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REPAIR AND RETROFITTING OF RC WALLS USING SELECTIVETECHNIQUESA. S. Elnashaia; R. Pinhoa

a Engineering Seismology and Earthquake Engineering Section, Imperial College Imperial CollegeRoad, London SW7 2BU, UK

To cite this Article Elnashai, A. S. and Pinho, R.(1998) 'REPAIR AND RETROFITTING OF RC WALLS USING SELECTIVETECHNIQUES', Journal of Earthquake Engineering, 2: 4, 525 — 568To link to this Article: DOI: 10.1080/13632469809350334URL: http://dx.doi.org/10.1080/13632469809350334

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Journal of Earthquake Engineering Vol. 2, No. 4 (1998) 525-568 @ f rnperial College Press

REPAIR- AND RETROFITTING OF RC WALLS USING SELECTIVE TECHNIQUES

A. S. ELNASHAI and R. PINHO Engineering Seismology and Earthquake Enginedng Section, Imperial College

Imperial College Road, London S W7 ZBU, UK

Received 16 December 1997 Revised 26 January 1998

Accepted 2 February 1998

In the context of capacity' design philosophy, where a desired failure mode exhibiting adequate levels of energy absorption capacity is envisaged, control must be exercised on the member behaviour to safeguard the achievement of the target overall response. Therefore, local repair and retrofitting methods that result in unquantifiable effects on seismic response characteristics should be re-assessed. In contrast, techniques to affect, in a controlled and easy-ternonitor fashion, individual design response parameters, i.e. stiffness, strength and ductility, may provide a new framework for repair and retrofitting earthquake-damaged structures to mirror 'capacity design' principles used for new structures. Such an approach is discussed in this paper and possible scenarios where selective intervention may be required are identified. A number of tests on RC walls are also reviewed to confirm the feasibility of the proposed intervention techniques. Finally, extensive parametric studies are carried out, using verified analytical models, leading to the derivation of selective re-design expressions and guidelines.

Keywords: selective, repair, retrofitting, walls, capacity re-design, RC structures

1. Introduction

Conventionally, the philosophy behind repair/retrofit ting schemes has been one of over-strengthening. However, in the light of modern 'capacity design' concepts used in seismic codes in which a significant role is assumed by the control of the overall response of RC structures, such an approach can be counter-productive. Structures designed to conform to a particular failure mode rely heavily on individual design response parameters of its members, such as stiffness and strength .in shear and flexure, as well as ductility. Accordingly, repair or ret refitting methods which will affect these characteristics should consider not only the local but also the global effects of the intervention. In fact, local over-strengthening of individual members may cause stiffness irregularities or disturb the sequence of plastic hinge formation, thus jeopardising the whole retrofitting process.

Moreover, several recent studies [Moehle, 1992; Calvi and Pavese, 1995; Kowal- sky et aL, 19951 have introduced the concept of 'displacement-based design' as a

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526 A. S. Elnashai E9 R. Pinho

logical and rational alternative to the currently used 'force-based design' methodology. In this new approach, a structure is designed to meet a target deformation criterion whilst strength and stiffness become end-products of the design procedure.

"

Since capacity design requires control on the deformational demand and supply at dissipative zones, it blends perfectly with displacement- (or more generally, deformation-) based design. Such an approach to seismic design clearly requires a higher level of control over the local behaviour of members and their global effect on the seismic response of a structure.

Therefore, methods of structural intervention, especially of RC structures, have to address these new requirements of local deformational behaviour control by providing tools for affecting individual design response parameters: stiffness, strength and ductility. This would allow the fine-tuning of the local response characteristics in favour of a desired global performance, enabling tighter control of the behaviour and failure modes of RC structures, thus leading to a more rational assessment and repair/ret rofit ting solution.

The three parameters governing displacement-based design (DBD) are period, equivalent damping and global displacement. Since the period in DBD is the secant value at the target displacement, it becomes a function of the initial stiffness, strength and maximum displacement. The equivalent damping is a function of the Level of ductility, for it is mainly contributed to by hysteretic energy dissipation. If separate control of stiffness, strength and ductility is afforded to the designer (in a, displacement- based assessment leading to repairlretrofitting design), then more than one solution to achieve the target DBD objective is availed of. Hence, selective intervention blends well with displacement-based assessment and re-design.

Such intervention philosophy is conceptually described in Fig. 1. The original structure may have a ratio between capacity (A,) and demand (Ad) displacements that does not meet the target safety requirements. The three intervention scenarios present different solutions to address such a situation, either by targeting the structure initial stiffness ( K i ) , its strength (F,) or ductility ( p ) . Which solution is more economical and feasible will depend on the case under consideration, keeping in mind both the structure characteristics and the displacement spectrum. Whilst an increase in the level of equivalent damping (C) will decrease the displacement demand, changes in the effective period of vibration of the structure (Tefj) may or may not be beneficial depending on the spectrum shape. It is clear, though, that this view provides more degrees of freedom for the designers of intervention schemes.

In this paper, tests performed at Imperial College [Elnashai and Salama, 19921 to investigate the feasibility of affecting one response parameter with little or no effect on others are re-assessed. An analytical model is assembled to represent the experiment aLy-verified intervention mechanisms for stitfness-, strength- and ductility-only scenarios- The model realism is confirmed by comparison with the available test data and M h e r employed in a parametric investigation. Sim- ple design-oriented expressions are derived, then analytically tested, to provide


Repair and Rettofitting of RC Walls Using Selective Techniques 527

Fig. 1. Variation in DBD design parameters due to selective intervention: (a) stiffness; (b) strength; and (c) ductility.

relationships between the physical characteristics of the intervention and the per- centage effect on the target response parameter. Finally, worked numerical examples are given to demonst rate the potential for application of the derived expressions.

2. Review of Recent Work on Repair and Retrofitting of RC Structures

There is very considerable literature on general repair and strengthening methods for RC structures, many of which are relevant to earthquake-relatedissues. For example, Japanese work on this subject is summarised up to 1986 by the Japanese Ministry of Construction [P WRI, 19861. Whole conference proceedings have also been dedicated to this important topic [UJCEERP, 19811 and, more recently, spe- cial issues of journals have focused on repair techniques [EEFU, 19961. A review of general repair and strengthening techniques, however, falls beyond the scope of this paper. Consequently, only work aimed at affecting selected response parameters, whilst intentionally avoiding affecting others, is cited. These focus on the seismic upgrading of reinforced concrete columns by selectively affecting their ductility capacity.

Aboutaha e t aL [1996] investigated the effectiveness of thin rectangular steel jackets for seismic strengthening of large rectangular non-ductile reinforced concrete columns. Tested specimens represented typical building columns designed .

and constructed in the 1960s in the United Sates. These were typically deficient in the level of concrete confinement and had inadequate lap splices in the longitudinal reinforcement. Different configurations of 6.3 mm thick steel jackets were applied with and without adhesive anchor bolts to seven full-scale specimens subjected to


528 A. S. E l w h a i E4 R. Pinho

cyclic loading. The test results show significant increase in the ductility of the reinforced concrete members, whilst minimum change in the initial stiffness of the members was observed. The ductile flexure-dominated resporise of the retrofitted models enabled their full flexural capacity to be developed, hence a significant increase in strength was also recorded.

Aviles et aL 119961 conducted a similar set of experiments on 18 column specimens. Some of the models were deficient in the level of concrete confinement at the foundation level. These were retrofitted with 1.2 mm thick steel plate wrapping combined with anchor bolts. The effects of such interventions were visible only in the increase of deformation capacity of the specimens, whilst no change in either stiffness or strength was verified.

Saadatrnanesh et oL [I9971 carried out experimental work on the application of high-strength fibre-reinforced plastic (FRP) composites straps to retrofit rectangular bridge columns. Five 115-scale specimens were tested under reversed cyclic loading. Both oval and rectangular shapes were used, and active confinement was applied in one of the specimens by means of pressure injection of epoxy resin. The increase in the level of ductility of the upgaded models is clearly shown in this work. Shear failure was avoided, thus enabling full attainment of the initial flexural capacity of the members.

