### Abstract

This project entitled aims at the investigation of the effect of structural pounding to the dynamic response of structures subject to strong ground motions. In many cases structural pounding during earthquake may result in considerable and incalculable damages. It usually need to be accounted for in the case of adjacent structures, bridges, base isolated buildings, industrial and port facilities, and in ground pipelines. The phenomenon of that impact force pounding has been noted by researchers and engineers over the past several decades. As we see through dull historical strokes and performance, in different investigations of past and recent earthquakes damage have illustrated several cases of pounding damage such as those that have occurred in the Imperial Valley (May 18, 1940), the Sequenay earthquake in Canada (1988), Kasai & Maison (1991), the Cairo earthquake (1992), the Northridge earthquake (1994), California (1994), Kobe, Japan (1995) Turkey (1999), Taiwan (1999) and Bhuj, Central Western India (2001). Some of the most memorable seismic events were in the 1972 Managua earthquake, when the five-storey Grant Hotel suffered a complete collapse, also in the 1964 Alaska earthquake, the 14-storey Anchorage Westwood hotel pounded against its low rise ballroom and the most recently extent of pounding in Mexico City in 1985 confirmed this as a major problem. Those all evidences have continued to illustrate the annihilation of earthquakes, with devastation of engineered in both buildings and bridges structures. Amongst the feasible structural destructions, seismic produced pounding has been frequently distinguished in numerous earthquakes, as a result this phenomenon plays a key role to the structures. As engineers, we have a responsibility to prevent it or take the necessary steps to mitigate it for the future constructions by considering the properties that affect and led pounding to occur. In order to examine the effect of the various parameters associated with pounding forces on the dynamic response of a seismically excited structure, a number of simulations and parametric studies have been performed, using SAP2000. By more precise investigations that have been done from professional earthquake investigators and engineers pounding produces acceleration and shear at various story levels. Also, significantly depends on the gap size between superstructure segments, which we will examine later on in the project. The main aim of the project is to conduct a detailed investigation on pounding-involved response structure during a seismic event as well as observed the structural behaviour as the result of ground motion excitation by examine the properties that affect pounding and determine the solutions and the mitigations that we have to take into account before we construct a structure in order to avoid future disasters.

### INTRODUCTION

### 1.1 Seismic Pounding effect (Overview)

Looking throughout the time, investigations and observations of the effects of historical earthquakes have demonstrated that many structures are susceptible to significant damage which may lead to collapse. Numerous devastating earthquakes have hit various seismically active regions. Some investigations that have been followed after those seismic events are distinguished fact providing that, an earthquake within the range of six is capable of creating and generating incalculable and irreversible damages, of both buildings and bridges. Those seismic losses have further consequences, most likely to present economical problem to the community hit. The main target of most seismic excitations are, the primary frequencies of rigid buildings between the ranges of low to medium height, resulting by this in significant accumulations of soil acceleration. Also, addition to this is the causing the presence of the inevitable enduring seismic loads in engineered structures, creating inflexible responses. In recent years it becomes more urgent need to minimize seismic damage not only to avoid structures failures but especially in crucial building facilities such as hospitals, telecommunications etc. as well as the protection of the critical equipment that is accommodated by those buildings.

(a)barrier rail damage (Northridge earthquake 1994)

(b)Connector collapse (Northridge earthquake 1994)

In seismically active areas the phenomenon of pounding may need to be accounted for, in the case of closely spaced structures to avoid extensive damages and human losses. The phenomenon of that impact force-pounding has been noted by earthquake investigators over the past several decades when the presence of pounding occurred into an extent. Looking throughout the time, some historical performance of pounding has been denoted, different investigations of past and recent earthquakes damage have illustrated several cases of pounding damage such as those that have occurred in the Imperial Valley (May 18, 1940), California (1994) the Northridge earthquake, Kobe, Japan (1995) and etc. in both engineered structures, buildings and bridges. One of the most remarkable example of pounding-involved destruction resulted from interactions between the Olive View Hospital main building and one of its independently standing stairway towers during the San Fernando earthquake of 1971. The extent of pounding was recently observed in Mexico City in 1985, which then it follows the most recent one in Central Western India (2001). Considerable pounding was observed at sites over 90 km from the epicentre thus indicating the possible catastrophic damage that may occur during future earthquakes having closer epicentres. Is remarkable to denote that pounding of adjacent buildings could have defective damage such as adjacent structures with different dynamic characteristics which vibrate out of phase and there is inadequate separation gap or energy diffusion system to board the relative moderate motions of adjacent buildings.

