Seismic safety evaluation methodology for masonry building and retrofitting using splint and bandage technique with wire mesh

Abstract

The paper presents a seismic safety assessment of unreinforced masonry (URM) building using two approaches. The first approach uses the ‘Pier Analysis’ method, based on the concept of equivalent lateral stiffness, where in-plane and out-of-plane actions are considered independently. The second approach is developed with the program SAP2000, where the linear response is evaluated using continuum ‘finite element modelling’ (FEM). Both methods are compared to evaluate the safety of wall piers and the differences in the outcomes under combined gravitational and lateral seismic forces. The analysis results showed that few wall elements are unsafe in in-plane and out-of-plane tension. It is also observed that the pier analysis method is conservative compared to FEM, but can be used as a simplified and quick tool in design offices for safety assessment, with reasonable accuracy. To safeguard the URM wall piers under lateral loads, a retrofitting technique is adopted by providing vertical and horizontal belts called splints and bandages, respectively, using welded wire mesh (WWM) reinforcement. The study using the ‘Pier Analysis’ shows that the lateral load capacity of unsafe URM piers can be enhanced up to 3.67 times and made safe using the applied retrofitting technique. Further, the retrofitting design methodology and recommendations for application procedures to on-site URM buildings are discussed in detail.

Graphical abstract

Keywords

unreinforced masonry / seismic in-plane and out-of-plane forces / pier analysis / finite element modelling / splint and bandage technique with wire mesh

1 Introduction

Unreinforced masonry (URM) has been the most extensively used building construction technique [1–4]. Even today, in the form of residential, institutional, commercial, and public buildings (including historical monuments), URM provides a large proportion of construction all over the globe, despite the widespread use of modern manufactured materials like concrete and steel [5]. As per 2011 census data on housing, from The Government of India, about 85% of the existing building stock present in India contributed to masonry structures (nearly 47% of masonry walls were constructed using burnt bricks, 14% were made with stones, and the remaining 24% were made of mud and unburnt bricks) [6]. Thus, over half of India’s population still lives in URM houses. For masonry construction in India, materials like clay, adobe, stone, and concrete are most commonly used to manufacture bricks or blocks [7]. URM is popular owing to its advantages such as simplicity in construction, easiness of future alterations, usability of local materials, thermal comfort, low skill level, and relatively lower labour cost, etc. Despite these advantages and being strong in compression, masonry has a low flexural (tensile) strength, making the URM building vulnerable to sudden and fragile failure when subjected to certain modes of lateral forces due to earthquake. The earthquake resistance of existing masonry construction in India is notoriously very poor and construction is regarded as non-engineered [6]. The existing housing stock of residential buildings in India constructed out of masonry with almost no earthquake-resistant features is a worrying situation.

When subjected to earthquake ground motion, seismic forces are directly proportional to the building element masses, and induced accelerations cause vibration of the structure. As a result of vibration, internal stresses in the form of bending and shear develop, which often exceed the material strength and cause damage to the load-bearing elements. Masonry, which is not a suitable material for withstanding bending and shear stresses suffers severe damage which often results in the collapse of the building [8–10]. Past earthquakes have revealed the devastating and grim reality of the seismic performance of URM buildings [11–14]. Tab.1 presents a list of the most devastating earthquakes in India and the neighbouring countries in the past century, which have resulted in the loss of thousands of lives, considerable damage to infrastructure, and displacement of millions of people for an extended period. For example, 1) The 2015 Nepal earthquake, which affected both Nepal and neighbouring states in India, caused more than 8900 deaths, injured about 21950, and triggered the widespread destruction of structures [15]; 2) The 2001 Gujrat (Bhuj) earthquake killed about 20000 people, injured about 166800 people, and destroyed about 400000 homes [16,17]; and 3) In the 2005 Kashmir earthquake, 87350 fatalities were recorded, and about 75200 people were injured [18,19]. In most earthquake events, failure and collapse of the URM buildings are observed due to excess tension under in-plane shear, lack of anchorage, and also due to out-of-plane flexural tension [20–24]. The details of these failure modes are explained in detail in the next section.

1.1 Failure modes of unreinforced masonry buildings

Bruneau [25] classified the URM failures as: 1) in-plane failures; 2) out-of-plane failures; and 3) lack of anchorage & diaphragm failures.

1.1.1 In-plane failure of walls

In-plane actions are considered, when the lateral forces acting on the URM walls are parallel to plane of the wall (Fig.1(a)). The URM walls have sufficient strength under in-plane forces due to considerable depth in their plane of bending. However, the wall openings are the weak points, initiating failure in the form of diagonal X-shaped cracks (Fig.1(a)) originating from the corners of the openings; such cracks reduce the effective cross-sectional area of wall resisting the seismic forces [26]. Further, the integral box action is also hampered by weakening of the joints, as the openings are very near to corners. The wall piers between openings undergo higher stresses than the top and bottom portions of the wall openings. The development of shear or flexural stresses beyond the ultimate limit can cause in-plane failures based on the height-to-length ratio (also called aspect ratio) of the wall, wall thickness, compressive strength of masonry, and axial stress [3,27–29]. As observed by several authors [1,29–32], the height-to-length ratio has a significant impact on the failure mode of the walls. A low height-to-length ratio generates in-plane shear failure, whereas high values lead to in-plane bending of a wall. Based on the combined effect of aspect ratio and the axial stress, the in-plane failures are classified as rocking (which governs the response at the low level of axial stress and high aspect ratio), toe crushing (common at a high level of axial stress and high aspect ratio), bed-joint sliding (which occurs at a low level of axial stress and low aspect ratio), and diagonal tension (which corresponds to a high level of axial stress and low aspect ratio) [33–37].

1.1.2 Out-of-plane failure of walls

Out-of-plane failure of walls is considered as the most recurring seismic damage to masonry buildings [38–42]. This is because the seismic resistance of the wall, by virtue of its weight and the tensile strength of masonry, is very small. When the lateral forces are acting perpendicularly to the plane of the wall, it experiences flexural deformation (Fig.1(a)). Due to out-of-plane forces in walls, cracks first appear at the corners and junctions of walls (Fig.1(b)), and the support from orthogonal walls is lost [38]. This results in the walls transferring the seismic force primarily by spanning vertically between the floors. These walls need support from the roof/floor, and that is the reason why even thick walls are prone to failure during seismic events. The out-of-plane failure is commonly observed when the URM building is constructed with a flexible diaphragm [43–47]. Aspect ratio (H/L) and the boundary conditions are the other important factors that govern the cracking patterns (refer to Fig.2 and Tab.2) of the masonry walls subjected to out-of-plane forces [48]. Generally, URM wall cracks in out-of-plane, at a low acceleration level, due to excess of bending stresses caused by seismic forces [49–51]. In successive cycles of earthquake loading, the cracked wall’s stiffness decreases and result in out-of-plane failure [52,53]. Out-of-plane damage not only causes collapse on its own but also has a strong negative impact on the behavior of a wall under in-plane loads. These damages impair the in-plane capacity of the walls and can dramatically trigger collapse under static loads.

