Introduction

The historical masonry structures serve as portals to the past, erected worldwide through diverse architectural styles and construction methods. These creations exhibit an amalgamation of brick and stone masonry techniques (D'Ambrisi et al., 2012). Through a retrospective examination of ancient constructions spanning a variety of forms—such as buildings, mosques, churches, cathedrals, domes, arches, and towers—it becomes evident that these structures were accurately made with symmetrical methodologies and materials. Preserving these cultural treasures demands meticulous attention and an exhaustive examination to pinpoint areas of structural vulnerability (Brandonisio et al., 2013; Colapietro et al., 2013).

India’s historical edifices are prime examples of masonry craftsmanship, employing stone and brick in their construction. However, insufficient retrofitting and a lack of maintenance make these architectural gems susceptible to partial or complete collapse when subjected to static and dynamic forces. Brick masonry, a pivotal construction material for monumental buildings, exhibits considerable mass and stiffness but limited tensile strength, rendering masonry structures vulnerable to lateral forces such as wind and earthquakes (Bilgin & Korini, 2012). Masonry systems fall into engineered or non-engineered categories, further classified as unreinforced, confined, or reinforced masonry (Acito et al., 2014; Choudhury et al., 2014; Milani, 2013). The evaluation of masonry structures’ safety is of paramount importance from artistic, cultural, social, and historical standpoints. These structures, which represent the heritage of the past, necessitate careful consideration to ensure their preservation for future generations.

The historical constructions, spanning various architectural styles, were erected devoid of seismic considerations, utilising local materials for diverse purposes. These structures have been devised with multiple utilities, serving as (i) cityscape features, (ii) open spaces for general use, (iii) venues for public gatherings such as churches, theatres, cathedrals, institutes, mosques, and temples, and (iv) isolated and inaccessible sites. These edifices exhibit spacious and open designs, employing an array of materials in symmetrical and asymmetrical patterns (2015b; Casolo et al., 2013; Choudhury et al., 2014; Lourenço, 2005; Milani & Valente, 2015a; Saloustros et al., 2015).

The materials used in construction have played a crucial role in assembling structural elements, binding, plastering, and decorative features. Previous research predominantly focussed on visual inspection surveys and thorough assessments of structures to comprehend their actual conditions concerning materials and structure (Aguilar et al., 2015; Ceroni et al., 2007; Fortunato et al., 2017; Lourenço, 2005; Lourenço et al., 2007; Parisi & Augenti, 2013; Ramos et al., 2006; Shakya & Kawan, 2016). Over time, specific structures have transformed from stable states to vulnerability due to soil settlements, prolonged seismic activity, and changing climate, often exacerbated by inadequate maintenance, varying load conditions, and insufficient retrofitting. Numerous historic monuments bear the brunt of past earthquakes, leading to collapses and severe damage to structural elements in buildings, churches, towers, mosques, domes, cathedrals, and vaults (Petromichelakis et al., 2014; Ramaglia et al., 2016; Roca et al., 2010; Viggiani, 2006). One can read more on finite-element modelling and analysis of various structures (Kaveh, 2014). The aftermath of earthquakes exposes deficiencies, including extensive openings in load-bearing walls, absence of vertical confining elements, subpar mortar quality, heavy balconies, and unconfined slanted walls (Akhaveissy & Milani, 2013; Betti et al., 2014; Indirli et al., 2000; Lourenço et al., 2013).

Thorough investigation, both documented and verbal, holds significance for understanding these structures architecturally and traditionally (Colapietro et al., 2013). Presently, many structures succumb to damage and collapse due to substantial cracks, material loss, continual deterioration, and various atmospheric factors (Anzani et al., 2010; Ceroni et al., 2012; Dolce et al., 2006; Dal Cin & Russo, 2016). Researchers have extensively examined old structures to uncover the materials used and their properties during construction.

The clock tower of the Senate Hall building has endured multiple seismic events, including the 1934 Bihar–Nepal earthquake and the 2015 Nepal–India earthquakes with magnitudes of 7.8 and 7.3, respectively. These earthquakes resulted in significant structural cracks, necessitating periodic repairs (Kumar N, personal communication). Noticeable extensive cracks are apparent on the first-floor level and at the junction where the tower meets the masonry wall of the building.

