Masonry Arches Retrofitted With Carbon Fibre

Introduction

When the term masonry arch is mentioned what comes to mind are ancient buildings and cathedrals of the Catholic Church. It must indeed be acknowledged that masonry arches form the pillar upon ancient buildings and engineering was founded upon. A study of ancient building shows that arches have been used in the construction of bridges, and gigantic buildings and the success of this engineering feat has stood the test of time to become tangible evidence to the modern world.

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The earliest types of arches of architecture were seen in ancient Arab culture through what is known as the corbelled arch. However, this type of construction has been dismissed by modern day scientists as not being a proper engineering arch. This is because scholars argue that this type of arch can only be used in limited span lengths and when the sides are steeply inclined. True arches are defined by their ability to withstand the test of time and the forces of nature which may include earthquakes, storms, alternating expansion and contraction. This property can be clearly seen in the ancient arches that have been around for a long time and that continue being subjected to deforming forces without fail. Secondly, masonry arches were built using non uniform materials which include clay bricks yet maintain consistency and strength when the gaps between these tiles are filled with mortar. This is another advantage of true arches in that they can be built from irregular materials and thus broadening the possibility of materials that could be used (Valluzi et al., 2001).

Masonry arches have proven very effective in the construction of ancient bridges. The reason for this was that brick and mortar were readily available and were easy to construct using. During the ancient days the technology of using composite materials was not present and thus it was not possible to use reinforcement sin the construction of bridges and any other structure that had a long span. Arches provided a way through which bridges could be built over a wide span using only brick and mortar only. The strength of arches lies in the fact that they do not have any form of tensile stress which is a blind spot of masonry. However this principle has been questioned over time since there must always exist a balance between the forces and if compressive force is exerted at a point a resultant and equal tensile force must be formed. Studies on the force distribution of masonry arches reveal the fact that the tensile forces exerted on masonry arches are exerted at the base of the arch in the ground. Further studies show that this force if often not very strong but are stronger near the abutments due to the increased volume through which the forces are diffused over.

Despite the good properties of masonry arches they have found less and less use in the modern day engineering. The main reason is that cheaper and newer ways of constructing buildings and structures of gaps have been found. The disadvantage of masonry arches includes the fact that much more volume in terms of brick/ stone and mortar is used. Modern day technology makes use composite materials that reduce the weight of the bridge and at the same increase the strength of the bridge making it capable of withstanding higher tensile and compressive forces (Enevoldsen, 2001).

The science behind the construction of arches in the ancient times was very simple as it involved the creation of voussoirs which were carefully placed in a semi circled arch and then the gaps were later filled in with normal construction materials (stone/ brick and mortar) also known as the spandrels. In historical ages a frame made of wood- easily available material that was easy to shape and craft- was used at the onset of construction. Voussoirs are then laid on the frame until they are self supporting. This was an intricate process as the voussoirs provided the strength and resistance to deformation of the structure. Once the voussoirs had been inspected the spandrels were later constructed. Historical evidence shows that this was a risky process as improperly placed voussoirs had the tendency to collapse once the wooden frame was removed.

Arches have also been used in the construction of other structures such as dams due to their ability to theoretically eliminate tensile forces which most building materials fail under. An example of is the Roosevelt dam which has the ability to withstand tremendous forces. It must be acknowledged that arches form a central point in engineering and they have not only been used for functional purposes but also for aesthetic purposes. This is seen in landmarks such as Frances Arch of triumph that has added beauty to the environment and is also a source of revenue from the number of tourists it attracts.

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However, arches are under pressure from natural forces and the effects of the environment on them. This has resulted in a gradual weakening and deterioration of ancient masonry arches. It is appreciated that arches form a pillar in the heritage and culture of people and there is a need to conserve them for future generations. This has raised the question as to what could be done so as to maintain the structural integrity of ancient arches while at the same time maintain he aesthetic value of these arches. New technology has exposed the possibility of using carbon fiber that is retrofitted into masonry arches so as to increase in the structural strength without affecting the appearance of these structures. This study will take an in depth look at this technology and the effects of retrofitting with carbon fiber.

Literature Review

Failure in masonry arches

It has been contested as to whether masonry arches are prone to crushing forces. However stress analysis show that masonry arches are resistant to crushing forces due to the high normal action of such structures. This means that they can be able to withstand extremely high loads. Exceptions to this rule have been spotted in flat arches that have been made of poor masonry. Therefore the resistance to crushing of masonry arches is greatly dependent on the quality of craftsmanship involved in the construction of the structure. Saadtmanesh (1994) notes that geometric inaccuracies can also cause failure of arches under a crushing force. A general model however shows that masonry arches are resistant to failure through crushing unless in some special circumstances.

Another way through which masonry arches could fail is through sliding motion. This type of failure occurs when there is a parallel movement between components in the arch which results in the failure of the voussoirs. However some scholars claim that this would be impractical due to the structural design of masonry arches. These scholars claim that such an occurrence could only occur in very thick arches. Incidentally studies show that most arches that were used in the ancient times and in the modern world do not meet the criteria which would lead to failure through sliding motion. Therefore failure through sliding motion is a theoretical claim that does not affect masonry arches in practice; sliding load can hardly exceed the hinge mode load.

Masonry arches are made up of small arches that are joined at certain interval points. This is particularly common in ancient architecture and was so because it was rather difficult to construct continuous arches due to the lack of materials of such properties. In fact in many ancient arches it can be noted that the voussoir is made up of individual stones/bricks that are joined together to form the arch. These joints often act as if they are hinged and they constitute the major weaknesses in masonry arches.