1.1.3 Failures due to lack of anchorage and diaphragm service

It has been observed from the past earthquakes (Tab.1) that the integral box action is essential to ensure the safety of masonry buildings against lateral loading, for which integrity of cross-walls and presence of rigid floor/roof diaphragm capable of transferring the seismic forces developed in out-of-plane walls to the in-plane walls are indispensable [6]. Seismic lateral forces that originate in all the components of a structure are transferred to rigid diaphragms through connections. The diaphragms then distribute the seismic forces to different elements of the structure based on relative stiffness. Therefore, the in-plane rigidity of the floors/roof acting as horizontal diaphragms is crucial. The in-plane stiffness of masonry walls being much higher than the out-of-plane stiffness, the walls resist lateral loads primarily through in-plane action. The out-of-plane seismic forces developing in the walls are transmitted to the diaphragms above and below and then to the in-plane walls. Therefore, adequate anchorage between the diaphragm and the vertical elements is essential for the satisfactory transfer of seismic forces [43,54–56]. The roofs and floors, if they are stiff, flat, and attached to the masonry using good quality mortar, have a beneficial impact on the performance of masonry buildings during earthquakes.

In contrast, buildings having flexible diaphragms (e.g., sloping roof, floor with tiles on the joist, a flat roof without proper anchorage or bearing) are subjected to more damage due to out-of-plane failure of walls unless supported by external ties or seismic bands/belts [44,45,57–59]. In flexible roof buildings, the only mode for transfer of out-of-plane seismic force is the horizontal flow to cross-walls through corners. Hence, insufficient anchorage of the roof diaphragm to a masonry wall can lead to the loss of support and results in bending of walls as cantilevers in an out-of-plane direction, leading to their failure, which in turn results in complete collapse.

1.2 Retrofitting of unreinforced masonry buildings

Initial assessment of earthquake-damaged buildings is followed by a long-term process of renovation and retrofitting. Renovation alone is not sufficient because it would bring the damaged structure to a pre-earthquake condition characterized by inadequate seismic resistance. It is extremely important to increase the seismic resistance of existing buildings to improve their behaviour during future seismic events. In addition to traditional retrofitting methods, such as reinforced concrete (RC) jacketing or grouting, the use of modern techniques with recent materials present numerous advantages [6]. Newer materials include fibre reinforced polymers (FRP). Over the years, several studies have been conducted with regard to the use of FRP for strengthening numerous types of structures made of various materials [41,53,60,61]. The main advantages of FRP lie in low self-weight and high strength. Despite many advantages of FRP, this material also presents certain disadvantages such as diminished performance at elevated temperatures, requirement of protective coatings, degradation of mechanical properties after long-term exposure to certain environmental conditions (like extensive moisture intrusion and frequent wet freezing-and-thawing cycles), higher level of site supervision, skilled workers, and inspection required. These disadvantages have encouraged the development of innovative high-quality textile reinforced mortars (TRM) [62–67] and wire-reinforced mortar [65,68–70].

The integral box action of URM buildings during an earthquake is the basic principle of seismic safety. The box action involves considerable interaction between in-plane and out-of-plane walls at the corner junctions. In past earthquakes, it has been witnessed that the damage often begins at the corners, resulting in the loss of box action and the walls acting independently, eventually leading to the building’s collapse. Hence, strategies like use of seismic bands (for new masonry construction) and belts (for existing masonry) have been introduced for good box action between all the elements of the building, i.e., between roof, walls, and foundation.

1.2.1 Seismic bands for new masonry construction

For earthquake-resistant design and construction of new masonry buildings, the use of vertical corner reinforcement and horizontal RC bands (also called tie beams) are commonly used to maintain the integrity of orthogonal walls and to achieve box action behaviour. Arya [71] proposed the concept of box action as the first major initiative for the retrofit of masonry buildings in India. After the Dhamar earthquake in the Yemen Arab Republic in 1982, Arya et al. [72] recommended the use of horizontal steel reinforcement in the form of bands at the critical levels. They also suggested the use of vertical reinforcing bars at the junctions of wall corners and near the sides of the opening (jambs). These bands are suggested to be provided just below the roof or floors, at the lintel level, and the top of gable masonry below the purlins. Further, several researchers [73–77] studied the efficacy of RC tie beams in load bearing walls at the floor and roof levels as well as at intermediate ones (at the lintels and the window sills). They reported that if tie beams are firmly connected to the floor or roof elements, then that can increase their in-plane stiffness and improve the transfer of lateral horizontal loads to the walls. They also observed that the tie beams are effective in reducing the tensile stresses in masonry by up to 50%. Later, IS 4326 [78] also recommends the use of RC seismic bands over the full width of wall, not less than 75 mm in depth and reinforced with longitudinal steel bars. These bands are usually constructed using RC of 1:2:4 grade (i.e., 1 part of cement, 2 parts of sand, and 4 parts of coarse aggregate) or reinforced brickwork in 1:3 cement-sand mortar, as a strengthening arrangement.

1.2.2 Seismic belts for existing masonry

After the Latur earthquake in 1993, Arya [79] proposed ferrocement seismic belts for the retrofitting of existing masonry houses in Marathwada. These seismic belts have been recommended to be provided above the door lintel level. The welded wire mesh (WWM) used in ferrocement must be connected to the wall using dowel bars or long nails and covered with cement-sand mortar on both sides of the walls [41,65]. IS 13935 [80] also recommends the use of splint (vertical seismic belt) and bandage (horizontal seismic belt) strengthening technique around the door and window openings. Among the various methods of retrofit, splint and bandage technique providing with galvanized WWM is the most economical and technically feasible one [81]. In Pakistan, quasi-static load tests have been conducted on scaled brick masonry walls to investigate the effects of ferrocement overlays on brick masonry and confined masonry walls [82]. The study demonstrates that this technique is effective for URM walls. Under cyclic load testing, the same retrofit technique, along with grout injection, has been used on a full-scale URM damaged building. They observed a significant increase in the retrofitted damaged building’s lateral load-carrying capacity [82].

Chellappa and Dubey [69] and Kadam et al. [70] have performed experimental studies using ‘shake-table’ and ‘shock-table’ testing, respectively, on half-scale single-story models. Splints and bandages technique with WWM has been used for strengthening the models and then compared to the URM building models. The results reported that the strengthened models performed significantly better with only minor damage. Later, the authors, Padalu et al. [65] of the present study tested the H-shape wall strengthened using WWM seismic belt (horizontal bandage at lintel level) under an out-of-plane reversed cyclic quasi-static airbag testing facility. They observed that the seismic belt prevented the vertical cracks from propagating. The cracks developed parallel to the horizontal bandage and dividing the wall into two separate zones, i.e., above and below the bandage. The results showed that the applied technique of horizontal bandage is very effective in enhancing flexural tensile strength and deformation capacity of masonry walls. As discussed in the literature, the use of seismic belts has been proved to be an effective retrofitting system and acts as a promising economical solution for existing URM buildings in the Indian subcontinent. However, the design methodology of retrofit using splint and bandage technique is still lacking. The application procedure of providing vertical and horizontal seismic belts and its detailing on URM walls suggested by IS 13935 [80] need modifications considering the practical issues encountered on-site based on the experimental studies. Hence, there is a need to work towards bridging this knowledge gap.

