Comparative Analysis of Single Pile with Embedded Beam Row and Volume Pile Modeling under Seismic Load

Cyclic loading increases deflection and bending moment in short-term loading. Isenhower et al. [7] reported several studies with bored piles under cyclic lateral loading in overconsolidated clay soils without free water. The pile deflection at ground level is 25 mm during cyclic loading. After the load is removed, a gap appears in a pile (Figure 1). Thus, cracks are visible from the front [7].

Figure 1

Cyclic loading of piles in sandy soil in one direction will permanently deflect piles in the direction of loading. For example, a relatively sizable cyclic load is applied in one direction and the pile top will allow soil particles. Therefore, no cohesion is observed to fall into the open gaps at the back of the pile (Figure 1). Moreover, the pile cannot return to the original position after the cyclic loading and causes the development of permanent deflection [7].

Figure 2

The soil reaction to the pile (p) is related to the pile deflection (y) through a nonlinear load-deflection curve. The main drawback of the p–y method is the soil is not a continuum, but a series of discrete springs (i.e., the Winkler model). Winkler's approach is a good representation of the important pile–soil interaction in evaluating the response of pile to earthquake shaking. Winkler's approach to lateral pile analysis is widely used in practice because of its easy of nonlinear modeling and mathematical and computational efficiency.

Soil properties, pile geometry, and load properties are the most influential factors on the p–y curve. Soil properties are principally confined to the soil zone close to the pile friction, whereas soil masses of several pile diameters are pressured when lateral deflection occurs [8].

The substructure is a reinforced concrete bored pile. Soil evaluation was conducted by the Laboratory of Soil Mechanics and Geology, Faculty of Engineering, Brawijaya University, from two SPT (Standard Penetration Test) and four CPT (Cone Penetration Test) of 2.5 tons. The study location is presented in Figure 3 around the DB. 1 drill (Figure 3).

Figure 3

The bored pile elevation starts at 4.325 m below the ground level (Figure 4). The bored pile elevation at 4.325 m below the ground level is assumed to be 0.00 m in modeling for finite element software. SPT elevation is 6.00 m below the ground surface and is assumed at a depth of −1.675 m in the case of groundwater level.

Figure 4

The main function of the structure is as an educational facility and has a hazard category IV. The combination of lateral loads consists of equivalent static earthquake loads and live loads in the semi-basement based on Standard National Indonesia (SNI) 1726 [15]. Lateral earth pressure was calculated using the Coulomb method based on Das [16]. The loading consists of three conditions based on the acceleration spectral response parameter for a short period (S_s) and for 1.0-s period (S₁), including the first condition with S_s = 0.80, S₁ = 0.30, condition 2 with S_s = 0.90, S₁ = 0.40, and condition 3 with S_s = 1.00, S₁ = 0.50. The combination lateral load value of the single pile load is 542.453 kN for the first condition, 690.240 kN for the second condition, and 822.309 kN for the third condition.

Poulos & Davis [17] proposed a method for classifying piles into different categories based on the flexibility factor, Kr (Kr = E_pI_p/E_sL_p4), where I_p is the inertia moment of pile and L_p is the pile length. The classification of the bored pile at Brawijaya University consists of a flexibility factor of 44 ′ 10⁻⁵ from E_p1 = 20.75 MPa, 52 ′ 10⁻⁵ from E_p2 = 29.05 MPa, and 59 ′ 10⁻⁵ from E_p3 = 37.35 MPa. From this value, based on Li et al. [18], the piles are categorized as very flexible piles with a flexibility factor of 10⁻⁵.

Based on the SPT and V_s values calculated using the approach of Hasancebi and Ulusuay in Hammam and Eliwa [12], Maheswari et al. [13], and Tsiambaos and Shabatakakis [14], the site classification is in the medium soil category (SD) based on SNI 1726 [15]. Moreover, the values of N and V_s are 15–50 and 175–350, respectively. The value of the shear wave velocity is used to determine the value of G_max (Table 2). In the finite element analysis, the pile is modeled linear elastic. The failure criteria are evaluated based on Mohr–Coulomb's strength parameters (friction angle) and c (cohesion).

A single pile is modeled with the material embedded beam rows (Figure 5a) for 2D analysis in PLAXIS 2D and a volume pile for 3D analysis in PLAXIS 3D (Figure 5b). The embedded beam row feature creates new possibilities for element modeling with soil–structure interactions. Embedded beam row has several advantages of plate and node to anchor nodes. It has a similar plate and meshes elements to node anchorage [19]. For software input, in the case of static equivalent load, the axial and lateral loads are point loads with a load value equal to the allowable axial bearing capacity and three conditions of combination lateral loads. The allowable axial bearing capacity value is 956.495 kN, that calculated by the laboratory method from FHWA-NHI-10-016 [20] for cohesive soils and Yu et al. [21] for cohesionless soil. The values of x-max, x-min, y-max, and y-min are obtained as 5D from the global coordinator. The x-max and y-max value is 4 m, and the x-min and y-min value is −4 m. The modeled pile is 20 m long.

