ABSTRACT: Pile foundations, either precast or castprojects such as bridges in transportation networks, or jetties in harbor areas, strategic structures count to a great extent on the serviceability of the carrying foundations or piles. Thus, the integrity ofpile-foundation systems governs sharply the service life of the supported structures. Moreover, include using materials as steel and concrete. Such materials when used in harsh environments such as sea water or salty soil layers suffer severe deterioration including loss of concrete durability, steel corrosion, and sometimes marine borer attacksConsequently, high repair or replacement costs of the foundation systems led researchers the feasibility of using FRP composite piles, such as concretebenefits of easier construction and repair, terms of life cycle analysis. In spite of that, one of the main drawbacks of composite piles is their relatively short track performance and absence of long-term durability data. tubes piles on the seismic behavior of the supported structures. This concerns the soilbehavior of the composite system. This paper describes a with concrete-filled tubular FRP piles under earthquakeson the lateral capacity of structures.

KEY WORDS: Seismic; Response; Concrete; FRP; Pile foundations

1 INTRODUCTION

Traditional construction of piles in bridge foundations includes using materials as steel, concrete, and timber. However, on using such materials in the construction of piles especially in harsh environments as sea water or salty soil layers, piles suffer a limited service life in addition to enlarging the maintenance costs. Associated problems include loss of concrete durability, steel corrosion,marine borer attack or degradation of timber piles. of deteriorated conventional piles in harsh environments shown in Figure 1.

Corrosion in steel piles Degradation in concrete piles

Severe damage in wooden piles

Figure 1. Degradation of Conventional

Studying the Impactfoundations on the Seismic Resp

Mohamed I.S. Elmasry 1 Construction & Building Engineering Department, Arab Academy for Science & Technology & Maritime Transport,

Pile foundations, either precast or cast-in-situ, are popular for usage worldwide in many important and costly projects such as bridges in transportation networks, or jetties in harbor areas, etc. In addition, the stability and safety of such

rategic structures count to a great extent on the serviceability of the carrying foundations or piles. Thus, the integrity offoundation systems governs sharply the service life of the supported structures. Moreover,

nclude using materials as steel and concrete. Such materials when used in harsh environments such as sea water or salty soil layers suffer severe deterioration including loss of concrete durability, steel corrosion, and sometimes marine borer attacks

equently, high repair or replacement costs of the foundation systems led researchers in the last few the feasibility of using FRP composite piles, such as concrete-filled tubular FRP piles. These piles are non

and advantages as improved durability in harsh environments and cost savings in terms of life cycle analysis. In spite of that, one of the main drawbacks of composite piles is their relatively short track

term durability data. The main focus in this paper is to study the effect of having FRP filled tubes piles on the seismic behavior of the supported structures. This concerns the soil-structure interaction an

This paper describes a proposed methodology to assess the structural capacity of foundations filled tubular FRP piles under earthquakes. Results are presented to verify the expected benefits versus the effects

Seismic; Response; Concrete; FRP; Pile foundations.

Traditional construction of piles in bridge foundations includes using materials as steel, concrete, and timber.

s in the construction of piles especially in harsh environments as sea water or salty soil layers, piles suffer a limited service life in addition to enlarging the maintenance costs. Associated problems include loss of concrete durability, steel corrosion, and sometimes marine borer attack or degradation of timber piles. Examples

in harsh environments are

Degradation in concrete piles

Severe damage in wooden piles

. Degradation of Conventional Piles [1].

Consequently, in the construction of concrete piles as a popular reliable type for bridges crossing over lakes or bays, a popular protection alternative, that had a wide acceptance in the engineering community, was to useupper portion of the piles lying between the bedthe pile caps [2,3]. However, this give the sufficient improvement oin addition to the high cost of attributed to the susceptibility of steelin salty environments.

Thus, researchers worldwide in the last few decades started to investigate the feasibility of using other materials thawould better sustain such harsh environments, without adding considerably to the overall construction costs. For example, FRP composite piles as concretechosen by many researchers as a possible foundation alternative for projects located in harsh marine environments. This was clear given the wide range of research that studied such type of piles [1,3,4]. Thesebenefits of easier construction and repair, as well as having other advantages including improved durability in harsh environments and cost savings in terms of life cycle analysis [3,4,5].

