Driven Pile Effects on nearby Cylindrical and Semi-Tapered Pile in Sandy Clay

: A pile foundation is commonly adopted for transferring superstructure loads into the ground in weaker soil. They diminish the settlement of the infrastructure and augment the soil-bearing capacity. This paper emphases the pile-driving effect on an existing adjacent cylindrical and semi-tapered pile. Driving a three-dimensional pile into the ground is fruitfully accomplished by combining the arbitrary Lagrangian–Eulerian (ALE) adaptive mesh and element deletion methods without adopting any assumptions that would simplify the simulation. Axial forces, bending moment, and lateral displacement were studied in the neighboring already-installed pile. An investigation was made into some factors affecting the forces and bending moment, such as pile spacing and the shape of the already-installed pile (cylindrical, tapered, or semi-tapered). An important response was observed in the impact of the driven pile on the nearby existing one, the bending moment and axial forces were not negligible, and when the pile was loaded, it was recommended to consider the coupling effect. Moreover, the adjacent semi-tapered pile was subjected to less axial and lateral movement than the cylindrical one with the same length and volume for taper angles smaller than 1.0 ◦ , and vice versa for taper angles greater than 1.4 ◦ .


Introduction
Piles could be adopted as a deep foundation for transferring loads of structures into the ground. They are commonly used when the ground is not able to support the structures individually. During earthquakes, some structures supported by a pile foundation collapse sometimes [1]. These collapses could be related to the exclusion of axial forces from some codes. Different techniques could be adopted for pile installations inside the ground going from drilling holes, boring, jacking, and driving the pile or cast in place. The driven pile is broadly adopted in modern engineering practices (improves the soil in case of seismic hazards and increases the soil stiffness in the weaker zone) and gained popularity in the past years because of their large tip and skin resistance [2,3]. Sadly, driven piles are associated with vibrations during the installation, noise, and reduced resistance issues [4]. Poulos [5] revealed that the driving of a pile involves a ground movement which will result in additional forces, bending moment, and displacement of nearby foundation structures. Severe damage or collapse of structures have been noticed after earthquakes, especially in weaker soil areas [1,6]. The bending moment and axial force experienced by piles during the event would have exceeded the bending moment and axial force of the section.
Tapered or semi-tapered piles are characterized by a difference at the bottom and top of the axial pile diameter. They are adopted into real engineering given the limited ground vibrations during the driving process. Tavasoli and Ghazavi, and Sormeie and Ghazavi [7,8] studied the ground motion related to tapered, cylindrical, and semi-tapered piles driven into the ground. The results showed that the non-uniform pile cross-section reduced working time, noise, and energy consumption. Nonetheless, the performance of tapered piles subjected to loading is not fully understood. Under harmonic loading, Peak vertical velocity [41][42][43][44]: (1)

Wave Propagation and Determination of Soil Damping Ratio
Damping is a vast topic in dynamics; it tends to be confused with phenomena that produce amplitude reduction. In a static analysis, the deflection of the structure is controlled by stiffness. Nevertheless, in dynamic analysis, the response switches between damping, mass, or stiffness. Damping is essential for calculating the response of the structures subjected to dynamic excitation [45]. Madheswaran et al. [46] revealed that the extreme of the vibration energy affecting adjacent structures was transferred by the Rayleigh waves that circulate near the ground surface. The waves generated by vibrations reproduce in the soil and could interrelate and damage adjacent constructions. It also could induce liquefaction, densification, and permanent settlement in the soil. The circulating waves close to the pile could be divided into (1) on the surface: the Rayleigh wave; (2) around the pile toe: the body wave; and (3) around the shaft: the vertical shear wave. Far away from the field, the soil response was controlled by the Rayleigh waves, and the body waves were considerably reduced. Near the field, the response of the soil was controlled by the shear waves [47].

Soil-Pile Interaction
The friction coefficient of the pile is evaluated according to the type of pile (steel or concrete), the type of soil (fine or coarse), and their properties. For sandy clay and concrete piles, the value varies between 0.2 and 0.4. They were conferring to the Technical Manual TM 3-34.22 (U.S. Army 2013). Farshi and Hamidi [16] proved that an augmentation in PPV conducted an upsurge friction coefficient principally near to the pile axis. Therefore, the friction coefficient reduction by adopting a steel pile rather than a concrete pile induced attenuation of ground vibrations. The pile-soil friction coefficient was taken as 0.35 in this paper, according to [15,16,48].