(a)Collapse of a department store building (Northridge earthquake 1994)

(b)Collapse of the first story of a wooden residential building (Northridge earthquake 1994)

Several researchers considered the topic of pounding between adjacent buildings (Anagnostopoulos 1988; Maison & Kasai, 1990; Papadramakis et al, 1996) with proving or deriving mathematical expression in order to evaluate and calculate the pounding force, by using experimental procedures. But few people have actually addressed the topic of pounding between adjacent buildings (Tsai, 1997; Malhotra, 1997; Matsagar & Jangid, 2003; Komodromos et al 2007) for which the behaviour and the requirements differ from the conventional structures. Likewise, those projects are limited especially to the study and investigation of pounding between adjacent buildings and based isolated buildings without investigating the case of conflict with neighbouring buildings and the resulting of great deformations of the superstructure.

In the past engineers couldn’t prevent the pounding due to some factors such as the past seismic codes did not give explicit guidance, because of this and due to particular economical factors and considerations, that are concerning the maximum land usage requirements, especially in the high density populated areas of cities pounding was unavoidable. Due to that, we are able to identify and investigate many buildings in global system which are already been built in contact or overmuch close to another that could easily cause them to suffer from pounding damage in future earthquake strikes. A large rupture is controvertible from both aspects. The overcrowded construction system in many cities complements a dominant apprehension for seismic pounding damage. For these major reasons, it has been comprehensively acquired that pounding is a disastrous phenomenon that should be anticipated or mitigated. Acceleration range will guidance in many cases to quake activities which are appreciably higher than designed by the design codes that have been used up to now.

The most affordable and easy active way for mitigating pounding effects and diminishing pounding damage, is to consider enough separation gap size between close adjacent structures, this causing difficulties to be accomplished, owing to the detailing engineered work that supposed to be done and the high cost of land in this present time. A flipside to the seismic separation gap precaution in the construction design is to reduce the effect or pounding force through devaluating lateral motion, some researchers involved in extent with lateral ground motions due to pounding such as (Kasaiet al. 1996, Abdullah et a.2001, Jankowski et al 2000, Ruangrassamee & Kawashima 2003, Kawashima & Shoji 2000). This procedure can be accomplished by joining adjacent structures at critical locations of the supports so that their motion could be in-phase with one another or by lessening the pounding buildings damping capacity by means of passive structural control of energy dissipation system.

### 1.2 Pounding force and impact element

Various impact elements are usually used to illustrate the pounding between adjoining construction buildings or bridge structures. Pounding between two conflicting structures, is often simulates by using contact force-based impact models such as the linear spring, Kelvin-Voigt element and Hertz contact model element, and additionally the restitution momentum-based stereo mechanical method.

(a)

(b)

(c)

Figure 1.2.1 shows the pounding problem in: (a) bridge structures [1] S. Mithikimar and R. DesRoches 2006; (b) adjacent buildings with link elements [2] V. Annasaheb Matsagar and R. Shyam Jangid 2005; (c) adjacent building with gap size structures [1] S. Mithikimar and R. DesRoches 2006;

Also another view of pounding effect beyond that in buildings is on the bridges. Many damages during strong earthquakes have occurred in bridge due to pounding between the girders when the gap is not sufficient. From many experimental studies that have been made showed that pounding damage of a bridge can have severe after-effects as it has been observed in many major earthquakes, such as the 1994 Northridge earthquake etc. As we can see from our daily routine bridges belong to one of the important lifeline systems, their proper function play major role in both our life and in the culture, especially after a devastating earthquake in order to survive and/or recovery.