1.3 Modelling strategies

The URM consists of units bonded together with mortar. The heterogeneous and anisotropic nature of masonry contributes to its composite character. Therefore, the analysis of masonry structures has always been a challenging task, because of the geometrical complexity, lack of knowledge of the used materials, and structural modifications during the time and ageing of materials [6,83,84]. One method of modelling masonry involves either explicit modelling of the brick unit, mortar, and the brick-mortar interface, or modelling it as an equivalent homogenous continuum, called the micro-modelling approach [85,86]. The other extremity involves modelling masonry as equivalent frame elements, termed as macro-modelling [87–89]. In the micro-modelling approach, finite element method/modelling (FEM), discrete element method (DEM), and applied element method (AEM) are the three promising tools to explore the detailed behaviour (i.e., crack initiation and damage pattern) of the structure. In FEM, the model is discretized into a mesh of finite elements maintaining continuity in the field and capable of simulating the anisotropic behaviour of masonry [47,83,86,89]. In DEM, the masonry structure is considered as a collection of distinct bodies, and the contact elements are used in between two masonry units that simulate the contact forces and are capable of simulating the collapse mechanisms [85,90–92]. Whereas, in AEM, the structural member is discretized into masonry units interconnected by normal and shear springs [93].

These methods are based on various theories or approaches, leading to varying degrees of complexity, analysis time, and cost. It is also reasonable to expect that the outcomes of various approaches also differ [94]. The micro-modelling of masonry structures (continuum or discontinuum) suitably describes the non-linear behaviour of masonry. In this approach, non-linearity is defined at the material level in terms of a constitutive relation [89]. Hence, a large number of input parameters, i.e., fracture energy in tension and compression, plastic strain at peak stress, the compressive and tensile strength of unit and mortar, elastic and shear modulus of unit and mortar, etc., are required and this proves to be a significant impediment to the adoption of the micro-modelling approach [95–97]. The requirement of an advanced computing facility is another major constraint in the application of micro-modelling to masonry buildings [92]. These limitations can be overcome by employing macro-modelling techniques, which allow for more intuitive visualization of structural behaviour as well as reasonably accurate results with minimal computational effort [88].

The pier analysis method [2,98–100] and equivalent frame modelling (EFM) [1,88,89,101–103] are the two simple macro-modelling techniques that have been widely used. In the EFM approach, the masonry structure is idealized as a collection of horizontal (spandrel) and vertical (piers) elements connected by rigid offsets and each element is modelled by appropriate constitutive laws using Timoshenko beam elements [89]. In the EFM method, a linear isotropic material is used, and the non-linearity is represented at the element level in terms of force-displacement relationships. In the last few decades, several simplified non-linear methods and computer programs based on EFM have been developed to perform seismic analysis on masonry buildings. The computer programs that have been developed include pushover response––POR method [104], Raithel Aldo and Augenti Nicola method––RAN [97], simplified analysis of masonry buildings––SAM [105], and TREMURI [87,106]. Despite the EFM-based analysis software’s advantages such as low computational demand, the modelling idealizations in the EFM approach have led to non-conservative seismic assessment [107]. This is because the EFM approach only simulates the in-plane behaviour of masonry walls and neglects the interaction of out-of-plane effects with the global response.

The pier method of analysis, on the other hand, considers both the in-plane and out-of-plane behaviour of masonry walls with appropriate end conditions. The EFM method is relatively more accurate than the pier method, in predicting the in-plane behaviour, as the flexibility of the spandrel is considered, whereas in the pier analysis method the spandrels are considered to be rigid (i.e., the piers are subjected to deformation) [2]. In case of the pier analysis method, the rigidity calculations for in-plane walls have been well established by considering the appropriate boundary conditions. The main advantage of considering the pier analysis method is that the calculations can be performed very easily by hand and the decision on pier safety along with corresponding retrofitting measures can be made quickly based on the outcomes. However, the standardized safety assessment procedure for masonry buildings subjected to in-plane and out-of-plane actions using the pier method is not fully developed and it is important to work in this direction.

1.4 Research significance

The novelty of the present study is to present a simple, quick, and detailed methodology using the pier analysis method (linear static analysis) for the initial seismic safety assessment of a typical URM building considering in-plane and out-of-plane actions. The developed approach creates confidence amongst the structural engineers that URM buildings may be analyzed as engineered constructions and can be designed with less computational effort in design offices. The primary objective of the present study is to detail the application of pier analysis to the typical URM building followed by the application of the same method to buildings in retrofitted conditions. For comparison, a linear dynamic analysis has also been performed using continuum FEM. The non-linear analysis of considered URM building is not covered under the scope of the present study. In the present study, a single-story URM building of a primary health centre located in a rural area is analyzed under combined gravity and earthquake loads to determine the compressive, tensile, and shear stresses. Based on the outcomes, the adequacy of a retrofit scheme of the considered URM building, using splint and bandage technique with WWM as reinforcement following the guidelines of IS 13935 [80] is highlighted. Further, the procedure for design, detailing and application of the seismic belts using wire mesh and ferrocement or cement-sand mortar is also demonstrated.

2 Structural evaluation

A building plan shown in Fig.3, a single-story typical URM primary health centre building with plan dimensions of 6.2 and 4.0 meters in X- and Y-direction, respectively, is considered. Fig.4 shows the front elevation of all the walls. The building has a height of 3.0 meters. A detailed structural analysis of the considered building is carried out to ascertain its structural capacity following the current relevant codes/manuals [108–113]. The considered portion of the building consists of four walls as shown in Fig.3, in both the orthogonal directions. The URM building’s walls are made of solid clay bricks with a 1:6 cement-sand mortar mix (i.e., M2 grade, according to IS 1905 [111]). Bricks of size 230 mm × 110 mm × 75 mm with compressive strength of 30 MPa are used for the construction. The roof is of RC slab (rigid diaphragm) of M-20 grade concrete over the wall top. The brick walls and RC slab have a thicknesses of 230 and 150 mm, respectively. Seismic evaluation is an essential component of the structural analysis, where the level of seismic demand is selected as a design basis earthquake (DBE). For seismic analysis, the building is considered to be located in seismic zone IV (under Category-E according to IS 4326 [78] and IS 13828 [114]) and resting on medium soil. The finish and live load on the roof are selected as 1.0 and 0.75 kN/m², respectively, as per the standards of IS 875 (Part-1 and 2) [109,110]. Tab.3 summarizes the material properties used in the present study.

2.1 Modelling and analysis of unreinforced masonry building

The seismic behaviour of URM building can be simulated using either a macro-modelling or continuum finite element method. The macro-modelling approach is preferred due to its simplicity and low computational expense. The ‘Pier analysis’ method is the most promising macro-modelling method, which can be used in design offices for modelling and analysis of masonry buildings, due to its simplified approach and low computational time. Continuum FEM is another versatile method that can consider the relevant material properties, geometric properties, and boundary conditions and can provide a better understanding of structural behaviour.

2.2 Pier analysis

In the present study, it is considered that the load-bearing walls act as in-plane shear walls when subjected to lateral forces in the direction parallel to the plane of a wall; while out-of-plane bending of wall occurs when it is subjected to seismic forces normal to its face (Fig.1(a)). The following fundamental assumptions are used to develop the pier analysis method [2,98–100].

1) The behaviour of masonry walls in in-plane and out-of-plane actions are studied independently [98].

2) The in-plane behaviour of walls is simulated by an assemblage of piers (i.e., the vertical members consisting of the masonry between the door and window openings from sill/plinth level to lintel level), and the spandrels (i.e., horizontal members above the openings and extending to the top) are assumed to be rigid [2].

3) The rotational deformations of the portions above and below the openings are much smaller than those of the piers between the openings and are neglected [98].

4) The vertical piers connected at their top by a spandrel attract the lateral forces such that they undergo equal displacement at their top. This is because of the rigid diaphragm action and the in-plane rigidity of the spandrel, together [2].

