, H. & Park, H. S. 1996. Hybrid CPN-Neural Dynamics Model for Discrete Optimization of Steel Structures, Microcomputers in Civil Engineering, 11 (5), 355–66.

[3] Adeli, H. & Wu, M. 1998. Regularization Neural Network for Construction Cost Estimate, Journal of Construction Engineering and Management , ASCE, 124 (1), 18–24.

[4] Adeli, H. 2001. Review article, Neural Net-works in Civil Engineering:1989-2000, Computer Aided and Civil and Infrastructure Engineering 16, 126-142.

[5] Attoh-Okine, N.O. 2001. Grouping Pavement Condition Variables for Performance Modeling Using Self-organizing Maps, Computer-Aided Civil and Infrastructure Engineering, 16, (2), 112-25

[6] Basheer, I. A. 2000. Selection of Methodlogy for Neural Network Modeling of Constituteve Hysteresis Behavior of Soils, Computer-Aided Civil and Infrastructure Engineering 15 (6), 445–63.

[7] Berke, L., Patnaik, S. N. & Murthy, P. L. N. 1993, Optimum Design of Aerospace Structural Components Using Neural Networks, Computers and Structures 48 (6), 1001–10.

[8] Bozinovski, S. 1994. The Artificial Intelligence (in Macedonian), Gocmar, Bitola

[9] Bozinovski, S. 1995. Consequence Driven Systems, Teaching, Learning and Self-learning Agents, Gocmar Press, Athol.

[10] Bozinovski, S. 1985 , Adaptation and Training: A Viewpoint, Automatica 26, Zagreb, 137-144

[11] Bozinovski, S. 1982. A Self-learning System Using Secondary Reinforcement, in R. Trappl (Ed.) Cybernetics and Systems Research, North Holland. (397-402)

[12] Cal, Y .1995. Soil Classification by Neural Network, Advances in Engineering Software, 22, 95-7.

[13] Eldin, N.N. & Senouci, A.B.1995. A Pavement Condition Rating Model Using Backpropagation Neural Network, Microcomputers in Civil Engineering , 10 (6), 433–41.

[14] Goh, A.T.C.1995. Neural Networks for Evaluating CPT Calibration Chamber Test Data, Microcomputers in Civil Engineering 10 (2), 147–51.

[15] Grossberg S.1972, Neural Expectation: Cerebellar and Retinal Analogies of Cells Fired by Unlearnable and Learnable Pattern Classes, Kybernetik.

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[17] Hecht-Nelsen, R.1988. Applications of Counterpropagation Networks, Neural Networks 2.

[18] Hertz, J., Krogh, A., and Palmer, R. G. 1991. Introduction to the Theory of Neural Computation, Addison-Wesley Publishing Company, New York, pp. 130–141.

[19] Hopfield, J. J. 1982. Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proceedings of the National Academy of Sciences , 79 , 2554–8.

[20] Hopfield, J. J. 1984. Neurons with Graded Response Have Collective Computational Properties Like Those of Wostate Neurons, Proceedings of the National Academy of Sciences 81, 3088–92.




[21] Juang, C. H. & Chen, C. J. 1999. CPT-Based Liquefaction Evaluation Using Artificial Neural Networks, Computer-Aided Civil and Infrastructure Engineering 14 (3), 221–9. [22] Klopf, H.1972. Brain Function and Adaptive Systems: A Heterostatic Theory, Air Force Research Laboratories Report.

[23] Kohonen, T., 1982. Self-organized Formation of Topologically Correct Feature Maps, Biological Cybernetics, Vol. 43, 1982, pp. 59–69. [24] Mohammed, H. A., Abd El Halim, A. O. & Razaqpur, A. G. 1995. Use of Neural Networks in Bridge Management Systems, Transportation Research Record No. 1490, Washington, pp. 1–8.

[25] Parker, D. B. 1985. Learning Logic, Technical Report TR-47, Center for Computational Research in Economics and Management Science, Massachusetts Institute of Technology, Cambridge, MA. [26] Petruseva, S. 2008, Emotion Learning: Solving a Shortest Path Problem in an Arbitrary Deterministic Environment in Linear Time with an Emotional Agent, International Journal of Applied Mathematics and Computer Science.

[27] Rosenblatt, F.1962. Principles of Neurodynamic, Spartan Book.

[28] Rumelhart, D. E., Hinton, G. E. and Williams, R. J. 1986. Learning

Representations by Back-Propagating Errors, Nature, Vol. 323, pp. 533–536. [29] Senouci, A. &Adeli, H. 2001, Resource Scheduling Using Neural Dynamics Model of Adeli and Park, Journal of Construction Engineering and Management, ASCE, 127 (1).

[30] Sipson, P. 1987, A Survey of Artificial Neural Networks, Naval Ocean Systems Center Technical Document TD 1106.

[31] Subcommitee on Neural Nets and Other Computational Intelligence – Based Modeling Systems A2K05(3), 1999. Use of Artificial Neural Networks in Geomechanical and Pavement Systems, Number E-C012, ISSN 0097-8515.

[32] Tashakori, A. & Adeli, H. 2001.Optimum Design of Cold-formed Steel Space Structures Using Neural Dynamics Model, Journal of Structural Engineering , ASCE, 127.

