Seismic analysis of extended piles in sand considering effect of scouring and effect of water as added mass

Scouring is one of the major causes of the failure of bridges and offshore wind turbines. Piles under extreme scouring and earthquake loads are vulnerable to failure and need to be investigated thoroughly. In this study, the seismic responses of an extended concrete pile with no scour and four scouring depths conditions are investigated under an input motion based on a Kobe earthquake record. The effect of water during an earthquake has a significant impact on the structure as hydrodynamic pressure; however, it is generally ignored in the seismic analysis of piles. The present study uses the concept of added mass to consider the effects of water. The combined soilstructure-interaction and shear beam model is used to simulate pile and soil using the beam-on-nonlinear-Winkler foundation (BNWF) method. Soil is divided into multiple layers with increasing shear modulus and the mass of each soil layer is lumped into two nodes of the layer. Modal analysis and nonlinear time history analysis are performed on different models. Results of the modal analysis show the decrease in fundamental frequencies of the pile with increasing scouring depths. The time history analysis results are reported in the form of Arias and Housner intensities, envelopes of acceleration, velocity, displacement of pile top, and envelopes of shear force and bending moment of the pile. Results show significant changes with scouring depth and the effect of water.


Introduction
Scouring is one of the major causes of failure of piles, bridges, offshore wind turbines, and structures buried underwater because of the removal of soil supports around the piles [1,2,3]. Scour can occur in sand as well as clay, and is classified as general scour (removal of the entire soil layer) and local scour (formation of the hole around the pile circumference) [4,5]. Due to the scouring effect, significant removal of bed materials around the structure led to a reduction in foundation stiffness and ultimately led to structural failure [6]. Many studies have been done considering the effect of scouring in the analysis with a primary focus on the lateral behavior of piles under constant horizontal loads or cyclic loads. However, limited studies have been done considering the combined effects of scouring and seismic loads. Reese et al. [7] introduced the formation of scour in clayey soil and investigated the formation of a gap at the pile-soil interface under the application of cyclic loads and concluded that the formation of the gap increases with a large number of cyclic load cycles and hence reduction in the lateral capacity of piles. Bennett et al. [8] investigated the Kansas bridge, founded on group piles subjected to scouring and reported a reduction in the lateral capacity of the bridges due to significant changes in bending moment and soil deformation. l-g model tests were performed on piles founded in marine clay subjected to scouring under monotonic and cyclic loads and found that scouring results in a significant increase in bending moment and pile deflection [9]. Mostafa [10] performed numerical analysis to investigate the effect of general and local scours in sandy and clayey soil and found that the general scour has more significant effects than the local scour and scouring in sandy soil is more critical in nature. Prendergast et al. [2] performed numerical analysis and verified experimentally to observe the effect of general scour on the frequency of the system and found that the fundamental frequency of the system decreases with increasing scour depths. Wang et al. [11] introduced a simplified method to study the dynamic interactions of saturated layered soils and piles considering general and local scouring subjected to different excitation frequencies and pile length-diameter ratios and found that the location of maximum bending moment shifted downward with increasing scour depths and length-diameter ratios.
Studies on piles considering both scour and seismic effects are limited. Therefore, the primary purpose of this study is to investigate the effect of general scouring in air and along with the effect of water under seismic loading. Before performing time history analysis, modal analysis is performed to observe the change in frequencies in different modes of vibration with increasing scouring depths and the results when the pile is in the air are compared with those when the pile is partially submerged in water. The effect of water is simulated using the concept of added mass and lumped into nodes of pile elements. For the time history analysis, the ground motion of the Kobe earthquake is selected. The pile is modelled with beam element and horizontal soil springs are modelled using a combination of linear and multi-linear plastic springs in a soil-structure-interaction model. The vertical soil is modelled using linear and multi-linear plastic springs in the shear beam model with a mass of each layer lumped at nodes of each layer. These two models are combined to perform the analysis. The results of the modal analysis show that the fundamental frequency of the system decreases with increasing scour depths. The second mode of vibration shows that frequencies increase with scouring depths. The time history analysis results are presented in the form of envelopes of acceleration, velocity and displacement of pile top and envelope of bending moment and shear force. The results show that the scouring effect and effect of water have a significant influence on the seismic analysis of piles.

