Efficiency and Critical Points of Strengthening Masonry

Structures with FRP

Jiri Witzany

Prof., Department of Building Structures, CTU in Prague, Czech Republic

Tomas Cejka

Lecturer, Department of Building Structures, CTU in Prague, Czech Republic

Radek Zigler

Lecturer, Department of Building Structures, CTU in Prague, Czech Republic

ABSTRACT

This paper presents the results of theoretical and experimental research focused on the explanation of the problems related to dramatic differences in the deformation characteristics of FRP fabrics and brick masonry. It investigates the mutual interaction of masonry possessing a relatively lower modulus of deformation Ed and a strengthening FRP layer with a relatively high modulus of elasticity ECFRP (ECFRP to Ed ratio ≈ <50;70>), the problems of the interaction of strengthening FRP layers with masonry in areas exposed to pressure (FRP buckling) and the problems related to efficient exploitation of mechanical characteristics of FRP with regard to specific mechanical characteristics of masonry. Special attention within the experimental research is focused on the strengthening of masonry pillars exposed to the external environment and damaged by tensile cracks in the case of reconstructions of historic buildings jeopardized by further cumulative failures and on-going disintegration and the failure mechanism of masonry pillars under low-cycle alternating load. The paper was written with support from Research Plan MSM 6840770001 “Reliability, optimization and durability of building materials and structures“.

KEYWORD

carbon fiber, masonry, experimental research, strengthening

T1A03

1. INTRODUCTION Unlike the strengthening of concrete structures with FRP fabrics [1], the strengthening of masonry structures loaded with concentric compression with FRP still has not been adequately verified. The majority of research projects are primarily focused on the issues of enhancing the resistance of masonry to seismicity-induced vibrations [2, 3]. In this respect, the current insufficient knowledge has not allowed formulating reliable relationships for the design of masonry reinforced with FRP (necessary mainly in reconstruction projects of historical buildings). The results of some experimental works of strengthening masonry with FRP published up to date are still way below the level of generalised conclusions. 2. THE INTERACTION OF MASONRY MEMBERS AND MORTAR IN COMPRESSED MASONRY STRUCTURES Masonry is a non-homogeneous, unisotropic, relatively brittle material composed of two substances with different characteristics. The variable mechanical characteristics of not only individual component parts of masonry, masonry members and the binder, but also the variability of these characteristics within individual masonry members and the binder, all these are the cause of a relatively complex stress state with particularly the tensile components of normal or principal stresses as the major agent in the appearance and development of cracks. The failure mechanism of masonry under concentric compression and the exhaustion of its load-bearing capacity in compression are characterized by the appearance and development of vertical, predominantly tensile cracks; the first cracks arise in the points of a masonry structure where the acting normal tensile stress σσσσx (principal stress σ1) has exceeded the local tensile strength of masonry fmst, or where the value of the transverse deformation εx (or ε1) has exceeded the value of the relative tensile deformation limit εx,m. Due to this mechanism, the compressive strength of masonry depends not only on the compressive strength of bricks fuc, the compressive strength of mortar fmc, but also on the tensile strength of bricks fut, or the tensile strength of mortar fmt. Due to the effect of the differences in the structure of the brick-making raw material and due to the effect of different setups of testing devices for measuring fut, different values of the fut /fuc ratio

are stated in professional literature, ranging, as a rule, in the interval of (0.05;0.09) for the compressive strength of bricks fuc in the interval of (10 MPa, 24 MPa) [4]. The investigation of masonry structures performed to-date has been limited to determining only the strength fuc, but not the strength fut. The tensile strength of bricks fut

applies mainly under loads approaching the masonry load limit, i.e. to masonry with initiated crack development in masonry with poorer-quality mortar being, therefore, of principal significance for the residual load-bearing capacity of masonry. In common types of masonry with a binder with a strength of 2 – 5 MPa, the bond of the mortar and bricks, and thus also their identical transverse deformation, are ensured by their mutual interaction. As a result of this mutual interaction, mortar, which is prone to greater transverse deformations (Em < Eb → εx,m > εx,b), is transversally “pushed“ (exposed to triaxial compressive stress states), while, on the contrary, bricks are transversally “pulled“. As a consequence of mutual interaction, the ultimate strength of masonry f msc is lower than the strength of its component with the higher bearing capacity (e.g. bricks fuc), but tends to be higher than the strength which would correspond to the strength of a body manufactured of the masonry component with the lower bearing capacity (e.g. mortar fmc).