In spite of that, long-term service of typical bridge piles requires them to sustain severe loading as earthquakes in addition to being sometimes under sconditions [6,7,8]. Moreover, when subjecting piles to abrupt loads such as the case of seismic loads, piles may suffer structural damage that would supported structures [6,7]. This is reflected in some caswhere extreme effects sometimes took place after some

Impact of Using Tubular Concrete-Filled FRP foundations on the Seismic Response of Structures

Mohamed I.S. Elmasry 1, Tareq M. Abd-El-Aziz 1, Ahmed M. KamelConstruction & Building Engineering Department, Arab Academy for Science & Technology & Maritime Transport,

P.O. Box: 1029, Alexandria, Egypt E-mail: elmasryi@aast.edu

situ, are popular for usage worldwide in many important and costly . In addition, the stability and safety of such

rategic structures count to a great extent on the serviceability of the carrying foundations or piles. Thus, the integrity of the foundation systems governs sharply the service life of the supported structures. Moreover, traditional pile foundations

nclude using materials as steel and concrete. Such materials when used in harsh environments such as sea water or salty soil layers suffer severe deterioration including loss of concrete durability, steel corrosion, and sometimes marine borer attacks.

in the last few decades to investigate These piles are non-corrosive with

advantages as improved durability in harsh environments and cost savings in terms of life cycle analysis. In spite of that, one of the main drawbacks of composite piles is their relatively short track record of

The main focus in this paper is to study the effect of having FRP filled structure interaction and the expected

ethodology to assess the structural capacity of foundations to verify the expected benefits versus the effects

Consequently, in the construction of concrete piles as a popular reliable type for bridges crossing over lakes or bays, a popular protection alternative, that had a wide acceptance in

e engineering community, was to use steel jackets in the upper portion of the piles lying between the bed-level up till

However, this protection method does not give the sufficient improvement on the life span of the piles,

of steel jackets. This may be attributed to the susceptibility of steel by nature to corrosion

Thus, researchers worldwide in the last few decades started to investigate the feasibility of using other materials that would better sustain such harsh environments, without adding considerably to the overall construction costs. For example, FRP composite piles as concrete-filled tubular FRP piles were chosen by many researchers as a possible foundation

ojects located in harsh marine environments. This was clear given the wide range of research that studied

These piles are non-corrosive with benefits of easier construction and repair, as well as having

ng improved durability in harsh environments and cost savings in terms of life cycle analysis

term service of typical bridge piles requires them to sustain severe loading as earthquakes in addition to being sometimes under severe environmental

Moreover, when subjecting piles to abrupt loads such as the case of seismic loads, piles may suffer

would threaten the integrity of the This is reflected in some cases

where extreme effects sometimes took place after some

illed FRP Pile onse of Structures

Kamel 1

Construction & Building Engineering Department, Arab Academy for Science & Technology & Maritime Transport,

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)ISSN: 2311-9020; ISBN: 978-972-752-165-4

477

seismic events tragically in terms of human lives losses, material and financial losses like what happened in Nigata earthquake (1964) in Japan and Izmit earthquake (1999) in Turkey [6,7]. The challenge however remains in testing or modeling reliably the pile-foundation system so that to expect the transferred excitation to the main structure. This is the case where a model for the soil structure interaction is needed.

Therefore, the main focus in this paper is to study the effect of having FRP filled-tube piles on the seismic behavior of the supported structures. This concerns the soil-structure interaction and the expected behavior of the composite system. The paper describes a proposed methodology to assess the structural behavior of foundations with concrete-filled tubular FRP piles under earthquakes, and the consequences on the transmitted excitation to the superstructure. The results are to verify the expected benefits versus the effects on the lateral capacity of structures. This is done in addition to taking into consideration the weakness points in the system including the connection between piles and pile caps as well as FRP-Pile-Soil interaction, etc.

2 PROBLEM DEFINITION

FRP composite piles, if found reliable, could offer the answer for improved durability in harsh environments and cost savings in terms of life cycle analysis. However, one of the main drawbacks of composite piles is their relatively short track record of performance and absence of long-term durability data [4,5].

For example, ongoing research at Virginia Tech has found that moisture is the dominant damage mechanism, influencing the long-term durability of concrete-filled tubular FRP piles [4]. In contrast, the implicit behavior of the structure under earthquakes needs to be studied if it is constructed using FRP filled-tube concrete piles as a foundation system. This is done in order to assess the consequences compared to the benefits of using such type of piles. Thus, a research study is needed to show the impact of FRP usage on piles behavior and whether having a negative or positive effect on improving the pile behavior properties.

3 LITERATURE REVIEW

The use of fiber-reinforced polymer or plastic (FRP) composite materials can be traced back to the 1940s in the military and defense industry, particularly in aerospace and naval applications [5]. Because of their excellent properties such as lightweight, noncorrosive, nonmagnetic, and nonconductive properties, composites can meet the high performance requirements of space exploration and air travel, and for this reason, composites were broadly used in the aerospace industry during the 1960s and 1970s [14]. Starting from the 1950s, composites have been increasingly used in civil engineering for semi-permanent structures and rehabilitation of old buildings [9,10]. A concise review on FRP composites for construction applications in civil engineering is given by Bakis et al. [14].

