Designing structures subjected to dynamic loads is quite complex and involve structural, mechanical, geotechnical engineering and the theory of vibration. Machines, buildings under seismic effect, and wind turbines induce both dynamic and static loads on their foundations. If these structures are supported on piles, a full understanding is required of the dynamic interaction between individual piles and soil (pile-soil interaction) and between adjacent piles (pile-soil-pile interaction). Due to the complexity of this problem, codes and manuals recommend the use of approximate approaches. However, there is a general lack in research concerning the accuracy of these approaches. The present paper aims to help filling this gap by comparing the recommendations from selected codes and manuals with the results obtained from the numerical analysis. The codes and manuals considered in this paper are the Egyptian Code (EC), ACI, and the Canadian Manual (CM). This comparison is held over a range of parameters including excitation force frequency (f), soil modulus of elasticity (Es), pile slenderness Ratio (L/D), dimensionless spacing ratio (S/D) and pile group size (ng). At the end of this study, advantageous and downfalls of these approaches are discussed.
The design of foundations under dynamic loads is complex and should involve structural, mechanical, geotechnical engineering in addition to the theory of vibration. The geotechnical engineer decides to support a structure on a shallow or deep foundation system based on many factors including the subsurface conditions and the induced dynamic and static loads. In case of using a deep foundation system, the design requires a full understanding of the dynamic interaction between the piles and the soil (pile-soil interaction) and between adjacent piles (pile-soil-pile interaction).
The current paper aims to evaluate the recommendations provided in the ACI, Canadian Manual (CM) and the Egyptian Code (EC) concerning the dynamic behavior of pile foundations under vertical and lateral vibrations. This is accomplished by comparing the results from numerical analysis with the results obtained from these codes and manuals. First, the paper thoroughly explains the 3D finite element model used in current present research. Then, it discusses the results for individual piles before moving to the pile group results in the final part of this paper. The parametric study includes excitation force frequency (f), soil modulus of elasticity (Es), piles slenderness ratio (L/D), dimensionless spacing ratio (S/D) and pile group size (ng).
The verification work of the numerical model capability to capture the dynamic behavior of deep foundation is thoroughly discussed in Khalil et al. . This model is based on the laboratory work of Hetland  which is concerned with the dynamic behavior of offshore monopile wind turbines. Similar to the verification model, the numerical simulation for the current research is performed using the finite element software PLAXIS 3D. The simulated soil domain dimensions are 14 m x 14 m with a depth ranging between 12 m and 15 m (Figure 1). To limit the effect of wave reflection, soil boundaries are placed at a distance ranging between 18 and 23 times the diameter of the piles . Moreover, viscous boundaries are used at all sides of the soil domain, except the top surface. An overburden pressure of 20 kPa is assumed at the model surface to simulate the weight of the backfill soil.Dynamic behavior of pile foundations under vertical and lateral vibrations: review of existing codes and manualsAll authorsMohamed M. Khalil, Asmaa M. Hassan & Hussein H. Elmamlouk online:25 February 2020Figure 1. Proposed finite element model. (a) 3D model, (b) 3D mesh
The dynamic behavior of a single pile is studied under a wide range of excitation frequencies (f) varying between 0.5 Hz and 60 Hz. This range covers low frequency loads such as wind and sea waves, frequencies of reciprocating and some rotating machinery as well as seismic waves. Figures 5 and 6 show the variation of stiffness (Ks), damping (Cs), and peak displacement for a single pile undergoing vertical and lateral dynamic motions. The finite element model (FE) shows that as the excitation frequency increases, Ks increases and Cs decreases under both types of vibrations. The rate of change (increase in Ks and decrease in Cs) is the highest at frequencies less than 5 Hz. The rapid variation of impedance parameters at such low frequencies is attributed to the fact that the system is transitioning from static to dynamic behavior. The same trend was observed in the rigorous solution of Kaynia and Kausel . These results prove that the dynamic pile-soil interaction depends on the excitation frequency [5,19]. It is also found that the rate of increase of stiffness is higher than the rate of decrease of damping (for f > 5 Hz). This leads to attaining lower values of peak displacement at higher frequencies as seen in Figures 5(c) and 6(c).Dynamic behavior of pile foundations under vertical and lateral vibrations: review of existing codes and manualsAll authorsMohamed M. Khalil, Asmaa M. Hassan & Hussein H. Elmamlouk online:25 February 2020Figure 5. Vertical dynamic behavior of single pile: (a) stiffness, (b) damping, (c) peak displacement (L/D = 20, 100%Es)