Let us express ∫=∆2/

0

, .1 x

x dxt

τσ τ (1)

where t is the height of the bed joint of mortar,

∫2/

0

.x

dxτ is the normal force per unit

length of the joint exerted by the shear flow τ arising in the butt (contact) “mortar – brick” joint due to their mutual interaction. The compatibility condition (of identical transverse deformation of masonry and mortar in close proximity to the bed joint) εx,b = εx,m may be roughly written in the form: εx,b +εx,bN = εx,m - εx,mN (2)

or m

xmy

b

xby

EEιτ σµσσµσ ,, . ∆−

=∆+

(3)

where εx,b and εx,m are free specific elongations of a brick body and mortar in the direction of the horizontal axis x, εx,bN and εx,mN are induced relative deformations of bricks (elongation) and mortar (compression), σy is the vertical normal stress, µb(m) is Poisson’s constant for bricks (mortar), Eb(m) is the modulus of elasticity of bricks

(mortar). With the growing height of the bed joint, the favourable effect of transverse compressive stresses - ∆σx,τ on the resulting strength of mortar is gradually limited only to the cross-sections adjoining the “mortar – brick” butt joints. In more remote cross-sections, the bed joint mortar is pushed out and disintegrated (the compressive strength of mortar being lower here due to higher tensile stresses σx (-∆σx,τ → 0 ⇒ εx,mN → 0).

Fig. 1 a) Condition of masonry compatibility, b) The pattern of principal stresses σ1 in a

compressed masonry pillar 450 mm thick in relation to the Eb : Em ratio and the bed joint

thickness Adopting a slight simplification, this spatial mechanism of mutual interaction of masonry members and the binder may be transformed into a planar stress state described by the components σx, σy, τxy (εx, εz, γxy [5]). The interaction mechanism

of both of the masonry components and the results of the microanalysis of a compressed masonry unit for the respective ratio of the strength f, or the modulus of elasticity E, are displayed in Fig. 1. The pattern of the principal stress σ1 clearly shows the effect of different values of the modulus of elasticity of bricks (Eb) and mortar (Em) and the bed joint thickness. By dividing a masonry pillar by continuous vertical cracks into individual “stanchions”, the ultimate bearing capacity of the masonry pillar is successively reached. The major agent in the appearance and development of tensile cracks in compressed masonry is the tensile strength of a brick, which has a significant share in the disintegration of masonry due to transverse tension. By expressing the strength of a brick under biaxial stress state [6] in the σ1 x σ2 coordinate system where the extreme strength values at the zero value of one of the principal stresses correspond to the ultimate strength set for uniaxial stress state, i.e. σ2 = the ultimate compressive strength fuc and σ1 = the ultimate tensile strength fut, the condition of the ultimate strength of masonry under biaxial stress state in the σ1 x σ2 coordinate system, e.g. for the ratio of ultimate strengths fuc/fut of 1/0.083, may be roughly expressed by the expression (Fig. 2): σ1 + 0.0883σ2

2 – 0.0071σ2 – 0.0831 ≤ 0 (4)

Fig. 2 Part of the envelope curve (“tension – compression“ quadrant) of brick strength expressed in the σ1 x σ2coordinate system

The condition of masonry failure may analogically be expressed in the ε1 x ε2 coordinate system – hence e.g. for a selected ratio of ultimate strengths fuc/fut of 1/0.021 it follows: ε1 + 0.2434ε2

2 – 0.0388ε2 – 0.2097 ≤ 0 (5)

The values of principal stresses +σ1 as the function of the Em/Eb ratio for the selected thicknesses of the bed joint may be determined from the results of numerical analysis of masonry under concentric compression (Fig. 3). The masonry strength dependence expressed in the σ1 x σ2 or ε1 x ε2 coordinate system allows making the non-linear elastic analysis of masonry failure due to tensile cracks in relation to the strength of masonry members in tension (bricks). The working diagram of a compressed masonry member N x δy is characterized by a very narrow area of elastic deformations and a prominent area of non-linear elastic and plastic deformations with a gradual growth of permanent deformations starting already at a low level of the growing load. The ability of plastic deformation of masonry under biaxial stress state is of exceptional importance for the rehabilitation of compressed masonry pillars (activation of the strengthening structure by the deformation of strengthened masonry) and for buildings exposed e.g. to extreme settlement (part of deformation is absorbed by the more yielding masonry component – mortar).