Structures made of FRP composites have been shown to provide efficient and economical applications in bridges and piers, retaining walls, airport facilities, storage structures exposed to salts and chemicals, and others. In addition to light-weight, noncorrosive, nonmagnetic, and nonconductive

properties, FRP composites exhibit excellent energy absorption characteristics which might be suitable for seismic response as well as high strength, fatigue life, and durability. Advantages also include competitive costs based on load capacity per unit weight and ease of handling, transportation, and installation [5]. Thus, FRP materials offer the inherent ability to alleviate or eliminate the following four construction related problems adversely contributing to transportation deterioration worldwide: corrosion of steel, high labor costs, energy consumption and environmental pollution, and devastating effects of natural hazards [5]. Consequently, a great need exists for these relatively new materials and methods to repair and/or replace deteriorated structures at reasonable costs.

Furthermore, FRP piles have been studied extensively in the last few decades as an alternative for traditional cast-in-place or precast concrete piles especially for piles existing in harsh environments like the undergone research on the Route 40 bridge at Virginia city, USA in 2003, e.g., A. Fam, M. Pando, and S. Rizkalla [4], and H. Hu and R. Seracino in 2013 [3]. In addition, other research applications, as that performed by A. Fam and S. Rizkalla) [11], and A. Mirmirn, Y. Shao and M. Shahawy) [12] studied the capacity and the behavior of FRP piles under axial loading and under mechanical driving loads.

In spite of that, though research proves that FRP piles are sustainable under harsh environments [3,4,5], yet estimating their behavior under different types of special loading is not clearly developed. In general, the behavior of piles under earthquakes was extensively studied for different types of piles in terms of material and construction, e.g. Shamsher Prakash and Vijay K. Puri [7]. However, the behavior of FRP piles under seismic loads is not yet clearly determined. This is the case given the fact that bridge structures behaviors under earthquakes are clearly affected by the soil structure interaction and by the type of the foundation system underneath [7].

4 PROBLEM IDEALIZATION

The complexity of the problem is reflected in the fact that piles are buried elements in the soil. In addition, Soil properties vary considerably from construction site to another in terms of dynamic and physical properties. Nevertheless, many difficulties are associated with performing in-situ tests for actual piles under service loads from actual bridges. This is the case especially when the piles penetrate through water depth in addition to soil layers beneath the water bed. However, given the importance of studying the effect of dynamic loads as seismic loads on FRP composite piles, it would be appropriate to represent the problem analytically, and interpret results based on modeling the problem mathematically.

4.1 Case study

The general case study herein is a near shore bridge that is considered as an important traffic hub. Figure 2 shows an example of such near shore bridges that exists in Alexandria, Egypt. In addition, the bridge is assumed to lie in a seismic active area. Moreover, the precise case study in this paper that deals with the core of the problem is a group of concrete-filled tubular FRP piles lying under a floating pile cap. It is assumed

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that the latter piles-cap system form a part of the foundatsystem of the studied near shore bridge. The pile cap assumed to exist above water zero level with a sufficient height, and supports the column of a carrying supports the bridge. The pile cap thus carries a vertical load coming from the frame column. A schematic of the pile cap foundation system is shown in Figure 3, where height of each pile, hs is the submerged heightpile, and db is the buried depth of each pile.

Figure 2. Stanly bay bridge in Alexandr

Figure 3. Studied pile cap system

5 PROPOSED APPROACH

A suitable analytical solution is required dynamic response of the piles-cap system studied within the context of this paper. As stated earlier, the studied foundation system is composed of floating rigidly capped groups with due consideration to pile-soil-pile interaction. group of floating piles is assumed embedded in a uniform stratum or half space and subjected to an earthquake buried depth of the pile. The applied dynamic forces are transmitted onto each pile through the buried part of the pile

5.1 FRP Composite piles and soil properties

In this paper, FRP composite piles refer to FRP with concrete piles and without steel reinforcementbonding between FRP jacket and concrete is

hc

hs

db

Water

Homogeneous Sandy Soil

Pile cap

form a part of the foundation near shore bridge. The pile cap is also

above water zero level with a sufficient the column of a carrying box frame that

carries a vertical load A schematic of the pile cap

, where hc is the clear is the submerged height in water of each

lexandria, Egypt.