Historically, the emphasis in structural practices has primarily been on vertical loads, with limited analysis of lateral loads. Consequently, the original construction of these structures centred around vertical forces alone. As proposed by Bartoli et al. (2013), an accurate structural assessment should be grounded in an in-depth understanding of various factors: (i) the building’s historical evolution, (ii) its geometry, (iii) structural intricacies, (iv) patterns of cracks and material deterioration, (v) techniques and materials employed in masonry construction, (vi) mechanical properties, and (vii) overall behaviour (Valente & Milani, 2016).

The current research encompasses all the parameters above for examination. The impact of dead load and site-specific ground motion has been evaluated, incorporating seismic parameters pertinent to the region. The study employs a stochastic model to present a comprehensive analysis of the static and dynamic performance of the historical masonry clock tower, with certain limitations regarding material property assessment.

Mechanical properties have been factored in by retrospectively examining previous studies on ancient monuments. These properties have been selected from established codes, case studies, and structural assumptions corresponding to the periods in which the structures were erected. The study relies solely on the anticipated mechanical characteristics of the structural materials, namely brick masonry and stone.

Following an extensive survey of the 108-year-old clock tower, the second tallest masonry tower in Allahabad, standing at 30.48 m and situated on the premises of Allahabad University (see Fig. 1), the tower’s response to various loadings is assessed. The clock tower of Allahabad University is a notable example of construction by British engineers. The endeavour to safeguard such venerable architectural treasures underscores the importance of ensuring life safety during significant earthquakes. Vulnerability in structures often arises from material decay, alterations in structural configuration, and inadequate maintenance practices.

Fig. 1
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Clock tower view of the east entrance gate of the Senate Hall building

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About Allahabad University

Prayagraj (previously known as Allahabad), a well-known ancient city in India, stands at the confluence of three sacred rivers: the Ganga, Yamuna, and Saraswati. Throughout its history, Allahabad served as a capital during the Mughal era, and later, during British rule, the city experienced steady growth with the creation of various landmarks, including the Mayo Memorial Hall, All Cathedral Church, and Allahabad University and Library (Misra, 2016). These structures have evolved into significant historical monuments, some repurposed for different uses and others becoming prime tourist attractions.

The city has a collection of historical monuments built across different epochs, each holding a wealth of historical evidence from its respective era. In this context, the current study delves into the clock tower, a pivotal element of the Senate Hall building. The Senate Hall building, part of the Allahabad University, is a testament to the city’s history. With its inception on September 23, 1887, Allahabad University ranks as India’s fourth oldest university, trailing only behind Calcutta, Bombay, and Madras (Misra, 2016). The architectural style of public edifices in Allahabad reflects the “Indo-Saracenic” design, as exemplified by the Senate Hall building. The year 1909 marked the selection of the current site for the Library, Senate House, and Law colleges. These edifices, now housing the Registrar's Office, Senate Hall, and English Department, were conceived by “Sir Swinton Jacob,” receiving approval for construction in 1910. “Sir John Havett,” the Chancellor, laid the foundation stone of the Senate House on January 17, 1910. The project encompassing the Senate Hall, Law College, and former Library building commenced in 1910 and concluded in 1915.

The Senate Hall building is an expansive and capacious structure, facilitating various activities such as examinations, conferences, convocations, meetings, and cultural events. The ground floor hosts three major halls, each encompassed by a wide peripheral verandah. The central hall, particularly grand in scale, accommodates more than 600 individuals simultaneously (Misra, 2016).

Clock tower

The clock tower stands prominently at the building’s frontal (East) entrance gate. It distinguishes itself as one of the tallest towers within the Senate Hall complex, precluding the need for additional tower construction. The tower's design adheres to symmetrical construction techniques, featuring a rectangular cross-sectional geometrical view for each storey. Constructed primarily from unreinforced brick masonry elements, the tower’s composition incorporates substantial construction materials in walls, roofs, and dome elements. However, stone materials take precedence in the design of stairs and decorative facets of the tower.

Internally, the masonry construction is fortified with thick plaster materials, while the external aspect of the entire tower is coated with a red paint finish. The ground and first-floor levels are seamlessly connected through expansive verandahs. These verandahs, positioned on both sides of the tower, are equipped with generous openings that provide access to the building. Beyond the first-floor level, the junctions between masonry constructions (specifically the intersections of roof levels across floors and each corner formed by brick masonry) are adorned with stone chips and decorative stone elements, as illustrated in Fig. 1.

