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Journal of Coastal Research SI 73270-276Coconut Creek, Florida Winter 2015 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai University Nanjing 210000, China Numerical Analysis on Dynamic Responses of the Sheet-Pile Wharf with Separated Relieving Platform under Horizontal Seismic Loads Zhibin Jiao, Huiming Tan*, Taotao Mei, and Xiangqian Hu ABSTRACT Jiao, Z.; Tan, H.; Mei, T., and Hu, X., 2015. Numerical analysis on dynamic responses of the sheet-pile wharf with separated relieving platform under horizontal seismic loads. In: Mi, W.; Lee, L.H.; Hirasawa, K., and Li, W. (eds.), Recent Developments on Port and Ocean Engineering. Journal of Coastal Research, Special Issue, No. 73, pp. 270-276. Coconut Creek (Florida), ISSN 0749-0208. The dynamic responses of a new kind of sheet-pile wharf under horizontal seismic loads have been simulated by using the finite element method, and the influences of earthquakes characteristics have been analyzed in detail. Compared with the traditional sheet-pile wharf, the separated relieving platform system has been adopted for the new wharf and the dock basin could be much deeper for larger ships. The results of the numerical calculation show that the separated relieving platform system is still effective under seismic loads, and the maximum internal force of structural elements doesnt change when earthquake acceleration reaches the peak value. With the increase of the earthquake peak ground acceleration value, the maximum internal force of structural elements all increases at different degrees, the amplification of the bending moment is the largest, those of tie rods tension force and anchor walls bending moment are a bit smaller than that of the front wall, and those of front pile and back piles bending moment are the smallest. The amplification coefficients of all internal force under the Kobe wave loads are always bigger than those under the EL-Centro wave with the same PGA value, which indicates that, in addition to the earthquake wave peak value, the responses are also affected by other earthquake characteristics, such as spectrum, wave energy density and wave total energy. ADDITIONAL INDEX WORDS: Sheet-pile wharf, dynamic responses, earthquake waves, structural force. _ INTRODUCTION The sheet-pile wharf, one of the three typical wharf structures, has many advantages, such as convenient construction, low cost, and good durability, making the wide use of sheet-pile possible. With the large-scale development, the excavation depth of harbor basin becomes deeper. Sometimes, the height difference between sea and land can be ten meters and more, and the front wall has to undertake much bigger horizontal soil pressure. To solve the problem, a new type of sheet-pile wharf with separated relieving platform has been designed (Liu, 2006). It is composed of front wall, anchor wall, pull rod and relieving platform system. Compared with the traditional sheet-pile, it is featured by the relieving platform system with piles and relieving platform. For the whole wharf, there is a gap between relieving platform and front wall, so this new wharf structure is called sheet-pile wharf with separated relieving platform. The purpose of installing the relieving platform system is to minimize the load on the front wall. By now, this new type of sheet-pile wharf has been applied successfully to the 100,000 ton dock in Tangshan harbor district, and the application is satisfactory. Some scholars have made studies on this new sheet-pile wharf. With centrifugal model experiments and numerical calculations, Gong (2007) analyzes this new type of wharf structure. She thinks that loading conditions of the sheet-pile wharf with separated relieving platform have improved. Compared with the wharf with single anchor on the same scale, the bending moment of front wall and the displacement decrease obviously, which indicates the structural form is effective. Through centrifugal model experiments, Xu et al. (2010) has studied the influences of the relieving platform structure on the front wall, the results of which show that the relieving platform can obviously minimize the bending moment State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Nanjing Hydraulic Research Institute Nanjing 210000, China College of Harbor Coastal and Offshore Engineering Hohai University Nanjing 210000, China School of Transportation Southeast University Nanjing 210000, China www.JCR _ DOI: 10.2112/SI73-048.1 received 5 August 2014; accepted in revision 17 November 2014. *Corresponding author: thming Coastal Education Sumer et al., 2007; Susumu, 2010). Park et al. (2009) analyze to determine the representative earthquake scenarios and the diachrony of ground motion before the results are applied to simplified and advanced liquefaction analyses at ports located in the southern parts of Korea. Relevant scholars have also conducted researches on the responses of the traditional sheet-pile wharf under earthquakes. Seismic design of the sheet-pile wharf mainly uses pseudo-static analysis and effective-stress analysis. The priority of pseudo-static analysis is the overall stability and the internal force of structure elements of the wharf structure. Christie (2010) analyzes the sheet-pile wharf in the finite element analysis method, and then compares the results of pseudo-static analysis. The comparison shows that the results of dynamic analysis and pseudo-static analysis are equal to each other in dynamic augment, but are different from each other in soil pressures. Jamshidi et al. (2010) discusses the influences of fiber reinforced backfill characteristics on the dynamic deformation of sheet pile walls by using the shaking table test. The seismic design has been introduced after the 1993 earthquake caused great damage to the uniform wharf (Arulmoli et al., 