Earthquake Response of a Historical Castle

ةصلاخ : ةقيقح ربتعي نامع ةنطلس يف لازلز عوقو رطخ نإ ، ةنس نيب تعقو ةيضرأ تازهل ريراقت ةدع كانه نأ ذإ 977 و م ةنـس 1998 م تاءاشنلإا ىلع رارضأ ثودح نود نكلو . ةيلازلز ةطراخ لمع ىلإ ةجاح كانه ل ع نم ىرخأ تانايب عمجو نام ةيلازلزلا ىوقلا دض تاءاشنلإا ميمصتل ةماع تافصاوم عـضو لـجأ . مييقت مت ةيملعلا ةقرولا هذه يفف رثأت ىدم ىوزن ةعلق ةيـخيراتلا ب لازلزلا ىوـق إب ينابملل ةماعلا تافصاوملا مدختس ) Uniform Building Code .( اذه نع تامولعملا بايغبو لزلا ةقطنملا لماع ةبسانم ميق ضارتفإب تمت ةزهلا نع جتانلا لعفلا در ةسارد نإف عقوملا لماعمو ةيلاز و تارثؤملا هذهل ريشت جئاتنلا اهيلإ انلصوت ىتلا ةيوقت لامعأ ضعب ءارجإ ىلإ ةجاحلا ىلإ ةعلقلل نكمتتل نم لزلازلا ةمواقم ةلمتحملا . ABSTRACT: The earthquake hazard potential in the Sultanate of Oman is considered real as there are several reports of felt earthquakes in the Sultanate of Oman during the period from years 977 to 1998, although no damage to the existing structures has been reported due to earthquakes. In Oman, seismic zoning map and other basic data are required for the development of a standard code for seismic design of structures. In this paper, seismic response of a historical Nizwa castle in Oman is assessed employing the methodology of Uniform Building Code (UBC, 1994). Also, in the absence of data pertaining to the seismic zone factor and the site coefficient, the seismic response study is carried out by assuming appropriate values of these parameters. The results of such investigation are presented in this paper. The results show that some retrofitting measures have to be undertaken in order that the existing historical building may survive in a possible damaging earthquake.

he assessment of earthquake hazard involves collecting and evaluating a wide range of data pertaining to the history and occurrence of earthquakes in a region and to their origin.There are several reports of felt earthquakes in the Sultanate of Oman (Figure 1) during the period from years 977 to 1998 (Table 1).Although Oman does experience earthquake ground motions from time to time, no structural damage has been reported due to earthquakes.The historical records, however, suggest a possibility of such damage during the Qalhat earthquake of 15 th century (Dickson, 1986).Some major events, however, that occurred at a great distance away in southern Iran, Pakistan or Yemen have been reported in Oman.For example, several individuals reported (Dickson, 1986) the effects of 27 November 1945 earthquake (M = 8.2) whose epicenter was just off the southeastern Iranian Makran Coast about 470 km from Muscat (in Oman).One witness reported damage, casualties, and a Tsunami surge.Also, 18th April 1983 earthquake event (M = 6.5) that occurred in Baluchistan was felt by some persons residing in multistory buildings in Muscat (590 km from place of earthquake occurrence) and was also felt in Buraimi (in Oman) at an even greater distance (Dickson, 1986).The Yemen earthquake (M = 5.7) of 13 th December 1982 was also felt by residents in Salalah region (Southern Oman) but not in Northern Oman (Dickson, 1986).Some faults were reported in the Batinah Coastal Plain in Northen Oman north to the Daymaniyat islands (Figure 2).Khaboura fault zone (Dickson, 1986) is located in south of Sohar about 80 km to the vicinity of Ras A'ssawadi along the coast (Figure 2).No systematic investigations concerning the seismic activity in Oman was undertaken before 1985.Earthquakes magnitudes recorded along the northeastern margin of the Arabian Plate have reached the most severe record magnitude of 8.2 (27 November 1945) (Dickson, 1986).The National Geophysical Data Center in Denver, Colorado (U.S.A) has some seismic data from about almost all regions of the world.It turns out from such seismic data that all the earthquakes that occurred in an area between 45.0º E to 65.0º E and 10.0º N to 30.0º N (Figure 3) show that a significant seismic activity is concentrated along the Zagrous fault zone in Iran.Also, it can be seen from Figure 3 that there are numerous epicenters along the Batinah Coastal Plain and offshore of Oman.Prior to 1980 very few earthquakes had been recorded in Oman mainly because of the lack of the local seismographic stations or sensitivity of the world seismic network or perhaps it was difficult to receive signals from events in the Oman area because of placement of seismic stations (Dickson, 1986).It is important to note that nearly all of the earthquakes after 1980 were reported by new stations in Norway, Sweden and England.The magnitude of these earthquakes ranges from 3.9 to 4.9 on modified Ritcher scale.Considerable efforts have already been made for assessing seismic hazard in the Sultanate of Oman and various other aspects of seismic monitoring in the Sultanate of Oman.Through these efforts, it turns out that several recent earth movements have occurred in Jabal Salak, Jabal Khubayb and Batinah coastal plains area (Dickson, 1986).An investigation has been undertaken to assess the response to seismic forces of an existing historical masonry structure (Nizwa castle) in the Sultanate of Oman.Seismic analysis of the existing building has been made employing the methodology of the Uniform Building Code (UBC), 1994.In the absence of data concerning the seismic zone factor and the site coefficient, the seismic response study is carried out selecting the appropriate basic data for the earthquake response computation.The results of such investigation are presented in this paper.