Ghobarah et (11. [I9981 tested three 1/3-scale columns to investigate the effectiveness of corrugated steel jacketing in the rehabilitation of reinforced concrete columns. The jackets were constructed from commercially available corrugated steel sheets and the gaps between the concrete and the steel jacket were filled with grout to provide continuity between the two elements. Furthermore, the undulated shape exhibits an out-of-plane stiffness which increases its efficiency in providing external passive confinement to the rehabilitated members. These exhibited a significant increase in deformation capacity, without any significant change in their initial stiffness.

The above research shows excellent results in the increase of ductility of reinforced concrete columns. Since a gap is provided between the steel/composite jackets and the foundation, no change in the original fleiural capacity of the member is introduced.. Similarly, significant modifications in the stiffness of the columns are prevented by the use of thin steel plates or high-strength composite materials. The latter will induce changes in initial stiffness up to a maximum of 5% as opposed to a 75% change if conventional concrete jacketing is used [Priestley et aL, 1996).

3. Design Scenarios Requiring Selective Intervention

3.1. Stiffness-only scenarios

3.1 .l. Repair of lightly damaged stnrctums

RC structures subjected to small earthquakes may suffer significant stiffness reduction due to heavy cracking of concrete members. However, il concrete crushing and buckling of reinforcement bars do not occur, the flexural strength of the members


Repair and Retrofitting of RC Walk Using Selective Techniques 529

will not necessarily be adversely affected. Hence, an effective intervention targeting. stiffness of cracked members reinstatement without changing their strength is the more economical'and logical approach.

For such situations, epoxy resin injection is widely used. Yet the end result of such intervention is extremely difficult to forecast and control, since it is highly dependent on the workmanship, the viscosity of the applied epoxy, the injection pressure and the crack width and configuration. The latter is particularly un- predictable, especially in the case of an earthquake-damaged wall where a complex crack configuration has developed due to the loading characteristics and dimensions of the member. Consequently, the degree of epoxy mortar penetration is uncertain and the level of stiffness reinstatement becomes doubtful.

This technique was tested by Elnashai and Salama [I9921 at Imperial College, amongst others, in a scaled wall subjected to severe cyclic loading. The stiffness vs. maximum cyclic displacement plots extracted from this experiment (Fig. 2) show that even under laboratory conditions, complete reinstatement of the initial stiffness of the tested specimen was not achieved due to the difficulty in making the epoxy resin penetrate cracks with width less than 0.05 mm (the height of the model was 1.2 m, thus the results are only satisfactory beyond 1% drift). The use of the stiffness-only selective repair technique, described ahead, will overcome such difficulties.

0.0 5 .O 10.0 15.0 20.0 25.0 30.0

Displacement (rnm)

15.0 ---...... .. --..---------- --...---.-..-..--.-, --" .. . . . . . . . . . . . . . . 2. . . . . .-- .......................

Fig. 2. Experimental results of intact and epoxy resin repaired walls [Elnashai and Salama, 19921.

- 12.5

2 VI VI s 10.0

'3.1.2. Correction of stzmess irtegularities

\ Intact . . . . . . . . .. . . . . . . . . 1: \ , . .

. \ Repaired . . ................................................................................ -

I-- / .

*-. ....-... .--. ---->-. --..:

A structure may have an irregular stiffness distribution due to incorrect design a p proach, architectural constraints or to the use of a more lenient code at the.time of its construction. To upgrade such a structure in order to improve its behaviour or

.-...... -", ........-.....K-.-..-.......---...I_...-.__---_.--..-I .. .... .-_. - U Y

....... - .............................

2.5 ---- ,---------.-----.-----.--.-......-.-------


530 A. S. Elnashai @ R. Pinho

to make it comply with new modern code design criteria, a selective intervention that will enable the designer to concentrate uniquely on the parameter in question is required. Otherwise, if repair or retrofitting methods which affect not only the stiffness of the members but also their flexural capacity are applied, then a complete structural redesign is needed, resulting in a more costly and time-consuming solution.

3.2. Strength-only scenarios

3.2.1. Capacity re-design

New code design philosophy requirements or an increase in seismic loads can lead to a requirement for structural upgrading. If the structure had been designed according to conventional direct design principles, then altering the sequence of plastic hinge formation to achieve a predetermined failure mode (in harmony with the capacity design concept) becomes imperative. This will require an increase in the strength of strategically. located members. However, if the serviceability limit states are still met with the existing stiffness distribution, an increase in this parameter is not required. Furthermore, if the stiffness distribution is in accordance with code prerequisites, changes could result in code violat ion. Thus full dynamic analysis and redesign would be required.

It is, therefore, clear that for such situations a selective intervention altering only the strength of the members, without affecting their stiffness, is required.

3.2.2. Strength eccentricity

Adverse torsional effects caused by stifhess eccentricity are widely known and relatively well addressed in seismic codes, where they are considered in simplified approaches whenever. possible. In contrast, strength eccentricity is not mentioned.

However, in a study by Xian 119921, it was shown that the inelastic response is indeed altered by this factor, resulting in an increase in ductility demand. Such a situation may arise, for ixtance, in a dual structural system, where in order to achieve stiffness symmetry, structural walls are used to balance the eccentric stiffnpss distribution. Since the relationship between strength and st ifFness of both systems is by no means similar, even though their relative stifiesses are in equilibrium, the strength distribution may be eccentric. Only a selective strength-only intervention can be effective in addressing such deficiency.

3.2.3. Variability in materials

The hazardous effects of variability in material properties are largely acknowledged,. particularly in the case where a predefined sequence of plastic hinge formation is required to advance the design process. However, even in more recent seismic codes, very little guidance on ways of controlling such effects is available. In the case of steel yield strength, the effects of its variability can be extremely adverse, as highlighted


Repair and Retmjitting of RC Walls Using Selective Techniques 531 '

Table 1. Effect of material variability on response p* rameters of a RC frame [Alexandrou, 19911.

Displacement Energy Behaviour Ductility Absorption Fact or

Pd kNm lq' ,

Max. 10.11 73.05 5.50

Min. 6.57 24.89 3.75

% change 54% 192% 4wo

in a study carried out by Alexandrou [I9911 on the global behaviour of RC frames subjected to seismic loading. In Table 1, the results from a study on a two-storey frame are presented. The steel yield was varied between practical limits and the ensuing population of nominally identical frames was analysed.

It can be observed that although the variations of yield strength correspond to realistic values, the effects of this factor on the global behaviour of the structure are critical, resulting in a variation of 47% in q factor, defined as the ratio between the linear elastic and non-linear response spectra. In such scenarios, only the strength of some critical members needs to be affected so as to ensure the structural, behaviour envisaged at the initial design s t age is reinstated. Therefore, a selective intervent ion targeting exclusively on strength enhancement should be applied.

3.3. Ductility-only scenarios

This is probably the most common situation where selective intervention is required. Problems with lack of ductility supply may arise if the members are poorly detailed due to inappropriate design, inadequate construction or lack of sufficient code requirements, as was the case of old building regulations. The effects of such deficiency can be extremely hazardous since ductility plays a critical role in guaranteeing that a structure can deform without significant loss of strength, thus avoiding collapse.

Traditionally, for such cases, the use of concrete jacketing has proved to be a very popular solution due to the ease of application and comparatively low cost. However, these retrofitting schemes are normally applied only a t the lower floors of a building, where higher levels of ductility demand are expected, thus causing changes in the global behaviour of the structure that can be extremely disadvanta- geous. For example, a 200 x 1000 rnm wall with a 100 mm concrete jacket (minimum required thickness for practical purposes) will have over 250% gain in elastic stiffness. Consequently, the structure will now attract higher seismic loads which the unstrengthened storeys will not withstand. Moreover, changing stiffness distribution in elevation may cause an increase in higher modes contribution to the deformed shape, making design according to simplified static analysis totally inadequate. Therefore, in the event of an earthquake, the retrofitted structure may suffer severe damage in its upper storeys, or even total collapse, as already observed in many post-earthquake field expeditions.


532 A . S. Elnashai R. Pinho

For such design scenarios, where only lack of member ductility needs to be addressed, the most effective and straightforward way of intervening is through a selective approach that will controllably affect the defective parameter alone.

