Gyula Bögöly MSc (CE)

BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS

DEPARTMENT OF ENGINEERING GEOLOGY AND GEOTECHNICS

ENGINEERING GEOLOGICAL CHARACTERIZATION AND NUMERICAL MODELLING OF STONE MASONRY ARCHES

New scientific results

Gyula Bögöly MSc (CE)

Supervisor: PhD, Péter Görög Assistant Professor

Budapest, 2016.

Engineering geological characterization and numerical modelling of stone masonry arches

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Table of contents

1. Background and motivation .................................................................................................. 2

2. Objectives of the dissertation ................................................................................................ 2

3. Summary of the related literature ........................................................................................ 3

4. Methodology ........................................................................................................................... 4

4.1. Load-bearing capacity analyses of masonry arch bridges ................................................ 4

4.2. Laboratory and numerical modelling of masonry arches ................................................. 5

5. New scientific results .............................................................................................................. 8

5.1. Theses regarding load-bearing capacity analyses of masonry arch bridges .................... 8

1. Thesis [5, 6] .......................................................................................................................... 8

2. Thesis [11] ............................................................................................................................ 9

3. Thesis [11] ............................................................................................................................ 9

5.2. Theses regarding laboratory and numerical modelling of masonry arches ................... 10

4. Thesis [7, 9, 11, 14] ............................................................................................................ 10

5. Thesis [13, 14] .................................................................................................................... 14

6. Applications of the results, outlook and future work ....................................................... 16

7. References ............................................................................................................................. 17

8. Main publications on the subject of the dissertation ........................................................ 20

9. Acknowledgement ................................................................................................................ 21

New scientific results Gyula Bögöly

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1. BACKGROUND AND MOTIVATION

Stone masonry arches are one of the most ancient forms of the engineering structures. Although

in these days new stone masonry arches are seldom built, the maintenance and restoration of the

old ones represent a special challenge at the present time as well. In historic times masonry arches

and vaults were widely used all over the world in large range of structures, even so their modelling

and analysis brings up many questions even today. In Hungary there are no methods commonly

used for controlling and investigating stone masonry arches and arch bridges thus the calculation

of load-bearing capacity of such structures causes difficulties in many cases. Due to the age of these

kind of structures the condition of most of them increasingly deteriorates. Moreover, the traffic and

related load has increased significantly, thus these old structures have to fulfil new expectations.

As a consequence, their stability control and verification of their load-bearing capacity became

necessary in many cases.

One of the most frequently investigated stone structures are the stone masonry bridges. Only in the

United Kingdom there are approximately 40000 (McKibbins et al., 2006), and in Hungary the

number of these bridges is also more than 1500 (Gálos & Vásárhelyi, 2005). Thus my research

primarily focuses on the analysis of the load-bearing capacity of stone masonry arch bridges thus

as a first step investigations were made in case of several arch bridges from the in situ diagnostics

through the laboratory investigations to the different stability analyses. My research pointed out

that in case of investigations of existing arches it is difficult to determine adequate input parameters

for the numerical modelling from the measurable data even for the simplest methods for instance

trust line analysis and rigid block method. The scope of effect of these input parameters is unclear

as well. In addition, the analysis of the structural behaviour also brings up further questions.

2. OBJECTIVES OF THE DISSERTATION

Based on the above mentioned findings my dissertation concerned with two major topics:

analyses of load-bearing capacity of stone masonry arch bridges and the effect of their input

parameters, and the usage of more difficult numerical modelling for investigating the structural

behaviour. Analysis of spatial behaviours, fatigue, skew or multiring arches, analysis of the soil-

structure interaction, effects of lateral loading do not belong to the scope of the research. The

objectives of the dissertation are the followings:

- comparison of the results of different load-bearing capacity analyses (MEXE method,

thrust line analysis, rigid block method)

- evaluation of the effect of the input parameters on the load-bearing capacity calculation by

means of sensitivity analysis


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- comparison of the results of laboratory experiments and numerical models to investigate if

a hybrid finite element program is capable of analysing the structural behaviour

- investigation of the applicability of a hybrid finite element program for the analysis of

carbon fiber reinforced polymer (CFRP) strengthened masonry vaults

3. SUMMARY OF THE RELATED LITERATURE

Since the cultural significance of stone masonry arch bridges is high and their structural

behaviour is unique, several papers, studies and researches are concerned with some aspects of

masonry structures. Modern equilibrium analyses of masonry arches were based on Heyman (1966)

work. His articles have been published since the 1960s and 1970s, and with his work he laid down

the basis of the plastic analyses of masonry arches. Heyman (1995) summarizes most of his

findings. There are a great many researchers of this topic, the works of Harvey (1988), Page (1988),