5) A single solid wall or a spandrel located in the upper portion of a cantilevered in-plane wall fixed at the bottom and with the top free to translate and rotate is considered as a cantilever wall or pier, respectively (Fig.5). This is like a cantilever beam that deflects and rotates at the ends [99].

6) A pier tied at the top by the rigid spandrel located above the opening and at the bottom by the foundation (e.g., under a door or opening) or a masonry element (e.g., under a window) is considered as a fixed pier (i.e., restrained against rotation at top and bottom) (Fig.6). This is similar to a beam fixed at both ends [98,100].

7) The in-plane walls attract the lateral load in direct proportion to its equivalent stiffness or rigidity, determined from the equivalent spring model of the wall [98,99].

8) Points of contra-flexure are assumed at the mid-height of the piers. Further, the top of piers in a wall, interconnected by spandrels and rigid diaphragm is assumed to move by an equal amount, and the distribution of shear among the piers is made accordingly [100].

9) In out-of-plane action, the walls are assumed to span vertically between the supports if supported by rigid roof/floor slab with adequate bearing, or seismic bands/belts are provided at the floor/roof level. The walls are assumed to have cantilever action if a flexible roof/floor slab has been provided, or the bearing of a rigid floor/roof diaphragm is inadequate, and no seismic band/belt is provided [100].

2.2.1 Boundary conditions

As previously stated, the piers end conditions (i.e., top, and bottom edge) are assumed to be either fixed or free, depending on the expected restraint provided by the foundation and walls above. Therefore, all the wall pier elements shown in Fig.4 are assumed to be fixed at both ends, except the upper end of the topmost members (e.g., element-1 of WX1, WX2, WY1, and WY2 as shown in Fig.4 and Tab.4), which do not have restraining forces, and are assumed to be free. The topmost pier of wall element-1 is actually a spandrel, where bending takes place between two piers. However, in the present study, the topmost pier is assumed as rigid in bending in vertical direction and only in-plane deformations in horizontal direction are considered. For a cantilever and fixed pier, the deflection resulting from a force, Q can be expressed as shown in Eqs. (1) and (2), respectively.

(1){\mathrm{\Delta }}_{\text{c}}={\mathrm{\Delta }}_{\text{m}}+{\mathrm{\Delta }}_{\text{v}}=\frac{Q{h}^3}{3E_{\text{m}}I}+\frac{1.2Qh}{A{G}_{\text{m}}},

(2){\mathrm{\Delta }}_{\text{f}}={\mathrm{\Delta }}_{\text{m}}+{\mathrm{\Delta }}_{\text{v}}=\frac{Q{h}^3}{12E_{\text{m}}I}+\frac{1.2Qh}{A{G}_{\text{m}}},

where Δ_m denotes the deflection due to flexural deformation (Fig.7(a)), Δ_v represents the deflection due to shear deformation (Fig.7(b)), Q stands for the lateral force on the pier, h means the height of pier, A signifies the cross-sectional area of the pier (equal to tD), t suggests the thickness of the pier, D indicates the length of pier, I depicts the moment of inertia of pier in the direction of bending (equal to tD³/12), E_m reflects the elastic modulus of masonry, G_m symbolizes the modulus of rigidity of masonry (equal to 0.4 E_m), and 1.2 multiplier in the numerator of Eqs. (1) and (2) represents shape factor for a rectangular section of the wall [99].

2.2.2 Equivalent rigidity of wall

The wall stiffness is estimated by considering the in-plane stiffness or rigidity of the ith pier, which is governed by the dimensions, material properties, and boundary conditions. The rigidity of a wall pier, R_i based on its end conditions is determined using Eqs. (3) and (4), respectively.

(3){R_i}_{\text{c}}=\frac{1}{{\mathrm{\Delta }}_{\text{c}}}=\frac{E_{\text{m}}t}{4{\left({\displaystyle \frac{h}{D}}\right)}^3+3\left({\displaystyle \frac{h}{D}}\right)},

(4)R_{i\text{f}}=\frac{1}{{\mathrm{\Delta }}_{\text{f}}}=\frac{E_{\text{m}}t}{{\left({\displaystyle \frac{h}{D}}\right)}^3+3\left({\displaystyle \frac{h}{D}}\right)}.

The elevation of a wall-WX1 with pier numbering and its equivalent spring model is shown in Fig.8. In the present study, the following steps are performed for determining wall rigidities: 1) deflection of the solid wall is determined considering as a cantilever wall, Δ_solid(c); 2) this step removes the entire portion of the wall containing all the openings by subtracting the cantilever deflection of an interior strip with a height equal to that of the highest opening from the solid wall deflection, Δ_strip(c); 3) deflections of all the piers within that interior strip are determined by their rigidities, considering as fixed condition, Δ_piers(f); 4) total deflection of an actual wall with openings is determined by adding the deflection of piers to the modified wall deflection as shown in Eq. (5).

(5){\mathrm{\Delta }}_{\text{total}}={\mathrm{\Delta }}_{\text{solid(c)}}-{\mathrm{\Delta }}_{\text{strip(c)}}+{\mathrm{\Delta }}_{\text{piers(f)}}.

The reciprocal of the total deflection becomes the equivalent lateral rigidity of the wall (R_w = 1/Δ_total). Also, the lateral rigidity, R_w of walls is determined using the equivalent spring model (Fig.8) and using Eq. (6); the two methods are found to yield almost the same value.

(6)R_{\text{w}}={\displaystyle \frac{1}{{\displaystyle \frac{1}{R{}_{\text{1c}}}}+{\displaystyle \frac{1}{R_{\text{2f}}+{\displaystyle \frac{1}{R_{\text{3f}}+R_{\text{4f}}}}+{\displaystyle \frac{1}{R_{\text{5f}}}}}}}}.

The total lateral rigidity of building, R_b in X and Y directions is determined as the sum of the rigidities of all the walls along X and Y directions, respectively, and is summarized in Tab.4.

2.2.3 Torsional and translational stiffness

After rigidity calculation, the coordinates of the centre of mass (CM) and centre of stiffness (CS) are determined by considering the distribution of mass and stiffness, respectively. The CM is considered as the point at which the entire mass of a building is lumped or concentrated; whereas the CS corresponds to the point through which the resultant of the restoring forces acts. The CM and stiffness are determined by taking static moments of a point, using the respective lumped weight of the members and relative stiffnesses of the walls as forces in the moment summation as shown in Tab.5 and Tab.6, respectively. The difference between CM and CS creates static eccentricity (Fig.9), which gives rise to torsional motion. The design eccentricity to be used is determined using Eq. (7) [108], and the maximum values are considered and summarized in Tab.7.

(7)e_{\text{d}}=\{\begin{array}{c}1.5e_{\text{s}}+0.05b,\\ e_{\text{s}}-0.05b,\end{array}

where e_s denotes the static eccentricity (i.e., the distance between CM and CS as shown in Fig.9), b denotes the plan dimension of a floor, perpendicular to the direction of a force, factor 1.5 represents the dynamic amplification factor, and 0.05b represents the accidental eccentricity of 5% of the building’s base dimension.

The translational stiffness in each direction (X and Y ) is obtained by simply adding the rigidity of all the walls in a particular direction, whereas the torsional rigidity of story is determined using Eq. (8) and the value is presented in Tab.8.

(8)R_{\text{θ}}=\sum R_x{d_y}^2+\sum R_y{d_x}^2,

where R_x and R_y are the relative lateral rigidity of the wall parallel to X and Y directions, respectively, and d_x and d_y are the distances to the CS from the center of the wall.