4. Feasibility of Selective Intervention Methods

The previous section emphasised the necessity for developing selective assessment and intervention techniques which allow the application of the new capacity design methodology in the repair and retrofitting of RC structures. Conceptually, the principles of such intervention philosophy can be applied to any type of structural member. However, its employment in the repair and retrofitting of vertical members assumes particular importance in the light of current seismic design practice.

The initial development of selective intervention techniques carried out by Elnashai [I9921 targeted its application to structural walls. The latter have b e come increasingly popular in the past thirty years, since its use in the design of earthquake-resistant high-rise buildings will prevent overdesign of the columns due to drift control, thus leading to more economical solutions generally. Nevertheless, the employment of the proposed schemes to repair and retrofitting, of columns is also feasible, although such study is not covered in the present work.

4.1. Experimental pmgmmme

In order to assess the feasibility of the proposed intervention schemes,. several scaled models were tested at Imperial College under cyclic loading conditions by Elnashai and Salama (19921. The tests are at a scale of approximately 1 : 2.5 and prototype steel and concrete could be used. In Fig. 3, the dimensions and reinforcement detailing of a typical specimen are described, together with the material properties obtained through tests carried out in parallel with t h e wall-testing programme.

f,' = 48.4 MPa

f, = 450 MPa

Fig. 3. Elevation and cross-section of a typical model.


Repair and RetroFtting of RC Walb Using Selective Techniquw 533

Selective techniques were applied both as repair to previously damaged walls, and as retrofitting in intact walls. The models were then tested, until collapse, under severe cyclic loading with at least two cycles at each level of displacement, expressed as multiples of the yield displacement.

Discussion of results and analysis of the effectiveness of the proposed intervention schemes constitute the main objectives of this presentation, hence only results relevant to these aims are covered. Nevertheless, an in-depth discussion of the tests results regarding other topics studied in this experimental programme, together with a detailed description of the test set-up and the design and construction of the models can be found elsewhere [Elnashsi and Salama, 19923.

4.2. Stimess-only intervention

Increase in stiffness without change in strength can be obtained through the use of .

External Bonded Steel Plates (EBSP) glued to the wall with epoxy mortars (Fig. 4). The plates should span at least the expected flexural plastic hinge length (1,) or the heavily cracked zone for the cases of retrofitting and repair, respectively.

Steel

Discontinuity gap

Fig. 4. Stiffness-only intervention - tested specimen [Elnashai and Salama, 19921.

minimum gap be&n the plates and the foundation or loading beam needs to be imposed in order to avoid plate bearing due to flexural deformation. Since there is no continuity between the plates and the loading beam or foundation, the critical section remains the same, hence the flexural capacity is unaltered. Furthermore,


534 A. S. Elnushai & R. Pinho

the increase in the level of stiffness is totally controlled by the position of the plates, their height, width and thickness, as demonstrated later.

The photograph of the specimen tested at Imperial College (shown in Fig. 4), corresponds to a model repaired with 3.6 mm steel plates after being previously damaged through cyclic loading with limited post-yielding deformation. The corresponding experimental results indicate that, unlike epoxy resin injection, the use of EBSP enables full reinstatement of the initial stiffness of damaged walls (Fig. 5). Moreover, steel plate adhesion is often used in repair and strengthening following earthquakes, hence this scheme is practical.

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Displacement (mrn)

Fig. 5. Experimental results of inti& and selectively repaired walls (Elnashai and Salama, 19921.

The presence of the steel plates will evidently affect the spread of inelasticity, hence the relationship between local and global ductility. This can be overcome by using plates with slits and/or thin (yielding) plates, to avail the development of a plastic hinge along the height. This issue needs further investigation.

4.3. Stmngth-only intervention

Two possible ways of achieving an increase in strength without affecting stiffness are by the addition of External Unbonded Reinforcement Bars (EURB) or of External Wnbonded Steel Plates (EUSP) to the walls, in conjunction with an Interaction Delay Mechanism (IDM). These are illustrated in Fig. 6.

When loaded horizontally, the wall will undergo vertical elongat ion (due to rotation and cracking) which will axially extend the exiernal re-bars or steel plates. A delay mechanism is designed such that the added bars or plates will only contribute to the flexural capacity after an initial displacement is exceeded. Hence, if this corresponds to yielding of the wall, for instance, then the wall will have its pre-yield behaviour unaltered.


Repair and Retrafitting of RC Walk Using Selective Techniques 535

- As for the compression, there is no contribution from the external mechanisms, since the associated vertical displacements are normally considerabIy smaller than the gap. Nevertheless, if this tolerance is exceeded and compressive contact occurs, both the EURB and EUSP will buckle and their strength contribution can thus be neglected.

Fig. 6. Strength-only intervention - tested specimens: (a) EURB; (b) EUSP (Elnashai and Salama, 19921.

In the first scheme, illustrated in Fig. 6(a), steel bars are fked to the top and bottom beams and a mechanical coupler with an initial slack is used to allow for a tolerance in displacement, beyond which the bars effectively contribute to the flexural strength of the wall. The bars were fixed to the foundation beam using high-strength epoxy patching mortar and to the top loading beam by means of a steel assembly fixed to the concrete wall.

In the second scheme, shown in Fig. 6(b), steel plates are bolted to the wall by steel angies and gusset plates. The IDM was achieved through the inclusion of slotted holes at the gusset plates located on the loading beam, which allowed the bolts to travel freely within the designed groove before bearing on the steel plate. Hence, additional resistance will only .be. .pro~ded..after .the .designed..displacement gap is exhausted.

The leveI of strength increase can be easily controlled by the area and position of the steel plates or rebars. Moreover, the displacement tolerance used in the delay mechanism can also be manipulated to provide the designer with the


536 A. S. Elnashai &f R. Pinho

possibility of choosing the ideal point from which the external mechanism should start contributing to the flexural strength. This is demonstrated in subsequent sections of the present paper.

The force vs. maximum cyclic displacement plot resulting from the test of the scheme presented in Fig. 6(b) is shown in Fig. 7, where it is compared with the behaviour of the reference model. The point where the external plates start interacting with the wall is clearly visible, as was intentionally designed. The increase in the specimen strength is also evident, whilst its initial stiffness remains unaltered.

, Displacement (mm)

Fig. 7. Experimental results of original 'md selectively strengthened walls (Elnashai and Salama, 19921.

This scheme can be successfully applied in practice by fixing the external bars or plates to the top and bottom slabs. These should then be encased in a ductile material or a plastic duct that will protect the steel from corrosion, provide fire protection and allow for the free movement of the delay mechanism. Furthermore, couplers are frequently used as an effective means of splicing reinforcement bars, hence the EURB are only one step ahead of currently applied practice. Also, there may be other more practical means of achieving the same end, e.g. by cutting bars of longer length than required for immediate load transfer.

Finally, it is worth noting that this intervention can only be successful if the wall has sdlicient capacity to withstand the increased demand on both shear and concrete compression triggered by the strengthening scheme. This issue is M h e r analysed later in this paper.


Repair and Retrofitting of RC Wdls Using Selective Techniques 537

4.4. Ductility-only intervention

In this design scenario, U-shaped ExternaI Confinement Stel'Plates (ECSP) may be added to the area where additional ductility is required. These should be glued to the wall by means of epoxy resin or any other material that will enswe a monolithic interaction between the two elements. To guarantee an effective confinement system, the fourth (open) side of the plates needs to be closed using a prestressed bolt (Fig. 8).

Due to the space between plates, crack arrest is minimised hence stiffness is not altered. Also, since there is no continuity between the plates and foundation, no increase in strength is provided. Moreover, it is well established that the increase in concrete strength due to confinement has a small effect on flexural capacity, especially for low levels of axial force, as in the case of structural walls.

Fig. 8. Ductilitysnly intervention - tested specimen [Elnashai and Salama, 19923.

This technique was experimentally tested on a scaled wall initially designed and built without any confinement reinforcement (Fig. 8). The 3.6 mm thick ECSP were designed to provide the specimen with the same ductility capacity of an identical model-confined .with -internal steel-hoops. Both walls-were subject& to similar cyclic loading regime until failure. The results h m these two experiments are compared in Fig. 9, where it can be seen that the target ductility level was achieved with the application of the external plates, without any significant changes in either stiffness or strength.