Evaluation of Pile Axial Ultimate Capacity
Methods for evaluating the pile's ultimate capacity in compression generally involve adding the end-bearing capacity to the shaft resistance (McCarron [49]).
where D = diameter of the pile, q = unit end bearing, and f (z) = unit skin friction. However, in this study, the piles were installed through the driven process; only the skin friction was mobilized (the shaft resistance was exclusively evaluated in this work). The final pile installation depth did not reach the bedrock. Equation (2) is simplified as The unit skin friction can be evaluated using Equation (4). f (z) = δS u (4) where α is a coefficient without dimension and S u is evaluated at the point in question and nominated the undrained shear strength of the soil. The formula proposed by the American Petroleum Institute API (1984,1987) advocates values for δ in relation to c u as follows Using the Mohr-Coulomb failure criterion the undrained shear strength is: And where σ 1 = kγz and σ 3 = γz. k is the lateral earth pressure factor, γ is the soil density, and z is the depth of the point in question. k can be evaluated by [34,50]

Numerical Model and Verification
The analysis method used in this paper involved two steps: (1) driving a single pile into the soil without any other structures and comparing the results with the field measurement presented by Wiss (1981) [51]; (2) driving the pile adjacent to the nearby existing pile and carrying out parametric studies on the pile shape and pile spacing effects, pile bending moment, axial force, and lateral movement. The Abaqus/explicit [38] was adopted to drive the pile from the initial depth to the final position. A three-dimensional model was chosen to complete the simulation phase, and the results were compared with the case study by Wiss (1981).
The driven pile induced soil movement, which developed a bending moment and axial forces on the existing nearby piles. Damage or cracking (concrete pile) could occur caused by these developed forces. The response of the adjacent piles during the vibration procedures could be studied by means of parametric values such as pile shape and pile spacing to observe the influence of these parameters on the generated axial forces, bending moment, and lateral movement. Commonly, the pile is driven until it reaches a harder stratum. Figure 1 shows the fundamental problem and describes some of the same parameters of the geometric as the one provided by [51].