Gilbert & Melbourne (1994), Vermeltfoort (2001), Fanning & Boothby (2001) Cavicchi &

Gambarotta (2006), Milani et al. (2008), Gibbons & Fanning (2010) ought to be mentioned in the

first place. The most comprehensive work about the assessment of masonry arch bridges from the

in situ diagnostics to the different calculations is presented by McKibbins et al. (2006). CFRP

strengthening in case of masonry arches is a relatively new topic. The papers of Foraboschi (2004),

Oliveira et al. (2010), Oliveira et al. (2011), Basílio et al. (2014), Maruccio et al. (2014) give an

outline of this research area.

In the home literature Kalinszky (1961), Dulácska (1994a), Peck (2003), Czeglédi (2005), Peck

& Sajtos (2005), Déry (2010), Pattantyús-Ábrahám (2011), Hegyi (2012) are concerned with the

different aspects of masonry arches. Regarding the numerical modelling of such structures Ther et

al. (2010), Ther & Kollár (2014), Bagi (2014), Simon & Bagi (2014), Lengyel & Bagi (2015)

provide information. Some other aspects of masonry structures are presented in Dulácska (1994b),

Sajtos (2001), Sajtos (2004), Fódi (2011), Haris & Hortobágyi (2012). Kiss et al. (2002a), Kiss et

al. (2002b) address theCFRP strengthening of masonry walls.

In Hungary papers of Orbán (2006a), Orbán (2006b), Orbán (2008), Orbán & Lenkei (2009),

Orbán & Gutermann (2009), Orbán (2014), Orbán & Juhász (2016) deal with the most area of the

topic. The most comprehensive work about the assessment of masonry arch bridges is Magyar

Útügyi Társaság (2006). Berkó (2003), Gálos & Vásárhelyi (2005), Gubányi-Kléber & Vásárhelyi

(2004), Tóth et al. (2009), Turi et al. (2013) give examples of different researches of arch bridges.

The Hungarian masonry arch bridges are demonstrated in Gáll (1970) and Imre et al. (2009).

In the home literature there are no previous papers regarding the laboratory experiments and

numerical modelling of masonry arches.


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4. METHODOLOGY

4.1. Load-bearing capacity analyses of masonry arch bridges

In order to get familiar with the practical difficulties and the whole process of load-bearing

capacity calculations of masonry bridges, investigations were made in case of seven arch bridges

(Benta-brook bridge in Sóskút, Mill-bridge in Sóskút, Bükkös-brook bridge in Szentendre, Derék-

brook bridge in Patak, Lókos-bridge in Romhány, Bér-brook bridge in Héhalom, Rédei-Nagy-

brook bridge in Gyöngyöspatai) from the in situ diagnostics through the laboratory investigations

to the different stability analyses. Comparison was made between the results of an approximate

calculation with the MEXE method (MEXE, 1963), the thrust line analysis and the rigid block

method. For the calculations the ARCHIE-M software (Obvis, 2016) and the LimitState Ring

program (LimitState Ltd, 2011) developed by the University of Sheffield were used. By means of

the results of the load-bearing capacity calculations the applicability of the MEXE method in case

of multispan bridges with stocky piers was analysed. The investigation based on the work of

Melbourne et al. (1997) and Magyar Útügyi Társaság (2006). Finally, sensitivity analyses were

carried out with the rigid block method to investigate the scope of effect of the input parameters to

the load-bearing capacity. Figure 1 demonstrates the different steps of the research.

Fig. 1. Flowchart of the research of load-bearing capacity analyses of masonry arch bridges

IN SITU TESTING - geometriai adatok felmérése

- identification of the lithotypes

- mapping the damages of the stucture

- identification of the fill material

- condition assessment of the mortar

- condition assessment of the dimension

stones ( Schmidt‐hammer, moisture)

- sampling

LABORATORY MATERIAL TESTING 1. Rock material testing

- specimen forming

- saturation or drying

- measuring mass and geometric data

- set up of testing system and sensors

- compressive strength test

- tensile strentgh test

- assessment of the measurements

SENSITIVITY ANALYSES - set up of parameter intervals

- bearing capacity calculations with the

rigid block method (LimitState Ring

program) concerning the different

parameter values, for all of the bridges

- drawing the diagrams of the sensitivity

analyses

BEARING CAPACITY CALCULATION OF BRIDGES

- MEXE method

- thrust line analysis

(Archie‐M program)