538 A. S. Elnashai 0 R. Pinho

Fig. 9. Experimental results of internal and externally confined walls [Elnashai and Salama, 1992).

The proposed ductility-only intervention technique proved to be extremely efficient and should be used as a tool for upgrading structures in which improper detailing leads to insufficient ductility capacity. From a practical view point, use of external confinement is widespread, especially on bridge piers, and the only additional feature in the proposed scheme is the closing bolt. The latter can be achieved by use of fasteners commonly used in RC structures (e.g. Hilti bolts).

Later in the paper, it is shown that the thickness, height and spacing of these external U-shaped plates can be controlled in order to achieve the desired confinement level and, consequently, the level of ductility capacity enhancement introduced by this selective scheme.

4.5. Shear-strength intervention

RC walls with shear-dominated deformational behaviour will respond in a brittle mode. Such a situation is undesirable since it will not allow the development of a ductile controlled failure mode, as required in modem seismic design. An intervention scheme aiming at the rectification of such shortcomings was also tested at Imperial College. The technique consisted of bonding horizontal steel plates to the wall by means of epoxy resin, as shown in Fig. 10. These should be attached to both sides of the wall in a staggered manner and bent through 90" at the extremities to prevent end splitting. Since no load path is provided by the alternate horizontal plates and flexural cracks can still develop, there is no change in either the flexural wall capacity or its initial stfiess.

The experimental test consisted of a repaired wall (Fig. 10) which had been previously subjected to cyclic loading and had failed due to excessive shear deformation. Contrary to what was verified with the intact specimen, the repaired wall


Repair and Retmfitting ol RC Walls Using Selective Techniques 539

Rear Plat - Front Plates

Fig. 10. Shear-strength intervention - tested specimen [Elnashai and Sakima, 19921.

responded in a more ductile mode and its ultimate flexural strength was fully developed (Fig. 11). Concrete crushing was recorded at the boundary elements rather than the web, as was originally the case.

These test results show that the shear strength of RC structural walls can be fully reinstated and, if required, enhanced by bonding external horizontal steel plates to the damaged wall without the need of epoxy resin injection. However, the use of the latter would improve the shear stiffness further, increase the energy absorption capacity and ensure higher durability for the retrofitting scheme.

The application of the shear-strength intervention technique may assume a vital role in guaranteeing that retrofitted structures respond to dynamic loading in a flexural-dominated behaviour, consistent with the redesign philosophy introduced previously. However, since the analytical work developed in this paper focuses solely on the flexural component of the seismic response of reinforced concrete walls, this selective intervention scheme is not studied in the following sections.

5. Finite Element Modelling

In Sec. 6 of this paper, an extensive analytical parametric study of the stiffness-, strength- and ductility-only intervention techniques is carried out so that a full understanding of such repair and retrofitting methods can be attained. The present section is concerned with developing analytical models which represent as


540 A. S, Elnashai 0 R. Pinho

Fig. 11. Experimental results of Saiama, 19921.

accurately as possible these

tested walls: (a) intact; (b) selectively repaired (Elnashai and

selective schemes. These are then verified by comparisons made with the test results and by conceptual undentandment of their behaviour .

5.1. Computer code

The study was- carried out using the finite element analysis program ADAPTIC [Izzuddin and Elnashai, 19891 developed at Imperial College. This program is capable of predicting the large displacement behaviour of plane and space kames under static or dynamic loading, taking &to account both geometric and material non- linear behaviour. Several concrete and steel material models are available, together


Repair and Rettofitting of RC Walls Using Selective Techniques 541

with a large library of 2D and 3D elements which can be used with a wide choice of typical predefined steel, concrete and composite section configurations.

For the purpose of this work, ten cubic plastic elements capable of modelling . distributed inelasticity are used to represent the test specimens. Each element has -

two Gaussian sections, subdivided into 150 fibres where strains and stresses are calculated. The concrete material represent ation is based on the uniaxial constant confinement model proposed by Mander et al. [1988]. However, the cyclic rules have

been improved to enable the prediction of continuing cyclic degradation of strength and stiffness, as well as better numerical stability under large displacement analysis [Martinez-Rueda and Elnashai, 19971. The behaviour of the reinforcement bars is represented using the mult i-surface plasticity model for steel, suggested by Pe- terson and Popov [1977]. This complex model is suitable for comparisons with experimental results since it has the ability to represent a yield plateau and non- linear strain hardening, as well as cyclic degradation. Experimental monotonic and cyclic steel tests results available in the literature are used for the calibration of its parameters [Martinez-Rueda, 19971. The external plates and re-bars are modelled using a bi-linear elastopIastic steel model with kinematic strain hardening since they are not expected to undergo significant inelastic load reversals.

The modelling of the stiffness-only intervention scheme is carried out using an eccentric steel section, whilst gap elements are utilised for the representation of the strength-only intervention. As for the case of ductility-only intervention, a physical representation of the intervention scheme is not sought. Instead, the effects of this selective met hod are introduced directly in -the concrete st ress-st rain relationship through the use of a confinement factor, described later.

5.2. Assessment of FE models and comparison to test results

As mentioned earlier, one of the main objectives of the proposed work is to provide the engineer with a set of re-design tools which will enable the fine-tuning of the member response characteristics in harmony with capacity and displacement-based design philosophies. Since the latter rely heavily on the quantification of three flexural design parameters, namely stiifness, strength and ductility, the development and study of selective intervention techniques focused on these three variables. Other important factors not normally quantified in design methods, such as bond slip, shear distort ion a t the plastic hinge region, inclined flexural-shear cracks and in- complete crack healing, which affect the energy dissipation capacity of reinforced concrete members are therefore not considered in the analysis.

Consequently, comparisons between analytical and experimental results can be carried out using the force vs. displacement hysteresis envelope of the flexural response of the wall. The latter is estimated by integration of the experimental rotation profile of the wall derived from vertical and horizontal displacement readings in trinsducers located at various levels along the wall height.


5.2.1. Intact wall

. Good agreement between the experimental and analytical results of the intact wall, used as the reference specimen for all the interventions, is fundamental to the success of this study. Focus can then be placed on the modelling of the selective techniques alone.

Displacement (mm)

Fig. 12. Force vs. flexural-displacement hysteresis envelope of intact wall.

In Fig. 12, the envelopes of the flexural cyclic response of the intact wall obtained in the experiment and using ADAPTIC, are shown. The results are in good, agreement thus leading to the conclusion that the FE modelling adopted accurately represents the flexural cyclic behaviour of the tested specimens (similar agreement was obtained for a number of wall analyses in this study, and for other structural members in previous studies [Elnashai and Elghazouli, 1993; Broderick and Elnashai, 19941).

The hardening effect obtained in the analysis at 12 mm (1% drift), which was not observed during the test, may be attributed to the model used for the steel bars, since this was not specifically calibrated to the steel employed in the experiments.

5.2.2. Stzfiess-only intervention

Experimental results of the stitfnessonly intervention cover solely repair applications, hence direct comparison with the analytical modelling is not possible since only upgrading schemes were modelled. Nevertheless, conceptual verification of the modelling adopted can still be carried out by comparison between the results of two monotonic analyses using one bare and one retrofitted wall (Fig. 13). A clear increase in stiffness can be observed whilst no change in strength occurs, confirming the experimental obsedions.


Repair and Retrofitting of RC Walls Using Selective Techniques 543

o ! : : : : : : : : i : : : : : : : : : : : : : : : : : : : : : : : : I 0 10 20 30 40 50 60 70 80

Displacement (mm)

Fig. 13. Force vs. displacement of stiffness-only intervention.

Furthermore, analyses carried out in the parametric study described in Sec. 6.1, undoubtedly demonstrate the effectiveness of the modelling adopted by providing results which can be physically interpreted and understood. It is therefore possible to conclude that the developed FE model accurately represents this selective scheme.

Comparison between the test results and the analytical modelling is possible for this intervention as shown in Fig. 14, where the hysteretic envelopes of the experimental and FE results are reproduced. The comparison between the two is excellent, validating the analytical model used for the strengt h-only intervention.