Study of arch failures show that the majority of failures occur from the separation of arch rings. This is particularly true in multi ring arches as there exist weaknesses at points where consecutive arches are joined onto each other. Sykora and Holicky (2010) in his experimental studies was able to find that arches were particularly prone at junctures where consecutive arches are joined together. He advocates for single ring arches as they are less prone to this type of failure. However the majority of failures of this type are due to failure in the mortar used to join these arches and is blamed on poor craftsmanship/ preparation of the mortar. It is due to this fact that another scholar Ellingwood (1981) advocates for the single ring arch as it eliminates the human element of error.

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Arches can also fail at the base and this is often due to scouring. Luchesi et al. (1994) in his research on ancient arches notes that the majority of failed arches due to the base occur as a result of weakened foundations and/ or sinking of the base. When the base sinks or is destroyed by water seepage and through the action of the environment this results in the failure of the structure from the base. Slippages are also common among foundation failures and they result when the shearing forces on the base exceed the foundation’s capacity to withstand these forces.

According to Luchesi et al (1994), ancient masonry arches are prone to failure from several forces which include but are not limited to the degradation of constructing materials, overloading to the increasing functional pressure, foundation settlements and structural changes that are constantly carried out on these structures. The susceptibility of masonry arches to collapse is magnified in areas that suffer from frequent earthquakes or at risk of suffering from earthquakes. Earthquakes challenge the ability of ancient masonry arches to withstand collapse. Enevoldsen (2001) notes that the frequency of occurrence of earthquakes in the world is on the rise coupled with the increasing magnitude of the quakes it is up to engineers to devise better ways of construction and of reinforcing what has already been built so as to preserve it. The seriousness of earthquakes and their destructive power can clearly be seen in past events that have destroyed structures of great heritage, aesthetic and social value such as the Assisi Basilica of Italy and the Citaladel Bam that is located in Iran. Both of these were of great cultural and aesthetic value to the local communities and to the nations involves, not to mention the damage of property and human injuries that result from such failures.

In fact Valluzi at al. (2001) purports that modern day engineers need to devise a limit value that each and every ancient building should be able to withstand. He also emphasises the need of setting higher limit values so that reinforcement procedures can provide long lasting service as well as cushion from unexpected occurrences.

The failure of masonry arches is explained through the static analysis principle. However this explanation has been highly contested due to several assumptions that it poses. The principle states that arches and dome have infinite amounts of compressive strength, have zero tensile strength and thus sliding failure can never occur. According to this principle an arch or dome can only fail when there is the formation of hinges that are not dissipative that result in bending motions. This principle also assesses the stability of an arch under a loading force and notes that the stability of such structures is determined by the shape/ geometry of the arch. Based on this principle extensive studies have been carried out on the mode of failure in single ring arches and multiple ring arches. This has been done so as to identify how each type of arch fails and to derive ways through which modern day monumental structures can be preserved. As Marfia and Sacco (2001) notes, many ancient time structures were constructed using arches since this was the technology that was most reliable at the time. Therefore modern day engineers have no option but to go back to this ancient engineering technique and improve it so as to preserve the valued monuments and structures that exist up to this date.

It has however been noted that the study of masonry arches has not been given enough emphasis. In support of this is Sykora and Holicky (2010) who note that in the majority of analyses carried on masonry arches test the behavior of these arches when subjected to constant vertical and horizontal accelerations. The scholar claims that this type of stability analysis is purely based on the geometry and custom scales that would determine that amount of force required to cause failure to the arch. He claims that this technique is limited as it can only be used to develop the lower limit of failure of a masonry arch. It is due to the limitations of static analysis that dynamic analysis of masonry arches was introduced. Pioneers in this study include Oppenheim who studies the response of a masonry arch when subjected to a base acceleration. In this study the arch is considered to be a rigid body that has a four link mechanism. However this technique did not completely get rid of static analysis as this test was carried out prior to the dynamic analysis so as to establish where the hinges were located; four point geometry. The motion of the arch was determined from the dynamics of the rigid body. An assumption of this technique was that failure occurring from a single cycle could be used to determine the ‘impulse magnitude duration failure’; which was used in determining the effect of impact on the structure. Improvements on Oppenheim’s work were carried out through the analysis of free vibrations within the arch structure that resulted from base acceleration of sinusoidal nature. It must however been acknowledges that even Clemente’s study had inherent limitations such as its failure to study how energy was dissipated in the event of impact. Critics of Oppenheim’s technique of dynamic analysis claim that it is inappropriate because there is a possibility that an arch may fail during the second cycle of motion since this technique used the distinct element method (Enevoldsen, 2001).

Finite element modeling has become a useful tool in the study of the stresses and failure behavior of masonry. However it has been found that discrete element modeling has much more to offer because it takes into consideration the discontinuous nature of structures and therefore gives room for dynamic analysis with the use of large displacements. Discrete element analysis has proven useful as it is able to facilitate analysis with respect to the fact that structures are made up of numerous individual blocks to form a single structure. These programs also allow the definition of the individual characteristics and properties of each block. Through a time stepping scheme this program is then able to solve motion equations. It is important to note that these programs also have several limitations which lie in their assumptions for example the contact forces on the individual blocks are in proportion to the inter penetration between these individual blocks. It is also important to note that this technique is prone to errors and mistakes if careful consideration is not carried out since numerous parameters such as out of balance force must be considered.