- rigid block method

(LimitState Ring program)

Permissible axle load

EVALUATION - comparsion of the results of the

different methods - comparsion with literary data - evaluation of the effect of the

parameters on the bearing capacity - conclusions


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In situ tests included the identification of lithotypes. Weathering forms were classified

according to Fitzner et al. (1995), Török (2002) and ICOMOS (2008). For the assessment of the

condition of the stone materials N-type Schmidt hammer was use. Laboratory tests and

measurements were made in the material testing laboratory of the Department of Construction

Materials and Engineering Geology. The investigations were made with calibrated instruments.

Determination of bulk density was made according to the MSZ EN 1936:2007 standard. Rock

strength tests were performed on oven-dry and water-saturated cylindrical specimens with a length-

to-diameter ratio of 2:1 at ambient temperature. Tensile strength tests were carried out according

to the MSZ 18285/2-79 Hungarian standard, uniaxial compressive strength tests were performed

according to the MSZ EN 1926:2007 standard. Elastic modulus and Poisson ration were measured

according to the suggestions of the ISRM (2014).

There are no unified method for taking into account the different damages of masonry

structures. Few damages can be considered in different extent and in different ways depending on

the different calculation methods. Present results take into account the effect of mortar loss, the

decreasing of the effective width of the vault due to lengthwise cracks of the arch. Displacements

of the abutments, foundation settlements, occasional backing, fallen blocks, stiffener effect of the

spandrel wall, partial collapses are not considered.

4.2. Laboratory and numerical modelling of masonry arches

In foreign researches it is an accepted procedure to verify the applicability and the accuracy of

new methods and software by means of laboratory experiments. Such validations are presented in

Melbourne & Gilbert (1995), Vermeltfoort (2001), Milani et al. (2008). Following the international

examples present research validate a hybrid finite element program (Rocscience RS2) by means of

laboratory experiments of small scale arches. The aim of the validation was to decide if the

mentioned numerical method is capable of analysing the structural behaviour, estimating the load-

bearing capacity accurately enough. Figure 2 summarizes the different part of the research.

Construction materials used for the experiments were tested as it was shown above in Chapter

4.1. Bending and compressive strength tests of the mortar were performed according to the MSZ

EN 1015-11:2000 standard. Bonding strength tests were measured by following the instructions of

the e-ÚT 07.03.21:2000 [ÚT2-3406] Hungarian standard. The tests were performed on an arch

(Figure 3) and on two barrel vaults with the same geometry with and without reinforcement (Figure

4). On the strengthened arch carbon fiber reinforced polymer (CFRP) plates were used to increase

the load-bearing capacity thus it was also observed if a calibrated numerical model can calculate

the strengthening effect. During the laboratory experiment the arches were loaded to collapse then


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the results were compared to the results of the numerical modelling. The most parts of the

laboratory experiments represent the results of the work together with Richárd Varró. The results

of the experiments are also presented in Varró et al. (2013), Varró et al. (2014). Further information

can be found in Varró (2012) and Varró (2015).

The constructed small scale vaults are semi-circular arches built from sandstone blocks with a

size of 3 x 3 x 4 cm. The normal size masonry arch has a segmental shape. It was built from standard

sized brick. The joints of all three arches were filled with traditional lime mortar. For the

strengthening of one of the small scale vaults SIKA CarboDur M-514 type CFRP strips were used

with a width of 50 mm. The strips were pasted up to the full length of the extrados and intrados

with a special mortar, the Sikadur-30 which is a 2-component, moisture-tolerant, high-strength,

structural epoxy paste adhesive for bonding external reinforcement.

Fig. 2. Flowchart of the research of laboratory and numerical modelling of masonry arches

LABORATORY EXPERIMENTS - preliminary investigations

- building the centre and the foundations

- preparing blocks and mortar

- construction of the arches, strengthening

with CFRP strips


- loading the arches till collapse

- observing failure load and mechanism

LABORATORY MATERIAL TESTING 1. Testing the material of the blocks

- specimen forming

- saturation or drying



- compressive strength test

- tensile strentgh test


2.Testing the mortar

- mixing mortars with different recipies

- preparing specimens


- bending‐, and compressive strength

test

- bonding strength test


- choosing recipe for mortar

3.Testing the CFRP strips

- bonding strength test of the special

mortar on different materials


NUMERICAL MODELLING - set up required parameters for the

modelling

- 2D hybrid finite element modelling

(Rocscience RS2 program)