[33] Vanluchene, R. D. & Sun, R. 1990. Neural Networks in Structural Engineering, Micro-computers in Civil Engineering 5 (3), 207–15.

[34] Venayagamoorthy, V., Allopi, D., Vena-yagamoorthy, G.K. 2004. Neural Network Based Classification of Road Pavement Structures, ICISIP, IEEE. [35] Werbos, P.1974. Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences, Ph. D. Dissertation, Harvard University.

silvana Petruseva



Numerical Modeling of Unreinforced and Jacketed Masonry Buildings 1 | P a g e

AUTHORS

Sergey Churilov Ph.D. Assistant Professor Ss. Cyril and Methodius University Faculty of Civil Engineering–Skopje [email protected]

Elena Dumova-Jovanoska Ph.D. Professor Ss. Cyril and Methodius University Faculty of Civil Engineering–Skopje [email protected]

NUMERICAL MODELING OF UNREINFORCED AND JACKETED MASONRY BUILDINGS Presented in this paper is application of a displacement-based approach, based on the capacity spectrum method (CSM), to investigate the behaviour of unreinforced and strengthened masonry buildings under seismic loads. New analysis module was developed in a software program for static non-linear analysis of masonry buildings based on design provisions and failure mechanisms for masonry. The non-linear effects of masonry are introduced as bilinear curves and the capacity curve of a building is created following an iterative procedure. The methodology for analysis is illustrated on an existing masonry building. CSM was applied in a numerical model of a school building for two cases of structural material, existing building - unreinforced masonry and strengthened building - RC jacketed masonry. It was found that the jacketing method significantly increased the seismic capacity of the building.

Keywords: masonry, unreinforced, RC jacketing, capacity spectrum method, capacity curve.

INTRODUCTION The importance of numerical modelling and analysis of masonry structures has been increasing over the past decade. A great significance has been given to sophisticated numerical tools that can predict the behaviour of a structure starting from the elastic region, through occurrence of cracks and stiffness degradation, to complete loss of strength. To completely understand the collapse mechanisms and assess the structural safety within reliable limits, precise constitutive models in addition to advanced methods for solving systems of equations resulting from finite element discretizations are often needed. Consequently, the use of the finite element method is assumed for global behaviour simulation of a masonry structure. Recently, numerical research in masonry has been focused on advanced numerical tools since the difficulty in application of the existing numerical tools has been increased due to several characteristics of structural masonry.

The solution of a certain structural analysis problem is normally achieved by establishing idealization of the material behaviour. The description of the material behaviour, together with the geometry idealization (2D or 3D), enables inclusion of complex effects related to masonry behaviour as well as more expensive solutions. The idealizations, which are commonly applied to the behaviour of masonry material are elastic, plastic and non-linear material behaviour. The recommended approach in engineering

69.046.2


sergey churilov, elena dumova-Jovanoska Scientific Journal of Civil Engineering • Volume 2 • Issue 1 • July 2013

2 | P a g e Numerical Modeling of Unreinforced and Jacketed Masonry Buildings

practice and analysis of masonry structures is to perform non-linear analysis after linear analysis. Basically, the linear analysis can predict the sections of a structure which are more susceptible to non-linearity and consequently study that part in detail with non-linear material behaviour. However, the resources for application of non-linear analysis methods to masonry buildings are difficult considering the complex behaviour of the masonry.

This paper presents application of an analytical model in simplified non-linear analysis of masonry buildings by using a displacement-based verification method. The methodology for analysis is illustrated on an existing masonry building with the aim to verify its seismic capacity [1]. The dynamic characteristics of the building were determined by ambient vibration tests and experimental analysis methods. The test results were used to update the material properties of the initial calculation model through a manual updating technique, by matching the test results and the results from the numerical modal analysis. The updated material parameters were used in the displacement-based method for analysis on the basis of the Capacity Spectrum Method (CSM). The analytical models based on DIN Eurocode 6/NA [2] and Tomaževič [3] for unreinforced and reinforced masonry walls were chosen, considering the correlation of the results from the research work of Churilov [1].

The analytical models were implemented in the MINEA software package [4], through a newly developed analysis module. A comparison of the results obtained for two cases of structural material (unreinforced and strengthened) applied to the building is presented.

Ambient vibration tests are not a prerequisite for the subsequent non-linear analysis, but enable a good assessment of the material properties of the existing buildings.

DISPLACEMENT- BASED ANA - LYSIS OF MASONRY BUIL -DINGS The adopted approach to non-linear static analysis and seismic design of masonry

buildings is based on the capacity spectrum method. A new displacement-based design concept has been developed by the Chair for Structural Statics and Dynamics, RWTH University of Aachen [5, 6]. This concept follows the new trend in the seismic design of structures, namely, the performance based design, which examines the deformation properties of a structure. It was generalized to 3D buildings considering torsional effects and the modified structural vibration shape because of its stiffness degradation.

The analysis procedure is based on the capacity spectrum method by comparing the seismic action with the loading capacity of the building, considering the non-linear behaviour with its post peak capacity. Masonry failure modes and hysteretic damping are considered and the concept does not require additional use of empirically determined correction coefficients. The non-linear push-over curve of the entire building is obtained from the force-displacement curves of the individual masonry walls. As an input, force-displacement curves of individual walls are required.