Some scholars express concerns on the suitability of discrete element modeling as a measurement technique for use in masonry structures. However Trinatafillou and Fardis (1997) support the use of this modeling technique in masonry structures. In his studies he was able to find that discrete element modeling was an effective way of identifying the effect of a harmonic force on a group of individual blocks. To verify whether these results were valid he compared the results acquired from discrete element modeling to those acquired in actual laboratory results and found that they were consistent. However most scholars appreciate that frameworks with discontinuous modeling are indeed effective in the determination of the structural properties of a construction and in determining the mechanism through which such structures fail when subjected to a load. Based on this study it has been noted that if an analytical method is proposed for certain study this must be accompanied by a method through which the impact problems involved will be tackled. It has also been described that the purpose of analytical analysis of failure in masonry arches is to investigate the failure characteristics of the arch when subjected to an acceleration force in the horizontal axis and to provide a practical solution that can be compared with those that have been earlier acquired.

Restoration of old masonry arches

Studies show that many historic buildings and structures that make use of arches are still in use in the modern day world. These structures apart from having a functional value, hold immense cultural and artistic value to their communities. However due to the age of these structures and the increasing loads that they are required to withstand there is a need for improvement on the load bearing capacities of masonry arches.

This is because such arches are particularly vulnerable under asymmetrical loading. In such loading the live to dead ratio may be high and thus result in the failure of such arches. Investigation not this phenomenon shows that this ratio is often high due to the asymmetrical distribution of live loads. Modifications are often made on arches in masonry so as to meet the rules and regulations of the concerns architectural bodies. Some of the popular changes that have been noted include the removal of tie rods and buttresses, the cutting of openings, the replacement of spandrel material and new columns/ walls may be raised on the extrados of the structure’s shell. It has also been found that majority of the shells used in such instances do not meet the required infrastructural requirements and code of building. This has proven to be a challenging task for structural engineers since the safety margins for masonry shells are constantly changing so as to meet the needs of the time. This in turn makes the task of restoring and upgrading ancient masonry arches very challenging (Trinatafillou and Fardis, 1997).

There is an evident need to find new ways to reinforce masonry arches since traditional forms have been found ineffective. His is because despite their ability to increase a structure’s strength, ductility and stiffness they tend to be very expensive due to the labor involved. Furthermore such forms of reinforcement have a short life span and violate the aesthetic and cultural requirements of such restoration procedures. It is due to these limitations of traditional reinforcement techniques that the concept of carbon retrofitting was developed.

Arch reinforcement techniques

It is important to study alternative approaches to arch reinforcement so as to be able to compare these approaches to carbon fiber reinforcement and make recommendations based on this study. This is because the advantages and weaknesses of carbon fiber reinforcement can only be appreciated if a critical understanding of other reinforcement techniques is acquired

Grout reinforcement

Grout has increasingly been used as a reinforcement material in ancient arches and structures of monumental value. Studies have however shown that the effectiveness of grout as a bonding material in the reinforcement of structures depends on the ration with which water, cement and sand have been mixed. Valluzi et al. (2001) in their experiments were able to show that the quality of sand and cement used in grout based remedies greatly determined the effectiveness of this technique. It has also been found that grout with fine sand has the best properties when it comes to the reinforcement of masonry arches.

A simple yet popular technique is what is known as grout injection. In this technique the strength of an arch is first of all assessed and then the spacing of the ties is calculated. After the spacing has been determined and the arch has been marked a drill is run through the intrados into the abutment. Through the use of the specialized drill the drill is able to inject grout and steel composite onto the cavity on removal. This results in the formation of a series of injects that hold the arch and the abutment together.

In Enevoldsen (2001) some studies it is seen that grout injection offers a fast and cheap way through which masonry arches could be restored and strengthened. He further adds that this technique is able to preserve the cultural and aesthetic values of the masonry arches. Some scholars strongly criticize this technique and claim that minimal research has been done on the long term performance of grout injections. It has also been found that this technique has been popularized and promoted due to commercial interests and that more scientific research needs to go into the study of this technique. Due to the limitation in the equipment and machines available this may not be a practical alternative for large arches such as those in bridges. Commercial equipment in use can be able to inject grout up to a length of 1.5 meters, but to make this technique viable for large project injectors of up to 10 meter length will be required. From this standpoint, grout injection would be an expensive and involving exercise. It is hypothesized that grout injection technology when used on a large scale can be able to impart some tensile strength into ancient arches and increase their resistance to quakes and other types of deforming forces. The principle behind this argument is that steel cables when used in a composite with grout will allow the structure to increase its tensile strength without affecting its compressive strength (Trinatafillou and Fardis, 1997).

Sykora and Holicky (2010) are in support of grout injection as a reinforcement technique and claim that it is much better compared to carbon fiber retrofitting since the steel cords that are impregnated into the grout are better in terms of ductility and tensile strength coupled with lower costs. He also notes that the selection process of a reinforcement technique should not only consider structural properties but other factors such as environmental impact and resistance to fire. He claims that carbon fiber reinforcement is prone to fires unlike grout injection and thus proposes the use of grout based composites in the reinforcement of masonry arches.

However care must be taken in the selection of composite materials to be used in such injection processes. Experimental data shows that steel cords with similar composition to what is used in the manufacture of vehicle tires should be applied. Studies show that this type of steel performs best under the deforming forces that arches in bridges and buildings face. In addition to this, such steel would be able to sustain a structure and sustain the internal vibrations that result in the event of an earthquake, landslide or successive loading and unloading. Bridges have been found to undergo such strenuous forces and thus it is important to impart some tensile forces. Studies also show that majority of cracks in bridges and houses are caused by a lack of tensile force in old masonry and the use of composite materials can prevent the occurrence of such cracks; the use impregnated steel cables. This type of steel cable is able to imitate the desirable properties of high strength steel that is often used in the construction of pre-stressed concrete structures.