- creating different modell set‐ups

concerning the geometrical idealization,

looking for the best fitting one

Failure load Failure mechanism

- using the validated numerical modell

for analysing the CFRP strengthened

vault

- verification of he results with the new

laboratory experiment

EVALUATION - comparison of the results of the laboratory experiments and the numerical models

- comparison of the different numerical modell set‐ups - revalidating the CFRP strengthened model - conclusions


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Fig. 3. Small scale vault with geometrical data (left), vault strengthened with CFRP strips (right)

Fig. 4. Normal size masonry arch with geometrical data

The numerical modelling was carried out with the Rocscience RS2 (Rocscience, 2014) two-

dimensional hybrid finite element program. Plane strain analysis was used with homogeneous,

isotropic, linear elastic, six nodded triangle finite elements. The connections between the blocks

were taken into account as joints. A joint represents an interface along which movement could take

place. A joint was assigned strength and stiffness properties in accordance with the Mohr-Coulomb

failure criterion. Residual values of strength parameters can be adjusted thus the behaviour of a

yielded joint can observed. Figure 5 shows the mechanical model of the joints. Normal and shear

stiffness were carried out by using the findings of Senthivel & Lourenço (2009).

jkn~normal stiffness, jks~shear stiffness, jten~tensile strength, jfric~friction angle, jcoh~cohesion

Fig. 5. Behaviour of the joints (Sarhosis et al., 2015)


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5. NEW SCIENTIFIC RESULTS

5.1. Theses regarding load-bearing capacity analyses of masonry arch bridges

1. Thesis [5, 6]

I have demonstrated by the comparison of the results of numerical modelling (with thrust

line analysis and rigid block method) and approximate calculation (MEXE method) of five

multi-span masonry arch bridges with stocky piers that in case of the investigated multi-span

bridges (rigid abutments, 0.11-0.87 pier height/thickness ratio, 3.6-9.2 m long span, 2.11-3.83

span/rise ratio) the MEXE method is applicable for calculating the permissible axle loads. In

case of the investigated bridges the load-bearing capacity calculated with the MEXE method

is 55-70 % of the results of the calculation with the rigid-block method.

The investigation based on the work of Melbourne et al. (1997) and Magyar Útügyi Társaság

(2006) according to which the vaults of multi-span arch bridges work independently if their piers

considered to be stocky. Since the approximate calculation of MEXE method is only applicable for

single span bridges, the statement of the 1. Thesis extends the boundary conditions and the

applicability of the method. The verification was carried out with the thrust line analysis and the

rigid block method to which Figure 6 and 7 provide examples. Table 1 summarizes the results of

the different calculation methods, the permissible axle loads are presented in the ratio of the rigid

block method. Bridges with grey coloured background are single span bridges. In case of the

Lókos-bridge (“e”) the MEXE method overestimates the permissible axle load which is a known

defect of the calculation. It can occur in case of bridges with short span and thin layer of surface

fill. In the other cases the approximation was as accurate as it was expected.

Fig. 6. Thrust line analysis in case of the Bér-brook bridge (39.06 t)

Fig. 7. Failure mechanism by the rigid block method in case of the Bér-brook bridge (49.0 t)


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Table 1. Permissible axle loads of different bridges in the ratio of the rigid block method

a b c d e f g

MEXE method 0.55 0.74 0.89 0.70 2.08 0.57 0.67

Thrust line a. 0.64 0.41 0.75 1.15 0.96 0.81 0.82

Rigid block m. 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Legend: a~Sóskút, Benta-brook. b., b~Mill-bridge, c~Szentendre, Bükkös-b. bridge,

d~Patak, Derék-b. bridge, e~Romhány, Lókos-bridge, f~Héhalom, Bér-b. b., g~Gyöngyöspata, Rédey-Nagy-b. b.

2. Thesis [11]

I have demonstrated by the sensitivity analyses of seven stone masonry arch bridges (2

single span, 2 double span, 3 triple span) carried out with rigid block method that the friction

coefficient has the largest effect on the load-bearing capacity. The other five tested

parameters (compressive strength of blocks, unit weight of blocks, unit weight of backfill,

angle of friction of backfill, angle of dispersion of surface fill) effected less the load-bearing

capacity of the investigated bridges (rigid abutments, 0.11-0.87 pier height/thickness ratio,

3.6-9.2 m long span, 2.11-3.83 span/rise ratio).