Further, to confirm the delay mechanism is working as intended, the displacements obtained in the IDM are studied in Fig. 15. It can be observed that the two mechanisms are working in opposite directions, as expected, and that the ex- tensions are never higher than the imposed limit (3 rnm, in this case). On the contrary, when subjected to compression, the IDM displacements do not have any limit, reflecting the intended characteristic of plate or bar buckling under compression.

It is also important to relate the previously described displacement behaviour of the delay mechanism with the axial force carried by the external steel plates. In Fig. 16, it is shown that the 'plates work only in tension and always in an alternate fashion, in harmony with the IDM displacement behaviour. Furthermore, comparison between Figs. 15 and 16 shows that the EUSP start carrying load only when the displacement in the delay mechanism has reached its tolerance gap. Therefore, the


-20 - I S - 10 -5 0 5 10 15 20 Displacement (mm)

Fig. 14. Force vs. flexural-dispIacement hysteresis envelope of wall retrofitted with EUSP.

0 2 4 6 8 10 12 14 16 18 20 22 24 No. of cycles

Fig. 15. Displacement in delay mechanisms.

proposed model appears to simulate this selective technique rather well, providing a useful tool for the upcoming parametric study.

5.2.4. Ductility-only intervention

Comparison between analytical and experimental results for the ductility-only intervention (Fig. 17) is not as close as for the previous cases. This can be explained by the aforementioned fact that the intervention scheme was not physically modelled in the computer code but instead is introduced by changes in the concrete stressstrain relationship, as described in subsequent sections.


Repair and Retrofitting of RC Walls Using Selective Techniques 545

10 12 No. of cycles

Fig. 16. Axial force in external steel plates.

-20 -15 -10 -5 0 5 10 15 20 Displacement (rnrn)

Fig. 17. Force vs. flexural-displacement hysteresis envelope of wall retrofitted with ECSP.

In Fig. 18, plots of force vs. displacement of a monotonically loaded wall with different intervention schemes are shown. The effects of the intervention on ductility are clear whilst no change in the initial wall stiffness is noticed, confirming the experimental observations;

Furthermore, in the extreme case of an increase in displacement ductility by a factor of about 10, only a 30% increase in the member strength is obsemed.


546 A. S. Elmshai 0 R. Pinho

0 10 20 30 40 50 60 70 80 90

Displacement (mm)

Fig. 18. Effect of ECSP configuration on ductility of upgraded wall.

6. Analytical Parametric Investigations and Design Expressions

In this section, the analytical models are verified and tested further. The design parameters affecting the response of selective techniques are assessed and the form of useful design expressions appraised. Extensive parametric analyses are undertaken for the three repairlretrofitting tools of stiffness-, strength- and ductility-only interventions, leading to the development of design guidelines and expressions.

To evaluate the three fundamental design response parameters being studied, the simplistic approach described in Fig. 19 [Paulay and Priestley, 19921 is followed. This elasto-plastic bilinear approximation for the force-displacement monotonic response of a reinforced concrete member has its principal applicability at design

Observed response

Idealised response

Fig. 19. Typical load-displacement relationship for a reinforced concrete element (Paulay and PriestIey, 19921.



level, where knowledge of the real non-linear behaviour of the member is not generally pursued. It is therefore most suitable to the objectives of the present work which, as mentioned earlier, focus on the development of practical analytical tools for redesign of RC structures.

The slope of the idealised linear elastic response, K = S,/ A,, is used to quantify stiffness. It should be based on the effective secant stiffness to the real load- displacement curve at a load of about 0.75Sy. An acceptable approximation is to calculate this point based on the first yield of reinforcement [Paulay and Priestley, 19921. The yield value of the equivalent elasto-plastic response, i.e. the ideal or '

yield strength of the member, can thus be estimated as being S, = 1.33s;. Finally, a convenient quantity to evaluate the member ductility capacity is the ultimate displacement ductility, defined as pa = A,/A,. In the following sections, these definitions are used to calcuiate the design response parameters of the walls.

6.1. Stiffness-only intervention

The variable FK, defined as the ratio between the upgraded/repaired and orig- inalldamaged stiffnesses of the member, is used to quantify the outcome of the intervention:

The parameters needed to fully describe such a scheme are the height of the steel plates (h , ) , their thickness ( t p ) , width ( I p ) and distance to the geometric centre of the wall cross-section (e,), as depicted in Fig. 20.

Fig. 20. PIate position and section dimensions for stiffness-only intervention.

6.1.1. Height of the plate

If an efficient stiffness-only intervention is sought, the height of the plate should always be greater than, or equal to, the expected flexural plastic hinge length. This will guarantee that the area where severe cracking of the concrete occurs is covered by the steel plates.


Fig. 21. (a) Curvature at maximum response; (b) Stiffness improvement vs. height of steel plates.

In Fig. 21(a) the curvature distribution at maximum response of a RC flexural wall is illustrated and inelasticity is observed up to a height of about 40% of the full height of the wall (h,). A stiffness improvement vs. height of steel plates plot resulting from the analysis of the same wall with different st iffness-only configurations is shown in Fig. 21(b). It is possible to observe that increasing the height of the plates to values close to 0.5h, has an important effect on the success of the intervention. However, from this point onwards, the effect of this parameter diminishes, as expected.

In the parametric study that follows, where design expressions and curves are derived, the plates are always considered to be spanning the whole height of the wall. This seemed to be the most logical approach since, as shown in Fig. 21(b), it will enable maximum efficiency. Nevertheless, if a different solution is sought, the latter figure can be consulted for guidance.

6.1.2. Plate position and section dimensions

In Fig. 22, the influence that thickness, width and position of the steel plates have on the outcome of this selective scheme is analysed. It can be observed that increasing the dimensions of thesteel plates and their distance to the symmetry axis of the wall will enhance the effect of the intervention. This is expected since larger plates and eccentricity will increase the moment of inertia of the section and the effectiveness of crack arrest. However, the significance of such effect varies considerably with the d u e s of these geometric parameters.

When steel plates are located close to the geometric centre of the section (e, + 0) , the significance of their dimensions relative to this distance is great. Thus, wider plates will induce a higher stifhess improvement since they will cause an important geometric eccentricity effect. As the plates are placed further away from the wall symmetry axis, the narrower plates (1, -t 0) will be more beneficial since it will be possible to achieve larger eccentricities. Hence, sharpest increases in the value


Repair and Reh.oFtting of RC Walk Using Selective Techniques 549

tp=6.0 rnrn

6=1.8 mrn

tp=0.3 mm

=P

Fig. 22. ~nfluence of plate dimensions and position in the wall.

of FK are obtained in the range of smaller values of 1,. Such effect can be clearly observed in 'Fig. 22, particularly for the surface corresponding to t , = 6.0 mm.

Moreover, because flexure cracking is concentrated at the wall edges, having a thicker but narrower plate shifted to the sides will be a more efficient way of gaining stiffness than using a wider but slimmer plate. Nevertheless, care should always be taken to ensure that the plates possess a contact surface with the wall sufficiently wide to avoid problems of lack of bonding.

In the following parametric study, two different approaches are adopted for the development of analytical tools for this intervention. The first approach aims at the development of a single design expression, derived by regression analysis, which returns the value of FK. This methodology is, however, too simplistic given the complex influence of the plates geometric characteristics on the outcome of the intervention. Therefore, alternatively, design curves which consider the influence of each variable separately, are also developed. These give the designer better insight and control on the effects of the intervention. Nevertheless, the simplicity of the first method perhaps renders it more appropriate for design situations.

6.1.3. Single-panzmeter approach

A non-dimensional parameter SK, capable of unambiguous characterisation of this intervention is created. This includes both the wall and plates properties that are most likely to influence the intervention result, and is defined by

- - - . . . - -- -A; ep - 4%,lp - t d p e p SK = constant x - x - = 100 x - x 2 = 400- ,

Aw lw bwlw lw bwL2 (6.2)

where A, and A, represent the total cross-section area of the plates and wall, respectively.


Fig. 23. Polynomial fit to stiffness-only results.

A large number of analyses were carried out, varying the thickness, width and position of the plates. The values of FK are plotted against the corresponciing SK in Fig. 23, where it is shown that a bi-linear polynomial fit to the data provides excellent results with considerably high global correlation factors (R2).

