Earthquake Analysis of an Old RC Minaret Retrofitting with Shape Memory Alloy

Abstract

Existing seismic vulnerability has become a topical of actuality, concerning both new and old buildings. Several techniques have been used to allow structures to better resist seismic events. In recent years, these have been so-called intelligent materials such as shape memory alloys (SMAs) due to their superelasticity and their ease in returning to their initial state after deformation, which can reach 10%. In the present article, nickel–titanium SMA is considered in a minaret of an old church transformed into a mosque to control the seismic response in terms of displacements, stresses and accelerations. The assessment of the seismic behavior was performed based on a modal and then transient analysis with Ansys software. The main objective was to determine the effectiveness of the addition of shape memory alloys by varying their number.

1. Introduction

Earthquakes are one of the natural disasters that cause the most damage in the world in human and material terms, such as the recent earthquake that hit Turkey and Syria with a magnitude of 7.8 and caused the deaths of 44,218 people in Turkey and 5914 in Syria [1]. With seismic tremors below 3 almost daily, Algeria has not escaped this kind of calamity. Indeed, all of the northern part located on the African and Eurasian plate is very vulnerable to earthquakes; some have exceeded magnitude 6.5 on the Richter scale. Algeria has experienced several violent earthquakes in recent years, some of which were very devastating, such as the El Asnam earthquake of 1980 (Ms = 7.3 and intensity MMI = X), which caused more than 3000 deaths, 8369 injuries, 20,000 buildings destroyed and more than 480,000 homeless, and Boumerdes in 2003 (Ms = 6.8; MMI = X) with a balance sheet of 2287 deaths, 1000 injured, 19,000 buildings destroyed and more than 100,000 made homeless. The recording of the Boumerdes earthquake is used in the simulation of the seismic behavior of the minaret of the mosque, which is the objective of our work [2,3]. It is necessary to continuously monitor the health of buildings in order to detect damage or to locate areas that need to be rehabilitated. Sometimes we use more sophisticated means such as sensors [4]. Rehabilitation of old buildings is becoming an important part of civil engineering and will minimize the negative effects of earthquakes by saving human lives and their property; this rehabilitation will increase the longevity of buildings and reduce collapses. In addition to the safety of people, we will gain an economic benefit that will be more advantageous. Several parameters for rehabilitation exist, based on the strength-improving type, the ductility-improving type, and the seismic dissipation/isolation type. Steel frame sub-structures and external frame-brace substructures [5] are employed. The intelligent materials developed at the beginning of the 1980s concern all sectors of activity. These intelligent materials are sensitive, adaptive and evolutionary. They have functions that allow them to behave like a sensor (to detect signals) or like an actuator by interacting with their environment, and sometimes like a processor treating and storing information. This rehabilitation starts with the control of the health of the structures. During recent years, the use of intelligent materials has become more and more widespread and touches even developing countries. For example, piezoelectric sensors, when they are subjected to electric field, deform, as well as inducing the opposite effect: when they deform, they generate an elastic field [6,7]. Many types of passive control exist. A comparison was made between steel restraints and SMA devices with metal dampers and viscoelastic dampers in a bridge. The period ratios of the two frameworks to the ratio of the ductility of the framework were different. Their objective was the determination of their effect on the joint-opening response. The results demonstrated that steel restraining devices are the least effective at limiting the opening of the seam on bridges, in contrast to SMA devices, which are very efficient in moderate and very high ratios [8]. The other variant of smart materials are the SMAs which can be associated with an insulator, generally formed by inclined bars, to dissipate the energy during the movement [9]. A probabilistic method about seismic hazard and fragility, PDEM (probability density evolution method), integrates into performance-based earthquake engineering the statistical information about PGAs that are introduced with different earthquakes [10].

The engineering is developing more and more, adapting to new technologies by using materials created from other materials such as alloys. Among the latest technologies are the shape memory alloys (SMAs), which are part of the range of intelligent materials. They offer the possibility of working in non-linearity and dissipating a large amount of energy due to their thermomechanical properties, high ductility and good corrosion resistance. SMAs are based on iron [11], copper [12] or nickel [13]. SMAs have the functionality to return to their original shape after unloading or heating. SMAs have been used in several fields, such as biomedicine, aeronautics and civil engineering. Thanks to the development of computational resources, modeling based on the finite element method has become more accessible and allows for testing solutions to assess their eventual benefits to the structural behavior. Considerable progress has been made in civil engineering using SMAs in recent structures or in rehabilitation such as the San Francisco de Asis Church in Italy [14]. Also worth mentioning is the use of SMAs in stability pucks [15], column–beam joints [16] and bridges [17]. They are also found in masonry walls subjected to out-of-plane loading [18]. SMAs have also been used in historical monuments [19] or in old buildings that may have experienced several earthquakes. The mosque of El-Badr, the subject of our work, has also suffered several earthquakes, including that of May 2014.