Effect of water as added mass
The water around the pile has certain effects in the analysis especially when structures are in vibration due to dynamic loads. The effect of water as hydrodynamic pressure may arise under seismic load however, it is generally neglected in the analysis due to the complexity of considering fluid-structure-interaction along with soil-structure-interaction. The effect of water can be included simply by using the concept of added mass, which can be defined as the analytical expression of hypothetical mass differing from the virtual mass that represents the total effective mass of the system considering vibration [12]. The effect of water can be included as an added mass in the analysis using added mass lumped at each submerged structural element of the pile nodes. The concept of added mass to consider hydrodynamic pressure due to water is not new and previously successfully applied on other structures such as in gravity dam [13], on cylindrical tank [14], structure in the fluid medium [15], in the tower [16], structures under earthquake loads that can be converted to equivalent static loads [17] and circular cylinders subjected to low and high-frequency vibration [18]. The effect of hydrodynamic pressure as added mass due to water in the inner and outer wall of the elliptical hollow cylinders under earthquake was studied [19] and later on modified by Zhang et al.,  [20] for a single circular pile used in this analysis. The mathematical expressions are as follows [20]: = 0.918 . + 0.155 .
(2) = 1.248 . + 2.156 (3) where, m(z̄) is an added mass, z̄=z/h, l=D/h, z is the distance above river bed level, D is the diameter of the pile, h is the height of water from the river bed level and ρ w is density of water.

Problem statement
An extended concrete pile having a length of 35m and a diameter (D) of 2m embedded in dense sand is subjected to four general scouring depths with an increment of 1D depth. The deck on the pile has a dimension of 4.5m x 4.5m x 2.5m, which is replaced with a rigid bar with an equivalent length of 1.25 m, a mass of 121.27Mg and moment of inertia of 267.804 Mg-m 2 (Fig.1). The concrete used in the pile having a unit weight of 23.5 kN/m 3 , Poisson's ratio of 0.2, and Young's modulus of 2.49 x 10 7 kN/m 2 is adopted. For the rigid bar, the value of Young's modulus of 2.49 x 10 8 kN/m 2 is used. Initially, an embedded depth of 25m in saturated dense sand with the angle of friction of 39°, saturated unit weight of 20.5 kN/m 3 , and a relative density of 75% is adopted. The soil layers are divided with a thickness of 0.5m and the mass of each soil layer can be calculated using ρ s . A.t (ρ s = density of soil, A= crosssectional area of the soil column (100m x 100m adopted) and t is the thickness of each layer) and lumped at each node of the layer. The effect of water is considered using an added mass (Eq. 1) and lumped at the nodes of submerged beam elements of the pile (Fig. 1). The Kobe earthquake ground motion [21] recorded at the JMA site with a 1km closest distance to fault in 1995 is used in this analysis (shown in Fig.2). It has a peak ground acceleration (PGA) of 0.805 g with a predominant frequency of 2.898 Hz and Arias intensity of 8.39 m/s.   [22] is modified for saturated soil that can include the effect of water as added mass. The shear beam model includes linear and nonlinear soil springs and is capable of measuring and applying the amplified ground response at different soil layers. Initially, the ground response is applied at the base of the pile. The structure-pile-soil interaction model is based on a beam on Winkler foundation method (pile as structural beam elements and soil reaction as linear and nonlinear spring elements) is combined with shear beam model to simulate combined effects (Fig 3). For a more detailed description of this model, one can refer to Chiou et al. [22].

Results and discussion
It is anticipated that with increasing scouring depths, the fundamental frequency of the pile will decrease. However, it is not clear for other modes of vibrations and how they will behave when the effect of water is considered. Therefore, modal analyses of piles in air and water are performed for different scouring depths. The combined soil-structure-interaction and shear beam models and modal shapes are shown in Fig. 4. The variation of frequency with scouring depths is plotted and compared for with and without the effect of water as added mass (Fig. 5). From Fig.5, it is observed that the fundamental frequencies decrease with scouring depths and due to the inclusion of water in the analysis, each condition produced more than 3 to 4% decreased in frequencies (3.04% for 0D, 3.39% for 1D, 3.67% for 2D, 3.96% for 3D and 4.2% for 4D scouring depths). 2 nd and 5 th modes of vibrations show an increase in frequencies with scouring depths while 3 rd and 6 th show first increase than decrease in frequencies. 2 nd Mode of vibration shows the least effect of water as added mass. 3 rd mode shows a negligible change in 0D and 1D however, for higher scouring depths, it shows more than 14% decrease in frequencies. 4 th mode shows a 15% decrease in 0D and 1D scouring depths with negligible effects in higher depths. 5 th Mode shows a 13% decrement due to water for 4D scouring depth with negligible effects on other scouring depths. The 6th mode of vibration shows a decrement of 7% for 2D and 10% for 3D scouring depths with negligible effects in other scouring depths. These variations are due to the inertial and kinematic effects.

