On vibration mode of pultruded FRP sheet piles

Transcription

1 Fourth International Conference on FRP Composites in Civil Engineering (CICE2008) 22-24July 2008, Zurich, Switzerland On vibration mode of pultruded FRP sheet piles G. Boscato & S. Russo University Iuav of Venice, Venice, Italy ABSTRACT: the application of PFRP (pultruded fiber reinforced polymer) sheet piles in civil engineering field with protection or structure function represents by then an effective alternative to steel piles especially because of their high durability. In spite of all that, application of PFRP material is not yet so wide, being probably even if erroneously because of cost and high deformability. In fact, also using steel the added costs that are needed to improve durability are really high; with the use of PFRP it is also possible to limit the depth of sheet piles to meters. Therefore this study wants to show, first of all, a typical application of PFRP sheet piles in the Venetian lagoon where the longitudinal and transversal vibration modes have been detected by accelerometers. In detail, the test shows the dynamic response of PFRP piles during the insertion in the ground for two different conditions: the first with a singular pile and the second, the real configuration, where the sheet pile is constrained to previous sheet piles. This research shows, finally, the comparison between experimental values and numerical data to complete the information on PFRP sheet piles for what concerns structure performance and application of the new technology rather than steel piles. 1 INTRODUCTION Recently, also in the structural engineering field regarding the sheet piles employment, the fiber reinforced polymer material (FRP) produced by pultrusion process has been employed. This is especially due to the possibility to use a very light and durable structural material with not negligible benefits for enliven, transport and insertion in the ground. This paper presents the first experimental tests and numerical results on vibration mode of sheet GFRP (with glass fibers) piles during the insertion in the ground through dynamic action directly applied to the piles. Generally speaking, this item is relatively innovative if we look at the usual employment of FRP material for reinforcement of existing structures or for new light structures, on which several applications and researches were made until now in fact at the present time applications and studies, Bastianini et al. (2007), Russo (2007) and Shao (2006), are still not many. Vice versa the use of FRP piles instead of steel piles seems to be very promising and moreover the area of draft and technical recommendations is appearing widespread. In the detail this research illustrates the evaluation of the first vibration mode, acceleration and distribution of lateral displacement along sheet piles of glass fiber and vinilester matrix, similar in shape to the steel Larseen sheet piles. The test was carried out applying the accelerometers along the surface of each sheet pile for two different types of dynamic action equal to 380 Hz and 760 Hz and in correspondence of two types of application, i.e. in presence of a singular sheet piles and in presence of a pair of sheet piles previously bonded with resin and mechanical longitudinal connection. To make a comparison between experimental and numerical results of first mode of vibration and evaluation of lateral displacement, Finite Element Analysis is shown together with the deepening of the resonance phenomenon

2 Finally, some considerations regarding the performance of a steel sheet piles with the same geometrical characteristic than the GFRP sheet piles are here presented. 2 MECHANICAL CHARACTERISTICS OF GFRP SHEET PILE AND TEST SETUP The mechanical and geometrical characteristics of the GFRP sheet piles are shown in Table 1, the x, y, and z axis direction are illustrated in Figure 1. The sheet pile were made by 48% in volume of glass fibre type E, and vinilester matrix. Figure 1 shows also in detail the shape of the GFRP sheet piles indicating the accelerometer position along each sheet pile. The 8 accelerometers employed are piezoelectric sensing elements featuring a cylindrical shear stress configuration with sensibility equal to 1000 mv/g, variation field assumed ± 10g and resolution of 1x10-5 g in the frequency variation from 0.25Hz to 800 Hz. Each sensor is equipped with integral charge preamplifier and is connected to the digitizer unit by means of high stability coaxial cables. The digitizer unit is based on commercial 13-bit data acquisition boards (Data Shuttle Express). The signal has been acquired with a lowpassing hardware elaboration equal to 2 khz; the signal s scansion is of 1000Hz. The level of dynamic load-vibration applied through traditional machine usually employed to insert the piles in the ground came from 380 to 760 Hz; the external sinusoidal load is equal to the self weight of insertion machine; the dead load of the clasped system is equal to 10000N Table 1. Mechanical and geometrical characteristics of sheet pile E xx E yy E zz G Density ν (MPa) (MPa) (MPa) xz ν zy ν yz (MPa) (kg/cm 3 ) A (cm2 ) J xx (cm 4 ) J yy (cm 4 ) Where E is the elastic modulus, ν is the poisson s ratio, G is the shear modulus, A is the area of cross section and J is the moment of inertia. Figure 1. Sheet pile shape and accelerometer location The acceleration measured through accelerometers in time domain of the insertion of a single sheet pile two meters deep in the ground is shown in Figure 2. Particularly, the number of oscillations detected by sensor n.6 from 20 to 30 till the end of dynamic action is enlightened. In detail, sensor 7 and 8 fixed to the web show the different oscillation amplitude influenced by different stiffnesses of webs; in the same way, the frequency domain calculated by Fast Fourier Transform is shown in Figure