Figure 5

The pile interface is represented by spring at numerical stiffness in the axial and lateral directions for 2D analysis [19]. In the 3D finite element (Figure 5b), the interface presents the interaction between the structural element and the soil with a value below 1.0 to indicate friction between the structural element and the soil [22]. The mesh is a triangular element 15-node for 2D analysis and is tetrahedral 10-node for 3D analysis. The mesh becomes denser the closer it is to the pile [4]. This is different in 2D finite element analysis with embedded beam rows, where the mesh has the same size, while in 3D finite element analysis, it is appropriate that the mesh is getting denser as it gets closer to the pile structure.

Finite element analysis shows the flexible pile features [6]. According to this study, it is in the very flexible pile category. This is also the mechanism of pile failure in this study, characterized by pile buckled to the right from a depth of 0.00–6.00 m for 2D finite element analysis and 0.00–4.00 m for 3D finite element analysis (Figure 6a, b). Small-diameter piles show a passive wedge collapse up to 5D at shallow depth, with deflection decreasing to zero at more than 8D below the surface (Wang et al., 2020). If gaps in the soil–pile interface occur, pile stiffness can impact the depth of the gap. This is because the depth of gap expansion must be limited to the depth of the point of rotation. Below the point of rotation and on the back side of the direction of loading, the pile shifts concerning the ground. Due to suction, the transition depth from wedge failure to flow around the failure is potentially reduced for flexible piles [23]. In addition, the mechanism of the pile collapse can also be clarified by the direction of the vector which points to the right, namely, the direction of the pile fracture (Figure 6c, d).

Figure 6

Lateral mobilization of the soil by the pile is calculated from the distribution of shear forces on the embedded beam row and volume pile. Then, it is assessed whether the lateral capacity of the soil is exceeded. Figure 7 shows a graph of the lateral load that the pile can withstand and the value of the deflection. If the pile is given a load of 542.453 kN for condition 1, 690.240 kN for condition 2, and 822.309 kN for condition 3, the combination of lateral loads’ effect, pile stiffness, and soil stiffness effect on a single pile 3D analysis can withstand a load of 300 kN lower than the given load under these three conditions. 2D analysis can withstand a 400–600 kN load lower than the given load under these three conditions. The value of the lateral capacity above is within safe limits because the ultimate lateral bearing capacity of the pile (P_ult) happens at a load of 1,000 kN.

Figure 7

In 2D finite element analysis, as the combination of lateral loads increases (Figure 7a), the lateral loads increase, followed by increasing deflections. In contrast to the effects of pile stiffness (Figure 7b) and soil stiffness (Figure 7c), the pile stiffness increases, deflection decreases, and lateral loads decrease. Regarding the effect of soil stiffness, where the soil stiffness increases, the deflection decreases, but the lateral load increases. This is in agreement with the results of [24], which states that when E_s increases, the deflection does not increase significantly.

As is the case in 3D finite element analysis, when the combined lateral load increases, the deflection increases and the lateral load increases. Regarding the effect of pile stiffness, with increasing flexural stiffness, the pile behavior is still governed by the wedge failure mechanism [6]. In addition, as the pile stiffness increases, the deflection decreases, but the lateral load increases, contrary to the results proposed by Wang et al. [6] that stiffer pile deflection under the same lateral load is slightly underestimated and due to the more considerable flexural stiffness, for the same deflection at ground level, a larger soil zone is mobilized. The depth of the effect of wedge failure also increases. With regard to the effect of soil stiffness, where the stiffness of the soil increases, the deflection decreases, followed by a decrease in the lateral load. According to the study by Zhou et al. [24], the displacement of the tip of the pile decreases with increasing E_s. It can be seen that 2D has different behavior from 3D finite element analysis on the effects of pile stiffness and soil stiffness. The 3D numerical model is reliable for improving the soil–pile reaction while decreasing the overall flexural stiffness of the pile friction [25]. The 3D finite element analysis is related to the soil response [26], as evidenced by the deflection occurring less than 25 mm, by the permissible deflection for the lateral pile based on Isenhower et al. [7], while the 2D analysis has a deflection more significant than 25 mm (Figure 7).

Furthermore, the 3D finite element showed the deflection was 1%D and the 2D finite element showed the deflection was 4%–8%D. The lateral load-deflection curves calculated from the 3D finite element analysis correspond to the validation for lateral load–soil interaction [27]. It can be seen that the deflection of the 2D finite element analysis on the effect of soil stiffness is inversely related to the lateral load, and the deflection of the 3D finite element analysis on the effect of pile stiffness is also inversely related to the lateral load.