Studied pile cap system

for computing the cap system studied within the

he studied foundation of floating rigidly capped cylindrical pile

pile interaction. The embedded in a uniform

n earthquake along the The applied dynamic forces are thus

buried part of the pile.

and soil properties

refer to FRP case filled without steel reinforcement. Perfect

between FRP jacket and concrete is assumed [15].

The FRP jacket or case covers and extend up till the pile cap works as protection for pile environmental attack, and work also as an external reinforcement for the concrete core incross section of the studied FRP in Figure 4.

Figure 4. A cross section in the studied FRP composite pile

The soil stratum in which the studied FRP piles are embedded is assumed homogenous sandy soil along the depth of the pile shaft. Moreover, the soil is modeled as a linear hysteretic material of Young’s modulusmaterial damping ratio ζ, and shear velocity

5.2 Modeling of piles-cap system

The mathematical model for divided along the vertical direction into horizontal strips as shown in Figure 5. Dividing the mass of each strip is assumed lumped and of the whole piles-cap system can thus be dealt with as a shear building model as shown in Figure of the pile cap and mi is the mass of the the context of this paper, only considered for lateral response pile groups.

Figure 5. Mathematical model of FRP pile

The lumped mass of each strip is evaluated as per the volume of the strips and the surrounding interactive soil

Earthquake Excitation

the full length of the pile shaft the pile cap bottom level. The FRP jacket

for pile concrete core from harsh and work also as an external

reinforcement for the concrete core inside. An explanatory the studied FRP composite pile type is shown

section in the studied FRP composite pile

The soil stratum in which the studied FRP piles are embedded is assumed homogenous sandy soil along the depth

he soil is modeled as a linear hysteretic material of Young’s modulus, E, Poisson’s ratio, ν,

, and shear velocity Vs [13].

cap system

The mathematical model for the piles considers piles are divided along the vertical direction into horizontal strips as

. Dividing the piles group into strips, the trip is assumed lumped and the dynamic model

can thus be dealt with as a shear building model as shown in Figure 5, where mp.c. is the mass

is the mass of the i th strip. Thus, within paper, only horizontal oscillations are

and studied for rigidly-capped

Mathematical model of FRP piles-cap system

The lumped mass of each strip is evaluated as per the e strips and the surrounding interactive soil

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479

wedge. The strips in the proposed model are considered of equal heights. However, the uppermost mass will also include the mass of the pile cap, mp.c., in addition to the strip mass. Furthermore each mass is assumed to have a single degree of freedom such that the number of degrees of freedom is relative to the number of masses.

Similarly, the stiffness of each strip is estimated as per the designed cross section of the pile group within the clear height above water and the submerged height within the water level. Moreover, the method introduces some approximations in evaluating the stiffness of each strip, and considers the interference of the piles and the surrounding soil wedge around each pile, originating along each pile shaft within the buried depth of the piles.

5.2.1 Bottom fixation length

FRP composite piles are assumed fixed at their bottom part. Thus, it is assumed that the lowermost part of the pile is replaced by a fixed support. The following equations will be useful to calculate the required fixation length of pile [8,16]:

Lf = L` - Ls (1)

Where L`: length of pile shaft buried under soil Ls: length of pile shaft between the sea bed level and the assumed starting point of fixation Lf: the fixation length of the pile shaft

Such that to calculate Ls, the following equation applies [8]:

Ls = 1.8 �� ���

� (2)

where E: Modulus of elasticity of concrete (20 GPa) I: Moment of inertia for the FRP Composite pile cross section Nh: horizontal sub grade reaction Constant (rate of increase with depth) such that,

Nh = �

�� (3)

where

dequ. : Equivalent pile diameter nh = horizontal sub grade reaction, obtained from H.G. Poulos [15] = 34 t/ft3 = 1.068 × 10-5 kN/mm3.

5.2.2 Piles-cap connection

The FRP piles-cap connections are assumed rigid. This is assumed to be achieved by adding a linking reinforcement cage at the top of the FRP composite piles [4], as shown in Figure 6. The linking bars are assumed to extend for the sufficient anchorage length (60 times the rebar reinforcement diameter as per Egyptian standards [17]) inside the pile cap as well as the fixed pile to the cap. It is assumed that the linking cage is composed of 9 T 25 rebar along the circumference of each FRP composite pile.

Figure 6. Linking reinforcement between the cap and FRP piles

5.2.3 Mass Estimates

On calculating the piles group mass at each strip, the pile shaft is divided into three zones. The upper zone of the pile lies above the water zero level up till the bottom of the pile cap with a height, hc. The second zone is the part of the pile submerged in water with depth, hs. The third and lowermost zone is the part of the pile buried in the soil with a depth, db.