Methodology for Earthquake Response
The method for earthquake response determination presented in this section is based on the requirements of the UBC, 1994.The UBC is most extensively used in the U.S.A., particularly in the western part of that country.This building code is intended to provide guidelines, and formulas, which constitute minimum legal requirements for design and construction within a particular region.These requirements are intended to achieve satisfactory performance of the structure when subjected to earthquake ground motion.The safety of the structure is not assured in the event of a major earthquake.The objective of the code is that a minor or moderate earthquake will not damage the structure and that a major earthquake will not produce collapse of the structure.Whenever a building is subjected to an earthquake, its foundation will start to move randomly because of soil movement of the site under the building.Then, the whole building moves due to the movement of its foundation, which causes deformations in the building.The earthquake forces can be divided into three components: vertical and two horizontals.In the present investigation, the vertical component of the ground motion is ignored.Only horizontal earthquake motion is considered in two orthogonal directions, but considering one component at a time.

Building Idealization
Details of the Nizwa castle's structural system are reported elsewhere (Al-Shariqi, 1998).Load bearing masonry walls have been employed as a structural system in the castle.In view of this, the castle is idealized as a three-storied lumped-mass-stiffness shear building system.The earthquake response of the building is completely defined by the physical properties of its structural elements, such as its mass, stiffness, damping and load-displacement characteristics on one hand, and time varying accelerations introduced at its foundation support on the other hand.Thus, the evaluation of structural properties and the selection of earthquake input are the most critical factors in the earthquake response analysis.In the present investigation equivalent static approach of earthquake analysis of multistory structures is employed (UBC, 1994).

Equivalent Static Approach
This method is adopted in most of the building codes for moderately high buildings due to its simplicity and due to the fact that many structures designed on the basis of code coefficients have satisfactorily withstood past earthquakes.Static horizontal forces are applied based on the values of seismic coefficients to simulate the effects of the designed earthquake.The distribution of the shear forces along the height of the building is adopted to be similar to that obtained by dynamic analysis.Design forces specified by most codes are smaller than those indicated by dynamic elastic analysis.However, to design any building in accordance with UBC-94, many factors should be taken into account by which the building shall be designed and constructed to resist a minimum lateral seismic force applied statically and independently in the direction of each of the two main axes of the structure.The equivalent static method used in the present study is briefly described in the following paragraphs.
TOTAL BASE SHEAR FORCE: The total base shear force (V) of the structure is determined by using the relation (UBC, 1994): where, W is the seismic weight of the structure, Z, the seismic zone factor, I, the occupancy importance coefficient, R w , the structural factor and C (dynamic factor) = 1.25S/T 0.66 ≤ 2.75 in which S is the site coefficient, T is the fundamental period of the building and is equal to C t (h N 0.75 ) while h N is the total height of the building in feet.C t is the time coefficient factor which depends on the structural system of a structure to be analyzed.
DISTRIBUTION OF LATERAL FORCES: The lateral force (F x ) at a height level x above the base is determined as: where F t = 0 for T < 0.7 sec or F t = 0.07TV < 0.25 for T > 0.7 sec, N is the total number of stories above the base of the building, F x , F i , F N are the lateral forces applied at level x, i and N, F t is the portion of the base force (V) at the top of the structure in addition to F N, h x , h i are the heights of level x and i above the base of the building, W x , W i are the seismic weights of ith level.
STOREY SHEAR FORCE: The shear at ith storey (V x ) is calculated using the formula: DRIFT AND STOREY LATERAL DISPLACEMENT: Drift (∆ x ) and storey lateral displacement (δ x ) are computed employing ∆ x = V x / K x and δ x = Σ∆ x ,where, K x is the flexural stiffness for ith storey.The code stipulates that the storey drift should not exceed (0.04/R w ) times the storey height or 0.005 times the storey height.
NATURAL PERIOD OF THE BUILDING: The natural period of the building is determined using Rayleigh's method.
OVERTURNING MOMENT: The overturning moment at ith level (M x ) of the building is computed by the following equation: HORIZONTAL TORSIONAL MOMENT: Diaphragms are considered flexible when the maximum lateral deformation of the diaphragm is more than twice the average storey drift of the associated stories.The provisions (UBC-1994) have been made for the increased shear force resulting from horizontal torsion where diaphragms are flexible.The accidental torsional moment (T x ) is 0.05DV x , where D is the dimension of the building perpendicular to the direction under consideration.
P-DELTA (P-∆) EFFECT: The ratio (θ x ) of the secondary moment at ith storey (M xs ) resulting from P-∆ effect to the primary moment at ith storey (M xp ) is estimated by the following equation where M xs is the secondary moment at xth storey, M xp is the primary moment at xth storey, P x is the total weight at xth storey and above, H x is the height of xth storey.According to the provision of the code, when θ x at each storey level of the building is less than 0.10, there is no need to account for the P-∆ effect.
DIAPHRAGM DESIGN FORCE: The code requires that horizontal diaphragms (floors and roofs) be designed to resist the following force given by: in which W px is the weight of the diaphragm and attached parts of the building at the ith storey.The code states that F px need not exceed 0.75ZI W px , but it shall not be less than 0.35ZI W px .