A wooden floor, supported by approximately 9-inch-thick sleepers, extends from the third-floor level to the dome access. These wooden sleepers are aligned longitudinally along the tower’s direction and are supported by the robust brick masonry walls. The design of the wooden stairs follows a cantilever pattern, firmly anchored to the masonry walls on one side while being supported by sloping wooden sleepers and iron clamps on the opposite side.

At the sixth-floor level, a circular clock is positioned on all four sides of the tower. This clock design seamlessly transitions into the base of the dome below it. The architectural configuration of the tower features a rectangular cross-section across its distinct floor levels. Notably, the clock tower at Allahabad University a height of 30.48 m and a nearly rectangular cross-section. The front side has a base width of 9.60 m, while the adjacent side spans 6.60 m, as illustrated in Fig. 2. The base quoin, rising to approximately 6.10 m, contributes to the tower’s overall aesthetic.

Fig. 2
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Visual inspection survey of clock tower

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The tower’s construction occurred during the latter part of the eighteenth century (1887–1910). Its foundation comprises rectangular masonry blunted bricks designed to accommodate a five-storey belfry. The external dimensions of the foundation are extended upward, measuring 1.07 m in height. The external wall thickness measures 1.22 m, while the internal wall width is 1.0 m at the ground floor level. Wall thickness gradually tapers from 1.22 m on the first floor to 0.61 m on the third floor.

The clock portion’s cross-section assumes an almost square shape, measuring 5.94 m by 6.40 m, culminating in a dome atop the tower. This dome boasts a height of 3.35 m and a radius of 3.04 m. Across all floor levels, openings have been thoughtfully incorporated in varying dimensions, encompassing both height and width considerations. The first-floor level is directly connected to the front verandah, serving as an entranceway to the building. Subsequent levels are exclusively designed, and a spiral-shaped cantilever staircase adheres to the masonry walls to facilitate movement within. The geometrical cross-sectional plan and elevation drawings have been accurately prepared through visual inspections of the tower’s structure and detailed drafting processes.

Cracks and damages

Following a comprehensive examination of the tower, a wealth of information about its structural design, construction methodologies, materials, and the presence of cracks and damages has been obtained. For evaluation, the assessment was restricted to the second-floor level due to the conspicuous presence of extensive cracks and material degradation on the structural elements. Notably, substantial cracks and plaster erosion observed on the masonry walls and tower connections have confined assessment beyond the current floor level. This measure is taken in the interest of public safety, leading to the closure of access to subsequent levels.

The visual inspection survey was conducted across the entire tower after the 2015 Nepal earthquake. The tower’s initial performance and structural mechanisms exhibited a favourable state on the ground floor level. However, a marked decline in condition was evident on the subsequent floor levels, manifesting as substantial losses in structural elements and materials. The tower’s architectural composition includes four expansive arches complemented by substantial columns and facade walls. While minor cracks were discernible on the facade walls and arch elements of the ground and first-floor levels, pronounced cracks manifested at the junctions of the roof and walls, as illustrated in Fig. 2b.

The degradation of construction materials has been a recurring issue, particularly at the connections between floors and within roof elements. Brick components have experienced erosion and diminished strength due to various atmospheric factors, particularly when coupled with plastered masonry walls. In contrast, load-bearing stone elements have displayed relatively better performance when devoid of plaster. Although minor, almost inconspicuous cracks have emerged on load-bearing stone features such as arches, columns, stone facades, and vaults, significant damage and failure are noticeable in the context of decorative structural elements and openings.

The survey underscores the compromised performance of structural components and construction materials, attributed mainly to prolonged atmospheric exposure. The tower has suffered substantial losses primarily due to the accumulation of rainwater, moisture, and temperature fluctuations. Prolonged moisture retention within materials and structural elements has instigated the deterioration of binding agents, contributing to significant degradation. Notably, an algae layer has become visible at the juncture between stone facades and brick masonry walls on the first floor. The persistent moisture environment has facilitated the growth of minor vegetation, including plants and grass.