2.2.4 Design seismic force

The design lateral force along the considered direction of the earthquake is determined as per IS 1893 (Part 1) [108] using Eqs. (9) and (10):

(9)V_{\text{b}}=A_{\text{h}}W,

(10)A_{\text{h}}=\frac{Z}{2}\frac{I}{R}\frac{S_{\text{a}}}{g}\beta \left(\xi \right),

where A_h denotes the horizontal seismic coefficient of the building; Z denotes the seismic zone factor (equal to 0.24 for zone-IV) representing the peak ground acceleration and factor 2 in the denominator is used to reduce the seismic forces for DBE level from the maximum considered earthquake (MCE) level hazard; I denotes the importance factor, which depends on the building’s functional use, and is categorized by the risk of failure, post-earthquake functional needs, historical value, or economic significance (equal to 1.5 for a health facility); R denotes the response reduction factor, and depends on the structure’s perceived seismic performance, and is categorized by ductile or brittle response (equal to 1.5 for URM building without seismic belts or RC bands); S_a/g denotes 5% damped spectral acceleration coefficient, depends on the fundamental period of building and the soil type; β(ξ) denotes the factor to take into account the effect of damping ratio, ξ (equal to 1.0 for 5% damping); and W denotes the seismic weight of the building including the weight of roof and walls.

The vertical force acting on walls is obtained by taking the summation of self-weight of roof/floor. The load transferred from the floor on the wall is distributed based on the tributary area as per the yield line pattern. The total vertical load on a wall (dead and live load is considered separately) is uniformly distributed over the full length of the wall, and the share of each pier in a wall is obtained considering the tributary length. For seismic weight calculation, linear triangular variation is considered, and only 50% of wall weight (109.6 kN) is lumped. The contribution of floor dead load (96.86 kN) and live load on the roof is taken as 100% and zero, respectively. The seismic weight of the building is 206.46 kN. The approximate fundamental period of the URM building is determined using the empirical formula, as shown in Eq. (11) [108].

(11)T=\frac{0.09H}{\sqrt{B}},

where H denotes the height of the building (in meters), and B denotes the base dimension of the building along the considered direction of the seismic forces (in meters).

Using Eq. (11), the design period of the considered building is 0.11 and 0.13 seconds in X and Y directions, respectively. The design horizontal seismic coefficient, A_h is 0.30. Considering the ‘medium soil’ type and the obtained period, the design acceleration coefficient is 2.5 for both X and Y directions. Therefore, the design base shear of the single-story URM building is obtained as 61.94 kN.

2.2.5 Direct and torsional shear forces

For the rigid diaphragm, it is assumed that all the walls are tied together with the RC slab. Hence, the total force, Q acting on the wall is distributed to the different piers in direct proportion to their relative lateral stiffness using the equivalent spring model (Fig.8). The total shear force, Q on individual walls is estimated as the algebraic sum of the forces due to uniform translation, F (Eqs. (12) and (13)), and due to torsion, ΔF (Eqs. (14) and (15)) and summarized in Tab.9.

(12)F_x=V_{\text{b}x}\frac{R_x}{\sum R_x},

(13)F_y=V_{\text{b}y}\frac{R_y}{\sum R_y},

(14)\mathrm{\Delta }{F}_x=M_{\text{T}x}\frac{R_x{d}_y}{R_{\text{θ}}},

(15)\mathrm{\Delta }{F}_y=M_{\text{T}y}\frac{R_y{d}_x}{R_{\text{θ}}},

where M_Tx and M_Ty are the torsional moments induced that are equal to V_bx × e_dy (for X-direction) and V_by × e_dx (for Y-direction), respectively.

2.2.6 Overturning moment

Buildings experience severe overturning moments as a result of lateral earthquake forces. If the overturning moment is large enough, it can overcome the structure’s dead weight, causing tension at the pier ends. In addition to the dead and live loads, it may cause high compressive forces in the wall piers, which may increase the axial load. As a result, the axial load increase in piers due to overturning moment on the wall is estimated using Eqs. (16) and (17), respectively.

(16)M_{\text{ovt}}=Qh,

(17)P_{\text{ovt}}=M_{\text{ovt}}\frac{L_i{A}_i}{I_{\text{n}}},

where P_ovt denotes the load due to overturning; M_ovt denotes the overturning moment (refer Tab.9); h denotes the height of the wall; L_iA_i denotes the centroid of a net section of wall (CG = ΣA_il/ΣA_i), l denotes the distance from the left edge of the wall to the centroid of a pier, L_i denotes absolute distance to the extreme fibres of the considered pier section from the centroidal axis (C.G.-l), and I_n denotes the corresponding moment of inertia (I_n = I + A_iL_i²) and its values are presented in Tab.10.

2.2.7 In-plane stresses

The in-plane shear in individual piers is obtained from the total shear acting on each wall, based on the relative stiffness. In the case of in-plane bending, the moment is determined for fixed and cantilever end piers using Eqs. (18) and (19), respectively:

(18)M_i=Q_i\frac{h_i}{2},

(19)M_i=Q_i{h}_i,

where M_i denotes the in-plane bending moment in ith pier, Q_i is the in-plane shear in ith pier, and h_i is the height of ith pier.

To estimate the in-plane safety of the walls, the normal stresses due to gravity load is determined. These stresses are combined with the bending stresses, developed due to lateral load to obtain the net tensile stress, f_t (Eq. (20)) and combined compressive stress, f_c (Eq. (21)). The in-plane shear stress, τ in a pier is determined using Eq. (22). The estimated net tensile stress, compressive stress, and shear stress values are summarized in Tab.11.

(20)f_{\text{t}}=\frac{P_{\text{t}}}{A}-\frac{M_i}{Z},

(21)f_{\text{c}}=\frac{P_{\text{c}}}{A}+\frac{M_i}{Z},

(22)\tau =\frac{Q_i}{A},

where P_t and P_c denote the total vertical load at the critical section of the pier for tension and compression, respectively (Eqs. (23) and (24)), Z denotes the section modulus of a pier (equal to tD²/6), and M_i denotes the in-plane bending moment in the ith pier, developed due to the lateral load acting at the top of the pier and other eccentric loads (Eqs. (18) and (19)):

(23)P_{\text{t}}=P_{\text{d}}+P_{\text{l}}-P_{\text{ovt}},

(24)P_{\text{c}}=P_{\text{d}}+P_{\text{l}}+P_{\text{ovt}}.

The dead load, P_d and live load, P_l acting on a pier are determined using Eqs. (25) and (26), respectively:

(25)P_{\text{d}}=\left(P_{\text{a}}\times b_{\text{eff}}\right)+P_{\text{w}},

(26)P_{\text{l}}=P_{\text{b}}\times b_{\text{eff}},

where P_a denotes the total dead load acting on the wall per meter length, which includes the self-weight of wall (equal to h_itγ_m) and dead load of RC slab (equal to [self-weight of RC slab + finish load] × tributary area, based on yield line pattern of loading) and P_b denotes the total live load acting on the wall per meter length (equal to live load intensity × tributary area), b_eff denotes the effective loading width of the pier (equal to length of the pier, D + half of each adjoining opening of the pier), and P_w denotes the self-weight of the pier including the weight from the upper pier if any.