According to some studies [3] Chouw and Hao (2003) and [4] Hai SUI et al. (2004) showed that gap size in the bridges plays the major key role for a bridge to survive under a pounding impact force. The examined the gap size and the outcomes showed that a smaller gap size can expect larger pounding force; therefore the possibility of damage of bridge decks is higher. So on in general designs a small gap should be avoided, if is possible. Moreover according to their experiment the results showed that friction device can decrease pounding impact force that works in different earthquakes.

a) Multiple-pier bridge model [4] H. SU, et al 2004;

b) Two Single degree of freedom model [4] H. SU, et al 2004;

An adequate gap size can contribute to the reduction of pounding effect, but nevertheless in real life the gap size for the designs is unavoidable and due to the limited space that we have to build the design the gap size end up to has smaller values. And thus we resort to other solutions in order to reduce the pounding effect, such as the friction device and bumpers (steel spring with viscous damper). Moreover friction device is much more practical and effective than bumpers. Bumpers can avoid the immediate damage but they cannot reduce the pounding force between the bridge girders, in the other hand friction device can be applied to any earthquake and also is less sensitive to various ground movements.

### Linear spring element

The linear spring element is the easiest and simplest contact element that used to model impact. When the gap between the adjoining structures adjournments, the spring take effect and is presentational of the force established in the meanwhile of impact force. According to Maison & Kasai [5] (1992) have used this model widely, to study further analyse pounding between adjacent buildings. Nonetheless, the linear spring cannot resolve the energy dissipation during impact. The linear spring element illustrated in Figure 1.2.3(a).

### The Kelvin-Voigt Element

The Kelvin-Voigt element can be described by a linear spring in parallel with a damper, as depicted in Figure 1.2.3(b), this model has been used in some studies [6] Anagnostopoulos, 1988; [7] Anagnostopoulos and Spiliopoulos, 1992; [8] Jankowski 2005; The linear spring illustrates the force during impact and the damper accounts for the energy dissipation during impact and is mostly used. The damping coefficient (ck) can be related to the coefficient of restitution (e), by equating the energy dissipations during impact, following the form of equations below:

Where, and Kk is the stiffness of the contact spring, and m1, m2 are the masses of the colliding bodies.

### Hertz contact law

Additionally, a non linear spring based on Hertz contact law can be used to model impact, as depicted in Figure 1.2.3(c). Nonetheless, the Hertz contact law is a characteristic representing of the static contact between elastic bodies and fails to contain energy loss during impact. The impact force can be expressed in the form of the equation below:

Where R is the impact stiffness parameter that depends on the material properties of the colliding structures and the contact surface geometry, g is the at-rest separation and n is the Hertz coefficient.

The use of the Hertz contact law has an intuitive appeal in modelling pounding, since one would expect the contact area between the colliding structures to increase as the contact force increases, leading to a non-linear stiffness described by the Hertz coefficient n which typically is taken ad 1.5. Several analysts have adopted this approach, including [9] Davis 1992; [10] Pantelides and Ma 1998; [11] Chau and Wei 2001; and [3] Chau et al. 2003;

More, for pounding simulation we can also meet the Hertzdamp model, which is a contact model based on the Hertz contact law and using a non linear hysteresis damper. According to experimental theories, for low peak ground acceleration levels, Hertz model produces sufficing results and the Hertzdamp model can be used in advance for moderate and high peak ground acceleration levels (PGA).

The contact element approach has its limitations, with the exact value of spring stiffness to be used, being unclear. Uncertainty in the impact stiffness arises from the unknown geometry of the impact surfaces, uncertain material properties under loading and variable impact velocities. The contact spring stiffness is typically taken as the in plane axial stiffness of the colliding structure (Maison and Kasai, 1990). Another reasonable estimate is twenty times the stiffness of the stiffer structure [6] Anagnostopoulos, 1988; However, using a very stiff spring can lead to numerical convergence difficulties and unrealistically high impact forces. The solution difficulties arise from the large changes in stiffness upon impact or contact loss, thus resulting in large unbalanced forces affecting the stability of the assembled equations of motion.