The dome’s upper surface exhibits minor, scarcely perceptible cracks, while the original white colouration has substantially faded to black. It is imperative to recognise that these minor and seemingly negligible failures have the potential to amplify into substantial losses over time, warranting attention and remedial action.

Finite-element modelling

Finite-element modelling (FEM) serves as a powerful tool for highlighting both micro and macro-level structural aspects, catering to a wide array of analytical objectives (Camata et al., 2008; Milani et al., 2018; Peña et al., 2010). Following a thorough visual assessment of the tower, comprehensive insights were gained concerning geometric cross-sectional intricacies, structural craftsmanship, construction materials and methods, and patterns of cracks and damage (Casolo et al., 2012; Tiberti et al., 2016; Valente & Milani, 2016).

The geometric representation of the tower is derived from documentation and on-site surveys, presenting a symmetrical 3D depiction of the masonry tower about the longitudinal y-axis, as depicted in Fig. 3. The clock tower, in its entirety, is individually modelled using actual dimensions and an emphasis on geometric accuracy. The modelling process employs ANSYS Workbench 14.0 (SAS IP, 2005) and adopts a macro- and homogeneous modelling approach, incorporating load-bearing elements into consideration.

Fig. 3
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Finite-element model of the clock tower (SAS IP, 2005)

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The 3D model of the tower authentically incorporates true structural dimensions, meticulously representing mechanisms such as vaults, arches, columns, domes, and openings. However, smaller decorative elements are omitted during the modelling phase due to computational considerations. The dome, for instance, is fashioned using a revolved arch featuring a crown height of 3.35 m and a radius of roughly 3.0 m. Masonry block behaviour is governed by the von-Mises criterion.

The 3D mesh configuration comprises an impressive 654,366 nodes and 385,465 SOLID187 elements. A mesh size of 100 mm is employed, with an edge length of approximately 32.92 mm. The meshing technique, implemented as an active assembly mechanism, yields accurate responses during analysis. Notably, SOLID187 is employed as a higher-order 3D element, precisely a 10-Noded tetrahedral solid element, with three degrees of freedom at each node, accounting for translations in the x, y, and z directions (SAS IP, 2005).

The base of the finite-element mesh is subject to fixed boundary conditions. The meshing size of 100 mm is utilised throughout the clock tower to capture the authentic behaviour of the overall structure and its varying structural components across different floor levels. A refined mesh approach is implemented in areas of particular stress concentration, such as load-bearing masonry walls, stone columns, arches, and openings. This is especially crucial given the evident deterioration of structural elements and construction materials observed during the visual inspection survey. Consequently, fine meshing with minimal tolerance is employed for arches and opening elements to accurately capture their connection to robust load-bearing structural components.

Historical structures stand as global testaments to significant periods in history, culture, and architectural perspectives. These worldwide monuments comprise various materials available during their respective eras. Presently, these structures hold immense significance. While extensive research has been conducted on ancient structures, comprehensive evaluations of the mechanical properties of aged materials have been lacking. Previous studies have relied on approximated mechanical properties derived from non-destructive and minimally destructive testing. These properties have been employed to assess the performance of historic monumental structures from the same era.

In historical construction practices, many materials were utilised for construction, binding, ornamentation, plastering, and painting. However, the present study narrows its focus to brick masonry and stone, as these materials are prominently visible from 1890 to 1920 constructions and play pivotal roles in the load transfer mechanism. In the current investigation, mechanical properties were determined through an exhaustive survey of historical monumental structures dating from the same periods. The mass density values for lime mortar and masonry brick fall within the range of 1600–1840 kg/m3 and 1920 kg/m3, respectively, as specified in the Indian Standard IS: 875 (Part-1) (IS 875 Part-1 (1987)). These values, as presented in Table 1, were individually incorporated into the finite-element model of the clock tower. This approach facilitates obtaining both static and dynamic responses using established standard codes.