Data for Seismic Response
In the absence of appropriate data for seismic response study, it is assumed that the Nizwa castle is located in a seismic zone equivalent to seismic zone 3 (UBC-94) and hence seismic zone factor Z = 0.3.Seismic zone 3 has been selected in view of the historical importance of the Nizwa castle.Further, the foundation soil of the castle is considered such that the site coefficient S = 1.2.The structural factor (R w ), the occupancy importance factor (I) and the time coefficient factor (C t ) are selected as 6.0, 1.0 and 0.02, respectively, in accordance with the appropriate building material and building system of the Nizwa castle.

Seismic Weight Determination
Seismic weight of the three storied Nizwa masonry castle has been determined employing its appropriate material and mechanical properties.Details of the seismic weight determination are reported elsewhere (Al-Shariqi, 1998).The results of the seismic weight computation of the masonry building are shown in Table 2.

Stiffness Determination of Shear Walls
Determination of the shear wall stiffness is reported in this section.A new methodology (Qamaruddin, 1999) has been employed in determining the wall stiffness.In this method, the wall is divided into three elements: namely pier, top spandrel and bottom spandrel.Then the three nondimensional parameters (pier aspect ratio, top and bottom spandrel aspect ratio) are evaluated for different walls.Employing the appropriate tables (Qamaruddin, 1999), the stiffness of the walls has been determined.In the present study, the stiffness of the walls parallel to transverse (T) and longitudinal (L) directions of the building has been computed separately.
This has been done in view of the assumption that the walls located parallel to the transverse direction of the building would resist any expected ground motion occurring parallel to the transverse direction of the structure.Similar is the condition for the walls located in the longitudinal direction of the building, for the expected earthquake motion in the longitudinal direction of the building.The results for the story-wise lumped stiffness of the shear walls located parallel to the transverse and longitudinal directions of the building are also tabulated in Table 2. Details of the stiffness determination of the shear walls are reported elsewhere (Al-Shariqi, 1998).

Seismic Response of the Castle
Earthquake response has been determined using the methodology of UBC-94 for the masonry building subjected to two orthogonal horizontal ground motions separately, taking them one at a time.The results of such response computation have been shown in Tables 3 to 7. * T-shear walls parallel to earthquake motion in transverse direction of the castle.+ L-shear walls parallel to earthquake motion in longitudinal direction of the castle.

Results and Discussions
The Nizwa castle is subjected to earthquake ground motion in two orthogonal directions, i.e., longitudinal and transverse separately.The discussion of the results thus obtained (Tables 3 to 7) is described in the following sub-sections.* Earthquake ground motion in transverse direction of the castle.+ Earthquake ground motion in longitudinal direction of the castle.