(a) Linear spring element

(b) Kelvin Voigt Element

(c) Hertz non-linear spring element

Figure 1.2.3: Various impact models and their contact force relations [12] Thomas G.Mezger 2006;

### 1.3 Method of Seismic Analysis

### 1.3.1 Non-linear Dynamic Analysis

Non-linear Dynamic analysis involves step-by step in time integration of the non-linear governing equations of motion, a powerful analysis that can evaluate any given seismic event motion. An earthquake accelerogram is correlated and the consistent response-history of a structural model during seismic events is evaluated. Computer software’s have been designed for these kinds of purposes. Sap can utilized a non-linear dynamic analysis for both linear elastic and non-linear inelastic material response, using step by step integration methods. Is a suitable computer program that is able to evaluate and analyze the response of a two-dimensional and a three-dimensional non-linear structure taking as an input the accelerogram component of an Earthquake? This program will be used to analyse our structural model and to produce a real time of time-history displacement. In a nonlinear dynamic procedure the building model followed static procedures incorporating directly the inelastic material response using in general finite elements. Because this program is using step-by step integration method of analysis the response of the structure, is one of the most sophisticated analysis procedure for predicting forces and displacements under seismic input. However, the calculated response can be very sensitive to the characteristics of the individual ground motion used as seismic input; therefore several time-history analyses are required using different ground motion records. The main value of nonlinear dynamic procedures has the objective to simulate the behaviour of a building structure in detail.

### 1.4 Main Objectives of this project

The main focus of this project is the development of an analytical model that pounding force will present based on the classical impact theory by using parametric study to identify the most important parameters that affecting pounding. Those factors that give arise to that impact force, therefore investigate of the different practical types of structures that pounding can be occurred. The main objective and scope of this study are, to explore the global response of buildings structures when the pounding effects take place under seismic events, therefore to review the main outcomes of the literature and how the impact theory come across to the practical cases. Create a structural modelling and perform a non linear time history analysis on it. Examine the realistic model of pounding that we will create if it satisfies the properties in order for the structure to work. Determine the relative importance of the dynamic characteristics of pounding.

Dynamic analysis will be carried out on the model structure to observe the displacement of the structure due to earthquake excitation. When we examine the main structure we are mainly concerned with displacement, velocity and acceleration, the general dynamic behaviour of the structure under the action of dynamic loads such as earthquake lateral loads. For the purpose of the project appropriate computer software will be used for its purposes (e.g. SAP2000). Creation and versatile of the model, accomplishment of the analysis, and checking and breakthrough of the design must be all done through this interface. Graphical displays of the results, including the real-time of time-history displacements will be easily produced by the use of that software.

At the end of that modelling analysis by gathering all the necessary and useful outcomes and explored in deep the main parameters derived by this, the conclusion and results of what we have to adopt as engineering before retrofitting a structure. The appropriate structural parameters are the separation gap size between adjacent structures (storey mass, structural stiffness and yield strength etc.), the dynamic behaviour of a damped multi-degree of freedom bridge system separated by an expansion joint, considering the limited width of clearance around a seismically isolated buildings, that pounding can cause high over stresses when the colliding buildings have different height, periods or masses and the isolators in bridge structures are effective in mitigating the induced seismic forces, cable restrainers etc.

Engineers should adopt those realistic facts before they construct new structures in order to succeed future sustainability of the structures and avoiding by this the impact phenomenon of pounding. Accomplish to mitigate the phenomenon of pounding in order to prevent future collisions and/or engineering disasters when seismic events occur.

### REVIEW OF LITERATURE

### 2.1 Practical Cases

Pounding-impact force generated by earthquakes between different analytical structure models may provoke extensive damage and in general most of the times the result of that force is not pleasant, it may lead the structure to a total collision as it can be seen from different practical cases. Pounding problem is phenomenon that has been observed during earthquakes and in accordance to ground motions, and has been extensively investigated by various researchers’ that have used a variety of impact analytical models. Because of the importance of what pounding will have as a result of different engineering structures, attracted the attention of several scientists and analyzers? This absorption is a consequence fact of a plenty growing amount of evidence, which can be found in reports and journals, which have been created after dominant exceeding earthquakes. Demonstrating, the power of that certain impact force which may cause considerable damage. The conclusions and results of successive series of various numerical, integrated analytical and experimental studies have been conducted using individual structural models and administering different models of practical cases confirm that pounding, due to constraining additional impact forces, may result in damage as well as significantly increase the structural response.