Fig. 3 Dependence of values of principal stresses σ1 on the Em : Eb ratio and the bed joint thickness

3. ANALYSIS OF THE RESULTS OF EXPERIMENTAL RESEARCH OF THE BEHAVIOUR OF MASONRY PILLARS UNDER CONCENTRIC COMPRESSION The research plan “Reliability, optimization and durability of building materials and structures“ involves experimental research focused on the behaviour of brick pillars wrapped (strengthened) by strips of carbon fibre of variable height and different placement along the height of masonry pillars. Special attention within the experimental research is focused on the strengthening of masonry pillars exposed to external environment (experimental series IV) and

damaged by tensile cracks in the case of reconstructions of historic buildings jeopardized by further cumulative failures and on-going disintegration and the failure mechanism of masonry pillars under low-cycle alternating load. Fig. 4 displays the experimentally obtained dependences of N x δy of unreinforced masonry pillars under concentric compression (experimental series I and IV)1).

Fig. 4 N x δy dependence of concentrically compressed unreinforced masonry pillars

The experimentally obtained patterns of N x δy dependences of unreinforced masonry pillars (experimental series I and IV) loaded by concentric compression force are characterized by: • nearly zero (negligible) width of the area of

initial elastic deformations not exceeding the value of 0,05 of the total width of deformations δy,0 - δy,m of the N x δy dependence;

• gentle progressive growth in total vertical deformations δy;

• decline in the relative permanent vertical deformation δy,p in relation to the total deformation δy,t under growing load with the compressive force N, δy,p/δy,t ϵ (0,92;0,56) – series I and δy,p/δy,t ϵ (0,84;0,72) – series IV (Fig. 5);

• continuous growth in horizontal (transverse) deformations δx in relation to the load N, δx,m ϵ (0,18; 0,33) – series I, δx,m ϵ (0,35; 0,50) – series IV (Fig. 6)

Note 1) The pillars were made in dimensions of 300 x 300 x 900 mm, of solid bricks (CP 20) with a strength of 20 MPa placed in lime mortar (MV 2) of compressive strength of 2 MPa, the thickness of joints (bed and butt) was ca 15 mm. Experimental series IV masonry pillars were exposed for a duration of one year to the effects of external environment, so that a partial masonry degradation could occur.

Fig. 5 N x δy,p/δy,t dependence of concentrically

compressed unreinforced masonry pillars

Fig. 6 N x δx dependence of concentrically compressed unreinforced masonry pillars

The first visually observable cracks (Fig. 7) in the central part of the unreinforced masonry pillar loaded with concentric compressive force appeared under the load of 480 kN, i.e. at 156% of the design (characteristic) load limit (ČSN EN 1996-1-1) – series I, and under the load of 300 kN, i.e. at 140% of the design (characteristic) load limit (ČSN EN 1996-1-1) – series IV. The total failure of the unreinforced masonry pillar loaded with concentric compressive force was reached under the load of 707 kN, i.e. at 229% of the design load limit (ČSN EN 1996-1-1) – series I, and under the load of 375 kN, i.e. at 175% of the design load limit (ČSN EN 1996-1-1) – series IV. The monitored patterns of vertical (δy) and horizontal (δx) deformations on loading (N) dependencies and the ultimate loads (Nu) show the influence of external environment on the decrease of masonry’s load bearing capacity and stiffness

(the ultimate load of the exposed pillars is approximately 53% of the ultimate load of non-exposed pillars). By preventing the premature appearance and development of tensile cracks in the masonry of the pillar arising due to the effect of contraction and mutual interaction of the masonry members and the binder, a better utilization of the load bearing capacity of the masonry in compression may be achieved in relation to the strength of its individual components. The reinforcement of a masonry pillar or a wall with fabrics of carbon fibres with a high modulus of elasticity (Ecfrp/Ed ϵ <50;70>) and a high tensile strength, e.g. ft,cfrp = 980 MPa, creates an external transverse reinforcement of compressed masonry taking over transverse tensile stresses in the masonry and increasing the value of the deformation limit δy,m

and the load limit Nu at failure.