2.2.8 Out-of-plane stresses

The end condition of walls is considered as simply supported at the top and bottom for out-of-plane action. Due to force in the horizontal direction, the wall bends in a vertical plane under uniformly applied pressure. The critical section for tension is considered to be at the mid-height of the wall, as the floor is rigid. Therefore, the out-of-plane bending moment can be estimated using Eq. (27):

(27)M_{\text{oop}}=\frac{p{h}^2}{8},

where p denotes the out-of-plane pressure acting on the wall due to seismic force and depends on the design horizontal seismic coefficient, A_h, unit weight of masonry (γ_m), and the thickness of the wall (t) and can be expressed as:

(28)p=A_{\mathrm{h}}^{\prime }{\gamma }_{\mathrm{m}}t,

where A_{\mathrm{h}}^{\prime } denotes the amplified horizontal seismic coefficient of building and can be determined as:

(29)A_{\mathrm{h}}^{\prime }=A_{\mathrm{h}}\left(1+2\frac{x}{H}\right),

where x denotes the distance to the mid-height of a considered story as measured from the base of the building, and H denotes the height of the building (equal to 3.0 m).

For the present study, the value of A_{\mathrm{h}}^{\prime } and p are found to be 0.60 and 2.76 kN/m², respectively. To estimate the out-of-plane safety of the walls, the net compressive and tensile stresses are determined using Eqs. (30) and (31), respectively, and the values are presented in Tab.12.

(30)f_{\text{c}}=\frac{P}{A}+\frac{M_{\text{oop}}}{Z},

(31)f_{\text{t}}=\frac{P}{A}-\frac{M_{\text{oop}}}{Z},

where P denotes the total vertical load which includes dead load of RC slab denoted as P_d (equal to [self-weight of RC slab + finish load] × tributary area based on yield line pattern of loading) and the weight of wall per meter length up to critical section represented as P_s (equal to 1 × γ_mth/2), A denotes the cross-sectional area of wall per meter length (equal to 1 × t = 0.23 m²), Z denotes the section modulus per meter length of the wall (equal to 1 × t²/6 = 0.009 m³), t denotes the thickness of the pier (equal to 0.23 m), and M_oop denotes the out-of-plane bending moment acting on the wall (equal to 3.11 kN·m).

2.2.9 Allowable stresses

The allowable compressive stress in masonry is determined using Eq. (32) [111] and summarized in Tab.13.

(32)f_{\text{cp}}=f_{\text{cb}}{k}_{\text{s}}{k}_{\text{a}}{k}_{\text{p}}.

The value of basic compressive stress, f_cb in Eq. (32) is obtained as equal to 0.25 times the compressive strength of masonry, f_m (=1.50 MPa). The stress reduction factor, k_s is determined by considering the second order effects in terms of the masonry element’s slenderness ratio and the loading eccentricity. For the present case, the RC slab supports on the full width of the external masonry walls and also the span is not exceeding 30 times the thickness of the wall. Hence, the axial loads acting on the wall are without any eccentricity. The slenderness ratio, λ is determined as the ratio of effective height, h_eff to the effective thickness, t_eff. The effective height of wall piers is obtained by considering the wall has full restraint at the top due to the rigid concrete slab. The value of h_eff is determined for both the orthogonal directions, i.e., normal to the plane of a wall (Eq. (33)) and parallel to the plane of a wall (Eq. (34)) and the maximum value is considered for the analysis.

(33)h_{\text{eff\_N}}=0.75h+0.25H_1,

(34)h_{\text{eff\_P}}=h,

where h denotes the height of the pier, and H₁ denotes the height of the taller opening.

For solid wall cross-section, the effective thickness, t_eff is considered as the actual thickness of the wall. The area reduction factor, k_a considers the smallness of the area of masonry cross-section (i.e., accounting for the variability in masonry), and the value is considered as 1.0 since the cross-sectional area of all the piers is more than 0.2 m². The shape modification factor, k_p considers the shape of the masonry unit (i.e., it accounts for changes in the number of bed-joints because of the way the bricks are being laid), and the factor is observed to be 1.0, as the height to width ratio of the masonry unit is found to be less than 0.75.

The allowable tensile stress, f_tp in masonry is considered as 0.05 MPa [111] for the vertical bending, where flexural tension develops perpendicular to the bed-joints. The allowable shear stress, τ_p in masonry is determined on the area of bed-joint using Eq. (35) and presented in Tab.13.

(35){\tau }_{\text{p}}=0.1+\frac{f_{\text{d}}}{6}⩽0.5\text{MPa},

where the value 0.1 refers to the cohesion, i.e., the bond between the brick unit and mortar, f_d denotes the compressive stress due to dead loads in MPa, and the value 1/6 refers to the frictional resistance, i.e., coefficient of friction.

2.3 Finite element analysis

The SAP2000 programme [115] is used to create a FEM of a typical single-story URM primary health centre building. The structure consists of masonry walls and a RC slab. The 3-D model of the URM building is created with the assumption that walls are the load-bearing elements, and floors are planar stiffening elements (rigid diaphragm), on which the horizontal effects are distributed between the connected walls. The connections between the floor diaphragms at the top and bottom, and the cross-walls at the two edges, are modelled as ‘integral’ in the FE model. URM walls and roof slab of the building are modelled using a four-node quadrilateral shell element that combines membrane and plate bending behaviour as shown in Fig.10. For shell elements, a thick-plate (Mindlin/Reissner) formulation is used. As masonry is a heterogeneous and anisotropic material, it is essential to consider the orthotropic properties of masonry in continuum modelling. However, due to the lack of adequate data, modelling is done using isotropic properties available from the existing literature, as shown in Tab.3. The present study uses the continuum finite element method to obtain the linear response. This study does not deal with the non-linear response of masonry, which is quite complex. However, the application of FEM to the linear analysis of continuum is quite straight forward and it has been calibrated and validated by several researchers [116–118] in the past.

In FE analysis, in-plane, and out-of-plane actions (forces and moments) are acting simultaneously. But as the linear procedure has been adopted, the stresses can be superimposed due to in-plane and out-of-plane bending. Each pier consists of different finite elements (as they are discretized) and hence, stresses are different for each discretized element and also vary across the area and thickness of the element. Hence, in-plane stresses (compressive and tensile) are obtained for the extreme elements close to the two edges at the base of pier and the average stresses at the mid-surface are considered. Similarly, the out-of-plane stresses are obtained at the mid-height of the pier at the two extreme faces (inner and outer). The out-of-plane action causes compressive stress on one face, and tensile stress on the other, whereas the stresses obtained from the FE analysis are combined with the in-plane stresses. Therefore, the true out-of-plane stresses are determined by deducting the average in-plane compressive and tensile stresses from the stresses obtained at the extreme faces. On the other hand, shear stress values are obtained by taking the average of the stresses obtained at the centre of all the discretized elements at the base of a pier.

The mesh convergence study is conducted by modelling one of the walls (WX1) in the building and analyzing under combined axial and lateral loads. For different mesh sizes, the compressive and tensile stresses are reported at the mid-surface of the extreme elements near the edges of a pier; whereas, the shear stress is reported at the centre of the pier. All the stresses are obtained at three different levels, viz. top, middle, and bottom level of wall pier, and compared in Tab.14. It is observed that there is hardly any difference between results for mesh size of 2.5 and 5.0 cm, and hence optimum mesh size of 5.0 cm is selected.