Hence, it is assumed that the masses of the strip elements within the clear height, hc, and the submerged depth, hs, have the same mass which is calculated based on the available information about the designed section only. However, for masses of strip elements under the sea bed level, buried in soil, the mass of each strip includes not only that of the pile cross section but also the interactive volume of the soil wedge that surrounds each embedded pile in the group. Figure 7 shows the expected elevation of the interactive soil wedge surrounding each FRP pile during lateral excitation [18].

Figure 7. An elevation view showing the projection of the interactive soil wedge surrounding the FRP pile during

lateral excitation of the piles-cap system

This is the case such that the angles βa and βp are obtained as

βa= 45- �� (4)

and

βp= 45+ �� (5)

where φ is the angle of friction of the sandy soil stratum. As evident from Figure 7, it can be easily concluded that the

cross section of the interactive soil wedge is nearly elliptical [18] such that the longer dimension of the oval shape can be obtained from:

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480

Dy = H × (tan βa +tan βp )+ d

and the shorter dimension can be assumed from

Dx ≅ �� × H × (tan βa +tan βp ) + d

where Dx = shorter ellipse dimension in X-axisDy = Longer ellipse dimension in Y-axisd = Pile diameter H = Full height of the FRP pile excluding fixation length

For large values of Dx and Dy, it is expected that between the effective soil surrounding each it is advisory to draw the soil wedge for each pile in terms of contour lines as shown in Figure 8 and evaluate soil masses excluding the overlap areas or volumes for each strip

Figure 8. A schematic showing the effective soil wedge around the FRP pile in terms of contour lines

5.2.4 Stiffness Estimates

Similarly to mass evaluations, on calculating the piles group stiffness for each strip, the pile shaft is divided into three zones. The upper zone of the pile that lies above the water zero level up till the bottom of the pile cap with a height, The second zone is the part of the pile submerged in water with depth, hs. The third and lower part comprises embedded part of the pile. Thus for the two upper zones, the stiffness of the strip element can be obtained from

Ki = �� � �

��

Where k: single pile strip stiffness E: Modules of elasticity h: strip element height

Meanwhile, to calculate the single pile stiffnessembedded in the sandy soil stratum, engineering software (AllPile) is used. AllPile directly uses COM624S calculation methods for lateral analysis. For details on COM624, please refer to the FHWA publications

In summary, COM624S uses the four nonlinear differential equations to perform the lateral analysis. They are:

EI ��

�� + Q

² �

�² + R – Pq = 0

where Q = axial compression load on the pile y = lateral deflection of pile at depth z z = depth from top of pile R = soil reaction per unit length E = modules of elasticity of pile I = moment of inertia of the pile Pq = distributed load along the length of pile

EI �

� + Q

�

� = P

d (6)

dimension can be assumed from

d (7)

axis axis

ull height of the FRP pile excluding fixation length , it is expected that the overlap

between the effective soil surrounding each pile is large. Thus, l wedge for each pile in terms of

es as shown in Figure 8 and evaluate soil masses or volumes for each strip.

showing the effective soil wedge

around the FRP pile in terms of contour lines

s, on calculating the piles group stiffness for each strip, the pile shaft is divided into three

lies above the water zero level up till the bottom of the pile cap with a height, hc.

pile submerged in water part comprises the

. Thus for the two upper zones, the strip element can be obtained from

(8)

calculate the single pile stiffness in the strips the geotechnical

. AllPile directly uses COM624S calculation methods for lateral analysis. For details

publications [19,20]. nonlinear differential

equations to perform the lateral analysis. They are:

= 0 (9)

= distributed load along the length of pile

(10)

where P = shear in the pile

�

� = S

and

EI ²

where St = slope of the elastic curve defined by the axis of pileM = bending moment in the pile

5.2.5 Damping Estimates

Dividing the pile height into threit is evident that no damping within the top zone above waterthe strip elements of the shaft aboveHowever, within the second and third zone of the pile that is submerged in water, water is assumed as source acting on the piles-cap system within the submerged height, hs and the buried depth, water height and soil layers is assumed 3effect within soil layers is neglected and only the stiffness coming from the associated soil wedge along the pile shaft with each pile is considered.