The University of Bath carried out tests on the performance of grout injection versus carbon fiber reinforcement and was able to find out that composites, in particular grout injection has the ability to increase the load bearing capacity of arch compared to externally bonded fiber reinforcements. This was as a result of actual laboratory tests that were carried out on 10 samples. The study was also able to show that composites had lower mechanical properties but were able to increase the load bearing capacity both in the intrados and the extrados. Similar to other studies it was also found that grout injection offers improved ease of application, greatly reduces installation and material costs and can be used in similar applications as those used in reinforced fibres. This discredits statements by Luchesi et al (1994) that grout injection is an expensive technique when compared to fibre reinforcement. A study of the stress distribution in the same study shows that grout injection reinforcement offers a better distribution of these forces in terms of the substrate and laminate solution when compared to fibre reinforcement. These results show that the steel cable is incorporated into the structure effectively and is able to carry a great of stresses due to the ability of grout to marry it into the arch. Another advantage of grout injection is that it facilitates the use of techniques that would be unacceptable in external fibre reinforcement techniques. These include the use of mechanical anchoring which is able to improve the performance of bridges and other arches as it allows these structures to acquire increased stiffness and stability. Limitations of grout injection include the fact that the steel cables involved have a higher sensitivity to temperature changes i.e. high thermal expansion coefficient.

Reinforcing steel strips

Study of failed ancient arches shows that these structures are able to distribute the resultant strain along the mortar joints and this avoids the occurrence of cracks. However the majority of failure mainly occurs from the inability of a structure to be able to support vertical and the horizontal displacement that are caused by the abutments. Therefore it with this factor in mind that reinforcement technique should be weighed against.

Flexible steel cable reinforcement.
Fig. 1: Flexible steel cable reinforcement.

Another alternative to grout injection and external fiber reinforcement is the use of reinforcing steel strips. These strips are able to increase the resistance of an arch against bending moments and axial loading. This is facilitated through radial loading of the arch using pre stressed strips that are applied on the arch or vault. This technique increases the compressive force of the arch and thus its resistance against incidental loading. This is done through the use of steel strips that are placed on the extrados of the arch. These strips are attached to the arch’s surface and tension is then applied. The principle behind this technique is based on the appreciation of the fact that arches have infinite compressive strength and that the application of radial strength does not have harmful effects on the properties of an arch. Further to this understanding, the axial internal load is increased so as to avoid the formation of collapse hinges. In addition to this the strips restore the compressive strength of the arch to what it was during its construction and also prevents the formation of cracks. Scholars who prefer this option claim that it gives the due respect to the internal composition of arches and does not tamper with the structural integrity of such constructs (Trinatafillou and Fardis, 1997).

Base for attachment of steel cable.
Fig. 2: Base for attachment of steel cable.

Critics of this method claim that it is ineffective because of the variation in arch curvature. However studies show that these strips are in fact strongest in areas where the radius of curvature is smaller. Limitations of this technique include the fact that it is based on the assumption that the piers are able to withstand the thrust that is exerted in a lateral direction as a result of the arch. Practical applications have shown that some ancient arches have weak piers and thus this technique has been rendered impractical in such instances. Simulations of such an occurrence show that weak piers would be unable to withstand the lateral thrust and thus the arch would fail at the keystone and/or springing. Another risk of the reinforcing steel strip is the fact that the arch could fail due to sliding motion. This can occur due to an imbalance of forces and improper application of this remedial technique.

This technique is applied through the use of a pre-stressing device that has been designed to maximize on the safety of the operation. Two sheets of steel reinforced grout are then placed on the extrados of the arch. The sheets are fixed to the piers and in cases where the integrity of the pier is questioned, fixed to the base of the piers and then tensioned. The resultant effect is that radial forced will be applied through the steel reinforced grout. This technique has been found to be useful in particular in increasing the flexion of arches due to the asymmetrical shapes and sizes of the building materials. It is important to note that the tension applied to the strips is applied to a low threshold value of approximately 4 – 8% so as to allow the structure to respond to low vibrations and displacements ; seismic activities.

Reinforcement through Carbon fibre retrofitting reinforcement

Fibers are increasingly becoming suitable materials for use in the reinforcement of masonry arches, domes and vaults. There are several properties of these materials that have resulted in their selected use and these include their light weight, resistance to corrosion, their ability to be formed in long lengths and customizable dimensions and their relative mechanical strength. It has also noted that these fibers are easy to apply on the required surfaces and thus their continued use.

Early tests on the response of carbon fiber reinforcement on masonry arches were carried out by Marfia and Sacco (2001) who were able to finds out that the fiber was able to increase the strength of masonry arches. Further studies have been carried out since this time with the majority of the studies pointing out that fiber bonding to the surface of masonry arches was able to increase the strength of the structure and its ability to withstand horizontal and vertical displacements. Further studies on the ability of carbon to withstand Luchesi et al (1994) who carried out studies on unidirectional carbon fibers and the effect that they have on masonry arches. The effect of these fibers when applied to the extrados and intrados have also been carried out and comparisons of the results carried out. It can however be said that the strength of fiber reinforcements in masonry arches is greatly dependent on the material used and the density of fibers used. Majority of these tests however indicate that the use of fiber reinforcement sin masonry arches was not only able to improve on the strength of the structure but were also able to improve on the ductility and reducing the effects of shear deformation (Ellingwood, 1981).