It was also verified that an accurate representation of the role played by the existence of different levels of longitudinal reinforcement or the presence of axial load would require these variables to be included in the design expression. Hence, further studies were carried out to include two additional parameters - reinforcement ratio (p,) and normalised axial force ( v ) . The former is defined by Eq. (6.3), where A, represents the total area of longitudinal reinforcement in the wall, and was considered in the range of 0.4 5 p, 5 (4%), as is generally adopted in design applications. The variable v is defined by Eq. (6.4), where N stands for axial force and f: is the concrete compressive strength. For the purpose of this study, the value of v was wried in the range of 0 5 v 5 0.10, as it is commonly observed in practice.

The final design expressions for this intervention can, therefore, be expressed as follows:


Repair and Retrofitting of RC WdLP Using Selective Techniques 551

The procedure followed to define the expressions shown above, with the inclusion of axial force and reinforcement ratio effects, involved extensive parametric studies and regression analysis, similarly to that outlined above for parameter SK. However, for the sake of brevity, details of these have been omitted and can be found elsewhere [Pinho, 19991 together with a more in-depth discussion of the effects that these parameters have on the outcome of the intervention.

6.1.4. Multi-parameter approach

Here, three non-dimensional parameters are derived to allow for the elaboration of the design curves shown in Figs. 24 to 28, which represent the effects of the plate posit ion and section dimensions on the outcome of the selective intervent ion. Parameters a and p relate to the plate thickness and width, respectively, and are defined by Eqs. (6.6) and (6.7), whilst parameter 7, defined by Eq. (6.8), accounts for the influence of the plate position in the wall.

Fig, 24. Proposed design curves for 7 = 0.


552 A, S. Elnashai & R. Pinho

B

Fig. 25. Proposed design curves for y = 0.25.


By definition, parameters /3 and 7 have an upper bound value of unity, whilst in the case of a an upper Limit value of 0.1 was assumed. The design curves shown in Figs. 24 through to 28 give the possibility of individual manipulation of each parameter in order to obtain a target FK.

As explained in Sec. 6.1.2, the Merences in the shape of c w e s corresponding to Merent categories of 7, reflect the important effect the position of the plates has on stifmess enhancement. It is clear that with a higher eccentricity, the optimum


Repair and RetroJitttng of RC Wdls Using Selective Techniques 553

y = 0.75


Fig. 28. Proposed design curves for 7 = 1.

level of a plate with a particular thickness is reached for smaller values of width (Fig. 28). This confirms the statement made previously, where it is proposed that maximum of stiffness-only intervention effect can be achieved by using relatively narrow plates located as close as possible to the wall extremities. Further, for values of 7 = 1, Fig. 28 seems to suggest that ideal solutions should be obtained for b p I L / 4 (0 10.5).


The influence of longitudinal reinforcement and axial load is included by apply- ing additional calibration factors to the value of FK obtained from the curves, as follows:

Both the design curves and expressions derived by regression analysis revealed a maximum coefficient of variation of 15% when compared with a wide range of results obtained by finite element analyses on a large variety of walls. These results confirm that the parameters defined to characterise the selective intervention and the derived design expressions (or curves) appropriately account for all the variables that most influence the effectiveness of this repair scheme.

6.2. Strength-only intervention

The variable Fs, defined as the ratio between the upgraded and original strength of the member, is used to quantify the outcome of the intervention:

In Fig. 29, a description of the relevant characteristics of this repair method is given. These are the distance of the external steel plates or re-bars to the edge of the wall (d,), and their cross-sectional area (A,) and yield strength (f:).

A,, f,!

/-

Fig. 29. Strength-only intervention parameters.


Repair and Retn$tting of RC Walls Using Selective Techniques 555

0 10 20 30 40 50 60 70 80

Displacement (rnm)

Fig. 30. Influence of ~ I D M on the response of the strengthened wall.

6.2.1. Interaction delay mechanism

The most critical parameter in this intervention is the value of the design gap (gIDM) adopted in the delay mechanism. This value should he such that the strength-only intervention does not begin interacting with the structure too early, thus affecting the member stiffness, or too late, by which time significant damage may already have occurred (Fig. 30). Moreover, when the mechanism starts contributing to the flexural resistance at a late stage, two levels of ductility are created, which would be a difficult situation to address in the light of current definitions of ductility.

If an idealised bi-linear load-displacement relationship, as suggested in Fig. 19, is considered, then a simple way of evaluating the design gap for the IDM can be derived. This should be designed to allow the mechanism to contribute to the flexural resistance a t a point somewhere in between the first yield strength (Sb) and the global yield strength (S,) of the wall. In this manner, the original stiffness will be maintained and the dynamic characteristics of the member will remain unaltered.

An estimate of the vertical displacement in the edges of the wall for these two loading stages is required for the determination of the design gap. This may be achieved by calculating the rotation (9) and the neutral axis depth (c) a t the top of the wall. If these values are known, then the vertical displacement in the external plates or re-bars (A;) is given by:

Rom section analysis, the value of curvature at the point of first yield. (4;) and the corresponding neutral axis depth (c&) can be easily determined at the foundation level. At this loading stage, it is also possible to assume the latter as constant throughout the height of the wall, whilst the c u p t u r e varies linearly. Finally, taking into consideration the relationship between S, and Sb, suggested


556 A. s.' Elnashai l3 R. Pinho

earlier, a lower and upper bound limit for the design gap of the delay mechanism is defined by:

Alternatively, simplified methods of seismic design in which a behaviour factor is used to obtain the design load, i.e. the ideal or global yield strength of a reinforced concrete member (SY), can also be used . - to obtain the upper bound limit for the IDM gap value. In this way, the design of the strength-only rnecha&sm would be. consistent with the wall original design philosophy. By characterising the curvature at the base of the wall as

where F, represents the elastic horizontal load, q stands for behaviour factor and I, is the equivalent moment of inertia of the cross-section at first yield in the extreme fibre, and substituting (6.13) in (6.12), the following alternative expression can be used to define the value of ~ I D M :

It is, nevertheless, important to notice that these expressions are derived from principles which apply to monotonic loading only. Under cyclic regimes, cumulative plastic deformations, mainly associated with cracks that remain open after load reversal, will raise uncertainties regarding the vertical elongation of the wall. These factors cannot be addressed by the expressions suggested above. Further, because these expressions are derived assuming linear curvature distribution at point of first yield, their application in design situations where such an assumption is not valid (for instance, high axial load), will produce slightly inaccurate results. Still, they do provide a first insight into the control of this intervention parameter, and should be used a t design level provided there is awareness of its limitations.

6.2.2. Distance to the wall

The external steel plates or re-bars contribute to the flexural strength at the location . of their longitudinal axes. A force criterion can thus be used to define the input

of strength introduced by the intervention. However, the distance to the wall of the external strengthening mechanism should also be considered when designing these intervention schemes. The use of large re-bars very close to the wall will induce a significant decrease in the ductility of the wall since the gain in extension deformation capacity caused by the intervention is not balanced on the compressive side. Hence, the concrete will be subjected to much higher compressive strains and eventually the wall will fail earlier due to concrete crushing. On the contrary, if


Repair and RetroJitting of RC Walk Using Selective Techniques 557

0 10 20 30 40 SO 60 70 80 Displacement (rnrn)

Fig. 31. Influence of d p on the response of the strengthened wall.

smaller external plates or re-bars are placed at greater distances from the wall, the same strength can be obtained with a smaller ductility decrease.

In Fig. 31, the plots of analyses carried out for two identical walls with different configuiations of strength-only intervent ions are shown. Although both walls ex- hibit identical strength enhancement, their ductility is completely different. The use of larger distances between the external mechanism and the wall proves extremely efficient in avoiding high levels of ductility degradation. Hence, such configuration should be applied in the upgrading of walls in which the available ductility does not comply with the demands arising from a 'short-dist ance' st rengt h-only intervention. Moreover, its applicability is still feasible, particularly if there are infill panels by the sides of the wall, since the external mechanism can be located a t a greater distance embedded in the infill panel without adverse architectural effects.