Therefore, the complete structure is discretized using a mesh size of 5 cm, as shown in Fig.11. To connect all the mismatched shell meshes, an edge constraint is used to ensure compatibility between the nodes. Further, the diaphragm constraint is used between the adjacent nodes to ensure the rigid diaphragm effect (i.e., in-plane rigidity). Fixed support is assigned to all nodes at the base level. Live loads and finish loads on the roof slab are applied as a uniform load on the shell element. The seismic loads (EQ) are applied in the form of response spectrum (linear dynamic analysis) using IS 1893 (Part-1) [108], in two principal directions (X and Y) of the building. It has been observed that the out-of-plane behaviour of walls might not be adequately simulated using the limited number of modes considered, as out-of-plane vibrations have much higher frequencies. Hence, the out-of-plane behaviour of walls has been simulated by subjecting the structure to uniform acceleration, obtained using Eqs. (28) and (29). The various actions have been combined as DL + LL ± EQ; where DL denotes the dead load, LL denotes the live load, and EQ denotes the seismic loads for horizontal shaking in two principal directions.

2.4 Results and discussion

The comparison of results from the FEM and pier analysis for in-plane and out-of-plane stresses is presented in Tab.15 and Tab.16, respectively. The estimated tensile stress, compressive stress, and shear stress values have been compared with the allowable values shown in Tab.13 to evaluate the in-plane and out-of-plane safety of the piers/walls. Tab.15 shows that in most of the cases (48 out of 51), the in-plane stresses obtained from the pier analysis are mostly conservative compared to FEM. However, in few cases, the in-plane stress values are found to be non-conservative; whereas Tab.16 shows that for all the cases, the out-of-plane tensile stresses obtained from the pier analysis are found to be conservative compared to FEM. From the results, it is observed that all 17 piers are safe in in-plane compression and in-plane shear, while 6 piers are unsafe in in-plane tension (35%). For out-of-plane action, all 4 walls are found to be safe in compression, but they fail in out-of-plane tension. Therefore, retrofitting is required to make the piers/walls safe in in-plane and out-of-plane tension.

Further, the results shown in Tab.15 indicate some difference between the in-plane results obtained from both the analyses. The variation in in-plane stresses obtained from the pier analysis method and FEM is found to be in the range between 3% and 39% for shear stress, 2% and 40% for compressive stress, and 12% and 41% for tensile stress. This is because of the assumptions made in the pier analysis, that there is no interaction between in-plane and out-of-plane walls, i.e., both act independently, whereas, in FEM, the interaction between in-plane and out-of-plane action of walls are considered explicitly. Tab.16 indicates the difference between the out-of-plane stresses obtained from FEM and pier analysis, where the variation ranges between 42% and 56%. The possible reason is understood to be the difference in the boundary conditions assumed in pier analysis and that is being simulated in the FEM. In pier analysis, the critical condition for out-of-plane walls is considered by assuming that there is no support from cross-walls and by considering simply supported conditions at the top and bottom. In contrast, in the FEM, as the linear analysis is being performed, masonry can take tension, and hence fixity can be achieved with floor slabs and cross-walls. Overall, the pier analysis method is conservative compared to FEM. However, pier analysis is a quick and simplified tool and can be used for initial seismic safety evaluation for masonry buildings.

3 Retrofit design and detailing

Using the results of ‘Pier Analysis’ method, the URM walls are retrofitted using seismic belts (i.e., splints and bandages) with wire mesh reinforcement against the in-plane and out-of-plane actions. The effectiveness of the retrofitting technique is also discussed. The following provides the complete design methodology and retrofit procedure recommendations.

3.1 Design of splint at wall corners and near the openings

From the analysis, it is observed that retrofitting of the building is required, as the expected performance of the URM piers is estimated to be unsatisfactory. Hence, vertical reinforcement in the form of WWM splints is designed following the guidelines of IS 13935 [80], to make the piers safe in in-plane tension. It is assumed that masonry cannot carry any tensile stresses, and therefore the contribution of masonry strength in tension is neglected. Hence, WWM resists the full tensile force acting on the pier under the combined action of gravity and lateral load. The linear triangular distribution of stresses across the masonry pier section is shown in Fig.12. Depth of the neutral axis (x) is obtained using the compressive and tensile stress block of masonry by means of similarity of triangle approach as shown in Fig.12(b). The reinforcement area is obtained by equating the tensile force (T) obtained from an area of the tensile stress block (Fig.12(b)) and the allowable tensile force resisted by the WWM (Fig.12(c)), as expressed in Eq. (36).

(36)T_{\text{per}}=0.6f_{\text{y}}\times 1.33A_{\text{st}},

where f_y denotes the grade of steel (WWM is made of Fe 250, and therefore, the yield stress of 250 MPa is used), A_st is the area of reinforcement, and factor 1.33 denotes the increase in the allowable stresses in case of seismic loading as per IS 1893 (Part-1) [108].

The required area of reinforcement ranges between 3.36 and 23.64 mm² which is too small to provide. Therefore, the minimum reinforcement of 116.14 mm² (vertical reinforcement = 3.25 mm diameter galvanized wire mesh including 14 wires with 25 mm grid spacing, and width of splint = 400 mm) recommended by the IS 13935 [80] is provided and summarized in Tab.17.

3.2 Design of bandage at lintel level

The walls also fails in tension due to out-of-plane bending, as masonry has very low tensile strength. Therefore, the vertical span of the wall is reduced by providing a seismic belt or bandage at the lintel level. The bandage is provided in the form of a strip of WWM covered with 1:3 ferrocement or inorganic matrix (i.e., cement-sand mortar). This horizontal bandage provides additional support in out-of-plane direction and reduces the effective span. The use of ferrocement bandage to retrofit URM walls results in the formation of a composite beam that supports the wall at lintel level, dividing the vertical span into two parts (see h₁ and h₂ in Fig.13). But in the analysis, it is idealized as h/2 rather than taking h₁ and h₂, resulting in much reduced bending moment in the wall, as expressed in Eq. (37)：

(37)M_{\text{t}}=p\frac{\left({\displaystyle \frac{h_1+h_2}{2}}\right)L^2}{10},

where M_t denotes the moment developed at bandage level, h₁ denotes the height of lintel from the floor, h₂ denotes the height of roof from the lintel, and L denotes the length of the wall.

The reinforcement required has been estimated as per the guidelines of IS 13935 [80] taking into account the composite action of masonry and WWM as a horizontally spanning beam supported by cross-walls. Fig.12(c) shows the distribution of bending stress across the section of the URM-bandage composite beam. It is assumed that the WWM reinforcement is effective only in tension, as the wires are too thin to resist buckling under compressive load. Depth of the neutral axis (x) is determined by equating the compressive force (C) with the tensile force (T) as shown in Fig.12. The compressive force (C) is obtained from the area of compressive stress block, whereas the tensile force resisted by the reinforcement is estimated using Eq. (36), ignoring the tensile strength of masonry. The moment capacity of the composite beam is determined using the working stress method and can be expressed as in Eq. (38)：

(38)M_{\text{band}}=T_{\text{per}}{J}_{\text{d}},

where J_d denotes the lever arm distance.

