Physical Modelling for Investigation Walls due to Thermal Movements of Cracking in Masonry of an Overlying Slab

This paper describes the use of 1/3 scale physical models to investigate the deformations generated and cracking in walls due to the thermal movements of an overlying slab. In this study three models were constructed to identify the effect of the structural form and aspect ratio of the wall on the formation+ of cracks. Temperature variations in the models, strains generated and formation of cracks were observed. The effect of the structural form and aspect ratio of the walls on the above phenomena were identified. The results were compared with numerical and field survey studies.


Introduction
Concrete slabs exposed to direct sunlight experience temperature related horizontal movements.In addition, temperatures on the top surface will be higher than those on the underside of the slab, causing an upward movement of the slab during heating.In a typical building, masonry and concrete structural elements are connected to each other at their respective interfaces.Therefore, significant movements may be generated in the masonry walls due to the movement of the roof slab.These movements can result in overstressing and cracking in masonry.Even though such non structural cracking of masonry is not a normal structural design consideration, these cracks lead to considerable problems with respect to the performance and appearance of a buiiding.Hence studying these cracks and factors causing them is important, in order to propose remedial measures.
Masonry structures represent one of the oldest forms of construction and different types of masoruy components have evolved over the years both in this country and all over the world.Before the development of numerical tools and advanced computer techniques, the design of masonry structures has been in the main based on empirical rules supported by analytical and experimental observations.The main advantage of a physical model over an analytical model is that it portrays the behavioul of a complete structure loaded to a failure state.Also, physical models represent a better idealization of the actual structures than numerical models, especially with respect to the boundary conditions and the anisotropic nature of materials.
The prime motivation to conduct experiments on structures at a reduced scale is to reduce the cost and the difficulties in testing.The choice of the geometric scale factor for a specific type of model depends on a number of factors including the available loading system, fabrication facilities and adequacy of representation.
This paper describes an investigation that used 1/3 scale physical models.In this study three models were constructed to identify the effect of structural form (using models representing 6 m long load bearing and concrete framed walls) and the effect of aspect ratio (using models representing 3 m long and 6 m long load bearing walis) on the above phenomenon.The movements generated on the model walls when the roof slab is subject to thermal loads due to direct sunlight were carefully monitored.The results were compared with corresponding numerical and field survey observations.The objective of the physical modelling was not to establish an equivalence between model and prototype.Rather the objective of the study was more limited, i.e. to investigate the movements developing and cracks forming on the masonry walls and to understand the relative importance of factors that cause cracking, such K.G.S. Dilruksli, BSc Eng (Horts), PhD is a Senior Lectrter in Ciztil Ertghteering at the Uniuersity of Morntuwg.
as the structural form of wall (i.e.whether the wall is load bearing or within a concrete frame) and aspect ratio of wall, and also to validate the numerical model.

Literature review
The literature shows that, depending on the requirement, reduced size strucfural models have been customarily used in research studies and widely employed in research programs in such applications as: 1) Development of experimental data for verification of the proposed t analytical methods.
2) Study of basic behaviour of complex structural forms such as sheIls.
3) Parametric studies on member behaviour.4) Behaviour of complex structural systems subject to complex loading histories.
Even though the methodology of using small scale modelling in structural research and design dates back many years, the techniques have improved considerably in the past few decades due to the improvements in instrumentation.The small scale modelling technique has been successfully applied to investigate problems in masonry and has proven to be a powerful technique that is an economical aiternative to full scale testing.
The literature (Gajanan et al. 1983;Bechara et al. 1990) states that the first successful attempt to modei masonry strllctures was made in England by Vogt in the mid 1950s using Lf 4 scale bricks and Iater L/10 scale bricks.The subsequent work of Hendry, Murthi and Sinha at the Edinburgh University in the 1960s on brickwork using L/3 and 1/6 scale models is considered as a successful development in masonry modelling.Later the technique has been developed and used by many researchers for their investigations.
Samarasinghe (1981) has used 1/6 scale brick masonry specimens to investigate in-p1ane behaviour of masonry and developed bi-axial failure criteria for masonry.To study behaviour of unreinforced masonry under biaxial pseudo dynamic ioading, Senthival and Uzoegbo (2004) have used 1/2 scale modeis.Around 700 tests of large and small scale static and dynamic tests have been considered to evaluate lateral load resistance of masonry infill walls by Henderson et al. (2003).
Hughes and Kitching (2000) have used L/6 and 1f 72 scale models to determine the properties of a range of brickwork composed of different model mortars in a number of different geometric test configurations.
Any given modei built in a laboratory has an optimum geometric scaie factor.Very small models require light loads but can present great difficulties in fabrication and instrumentation.Large models are easier to build but require much heavier loading equipment.
3. Materials and methods