6.2.3. Design ezpressions

Similarly to the study in Sec. 6.1.3, the adoption of a single parameter which enables a clear representation of all the important factors influencing the effectiveness of this scheme is sought. In this case, both the wall and external plates material properties are of importance, and were included in the strengt h-only selective intervention parameter Ss:

A p e dp + L / 2 S, = constant x - x

AP f y P dp + l u / 2 = lo---- (6.15) A3 fi, 1, A s f, 4"

where f, represents the yield strength of the longitudinal reinforcement of the wall.


558 A. S. Elnashai & R. Pinho

Fig. 32. Polynomial fit to strengt h-only results.

In Fig. 32, the polynomial fit to the results of the parametric investigations without axial load is shown. A global correlation factor of 0.97 indicates the adequacy of the linear regression used.

The final design expression, which includes the variables discussed above together with the existent level of axial load, becomes

The results obtained by Eq. (6.16) compare extremely well with the values given by finite element analysis of several different RC walls, revealing a maximum coeE ficient of variation of 4%. Hence, it is concluded that all the wall properties and retrofitting scheme characteristics, which are most relevant for the outcome of the intervention, are considered in the proposed methodology.

6.3. Ductility-ody intervention

It wodd not be feasible to address this intervention scheme in a similar manner to the procedure adopted for the two previous cases. Relating the physical char- acterist ics of t his intenrent ion to the global ductility increase is neither practical nor effective. The uncertainties in the definition of yield and failure criteria would not allow the development of a simple and accurate methodology. Instead, an approach similar to that widely used in the design of reinforced concrete members confined with internal steel hoops is followed. In this procedure, the concrete stress- strain relationship is changed by the application of a confinement factor dependent on the configuration of the stirrups and dimensions of the section. Accordingly, the ductility-only selective intervention parameter (kD), described by Eq. (6.17),


Repair and Retrofitting of RC Wails Using Selective Techniques 559

is defined as the ratio between the externally confined and unconfined concrete compressive strength, . f:, and f: , respectively.

6.3.1. Design eqression

This intervention technique requires the definition of three main geometric variables, namely the thickness of the plates ( t , ) , their height (h,) and spacing (s,), together with the bolt prestress force (Pb) , as shown in Fig. 33.

Effectively confined core

\

Fig. 33. Ductility-only intervention parameters.

A simplified methodology to evaluate ko based on the approach proposed by Mander et al. [1988] is followed. Although the latter was initially developed to be used with circular or rectangular internal steel hoops, an adaptation to the duct ility-only technique is undertaken below.

The discontinuities between plates and, more importantly, those caused by the presence of a bolt as the fourth closing side of the external confinement system, were studied through the use of formulations for soil and rock mechanics [Poulos and Davis, 19741. The analysis of the path of the compression confinement stresses between plates and bolts leads to the conclusion that an arching effect similar to that suggested by Mander et al. [I9881 can be used to delimit the effectively confined concrete core in this intervention. Hence, the following assumptions are made:

(i) the U-shape steel plates are stiff enough to avoid being pushed outwards due to lateral confinement pressure, therefore reduction in plan of the effectively confined concrete core due to arching occurs only in the vicinity of the closing bolt (see Fig. 33);


560 A.

(ii)

(iii)

6.1

in elevation, reduction of effectively confined concrete core occurs due to arching effects between consecutive external plates and bolts, as shown in Fig. 34; the arching effects are modelled as second-degree parabolas with an initial tangent slope of 45'; the prestressed bolt is capable of fully transmitting the lateral confining pressure to the steel plates, thus representing adequately a closed hoop behaviour of the whole assembly, albeit locally.

- - -

Effective1 y confined core

Front elevation Side elevation

Fig. 34. Effectively and ineffectively confined core.

Consequently, the effectively confined concrete core area (A,) at the most un- favourable location (midway through two consecutive plates) is given by

and the confinement effectiveness coefficient becomes

with pcc representing the ratio of longitudinal reinforcement to the confined concrete core area (Acc).

The prestressed bolt is designed to work as the fourth side of the external hoop, capable of transmitting the lateral stresses to the steel plates. To guarantee equilibrium of confining stresses, the bolt should be designed so as to assure that its axial capacity equals that of the opposite plate. This may involve the use of a prestress force such that

f i ~ p = fyb%+%, (6.20)



where Ab and A, represent the cross-section area of the bolt and steel plate, respectively, whilst their yield strength values are introduced in the expression by f,b and f; ..

Since k, takes into account all the discontinuities present in this scheme, and the bolt is designed to ensure a closed hoop behaviour of the whole assembly, the effective section area ratios of transverse reinforcement (p, and p,) 'can be defined

by

By virtue of force equilibrium between the lateral confinement stress resultants and the tension forces in are determined by

the plates, the effective lateral confining stresses (fl, and fl,)

Finally, by using the general solution curves described in the work of Mander et al. [1988], the ductility-only selective intervention parameter kD can be determined, and the stress-strain relationship of the concrete adjusted to incorporate the effect of the intervention.

As mentioned earlier, this approach is equivalent to methods currently used in the design of reinforced concrete members confined with internal steel hoops. Hence, its application in design situations is equally practical and straightforward.

6.3.2. Thickness, height and spacing of the steel plates

In this section, the influence of the thickness, height and spacing of the external confinement steel plates on the outcome of this repair scheme is studied. The selective intervention parameter kD is used to quantify the result of the intervention.

In Fig. 35, it is observed that the smaller the spacing, the higher the confinement level achieved by the intervention. Nonetheless, in order to avoid changes in stiffness, a sensible spacing should always be left between plates to minirnise crack arrest.

Together with the decrease in spacing of the plates, an increase in the effect of this selective scheme can also be obtained by means of greater height or thickness of the plates. However, fesults from analyses on retrofitted walls in which these two parameters are varied, lead to the conclusion that the most effective way of gaining ductility with this type of external intervention is by increasing the height of the plates, not their thickness. In Fig. 36, it is shown that if, for instance, a target confinement ratio is set as kD = 1.9, then using thicknesses of 10, 5 and 3 mm, will result in heights of 38, 55 and 69 mrn, leading to a steel plate section area of


Fig. 35. Influence of sp in the ductility-only intervention parameter.

Fig. 36. Effect t, and hp in the ductility-only intervention parameter.

380, 275 and 207 mm2, respectively. Therefore, using high plates closely spaced is the most efficient way of achieving a confinement factor that will satisfy a target ductility.

7. Closing Remarks

The effects on structures of currently used methods of repair and retrofitting reinforced concrete members are generally not easy to quantlfy or control and their influence on the global behaviour of RC structures may not optimise the overall seismic response. New earthquake-resistant design trends require that the global response and failure mode are fully controlled, an objective not readily achieved



by the majority of available structural intervention techniques. In order to at- tain such an aim, selective methods of repair and retrofitting, capable of individ- ually affecting a single design response parameter, need to be developed. Practi- cal schemes were presented and described in this paper, toget her with test results from an experimental programme by which their feasibility and effectiveness were confirmed.

Full control over such techniques prior to their application can be accomplished with the definition of simple design expressions. The selective schemes, tested previously a t Imperial College, were modelled using the finite element package ADAP- TIC. The ingredients of the models were verified as well as their collective response through comparison with experiments and conceptual understanding of their physical characteristics. Extensive parametric studies were carried out, enabling a deeper understanding of such novel repair or retrofitting techniques and the development of useful design expressions. Further, design guidelines for practical application in the seismic re-design of structures were given in the body of the study, the most important of which are summarised below:

1. Stiffness-only intervention: best results are obtained by using narrow plates (1, < 1,/4) placed as near the edges as possible, in order to improve geometric eccentricity effects and to maximise flexural crack arrest. Although stiffness improvement is at its highest when the steel plates span the whole height of the wall, a successful intervention can still be achieved by providing plates spanning the anticipated zone of inelasticity.

2. Strength-only intervention: best results are achieved by using a longer lever arm and smaller plates or yield strength. In this way, reduction of ductility of the wall is rninimised. The design gap should have a value corresponding to vertical elongation of the wall at the point of yield, to ensure that stiffness is not altered.

3. Ductility-only inte~ention: best resuits are achieved if spacing between the steel plates is minimised and the height of these is maximised. However, to assure that minimum effect on the member stiffness is induced, a sensible gap between consecutive U-shaped plates should always be kept.