It is important to note that the majority of studies carried out on the effect of fibers on masonry arches show that the majority of the fibers have the ability of increasing the load bearing capacities of these arches by a percentage of between 5000% and 10000%. These results were able to bring to the table impressive observation that demonstrates a very high strength to weight increment ratio in the case of fiber reinforcement. It is due to the low weight of these reinforcements that give them a competitive edge over other reinforcement techniques. It is noted that due to their light weight, fiber reinforcement is cheaper to transport and to install compared to other techniques such as grout injection. However literature exposes differing opinions among scholars as to which technique is cheaper and easier to implement. Therefore this is seen to depend on the individual interests and preferences and a blanket statement would be inappropriate.

Ellingwood (1981) in their experiments were able to test the behavior of carbon fiber reinforcements that were mixed with a cement matrix. In their study a mixture of carbon fiber and the cement matrix was applied onto the extras of the arch. The results were similar to those carried out in other studies and portray improved properties. However studies carried out by Luchesi et al (1994) compare the properties of reinforced glass fiber to that of carbon and find that glass has better properties in terms of ductility, and ability to withstand deformation. In this experiment the scholars were able to reproduce real life occurrences of an earthquake. In addition to this scaled models of monumental masonry arches were also developed. These models were made up of arches with a rather soft abutment section that was reinforced in the intrados. The models were then subjected to vertical and horizontal loads to simulate the forces that would be experienced in an actual earthquake. This study was able to reveal that strengthening using carbon fiber in the presence of compressive stresses resulted in reduced effectiveness of the reinforcement. Carbon fibers were noted to detach in when presented under vertical loading forces and this makes it less suitable for use in seismic reinforcement. On the other hand glass reinforcements were found to have better compression and traction strengths. An investigation into this phenomenon shows that this is due to the cement matrix that is involved in this process. The experiment also shows that glass fiber reinforcements have superior properties that make it more suitable when it comes to withstanding horizontal loading. It should be keenly noted that these findings could be as a result of the increase in sectional area of the arch due the use of glass reinforcements. Therefore this observation is open for further testing and discussion and may not necessarily represent accurate results.

In this type of reinforcement epoxy bonded carbon fibers are bonded to the structure of masonry and enable the structures to bear the greater stresses. Through this the structure is able to bear greater forces at a reduced cost in terms of cost of reinforcement, materials and the labor involved. In addition to this type of reinforcement does not tamper with the cultural and aesthetic value of an arch.

Carbon fiber is preferred as a bonding material mainly because it is well adapted to curved surfaces and difficult to access areas. In studies carried out on ancient arches it has been found that most of them are curved and are located in some difficult to access areas making carbon an effective bonding material. Therefore with this in mind carbon is extensively being researched as a suitable bonding material for each reinforcement. In the selection of bonding materials it is important to note the kind of occurrences that lead to failure in arches. It as been noted that server cracks are the main cause of failure in masonry arches. Due to cracking the shells are split into numerous slices with each slice acquiring the characteristics of an independent arch. Therefore the load is eventually carried out by individual arches which are dependent on the pattern of cracking. The study of cracks in masonry shells has been the cause of numerous arguments since some critics argue that no type of reinforcement can be able to prevent the occurrence of cracks. However tests carried out on carbon reinforced arches shows that even in the event of cracking the retrofitting prevents the formation of small independent arches through the stitching action of the reinforcement (Ellingwood, 1981).

It is a general observation that carbon reinforced fibers are effective reinforcement materials that can protect bridges from the forces encountered due to springing. This is in particular reference to monumental bridges that are continuously subjected to heavy loads. The literature review was able to show that the success of carbon fiber reinforcement eventually depends on the mode through which the pre-stressed system of laminates are connected to each other. It has also been noted that extensive testing and designing is required in regions of tensile stress within a masonry arch. Some studies show that pre-twisted carbon fiber tendons would be an effective reinforcement material as they would be able to impart the required properties into a bridge. However due to the stresses imparted on the tendons there is a necessity of anchoring of these fibers of the base (pier) of the arch. It was also found that carbon fiber reinforcement is an effective way through which the formation of the four hinges can be prevented. This was evident from the earlier mentioned experiments that were conducted by the said scholar on the effect of carbon fiber reinforcement on the intrados and on the extrados. It was found that fiber reinforcement on the intrados was less effective in preventing the formation of the four hinges when compared to application on the extrados. Therefore based on this experiment it would be recommended that carbon fiber reinforcements be applied to the extrados as they are able to increase the compressive strength of the arch, prevent cracking, prevent the formation of the four hinges and impart a reasonable degree of tensile strength onto the structure (Luchesi et al, 1994).

It has been noted that gaps exist in the knowledge of the stresses that are experienced in between the mortar joints. This is because most experiments have focused on the behavior of the reinforcement materials and on the four hinges of collapse with minimal emphasis being given to the mortar joint. This calls for further studies on the impact of carbon fiber reinforcement on mortar joints.

Types of carbon fibers

There are different types of carbon fiber reinforcement that are used in civil engineering processes and they include Sika Wrap 300c, Sika CarboDur, SikaCarbo Shear, Sika Wrap Hex 230 c, Sika CarboDur plates. These are but trade names used by the Sika Group of manufacturers to differentiate different products and note their characteristics. This is one of the leading companies that specializes in the production of these fibers. It is worthwhile to understand that there are many manufacturers that deal in reinforcing fiber production and it would be impossible to review all their products. However the properties of most of these fibers are similar it is only the trade name that if often different. Below is a table to the mentioned fibers and their properties:

Name Properties
Sika Wrap 300c Made of woven fabric in which the strands go in one direction
Sika CarboDur Used for heavy duty applications
SikaCarbo Shear Used for adding strength against shearing forces
Sika Wrap Hex 230 c Similar material to 300c but differ in the arrangement of fibers
Sika CarboDur plates These are carbon plates that have undergone pultruding

It is important for a structural engineer to understand his application and the requirements of the time so as to select a suitable reinforcement fiber. Despite recommendations from manufacturer testing (XXXX) notes that this decision should be left to the experience and preference of the builder.