Choice of scale and models
The review of literature has shown that models built to the reduced scale of 1/3 to 1./6 are considered as suitable for studying masonry structures.In this study, the scale factor of 1f 3 was selected to construct the models considering factors such as availability of materials, controlling workability and ease of monitoring.
Observations from the building survey and results of numericai modelling (Dilrukshi and  Dias 2008; Dilrukshi 2008) indicate that the length of load bearing walls has a significant effect on the location and the orientation of these cracks.Therefore, to capture this effect, models were constructed to represent 3 m and 6 m long load bearing walls.It was also understood that the structural form of the wall has a significant effect.To investigate this effect, a model which represented a 6 m long concrete framed wall was constructed in addition to the load bearing walls.The details of the models used in this investigation are shown in Table 1.The models were simplified to represent the effect of the concrete slab on walls which are typically 3 m apart in plan.The area of slab r,r,hich experiences an upward deflection has a direct influence to generate movements on the wall.Hence, for simpliciiv we were only concerned about this area of the slab, which was considered as approximately equal to a length of L/4 to each side from the centre of the wall (where L is the span of the slab between two supports).The details of this simpiification are showrr in Figure 1.
hard laterite and hence the possibility of settlements was minimal.Moreover the loads from the models are very smali, and r,ve could assume that settlement would not be the cause of any cracking.
Two models of length 1 m and 2 m were constructed to represent load bearing walls of length 3 m and 6 m respectively.The 1 mheight of both walls represented 3 m.A 4 mm ihick mortar joini (representing around 10 -L2 mm jn the prototype) was maintained between the brick ur-rits.Walls were constructed according to the standard English bond pattern.Bricks were imrnersed in water for about 10 minutes before the construction of wall panels.One of the major variables in brickwork construction is the standard of workmanship.In order to reduce the variability in workmanship, the same experienced brick layer was employed to build all the models.A 50 mm thick slab was constructed to represent the 150 mm slab of the prototype.The maximum size of coarse aggregate was lirnited to 10 mm in the concrete mix and 6 mm diameter mild steel was used as the reinforcement.
A concrete framed model with two columns of size 100 x 100 mm at the edges and a beam of 100 x 170 mm was'constructed to represent a 6 m long wall in the prototype.Mild steel reinforcement of size 6 mm diameter was used for the construction of both beam and columns.
The columns were constructed first and the masoruy wall was constructed later as an infill wail.The methodology used for the construction of the load bearing wall models was used for the construction of the infill wall and roof slab.
A 5 mm thick plaster was used in all walls of the 1/3 scale model to represent the 15 mm thick plaster of the prototype.A mortar mix of 1:5 (cement: sand) was used for the plastering, once again with a maximum aggregate size of 1.4 mrn.
Curing of masonry and concrete was done for a period of 28 days under damp hessian and the modei walls were protected against direct solar radiation by covering them witl-r plywood sheets, in order to ensure that solar radiation was experienced only by the siabs and not the walls.The long curing period was to make the materials as strong as possible, with correspondingly high E value, so that the generation of cracks due to movements would be encouraged.The bricks employed in this project were clay bricks normally available in the iocal market.Bricks were cut to the size of 75 x 36 x 24 mm, i.e. 1. /3 scaie of the standard size bricks.
A diamond cutter was used to cut bricks according to the requirements.The aggregate passing through a 4 mm sieve is defined as the fine aggregate for normal (prototype) construction.In order to satisfy the 1,/3 ratio in the models, the maximum aggregate size was taken as approximately 1/3 of 4 mm (1.33 mm) and aggregate passing through the 1.4 mm sieve was used for the studv.
A mortar mix of f ,O 1."*"r,t: sand) by volume was used for the construction of wall panels.
This mortar mix is usually used by masons for construction of brick masonry walls in Sri Lanka.The water/cement ratio used for our mortar mix was around 1.2, which was just sufficient as judged by the brick layer.This is not rnuch higher than that used for usual construction, in spite of the fine sand particles in the mortar used for the model.
A location that receives long hours of sunlight was selected for the construction of models.The intention was to obtain the maximum amount of thermal radiation from the sun.The ground was firmly levelled and plecast concrete beams were piaced on the ground as the foundations 'for the rnodels.The soii at this location was