Moreover, there are many practical case histories of engineered buildings with different dynamic properties and characteristics, which have been constructed under the old earthquake resistant design codes. Analogous conditions concern also bridge constructions. When a structure is under earthquake vibrations will move according to ground motions. These vibrations can be entirely exaggerated, creating at the same time stresses and deformations throughout the structure. Evaluation of methods can be carry out in engineering practise to estimate the parameters that give a rise to pounding. The accuracy and the ability of computational appliance have increased a lot this century by helping us evaluate the seismic structural response of structure, a variety of software’s computing programs have been designed for those purposes, and can accomplished to calculate the dynamic seismic response of a structure which help engineers mitigate pounding effects in structure by avoiding future disasters . Linear and nonlinear models are realistic pounding models that have been used for studying the performance of a structural system under the mode of structural pounding effect under seismic events. Significance to notice in seismically active areas the serious hazard that pounding can cause and in what practical cases does it occurs by review of some critical and enlightened journals and reports, according to history performance of an exceeding major earthquakes. Also a time history analysis is a dynamic tool for the investigation of a structural seismic enforcement. Because of all the above reasons, investigations have been carried out on pounding mitigation in order to improve the seismic response.

### 2.1.1 Linear and non-linear pounding of structural systems

Pantellides and Ma [13] examined by experimental procedures, the dynamic response of a damped single degree-of-freedom structural model during a seismic event. They analysed the structural behaviour of SDF with both elastic and inelastic structural impact response by using realistic parameters for the pounding model in numerical calculations of the earthquake response. The method of analysis that they used can be used to examine pounding in both buildings and bridges. In order to accomplished to evaluate the effects that concerning pounding force during earthquake in structures, they made a comparison between linear and non-linear models. In the non-linear pounding model they produced results that showed the one-sided pounding model produces more dangerous effects than the two-sided. In their analysis they derived a mathematical equation that concerns the impact force effects in order to represent pounding model for both elastic and inelastic structures.

A realistic pounding element was used for this studying and numerical simulations have demonstrated that pounding impact behaviour is not responsive to the values of the stiffness parameter. Furthermore, their experimental results for both elastic and inelastic structures in order to balance damping levels have showed that the higher deformation occurred in the elastic model. According to some observations that have been made the values of pounding force is relatively small in the inelastic structures in comparison to the elastic structures. The value codes of moderate the damping levels are controlled as compared to the actual seismic separation gap size found through the analysis of SDF structural model. The value of seismic gap is decreased considerably as the damping capacity of the pounding structural model is increased.

Jankowski [14], addressed to an extent of a non-linear modelling due of earthquake that generated pounding of structural buildings, by deriving the essential fundamental mathematical expressions, involving the function and the applications of the non-linear analysis. By analysing various earthquake records, he derived appropriate mathematical expressions showing the limitation and the feasibility of a non-linear model, in anticipating values for a seismic pounding gap size as well as values for mass, elastic stiffness and damping coefficients between buildings. In his analysis of two inadequately separated buildings with different dynamic characteristics, modelled by elastoplastic multi-degree-of-freedom lumped mass models are used to simulate the functioning structural behaviour and non-linear viscoelastic impact specificity elements are applied to a model collision. The results of the study demonstrate that pounding has an indicative impact on the behaviour of structural buildings, and furthermore the results that he derived confirm the performance of the non-linear, viscoelastic model which endures to simulate the pounding phenomenon more accurately.

### 2.1.2 Seismic Pounding Effects between adjacent buildings

In these last decades, the pounding phenomenon between closely spaced building structures can be a serious hazard especially in seismically active areas with strong ground motion. Because of that critical fact a beneficial awareness of pounding response on engineer structures and numerical formulas for calculating building separation gap size based on linear or analogous linear methods have been introduced.