Capacity spectrum method

The capacity spectrum method was originally developed by Freeman et al. [7] in 1975. It requires definition of the force-displacement capacity of a building and a corresponding site response spectrum. The procedure consists of finding the displacement demand during ground motion of a building in the inelastic range by the point where both the demand and the capacity curves intersect. The effective damping (ξeff) is used to define the demand spectral value, which corresponds to the damping that occurs when the structures is pushed into the inelastic range. In this procedure, it is viewed as a combination of viscous and hysteretic damping. The effective damping is obtained from ξeff=λξ0+0.05, where λ is a modification factor to account for the approximation involved in describing the hysteretic response of the building by the bilinear idealisation of the capacity curve. It ranges from 0.3− 1.0 depending on the type of the structural system, being 0.3 for systems with poor and unreliable hysteretic behaviour and 1.0 for well-detailed elements with stable hysteresis loops. The value of 0.05 represents the viscous damping inherent in the system.


nuMericAL ModeLinG of unreinforced And JAckeTed MAsonry buiLdinGsScientific Journal of Civil Engineering • Volume 2 • Issue 1 • July 2013


An iterative procedure is applied to obtain the displacement demand of the building. To initiate the process, the initial stiffness and an arbitrary value of the effective damping (for instance ξeff=5%) are used. With these values, a displacement demand is obtained from the demand acceleration-displacement spectra for this period of natural vibration and 5% damping, corresponding to point (0) in Figure 1. The displacement demand for this period and damping is obtained and marked as δ0. From the intersection point of the displacement demand and the capacity curve, a new effective period Teff(1) compatible with this displacement is obtained and the effective damping ξeff(1) is computed. A new calculation cycle is initiated. It uses the new period and damping value to obtain the new displacement demand, δ1. The procedure is repeated until the displacement demand δm matches the spectral value for the period Teff and the damping ξeff employed. The displacement demand δm is compatible with the strength and the stiffness of the building as well as the ground motion.

Capacity curve of the building masonry walls

The developed analysis concept requires definition of the capacity curves for the individual masonry walls at the ground floor of the building. These curves can be determined by experimental investigation, numerical simulation and analytical computation.

Based on the obtained test results in the cited research work [1], analytical formulation for the capacity curves of the individual masonry walls was used. The analytical models according to DIN Eurocode 6/NA [2] and Tomaževič [3] considering diagonal shear, flexural and sliding shear failure modes were implemented as a new module in the software package MINEA software package [4]. Three parameters are necessary for the development of the capacity curve for each wall: initial stiffness, maximum resistance (load bearing capacity) and ultimate displacement, see Figure 2. A database consisting from capacity curves and damping curves at different levels of vertical load and different height to length ratios was created.

Capacity curve of the building

The capacity curve of the entire building is determined from the capacity curves of the individual walls in the direction of the seismic action. Hence, several approximations are made:

The structure is assumed to have continuous walls over the height of the building,

The upper floors are considered to behave linearly elastic,

The failure modes are limited to the walls at the ground floor, and

The floor slabs are assumed to be fully rigid horizontal diaphragms, which transfer the horizontal forces from the seismic action to the masonry walls.

Figure 2. Bilinear capacity curve representation with the necessary parameters

Figure 1. Capacity spectrum method




Figure 3. Calculation of the building capacity curve by iterative algorithm

For symmetrical ground plans with symmetrical mass distribution, the capacity curve of a building can be computed by simple superposition of the capacity curves for the individual masonry walls. In case of unsymmetrical ground plans, the torsional effects have to be considered as a result of the rotation and displacement perpendicular to the direction of action. Therefore, the capacity curve is determined by using double iterative algorithm. First, a displacement step is imposed to the ground floor (let us assume that it is in x- direction), see Figure 3. With the imposed displacement, the resulting forces in all masonry walls are evaluated and the

resulting moment is computed. Then, a double iterative algorithm is applied with a procedure consisting of rotating and translating the system around the mass centre until the floor finds an equilibrium, .0,0 yFM The resulting pair of imposed displacement and reaction force in the direction of the action create one point on the capacity curve of the building. The whole curve is calculated by repeating the described procedure.

This approach is sufficiently accurate for buildings with few floors. A more refined approach can be applied to take into account the stiffness change at all floors.

DEVELOPMENT OF A NEW ANALYSIS MODULE IN MINEA For the purposes of the analysis performed with the MINEA software program [4], each wall needs to be described by a capacity curve. As described earlier, a capacity curve of a wall needs three parameters: initial stiffness, maximum resistance and ultimate displace-ment.