From the design, it is observed that for walls WX1 and WX2, the allowable tensile force (T_per) resisted by WWM reinforcement, and the depth of neutral axis (x) are found to be 23.17 kN and 61.12 mm, respectively. The moment capacity of the horizontal bandage (M_band = 4.85 kN·m) is found to be smaller than the applied moment (M_t= 15.91 kN·m), and therefore found to be unsafe. In the case of wall WY1 and WY2, the applied moment (M_t= 6.62 kN·m) is found to be again larger than the capacity of the URM-bandage composite section (M_band = 4.85 kN·m). Hence, WWM reinforcement alone is inadequate and therefore an additional 2 steel reinforcing bars (Fe 500 grade i.e., the yield stress of 500 MPa) of 10 mm diameter are provided to resist the balance moment (M_bal) and support the walls in out-of-plane action. The amount of WWM reinforcement provided in horizontal bandage is similar to that of vertical splints, except for the width of bandage (H = 380 mm). The design details are presented in Tab.18.

After retrofitting the URM building, the stresses in all the piers/walls are found to be within the allowable limit and safe. In Fig.14 and Fig.15, detailed drawings of the typical arrangement for splints and bandages in a retrofitted URM wall are presented based on retrofit calculations and guidelines. The designed vertical splints are applied at the corners of rooms (i.e., junctions of walls) and jambs of window and door openings, to prevent the initiation of in-plane shear cracks. The designed horizontal bandages are provided at the lintel level of all the walls to resists the seismic force by spanning between the top roof and bottom floor, and its role is even more crucial in the out-of-plane action of walls.

3.3 Recommendations for retrofit procedure

To ensure the integral box action of URM buildings and strengthening of walls in in-plane and out-of-plane action, the vertical and horizontal seismic belts (splints and bandages) must be applied carefully and continue on both the faces of all the walls. Some of the main issues in the use of splint and bandage technique are identified based on the on-site full-scale experimentation investigated by the researchers [69,70], authors of the present study [65], and their preventive measures are suggested as follows.

1) Proper adhesion and bonding of the splints and bandages with the existing masonry must be ensured to transfer the shear stresses developing at the interface. This can be ensured by raking of the masonry joints, use of a cement slurry bond coat, and use of dowel bars at regular intervals for transfer of shear between the ferrocement and the URM wall.

2) To avoid corrosion of reinforcement in the ferrocement belt, galvanized WWM reinforcement must be used, or it must be epoxy painted.

3) The added ferrocement belts must be thicker than the plaster usually applied on masonry walls. These thicker belts should be neatly finished to look aesthetically pleasing and provide a sense of security to the occupants.

Further, the proposed step-by-step procedure of applying the ferrocement strips (seismic belts) on a typical masonry building is as follows.

Step-1: Measurement and marking of splints and bandages must be made on the masonry walls using a coloured thread. The dimensions of the splints and bandage must be obtained from the drawings shown in Fig.14 and Fig.15. The splints must be marked along with all the corners of a room. Jambs of the openings and bandages must be marked horizontally above the doors and windows as shown in Fig.16(a).

Step-2: The plaster on the marked area must be removed using a disk cutter (Fig.16(b)) and chisel (Fig.16(c)).

Step-3: The masonry joints must be raked up to a depth of 15 mm, as shown in Fig.16(d), and cleaned with water to have a good bond with the ferrocement. A pit must be made in the floor to a depth of at least 300 mm to anchor the splints (Fig.16(e) and Fig.16(f)). Similarly, in the case of a multi-story building, a hole must be made in the slab of the upper floors for continuity of splint.

Step-4: A bond coat of cement slurry must be applied over the masonry (Fig.16(g)).

Step-5: Cement-sand plaster of 1:3 mortar with 10 mm thickness must be applied over the masonry substrate, as shown in Fig.16(h) to fill the raked joints. The plastered surface must be kept rough (Fig.16(i)) for a better bond with the second layer of mortar or ferrocement.

Step-6: A strip of galvanized WWM must be cut in the required size with the required number of wires (Fig.16(j)). If galvanized WWM is not available, then it should be painted with epoxy to safeguard against corrosion (Fig.16(k)).

Step-7: The wire mesh must be fixed to the plastered surface on either face using 4 mm diameter dowel bars at a spacing of 300 mm centre to centre (Fig.14 and Fig.15), properly connecting the wire mesh on both sides of the walls. The holes are drilled (Fig.16(l)) to pass the dowel bars through the wall must be cement grouted after placement. It may be noted that in some cases, WWM reinforcement may not be adequate, and therefore steel rebars also need to be used (Fig.16(m)).

Step-8: A bond coat of cement slurry and the second layer of plaster with 25 mm thickness must be applied (Fig.16(n)). The cement slurry provides a good bond between the two layers of plaster and protects the WWM from corrosion. However, it must be applied immediately before the application of the second layer of plaster. (Note: An alternative to applying cement plaster in two layers can also be replaced using ‘shotcrete’ or ‘guniting’. In this process, micro-concrete (M-20 grade) must be sprayed on the surface of masonry under pressure (Fig.16(o)). Micro-concreting provides a stronger layer and better bond with the wall and WWM. It also provides better protection of the wires against corrosion. However, care must be taken in placing of WWM, and a clear gap of 10 mm must be maintained between the wall and the WWM using precast concrete spacers (Fig.16(p)).

Step-9: A good finish to the plastered/guniting surface must be provided with neat edges (Fig.16(q)). The plaster on the splints and bandages is thicker than the usual thickness of wall plaster, and hence they are prominently visible (Fig.16(r)). Sufficient curing of the plastered surface must be done by sprinkling water for about 28 d.

4 Conclusions

Seismic evaluation of a typical URM building has been presented, using pier analysis and finite element method. The adequacy of a retrofit technique using ferrocement splints and bandages has been illustrated. The following are the findings of the study.

1) The pier analysis is a simple but approximate method and suitable for hand calculations. Its comparison with the more sophisticated continuum finite element method has been performed using linear dynamic analysis and isotropic properties of masonry for the URM building. However, for the retrofitted building, FEM could not be performed due to the limitation of the software and lack of detail of the orthotropic properties of masonry. The results of pier analysis have been compared with those of FE analysis. The stresses in the in-plane actions, obtained using the two methods of analysis, are reasonably comparable. However, a large difference between pier analysis and FEM has been observed in tensile stresses under the out-of-plane action of walls. This variation is due to the difference in the boundary conditions assumed in the pier analysis and the finite element model. In pier analysis, out-of-plane walls have been assumed to have no support from cross-walls and to be simply supported at the top and bottom. In contrast, in the FE model, an integral connection with floor slabs and cross-walls has been simulated.

2) The results of the pier analysis method are conservative compared to the FEM due to the simplifying assumptions. However, the pier analysis method can be used as a quick and simplified tool in design offices to evaluate the seismic safety of contemporary and heritage masonry buildings. The pier method also identifies the need for retrofitting of individual walls or piers under expected seismic action.

3) Based on the analysis, unsafe URM piers have been retrofitted using ferrocement splints (vertical belt) and bandages (horizontal belt) with WWM. These belts serve two purposes. They act as ties and integrate the walls to achieve box-action, and at the same time, they strengthen the walls in out-of-plane action. After the retrofitting, the lateral load capacity of the wall piers increased up to 3.67 times, such that all the piers have enhanced safety under gravity, and seismic in-plane and out-of-plane loads.

4) The developed assessment procedure, design methodology, detailing, and recommendations proposed for the application of splint and bandage retrofitting technique to URM buildings can be implemented using the guidelines of IS 13935 [80] for practical design and execution on-site. The reliability of the retrofit scheme needs to be further evaluated using experimental and more detailed analysis methods considering the orthotropic and non-linear properties of masonry. Further, the present study is limited to buildings with rigid diaphragms. It may be extended for other floor and roof types and their connections with the walls.

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