In this research, the behavior of an old minaret is investigated before and after being retrofitted using SMA dampers and Ni–Ti alloys. The effectiveness of such a technique is evaluated on the basis of the action of the recent Algerian earthquake, the earthquake of Boumerdes of 21 May 2003 of intensity X and magnitude 6.8, which caused 2278 victims, 11,450 injured and 182,000 inhabitants who lost their houses [20,21].

2. Shape Memory Alloys Overview

In the 1930s, several physicists, such as Cheng and Read, noticed that when a material is deformed out of its elastic shape, it returns to its initial shape. In 1960, other scientists such as Buchlert Wiley (US Naval Ordnance Laboratory) discovered the effect of shape memory on a Ni–Ti alloy called Nitonol, and it was only in the 1960s that SMAs became of interest in research and found commercial potential [22].

2.1. Superelastic Effect

This effect is observed when a force is applied to an SMA which is at the beginning of its austenitic state and whose temperature is (T > AF). It undergoes an elastic transformation when the maximum stress of the beginning of the transformation is reached (${\mathsf{\sigma }\mathrm{M}\mathrm{S}}^{}).$ The orientation of the martensite formed indicates deformation that reaches 6% for Ni–Ti, and reaches ${\mathsf{\sigma }\mathrm{M}\mathrm{f}}^{}$ after unloading the alloy returns it to its initial position, presenting a 100% austenite phase [23].

2.2. Shape Memory Effect

We apply to an SMA, at a temperature T < Mf, constraint, and when it attains its austenitic state, the martensite starts to orient itself, arriving at the end of the direction beyond the elasticity deformation of the martensite. After liberation, there is a deformation. The alloy is heated to a temperature T > Af; the point E is the direct transformation (austenite martensite). The alloy is allowed to cool, with the result of attached martensite [23].

We examined other effects of SMAs; however, in this research, the superelastic effect is used, as in the retrofitting of an old church in Italy [24].

2.3. Mechanical Proprieties of Shape Memory Alloy

Certain mechanical properties of the SMA must be discussed ahead of the potentials and efficacy of SMA.

Within earthquake retrofit applications, strain effect and temperature effect can be assessed as cyclical properties, wherein a Ni–Ti alloys in its austenite phase is subjected to cyclic loads. A number of reservations could be made. For starters, repeated cyclical loading causes gradual increases in residual strains. Another finding is that as cyclical loading increases, forward transformation stress decreases. This is also due to microstructural slips, which prevent the formation of stress-induced martensite upon further cycling. The martensitic forward transformation stress is reduced as a result. Larger amounts of cold working, annealing at lower temperatures, cycling under lower stresses, and cycling at faster rates could enhance the degradation of the cyclical properties of the SMAs, known as fatigue. Several studies have been conducted to investigate the effects of prestressing SMA wires prior to cycling. Several studies have shown that SMA wires must be pretensioned to half of their maximum strain and cycled around the prestrained value for efficient energy dissipation [23].

2.4. Strain Rate Effect

Several studies have been conducted to investigate the effects of prestressing SMA wires prior to cycling. Several studies have shown that SMA wires must be pretensioned to half of their maximum strain and cycled around the prestrained value for efficient energy dissipation. The research described in [23] used the same reasoning.

2.5. Temperature Effect

When predicting the behavior of shape memory alloys, temperature is most likely the single most important factor. Shape memory is a thermoelastic process, which means that a decrease in temperature equals an increase in stress. As a result, as temperature decreases, stress increases, requiring a lower stress value to induce transformation. A low-temperature specimen will exhibit the shape memory effect, whereas a high-temperature specimen may exhibit the superelastic effect. If the operating temperature of SMAs is not known within a reasonable bound, this can cause significant design issues [23].

2.6. Shape Memory Alloy Application as Connection

SMA bolts, SMA Belleville washer springs, and SMA ring springs were all considered as kernel elements for these connections. The use of multiple types of SMA elements was also attempted. The influence of the slab system on the behavior of self-centering connections is discussed, with the issue of frame expansion being raised and addressed in particular.