Fig. 3.
Combined soil-structure-interaction and shear beam model [22].   Results of time history analysis are presented in the forms of the envelope of acceleration, velocity, displacement of the pile top in Fig 6, and then followed by the envelope of shear force and bending moment of the pile in Fig. 7, and finally Arias and Housner intensities in Fig.8. The envelopes of pile top in terms of acceleration, velocity and displacement are shown in Fig. 6. (a), (b), and (c) respectively. Initially, acceleration response decreases sharply with scouring effects and with higher scouring depth change is not very high. Effect of water reduces the acceleration response by 4.4, 6.3 and 0.5% for scouring depths 0D, 1D and 3D while increases by 7 and 5% for scouring depths 2D and 4D respectively. Effect of water produces a higher acceleration response for some scouring depths and therefore, ignoring it may lead to stability issues. From Fig. 6(b), it can be seen that initially, peak velocity response decreases with scoring depth and then sharply increases with scouring depths. Effect of water reduce the velocity response for 0D scoring depths by 7% and 0.17% for 3D scoring depths. However, it increases 15.4% at 2D and 15.8% at 4D scouring depths respectively. More than a 15% increase in velocity response cannot be ignored in the analysis, therefore an inclusion of the effect of water in the analysis is very important. Fig. 6(c) shows a small change in peak displacement for scouring depths up to 2D and then the displacement sharply increases for higher scouring depths. The effect of water is also significant for scouring depths 2D or higher. Scouring depths 2D, 3D, and 4D show 2%, 7.8%, and 24% increases in the peak displacement response. For higher scouring depths, the displacement increment is very large because scouring and the effect of water increase the response significantly.   Fig. 7(a) and (b) show the variation of peak shear force and bending moment with the scouring depth of the pile in air and submerged in water. Initially, shear force reduced with increasing scouring depth and start increasing with higher scouring depths. A similar pattern is observed in the bending moment too. The effect of water as added mass shows significant change with higher scouring depths for shear force and bending moment both and therefore, the effect of water cannot be ignored in the seismic analysis.  Fig. 2). Arias intensity starts attenuated with increasing scouring depth from 0D to 2D scoring depths, increases again for 3D and decreases for 4D scoring depths. Added mass produces higher Arias intensities for all scouring depths; however, it is maximum at a scoring depth of 3D. Housner intensities are amplified with increasing scouring depths and also the effect of added mass increases with scouring depths and shows maximum differences at scouring depth 3D thereafter, the effect is lesser. These two intensity parameters depend on the peak acceleration, spectral acceleration and spectral velocity respectively. Therefore, they can capture the effect of the earthquake better than the individual parameters of acceleration, velocity and displacement.

Conclusion
From this study, the following conclusions can be drawn: 1. From the modal analysis, it is observed that the fundamental mode of vibration is critical under scouring effects and the effect of water should not be neglected. 2. The acceleration envelope of the pile top shows that the scouring initially attenuates the response and then it starts to be amplified with higher scouring depths. The effect of water produces a higher acceleration response for some scouring depths and therefore, ignoring it may lead to stability issues. 3. The velocity and acceleration envelopes show higher responses with increasing scouring depths and higher scouring depths produce higher (>15%) increases in responses due to an inclusion of the effect of water as added mass. Therefore, the hydrodynamic effect of water cannot be ignored in the seismic analysis of piles. 4. Arias and Housner intensities are able to observe the overall effect of the earthquake impact and either can be utilized in the design of piles instead of three different parameters of acceleration, velocity, and displacement.