Fig. 7 Appearance of visually observable cracks in concentrically compressed unreinforced masonry

pillars and failure after reaching the load limit

Reinforcing fabrics and mats are produced of high-modular carbon fibres, glass, polyester and aramid fibres with comparable characteristics. Carbon fibres possess a high modulus of elasticity

of 240 000 MPa, resistance to fatigue (very high fatigue strength – ca 106 cycles under a load of ca 0.8 of the ultimate strength), chemical substances, corrosion, temperature changes (a low coefficient of thermal expansion – up to 50x lower than the coefficient of thermal expansion of concrete). The ultimate elongation of carbon-fibre fabric is much lower than the ultimate elongation of masonry the reaching of which is accompanied by the appearance of tensile cracks in the masonry. The working diagrams of fabrics of carbon fibres are significantly different from the working diagram of masonry. The relative deformation (elongation) at breaking of fabrics of carbon fibres is 1.0%. For the dimensioning of strengthened masonry structures, however, the relative deformation at breaking in relation to the type of loading should not exceed 50% of the respective value. The significant difference of the working diagram of masonry and that of fabrics of carbon fibres poses a serious problem requiring experimental research of the mutual interaction of these two different components (e.g. the problem of the buckling of the fabrics of carbon fibres in compressed areas). The pattern of experimentally determined N x δy dependences of masonry pillars (Fig. 8) under concentric compression reinforced with strips of fabrics of carbon fibres (Fig. 9) as compared to experimentally determined N x δy dependences of unreinforced masonry pillars (Fig. 4) apparently shows the following: • the reinforcement of masonry pillars under

concentric compression with carbon-fibre fabric have a significant effect on the magnitude of horizontal (transverse) deformations δx as compared to horizontal deformations of an unreinforced pillar (for identical loading levels, Fig. 10). Ultimate vertical deformation δx,t of masonry pillars under concentric compression reinforced by carbon fiber strips lies approx. between 394% (series IV) and 573% (series I) of ultimate vertical deformation δx,t of unreinforced pillars. The carbon fabric is activated successively, after the appearance and development of cracks (i.e. analogically to reinforcement in reinforced concrete structures);

• the working diagrams of unreinforced and reinforced masonry pillars under concentric compression are characterized by a gradual growth of deformations δy, in this case the

appearance of visually observable cracks is not accompanied by a steeper growth of total vertical deformations δy,t. Ultimate vertical deformation δy,t of masonry pillars under concentric compression reinforced by carbon fiber strips lies approx. between 327% (series IV) and 340% (series I) of ultimate vertical deformation δy,t of unreinforced pillars;

Fig. 8 Reinforcement of masonry pillars with

carbon fibre strips (series I and IV)

Fig. 9 N x δy dependence of masonry pillars under concentric compression reinforced with strips of

fabric of carbon fibre

• the working diagrams of unreinforced and reinforced masonry pillars under concentric compression are characterized by a negligible area of elastic deformations lacking a wide transition area from elastic deformations to the elastic-plastic deformation area, i.e. the area before and after the crack appearance. The phase preceding the first cracks during which non-elastic masonry pushing occurs is characterized by higher values of the ratio of permanent and total vertical deformations

δy,p/δy,t ϵ (0,92;0,51) as compared to the phase after the appearance of cracks δy,p/δy,t ϵ (0,7;0,5) – series I, and δy,p/δy,t ϵ (0,88;0,75) as compared to the phase after the appearance of cracks δy,p/δy,t ϵ (0,75;0,72) – series IV;