Table 1 Mechanical properties used to model the tower
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Static and dynamic analyses

Both static and dynamic analyses have been conducted on the masonry clock tower. The tower’s examination adheres to Indian code stipulations and considers approximate mechanical properties detailed in Table 1. For the static analysis, Gravity analysis following IS: 875–1987 (Part-1) was executed (IS 875 Part-1 (1987)). The analysis encompasses fixed (bonded) boundary conditions at the base (plinth) level. Junctions up to the second floor have been assigned restricted boundary conditions, combining fixed and hinged elements within walls, facades, panels, and roof components. Gravity load (self-weight) analysis involves restraining nodes at the base, illustrated in Fig. 4. Linear analysis employing the von-Mises stress mechanism is employed to ascertain stress distribution within the clock tower. Results of the numerical model under gravity load reveal a total deformation of 3.76 mm at the dome’s apex, as depicted in Fig. 5a. However, this numerical model’s deformation prediction falls notably short of actual structural behaviour, as it does not account for deformation occurring over the tower’s lifespan.

Fig. 4
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Stress and deformation response during dead load of clock tower

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Fig. 5
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Stress and deformation response during wind load of clock tower

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The von-Mises equivalent stresses peak at 1.81 MPa at the joint of the clock tower’s first-floor level, as shown in Fig. 5b. Compressive stresses induced by self-weight and live load remain below the compressive strength of the masonry, as specified in IS: 1905–1987. Consequently, the clock tower’s masonry structural configuration demonstrates sufficient capacity to endure gravity loads. This analysis identifies critical and vulnerable points across the structural system and connections. The assessment of stresses contributes to evaluating the performance of stress distribution that might lead to severe structural crack damage.

Equivalent static analysis under horizontal (wind) loads

The foundational connections of the examined clock tower are assumed to be fixed. Wind pressure is exerted from the southwest direction onto the tower. The tower’s designated side for wind load application at varying heights aligns with the specifications of IS: 875 (Part-3) (‘IS 875 (Part-3): 2015’, 2015).

In addition, the bottom floor, situated at a height of 6.09 m, is excluded from wind load considerations due to its enclosure by surrounding structures, rendering it less susceptible to influence. The computation of wind load adheres to established standards, employing parameters outlined in wind codes. The calculation of wind load follows documented methods, where the design wind speed (\({V}_{z}\)) is determined following IS: 875 (Part-3) (‘IS 875 (Part-3): 2015’, 2015), utilising the subsequent equations:

$${V}_{z}= {V}_{b}\,{k}_{1}\,{k}_{2}\,{k}_{3}$$

\(p_{z} = 0.6 V_{z}^{2}\), where \(p_{z}\) is design wind pressure in N/m2.

In the direction of the applied wind load, as illustrated in Fig. 5a, the tower exhibits a displacement of 5.17 mm at its uppermost point. As anticipated, the stresses generated are more significant on the downwind side than the upwind side, manifesting as compressive forces. The maximum stress is concentrated at the base of the tower’s downwind side, measuring 1.51 MPa, while the minimum stress registers at 2.10 × 10–4 MPa, as depicted in Fig. 5b. Notably, the tower remains unburdened from forces originating in all directions until the first-floor level. Primarily, the influence of the wind is prominent on the tower’s eastern and western faces.

Modal (vibration) analysis

Modal analysis is a fundamental method to assess dynamic responses in historic structures. The masonry tower’s vibrational behaviour was determined using 3D modal analysis with the same conditions as dead load. Modal shapes, frequencies, and masses were obtained using the Block Lanczos Method (BLM). The modal analysis encompassed free and forced (wind-induced) vibrations, revealing Eigen frequencies, mode shapes, and effective masses as shown in Table 2. Wind load was considered for forced vibration analysis, following Indian codes, with wind pressure above 10 m in the east direction. Tower obstruction by adjacent structures led to wind influence from three sides. The tower’s first three modal frequencies were 1.732, 2.147, and 3.922 Hz for free vibration (Fig. 6). Forced vibration closely mirrored free vibration for the first three modes. The tower was constructed using full-bodied, unreinforced masonry techniques and exhibited stone exteriors on its lower and initial floors. They were surrounding edifices protected against the impact of winds.

Table 2 Natural frequency during free vibration
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Fig. 6
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First three free vibrational modal shapes and natural frequencies response of clock tower

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Table 3 displays mass participation in the X and Z directions, accounting for approximately 55% of total mass across the initial two modes. Minor deviations in participation factor arise from slight configuration changes in these directions. The symmetry along the longitudinal axis underpins comparable free vibration behaviour in the X and Z directions.