The available experimental studies on these novel connections are represented, allowing for a thorough understanding of their key performance characteristics, such as moment–rotation response, ductility, self-centering capability, energy dissipation and possible failure modes. Beam-to-column connections, abbreviated as connections, play an important role in ensuring structural safety against seismic hazards. These could include hybrid connections with washers and bolts as well as SMA ring springs [24].

3. Presentation of the Case Study

The El-Badr Mosque is a former church previously named Church of St. John the Baptist located in downtown Mostaganem in Algeria. The Church of St. John the Baptist was built in 1839 and restored in 1953, and was transformed into a mosque after the modification of the bell tower into a minaret (Figure 1). It received the name of El-Badr Mosque in the 1970s.

The minaret has a total height of 30.2 m (see Figure 2) and is composed of a rectangular part with a height of 4 m and a door, above which is a polygonal tower with eight sides, with a maximum width of 3.4 m and a height of 20.2 m, and another tower with a height of 4 m. The whole structure has 24 windows. Figure 3 shows the cross section of the minaret.

The minaret is constructed of reinforced concrete. The mechanical and physical properties are described as follows (

Table 1. Mechanical proprieties of the RC minaret.

Young’s Module (MPa)	Volume Weight (kN/m3)	Poisson Ratio	Compressive Strength (MPa)
13.000	23	0.2	25

). The determination of the physical and mechanical properties of the reinforced concrete of our minaret is based on the results obtained from the work of a research team at the University of Mostaganem, wherein they carried out the ambient vibration test on said minaret. The fundamental period of the minaret is estimated at 0.338 s. After several attempts to calibrate the digital model, we found the following characteristics.

4. Numerical Model of the Minaret

The choice of Ansys Apdl was made because it provides the possibility to integrate SMAs by introducing their thermomechanical proprieties. The SMAs were fixed between their two sides with a metallic belt. To model the following elements, solid 45 was used for the structure in reinforced concrete and solid 185 for the SMA and the metallic belt. The SMA could be modeled with plane or solid element (PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, and SOLSH190), available in Ansys software [25]. Thus, the 3-D eight-node structural solid element SOLID185 with a height of 4 m at point A is shown in Figure 4.

The method used to mesh was a tet shape with a free mesh in volume. The command “vmesh” was used for the reinforced concrete part and the SMA.

In a first phase, we considered the modal obtained by the finite element method in order to find the frequencies and modes shapes of the structure under study. Then, a transient analysis was developed to calculate the seismic response of the structure in terms of stresses, displacements and accelerations. Two points of study were chosen on the minaret. Point A, which represents a strong concentration of stress, is located at a height of 4 m. Point B is located the top of the structure at 30.2 m, the place of maximum displacements (Figure 5).

Modal Analysis

The modal analysis was established by Ansys software, and the results are described in

Table 2. List of periods and frequencies without SMA.

Mode	Frequency (Hz)	Period (s)	Mode Type
1	3.019	0.331	Translation x
2	3.049	0.327	Translation y
3	16.698	0.059	Translation x
4	16.919	0.059	Translation y
5	21.293	0.046	Torsion
6	24.529	0.040	Translation z
7	29.517	0.033	Translation x
8	29.851	0.0219	Translation y

and in Figure 6. The different modes with their frequencies and the directions of their displacement are represented. Modes 5 and 6 correspond to torsion and translation along z; modes 1, 3, 7 and 2, 4, 8 correspond respectively to translation along x and y. The fundamental period is 0.331 s.

Table 3. List of periods with SMA.

Mode	Period Without SMA (s)	Period 4 SMA (s)	Period 6 SMA (s)
1	0.331	0.348	0.348
2	0.327	0.33	0.338
3	0.059	0.326	0.336
4	0.059	0.315	0.315
5	0.046	0.305	0.305
6	0.040	0.283	0.283
7	0.033	0.283	0.268
8	0.0219	0.243	0.243

shows that there was a very small variation in the period between the virgin state of the structure and the state with 4 and 6 SMAs in fundamental mode shapes. Additionally, the period increased in the other modes.