Further tests are planned for the immediate future under the auspices of the Europear. network ICONS (Innovative Concepts for Seismic Design of New and Ex- isting Structures) and supported by ECOEST 11 (European Consortium of Earth- quake Shaking Tables). These will focus on testing the design expressions under simulated earthquake action and assessing the efficiency of mixed intervention types under both repair and retrofitting design scenarios. Moreover, in the strengt h-only scheme, an interaction device such as a spring mechanism will be developed in order to reduce the abrupt stress increase caused by earthquake loading in the delay mechanism.


564 A. S. Elnashai 0 R. Pinho

Acknowledgements

The experimental work was carried out by Dr. A. I. Salarna, as part of his doc- toral thesis at Imperial College. The tests were funded by the UK Science and Engineering Research Council. The current work is supported financially by the European Community through the research network ICONS (Innovative Concepts for Seismic Design of New and Existing Structures) and by the Calouste Gulbenkian Foundation.

Appendix

Examples of application of the design ezpressions

For the purpose of this example, let us consider a 200 x 1500 x 3000 rnm wall. The concrete compressive strength is fi = 30 MPa and the yield stress of the steel re-bars is f, = 400 MPa. The longitudinal reinforcement in the boundary elements is made of six 12 mm bars, whilst in the web 10 mm bars spaced at 200 rnm are used as vertical reinforcement (four bars at each face). Confinement reinforcement is not available.

b, = 200 mm; I , = 1500 mm; h, = 3000 mm;

f: = 30 MPa; f, = 400 MPa

Stimess-only intervention

The objective of the intervention is to increase by 50% the stiffness of the wall using 4-mm thick steel plates. It is assumed that due to architectural constraints the external plates can o d y be applied at a distance of 100 mm from the wall edges. An axial load of 200 kN is also considered.

v = 200 x 103

= 0.022; FK = 1.5; t p = 4 mm; 200 x 1500 x 30 . .

I , =?; e, =? (free edge 3 100 mm)

The value of the selective intervention parameter SK is determined using Eq. (6.5a):

Expressing e, as a function of lp (see Fig. 20)

e, = 1500/2 - l p / 2 - 100 = 650 - 1,/2


Repair and Retmjitting of RC Walls Using Selective Techniques 565

and using Eq. (6.2), the value of tp can be determined:

Hence, the solution is to use 100 x 4 mm plates at a distance of 600 rnm from the centre of the wall.

Strength-only intervention

The objective of the intervention is to achieve an increase of 30% in the flexural capacity of the wall by means of external re-bars with yield strength of 500 MPa. A maximum distance of 300 mm is allowed between the re-bars and the wall sides. It is also assumed that the wall had been designed for an elastic load of 350 kN and a behaviour factor of 2.

F, = 350 kN (q = 2); Ec = 4 . 7 m .;: 26 GPa; Fs = 1.3;

f,P = 500 MPa; d, = 300 mm; A, =?; gID, =?

The value of the selective intervention parameter Ss is determined from Eq. (6.16),

Using Eq. (6.15), the area of the plates to be used is obtained:

Assuming the following values computed from sect ion analysis

#; = 1.6 x mm-'; cb = cd = 240 mm; 1. = 9.46 x lo9 mm4

and using Eq. (6.14), lower and upper bounds for the IDM gap design value are

Hence, the selective intervention would consist on using four 10 mm reinforcement bars placed a t a distance of 300 rnm from the wall edges, with a delay mechanism allowing for a design vertical tolerance of about 5 mm.


566 A. S: Elnashai 0 R. Pinho

Ductility-only intervention

The objective of the intervention is to achieve a ratio of five between the ultimate and peak confined concrete strain, by means of external U-shaped plates with yield strength of 275 MPa. These are 4 mm thick and spaced by 20 mm to avoid crack arrest. The wall boundary elements are 250 mm wide and 200 rnm deep.

6 x n x 1 2 ~ 1 4 I Pcc = = 0.014; E ~ ~ / E ~ ~ = 5; t p = 4 mrn; S, = 20 mm; h, =?

250 x 200

An initial value of 100 mm is arbitrated for the plates height in order to initiate the trial procedure. The spacing between plates s, thus becomes equal to 120 mm (see Fig. 34). By substituting in Eq. (6.19) the confinement effectiveness coefficient is evaluated:

Using the general solution curves described in the work of Mander et al. (19881, the ductility-only selective intervention parameter kR can be determined:

2 x 100 x 4 275 I' = 0.72 x 0.033 x - = 0.22 200 x 120 30 blander s t al. [1988] 2 x 100 x 4

, k D " 2 = 0.027 275

'250 x 120 - = 0.72 x 0.027 x - 3 0

= 0.18

The peak and ultimate confined concrete compression strains are estimated by the following expressions [Paulay and Priestley, 19921 :

E~~ = 0.002[1+ 5(ko - l)] = 0.002[1 + 5(2 - l)] = 0.012

Thus, the ratio between peak and ultimate compressive strain becomes equal to 0.062/0.012 = 5.2, which satisfies the proposed target. The closing bolts are designed to satisfy Eq. (6.20):

assuming fi = 275 MPa and f i = 0 275 x 100 x 4 = f,b7r#i/4+ P6 > &, = 40 mm

Hence, the retrofitting solution consists of utilising U-shaped steel plates with a thickness of 4 mm, and a height of 100 mm, together with 40 mm bolts.

References

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Repair and RetrojWng of RC Walls Using Selective Techniques 567

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Ghobarah, A., Ashraf Biddah and Mahgoub, M. 119971 "Rehabilitation of reinforced con- cret e columns using corrugated steel jacketing," J. Earthq. Engrg. 1(4), 65 1-673.

Izzuddin, B. A. and Elnashai, A. S. [1989] 'LADAPTIC, a program for adaptive large displacement elastoplastic dynamic analysis of steel, concrete and composite frames," Research Report ESEE-89/7, Engineering Seismology and Earthquake Engineering Sec- tion, Imperial College, London.

Kowalsky, M. J., Priestley, M. J. N. and MacRae, G. A. (19951 "Displacement-based design of RC bridge columns in seismic regions," Eorthq. Engrg. struct. Dyn. 24(12), 1623-1643.

Mander, J. B., Priestley, M. J. N. and Park, R. [I9881 "Theoretical stress-strain model for confined concrete," J. Stmct. Engrg., ASCE 114(8), 1804-1826.

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Martinez-Rueda, 3. E. [1997] "Energy dissipation devices for seismic upgrading of RC structures," Ph.D. Thesis, Imperial College, University of London, London.

Moehle, J. P. [I9921 "Displacement-based design of RC structures subjected to earthquakes," Earthquake spectm 8(3), 403-428.

Paulay, T. and Priestley, M. J. N. [1992] Seismic Design of Reinforred Concrete and Ma- sonry Buildings (John Wiley & Sons, Inc., New York).

Petersson, H. and Popov, E. P. [1977] "Constitutive relations for generalised loadings," J. Engrg. Mech. Div., ASCE 103(4), 611-627.

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POU~OS, H. J. and Davis, E. H . (19741 E l ~ t z c Solutions for Soil and Rock Mechanics (John Wiley & Sons, Inc., New York).


568 A. S. Elnashai & R. Pinho

Priestley, M. J. N., Seible F. and Calvi, G. M . (19961 Seismic Design and Retmfit o j Bridges (John Wiley & Sons, Inc., New York).

P WRI (19861 Public Works Research Institute, Manual for Repair Me tho& of Civil Engi- neering Structures Damaged by Earthquakes, Ministry of Construction, Japan.

Saadatmanesh, H., ELani, M. R. and Jin, L. [I9971 cLSeismic retrofitting of rectangular bridge columns with composite straps," Earthquake Specha 13(2), 281-304.

Xian, D. [I9921 "Inelastic response and effective design of asymmetric buildings under strong earthquake loading," Ph.D. Thesis, University College, University of London, London.

U JCEERP (198 11 US/ Japan Cooperative Earthquake Engineering Research Program, Pmc. Second Seminar on Repair and RetroJit of Structures, Tsukuba, Japan.


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