Table 3 Effective % mass participation factor of free vibration
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Dynamic time history analysis using synthetic site-specific acceleration

Dynamic time history analysis is crucial for assessing seismic response in historical monuments. Pushover analysis, time history analysis, and kinematic analysis employing linear and nonlinear material behaviour have been employed in various studies (Acito et al., 2014; Betti & Vignoli, 2011; D’Ambrisi et al., 2012; Valente & Milani, 2016). One can use to optimise these structures by employing methods given by Kaveh (Kaveh, 2006, 2013). Monumental structures rely on a combination of elements (walls, arches, vaults, domes) and materials (bricks, stone, iron, and timber) designed with spacious and robust construction techniques. Seismic activity, driven by tectonic plate movements, induces short- and long-duration responses. Although short-duration events are manageable due to structural bonding and stiffness, extended events cause significant deformities and damage. Previous researchers conducted post-earthquake diagnostic investigations, seismic vulnerability analyses, and seismic capacity evaluations using finite-element modelling (Bilgin & Korini, 2012; Casolo et al., 2013; Saisi & Gentile, 2015; Tiberti et al., 2016) and identifying critical weak points through crack and damage assessments guides necessary strengthening and retrofitting efforts for heritage preservation.

Utilising seismic guidelines (revised code IS:1893–2016) (IS 1893 (part 1), 2002), dynamic time history analysis was conducted on the masonry clock tower. Acceleration ground motion response was applied in the longitudinal (X-direction) at the tower’s base. The tower’s boundary condition was fixed (bonded) at the plinth level, encompassing connections to walls, roofs, and facades. The response was generated from past seismic events on the ground floor. Synthetic ground motion, derived from unavailable strong motion data for Allahabad city, was synthesised using Boore’s stochastic method (1983) (Boore, 1983). The amplitude spectrum for the target ground motion was determined based on magnitude, distance, and duration properties, as Motazedian and Atkinson (2005) outlined (Motazedian & Atkinson, 2005):

$$A_{j} \left( {r,f} \right) = \frac{{R_{\theta \phi } \cdot F \cdot V}}{{4\pi \rho v_{s}^{3} }} \cdot \left( {2\pi f} \right)^{2} \cdot \frac{{M_{0ij} }}{{\left[ {1 + \left( {\frac{f}{{f_{0ij} }}} \right)^{2} } \right]}} \cdot G \cdot e^{{\frac{{ - \pi fr_{eff} }}{{v_{s} Q\left( f \right)}}}} e^{ - \pi kf}$$
(1)

Applying this factor is necessary due to the specific stress drop conditions Wells and Coppersmith (1994) considered (Wells & Coppersmith, 1994), which may not align with the study context. Kayal (2008) assigns a stress drop range of 50–200 bars for the IGP region (Kayal, 2008), with a reference stress of 100 bars. The time history produced from the Allahabad fault is depicted in (Fig. 7), exhibiting a PGA of 1.29 m/s2. The clock tower model’s dynamic response, including infills, corresponds to a specified time history compatible with the IS code spectrum for 5% damping (IS 1893 (part 1), 2002).

Fig. 7
figure 7

Ground motion acceleration 1.29 m/s2 of Allahabad city

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Acceleration responses for each floor level are depicted in Fig. 8. Notably, the clock tower’s acceleration de-amplifies across all levels, from the first floor to the top dome. The first floor and dome elements exhibit acceleration responses of \({1}.{95} \times 10^{ - 4} {\raise0.7ex\hbox{${\text{m}}$} \!\mathord{\left/ {\vphantom {{\text{m}} {{\text{s}}^{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{s}}^{2} }$}}\) and \({1}.{98} \times 10^{ - 3} {\raise0.7ex\hbox{${\text{m}}$} \!\mathord{\left/ {\vphantom {{\text{m}} {{\text{s}}^{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{s}}^{2} }$}}\), respectively. These responses align with critical stress locations identified in static analysis. The tower performs superior on the ground and first floors, attributed to consistent thick construction techniques, structural symmetry, mass distribution, and integrity.

Fig. 8
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Acceleration response

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As illustrated in Fig. 9, the clock tower exhibits negligible deformation and velocity responses. The tower manifests symmetrical responses throughout its entire floor levels through dynamic analyses. Significantly heightened responses are notable at the connection between the tower and the façade wall on the first floor and at the dome element’s apex. Minor deformation responses are evident at ground and first-floor levels within the masonry construction. However, responses escalate on the subsequent floor due to decreased wall thickness; symmetrically constructed sections from the third to fifth-floor exhibit consistent deformation responses.