The average difference in the lateral resistance of the 2D single pile analysis compared to the 3D single pile analysis was 50%–70% (Table 3) and the deflection was 70%–90% (Table 4). It can be seen that the difference between 2D and 3D analyses is vast, where 2D finite element analysis reduces the lateral resistance but increases the deflection at the pile surface. Considering that the friction factor is related to the strength properties of the soil layer, this is because there is no friction factor or interface in the embedded beam row model. The interface is represented by a spring. The spring is most likely to cause a decrease in stiffness and friction between the soil and piles. Thus, the deflection is large and the strength of the soil layer decreases due to the interaction between the piles in contact. So, they do not slip over each other. This is different from Sluis et al. [1] which reports that the shear force of structural elements in the 2D model will be greater than in the 3D model. Based on these results, the behavior of the lateral pile using 2D finite element analysis is considered inconsistent.

In addition, 3D finite element analysis has a friction factor (interface), which can increase the interaction between the pile and soil by slipping the two materials against each other. This makes the 3D numerical model appropriate to be relied upon to improve the pile–soil reaction.

The mobilization of the lateral bearing capacity of the soil by the pile is calculated based on the equivalent force of the soil stress that occurs in the x direction. This assessment is carried out per unit meter depth over the total pile length (Figure 8). Combination lateral loads effect, pile stiffness effect, and soil stiffness effect do not affect the soil's lateral bearing capacity because the soil's lateral bearing capacity is based on soil characteristics such as soil unit weight and friction angle. The ultimate lateral bearing capacity, p_u, increases with increasing depth [6,27]. The ultimate lateral bearing capacity has the largest value based on the 3D finite element method. The lateral bearing capacity of the soil is fully mobilized along the full depth of the pile, lowering the ultimate resistance of the soil at shallow depths and increasing it in the deep zone. This agrees with [6,9,27] that the ultimate lateral bearing capacity, p_u, increases with increasing depth.

Figure 8

4.2.1

The p–y Curve

The p–y curve was obtained with the help of finite difference software for a single pile calculated using the p–y API approach [9]. Pile modeling at the finite difference method is identical to the 3D finite element method, and the relationship between soil resistance and deflection (p–y curve) was taken at a depth of 20.00 m to match the pile group's deflection output from the 3D finite element analysis. The FDM – API method has the highest lateral soil resistance value, followed by the method of Klinkvort (2012), Liang et al. (2018) [10] in the second place, and Hyunsung and Sangseom (2018) [11] are the lowest. In contrast to a study by Wang et al. [27], the Klinkvort method increases k_ini at greater depths. The Klinkvort method has lower soil lateral resistance values [6,27]. The three methods continue to increase until it reaches the maximum lateral soil resistance at maximum deflection (Figure 9). Meanwhile, it increases until it reaches the maximum lateral soil resistance at a deflection of 0.125%D and then becomes constant until the maximum deflection is achieved.

Figure 9

The load–displacement relationship calculated by the FDM – API presents a good agreement with the 3D finite element analysis with a difference of 30% (Table 5). The 3D finite element analysis increases soil stiffness at greater depths. It is appropriate that the API method estimates the lateral pile–soil resistance due to the API method [9], inducing an overestimation of the initial stiffness, and the API method [9] provides reasonable predictions for small-diameter piles [6,27]. The FDM – API method significantly overestimates the present value at all depths (Figure 9). Moreover, the API method [9] is defined as a cyclic p–y curve related to small-diameter flexible piles, and therefore, it overestimates the soil reaction at higher depths. The increase in soil reaction might be due to an additional component of the soil reaction by pile rotation to the simple lateral translational mode of pile deformation [5,6]. The p–y curve is more rigid than the other methods, considering the initial stiffness and the final lateral stress [28]. In addition, the load–displacement relationship calculated by Hyunsung and Sangseom [11] agrees well with the 2D finite element (Table 5). In contrast to 3D finite element analysis, in 2D finite element analysis, it is possible to reduce stiffness because there is no friction between the soil and piles.

Table 5

The difference in deflection with the FEM 3D.

	Lateral resistance (kN)	The difference in deflection with FEM 3D (%)	The difference in deflection with FEM 2D (%)
FEM 3D	10,410.00	-	81.220
FEM 2D	1,955.00	81.220	-
FDM – API (2011)	7,025.381	32.513	72.172
Klinkvort (2012)	3,931.621	62.232	50.275
Liang et al. (2018) [10]	4,441.177	57.337	55.980
Hyunsung and Sangseom (2018) [11]	1,306.272	87.452	33.183