3. Thesis [11]

I have demonstrated by the sensitivity analyses of seven stone masonry arch bridges (rigid

abutments, 0.11-0.87 pier height/thickness ratio, 3.6-9.2 m long span, 2.11-3.83 span/rise

ratio) carried out with rigid block method that load-bearing capacity of the investigated

bridges is more sensitive to the unit weight of the backfill than to the compressive strength of

the blocks. The average variation of the load-bearing capacity of the investigated bridges due

to ±10% alteration of compressive strength is ±1.88%, due to ±10% alteration of unit weight

of backfill is ±4.80%.

Figure 8 and 9 give examples of the results of sensitivity analyses. According to these results

in case of arch bridges the friction coefficient and the soil physical properties have the largest effect

on the load-bearing capacity. It confirms also that the backfill has a multiple role in forming the

forces and behaviour of the structure. The results show that the emergent failure mechanism could

affect significantly the rate of the influence of the parameters. Therefore it is suggested to pay

attention to the accuracy of the parameters depending on the failure mechanism. In case of sliding

only failure mechanism (Figure 8) the accuracy of the value of friction coefficient is especially

determining. In case of the investigated bridges minor alteration of this coefficient causes

significant difference in the failure load (10% alteration could cause 28% difference on the

average).


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Fig. 8. Results of the sensitivity analysis in case of the Derék-brook bridge

Fig. 9. Results of the sensitivity analysis in case of the Réday-Nagy-brook bridge

5.2. Theses regarding laboratory and numerical modelling of masonry arches

4. Thesis [7, 9, 11, 14]

I have demonstrated by numerical modelling supported by laboratory experiments that

a hybrid finite element method (Rocscience RS2) is capable of analysing the structural

behaviour of segmental masonry arches and vaults, and it can estimate the load-bearing

capacity of the analysed structures accurately (83-97 % of the results of the laboratory

experiments). To achieve the mentioned accuracy it is necessary to use the accurate geometry

for setting up the model instead of idealized geometry that is to say it is necessary to take into

consideration the real form of the blocks and the real width of the mortar. The numerical

model made with idealized geometry overestimated the load-bearing capacity of the tested

arch, and the failure mechanism also differed from the laboratory results. In case of the

numerical model with the accurate geometry the calculated result gave a conservative

approximation (83 % of the result of the laboratory experiment) and the failure mechanism

of the model was equivalent to the observed results of the laboratory experiment.


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Table 2 summarizes the calculated failure loads as results of the numerical modelling and the

measured failure loads as results of the laboratory experiments in case of the brick arch and the

small scale sandstone vault. The results show good correspondence in both cases, the method was

suitable for calculating the load-bearing capacity with adequate accuracy. The numerical model of

the brick arch can be seen in Figure 10. Figure 15 shows the numerical model of the sandstone

vault. In the figures mentioned above the emergent displacements at the moment of collapse are

illustrated with a range of colours, and the cracked parts of the cross sections are highlighted with

red colour. Beyond the values of the failure loads, the numerical models gave a good

correspondence of the failure mechanism as well. The emergent failure mechanisms of the brick

arch can be seen in Figure 11 and in case of the sandstone arch Figure 12 presents the results. In

both cases the arches were lost their stability after the four hinges failure mechanism occurred.

Table 2. Comparison of the failure loads from the numerical models and the laboratory experiments

Numerical models Laboratory experiments

Calculated failure load Calculated/Measured

failure load Measured failure load

arch 0.25 kN (2 x 0.125 kN) 97 % 0.258 kN (2 x 0.129 kN)

vault 0.16 kN (2 x 0.08 kN) 83 % 0.193 kN (2 x 0.097 kN)

Fig. 10. Failure load of the brick arch and the emergent displacements at the moment of collapse

In case of masonry arches built from stone materials it is frequent that the masonry consists of

irregular blocks with different shape and different sizes. On the other hand, in case of numerical

models idealized geometry is used in most cases with regular uniform shaped and sized blocks.

The effect of these differences was analysed in case of the sandstone vault which was built from

irregular blocks. In such cases there are different approaches to create the numerical model

considering the geometry of the blocks. The model can be built from idealized blocks with the same

size and shape (Figure 13). One other option is to using the real geometry of the blocks (Figure 14)


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or using the real geometry of the blocks and the mortar thickness (Figure 15) as well. Due to the

small scale of the sandstone vault the influence of the real thickness of mortar has higher

significance in this experiment.