LATERAL FORCES COMPARISON:
The results from Table 3 show that the lateral forces developed in the structure subjected to ground shaking in the T-direction are about 13.5 % larger than the corresponding lateral forces values obtained for the ground motion in the L-direction in all the stories of the castle.
COMPARISON OF BASE SHEAR FORCES: It can be seen from Table 3 that the values of the shear forces in the respective stories of the structure subjected to ground motion in the T-direction are also about 13.5 % higher than the corresponding values obtained for the earthquake ground motion in the L-direction.4, it is seen that the values of the storey drift show different variation trends in the building as obtained by the static method.For example, the storey drift values obtained in stories 1 and 2 are respectively about 11% and 30% higher when the structure is subjected to the L-direction of the earthquake ground shaking in comparison with the corresponding values as obtained for T-direction of the ground motion.Unlike this trend, the storey drift value obtained in third floor is about 53% higher for the T-direction of the ground motion compared to the L-direction one.The above trend of storey drift variation may be attributed mainly to the variation of the storey stiffness (Table 2).

COMPARISON OF STOREY DRIFTS:
According to the UBC-94 code, the maximum permissible storey drift for the castle is determined as 0.020 m.From Table 4, it is established that the storey drifts determined in all the stories of the castle are less than the maximum permissible value of the storey drift.In view of this, the serviceability requirement of the historical castle is met VARIATION OF LATERAL DISPLACEMENTS: It can be observed from Table 4 that the storywise lateral displacements of the building under the L-direction of earthquake force are about 11% and 18% higher in the first and second stories respectively in comparison with the corresponding values obtained for the T-direction of the ground motion.In contrast to this observation, the lateral displacement of the third storey in the L-direction of earthquake motion is about 10.5% lower than that obtained for the T-direction.5, it is observed that the overturning moment in all the stories of the structure subjected to the T-direction of the ground shaking are about 13.5% larger than those obtained for the ground motion in the L-direction.This trend is true because the lateral forces developed in the structure under the T-direction of the ground motion are more than their corresponding values for the L-direction of the earthquake shaking.But, the torsional moment values in all the stories of the masonry castle are about 26.3% higher when the structure is subjected to the ground shaking in the L-direction in comparison with the response obtained for the Tdirection of the ground motion.
VARIATION OF SECONDARY MOMENTS: It is observed from Table 6 that there is a different trend in the story-wise development of the secondary moment.For example, the Table 6 shows greater values of the secondary moments in the first and second stories of the masonry castle subjected to the Tdirection of the ground motion than the corresponding values in the L-direction of the earthquake force.But, the secondary moment in third storey of the structure for the L-direction of earthquake is greater than the corresponding secondary moment in the T-direction.6 that the ratios (θ x ) of the secondary moment (M xs ) resulting from P-∆ effect to the primary moment (M xp ) in all the stories of the masonry castle are much less than 0.10.This statement is true for the castle subjected to the T-as well as L-directions of earthquake ground motion.Therefore, there is no need to account for P-∆ effect in the design of the castle because according to the provision of the UBC-94 code, θ x at each storey level of the building should be less than 0.10.
DIAPHRAGM FORCES VARIATION: Table 7 shows that the diaphragm forces developed in the roofing/flooring systems of the castle subject to ground shaking in the T-direction are higher than the corresponding values for the earthquake motion in the L-direction.It can also be seen from the table that the diaphragm forces developed in the third storey are more than the maximum diaphragm force permitted by the UBC-94 code.In view of this observation, it is established that the roofing system of the castle may fail in any future earthquake consistent with basic data considered in the seismic response determination of the Nizwa masonry castle.

Conclusions
Firstly, the seismic activity in the Sultanate of Oman has been studied through available literature.Then, the seismic response of the Nizwa castle subjected to the expected earthquake ground shaking has been determined.Based on the present study, the following conclusions can be drawn: 1.
Since the Sultanate of Oman is situated within the seismic belt, contrary to past belief, there is a possibility of occurrence of earthquakes, especially in Batinah Coastal plain.

2.
The earthquake response analysis of the three storied Nizwa castle show that there is no definite trend in the variation of different seismic responses.

3.
The seismic response results may be used in the evaluation of seismic capability of the structural elements of the existing Nizwa castle.If required, strengthening measures will have to be undertaken to guard against possible failure of this structure during any future earthquake.

Figure 2 .
Figure 2. Epicenters and Active Faults along the Batinah Plain and Offshore in Oman.

Table 1 :
(Dickson, 1986)s in Oman(Dickson, 1986) * Numbers in parenthesis indicate number of felt earthquakes in a particular year.

Table 2 :
Data for Seismic Response Computation

Table 3 :
Lateral Force and Shear Force

Table 4 :
Storey Drift and Lateral Displacement

Table 5 :
Overturning and Torsional Moment

Table 6 :
Primary (M xp ) and Secondary (M xs ) Moment