5.2.6 Group interaction effects

Due to the fact that the distances between the piles are relatively small, it is expected that the interference between the soil wedges around the piles should result in reduction of the group total stiffness rather than summing the each pile. Thus, a reduction factor for group effect is used[22]. Figure 9 [22] shows the values of the

Figure 6. Piles group reduction factors

The fm value, as indicated in Figure 9,number of rows of piles increasesdecreases as well on decreasing the spacing of the rows. The values of fm are relative to the load carried by each row of piles. The chart shows that the leading row takes most of the input energy. For piles spaced more than six diamethe values of fm are equal to 1.0, indicating that group interaction effects are negligible

5.2.7 Modeling Earthquake Excitation

In addition, the earthquake excitation is assumed to affect the piles-cap system along the buried depth of the pilestrips under the soil top layer areexcitation momentarily. This is the case where the seismic

= St (11)

² �

�² = M (12)

= slope of the elastic curve defined by the axis of pile ent in the pile

three zones as mentioned earlier, damping exists on the pile-cap system

within the top zone above water. Thus, the damping ratio for shaft above water table is neglected.

However, within the second and third zone of the pile shaft water is assumed as damping

cap system within the submerged and the buried depth, db. The damping ratio within

is assumed 3% [21]. The damping effect within soil layers is neglected and only the stiffness coming from the associated soil wedge along the pile shaft

Group interaction effects

he fact that the distances between the piles are small, it is expected that the interference between

the soil wedges around the piles should result in reduction of the group total stiffness rather than summing the stiffness for

a reduction factor for group effect is used the values of the P-multipliers (fm).

reduction factors [22].

, as indicated in Figure 9, decreases as the number of rows of piles increases. In addition, the fm value

as well on decreasing the spacing of the rows. The relative to the load carried by each row of

piles. The chart shows that the leading row takes most of the input energy. For piles spaced more than six diameters apart, the values of fm are equal to 1.0, indicating that group interaction effects are negligible [22].

Excitation

In addition, the earthquake excitation is assumed to affect the cap system along the buried depth of the piles. Thus, all

are excited with the same lateral excitation momentarily. This is the case where the seismic

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481

wave acting on the pile is assumed to have the same magnitude along the pile depth in the soil. Moreover, since the number of piles in the studied group is relatively large and the pile spacing, S, is equal to three times the pile diameter (relatively small), it is assumed that the lateral responses of all embedded piles will have the same phase.

Furthermore, the dynamic time-domain responses of the shear building model of the system is obtained using a linear state space model using Matlab software [23]. Thus, consider a linear structural model of the form:

ƒbKxxCxM =++ d &&& , ƒdxCxCy ++= 21 & (13)

where M, K, and Cd are the mass, stiffness and damping matrices of the system, and C1, C2, and d are the output influence matrices for the displacement, velocity and the external force, f. Thus, one can write the model in a state-space form

ƒBqAq~

+~

=& , ƒDCqy += (14)

where

[ ]TTT= xxq & (15)

is the state vector, A~

is the system state matrix which is dependent on the mass M, damping C, and stiffness K matrices of the structural system such that,

�� = � �����×���� �����×����(−"#�$)����×���� (−"#�&)����×����

' (16)

where nDOF is the number of degrees of freedom of the system.

In addition, f is an excitation force, and y is a vector of

measured responses. Moreover, B~ is the input influence

matrix, C is the output influence matrix for the state vector q, and D is the direct transmission matrix. The latter matrices have different forms depending on the assigned type of input excitations and the desired output measurements.

5.3 Numerical Example

As mentioned earlier, the case study is a near shore bridge located in Egypt – Alexandria in shallow water depth where the foundations are established by using deep foundation (piles-cap) system having the following properties:

• Glass Fiber Reinforcement Polymer (GFRP) Tube filled by Concrete “Composite pile”.

• Driven pile. • Pile diameter (d) = 0.625 m • GFRP Tube thickness 5 mm • Pile capacity design load 667.5 KN and ultimate

load 4000 KN • Pile full length is 30 m and the buried depth is 20 m. • Water depth 6.00 m. • Pile head height from sea water table 4.00 m. • Pile cap thickness 1.00 m • Pile Material properties:

o See Table 1 for FRP material properties o Modules of Elasticity of concrete 20GPa o Cubic strength of concrete is 45MPa

Table 1. Mechanical properties of GFRP Tube [4,24]

In addition, it is assumed that the pile cap supports an axial load of 16000kN coming from the bridge supporting frame. Thus, assuming the capacity of each pile is 667.5kN [4] then nearly 25 FRP piles under the pile cap are required. Moreover, the piles are distributed as a 5×5 array form. Assuming the spacing between piles, S, equals to 3D, then, the dimension of the square pile cap is evaluated to be 9.4m, see Figure 10 for the studied foundation system layout.