Loacling
The main load associated with this study is the thermal ioad on the slab due to direct solar radiation.
Modelling of the dead weight stresses is not easy in structural engineering studies using small scaie models.In this study, special attention was not paid for modelling of dead weight because it was understood that lower dead weight would help to magnifying the upward movement and hence facilitate the study ef the thermal phenomena.
gauge.The results of a preliminary numerical model study (Dilrukshi 2008) were used to identify the locations and directions in which datum discs had to be fixed.A description of the selected locations and their directions for the instailation of strain gauges is given in Table 2 and Figure 2 (l is the length of the wall).
The datum discs were placed on both the East face (Face 1) and the West face (Face 2).
The distance between a pair of datum discs was kept at around 4 cm.The measurements were taken once a .week on a selected sunny day.To capture the diurnal variation of movements, readings u'ere taken at 7.00 a.m., l-0.30a.m., 12.30 p.m., 3.00 p.m. and 6.00 p.m. on each seiected day.

Strain rnessuretnents str&ht geuqe
The movements initially measured using ttsing a nlechanical of the wails were a mechanical strain Locations selected to install strain gauges are tire sarne as above.The time interval for measurements was set to 10 minutes.
Measurements were started 6.30 a.m. and continued for a period of 36 hours.
The strain gauges are subject to expansions and contractions due to the temperature variations of the gauge itself.The strain values which are recorded by the data logger contain these temperature induced strains.Therefore to obtain actual values of the masonry strains we need to remove this temperature effect from the readings.The ternperature of the strain gauges will be almost equal to the ternperature of the masonry wall.The corrected reading (yJ can be obtain as; y" = y, -(ttr)tt where; y,-Corrected strain rending y,-Strain reading obtained by data logger t -Temperature corresponding to reading to -Reference temperature (temperature qt 6.30 a.m.) k -Temperature coeficient of gauge factor of the strain gauge (+ 0.00011.5% / oC) 3, 6 T emp er atur e m e asur ement s Diurnal temperature variations of the top and the bottom surfaces of slabs, walls and beam (in the framed wall) were measured simultaneously with the strains.A multi meter with surface probe was used for these measurements. ,,.