2013; Klusmeyer, Yan, and Firat, 2013). The design of the new wall focuses on the alignment of the wharf surface and reduces the risks of potential soil liquefaction during future events, and the new wall is expected to meet the performance criteria for Level 1 and 2 earthquakes. The mechanisms of large ground deformation caused by soil liquefaction and the fact of the pile group behind quay walls subject to the lateral soil displacement have been studied by Ramin and Ikuo (2010), based on shaking table model tests. The results show that the effect of pile-head constraint on the profiles of the monotonic bending moment is found important as it produces a bending moment at the pile-head in the opposite direction to the bending moment at the bottom. Moreover, this constraint considerably reduces the pile deflection. FIELD TEST Subsoil Investigation The testing field is located in Tangshan port, the Bohai bay area in China. The test port is a 100,000 ton cargo berth. The main coastal distribution is sandy soil, and the thickness distribution can be more than 80 m. Through the field drilling sampling and laboratory tests, each soil layers physic-mechanical index are obtained. Wharf Design The main design scheme of testing the wharf structure is: the sea side piles are 4.0 m away from the wharf apron, and is made up of 1200 mm 1600 mm (bending direction) square piles; the land side piles are 1200 mm 1200 mm piles; the thickness of concrete bearing platform is 1.0 m. The tie rod-which connects breast wall and anchor wall is Q34595 in size; the thickness of anchor wall is 1.1 m. NUMERICAL COMPUTATION Numerical Model In the calculation model, wall and piles are made of reinforced concrete, whose compressive strength is 30 MPa. Because concrete modulus is far bigger than soil modulus, the deformation of structures is elastic, and walls and piles are simulated by linear elastic material. In the 2D finite element calculation, based on the principle of equal flexural rigidity, piles are regarded as plates, and the thickness of equivalent plates for front pile and back pile are 0.98 m and 0.73 m respectively. Rod is simulated by an anchor rod, namely a fixed axial rigidity spring with two nodes. In order to reflect the actual working status of the tie rod in calculation, 50 kN/m tension is applied in advance. In the whole construction of the wharf, excavation and dredging of the wharf apron is the most important period in terms of load bearing. During that period, the soil body is in unloading status and modulus will increase. Therefore, hardening soil model (Schanz and Vermeer, 1996) is used in this calculation. Besides soil constitutive model and interface parameters, the damping of material must be also considered in dynamic calculation. Material damping of soil is in general caused by the development of viscous characteristics, friction and plasticity. Rayleigh damping formula is used to simulate material damping in this calculation. There are many ways to confirm damping factors (Park and Hashash, 2004). The practical calculation parameters of soil and contact interface can be seen in Table 1. Table 1. Properties of soils and soil-structure interfaces. Properties Silty to fine sand Mucky clay Fine to medium sand Silty clay Saturated unit weight kN/m3 17 16 19.5 19 Unsaturated unit weight kN/m3 16 15.6 18.7 18.1 Stiffness modulus for reference MPa 5.1 2.15 11.9 3.78 Unload-reload modulus MPa 14.5 6.9 30.9 11.8 Power exponent of modulus stress 0.5 0.5 0.5 0.5 Poissons ratio 0.3 0.35 0.3 0.3 cohesion kPa 0.21 12 0.2 18 Friction angle 26 17 31 19.6 Reduction factor of interface intensity 0.7 0.7 0.7 0.7 Rayleigh damping factor 0.01 0.01 0.0.1 0.01 272 Tan et al. Journal of Coastal Research, Special Issue No. 73, 2015 In static calculation, load mainly means the gravity of structure and soil, and the underground water level is -1.5 m. In dynamic calculation, horizontal dynamic acceleration diachrony is applied to model bottom. To analyze the impact of earthquakes of various intensity-on the wharf structure, the acceleration diachrony is modified based on Equation (1). max max ( ) ( ) a t a tA A = (1) ( )a tand ( )a t are original acceleration time and adjusted acceleration time respectively, max A and max A are the initial earthquake peak ground acceleration (PGA) value and the adjusted PGA respectively. Moreover, to analyze the impact of different acceleration time histories on dynamic responses of covered sheet-pile wharf, EL-Centro wave and Kobe wave are applied at model bottom. Standardized seismic wave ( 2 max 1.0/Am s=) acceleration time-histories can be seen in Figure 2. Form the earthquake type, Kobe wave is a kind of seismic wave caused by the straight down type of earthquake, and approximately transmits in the vertical direction. EL-Centro wave is not caused by the straight down type of earthquake. Figure 3 shows the Fourier spectrum of two seismic waves, and the distinction between them is clear. On the other hand, the total energy of EL-Centro wave is much bigger if these two kinds of wave have the same PGA value. However, the time-varying spectrum in reference (Fan, Lu, and Zhang, 2010; Nozu, Ichii, and Sugano, 2004) shows that the maximum value of energy density of Kobe wave is much bigger than that of EL-Centro wave, which means that energy of Kobe wave is more intensive. (a) (b) Figure 2: (a) Acceleration time-histories of standardized EL-Centro wave; (b) Acceleration time-histories of standardized Kobe wave. VERIFICATION To verify the rationality of infinite element calculation results, the results of the finite element static calculation are compared with those of the field test observations. In the field test, only the stress data of front wall and front pile are obtained. The data are used to verify the rationality and accuracy of calculation of finite element calculation results. Front wall