The impact of changing the soil stiffness (Es) is investigated on the vertical dynamic behavior of a pile group of four as shown in Figure 11. As a result of decreasing the soil stiffness (Es) by 50%, the finite element model shows a non-uniform reduction in Kg. The reduction varies from as low as 4% (between 25 Hz and 35 Hz) to as high as 39% at f = 60 Hz. Meanwhile, Figure 11(b) shows that Cg slightly increases (by less than 5%) between 10 Hz and 27 Hz. For frequencies larger than 27 Hz, Cg decreases by a value up to 39%. Accordingly, a general increase in the peak displacements is depicted. However, this increase is variable along the studied frequency range and is found to vary between 8% and 52% (Figure 11(c)). The same trends are found when the Canadian Manual approach is applied which have already been reported by many researchers [8,9]. The length of a stress wave traveling through a soil media is, basically, dependent on its velocity through this media and the excitation frequency. Therefore, changing the stiffness of the soil (Es) alters the compression and shear wave velocities and, consequently, the length of the stress waves traveling between adjacent piles. Therefore, the phase in which the stress waves are emitted from the vibrating piles and reaching the adjacent piles changes. This change can be in phase or out of phase with the adjacent piles movement. As a result, the impedance parameters may decrease, increase or remain almost constant. On the other hand, ACI depends on the static interaction coefficients. These interaction factors do not take into account the effect of the stress waves considered in other approaches. Therefore, uniform reductions in Kg and Cg and increase in peak displacements are obtained.Dynamic behavior of pile foundations under vertical and lateral vibrations: review of existing codes and manualsAll authorsMohamed M. Khalil, Asmaa M. Hassan & Hussein H. Elmamlouk online:25 February 2020Figure 11. Effect of soil stiffness on vertical dynamic behavior: (a) stiffness, (b) damping, (c) peak displacement (ng = 4, L/D = 20, S/D = 5)
Figure 13 shows that the pile slenderness ratio (L/D) has a slight impact on the dynamic behavior of pile group subjected to either vertical or lateral vibrations. This is proved via the results obtained from the finite element solution. Increasing the pile slenderness ratio from 20 to 30 leads to a decrease in peak displacements by less than 5% (under vertical vibrations) and less than 7% (under lateral vibrations). The same trend is observed while using the Canadian Manual. Meanwhile, according to ACI, L/D has a negligible to no effect on the peak displacements.Dynamic behavior of pile foundations under vertical and lateral vibrations: review of existing codes and manualsAll authorsMohamed M. Khalil, Asmaa M. Hassan & Hussein H. Elmamlouk online:25 February 2020Figure 13. Effect of pile slenderness ratio under (a) vertical vibrations (b) lateral vibrations (ng = 4, L/D = 20, S/D = 5, 100% Es)
The effect of pile group size is investigated via the group stiffness/damping efficiency. Group stiffness/damping efficiency is defined as the ratio of the average stiffness/damping per pile in the group to the stiffness/damping of a comparable single pile. Figure 14 shows the variation of group stiffness efficiency, group damping efficiency and peak displacement for groups of four and nine piles undergoing lateral dynamic motion.Dynamic behavior of pile foundations under vertical and lateral vibrations: review of existing codes and manualsAll authorsMohamed M. Khalil, Asmaa M. Hassan & Hussein H. Elmamlouk online:25 February 2020Figure 14. Effect of group size on lateral dynamic behavior: (a) stiffness group efficiency, (b) damping stiffness group efficiency, (c) peak displacement (100%Es, L/D = 20, S/D = 5)
The dynamic behavior of the pile group calculated according to the Canadian Manual shows a similar trend to the finite element model. ACI is less accurate in capturing the dynamic behavior. ACI underestimates stiffness under high frequencies, consequently, peak displacements are over-predicted. Therefore, ACI is suitable to conduct preliminary calculations for small and medium size machine foundations only. Meanwhile, the Egyptian Code does not provide any method to evaluate the dynamic behavior of pile groups. Finally, it is found that the procedure proposed by the Canadian manual is the most capable of simulating the dynamic behavior of single piles and pile groups. 2b1af7f3a8