Methodology

Model arch

A round arch will be selected for this study. Study of existing monuments shows that a good number of round arches are in need of restoration/improvement. Furthermore a lot of study has been done on semi circular arches with less research being carried out on circular arches. A scaled arch will be rebuilt so as to reproduce the type of arch that would be found in a monumental building. This will be done through the measurement of forces that a real life arch undergoes and a scaled model was constructed in the lab. This was done through blocks without the use of mortar This is with respect to the fact that many ancient and monumental arches were built without mortar between the joints. In addition to this would uncover new ground as most related experiments are done with joints that have been mortared. So as to represent the actual arches the constituency of block is measured and this is also used in the construction of the model. The blocks were made from 77% clay and 23% cement. A low proportion of cement (23%) so as to imitate the properties of aged bricks that have undergone environmental degradation. The compressive strength of the scaled blocks is then measured and found to be 58Mpa. This compressive strength is based on the study of ancient architecture that shows that limestone was a popular material that was used in the construction of Roman buildings. Tests on these blocks show that they have a compressive strength of about 60Mpa which means that materials with compressive strength within this range would accurately represent the ancient limestone. Below is a list of the properties of the model block

Youngs modulus = E m = 40, 000 Mpa

Poisson coefficient = v m = 0.199

Material density = 0. 0025 kg/ mm3

The arches are built to a dimension of 1.6 meters in span. The height of the bricks is 30cms and the width is 16 cms. A model arch is then constructed using the exact processes that would have been used in ancient times. This is through a frame that is eventually removed to leave the arch in a stationary state. As mentioned earlier the purpose of the most reinforcement procedures is to increase strengthen and maintain the aesthetic value of a structure. To do this therefore, the reinforced carbon fibers will be placed on the intrados and on the extrados of the arch. The effect of these reinforcements will be measured based on two comparative tests whereby an unreinforced sample will be compared to the reinforced one.

The carbon fibre sheets are selected for the reinforcement procedure is the Sika Cabo Dur. The characteristics of this fiber are shown in the list below:

Young’s modulus = E m = 39, 000 Mpa

Carbon fiber strength = 3, 500 Mpa

The values shown above are not those shown by the manufacturer but were acquired from laboratory tests. This is based on the understanding that manufacturer specifications often vary due to manufacturing errors and the testing equipment used. Furthermore no test is 100% accurate and slight differences could be acquired due to truncated and rounded off values.

Aft the models had been constructed they were then subjected to a point load on the top of the arch. However the force was not exerted at the center but was move 0. 8 cms to the side of the keystone. This is with respect to the fact that the keystone bears most of the forces that are involved in an arch and thus the need to exert point force on it in the experiment.

Scale model of arch.
Fig. 3: Scale model of arch.

The concrete blocks are assembled into an arch shape. However before this is done the blocks are tested so as to ensure that they were of the same consistency in terms of size, weight strength and their elastic modulus. This was a control procedure to minimize the occurrence of errors in the experiment. Several arches are built due to the fact that repeat experiments were carried out in instances where the results were unclear or suspect plus the fact that experiments on the effect of carbon reinforcement on the intrados and extrados was compared to an unreinforced arch.

Data collection

Force is applied to the arch by the use of a hydraulic operated jack. This jack is calibrated so that measurements of the mount of force exerted on the arch can be taken. Force is continuously and steadily applied through the jack and the point at which failure occurs through the four point mechanism occurs is recorded. The first test involves a non reinforced arch that is subjected to a steady load until it collapses. After these readings have been taken (control experiment) an arch that has been reinforced on its extrados and one lateral side is mounted under the jack and a repeat of the above mentioned procedure is carried out. The dimensions of the reinforcement are 20 cms in width on the extrados and 10 cms on the lateral side of the arch.

As mentioned in the literature review section an important function of any reinforcement material is to protect the arch from horizontal and vertical displacement which often causes collapse/ failure. To measure this phenomenon the experiment integrates the use of displacement transducers that are located at 10 points along the arch.

The second experiment involves the reinforcement of the blocks on the extrados only. In this experiment the carbon reinforcement on the lateral side is removed so as to investigate whether this type of reinforcement has an effect on the. This is with consideration of the fact that limited research has been done on the effects of lateral carbon fiber reinforcement versus that of the extrados and of the intrados. The final experiment involves the reinforcement of the intrados alone so as to compare reinforcement characteristics between he intrados and the extrados.

Other visible indicators such as the appearance of cracks on the masonry and reinforcement are also noted at respective forces. This is because this information would prove useful in the analysis of the pattern of failure and the effect of different forces on the structure.

Results and Discussion

Unreinforced arch

Initial tests were carried out on the unreinforced arch and it was found that this type of arch failed at relatively low forces. This was not out of the ordinary as it was a general expectation that this type of arch would yield considerably low forces. However what was of interest was that the arch in this category failed at extremely low forcers, lower than expected. At 1.8 KN the arch was seen to fail as the keystone is dislodged from its position. As a result of this, there was formation of the four point hinges and the failure of the whole structure. No cracking was noticed along the arch and this was recorded for comparison with other experimental results. The transducers were able to shown that failure mainly occurred from vertical displacement which led to the horizontal displacement and then collapse. This is because the force applied on the arch is directional; vertical force.