4.L T emp erature o ariation
The temperature variations observed on the 2 m load bearing and the 2 m concrete framed model walls within a period of 36 hours starting from 6.30 a.m. are shown in Figure 3 and Figure 4 respectively.The variations are cyclic in both models.At 6.30 a.m. in the morning, the temperature of the structures stood at around 230 C. It increased gradually and reached a peak by 2 p.m. and then started to decrease.During the night the temperature was much lowei.The maximum temperature gradient across the slab also occurred around 2 p.m.At the troughs, the temperature of the whole structure seems similar.This means that the models have achieved thermal equilibrium with the surrounding temperature.At peaks there is a gradient of temperature through the depth of slab, because of the solar radiation.
Normally the upper surface of the slab should reach higher temperatures earlier than the cooler lower layers.Therefore the top surface of the slab reaches its peak before the bottom.This can be clearly observed at the second peak in both cases.The difference of the temperature from top surface of the slab to the wall is higher in the framed wall than the load bearing wall (Table 3).The greater concrete depth due to the presence of a beam is the reason for this difference.In general, the observations from the study show that the models have experienced a thermal gradient approximately equal to that estimated for the prototype.Around 1-.5 months after the construction of models, cracks were noticed in the concrete framed wall (Figure 5, with crack lines enhanced for clarity).A crack had been formed horizontally under the beam (Figure 5(a)) and had become diagonal towards the column at the edge of the wall (Figures 5(c) and (d)).The inclinations of diagonal cracks were around 450 to the horizontal.This is similar to the observations on the concrete framed walls in the building survey (Dilrukshi and Dias 2008).
It is also similar to the principal stress directions identified in the numerical modelling for concrete framed walls.The diagonal cracks have formed at the panel edge near the column on one end of the wall on both faces (Figure 5(c) and (d)).However, we can not see these diagonal cracks on the other end of the wall once again.Differences in workmanship below the beam level may be the cause for this variation.
Two years after construction, hair line cracks (inclination around    In the concrete framed wall, the results were obtained after the formation of cracks (Figure 10).Since the stresses generated on the walls are released through formation of cracks, strain measutements do not give a clear picture about stress variations in the various directions.However the maximum stresses have been generated at the locations of cracks and their directions are perpendicular to the direction of cracks.
4.4 Strain obseraations using digital strain 8eu8es Later these movements were monitored using strain gauges and a data logger.Since these instruments are more sensitive than the mechanical strain gauge, the measutements are more accurate than the earlier ones.The strain observations are shown in Figures 11 and 12 These strains have the same pattern as the temperature variations of the roof slab (Figures 3 and 4).Hence it is clear that the cause for wall strains is the movements of the roof slab as a result of temperature variation in the slab.
The observations on the 2 m load bearing wall model in Figures 9 and 11 indicate that the maximum strain and hence the maximum movement of the wall has occurred in a diagonal direction at the edges while it is Expansive strains in of walls during a single day were measured over a period of a year using a mechanical strain gauge.The readings were taken weekly.Since these expansive strains would be related to the overall temperature difference in the roof slab, expansions per degree of thermal gradient of roof slab were calculated.The average maximum daily expansions of walls observed are shown in Figures 8 to10.
In the 1 m load bearing wall model the maximum expansion has occurred in the horizontal direction (H t V, D1 and D3, see Figure 8), while'the maximum expansion of the 2 m load bearing wall model is diagonal (D1., D2, D3 and D4 > H and V, see Figure 9)' This gives an indication about the effect of the aspect ratio of the wall on the movements of the load bearing walls.Since the results were obtained before the formation of cracks, this gives a clear picture about the elastic behaviour of the system.A considerable amount of strain has been recorded in the horizontal direction at the centre too.Observations of movements using the mechanical strain gauge in the load bearing walls showed that when the aspect ratio of the wall is 1.0 the horizontal strain at the centre is higher than the diagonal strain at the edges (Figure 8).
Therefore there is a possibility of crack generation vertically close to the panel centre and downward inclined at the panel edge.
Vertical cracking is more likely to occur when the wall is short and diagonal cracking when it is long.Flowever, depending on the level of stress generated on the wall, the formation of both vertical and diagonal cracks are possible in long walls.The observations from the building survey also demonstrate this crack pattern on load bearing walls (Dilrukshi and Dias 2008).
In the concrete framed wall, cracks were present at the time of these strain measurements.The majority of planned strain gauging locations were across these cracks.
These observations show that the methodology used to select the strain gauging locations is sound.The cracks that have deviated from the expected locations are probably due fo material non homogeneity and workmanship deficiencies.The observations of strains at the uncracked locations of the framed wall are shown in Figure 12.The figure illustrates that all the strains have followed the pattern of diurnal temperature variations in the roof slab.
The crack pattern can be described as being horizontal under the beam at the centre and downward inclined at the panel edge near the column as regularly observed in concrete framed buildings during the building survey.Also, the results of the numerical simulations con-firm this (Dilrukshi and Dias 2008).The above results show that the stratn observations of the physical model and the results of numerical simulation have reasonable agreement with each other, except at the location V. Therefore the numericai model developed using SAP2000 can be considered as being reasonably well validated.