Numerical Model and Verification
The analysis method used in this paper involved two steps: (1) driving a single into the soil without any other structures and comparing the results with the field m urement presented by Wiss (1981) [51]; (2) driving the pile adjacent to the nearby exis pile and carrying out parametric studies on the pile shape and pile spacing effects, bending moment, axial force, and lateral movement. The Abaqus/explicit [38] w adopted to drive the pile from the initial depth to the final position. A three-dimensio model was chosen to complete the simulation phase, and the results were compared w the case study by Wiss (1981).
The driven pile induced soil movement, which developed a bending moment axial forces on the existing nearby piles. Damage or cracking (concrete pile) could oc caused by these developed forces. The response of the adjacent piles during the vibra procedures could be studied by means of parametric values such as pile shape and spacing to observe the influence of these parameters on the generated axial forces, be ing moment, and lateral movement. Commonly, the pile is driven until it reaches a har stratum. Figure 1 shows the fundamental problem and describes some of the same par eters of the geometric as the one provided by [51].  show the geometry of the soil and pile models. A uniform soil layer was taken (sandy clay), the diameter of the concrete pile was 0.5 m, the length was evaluated as 10 m, and 60 • was taken as the conical tip angle. A total of 25,120 nodes and 25,120 elements were used to build the model.  Figures 2 and 3 show the geometry of the soil and pile models. A uniform soil layer was taken (sandy clay), the diameter of the concrete pile was 0.5 m, the length was evaluated as 10 m, and 60° was taken as the conical tip angle. A total of 25,120 nodes and 25,120 elements were used to build the model.  The material properties adopted are listed in Table 1. Their characteristics were the same as the model proposed by [15,51,52]. Hence, the reliability of the method was evaluated by comparing the results with the field measurement presented by Wiss (1981). An elastic model was used to capture the pile behavior, and the Drucker-Prager model was used to define the elastoplastic behavior of the soil with the friction angle (ϕ) set to 25°, the flow stress ratio (K) set to one, and the dilation angle (ψ) set to 1°. Due to the computer size limitation during the dynamic simulation, only one part of the model was mapped in a computational domain. Generally, the part of the ground that was expected to have a significant effect was mapped. The remaining area was taken into account in the definition of the boundary conditions, which intended to limit the wave reflection. These boundary conditions were intended to capture the wave reflection during a dynamic simulation of pile driving. The reflection of the outward-propagating wave could be caused by the fixed boundary conditions, by adding energy inside the model.   Figures 2 and 3 show the geometry of the soil and pile models. A uniform soil layer was taken (sandy clay), the diameter of the concrete pile was 0.5 m, the length was evaluated as 10 m, and 60° was taken as the conical tip angle. A total of 25,120 nodes and 25,120 elements were used to build the model.  The material properties adopted are listed in Table 1. Their characteristics were the same as the model proposed by [15,51,52]. Hence, the reliability of the method was evaluated by comparing the results with the field measurement presented by Wiss (1981). An elastic model was used to capture the pile behavior, and the Drucker-Prager model was used to define the elastoplastic behavior of the soil with the friction angle (ϕ) set to 25°, the flow stress ratio (K) set to one, and the dilation angle (ψ) set to 1°. Due to the computer size limitation during the dynamic simulation, only one part of the model was mapped in a computational domain. Generally, the part of the ground that was expected to have a significant effect was mapped. The remaining area was taken into account in the definition of the boundary conditions, which intended to limit the wave reflection. These boundary conditions were intended to capture the wave reflection during a dynamic simulation of pile driving. The reflection of the outward-propagating wave could be caused by the fixed boundary conditions, by adding energy inside the model. The material properties adopted are listed in Table 1. Their characteristics were the same as the model proposed by [15,51,52]. Hence, the reliability of the method was evaluated by comparing the results with the field measurement presented by Wiss (1981). An elastic model was used to capture the pile behavior, and the Drucker-Prager model was used to define the elastoplastic behavior of the soil with the friction angle (φ) set to 25 • , the flow stress ratio (K) set to one, and the dilation angle (ψ) set to 1 • . Due to the computer size limitation during the dynamic simulation, only one part of the model was mapped in a computational domain. Generally, the part of the ground that was expected to have a significant effect was mapped. The remaining area was taken into account in the definition of the boundary conditions, which intended to limit the wave reflection. These boundary conditions were intended to capture the wave reflection during a dynamic simulation of pile driving. The reflection of the outward-propagating wave could be caused by the fixed boundary conditions, by adding energy inside the model. An infinite element at the side and bottom part of the finite element mesh to prevent wave reflection was used in [17,20]. The boundary element was proposed by [47] to capture the soil behavior. Other papers used artificial boundaries to absorb the wave deriving from the driven pile [15,16,48,52]. A regular augmentation of the damping was adopted for absorbing the wave and its limited the errors before model verification [53]. An artificial boundary can be summarized in the following steps:

1.
Divide the side and bottom part of the finite element mesh into subzones 2.
Increase the damping gradually in these subzones Figure 2 shows the five subzones of the artificial boundary definition to avoid a reflection of the wave.
The damping was gradually increased in these zones from 7.5-17.5%. Zhang and Tao evaluated the limit of the Rayleigh damping from 2.4-15.4% for clays and from 1.5-17.5% for sands. The soil damping was taken as 7% as provided by [15,16] for a similar soil layer. The depth of the soil was seized large enough to allow the natural damping of the waves at the bottom boundary.
Driving a pile is a process that involves large deformation in the soil surrounding the pile toe. This caused soil distortion and resulted in the abortion of the simulation. Therefore, an ALE technic was used to prevent abortion of the calculation. The use of the ALE could change the system over time (Figure 2). The element mesh shape is optimized due to its erratic movement. Both the arbitrary Lagrangian-Eulerian zone and pile were modeled using C3D8R (8-node linear brick elements with reduced integration and hourglass control coefficients reduction), and the rest of the soil layer was modeled using tetrahedral mesh. Furthermore, due to the large displacement in the soil zone surrounding the pile toe, an ALE mesh was carried-out to permit an automatic re-mesh for optimizing the element shape and to avoid cessation of the simulation afterward due to large element distortion. The element deletion technic was also adopted to delete the element that failed.
Modeling the hammer impact directly beyond some simplifications could be fastidious due to the complex equipment of the impact hammer (ram, cushion, and an anvil). Some analytical method representing each impact hammer was developed to simplify the simulation formula. The model given by Deeks and Randolph (1993) [54] was used to find the equivalent concentrated force for each hammer at the pile head blow (Figure 4).   The driven-pile installation from the initial position to the final depth was realized in three steps: (1) running the initial conditions of the site by applying gravity load, (2) taking a short time of 0.25 s to permit a primary pile penetration inside the soil caused by its weight, and (3) executing successive impact hammering on the head of the pile until it reached its final penetration depth.
The validity of the numerical simulation should be estimated by comparing some results with previous evaluated field monitoring results. The closeness of the results to the Appl. Sci. 2021, 11, 2919 7 of 13 field measurement was the criteria that defined the reliability of the results. The recorded values by Wiss (1981) were adopted to approve the proposed method. The comparison between the peak particle velocity (PPV) of numerical and measure values was conducted at some radial distances from the surface of the ground, as plotted in Figure 5. Conferring to Figure 5, the simulation results were feasible using the field measurement. The simulated and experienced PPV values were compared in a large distance of 1-45 m, to assure the reliability of the results.

Axial Reaction
The pile was modeled as a three-dimensional finite element. A 4-node doubly thick or thin shell, finite membrane strains, hourglass control, and reduced int (S4R) were adopted to model the pile. The sandy clay soil parameters were con reasonably typical for medium-stiff clay. Some simplifications were applied in m proaches, in particular: (1) Young's modulus was taken for the pile-skin friction constant with depth; (2) the effects of the driven pile were manifested in horizo placements at the existing pile location, and as statically vertical. No attention w the potential dynamic impacts emanating while driving the pile. The moment a forces were the integration of the shell stresses, and they were given per unit le the element.
At the beginning of the simulation, the soil moved downwards (taken neg this paper); nonetheless, when the penetration upsurged, the soil adjacent to the moved positively, and a heave happened. At the end of the simulation (L1/L = 1), arose in the soil at all levels. In analyzing these responses, a sequential (subsequ ditional calculation was completed beginning from a primarily stress-free pile, taining the free-field movements in order for three pile penetration depths L1/L =