Reinforced extrados and lateral side

The second experiment involved the reinforcement of the extrados and one of the lateral sides with carbon reinforcements. It is found that with the application of a small amount of load the carbon reinforcement that was applied on the lateral side starts peeling off the blocks. The experiment was paused so as to investigate whether there were signs of damage on the arch itself. Surprisingly it was established that the arch itself did not have any cracks and did not show any signs of failure. This led to the conclusion that carbon reinforcement on the lateral side was an effective way of reinforcing masonry arches. Further investigations show that carbon fiber reinforcement on the lateral did not bear any load and therefore there was no need for such reinforcement. The peeling of the reinforcement was due to the slow deformation of the arch itself since the carbon fiber did not bear any load. Cracking of the arch was noted at 110 KN when fissures were noted at the top of the keystone directly above where the jack applied its point pressure. There are different interpretations into this and one is that the due to the nature of the force being applied these cracks were as a result of the jack and not the inability of the arch to sustain the forces exerted. In practical applications the force would be exerted on the center of the keystone and not towards one edge. This experimental difference could be hypothesized to be reason for the cracking. Another interpretation is that at 110 KN the edge of the keystone could not support the arch and thus this resulted to cracking. Due to the differences in interpretation with regard to this matter, more load was exerted onto the arch until it collapsed. Therefore in such a case the term failure would refer to the collapse of the masonry arch and not cracking i.e. Cracks are interpreted to be warning signs of failure but not a failure in actual sense. In this experiment the arch is seen to fail at 300 KN.

Reinforced extrados

In this experiment the carbon fiber reinforcement is applied on the extrados of the arch alone. This was done so as to compare the figures at which failure occurs to that of reinforcement on both the extrados and the lateral side if the arch. Similar to other experiments the extrados was roughened so as to facilitate better bonding of the carbon fiber composite to the surface of the arch. In this experiment cracking occurs at the keystone at 140 KN. After the steady increase of the load applied the arch was noted to fail at 293 KN. It was expected that failure of the arch this experiment would occur at a much lower load since only the extrados had been reinforced. The results of this study show that reinforcement on the laterals does not have an effect on the strength and load bearing capacities of an arch. This does not only shed some light on carbon reinforcement but on all forms; the extrados is more effective compared o the intrados. This explains the process of flexible steel strengthening strips as they are also applied on the extrados of an arch.

Finite element analysis

Finite element analysis is chosen over discrete element analysis due to its simplicity of interpretation and ease of study. This technique will be used to measure the way in which a specific arch responds to the point loading of the hydraulic jack. Previous studies have shown that finite element analysis has enabled researchers to identify the areas in an arch where there is maximum stress and thus failure. Through finite element analysis researchers can able to predict the response of certain materials to certain loads without necessarily conduction real experiments. In instances where real experiments have been carried out this technique can be used to confirm and explain certain phenomena. Planes stresses in two dimensions are analyzed using the finite element analysis method.

The arches are made up of six individual blocks. This separate nature of these blocks is also fed into the analysis software (MATLAB) so as to facilitate effective simulation. The simulation will also be done in line with the four point hinge theory. This means that four nodes will be fed into the software for simulation. The stresses and forces encountered at points where one block joins the next are noted and a finite width is also noted.

A simulation of the point force application form the hydraulic jack is simulated. This simulation is done with regard to the amount of force exerted by the jack. Since the experimental results show that the reinforced extrados fails at 290 KN, a similar point force is simulated in by the software. A linear and elastic model is simulated by MATLAB and the analysis results noted. The analysis of the reinforced arch was able to give results as shown below:

Finite element simulation of unreinforced arch.
Fig. 4: Finite element simulation of unreinforced arch.

The results of finite element analysis show that the data collected in the experiment was accurate. This is because at 2KN an unreinforced arch was seen to collapse according to the simulation. This amount of loading was reached through step by step increment of the load using the software. The shape of the arch at the time of collapse was also simulated as shown below. From the above diagram it can be noted that the four point hinges have occurred and have resulted in a sort of cantilever that leads to the failure of the arch. The difference of 0.01 KN between the experiment and analysis results are due to the possibility that experimental errors could have occurred either due to faulty equipment of small inconsistencies in the material properties.

The second simulation is done on a reinforced arch with carbon fiber reinforcement on the extrados. This is done so as to gain a different perspective on the influence that this reinforcement has on the mechanical properties of the arch. The carbon fiber is modeled through the use of a two node truss. However it is impossible to define the relationship between the reinforcing fiber and the surface of the arch blocks. Therefore it is assumed that these two have a perfect bond despite the fact that this is unlikely in a practical experiment. The reinforcement material is defined as having some form of linear elasticity and the interfaces are further assumed to have no tension. It is critical to understand that in such analyses it is important to define the type of model that should be simulated for parts in tension and those in compression.

Load to displacement diagram.
Fig. 5: Load to displacement diagram.

In this study four models are studied and these include the linear elastic model, the zero tension models, the Von Mises model for compression forces and the damage model for compression forces. The respective loads and the vertical displacement are then simulated on a graph. These results are found to be similar in pattern to those acquired from other studies. This shows that the behavior of arches is similar despite the shape and the size of the blocks being used.

Finite element simulation of reinforced arch.
Fig. 6: Finite element simulation of reinforced arch.