Initial stiffness

The lateral initial stiffness, eK of a wall is defined by the secant stiffness at the formation of the cracks. It is calculated as a sum of the lateral deformations due to bending and shear of the wall generated by a lateral load. A linear elastic theoretical model assuming total deformation d of fixed ended masonry walls partly due to bending and partly due to shear was used. Thus, the following formulas were used to calculate the lateral stiffness for fully fixed boundary conditions:

dHK u

e (1)

W

u

E

u

GAhH

EIhHd

12

3 (2)

where, Hu is ultimate horizontal resistance of the wall, h is height of the wall, E is modulus of elasticity of masonry, G is shear modulus of masonry, IE is reduced moment of inertia of the wall’s cross-section, Aw is area of the horizontal cross-section of the wall, is shear coefficient, for rectangular cross-section

.2.1

For practical applications, the effective stiffness derived from the elastic theory can be reduced to better match the experimental results. As pointed out by Gellert [8], based on analysis of several experimental results, the effective stiffness can be calculated by considering a reduced moment of inertia, as presented in Eq.3.

W

W

WE

GAhEI

II

264.31

(3)

where, IW is moment of inertia of the wall’s cross-section.

sergey churilov, elena dumova-Jovanoska




Maximum resistance

The maximum resistance was obtained with respect to the failure modes for unreinforced and reinforced masonry walls, as presented in Churilov [1]. It was obtained by adopting the lowest of the resistances calculated for a wall failing in shear or bending. The models for unreinforced and strengthened masonry walls proposed in DIN Eurocode 6/NA [2] and Tomaževič [3] were used to calculate the maximum resistances for each wall.

Tomaževič provisions

According to the provisions given by Tomaževič [3], the maximum resistance of the walls falling in shear was calculated with respect to Eq. 4.

urumhsu HHCH , (4)

where, Hu,s is the maximum resistance of the wall failing in shear; Ch is the maximum resistance degradation factor, (Ch=0.85); Hum is the resistance of the masonry; and Hur is the resistance of the reinforcement.

The resistance of masonry was calculated by using Eq. 5, where the tensile strength of masonry ft was evaluated by use of Eq. 6. For the shear stress distribution factor b, three limit states were considered, see Eq. 7.

10 t

twum fb

fAH (5)

22

02max

20

bft (6)

where, ft is tensile strength of masonry, max is average shear stress in horizontal section of the wall at maximum horizontal load Hmax and σ0 is average compressive stress in horizontal section of the wall due to constant vertical load.

5.1 if5.15.11.1 if

1.1if1.1

LhLhLh

Lhb (7)

The contribution of the reinforcement was introduced through the resistances calculated for the horizontal and the vertical reinforcement, Eq. 8.

yvmsvyhshur ffAfAH 026.13.0 (8)

where, As h is the area of horizontal reinforcement, Asv is the area of vertical reinforcement, fyh is the yield strength of horizontal reinforcement, fyv is the yield strength of vertical reinforcement, fm is the compressive strength of mortar.

The formulas for bending resistance of unreinforced and reinforced masonry wall were implemented in the analysis module, as well. To obtain the flexural capacity of the section through the corresponding ultimate bending moment, MRu, the equilibrium of sectional forces in the most stressed section of the wall was assessed. The ultimate bending moment can be calculated by Eq. 9. The flexural resistance of the wall, Hu,f, can be determined depending on the boundary conditions, Eq. 10.

kRu f

tLM85.0

12

02

0 (9)

hMH Ru

fu , (10)

where, fk is characteristic compressive strength of masonry and α defines the boundary conditions at the bottom and the top of the wall, (α=0.5 for fixed ended wall, α=1.0 for cantilever wall).

The bending resistance of reinforced masonry can be calculated by adding the contribution of the reinforcement to the flexural capacity of the cross-section of an unreinforced masonry wall. Considering that RC jacketed walls have uniform reinforcement distribution over the wall surface, the original formulation of Tomaževič [3] was modified to take into account this distribution, as shown in Eq. 11.

n

iiyvsv

kstrRu

lnlfA

ftLM

1

'

02

0,

2

85.01

2

(11)

where, n is number of vertical bars, n=L/s and s is horizontal distance between the vertical reinforcement bars. The flexural resistance of the wall Hstr,f can be determined depending on the boundary conditions, Eq. 12.




hM

H strRufstr

,, (12)

DIN Eurocode 6/NA provisions

The design provisions for maximum resistance of masonry walls given in Eurocode 6 [9] and DIN Eurocode 6/NA [2] were implemented in the analysis module as a second option for definition of the capacity curves.

The shear resistance calculation for the unreinforced masonry walls was done according to Eq. 13, while two ultimate criteria for calculation of the characteristic shear strength of masonry (fvk) were established.

cM

vksu tlfH

, (13)

where, Hu,s is the design shear resistance of the URM wall, lc is the length of the compressed part of the wall, ignoring the part of the wall that is in tension, and t is thickness of the wall.

The analysis value of fvk was adopted as the smallest between fvlt1 and fvlt2 which consider sliding shear failure (fvlt1) and diagonal shear failure of masonry (fvlt2),

001 4.0 vkvlt ff (14)

calbtcalbtvlt f

ff,

0,2 145.0

(15)

where, fvk0 is the characteristic shear strength of masonry under zero compressive stress.

The calculation tensile strength of the masonry units, fbt,cal, was adopted in relation to the unit type according to DIN Eurocode 6/NA [2]. Due to the fact that the shear resistance of the unreinforced walls depends on the stress state governed by the level of the vertical and horizontal loads, a simplification for calculation of the length of the compressed part of the wall (Lc) was made. In MINEA [4], the Lc parameter was considered to be equal to the wall length L. This assumption was supported by the fact that the horizontal loads needed for calculation of the actual stress state inside the wall are not known prior to distribution of the horizontal forces on each wall. This distribution is not performed in MINEA [4], because only the individual capacity curves of the walls are needed as an input parameter.