Fig. 11. Emergent failure mechanisms of the arch: laboratory model (above), numerical model (below)

Fig. 12. Emergent failure mechanism of the vault: laboratory model (above), numerical model (below)


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Table 3 demonstrates the differences between the calculated failure load in case of the three

different model set-ups and the result of the laboratory experiment. According to the results the

idealized model set-up significantly overestimates the real failure load. The model with real block

geometry and mortar gave the best approximation of the measured laboratory results. Figure 13-15

show that depending on the model set-up the geometry effected the failure mechanism as well.

Emergent displacements at the moment of collapse are illustrated with a range of colours, and the

cracked parts of the cross sections are highlighted with red colour.

Table 3. Comparison of the failure loads of the different model set-ups with the result of the laboratory experiment

Numerical models Laboratory experiments

Model set-up Calculated failure load Calculated/Measured

failure load Measured failure load

Idealized model 0.8 kN (2 x 0.4 kN) 414 %

0.193 kN (2 x 0.097 kN) Model with real block geometry

0.28 kN (2 x 0.14 kN) 145 %

Model with real block geometry and mortar

0.16 kN (2 x 0.08 kN) 83 %

Fig. 13. Failure load and displacements at the moment of collapse in case of the idealized model

Fig. 14. Failure load and displacements at the moment of collapse in case of the model with real block geometry


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Fig. 15. Failure load and displacements at the moment of collapse in case of the model

with real block geometry and mortar

5. Thesis [13, 14]

I demonstrated by laboratory experiment of a masonry vault strengthened with carbon

fiber reinforced polymer (CFRP) strips on the full length of the intrados and extrados that

the effect of the strengthening can be calculated with the calibrated numerical model (using

Rocscience RS2) and the altered failure mechanism can be predicted.

By means of the experiment validated numerical model of the small scale vault it was tested if

the calculation works properly in further investigations. Thus the strengthening effect of the CFRP

strips was analysed with the validated model and the results of the calculation were compared to

the laboratory experiment. The failure load of the strengthened laboratory vault was (2 x 11.25 kN)

24.5 kN. According to the previous findings the model was made with the real block geometry and

mortar width. The accuracy of the calculation was proved to be adequate again, the approximated

failure load was 91 % of the measured value in the laboratory (Table 4).

Table 4. Comparison of the failure load from the numerical model and from the laboratory experiment of the CFRP strengthened vault

Numerical model Laboratory experiments

Calculated failure load Calculated/Measured failure

load Measured failure load

22.4 kN (2 x 11.2 kN) 91 % 24.5 kN (2 x 11.25 kN)


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Fig. 16. Failure load and displacements at the moment of collapse in case of the CFRP strengthened vault

Figure 16 shows the emergent displacements of the vault at the moment of collapse. Till the failure

occurred all of the joints of the structure cracked through. Still the arch did not collapse since

simultaneously the rotations and the formation of the four hinges mechanism were hindered with

the CFRP strips. The altered failure occurred due to the debonding of the strips and the sliding of

the blocks near to the exerted loads (Figure 17). The numerical model simulated the real behaviour

of the arch suitably.

Fig. 17. Emergent failure mechanism of the strengthened vault: laboratory model (above), numerical model (below)


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Typical failure mechanism of masonry arches is the four-hinge mechanism. Since CFRP strips

hinder the formation of rotation, hinges mechanism are blocked. Therefore the failure mode of

strengthened arches will be completely different. In such cases crushing of the blocks, sliding,

debonding of the strips, or rupture of the CFRP strips can occur (Foraboschi, 2004). The altered

failure mode in this case started with the debonding of the strips which lead to sliding between

blocks.

6. APPLICATIONS OF THE RESULTS, OUTLOOK AND FUTURE WORK

The presented new scientific results help the investigation of the bearing capacity of masonry

arch bridges and the analysis of the structural behaviour of arches and vaults. With my results I

extended the potential use of a simple and common approximate calculation (MEXE method) for

multi-span bridges with stocky piers. By this I enabled an easier way to examine many other bridge

in practice.

From the results of the sensitivity analysis I concluded that the accuracy of the various input

parameters should be taken into account depending on the failure mechanism. The results of my

research draw attention to those parameters (e.g. friction between blocks), of which inaccuracy

influences significantly the load-bearing capacity. Therefore these results could be a guideline for

the engineers in case of practical investigations. An interesting result is that the load-bearing

capacity is more sensitive to the uncertainty of the unit weight of the backfill than to the

compressive strength of the blocks. This statement highlights the importance of the investigation

of the backfill for these calculations. Since the friction coefficient between the blocks cannot be

measured, but it is an important parameter in terms of the calculation, the setting up of these values

opens the door to further researches with the laboratory examination of different stone materials

and different mortars.