5. Minaret Transient Analysis

5.1. Without SMA

In order to see the response of the minaret during an earthquake without taking into account the SMA, we made a transient analysis, which is non-linear because of the behavior of the SMA. We used the earthquake at Boumerdes, which occurred in Algeria in the city of Boumerdes on 21 May 2003, and which was the most violent since the earthquake of El Asnam in 1980. The accelerogram of this earthquake is provided by the Center for Applied Research in Earthquake Engineering (CGS) in Algiers, as shown in the following figure (Figure 7).

There is still no reliable way to predict the seismicity of a region in advance. The search for precursors has not evolved, but it is possible to record historical seismic information thanks to instrumental data that started about a century ago; one can thus calculate the probability that the intensity reaches or exceeds a certain threshold. However, the number of earthquakes with high intensity is quite limited for statistical analysis. The calculation of a PGA (peak ground acceleration) of PGA = 0.58 g [26] for the earthquake of Boumerdes was determined from the values of the horizontal behavior of the ground movement, and in general, it is considered for two defined periods, which are T = 475 years, P = 10% (DBE) and T = 2475 years, P = 2% (MCE) for t = 50 years; these quantities are related by the following formula from the fish law:

$$T=\frac{t}{\log (1-P)}$$

(1)

P: the probability that the event will occur; t: exposure time; T: mean return period.

For the calculation of the MCE (maximum considered earthquake): MCE = 3.81 +1. 920log L = 6.77 [27].

With L = length of the fault of Thénia/Boumerdes; L = 35 km.

DBE = (2MCE)/3 = 4.51.

The seismic response of the minaret is schematized by the following curves (Figure 8 and Figure 9), representative of the displacement stresses and accelerations at points A and B.

Table 4. Maximum seismic response at points A and B without SMA.

Position	Sizes	Value
Point A	Uxmax (cm)	0.19907
	Axmax (m/s²)	0.3531
	σxmax (MPa)	4.0814
Point B	Uxmax (cm)	17.1712
	Axmax (m/s²)	23.4494
	σxmax (MPa)	0.00418

gives the maximum values of displacement (Ux_,max), stress (σ_x,max) and acceleration (a_x,max) of the structure. It can be seen that at point A the stress is higher, and the displacement is lower; however, at point B the opposite is observed.

5.2. With SMA

In this part, we describe how our minaret was equipped with SMA. A polygonal metal belt (Figure 10) fixed the alloy to the concrete structure. An innovative solution suggests exploiting the special features of the SMA’s superelastic behavior under dynamic excitation. Prestressed SMA wires or trusses can be installed between the brick components, with the effects of limiting the vibration-induced relative displacements and, at the same time, allowing for energy dissipation [2]. 4 SMA was fixed at a height of 4 m at the bottom of the polygonal part of the minaret in a first case. In a second, 6 SMA was fixed at the same position. In a last test, 6 SMA was used with a different repartition: 4 SMA was fixed at height of 4 m and two others at a height of 24.2 m. Nickel–titanium SMA was used. The alloys had a length of 1.20 m and a diameter of 40 mm.

The physical and mechanical characteristics of the nickel–titanium SMA considered in our study are presented in

Table 5. Mechanical properties of the SMA.

Property	Value	Units
Nitinol
Density	6450	kg/m3
Young’s modulus	90,000	MPa
Poisson’s ratio	0.3
Tensile yield strength	1000	MPa
Tensile ultimate strength	1400	MPa
Superelasticity
Sigma SAS	520	MPa
Sigma FAS	600	MPa
Sigma SSA	300	MPa
Sigma FSA	200	MPa
Epsilon	0.063	mm−1
A	0.09

and are based on the physical and mechanical properties of the Ni–Ti SMA used [3]. The behavior model is illustrated in a diagram of stress versus strain in Figure 11 and Table 5.

The values of the loading and unloading constraints in the initial state ${(\mathsf{\sigma }\mathbf{s}}^{\mathit{A}\mathit{S}}$,${\mathsf{\sigma }\mathbf{S}}^{\mathit{S}\mathit{A}}$) relative to the final value (${\mathsf{\sigma }\mathbf{F}}^{\mathit{A}\mathit{S}},{\mathsf{\sigma }\mathbf{F}}^{\mathit{S}\mathit{A}}$) are represented; also observe the maximum residual deformation (εL) and the material compatibility parameter in tension and compression (α) as well as the mechanical characteristics of the SMA.

The seismic response is compared without and with SMA (4 SMA and 6 SMA). The SMA was installed at a 4 m height from the base.