3 Figure 2. Experimental evaluation of vibration response in time domain Figure 3. Experimental evaluation of vibration response in frequency domain 3 FINITE ELEMENT ANALYSIS To better understand the reliability of the experimental results given by the dynamic test, a first finite element analysis considering two different boundary condition to simulate the effective insertion in the ground in the first case with total length of 9 meters and simply supported, and in the second case with length of 7 meters with support and clamped condition was carried out. For what concerns the constitutive law assumed for GFRP material, linear elastic behaviour and perfect bond between fiber and matrix were assumed; for this analysis the damping ratio considered is equal to 2.5%, (Boscato 2007). For this analysis, Strauss 7 software release was used; the pultruded pile was modeled through plate elements. The analytical results of the first case application, with dynamic action equal to 380 Hz is shown in Figure 4; while the second case, with 760 Hz dynamic value of action is represented in Figure 5. In both figures the lateral displacement is illustrated, while the stress values are shown in Figures 6 and 7 for the two boundary conditions. In all figures, letters A, B and C show respectively the fundamental frequency, the natural frequency close to frequencies of applied dynamic loads and, finally, the frequencies of vibrations forced

4 Figure 4. Lateral displacement, scheme 1 Figure 5. Lateral displacement, scheme 2 Figure 6. Vertical stress, scheme 1-4 -

5 Figure 7. Vertical stress, scheme 2 To simulate the real performance of GFRP sheet piles versus the steel sheet piles usually employed, a comparison between the mechanical response of a steel sheet pile and GFRP pile with the same cross section and length was carried out through finite element analysis. All the results are shown in Tables from 2 to 5. Table 2. Maximum results of displacement and stress values of GFRP sheet pile, scheme 1 Natural frequency-mode 1_8.45Hz Aging vibration 380Hz Table 3. Maximum results of displacement and stress values of GFRP sheet pile, scheme 2 Natural frequency-mode 1_11.17Hz Aging vibration 760Hz Table 4. Maximum results of displacement and stress values of steel sheet pile, scheme 1 Natural frequency-mode 1_13.78Hz Aging vibration 380Hz Table 5. Maximum results of displacement and stress values of steel sheet pile, scheme 2 Natural frequency-mode 1_20.32Hz Aging vibration 760Hz Where σ t and σ c are respectively the maximum values of tensile and compression stresses. 4 RESULTS COMPARISON The comparison between experimental results and values determined by FEM analysis is depicted in Figure 8; in detail, this figure points out the structural response of FRP element subjected to dynamic load equal to 760Hz following the first mode of vibration (37.7Hz as highlighted in Figure 3). The dynamic behaviour was recorded by each of the accelerometers for each depth of insertion (i.e. D1m = Depth 1 meter). The analytical values simulate the global behavior of the sheet pile, considering in this specific case the real boundary conditions of Winkler soil - with constant K= 1.2 Kg/cm3 - for the inserted part and sliding pin restrain at the end with dynamic load applied

6 lateral displ. along y axis (mm) Hz_mode 1 D1m_exp D2m_exp D3m_exp D4m_exp D1m_FEM D2m_FEM D3m_FEM D4m_FEM length (m) Figure 8. Comparison between experimental and FEM results The FEM values show a good agreement with the experimental results. The differences are caused by the difficulty to guarantee the perpendicular position of FRP element to soil during the experimental phase. 5 CONCLUSIONS By experimental results and finite element analysis it is possible to draw the first conclusions as follows: - the experimental results highlight the asymmetrical behavior of FRP sheet pile, mainly due to the different stiffness of the two flanges. - A good agreement between experimental and analytical results appears. - The response of 9 meters long sheet pile is controlled by global structural behavior; in the initial phase of the insertion, displacements involve exclusively the web - that is vulnerable mostly for applied external dynamic load. The greater stiffness of 7 meters is achieved by boundary conditions, in this case the displacements are really lower along the sheet pile; in the FE analysis negligible local instability is observable too. - The longitudinal stress values obtained by finite element analysis are negligible. - The higher deformability of pultruded elements is highlighted by finite element analysis in the free vibrations field; however this deformability decreases with the increment of vibration dynamic load. - The comparison between steel and GFRP materials carried out by FE analysis points out similar lateral displacement values. The fundamental frequency of steel sheet pile is higher than GFRP element; these values show the different stiffness of GFRP and steel materials. - Generally speaking, the whole insertion process of GFRP sheet piles can be done with the same operations usually employed for the steel sheet piles. REFERENCES Bastianini, F., Boscato, G., Russo & S., Sciarretta, F., (2007). Natural frequencies of pultruded profiles with different cross-section. Proceedings of ACIC 07, Advanced Composites in Construction, University of Bath, Bath, U.K. Boscato G., Russo S., (2007). Lo smorzamento nel comportamento dinamico degli elementi strutturali in composito fibrorinforzato, Atti del Workshop Materiali ed Approcci Innovativi per il Progetto in Zona Sismica e la Mitigazione della Vulnerabilità delle Strutture, Università di Salerno, Salerno, Italy Russo S., (2007). Strutture in Composito, Sperimentazione, Teoria e Applicazioni, Hoepli. Shao, Y., (2006). Characterization of a Pultruded FRP Sheet Pile for Waterfront Retaining Structure, Journal of Materials in Civil Engineering, Vol.18, No