The shear resistance of reinforced masonry walls was implemented according to the formulas given in Eurocode 6 [9] and DIN Eurocode 6/NA [2] without any modification.

The bending resistance of unreinforced and reinforced masonry walls was also included in the analysis module. Therefore, Eq. 10 was used to calculate the bending resistance of the unreinforced walls, while the ultimate bending moment was taken according to Eq. 16. The pv factor depends on the boundary conditions on the top and the bottom wall edges. According to Gellert [8], pv=1.3 for fully fixed walls and pv=1.0 for cantilever walls were assumed in the module.

kvRu f

tqpLqM 0

20 15.11

2 (16)

The bending resistance of the reinforced masonry walls was implemented according to Eq. 17.

24.0 dbfzfAM wkyvsvRu (17)

where, z is the lever arm between the compressive and tensile force, bw is the width of the wall (thickness of the wall), d is the effective depth of the section (length of the wall), .38.00 kfLd

The lever arm for a section where the maximum compression and tension are reached simultaneously, may be taken as:

ddfbfA

dzkw

yvsv 95.05.01

(18)

The flexural resistance of the wall (Hstr,f) can be determined according to Eq. 10.

Ultimate displacement

The deformation capability described by the ultimate displacement values was defined as a drift limit ( u ) from the wall height according to Eq. 19 and Table 1.

hd uu (19)

For implementation of the ultimate displacements, several drift limits defined in the literature and design codes were considered. The drift ratios given in EN 1998-3 [10], DIN Eurocode 6/NA [2], OPCM 3274 [11]





and FEMA 273 [12] were studied. Referenced drift limits for shear and bending failure modes for two damage states (significant damage –SD and near collapse - NC) were considered.

The drift ratio for the reinforced masonry was defined according to FEMA 273 [12] for non-linear static procedures. Here, FEMA 273 guidelines for reinforced masonry walls were used as a reference to limit the ultimate displacements. This was done considering the fact that no reliable limit values for reinforced masonry walls were defined in other design provisions studied previously.

General software description and features

MINEA software was developed by Dr.-Ing. Christoph Butenweg and his associates (SDA-engineering GmbH). It offers solution for effective analysis of masonry buildings under vertical and horizontal loads due to earthquakes and wind. It features an integrated database structure, with databases for masonry materials. Depending on the requirements of the specific project, the calculations can be performed on 2D or 3D models.

The seismic action can be described by a design spectrum according to DIN 4149-04 [13] and a user supplied free spectrum. The seismic action can be applied in arbitrary direction of the ground plan or the program can automatically determine the weakest direction of the building and apply the horizontal loads. The damping from code defined spectra can be defined as hysteretic or constant viscous damping, while for free spectra, the damping has to be included in the spectra.

The building is assumed to be composed of continuous walls along the height and the upper floors are considered as linear elastic.

The torsional effects are considered according to the code regulations.

The materials are classified according to their mechanical properties. A database of code defined and user supplied materials is available within the program. The building is defined in the plan view by including the continuous walls only. The openings, piers and spandrels are not considered, while the walls with openings should not be defined in the calculation. The walls are entered through a graphical environment by indicating start and end points of each wall. The floor slab is created within the graphical window by indicating the floor contour points. Openings in the floors can be considered.

The load distribution on the walls is performed according to the corresponding areas of influence.

The results are presented in tabular and graphical form. The graphical presentation of the results shows the diagrams of the capacity curves for the individual walls, the capacity curve of the entire building, the diagram from the CSM with the identified performance point, the frequency distribution and the damping of the building.

PRACTICAL APPLICATION The proposed methodology was applied for the public masonry building of the primary school “Vojdan Chernodrinski” in Skopje, Macedonia, Dumova-Jovanoska et al. [14]. This building was selected for research and application of the developed methodology as a typical example of a building from the city of Skopje due to several reasons. The building was constructed before the catastrophic 1963 Skopje earthquake and according to PIOVSP [15] it is classified in category I. It is extremely important for such buildings to survive future earthquakes without serious damage to the structural system and to protect the lives of the residing young children.

Description of the building

The original design project documentation on the building was found in the Archives of

Table 1: Ultimate displacements implemented in MINEA

Failure mode Unreinforced Reinforced %u %u Diagonal shear+sliding shear kf15.04.0 0 acc. FEMA 273, table 7-5 kf15.03.0 0 acc. FEMA 273, table 7-5 Bending Lh4.0




Macedonia. It was constructed in 1952 and consists of a ground floor and 2 upper floors with rectangular shape in layout and dimensions 53.58x10.18 m, see Figure 4. From the available documentation, it is evident that the structural system represents confined masonry. It is composed from solid brick units and mortar with unknown properties and regularly spaced RC columns made from concrete class MB16 and certain number of RC beams. The concrete beams of class MB22 were used to connect few columns, while the other beams were located over the openings. The floors were designed and constructed as ribbed slabs from concrete class MB22. The building was designed by taking into account vertical gravitational loads only as seen in the design documentation. Typical views of the building are given in Figure 5.