Axial Reaction
The pile was modeled as a three-dimensional finite element. A 4-node doubly curved thick or thin shell, finite membrane strains, hourglass control, and reduced integration (S4R) were adopted to model the pile. The sandy clay soil parameters were considered reasonably typical for medium-stiff clay. Some simplifications were applied in many approaches, in particular: (1) Young's modulus was taken for the pile-skin friction and soil constant with depth; (2) the effects of the driven pile were manifested in horizontal displacements at the existing pile location, and as statically vertical. No attention was set to the potential dynamic impacts emanating while driving the pile. The moment and axial forces were the integration of the shell stresses, and they were given per unit length for the element.
At the beginning of the simulation, the soil moved downwards (taken negative in this paper); nonetheless, when the penetration upsurged, the soil adjacent to the surface moved positively, and a heave happened. At the end of the simulation (L 1 /L = 1), a heave arose in the soil at all levels. In analyzing these responses, a sequential (subsequent) additional calculation was completed beginning from a primarily stress-free pile, and pertaining the free-field movements in order for three pile penetration depths L 1 /L = 1/3, 2/3, and 1. Thus, the preceding soil movement effect could be appropriately taken into account.
For one case (r/d = 8, d is the diameter of the pile), Figure 6  For one case (r/d = 8, d is the diameter of the pile), Figure 6 displays the simulated behaviors of the existing friction pile axial force. The pile's axial force increased with the driven pile penetration inside the soil, and (L1) upsurged until the ratio (L1/L = 0.7) when the axial force diminished with the length of penetration increased. The maximum compressive force was about 56.2% of the ultimate geotechnical shaft resistance of approximately 802.3 kN.  Figure 7 plots the simulated behavior of the produced bending moment in the existing pile for penetration depths L1/L of the newly installed pile. The already-installed pile's head and tip were free for movement. The bending moment values were significant when positioning the pile at r/d = 8 (nearby the driven pile), particularly for relatively large values of L1/L. The maximum value increased and fluctuated while the driven pile attended its final depth of penetration. Hence, when the head and tip of the existing pile were free to move, the analyses clearly showed the possibility of damage to the already-installed pile while a pile was driven adjacently. In addition, the pile was modeled to behave elastically, thus the simulated bending moments could surpass the values that would induce the yielding of the pile.  Figure 7 plots the simulated behavior of the produced bending moment in the existing pile for penetration depths L 1 /L of the newly installed pile. The already-installed pile's head and tip were free for movement. The bending moment values were significant when positioning the pile at r/d = 8 (nearby the driven pile), particularly for relatively large values of L 1 /L. The maximum value increased and fluctuated while the driven pile attended its final depth of penetration. Hence, when the head and tip of the existing pile were free to move, the analyses clearly showed the possibility of damage to the alreadyinstalled pile while a pile was driven adjacently. In addition, the pile was modeled to behave elastically, thus the simulated bending moments could surpass the values that would induce the yielding of the pile. driven pile penetration inside the soil, and (L1) upsurged until the ratio (L1/L = 0.7) when the axial force diminished with the length of penetration increased. The maximum compressive force was about 56.2% of the ultimate geotechnical shaft resistance of approximately 802.3 kN.  Figure 7 plots the simulated behavior of the produced bending moment in the existing pile for penetration depths L1/L of the newly installed pile. The already-installed pile's head and tip were free for movement. The bending moment values were significant when positioning the pile at r/d = 8 (nearby the driven pile), particularly for relatively large values of L1/L. The maximum value increased and fluctuated while the driven pile attended its final depth of penetration. Hence, when the head and tip of the existing pile were free to move, the analyses clearly showed the possibility of damage to the already-installed pile while a pile was driven adjacently. In addition, the pile was modeled to behave elastically, thus the simulated bending moments could surpass the values that would induce the yielding of the pile.

Lateral Movement Analysis
The already-installed pile head and tip were free to move. Figure 8 displayed the simulated behavior of the produced lateral movement in a pile for three penetration depths L 1 /L of the newly driven pile. A significant displacement value was noticed in a pile when positioning at r/d = 8, particularly at the end of the driving process (L 1 /L = 1). The maximum value increased while the driven pile attended its final depth of penetration. At the pile depth of penetration, the maximum lateral displacement inside the existing pile was located approximated at the pile depth equal to the depth of penetration of the driven pile ( Figure 8). This result is similar to the model proposed by Ni et al. [55]. simulated behavior of the produced lateral movement in a pile for three penetration depths L1/L of the newly driven pile. A significant displacement value was noticed in a pile when positioning at r/d = 8, particularly at the end of the driving process (L1/L = 1). The maximum value increased while the driven pile attended its final depth of penetration. At the pile depth of penetration, the maximum lateral displacement inside the existing pile was located approximated at the pile depth equal to the depth of penetration of the driven pile ( Figure 8). This result is similar to the model proposed by Ni et al. [55]. For small penetrations, the pile moved downward; however, for large penetrations L1/L of the driven pile bigger than around 0.5, the already existing pile movement was upward. When (L1/L = 1), a maximum value of the upward movements was attended (around 3% of the pile diameter) at a position of r/d = 8. Therefore, a fairly possible problem was observed when constructing the friction pile: (1) a heave would occur next to the existing pile, and (2) it could induce a loss of contact among the supporting soil and the pile tip and could induce the apparition of a gap. Once the load was applied on the pile and the resistance of the shaft was assembled entirely, a noticeable settlement could appear when the gap was closed previous to the tip re-touching the soil. These phenomena had been well-recognized and experienced in real engineering. The maximum lateral displacement decreased rapidly with an increase in r/d and became relatively small for spacings over around eight diameters. As plotted in Figure 9, the maximum displacement occurred for depths of penetration (L1/L) of about one. For small penetrations, the pile moved downward; however, for large penetrations L 1 /L of the driven pile bigger than around 0.5, the already existing pile movement was upward. When (L 1 /L = 1), a maximum value of the upward movements was attended (around 3% of the pile diameter) at a position of r/d = 8. Therefore, a fairly possible problem was observed when constructing the friction pile: (1) a heave would occur next to the existing pile, and (2) it could induce a loss of contact among the supporting soil and the pile tip and could induce the apparition of a gap. Once the load was applied on the pile and the resistance of the shaft was assembled entirely, a noticeable settlement could appear when the gap was closed previous to the tip re-touching the soil. These phenomena had been well-recognized and experienced in real engineering. The maximum lateral displacement decreased rapidly with an increase in r/d and became relatively small for spacings over around eight diameters. As plotted in Figure 9, the maximum displacement occurred for depths of penetration (L 1 /L) of about one.