Figure 10. Layout of the studied foundation system

The soil is assumed composed of dense sand stratum continuously for 30m depth. The internal angle of fraction (φ) is assumed 35°. The unit weight (ɣ) of the soil is taken as

18.5 KN/m3 and ( ɣeff ). 8.5 KN/m3. Furthermore, the height of each strip in the model is 2m.

Table (2) shows the values of the mass, stiffness and damping estimates for all strip elements of the piles group-cap model. Figure 11 shows the soil wedge contours that would move with the pile group when subjected to lateral excitation. The time history of the Aqaba earthquake of 1995 in the North-South direction is used to represent the earthquake excitation on the system. The latter earthquake record is normalized to 0.25g corresponding to the maximum expected acceleration in the fifth seismic active geographic zone in Egypt.

Material properties Axial Direction Hoop Direction Tensile Strength (MPa) 290 500 Comp. Strength (MPa) 150 N/A Elastic Modules (GPa) 15.13 17.69

Poisson Ratio 0.32 0.34 Unit Weight (KN/m3) 20.9 20.9

Earthquake Excitation

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482

Figure 11. Soil wedge contour that would move with the

pile group when subjected to lateral excitation

Table 2. Mechanical properties of GFRP Tube

6 Analysis of results

On studying the dynamic response of the FRP piles-cap system under the Aqaba earthquake (North-South direction), as shown in figure 12, the lateral acceleration responses of the model strips are observed, see Figures 13 to 16. As shown in the latter figures, it is clear that the accelerations were amplified beyond the maximum magnitude of the earthquake excitation especially in the part of the shaft above the sea bed. Moreover, the response of Strip-5 shows the transient response after the earthquake excitation might take clearly longer time before reaching zero motion. The case is even acute in the case of the pile cap response which indicates unstable condition after 50 seconds of the earthquake excitation, see Figure 16.

The above results can be attributed to the fact that the variation in stiffness between the Strip-5 and Strip-6 led to a soft story behavior. However, the fact that the modulus of elasticity of FRP is nearly less than one tenth that of steel, may have added considerably to the problem. In addition, given the fact that the connection between the FRP piles and the pile cap may not be fully rigid, this raises doubts about the consequences on the integrity of the supported structure.

Moreover, on studying the power spectral density of the lateral acceleration response of the model strip right under the

Figure 12. Normalized Aqaba earthquake ground acceleration time

history (North-South direction)

Figure 13. Lateral acceleration response of the bottom strip element of the model (Strip-1)

Figure 14. Lateral acceleration response of the strip element right under the sea bed (Strip-6)

Figure 15. Lateral acceleration response of the strip element right over the sea bed (Strip-5)

Figure 16. Lateral acceleration response of the pile cap

Element No.

Group stiffness

KN/mm

Group Mass Kg

Damping Ratio %

Pile Cap 1

- 1612.22

225178.40 39092.30

- -

2 1612.22 39092.30 -

3 1612.22 39092.30 3.00

4 1612.22 39092.30 3.00

5 1612.22 39092.30 3.00

6 114285.64 1073605.55 3.00

7 245556.90 822989.85 3.00

8 281149.46 605195.77 3.00

9 256227.40 419356.83 3.00

10 199579.11 263705.45 3.00

11 166607.09 55493.53 3.00

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Unstable condition

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

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sea bed, it is observed that the max response concerns the frequency domain between 3 Hz and 5 Hz with the peak at 4 Hz, as shown in Figure 17. In contrast, the power spectral density of the lateral acceleration response of the model strip right over the sea bed indicates that the max response concerns the frequency domain between 0.9 Hz and 3 Hz with the peak at 2 Hz, as shown in Figure 18. This shift in the frequency domain with maximum response may be explained by the fact that the considerable variation in stiffness between the two strips 5 and 6 resulted in a soft story behavior such that the relative displacements considerably increased. The latter condition should have definitely affected the stability of the foundation system.

Furthermore, the above discussion is reflected in the power spectral density of the lateral response of the pile cap, where the kinetic energy clearly increased such that the max response occurred in the zone that included the fundamental natural frequency of the system (0.44 Hz). Consequently, the response of the system was unstable and the integrity of the foundation system was questionable.

Figure 17. PSD for the response of the strip element right under the sea bed

Figure 18. PSD for the response of the strip element right over the sea bed

Figure 19. PSD for the response of the pile cap

7 Conclusions

FRP composite piles behavior under earthquake excitation was studied. The paper introduces a dynamic model for a piles-cap system that is supposed to sustain a vertical reaction from the supporting box frame of a near shore bridge. Results indicate that despite the durable behavior of FRP piles in

harsh environments, yet, the fact that the modulus of elasticity is relatively small, almost less than one tenth that of steel, reduces the lateral stiffness and affects considerably the efficiency of the foundation system when subjected to lateral earthquake excitation. Thus, such behavior should be accounted for on designing bridges in active seismic zones.