Identification of the dynamic properties

To determine the real geometry, detailed on-site measurements were performed confirming many of the design parameters, but also indicating some significant differences between the actual building configuration and that in the original documentation. The survey

of the documentation and the current state of the building verified the presence of RC columns which act as a confinement of the masonry. The floors were assessed to have sufficient in-plane rigidity and to be able to be treated as rigid diaphragm in the analysis. Complete information about the properties of the construction material was missing, except for the very few parameters given in the original documentation. Because it was impossible to perform destructive tests and extract test samples from the building, the only possible method to discover the material properties was to conduct non-destructive tests and to perform ambient vibration measurements. Therefore, a series of ambient vibration measurements were carried out and these results were used to update the FE model of the building [14].

An initial 3D calculation FE model of the building based on geometry survey was developed prior to the performance of the ambient vibration tests. The masonry walls and the floor slabs were modelled by a 4-node shell FE, while the RC beams and columns were modelled by frame elements. In order to determine the dynamic properties of the structure, modal analysis was performed.

Table 2 shows a comparison of the first two

Figure 4. Typical building floor plan

a) North-West view b) West-East view

Figure 5. Characteristic views of the building.





natural frequencies of the building obtained by dynamic testing and FE model updating. The FE model updating of the selected parameters further improved the determined parameters and thus an optimal model of the building was achieved. The sensitivity analysis of the Young’s modulus of masonry and the unit weight was conducted. These parameters, together with the identified natural frequencies, were used as input values for the masonry in the numerical model used for seismic verification analysis.

Displacement-based seismic verifi-fication

The condition of the existing building was assessed by using the displacement-based seismic verification concept described previously. The capacity curves of the individual walls were computed by means of the proposed idealisation according to DIN Eurocode 6/NA [2]. The vertical load levels of the walls were calculated using the load distribution areas. The idealised bilinear (elastic-plastic) capacity curves for each masonry wall included in the model were calculated within the software.

Input values for non-linear analysis of the building

All walls present in the building were inserted in the numerical model, see Figure 6. The window and door openings, as well as the spandrel walls were excluded from the analysis. Only continuous walls with rectangular shape were included for calculation of the building capacity curves, see

Figure 7. The wall height of the three stories was 3900 mm. As discovered from the original design project, three different thicknesses of the walls were modelled, namely 120 mm, 250 mm and 400 mm.

All walls were modelled from unreinforced masonry and were considered fully fixed at both edges (α=0.5). Additionally, two reinforced concrete rectangular columns (150x150 mm) were added to the model where the openings for the windows at the stairs were located. Moreover, due to the unknown properties of the RC columns for confinement at window piers, as well as their connection to the masonry, those elements were treated as unreinforced masonry piers. Following the basic assumptions of the software, the floor structure was regarded as RC rigid diaphragm. The slab thickness was 150 mm. The roof structure was modelled as rigid RC slab with thickness of 120 mm. The material data for the analysis are given in Table 3.

The jacketed masonry included in the analysis consisted of reinforcement meshes with diameter 8 mm at a mutual distance along vertical and horizontal direction of 100 mm. In total, the area of the reinforcement mesh was 503 mm2. The yield strength of the reinforcement mesh was 600 N/mm2.

In addition to the self-weight, live load with intensity 1.5 kN/m2 was applied in vertical direction on all slabs. Load combination

Table 2: Comparison of the dynamic properties of the building obtained by tests and after FE model updating

Mode AVT test Updated FE model

Percentage difference

(Hz) (Hz) (%) 1 4.49 4.17 6.9 2 5.08 6.78 28.7

Figure 6. Wall numbering at the ground floor

Figure 7. 3D numerical model for deformation based seismic verification




factors of ψ0=0.7 and ψ2=0.3 were applied for the office building. The roof was loaded with an additional load of 1.0 kN/m2.

The idealized capacity curves for each wall were calculated within the software with the analytical models provided in the previous section. First, the ultimate resistance of each wall was calculated for the case of shear and flexural failure mode, by using the respective formulas. The wall failure mode was determined with respect to the smaller value between both. Next, the initial stiffness, elastic displacement and ultimate displacement were calculated.

The seismic load was defined according to Eurocode 8 [16] for assumed ground type B and estimated site elastic ground acceleration of ag=2.94 m/s2 (~0.3g). The demand curves were represented by earthquake response spectra for various levels of damping. Three damped response spectra curves were used, 3%, 5% and 10%. The 3 percent damping was defined according to the results from the ambient vibration test. The 5 percent response spectrum is generally used to represent the demand when the structure is responding linearly elastic. Higher damped response spectra are used to represent inelastic response spectra to account for hysteretic non-linear response of the building as defined in Freeman [17].