Table 6. Maximum seismic response at points A and B for 4, 6 and without SMA.

Position	Sizes	Without SMA (1)	4 SMA (2)	6 SMA (3)	Difference (1 and 2)	Difference (1 and 3)	Difference (2 and 3)
Point A	Uxmax (cm)	0.19907	0.19936	0.20134	−0.00029	−0.00227	−0.0019
	Axmax (m/s²)	0.3531	0.2530	0.250016	0.1001	0.103084	0..0029
	σxmax (MPa)	4.0814	2.5152	2.1836	1.5662	1.8978	0.3316
Point B	Uxmax (cm)	17.1712	17.1431	18.2512	+0.0281	−1.08	−1.1081
	Axmax (m/s²)	23.4494	23.2067	25.922	0.2427	−2.4726	−2.7153
	σxmax (MPa)	0.00418	0.00425	0.004316	0	−0.00013	0

shows the relative differences between the results of the case of the model without alloys and that with 4 SMA, and between the case without alloys and that with 6 SMA.

The different curves show the variation of the above-mentioned quantities as a function of time.

The results show a decrease in stress for 4 SMA at points A and B compared to the structure without alloy (Figure 12 and Figure 13). This shows that the structure is less stressed, less prone to collapse; for 6 SMA the results are quite similar (Figure 14 and Figure 15), except the decrease in stress at point A and the increase in displacement and acceleration at point B are probably due to the non-linearity of the material. The table also shows that beyond 4 SMA the variations in the quantities are very small.

Table 7. Maximum seismic response at point A and B for 4, 4 + 2 SMA.

Position	Sizes	4 SMA	4 + 2 SMA	Difference
Point A	Uxmax (cm)	0.19936	0.19957	−0.00021
	Axmax (m/s²)	0.2530	0.2642	−0.0112
	σxmax (MPa)	2.5152	2.1884	0.3268
Point B	Uxmax (cm)	17.1431	17.1901	−0.047
	Axmax (m/s²)	23.2067	25.437	−2.2303
	σxmax (MPa)		0.003591	0.00066

presents the results of the arrangement of the 4 SMA at a height of 4 m as before, and with the addition of 2 SMA at a height of 24.2 m (4 + 2 SMA).

We noticed a very small difference between the magnitudes at points A and B. This shows us that the use of a larger number of SMA does not attenuate the seismic response.

In a last case, 4 SMA was placed at a height of 24 m and the result was compared with 4 SMA at a height of 4 m (

Table 8. Maximum seismic response at points A and B for 4 SMA at two different positions.

Position	Sizes	4 SMA (4M)	4 SMA (24 M)	Difference
Point A	Uxmax (cm)	0.19936	0.1878	0.01156
	Axmax (m/s²)	0.2530	0.284	−0.031
	σxmax (MPa)	2.5152	2.148	0.3672
Point B	Uxmax (cm)	17.1431	13.034	4.109
	Axmax (m/s²)	23.2067	20.611	−2.595
	σxmax (MPa)	0.00425	0.00323	0.00102

).

The results show that the use of the SMA at the height of 24 m is very effective and shows the best attenuation of the stress and displacement at point A, and also B; this demonstrates that this variant is more efficient.

6. Conclusions

Due to their mechanical properties, SMAs are increasingly used in the field of earthquake engineering. The application of nickel–titanium wire on the minaret of the El-Badr Mosque, thanks to Ansys Apdl software, has demonstrated the interest of these alloys. We have subjected our structure to a seismic excitation represented by the real record of the earthquake of Boumerdes in 2003, and compared the seismic response of the minaret in terms of stresses, displacements, and accelerations in its virgin state (without alloy) and with 4 and 6 alloys of the Ni–Ti type arranged in different ways. The results show that the use of 4 SMA resulted in a significant reduction in stress at point A, whereas at point B the decline was smaller. A small variation in displacements and accelerations was observed. A higher number of SMA was also considered; 6 SMA was placed at a height of 4 m and 2 SMA placed at a height of 24 m with 4 SMA at a height of 4 m. The results show that adding more SMA to the 4 initially considered does not show a natural variation. In a final distribution, we set the 4 SMA at a height of 24 m. The findings reveal a large drop in stress and displacement at points A and B. In general, it appears that the SMAs considerably reduce the seismic response, especially in terms of stresses, when they are placed judiciously with a well-predetermined number. The choice of 4 SMA at a height of 24 m is appropriate.