Fig. 10 N x δx dependence of masonry pillars under concentric compression reinforced with

strips of carbon-fibre fabric

• the width of the area of total deformations of the N x δy dependence of masonry pillars reinforced with carbon-fibre fabric under concentric compressive force as compared to the width of the deformation area of unreinforced masonry pillars under concentric compression is by many times greater (see Fig. 4 and Fig. 9). The experimentally determined value δy,m of reinforced masonry pillars under concentric compression reached magnitudes within the interval of (3,12;4,83) mm – series I and (6,58;10,87) mm – series IV, while the value δy,m of unreinforced masonry pillars under concentric compression reached magnitudes in the interval of (0,89;2,26) mm – series I and (2,56;2,86) mm – series IV;

• the greater width of the reinforcing strips of carbon-fibre fabric increases the width of elastic-plastic deformations (δy,m

150 = 9,64 mm; δy,m

75 = 6,69 mm) and increases the load-bearing capacity of the masonry pillar (experimental series IV) in compression (Num

150 = 520 kN; Num75 = 510 kN) – series IV

(Fig. 9); • the ratio of the permanent and total vertical

deformation δy,p/ δy,t of unreinforced masonry pillars under concentric compression and growing load by concentric compressive force (with growing vertical deformations δy) falls

from the initial value of (0,83;0,92) – series I and (0,84;0,88) – series IV to a value of (0,67;0,7) – series I and (0,72;0,75) – series IV, i.e. approx.128% (series I) and approx. 117% (series IV) of the initial values before the reaching of the ultimate bearing capacity (Fig. 5), whereas in pillars reinforced with the carbon-fibre fabric this decline before the reaching of the ultimate bearing capacity amounts to approx. 136% (series I) and approx 125% (series IV) of the initial value. This relative drop in the permanent deformation in relation to the total deformation is caused by the active effect of the carbon-fibre fabric significantly contributing to the increased bearing capacity of reinforced masonry pillars (Fig. 11);

Fig. 11 N x δy,p/δy,t dependence of masonry pillars

under concentric compression reinforced with strips of carbon-fibre fabric

• the increased bearing capacity of masonry pillars under concentric compression reinforced with carbon-fibre fabric is achieved by the utilization of the bearing capacity of masonry in the area of elastic-plastic deformations of masonry gradually disintegrated by vertical tensile cracks;

4. SUMMARY • By reinforcing a masonry pillar under

concentric compressive force with strips of carbon-fibre fabric its load limit in compression is increased. In the case of experimentally verified pillars, this increase in the load limit of masonry pillars in compression amounted to 136% (series IV) after wrapping by strips 75 mm in width, 148% (series I) and 138% (series IV) after wrapping by strips 150 mm in width as

compared to the load limit of an unreinforced masonry pillar under concentric compressive force (Fig. 12).

Fig. 12 Load limit of unreinforced and reinforced

pillars

• Masonry pillars under concentric compressive force reinforced with strips of carbon-fibre fabric have a significantly wider area of elastic-plastic deformations. In the case of experimentally verified pillars this increase in the deformation limit of masonry pillars strengthened by strips of carbon-fibre fabric in compression amounted to 246% (series IV) after wrapping by strips 75 mm in width and 257% (series I) and 355% (series IV) after wrapping by strips 150 mm in width as compared to the deformation limit of an unreinforced masonry pillar under concentric compressive force (Fig. 13).

• The carbon fabric starts to be fully manifested in the phase of crack propagation and development preventing, in the first place, the redistribution of compressive normal stresses, which is the cause of the growing non-uniformity in the distribution of compressive stresses along the cross-section of a masonry member. Despite the growing horizontal as well as vertical deformations (mainly in the central part), due to the wrapping by carbon-fibre fabric and local failure by tensile cracks, the masonry member is still able to transfer the growing compressive load; during this action the ultimate strength of individual components of masonry is gradually being exhausted.

• The greater width of the area of elastic-plastic deformations δx, δy of reinforced masonry pillars under concentric compressive force is positively manifested in terms of the action and response of the vertical masonry structure

under cyclic load (technical, induced and natural seismicity, cyclic temperature and moisture load).

Fig. 13 Vertical deformation limits of unreinforced

and reinforced pillars at reaching the load limit

ACKNOWLEDGEMENT

The paper was written with support from Research Plan MSM 6840770001 “Reliability, optimization and durability of building materials and structures“.

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