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Filled Tubular FRP Piles, The 3rd Int. Conf. on Composites in Infrastructure, ICCI '02, San Francisco, June 10-12, paper no. 80, pp. 1-12., 2002.

[2] L. Kappes, M. Berry, J. Stephens and L. MacKittrick, Concrete Filled Steel Tube Piles to Concrete Pile-Cap Connections, Chicago, Illinois, United States, 2012

[3] H. Hu and R. Seracino, Analytical Model For Frp-And-Steel-Confined Circular Concrete Columns In Compression, Journal of Composites for Construction, North Carolina State University, Raleigh, USA, 2013

[4] A. Fam, M. Pando, S. Rizkalla and G. Filz, Precast Composite Piles for Route 40 Bridge in Virginia, Invited Paper, Proceedings, CD-Rom, CSCE 2003, Special Session on Soil-Cylinder Interaction, Moncton, NB, Canada, June 4-7, 2003, GCT-570, pp.1-10, 2003 .

[5] J. Davalos, P. Qiao and L. Shan, Advanced fiber-reinforced polymer (FRP) composites for use in civil engineering, West Virginia University, West Virginia, USA, Chapter 4, 2005.

[6] V. Puri and S. Prakash, The Foundations For Dynamic Loads, Art of Foundation Engineering Practice Congress, West Palm Beach, Florida, United States, 2010.

[7] S. Prakash and V. Puri, Piles under Earthquake Loads, Sacramento, California, United States, 2008.

[8] F. Edmonds, A. Carr, P. Goldsmith, P. North, J. Wood and R. Preston, Seismic Design of Bridges Section 4 – Bridge Foundations, Bulletin of NZSEE Vol 13, No 3, Wellington, New Zealand, 1980.

[9] M. Seniwongse,, Rehabilitation and Strengthening of Concrete Structures Using Carbon Fiber Reinforced Polymer, Bulletin of NZSEE Vol 13, No 3, Denver, Colorado, United States, 2008.

[10] S. Rizkalla and T. Hassan, Rehabilitation Of Concrete Structures With Frp, North Carolina State University Raleigh, NC, USA, 2002.

[11] A. Fam and S. Rizkalla, Behavior of Axially Loaded Concrete-Filled Circular Fiber-Reinforced Polymer Tubes, Journal, 2001.

[12] A. Mirmirn, Y. Shao and M. Shahawy, Analysis and field tests on the performance of composite tubes under pile driving impact, North Carolina state university, USA, 2002.

[13] M. Randolph, Analysis The response of flexible piles to lateral loading, Cambridge University, USA, Volume 31, Issue 2,1981.

[14] Bakis et al, fiber-reinforced polymer composites for construction, journal of composites for construction 6(2):73-87,2002.

[15] I. Volety, modeling of fiber reinforced polymer confined concrete cylinders, B.E., Chaitanya Bharathi Institute of Technology, India, May 2006.

[16] H. Poulos and E. Davis, Pile Foundation Analysis and Design, John Wiley and Sans, 1980.

[17] The Egyptian Code of Practice for Design and Construction of Concrete Structures; Ministry of Housing and Public Utilities; Research Center for Housing, Building and Physical Planning, 2012

[18] Department of Civil and Environmental Engineering, Analysis of Laterally Loaded Long or Intermediate Drilled Shafts of Small or Large Diameter in Layered Soils, University of Nevada, Reno, Final Report, Report No. CA04-0252, Chapter 5, 2008.

[19] FHWA-SA-91-048, COM624P– Laterally Loaded Pile Program for the Microcomputer, Version 2.0

[20] AllPile User’s Manual, USA, Volume 2, Chapter 8, 2011. [21] H. Baesler, R. Boroschek and C. Vega, Experimental Determination of

Damping Ratio of a Transparent Pier with Steel Piles and Reinforced Concrete Board, 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, 2004.

[22] J. Clarke and J. Duncan, Revision of the CLM Spreadsheet for Lateral Load Analyses of Deep Foundations, Virginia Polytechnic Institute, Virginia, USA, 2001.

[23] MATLAB® (1999). The Math Works Inc., Natick, Massachustes. [24] Aslan 100 fiberglass rebar, Glass Fiber Reinforced Polymer (GFRP)

Rebar - Aslan™ 100 series FIBERGLASS REBAR, Hughes Brothers, Inc. 210 N. 13th Street Seward NE 68434, USA, 2011

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