Abdel Raheem [14] established and achieved a tool for the inelastic analysis of seismic pounding effect between buildings. He carried out a parametric study on buildings pounding response as well as proper seismic hazard mitigation practice for adjacent buildings. Three categories of recorded earthquake excitation were used for input. He studied the effect of impact using linear and nonlinear contact force model for different separation distances and compared with nominal model without pounding consideration. Therefore the results of these studies lean on the stimulation characteristics and the relationship between the buildings fundamental period. Furthermore because pounding produces acceleration and shear in various story levels that are greater than those from the no pounding case.

Westermo [16] suggested, in order improving the earthquake response of structures without adequate in-between space of the structures, to linking buildings by beams, which can carry the forces between the structures and thus annihilating collisions. Anagnostopoulos [6] analysed the effect of pounding for buildings under strong ground motions by a simplified single-degree-of-freedom (SDOF) model. Miller and Fatemi [17] explored in to an extent the phenomenon of pounding-impact force, of adjacent buildings subjected to harmonic motions by the vibroimpact concept. Maison and Kasai [18] modelled the buildings as multiple-degree-of-freedom systems and analysed the response of structural pounding with different types of idealizations. Papadrakakis et al. [19] studied the pounding response of two or more close separated buildings based on the Lagrange multiplier approach by which the geometric compatibility conditions due to proximity are constrained. A three-dimensional model developed for the simulation of the pounding behaviour of adjacent buildings is presented by Papadrakakis et al. [20]. In the evaluation of building separation, Jeng et al. [18] estimated the minimum separation distance required to avoid pounding of adjacent buildings by the spectral difference (SPD) method. Kasai et al. [4] extended Jeng’s results and proposed a simplified rule to predict the inelastic vibration phase of buildings based on the numerical results of dynamic time-history analyses.

Anagnostopoulos and Spiliopoulos [7] examined the behaviour of common pounding between adjacent buildings in city blocks to several strong earthquakes. In the study, the buildings were idealized as lumped-mass, shear beam type, multi-degree-of-freedom (MDOF) systems with bilinear force deformation characteristics and with bases supported on translational and rocking spring dashpots. Collisions between adjacent masses can occur at any level and are simulated by means of viscoelastic impact elements. They used five real earthquake motions to study the effects of the following factors: building configuration and relative size, seismic separation distance and impact element properties. It was found that pounding can cause high over stresses, mainly when the colliding buildings have significantly different heights, periods or masses. They suggest a possibility for introducing a set of conditions into the codes, combined with some special measures, as an alternative to the seismic separation requirement.

Figure 2.1.2-2 on the left there is a finite element mathematical model and on the right shows the elevation view of a 2 different height building with the separation gap size [14] Abdel Raheem 2006;

### 2.1.3 SEISMIC POUNDING EFFECT AND RESTRAINERS ON SEISMIC RESPONCE OF MULTIPLE-FRAME BRIDGES

DesRoches and Muthukumar [22] used analytical illustrations to check out, the factors and the parameters affecting the worldwide reaction and behaviour of a multiple-frame bridge as a result of pounding of adjacent frames. They have conducted parameter studies of one-sided and two-sided pounding, to dispose the effects of frame stiffness ratio, ground motion characteristics, frame yielding, and restrainers on the pounding behaviour of bridge frames. They showed that the addition of restrainers has a minor effect on the one-sided pounding response of highly out-of-phase frames. It is determined that the most important parameters are the frame period ratio and the characteristic period of the ground motion. The current study explores the effect that pounding impact-force and restrainers have on the worldwide appeal of bridge frames in a multi-frame bridge. They used investigations of two-sided pounding using MDOF models, which showed a favourable post impact response for the flexible frame and a detrimental effect for the stiff frame demand, for all period ratios. The results from both one-sided and two-sided impact reveal that the response of bridge frames due to pounding, irrespective of the ground motion period ratio, thus validating the recommendations suggested by Caltrans. Current recommendations by Caltrans for limitations in frame period ratios to reduce the effects of pounding are evaluated through an example case. The effect of restrainers on the pounding response of bridge frames is evaluated. The results show that restrainers have very little effect on the demands on bridge frames compared with pounding.

### 2.1.4 GIRDER POUNDING ON BRIDGES

Hao and Chouw [23] introduced a new design principle for anticipating