is one of the most important structure elements of the wharf. The measured value and the finite element calculation value in static condition are showed in Figure 4, and the measured value is the observed result at the end of observation term. In the field test, due to the influence of different conditions, such as changes in water level and other conditions, the maximum bending moment value of front wall does not occur in the observation term, but occurs in the observation period, where the maximum value is 769, and the maximum calculation value is 985.8. (a) (b) Figure 3: (a) Fourier spectrum of EL-Centro wave; (b) Fourier spectrum of Kobe wave. Figure 5 illustrates the bending moment distribution of front pile (seaside pile). The measured inflection points elevation is about -9 m, while the calculation inflection points elevation is about -15 m, which is approximate to front walls inflection point. The maximum measured value is 1240, and the finite element approach calculation value is 1314.6. That the maximum bending moment of the pile is bigger than that of front wall indicates that the relieving platform works well in undertaking the back soil pressure and upper load, and that it decreases the load working on front wall. The calculation result of the finite element approach basically indicates the internal force distribution rule of main members, such as front wall, pile, Numerical Analysis on Dynamic Response of Sheet-Pile Wharf 273 Journal of Coastal Research, Special Issue No. 73, 2015 tie rod and so on. So the finite element calculation model is acceptable. DYNAMIC RESPONSES OF WHARF STRUCTURE Wall With the effect of seismic loads, the internal force distribution of front wall is changing at different time, Figure 6 shows the distribution of front walls bending moments along depth at the acceleration peak value of 0.1 g under the effect of earthquake waves. From the figure, we can see that the bending moment at different time is different, but except for the difference in the depth, the basic distribution regularities are similar to static calculation results, and the inflection point is obvious. However, the location of inflection points and the maximum value of positive and negative moments are changing, so the maximum bending moment of front wall does not conform to that of the maximum acceleration time-histories s. Figure 4. bending moment of front wall. Figure 5. bending moment of front pile (seaside pile). Front Pile (Seaside Pile) With the effect of seismic loads, the internal force distribution of front wall is changing at different moment. Figure 7 is the distribution of front piles bending moments along depth at different moment under the effect of earthquake waves with different acceleration peak values. As can be seen from the figure, the bending moment is different at different time; however, the distribution along depth is basically the same as the results of static calculation. There is obviously inflection point, but the location of inflection point and the maximum bending moment are changing. The moment when the maximum bending moment of front wall occurs is different from the moment when the seismic acceleration time-histories peak value occurs. Figure 6. Bending moments of front wall under El-Centro waves (PGA=0.1g) at various time steps. Figure 7. Bending moments of front pile under El-Centro waves (PGA=0.1 g) at various time steps. 274 Tan et al. Journal of Coastal Research, Special Issue No. 73, 2015 Back Pile (Landside Pile) The internal force distribution of back pile is changing under the earthquake loads. Figure 8 is the bending moment distribution diagram of back pile along depth at different time under the effect of earthquake waves with peak acceleration at 0.1 g. From the figure, we can see that the bending moment is different at different time, and the biggest moment is negative moment, which appears at the upside of the pile (at about -6 m). Compared with the static status, its distribution along depth is varied in some moment, mainly including facts that negative moment will appear in the lower part of the pile, which indicates that deep soil bodys embedded function isnt always optimal. The moment when the maximum bending moment of the pile appears does not conform to the moment when the peak acceleration appears. Figure 8. Bending moments of back pile under El-Centro waves (PGA= 0.1 g) at various time steps. Anchor Wall With seismic loads, the internal force distribution of anchor wall is changing at different moment. Figure 9 is distribution diagram of bending moments of anchor wall along depth at different moment under the effect of earthquake waves with the peak acceleration at 0.1 g. As can be seen from the figure, the moment is different at different time steps, but the distribution regularities along the depth are similar to the results of calculation, most moments are positive, the moment when the biggest bending moment of anchor wall occurs does not conform to the moment when the seismic peak acceleration occurs. COMPARISON OF DIFFERENT SEISMIC EFFECTS Figure 10 shows the change rule of amplification coefficient of the maximum bending moment of front wall under different seismic loads. With the increase of peak acceleration of seismic waves, the loads undertaken by the front wall increase, and the maximum bending moment is constantly increasing, but the increase is not obvious. While the peak acceleration increases from 0.1 g to 0.5 g, the maximum bending moment of front wall increases from 1.6 to 3.5 or above. By comparing calculation results of EL-Centro wave and Kobe wave, we can notice that the calculation results of Kobe wave is always bigger than those of EL-Centro wave when the peak acceleration is the same, especially when the PGA is bigger than 0.1 g, this trend is much more obvious. Figure 9. Bending moments of anchor wall under El