Effect of the Pile Shape
Data about tapered and semi-tapered pile behavior during adjacent pile construction are scarce. In this section, the bending moment, axial force, and lateral movement on nonuniform pile cross-sections were caused by the driving of a friction pile. However, cylin-

Effect of the Pile Shape
Data about tapered and semi-tapered pile behavior during adjacent pile construction are scarce. In this section, the bending moment, axial force, and lateral movement on non-uniform pile cross-sections were caused by the driving of a friction pile. However, cylindrical and semi-tapered concrete piles with different geometries in terms of volume and length were adopted, as plotted in Figure 10. The cylindrical pile was 10 m long and 0.5 m thick. The semi-tapered pile was identical in volume and length to the cylindrical one and with the taper angle α taken as 0.7 • , 1.0 • , and 1.4 • as proposed by Manandhar and Yasufuku [56]. Thus, the obtained results may be used in practice.

Effect of the Pile Shape
Data about tapered and semi-tapered pile behavior during adjacent pile construction are scarce. In this section, the bending moment, axial force, and lateral movement on nonuniform pile cross-sections were caused by the driving of a friction pile. However, cylindrical and semi-tapered concrete piles with different geometries in terms of volume and length were adopted, as plotted in Figure 10. The cylindrical pile was 10 m long and 0.5 m thick. The semi-tapered pile was identical in volume and length to the cylindrical one and with the taper angle α taken as 0.7°, 1.0°, and 1.4° as proposed by Manandhar and Yasufuku [56]. Thus, the obtained results may be used in practice. From the obtained results, it was concluded that the semi-tapered pile was subjected to less axial forces and lateral movement than the cylindrical one with the same length and volume for a taper angle of less than 1.0° (Figures 11 and 12). For the taper angle with From the obtained results, it was concluded that the semi-tapered pile was subjected to less axial forces and lateral movement than the cylindrical one with the same length and volume for a taper angle of less than 1.0 • (Figures 11 and 12). For the taper angle with more than 1.4 • , large values of axial force and lateral movement were observed in the semi-tapered pile. Thus, the use of semi-tapered piles will be more beneficial than the cylindrical one with the same volume and length for a taper angle of less than 1.0 • .
Appl. Sci. 2021, 11, x FOR PEER REVIEW 11 of 14 more than 1.4°, large values of axial force and lateral movement were observed in the semi-tapered pile. Thus, the use of semi-tapered piles will be more beneficial than the cylindrical one with the same volume and length for a taper angle of less than 1.0°.

Conclusions
The study provided that the soil movements due to a driven pile can induce a large bending moment, lateral movement, and axial forces in an existing adjacent pile. Numerical simulation was adopted to evaluate these movements and forces.

Conclusions
The study provided that the soil movements due to a driven pile can induce a large bending moment, lateral movement, and axial forces in an existing adjacent pile. Numerical simulation was adopted to evaluate these movements and forces.

1.
In this paper, a reliable method to complete the driving of a pile was proposed. This involved combining the element deletion and arbitrary Lagrangian-Eulerian (ALE) mesh method.

2.
The adjacent semi-tapered pile was subjected to less axial and lateral movement than the cylindrical one with the same length and volume for a taper angle smaller than 1.0 • , and vice versa for a taper angle greater than 1.4 • .

3.
Moreover, the influence of the driven pile on the existing pile's responses was significant, the bending moment and axial force were not negligible, and the coupling effect in the case of the loaded pile should be factually considered. In fact, the pile's design subjected to lateral and axial load was usually treated as a separate problem.