Fig. 9
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Deformation and velocity response at critical locations of the clock tower

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Deformation remains marginal at the top of the dome (0.0035 mm) and first floor (0.00038 mm), as depicted in Fig. 9a. The tower’s ground and first-floor sections, connected to the Senate Hall building, exhibit satisfactory conditions owing to the robust wall, arch, and vault integrity. Nonetheless, connections and binding materials have suffered considerable degradation and losses from cracks. Figure 9b reveals a velocity response mirroring the minor deformation response in similar locations.

The stress distribution is evident across each floor level of the tower’s height, with critical zones identified during visual scrutiny due to notable cracks and damages. Immediate stress responses are notable at connections and on un-plastered walls (as shown in Fig. 10). Stress concentrations are at 2.47 × 10–4 MPa and 3.86 × 10–4 MPa on the tower’s first and second floors, respectively. At the same time, the dome element displays minimal stress. Corresponding major stress concentrations align with locations of prominent cracks and damages on construction and decorative elements. Minor stress reactions appear in brick masonry and stone elements at openings and arch crown positions. These responses reveal enhanced bonding behaviour among connections and binding materials within structural mechanisms, particularly at ground and first-floor levels. This region is inherently stable, facilitated by numerous strategically placed openings that effectively transfer substantial loads via arches and walls.

Fig. 10
figure 10

Stress response of clock tower

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Despite comprehensive construction efforts, certain sections exhibit cracks and material deterioration, necessitating the identification of critical vulnerabilities for requisite maintenance. Connections between the roof and walls exhibit minor cracks and degradation of binding material. Consistently, this analysis reaffirms stress response prevalence in locations congruent with those identified visually. Ultimately, strategic maintenance interventions are imperative to preserve the tower’s integrity, focussing on fortifying weak areas and addressing degradation concerns.

Conclusions

This research has comprehensively examined the ageing unreinforced masonry clock tower situated at the forefront of the Senate Hall building. The tower’s construction relies on a substantial brick masonry technique, accurately executed on each floor level, with internal plastered walls and a distinctive red exterior paint finish. Through thorough visual scrutiny, an intricate understanding of the tower’s condition has been established, revealing minor and inconsequential cracks on the ground floor masonry walls and various connections between walls and to the façade and roof.

However, the examination unveiled a more concerning scenario as one ascends. Notably, the second-floor level showcases severe cracks along exterior masonry walls, particularly at the interface between the stairs and peripheral walls. Deeper structural concerns are evident through severe damages in the masonry walls, roofs, and dome elements, encompassing connections and structural mechanisms up to the second floor. The static weight analysis revealed a significant revelation, highlighting a maximum stress of 1.81 MPa at the connections and a maximum deformation of 3.76 mm on the dome element.

The clock tower’s dynamic behaviour was effectively evaluated through modal response assessments. This dynamic analysis reflected responses that remained consistent and symmetrical from the ground floor to the dome, reflecting the tower’s robust masonry wall construction. Furthermore, the response metrics—encompassing acceleration, deformation, and velocity—showcased a progressive value increase as height escalated. Remarkably, stress responses remained minimal across each floor level, attributed to the tower’s durable, thick construction technique consistently upheld throughout its entirety.

Present findings underscore that the clock tower has displayed commendable resilience on the ground and first-floor levels due to its substantial construction materials and skilled craftsmanship. However, these strengths are counterbalanced by numerous structural elements and connections necessitating retrofitting and meticulous maintenance. This imperative is especially evident for walls with and without plaster, the roof, and the dome, all of which demand attention to stave off unchecked deterioration of construction materials. Notably, instances emerged where elements demanded complete renewal with new materials, owing to the degradation caused by moisture and the manifestation of substantial cracks.

The study has unveiled a nuanced perspective on the unreinforced masonry clock tower’s structural integrity. While it has demonstrated commendable stability on certain levels, there is an imminent requirement for substantial interventions to ensure its longevity and safeguard its historic significance. Through targeted retrofitting, meticulous maintenance, and the judicious incorporation of modern materials and techniques, the clock tower can stand as a testament to its historical legacy and capacity to endure into the future.