I proved with my results of the laboratory and numerical modelling of masonry arches that a

hybrid finite element method (Rocscience RS2) is able to calculate the failure load of the arches

with adequate accuracy and it is suitable to predict the fracture mechanisms in case of unreinforced

and reinforced arches by CFRP strips as well. The most important lesson of the numerical models

was that there may be significant differences between idealized modelling and modelling with

actual geometry. The modelling with idealized geometry overestimated the load-bearing capacity

of the arch significantly and it never gave back the failure mechanism. Therefore as far as possible

the geometric imperfections should be taken into account in case of the modelling of arches built

by blocks with irregular shape and different size. The results should be definitely validated for real-

size arches in the future. The numerical models demonstrated by the presented experiments are


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suitable for further studies, because these validated models are useable to analyse additional effects

(filling, horizontal forces, etc.).

All things considered it can be said that the investigation of stone masonry arches is a complex,

multidisciplinary research topic that provides more and more questions to be answered and

problems to be solved for engineers. With the development of the material sciences, measurement

technologies and numerical methods the interest of this theme shall intensify in the future. At

present, the accuracy of the available mechanical models is far superior to the measurement

accuracy of the individual material properties. Therefore in theory we can perform high precision

calculations, but in practice we can only calculate the carrying capacity of existing structures with

high estimation. Thus, in the future more effort should be put into the development of diagnostic

methods and into the closer cooperation of these connecting scientific areas.

7. REFERENCES

Bagi, K., 2014. When Heyman’s Safe Theorem of rigid block systems fails: Non-Heymanian collapse modes of masonry structures. International Journal of Solids and Structures 51, 2696–2705. doi:10.1016/j.ijsolstr.2014.03.041

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8. MAIN PUBLICATIONS ON THE SUBJECT OF THE DISSERTATION

[1] Bögöly, Gy., Görög, P., 2010. A Bükkös patak boltozott kőhídjának vizsgálata, in: Mérnökgeológia-Kőzetmechanika 2010. (In: Török Á., Vásárhelyi B. (Eds.)), Mérnökgeológia-Kőzetmechanika Kiskönyvtár. Presented at the Mérnökgeológia-Kőzetmechanika Konferencia, Konferencia helye, ideje: Budapest, Magyarország, 2010.03.25, Műegyetem Kiadó, Budapest, pp. 35–44.

[2] Bögöly, Gy., Görög, P., Seidl, Á., Török, Á., 2011. Gyöngyöspatai boltozott híd kőzetdiagnosztikai vizsgálata, in: Építményeink védelme-Műemlékeink védelme 2011 (In: Szalay L. (Ed.)). Presented at the Építményeink védelme - Műemlékeink védelme 2011., Konferencia helye, ideje: Ráckeve, Magyarország, 2011.03.29-2011.03.31., Konferencia Iroda Bt., Budapest, pp. 1–9.

[3] Bögöly, Gy., Görög, P., Török, Á., 2011. Diagnostics and stability analysis of stone masonry arch bridges, a case study from Hungary, in: Building Materials and Building Technology to Preserve the Built Heritage (In: Drochytka R, Bohus S. (Eds.)). Presented at the 2nd WTA International Ph.D. Symposium, Brno, Csehország, Oct. 6-7. 2011., Academic Publishing CERM Ltd., Brno, pp. 98–107.

[4] Bögöly, Gy., Görög, P., Török, Á., 2011. Boltozott hidak diagnosztikai módszerei. Díszítő- Építő- Mű- Terméskő XIII, 32–36.

[5] Bögöly, Gy., Görög, P., 2012. Kőszerkezetű hidak számítógépes modellezése, in: Építményeink Védelme-Műemlékeink Védelme 2012 (In: Szalay L. (Ed.)). Presented at the Építményeink védelme - Műemlékeink védelme 2012., Konferencia helye, ideje: Ráckeve, Magyarország, 2012.03.27-2012.03.29., Konferencia Iroda Bt., Budapest, pp. 49–56.

[6] Bögöly, Gy., 2012. Diagnostic and stability analysis of stone masonry arch bridges, in: Proceedings of the 9th Fib International PhD Symposium in Civil Engineering. KIT Scientific Publishing, Karlsruhe, pp. 167–173.