Assessment of the existing building

The main results obtained for the unreinforced masonry walls are given in Table 4. The results obtained for the analysed unreinforced masonry building showed that all walls oriented in Y direction of the global coordinate system would fail in shear, because their shear resistance was smaller than their flexural resistance. Also, most of the walls positioned in the global X direction would fail in flexure, 71%, while only 29% of the walls would fail in shear. A very interesting finding was that all walls that were assessed to fail in shear had a height to length (h/L) ratio smaller than 1.7, while flexural failure mode occurred in walls with h/L>1.7. The normal stress level achieved in the walls was in the range of σ0=0.18−0.75 N/mm2. The total resultant floor masses were: floors 1, 2 = 594.46 t and floor 3= 408.45 t.

The calculated capacity curves for the unreinforced masonry building in both orthogonal directions (X and Y) are shown in Figure 8. As can be seen from the figure, the capacity of the building in Y direction is about 2 times less than the capacity in X direction. This means that the building is more vulnerable in Y direction and that the first failures of the walls are expected to happen in the walls oriented with their plane in Y direction. The building has greater ductility in X direction. The assessed capacity was expected, considering the orientation of the walls in the floor plan layout.

The non-linear displacement-based method was applied in both directions of the building. The building’s capacity curve was converted into a spectral acceleration - spectral displacement diagram by using the dynamic characteristics of the fundamental mode to represent the structure as a single-degree-of-freedom structure. Thus, a capacity spectrum was obtained.

Both the capacity spectrum and the demand response spectrum were defined by the same set of coordinates and plotted together as shown in Figure 9. The intersection point in the diagram represents the "performance point",

Table 3: Material data for analysis of the existing state of the building

Material Compressive strength

Char. initial shear

Modulus of elasticity

Density Poisson’s ratio

(N/mm2) (N/mm2) (N/mm2) (kg/m3) URM 2.8 0.08 3108 1870 0.1 RC 20.5 / 31500 2500 0.2

Figure 8. Capacity curves of the URM building in the orthogonal directions





i.e., the inelastic response of the building. If the capacity curve intersects the demand curve, the building will survive the earthquake. In the case of the unreinforced masonry building, no performance point could be

established for 3, 5 or 10% damping. This indicates a critical situation and possible failure of the building at the ground floor.

Assessment of the strengthened building

Table 4: Results for the case of unreinforced masonry walls




The effectiveness of the strengthening method, which uses RC jackets, is illustrated by the presented application example. RC jacketing was applied to modify the original structural material, i.e. unreinforced masonry. Therefore, it was assumed that the steel reinforcing meshes had a bar diameter of Ø8 mm distributed at equal distances of 100 mm in both directions. The total reinforcement area was 503 mm2/m2. However, in respect to the test results obtained for the jacketed masonry walls without anchorage of vertical reinforcement in the floor beams [1], the participation of the vertical reinforcement in the seismic resistance of the walls was neglected in this example.

Figure 9. Determination of the "performance point"

for the unreinforced masonry building

The main analysis results obtained for the building with strengthened masonry walls (SM) are presented in Table 5. Only the results for the jacketed walls are presented. In X direction, jacketing was applied only to the walls that failed first during the analysis of the existing building. The wall failure sequences are automatically calculated by the program. In Y direction, strengthening was applied to all walls. The rest of the walls remained as unreinforced masonry wherefore the same results shown in Table 4 are valid for this case, as well. The strengthened masonry walls showed that each of them would fail by a flexure failure mode. The flexural and shear capacity of the jacketed walls was increased in comparison to that of the unreinforced walls. The flexural resistance was increased for 30%, while the shear resistance was increased in the range of 843− 2132%, or for about 1010% on the average. The increased resistance was due to the contribution of the horizontal reinfor-cement.

The capacity curves for the strengthened building in both horizontal orthogonal directions of the building were plotted on the same diagram with the capacity curves for the unreinforced building, see Figure 10. As can be seen, higher capacity of the strengthened

Table 5: Results obtained in the case of RC jacketed masonry walls





building was obtained in each direction in comparison with the unreinforced building. The seismic capacity of the strengthened building in X direction was about 7 times higher, while in Y direction, it was approximately 10 times higher than the capacity of the unreinforced building. Also, the ductility of the building with respect to the ultimate displacements was increased for about 30%. The results indicate that the applied strengthening method improved the seismic resistance of the building and changed the failure mechanism from shear to flexural. Flexural failure is considered ductile behaviour that can dissipate a lot of seismic energy. This is one of the reasons why it is the desired failure mode in seismic loading situations.

The capacity spectrum method was applied to the strengthened building to verify the seismic capacity, see Figure 11. The performance points were identified at the intersection of the capacity and the demand spectra for both directions. In both cases, the performance point lies in the ascending range of the capacity spectrum. For example, for 5% damped response spectrum, the performance point in Y direction was detected at a spectral acceleration of 7.123 m/s2 and a spectral displacement of 0.00178 m, giving a period of T=0.099 s.

From all the results shown above, it can be concluded that the jacketed masonry applied to the selected walls increased the seismic resistance and the global stability of the building for the given seismic intensity.

CONCLUSIONS

In this paper, application of a displacement-based analysis and seismic verification of masonry buildings are presented. The capacity spectrum method was applied in a numerical model of a school building. Based on the experimentally obtained capacity of unreinforced and jacketed masonry walls, analytical design relations for different failure modes were selected and included in a nonlinear analysis software. CSM was applied in two cases: unreinforced and RC jacketed masonry. Two essential findings from this comparison are summarized.