Comparison "f
results with sulTey ob s era ati ons an d num eri c al pr edi cti o ns In this study, small scale physical models were used to identify the effect of loof slab movements on solid walls.The main features associated with solid walls are the structural form and the aspect ratio of the wall.
According to the observations from the building survey (Dilrukshi 2008), cracks in load bearing wails can be identified as being vertical near the centre and inclined downward close to the ends of the wall.The inclinations of these diagonal cracks were around 500 -600 to the horizontal.
The observations of the physical models which represent load bearing walls have also confirmed this crack pattern.In the physical model wall which represented a short wall, the maximum strains were observed in the horizontal direction at the wall centre.In the wall which represented a long wall the strains measured in a diagonal direction close to the panel edge at 250 to the horizontal are the highest.The strains in the horizontal direction at the centre of this wall also dispiayed considerably high values.This implies that cracking in long load bearing walls is possible vertically at the centre and diagonally at the panel edges, as observed in the building survey.
The numerical modelling has also predicted the same phenomena (Dilrukshi and Dias 2008,  Dilrukshi 2008).The results indicate that the maximum principal stresses in the short load bearing walls is at the wall centre in the horizontal direction and that it is at 250 to the horizontal close to the panel edges in the long load bearing wall.
Horizontal cracking under the beam and diagonal cracking close to the column near panel edges were the most common types of cracks observed in the concrete framed walls during the building survey (Dilrukshi andDias 2008, Dilrukshi 2008).The direction of the diagonal cracking was around 450 to the horizontal.The cracks observed in the physical model which represented a concrete framed wall were also the sarle as the above.The strains observed in the vertical direction at the wall centre and diagonal directions (at 450 to the horizontai) at the panel edges are the highest in this wali.The numerical rnodels (Dilrukshi 2008) have also predicted diagonal cracking close to the waii edges (due to higher principal stresses in wall) and horizontal cracking under the beam (due to higher principal stresses in wall or higher tensile and shear stresses in the interface link elements).

Conclusion
Both the building survey and physical model observations demonstrate that the movements generated on walls due to the temperature of the roof siab follow the pattern of those diurnal temperature variations.
The pattern (type and location) of cracking depends significantly on whether the wall is load bearing or framed by the reinforced concrete elements.
Forrnation ol horizontal cracks under the beams is common in concrete framed walls.They can be formed in the wall just under the concrete beam or at the masonryconcrete beam interface, usually at the weaker of the two.
Both Both the building survey observations and the strain observations in physical models show that in addition to the diagonal cracking at the edges, vertical cracking close to the centre is also possible in load bearing walls.When the wali aspect ratio is ciose to one 1..
(short walls) such vertical cracking is more likely than diagonal cracking at the edges.In long walls the formation of diagonal cracks at the ends is more likely, but both types of cracks could form.
Figure 1-Simplification of the model

Figure 3 -
Figure 3 -Temperature variation of 2 m load

-Figure 5 -
Figure 5 -Cracks in 2 m concrete frame model (around L.5 months after the construction): (a) Horizontal crack immediately under the beam (the right hand side of the wall, West Face); (b) Horizontal crack below the beam level (the left hand side of wall, West Face); (c) Diagonal crack at the edge of the left hand side, East Face; (d) Diagonal crack at the edge of the right hand side, West Face. respectively.

Figure 6 -Figure 9 -
Figure 6 -Cracks in wall2 m load bearing wall model

Figure
Figure 7 -Cracks in 2 m concrete framed wall model 4.3 Strain obseraations using mechanical strain gauge

Figure 8 -
Figure8-Average maximum daily expansion of the 1 m load bearing wall(Model I)

Figure 1L -
Figure 1L -Shain measurements in 2 m load bearing wall model -West Face

Figure 12 -
Figure 12 -Strain measurements in 2 m concrete framed wall model -East Face 4.5 Quantitatioe aalidation of SAP2000 model

Table 1 -
Description of physical models used concrete 20 nm 600 to the horizontal) were seen on the 2 m load bearing wall model.The cracking observed on the 2 m load bearing wall and concrete framed wall models are compared in Figures6 and 7 Sincethe 1 m load bearing model wall collapsed accidentally during the attempted strain gauging operatiory it could not be observed for an extended duration.However, it did not display any cracking in the 14 months under observation.

Table 2 )
and the strain values obtained by the numerical simulation are shown inTable 4.

Table 4 :
Comparison of strains of 1rl3 scale types of structural arrangements give diagonal cracking near the ends of the walls, with the crack orientation steeper in load bearing walls.The diagonal cracks in concrete framed wails usually have inclinations of around 450 to the horizontal and in load bearing wal1s it is generally around 600.