[7] Varró, R., Bögöly, Gy., Görög, P., 2013. Kőboltozat laboratóriumi vizsgálatának tapasztalatai. Magyar Építőipar, 2013:(2), 63–68.

[8] Bögöly, Gy., Borbély, D., Görög, P., 2014. Előkészítő vizsgálatok kőboltozat laboratóriumi modellezéséhez. Magyar Építőipar 64, 141–145.

[9] Varró, R., Bögöly, Gy., Görög, P., 2014. Kőszerkezetű boltozatok teherbírásának vizsgálata, In: Köllő G. (Eds.). Presented at the XVIII. Nemzetközi Építéstudományi Konferencia: ÉPKO 2014. Konferencia helye, ideje: Csíksomlyó, Románia, 2014.06.12-2014.06.15., Erdélyi Magyar Műszaki Tudományos Társaság (EMT), pp. 333–337.

[10] Bögöly, Gy., Görög, P., Török, Á., 2015. Stone masonry arch bridges: In situ testing and stability analyses by using numerical methods; examples from Hungary, in: Engineering Geology for Society and Territory - Volume 8: Preservation of Cultural Heritage. pp. 503–506.

[11] Bögöly, Gy., Görög, P., 2015. Numerical Testing of a Small-Scale Stone Masonry Arch. Periodica Polytechnica Civil Engineering 59 (4), 567-573. doi:10.3311/PPci.7786

[12] Bögöly, Gy., Török, Á., Görög, P., 2015. Dimension stones of the North Hungarian masonry arch bridges. Central European Geology 58 (3), 230–245. doi:10.1556/24.58.2015.3.3

[13] Szakály, F., Bögöly, Gy., Varró, R., Berecz, A., Görög, P., 2015. Experimental and numerical analysis of small scale masonry arches, in: Proceedings of the 8th International Congress of Croatian Society of Mechanics (In: Ivica Kožar, Nenad Bićanić, Gordan Jelenić, Marko Čanađija (Eds..)). Presented at the 8th International Congress of Croatian Society of Mechanics, Croatian Society of Mechanics, Opatija, Croatia, 2015.09.29-2015.10.02., pp. 1–10.

[14] Bögöly, Gy., 2016. Kicsinyített boltozatok laboratóriumi és hibrid végeselemes modellezése, in: Mérnökgeológia-Kőzetmechanika 2016. (In: Török Á., Görög P., Vásárhelyi B. (Eds.)), Mérnökgeológia-Kőzetmechanika Kiskönyvtár. Presented at the Mérnökgeológia-Kőzetmechanika Konferencia, Konferencia helye, ideje: Budapest, Magyarország, 2016.05.18., Hantken Kiadó, Budapest, pp. 307–316.


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9. ACKNOWLEDGEMENT

Firstly, I would like to express my sincere gratitude to my advisor Prof. Péter Görög for his

help and the continuous support. Without his precious support in the last few years, it would not

be possible to conduct this research. Besides my advisor, I would like to thank the head of

department, Prof. Ákos Török, for his precious help in my articles and research and for his unfailing

support at my university work.

I would like to thank Prof. Katalin Bagi and Prof. Rita Kiss for reviewing my thesis version,

which was made for the discussion at the Department, and for their insightful comments and

recommendations.

I would like to acknowledge Orsolya Tasnádi and Olivér Himmel for their help and work at

the laboratory and field measurements. Especially I would like to thank Richárd Varró for his help

and work in the small-scale laboratory model tests. Thanks to Dániel Borbély for his help in

numerical modelling and for the joint work. I would also like to thank Prof. Nikoletta Rozgonyi-

Boissinot and Prof. Balázs Vásárhelyi for reading my Ph.D study and for their useful advices and

comments.

I am gratefully indebted to Sika Hungária Kft.for providing the necessary CFRP tapes and

other accessories for the experiments.

I would also like to thank Ildikó Nagyné Barsi, Ildikó Buocz, Nikolett Kocsisné Bodnár, Péter

Juhász, Zita Kárpátiné Pápay, Bálint Pálinkás, Gyula Emszt and all the employees of the

department for their dedicated support.

Finally, I must express my very profound gratitude to my wife, to my family and last but not

least to my friends for their patience and for providing me with continuous encouragement and

unfailing support.

This thesis is connected to the scientific program of the " Development of quality-oriented and

harmonized R+D+I strategy and functional model at BME" project. This project has been supported

by the New Széchenyi Plan (Project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002).

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Gyula Bögöly MSc (CE)

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