The assessment of the existing building in its present state showed that there was no performance point identified during this analysis. This important finding suggests that the building does not posses enough capacity to resist the loads from the applied seismic action. To improve the capacity of the building, a strengthening method with application of RC jackets was applied. The contribution of the vertical reinforcement to the overall seismic resistance was ignored.

The strengthening method was applied for selected walls in both orthogonal directions. The decision as to which walls should be strengthened was based on the detected wall failure sequence from the analysis of the unreinforced building. In X direction, only walls that failed first were selected, while in Y direction, all walls were strengthened. This was done because the Y direction was twice ‘weaker’ than the X direction in terms of maximum seismic resistance. It was proved that the strengthened, RC jacketed masonry improved the seismic capacity of the building in both directions. The performance points

Figure 10. Comparison of the capacity curves of the unreinforced and strengthened building

Figure 11. Determination of the "performance point" for the strengthened masonry building




were identified in both directions. With the applied strengthening material, the seismic safety of the building was increased.

ACKNOWLEDGMENTS

The authors are indebted to Dr.-Ing. C. Butenweg and SDA-engineering GmbH for the provided MINEA software.

REFERENCES

[1] Churilov, S. 2012. Experimental and Analytical Research of Strengthened Masonry. Ph.D. Thesis, Ss. Cyril and Methodius University, Faculty of Civil Engineering, Skopje, Macedonia.

[2] DIN Eurocode 6/NA. 2011. National Annex - Eurocode 6: Design of Masonry Structures - Part 1-1: General Rules for Reinforced and Unreinforced Masonry Structures. Berlin, DIN EN 1996-1-1/NA, DIN Deutsches Institut für Normung, April.

[3] Tomaževič, M. 1999. Earthquake-Resistant Design of Masonry Buildings, Volume 1 of Series on Innovation in Structures and Construction, Imperial College Press.

[4] MINEA. 2011. Design & Analysis of Masonry Buildings. SDA-Engineering GmbH, Research Version v2.3.54, edition, November.

[5] Gellert, C., Norda, H. and Butenweg, C. 2008. Nonlinear Behavior of Masonry Under Cyclic Loading. In 7th European Conference on Structural Dynamics - Eurodyn 2008, number E39, Southampton, UK, July, 7-9.

[6] Butenweg, C., Gellert, C., Reindl, L. and Meskouris, K. 2009. A Nonlinear Method for the Seismic Safety Verification of Masonry Buildings. In M. Papadrakakis, N.D. Lagaros, and M. Fragiadakis, editors, Compdyn 2009 - ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece, June, 22-24.

[7] Freeman, S. A., Nicoletti, J.P. and Tyrell, J.V. 1975. Evaluations of Existing Buildings for Seismic Risk. In Proceedings of 1st U.S. National Conference on Earthquake Engineering, volume 113-22, Berkeley, USA, EERI.

[8] Gellert, C. 2010. Nonlinear Analysis of Unreinforced Masonry Structures Under Earthquake Actions. PhD thesis, RWTH Aachen, LBB, December, (in German).

[9] Eurocode 6. 2005. Design of Masonry Structures - Part 1-1: General Rules for Reinforced and Unreinforced Masonry Structures. EN 1996-1-1:2005.

[10] EN 1998-3. 2005. Design of Structures for Earthquake Resistance - Part 1: Assessment and Retrofitting of Buildings. Brussels EN 1998-3:2005, CEN, June.

[11] OPCM 3274. 2005. Norme tecniche per il progetto, la valutazione e l’adeguamento sismico degli edifici. Testo integrato dell’allegato 2-edifici-all’ordinanza 3274 come modificato dall’opcm 3431 del 3/5/05. Roma n. 3274, Ordinanza del Presidente del Consiglio dei Ministri.

[12] FEMA 273. 1997. NEHRP Guidelines for the Seismic Rehabilitation of Buildings. Washington, D.C. FEMA, Federal Emergency Management Agency, October.

[13] DIN 4149-04. 2005. Bauten in deutschen Erdbebengebieten-Lastannahmen, Bemessung und Ausführung üblicher Hochbauten. Berlin, Deutsches Institut für Normung (DIN), April.

[14] Dumova-Jovanoska, E., Markovski, G. and Churilov, S. 2011. FEM Updating of Existing Structures Based on Ambient Vibration Measurements. International Conference - Innovation as a Function of Engineering Development, Volume 1, Nish, Serbia, November 25-26.

[15] PIOVSP. 1981. Code of Technical Regu-lations for the Design and Construction of Buildings in Seismic Regions. No. 50-3547/1 (25.2.1981), Official Gazette of (former) SFRY, No. 31, June.

[16] Eurocode 8. 2004. Design of Structures for Earthquake Resistance - Part 1: General Rules, Seismic Actions and Rules for Buildings. Brussels EN 1998-1:2004, CEN, December.

[17] Freeman, S. A. 1998. The Capacity Spectrum Method as a Tool for Seismic Design. Proceedings of the 11th European Conference on Earthquake Engineering, Paris, September 6-11. A.A.Balkema.


Volume 2Issue 1July 2013

volume 2 issue 1 july 2013

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