A study of the simulation also reveals that in the case of the reinforced arch there exist only three points of hinges compared to four in the unreinforced one. The results of the simulation show that the arch when reinforced with carbon fibers would fail at 436 KN which is slightly higher than the experimental results. This shows that either there are some inherent limitations in the experiment that could have caused this difference or due to the inability of the software to simulate the bonging characteristics between the arch and the fiber.

Conclusion

The study of arch failures shows that the majority of failures occur from the separation of the arch rings. This is particularly true in multi ring arches as there exist weaknesses at points where consecutive arches are joined onto each other. Experimental studies were able to find that arches were particularly prone at junctures where consecutive arches are joined together.

Ancient masonry arches of monumental value are prone to failure from several forces for example increasing functional pressure, foundation settlements and structural changes that are constantly carried out on these structure and degradation of constructing materials, overloading to the. The study shows that masonry arches are at a higher risk in areas that suffer from frequent earthquakes or at risk of suffering from earthquakes and other disasters such as flooding, landslides, hurricanes and tornados. Therefore it is up to engineers to devise better ways of construction and of reinforcing what has already been built so as to preserve it. A study on the load bearing capacities of ancient masonry arches shows that they risk collapsing under the pressure of modern day operations.

This is because such arches are particularly vulnerable under asymmetrical loading. In such loading the live to dead weight ratio may be high and thus result in the failure of such arches. Investigation not this phenomenon shows that this ratio is often high due to the asymmetrical distribution of live loads. Modifications are often made on arches in masonry so as to meet the rules and regulations of the concerned architectural bodies. Some of the popular changes that have been noted include the removal of tie rods and buttresses, the cutting of openings, the replacement of spandrel material and new columns and walls may be raised on the extrados of the structure’s shell. It has also been found that the majority of the shells used in such instances do not meet the required infrastructural requirements and local codes of building. This has proven to be a challenging task for structural engineers since the safety margins for masonry shells are constantly changing so as to meet the needs of the time. This in turn makes the task of restoring and upgrading ancient masonry arches very challenging.

There is an evident need to find new ways to reinforce masonry arches since traditional forms have been found ineffective. His is because despite their ability to increase a structure’s strength, ductility and stiffness they tend to be very expensive due to the labor involved. Furthermore such forms of reinforcement have a short life span and violate the aesthetic and cultural requirements of such restorative procedures. It is due to these limitations of traditional reinforcement techniques that the concept of carbon retrofitting was developed.

Alternatives to carbon fiber reinforcement that are worth noting include grout injection and flexible steel cable reinforcement. Grout injection reinforcement offers a better distribution of these forces in terms of the substrate and laminate solution when compared to fiber reinforcement. Another advantage of grout injection is that it facilitates the use of techniques that would be unacceptable in external fiber reinforcement techniques. These include the use of mechanical anchoring which is able to improve the performance of bridges and other arches as it allows these structures to acquire increased stiffness and stability.

On the other hand strips are able to increase the resistance of an arch against bending moments and axial loading. This is facilitated through radial loading of the arch using pre stressed strips that are applied on the arch or vault. This technique increases the compressive force of the arch and thus its resistance against incidental loading. This is done through the use of steel strips that are placed on the extrados of the arch. These strips are attached to the arch’s surface and tension is then applied. The principle behind this technique is based on the appreciation of the fact that arches have infinite compressive strengths and that the application of radial strength does not have harmful effects on the properties of an arch.

Benefits of carbon fiber include that they are increasingly becoming suitable materials for use in the reinforcement of masonry arches, domes and vaults. There are several properties of these materials that have resulted in their selected use and these include their light weight, resistance to corrosion, their ability to be formed in long lengths and customizable dimensions and their relative mechanical strength. It has also been noted that these fibers are easy to apply on the required surfaces and thus their continued use.

The specific findings of this study are:

  • Carbon fiber reinforcements are able to improve the load bearing capacity of an arch by 20000%. This is in comparison to previous studies that keep this figure at 10,000 % This figure is however based on the results acquired from finite element analysis.
  • The reinforcement of an arch with carbon fiber is able to reduce and/ or prevent the formation of the four point hinges of arch failure.
  • Grout injection could offer a more practical and cheaper way of strengthening masonry arches- based on literature review. This is despite earlier claims that carbon fiber reinforcement is cheaper.
  • There is a need to carry out extensive testing on the different carbon fibers that exist in the market so as to gain empirical knowledge of the respective failure loads, ability to bond to the surface and how they respond to the intrados and to the extrados.

References

Ellingwood, B., 1981. Analysis of reliability for masonry structures. Journal of structural division, 107(5), pp. 757 -773.

Enevoldsen, I., 2001. Experience with probabilistic based assessment of bridges. Structural Engineering International, 11(4), pp. 238- 246.

Luchesi, M. Paldonvani, C. and Pagni, A., 1994. A numerical problem for solving equilibrium problems of masonry like buildings. Meccanica, 29, pp. 175 -193.

Marfia, S. and Sacco, E., 2001. Modeling of reinforced masonry elements. International Journal of Solids and structures. 35, pp. 1723 – 1741.

Saadtmanesh, H., 1994. Fiber composites for new and existing structures. ACI Structural Journal, 91, pp. 346- 354.

Sykora, M. and Holicky, M., 2010. Probabilistic model for masonry strength of existing structures. Engineering mechanics, 17(1), pp. 61 -70.

Trinatafillou T. C. and Fardis, M. N., 1997. Strengthening of historic masonry arches with composite materials. Material and structures, 30, pp. 486- 496.

Valluzi, M. R. Valdemara, M and Modena, C., 2001. Behavior of brick masonry walls strengthened by FRP laminates. Journal of composites for construction, 5(3), pp. 163 – 169.

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